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4 years ago

PLEASE ANSWER ASAP AND PLEASE SHOW WORK

Mathematics

1 answer:

Scilla [17]4 years ago

6 0

(A)

y = 25x + 32

(B)

The y-intercept represents the original battery life.

(C)

The rate of change represents the rate at which the battery life changes.

(D)

y = 25(2.5) + 32

94.5% Battery life

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A lighthouse beacon can be seen 17mi in all directions. To the nearest square mile, what is the area over which the beacon can b

Alchen [17]

Imagine this as a circle. The circle will have a radius of 17mi and the lighthouse will be in the middle. The area of the circle will be the area over which the beacon can be seen.

$A=\pi r^{2}$ is the equation for the area of the circle where A is the area.

Now we simply plug in our information

A= $\pi (17)^{2}$
A=907.9 $mi^{2}$

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4 years ago

there are 318 fictiom books in the class library. the number of nonfiction booka os 47 less than the number of fiction books. ab

Mama L [17]

318-47= 271 There are 271 non-fiction books in the library. just subtract 47 from 318 to get the answer.

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4 years ago

Read 2 more answers

While conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modem

Kitty [74]

Answer:

We conclude that this is an unusually high number of faulty modems.

Step-by-step explanation:

We are given that while conducting a test of modems being manufactured, it is found that 10 modems were faulty out of a random sample of 367 modems.

The probability of obtaining this many bad modems (or more), under the assumptions of typical manufacturing flaws would be 0.013.

Let p = population proportion.

So, Null Hypothesis, $H_0$ : p = 0.013 {means that this is an unusually 0.013 proportion of faulty modems}

Alternate Hypothesis, $H_A$ : p > 0.013 {means that this is an unusually high number of faulty modems}

The test statistics that would be used here One-sample z-test for proportions;

T.S. = $\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion faulty modems= $\frac{10}{367}$ = 0.027

n = sample of modems = 367

So, the test statistics = $\frac{0.027-0.013}{\sqrt{\frac{0.013(1-0.013)}{367} } }$

= 2.367

The value of z-test statistics is 2.367.

Since, we are not given with the level of significance so we assume it to be 5%. Now at 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since our test statistics is more than the critical value of z as 2.367 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that this is an unusually high number of faulty modems.

6 0

4 years ago

9. Two points in the plane, A(−3,8) and ????(17,8), represent the endpoints of the diameter of a circle.

kherson [118]

Answer:

a) (7,8)

b) r = 10

c) $(x-7)^2+(y-8)^2=100$

Step-by-step explanation:

a) Given the endpoints the diameter of the circle as A(-3,8) and B(17,8)

we should realize that the center of the circle lies exactly at the midpoint of these two points. let's denote the midpoint as $(x_m,y_m)$

$(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)$

$(x_m, y_m) = \left(\dfrac{-3+17}{2},\dfrac{8+8}{2}\right)$

$(x_m, y_m) = (7,8)$

this is the coordinate of the center of the circle.

b) The radius of the circle can be easily found by using the distance formula between the center point and either of the two endpoints of the diameter.

the general distance formula is:

$r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

in our case the equation changes to: (selecting the centre and point B)

$r = \sqrt{(x_m-x_2)^2+(y_m-y_2)^2}$

$r = \sqrt{(7-17)^2+(8-8)^2}$

$r = 10$

side note: there are more alternate ways to find the radius for e.g (you can use the distance formula between the points A and B and that'll give you the length of the diameter which you can divide by 2 to get the radius) OR (you don't need to use the distance formula at all since in this particular case all the coordinates lie on the same horizontal line, so by simply subtracting the two x-coordinates of the center and either of A or B)

c) the ingredients needed to make the equation of the circle are the