The approximate distance between points T and U is 3.16 units, rounded to the nearest hundredth.(option c)
The problem states that we need to find the approximate distance between points T and U, rounded to the nearest hundredth. To solve this problem, we can use the distance formula, which is derived from the Pythagorean theorem. The formula is given as:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Here, (x₁, y₁) and (x₂, y₂) represent the coordinates of the two points, and √ denotes the square root operation.
Now, let's apply this formula to find the distance between points T and U. Suppose that T has the coordinates (-2, 1), and U has the coordinates (-1, 4). Then, we can plug in these values into the formula and simplify:
distance = √[(-1 + 2)² + (4 - 1)²]
= √[(1)² + 3²]
= √(1 + 9)
= √10
≈ 3.16
Therefore, we can see that the correct answer is (c) 3.16 units.
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BRAINLIEST IF RIGHT
6. MN=x-1, NP = 9x - 68, MP = 5x - 4
The value of x is 13.
What is a line segment?A line segment is a straight line formed by a continuous arrangement of series of points. As such, it can be divided into parts.
Considering the given question, it can be deduced that; MP is a line segment which has been divided into two parts MN and NP.
Thus we have;
MP = MN + NP
But we are given that; MN = x - 1, NP = 9x - 68, and MP = 5x - 4.
Then we can say that;
MP = MN + NP
5x - 4 = (x-1) + (9x - 68)
= 10x - 69
collect like terms
69 - 4 = 10x - 5x
65 = 5x
x = 65/ 5
= 13
The value of x is 13.
MP = 5x - 4
= 5(13) - 4
= 65 - 4
MP = 61
MN = x - 1
= 13 - 1
MN = 12
NP = 9x - 68
= 9(13) - 68
= 117 - 68
NP = 49
Therefore, the appropriate value of x is 13.
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The correct question is:
Range of x-values: 6. MN = x - 1, NP = 9x - 68, MP = 5x - 4.
solve for x
log4(2x)=5
Answer
=5
4^5=2x2x=1024x=512
We know that 3/4 of Australians work force are happly with their jobs. We know this because we surveyed 100 government employees aged 25-30 and found that 75 of them were satisfised with their postions. What in the statement makes the 3/4 a questionable figure?
The 3/4 is questionable figure in the statement because it is based on a limited and potentially unrepresentative sample.
The statement "We know that 3/4 of Australians work force are happily with their jobs" is based on the survey results of only 100 government employees aged 25-30. While this may provide an indication of job satisfaction among this particular group, it is not necessarily representative of the entire Australian workforce.
The sample size of 100 employees is relatively small, and the sample may not be representative of the larger population. Additionally, the sample only includes government employees aged 25-30, which further limits its generalizability. There may be significant differences in job satisfaction levels among different age groups or in different industries.
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The account balance on April 1st is $50.51. On April 15th a payment of $15.00 is made. On April 25th a purchase of $19.27 is made. The annual rate is 18%.
What is the unpaid balance? What is the finance charge using the unpaid balance method? What is the new balance?
Unpaid balance = $
Finance charge = $
New balance = $
In response to the stated question, we can state that The new balance is equation therefore $55.59.
What is equation?An equation is a mathematical assertion that establishes the equality of two expressions that are joined together by the equals sign ('='). For example, 2x – 5 = 13. 2x-5 and 13 are examples of expressions. The letter '=' connects the two expressions. A mathematical formula is called an equation if it contains two algebraic expressions on either side of the equal sign (=). It shows how the right and left formulas are equivalent to one another. Any formula will result in L.H.S. = R.H.S. (left side = right side).
We must ascertain the balance that is still owing after the payment and purchase transactions have been executed in order to calculate the unpaid balance.
The balance drops to $35.51 on April 15 ($50.51 - $15.00), a reduction of $15.00.
The account balance climbs to $54.78 ($35.51 + $19.27) on April 25.
The remaining balance is $54.78 as a result.
$44.29 * (0.18 / 365) * 30 = $0.81
The finance fee is therefore $0.81.
We combine the outstanding balance and the finance charge to determine the new balance:
$54.78 + $0.81 = $55.59
The new balance is therefore $55.59.
