Gail averages 153 points per bowling game with a standard deviation of 14.5 points. Suppose Gail's points per bowling game are normally distributed. Let X= the number of points per bowling game. Then X ∼ N ( 153 , 14.5 ) . z-score when x = 108 is _____. The mean is 153 . The z-score tell you that x = 108 is _____ standard deviations to the left of the mean.

The correlation coefficient is a statistical measure that indicates the strength and direction of the relationship between two variables.

Correlation coefficient is denoted by the symbol "r" and ranges from -1 to 1.

A correlation coefficient of 1 indicates a perfect positive correlation, where as one variable increases, the other variable also increases at the same rate.

A correlation coefficient of -1 indicates a perfect negative correlation, where as one variable increases, the other variable decreases at the same rate.

A correlation coefficient of 0 indicates no correlation between the two variables.

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Let's assume that Mr. and Mrs. Johnson bought x adult tickets and y children's tickets.

Since there are three children, we know that:

y = 3x

The total cost of the parents' tickets is 7x, and the total cost of the children's tickets is 4y. Substituting y = 3x, we get:

total cost of parents' tickets = 7x

total cost of children's tickets = 4(3x) = 12x

Therefore, the ratio of the total cost of the parents' tickets to the total cost of the children's tickets is:

(7x) / (12x) = 7/12

So the answer is 7/12, which cannot be simplified further. Therefore, the ratio is 7/12, which can be written in the form aib as 0+7/12i.

Answer: 7:6

Step-by-step explanation:

1. There are two adults (Mr. and Mrs. Jonhson) and three children. So let's make adults = y and children = x

2. Adult tickets cost $7. So we are going to multiply 7 x 2y = $14

3. Children's tickets cost $4. So we are going to multiply 4 x 3x = $12

4. The last step is to fully reduce [tex]\frac{14}{12}[/tex] = [tex]\frac{7}{6}[/tex]

5. So the answer is 7:6

The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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For an event based on order by sam for ham and coffee with different probabilities, then the probability that he will order neither ham nor coffee is equals to the 0.07.

We have sam is a regular customer at joe's diner. Let us consider two events be defined as A: sam will order ham

B: sam will order coffee

Now, the probability that sam will order ham, P( A) = 0.8

The probability that sam will order coffee, P( B) = 0.65

We have to determine the probability that he will order neither ham nor coffee.

Probability is chances of occurrence of an event. It is calculated by dividing the favourable response to total possible outcomes. Probability value always lies between 0 to 1. Apply probability law P( will order ham ) + P( will not order ham) = 1

=> Probability that sam will not order ham

[tex]P( \bar A ) [/tex] = 1 - 0.8 = 0.2

Probability that sam will not order coffee,

[tex]P( \bar A ) [/tex]= 1 - 0.65 = 0.35

Now, as we see both events A and B are independent events so, there corresponding also independent. Therefore, Probability that he will order neither ham nor coffee, [tex] P( \bar A ∩ \bar B) [/tex]

[tex]= P( \bar A) P(\bar B) [/tex]

= 0.2 × 0.35 = 0.07

Hence, required probability is 0.07.

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Answer:

-----------------------------

Standard form for the equation of a circle is:

where the center is (h, k) and the radius is r units.

Complete the square by adding missing parts of the identity:

Apply this to the given equation:

As per the standard form, the center is (h, k) = (2, - 4) and radius is r = 4 units.

The perimeter of the triangle is 23.623 units.

What is perimeter of triangle?

Finding the distance around a triangle entails determining its perimeter. The distance formula can be used to calculate the side lengths if you don't already know all of them. The simplest way to find a triangle's perimeter is to add up all of its sides' lengths.

The distance between two points (x1,y1) and (x2,y2) can be determined using the following formula: √(x₂-x₁)² + (y₂ - y₁)²

Let the given vertices are (-7, -2), (-2, -5) , and (2, 3).

Distance formula for two points is = √(x₂-x₁)² + (y₂ - y₁)²

Using the formula,

AB = √((-2)-(-7))² +((-5)-(-2))²

= √(-2+7)² + (-5+2)²

= √5² + (-3)²

= √25 + 9

= √31

Similarly, BC = √(2 - (-2))² + (3-(-5))²

= √(2+2)² + (3+5)²

= √4² + 8²

= √16+64

= √80

CA = √((-7)-2)² + (-2 + 3)²

= √(-9²) + 1

= √81+1

=√82

Perimeter of triangle = AB + BC + CA

= √31 +√81 +√82

= 5.5677 + 9 + 9.0553

= 23.623

Therefore, the perimeter of the triangle is 23.623 units.

