Find the value of the trigonometric ratio. Simplify the ratio if possible.
(Hint: You may need to use some pythagorean theorem first!)

Using the formula for the margin of error, it is found that a smaller confidence interval would be obtained as follow:

D. Increase the sample size to 64.

It is given by the following formula:

[tex]M = z\frac{s}{\sqrt{n}}[/tex]

In which:

For a smaller interval, we need to decrease the margin of error, which is possible increasing the sample size, hence option D is correct.

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Answer:

[tex]x=7,\\y=4\sqrt{2}[/tex]

Step-by-step explanation:

Draw an auxiliary line in the trapezoid forming a triangle and a rectangle. The dimensions of the rectangle are 3 x 4, so the length of the auxiliary line must be 4.

The auxiliary line also creates a 45-45-90 triangle. The auxiliary line itself makes up one leg of the triangle, and since we know it is 4, we can use the Pythagorean Theorem to find y:

[tex]4^2+4^2=y^2,\\y^2=32,\\y=\sqrt{32}=\boxed{4\sqrt{2}}[/tex]

The length of x can be found by adding the bottom leg of the 45-45-90 triangle and the bottom dimension of the rectangle:

[tex]x=4+3=\boxed{7}[/tex]

Answer:

The dimensions are four by two by two meters.

Step-by-step explanation:

The volume for a rectangular prism is given by:

[tex]V=\ell wh[/tex]

Where l is the length (or depth), w is the width, and h is the height.

Since the height and width are both two meters less than the depth, we can write that:

[tex]h=\ell -2\text{ and } w = \ell -2[/tex]

We are also given that the total volume is 16 cubic meters. Substitute:

[tex]16=\ell(\ell -2)(\ell -2)[/tex]

Expand:

[tex]16=\ell(\ell^2 -4\ell +4)[/tex]

Distribute:

[tex]16=\ell ^3-4\ell ^2+4\ell[/tex]

Isolate the equation. So:

[tex]\ell ^3-4\ell ^2+4\ell -16=0[/tex]

We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:

[tex]\ell ^2(\ell -4)+4(\ell -4)=0[/tex]

Factor:

[tex](\ell ^2+4)(\ell -4)=0[/tex]

Zero Product Property:

[tex]\ell ^2+4=0\text{ or } \ell - 4=0[/tex]

Solve for each case:

[tex]\ell^2=-4\text{ or } \ell =4[/tex]

Since we cannot take the square root of a negative number, we can ignore the first case.

Therefore, the length (or depth) of the storage space is four meters.

Thus, the dimensions are four by two by two meters.

Answer:

A. 320 ft²

B. 2,304 ft²

Step-by-step explanation:

A. Area of one triangular face = area of triangle = ½*b*h

Where,

b = 32 ft

h = 20 ft

A = ½*32*20 = 16*20

A = 320 ft²

Area of 1 triangular face = 320 ft²

B. Total surface area = area of the 4 triangular face + area of the base of the square pyramid

T.S.A = 4(320) + (s²)

Where,

s = 32 ft

T.S.A = 4(320) + (32²)

T.S.A = 1,280 + 1,024

= 2,304 ft²

Answer:

30ml of yellow

18ml of red

Step-by-step explanation:

5x6=30

3×6=18

Answer:

Step-by-step explanation:

a color

Answer:

333..%

Step-by-step explanation:

Step-by-step explanation:

165kg=330$

150*4=600$

600-330=270

espero te ayude :D

Answer:

p=5

Step-by-step explanation:

5+p=10

Hence, p=10-5

=5

Answer:

5

Step-by-step explanation:

1. Move the constant to the right- hand side and change its sign.

p=10-5

2. Subtract the numbers

p=10-5

the answer is 5

Answer:

Step-by-step explanation:

A trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula looks like this:

area_trapezoid1.gif or area_trapezoid2.gif

Where b1.gif is base1.gif, b2.gif is base2.gif, h.gif is height and · means multiply.

Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.

In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.

Answer:

x=28

y=v7vub8b9nf7v6v

Answer

2

Step-by-step explanation:

x^2-5x+2,

the greatest exponent seen in the polynomial is two (x squared), so the degree of this polynomial is 2 because of the number two x^2 -5x+2

Answer:

18

Step-by-step explanation:

Find the diagram attached

From the diagram

PR + RQ = PQ

PR + RQ = 38

PR = 38 - RQ

using similar triangle;

KQ/RQ = KP/PR

45/RQ = 50/38-RQ

Cross multiply

50RQ = 45(38-RQ)

50RQ = 1710 - 45RQ

50RQ + 45RQ = 1710

95RQ = 1710

RQ = 1710/95

RQ = 18

Hence the length of RQ is 18

Answer:

B .3.5 points of coffee did he drink

hope it helps

Answer:

Step-by-step explanation:

Answer:

4 feet of wall should be on each side of the painting.

Step-by-step explanation:

Given that a 4 foot wide painting should be centered on a 12 foot wide wall, to determine how many feet (X) should be on each side of the painting, the following equation must be solved:

(Total wide of the wall - wide of the painting) / 2 = X

(12 - 4) / 2 = X

8/2 = X

4 = X

Therefore, 4 feet of wall should be on each side of the painting.

Answer:

910*(1.2)^t

Step-by-step explanation:

Given data

Initial population= 910 quail

Rate= 20%

Let us use the model below

A= P(1+r)^t

r= 0.2

A= 910(1+0.2)^t

A= 910*(1.2)^t

Hence the expression to model the population is  910*(1.2)^t

An initial population of 910 quail increases at an annual rate of 20%.

So,

910*(1.2)^t

Step-by-step explanation:

Given data

Initial population= 910 quail

Rate= 20%

Let us use the model below

A= P(1+r)^t

r= 0.2

A= 910(1+0.2)^t

A= 910*(1.2)^t

Hence the expression to model the population is 910*(1.2)^t.

An exponential function is a mathematical function of the following form: f ( x ) = an x. where x is a variable, and a is a constant called the base of the function. The most commonly encountered exponential-function base is the transcendental number e, which is equal to approximately 2.71828.

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Answer:

use photo math. it will help

Answer:

Step-by-step explanation:

i cant see the answer

answer:

ABCD is not congruent to KLMN

ABCD cannot be mapped onto KLMN

Answer:

Graph A: (0,10) Graph B: (0,20)

Graph A: Height (feet) Graph B: Hight (feet)

Graph A: 138 Graph B: 120

Graph A: 32.6 Graph B: 43

Step-by-step explanation:

The smaller text was really blurry but I tried my best. Hope this helps!

Answer:

Step-by-step explanation:

I just pointed the answers, but quality of picture is poor: it's impossible to indicate the numbers on y-axis, and tell exact number on x-axis.

Answer:

$30.53

Step-by-step explanation:

Find total sum

30+25+35=90

90+24=114

114+40=154

154+35=189

…

You will get 458

458/15=30.53333

Answer:

I think the answer is would be C

Answer:

A. Neil did not make a mistake.

Step-by-step explanation:

Everything looks fine in this problem.

========================================================

Explanation:

Simply look at the "coef" column to find the values you need. The constant is the term that isn't attached to the variable. The mileage coefficient is basically the slope.

You can think of it like

price = constant + (mileage coefficient)*(mileage)

The mileage coefficient being negative tells us we have negative correlation going on here. As x increases, y decreases. This makes sense because the car's value is expected to go down the more mileage is added on it.

Answer:

0.52

Step-by-step explanation:

100% - 48% = 52%

[tex]\frac{52}{100}[/tex]

0.52

I hope this is help full to you

Answer:

The answer e i think

Step-by-step explanation:

Answer:

below

Step-by-step explanation:

15r kg therefore it would be 15r/5people

3r kg for each person

Answer:

the second one for #4 and the third one for #5

Step-by-step explanation:

4. The sum of x and y is 24, so x+y = 24. The difference is 15, so x-y = 15, or

y-x=15 (they didn't specify which was which). Therefore, A, C, and D are correct, so x = 15-y is the answer (x = 15-y is the same as x+y = 15, which is false).

5.

Matt = 6 apple pies + 4 lemon pies and he got 80 dollars.

Ming = 6 apple pies + 5 lemon pies and he got 94 dollars.

If apple pie is "a" and lemon is "l":

6a + 4l = 80

6a + 5l = 94,

so C is the answer