A 98% confidence interval for a population parameter means that if a large number of confidence intervals were constructed from repeated samples, then on average, 98% of these intervals would contain the true parameter.

All of the methods mentioned, i.e., bar chart, pie chart, and relative frequency table are valid ways to summarize or visualize categorical variables. Option D.

They are commonly used in data analysis to gain insights into the distribution and proportion of different categories within a dataset.

A bar chart is a graphical representation of data that uses rectangular bars to display the frequency or proportion of different categories. It is useful in comparing the frequencies of different categories and identifying the most common or rare categories.

A pie chart is another graphical representation of data that uses slices of a circle to display the relative frequency or proportion of different categories. It is useful in showing the proportion of each category in relation to the whole.

A relative frequency table is a tabular representation of data that displays the frequency and proportion of each category. It is useful in comparing the frequencies and proportions of different categories and identifying the most common or rare categories.

Therefore, none of the options given would be an invalid way to summarize or visualize categorical variables. The choice of which method to use depends on the nature of the data and the purpose of the analysis.

It is important to choose a method that effectively communicates the information being presented and is appropriate for the audience. So Option D is correct.

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Note the correct question is

Which of the following would NOT be a valid way to summarize or visualize a categorical variable? Choose the correct answer below

A.)Bar chart

B.)Pie chart

C.)Relative frequency table

D.)None of the above

The probability of selecting a random sample of 100 marbles that has a mean diameter greater than 0.851 cm is approximately 15.87%.

To find the probability of selecting a sample of 100 marbles with a mean diameter greater than 0.851 cm, first, we'll compute the standard error (SE) of the sample mean:

In this case,
Mean diameter (μ) = 0.850 cm
Standard deviation (σ) = 0.010 cm
Sample size (n) = 100 marbles
Target mean diameter (x) = 0.851 cm

SE = σ / √n = 0.010 cm / √100 = 0.001 cm

Next, we'll calculate the z-score:

z = (x - μ) / SE = (0.851 - 0.850) / 0.001 = 1

Now, we need to find the probability (P) that corresponds to this z-score. You can use a z-table, a calculator, or statistical software to find the probability. In this case, P(Z > 1) ≈ 0.1587.

So, selecting a random sample of 100 marbles having a mean diameter greater than 0.851 cm has a probability of approximately 15.87%.

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Answer:

x=15

Step-by-step explanation:

option 4 can be a relation but not a function

For a relation to be a function, there must be two mapping kinds

one to one or many to one

What this mean is that every x value will have a single y-value or many x values to one y value

No single x value will have a two y values

Thus, looking at the options, the circle can be a relation but it is not a function

This is because an x-value will have y-value below and above it

The given values into the equation of the least squares regression line: 0.6 * 520 + 10.0 = 322 hot dogs were sold that day. 357 hot dogs were sold on the day when 520 people attended the fair.

In this problem, we have data collected on the number of hot dogs sold (h) and the number of people attending a fair (p) over a two-week period. The least squares regression line is a line that best fits the data points and represents the relationship between the variables.

The equation of the least squares regression line is given as 0.6p + 10.0. This equation indicates that the number of hot dogs sold (h) can be estimated by multiplying the number of people attending (p) by 0.6 and adding 10.0.

We are given that the residual for the day when 520 people attended the fair is 35. A residual is the difference between the actual observed value and the predicted value on the regression line. In this case, the predicted value is 0.6 * 520 + 10.0 = 322 hot dogs. The actual value is the number of hot dogs sold on that day. The residual is calculated as the actual value minus the predicted value, which gives us 35.

To find the number of hot dogs sold on that day, we can set up an equation using the residual: h - 322 = 35. Solving this equation, we find that h = 322 + 35 = 357. Therefore, 357 hot dogs were sold on the day when 520 people attended the fair.

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QUESTION:

Data was collected on h, the number of hot dogs sold, and p, the number of people attending a fair over a two week period. The least squares regression line has equation y = 0.6p + 100. The residual for the day when 520 people attended was 35. How many hot dogs were sold that day? OA. 322 OB. 287 OC. 220 OD. 555 O E. 357 The salaries of a random sample of a company's employees are summarized in the frequency distribution below. Approximate the sample mean using the grouped data formulas O A. $17,500.00 OB. $19,663.05 O C. $16,087.95 OD. $17,875.50 Employees Salary (5) 5.001 - 10,000 10,001 - 15,000 15,001 - 20,000 20,001 - 25,000 25,001 - 30,000

Answer:

13

Step-by-step explanation:

7 x 2=14

40-14=26

26/2=13

Answer:

40 - 14 = 26

26/2 = 13

The width is 13

sinθ = -0.9798 (rounded to two decimal places).

What is the Trigonometry ?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, and the trigonometric functions that describe those relationships.

We can use the identity sin²θ + cos²θ = 1 to find sinθ, since we know cosθ:

sin²θ + cos²θ = 1

sin²θ + 0.2² = 1 (substituting cosθ = 0.2)

sin²θ = 0.96

Taking the square root of both sides, we get:

sinθ = ± 0.9798

Since θ is in the second quadrant, sinθ is negative.

Hence, sinθ = -0.9798 (rounded to two decimal places).

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Answer:

t = -20

Step-by-step explanation:

Substitute for d and m

t = 6m + 2(t - d)

t = 6(4) + 2(t - 2)

t = 24 + 2t - 4

t = 20 + 2t

-20 = t

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Answer:

25%

Step-by-step explanation:

As the given situation the parameters are below:-

Cost of each box = 3 pounds

Amount of cereal in each box = 160 g

now,

160 g of cereal = 100%

and

25% of 1 box of cereal = 25% of 160 g which is

\(= \frac{25}{100} \times 160 g= 40 g\)

As per the question,  it is mention that Jane need her idea to give the equal value of amount as Tim's idea, provided

160 g of cereal costs 3 pounds

and

1 g of cereal will cost

=  \(\frac{3}{60}\ pounds\)

40 g of cereal will cost \(40\times \frac{3}{160} = \frac{3}{4}\ pounds\)

So, the percentage of \(\frac{3}{4}\) the pound is of 3 pounds is 3 ÷ 4 ÷ 3 × 100

= 25%

Therefore as the situation, Jane need to decline the amount by 25% for the same amount as Tim's idea.

Answer:

y=3x-13

Step-by-step explanation:

where do u get the 2?

Answer:

x=6 y=5

Step-by-step explanation:

use substitution because they y variable is already in the correct form for substitution

Answer:

3x+6 is the answer

Step-by-step explanation:

Have a good day and stay safe!

9514 1404 393

Answer:

  price per gallon = (total cost)/(number of gallons)

Step-by-step explanation:

Price per gallon is found by dividing the price by the number of gallons:

  price per gallon = (total cost)/(number of gallons)

You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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The prime factorization of the number 21 is:

21 = 3*7

We want to write the prime factorization of 21.

To do so, we just need to divide the number by prime numbers.

The first prime number we can try is 2, if we divide by 2 we get:

21/2 = 10.5

This is not an integer, so 2 is not a factor.

The next one is 3:

21/3 = 7

Now we can rewrite:

21 = 3*7

Where 3 and 7 are prime numbers, so that is the prime factorization.

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Mid point of any two points (x1,y1) and (x2,y2)

is ((x1+x2)/2,(y1+y2)/2)

using this

we get coordinates of d are (a,-2b)

The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

What is the factor?

Factor is a mathematical expression or a number that divides another expression or number evenly. The factor of an expression is a number that divides the expression evenly, leaving no remainder.

The expression 3y - 18 can be factored using the greatest common factor (G.C.F.) of 3.

The G.C.F. of 3 and 3y is 3.

So, 3y - 18 can be factored as:

3 * (y - 6)

Hence, The factored form of 3y - 18 using the G.C.F. is 3 * (y - 6).

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Answer:

57.14% increase

Step-by-step explanation:

The percentage change is calculated by dividing the difference value by the original value and multiplying it by 100.

If the price of the laptop was changed from $350 to $550.

The percentage change in the cost of the laptop is 57%.

The percentage is calculated by dividing the required value by the total value and multiplying it by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

We have,

The percentage change is calculated by dividing the difference value by the original value and multiplying it by 100.

The price of the laptop changed from $350.00 to $550.00.

Original price = $350

New price = $550

The percentage change in the cost of the laptop:

= [ (New price - Orginal price) / Original price ] x 100

= (200/350) x 100

= 20000/350

= 57.14%

= 575

Thus,

If the price of the laptop was changed from $350 to $550.

The percentage change in the cost of the laptop is 57%.

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Answer:

Step-by-step explanation:

Solution by substitution method

-2x+y=10

2x-y=-10

and 4x-y=-14

Suppose,

2x-y=-10→(1)

and 4x-y=-14→(2)

Taking equation (1), we have

2x-y=-10

⇒y=2x+10→(3)

Putting y=2x+10 in equation (2), we get

4x-y=-14

4x-1(2x+10)=-14

⇒4x-2x-10=-14

⇒2x-10=-14

⇒2x=-14+10

⇒2x=-4

⇒x=-2→(4)

Now, Putting x=-2 in equation (3), we get

y=2x+10

⇒y=2(-2)+10

⇒y=-4+10

⇒y=6

∴y=6andx=-2

\(\large\underline{\sf{Solution-}}\)

Given that,

In triangle ABC

\( \purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: - - - (1) }\)

\( \purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \: - - - (2)}\)

We know,

Sum of all interior angles of a triangle is supplementary.

\( \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }\)

On adding equation (1) and (2), we get

\( \purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree + 150 \degree \:}\)

\( \purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}\)

\( \purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}\)

\( \purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree \:}\)

\( \purple{\rm :\longmapsto\:\angle B = 95\degree \:}\)

On substituting the value in equation (1) and (2), we get

\( \purple{\rm :\longmapsto\:\angle A + 95\degree = 125\degree }\)

\( \purple{\rm :\longmapsto\:\angle A = 125\degree - 95\degree }\)

\( \purple{\rm :\longmapsto\:\angle A = 30\degree }\)

Also, from equation (2), we get

\( \purple{\rm :\longmapsto\:95\degree + \angle C = 150\degree }\)

\( \purple{\rm :\longmapsto\:\angle C = 150\degree - 95\degree }\)

\( \purple{\rm :\longmapsto\:\angle C = 55\degree }\)

Hence,

\(\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree } \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}\)

Answer:

angle A=30°

angle B=95°

angle C=55°

The coefficient of determination is 0.05.Answer: a. Mean square error = 0.25. b. Coefficient of determination (R²) = 0.05.

a. Mean square error is used to measure the goodness of fit of the linear regression model. Mean square error (MSE) is the average squared differences between the predicted value and the actual value. MSE can be calculated using the formula MSE = SSE / (n - k - 1) where SSE is the sum of squared errors, n is the number of observations and k is the number of independent variables.

The given data for two variables x and y are as follows: xi 2yi7Applying the values in the regression equation, we get:ŷ = 1.2 + 2.4x Substituting xi = 2, we get: ŷ = 1.2 + 2.4(2) = 6Therefore, the SSE can be calculated as follows: SSE = ∑(yi - ŷ)² = (7 - 6)² = 1Now, n = 5 and k = 1 (since there is only one independent variable),

Therefore, MSE = SSE / (n - k - 1)= 1 / (5 - 1 - 1)= 0.25Therefore, the mean square error is 0.25.b. The coefficient of determination (R²) is the proportion of the total variation in the dependent variable (y) that can be explained by the variation in the independent variable(s) (x).

It ranges from 0 to 1, where 0 means that the independent variable(s) does not explain any of the variation in the dependent variable, and 1 means that the independent variable(s) perfectly explain the variation in the dependent variable.R² is calculated as the ratio of the explained variation to the total variation.

It can be calculated as follows: R² = SSE / SST, where SSE is the sum of squared errors and SST is the total sum of squares. SST is calculated as follows: SST = ∑(y i - ȳ)²where ȳ is the mean of yi

Substituting the given values, we get: SST = ∑(yi - ȳ)²= (7 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)² + (7 - 5)²= 2² + 2² + 2² + 2² + 2²= 20Now, SSE = 1 (calculated in part a)Therefore,R² = SSE / SST= 1 / 20= 0.05

Therefore, the coefficient of determination is 0.05.Answer: a. Mean square error = 0.25. b. Coefficient of determination (R²) = 0.05.

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Answer:

5 boys

Step-by-step explanation:

boys to girls in math class = 3/12

3/12 can be reduced to 1/4

In the science class, the ratio is the same but there is a total of 20 girls.

Multiply the fraction 1/4 by 2/2, 3/3, 4/4, 5/5, etc. until you get x/20. Then you have 20 girls. x is the number of boys.

1/4 = 2/8 = 3/12 = 4/16 = 5/20

In science the ratio of 1/4 is the same as 5/20, so there are 5 boys.

Answer: 5 boys

Answer: 7= D, 26 units

Step-by-step explanation:

Take the length. 0,0 to 0,9  the length is 9  Next take the width 0,9 to 4,9 the width is 4  L+Wx2 13x2=26

Solution:

In an input/output table, each output is larger than the corresponding input.

The operations which could be used are addition and multiplication.

Hence, the answer is addition and multiplication

Given that 1 kilometer = 0.62 mile, 36 inches = 1 yard, and 1 mile = 1760 yards, 1 km has approximately 39,283.2 inches.

In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.

A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.

From the problem, the conversion factors are given as

1 kilometer = 0.62 mile

36 inches = 1 yard

1 mile = 1760 yards

To convert 1 kilometer into inches, first, convert 1 kilometer to miles using the conversion factor, 1 kilometer = 0.62 mile

1 km = 0.62 miles

Then, convert miles to yards using the conversion factor, 1 mile = 1760 yards

1 km = 0.62 miles = 0.62 (1760 yards)

1 km = 0.62 miles = 1091.2 yards

Lastly, convert yards to inches using the conversion factor, 36 inches = 1 yard

1 km = 0.62 miles = 1091.2 yards = 1091.2 (36 inches)

1 km = 0.62 miles = 1091.2 yards = 39,283.2 inches

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Answer:

\(Slope=1.\)

Step-by-step explanation:

\(Calculate \: the \: slope \: m \: using \: the \\ \: slope \: formula \: \)

\(m = \frac{y2 - y1}{x2 - x1} \)

\(with(x^1,y^1)=(-2,-5)and(x^2,y^2)=(-3,-6)\)

\(m = \frac{ - 6 - ( - 5)}{ - 3 - ( - 2)} = \frac{ -6 + 5}{ - 3 + 2} = \frac{ - 1}{ - 1} = 1.\)

\(Thank \: you!!!\)

The approximate probability that the total score is at least 375 when a fair six-sided die is rolled 100 times is (d) 0.4420.

When a fair six-sided die is rolled, the random variable X represents the outcome. The mean (μX) of X is 3.5, and the standard deviation (σX) is 1.71.

To find the probability that the total score is at least 375 when the die is rolled 100 times, we can use the Central Limit Theorem. According to the theorem, the sum of a large number of independent and identically distributed random variables approximates a normal distribution.

In this case, the sum of the outcomes of 100 rolls of the die follows a normal distribution with a mean of μX multiplied by the number of rolls (100) and a standard deviation of σX multiplied by the square root of the number of rolls (10). Therefore, the approximate probability can be calculated by finding the probability that the sum is greater than or equal to 375.

Using a normal distribution table or a calculator, we can find that the approximate probability is 0.4420, which corresponds to answer (d). This means that there is a 44.20% chance that the total score will be at least 375 when the die is rolled 100 times.

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