What is the volume of this rectangular prism

The total number of possible outcomes for Yolanda’s card is 51.

A branch of mathematics concerned with the analysis of random phenomena, or occurrence of things.

Given that, Raj has a full deck of 52 cards. Sydney chooses the queen of clubs and holds onto it. Then Yolanda chooses a card.

Since, there is only 1 queen of clubs in a deck of cards, so, after choosing 1 card from deck there will be remaining only 51 cards.

Therefore, there will be 51 cards remaining for Yolanda to choose.

Hence, The total number of possible outcomes for Yolanda’s card is 51.

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Answer:

1/18

Step-by-step explanation:

Total 11: (5,6) (6,5)

2/36

1/18

Answer:

Correct option: (C)

Step-by-step explanation:

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

Or, if n such (1 - α)% confidence intervals are constructed then (1 - α)% of these interval will consist of the true parameter value.

It is provided that each of the 250 people taking statistics randomly takes a sample of 40 of these heights and constructs a 95% confidence interval for mean height of all students at the college.

So there sill be n = 250, 95% confidence intervals for mean height of all students at the college.

Then 95% of these 250 confidence intervals for mean will consist of the true mean height of the college students.

Thus, the correct option is (C).

Answer:

x=−1,  3/8

Step-by-step explanation:

Answer:

x= 3/8 or x=-1

Step-by-step explanation:

Step 1: Subtract 3 from both sides.

8x2+5x−3=3−3

8x2+5x−3=0

Step 2: Factor the left side of the equation.

(8x−3)(x+1)=0

Step 3: Set factors equal to 0.

8x−3=0 or x+1=0

x=3/8 or x=-1

Step-by-step explanation:

Putting the value of r

3 ( 1/6) 2

So 3 × (1/6) = 0.5 × 2 = 1

Answer:

No, the expression is not linear because the highest power of x is 2.

Answer:

No it isn't  it is Quadratic

Step-by-step explanation:

4x + 7° = 5x - 1°

5x - 4x = 7° + 1°

x = 8°

As OR~=OS

Answer:

The claim made by the CEO was correct.

Step-by-step explanation:

The CEO of a large electric utility claims that 80% of all his customers are very satisfied with the service they receive.

A one-proportion z-test can be used to determine whether the claim made by the CEO of a large electric utility  is correct or not.

The hypothesis can be defined as:

H₀: The proportion of customers that are very satisfied with the service they receive is 80%, i.e. p = 0.80.

Hₐ: The proportion of customers that are very satisfied with the service they receive is not 80%, i.e. p ≠ 0.80.

The information provided is:

[tex]\hat p[/tex] = 0.73

n = 100

α = 0.05

Compute the test statistic as follows:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.73-0.80}{\sqrt{\frac{0.80(1-0.80)}{100}}}=-1.75[/tex]

The test statistic value is -1.75.

The decision rule is:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

Compute the p-value of the two-tailed test as follows:

[tex]p-value=2\times P(Z<-1.75)\\=2\times [1-P(Z<1.75)]\\=2\times [1-0.95994]\\=0.08012 \\\approx 0.08[/tex]

*Use a z-table for the probability.

The p-value of the two-tailed test is 0.08.

p-value = 0.08 > α = 0.05

The null hypothesis was failed to be rejected at 5% level of significance.

Thus, it can be concluded that the claim made by the CEO was correct. The proportion of customers that are very satisfied with the service they receive is 80%.

Answer: 4 feet

Step-by-step explanation:

The formula for volume is length x width x height

Answer:

The answer to your question is 4 ft

Step-by-step explanation:

Data

length = 2 ft

height = 5 ft

Volume = 40 ft³

width = ?

Process

A crate is a rectangular prism, so to calculate the volume we use

       Volume of a rectangular prism = height x length x width

-Solve for width

        width = Volume / height x length

-Substitution

        width = 40 / (5 x 2)

-Simplification

        width = 40/10

-Result

       width = 4 ft

Answer:

(x+8)^2 = 127

Step-by-step explanation:

Answer:log2 (4x) = log2(4)+log2 (x) it is D

Step-by-step explanation:

Answer:

2.78% probability that he gets exactly 2 of the twenty questions wrong

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he knows the answer, or he does not. The probability of him knowing the answer for a question is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

On any question, the student knows the answer with probability .7.

This means that [tex]p = 0.7[/tex]

What is the probability that he gets exactly 2 of the twenty questions wrong, if his performance on different questions is independent

2 of 20 wrong, 20-2 = 18 correctly. So this is P(X = 18).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 18) = C_{20,18}.(0.7)^{18}.(0.3)^{2} = 0.0278[/tex]

2.78% probability that he gets exactly 2 of the twenty questions wrong

Answer:

infinity

Step-by-step explanation:

a) the expected value of this gamble in dollars is Infinity

i.e

expected value = [tex]\frac{1}{2}*2 + \frac{1}{4}*4 + \frac{1}{8}*8 + \frac{1}{16}*16 + ... + \to \infty (infinty) \\[/tex]

= [tex]1+1+1+1+1 + ... = \infty[/tex]

b)

When offered, most people say they would pay only less than $10 to play this game.

What are two reasons why people are willing to pay so much less than the expected value?

These people are ready to pay less than $10 to play this game due to the fact that people usually overlook the unlikely event when making decisions. In a bid to that logic, they gamble in order to double their amount of money and the probability that heads may never come is ignored by these people and they may hope for a likely event i.e a head every time they play the game.

Also, the expected value is so humongous that if and only if that the first head appears after a long series of tails which is  very less certain to occur, because mostly people would think that on an average the length of a series of tails ( or heads) is somewhat near 10 or so, but definitely infinity.

Let your friend's hourly wage last year be $x.

125% of x = 10.50

[tex]\frac{125}{100}[/tex] x = 10.5

[tex]\frac{5}{4}[/tex] x = 10.5

5x = 42

x = $8.40

Your friend's hourly wage last year was $8.40.

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

Answer:

it is $8.40

Step-by-step explanation:

sorry my answer got deleted :(

Answer:

Please see the attached file for the complete answer.

Step-by-step explanation:    

Please use mean = 3.5 instead of 3.1 and varience = 0.015 instead of 0.018 in the solution.

Answer:0.518518519

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

12(5x−2)

Step-by-step explanation:

i think this is the answer plz tell me if im wrong

Answer:

Step-by-step explanation:

Hello!

The objective is to test if the purchase frequencies of new-car buyers follow the distribution of the shares of the U.S. automobile market for 1990.

You have one variable of interest:

X: Brand a new-car buyer prefers, categorized: GM, Japanese, Ford, Chrysler and Other

n= 1000

Observed frequencies

GM 193

Japanese 384

Ford 170

Chrysler 90

Other 163

a) The test to use to analyze if the observed purchase frequencies follow the market distribution you have to conduct a Goodness to Fit Chi-Square test.

The conditions for this test are:

- Independent observations

In this case, we will assume that each buyer surveyed is independent of the others.

- For 3+ categories: each expected frequency (Ei) must be at least 1 and at most 20% of the Ei are allowed to be less than 5.

In our case we have a total of 5 categories, 20% of 5 is 1, only one expected frequency is allowed to have a value less than 5.

I'll check this by calculating all expected frequencies using the formula: Ei= n*Pi (Pi= theoretical proportion that corresponds to the i-category)

E(GM)= n*P(GM)= 1000*0.36= 360

E(Jap)= n*P(Jap)= 1000*0.26= 260

E(Ford)= n*P(Ford)= 1000*0.21= 210

E(Chrys)= n*P(Chrys)= 1000*0.09= 90

E(Other)= n*P(Other)= 1000*0.08= 80

Note: If all calculations are done correctly then ∑Ei=n.

This is a quick way to check if the calculations are done correctly.

As you can see all conditions for the test are met.

b) The hypotheses for this test are:

H₀: P(GM)= 0.36; P(Jap)= 0.26; P(Ford)= 0.21; P(Chrys)= 0.09; P(Other)= 0.08

H₁: At least one of the expected frequencies is different from the observed ones.

α: 0.05

[tex]X^2= sum \frac{(Oi-Ei)^2}{Ei} ~~X^2_{k-1}[/tex]

k= number of categories of the variable.

This test is one-tailed right this mean you'll reject the null hypothesis to high values of X²

[tex]X^2_{k-1;1-\alpha }= X^2_{4;0.95}= 9.488[/tex]

Decision rule using the critical value approach:

If [tex]X^2_{H_0}[/tex] ≥ 9.488, reject the null hypothesis

If [tex]X^2_{H_0}[/tex] < 9.488, don't reject the null hypothesis

[tex]X^2_{H_0}= \frac{(193-360)^2}{360} + \frac{(384-260)^2}{260} + \frac{(170-210)^2}{210} + \frac{(90-90)^2}{90} + \frac{(163-80)^2}{80} = 230.34[/tex]

The value of the statistic under the null hypothesis is greater than the critical value, so the decision is to reject the null hypothesis.

Using a 5% level of significance, there is significant evidence to conclude that the current market greatly differs from the preference distribution of 1990.

The chi-square test can be used to determine if there is a significant difference between the observed frequencies and the expected frequencies based on the shares of the U.S. automobile market in 1990. A calculated chi-square statistic greater than the critical value would indicate a significant difference between the current market shares and those of 1990.

The first step in the process is to calculate the expected counts for each category based on the shares of the U.S. automobile market in 1990. The expected counts for GM, Japanese manufacturers, Ford, Chrysler, and other amounts to 360, 260, 210, 90, and 80, respectively.

Given the observed frequencies, the chi-square statistic X² can be calculated. The formula for the chi-square test is X² = Σ[(O-E)²/E], where O represents the observed frequency and E represents the expected frequency. Using this formula, the chi-square statistic is calculated.

Finally, using a chi-square distribution table with 4 degrees of freedom (5 categories - 1), and an alpha level of 0.05, you can compare the calculated chi-square statistic to the critical value (9.488). If the chi-square statistic is larger than the critical value, you would reject the null hypothesis and conclude that the current market shares do differ from those of 1990. If the chi-square statistic is smaller than the critical value, you would not reject the null hypothesis and conclude that the current market shares do not significantly differ from those of 1990.

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The statement equivalent to 10^x is A,C and F.

We have to find the expression equivalent to 10^x.

Equivalent Statements are statements that are written differently but hold the same logical equivalence.

[tex]A.(50/5)^x\\=10^x[/tex]

This is equivalent to the 10^x.

[tex]10 \times 10^x-1\\=10 \times 10^x\times 10^-1\\=10^x[/tex]

This is equivalent to the 10^x.

[tex]50^x / 5^x\\=10^x[/tex]

This is equivalent to the 10^x.

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The expression 10^x represents a form of exponential notation, which includes any expression that has 10 as the base in the format a x 10^x. This is often used in scientific notation to conveniently write very small or large numbers. Such an expression could also be manipulated using rules of exponential arithmetic.

The expression 10^x is equivalent to any expression with exponential notation where 10 is the base. This includes expressions like 1.23 x 10^x or 3.6 x 10^-x, where the 'x' in the exponent can be replaced by any number. This introduces the concept of scientific notation, which allows very large and small numbers to be written compactly. For example, 1,230,000,000 can be written 1.23 x 10^9, and 0.00000000036 can be written 3.6 x 10^-10. Exponential Arithmetic further explains how these notations can simplify arithmetic operations. It explains that to multiply two numbers written in exponential form, one should multiply the numbers in the front and add the exponents.

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Answer:

Third one

4 + 2.5 > 5

Step-by-step explanation:

To form a triangle, the longest side should be less than the sum of the two shorter sides (triangular inequality)

Longest side < sum of the shorter ones

Longest side: 5

Shorter ones: 2.5 & 4

5 < 2.5 + 4

This is the same as:

4 + 2.5 > 5

Answer:

1 3 5

Step-by-step explanation:

Answer:

45 original books then 23 is sold = 22

next day 15 is sold so

23-15=7

7 books remain

Step-by-step explanation:

45-23-15=7

Answer:

In the diagram, the length of the external portion of the secant segment PN is x. The length of the entire segment LN is 36. The value of x is 17.75.

Step-by-step explanation:

I just did it on Edge.

Answer:

0.57 or 0.6

Step-by-step explanation:

Answer:

Only truck 1 can pass under the bridge.

Step-by-step explanation:

So, first of all, we must do a drawing of what the situation looks like (see attached picture).

Next, we can take the general equation of an ellipse that is centered at the origin, which is the following:

[tex] \frac{x^2}{a^2}+\frac{y^2}{b^2}[/tex]

where:

a= wider side of the ellipse

b= shorter side of the ellipse

in this case:

[tex] a=\frac{38}{2}=19ft[/tex]

and

b=12ft

so we can go ahead and plug this data into the ellipse formula:

[tex] \frac{x^2}{(19)^2}+\frac{y^2}{(12)^2}[/tex]

and we can simplify the equation, so we get:

[tex] \frac{x^2}{361}+\frac{y^2}{144}[/tex]

So, we need to know if either truk will pass under the bridge, so we will match the center of the bridge with the center of each truck and see if the height of the bridge is enough for either to pass.

in order to do this let's solve the equation for y:

[tex] \frac{y^{2}}{144}=1-\frac{x^{2}}{361}[/tex]

[tex] y^{2}=144(1-\frac{x^{2}}{361})[/tex]

we can add everything inside parenthesis so we get:

[tex] y^{2}=144(\frac{361-x^{2}}{361})[/tex]

and take the square root on both sides, so we get:

[tex] y=\sqrt{144(\frac{361-x^{2}}{361})}[/tex]

and we can simplify this so we get:

[tex] y=\frac{12}{19}\sqrt{361-x^{2}}[/tex]

and now we can evaluate this equation for x=4 (half the width of the trucks) so:

[tex] y=\frac{12}{19}\sqrt{361-(8)^{2}}[/tex]

y=11.73ft

this means that for the trucks to pass under the bridge they must have a maximum height of 11.73ft, therefore only truck 1 is able to pass under the bridge since truck 2 is too high.

Truck 1 and Truck 2 can both pass under the bridge.

To determine which truck can pass under the bridge, we need to compare the height of the truck to the height of the arch over the center of the roadway. The height of the arch is given as 12 feet. Truck 1 has an overall height of 11 feet, so it can pass under the bridge. Truck 2 has an overall height of 12 feet, which is equal to the height of the arch, so it can also pass under the bridge.

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Answer:

terminating and rational

Step-by-step explanation:

Answer:

C: Terminating and Rational

Step-by-step explanation:

A whole number is a number with no decimal places so the answer is not A.

A natural number is a whole number which is equal to or greater than 0, and since 0.46 is not a whole number, the answer is not B either.

A terminating number is a number which does not go on forever, like 3.86. A rational number is a number which can be expressed as a fraction, and 0.46 can be expressed as 46/100. Thus 0.46 is both terminating and rational, making C the answer.

Answer:

Option D) 0.014

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 1200

Sample proportion =

[tex]\hat{p} = 0.47[/tex]

We have to make a 95% confidence interval.

Formula for standard error:

[tex]S.E = \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

Putting the values, we get:

[tex]S.E = \sqrt{\dfrac{0.47(1-0.47)}{1200}} = 0.014[/tex]

Thus, the correct answer is

Option D) 0.014

The quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is [tex]\frac{20}{21}[/tex]

Recall:

The quotient of two quantities or values is the result you get by dividing one with the other.

Therefore, the quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is solved as shown below:

[tex]\frac{4}{7} \div \frac{3}{5} \\[/tex]

Change the division sign to multiplication sign and turn the second fraction upside down

[tex]\frac{4}{7} \times \frac{5}{3} \\[/tex]

Multiply both fractions together

[tex]= \frac{4 \times 5}{7 \times 3}\\= \frac{20}{21}[/tex]

Therefore the quotient of [tex]\frac{4}{7} $ and $ \frac{3}{5}[/tex] is [tex]\frac{20}{21}[/tex]

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Answer:

Choices A, C, D, and E are the right choices.

Step-by-step explanation:

Area of the given figure = [tex]174 \:ft^2[/tex]

Option A = 174

Option B = 150

Option C = 174

Option D = 174

Option E = 174

Answer:

Step-by-step explanation:

Hello!

Tha claim is those female employees have less probability of being selected for management training than the males employees of a supermarket chain.

The company denies this claim and assures that the employees are picked at random from an eligible pool, i.e. that there is no gender bias in the manager selection

If you consider the variables:

X₁: Number of female employees selected for management training

X₂: Number of male employees selected for management training

The parameter of interest would be

p₁: population proportion of female employees selected for management training

p₂: population proportion of male employees selected for management training

If the company claims that there is no gender bias in the management selection is true, then the proportion of female employees selected for management training and the proportion of male employees selected for management training should be the same, symbolically: p₁ = p₂

If the company's claim is incorrect, then these proportions should be different: p₁ ≠ p₂

I hope this helps!

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 7463

For the alternative hypothesis,

µ ≠ 7463

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7463 hours

x = 7163 hours

σ = 1080 hours

n = 81

b) z = (7163 - 7463)/(1080/√81) = - 2.5

Looking at the normal distribution table, the probability corresponding to the z score is 0.02

Recall, population mean is 7463

The difference between sample sample mean and population mean is 7463 - 7163 = 300

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 7463 - 300 = 7163

the x value for the right tail is 7463 + 300 = 7763

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area below z as 0.02

We would double this area to include the area in the right tail of z = 2.5. Thus

p = 0.02 × 2 = 0.04

It means that in a sample of size 81 light bulbs, we would observe a sample mean of 300 hours or more away from 7463 about 4% of the time by chance alone.

c) Confidence interval is written in the form,

(Sample mean - margin of error, sample mean + margin of error)

The sample mean, x is the point estimate for the population mean.

Margin of error = z × σ/√n

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.025 = 0.975

The z score corresponding to the area on the z table is 1.96. Thus, z score for 95% confidence level is 1.96

Margin of error = 1.96 × 1080/√81

= 235.2

Confidence interval = 7163 ± 23.2

a) Since alpha, 0.05 > than the p value, 0.04, then we would reject the null hypothesis. Therefore, at a 5% level of significance, there is evidence that the mean life is different from 7463 hours

Comparing the results of a and c, it is true that the population mean life is not 7463 hours.