In an all boys school, the heights of the student body are normally distributed with a mean of 70 inches and a standard deviation of 5 inches. Using the empirical rule, what percentage of the boys are between 65 and 75 inches tall?

Answer:

16

Step-by-step explanation:

Number = x

(3/4 of x) - (1/2 of x) = 4

3x/4 - x/2 = 4

3x - 2x / 4 = 4

x/4 = 4

x = 16

Answer: D

A is correct because when you convert 40% into a decimal the results will be .40 or .4

B is correct because 2/5 as a percent is 40%. It's like having 5 questions on a quiz and you get 2 right and 3 wrong. That means your grade is 40%.

C is correct because 40/100 means the decimal will be .4. 40÷100 will equal .4 which means 40/100 is also 40%.

D is incorrect due to the fact when you convert it to a fraction it'll be 4/25. When converting it to a percent the result will be 16%.

The number 40% in not equivalent to 0.04.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

The number is,

⇒ 40%

Now,

Since, The number is,

⇒ 40%

Hence, It can be written as;

⇒ 40% = 40/100

           = 4/10

           = 2/5

           = 0.4

Thus, The number 40% in not equivalent to 0.04.

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Answer:

It's one infinite solutions

Step-by-step explanation:

Any number can be put in for x beings there is no set answer to the equation. if there was a set number like 3x+9+4x+x=40 for instance, there would be only one solution, but since there's not, it is infinite solutions.

The required measure of the complementary angles is 82.1° and 7.9°.

Given that,
The measure of two complementary angles is 7x + 17 and 3x - 20. To find the measures of the angles.​

The angle can be defined as the one line inclined over another line.

Here,
the sum of the two complementary angles is equal to 90°. Implying
7x + 17 + 3x - 20 = 90
10x -3 = 90
10x = 93
x = 93 / 10
x = 9.3

Now,
The measure of angles
7x + 17 = 7 * 9.3 + 17
           = 82.1°  
3x - 20 = 3 * 9.3 - 20
             = 7.9°

Thus, the required measure of the complementary angles is 82.1° and 7.9°.

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Answer:

51/4

Step-by-step explanation:

To begin with you have to understand what is the distribution of the random variable. If X represents the point where the bus breaks down. That is correct.  

X~ Uniform(0,100)

Then the probability mass function is given as follows.

[tex]f(x) = P(X=x) = 1/100 \,\,\,\, \text{if} \,\,\,\, 0 \leq x \leq 100\\f(x) = P(X=x) = 0 \,\,\,\, \text{otherwise}[/tex]

Now, imagine that the D represents the distance from the break down point to the nearest station. Think about this, the first service station is 20 meters away from city A, and the second station is located  70 meters away from city A then the mid point between 20 and 70  is (70+20)/2 = 45 then we can represent D as follows

[tex]D(x) =\left\{ \begin{array}{ll} x & \mbox{if } 0\leq x \leq 20 \\ x-20 & \mbox{if } 20\leq x < 45\\ 70-x & \mbox{if } 45 \leq x \leq 70\\ x-70 & \mbox{if } 70 \leq x \leq 100\\ \end{array}\right.[/tex]

Now, as we said before X represents the random variable where the bus breaks down, then we form a new random variable [tex]Y = D(X)[/tex], [tex]Y[/tex] is a random variable as well, remember that there is a theorem that says that

[tex]E[Y] = E[D(X)] = \int\limits_{-\infty}^{\infty} D(x) f(x) \,\, dx[/tex]

Where [tex]f(x)[/tex] is the probability mass function of X. Using the information of our problem

[tex]E[Y] = \int\limits_{-\infty}^{\infty} D(x)f(x) dx \\= \frac{1}{100} \bigg[ \int\limits_{0}^{20} x dx +\int\limits_{20}^{45} (x-20) dx +\int\limits_{45}^{70} (70-x) dx +\int\limits_{70}^{100} (x-70) dx \bigg]\\= \frac{51}{4} = 12.75[/tex]

Answer:

123 days

Step-by-step explanation:

The minimum duration for which an empty apartment remains to update the kitchen appliances is approximately 120 days.

To find the minimum duration for which an apartment remained empty for the company to update the kitchen appliances, we need to find the duration that corresponds to the top 10% of durations. Since we know the distribution is approximately normal with a mean of 85 days and a standard deviation of 29 days, we can use z-scores to find the corresponding duration.

First, we need to find the z-score corresponding to the top 10%. We can use the z-table or a calculator to find that the z-score is approximately 1.28.

Next, we can use the formula z = (x - mean) / standard deviation to solve for x, the minimum duration:

1.28 = (x - 85) / 29.

Solving for x, we get x ≈ 120.12. Rounding to the nearest whole number, the minimum duration for which the apartment remained empty is 120 days.

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Answer:

a) The null and alternative hypothesis are:

[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]

c) Test statistic t=1.53

P-value=0.064

d) The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that students who complete the core curriculum are ready for​ college-level mathematics.  That is that the true score for the group is not significantly higher than 23.

Step-by-step explanation:

The question is incomplete:

a) State the appropriate null and alternative hypotheses.

c) Use the P-value approach at the 0.05 level of significance to test the hypotheses in part (a). ldentify the test statistic. (Round to two decimal places as needed.) Identfy the P-value. P-value (Round to three decimal places as needed.)

d) Write a conclusion based on the results. Choose the correct answer below. ? the null hypothesis and claim that there ? sufficient evidence to conclude that the population mean is ? than 20.

This is a hypothesis test for the population mean.

The claim is that students who complete the core curriculum are ready for​ college-level mathematics.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=23\\\\H_a:\mu> 23[/tex]

The significance level is assumed to be 0.05.

The sample has a size n=150.

The sample mean is M=23.4.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=3.2.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{3.2}{\sqrt{150}}=0.261[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{23.4-23}{0.261}=\dfrac{0.4}{0.261}=1.531[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=150-1=149[/tex]

This test is a right-tailed test, with 149 degrees of freedom and t=1.531, so the P-value for this test is calculated as (using a t-table):

[tex]P-value=P(t>1.531)=0.064[/tex]

As the P-value (0.064) is bigger than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that students who complete the core curriculum are ready for​ college-level mathematics.

Answer:

We conclude that the sodium content is same as what the nutrition label states.

Step-by-step explanation:

We are given that the nutrition label for Oriental Spice Sauce states that one package of sauce has 1100 milligrams of sodium.

The FDA randomly selects 40 packages of Oriental Spice Sauce and determines the sodium content. The sample has an average of 1088.64 milligrams of sodium per package with a sample standard deviation of 234.12 milligrams.

Let [tex]\mu[/tex] = average sodium content.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 1100 milligrams      {means that the sodium content is same as what the nutrition label states}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 1100 milligrams      {means that the sodium content is different from what the nutrition label states}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

                    T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample average sodium content = 1088.64 milligrams

            s = sample standard deviation = 234.12 milligrams

            n = sample of packages of Oriental Spice Sauce = 40

So, test statistics  =  [tex]\frac{1088.64-1100}{\frac{234.12}{\sqrt{40}}}[/tex]  ~ [tex]t_3_9[/tex]

                              =  -0.307

The value of z test statistics is -0.307.

Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 0.05 significance level the t table gives critical values of -2.0225 and 2.0225 at 39 degree of freedom for two-tailed test.

Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the sodium content is same as what the nutrition label states.

To determine if the sodium content of the Oriental Spice Sauce is different from what the label states, a confidence interval approach can be used. A t-test is used to compare the sample mean to the hypothesized population mean. If the p-value is less than the level of significance, the null hypothesis is rejected.

To determine if the sodium content of the Oriental Spice Sauce is different from what the nutrition label states, we can use a confidence interval approach.

Step 1: Define the null and alternative hypotheses. Null hypothesis (H0): The sodium content is the same as what the nutrition label states. Alternative hypothesis (Ha): The sodium content is different from what the nutrition label states.

Step 2: Calculate the test statistic and p-value. We can use a t-test to compare the sample mean to the hypothesized population mean (the sodium content stated on the label).

Step 3: Determine the level of significance and compare the p-value to it. If the p-value is less than the level of significance, we reject the null hypothesis and conclude that there is evidence that the sodium content is different from what the nutrition label states.

Answer:

84

Step-by-step explanation:

Answer:

84

Step-by-step explanation:

588/7=84

Answer: The distance of  Observer A from the radio antenna is what fraction  of the distance of Observer B from the radio  antenna?​

It is 1/4.

Step-by-step explanation:

We know that the intensity of electromagnetic waves decreases with the radius squared, this means that we can write a simple relation as:

Intensity(r) = A/r^2

Observer A measures 16 the intensity of observer B.

if Ia is the intensity that observer A measures and Ib is the intensity that observer B measures, we have that:

Ia = 16Ib

A/(ra)^2 = 16*A/(rb)^2

1/(ra)^2 = 16/(rb)^2

rb^2 = 16*ra^2

and we know that 16 = 4*4 = 4^2

rb^2 = (4*ra)^2

then rb = 4*ra

this means that the distance between observer B and the antenna is equal to 4 times the distance between observer A and the antenna.

The fraction is ra = rb/4

The distance of

Observer A from the radio antenna is what fraction of the distance of Observer B from the radio antenna?​

It is 1/4.

Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. The distance of Observer A from the radio antenna is 4 times the distance of Observer B.

Observer A measures the intensity of the signal to be 16 times the intensity measured by Observer B. Let's denote the distance of Observer A from the radio antenna as dA and the distance of Observer B as dB.

We can use the inverse square law to relate the intensity to the distance: Intensity is inversely proportional to the square of the distance.

So, we have:

IntensityA/IntensityB = (dA/dB)^2 = 16

Solving for dA/dB, we find:

dA/dB = sqrt(16) = 4

Therefore, the distance of Observer A from the radio antenna is 4 times the distance of Observer B.

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Answer:

Null hypothesis: [tex]\mu \leq 300[/tex]

Alternative hypothesis: [tex]\mu >300[/tex]

When we talk about a type I of error we are refering to a“false positive” and is associated when we reject a null  hypothesis when it is actually true.

And for this special case would be reject the null hypothesis that the true mean is lower or equal than 300 [/tex]\mu\leq 300[/tex] but that in fact is true.

This type of error is associated to the significance level [tex]\alpha[/tex] assumed for the statistical test

Step-by-step explanation:

For this case we define the random variable X as the number of automobiles pass at a location per hour and we are tryng to proof this:

Null hypothesis: [tex]\mu \leq 300[/tex]

Alternative hypothesis: [tex]\mu >300[/tex]

When we talk about a type I of error we are refering to a“false positive” and is associated when we reject a null  hypothesis when it is actually true.

And for this special case would be reject the null hypothesis that the true mean is lower or equal than 300 [/tex]\mu\leq 300[/tex] but that in fact is true.

This type of error is associated to the significance level [tex]\alpha[/tex] assumed for the statistical test

Answer:

7/12 of a can

Step-by-step explanation:

Answer:

Well all the distributive property is is just splitting up a number so you can distribute it to other numbers so you could do 2x(3x82)

Step-by-step explanation:

Answer:8pennies,16dimes,13nickels,13quarters

Step-by-step explanation:

total number of coin=50

16% are pennies

16% of 50

16/100 x 50=(16x50)/100=800/100=8

Pennies=8

32% are dimes

32% of 50

32/100 x 50=(32x50)/100=1600/100=16

Dimes = 16

5 more nickels than pennies

Pennies=8

nickels=8+5=13

nickels=13

8+16+13=37

50-37=13

13 quarters

pennies=8,dimes=16,nickels=13,quarters=13

Answer:

Width = (x + 8) inches.

Step-by-step explanation:

The  area of the quilt is the length times the width and if we know the area and the length we can find the width by area / length.

Area = x^2 + 18x + 80 = (x + 10)(x + 8) - now we know that the length is (x + 10) so the width must be (x + 8) inches.

Let me know if you require more explanation.

Answer:

3

Step-by-step explanation:

Range is the difference between

Answer:

  1350 square inches

Step-by-step explanation:

The area of the end trapezoid is ...

  A = (1/2)(b1 +b2)h = (1/2)(12 +36)(5) = 120 . . . . . square inches

The perimeter of the end trapezoid is ...

  P = 13 +12 +13 + 3×12 = 74 . . . . inches

so the total area of the rectangular surfaces (including the bottom) is ...

  (74 in)(15 in) = 1110 in²

The total area of the ramp is this rectangular area plus the two trapezoidal ends:

  total area = rectangle area + 2×trapezoid area

  = 1110 in² +2×120 in²

  total area = 1350 square inches

Answer:

a) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]

b) [tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]

c) For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower

d)   [tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

Solving for n we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

And replacing the info we have:

[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]

Step-by-step explanation:

Part a

For this case we have the following data given

[tex]\bar X = 78.25[/tex] represent the sample mean for the customer order totals

[tex]\sigma =22.50[/tex] represent the population deviation

[tex] n= 40[/tex] represent the sample size selected

The confidence level is 90% or 0.90 and the significance level would be [tex]\alpha=0.1[/tex] and [tex]\alpha/2 = 0.05[/tex] and the critical value from the normal standard distirbution would be given by:

[tex] z_{\alpha/2}=1.64[/tex]

And the confidence interval is given by:

[tex] \bar X -z_{\alpha/2} \frac{\sigma}{\sqrt{n}}[/tex]

And replacing we got:

[tex] 78.25- 1.64 \frac{22.50}{\sqrt{40}}= 72.416[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{40}}= 84.084[/tex]

Part b

The sample size is now n = 75, but the same confidence so the new interval would be:

[tex] 78.25- 1.64 \frac{22.50}{\sqrt{75}}= 73.989[/tex]

[tex] 78.25+ 1.64 \frac{22.50}{\sqrt{75}}= 82.511[/tex]

Part c

For this case when we increase the sample size the margin of error would be lower and then the interval would be narrower

Part d

The margin of error is given by:

 [tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

Solving for n we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

And replacing the info we have:

[tex]n=(\frac{1.640(22.50)}{5})^2 =54.46 \approx 55[/tex]

Answer:

63x

Step-by-step explanation:

3(21x)

= (3· 21)x

= 63x

Answer:63x

Step-by-step explanation:

Answer:

2 units

Step-by-step explanation:

As the radius is half of the  diameter. To work this out you would simply multiply 1 by 2, which gives you 2.

1) Multiply 1 by 2.

[tex]1*2=2[/tex]

Answer:

1 . Total time = 1 hr 55 minutes

2 Distance = 121 km

Step-by-step explanation:

Mattew journey

stage a

Distance = 20km

Speed = 30km/h

Time = distance/speed

Time = 20/30

Time = 2/3 h

Time = 40 minutes

Stage b

Distance = 50 I'm

Speed = 100 km/h

Time = distance/speed

Time = 50/100

Time = 0.5 h

Time = 30 minutes

Stage c

Distance = 30 km

Speed = 40 km/h

Time = distance/speed

Time = 30/40

Time = 3/4 h

Time = 45 minutes.

Total time taken =( 40 + 30 + 45 ) minutes

Total time = 115 minutes

Total time = 1 hr 55 minutes

2.

Speed =60 km/h

Time= 6 minutes + x

And x = 1 hr 55 minutes

Time = 1 hr 55 minutes + 6 minutes

Time = 2 hr 1 minute

Time = 2.01666667 hr

Distance covered = speed * time

Distance = 60*2.016667

Distance = 121 km

In this exercise we have to use the knowledge of time and distance, so we have to:  

1) Total time = 1 hr 55 minutes

2) Distance = 121 km

To calculate Matthew's journey we have to use the formula of :

[tex]Time= \frac{Distance}{Speed}[/tex]

Are doing the calculations for each Stage, like this:

Stage A, we know that:

[tex]Time = 20/30\\T = 2/3 h\\Time = 40 \ minutes[/tex]

Stage B, we know that:  

[tex]Time = 50/100\\T = 0.5 h\\Time = 30\ min[/tex]

Stage C, we know that:  

[tex]Time = 30/40\\T= 3/4 h\\Time = 45\ min[/tex]

1) So using all the values ​​calculated above, let's calculate the total value of the trip that will take place by:

[tex]Total =( 40 + 30 + 45 ) minutes\\Total = 115 \ minutes\\Total = 1 \ hr \ 55 \ minutes[/tex]

2) For the second part of this question we want to calculate the total distance of travel hours so:  

[tex]x = 1 \ hr \ 55 minutes\\Time = 1 \ hr\ 55 \ minutes + 6 \ minutes = 2 \ hr \ 1 minute\\Time = 2.01666667\\Distance = speed * time\\Distance = 60*2.016667\\Distance = 121 km[/tex]

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Answer: 36

Step-by-step explanation:

explicit

Answer:

the answer is D

Step-by-step explanation:

i guessed until it gave me the answer yw

Answer:

D

Step-by-step explanation:

Answer:

See explaination

Step-by-step explanation:

B. The equality relation on the real numbers is an equivalence relation.

This statement is true

C. If RR is a reflexive relation on a set S, then any two RR- related elements of S must also be R2R2 related.

This statement is true

F. The less than or equal relation on the real numbers fails to be an equivalence relation because it is reflexive and transitive but not symmetric

This statement is true

H. If RR is an equivalence relation, then R2

This statement is true

Answer:

c) Two sample t-test

Step-by-step explanation:

Given data

Golfer                          1             2                  3               4

Brand1 (x)                  93          88                112            79

Brand 2 (y)               95          86                 111            77

Mean of x =

                  [tex]\frac{93+88+112+79}{4} = 93[/tex]

            x⁻ = 93

Mean of y

                [tex]\frac{95+86+111+77}{4} = 92.25[/tex]

            y ⁻ = 92.25

Given data

Brand1 (x)         :         93            88                112            79

Brand 2 (y)       :        95             86                111             77

x- x⁻                 :        0                -5                19              -14

y -y ⁻                 :        2.75         -6.25           18.75        -15.25

(x- x⁻)²              :         0                 25             361            196

( y -y ⁻  )²         :       7.5625      39.0625      351.5625    232.5625

S² =     [tex]\frac{sum((x- x^{-} )^{2} +sum (y- y^{-} )^{2} }{n_{1}+n_{2} -2 }[/tex]

[tex]S^{2} = \frac{582+630.75}{4+4-2} = 202.125[/tex]

S = 14.21706

Null hypothesis: H₀: There is no significant difference between the means

Alternative hypothesis: H₁: There is significant difference between the means

Student's t test for difference for means

The test statistic

[tex]t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }[/tex]

[tex]t = \frac{93 -92.25}{\sqrt{202.125(\frac{1}{4 } +\frac{1}{4 } } }[/tex]

on calculation , we get

t = 0.0746

Degrees of freedom ν = n₁ +n₂ -2 = 4+4-2 =6

[tex]t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.447[/tex]

The calculated value t = 0.0746 < 2.447 at 0.05 level of significance

null hypothesis is accepted

Conclusion:-

There is no significant difference between the means

Final answer:

The matched pairs t-test is the correct method for analyzing the difference in golfers' scores with two different brands of clubs, as each golfer serves as their control.

Explanation:

The appropriate test to determine if the mean scores differ by brand of club is b. matched pairs t-test. Since the data consists of scores from the same golfers using two different brands of clubs in a controlled setting (meaning, the same golfer's scores are paired with each type of golf club), the analysis compares two related samples. In matched pairs designs, we test the differences by subtracting one measurement from the other. The golfers serve as their controls, eliminating variations between different individuals' performances, which could affect the scores. This is a classic scenario of a paired sample t-test, where each golfer's scores with Brand 1 are paired with their scores with Brand 2, and the difference in scores is analyzed.

Answer:

The value of the test statistic is [tex]t = -1.44[/tex]

Step-by-step explanation:

The null hypothesis is:

[tex]H_{0} \geq 432[/tex]

The alternate hypotesis is:

[tex]H_{1} < 432[/tex]

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

In this problem, we have that:

[tex]X = 426, \mu = 432, \sigma = 26, n = 39[/tex]

So

[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]t = \frac{426 - 432}{\frac{26}{\sqrt{39}}}[/tex]

[tex]t = -1.44[/tex]

The value of the test statistic is [tex]t = -1.44[/tex]

Answer:

Step-by-step explanation:

They sold 201 small bags

and they sold 83 large bags

hope this helps :)

Answer:

l + s = 299

4l + s = $662

121 large bags were sold.

178 small bags were sold.

Step-by-step explanation:

Quantity equation: l + s = 299. l is the amount of large bags and s is the amount of small.

Price equation: 4l + s = $662. This means each large bag earns 4 dollars and each small bag earns 1.

To solve this, you use the method elimination and subtract (l + s = 299) from 4l + s = 662.

So, after subtracting, the equation you are left with is 3l = 363. Divide both sides by 3 and you get l = 121. 121 large bags were sold.

Plug in 121 for l in the first equation, now it says 121 + s = 299. Subtract 121 from 299 and get 178. 178 small bags were sold.

Answer:

5

Step-by-step explanation:

split 20 into 4 and find out how much is one portion the four

Plz mark brainliest

Answer:

n=9 10 11

Step-by-step explanation:

Answer: 10

Step-by-step explanation: