Answer:
(3,0)
Step-by-step explanation:
To answer this, just find what was added to A to get to the midpoint, then add that to the midpoint for B.
So first, find how to get from (-1,3) to (1,2). If you add together -1 + 2, the answer is 1, the x value of the midpoint. If you subtract 3 - 1, the answer is 2, the y value of the midpoint.
Now, we just apply these to the midpoint, which should get us to the coordinates of B.
1 + 2 = 3
2 - 2 = 0
(3,0)
So, the coordinates of B are (3,0).
2) (10) Sue has a total of $20,000 to invest. She deposits some of her money in an account that returns 12% and the rest in a second account that returns 20%. At the end of the first year, she earned $3460 a) Give the equation that arises from the total amount of money invested. b) give the equation that results from the amount of interest she earned. c) Convert the system or equations into an augmented matrix d) Solve the system using Gauss-Jordan Elimination. Show row operations for all steps e) Answer the question: How much did she invest in each account?
From the solution, we can determine that Sue invested $1,750 in the account that returns 12% and $18,250 in the account that returns 20%.
a) Let x represent the amount of money invested in the account that returns 12% and y represent the amount of money invested in the account that returns 20%. The equation that arises from the total amount of money invested is:
x + y = 20,000
b) The interest earned from the account that returns 12% is given by 0.12x, and the interest earned from the account that returns 20% is given by 0.20y. The equation that arises from the amount of interest earned is:
0.12x + 0.20y = 3,460
c) Converting the system of equations into an augmented matrix:
[1 1 | 20,000]
[0.12 0.20 | 3,460]
d) Solving the system using Gauss-Jordan Elimination:
Row 2 - 0.12 * Row 1:
[1 1 | 20,000]
[0 0.08 | 1,460]
Divide Row 2 by 0.08:
[1 1 | 20,000]
[0 1 | 18,250]
Row 1 - Row 2:
[1 0 | 1,750]
[0 1 | 18,250]
Know more about augmented matrix here:
https://brainly.com/question/30403694
#SPJ11
How do you know what method (SSS, SAS, ASA, AAS) to use when proving triangle congruence?
Answer:
Two triangles are said to be congruent if they are exactly identical. We know that a triangle has three angles and three sides. So, two triangles have six angles and six sides. If we can prove the any corresponding three of them of both triangles equal under certain rules, the triangles are congruent to each other. These rules are called axioms.
The method you will use depends on the information you are given about the triangles.
--> SSS(Side-Side-Side): If you know that all three sides of a triangle are congruent to the corresponding sides of another triangle, then the two triangles are congruent.
--> SAS(Side-Angle-Side): If you know that two sides and the angle between those sides are equal to the another corresponding two sides and the angle between the two sides of another triangle, then you say that the triangles are congruent by SAS axiom.
--> ASA(Angle-Side-Angle): If you know that the two angles and the side between them are equal to the two corresponding angles and the side between those angles of another triangle are equal, you may say that the triangles are congruent by ASA axiom.
--> AAS(Angle-Angle-Side): This method is similar to the ASA axiom, but they are not same. In AAS axiom also you need to have two corresponding angles and a side of a triangle equal, but they should be in angle-angle-side order.
--> RHS(Right-Hypotenuse-Side) or HL(Hypotenuse-Leg): If hypotenuses and any two sides of two right triangles are equal, the triangles are said to be congruent by RHS axiom. You can only test this rule for the right triangles.
Answer:
So, there are four ways to figure out if two triangles are the same shape and size. One way is called SSS, which means all three sides of one triangle match up with the corresponding sides on the other triangle. Another way is called AAS, where two angles and one side of one triangle match two angles and one side of the other triangle. Then there's SAS, where two sides and the angle between them match up with the same parts on the other triangle. Finally, there's ASA, where two angles and a side in between them match up with the same parts on the other triangle.
The Sun has a radius of 7. 105 kilometers. Calculate the surface area of the Sun in square meters. Note that you can approximate the Sun (symbol ) to be a sphere with a surface area of A = 4TR¹² where Ro is the radius (the distance from the center to the edge) of the Sun. In this class, approximating = 3 is perfectly fine, so we can approximate the formula for surface area to be Ao 12R². x 10 square meters Hint: 1 km²: 1 (km)² = 1 kilo² m² = 1 ⋅ (10³)² m² = 100 m²
The surface area of the Sun is approximately 6.07 x 10¹² square meters.
To calculate the surface area of the Sun, we can use the formula A = 4πR², where R is the radius of the Sun. Given that the radius of the Sun is 7.105 kilometers, we need to convert it to meters before substituting it into the formula.
1 kilometer (km) is equal to 1000 meters (m). Therefore, the radius of the Sun in meters (Ro) is:
R₀ = [tex]7.105 km * 1000 m/km[/tex]
R₀ = 7,105 meters
Now, we can substitute the value of R₀ into the formula:
A = 4π(7,105)²
A = 4π(50,441,025)
A ≈ 201,764,100π
Since we can approximate π to 3, the surface area can be further simplified:
A ≈ 201,764,100 * 3
A ≈ 605,292,300 square meters
The surface area of the Sun is approximately 6.07 x 10¹² square meters.
Learn more about surface area
brainly.com/question/29251585
#SPJ11
Renee designed the square tile as an art project.
a. Describe a way to determine if the trapezoids in the design are isosceles.
In order to determine if the trapezoids in the design are isosceles, you can measure the lengths of their bases and legs. If the trapezoids have congruent bases and congruent non-parallel sides, then they are isosceles trapezoids.
1. Identify the trapezoids in the design. Look for shapes that have one pair of parallel sides and two pairs of non-parallel sides.
2. Measure the length of each base of the trapezoid. The bases are the parallel sides of the trapezoid.
3. Compare the lengths of the bases. If the bases of a trapezoid are equal in length, then it has congruent bases.
4. Measure the length of each non-parallel side of the trapezoid. These are the legs of the trapezoid.
5. Compare the lengths of the legs. If the legs of a trapezoid are equal in length, then it has congruent non-parallel sides.
6. If both the bases and non-parallel sides of a trapezoid are congruent, then it is an isosceles trapezoid.
To know more about trapezoids and their properties, refer here:
https://brainly.com/question/31380175#
#SPJ11
Given f(x)=x²−1,g(x)=√2x, and h(x)=1/x, determine the value of f(g(h(2))). a. (x²−1)√x
b. 3
c. 0
d. 1
the value of function(g(h(2))) is 1. Therefore, the answer is option: d. 1
determine the value of f(g(h(2))).
f(h(x)) = f(1/x) = (1/x)^2 - 1= 1/x² - 1g(h(x))
= g(1/x)
= √2(1/x)
= √2/x
f(g(h(x))) = f(g(h(x))) = f(√2/x)
= (√2/x)² - 1
= 2/x² - 1
Now, substituting x = 2:
f(g(h(2))) = 2/2² - 1
= 2/4 - 1
= 1/2 - 1
= -1/2
Therefore, the answer is option: d. 1
To learn more about function
https://brainly.com/question/14723549
#SPJ11
Does the equation 6x+12y−18z=9 has an integer solution? Why or why not? Find the set of all integer solutions (x,y) to the linear homogeneous Diophantine equation 14x+22y= 0. Find the set of all integer solutions (x,y) to the linear Diophantine equation 3x−5y=4
- The equation 6x + 12y - 18z = 9 does not have an integer solution.
- The set of all integer solutions (x, y) to the linear homogeneous Diophantine equation 14x + 22y = 0 is given by (11k, -7k), where k is an arbitrary integer.
- The set of all integer solutions (x, y) to the linear Diophantine equation 3x - 5y = 4 is given by (-14 + 5k, -8 + 3k), where k is an arbitrary integer.
The equation 6x + 12y - 18z = 9 does not have an integer solution. This is because the right-hand side of the equation is 9, which is not divisible by 6, 12, or 18. In order for an equation to have an integer solution, the right-hand side must be divisible by the greatest common divisor (GCD) of the coefficients on the left-hand side. However, in this case, the GCD of 6, 12, and 18 is 6, and 9 is not divisible by 6. Therefore, there are no integer solutions to this equation.
To find the set of all integer solutions (x, y) to the linear homogeneous Diophantine equation 14x + 22y = 0, we can first find the GCD of 14 and 22, which is 2. Then, we divide both sides of the equation by the GCD to get the reduced equation 7x + 11y = 0. Since the GCD is 2, the reduced equation still holds the same set of integer solutions as the original equation.
Now, we observe that both coefficients, 7 and 11, are relatively prime (i.e., they have no common factors other than 1). This implies that the equation has infinitely many integer solutions. In general, the solutions can be expressed as (11k, -7k), where k is an arbitrary integer.
To find the set of all integer solutions (x, y) to the linear Diophantine equation 3x - 5y = 4, we can again start by finding the GCD of the coefficients 3 and -5, which is 1. Since the GCD is 1, the equation has integer solutions.
To find a particular solution, we can use the extended Euclidean algorithm. By applying the algorithm, we find that x = -14 and y = -8 is a particular solution to the equation.
From this particular solution, we can find the general solution by adding integer multiples of the coefficient of the other variable. In this case, the general solution can be expressed as (x, y) = (-14 + 5k, -8 + 3k), where k is an arbitrary integer.
To know more about linear Diophantine equations, refer here:
https://brainly.com/question/30709147#
#SPJ11
What is the value of the expression (-8)^5/3
Write an explicit formula for
�
�
a
n
, the
�
th
n
th
term of the sequence
27
,
9
,
3
,
.
.
.
27,9,3,....
The explicit formula for the nth term (an) of the sequence 27, 9, 3, ... can be expressed as an = 27 / 3^(n-1), where n represents the position of the term in the sequence.
To find the explicit formula for the nth term of the sequence 27, 9, 3, ..., we need to identify the pattern or rule governing the sequence.
From the given sequence, we can observe that each term is obtained by dividing the previous term by 3. Specifically, the first term is 27, the second term is obtained by dividing 27 by 3, giving 9, and the third term is obtained by dividing 9 by 3, giving 3. This pattern continues as we divide each term by 3 to get the subsequent term.
