What is the volume of this prism?44 cubic units
88 cubic units
102 cubic units
Not enough information.

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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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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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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There will be about 105.28 pounds of radioactive material in the concrete vault after 140 years.

The function [tex]A = A_0e^{(-0.0077x)}[/tex] gives the amount A of the radioactive material, where A0 is the initial amount of the material, x is the number of years since it was put in the vault, and e is the mathematical constant approximately equal to 2.71828.

We are given that the initial amount of material put into the vault is 300 pounds.

Therefore, [tex]A_0 = 300[/tex].

We want to find the amount of material that will be left after 140 years. Therefore, x = 140.

Substituting these values into the function, we get:

[tex]A = A0e^{(-0.0077x)}\\A = 300e^{(-0.0077 * 140)}\\A = 105.28[/tex]

Therefore, after 140 years, approximately 105.28 pounds of radioactive material will be left in the concrete vault.

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

Step-by-step explanation:

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:

(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

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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Answer:

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

2x + 10 = 3x - 12

x = 22

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:  [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:

Les opinions des 450 élèves d'un lycée quant à savoir s'ils soutiennent le candidat A à la présidence du corps étudiant sont présentées ci-dessous. Masquez et mélangez toutes les valeurs. Prenez un échantillon aléatoire de 25 valeurs de la population. Sur la base de cet échantillon, trouvez la proportion de l'échantillon et utilisez cette valeur pour créer un intervalle de confiance à 95 % pour la véritable proportion de la population qui soutient le candidat A, en arrondissant au millième le plus proche.

Échantillon Oui : 19 Échantillon N° : 6 Échantillons : 25

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.

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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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:

Step-by-step explanation:

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Answer:

I think it’s

False

True

True

True

True

False

True

False

The volume of the rectangular prism which is as described in the task content is; 67½ cm³.

It follows from the task content that the value of the rectangular prism which is as described is required to be determined.

Since the rectangular prism has width as six centimeters, the length as two and a half centimeters and the height as four and a half centimeters;

Volume = l × w × h

Volume = 2½ × 6 × 4½

Volume = 5/2 × 6 × 9 / 2

Volume = 67½ cm³.

Ultimately, the volume of the prism is; 67.5 cm³.

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Answer:

Number three is D.

Step-by-step explanation:

Answer:

multiply the number of meters by 100

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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The slope of the line that cuts through the points (1, -5) and (3, 5) is equal to 2.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

By substituting the given data points into the slope formula, we have the following;

Slope (m) = (5 - (-5))/(3 - 1)

Slope (m) = (5 + 5)/(2)

Slope (m) = 10/2

Slope (m) = 2.

Based on the graph, the slope is the change in y-axis with respect to the x-axis and it is equal to 2.

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Answer:

the sum of Z1 and Z2 is 4.553 + j 5.326.

Step-by-step explanation:

To add two phasors, we add their real and imaginary parts separately.

Given:

Z1 = 2 / 63°

Z2 = 5 / 42°

Converting them to rectangular form:

Z1 = 2 cos(63°) + j 2 sin(63°) = 0.921 + j 1.862

Z2 = 5 cos(42°) + j 5 sin(42°) = 3.632 + j 3.464

Adding them:

Z1 + Z2 = (0.921 + 3.632) + j (1.862 + 3.464)

= 4.553 + j 5.326

Therefore, the sum of Z1 and Z2 is 4.553 + j 5.326.

hope this helped you!;))

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.

The proportion of the babies born

Given that

Uniform Distribution from 1 – 53

This means that

a = 1 and b = 53

So, we have

Mean = (a + b)/2 = (1 + 53)/2 = 27

Standard deviation = √[(b – a)² / 12] = √[(53 – 1)² / 12] = 15

After the 40th week of the year

The z-score is calculated as

z = (x - mean)/Standard deviation

So, we have

z = (40 - 27)/15 = 0.8667

So, we have

Proportion = P(z > 0.8667)

Proportion = 80.7%

Before the 10th week of the year

z = (10 - 27)/15 = -1.133

So, we have

Proportion = P(z < -1.133)

Proportion = 12.9%

Between the 10th and 40th week of the year

This is calculated as

Proportion = (-1.133 < z < 0.8667)

So, we have

Proportion = 67.8%

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Answer:

Step-by-step explanation:

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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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 volume of the cone is  37.70 cm³.

The volume of the cone is calculated as follows;

V = ¹/₃πr²h

where;

The radius of the cone is calculated by applying the following formula;

r = √ (5² - 4²)

r = 3 cm

The volume of the cone is calculated as;

V = ¹/₃πr²h

V = ¹/₃π(3)²(4)

V = 37.7 cm³

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