Using f(x) = -5x + 12, evaluate f (-2)

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:

[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].

The gradient of line A is -2. 67

Gradient = slope = Δy/ Δx

We have,

y2 = 3

y1 = -5

x2 = -3

x1 = 0

Substitute the values

Gradient = [tex]\frac{3 - (-5)}{-3 -0}[/tex]

Gradient = [tex]\frac{3 + 5}{-3}[/tex]

Gradient = [tex]\frac{8}{-3}[/tex]

Gradient = -2. 67

Thus, the gradient of line A is -2. 67

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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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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:

no because it would be flipped

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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Answer:

1

Step-by-step explanation:

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

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?

The Sample mean,Sample Variance, Standard deviation is mathematically given as

Generally, the equation for Sample mean is  mathematically given as

[tex]x = \frac{1}{N}(\sum xifi )[/tex]

Where

[tex]\sum xifi=80+135+220+145+72+258[/tex]

[tex]\sum xifi=910[/tex]

Therefore

x=1/42 (910)

x=21.66

Sample Variance

[tex]\sigma = \frac{1}{N-1}(\sum xi^2fi-(\frac{1}{N}(\sum xifi^2 )) )[/tex]

Where

[tex]\sum xi^2fi=640+2025+4840+4205+2592+11094[/tex]

[tex]\sum xi^2fi=25396[/tex]

Therefore

[tex]\sigma = \frac{1}{41}(25396-(\frac{1}{42}(910^2 )) )[/tex]

[tex]\sigma=138.52[/tex]

Standard deviation.

[tex]\mu=\sqrt{\sigma^2}\\\\\mu=\sqrt{138.52}[/tex]

[tex]\mu=11.769[/tex]

In conclusion,

x=21.66

[tex]\sigma=138.52[/tex]

[tex]\mu=11.769[/tex]

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Answer:

11 mushrooms

Step-by-step explanation:

Let's take two sets of numbers that fulfill the requirements (2 and 24 | 5 and  27)

In the first case, there are 26 mushrooms, and to have an equal amount they each need 13. Collin had to give 11 mushrooms to Sophie.

In the second case, there are 32 mushrooms, and they both need 16 each. So in this case, Collin also had to give 11 to Sophie.

The answer is 11 mushrooms.

Answer:

4p-3

Explaination

when we subtract

4p-3 -3p-6

it will give us p _9

Answer:

28 square meters.

Step-by-step explanation:

The total area - the grass area = the cement area.

36 - 8 = 28.

28 square meters.

Answer:

The answer is 0.55

Step-by-step explanation:

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

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:

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

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:

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

cos θ = [tex]\frac{-4\sqrt{65} }{65}[/tex], sin θ = [tex]\frac{-7\sqrt{65} }{65}[/tex], cot  θ  = 4/7, sec  θ = [tex]\frac{-\sqrt{65} }{4}[/tex], cosec  θ  = [tex]\frac{-\sqrt{65} }{7}[/tex]

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = [tex]\sqrt{7^{2} + 4^{2} }[/tex] = [tex]\sqrt{49+16}[/tex] = [tex]\sqrt{65}[/tex]

sin θ = opposite/ hyp = [tex]\frac{7}{\sqrt{65} }[/tex]

Rationalize, [tex]\frac{7}{\sqrt{65} }[/tex] x [tex]\frac{\sqrt{65} }{\sqrt{65} }[/tex] = [tex]\frac{7\sqrt{65} }{65}[/tex]

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - [tex]\frac{7\sqrt{65} }{65}[/tex]

cos   θ  = adj/hyp = [tex]\frac{4}{\sqrt{65} }[/tex]

By rationalizing and knowing that cos  θ  is negative, cos θ  = -[tex]\frac{-4\sqrt{65} }{65}[/tex]

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/[tex]\frac{4}{\sqrt{65} }[/tex] = -[tex]\frac{-\sqrt{65} }{4}[/tex]

cosec θ  = 1/sin θ  = 1/[tex]\frac{\sqrt{65} }{7}[/tex] = [tex]\frac{-\sqrt{65} }{7}[/tex]

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Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

Cost price is the amount we pay to buy an item at which it is available.

Here,

Selling price of a cake = 200 cedis

Discount because of sale = 10% on each unit.

                                              (Only if 4 cakes purchased at a time)

Amanda purchased 8 cakes

So, Amanda need to pay only 90 percent of the total amount.

Total cost price of 8 cakes for Amanda = (200 X 90%) X 8

                                                                  = 180 X 8

                                                                  = 1440

Thus, Amanda needs to pay 1440 cedis for purchasing 8 cakes on discounted price.

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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]

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 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 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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Answer:

assume X dollar is $100

If so then,

$100-10% =$90

Thus,

$90x125%=$112.5

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:

24/49

Step-by-step explanation:

Option d) is correct, i.e. a rotation, then a dilation. Transformation will create a pair of similar but not congruent triangles.

Which composition of transformations will create a pair of similar, not congruent triangles?

In congruent geometry, the shapes that are so identical. can be superimposed to themselves.

When triangle is rotated, than position of angles will change. Aftermath the dilation of the triangle would increase the proportion of the sides, but angles remains equal, by which the triangle remain similar but not congruent.

Thus, a rotation, then a dilation transformation will create a pair of siilar but not congruent triangles.

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Answer:

D. a rotation, then a dilation

Step-by-step explanation:

got it right on edge 23