A dietitian wants to know the average time spent on breakfast in a primary school. The dietitian randomly samples 16 students and finds that the average is 15.8 minutes with a standard deviation of 2.31 minutes. Assume that the distribution of the time spent on the breakfast is normally distributed. The dietitian finds a 90% confidence interval for this sample is (14.788, 16.812) Flag question Select one or more:_________. a. The margin of error is 1.012. b. The margin of error is 2.024 c. The margin of error is 0.950 d. We believe that the true mean time spent on breakfast in this primary school is between 14.788 and 16.812 minutes. e. If we take many other samples from this population, 90% of them will have a sample mean that is between 14.788 and 16.812. f. There is a 90% chance that the true mean is between 14.788 and 16.812 minutes.

Answer:

(0, -1)

Step-by-step explanation:

((4 + (-4))/2, (2 + (-4))/2) =

(0/2, -2/2) =

(0, -1)

The probability of not spinning a 5 and flipping heads in a coin toss, assuming a spinner with 10 numbers and a fair coin, is 0.45 or 45%. This is calculated by multiplying the individual probabilities of each independent event.

The question asked is related to the concept of probability, which refers to the likelihood of an event occurring. Specifically, it involves two independent events: spinning a number (other than 5) on a spinner, and flipping a coin to get heads. In this case, the two events do not affect the outcomes of each other.

Let's assume the spinner has 10 numbers (1 to 10) and the coin is fair (meaning the probabilities of getting heads and tails are equal). The probability of not getting a 5 on the spinner is 9/10 (because 9 out of the 10 possible outcomes meet this criterion), and the probability of getting heads on a coin flip is 1/2 (because 1 out of the 2 possible outcomes meets this criterion)

Since these are independent events, we can use the rule of product in probability to calculate the combined probability by multiplying the individual probabilities: (9/10) * (1/2) = 9/20, or 0.45. So, the probability of both not spinning a 5 and flipping heads is 0.45, or 45%.

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The student's question involves calculating the combined probability of independent events in a high school Mathematics context. It also touches on the law of large numbers, which predicts the long-term outcomes of random events. Additionally, the principles of entropy and orderliness in potential outcomes are discussed.

The question at hand deals with the concept of probability, specifically the likelihood of spinning a number other than 5 on a device, such as a spinner or die, and flipping a coin to get heads. When we assess the chance of getting either of these outcomes, if we presume each event to be independent, the combined probability is the product of their individual probabilities.

The statistical underpinning of this concept lies in the law of large numbers, which articulates that as the number of trials in a probability experiment increases, the observed or empirical frequency approaches the theoretical probability. This law reinforces why the outcomes of coin tosses and die rolls often do not match expected results exactly in small sample sizes but do over many repetitions.

Furthermore, when analyzing the microstate probabilities of coin tosses, we assume each result has an equal likelihood of occurring, which allows us to predict the macrostate frequencies. When tossing coins, we consider symmetrical outcomes such as 5 heads or 5 tails to be orderly and less likely than the more disorderly and common 3 heads with 2 tails.

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Answer:

slope = -3

Step-by-step explanation:

1) Rearrange eqn into slope intercept form

slope intercept form: y = mx + b

where...

m = the slope

b = the y-intercept (where the line crosses the y axis)

3x + y = 12

y = -3x+12

2) Know parallel rule. A line that runs parallel has the same slope but a different y-intercept

So the slope is: -3

Answer:

(a) The standard error of the mean in this experiment is $0.052.

(b) The probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c) The probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d) The likelihood that the sample mean is greater than $3.92 is 0.9726.

Step-by-step explanation:

According to the Central Limit Theorem if we have an unknown population with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from the population with replacement, then the distribution of the sample means will be approximately normally distributed.

Then, the mean of the distribution of sample mean is given by,

[tex]\mu_{\bar x}=\mu[/tex]

And the standard deviation of the distribution of sample mean is given by,

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

The information provided is:

[tex]n=40\\\mu=\$3.82\\\sigma=\$0.33[/tex]

As n = 40 > 30, the distribution of sample mean is [tex]\bar X\sim N(3.82,\ 0.052^{2})[/tex].

(a)

The standard error is the standard deviation of the sampling distribution of sample mean.

Compute the standard deviation of the sampling distribution of sample mean as follows:

[tex]\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}[/tex]

    [tex]=\frac{0.33}{\sqrt{40}}\\\\=0.052178\\\\\approx 0.052[/tex]

Thus, the standard error of the mean in this experiment is $0.052.

(b)

Compute the probability that the sample mean is between $3.78 and $3.86 as follows:

[tex]P(3.78<\bar X<3.86)=P(\frac{3.78-3.82}{0.052}<\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.86-3.82}{0.052})[/tex]

                               [tex]=P(-0.77<Z<0.77)\\=0.77935-0.22065\\=0.5587[/tex]

Thus, the probability that the sample mean is between $3.78 and $3.86 is 0.5587.

(c)

If the difference between the sample mean and the population mean is less than $0.01 then:

[tex]\bar X-\mu_{\bar x}<0.01\\\\\bar X-3.82<0.01\\\\\bar X<\$3.83[/tex]

Compute the value of [tex]P(\bar X<3.83)[/tex] as follows:

[tex]P(\bar X<3.83)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}<\frac{3.83-3.82}{0.052})[/tex]

                    [tex]=P(Z<0.19)\\=0.57535\\\approx 0.5754[/tex]

Thus, the probability that the difference between the sample mean and the population mean is less than $0.01 is 0.5754.

(d)

Compute the probability that the sample mean is greater than $3.92 as follows:

[tex]P(\bar X>3.92)=P(\frac{\bar X-\mu_{\bar x}}{\sigma_{\bar x}}>\frac{3.92-3.82}{0.052})[/tex]

                    [tex]=P(Z<1.92)\\=0.97257\\\approx 0.9726[/tex]

Thus, the likelihood that the sample mean is greater than $3.92 is 0.9726.

The standard error is 0.0522. The probability of the sample mean lying in a certain range and the difference from the population mean being less than a certain value can be determined using Z-scores and a Z-table. The likelihood of the sample mean being more than a certain value can also be determined in the same way.

An economist is using the average price of a gallon of milk to measure inflation. The average price ($3.82) and the population standard deviation ($0.33) is known. Here are answers to your questions:

a. Standard Error of the mean: The Standard error (SE) is calculated by dividing the standard deviation by the square root of the sample size. So SE = Standard Deviation / √n = 0.33 / √40 = 0.0522 per gallon.

b. Probability of the sample mean between $3.78 and $3.86: This is a Z-score question. Z = (X- µ)/SE. So, first find the Z-scores for $3.78 and $3.86, and then find the probability corresponding to these Z-scores from the Z-table. This probability is the chance that the sample mean is between $3.78 and $3.86.

c. Probability of the difference: Similarly, find the Z-score for the difference of $0.01 and look up the probability in the Z-table. This gives the likelihood of the sample mean being less than $0.01 away from the population mean.

d. Likelihood the sample mean is greater than $3.92: Use the same method to work out the Z-score for $3.92. The Z-table gives you the probability of the sample mean being less than $3.92, so subtract that from 1 to get the probability of it being more than $3.92.

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Answer:

1 2/4

Step-by-step explanation: 2/4 * 3 = 1 2/4

Answer:

It would be answer 3

Step-by-step explanation:

Because it is one in the actual maximum height

Answer:

Each value of time is associated with exactly one height.

Step-by-step explanation:

Answer:

0 is an inflection point

1/4 is a local maximum.

Step-by-step explanation:

To begin with you find the first derivative of the function and get that

[tex]h'(x) = 3x^2 - 12x^3[/tex]

to find the critical points you equal the first derivative to 0  and get that

[tex]3x^2 - 12x^3 = 0, x = 0,1/4[/tex]

To find if they are maximums or local minimums you use the second derivative.

