What is the constant of proportionality in this table?
X
2
5
7.5
y
31
77.5
116.25

The value of the x as shown in the graph will be 16.61 ft.

From the sine rule in the triangle,

In a triangle ABC, where a, b, and c are the side lengths opposite to the angles A, B, and C respectively, and where the opposite angles A, B, and C are opposite to sides a, b, and c respectively, the Sine Rule states:

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

Use the Law Of Sines to solve this:

(Sin 7)/9 = (Sin 13)/x

Cross multiply...

x(Sin 7) = 9(Sin 13)

Divide both sides by Sin 7

x = [9(Sin 13)]/(Sin 7)

x = 16.61254121

therefore, for the ramp, the value of the x will be 16.612 ft.

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The inequality represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks is 50 ≥ 3.5x + 5

We are given that Sydney started with no money in her piggy bank and adds $3.50 each day. Destiny started with $50 in her piggy bank and spends $5 of her money each day.

We need to find the equation or inequality that represents the number of days, x, needed for Destiny and Sydney to have the same amount of money in their piggy banks.

Sydney started with zero money in her piggy bank and adds $3.50 each day means 0 + 3.50 and Destiny started with $50 in her piggy bank and spends $5 of her money each day then

the inequality  becomes as ;

50 ≥ 3.5x + 5

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From 1970 to 2013, the price of postal stamps increased at an average yearly rate of 4.851%.

The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)[/tex]

where A represents the total sum, P represents the beginning sum, r represents the yearly interest rate, n is the number of times the interest is compounded annually, and t represents the number of years.

In this instance, we may consider the initial cost of postal stamps in 1970 as the principal and the rise in price as the interest. The yearly rate of rise, r, may be calculated using the formula.

Let P represent the price in 1970 ($0.06) and A represent the price in 2013 ($0.46). Let t be the duration, or 43 years, from 1970 to 2013.

Then, we can write:

[tex]A = P(1 + r)^t[/tex]

Substituting the values, we get:

[tex]0.46 = 0.06(1 + r)^{43[/tex]

Dividing both sides by 0.06, we get:

[tex]7.67 = (1 + r)^{43[/tex]

Taking the 43rd root of both sides, we get:

[tex](1 + r) = 7.67^{1/43}\\(1 + r) = 1.04851[/tex]

Subtracting 1 from both sides, we get:

r = 0.04851 = 4.851%

Therefore, the average annual rate of increase in the price of postage stamps from 1970 to 2013 is 4.851%.

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Answer:

(a) Area of the big circle

= π(9^2) = 81π square cm

(b) Area of both little circles

= 2π(4.5^2) = 40.5π square cm

= 81π/2 square cm

(c) Area of the blue section

= 81π - 40.5π = 40.5π square cm

= 81π/2 square cm

Measurement can be used to determine the amount of boxes that can fit into Truck H is 2(20 boxes) = 2 cubic yards

Algebraic expressions are defined as those mathematical expressions that consists of variables, terms, coefficients, constants and factors.

Algebraic expressions are also known  to be composed of arithmetic operations, such as;

From the information given, we have that;

For Truck G = 20 boxes

And 20 boxes = 1 cubic yard

Then,

Truck H = 2(Truck B)

Truck H = 2(20 boxes)

Truck H = 40 boxes

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Answer:

Number three is D.

Step-by-step explanation:

Answer: im pretty sure the answer is in the pdf, when you scroll down. its 126 cm^2

Step-by-step explanation:

According to the information, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.

To evaluate the elasticity at $p=2$, we need to use the formula for price elasticity of demand:

E = (dQ/Q) / (dP/P)

where:

E = price elasticity of demand

dQ = change in quantity demanded

Q = quantity demanded

dP = change in price

P = price

We are given the equation for the demand function:

x = 15000 - 3535√p

So, the quantity demanded at price $p$ is $Q = x(p) = 15000 - 3535\sqrt{p}$.

Taking the derivative of Q with respect to p:

dQ/dp = -3535/(2√p)

Now we can calculate the elasticity at $p=2$:

Q = 15000 - 3535√2

dQ/dp = -3535/(2√2)

P = 2

dP = 0

E = (dQ/Q) / (dP/P)

E = (-3535/(2√2)) / [(15000 - 3535√2)/2]

E ≈ -0.619

According to the above, the elasticity is 0.619, suggests that the demand is relatively insensitive to price changes.

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answer 95 I think that is the answer do you know it it is hard

Answer:

Total cost = $132

Step-by-step explanation:

We can find the total cost using the formula

total cost = (item 1 quantity * cost) + (item 2 quantity * cost)

We essentially find the sum of the product of item quantity and cost for each item:

Thus, for 2 chairs costing $37/chair and 1 table costing $58/table, the total cost is:

Total cost = (2 * $37) + (1 * $58)

Total cost = $74 + $58

Total cost = $132

Answer: Answer choice C: -1.3 and 1.3.

Step-by-step explanation:

We can start by using the formula for the distance, D, between the two trains as a function of time, T:

D = 55(T + 2.25) - 120T

Simplifying this equation, we get:

D = 55T + 123.75 - 120T

D = -65T + 123.75

To find the two values of T for which D = 40, we can set this equation equal to 40 and solve for T:

40 = -65T + 123.75

-85 = -65T

T = 1.31

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.31) + 123.75

D = 40.0375

Therefore, one solution is T = 1.31. To find the other solution, we can plug D = 40 into the equation and solve for T:

40 = -65T + 123.75

-83.75 = -65T

T = 1.29

Plugging this value back into the original equation, we can see that D is equal to 40:

D = -65(1.29) + 123.75

D = 40.0375

Therefore, the two values of T for which D = 40 are approximately 1.3 and 1.3, which rounds to answer choice C: -1.3 and 1.3.

The proportional relationship y = 15x represents the relationship between the variables, and it's graph is given by the image presented at the end of the answer.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

A student in a foreign language program learns 15 new word each week, hence the constant is given as follows:

k = 15.

Meaning that the equation is:

y = 15x.

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The surface area of the rectangular prism is 216 square cm

From the question, we have the following parameters that can be used in our computation:

10 cm by 3 cm by 6 cm

The surface area of the rectangular prism is calculated as

Area = 2 * (3 * 10 + 3 * 6 + 10 * 6)

Evaluate

Area = 216

Hence, the area is 216 square cm

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Answer:

D

Step-by-step explanation:

We know that the residual is the difference between the observed value and the predicted value for a given point. Let's assume that the predicted values for the three points in the data set are denoted by ŷ₁, ŷ₂, and ŷ₃, and the observed values are denoted by y₁, y₂, and y₃.

We can write the residuals as:

e₁ = y₁ - ŷ₁

e₂ = y₂ - ŷ₂

e₃ = y₃ - ŷ₃

We are given that two of the residuals are -7 and 4.
Let's assume that e₁ = -7 and e₂ = 4.

We can use these values to find the third residual e₃.Since the sum of residuals is always equal to zero, we have:

e₁ + e₂ + e₃ = 0

Substituting the values of e₁ and e₂, we get

:-7 + 4 + e₃ = 0

Simplifying, we get:

e₃ = 3

Therefore, the third residual is 3, which is option D.

Answer:

To simplify the expression (5^-3/5^-1), we need to use the rule of exponents that states when dividing two powers with the same base, we can subtract the exponents.

Using this rule, we get:

(5^-3/5^-1) = 5^-3 ÷ 5^-1 = 5^-3 × 5^1 = 5^-2 = 1/25

Therefore, Hector gave the correct answer.

The inverse of the function f(x) = 9x²- 12 is p(x) = √(x + 12)/9

Given that the domain of a function f is restricted to x ≥ 0, we need to find the inverse of the function

f(x) = 9x²- 12 for x ≥ 0.

To find the inverse of the function, we proceed as follows.

f(x) = 9x²- 12

Let f(x) = y

So, we have that

y = 9x²- 12

Adding 12 to both sides of the equation, we have that

y + 12 = 9x²- 12 + 12

y + 12 = 9x²

Dividing both sides by 9, we have that

(y + 12)/9 = 9x²/9

(y + 12)/9 = x²

Taking square root of both sides, we have that

√x² = √(y + 12)/9

x = √(y + 12)/9

Now, replacing x with y, we have that

x = √(y + 12)/9

y = √(x + 12)/9

Replacing y with f⁻¹(x), we have that

f⁻¹(x) = √(x + 12)/9

So, the inverse is p(x) = √(x + 12)/9

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Answer:

Step-by-step explanation:

Answer:

2(x + 5) = 3(x - 4)

2x + 10 = 3x - 12

x = 22

Answer:

The expression "34° (-1/2 x) °" can be simplified by multiplying 34° by the quantity (-1/2 x):

34° (-1/2 x) ° = (34°) * (-1/2 x)

To multiply two values with units, we can simply multiply the numerical parts and keep the units. Therefore, we get:

(34°) * (-1/2 x) = -17x°

So the value of "34° (-1/2 x) °" is simply -17x°.

We can see here that the probability that it is yellow is: 2.4.

Probability is a way to gauge how likely something is to happen. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.

Probability that the marble is yellow:

Total marbles = 12

Yellow marbles = 5

Probability that the marble is yellow: 12/5 = 2.4

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Answer:

the answer is 80

Step-by-step explanation:

1pound=16ounces

Answer:  [tex](x+7)^2 + (y+1)^2 = 9[/tex]

center = (-7, -1)

radius = 3

======================================================

Explanation:

The highest point on the circle is at (-7,2)

The lowest point is at (-7, -4)

Connecting these endpoints gets us one diameter of this circle.

Apply the midpoint formula to these endpoints.

[tex]\text{Endpoints: }(x_1,y_1) = (-7,2) \text{ and } (x_2,y_2) = (-7,-4)\\\\\text{Midpoint} = (x_m, y_m)\\\\\begin{array}{|l|l|}\cline{1-2}x_m = \frac{x_1 + x_2}{2} & y_m = \frac{y_1 + y_2}{2}\\ & \\x_m = \frac{-7 +(-7)}{2} & y_m = \frac{2 +(-4)}{2}\\ & \\x_m = \frac{-14}{2} & y_m = \frac{-2}{2}\\ & \\x_m = -7 & y_m = -1\\\cline{1-2}\end{array}\\\\\text{The midpoint is located at }(-7, -1)\\\\[/tex]

This midpoint of a diameter is also the location of the center of the circle. Recall that all diameters are a special type of chord that pass through the center of a circle.

The circle is centered at (-7, -1)

---------

Now compute the distance from the center (-7,-1) to a point on the circle's edge. Let's say we picked (-7,2)

The distance between these points is 3 units, which we can find by subtracting the y coordinates and using absolute value

distance = |2 -(-1)| = |2+1| = |3| = 3

You could use the distance formula, but it's probably easier to subtract and then use absolute value.

The distance of 3 units represents the radius of the circle. It's how far you need to go from the center to get to the circle's edge.

Circle radius = 3

---------

Summary

We plug those items into the circle template equation.

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-(-7))^2 + (y-(-1))^2 = 3^2\\\\(x+7)^2 + (y+1)^2 = 9[/tex]

That last equation is the final answer.

Answer:

Step-by-step explanation:

Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph Bar Graph

When graphing an equation on graph paper I have to have all of these but: B. work shown.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

In Mathematics and Geometry, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

In conclusion, you do not need to have your algebraic work shown when graphing an equation on graph paper.

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The skate park is approximately 6.4 miles from the ice cream parlor.

We can use the Pythagorean theorem to find the distance between the skate park and the ice cream parlor.

As per the information, we can see that the distance we're looking for is the hypotenuse of a right triangle with legs of length 4 miles (distance from school to skate park) and 5 miles (distance from school to ice cream parlor).

Using the Pythagorean theorem, we get:

c² = a² + b²

where c is the distance between the skate park and the ice cream parlor, and a and b are the distances from the school to the skate park and ice cream parlor, respectively.

Substituting the values we know, we get:

c² = 4² + 5²

c² = 16 + 25

c² = 41

Taking the square root of both sides, we get:

c = √41

c ≈ 6.4

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The probability that ten hats given to ten people will consist of more blue caps than red caps is given as follows:

a. 0.2.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes in which there are more blue than red caps are those in which the number of zeros is greater than the number of ones, hence the number of desired outcomes is of:

2. (simulation number 7 and simulation number 10).

Hence the probability is of:

p = 2/10

p = 0.2.

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The percentage increase by the given data is 25%.

We are given that;

Weight of plastic in october= 40

Weight of plastic in november= 50

Now,

To find the percentage increase of the amount of plastic from October to November, we need to find the absolute increase and divide it by the original amount, then multiply by 100 to get the percentage.

The absolute increase is the difference between the final amount and the initial amount, which is 50 - 40 = 10 pounds.

The original amount is the initial amount, which is 40 pounds.

10​/40×100=25%.

Therefore, by the percentage the answer will be 25%.

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The radius of the circle with central angle θ = 40° is r = 8.594 cm

Given data ,

A circular arc has measure 6cm and is intercepted by a central angle of 40°

Now , the radius r of the circle is given by

r = L / θ

where θ is in radians

So , 40° = 0.6981317007977318 radians

On simplifying , we get

r = 40 / 0.6981317007977318

Now , the measure of r = 8.594 cm

Hence , the radius is r = 8.594 cm

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Answer:

multiply the number of meters by 100