A solid right pyramid has a square base with an edge length of s units and a height of h units.
Which expression represents the volume of the pyramid?
One-fourth s^2h units^3
One-third s^2h units^3
s^2h units^3
3^s2h units^3

Answer:

D

Step-by-step explanation:

    [tex]\sf Sin \ \theta =\dfrac{opposite \ side }{hypotenuse} =\dfrac{12}{37}[/tex]

To find the adjacent side use  Pythagorean theorem.

      Opposite side² + adjacent side² = hypotenuse²    

                                  adjacent side² = hypotenuse² - opposite side²

                                                           = 37² - 12²

                                                           = 1369 - 144  

                                                           = 1225

                                  adjacent side = √1225

                                                          = 35

[tex]\sf tan \ \theta =\dfrac{Opposite \ side }{adjacent \ side}\\\\tan \ \theta = \dfrac{12}{35}[/tex]                                                                                                                                                              

The transformations and their respective descriptions are:

A. (x, y) ⇒ (3x, y) implies horizontal stretch by a scale factor of 3

B. (x, y) ⇒ (x+3, y) implies translation 3 units right

C. (x, y) ⇒ (x, 3y) implies vertical stretch by a factor of 3

D. (x, y) ⇒ (x, y+3) implies  implies translation 3 units up

E. (x, y) ⇒ (3x, 3y) implies dilation with a scale factor 3

Translation is an algebraic transformation of a shape by moving the vertices some units along the x or y axis.

When a shape is translated it may move to a new position depending on the orientation of the translation.

Analysis:

For A, the x coordinate was transformed three times its initial value stretching it horizontally.

For B, the x coordinate moved 3 units further away from its initial value making the new value x+3 and y remaining the same.

For C, the y coordinated was transformed to a value three times what it was, making it to be stretched vertically, since the y-axis is a vertical axis.

For D, the y coordinate was moves 3 units away from its initial position making it to be translated up, since 3 is positive.

For E, both coordinates were stretched 3 units as much as their original value making the shape to dilate.

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Answer:

assume X dollar is $100

If so then,

$100-10% =$90

Thus,

$90x125%=$112.5

Answer:

1

Step-by-step explanation:

[tex]i^4=1\\\\i^{36}=(i^{4})^9=(1)^9=1[/tex]

Answer:

[tex]3 \log 2[/tex]

Step-by-step explanation:

Given expression:

[tex]\log 2 + \log \left(\dfrac{3}{2}\right)+\log \left(\dfrac{4}{3}\right)+\log \left(\dfrac{5}{4}\right)+\log \left(\dfrac{6}{5}\right)+\log \left(\dfrac{7}{6}\right)+\log \left(\dfrac{8}{7}\right)[/tex]

[tex]\textsf{Apply the \underline{Log Product Law}}: \quad \log_ax + \log_ay=\log_axy[/tex]

[tex]\implies \log \left(2 \cdot \dfrac{3}{2} \cdot \dfrac{4}{3} \cdot \dfrac{5}{4} \cdot \dfrac{6}{5} \cdot \dfrac{7}{6} \cdot \dfrac{8}{7}\right)[/tex]

Cross out common factors:

[tex]\implies \log \left(\diagup\!\!\!\!2 \cdot \dfrac{\diagup\!\!\!\!3}{\diagup\!\!\!\!2} \cdot \dfrac{\diagup\!\!\!\!4}{\diagup\!\!\!\!3} \cdot \dfrac{\diagup\!\!\!\!5}{\diagup\!\!\!\!4} \cdot \dfrac{\diagup\!\!\!\!6}{\diagup\!\!\!\!5} \cdot \dfrac{\diagup\!\!\!\!7}{\diagup\!\!\!\!6} \cdot \dfrac{8}{\diagup\!\!\!\!7}\right)[/tex]

Therefore:

[tex]\implies \log 8[/tex]

Factor the number:  8 = 2³

[tex]\implies \log 2^3[/tex]

[tex]\textsf{Apply the \underline{Log Power Law}}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies 3 \log 2[/tex]

The value of the composition of functions f(g(3)) is given by (A) -1.

Here given that the functions are,

f(x) = 3x-7

g(x) = (x+1)/(x-1)

To find the value of g(3) we have to first substitute the value x = 3 in the given function g(x), doing that we get,

g(3) = (3+1)/(3-1) = 4/2 =2

Thus the value of g(3) = 2

Now in order to find the value of composition of functions f(g(3)) we have to substitute the value of x = g(3) = 2 in the given function f(x), doing that we get,

f(g(3)) = f(x = g(3)) = f(x = 2) = f(2) = 3*2-7 = 6-7 = -1

Thus the value of the required composition of functions f(g(3)) is given by -1.

Hence the correct option is given by (A).

The question is incomplete. Find the full content below.

Consider these functions:

f(x) = 3x-7

g(x) = (x+1)/(x-1)

What the value of f(g(3))?

(A) -1

(B) 0

(C) 3

(D) 5

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Answer:

The answer is 7.199 x 10^4 hectares

Step-by-step explanation:

Let's set x as the total land area in 2017.

x * (1 + 6.4%) = 76,600

x * (1 + 0.064) = 76,600

x * 1.064 = 76,600

x = 76,600 / 1.064

x = 71,992.48

x = 7.199 * 10^4 hectares

The value of u, number of hours walking up a hill based on the equation is 2.5

9(u – 2) + 1.5u = 8.25

where,

9(u – 2) + 1.5u = 8.25

9u - 18 + 1.5u = 8.25

9u + 1.5u = 8.25 + 18

10.5u = 26.25

u = 26.25/10.5

u = 2.5

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SOLUTION :-

AREA of sector = ( ∆/360° ) × πr²

∆ = given angle , r = radius

hence ,

AREA of sector for given angle

= ( 120°/360° ) × π 12² mi²

= ⅓ × π × 144 = 150.79 mi² = 151 mi² ( rounded off )

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Answer:

Sector area = 151 mi²

Step-by-step explanation:

We can use the formula for sector area:

Area = [tex]\frac{\theta}{360} \pi\ r^2[/tex]

where:
θ = central angle (120°),

r = radius of circle (12 mi) .

Substituting these values into the formula:

Area = [tex]\frac{120}{360} \pi\ \times (12)^2[/tex]

        ⇒ 48 π

        ⇒ 150.796

        ≈  151 mi²   (rounded to the nearest whole number)

Answer:

A

Step-by-step explanation:

The first picture shows the parent function,

A function assigns a x for only one y.

The inverse is opposite

The inverse assign a y for only one x.

So the answer is the table that swap x and y values.

The coordinates for the parent function are

(0,0)

(2,1)

(4,2)

So the inverse should have

(0,0)

(1,2)

(2,4)

A shows that, so a is the answer

The distance between the home plate and the second base is 127.3 feet

An equation is an expression that shows the relationship between two or more variables and numbers.

Let x represent the distance between the home plate and the second base. Using Pythagoras theorem:

x² = 90² + 90²

x = 127.3 feet

The distance between the home plate and the second base is 127.3 feet

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The distance between home plate and second base is  2√4050 feet.

In a square, all sides are equal in length.

If the distance between each pair of bases is 90 feet, it means that each side of the square (representing the distance along the edge) is also 90 feet.

Since home plate and second base are opposite corners of the square, they are connected by the diagonal of the square.

In a square, the diagonal forms a right triangle with the sides of the square.

Using the Pythagorean theorem, we can find the length of the diagonal (the distance between home plate and second base):

diagonal² = side² + side²

diagonal² = 90² + 90²

diagonal²= 8100 + 8100

diagonal² = 16200

diagonal =√16200

diagonal = 2√4050 feet.

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Answer:

[tex][0, \infty)[/tex]

Answer:

The answer is 0.55

Step-by-step explanation:

Because 55% = [tex]\frac{55}{100}[/tex] = 0.55

Answer:

[tex]2 * 10^3 * 1,02^t[/tex]

Step-by-step explanation:

Let [tex]S = 2000 = 2 * 10^3[/tex] dollars be our investment, [tex]r = 2\%[/tex] - our interest rate. In order to simplify things, I suggest bringing the variable [tex]p[/tex] into play: [tex]p = 1 + \frac{r}{100}[/tex]. So, after year [tex]1[/tex] we will have [tex]S_{1} = S + \frac{r}{100}S = S(1 + \frac{r}{100} ) = Sp[/tex]. After year [tex]2[/tex]: [tex]S_{2} = S_{1}p = Sp * p = Sp^2[/tex]. After year [tex]t[/tex]: [tex]S_{t} = S_{t - 1}p = Sp^t[/tex]. Besides, we can count [tex]p[/tex]. Indeed, [tex]p = 1 + \frac{r}{100} = 1 + \frac{2}{100} = \frac{100}{100} + \frac{2}{100} = \frac{102}{100} = 1,02[/tex]. Therefore, [tex]V(t) = Sp^t = 2 * 10^3 * 1,02^t[/tex].

Answer:

A. 33x-25=33x+25

C. 33x-33=33x+25

D.33x+33=33x+25

A. 33x-25=33x+25

33x-33x=25+25

0 = 50

This is incorrect equality, as it is not equal on both sides.

Therefore this equation has no solutions.

B. 33x+25=33x+25

33x−33x=25−25

0=0

This is correct equality, as it is equal to zero on both sides.

Therefore the equation has an infinite number of solutions.

C. 33x-33=33x+25

33x-33x=33+25

0=58

This is incorrect equality, as it is not equal on both sides.

Therefore this equation has no solution.

D. 33x+33=33x+25

33x−33x=25−33

0=−8

This is incorrect equality, as it is not equal on both sides.

Therefore this equation has no solution.

Hence, the equations which has no solution are;

A. 33x-25=33x+25

C. 33x-33=33x+25

D.33x+33=33x+25

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The 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).

The confidence interval for a population proportion for a given sample is given by the formula:

[tex](p-Z\sqrt{\frac{p(1-p}{n} } , p+Z\sqrt{\frac{p(1-p}{n} })[/tex],

where p is the population proportion, Z is the Z-score value for the confidence interval, and n is the sample size.

In the question, we are given a random sample of 81 8th graders at a large suburban middle school. This implies that the sample size, n = 81. Also, we are told that they indicated 87% of them were involved with some type of after-school activity. This implies that the population proportion, p = 87% = 0.87.

We are asked to find the 90% confidence interval that estimates the proportion of them that are involved in an after-school activity.

Z-score (Z) corresponding to a 90% confidence interval is 1.645.

Thus, we can find the confidence interval as follows:

(0.87 - 1.645√{(0.87(1 - 0.87))/81},0.87 + 1.645√{(0.87(1 - 0.87))/81})

= (0.87 - 0.061469,0.87 + 0.061469)

= (0.80853,0.93147).

Thus, the 90% confidence interval that estimates the proportion of 8th graders that are involved in an after-school activity is (0.80853,0.93147).

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Answer:

no because it would be flipped

The scale factor in the question given above is: 2 See the explanation below.

In math, the scale factor is the extent or ratio by which a geometrical shape is enlarged or reduced.

We know that:

Given the above, the distance from point Q to point A' is 2.50. This is double the distance from point Q to point A.

The scale factor is 2.

1.25 + 1.25 = 2.50

2.50 / 1.25 = 2

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The angle congruent to ∠6 are ∠8, ∠3, ∠9 and ∠14

When parallel lines are cut by a transversal, angle relationships are formed. They include corresponding , alternate and many more.

L║m

n ║ q

Therefore, the angles congruent to ∠6 by alternate or corresponding relationship are as follows:

∠6≅∠8≅∠3≅∠9≅∠14

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The height is increasing at the rate of (6/5π) ft/min.

It is given that Gravel is being dumped from a conveyor belt at a rate of 40 ft3/min. Also, its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

For this, we need to find the volume of a cone. Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

The volume of a cone is - V=1/3hπr²

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The blanks can be filled with definitions of property bisector,  Substitution property of equality, and Distributive property, respectively.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The given blanks can be filled as,

Hence, the blanks can be filled with definitions of property bisector,  Substitution property of equality, and Distributive property, respectively.

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Answer:

3x

Step-by-step explanation:

2x is the name, there are 2 x's, you are adding an x to the 2 x's therefore making 3 x's or 3x

Answer:

This is true.

Step-by-step explanation:

Congruence means the same shape and size. So if they line up, they will line up perfectly.

By the way, is there any question you need help with, or do you just need to see if this is true or false?

Let the numerator be x & denominator be y then,

ATQ,

x+1/y-1=12/11

11x+11=12y-12

11x-12y+11+12=0

11x-12y+23=0....(1)

&

x+3/y-3=14/9

9x+27=14y-42

9x-14y+27+42=0

9x-14y+69=0....(2)

Multiplying eq . 1 by 9 & eq. 2 by 11

We get,

99x-108y+207=0....(3)

99x-154y+759=0....(4)

Subtracting eq. 4 by eq. 3

99x-108y+207=0

99x-154y+759=0

______________

0 + 46y - 552 =0

______________

46y= 552

________

y=552/46

________

y=12

____

putting the value of y in eq. 1,

11x-12y+23=0

11x-12*12+23=0

11x-144+23=0

11x-121=0

11x=121

x=121/11

x=11

So, y = 12 & x = 11 & the fraction is 11/12

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The probability that she will choose one by each composer is 2/455.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability = (number of bach cds / total number of cds) x  (number of beethoven cds / total number of cds - 1) x  (number of Brahms cds / total number of cds-2) x  (number of Handel's cds / total number of cds-3)

= 4/15 x 6/14 x 3/13 x 2/12 = 2/455

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Answer:

24/49

Step-by-step explanation:

The a gallon of orange juice will cost $ 3.0 more than a gallon of milk.

The size of the orange juice in gallon is calculated as follows;

1 ounce = 0.0078125 gal

5.5 ounce = ?

= 0.043 gallon

Total volume of 6 pack = 6 x 0.043 gal = 0.258 gal

0.258 gal = $1.79

1 gal = ?

= $ 6.94

= $ 6.94 - $ 3.99

= $2.95

≈ $ 3.0

Thus, the a gallon of orange juice will cost $ 3.0 more than a gallon of milk.

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The intervals [-5,-1], [-4,-1], [-3,1],[-2,1] match with -8,-7,4,-3.

Given the value of function at x=-5 is 35, at x=-4 is 24, at x=-3 is 15,at x=-2 is 8,at x=-2 is 8,at x=-1 is 3, at x=0 is 0, at x=1 is -1.

Average rate of change of values refers to the average of differences in the values divided by the difference of values of x.

First finding the average rate of change of interval [-5,-1]

Average rate of change={f(-1)-f(-5)}/(-1+5)

=(3-35)/4

=-32/4

=-8

Finding the average rate of change of interval [-4,-1]

Average rate of change={f(-1)-f(-4)}/(-1+4)

=(3-24)/3

=-21/3

=-7

Finding the average rate of change of interval [-3,1]

Average rate of change={f(1)-f(-3)}/(-3-1)

=(-1-15)/-3-1

=-16/-4

=4

Finding the average rate of change of interval [-2,1]

Average rate of change={f(1)-f(-2)}/(1+2)

=(-1-8)/3

=-9/3

=-3

Hence the values which are to be filled in the boxes are -8,-7,4,-3.

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Answer:

The product is the difference of squares is [tex]$$\left(5k+6\right)\left(5k-6\right)=25{{k}^2}-36$$[/tex]

Step-by-step explanation:

Explanation

[tex]$$\begin{aligned}&(5 k+6)(5 k-6)=(5 k)^{2}-(6)^{2} \\&(5 k+6)(5 k-6)=25 k^{2}-36\end{aligned}$$[/tex]