[tex]h''(x) = 6x-36x^2[/tex]

since [tex]h''(0) = 0[/tex] is neither an inflection point, and since [tex]h''(1/4) = -3/4 <0[/tex] then 1/4 is a maximum.

Answer:

0.20 or 20%

Step-by-step explanation:

Brown shoes = 3

Black shoes = 2

Total shoes = 5

Brown pants = 1

Black shoes = 3

Total pants = 4

Brown socks =4

Black socks = 6

Red socks = 2

Total socks = 12

In order to choose shoes, pants and socks of the same color, Teddy can go either all black or all brown. For all black, there is a 2 in 5 chance he gets the right shoes, 3 in 4 chance for pants and 6 in 12 for socks. For all brown, there is a 3 in 5 chance he gets the right shoes, 1 in 4 chance for pants and 4 in 12 for socks.

[tex]P=P(All\ black)+P(All\ brown)\\P=\frac{2}{5}*\frac{3}{4}*\frac{6}{12}+ \frac{3}{5}*\frac{1}{4}*\frac{4}{12}\\P=0.20[/tex]

The probability that he chooses shoes, pants, and socks of the same color is 0.20 or 20%.

The exact value of cot(3π/4) is 1.

Cotangent (cot) is defined as the ratio of the adjacent side to the opposite side of a right triangle. In the case of 3π/4, which is a 45-degree angle in the third quadrant, we can use the reference angle of π/4 (45 degrees in the first quadrant) to find the corresponding values.

In the first quadrant, the tangent of π/4 is 1, meaning the opposite side is equal to the adjacent side. In the third quadrant the values are negated, so the opposite side becomes -1, and the adjacent side becomes -1.

Therefore, cot(3π/4) can be calculated as the ratio of the adjacent side (-1) to the opposite side (-1), resulting in:

cot(3π/4) = -1/-1 = 1.

So, the exact value of cot(3π/4) is 1.

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Answer:

Yes we need to convert measurements to same unit to determine whether she purchased the right amount of ribbon or not.

Mimi purchased 5 yards of ribbon which is less than what she needed that is 5.5 yards

Step-by-step explanation:

Yes we need to convert measurements to same unit to determine whether she purchased the right amount of ribbon or not.

We cannot compare two different units therefore, we are always required to convert all the measurements into a single unit for the sake of comparison.  

Mimi needs eleven pieces of rhinestone ribbon.

Each piece is 18-inch long.

So the total amount of ribbon that she need is

Total amount needed = 11*18

Total amount needed = 198 inches

Convert the amount of ribbon from inches to yards

1 yard is equal to 36 inches

Total amount needed = 198/36

Total amount needed = 5.5 yards

But Mimi purchased 5 yards of ribbon which is less than what she needed that is 5.5 yards.

Buying options:

$6 per yard

$55 for whole spool

Since Mimi needs 5.5 yards or round it to nearest whole because ribbon is sold in per yard basis so 6 yards of ribbon will cost

Cost = $6*6 = $36

$36 are less than $55 therefore, it is better to buy on per yard basis rather than the whole spool of ribbon.

Answer:

4(x-3)(x+6)

Step-by-step explanation:

Factor out the 4

4(x2 + 3x - 18)

what 2 numbers add to 3 and multiply to - 18?

-3 and 6

therefore 4x2 + 12x − 72 = 4(x-3)(x+6)

Answer:

(4x² + 24x)- (12x + 72)

4x( x+ 6)- 12(x + 6)

ans = (4x - 12)(x + 6)

Answer: the probability is 0.25

Step-by-step explanation:

We have 10 numbers:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Of those, the odd ones are:

1, 3, 5, 7, 9

So we have 5 odd numbers.

The probability that the outcome is an odd number is equal to the number of odd numbers divided the total number of numbers:

p = 5/10 = 0.5

For the second spin the probability is the same, p = 5/10, because the first outcome does not affect the results of the second spin.

The probability of spining an odd number both times, then is the joint probability for two times this same event:

P = (5/10)(5/10) = 0.5*0.5 = 0.25

or 25% in percent form

Answer:

foot = 12 inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

The diagram is shown in the image attached.

A tangent is a line that intercepts at one unique point. When we have a tangent about a circle, an important results is that the tangent is perpendicular to the radius, because a radius can be seen as perpendicular to any point of the circle.

That means, the triangle formed ADC is a right triangle, because [tex]\angle D= 90\°[/tex].

Now, we know that [tex]CD=23[/tex] and [tex]CA=28[/tex], which are leg and hypothenuse, respectively.

So, to find [tex]m \angle C[/tex] we just need to use trigonometric reasons, specifically, the cosine funtion, because it relates the adjacent leg and the hypothenuse.

[tex]cos(C)=\frac{CD}{CA}=\frac{23}{28} \\C=cos^{-1}(\frac{23}{28} ) \approx 35 \°[/tex]

Therefore, the measure of angle C is 35°, approximately.

The question seems to seek the measure of angle mZC using properties of tangents and circles, but the provided references don't offer a clear method to find it with the given data. Therefore, it is not possible to calculate the angle without additional information or a specific figure.

Given the information in the question, we are asked to find the measure of angle m√C in a circle where segment CD is tangent to the circle at point D, CD = 23, and CA = 28. The problem seems to be related to the properties of tangents and circles, specifically the tangent-secant theorem which states that if a tangent and a secant (or diameter) intersect at the point of tangency, the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external part (in this case, CD and DA).

However, the extracted references do not provide a clear or direct method for calculating the measure of angle m√C. The references are disjointed and relate to various other unrelated geometrical and physical contexts, like vector differences, spherical triangles, and integral segments.

Without a specific figure or more context, it is not possible to accurately determine the measure of angle m√C based solely on the information provided.

Answer:

The median number of miles that Sam drove during those months is 1044 miles

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

For a set of n values

First we order the values in an increasing way.

If n is odd, the median is the value at the position (n+1)/2

If n is even, the median is the average of the values at the positions n/2 and (n/2) + 1

In this problem:

6 values

Ordered in an increasing way:

880, 997, 1002, 1086, 1534, 1637

6 is an even value.

6/2 = 3. The third element is 1002

6/2 + 1 = 4. The fourth element is 1086.

Average: (1002 + 1086)/2 = 1044

The median number of miles that Sam drove during those months is 1044 miles

Answer:

Step-by-step explanation:

The given question is

A futsal team scored 60 goals, corresponding to four-sixths of the league's total goals. How many goals were scored in the league?

If 60 goals represents four-sixths of the total goals, then how many goals were scored?

Here we need to use the rule of three, where the given equivalence is

[tex]60 \ goals = \frac{4}{6}[/tex]

And the total number of goals is represents by 1, which is the 100% of goals.

[tex]x=1\frac{60 \ goals}{\frac{4}{6} }=\frac{360}{4} \ goals\\ x=90[/tex]

Therefore, the team scored a total of 90 goals.

O total de gols marcados no campeonato foi de 90, como calculado por meio de uma equação proporcional representada pela fração de gols marcados pelo time de futsal.

A questão relata que o time de futsal marcou 60 gols, o que equivale a quatro sextos do total de gols do campeonato. Para identificar o total de gols do campeonato, podemos configurar uma equação proporcional.

Se 4/6 corresponde a 60 gols, então 1/6 corresponde a 60 dividido por 4, que resulta em 15 gols. Uma vez que temos o valor representando 1/6, para obter o total de gols (ou seja, 6/6), simplesmente multiplicamos 15 por 6. Isso nos dá 90 gols.

Portanto, o total de gols marcados no campeonato foi de 90.

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Answer:

12.7

Step-by-step explanation:

If this is a right triangle then you just have to use pythagorean theorem. If fifteen is the hypotenuse then fifteen squared minus eight squared will give you x squared. Fifteen squared is 225 and eight squared is 64 so you subtract 64 from 225 to acquire the number 161. The square root of 161 is not exact but when rounded it is 12.7

Answer:

the answer is D

Step-by-step explanation:

67 x e is MPH

Answer:

(-2,0)   and (0,2)

Step-by-step explanation: I GOT IT RIGHT ON EDGINUITY

THANK ME LATER!!

Answer:

Step-by-step explanation:

Answer above is right!

Using the sine ratio (SOH), the approximate value of x to the nearest tenth is: 4.6 cm.

The sine ratio in Trigonometry is given as: sin ∅ = opposite/hypotenuse.

Thus, given:

∅ = 50°

Hypotenuse = 6 cm

Opposite = x cm

Plug in the values in to the sine ratio:

sin 50 = x/6

x = sin 50 × 6

x = 4.6 cm

Therefore, using the sine ratio (SOH), the approximate value of x to the nearest tenth is: 4.6 cm.

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Answer:

figure it out

Step-by-step explanation:

Answer:

We need a sample size of at least 1161.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error for the interval is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

For this problem, we have that:

[tex]\pi = 0.22[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

How large a sample should she take?

We need a sample size of at least n.

n is found when [tex]M = 0.02[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.02 = 1.645\sqrt{\frac{0.22*0.78}{n}}[/tex]

[tex]0.02\sqrt{n} = 1.645\sqrt{0.22*0.78}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.22*0.78}}{0.02}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.645\sqrt{0.22*0.78}}{0.02})^{2}[/tex]

[tex]n = 1160.88[/tex]

Rounding up

We need a sample size of at least 1161.

To estimate the proportion of defective parts with 90% confidence and 0.02 margin of error, the manager needs to use the formula for sample size, resulting in at least 1532 parts needed to be sampled.

This question involves the calculation of sample size in statistical inference. To estimate the proportion of defective parts with a 90% confidence interval, the production manager will need to use the formula for estimating sample size, which is n = Z² * P(1-P) / E².

In this formula, Z is the z-score associated with the desired confidence level (for a 90% confidence level, the Z value is 1.645), P is the estimated proportion of the population (in this case, 0.22), and E is the margin of error (in this case, 0.02).

By substituting these values into the formula, we get: n = 1.645² * 0.22(1 - 0.22) / 0.02² = 1531.025

Since we can't have a fraction of a sample, we round this up to the nearest whole number and the manager should sample at least 1532 parts.

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Answer:

I think you mentioned the problem “Five is the quotient of 120 divided by some number. What is the number?” In that case the answer is 24. Option b

Step-by-step explanation:

I got a 100 on the test!

Answer:

:C it not 24 it 20

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between triangle sides and trig functions. For the angle of interest, the diagram shows values for the Opposite side (12) and the Adjacent side (16.5). The mnemonic tells you that these are related to the Tangent of the angle:

  Tan = Opposite/Adjacent

  tan(θ) = (12/16.5)

Answer:

A) 120 cm^3

Step-by-step explanation:

area of triangle = 1/2 x 5 x 12 = 30

volume = 1/3 x 30 x 12 = 120

Answer:

A

Step-by-step explanation:

Answer:

(See explanation for further details)

Step-by-step explanation:

An approach is handling the trigonometric equation so that number of trigonometric functions can be reduce to one, in order to determine the periodicity of complete expression and therefore, to determine the complete set of solutions.

Answer:

5 Cars

Step-by-step explanation:

Let the number of cars to be sold to make the total pay equal be x.

The first company pays a salary of $12,500 plus commission of $1500 for each car sold.

The second company pays a salary of $17,500 plus a commission of $500 per car sold.

Equating both sides

12500+1500x=17500+500x

Collect like terms

1500x-500x=17500-12500

1000x=5000

Divide both sides by 1000

x=5

Therefore, when 5 cars are sold, the total pay would be the same.

Answer: 10y3 + 5x3 + 2

Step-by-step explanation: