how many 1/2 inch cubes does it take to fill a rectangular prism with a length of 1 inch, a width of 2 inches and a height of 3 inches

Answer:

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

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]

18% of residents in Minneapolis, Minnesota, are African Americans. Suppose a local court will randomly sample 100 state residents and will then observe the proportion in the sample who are African American.

This means that [tex]p = 0.18, n = 100[/tex]

So, by the Central Limit Theorem:

[tex]\mu = 0.18, s = \sqrt{\frac{0.18*0.82}{100}} = 0.0384[/tex]

How likely is the resulting sample proportion to be between 0.066 and 0.294?

This is the pvalue of Z when X = 0.294 subtracted by the pvalue of Z when X = 0.066. So

X = 0.294

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

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

[tex]Z = \frac{0.294 - 0.18}{0.0384}[/tex]

[tex]Z = 2.97[/tex]

[tex]Z = 2.97[/tex] has a pvalue of 0.9985

X = 0.066

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

[tex]Z = \frac{0.066 - 0.18}{0.0384}[/tex]

[tex]Z = -2.97[/tex]

[tex]Z = -2.97[/tex] has a pvalue of 0.0015

0.9985 - 0.0015 = 0.997

0.997 = 99.7% probability that the resulting sample proportion to be between 0.066 and 0.294

Answer:

63

Step-by-step explanation:

Answer/Step-by-step explanation:

Factor this. GCF=2

2(2cos2x+cos x-1)=0

2(2cos x -1)(cos x+1)=0 Set each factor equal to zero and solve

2cos x -1=0 Add 1 to both sides

2cos x =1 Divide by 2

cos x =1/2

x=π/3

x=5π/3

cos x+1=0 Subtract 1 from both sides

cos x=-1

x = π

Answer:

9

Step-by-step explanation:

Answer:

C.

Step-by-step explanation:

Answer:

37.68

Step-by-step explanation:

A= 3.14 x 4 x 4 = 50.24

50.24 ÷ 4 = 12.56

12.56 x 3 = 37.68

Answer:

Step-by-step explanation:

that means that x=z transitive prop of equality

if my answer helps please mark as brainliest

Answer:

14

Step-by-step explanation:

13-2=11 then 11x 3 =33 then 33-25=8+=14

Answer:

Step-by-step explanation:

PEMDAS is going to be your best friend bud. It stands for Parenthesis, Exponents, Multiplication/Division, Addition/Subtraction. This is the order you will use for all problems like this in the future. Start by solving everything inside the parenthesis.

6+3(11)-5^2=?

Now that all the parenthesis are gone we move on to exponents.

6+3(11)-(5*5)=?

6+3(11)-25=?

Now that all exponents are gone we solve for multiplication and division, whichever comes first when reading from left to right.

6+33-25=?

The final step is to add and subtract from left to right.

Hope this helps!

Answer:

The bench costs $375

Step-by-step explanation:

t + b = 793

t = b+43

(b+43) + b = 793

2b + 43 = 793

2b = 750

b = 375

The bench costs $375

Answer: c. The point estimate is 0.80 and the margin of error is 0.035.

Step-by-step explanation:

Given: The 95 percent confidence interval was (0.765, 0.835).

Confidence interval = Point estimate ± Margin of error.

I.e. Point estimate + Margin of error = 0.835       (i)

Point estimate - Margin of error = 0.765         (ii)

Add (i) and (ii), we get

2 (Point estimate)= 1.60

⇒ Point estimate = 0.80

Put this in (i), we get

0.80+Margin of error = 0.835

⇒ Margin of error = 0.835 -0.80

⇒ Margin of error = 0.035

Hence, the correct statement is:

c. The point estimate is 0.80 and the margin of error is 0.035.

Answer:

$77,886

Step-by-step explanation:

We solve this question by proportions, using a rule of three.

The table states that:

$201.6 in 2006 is worth $232.957 in 2013.

We want to find:

The value of $90,000 in 2013 in 2006:

$201.6 - $232.957

x - $90000

Applying cross multiplication

[tex]232957x = 201.6*90000[/tex]

[tex]x = \frac{201.6*90000}{232957}[/tex]

[tex]x = 77886[/tex]

$77,886 is the answer

Answer:

The estimate for the amount of tails is 146.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a head, or it is tails. Throws are independent. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

The probability of a head is 0.27.

This means that the probability of tails is [tex]p = 1 - 0.27 = 0.73[/tex]

The coin is thrown 200 times.

This means that [tex]n = 200[/tex]

Write an estimate for the amount of tails

This is the expected value, so:

[tex]E(X) = np = 200*0.73 = 146[/tex]

The estimate for the amount of tails is 146.

Answer:

45x happy to help ya :)

Step-by-step explanation:

Answer:

375 bags

Step-by-step explanation:

900/2.4=375 bags

Answer:

18

Step-by-step explanation:

its an isoceles triangle, the two sides (NP and Q) are equal

Answer:

18

Step-by-step explanation:

Answer:

y = 10 x = 4

Step-by-step explanation:

Answer:

y = 10x - 30

Step-by-step explanation:

x = 5

5 x 10 = 50

50 - 30 = 20

y = 20

x = 6

6 x 10 = 60

60 - 30 = 30

y = 30

x = 7

7 x 10 = 70

70 - 30 = 40

y = 40

x = 8

8 x 10 = 80

80 - 30 = 50

y = 50

Answer:

1 second

Step-by-step explanation:

The number of seconds for the ball to reach the maximum height is t = 1 s

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = -16t² + 32t + 128

The function h(t) gives the height of the ball at time t. The maximum height occurs at the vertex of the parabolic path, which is given by the formula:

t = -b / (2a)

where a = -16 and b = 32 are the coefficients of the quadratic term and the linear term, respectively.

Substituting these values into the formula, we get:

t = -32 / (2(-16)) = 1

Therefore, the ball reaches its maximum height after 1 second

Hence , the function is solved

To learn more about function rule click :

https://brainly.com/question/3760195

#SPJ2

Answer:

Step-by-step explanation:

Expresión x--12.5*y-612*x-3*y-2 = 9.5*y-611.0*x-2.0

Answer:

60

Step-by-step explanation:

There are sixty students.

15%   =   9

------------------

100% =  x

Cross muliply.

900

------

15x

Divide 15x by 15, and 900 by 15.

Answer is 60.

I hope this helps!

Brainliest would be awesome!

Answer:

pesaria 2.25 kilos

explicacion

Answer:

ummmm this is easy

Step-by-step explanation:

she has to spend $137.51 more, all you have to do is

$250 - $112.49 = $137.51

I am not sure if you were serious with this question or not but here is the answer lulu

hope this helps :) :) :) :)

Answer: 45 apples will be needed to fill 3 boxes

Step-by-step explanation: If there are an even amount of apples in each box, 15 times 2 is 30. So if there are 15 apples in each box, 15 times 3 is 45.

Answer:45 apples

Step-by-step explanation:

Since 15 apples are needed to fill 1 box, 45 apples are needed to fill 3 bboxes

Answer:

Probably unequal  ( B )

Step-by-step explanation:

experimental group = 10

using 85% ethanol gasoline

mean = 240 pounds per 100 miles

standard deviation = 20 pounds

control group = 14 vehicles

using regular gasoline

mean = 252 pounds per 100 miles

standard deviation = 15 pounds

comparing  the sample variance of each group shows that they are probably unequal using the equation below

Variance for a sample set of data = ∑ ( x - X ) ^2 / n - 1

where n = number of events

X = mean value

x = value of events

Answer:

216..................

Answer:

m=52

Step-by-step explanation:

ABC and FBE are congruent and we know that ABC is 52

90-38=52

so FBE is also 52

Hope this helps ^-^

Answer:

c = -6

Step-by-step explanation:

10c + 12 = -48

subtract 12 from both sides

10c = -60

divide by 10 on both sides

c = -6

Answer:

C = -6

Step-by-step explanation:

10c + 12 = - 48

      -12     -12

10c = -60

/10     /10

c = -6