A stereo speaker in the shape of a triangular pyramid has a height of 8.25 inches. The area of the base of the speaker is 22 square inches. What is the volume of the speaker in cubic inches?
A. 60.5 in3

B. 181.5 in3

C. 90.75 in3

D. 243 in3

Answer:

B. Z= -2.55

Step-by-step explanation:

To solve this question, first we need to understand the central limit theroem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction of normal variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

11 of 50 men believe that sexual discrimination is a problem:

This means that:

[tex]p_M = \frac{11}{50} = 0.22, s_M = \sqrt{\frac{0.22*0.78}{50}} = 0.0586[/tex]

19 of 40 women believe that sexual discrimination is a problem:

This means what:

[tex]p_W = \frac{19}{40} = 0.475,  s_W = \sqrt{\frac{0.475*0.525}{40}} = 0.079[/tex]

Difference between the proportion of men and women:

[tex]p_D = p_M - p_W = 0.22 - 0.475 = -0.255[/tex]

[tex]s_D = \sqrt{s_M^2+s_W^2} = \sqrt{0.0586^2+0.079^2} = 0.0984[/tex]

A powerful women's group has claimed that men and women differ in attitudes about sexual discrimination.

This means that the null hypothesis is that they do not differ, than is, the difference is 0. So

[tex]H_0: p_D = 0[/tex]

At the alternate hypothesis, we test that they differ, that is, the difference is different of 0. So

[tex]H_a: p_D \neq 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

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

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

For the sample, we calculated that:

[tex]X = -0.255, s = 0.0984[/tex]

The value of the test-statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.255 - 0}{0.0984}[/tex]

[tex]z = -2.59[/tex]

Closes answer is Z = -2.55, option B.

Answer:

1.66666666666666666667

Step-by-step explanation:

if rounded by the nearest tenth it is 1.7

Hope this helps :)

Answer:

10/6 = 1 and 2/3

Step-by-step explanation:

10 pounds of candy, 6 bags.

that means 10 divided by 6, or 10/6

simplify that 10-6 = 4, 6 can only be subtracted once, so it is 1 and 4/6 or 2/3

2/3 is 0.666666... so add it together and you get 1.66666... or 1 and 2/3

Answer:A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

Explanation:

To find a relationship modeled by the given function it is recommendable to factor it.

The function is: f(x)=4x3- 72 x2+320x

The first step to factor it is to extract common factor 4x: f (x)=4x(x2-18=80)

The second step is to factor the quadratic trinomial.

That is made by writing it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is: f(x)=(4x)(x-10)(x-8)

Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.

x is the desired (unknown) length

4x is 4 times the desired length

x - 10 is 10 less than the desired length

x - 8 is 8 less than the desired length

Thus, the volume of the prism is the product of the three factors:

Volume = (4x)(x-10)(x-8)

Answer:

B 113

Step-by-step explanation:

on edg

From the information given, the area of the circle is: "113 sq. cm".

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

The formula to find the area of a circle is,

Area = πr².

Now, Using the side as the radius of the circle, we can calculate the area of the base area.

Here,

Radius r = 6

Thus, We get;

A = π x 6²

A = (22/7) x 36

A = 3.14285714286 x 36

A = 113.12

A ≈ 113 square unit.

Hence, The area of the circle is,

⇒ A =  113 sq. cm.

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Answer:

I might be in highschool, but I'm sure I can still help.

Step-by-step explanation:

See the 45 degree angles? that means they're equal sides. So 4v2 = 5.65, right? so if you take 180 - 5.65, and then divide by two, you should have the length to each of those sides. They're equal, remember. So, the answer would be 180 - 5.65 = 174.35. 174.35 / 2 = 87.175. In this case, k = 87.175 :)

Answer:

1230 is how much he received for the bike

Step-by-step explanation:

Answer:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Step-by-step explanation:

Given

[tex]n = 125[/tex]

See attachment for proper table

Required

Complete the table

Experimental probability is calculated as:

[tex]Pr = \frac{Frequency}{n}[/tex]

We use the above formula when the frequency is known.

For result of roll 2, 4 and 6

The frequencies are 13, 29 and 6, respectively

So, we have:

[tex]Pr(2) = \frac{13}{125} = 0.104[/tex]

[tex]Pr(4) = \frac{29}{125} = 0.232[/tex]

[tex]Pr(6) = \frac{6}{125} = 0.048[/tex]

When the frequency is to be calculated, we use:

[tex]Pr = \frac{Frequency}{n}[/tex]

[tex]Frequency = n * Pr[/tex]

For result of roll 3 and 5

The probabilities are 0.144 and 0.296, respectively

So, we have:

[tex]Frequency(3) = 125 * 0.144 = 18[/tex]

[tex]Frequency(5) = 125 * 0.296 = 37[/tex]

For roll of 1 where the frequency and the probability are not known, we use:

[tex]Total \ Frequency = 125[/tex]

So:

Frequency(1) added to others must equal 125

This gives:

[tex]Frequency(1) + 13 + 18 + 29 + 37 + 6 = 125[/tex]

[tex]Frequency(1) + 103 = 125[/tex]

Collect like terms

[tex]Frequency(1) =- 103 + 125[/tex]

[tex]Frequency(1) =22[/tex]

The probability is then calculated as:

[tex]Pr(1) = \frac{22}{125}[/tex]

[tex]Pr(1) = 0.176[/tex]

So, the complete table is:

[tex]1 \to 22 \to 0.176[/tex]

[tex]2 \to 13 \to 0.104[/tex]

[tex]3 \to 18 \to 0.144[/tex]

[tex]4 \to 29 \to 0.232[/tex]

[tex]5 \to 37 \to 0.296[/tex]

[tex]6 \to 6 \to 0.048[/tex]

Answer:

your answer is 7 meters

I hope it's helps you ❤️

Answer:

4)

Step-by-step explanation:

This is in standard form. To change it to slope-intercept form, you would divide 2x by 3y and you would divide 6 by 3y. That would make the equation y = [tex]\frac{2}{3}[/tex]x + 2. y = mx + b, and slope = m, so on answer choice 4, slope would equal [tex]\frac{2}{3}[/tex].

Answer:

SAS

Step-by-step explanation:

Answer:

1/25

Step-by-step explanation:

days in a week is 7

odds of being born on each 7 days is equal

x born = 7 days

pr(one separate baby) = 1 ÷ 5

pr(second separate baby) = 1 ÷ 5

pr(both being born on a school day) = 1/5 × 1/5

= 1/25

Answer:

AB = √17     4.1

GH = 4√2    5.7

Step-by-step explanation:

AB = 1²+4²=c²

1+16=c²

17=c²

√17=c

c=4.1

GH = 4²+4²=c²

16+16=c²

32=c²

√32=c

4√2=c

C=5.7

Answer:

b

Step-by-step explanation:

The solution for system of two equations is simply the intersection of the two functions. Hence (b) is the answer

Answer:

8 boxes

Step-by-step explanation:

Surface area of the rectangular prism:

A=2(wl+hl+hw)

A = 2(5·4+7·4+7·5) = 166

The 166 represents the square ft of one box.

Take the total number of wallpaper she has, 1328 ft^2, and divide by 166 to find the number of boxes that she can cover.

[tex]\frac{1328}{166} = 8[/tex]

Hope that helps!

Answer:

Step-by-step explanation:

Firstly lets calculate the total surface area of the cuboid

Total surface area of cuboid (A1)

= 2( l*b+ b*h +l*h)

= 2( 7 * 5+ 5 * 4 + 7 * 4)

= 166 ft²

also given that

Total area of the wallpaper ( A2)= 1328 ft²

Now

Number of boxes that she can cover is

= A2 / A1

= 1328 / 166

= 8 BOXES.

hope it will help :)

Answer: 120cm squared

Step-by-step explanation: To do this you can cut off one of the 'triangle ends' on the trapezoid and add it to the other side to make a rectangle. Since the top is 10cm, each triangle will have a base of 5cm, so the bases will be 15cm when you subtract 20-5. Then you just have 8 * 15 which is 120cm SQUARED. This may have been a little confusing so i attachecd a diagram.

Answer:

(0,1.5)

Step-by-step explanation:

(x,y)

Answer:

Parameter = 0.5

Null hypothesis : H0 : P0 = 0.5

Alternative hypothesis ; H0 : P0 > 0.5

Pvalue = 0.99966

Step-by-step explanation:

The parameter defines a statistical value or calculation which is derived from the population.

The parameter in this scenario is the population proportion, P0 which is 0.5

The scenario above describes a scenario to test the difference in population.

The null hypothesis, that bride and groom are of the same age ;

H0 : P0 = 0.5

The alternative hypothesis ; the bride is younger Than the groom in more than half of the population.

H1 : p0 > 0.5

To obtain the Pvalue :

Test statistic : (phat - P0) ÷ √(p0(1 -p0) / n)

Phat = x/n

x = 67 ; sample size, n = 100

Phat = x / n = 67/100 = 0.67

P0 = 1 - 0.5 = 0.5

Tstatistic = (0.67-0.50) ÷ √(0.5(0.5) / 100)

Tstatiatic = 0.17 ÷ 0.05

Tstatistic = 3.4

P-value : p(Z < 3.4) = 0.99966 (Z probability calculator).

Answer:

4.9:13.1

Step-by-step explanation:

V=4/3*pi*r^3

Answer:

The second 1: Beaver dams can make water safer and cleaner

Step-by-step explanation:

Since Beaver dams create wetland = new plants and animals to area = clean water, so  beaver dams = clean water.

Answer:

I WANT POINTS

Step-by-step explanation:

NOTHING TO SAY ABOUT I-Ready.

Answer:

YES

Step-by-step explanation:

(3/8)·64 = 24 seats in the first class carriage are being used.

(7/13)·(78)·3 = 126 seats in the standard carriages are being used, for a total of ...

 24 + 126 = 150 . . . occupied seats

The number of available seats is ...

 64 +3·78 = 298

so half the seats on the train will be 298/2 = 149 seats.

 150 > 149, so more than half the seats on the train are being used.

Answer: $1.85

Step-by-step explanation: 21.55+2.25+3.89+1.95=29.64

29.64*(.0625)=1.8525

$1.85

29.64*(1.0625)=31.4925

$31.49

$31.49-$1.85=$29.64

Answer:

This question seems incomplete

Answer:

height of second rectangular prism is 5 meters

Step-by-step explanation:

Answer and Step-by-step explanation:

The radius of this circle is 5 cm.

This is because the radius of any circle is the distance from the middle of the circle to the edge of the circle. The diagram shows us 5cm as that distance.

#teamtrees #PAW (Plant And Water)

Answer:

The number of ways to choose a cone, if order matters, is 45.

Step-by-step explanation:

Given that a certain ice cream parlor offers fifteen flavors of ice cream, and you want an ice cream cone with three scoops of ice cream, all different flavors, to determine in how many ways you can choose a cone if it matters which flavor is on. top, which is in the middle and which is on the bottom, the following calculation must be performed:

15 x 3 = X

45 = X

The number of ways to choose a cone, if order matters, is 45.

There is 1820 ways of teams of 4 can she make without repetition using combination formula.

What is combination?

  Selections are another name for combinations. The choice of items from a predetermined group of items corresponds to combinations. We don't want to organise anything here. We are going to choose them. We use the notation nCr to indicate how many distinct r-selections or combinations there are among a set of n objects. A combination is distinct from an arrangement or a permutation. No matter how the objects are arranged, combinations are produced by choosing some or all of them.

Here There are 16 total swim team members and 4 swimmers that will be chosen for each relay team.

So, n=16 and r=4. Then

=> nCr =  [tex]\frac{n!}{r!(n-r)!}[/tex]

=> 16C4 = [tex]\frac{16!}{4!(16-4)!}[/tex]

=> 16C4 = [tex]\frac{16!}{4!*12!}[/tex]

=> 16C4 = [tex]\frac{16*15*14*13}{4*3*2*1}[/tex]

=>16C4 = 4*5*7*13 = 1820

Hence there is 1820 ways  of teams of 4 can she make without repetition.

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Answer:

17

Step-by-step explanation:

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Answer:

The person walked 1,056 feet in 6 minutes.

Mph 12