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The system of equations that could be used to determine the number of free throws Jason made and the number of two point shots he made are: x + y = 13 and 1x + 2y = 20

Let x be the number of free throws Jason made and y be the number of two-point shots he made.

Then, we can write a system of equations based on the given information:

x + y = 13  (total number of shots made)

1x + 2y = 20  (total number of points scored)

The first equation shows Jason's total number of shots, which include both free throws and two-point attempts.

The second equation indicates Jason's total amount of points, taking into account that two-point shots are worth twice as much as free throws.

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Answer: A Rectangular prism 

The average discount that is obtained by spinning the spinner is 17.7%.

Let, the probability of landing on an even number is denoted by P(E) and the probability of landing on an odd number is denoted by P(O).

We have that the pointer lands on an even number 135 times out of 250 spins.

So, the probability that is of landing on an even number is:

P(E) = Number of times the pointer lands on an even number / Total number of spins

P(E) = 135 / 250

Since, we have the sum of probabilities of all possible outcomes must be 1, we can find the probability of landing on an odd number as follows:

P(O) = 1 - P(E)

P(O) = 1 - (135 / 250)

Now, we know that even numbers get 20% off, and odd numbers get 15% off.

We find the average discount considering these probabilities:

Average Discount = (P(E) * 20%) + (P(O) * 15%)

Average Discount = (135 / 250) * 20% + [1 - (135 / 250)] * 15%

Now, let's perform the calculations:

Average Discount = (135 / 250) * 0.20 + [1 - (135 / 250)] * 0.15

Average Discount = 0.108 + (1 - 0.54) * 0.15

Average Discount = 0.108 + 0.46 * 0.15

Average Discount = 0.108 + 0.069

Average Discount = 0.177

So, the average discount that is obtained by spinning the spinner is 17.7%.

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complete question:

A clothing store has each customer spin this spinner to reveal a discount. Even numbers get 20% off and odd numbers get 15% off. The pointer lands on an even number 135 times out of 250 spins. find the average discount obtained by spinning the spinner?

Answer:

19.25

Step-by-step explanation:

You add up all three sides which would be 10+3.25+6 to get the awnser 19.25

Answer:

[tex]3.37 \times 9 \\ = 30.33[/tex]

hope it helps

Under the direct method, Gaulle will report cash collected from customers of $35,000.cash collected from customers is determined by adding the changes in Accounts Receivable to the revenues recognized during the period.

Beginning Accounts Receivable was $6,000 and ending Accounts Receivable was $9,000, indicating that customers owed Gaulle an additional $3,000 during the year.

Revenue for the year was $38,000, which represents the total sales generated by the company during the period. To calculate the cash collected from customers, we need to subtract the change in Accounts Receivable from the revenue recognized during the period.

Therefore, the cash collected from customers for Gaulle is calculated as follows:

Cash collected from customers = Revenue - Decrease in Accounts Receivable

= $38,000 - ($9,000 - $6,000)

= $35,000

Therefore, the answer is B. $35,000.

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Answer:

240m

Step-by-step explanation:

You need to find the area of each surface.

FORMULAS

A= L × W

A= 1/2(L × W)

SIDES

Base = 12×6 = 72

Top of triangle = 6×13 = 78

Side of triangle = 5×6 = 30

Triangular side 1 = 1/2(5×12) = 30

Triangular side 2 = 1/2(5×12) 30

Now you need to add all of the surface areas together.

72+78+30+30+30 = 240

Therefore, the surface area of the triangular prism is 240m.

IM SO SORRY IF THIS DOESN'T MAKE ANY SENSE!

If Kelly has 3 bags containing 8 pieces each, and Lori has 8 bags containing 6 pieces each, then Lori have 24 candies more than Kelly.

If Kelly has 3 bags which contains 8 pieces of candy in each bag,

then Total number of candies with Kelly is = 3×8 = 24 candies,

If Lori has 8 bags which contains 6 pieces of candy in each bag,

then Total number of candies with Lori is = 8×6 = 48 candies,

So, to find how much more candy Lori has than Kelly, we need to subtract the number of pieces of candy Kelly has from the number Lori has;

The equation to find the difference in candies is written;

⇒ Difference = (total candies with Lori) - (total candies with Kelly),

⇒ Difference = 48 - 24 = 24 candies;

Therefore, Lori has 24 more pieces of candy than Kelly.

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The value of the unknown number -12.

Given that: twice a certain number is added to 10 and the result is minus 14.

Let's assume that the number we are trying to find is "x".

We can represent the statement twice this number (2x) is added to 10, and the result is -14 in an algebraic equation.

2x + 10 = -14

We can solve for x by isolating it on one side of the equation. We can start by subtracting 10 from both sides of the equation:

2x + 10 - 10  = -14 - 10

2x = -14 - 10

Simplifying the right side of the equation, we get:

2x = -24

Finally, we can solve for x by dividing both sides of the equation by 2:

2x/2 = -24/2

x = -12

Therefore, the number we are looking for is -12.

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The volume and total surface area of each shape combined is calculated below.

For cone-hemisphere shape

Volume = volume of cone + volume of hemisphere

Volume = 1/3πr²h + 2/3πr³

where r = 9/2 = 4.5 m

h = √(13² - 4.5²)      (Pythagoras)

h = 12.20 m

Volume = 1/3πr²h + 2/3πr³

Volume = (1/3 * 3.14 * 4.5² * 12.2) + (2/3 * 3.14 * 4.5³)

Volume = 449.33 m³

Surface area = curved surface area of cone + curved surface area of hemisphere

Surface area = πrl + 2πr², where l = 13 m

Surface area = (3.14 * 4.5 * 13) + (2 * 3.14 * 4.5²)

Surface area = 310.86 cm²

For hemisphere-cylinder shape

Volume = volume of hemisphere + volume of cylinder

Volume =  2/3πr³ + πr²h

where r = 22/2 = 11 ft

height of cylinder (h) = 45 - 11 = 34 ft

Volume =  (2/3 * 3.14 * 11³) + (3.14 * 11² * 34)

Volume =  15704.19 ft³

Surface area = curved surface area of hemisphere + curved surface area of  cylinder + curved surface area circular base of cylinder

Surface area =  2πr² + πr² + 2πrh

Surface area =  3πr² + 2πrh

Surface area =  (3 * 3.14 * 11²) + (2 * 3.14 * 11 * 34)

Surface area = 3488.54 ft²

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To cover the entire area of pyramid, Serena would need approximately 63.36 square inches of paper.

The area of the square base is

4.8 in x 4.8 in = 23.04 sq in

The area of each triangular face is

(1/2) x base x height = (1/2) x 4.8 in x 4.2 in = 10.08 sq in

Since there are four triangular faces, the total area of the triangular faces is

4 x 10.08 sq in = 40.32 sq in

Therefore, the total surface area of the pyramid is

23.04 sq in + 40.32 sq in = 63.36 sq in

So, it would take 63.36 square inches of paper to cover the entire pyramid.

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Answer:

Step-by-step explanation:

Firms 1's structure is in the form of the cylinder. So the formula used for the calculation of the enclosed space or volume of the cylinder is:

Volume of the cylinder = πr²h               .........(i)

where r = radius of the structure

Diameter(d) = 70ft

Given r = 70/2 = 35ft

h = Height of the structure

Given h = 60ft

By substituting the values of radius (r) and height (h) in equation (i), we get

V = π(35)²(60)ft³

V = 3.14(35)(60)ft³

V = 6597.345ft³

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The angles formed by the bisector are equal in measure, adjacent, supplementary, form a linear pair, and are congruent.

When a line bisects an angle, it divides the angle into two equal parts. The resulting angles have several properties

They have equal measures: The two angles formed by the bisector have the same degree measurement.

They are adjacent: The two angles share a common side and vertex.

They are supplementary: The sum of the two angles formed by the bisector is 180 degrees.

They form a linear pair: The two angles, together with the adjacent angle on the other side of the bisector, form a straight line or a linear pair.

They are congruent: The two angles formed by the bisector are congruent to each other.

These properties are useful in solving problems involving angle bisectors in geometry.

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I have solved the question in general, as the given question is incomplete.

The complete question is:

What are some properties of the angles formed by the bisector?

Answer: is option (3) -4x²-6.

Step-by-step explanation: First, we need to add the two given polynomials:

4x^2 - x + 1 + (-6x^2 + x - 4) = -2x^2 - 3

Now, we need to multiply this sum by 2:

2(-2x^2 - 3) = -4x^2 - 6

Therefore, the polynomial that is twice the sum of 4x^2-x+1 and -6x^2+x-4

The answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7

A linear function is defined as a function that has either one or two variables without exponents. It is a function that graphs to a straight line.

The given plot displays the distribution of the number of roses purchased per day at a grocery store. The best measure of variability for this data would be the interquartile range (IQR) since it is robust to outliers and provides a measure of the spread of the middle 50% of the data.

To calculate the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data.

From the plot, we can see that there are a total of 11 data points: one at 1, two at 2, three at 6, three at 7, two at 8, and three at 9. The median (Q2) is 7 since it is the middle value when the data are arranged in order.

To find Q1, we need to find the median of the lower half of the data. Since there is one data point below 6 and three data points at 6, the lower half of the data consists of four points: 1, 2, 6, and 6. The median of this set is (1+2)/2 = 1.5.

To find Q3, we need to find the median of the upper half of the data. Since there are two data points at 8 and three data points at 9, the upper half of the data consists of five points: 8, 8, 9, 9, and 9. The median of this set is (8+9)/2 = 8.5.

Therefore, the IQR is Q3-Q1 = 8.5-1.5 = 7.

Therefore, the answer is "The IQR is the best measure of variability, and it equals 7. because the best measure of variability for the data is the IQR, and its value is 7

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Answer:

the answer to your question is x=3

Answer:

Option A: x = 3

Step-by-step explanation:

The lowest part of the parabola has an x-value of 3.

The total balance in a year after the simple interest is A = P ( 1 + r )

Given data ,

Let the total balance in a year after the simple interest is A

Now , the multiply the initial balance by (1 + r), where r is the annual interest rate as a decimal.

In this case, the interest rate is 7%, or 0.07 as a decimal.

Therefore, Cameron should multiply his current balance by (1 + 0.07) = 1.07 to find his total balance in a year in one step.

For example, if Cameron's current balance is $10,000, his total balance after one year with simple interest would be:

Total balance = $10,000 x 1.07 = $10,700

Hence , the total balance is given by A = P ( 1 + r )

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Once you have information with two quantitative factors, x, and y, and you watch a common slant that changes heading, one good method to decide in case there's a relationship between x and y and to form a show that permits you to anticipate the anticipated esteem of y based on x is to utilize polynomial regression.

Polynomial relapse may be a sort of relapse investigation in which the relationship between the free variable (x) and the dependent variable (y) is modeled as an nth-degree polynomial. By fitting a polynomial work to the information, you'll be able to capture the common drift of the information even if it changes course and utilizes it. to foresee the anticipated esteem of y based on a given esteem of x.

polynomial relapse can be a valuable method to analyze and show information with a changing drift and give experiences into the relationship between x and y. 

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We cannot have a fraction of a person in the sample, we need to round up to the next whole number, which is 1022.

So, you will need to sample at least 1022 individuals to achieve a 95% confidence level with a margin of error no more than 3%.

This means that the correct answer among the given options is "at least 1068".

To estimate the sample size needed for survey, you can use the formula for sample size calculation in a proportion estimation problem.

The formula is:
[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]
where:
n = required sample size
Z = Z-score, which corresponds to the desired confidence level (1.96 for a 95% confidence level)
p = estimated proportion (0.35 in this case)
E = desired margin of error (0.03 in this case)
Now, let's plug the values into the formula:
[tex]n = (1.96^2 * 0.35 * (1-0.35)) / 0.03^2[/tex]
n = (3.8416 * 0.35 * 0.65) / 0.0009
n = 0.919326 / 0.0009
n ≈ 1021.473.

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The two possible sets of dimensions for the rectangular plot are:

Length = 27 meters, Width = 4 meters

Length = 4 meters, Width = 15.5 meters

Let's denote the length of the rectangular plot by L and the width by W. We know that the total length of the fencing needed is 35 m, which we can use to create an equation:

L + 2W = 35

The area of the land is 132 square meters, which we can use to create another equation:

LW = 132

We can solve the first equation for L:

L = 35 - 2W

Substituting this into the second equation, we get:

(35 - 2W)W = 132

Expanding and rearranging, we get a quadratic equation:

2W^2 - 35W + 132 = 0

We can solve for W using the quadratic formula:

W = [35 ± √(35^2 - 4(2)(132))] / (2(2))

W = [35 ± √(841)] / 4

W = [35 ± 29] / 4

Solving for W, we get two possible values:

W = 4 or W = 15.5

If W is 4 meters, then L is:

L = 35 - 2W = 27

If W is 15.5 meters, then L is:

L = 35 - 2W = 4

Therefore, the two possible sets of dimensions for the rectangular plot are:

Length = 27 meters, Width = 4 meters

Length = 4 meters, Width = 15.5 meters

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Jow will need to pay a commision of $7.50. The total amount charged by the broker will be $17.50

Joes current portfolio is worth $50,000

A purchase price one share =  $15

He wants to purchase 50 shares of a company's stock

Using unitary method the cost of 50 shares would be,

C = 50 × 15

C = $750

Since his portfolio is less than $100000 the amount chanrged by the broker would be equal to the 1% commision plus fees per trade.

First we find the commision.

1 percent of $750

= 1/100 × 750

= $7.5

And the fees per trade = $10

So, the total amount charged by the broker = $10 + $7.5

                                                                     = $17.5

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Find the complete question below.

Volume of the square prism is 200 cm³

Surface area of the square pyramid is 55 cm²

Total volume is 212.5 cm³

The base of the square prism is a square with sides of 5 cm. The height of the prism is 8 cm. Therefore, the surface area of the square prism is:

Surface area of one face of the square prism = (5 cm x 8 cm) = 40 cm²

There are 6 faces in a cube, therefore total surface area of the square prism = 6 x 40 cm² = 240 cm²

Volume of the square prism = (5 cm x 5 cm x 8 cm) = 200 cm³

The base of the square pyramid is also a square with sides of 5 cm. The slant height of the pyramid is 3 cm. The height of the pyramid can be found using the Pythagorean theorem:

Height² = slant height² - (1/2 base length)² = 3² - (1/2 x 5)² = 9 - 6.25 = 2.25

Height = √2.25 = 1.5 cm

Surface area of the square pyramid = (0.5 x base perimeter x slant height) + base area = (0.5 x 20 cm x 3 cm) + (5 cm x 5 cm) = 30 cm² + 25 cm² = 55 cm²

Volume of the square pyramid = (1/3 x base area x height) = (1/3 x 5 cm x 5 cm x 1.5 cm) = 12.5 cm³

The total surface area of the decomposable solid is:

Total surface area = Surface area of square prism + Surface area of square pyramid = 240 cm² + 55 cm² = 295 cm²

The total volume of the decomposable solid is:

Total volume = Volume of square prism + Volume of square pyramid = 200 cm³ + 12.5 cm³ = 212.5 cm³

The cost of materials includes the cost of metal for the sculpture, silicone for filling the sculpture, and paint for painting the sculpture.

The cost of metal for the sculpture is:

Cost of metal = (Total surface area x Cost per 100 cm²) = (295 cm² x $12.25/100 cm²) = $36.14

The cost of silicone for filling the sculpture is:

The volume of the decomposable solid is 212.5 cm³

The cost of silicone is $0.25 per cm³

Cost of silicone = (Volume of sculpture x Cost per cm³) = (212.5 cm³ x $0.25/cm³) = $53.13

The cost of paint for painting the sculpture is:

The total surface area of the decomposable solid is 295 cm²

The cost of paint is $0.75 per 10 cm²

Cost of paint = (Total surface area x Cost per 10 cm²) = (295 cm² x $0.75/10 cm²) = $22.13

Therefore, the total cost of materials for the sculpture is:

Total cost of materials = Cost of metal + Cost of silicone + Cost of paint = $36.

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Answer: Assuming a significance level of 0.05 for each hypothesis test, the probability of committing a Type I error (rejecting the null hypothesis when it is actually true) in any given test is 0.05.

Therefore, the expected number of Type I errors in 1,900 hypothesis tests is:

Expected number of Type I errors = (0.05) x (1,900) = 95

So, we would expect to commit a Type I error about 95 times in 1,900 hypothesis tests, assuming the null hypothesis were true.

Step-by-step explanation: