One year, there were about 3,000 institutions of higher learning in the U.S. (including junior colleges and community colleges). As part of a continuing study of higher education, the Carnegie Commission took a simple random sample of 400 of these institutions. The average enrollment in the 400 sample schools was 3,700, and the SD was 6,500. The Commission estimates the average enrollment at all 3,000 institutions to be around 3,700; they put a give-or-take number of 325 on this estimate. There were about 600,000 faculty members at institutions of higher learning in the U.S. As part of its study, the Carnegie Commission took a simple random sample of 2,500 of these faculty persons. On the average, these 2,500 sample persons had published 1.7 research papers in the two years prior to the survey, and the SD was 2.3 papers. If possible, find an approximate 95%-confidence interval for the average number of research papers published by all 600,000 faculty members in the two years prior to the survey. If this isn't possible, explain why not.

Answer:

QR=17

Step-by-step explanation:

[tex](12)(x-2)=(3)(3x-1)\\12x-24=9x-3\\3x-24=-3\\3x=21\\x=7[/tex]                

 [tex]x=7\\\\QR=12+x-2\\=12+(7)-2\\QR=17[/tex]

a. x = 120°

b. x = 88°

c. x = 146°

Determining the value of x

A. We have that x and angle 80° as shown in the diagram is on a straight

Angles on a straight line = 180°

Then,

x + 80° = 180°

Make 'x' subject

x = 180° -  80°

x = 100°

B. From the diagram, we can see that 'x' at ∠BCD is alternate to ∠EDC which is 88°

It is important to note that alternate angles are equal

Then,

x =  88°

C. From the diagram, we can see that 'x' at CDE is on a straight line with ABC

Angles on a straight line are equal

Then,

x + 34° = 180°

Make 'x' subject of formula

x = 180° - 34°

x = 146°

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Answer:

The required linear equation satisfying the given conditions f(-5)=-4 and f(5)=2 is

[tex]$$y=\frac{3}{5} x-1$$[/tex]

Step-by-step explanation:

It is given that f(-5)=-4 and f(5)=2. It is required to find out a linear equation satisfying the conditions f(-5)=-4 and f(5)=2. To find it out, first, represent the given conditions in the form of points and then find the slope of a line passing through these two given points. Then consider one of the points to give the linear equation of the line in the form [tex]$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$[/tex]

Step 1 of 4

Observe, f(-5)=-4 gives the point (5,-4)

And f(5)=2 gives the point (5,2)

This means that the function f(x) satisfies the points (-5,-4) and (5,2).

Step 2 of 4

Now find out the slope of a line passing through the points (-5,-4) and (5,2).

[tex]$$\begin{aligned}m &=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\m &=\frac{2-(-4)}{5-(-5)} \\m &=\frac{2+4}{5+5} \\m &=\frac{6}{10} \\m &=\frac{3}{5}\end{aligned}$$[/tex]

Step 3 of 4

Now use the slope [tex]$m=\frac{3}{5}$[/tex] and use one of the two given points and write the equation in point-slope form:

[tex]$$\left(y-y_{2}\right)=m\left(x-x_{2}\right)$$\\ $$(y-2)=\frac{3}{5}(x-5)$$[/tex]

Distribute [tex]$\frac{3}{5}$[/tex],

[tex]$$\begin{aligned}&y-2=\frac{3}{5} x-\frac{3}{5} \times 5 \\&y-2=\frac{3}{5} x-3\end{aligned}$$[/tex]

Step 4 of 4

This linear function can be written in the slope-intercept form by adding 2 on both sides, [tex]$y-2+2=\frac{3}{5} x-3+2$[/tex]

[tex]$$y=\frac{3}{5} x-1$$[/tex]

So, this is the required linear equation.

Answer:

2 parts

Step-by-step explanation:

The rectangle has a 1/2 ratio, because there are 4 parts of the circle, you will shade 2. This is because 2/4 ratio is simplified to 1/2.

Answer:

b is not a polynomial

Step-by-step explanation:

b is not a polynomial because in y-3/y the y in denomination means y to the power -1 when it is taken to numerator and if power is negative then it is not a polynomial

Answer:

Step-by-step explanation:

Hi!

A is congruent to angle C. Because angle FCE is on the other side of the angle C which is equal to A, angle FCE has to equal A

Answer:

the chance is 1.5 out of 5

You can by 42 combinations of items from the store

The given parameters are:

Envelop = 7

Stamp = 6

The number of combination is:

Combination = Envelop * Stamp

So, we have:

Combination = 7 * 6

Evaluate

Combination = 42

Hence, you can by 42 combinations of items from the store

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Answer:

OC

Step-by-step explanation:

4×3=12m

5+1=6n

4÷1=4

Answer:

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

Step-by-step explanation:

Explanation

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

Work Shown:

| x-1 | < 2

-2 < x-1 < 2 ... see note1 below

-2+1 < x-1+1 < 2+1 ... see note2

-1 < x < 3

Answer:

-4

Step-by-step explanation:

The data is modeling a geometric sequence because they have a common ratio of 2.

The recursive formula to determine the time she will complete station 5

Part C:

The explicit formula to find the time she will complete the 9th station.

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Answer:

y + 1/2 = 3(x - 2)

Step-by-step explanation:

We have to think about this question in point-slope form, which is a form that explicitly gives us the slope of the line and a single point that it passes through. Point-slope form looks like this: y - y1 = m(x - x1), where m is the slope and (x1,y1) is a point that the line goes through. We are given that the line goes through (2, -1/2) which means x1 = 2 and y1 = (-1/2). We are also given that the slope is 3. We can plug these quantities into the equation to solve:

y - (-1/2) = 3(x - 2) OR y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

The correct option is (3).

The slope of a line indicates its direction and steepness. Finding the slope of lines in a coordinate plane can help predict whether the lines are parallel, perpendicular, or have no relationship at all without actually using a compass.

As per the given data:

We have to find out the equation of the line that passes through (2, -1/2) and has a slope of 3.

As we know a point at the slope of the line, we can use the point slope form:

[tex]y - y_1 = m(x-x_1)[/tex] , where m is the slope and [tex](x_1, y_1)[/tex] is the point through which the line passes.

y - (-1/2) = 3(x - 2)

y + 1/2 = 3(x - 2)

The equation of the line is y + 1/2 = 3(x - 2).

Hence, The equation of the line is y + 1/2 = 3(x - 2).

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Answer:

Step-by-step explanation:

I'm going to assume you want it to be a perfect triangle, so then we would have the equation 4x=24. So we can divide each side by 4 to get rid of the 4 and get x by itself. So 24/4= 5. So x=5

The expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

Given the expression below;

-0.5 (1.7 + 1.7)

According to the distributive law;

A(B+C) = AB + AC

Expand

-0.5(1.7) + (-0.5)(1.7)

-0.5(1.7) - 0.5(1.7)

2(-0.5(1.7))

Hence the expressions equivalent to -0.5(1.7+1.7) are -0.5(1.7) - 0.5(1.7)

and 2(-0.5(1.7))

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Hello,

[tex]Speed = \frac{Distance}{Time} = \frac{15 km}{3 h} = \boxed{5 km/h}[/tex]

Stan walked at 5 km/h

h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

In the question, we are given that during a local high school football game, the height of h feet of a football after t seconds can be represented by the quadratic function h(t) = -16t² + 58t + 2.

We are asked to find h(2.5) and explain its meaning.

To find h(2.5), we substitute t = 2.5, in the quadratic function h(t) = -16t² + 58t + 2.

Thus,

h(2.5) = - 16(2.5)² + 58(2.5) + 2,

or, h(2.5) = - 16(6.25) + 145 + 2,

or, h(2.5) = -100 + 147,

or, h(2.5) = 47.

Hence, h(2.5) = 47, and this mean that the height of the football after 2.5 seconds is 47 feet, using the quadratic function h(t) = -16t² + 58t + 2.

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Hence, the area of base is [tex]x^2 - 2x - 9[/tex]

Division in maths is breaking a number into equal parts and finding out how many equal parts can be made.

The volume of a rectangular prism is,

        Volume = Area x Height

Substituting the given expressions,

[tex]x^3 + 2x^2 - 17x - 36 = Area x (x + 4)[/tex]

Area = [tex](x^3 + 2x^2 - 17x - 36) / (x + 4)[/tex]

Now, let's use synthetic division,

-4 |    1    2    -17   -36

----    __-4___8___36

        1    -2     -9     0

The expression for the area is [tex]x^2 - 2x - 9[/tex]

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The probability of not winning of united is [tex]\frac{2}{5}[/tex] .

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given that the probability of winning of united is [tex]P(A)=\frac{3}{5}[/tex] .

Usually, we take the total probability is 1

So, the probability of not winning of united is [tex]1-\frac{3}{5}[/tex]

                                                                        [tex]=\frac{5-3}{5}\\=\frac{2}{5}[/tex]

Therefore, the probability of not winning of united is [tex]\frac{2}{5}[/tex] .

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A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

In this question we have two rigid transformations to be defined: (i) Rotation, (ii) Translation. Rigid transformations are transformations applied on geometric loci such that Euclidean distance is conserved. Herein we must describe the characteristic of a rotation and a translation.

A translation is a transformation in which an object at every point according to a given vector and a rotation is a transformation in which an object is moved angularly with respect to a point.

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Answer:

A rotation is a transformation where an object-

moves in a circular arc around a point

A translation is a transformation where an object-

moves a specified distance along a line parallel to a specified line

Step-by-step explanation:

Plato answer

The game is profitable since the payout is always less than what you earn.

Given that a fair game with 4 or more outcomes using a binomial situation presented in this lesson (simulated with a spinner or random number) and adjust the point values the  so cost of the 10 points will make the game profitable.

Let's discuss the Lucky 7 game

The game is played with the two fair dice rolls.

You put your money on either of 3 things: Above 7, Lucky 7 or below 7

The game below is designed in Excel:

Each cell formula to generate the game:

They are 36 possible outcomes.

7 is the most likely number coming up

6/36=1/6

of the time.

Thus the expected value of the bet is:

(5/12)x₂+(5/12)x₂+(1/6)x₃=26/12

Which, of course, can not make any sense. so, the good idea from the standpoint of the bank is to pay two times on only one of the two possibilities, not a seven, and to give the bet back on the 7. This then gives:

(5/12)x₂+(5/12)x₀+(1/6)x₁=12/12=1

Which is a perfectly fair game.

Of course, the bank wouldn't approve either, so we probably need more restrictions. The way 7 comes out is: 2 ways for each case, (1,5), (2,5), (3,4), then a constraint like not to pay on (5,1) would be added.

Then the 7 returns the money

4/36 = 1/9.

The new case then yields:

(5/12)x₂+(5/12)x₀+(1/9)x₁=34/36=17/18

This says that for every $18 handled in bets the bank expects to pay out $17.

Hence we can say that the game is profitable since the payout is always less than what you earn.

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Option (A) :  least: 10 hours; greatest: 14 hours

The function f(x) = sin x has all real numbers in its domain, but its range is

−1 ≤ sin x ≤ 1.

How to solve such range questions?

Such questions in which every term is in addition and its range is asked is simplest ones to solve if we know the range of each of term. This can be seen from this question

Given: d(t) = 2sin(xt) + 12

=  −1 ≤ sin (xt) ≤ 1.

=  −2≤ 2 sin (xt) ≤ 2.

=  10 ≤ 2sin (xt) + 12 ≤ 14

=   10 ≤d(t) ≤ 14

Thus  least: 10 hours; greatest: 14 hours

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Answer:

the Slope: 11

the y-intercept: (0, - 8) x        y

                                     0       -8

                                     1         3

Step-by-step explanation:

Answer:

[tex]y=\frac{11}{8}x+\frac{1}{2}[/tex]

Based on the calculations, the scale factor for this dilation is equal to 1/3.

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

its 1/3

Answer:

Step-by-step explanation:

Since the sum of all exterior angles in a polygon is 360°, we have to divide 360 by 6 to find the number of sides.

360/6 = 60.

So, the polygon has 60 sides.

Hope this helps! (:

Answer:

14

Step-by-step explanation:

because it is a small angle that will indooor more sides

Answer:

Vertex: (-2, 0)

Axis of symmetry: x = -2

Direction of opening: Upwards

Min: 0

Y-intercept: 4

Step-by-step explanation:

    Let us graph this line, and then pull out the details we need. See attached.

    What do all of these different things mean?

Vertex: This is where the graph intercepts the axis of symmetry (x = -2, see below) and is at point (-2, 0) for this graph.

Axis of Symmetry: This is the line that the graph is symmetrical across. The "center" of the graph. Here, it is x = -2.

Direction of Opening: The direction that the graph is going/opening towards. In this case, it is upwards.

Min: The minimum (in this case) value, the lowest y-coordinate. This is 0 here.

Y-intercept: The point at which the line intercepts the y-axis. This is 4 here.

The system of inequalities represents the number of color copies, x, and grayscale copies, y, that julissa can print to meet her goal is;

x + y ≥ 8

x + y ≥ 84x + 2y ≤ 25

let

x + y ≥ 8

4x + 2y ≤ 25

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