The exact value of cos(-n/12) is equal to cos(n/12).
The cosine function (or cos function) in a triangle is the ratio of the adjacent side to that of the hypotenuse.
The value of cosine function is periodic with a period of 2π. Therefore, we can use the property cos(x) = cos(x + 2πk) for any integer value of k.
In this case, we have cos(-n/12). To find the exact value, we can use the fact that cos(x) = cos(-x) for any angle x. Therefore, we can rewrite cos(-n/12) as cos(n/12).
So, the exact value of cos(-n/12) is equal to cos(n/12).
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the current in the electronic circuit in the mobile phone was 0.12a the potential difference across the battery was 3.9V. calculate the resistance of the electronic circuit in the mobile phone
Answer:
Step-by-step explanation:
V = 3.9V
I = 0.12A
Ohm's Law, V = IR
Rearranging Ohm's Law, R = V/I
R = 3.9/0.12 = 32.5Ω
Round to the nearest hundredth place.
7.2 ft
15.1 ft
The volume of the tarp shelter is 65.37 ft³ .
Given,
Conic tarp shelter with radius 5.1 ft and height 7.2 ft .
Now,
Volume of cone = 1/3 × π × r² × h
Substitute the values in the formula,
Volume of cone = 1/3 ×3.14 × (5.1)² × 7.2
Volume of cone = 65.37 ft³ .
Hence volume of tarp shelter will be 65.37 ft³ .
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Use an associative law to find an expression equivalent to
s + (r + 75)
As you can see below, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.
The associative law in mathematics states that the grouping of numbers in an addition or multiplication operation does not affect the result. In other words, you can regroup terms within parentheses without changing the value of the expression.
Using the associative law, we can regroup the terms in the expression s + (r + 75) by removing the parentheses and rearranging the terms:
s + (r + 75) = (s + r) + 75
The expression (s + r) + 75 is equivalent to s + (r + 75) because the addition operation is associative.
Let's take an example to illustrate this:
Suppose s = 10 and r = 20.
Using the original expression:
s + (r + 75) = 10 + (20 + 75) = 10 + 95 = 105
Using the expression with regrouped terms:
(s + r) + 75 = (10 + 20) + 75 = 30 + 75 = 105
As you can see, both expressions result in the same value of 105. This demonstrates the application of the associative law in regrouping terms and maintaining the equivalence of the expression.
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In a health club, research shows that on average, patrons spend an average of 42.5 minutes
on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally
distributed variable. Find the probability that randomly selected individual would spent
between 30 and 40 minutes on the treadmill.
0,30
0.70
0.40
Less than 1%
Answer:
0.30
Step-by-step explanation:
To find the probability that a randomly selected individual would spend between 30 and 40 minutes on the treadmill, we need to calculate the z-scores corresponding to these values and then use the z-table or a statistical calculator to find the probability.
First, we calculate the z-scores using the formula:
z = (x - μ) / σ
where x is the value (in this case, 30 and 40), μ is the mean (42.5), and σ is the standard deviation (4.8).
For x = 30:
z = (30 - 42.5) / 4.8 ≈ -2.604
For x = 40:
z = (40 - 42.5) / 4.8 ≈ -0.521
Next, we look up the probabilities associated with these z-scores in the z-table or use a statistical calculator.
From the z-table or calculator, the probability corresponding to z = -2.604 is approximately 0.0047, and the probability corresponding to z = -0.521 is approximately 0.3015.
To find the probability between 30 and 40 minutes, we subtract the probability associated with z = -2.604 from the probability associated with z = -0.521:
P(30 ≤ x ≤ 40) = P(z = -0.521) - P(z = -2.604)
≈ 0.3015 - 0.0047
≈ 0.2968
Therefore, the probability that a randomly selected individual would spend between 30 and 40 minutes on the treadmill is approximately 0.2968, which is equivalent to 29.68%. Rounding up we will get 0.30.
Hope this helps!
Can you factor 5v²-30v+70
Answer: Unfactorable
Step-by-step explanation:
5v^2-30v+70
5(v^2-6v+14)
You can't factor v^2-6v+14 with rational numbers
Which scenarto could be modeled by the graph of the function A) & 10041.002)4
A
An ant colony that has an initial population ef 100 increases by 0.296 per year.
An ant colony that has an Infal population of 100 increases at a constant rate of 0.2 per year.
An ant colony that has an intal population of 100 decreases by 0.2% per year
D
An ant colony that has an Infial population of 100 decreases at a constant rate of 0.2 per year.
The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.
We have,
The function A(x) = 100 + 4x represents a linear relationship between the variable x (representing time in this case) and the variable A(x) (representing the population of the ant colony).
The term 100 in the function represents the initial population of the ant colony.
It indicates that at the starting point (x = 0), the population is 100.
The term 4x in the function represents the rate at which the population increases over time. Since the coefficient of x is positive (4), it indicates that the population is increasing.
For every unit increase in x (in this case, for every year that passes), the population increases by 4.
Therefore,
The function A(x) = 100 + 4x describes the scenario of an ant colony that starts with an initial population of 100 and experiences a constant rate of increase of 4 ants per year.
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PLS HELP, BRAINLEST ANSWER GIVEN
This fraction is equivalent to
Answer: A -6x² + 2x -4
Step-by-step explanation:
[tex]\frac{-12x^{3}+ 4x^{2} -8x}{2x}[/tex] >Divide each of the top terms by 2x[tex]=\frac{-12x^{3}}{2x} +\frac{4x^{2} }{2x} -\frac{8x}{2x}[/tex]
= -6x² + 2x -4
What is an improper fraction for 1 3/4
Answer:
An improper fraction for 1 3/4 is 7/4.
Step-by-step explanation:
[tex]\frac{7}{4}[/tex]
To find the improper fraction of a mixed number fraction. You first have to remove the whole number from the fraction (the big one bending the fraction)
Do this by multiplying the denominator (4) by the whole number (1)
4 x 1 = 4
Then add this number with the numerator (top number) which is 3.
4+3 = 7
Seven is our new numerator, our denominator stays the same (4)
So our new improper fraction is:
[tex]\frac{7}{4}[/tex]
what is equivalent to 3³
Answer:
Step-by-step explanation:
3x3x3= 27
If 15% of the customers total is $98,880, then the sum total equals what
Answer:
Step-by-step explanation:
The distance that a freefalling body falls in each second starting with the first second is given by the arithmetic progression 16, 48,80,112
find the distance, the body falls in the seventh second
Answer:
208 units
Step-by-step explanation:
The first term is given as 16, which means a = 16.
The second term can be obtained by adding the common difference to the first term: 16 + d = 48.
The third term is obtained by adding the common difference to the second term: 48 + d = 80.
The fourth term is obtained by adding the common difference to the third term: 80 + d = 112.
We can solve these equations to find the value of 'd':
16 + d = 48
d = 48 - 16
d = 32
48 + d = 80
32 + 48 = 80 (valid)
80 + d = 112
32 + 80 = 112 (valid)
Therefore, the common difference is 32.
Now that we have the common difference, we can find the distance the body falls in the seventh second.
The formula for finding the nth term of an arithmetic progression is:
a_n = a + (n - 1) * d
where a_n is the nth term, a is the first term, n is the position of the term, and d is the common difference.
Plugging in the values, we can find the seventh term:
a_7 = 16 + (7 - 1) * 32
a_7 = 16 + 6 * 32
a_7 = 16 + 192
a_7 = 208
Therefore, the distance the body falls in the seventh second is 208 units.
Suppose that point P is the point on the unit circle obtained by rotating the initial ray through θ° counterclockwise. What is the length of segment OP?
The length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
To determine the length of segment OP on the unit circle, we need to use trigonometry. Let's break down the problem step by step:
Definition: The unit circle is a circle with a radius of 1 centered at the origin (0, 0) in the Cartesian coordinate system.
Initial Ray: The initial ray is a line segment that starts from the origin (0, 0) and extends to a point on the unit circle. It forms an angle with the positive x-axis.
Rotation: We are rotating the initial ray counterclockwise by θ degrees. This means we are essentially finding a new point on the unit circle based on the angle θ.
Trigonometric Functions: The trigonometric functions sine (sin) and cosine (cos) are particularly useful for calculating the coordinates of points on the unit circle.
sin(θ) gives the y-coordinate of a point on the unit circle.
cos(θ) gives the x-coordinate of a point on the unit circle.
Coordinates of Point P: Since we are rotating the initial ray counterclockwise by θ degrees, the coordinates of point P on the unit circle can be obtained as follows:
x-coordinate of P: cos(θ)
y-coordinate of P: sin(θ)
Distance from the Origin (Length of Segment OP):
Using the coordinates of point P, we can calculate the distance between the origin (0, 0) and point P using the distance formula.
The distance formula states that for two points (x1, y1) and (x2, y2), the distance between them is given by:
d = √((x2 - x1)² + (y2 - y1)²)
In this case, point P has coordinates (cos(θ), sin(θ)), and the origin is (0, 0). Thus, the distance (length of segment OP) is:
d = √((cos(θ) - 0)² + (sin(θ) - 0)²)
= √(cos²(θ) + sin²(θ))
= √(1) [Using the trigonometric identity: sin²(θ) + cos²(θ) = 1]
= 1
Therefore, the length of segment OP, which represents the distance from the origin to point P on the unit circle, is always equal to 1.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / fc
The degree of the function (x) = (x + 1)2(2x-3)(x+2) is
Reset
, and its y-intercept
Next
A vet records the weight of all the dogs she has seen in the last week the data is recorded bellow in pounds. 61, 10, 32, 19, 22, 22, 29, 36, 14, 49, 3 What is the mean Median, mode, standard deviation, and the outlier (if any)?
Answer:
Mean: 27
Median: 22
Mode: 22
Standard deviation: 17
No outlier (61 might be one just check with people you know and see if they have an outlier or not)
Step-by-step explanation: Give a definition of mean, median, mode…and just add your answers.
A ball is thrown into the air. The function h(x) = -16x2 + 64x + 8 models the height, in feet above ground, of the ball after x seconds.
What was the height of the ball at the time it was thrown?
How many seconds after being thrown did the ball reach its maximum height?
Answer:
At the time the ball was thrown, it was 8 feet above the ground.
h'(x) = -32x + 64 = 0, so x = 2
The ball reaches its maximum height after 2 seconds.
is 72 and has an IRA with a fair market value of
Use
Table
45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the
distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a
vacation?
May Kawasaki's required minimum distribution (RMD) is $3,808. This is calculated by dividing her IRA balance of $98,000 by the distribution period of 26.2, which is found in the Uniform Life Table on page 45 for a 72-year-old.
How to explain the informationb) If May Kawasaki fails to take her RMD, she will incur a 50% penalty on the amount she should have withdrawn. In this case, the penalty would be $1,904.
c) If May Kawasaki had made an early withdrawal of $10,000 to take a vacation, she would have paid a 10% penalty on the amount withdrawn. In this case, the penalty would have been $1,000.
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1. May Kawasaki is 72 and has an IRA with a fair market value of $98,000. a) Use the Uniform Life Table on p. 45 to determine her required minimum distribution. b) What penalty would she incur if she failed to take the distribution? c) What penalty would she have paid if she had made an early withdrawal of $10,000 to take a vacation?
Help pls i don't understand
ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
What is Angle- Angle - Side theorem?The angle-angle-side theorem, or AAS, tells us that if two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are congruent.
If we consider triangle FSH and triangle FSI, we will observe the following;
angle HFS = angle IFSangle FSH = angle FSIlength HS = length SISo based on the angle-angle-side theorem, or AAS, we can see that triangle FSH is congruent to triangle FSI.
Thus, our answer will be; ΔFSH ≅ ΔFSI by the rule of angle-angle-side theorem, or AAS.
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Need the correct answers for this. Can you help me?
The length of PQ is 3√5 and its slope is -2
The length of SR is 3√5 and its slope is -2
The length of SP is 5√2 and its slope is -7
The length of RQ is 5√2 and its slope is -1
So PQ ≅ SR and SP ≅ RQ. By the Perpendicular Bisector theorem, adjacent sides are perpendicular. By the selection of side, ∠PSR, ∠SRQ, ∠RQP and ∠QPS are right angles. So, the quadrilateral is a rectangle.
Understanding QuadrilateralTo find the lengths and slopes of the sides of the quadrilateral PQRS, we apply the distance formula:
D = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
and the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
1. Length PQ:
Using the distance formula, the length PQ can be calculated as follows:
PQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((3 - 0)² + (-4 - 2)²)
= √(3² + (-6)²)
= √(9 + 36)
= √45
= 3√5
2. Length SR:
Using the distance formula, the length SR can be calculated as follows:
SR = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - (-2))² + (-5 - 1)²)
= √((1 + 2)² + (-6)²)
= √(3² + 36)
= √(9 + 36)
= √45
= 3√5
3. Length SP:
Using the distance formula, the length SP can be calculated as follows:
SP = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((1 - 0)² + (-5 - 2)²)
= √(1² + (-7)²)
= √(1 + 49)
= √50
= 5√2
4. Length RQ:
Using the distance formula, the length RQ can be calculated as follows:
RQ = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]
= √((-2 - 3)² + (1 - (-4))²)
= √((-2 - 3)² + (1 + 4)²)
= √((-5)² + 5²)
= √(25 + 25)
= √50
= 5√2
Now, let's calculate the slopes of the sides:
1. Slope PQ:
The slope of PQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-4 - 2) / (3 - 0)
= -6 / 3
= -2
2. Slope SR:
The slope of SR can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 1) / (1 - (-2))
= -6 / 3
= -2
3. Slope SP:
The slope of SP can be calculated using the slope formula:
m =[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (-5 - 2) / (1 - 0)
= -7 / 1
= -7
4. Slope RQ:
The slope of RQ can be calculated using the slope formula:
m = [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
= (1 - (-4)) / (-2 - 3)
= 5 / (-5)
= -1
Therefore, the lengths and slopes of the sides of the quadrilateral PQRS are:
Length PQ: 3√5
Length SR: 3√5
Length SP: 5√2
Length RQ: 5√2
Slope PQ: -2
Slope SR: -2
Slope SP: -7
Slope RQ: -1
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Part A
Study the two functions shown, A(t) and 12∙J(t). Based on the graph and the data, what kinds of functions are they? Choose among linear, quadratic, and exponential. Describe the features of each function that gave you clues.
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Part B
The equation A = Pert describes a bank loan that compounds continuously. The variables in the equation are described in the table:
Variable Definition
A This is the principal and interest on the loan. Principal is the amount of money borrowed. Interest is a graduated fee paid to the bank for the privilege of borrowing its money.
P This is the principal, or the amount of money borrowed. Don’t confuse P in the compounding interest equation with P in the profit equation. One is principal, the other is profit.
e This is Euler’s number, e ≈ 2.7, used in exponential functions that are continuously compounding.
r This is the interest rate expressed as a percentage.
t This is the time allotted, in years, to repay the loan. It’s also called the life of the loan.
For the sake of this activity, assume that you will collect profit from sales for a number of months and then use a portion of that profit to pay off the entire loan in one lump-sum payment once the loan terminates. Based on this assumption, what does the intersection of the 12∙J(t) curve and the A(t) curve represent? Explain using your own words.
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Part C
Take some time to gradually increase P in increments of $100,000 while keeping r and J(t) constant. What happens to the relationship between the two curves? What does this mean with respect to the bank loan? Why is this a dangerous situation with respect to the financial health of your business? Why would banks put safeguards in place to prevent this from occurring?
15px
Part A:
A(t) is a linear function, and 12∙J(t) is an exponential function. The straight line nature of A(t) indicates linear growth, while the curve of 12∙J(t) suggests exponential growth.
Part B:
The intersection of the 12∙J(t) curve and the A(t) curve represents the point where the accumulated profit from sales is sufficient to pay off the entire loan in one lump-sum payment.
Part C:
As P increases while keeping r and J(t) constant, the relationship between the two curves shifts, indicating a higher profit requirement to cover the increased loan amount. This is dangerous for business financial health and banks have safeguards to prevent excessive debt and defaults.