Therefore, we can express the nth term, denoted as aₙ, as:
aₙ = 27 / 3^(n-1)
This formula states that to obtain the nth term, we start with 27 and divide it by 3 raised to the power of (n-1), where n represents the position of the term in the sequence.
For example:
When n = 1, the first term is a₁ = 27 / 3^(1-1) = 27 / 3^0 = 27.
When n = 2, the second term is a₂ = 27 / 3^(2-1) = 27 / 3^1 = 9.
When n = 3, the third term is a₃ = 27 / 3^(3-1) = 27 / 3^2 = 3.
Using this explicit formula, you can calculate any term of the sequence by plugging in the value of n into the formula.
for such more question on sequence
https://brainly.com/question/27555792
#SPJ8
What is the area of this figure?
Enter your answer in the box. Cm² 4 cm at top 5cm to right 5cm at bottom
The area of the given figure, we can divide it into two separate shapes: a rectangle and a right triangle. The area of the given figure is 30 cm².
First, let's calculate the area of the rectangle. The width of the rectangle is 5 cm, and the height is 4 cm. The area of a rectangle is given by the formula: A = length × width. Therefore, the area of the rectangle is:
Area of rectangle = 5 cm × 4 cm = 20 cm².
Next, let's calculate the area of the right triangle. The base of the triangle is 5 cm, and the height is 4 cm. The area of a triangle is given by the formula: A = 0.5 × base × height. Therefore, the area of the right triangle is: Area of triangle = 0.5 × 5 cm × 4 cm = 10 cm².
To find the total area of the figure, we add the area of the rectangle and the area of the triangle:
Total area = Area of rectangle + Area of triangle = 20 cm² + 10 cm² = 30 cm².
Therefore, the area of the given figure is 30 cm².
Learn more about rectangle here
https://brainly.com/question/2607596
#SPJ11
Each unit on the coordinate plane represents 1 NM. If the boat is 10 NM east of the y-axis, what are its coordinates to the nearest tenth?
The boat's coordinates are (10, 0).
A coordinate plane is a grid made up of vertical and horizontal lines that intersect at a point known as the origin. The origin is typically marked as point (0, 0). The horizontal line is known as the x-axis, while the vertical line is known as the y-axis.
The x-axis and y-axis split the plane into four quadrants, numbered I to IV counterclockwise starting at the upper-right quadrant. Points on the plane are described by an ordered pair of numbers, (x, y), where x represents the horizontal distance from the origin, and y represents the vertical distance from the origin, in that order.
The distance between any two points on the coordinate plane can be calculated using the distance formula. When it comes to the given question, we are given that Each unit on the coordinate plane represents 1 NM.
Since the boat is 10 NM east of the y-axis, the x-coordinate of the boat's position is 10. Since the boat is not on the y-axis, its y-coordinate is 0. Therefore, the boat's coordinates are (10, 0).
For more such questions on coordinates, click on:
https://brainly.com/question/17206319
#SPJ8
Jocelyn estimates that a piece of wood measures 5.5 cm. If it actually measures 5.62 cm, what is the percent error of Jocelyn’s estimate?
Answer:
The percent error is -2.1352% of Jocelyn's estimate.
If y varies directly as x, and y is 48 when x is 6, which expression can be used to find the value of y when x is 2?
Answer:
y= 8x
Step-by-step explanation:
y= 48
x= 6
48/6 = 8
y= 8x
x=2
y= 8(2)
y= 16
If a media planner wishes to run 120 adult 18-34 GRPS per week,
and if the Cpp is $2000 then the campaign will cost the advertiser
_______per week.
If a media planner wishes to run 120 adult 18-34 GRPS per week, the frequency of the advertisement needs to be 3 times per week.
The Gross Rating Point (GRP) is a metric that is used in advertising to measure the size of an advertiser's audience reach. It is measured by multiplying the percentage of the target audience reached by the number of impressions delivered. In other words, it is a calculation of how many people in a specific demographic will be exposed to an advertisement. For instance, if the GRP of a particular ad is 100, it means that the ad was seen by 100% of the target audience.
Frequency is the number of times an ad is aired on television or radio, and it is an essential aspect of media planning. A frequency of three times per week is ideal for an advertisement to have a significant impact on the audience. However, it is worth noting that the actual frequency needed to reach a specific audience may differ based on the demographic and the product or service being advertised.
Learn more about Gross Rating Point (GRP) here: https://brainly.com/question/29454398
#SPJ11
What is the x -intercept of the line at the right after it is translated up 3 units?
The x-intercept of the line at the right after it is translated up 3 units is x = (-b - 3)/m.
The x-intercept of a line is the point where it intersects the x-axis, meaning the y-coordinate is 0. To find the x-intercept after the line is translated up 3 units, we need to determine the equation of the translated line.
Let's assume the equation of the original line is y = mx + b, where m is the slope and b is the y-intercept. To translate the line up 3 units, we add 3 to the y-coordinate. This gives us the equation of the translated line as
y = mx + b + 3
To find the x-intercept of the translated line, we substitute y = 0 into the equation and solve for x. So, we have
0 = mx + b + 3.
Now, solve the equation for x:
mx + b + 3 = 0
mx = -b - 3
x = (-b - 3)/m
Read more about line here:
https://brainly.com/question/2696693
#SPJ11
You are looking for a new cell phone plan. The first company, Cellular-Tastic (f) charges a fee of $20 and 0
$0.11 per minute of use. Dirt-Cheap Cell (g) charges a monthly fee of $55 and $0.01 per minute of use.
a. How many minutes would you need to use for the cell phones to cost the same amount?
b. Create a graph to model this situation.
c. Using your graph, explain when each company would be a better option.
a) the two cell phone plans would cost the same amount when using 350 minutes.
b) The graph will intersect at the point where the two total costs are equal.
c) . The intersection point represents the threshold where the costs are equal, making it a crucial point to consider when choosing between the two plans based on expected usage.
a. To find the number of minutes needed for the cell phones to cost the same amount, we can set up an equation where the total cost from Cellular-Tastic (f) is equal to the total cost from Dirt-Cheap Cell (g). Let's denote the number of minutes as m.
For Cellular-Tastic (f):
Total cost = $20 (monthly fee) + $0.11 per minute * m
For Dirt-Cheap Cell (g):
Total cost = $55 (monthly fee) + $0.01 per minute * m
Setting these two expressions equal to each other, we have:
$20 + $0.11m = $55 + $0.01m
Simplifying the equation:
$0.1m = $35
m = $35 / $0.1
m = 350 minutes
Therefore, the two cell phone plans would cost the same amount when using 350 minutes.
b. To create a graph modeling this situation, we can plot the total cost on the y-axis and the number of minutes on the x-axis. The graph will have two lines, one representing Cellular-Tastic (f) and the other representing Dirt-Cheap Cell (g).
The y-intercept for Cellular-Tastic will be $20, and the slope will be $0.11 per minute. The y-intercept for Dirt-Cheap Cell will be $55, and the slope will be $0.01 per minute. The graph will intersect at the point where the two total costs are equal.
c. Using the graph, we can determine when each company would be a better option.
For a lower number of minutes, Cellular-Tastic (f) would be a better option as its monthly fee is lower compared to Dirt-Cheap Cell (g). The graph will show that the Cellular-Tastic line is initially lower than the Dirt-Cheap Cell line.
As the number of minutes increases, there will be a point where the two lines intersect. At this point (350 minutes), both plans will cost the same amount.
Beyond the intersection point, Dirt-Cheap Cell (g) becomes the better option for higher usage. As the number of minutes increases further, the Dirt-Cheap Cell line will be lower than the Cellular-Tastic line, indicating a lower total cost for Dirt-Cheap Cell.
For more such questions on intersect visit:
https://brainly.com/question/30915785
#SPJ8
Bearing used in an automotive application is supposed to have a nominal inside diameter 1.5 inches. A random sample of 25 bearings is selected, and the average inside diameter of these bearings is 1.4975 inches. Bearing diameter is known to be normally distributed with standard deviation σ=0.1 inch. We want to test the following hypothesis at α=0.01. H0:μ=1.5,H1:μ=1.5 (a) Calculate the type II error if the true mean diameter is 1.55 inches. (b) What sample size would be required to detect a true mean diameter as low as 1.55 inches if you wanted the power of the test to be at least 0.9 ?
(a) Without knowing the effect size, it is not possible to calculate the type II error for the given hypothesis test. (b) To detect a true mean diameter of 1.55 inches with a power of at least 0.9, approximately 65 bearings would be needed.
(a) If the true mean diameter is 1.55 inches, the probability of not rejecting the null hypothesis when it is false (i.e., the type II error) depends on the chosen significance level, sample size, and effect size. Without knowing the effect size, it is not possible to calculate the type II error.
(b) To calculate the required sample size to detect a true mean diameter of 1.55 inches with a power of at least 0.9, we need to know the chosen significance level, the standard deviation of the population, and the effect size.
Using a statistical power calculator or a sample size formula, we can determine that a sample size of approximately 65 bearings is needed.
to know more about hypothesis test, visit:
brainly.com/question/32874475
#SPJ11
What is the value of θ for the acute angle in a right triangle? sin(θ)=cos(53°) Enter your answer in the box. θ= °
Answer:
the value of θ for the acute angle in a right triangle, where sin(θ) = cos(53°), is 37 degrees.
Step-by-step explanation:
In a right triangle, one of the angles is always 90 degrees, which is the right angle. The acute angle in a right triangle is the angle that is smaller than 90 degrees.
To find the value of θ for the acute angle in a right triangle, given that sin(θ) = cos(53°), we can use the trigonometric identity:
sin(θ) = cos(90° - θ)
Since sin(θ) = cos(53°), we can equate them:
cos(90° - θ) = cos(53°)
To find the acute angle θ, we solve for θ by equating the angles inside the cosine function:
90° - θ = 53°
Subtracting 53° from both sides:
90° - 53° = θ
θ= 37°
Therefore, the value of θ for the acute angle in a right triangle, where sin(θ) = cos(53°), is 37 degrees.
You can define the rules for irrational exponents so that they have the same properties as rational exponents. Use those properties to simplify each expression. 9¹/√₂
The simplified form of 9^(1/√2) is 3.
By defining the rules for irrational exponents, we can extend the properties of rational exponents to handle expressions with irrational exponents. Let's simplify the expression 9^(1/√2) using these rules.
To simplify the expression, we can rewrite 9 as [tex]3^2[/tex]:
[tex]3^2[/tex]^(1/√2)
Now, we can apply the rule for exponentiation of exponents, which states that a^(b^c) is equivalent to (a^b)^c:
(3^(2/√2))^1
Next, we can use the rule for rational exponents, where a^(p/q) is equivalent to the qth root of [tex]a^p[/tex]:
√(3^2)^1
Simplifying further, we have:
√3^2
Finally, we can evaluate the square root of [tex]3^2[/tex]:
√9 = 3
To learn more about rational exponents, refer here:
https://brainly.com/question/12389529
#SPJ11
Fifty tickets are entered into a raffle. Three different tickets are selected at random. All winners receive $500. How many ways can 3 different tickets be selected? Select one: a. 117,600 b. 125,000 c. 19,600 d. 997,002,000
There are 19,600 ways to select three different tickets from the given pool of fifty tickets, the correct option is: c. 19,600
To determine the number of ways three different tickets can be selected from a pool of fifty tickets, we can use the concept of combinations. The number of combinations of selecting r items from a set of n items is given by the formula nCr = n! / (r!(n-r)!), where n! represents the factorial of n.
In this case, we need to calculate the number of ways to select 3 tickets from a pool of 50 tickets. Applying the formula, we have:
50C3 = 50! / (3!(50-3)!)
= 50! / (3!47!)
Simplifying further:
50C3 = (50 * 49 * 48 * 47!) / (3 * 2 * 1 * 47!)
= (50 * 49 * 48) / (3 * 2 * 1)
= 19600
Therefore, the correct answer is: c. 19,600
Learn more about Tickets
brainly.com/question/183790
#SPJ11
(a) Find the work done by a force 5 i^ +3 j^ +2 k^ acting on a body which moves from the origin to the point (3,−1,2). (b) Given u =− i^ +2 j^ −1 k^and v = 2l −1 j^ +3 k^ . Determine a vector which is perpendicular to both u and v .
a) The work done by the force F = 5i + 3j + 2k on a body moving from the origin to the point (3, -1, 2) is 13 units.
b) A vector that is perpendicular to both u = -i + 2j - k and v = 2i - j + 3k is -6i - 7j - 3k.
a) The work done by a force F = 5i + 3j + 2k acting on a body that moves from the origin to the point (3, -1, 2) can be determined using the formula:
Work done = ∫F · ds
Where F is the force and ds is the displacement of the body. Displacement is defined as the change in the position vector of the body, which is given by the difference in the position vectors of the final point and the initial point:
s = rf - ri
In this case, s = (3i - j + 2k) - (0i + 0j + 0k) = 3i - j + 2k
Therefore, the work done is:
Work done = ∫F · ds = ∫₀ˢ (5i + 3j + 2k) · (ds)
Simplifying further:
Work done = ∫₀ˢ (5dx + 3dy + 2dz)
Evaluating the integral:
Work done = [5x + 3y + 2z]₀ˢ
Substituting the values:
Work done = [5(3) + 3(-1) + 2(2)] - [5(0) + 3(0) + 2(0)]
Therefore, the work done = 13 units.
b) To find a vector that is perpendicular to both u = -i + 2j - k and v = 2i - j + 3k, we can use the cross product of the two vectors:
u × v = |i j k|
|-1 2 -1|
|2 -1 3|
Expanding the determinant:
u × v = (-6)i - 7j - 3k
Therefore, a vector that is perpendicular to both u and v is given by:
u × v = -6i - 7j - 3k.
Learn more about force
https://brainly.com/question/30507236
#SPJ11
Pleeeeaase Answer ASAP!
Answer:
Step-by-step explanation:
Domain is where x direction part of the function where it exists,
The function exists from 0 to 9 including 0 and 9. Can be written 2 ways:
Interval notation
0 ≤ x ≤ 9
Set notation
[0, 9]
How long will it take $1298 00 to accumulate to $1423.00 at 3% pa compounded send-annualy? State your answer in years and months (hom 0 to 11 months) The investment will take year(s) and month(s) to mature In how many months will money double at 6% p a compounded quarterly? State your answer in years and months (from 0 to 11 months) In year(s) and month(s) the money will double at 6% p. a. compounded quarterly CETEED A promissory note for $600.00 dated January 15, 2017, requires an interest payment of $90.00 at maturity. It interest in at 9% pa. compounded monthly, determine the due date of the ne 0.00 The due date is (Round down to the neareskry) What is the nominal annual rate of interest compounded monthly at which $1191 00 will accumulate to $161453 in eight years and eight months? The nominal annual rate of interest in %. (Round the final answer to four decimal places as needed Round all intermediate values to six decimal places as needed) At what nominal annual rate of interest will money double itself in four years, three months if compounded quarterly? CETTE Next que The nominal annual rate of interest for money to double itself in four years, three months is % per annum compounded quarterly (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.) A debt of $670.68 was to be repaid in 15 months. If $788,76 was repaid, what was the nominal rate compounded monthly that was charged? The nominal rate compounded monthly is. (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.) What is the effective annual rate of interest if $1300.00 grows to $1800.00 in four years compounded semi-annually? KIER The effective annual rate of interest as a percent is % (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.) An amount of $1000.00 earns $400.00 interest in three years, nine months. What is the effective annual rate if interest compounds quarterly? Em The effective annual rate of interest as a percent is% (Round the final answer to four decimal places as needed Round all intermediate values to six decimal places as needed.) Sarah made a deposit of $1384 00 into a bank account that earns interest at 7.5% compounded quarterly. The deposit eams interest at that rate for four years (a) Find the balance of the account at the end of the period (b) How much interest is earned? (c) What is the effective rate of interest? (a) The balance at the end of the period is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed) (b) The interest eamed is $ (Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed) (c) The effective rate of interest is (Round the final answer to four decimal places as needed. Round all intermediate values to six decimal places as needed.)
The investment will take 1 year and 4 months to mature. In 16 months, the initial amount of $1298.00 will accumulate to $1423.00 at a 3% annual interest rate compounded semi-annually.
To calculate the time it takes for an investment to accumulate to a certain amount, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount ($1423.00)
P = Principal amount ($1298.00)
r = Annual interest rate (3% or 0.03)
n = Number of times interest is compounded per year (2 for semi-annual)
t = Time in years
We need to solve for t in this equation. Rearranging the formula:
t = (1/n) * log(A/P) / log(1 + r/n)
Plugging in the values:
t = (1/2) * log(1423/1298) / log(1 + 0.03/2)
Calculating this equation, we find t to be approximately 1.33 years, which is equivalent to 1 year and 4 months.
compound interest calculations and the formula used to determine the time it takes for an investment to accumulate to a specific amount.
Learn more about accumulate
brainly.com/question/32115201
#SPJ11
Has a ulameter of 30 mm. - (10 points) If the force P causes a point A to be displaced vertically by 2.2 mm, determine the normal strain developed in each wire. P 600 mm 30° 600 mm 30°
The normal strain developed in each wire is 0.00367 or 0.367%.
To determine the normal strain developed in each wire, we need to consider the relationship between strain, displacement, and original length.
Ulameter length: 30 mm
Displacement of point A: 2.2 mm
To find the normal strain, we can use the formula:
strain = (displacement) / (original length)
For the upper wire:
Original length = 600 mm
Strain in upper wire = (2.2 mm) / (600 mm) = 0.00367 or 0.367%
For the lower wire:
Original length = 600 mm
Strain in lower wire = (2.2 mm) / (600 mm) = 0.00367 or 0.367%
Therefore, the normal strain developed in each wire is 0.00367 or 0.367%.
Learn more about strain at brainly.com/question/27896729.
#SPJ11
Given the system of equations:
4x_1+5x_2+6x_3=8 x_1+2x_2+3x_3 = 2 7x_1+8x_2+9x_3=14.
a. Use Gaussian elimination to determine the ranks of the coefficient matrix and the augmented matrix..
b. Hence comment on the consistency of the system and the nature of the solutions.
c. Find the solution(s) if any.
a. The required answer is there are 2 non-zero rows, so the rank of the augmented matrix is also 2. To determine the ranks of the coefficient matrix and the augmented matrix using Gaussian elimination, we can perform row operations to simplify the system of equations.
The coefficient matrix can be obtained by taking the coefficients of the variables from the original system of equations:
4 5 6
1 2 3
7 8 9
Let's perform Gaussian elimination on the coefficient matrix:
1) Swap rows R1 and R2:
1 2 3
4 5 6
7 8 9
2) Subtract 4 times R1 from R2:
1 2 3
0 -3 -6
7 8 9
3) Subtract 7 times R1 from R3:
1 2 3
0 -3 -6
0 -6 -12
4) Divide R2 by -3:
1 2 3
0 1 2
0 -6 -12
5) Add 2 times R2 to R1:
1 0 -1
0 1 2
0 -6 -12
6) Subtract 6 times R2 from R3:
1 0 -1
0 1 2
0 0 0
The resulting matrix is in row echelon form. To find the rank of the coefficient matrix, we count the number of non-zero rows. In this case, there are 2 non-zero rows, so the rank of the coefficient matrix is 2.
The augmented matrix includes the constants on the right side of the equations:
8
2
14
Let's perform Gaussian elimination on the augmented matrix:
1) Swap rows R1 and R2:
2
8
14
2) Subtract 4 times R1 from R2:
2
0
6
3) Subtract 7 times R1 from R3:
2
0
0
The resulting augmented matrix is in row echelon form. To find the rank of the augmented matrix, we count the number of non-zero rows. In this case, there are 2 non-zero rows, so the rank of the augmented matrix is also 2.
b. The consistency of the system and the nature of the solutions can be determined based on the ranks of the coefficient matrix and the augmented matrix.