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Suppose you have been tasked with regulating a single monopoly firm that sells 50-pound bags of concrete. The firm has fixed costs of $10 million per year and a variable cost of $3 per bag no matter how many bags are produced.
the optimal price and quantity for the bags of concrete should be amount $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.
Q = 10,000 - 100P
Where Q is the quantity of bags and P is the price per bag.
The goal of the regulation is to maximize total economic surplus.
To maximize total economic surplus, the optimal price and quantity for the bags of concrete should be determined. The total economic surplus for this situation can be calculated by finding the area of the triangle formed between the demand curve and the price line.
The optimal price is calculated by setting the demand equation equal to zero, giving P = 100.
The optimal quantity is calculated by substituting the optimal price into the demand equation, giving Q = 10,000.
The total economic surplus is calculated by finding the area of the triangle formed between the demand curve and the price line, which is (100*10,000)/2 = $500,000 amount.
Therefore, the optimal price and quantity for the bags of concrete should be $100 and 10,000 bags, respectively. This combination would yield a total economic surplus of $500,000.
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El tangram es un rompecabezas chino de 7 piezas que salen de cortar un cuadrado en 5 triángulos, un paralelogramo y un cuadrado como se muestra en la figura; el juego consiste en usar las piezas para construir diferentes formas Cuatro amigos están reunidos formando figuras con las piezas del tangram, uno de ellos preguntó: ¿Qué fracción del cuadrado representa la figura que he construido, considerando que el cuadrado formado por las 7 piezas es la unidad?
The fraction of the square represented by a figure constructed with pieces of a tangram can be calculated by dividing the area of the figure by the area of the square.
The fraction of the square that a figure constructed with the pieces of a tangram represents can be calculated by dividing the area of the figure with the area of the square. The area of a square can be determined using the formula A = s2, where s is the side length of the square. The area of the figure can be calculated by adding together the area of the individual pieces of the tangram. For example, if the figure is composed of two triangles with base lengths of b1 and b2 and heights h1 and h2, then the area of the figure can be calculated using the formula A = b1h1 + b2h2. The fraction of the square represented by the figure is calculated by dividing the area of the figure by the area of the square.
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A hot-air balloon is floating over a river valley. At noon, the pilot increases the balloon's altitude to get a better view of the surroundings. This situation can be modeled as a linear relationship. What does the slope of the line tell you about the situation?
The slope of the line in this situation tells us the rate of change of the balloon's altitude with respect to time.
The slope of a line represents the ratio of the change in the vertical coordinate (altitude) to the change in the horizontal coordinate (time). In this scenario, as the pilot increases the balloon's altitude to get a better view of the surroundings, the altitude changes with respect to time.
Thus, the slope of the line represents the rate of change of the balloon's altitude with respect to time. A steep slope indicates a rapid change in altitude over time, while a gentle slope indicates a slower change. By analyzing the slope, the pilot can adjust the altitude of the balloon as needed to achieve the desired view.
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the 12-foot bed of a dump truck loaded with heavy stone must rise to an angle of 36 degrees before the stone will spill out. Approximately how high must the front of the bed rise (x) to unload?
The approximate height of the front bed 8.1ft
What is trigonometry?
The study of the relationships and characteristics of angles, triangles, and the trigonometric functions is the focus of the mathematic branch known as trigonometry (sine, cosine, tangent, cotangent, secant, and cosecant). It entails using algebraic methods and geometric principles to solve problems involving triangles and angles, such as measuring angles, computing triangle sides and angles, and analysing periodic events like waves and oscillations.
We use trigonometry to solve the problem
we have
tan (36) = opposite side/ adjacent side
tan(36) = opposite side / 12
Opposite side = tan(36) *12
Opposite side = 8.1 ft
Hence, the approximate height of the front bed 8.1ft
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This is for highschool geometry
The side length of dilated cubes is 10.08 units. Then the surface area of the dilated cube is 609.6384 square units.
What is dilation?
Dilation means the changing of the size of the object without changing the shape. The size of the object may be increased or decreased based on the scale factor.
A solid has a volume of 2 cubic units and a surface area of 10 square units.
The solid is dilated, and the image has a volume of 128 cubic units.
Let the original side length of the cube be a and dilated length of the cube be b.
MsReid CTEA
The total cost of producing a type of car is given by
C(x)=25000−40x+0.02x^2, where x is the number of cars produced. How
many cars should be produced to incur minimum cost?
The corporation should make 1000 of a certain sort of car in order to reduce production cost using minimal cost function and derivatives.
Finding the value of x that minimizes the cost function will help us determine the optimal number of automobiles to construct. [tex]C(x) = 25000 - 40x + 0.02x^2[/tex].
The derivative of C(x) with respect to x can be taken, set to zero, and then the value of x can be determined.
[tex]C'(x) = -40 + 0.04x = 0 0.04x = 40 \sx = 1000[/tex]
Hence, when 1000 cars are created, the least cost is incurred. We can check the second derivative of C(x) at x = 1000 to make sure this is a minimum.
[tex]C''(x) = 0.04 > 0[/tex]
The fact that the second derivative is positive demonstrates that the minimum of C(x) occurs at x = 1000.
As a result, the corporation should make 1000 of a certain sort of car in order to reduce production costs. Cost is reduced to $21000 at this manufacturing level.
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how much is x?
44=-7+x
Answer: x=51
Step-by-step explanation: Add 7 to both sides of the equation.
Please give brainliest !!
Answer:
x = 51
Step-by-step explanation:
44 = -7 + x
+7 +7
51 = x
x = 51
The net of a solid figure is shown below: Four squares are shown side by side in a row. The second square has a square above it and a square below it. All the squares have side length equal to 3 inches Which calculation will give the total surface area of the solid figure? (1 point) a 3 × 6 × 6 square inches b 6 × 3 × 3 × 3 square inches c 3 × 6 × 6 × 6 square inches d 6 × 3 × 3 square inches
6 × 3 × 3 square inches will give the total surface area of the solid figure.
What is surface area?
The surface area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface.
We are given a figure which contains six squares and the dimensions of each square are 3 inches each.
Area of one square = 3 × 3 square inches
Total surface area = 6 × 3 × 3 square inches
Hence, 6 × 3 × 3 square inches will give the total surface area of the solid figure.
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The missing figure of the question has been attached below.
An express railroad train between 2 cities carries 10 000 passengers per year at a one - way fare of $50. If the fare goes up, ridership will decrease, since more people will drive. It is estimated that each $10 increase in fare will result in 1000 fewer passengers per year. What fare will maximize revenue?
The fare that would maximize revenue is $70.
To prove this, we must first calculate the number of passengers who will use the train at different fares. This is because the revenue formula for this is:
Revenue = Fares x Passengers
where revenue is a function of both the fare and the number of passengers using the train. From the given data, we have:
Initial Fare = $50
Initial Passengers = 10,000
Assuming X = Increase in fare (in dollars) and Y = Decrease in passengers, we can derive the following table:
Fare ($)|Passengers|Revenue ($)
--|--|--
50|10,000|500,000
60|9,000|540,000
70|8,000|560,000
80|7,000|560,000
90|6,000|540,000
Here's how we computed it:
Starting at the $50 fare, every additional $10 fare increase decreases the number of passengers by 1000 (see the problem statement). So, at $60, the number of passengers is 10,000 – 1,000 = 9,000. Similarly, at $70, the number of passengers is 10,000 – 2,000 = 8,000. Continuing this way, we can fill in the table. Then, we can plug in the values of fares and passengers into the revenue formula to obtain the revenue values in the last column.
Note that the revenue maximizes at a fare of $70 because at that point, the revenue is the highest ($560,000) compared to any other fare in the table. Therefore, the fare that maximizes revenue is $70.
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For each of the figures, write an absolute value equation to satisfy the given solution sets: -8 and -2
An absolute value equation to satisfy the given solution sets: -8 and -2 is |x+5|=3
Define equationIn mathematics, an equation is a statement that two expressions are equal. An equation consists of variables, constants, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, etc.). The variables in an equation are often represented by letters, and the equation indicates that certain combinations of these variables and constants have the same value. Equations are commonly used in mathematics, physics, engineering, and many other fields to model and solve problems.
From the diagram you can see that the solutions of the equation are and
1. Determine the middle number between -8 and -2:
1/2(-8-2)=-5
2. Find the distance between points x=-5and x=-2:
d=-2+5=3
3. Writhe an absolute value equation :
|x+5|=3
Image is attached below.
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After 12 hours, half of a 16-gram sample of a radioactive element remains. Find the constant k for this element for t hours, then write the equation for modeling its exponential decay
The equation for modeling its exponential decay is N(t) = 16 * e^(-0.0578t) where N(t) is the amount of radioactive element remaining after t hours.
We can use the formula for exponential decay to model the decay of the radioactive element. The formula is:
N(t) = N0 * e^(-kt)
where N(t) is the amount of the radioactive element remaining after t hours, N0 is the initial amount of the element, e is the mathematical constant approximately equal to 2.71828, and k is a constant that represents the rate of decay.
We are given that half of the initial 16-gram sample remains after 12 hours. That means the initial amount N0 is 16 grams and the amount remaining after 12 hours is 8 grams. We can use these values to solve for k.
8 = 16 * e^(-k*12)
Dividing both sides by 16, we get:
0.5 = e^(-12k)
Taking the natural logarithm of both sides, we get:
ln(0.5) = -12k
Solving for k, we get:
k = -ln(0.5)/12
k ≈ 0.0578
Therefore, the constant k for this radioactive element is approximately 0.0578. The equation of modeling its exponential decay is
N(t) = 16 * e^(-0.0578t)
where N(t) is the amount of radioactive element.
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Step by step please
Answer:
17/25
Step-by-step explanation:
You want to know which of 5/16 or 17/25 is closer to 1/2.
ComparisonFor the sake of argument, let's assume that 17/25 is closer to 1/2. This means the difference from 1/2 is smaller than for 5/16:
(17/25 -1/2) < (1/2 -5/16)
We can add (5/16 + 1/2) to both sides and we get ...
17/25 + 5/16 < 1
The sum on the left is easily computed:
(17·16 +25·5)/(25·16) < 1
(272 +125)/400 < 1
397/400 < 1 . . . . . . true
Our original premise is true: 17/25 is closer to 1/2.
__
Additional comment
A straightforward solution involves finding the positive difference of each number from 1/2, then comparing those differences. The attached calculator screen does that. It shows the difference of 17/25 from 1/2 is smaller than for 5/16, in agreement with the above.
Effectively, we're comparing the midpoint between the two numbers to 1/2. If it is below 1/2 (which it is), then the upper number doesn't have as great a distance from 1/2 as the lower number does.
This sort of comparison only works if the numbers are on either side of 1/2. If they are on the same side, the sign of their difference tells the tale.
José y Damián son montañistas,cada uno de ellos ha tomado un camino diferente para ascender a una montaña José camina en línea recta 365m y en ascenso 584m, mientras que Damián camina en ascenso 465m y en línea recta 208 m para llegar al punto de encuentro. ¿cuántos metros de diferencia hay en el recorrido de los dos montañistas para llegar al punto de encuentro
The difference in the distance of the route of the two mountaineers to reach the meeting point is approximately 311.67m.
To solve this problem, we need to find the total distance each mountaineer traveled to reach the meeting point. Then we can compare the two distances to find the difference.
Let's start with José's route. We can use the Pythagorean theorem to find the total distance he traveled:
total distance = √(365² + 584²) ≈ 694.36m
Now let's find the total distance for Damián's route. Again, we can use the Pythagorean theorem to find the distance he walked on the ground:
distance on the ground = √208² + (584 - 465)² = √208² + 119² ≈ 236.98m
And we can add the distance he ascended:
total distance = 236.98m + 465m = 701.98m
Finally, we can find the difference in distance between the two routes:
difference = 701.98m - 694.36m ≈ 7.62m
Therefore, there is a difference of approximately 7.62 meters between the route of the two mountaineers to reach the meeting point.
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The question is -
José and Damián are mountaineers, each of them has taken a different path to climb a mountain. José walks straight for 365m and climbs 584m, while Damián climbs 465m and walks straight for 208m to reach the meeting point. How many meters of difference are there in the path taken by the two mountaineers to reach the meeting point?
Noah loves the half tens fact and often uses them to solve multiplication problems. Make up a 2 digit number and 3 digit multiplication problem for which using half ten fact is efficient. Then solve the problem using that strategy
Using the half ten fact for rounding and distributive property helped us efficiently solve the multiplication problem of 47 x 550.
Let's take the 2-digit number 47 and multiply it by the 3-digit number 550:
To use the half ten fact, we can first round the 3-digit number to the nearest half ten, which in this case would be 550 rounded to 550 + 50 = 600.
Then, we can split the 2-digit number into its tens and ones digits: 47 = 40 + 7.
Next, we can use the distributive property of multiplication to simplify the problem:
47 x 600 = (40 + 7) x 600 = 40 x 600 + 7 x 600
Now, we can use the half ten fact for the first term: 40 x 600 = (20 x 10) x 600 = 20 x (10 x 600) = 20 x 6000 = 120,000.
For the second term, we can use the fact that 7 x 6 = 42:
7 x 600 = 7 x (10 x 60) = (7 x 10) x 60 = 70 x 60 = 4,200.
Finally, we can add the two terms to get the final answer:
47 x 550 = 47 x 600 - 47 x 50 = 120,000 + 4,200 - 2,350 = 121,850.
Therefore, using the half ten fact for rounding and distributive property helped us efficiently solve the multiplication problem of 47 x 550.
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(3x+19) and (5x-9) set equal
The expressions (3x+19) and (5x-9) when set equal gives the solution x = 14
How to solve equivalent equation?Equivalent equation is an assertion that two expressions are equal, expressed by writing the two expressions separated by an equal sign from which one is to determine a particular quantity.
(3x + 19) = (5x - 9)
open parenthesis
3x + 19 = 5x - 9
combine like terms
3x - 5x = -9 - 19
-2x = -28
divide both sides by -2
x = -28/-2
x = 14
Therefore, x = 14 is the solution to the expressions when set equal.
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Help
Me please please
The average rate of change is $22.50 per class
The total amount for 5 classes is $117.5The first class is $27.50 due to the studio charging $5 as the registration fee How to determine the average rate of changeThe table of values represent the given parameter
The average rate of change is calculated as
Rate = Change in T(c)/Corresponding change in c
So, we have
Rate = (50 - 27.50)/(2 - 1)
Rate = 22.50
The total amount for 5 classesWe start by calculating the function from
T(c) = mc + b
Where
m = Rate = 22.50
So, we have
T(c) = 22.5c + b
Using the points, we have
22.5 * 1 + b = 27.50
So, we have
b = 5
So, we have
T(c) = 22.5c + 5
For 5 classes, we have
T(5) = 22.5 * 5 + 5
T(5) = 117.5
Why the first class is 27.50The first class is 27.50 because the studio charges a registration fee of $5
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Maddie buys a drink and a frozen yogurt. The frozen yogurt is priced by the ounce. The equation y= 0.50x + 2.25 can model the total cost of maddies purchases. What does the value of the function at x = 0 represent?
Answer: x = 0 represents the price of the drink
Step-by-step explanation:
The equation 71. 40=(11. 9)6 shows how much it cost for a
company to buy 6 new uniforms. How much does it cost per
uniform?
Please please help me quiz.
If the cost for the 6 new uniforms is denoted by 71.40 = (11.9)6 , then the cost per uniform is $11.9 .
The equation which shows how much it cost for a company to buy 6 new uniforms is represented as : 71.40 = (11.9)6 ,
In order to find the cost per uniform, we need to divide both sides of the cost equation by 6:
On dividing both the sides of cost-equation by 6,
We get;
⇒ 71.40/6 = [(11.9)6]/6,
On simplifying ,
We get,
⇒ 71.40/6 = 11.9
Therefore, it cost the company 11.9 dollars each for the new uniform.
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What are the next four numbers in the pattern below? ¼, ¾, 1 ¼, 1 ¾...
Answer:
Answer below
Step-by-step explanation:
2 1/4, 2 3/4, 3 1/4, 3 3/4
Answer:[tex]2\frac{1}{4} , 2\frac{3}{4} , 3\frac{1}{4} , 3\frac{3}{4}[/tex]
Step-by-step explanation:
This series is in arithmetic progression, where all the elements in this series increase progressively. They have a common difference. You can find the common difference by substracting any term by its preceding term as:
d = t(n+1) - t(n)
In this case:
[tex]\frac{3}{4} - \frac{1}{4} = \frac{1}{2}[/tex]
You can use the cd. to find the remaining elements by adding the difference to the 4th term to find the 5th term, and adding it to 5th term to get the 6th term and so on.
1. What assumptions may not necessarily be valid for a typical family regarding both the loan rate and savings plan rate?
The loan rate assumptions are:
1) Assumption that the family has good credit
2) Assumption that the family is borrowing for a large purchase
3) Assumption that the loan is secured
Savings Plan Rate Assumptions are:
1) Assumption that the family has a significant amount of disposable income
2) Assumption that the family has a long investment horizon
3) Assumption that the family has a high tolerance for risk
There are a few assumptions that may not necessarily be valid for a typical family regarding both the loan rate and savings plan rate. Some of these assumptions include:
Loan Rate Assumptions:a. Assumption that the family has good credit: Most loan rate calculators assume that the borrower has good credit.
b. Assumption that the family is borrowing for a large purchase: Many loan rate calculators assume that the family is borrowing for a large purchase, such as a house or a car.
c. Assumption that the loan is secured: Many loan rate calculators assume that the loan is secured by collateral, such as a house or a car.
Savings Plan Rate Assumptions:a. Assumption that the family has a significant amount of disposable income: Many savings plan calculators assume that the family has a significant amount of disposable income to invest in a savings plan.
b. Assumption that the family has a long investment horizon: Many savings plan calculators assume that the family has a long investment horizon, such as 10 or 20 years.
c. Assumption that the family has a high tolerance for risk: Many savings plan calculators assume that the family has a high tolerance for risk and can invest in high-risk investments that offer a higher rate of return.
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1.
An artist wants to sell prints of her paintings. She orders a set of prints for each of two of her paintings.
Each set contains regular prints and glossy prints, as shown in the table. Find the cost of one glossy
print.
The cost of one glossy print is $7.84.
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, where the largest exponent of the variable is 2.
An example of a quadratic equation is ax^2 + bx + c = 0, where a, b, and c are constants and x is the variable.
Let the cost of one regular print be "x" and the cost of one glossy print be "y".
From the first row, we can set up the equation:
45x + 30y = 465
From the second row, we can set up another equation:
15x + 10y = 155
We can solve for one variable in terms of the other in the second equation:
15x + 10y = 155
10y = 155 - 15x
y = (155 - 15x)/10
We can substitute this expression for y into the first equation:
45x + 30y = 465
45x + 30((155 - 15x)/10) = 465
Multiplying both sides by 10 to eliminate the fraction:
450x + 300(155 - 15x) = 4650
Simplifying:
450x + 46500 - 4500x = 4650
-4050x = -41850
x = 10.32 (rounded to the nearest hundredth)
Now we can substitute this value for x into the expression for y:
y = (155 - 15x)/10
y = (155 - 15(10.32))/10
y = 7.84 (rounded to the nearest hundredth)
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determine whether the formula is explict of recursice then find the first five terms of the sequence a n-2^a n -1+1 where a 1=3
The sequence type is a recursive function and the first five terms cannot be determined from the formula
How to determine the sequence typeFrom the question, we have the following parameters that can be used in our computation:
a(n-2)ᵃ⁽ⁿ ⁻ ¹⁾ + 1 where a1 = 3
The formula a(n-2)ᵃ⁽ⁿ ⁻ ¹⁾ + 1 is recursive because it defines the nth term in terms of the two previous terms a(n-2) and a(n-1).
To find the first five terms of the sequence, we can use the initial value a1=3 and the recursive formula.
So, we have
a1 = 3
a2 = a(0)ᵃ¹
The second term cannot be calculated because we do not have a(0)
This means that other terms cannot be calculated with the formula
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Using trigonometry, work out the length y Give your answer in centimetres to 1 d.p. Y 6.1 cm 39° Not drawn accurately
The length of y is given as follows:
y = 7.8 cm.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.In the context of this problem, we have that y is the hypotenuse, while 6.1 cm is the side length adjacent to the angle of 39º, hence:
cos(39º) = 6.1/y
y = 6.1/cosine of 39 degrees
y = 7.8 cm.
Missing Information6.1 cm is adjacent to the angle of 39º, while y is the hypotenuse.
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Consider the first five terms of the following sequence. 2, 6, 18, 54, 162,. Of The sequence defines a function, what is a reasonable domain and range of the function?A. Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}Domain: {1, 2, 3, 4, 5, …}; Range: all real numbers. Domain: all real numbers; Range: {2, 6, 18, 54, 162, …}D. Domain: all real numbers; Range: all real numbers
The reasonable domain and range of the function is option (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
The sequence appears to be an exponential sequence with a common ratio of 3. That is, each term is obtained by multiplying the previous term by 3.
If this sequence defines a function, a reasonable domain would be the set of positive integers starting from 1 since the sequence begins with the first term being 2.
The range of the function appears to be the set of positive powers of 3 since each term is a power of 3 multiplied by the initial term, 2. Therefore, a reasonable range would be the set {2, 6, 18, 54, 162, ...}.
Therefore, the correct option is (A) Domain: {1, 2, 3, 4, 5, …}; Range: {2, 6, 18, 54, 162, …}.
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exponential and logarithmic functions
The half-life of Potassium-40 is 1.25 billion years. The decay equation for Potassium-40 can be expressed as N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant.
What is decay constant?Decay constant is a measure of the rate at which a radioactive sample decays. It is usually expressed as the probability of a given radioactive nucleus decaying per unit time. It is related to the half-life of a radioactive sample, which is the time it takes for half of the sample to decay.
To answer part b, we need to solve N(t) = 15 mg. When rearranged, this equation becomes t = ln(15/N0)/(-k). Using the given initial amount of 36 mg and the calculated decay constant of 0.00056, we find that it will take 1.44 billion years for the specimen to decay to 15 mg.
For part c, we can use the same equation and solve for N(t). We get N(t) = N0e-kt, where N(t) is the amount of Potassium-40 at time t, N0 is the initial amount of Potassium-40, and k is the decay constant. Using the initial amount of 36 mg and the decay constant of 0.00056, we find that after 300 million years, there will be 27.72 mg of Potassium-40 left.
For part d, we can solve N(t) = N0/8. When rearranged, this equation becomes t = ln(N0/8)/(-k). With the initial amount of 36 mg and the decay constant of 0.00056, we find that it will take 2.68 billion years for Potassium-40 to decay to one-eighth of its original amount.
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Managed timber stands average 150 trees per acre with standard
deviation of 40. Assume acres are normally distributed. Find
probability of a randomly selected timber stand having more than 92
trees
The probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.
Managed timber stands average 150 trees per acre with a standard deviation of 40. Assume acres are normally distributed.To find the probability of a randomly selected timber stand having more than 92 trees.We have to calculate the Z-Score using the formula,Z= (X-μ)/ σWhere X= 92 treesμ = 150 treesσ= 40Using the formulaZ= (X-μ)/ σZ= (92-150)/40= -1.45We know that the area under the normal distribution curve is 1. To find the probability of a random variable that falls between two points, we need to find the area between those points.A normal distribution curve is shown below:To find the probability of a randomly selected timber stand having more than 92 trees, we need to find the area to the right of Z= -1.45 using a normal distribution table. The probability is 0.0744 or 7.44%.Therefore, the probability of a randomly selected timber stand having more than 92 trees is 0.0744 or 7.44%.
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