Part A:
From the given information, we have two functions: A(t) and 12∙J(t). Let's analyze their features to determine their types.
A(t) is a linear function:
A linear function is characterized by a constant rate of change and forms a straight line on a graph.
In the given graph, A(t) is represented by a straight line, indicating a linear relationship between the variables.
This suggests that A(t) is a linear function.
12∙J(t) is an exponential function:
An exponential function is characterized by a constant ratio or base and shows exponential growth or decay.
In the given graph, 12∙J(t) is represented by a curve that exhibits exponential growth.
The increasing rate of change as time progresses indicates an exponential relationship.
Therefore, 12∙J(t) is an exponential function.
Part B:
The intersection of the 12∙J(t) curve and the A(t) curve represents the point at which the profit generated from sales is sufficient to pay off the entire loan in one lump-sum payment. In other words, it represents the point in time when the accumulated profit matches the amount of the loan.
At this intersection point, the profit generated from sales has reached a level where it can fully cover the principal and interest owed on the loan. This indicates that the business has generated enough funds to repay the loan in its entirety.
Part C:
As the principal (P) is increased while keeping the interest rate (r) and 12∙J(t) constant, the relationship between the two curves changes. Specifically, the intersection point between the curves shifts to the right on the graph.
This change in the relationship between the curves signifies that the business needs a higher level of profit to cover the increased loan amount. It suggests that the business has taken on a larger loan, which requires a higher profit to repay.
This situation is considered dangerous for the financial health of the business because it increases the risk of not generating sufficient profit to repay the loan. If the business fails to generate enough profit to cover the loan payments, it may lead to financial instability and potential default on the loan.
To mitigate such risks, banks put safeguards in place to prevent businesses from taking on excessive debt. These safeguards include conducting thorough evaluations of the business's financial health, setting limits on loan amounts based on the business's income and creditworthiness, and assessing the repayment capacity of the borrower. These measures aim to minimize the risk of defaults and protect both the borrower and the lender.
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Solve the equation below for x by graphing
3x =8_2x
The solution to the equation 3x = 8 - 2x is x = 1.6.
To solve the equation 3x = 8 - 2x by graphing, we can plot the two sides of the equation as functions of x and find the point(s) where they intersect. Here's a step-by-step explanation:
Express the equation in the form of y = f(x). Rearrange the equation:
3x + 2x = 8
5x = 8
x = 8/5 or 1.6
Graph the functions y = 3x and y = 8 - 2x on the same coordinate plane. The line represented by y = 3x is upward sloping, and the line represented by y = 8 - 2x is downward sloping.
Plot the points (1.6, 3(1.6)) and (1.6, 8 - 2(1.6)) on the graph.
The point of intersection represents the solution to the equation. In this case, the lines intersect at (1.6, 4.8).
Therefore, the solution to the equation 3x = 8 - 2x is x = 1.6.
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Help me! Make sure to do step by step! (I need to see the steps)
Simplify
(9x^8y^2z^6)^1/2
Answer: [tex]3x^4yz^3[/tex]
I'm hoping this is your equation: [tex](9x^{8}y^{2}z^{6})^{1/2}[/tex]
and not: [tex](9x^{8y^{2z^{z^6}}})[/tex]
Step-by-step explanation:
The square root of a number can be shown as a 1/2 power
We'll use the exponent rule:
= [tex]9^{1/2}(x^8 )^{1/2}(y^2)^{1/2}(z^6){1/2}[/tex]
Then we'll do each term individually
the square root of 9 is 3
for [tex](x^8)^{1/2}[/tex] the exponents multiply which give us [tex]x^4[/tex]
[tex](y^2)^{1/2}[/tex] gives us y
[tex](z^6)^{1/2}[/tex] gives us z^3
After doing all this we get [tex]3x^4yz^3[/tex]
1/27^{4-x}=9^{2x-1}
Please if you could explain how you get your answer, that would be great.
The solution of the given equation is x = -10.
We are given that;
The equation 1/27^{4-x}=9^{2x-1}
Now,
This is an exponential equation that can be solved by using the properties of exponents and logarithms. Here are the steps to solve it:
Rewrite both sides of the equation using the same base. Since 27 and 9 are both powers of 3, we can use 3 as the base. We have:
(3(-3))(4-x) = (32)(2x-1)
Apply the power rule of exponents to simplify the expressions. The power rule states that (ab)c = a^(bc). We have:
3^(-12+3x) = 3^(4x-2)
Since the bases are equal, we can set the exponents equal to each other and solve for x. We have:
-12 + 3x = 4x - 2 -10 = x
Therefore, by the given equation the answer will be x = -10.
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4. The perimeter of the rectangle is represented by 8y metres and the area is represented by
(6y + 3) square metres.
X+8
x+6
a. Write two equations in terms of x and y: one for the perimeter and one for the area
of the rectangle.
b. Determine the perimeter and the area of the rectangle.
a) The two equations in terms of x and y: one for the perimeter and one for the area of the rectangle are:
y = 0.5x + 3.5
6y + 3 = x² + 14x + 48
b) The area and perimeter of the rectangle are:
Perimeter = 30 m
Area = 15 m²
How to find the perimeter and area of the rectangle?The formula to find the area of a rectangle is:
Area = Length * Width
The formula to find the perimeter of a rectangle is:
Perimeter = 2(Length + Width)
We are given that:
Perimeter = 8y meters
Area = (6y + 3) square meters
From the image, we see that:
Length = x + 6
Width = x + 8
Thus:
Perimeter equation is:
8y = 2(x + 6 + x + 8)
8y = 4x + 28
y = 0.5x + 3.5
Area equation is:
6y + 3 = (x + 6)(x + 8)
6y + 3 = x² + 14x + 48
Thus:
6(0.5x + 3.5) + 3 = x² + 14x + 48
3x + 24 = x² + 14x + 48
x² + 11x + 24 = 0
Using quadratic equation calculator gives:
x = -8 or -3
Thus, we will use x = -3 and we have:
Length = -3 + 6 = 3 m
Width = -3 + 8 = 5 m
Perimeter = 2(3 + 5) = 30 m
Area = 3 * 5 = 15 m²
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What are the minimum and maximum values of the function?
The minimum value of [tex]f(x) = -2^3 \sqrt\(5-4x+3)[/tex] on the interval [1, 8] is -3 and the maximum value is 5. To find the minimum value, we can start by finding the critical points of the function.
The critical points are the points where the derivative of the function is equal to zero. In this case, the derivative of the function is
[tex]f'(x) = -2^3 \times (5-4x+3) ^(-3/2) \times (-4)[/tex]
The critical points of the function are x = 1 and x = 5.
We can now evaluate the function at each critical point and at the endpoints of the interval to find the minimum and maximum values. The values of the function at the critical points and at the endpoints are
x | f(x)
-- | --
1 | -3
5 | 5
8 | 9
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Desperate Need Of Help
The domain and range of the graph above in interval notation include the following:
Domain = [-6, 3]
Range = [-3, 3]
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:
Domain = [-6, 3] or -6 ≤ x < 3.
Range = [-3, 3] or -3 < y < 3
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A line that passes through the points (–4, 10) and (–1, 5) can be represented by the equation y = - 5/3(x – 2). Which equations also represent this line? Select three options.
y=-5/3x-2
✅y=-5/3x+10/3
✅3y = –5x + 10
3x + 15y = 30
✅5x + 3y = 10
Can someone tell me if I chose the right answers
Options 2, 3, and 5 are correct representations of the line passing through the given points.
The equation y = -5/3(x - 2) represents a line passing through the points (-4, 10) and (-1, 5).
Let's verify each option:
y = -5/3x - 2: This equation does not represent the same line. The constant term is different (-2 instead of +10/3).
y = -5/3x + 10/3: This equation represents the same line. It has the same slope (-5/3) and the same y-intercept (10/3).
3y = -5x + 10: This equation represents the same line. It can be simplified by dividing both sides by 3, resulting in the same slope (-5/3) and the same y-intercept (10/3).
3x + 15y = 30: This equation does not represent the same line. The coefficients of x and y are different, resulting in a different slope.
5x + 3y = 10: This equation represents the same line. It has the same slope (-5/3) and the same y-intercept (10/3).
Therefore, options 2, 3, and 5 are correct representations of the line passing through the given points.
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4. In a lab experiment, 5300 bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every 12 hours. Write a function showing the number of bacteria after t hours, where the hourly growth rate can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per hour, to the nearest hundredth of a percent.
The function representing the number of bacteria after t hours is N(t) = 5300 * (1 + 0.0592)^t, and the growth rate per hour is approximately 5.92%.
To represent the number of bacteria after t hours, we can use the exponential growth formula:
N(t) = N₀ * (1 + r)^t,
where N(t) is the number of bacteria after t hours, N₀ is the initial number of bacteria, r is the hourly growth rate, and t is the time in hours.
In this case, the initial number of bacteria is 5300, and the hourly growth rate can be determined from the doubling time of 12 hours. The growth rate can be calculated using the formula:
r = 2^(1/t_double) - 1,
where t_double is the doubling time in hours.
Substituting the given values, we have:
r = 2^(1/12) - 1 ≈ 0.0592.
Now we can write the function for the number of bacteria after t hours:
N(t) = 5300 * (1 + 0.0592)^t.
To determine the percentage of growth per hour, we can calculate the relative growth rate as a percentage:
percentage_growth = r * 100 ≈ 5.92%.
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Stephanie wanted to solve the equation 16=3x+1. Which inverse operations should she use to find the solution?
Subtraction and Division
Step-by-step explanation:Inverse operations help find the solution to equations.
Defining Inverse Operations
Firstly, let's define an operation. An operation in math is a function that can manipulate a value. Inverse operations are operations that are opposite operations that undo each other. For example, addition and subtraction are inverse operations because subtraction undoes addition. Multiplication and division are also inverse operations.
Solving the Equation
The equation 16 = 3x + 1 involves both addition and multiplication. So, to solve this, we can use the inverse operations of subtraction and division. First, subtract 1 from both sides.
15 = 3xThen, divide both sides by 3.
5 = xThis shows that by using subtraction and division, we can undo the addition and multiplication used in the equation. This allows us to find the value of x.
Which route of delivery would be most appropriate for a patient with a bacterial sinus infection?
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. You have a credit card with a balance of $754.43 at a 13.6% APR. You have $300.00 available each month to save or pay down your debts. a. How many months will it take to pay off the credit card if you only put half of the available money toward the credit card each month and make the payments at the beginning of the month? b. How many months will it take to pay off the credit card if you put all of the available money toward the credit card each month and make the payments at the beginning of the month? Be sure to include in your response: • the answer to the original question • the mathematical steps for solving the problem demonstrating mathematical reasoning
a. It will take 7 months to pay off the credit card.
b. it will take 4 months to pay off the credit card.
Since, APR stands for Annual Percentage Rate. It is the interest rate charged on a loan or credit card, expressed as a yearly percentage rate. The APR takes into account not only the interest rate, but also any fees or charges associated with the loan or credit card.
a. If you put half of the available money each month toward the credit card, then you are paying $150.00 per month towards the credit card balance.
We can use the formula for the present value of an annuity to find how many months it will take to pay off the credit card:
PV = PMT × ((1 - (1 + r)⁻ⁿ) / r)
where:
PV is the present value of the debt
PMT is the payment amount per period
r is the monthly interest rate
n is the number of periods
Substituting the values, we get:
754.43 = 150 × ((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV ×r / PMT)) / log(1 + r)
n = log(1 + (754.43×0.011333 / 150)) / log(1 + 0.011333)
n = 6.18
Therefore, it will take 7 months to pay off the credit card if you put half of the available money each month toward the credit card.
b. If you put all of the available money each month toward the credit card, then you are paying $300.00 per month towards the credit card balance.
754.43 = 300 ×((1 - (1 + 0.011333)⁻ⁿ) / 0.011333)
Simplifying and solving for n, we get:
n = log(1 + (PV × r / PMT)) / log(1 + r)
n = log(1 + (754.43× 0.011333 / 300)) / log(1 + 0.011333)
n = 3.43
Therefore, it will take 4 months to pay off the credit card if you put all of the available money each month toward the credit card.
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