Since the rank of the coefficient matrix is 2, and the rank of the augmented matrix is also 2, we can conclude that the system is consistent. This means that there is at least one solution to the system of equations.
c. To find the solution(s), we can express the system of equations in matrix form and solve for the variables using matrix operations.
The coefficient matrix can be represented as [A] and the constant matrix as [B]:
[A] =
1 0 -1
0 1 2
0 0 0
[B] =
8
2
0
To solve for the variables [X], we can use the formula [A][X] = [B]:
[A]^-1[A][X] = [A]^-1[B]
[I][X] = [A]^-1[B]
[X] = [A]^-1[B]
Calculating the inverse of [A] and multiplying it by [B], we get:
[X] =
1
-2
1
Therefore, the solution to the system of equations is x_1 = 1, x_2 = -2, and x_3 = 1.
Learn more about Gaussian elimination:
https://brainly.com/question/30400788
#SPJ11
4) If f (x)=4x+1 and g(x) = x²+5
a) Find (f-g) (-2)
b) Find g¹ (f(x))
If g¹ (f(x)) = 16x² + 8x + 6and g(x) = x²+5 then (f - g) (-2) = 4(-2) - (-2)² - 4= -8 - 4 - 4= -16 and g¹ (f(x)) = 16x² + 8x + 6.
Given that f(x) = 4x + 1 and g(x) = x² + 5
a) Find (f-g) (-2)(f - g) (x) = f(x) - g(x)
Substitute the values of f(x) and g(x)f(x) = 4x + 1g(x) = x² + 5(f - g) (x) = 4x + 1 - (x² + 5) = 4x - x² - 4
On substituting x = -2, we get
(f - g) (-2) = 4(-2) - (-2)² - 4= -8 - 4 - 4= -16
b) Find g¹ (f(x))f(x) = 4x + 1g(x) = x² + 5
Let y = f(x) => y = 4x + 1
On substituting the value of y in g(x), we get
g(x) = (4x + 1)² + 5= 16x² + 8x + 1 + 5= 16x² + 8x + 6
Therefore, g¹ (f(x)) = 16x² + 8x + 6
Learn more about g¹ (f(x)) at https://brainly.com/question/32930384
#SPJ11
c. For the following statement, answer TRUE or FALSE. i. \( [0,1] \) is countable. ii. Set of real numbers is uncountable. iii. Set of irrational numbers is countable.
c. For the following statement, answer TRUE or FALSE. i. [0,1] is countable: FALSE. ii. The set of real numbers is uncountable: TRUE. iii. The set of irrational numbers is countable: FALSE.
For the first statement, [0, 1] is an uncountable set since we cannot count all of its elements. For the second statement, it is correct that the set of real numbers is uncountable. This result is called Cantor's diagonal argument and is one of the most critical results of mathematical analysis. The proof of this theorem is known as Cantor's diagonalization argument, and it is a significant proof that has made a significant contribution to the field of mathematics.
The set of irrational numbers is uncountable, so the statement is false. Because the irrational numbers are the numbers that are not rational numbers. And the set of irrational numbers is not countable as we cannot list them.
You can learn more about real numbers at: brainly.com/question/31715634
#SPJ11
A kilogram of sweet potatoes costs 25 cents more than a kilogram of tomatoes. if 3 kg of sweet potatoes costs $12.45, find the cost of a kilo of tomatoes (aud)
Answer:
Step-by-step explanation:
If a kilogram of sweet potatoes costs 25 cents more than a kilogram of tomatoes and 3 kilograms of sweet potatoes cost 12.45 you need to divide 12.45 by 3 to get the cost of 1 kilogram of sweet potatoes.
12.45/3=4.15
We then subtract 25 cents from 4.15 to get the cost of one kilogram of tomatoes because a kilogram of sweet potatoes costs 25 cents more.
4.15-.25=3.9
A kilogram of tomatoes costs 3.90$.
Witch expression is equal to 1/tan x + tan x
A 1/sin x
B sin x cos x
C 1/cos x
D1/sin x cos x
The expression 1/tan(x) + tan(x) is equal to cos(x) + sin(x). Therefore, option B. Sin(x)cos(x) is correct.
To simplify the expression 1/tan(x) + tan(x), we need to find a common denominator for the two terms.
Since tan(x) is equivalent to sin(x)/cos(x), we can rewrite the expression as:
1/tan(x) + tan(x) = 1/(sin(x)/cos(x)) + sin(x)/cos(x)
To simplify further, we can multiply the first term by cos(x)/cos(x) and the second term by sin(x)/sin(x):
1/(sin(x)/cos(x)) + sin(x)/cos(x) = cos(x)/sin(x) + sin(x)/cos(x)
Now, to find a common denominator, we multiply the first term by sin(x)/sin(x) and the second term by cos(x)/cos(x):
(cos(x)/sin(x))(sin(x)/sin(x)) + (sin(x)/cos(x))(cos(x)/cos(x)) = cos(x)sin(x)/sin(x) + sin(x)cos(x)/cos(x)
Simplifying the expression further, we get:
cos(x)sin(x)/sin(x) + sin(x)cos(x)/cos(x) = cos(x) + sin(x)
Therefore, the expression 1/tan(x) + tan(x) is equal to cos(x) + sin(x).
From the given choices, the best answer that matches the simplified expression is:
B. sin(x)cos(x)
for such more question on equivalent
https://brainly.com/question/9657981
#SPJ8
Solid A and solid B are
mathematically similar. The ratio
of the volume of A to the volume
of B is 125: 64
If the surface area of A is 400 cm
what is the surface of B?
The surface area of solid B is 1024 cm².
If the solids A and B are mathematically similar, it means that their corresponding sides are in proportion, including their volumes and surface areas.
Given that the ratio of the volume of A to the volume of B is 125:64, we can express this as:
Volume of A / Volume of B = 125/64
Let's assume the volume of A is V_A and the volume of B is V_B.
V_A / V_B = 125/64
Now, let's consider the surface area of A, which is given as 400 cm².
We know that the surface area of a solid is proportional to the square of its corresponding sides.
Surface Area of A / Surface Area of B = (Side of A / Side of B)²
400 / Surface Area of B = (Side of A / Side of B)²
Since the solids A and B are mathematically similar, their sides are in the same ratio as their volumes:
Side of A / Side of B = ∛(V_A / V_B) = ∛(125/64)
Now, we can substitute this value back into the equation for the surface area:
400 / Surface Area of B = (∛(125/64))²
400 / Surface Area of B = (5/4)²
400 / Surface Area of B = 25/16
Cross-multiplying:
400 * 16 = Surface Area of B * 25
Surface Area of B = (400 * 16) / 25
Surface Area of B = 25600 / 25
Surface Area of B = 1024 cm²
As a result, solid B has a surface area of 1024 cm2.
for such more question on surface area
https://brainly.com/question/20771646
#SPJ8
ion 1 et ered ed out of g ion Work Problem [15 points]: Write step-by-step solutions and justify your answers. = Use Euler's method to obtain an approximation of y(2) using h y' = 4x − 8y + 10, 0.5, for the IVP: y(1) = 5.
The Euler's method with h = 0.5, the approximation of y(2) for the given initial value problem is -11.5.
Using Euler's method with a step size of h = 0.5, we can approximate the value of y(2) for the given initial value problem y' = 4x - 8y + 10, y(1) = 5.
Euler's method is an iterative numerical method used to approximate solutions to ordinary differential equations. It involves dividing the interval of interest into smaller steps and approximating the solution at each step based on the slope of the differential equation at that point.
To apply Euler's method, we start with the initial condition (x₀, y₀) = (1, 5) and compute the next approximation using the formula:
yₙ₊₁ = yₙ + h * f(xₙ, yₙ),
where h is the step size and f(x, y) is the differential equation.
In this case,
f(x, y) = 4x - 8y + 10.
Using h = 0.5,
we can calculate the approximation of y(2) as follows:
x₁ = x₀ + h = 1 + 0.5 = 1.5,
y₁ = y₀ + h * f(x₀, y₀) = 5 + 0.5 * (4 * 1 - 8 * 5 + 10) = -11.5.
Therefore, using Euler's method with h = 0.5, the approximation of y(2) for the given initial value problem is -11.5.
Learn more about Euler's method from the given link:
https://brainly.com/question/33067517
#SPJ11
The approximation of y(2) from the differential equation using Euler's method with a step size of 0.5 is 29.
What is the approximation of the function?To approximate the value of y(2) using Euler's method, we'll follow these steps:
1. Define the given differential equation: y' = 4x - 8y + 10.
2. Determine the step size, h, which is given as 0.5.
3. Identify the initial condition: y(1) = 5.
4. Set up the iteration using Euler's method:
- Start with the initial condition: x(0) = 1, y(0) = 5.
- Calculate the slope at (x(0), y(0)): m = 4x(0) - 8y(0) + 10.
- Update the next values:
x(1) = x(0) + h
y(1) = y(0) + h * m
Repeat the above step until you reach the desired value, x = 2.
5. Calculate the approximation of y(2) using Euler's method.
Let's go through the steps:
Step 1: The given differential equation is y' = 4x - 8y + 10.
Step 2: The step size is h = 0.5.
Step 3: The initial condition is y(1) = 5.
Step 4: Using Euler's method iteration:
For x = 1, y = 5:
m = 4(1) - 8(5) + 10 = -26
x(1) = 1 + 0.5 = 1.5
y(1) = 5 + 0.5 * (-26) = -7
For x = 1.5, y = -7:
m = 4(1.5) - 8(-7) + 10 = 80
x(2) = 1.5 + 0.5 = 2
y(2) = -7 + 0.5 * 80 = 29
Step 5: The approximation of y(2) using Euler's method is 29.
Learn more on Euler's method here;
https://brainly.com/question/14091150
#SPJ4