A student was asked to find the difference (4x - 3x + 6.7") - (2x - 6x + x'). The student's work is shown at right. Identify the student's error and give the correct difference.

The sample should be taken to provide a 95% confidence interval is 200.

A confidence interval is made up of the mean of your estimate plus and minus the estimate's range. This is the range of values you expect your estimate to fall within if you repeat the test, within a given level of confidence.

Confidence is another name for probability in statistics.

Given the planning value for the population proportion,

probability, p = 0.25

q  = 1 - p = 1 - 0.25

q = 0.75

margin of error = E = 0.06

value of z at 95% confidence interval is 1.96,

the formula for a sample is,

n = (z/E)²pq

n = (1.96/0.06)²*0.25*0.75

n = 200.08

n = 200 approx

Hence sample size is 200.

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Answer:

The answer is -14

Step-by-step explanation:

P.S Can I have brainliest?

Answer:

1/8 because pretend that you have 1/4 of a pie you divide that quarter by two you have 1/8.

Answer:

1/4 ÷ 2 = 1/8 in fraction form. 1/4 ÷ 2 = 0.125 in decimal form.

Step-by-step explanation:

Hope it helps :)

5. The quadratic function for the height of the rock, h = -16·t² + 79·t + 50, indicates;

a. The height of the rock will be 125 feet above the beach at 1.28 seconds and 3.66 seconds after it is thrown

b. The maximum height reached is about 147.5 feet

The time it takes the rock to reach the maximum height is about 2.47 seconds

A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where, a, b, and c are numbers, and a ≠ 0.

The initial velocity of the rock = 79 ft/s

Height of the cliff above the beach from which the rock is thrown = 50 feet

The function for the height of the rock above the beach is; h = -16·t² + 79·t + 50

Please find attached the graph of the height of the rock as a function of time, created with MS Excel.

Required; When the height of the rock will be 125 feet above the beach

When the height of the rock is 125 feet, we get;

h = 125 = -16·t² + 79·t + 50

-16·t² + 79·t + 50 - 125 = 0

-16·t² + 79·t - 75 = 0

The value of t obtained using an online tool are;

t = (79 + √(1441))/32 ≈ 3.66 and t = (79 - √(1441))/32 ≈ 1.28

The times at which the height of the rock will be 125 feet above the beach are; 1.28 seconds and 3.66 seconds after the rock is thrown

b. The maximum height of the rock can be obtained from the formula for finding the maximum height of a quadratic equation of the form; f(x) = a·x² + b·x + c, which is;

At the maximum point, x = -b/(2·a)

The function for the height; h = -16·t² + 79·t + 50, indicates that we get;

a = -16, b = 79, and c = 50

Therefore;

The time it takes the rock to reach the maximum height, t(max), is therefore;

t(max) = -79/(2 × (-16)) ≈ 2.47

It takes about 2.47 seconds for the rock to reach the maximum height

The maximum height, h(max) = -16 × 2.46875² + 79×2.46875 + 50 ≈ 147.5

The maximum height reached by the rock is about 147.5 feet

Possible part of the question, obtained from a similar online question, includes;

a. The time it takes the rock to reach a height of 125 feet above the beach
b. The maximum height reached by the rock and the duration it takes the rock to reach the maximum height.

Please find attached the possible graph in the question, created with MS Excel, using the function for the height of the rock.

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The statement "In both cases, subtract 6 from both sides, but reverse the inequality sign when doing that for the inequality" best describes the process used to solve the equations.

In the equation -3x + 6 = 21, to isolate the variable x, we subtract 6 from both sides of the equation, which yields -3x = 15. Then, we divide both sides by -3 to solve for x, resulting in x = -5. This process is applicable to equations where we aim to find the exact value of the variable.

Similarly, in the inequality -3x + 6 < 21, we want to find the range of values for x that satisfy the inequality. By subtracting 6 from both sides, we obtain -3x < 15.

However, since we performed the same operation on both sides of the inequality, the direction of the inequality sign remains the same.

Thus, the correct inequality is -3x < 15. To isolate x, we divide both sides by -3. However, since we reversed the inequality sign, we must also reverse it again, resulting in x > -5.

This process allows us to determine the range of values for x that satisfy the inequality.

Therefore, the statement accurately describes the process for solving both the equation and the inequality, highlighting the significance of reversing the inequality sign when manipulating inequalities.

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Answer:

Null Hypothesis:-H₀: P = 0.12

There is no difference between the percentage of volunteers selected from the college students.

Alternative Hypothesis:-H₁: P ≠ 0.12

There is a difference between the percentage of volunteers selected from the college students.

The calculated value Z = 0.5543 < 2.376 at 0.01 level of significance

The null hypothesis is accepted

There is a difference between the percentage of volunteers selected from the college students.

Step-by-step explanation:

Step(i):-

Given that the Population proportion P= 12% = 0.12

Given that the 331 randomly selected students who receive financial aid, 43 of them volunteered their time.

Sample proportion

                      \(p = \frac{x}{n} = \frac{43}{331} = 0.1299\)

Step(ii):-

Null Hypothesis:-H₀: P = 0.12

There is a difference between the percentage of volunteers selected from the college students.

Alternative Hypothesis:-H₁: P ≠ 0.12

There is no difference between the percentage of volunteers selected from the college students.

Step(iii):-

Test statistic

        \(Z = \frac{p-P }{\sqrt{\frac{PQ}{n } } }\)

        \(Z = \frac{0.1299-0.12 }{\sqrt{\frac{(0.12)(0.88)}{331 } } }\)

      Z = 0.5543

Level of significance = 0.01

Critical value Z₀.₀₁ = 2.376

Final answer:-

The calculated value Z = 0.5543 < 2.376 at 0.01 level of significance

The null hypothesis is accepted

There is a difference between the percentage of volunteers selected from the college students.

Answer:

a

Step-by-step explanation:

Answer: y = 3x^2 -x + 2

Step-by-step explanation:

We can see that the dot plot is seen below.

We can see here that An example of a graphical representation of data is a dot plot. It is a number line with dots above each value to indicate the frequency or count of that value.

Depending on the type of data being shown, the dots are often arranged either horizontally or vertically.

Dot plots are known to be useful for showing the distribution of data, particularly for small data sets.

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Answer:

Graph 3 is B

Graph 4 is D

Graph 5 is C

Graph 6 is B

Step-by-step explanation:

If there were 50 workers, they would set 2,500 stones each day.

Total number is a term used to describe the sum of all the values or items within a set. It is usually used to calculate an aggregate or grand total, such as the sum of all the numbers in a list or the total number of people in a population. Total number can also be used to describe the absolute value or quantity of something, such as the total number of days in a year.

Assuming each worker set the same number of stones each day, the total number of stones set each day would be 50 times the number of workers. For example, if there were 20 workers, they would set 1,000 stones each day.
The number of stones set each day could also vary depending on the number of workers and the number of days they worked in a week. For example, if the workers worked a six day week and worked 50 out of the 52 weeks each year, the total number of stones set each day would be 50 times the number of workers multiplied by six. For example, if there were 20 workers, they would set 12,000 stones each day. If there were 50 workers, they would set 30,000 stones each day.

The number of stones set each day can also be affected by the production rate of the workers, the quality of the stones, and the amount of time required to set each stone. If the production rate was low, the number of stones set each day would also be lower. Similarly, if the quality of the stones was poor, the workers would likely take longer to set each stone, thus reducing the number of stones set each day.

Overall, the exact number of stones set each day depends on the number of workers, the number of days they work each week, their production rate, and the quality of the stones.

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No, the given experiment does not have a sample space with equally likely outcomes.

The term "loaded" means that the die is not fair, and certain numbers are more likely to appear than others. This means that the probabilities of each possible outcome are not equal, and therefore the sample space does not have equally likely outcomes. For example, if a die is loaded to favor rolling a 6, then the probability of rolling a 6 is higher than the probability of rolling any other number. Therefore, the sample space of this experiment is not uniform, and outcomes are not equally likely.

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Answer:

<

Step-by-step explanation:

1) Substitute 5 into the question

2) Work out the sides

3) Put it into an inequality

5 < 7

Hope this helps, have a great day!

Answer:

common ratio =r=3

Step-by-step explanation:

Answer:

−4194304

Step-by-step explanation:

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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The mode will not change.

Given data,

58,60,53,54,60,35,58,60

Outlier is the value in a set of data that much higher or lower than other values in data.

from given data, outlier is 35.

Mode is the value in a set of data that occurs more frequently in set of data.

from given data, 60 occurs more frequently.

Hence, 60 is the mode of data.

If outlier is removed from the data set then it will not affect the mode of the data

Thus, the mode will not change.

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Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

11 people could enter for $100

Step-by-step explanation:

According to the information given:

$28=3 people

$20=2 people

so it goes up by 8 dollars for every person added

20-8= 16, the original fee, meaning the sequence formula would be:

8n+8 (n being the number of people)

if 8n+8=100

8n=92

n=11.5 rounded down would be 11

32π is the value of F by Stokes' theorem.

What exactly does Stokes Theorem mean?

In accordance with the Stoke's theorem, "the surface integral of the curl of a function over a surface bounded by a closed surface is equal to the line integral of the specific vector function around that surface."

Since F = −16yzi+16xzj+13(x2+y2)zk

     Here  x² + y²  = 1

put   x = 1 cos t     y = sin t     z = 1

F = - 16 Sin t i + 16cos t j + 13 . 1 k

       = -16 Sin t i + 16cos t j + 13k

C : Y(t) =  < x,y,z >

            = < cost , sint , 1 >

    dr = < -sint , cost , 0 >

 we know that stokes' theorem

         ∫∫s = Curl F. ds = ∫c F . dr

   ∫∫s curl F . ds = ∫₀²π < -16 sint , 16cost , 13> < - sint , cost , 0 >dt

                          = ∫₀²π ( 16 sin² t + 16 cos² t + 0 ) dt

                       = ∫₀²π 16( sin² t + cos² t ) dt

                        =  ∫₀²π 16 . 1  dt

                         = 16 [ t ]₀²π  = 16 * 2π  ⇒32π

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The probability that the student lived in the Gold dorm and was an underclassmen is of:

0.035 = 3.5%.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

The parameters for this problem are given as follows:

Hence the probability that the student lived in the Gold dorm and was an underclassmen is calculated as follows:

p = 0.7 x 0.05 = 0.035 = 3.5%.

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

Answer:

Test statistic t = -1.8246

P-value = 0.0737

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean GPA of night students is different from the mean GPA of day students.

Step-by-step explanation:

This is a hypothesis test for the difference between populations means.

The claim is that the mean GPA of night students is different from the mean GPA of day students.

Then, the null and alternative hypothesis are:

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2\neq 0\)

The significance level is 0.05.

The sample 1, of size n1=30 has a mean of 2.35 and a standard deviation of 0.46.

The sample 2, of size n2=25 has a mean of 2.58 and a standard deviation of 0.47.

The difference between sample means is Md=-0.23.

\(M_d=M_1-M_2=2.35-2.58=-0.23\)

The estimated standard error of the difference between means is computed using the formula:

\(s_{M_d}=\sqrt{\dfrac{\sigma_1^2}{n_1}+\dfrac{\sigma_2^2}{n_2}}=\sqrt{\dfrac{0.46^2}{30}+\dfrac{0.47^2}{25}}\\\\\\s_{M_d}=\sqrt{0.007+0.009}=\sqrt{0.016}=0.1261\)

Then, we can calculate the t-statistic as:

\(t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-0.23-0}{0.1261}=\dfrac{-0.23}{0.1261}=-1.8246\)

The degrees of freedom for this test are:

\(df=n_1+n_2-2=30+25-2=53\)

This test is a two-tailed test, with 53 degrees of freedom and t=-1.8246, so the P-value for this test is calculated as (using a t-table):

\(\text{P-value}=2\cdot P(t<-1.8246)=0.0737\)

As the P-value (0.0737) is greater 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 the mean GPA of night students is different from the mean GPA of day students.

cos 36 × cos 72 = 0.25

cos 36 × cos 72 =

0.309 x 0.809 = 0.249 = 0.25

Answer:

4/610=0.00655737704918

Step-by-step explanation:

Answer

0.00655737704

4/610 ≈ 0.007 or 0.01

Step-by-step explanation:

1) 4/610 = 0.00655737704

2) Since the number is too long, you can also round it to the nearest thousandth which is 0.007 or you can round to the nearest hundredth which is 0.01

However, the answer 0.00655737704 is the most accurate.

Hope this helps!

Answer:

2(x)=y  only because 20 is half of 40 and the first section in the table is 20=40y

Step-by-step explanation:

Hope this helped.

A brainliest is always appreciated.

There is only 1 possible 11-card hand that can be formed from a 20-card deck.

To determine the number of 11-card hands possible with a 20-card deck, we can use the concept of combinations.

The number of combinations, denoted as "nCk," represents the number of ways to choose k items from a set of n items without regard to the order. In this case, we want to find the number of 11-card hands from a 20-card deck.

The formula for combinations is:

nCk = n! / (k!(n-k)!)

Where "!" denotes the factorial of a number.

Substituting the values into the formula:

20C11 = 20! / (11!(20-11)!)

Simplifying further:

20C11 = 20! / (11! * 9!)

Now, let's calculate the factorial values:

20! = 20 * 19 * 18 * ... * 2 * 1

11! = 11 * 10 * 9 * ... * 2 * 1

9! = 9 * 8 * 7 * ... * 2 * 1

By canceling out common terms in the numerator and denominator, we get:

20C11 = (20 * 19 * 18 * ... * 12) / (11 * 10 * 9 * ... * 2 * 1)

Performing the multiplication:

20C11 = 39,916,800 / 39,916,800

Finally, the result simplifies to:

20C11 = 1

Consequently, with a 20-card deck, there is only one potential 11-card hand.

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Answer:

You can measure from the inside of the tank or measure the outside and subtract the width of the tank walls to find the inside measurement. Next multiply the length width and depth measurements to find the cubic volume in cubic inches

Step-by-step explanation: