Suppose sonar on the surface of the sea locates an
object at an angle of depression of 65° and a distance
of 320 feet.
How deep is the object?

Answer:

The p-value for this test is 0.1375.

Step-by-step explanation:

A student believes that the average grade on the statistics final examination was 87. The student wants to test whether the average is different from 87 at 90% level of confidence.

At the null hypothesis, we test if the average is 87, that is:

[tex]H_0: \mu = 87[/tex]

At the alternate hypothesis, we test if the average is different from 87, that is:

[tex]H_a: \mu \neq 87[/tex]

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]s[/tex] is the standard deviation of the sample and n is the size of the sample.

87 is tested at the null hypothesis:

This means that [tex]\mu = 87[/tex]

The average grade in the sample was 83.96 with a standard deviation of 12. Sample of 36

This means that [tex]X = 83.96, s = 12, n = 36[/tex]

Value of the test-statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{83.96 - 87}{\frac{12}{\sqrt{36}}}[/tex]

[tex]t = -1.52[/tex]

Pvalue:

Probability of the sample mean differing of 87, which means that we have a two-tailed test, with t = -1.52 and 36 - 1 = 35 degrees of freedom.

With the help of a calculator, the pvalue is of 0.1375.

The p-value for this test is 0.1375.

Answer:

89.44

Step-by-step explanation:

[tex]120^2-80^2=8000[/tex]

[tex]\sqrt{8000} = 89.44[/tex]

Answer:

x = 12 and y = 11

Step-by-step explanation:

4x+3y=-15 -----equation 1st

4x-y = -27 ____equation 2nd

then,

Multiple equation second by 3 and slove it with equation first

4X +3Y = -15

12X -3Y = -81 (Multiples it with 3)

-8x = -96 (subtracted)

x=-96/-8

therefore, x=12

again,

from equation first

4x+3y = -15

or 4 × 12 + 3y = -15

or 3y = -15+48

or 3y= 33

or y=33/3

therefore, y =11

I hope this helps. If you have any doubt feel free to ask!!

Answer:

x = -6,  y = 3

Step-by-step explanation:

1)  4x + 3y = -15

2)  4x - y =  -27

     0 + 4y = 12       subtract equation (2) from equation (1)

4y = 12

y = 12/4 = 3         substitute y = 3 into either equation 1 or 2 and solve for x

4x + 3(3) = -15

4x = -24

x = -6

Check your answers by plugging x = -6, y = 3 into the equations:

4(-6) + 3(3) = -15   correct!

4(-6) - 3 = -27        correct!

Answer:c=35

Step-by-step explanation:

i just did this

Answer:

depends on the size of the house

let's say the house is 10 square meter then you would need 5 gallons

let's the house is 60 square meter then you would need 30 gallons

Step-by-step explanation:

whatever the square meter just divide it with 2 and that should be your answer

Step-by-step explanation:

The figure is made up of an 8x8 square and 4 identical triangles with 8-ft bases and 4 ft in height. Each triangle has an area = (1/2)bh = (1/2)(8)(4) = 16 ft^2. The square part has an area of 8x8 = 64 ft^2. Therefore, the total area of the figure is

A = (area of square) + 4×(area of triangle)

= 64 ft^2 + 4(16ft^2)

= 128 sq ft

Answer:

3.6

Step-by-step explanation:

tan61=x/2

2(tan61)=x

3.6=x

Answer:

$1,158.08

Step-by-step explanation:

The value of the car in year 10 is $1158.08

From the table, we have the following points

(x, y) = (1,5000) and (2,4250)

Start by calculating the rate of depreciation using:

r = y2/y1

So, we have:

r = 4250/5000

Evaluate

r = 0.85

The value of the car in nth year is calculated using:

y = y1 * r^(n - 1)

For the 10th year, we have:

y = 5000 * 0.85^(10 - 1)

Evaluate the product

y = 1158.08

Hence, the value of the car in year 10 is $1158.08

Read more about depreciation at:

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Option A. They led the most powerful of the Allied countries.

Answer:

280

Step-by-step explanation:

a) The process to find the limit is given as follows:

b) When a function does not have any discontinuity at x = 1, the procedure is the same as calculating f(1), however in the case of a discontinuity, such as for f(x), the discontinuity first has to be removed, if possible.

The first step in calculating the limit of a function is calculating the numeric value of the function at the value of x which the function approaches.

Hence:

For the case of g(x), there is a discontinuity, meaning that the function has to be factored to remove the discontinuity.

Applying the subtraction of perfect squares, we have that:

x² - 1 = (x - 1)(x + 1).

Then:

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

Meaning that the limit is then calculated as follows:

lim x -> 1 g(x) = lim x->1 x + 1 = 1 + 1 = 2.

More can be learned about limits at brainly.com/question/26104792

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Answer:

Below

Step-by-step explanation:

f(t) = 4.1 (sin pi/6 t  - pi/3) + 19.7    <===will be a maximum when the sin portion is equal to 1

   so    sin ( pi/6 t - pi/3) = 1     given that sin is equal to one   at 0 and pi and 2 pi  and 3 pi    and 4 pi   etc

              pi/6 t - pi/3 =  0  or pi , 2 pi, 3 pi  , 4 pi

                  then t = 2 and 8 and 14   and 20 hrs  ( every 6 hrs starting with t = 2)

Answer:

To answer this problem, first let us calculate for the theoretical probability obtained from the study conducted:

Theoretical Probability = 6,670 / 40,000

Theoretical Probability = 0.16675 = 0.17

From the given choices, the list of words which can give this similar amount of probability is:

“to, sarcastic, epithet, for, less, corruptible, than, the, offspring, open, any, primary, loyalty, table, out, whom, example, who, mention, say”

In this set of words, the number of words starting with letter T is 4. Calculating for the probability of getting a word starting with T in this set is:

Sample probability = 4 / 20

Sample probability = 0.20

Step-by-step explanation:

Answer: spinning a spinner with 4 equal sections 50 times

Step-by-step explanation:

The models that one can use to simulate the outcome of guessing the correct answers to a 50-question test will be to spinn a spinner with 4 equal sections 50 times.

Flipping a coin 50 times is wrong since the coin only has two outcomes which are head and tail. Rolling a 6-sided die 50 times is also wrong.

Therefore, the correct option is B.

Answer: QP=11.18cm;

QP=11.18cm;

m<Q=42;m<R=48*

Step-by-step explanation:

Hope this helps and the 48 degree

Answer:

174 ft²

Step-by-step explanation:

The polygon cam be decomposed into two rectangles.

The area of the polygon = rectangle A + rectangle B

Area of rectangle A = L* W

L = 18 ft

W = 9 ft

Area of rectangle A = 18*9 = 162 ft²

Area of rectangle B = L* W

L = 20 - 18 = 2 ft

W = 6 ft

Area of rectangle A = 2*6 = 12 ft²

✔️Area of the polygon = 162 + 12 = 174 ft²

Answer:

5 Hours

Step-by-step explanation:

2 : 30 = 1 : 15

75 ÷ 15 = 5

Answer:

5 hours

Step-by-step explanation:

30/2 = 15 miles per hour

75/15 = 5 hours

Step-by-step explanation:

When the slope of the function is positive, it is increasing

when the slope of the function is negative, it is decreasing

just like with the line function  y = mx + b

so if you put a line tangent to the function at every point the slope of the line will indicate a increasing or decreasing point of the function

also beware where the slope is zero  it is not increasing or decreasing

there are two intervals of increasing, one interval of decreasing and two point of zero slope or neither increasing or decreasing

increasing interval  1)  x < -2     2) x > 1.5

decreasing interval   1)     -2 <  x < 1.5

at -2 and 1.5 the slope is zero

If the slope of a function is positive at all the points of the curve in a interval, function will be increasing.

f'(x) > 0

If the slope of a function is negative at all the points of the curve in a interval,

function will be decreasing.

f'(x) < 0

As we can see from the graph slope of the curve is positive in the intervals (-∞, -2) and (1.5, ∞) and decreasing in the interval (-2, 1.5).

Therefore, function is increasing in the intervals → (-∞, -2) and (1.5, ∞).

And the function is decreasing in the interval → (-2, 1.5)

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Answer:

3 decimal places

Step-by-step explanation:

square root of 11.737476 is 3.426

Answer:

3•426

having 3 decimal places

Answer:

a, d, f

Step-by-step explanation:

3 - 3= 0

6 = 2(3)

3^2 = 9

Answer and Step-by-step explanation:

To find all equations where x = 3 is a solution, solve all equations for x and see if it is equal to 3.

A. x - 3 = 0

x = 3

B. 1 + x = 2

x = 1

C. 9 - x = 3

x = 6

D. 6 = 2x

x = 3

E. [tex]\frac{1}{5} x = 3[/tex]

x = 15

F. [tex]x^2 = 9[/tex]

x = 3

A, D, and F are the answers.

#teamtrees #PAW (Plant And Water)

Answer:

To find the radius..just divide them by two

For the diameter multiply by two

Circumference formula is

[tex]2\pi \: r[/tex]

Answer:

D

Step-by-step explanation:

i think i do am not si sure

Answer:

A, the first option

Step-by-step explanation:

1. Add 15 to both sides to cancel out the 15 from the left. (5x < -50)

2.  Divide both sides by 5 to cancel out the 5 from the left. ( x < -10)

This inequality does not include the -10 because it's less than -10 not less than or equal to. So, the point at -10 should not be filled in.

x has to be LESS than, so the graph should include numbers that are less than -10 which leads us to our answer, A.

Answer:

20 is the answer

Step-by-step explanation:

I did the math.hope it helps :)

Answer:

45 degrees

Step-by-step explanation:

Answer:

The fourth graph since it passes the vertical line test.

Each input has one output.

Hope this helps :)

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

Slope "m"

y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex] )

~~~~~~~~~~~~~~

( 4 , - 7 )

m = [tex]-\frac{1}{2}[/tex]

y - ( - 7 ) = [tex]-\frac{1}{2}[/tex] ( x - 4 )

y + 7 = [tex]-\frac{1}{2}[/tex] ( x - 4 )

Answer:

463 rounded

Step-by-step explanation:

4/3 times pi times r times r times r.

4.8 x 4.8 x  4.8 = 110.592 x 3.14 x 4/3 = 463

Volume of sphere is 463.01 [tex]cm^{3}[/tex].

The volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.

Volume of sphere = [tex]\frac{4}{3}\pi r^{3}[/tex]

Given

Radius of sphere r = 4.8 cm

Volume of sphere

V = [tex]\frac{4}{3}\pi r^{3}[/tex]

V = [tex]\frac{4}{3} \pi (4.8)^{3}[/tex]

V = 463.01 [tex]cm^{3}[/tex]

Volume of sphere is 463.01 [tex]cm^{3}[/tex].

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Answer:

it's C

Step-by-step explanation:

-16 means where the line crosses y axis