Which of the following is equivalent to 5/13^3

Given:

The given figure ABCD is a trapezoid.

The measure of ∠A is (2x + 32).

The measure of ∠B is 112°

The measure of ∠C is y.

The measure of ∠D is 46°

We need to determine the value of x and y.

Value of x:

We know the property that the adjacent angles in a trapezoid are supplementary.

Thus, we have;

[tex]\angle A+\angle B=180[/tex]

Substituting the values, we get;

[tex]2x+32+112=180[/tex]

       [tex]2x+144=180[/tex]

                 [tex]2x=36[/tex]

                   [tex]x=18[/tex]

Thus, the value of x is 18.

Value of y:

The value of y can be determined using the property that the adjacent angles of a trapezoid are supplementary.

Thus, we have;

[tex]\angle C+\angle D=180[/tex]

    [tex]y+46=180[/tex]

            [tex]y=134[/tex]

Thus, the value of y is 134.

Hence, Option c is the correct answer.

Answer:

6000000 mm squared

Step-by-step explanation:

We first convert the meters to millimeters. We got 4000 and 3000. The area of a triangle is base times height divided by 2. So we get 12000000 divided by 2 or 6000000 mm squared

Answer:

the dimensions xyz of a box with volume 10 cubic feet that has minimum cost is;

x = 1.68 ft

y = 1.68 ft

z = 3.54 ft

Step-by-step explanation:

See attachment for the full explanation.

Answer:

it would be a distance of 7 units

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

the absolute value of -5 - 2 = 7

Answer:

[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]  

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]

Since is a one side test the p value would be:

[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]

And the best option for this case would be:

None of the above (it should be t(38) = 5.07, p < .01)

Step-by-step explanation:

Data given and notation

[tex]\bar X_{1}=7[/tex] represent the mean for the sample 1

[tex]\bar X_{2}=10[/tex] represent the mean for the sample 2

[tex]s_{1}=\sqrt{2.5}= 1.581[/tex] represent the sample standard deviation for the sample 1

[tex]s_{2}=\sqrt{4.5}= 2.121[/tex] represent the sample standard deviation for the sample 2

[tex]n_{1}=20[/tex] sample size selected for 1

[tex]n_{2}=20[/tex] sample size selected for 2

[tex]\alpha[/tex] represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the group 1 is higher than the mean for group 2, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{2} \leq \mu_{1}[/tex]

Alternative hypothesis:[tex]\mu_{2} > \mu_{1}[/tex]

If we analyze the size for the samples both are less than 30 so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{2}-\bar X_{1}}{\sqrt{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}}[/tex] (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other".

Calculate the statistic

We can replace in formula (1) the info given like this:

[tex]t=\frac{10-7}{\sqrt{\frac{1.581^2}{20}+\frac{2.121^2}{20}}}}=5.07[/tex]  

P-value

The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{1}+n_{2}-2=20+20-2=38[/tex]

Since is a one side test the p value would be:

[tex]p_v =P(t_{(38)}>5.07)=5.33x10^{-6}[/tex]

And the best option for this case would be:

None of the above (it should be t(38) = 5.07, p < .01)

Answer:

See explanation

Step-by-step explanation:

Solution:-

The random variable, Y be the temperature of chemical reaction in degree fahrenheit be a linear expression of a random variable X : The  temperature in at which a certain chemical reaction takes place.

                             Y = 1.8*X + 32

- The median of the random variate "X" is given to be equal to "η". We can mathematically express it as:

                             P ( X ≤ η ) = 0.5

- Then the median of "Y" distribution can be expressed with the help of the relation given:

                             P ( Y ≤ 1.8*η + 32 )

- The left hand side of the inequality can be replaced by the linear relation:

                             P ( 1.8*X + 32 ≤ 1.8*η + 32 )

                             P ( 1.8*X ≤ 1.8*η )   ..... Cancel "1.8" on both sides.

                            P ( X ≤ η ) = 0.5 ...... Proven

Hence,

- Through conjecture we proved that: (1.8*η + 32) has to be the median of distribution "Y".

b)

- Recall that the definition of proportion (p) of distribution that lie within the 90th percentile. It can be mathematically expressed as the probability of random variate "X" at 90th percentile :

                             P ( X ≤ p_.9 ) = 0.9 ..... 90th percentile

- Now use the conjecture given as a linear expression random variate "Y",

          P ( Y ≤ 1.8*p_0.9 + 32 ) = P ( 1.8*X + 32 ≤ 1.8*p_0.9 + 32 )

                                                 = P ( 1.8*X ≤ 1.8*p_0.9 )

                                                 = P ( X  ≤ p_0.9 )

                                                 = 0.9

- So from conjecture we saw that the 90th percentile of "X" distribution is also the 90th percentile of "Y" distribution.

c)

- The more general relation between two random variate "Y" and "X" is given:

                            Y = aX + b

Where, a : is either a positive or negative constant.

- Denote, (np) as the 100th percentile of the X distribution, so the corresponding 100th percentile of the Y distribution would be : (a*np + b).

- When a is positive,

                   P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )

                                                 = P ( a*X ≤ a*p_% )

                                                 = P ( X  ≤ p_% )

                                                 = np_%        

- When a is negative,

                   P ( Y ≤ a*p_% + b ) = P ( a*X + b ≤ a*p_% + b )

                                                 = P ( a*X ≤ a*p_% )

                                                 = P ( X  ≥ p_% )

                                                 = 1 - np_%        

In a temperature conversion equation Y = 1.8X + 32, medians and percentiles of Y are related to the corresponding values of X through the equation itself. For an arbitrary linear transformation Y = aX + b, percentiles of Y and X are related as aX + b, with ordering depending on the sign of a.

Lets start by talking about the relationship between X and Y. In the context of the temperature conversion between Celsius (X) and Fahrenheit (Y), Y equals to 1.8 times X plus 32.

1. If the median of X is M, substituting M into the equation Y = 1.8X + 32 gives the median of Y as 1.8M + 32, since the transformation is linear.

2. The 90th percentile of the Y distribution will relate to the 90th percentile of X distribution in a similar fashion. If we denote the 90th percentile of X as P, then the 90th percentile of Y will be 1.8P + 32.

3. For a general linear transformation Y = aX + b, where a is non-zero, any percentile of Y is related to the corresponding percentile of X as aX + b. If a is positive, the transformation will preserve the ordering of percentiles (e.g., higher values of X correspond to higher values of Y). If a is negative, it will reverse the ordering of percentiles (e.g., higher values of X will correspond to lower values of Y).

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Answer:

A: (m + p, n + r)

Step-by-step explanation:

[tex]Midpoint \: of \: AC \\ = \bigg( \frac{2m + 2p}{2} \: \: \frac{2n + 2r}{2} \bigg) \\ \\ = \bigg( m + p, \: \: n + r \bigg)[/tex]

Answer:

a.  [tex]\int\limits^5_0 {f(x)} \, dx[/tex]

Step-by-step explanation:

Since f(x) is the function for the populational density at a certain sidewalk for a 5 mile stretch, a definite integral of that function will yield the total number of people within the integration intervals. If we are interested in the number of people in the whole 5 mile stretch, we must integrate f(x) from x = 0 miles to x = 5 miles:

[tex]\int\limits^5_0 {f(x)} \, dx[/tex]

Therefore, the answer is alternative a.

Answer:

160 plus 35 = 185

Step-by-step explanation:

8×20

hopefully this helps you

Answer:

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Step-by-step explanation:

Problems of normally distributed samples are solved using 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.

In this problem, we have that:

[tex]\mu = 6492, \sigma = 1025[/tex]

He decides to sell boats that will appeal to the middle 66% of the market in terms of price.

50 - (66/2)  = 17th percentile

50 + (66/2) = 83rd percentile

17th percentile

X when Z has a pvalue of 0.17. So X when Z = -0.955.

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

[tex]-0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = -0.955*1025[/tex]

[tex]X = 5513[/tex]

83rd percentile

X when Z has a pvalue of 0.83. So X when Z = 0.955.

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

[tex]0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = 0.955*1025[/tex]

[tex]X = 7471[/tex]

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

The marine sales dealer plans to sell boats between $5467 and $7517 to appeal to the middle 66% of market prices. These figures are computed by adding or subtracting one standard deviation from the average price.

In this scenario, the marine sales dealer wants to price boats that appeal to the middle 66% of the market, which means the dealer wants to avoid the top and bottom 17% of the market (as 100%-66%=34% and 34%/2=17%). Therefore, we need to find the boats' prices that are 1 standard deviation away from the mean, since in a normal distribution, approximately 68% of values lie within 1 standard deviation from the mean (closest to 66%).

The standard deviation given is $1025. Thus, the maximum price of the boats the dealer will sell is the mean price plus one standard deviation:

$6492 + $1025 = $7517

And the minimum price is the mean price minus one standard deviation:

$6492 - $1025 = $5467

Therefore, the dealer will sell boats priced between $5467 and $7517 to appeal to the middle 66% of the market.

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Answer:

The probability that he makes one of the two free throws is 0.38

Step-by-step explanation:

Hello!

Considering the situation:

A pro basketball player shoots two free throws.

The following events are determined:

A: "He makes the first free throw"

Ac: "He doesn't make the first free throw"

B: "He makes the second free throw"

Bc: "He doesn't make the second free throw"

It is known that

P(A)= 0.48

P(B/A)= 0.62

P(B/Ac)= 0.38

You need to calculate the probability that he makes one of the two free throws.

There are two possibilities, that "he makes the first throw but fails the second" or that "he fails the first throw and makes the second"

Symbolically:

P(A∩Bc) + P(Ac∩B)

Step 1.

P(A)= 0.48

P(Ac)= 1 - P(A)= 1 - 0.48= 0.52

P(Ac∩B) = P(Ac) * P(B/Ac)= 0.52*0.38= 0.1976≅ 0.20

Step 2.

P(A∩B)= P(A)*P(B/A)= 0.48*0.62= 0.2976≅ 0.30

P(A)= P(A∩B) + P(A∩Bc)

P(A∩Bc)= P(A) - P(A∩B)= 0.48 - 0.30= 0.18

Step 3

P(Ac∩B) + P(A∩Bc) = 0.20 + 0.18= 0.38

I hope this helps!

The probability that the player makes one of the two free throws using the multiplicative rule is 0.4952 or 49.52%.

To find the probability that the player makes one of the two free throws using the multiplicative rule, we need to consider the two possible ways he can do this:

We can calculate the probability for each case and sum them up to find the total probability:

p(make 1st and miss 2nd) = (0.48) * (0.62) = 0.2976

p(miss 1st and make 2nd) = (0.52) * (0.38) = 0.1976

Total probability = p(make 1st and miss 2nd) + p(miss 1st and make 2nd) = 0.2976 + 0.1976 = 0.4952

Therefore, the probability that the player makes one of the two free throws is 0.4952, or 49.52%.

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Answer: j=-5 as long as you follow my steps you will also be able to show your work.

Combine multiplied terms into a single fraction

Distribute it then

Multiply all terms by the same value to eliminate fraction denominators.

Answer:

4

Step-by-step explanation:

use the order of operations- (parentheses, exponets, multiply, divide, add, subtract...)

54-200/4

-200/4=-50

54-50=4

Answer:

The calculated p-value is greater than the significance level at which the test was performed, hence, we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

Step-by-step explanation:

For hypothesis testing, we first clearly state our null and alternative hypothesis.

For hypothesis testing, the first thing to define is the null and alternative hypothesis.

In hypothesis testing, especially one comparing two sets of data, the null hypothesis plays the devil's advocate and usually takes the form of the opposite of the theory to be tested. It usually contains the signs =, ≤ and ≥ depending on the direction of the test.

The alternative hypothesis usually confirms the theory being tested by the experimental setup. It usually contains the signs ≠, < and > depending on the direction of the test.

For this question, we are to investigate that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

The null hypothesis would be that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate. That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

The alternative hypothesis is that there is significant evidence to suggest that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

This is evidently a one tail hypothesis test (we're investigating only in one direction; less than the claim

Mathematically, the null hypothesis is

H₀: μ ≥ 15

The alternative hypothesis is

Hₐ: μ < 15 minutes

To do this test, we will use the z-distribution because the population standard deviation is known.

So, we compute the z-test statistic

z = (x - μ₀)/σₓ

x = sample mean = 13 minutes

μ₀ = the advocate's claim = 15 minutes

σₓ = standard error of the poll proportion = (σ/√n)

where n = Sample size = 50

σ = population standard deviation = 11 minutes.

σₓ = (σ/√n) = (11/√50) = 1.556

z = (13 - 15) ÷ 1.556 = -1.29

checking the tables for the p-value of this z-statistic

p-value (for z = -1.29, at 0.05 significance level, with a one tailed condition) = 0.098525

The interpretation of p-values is that

When the (p-value > significance level), we fail to reject the null hypothesis and when the (p-value < significance level), we reject the null hypothesis and accept the alternative hypothesis.

So, for this question, significance level = 5% = 0.05

p-value = 0.098525

0.098525 > 0.05

Hence,

p-value > significance level

This means that we fail to reject the null hypothesis & conclude that there is no significant evidence to say that the actual mean waiting time turned out to be significantly less than the 15-minute claim made by the taxpayer advocate.

That is, the true mean waiting time is equal to or greater than the 15-minute claim by the taxpayer advocate.

Hope this Helps!!!

Daniel appears to be paying more for auto insurance compared to the average amount his friends pay based on the data from nine friends. However, as the data only represents a sample, and auto insurance rates can vary widely, additional comparison or the advice of an insurance specialist is recommended.

To determine if Daniel is overpaying for his auto insurance, we can compare his insurance cost to the average price paid by his friends. To do this, we need to calculate the mean (average) of his friends' insurance amounts.

Here are the amounts his friends pay: 564, 578, 478, 507, 621, 564, 489, 612, 538.

Adding these together gets a total of 4951. There are nine friends, so we divide 4951 by 9 to get an average cost of 550.

Since Daniel is paying $600, which is more than the average of $550, it seems he's spending more than his friends for auto insurance.

However, we only have the data from a sample of his friends. The insurance amounts can have a wide range, depending on several factors like age, driving records, the type of vehicle insured, and geographic location. Therefore, it's recommended that Daniel compare his rate with more people or consult with an insurance specialist for a more accurate conclusion.

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The question revolves around calculating queueing system performance measures for a software company's call center and adjusting the service rate to maintain consistent service levels during an operational change. Calculations would apply queue theory but specifics require further details about the model type, such as M/M/1 or M/M/2. Algebraic methods would be needed to adjust the service rate to keep waiting times consistent.

The question deals with determining key performance measures (L, Lq, W, Wq) for a queueing system at People's Software Company call center, under two different operational scenarios, and solving for the service rate (μ) that equates waiting times between these scenarios. The system initially with two representatives and an arrival rate of 10 calls per hour, transitioning to one representative and a decreased arrival rate of 5 calls per hour, is examined assuming exponential service times with a mean of 5 minutes.

For the current system with two technical representatives and ten calls arriving per hour, assuming the call arrival rate follows a Poisson process and service times are exponentially distributed, key performance measures could be calculated utilizing formulas from queueing theory. However, these formulas depend highly on the specifics of the queueing model used, such as M/M/1, M/M/2, etc., and are not directly provided here.

For next year's system with a reduction in technical representatives and a halved arrival rate, similar analytical methods could be applied to predict performance based on the adjusted arrival rate and the assumption of unchanged service time distributions.

Regarding the adjustment of μ to maintain the same waiting time (W), algebraic solutions involving the exponential service time distribution and Poisson arrival processes must be derived, factoring in the reduction of workers and the change in arrival rate, to find the new service rate (μ) that would ensure continuity in service level expectations.

Answer:

68/99

Step-by-step explanation:

.68686868686 repeating

Let x= .68686868668repeating

Multiply by 100

100x = 68.686868686repeating

Subtract x = .68686868repeating from this equation

100x = 68.686868686repeating

-x = .68686868repeating

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

99x = 68

Divide each side by 99

99x / 99 = 68/99

x = 68/99

Answer:

68/99 I agree with the other person

Step-by-step explanation:

Answer: -3 1/4 or -13/4

Step-by-step explanation:

Answer:

[tex]\frac{-7}{4}[/tex]

Step-by-step explanation:

-3*3/4-1/2

-9/4+1/2

-9/4+2/4

(-9+2)/4

-7/4

Answer:

$6,376.92

Step-by-step explanation:

-Let d be the rate of depreciation per year.

-Therefore, the value after n years can be expressed as:

[tex]A=P(1-d)^n\\\\A=Value \ after \ n \ years\\P=Initial \ Value\\d=Rate \ of \ depreciation\\n=Time \ in \ years[/tex]

#We substitute for the years 2009-2013 to solve for d:

[tex]A=P(1-d)^n\\\\19000=41000(1-d)^4\\\\0.475=(1-d)^4\\\\d=1-0.475^{0.25}\\\\d=0.1698[/tex]

#We then use the calculated depreciation rate above to solve for A after 10 yrs:

[tex]A=P(1-d)^n\\\\=41000(1-0.1698)^{10}\\\\=\$6,376.92[/tex]

Hence, the value of the car after 10 yrs is $6,376.92

To find the future value of a car in 2019, we calculate the percentage decrease in value from 2009 to 2013 and apply it for 6 years.

To find the future value of the car in 2019, we need to determine the percentage decrease in value each year. From 2009 to 2013, the car depreciated from $41,000 to $19,000.

This is a decrease of $22,000. To find the percentage decrease, divide this by the initial value: 22,000 / 41,000 = 0.5366 (approximately).

To find the future value in 2019, we need to apply this percentage decrease continuously for 6 years. Multiply the current value by the percentage decrease repeatedly.

= 19,000 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366 * 0.5366

= $5,862.54 (approximately).

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Answer:

4

Step-by-step explanation:

4 data points are between 13 and 18 they are 13, 14, 15, and 18.

Answer:

4

Step-by-step explanation:

i took test

Answer: 12

Step-by-step explanation: To find the radius you have to do the opposite of 2r(pi). So you divide 75 by 2 and then by 3.14, getting 11.9, which rounds to 12

Answer:

1)  12in

Step-by-step explanation:

The circumference is 75, so to find the diameter you have to divide 75 by 3.14. You get 24 approximately. Then divide the diameter by 2, so 24/2=12.

Answer:

y = 18x

72 cupcakes = 18 cups of flour

Step-by-step explanation:

y= cupcakes

x=flour

4/1

72/18

18x4=72

Answer:

72 cupcakes

Step-by-step explanation:

Take 4 and multiply it by 18! Simple! :)

Step-by-step explanation:

[tex]2 {y}^{2} (35 - 4y) \\ = 2 {y}^{2} \times 35 - 2 {y}^{2} \times 4y \\ = 70 {y}^{2} - 8 {y}^{3} \\ = \red { \bold{ - 8 {y}^{3} + 70 {y}^{2} }} \\ is \: in \: the \: standard \: form.[/tex]

Answer:

8.2*10^-3

Step-by-step explanation:

Answer:

0.0082

(scientific notation)-step explanation:

Answer:

No.

Step-by-step explanation:

This is not a perfect square because the exponent would need to be even, not odd. The 100 is a perfect square. If you were to simplify it, it would be (10x^2) * (10x). In order for it to be truly a perfect square, they both need to be the same.

Answer:

a) The large sample size 'n' = 1320.59

b) If the standard deviation and the margin of error are both doubled also the sample size is not changed.

Step-by-step explanation:

Explanation:-

a)

Given data the standard deviation of the population

σ = 70.5

Given the margin error = 5 units

We know that the estimate of the population mean is defined by

that is margin error = [tex]\frac{z_{\alpha } S.D }{\sqrt{n} }[/tex]

            [tex]M.E = \frac{z_{\alpha } S.D }{\sqrt{n} }[/tex]

cross multiplication , we get

[tex]M.E (\sqrt{n} ) = z_{\alpha } S.D[/tex]

[tex]\sqrt{n} = \frac{z_{\alpha } S.D }{M.E }[/tex]

[tex]\sqrt{n} = \frac{2.578 X 70.5}{5} }[/tex]

√n = 36.34

squaring on both sides , we get

n = 1320.59

b) The margin error of the mean

   [tex]\sqrt{n} = \frac{z_{\alpha } S.D }{M.E }[/tex]

the standard deviation and the margin of error are both doubled

  √n = zₓ2σ/2M.E

  √n = 36.34

squaring on both sides , we get

     n = 1320.59

If the standard deviation and the margin of error are both doubled also the sample size is not changed.

Answer:

1.  3/4 + 3/4 + 3/4 +3/4

2. 0.75 * 4

Step-by-step explanation:

1. add 3/4 four times

3/4 + 3/4 + 3/4 +3/4

2. You can turn 3/4 into a decimal.  3/4 =0.75

0.75 * 4

Final answer:

3/4 × 4 can be solved through repeated addition by adding 3/4 to itself four times to get 9/4 or 2 1/4. Alternatively, by simplifying before multiplying, recognizing that 4 is the reciprocal of 1/4, we easily find that the product is 3.

Explanation:

When solving 3/4 × 4 using repeated addition, we use the concept that multiplying a number by a whole number is the same as adding that number to itself that many times. In this case, 3/4 is added to itself 4 times:

We have four 3/4's, and when we add them up, we get:

When we add 3/2 (1 1/2) and 3/4, we can convert 1 1/2 into 6/4 to make it easier to add the fractions, obtaining:

Therefore, 3/4 × 4 equals 9/4 or 2 1/4 through repeated addition.

Another way to approach the problem is by simplifying before multiplying. Since we are multiplying by 4, which is the reciprocal of 1/4, we can simplify by understanding that:

Thus, by canceling out the common factors (4 in the numerator and 4 in the denominator), the multiplication becomes 3 × 1, which equals 3. This satisfies the condition that as long as we perform the same operation on both sides of the equals sign, the expression remains an equality.

Answer:

0.8 gallons

Step-by-step explanation:

4 gallons of juice divided into 5 pitchers equally, 4/5=0.8 per pitcher.

Answer:

Im not 100% sure but i think its first row second

Answer: all the triangle are similar

Step-by-step explanation: ;)