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4 years ago

9

When 440 junior college students were surveyed, 200 said they have a passport. Construct a 95% confidence interval for the propo

rtion of junior college students that have a passport.

1 answer:

nekit [7.7K]4 years ago

7 0

Sample proportion: 190/425 = 0.45
ME = 1.96*sqrt[0.45*0.55/425] = 0.047
-----
95% CI: 0.45-0.047 < p < 0.45+0.047

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For triangle ABC, angle A=110, angle B=43, and side b=15. Find side c.

vredina [299]

Answer: 10

<u>Step-by-step explanation:</u>

First, find m∠C by using the Triangle Sum Theorem:

∠A + ∠B + ∠C = 180°

110 + 43 + ∠C = 180°

153 + ∠C = 180°

∠C = 27°

Next, Use the Law of Sines to solve for c:

$\dfrac{b}{sin\ B}= \dfrac{c}{sin\ C}$

$\dfrac{15}{sin\ 43}= \dfrac{c}{sin\ 27}$

$\dfrac{15\ sin\ 27}{sin\ 43}= c$

$10 = c$

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3 years ago

If you are offered one slice from a round pizza (in other words, a sector of a circle) and the slice must have a perimeter of 24

VARVARA [1.3K]

Answer:

A 12 in diameter will reward you with the largest slice of pizza.

Step-by-step explanation:

Let $r$ be the radius and $\theta$ be the angle of a circle.

According with the graph, the area of the sector is given by

$A=\frac{1}{2}r^2\theta$

The arc lenght of a circle with radius $r$ and angle $\theta$ is $r \theta$

The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length

$2r+r\theta=24 \:in$

We need to express the area as a function of one variable, to do this we use the above equation and we solve for $\theta$

$2r+r\theta=24\\r\theta=24-2r\\\theta=\frac{24-2r}{r}$

Next, we substitute this equation into the area equation

$A=\frac{1}{2}r^2(\frac{24-2r}{r})\\A=\frac{1}{2}r(24-2r)\\A=12r-r^2$

The domain of the area is

$0$

To find the diameter of pizza that will reward you with the largest slice you need to find the derivative of the area and set it equal to zero to find the critical points.

$\frac{d}{dr} A=\frac{d}{dr}(12r-r^2)\\A'(r)=\frac{d}{dr}(12r)-\frac{d}{dr}(r^2)\\A'(r)=12-2r$

$12-2r=0\\-2r=-12\\\frac{-2r}{-2}=\frac{-12}{-2}\\r=6$

To check if $r=6$ is a maximum we use the Second Derivative test

if $f'(c)=0$ and $f''(c)$ , then f(x) has a local maximum at x = c.

The second derivative is

$\frac{d}{dr} A'(r)=\frac{d}{dr} (12-2r)\\A''(r)=-2$

Because $A''(r)=-2$ the largest slice is when r = 6 in.

The diameter of the pizza is given by

$D=2r=2\cdot 6=12 \:in$

A 12 in diameter will reward you with the largest slice of pizza.

3 0

3 years ago

The graphs show the amounts in two different bank accounts over several months.

Neko [114]

Answer:

where are the graphs?

Step-by-step explanation:

3 0

3 years ago

Interpret the following sine regression model.

natita [175]

Answer:

The question is incomplete, so I will describe the sine regression model.

The function

y = 0.884 sin(0.245x - 1.093) + 0.400

correspond to the general equation:

y = a sin(bx - c) + d

where:

a = 0.884

b = 0.245

c = 1.093

d = 0.400

The amplitude of the function is computed as follows:

amplitude = |a| = 0.884

The period of the function is computed as follows:

period = 2π/|b| = 25.6456

The phase shift of the function is computed as follows:

phase shift = c/b = 4.4612 to the right (because there is a minus sign before c in the equation)

The vertical shift of the function is computed as follows:

vertical shift = d = 0.400

3 0

4 years ago

Write the resultant of the two vectors as an ordered pair. –6 5 and 6 –5

RideAnS [48]

Answer:

Resultant vector of two vectors is (0, 0).

Step-by-step explanation:

in this question two vectors having ordered pair (-6, 5) and (6, -5) have been given.

We can represent these vectors in the form of

$\vec{A}=-6\hat{x}+5\hat{y}$

and $\vec{A'}=6\hat{x}+(-5)\hat{y}$

Now the resultant of these vectors will be = A + A'

A + A' = $\vec{A}=-6\hat{x}+5\hat{y}$ + $\vec{A'}=6\hat{x}+(-5)\hat{y}$

So the resultant vector = (0 + 0)

Therefore the resultant will be (0, 0)

8 0

3 years ago

Read 2 more answers