which of the following refers to a set of procedures in which the sample size and sample statistics are used to make estimates of population values or facts?

Answer:

d

Step-by-step explanation:

The amount cheaper is the car washes Malcolm orders than the car washes Martha's order is $13.

The correct answer choice is option B.

Malcolm's gift card = $50.

Cost Malcolm's car wash per visit = $7

Martha's gift card = $180

Cost Martha's car wash per visit = Difference between gift card balance of first and second visit

= $180 - $160

= $20

How cheap is the car washes Malcolm orders than the car washes Martha's order = $20 - $7

= $13

Therefore, Malcolm's car wash is cheaper than Martha's car wash by $13

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The critical values are 0.622, 0.707, 0.789 and 0.834

The sample size is given as:

n = 8

Calculate the degrees of freedom using

df = n - 2

So, we have:

df = 8 - 2

df = 6

Using the table of values of critical values, we have:

Critical values = 0.622, 0.707, 0.789 and 0.834

By comparing the critical values and the linear correlation coefficient, we can conclude that there is no significant linear correlation.

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Answer:

I think answer is D but it could be wrong not sure

Answer:

Solution given:

<C=90°

<B=48.7°

a=?

<A=?

b=?

Now

In right angled triangle

<A+<B+<C=180°[Sum of interior angle of a triangle is 180°]

<A+48.7+90=180°

<A=180-90-48.7

<A=41.3°

again

Sin 48.7=perpendicular/hypotenuse=b/c

b=sin 48.7°×16

b=12

again

Cos 48.7°=base/hypotenuse=a/c

a=Cos 48.7°×c

a=Cos 48.7°×16

a=10.6

So ,answer is:D.m<A=41.3°,a=10.6 and b=12.

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

From the question, we have the following parameters that can be used in our computation:

x + y > 3

x - 3y < 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (6, 2)

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Answer:

none of these

Step-by-step explanation:

Answer:

26 inches

Step-by-step explanation:

You find out that 1 foot equals 12 inches

times 2 by 12 equaling 24

24 added by 2 is 26

1/6 as a decimal is 1.83 infinitive 3 which is rounded to 2 as the whole number

makes your answer 26 inches

Hope that helps

Answer:

D. 5 units

Step-by-step explanation:

To work out the length use formula:

\(length = \sqrt{(y₂-y1) {}^{2} + (x₂-x1) {}^{2}} \)

length of AB:

\(AB = \sqrt{( - 4 - 5) {}^{2} + ( - 6 - ( - 2)) {}^{2} } = \sqrt{97} \)

length of AC:

\(AC = \sqrt{( - 7 - 5) {}^{2} + ( - 2 - ( - 2)) {}^{2} } = 12\)

length of BC:

\(BC = \sqrt{( - 7 - ( - 4)) {}^{2} + ( - 2 - ( - 6)) {}^{2} } = 5\)

as you can see BC has the shortest side of 5 units

Answer:

Hello your question has some missing information attached below is the missing information

answer :

i) ( 0.158 , - 1.018 )

ii)  the difference in expected earnings can be computed as

( \(X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}\)

Step-by-step explanation:

i) Construct a 95% confidence interval ( between Juanita and Molly )

Expected difference in earnings = ( X\(_{6}\)\(_{,A}\) - X\(_{6.B}\)) = \(\beta _{0}\)= ( \(\beta + \beta _{6}\) )

∴ 95% confidence interval

-0.43 ± 1.96 * 0.30 = [ -0.43 ± 0.588 ] =  ( 0.158 , - 1.018 )  ( hence confidence interval at 95% = 1.96 )

ii) Construct a 95% confidence interval ( between Juanita and Jennifer )

Juanita is a student from the south and Jennifer is a student from Midwest

therefore the difference in expected earnings can be computed as

( \(X_{6,A} - X_{5,C} ) = \beta _{0} + \beta _{6} - ( \beta _{0} - \beta _{5} ) = \beta _{6} - \beta _{5}\)

therefore a 95% confidence interval can be calculated with the above regression model.

In step 5 of the experimental procedure, the design of a WDM coupler is discussed to combine two signals of λ=1300nm and 1550nm.

The separation between waveguides is chosen as d=3μm, and the task is to estimate the total length of the coupler needed to combine the signals. To achieve this, K and γ are calculated for each wavelength using the equation.

Then, the coupling length for each wavelength is computed. After this, a length L is found for the coupler such that it consists of approximately an even number of coupling lengths for one wavelength and an odd number for the other wavelength, keeping the device length under 3 cm. Finally, using equation (4.4) and the value of L in part (b), the fraction of each of the two wavelengths that end up in the same waveguide is calculated.

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The steps you have are correct. I'll fill in the gap between step 2 and step 3.

\(0.4245 = \frac{2.5}{\text{x}}\\\\0.4245\text{x} = 2.5\\\\\text{x} = \frac{2.5}{0.4245}\\\\\text{x} = 5.8892815\\\\\text{x} = 5.9\\\\\)

I multiplied both sides by x, then divided both sides by 0.4245 to isolate the variable.

With the exception of 2.5, every other decimal value mentioned is approximate.

To get the average annual cost :

Divide the cost by the product of number of years and number of items

From the given problem :

There are two types of sweatshirt

1. $54 for 3 cheap sweatshirts that lasted for 6 months

Cost = 54

year = 6 months or 0.5 year

number of items = 3

Ave = 54/(3 x 0.5) = $36

2. $28 for 3 quality sweatshirts that lasted for 2 years

Cost = 28

year = 2 years

number of items = 3

Ave = 28/(2 x 3) = $4.67

So the difference between the average annual cost for each type of sweatshirt is :

36 - 4.67 = $31.33

The correct answer is None of these choices are correct.

The numbers can be a solution for the inequality 32+a>44 is 13 and 14.

If the equation or inequality have variable terms, than there might be some values of those variables for which the equation or inequality might be correct. Such values are known as solution to that equation or inequality. To set of such values are called solution set to be considered equation or inequality.

Given that;

The inequality= 32+a>44

To solve the inequality 32 + a > 44, we need to isolate the variable "a" on one side of the inequality.

32 + a > 44

Subtract 32 from both sides:

a > 44 - 32

a > 12

This means that any number greater than 12 can be a solution to the inequality.

Therefore, the inequalities numbers 13 and 14 can be solutions, but 11 and 12 cannot.

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Answer:

Linear decreasing

Step-by-step explanation:

Ape.x

Answer:

78.5

Step-by-step explanation:

A=πr^2 is the formula. Since you're using pi as 3.14, 3.14 times 5^2 is 78.5 (5^2 is 25 because 5x5=25)

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The unit cost C depends on the number of engines made. If x engines are made, then the unit cost is given by the function:

C(x)=0.2x²+ 248x +21,748 is $12917, which is the minimum unit cost.

Unit cost, also known as the break-even point, is the lowest price at which a company must sell a product to avoid losses. For example, a product with a breakeven unit cost of $10 per unit must sell above that price. Revenues above this price constitute the company's profit.

The calculates the unit cost of production as the break-even point. This cost constitutes the base price that the company uses to determine its market price.

In general, a unit must sell for more than its unit cost to generate a profit. For example, a company manufactures 1,000 units of a product that costs $4 each and sells them for $5 each. The profit is $5 minus $4, or $1 per unit of income. If a unit is priced at $3 per unit, there is a loss because $3 minus $4 (cost) is a loss of $1 per unit.

By the definition of average cost, we know it is the ratio of the total cost to the number of manufactured products. The total cost here is also termed as unit cost, which is equal to the sum of fixed cost and variable cost.

Hence, Average cost = Total cost/Number of units

                                    =  (Fixed cost + Variable cost)/Number of units.

According to the Question:

The minimum unit cost is $12197.

Take the derivative and set = 0  solve for x

C'(x) = 2x -360 = 0

x = 180 engines

C(180)  = (180)² -360(180) + 44,597

           = 44,597 - 32400

           = $12,197  minimum cost.

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Answer:

Step-by-step explanation:

The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.

Step 1: Evaluate the expression inside the parentheses.

7.4 - 3.6 = 3.8

After evaluating the expression inside the parentheses, the expression becomes:

12 ÷ 3.8 + 8 - 2

Step 2: Perform the division.

12 ÷ 3.8 = 3.158

After performing the division, the expression becomes:

3.158 + 8 - 2

Step 3: Perform the addition and subtraction from left to right.

3.158 + 8 = 11.158

11.158 - 2 = 9.158

Therefore, the value of the given expression is approximately 9.158.

The first step is:

Work/explanation:

The expression is:

12 ÷ (7.4 − 3.6) + 8 − 2

Let's recall the order of operations first:

So we evaluate

\(\sf{12\div(7.4-3.6)+8-2}\)

\(\sf{12\div3.8+8-2}\)

Next, division:

\(\sf{3.158+8-2}\)

Next, addition & subtraction:

\(\sf{9.158}\)

Answer:   \(\;\;\frac{1}{6} , \;\; 0.16667,\;\; \text{or about}\;\;17\%\)

Step-by-step explanation:

   A regular dice has 6 sides, and only one of those sides side has a six.

        We write probability as;

   \(\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} = \frac{\text{number of times six is on the dice}}{\text{number of numberss on the dice}} =\frac{1}{6}\)

Hi, there!

 _______

\(\boxed{\boxed{\sf{Probability=\dfrac{Favorable \ Outcomes}{Total \ Outcomes}}}}\)

Here,

» Favourable Outcome(s) -> getting a 6 on a die (1 outcome),  because only one side of a die has a six on it

» Total Outcomes -> 6 (you can only get 1, 2, 3, 4, 5, 6 if you roll one die)

So,

\(\sf{Probability_{(6)}=\dfrac{1}{6}}\)

Hope the answer - and explanation - made sense to you,

happy studying!!

                                                                                                        \(\tiny\textit{frozen \ melody}\)

Answer:

1. \(Expression: 3(5a + 2)\)

2. \(Total\ charges = 6.25(s+g)\)

3. \(Total = 65x + 18 + 65y\)

4. Michelle

5. 20 friends

6. Thor

8. \(x\leq 5\)

9. \(x + x + 5 = 32\)

10. \(7n + 9 \leq 44\) so: \(n \leq 5\)

11. \(40 + 5n \leq 70\) So: \(n \leq 6\)

12. \(10.01 p + 9.96 \leq 50\) so \(p \leq 4\)

Step-by-step explanation:

1. Given

\(Expression: 15a + 6\)

Required

Determine the equivalent expression

\(Expression: 15a + 6\)

Expand:

\(Expression: 3 * 5a + 3 * 2\)

Factorize:

\(Expression: 3(5a + 2)\)

Hence, the equivalent expression of the given expression is \(3(5a + 2)\)

2.

Given

\(Charges = \$6.25\)

s = seventh grade students

g = eight grade students

Required

Determine the total charges

First, we need to calculate the total number of charges:

\(Total=s+g\)

\(Total\ charges = Charges * Total\)

\(Total\ charges = 6.25(s+g)\)

3. Given

Ken

\(Duration = x\ weeks\)

\(Extra\ Earnings = \$18\)

\(Weekly\ Earnings = \$65\)

Paul

\(Weekly\ Earnings = \$65\)

\(Duration = y\ weeks\)

Ken's total charges is:

\(Weekly\ Earnings * Duration + Extra\ Earnings\)

\(65 * x + 18\)

\(65x + 18\)

Paul's total charges is:

\(Weekly\ Earnings * Duration\)

\(65 * y\)

\(65 y\)

\(Total = Ken + Paul\)

\(Total = 65x + 18 + 65y\)

4.

To calculate the percentage, we simply divided the number of pop albums by the total number of albums.

For Michelle.

\(\%Pop = \frac{33}{60} * 100\%\)

\(\%Pop = \frac{3300\%}{60}\)

\(\%Pop = 55\%\)

For Sasha

\(\%Pop = \frac{36}{78} * 100\%\)

\(\%Pop = \frac{3600\%}{78}\)

\(\%Pop = 46.2\%\)

For Kat:

\(\%Pop = \frac{40}{89} * 100\%\)

\(\%Pop = \frac{4000\%}{89}\)

\(\%Pop = 44.9\%\)

For Monica:

\(\%Pop = \frac{24}{59} * 100\%\)

\(\%Pop = \frac{2400\%}{59}\)

\(\%Pop = 40.7\%\)

From the calculation above, Michelle has the highest percentage of Pop music

5.

\(People = 80\)

\(Fortnite = 0.55\)

\(Among\ Us = 30\%\)

Required

Determine number of friends that prefer fortnite more than among us

First, we need to calculate the number of people that prefer Fortnite.

\(Fortnite = 0.55 * 80\)

\(Fortnite = 44\)

Next, we need to calculate the number of people that prefer Among Us.

\(Among\ Us = 30\% * 80\)

\(Among\ Us = 24\)

The difference is:

\(Difference = 44 - 24\)

\(Difference = 20\)

Hence, 20 more people preferred Fortnite to Among Us

6.

\(Hulk = 0.25\)

\(Iron\ Man = 12\)

\(Thor = 35\%\)

Captain America cleaned the rest

\(Total = 60\)

Number of cities by each is:

\(Hulk = 0.25 * 60\)

\(Hulk = 15\)

\(Iron\ Man = 12\)

\(Thor = 35\%\)

\(Thor = 35\% * 60\)

\(Thor = 21\)

\(Captain\ America = 60 - 15 -12 - 21\)

\(Captain\ America = 12\)

By comparison, Thor cleaned the highest number of cities

7. This question is not clear

\(Total = \$70\)

\(Glass = \$30\)

\(Each\ Cape = \$8\)

Let the number of cape be x.

We have that:

\(8 * x + 30 \leq 70\)

\(8 x +\leq 70 - 30\)

\(8 x +\leq 40\)

\(x\leq 5\)

9.

Let the first number be x and the second be y

\(x + y = 32\)

\(y = x + 5\)

Substitute x + 5 for y in the first equation

\(x + x + 5 = 32\)

10.

\(Savings = \$9\)

Earnings = $7 per hous

Total = $44

The inequality is:

\(7 * n + 9 \leq 44\)

\(7n + 9 \leq 44\)

\(7n \leq 44 - 9\)

\(7n \leq 35\)

\(n \leq 5\)

11.

Earnings = $40

Extra = $5 per lasso

Total Earnings = At least $70 daily

The inequality is:

\(40 + 5n \leq 70\)

\(5n \leq 70 - 40\)

\(5n \leq 30\)

\(n \leq 6\)

12.

\(Each\ Cake = \$0.01\)

\(Shipping = \$9.96\) per order

\(Available = \$50\) --- maximum

The inequality is:

\(10.01 * p + 9.96 \leq 50\)

\(10.01 p + 9.96 \leq 50\)

\(10.01 p \leq 50 - 9.96\)

\(10.01 p \leq 40.04\)

\(p \leq 4\)

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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Answer:

a) Options E, F, G and H are all correct.

The distribution of X can be modelled by a binomial distribution because

E. The trials are independent.

F.There are a fixed number of bids.

G. There is the same probability of success for each trial (bid).

H. The data are binary (you either win the bid or not, that is, success or failure).

b) The probability of winning exactly 1 bid = 0.4410

c) The probability that you win 1 bid or fewer = 0.7840

d) The probability that you win more than 1 bid = 0.2160

Step-by-step explanation:

Complete Question

You are bidding on three items available on an online shopping site. You think that for each bid you have a 30% chance of winning it, and the outcomes of the three bids are independent events. Let X denote the number of winning bids out of the three items you bid on.

a. Explain why the distribution of X can be modeled by the binomial distribution.

A. The trials are dependent.

B. The data are not binary.

C. Probabilities of success for trials (bids) differ for each trial

D. The number of bids varies.

E. The trials are independent

F.There are a fixed number of bids.

G. There is the same probability of success for each trial (bid)

H. The data are binary

b. The probability of winning exactly 1 bid is (Round to four decimal places as needed.)

c. Find the probability that you win 1 bid or fewer.

d. Find the probability that you win more than 1 bid.

Solution

a) A binomial experiment is one in which the probability of success doesn't change with every run or number of trials.

It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.

Hence, the correct options are

E. The trials are independent.

F.There are a fixed number of bids.

G. There is the same probability of success for each trial (bid).

H. The data are binary (you either win the bid or not, that is, success or failure).

b) Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = total number of bids available = 3

x = Number of successes required = winning exactly 1

p = probability of success = probability of winning a bid = 30% = 0.30

q = probability of failure = probability of NOT winning a bid = 1 - p = 1 - 0.30 = 0.70

P(X = 1) = ³C₁ (0.3)¹ (0.7)³⁻¹ = 0.4410 to 4 d.p.

c) The probability that you win 1 bid or fewer.

n = total number of sample spaces = total number of bids available = 3

x = Number of successes required = winning 1 or fewer bid = ≤ 1 = 0, 1

p = probability of success = probability of winning a bid = 30% = 0.30

q = probability of failure = probability of NOT winning a bid = 1 - p = 1 - 0.30 = 0.70

P(X ≤ 1) = P(X = 0) + P(X = 1)

P(X = 0) = ³C₀ (0.3)⁰ (0.7)³⁻⁰ = 0.343

P(X = 1) = 0.441 (as calculated in (b) above)

P(X ≤ 1) = 0.343 + 0.441 = 0.784

d) Probability that you win more than 1 bid

n = total number of sample spaces = total number of bids available = 3

x = Number of successes required = winning more than 1 bid = >1 = 2, 3

p = probability of success = probability of winning a bid = 30% = 0.30

q = probability of failure = probability of NOT winning a bid = 1 - p = 1 - 0.30 = 0.70

P(X > 1) = P(X = 2) + P(X = 3)

P(X = 2) = ³C₂ (0.3)² (0.7)³⁻² = 0.189

P(X = 3) = ³C₃ (0.3)³ (0.7)³⁻³ = 0.027

P(X > 1) = 0.189 + 0.027 = 0.2160

Hope this Helps!!!

The area as a product and as a sum will be (x - 5)(x + 3) and x² - 5x + 3x - 15, respectively.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The dimensions (outside parts) of the Area Model are below.

x²        - 5x

3x        - 15

Then the sum is given as,

⇒ x² - 5x + 3x - 15

Factorize the expression, then we have

⇒ x² - 5x + 3x - 15

⇒ x(x - 5) + 3(x - 5)

⇒ (x - 5)(x + 3)

The area as a product and as a sum will be (x - 5)(x + 3) and x² - 5x + 3x - 15, respectively.

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9514 1404 393

Answer:

  $51.72 each

Step-by-step explanation:

There are several ways to go at this. Let's try this one:

Marcus paid a price that was 3/4 off the original, so was 1/4 of the original price. Then the original price was 4 times what Marcus paid:

  29.79 × 4 = 119.16 . . . . . original price of 3 pants and 2 shirts

The original price of the pants was 5.24 each, so the 3 pairs originally cost ...

  5.24 × 3 = 15.72

The two shirts then account for the difference between this amount and the original cost.

  2s = 119.16 -15.72 = 103.44

  s = 51.72

The shirts were originally $51.72 each.

Answer: Step-by-step explanation:

To find the average rate of change of a function over an interval, we can use the following formula:

average rate of change = (y2 - y1)/(x2 - x1)

Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.

In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.

For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (g(3) - g(-1))/(3 - (-1))

= (9 + 18 - (1 - 6))/(4)

= 27/4

= 6.75

For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:

average rate of change = (f(3) - f(-1))/(3 - (-1))

= (2 - 2)/(4)

= 0

Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.

I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?

Answer:

2/3 x + 20/21

Step-by-step explanation:

Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line