Elise and her dad are planning to attend the state fair. An adult ticket is $21.00. The price of an adult ticket is $10.00 more than 2/3 the of a student ticket. Write an equation to determine how much Elise will pay for a student ticket ​

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

Given,

Number of smokers; Sample size, n = 40

Mean of the sample, μ = 172.5

Standard deviation, σ = 119.5

We have to find the 90% confidence interval estimate of the mean cotinine level of all smokers.

Here,

The confidence interval is given as;-

x − E < μ < x + E

E is the margin of error.

Margin of error,

E = zα/₂ σ/√n

E = 1.644854 119.5/√40

E = 31.07887

Then,

The confidence interval is;

x − E < μ < x + E

141.4211 < μ < 203.5789

That is,

The 90% confidence interval estimate of the mean cotinine level of all smokers is 141.4211 < μ < 203.5789

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An exponential equation for the growth of the balance in her account is \(10(1.06)^t\).

Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.

Compound Interest =\(P(1+r/n)^rt\)

We have been given that Quincy has $10 in a savings account. The interest rate is 6%, compounded annually.

The compound interest will be;

Compound Interest =\(P(1+r/n)^rt\)

\(10(1+6/100)^t\\\\10(1+ 0.06)^t\\\\10(1.06)^t\)

Hence, an exponential equation for the growth of the balance in her account is \(10(1.06)^t\).

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The probability of selecting two orange markers is 2/6 * 1/5 = 1/15.

What is non-replacement event?

Components that have not been altered typically have content that is present within the document, whereas elements that have been replaced typically have content that is present outside of the document.

Given that there are 3 green, 1 purple, and 2 orange markers.

Total number of markers is (3 + 1 + 2) = 6.

The probability of an event is the ratio of the number of outcomes of a favorable event to the total number of outcomes.

The probability that the first marker is orange is 2/6 = 1/3.

After picking the number of markers that left is (6 - 1) = 5.

The number of orange marker that left is 2 - 1 = 1.

The probability that the second marker is orange is 1/5.

The probability of selecting two orange markers is (1/3) × ( 1/5) = 1/15.

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Answer:

Step-by-step explanation:

Question 1:

The best measure of center for the given data is the median, which is equal to 7. This is because the data is skewed and has some outliers, which could heavily impact the mean. The median is the middle value when the data is arranged in order, and it is less sensitive to outliers compared to the mean.

Answer: The median is the best measure of center, and it equals 7.

Question 2:

The appropriate measure of center for the given data is the median of 49. This is because the data is skewed, with a long tail towards the higher end, and there are some outliers present. The median is less sensitive to outliers and better represents the center of skewed data compared to the mean.

Answer: The median of 49 is the most accurate measure of center to use.

Question 3:

The appropriate measure of variability for the given data is the interquartile range (IQR), which is equal to 6. The IQR is a good measure of variability for skewed data because it is not affected by extreme values or outliers, and it gives a sense of the spread of the middle 50% of the data.

Answer: The IQR is the best measure of variability, and it equals 6.

Question 4:

The appropriate measure of variability for the given data is the range, which is equal to 29 (49 - 20). The range is a good measure of variability for small datasets and provides an idea of the spread of the data.

Answer: The range is the best measure of variability, and it equals 29.

Question 5:

The best measure of variability for the given data is the interquartile range (IQR), which is 1.5 for Player A and 3.5 for Player B. A smaller IQR suggests more consistent data as the middle 50% of the data is less spread out, and there are fewer outliers.

Answer: Player A is the most consistent with an IQR of 1.5.

Question 6:

The appropriate measure of center for the given data is the median because there are outliers present. The median is less sensitive to outliers and provides a better representation of the central tendency of the data.

Answer: The median is the best measure of center because there are outliers present.

Question 7:

The appropriate measure of center for the given data is the median, which is equal to 11. The data is skewed, and there are outliers present, which could heavily impact the mean. The median is less sensitive to outliers compared to the mean and provides a better representation of the central tendency of the data.

Answer: The median is the best measure of center, and it equals 11.

The probability that at most two students will join the sports club is 0.7499.

A simple way to calculate the probability of this experiment is explained below.

Given that experience has shown that twenty percent of the new students who enroll at Unisa also join the institution's sports club. Therefore, the probability of joining a sports club P (A) = 0.2 (twenty percent), and the probability of not joining P (A') = 0.8 (one minus 0.2).

The question is to find the probability that at most two students will join the sports club. Therefore, we need to find the probability of 0, 1, or 2 students joining the sports club.

That is P (0) + P (1) + P (2).

The probability of 0 students joining a sports club: P (0) = (¹⁴C₀) (0.2)⁰(0.8)¹⁴ = 0.8¹⁴ = 0.0563.

The probability of 1 student joining a sports club: P (1) = (¹⁴C₁) (0.2)¹ (0.8)¹³ = 0.2682.

The probability of 2 students joining a sports club: P (2) = (¹⁴C₂) (0.2)² (0.8)¹²= 0.3559.

Therefore, P (0) + P (1) + P (2) = 0.0563 + 0.2682 + 0.3559 = 0.6804. Hence, the probability that at most two students will join the sports club is 0.6804. Therefore, the correct option is option B, 0.7499.

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Answer:

32

Step-by-step explanation:

p=sample proportion

p=number of defective parts/size of sample = 4/25

Estimate:

(sample proportion)x(size of population) = (4/25)x(200)=32

fish tested = 5x5=25

fish population = 40x5=200

Answer:

Check the attachment.

The correct answer is 2 (C) - 2 days is the total slack for activity F. To determine the total slack for activity F, we need to calculate the slack for each activity in the network. Slack refers to the amount of time an activity can be delayed without affecting the project completion time.

1. First, let's draw the network using the information provided:
  - A is the start node and G is the stop node.
  - Activity A has a duration of 5 days and has no predecessor.
  - Activities B, C, and D have durations of 8, 7, and 6 days respectively, and their predecessors are A.
  - Activity E has a duration of 9 days and its predecessors are B, C, and D.
  - Activity F has a duration of 10 days and its predecessors are B, C, and D.
  - Activity G has a duration of 5 days and its predecessors are E and F.

                 A
                /|\
               / | \
              /  |  \
             B   C   D
              \  |  /
               \ | /
                \|/
                 E
                 |
                 F
                 |
                 G

2. Now, let's calculate the slack for each activity:
  - Slack is calculated by subtracting the earliest start time of an activity from the latest start time without delaying the project completion time.
  - The earliest start time for activity F is 17 days.
  - The latest start time for activity F is 19 days (project completion time is 22 days).
  - Total slack for activity F = latest start time - earliest start time = 19 - 17 = 2 days.

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The area of a square can be found by using the following expression:

where "A" is the area and "l" is the length of each side of the square. The square on this problem has an area of 9 cm², so we can find the sides by replacing A for 9 on the expression above.

To solve it we need to take the square root on both sides of the equation.

Each side of the square has a length of 3 cm, so the sides are 3 cm x 3 cm.

Answer:

y = -3

Step-by-step explanation:

3x + 4y = -6   then,   3x = -4y - 6,     x = (-4y - 6)/3

5x + 2y = 4

substitute for x:

5(-4y - 6)/3 + 2y = 4

simplify:

(-20y - 30)/3 = 4 - 2y

-20y - 30 = (3)(4 - 2y)

-20y - 30 = 12 - 6y

-14y = 42

y = -3

check:

5x + 2(-3) = 4

5x = 10

x = 2

3(2) + 4(-3) = -6

6 - 12 = -6

-6 = -6

5(2) + 2(-3) = 4

10 - 6 = 4

4 = 4

Answer:

Step-by-step explanation:

5x - 3x -1 = -1

2x - 1 = -1

      +1     +1

2x = 0

/2     /2

x = 0

If two angles are supplementary, then

the sum of their measures is 180°.

So if the measure of an angle is 77°,

the measure of its supplement is 103°.

We can find the measure of its supplement by taking 180 minus the measure of the original angle which in this case is 180 - 77 or 103°.

Answer:

then the other angle measures _1_0_3_.

In space, there can be infinitely many planes that are perpendicular to a given line at a given point on that line.

The correct answer is Option D.

The key concept here is that a plane is defined by having at least three non-collinear points.

When a line is given, we can choose any two points on that line, and then construct a plane that contains both the line and those two points. By doing so, we ensure that the plane is perpendicular to the given line at the chosen point.

Since we can select an infinite number of points on the given line, we can construct an infinite number of planes that are perpendicular to the line at various points.

Thus, the correct answer is D. infinitely many planes can be perpendicular to a given line at a given point in space.

The correct answer is Option D.

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A right triangle with 45 degree angles mean bot the height and the base are the same, so Y would be 9.

The hypotenuse, which is labeled x is the length of the side multiplied by the square toot of 2.

Answer: X = 9√2

Answer:

12 - 4 m

Simplify: -4(m -3)

Step-by-step explanation:

1:  Solve the expression by using the distribute property

2: Simplify -4(m -3)

3: Done

Answer: 12 - 4 m

Hope this helps.

To determine the sample size necessary for this study, we use the formula: n = (Z^2 * p * q) / E^2. The necessary sample size is approximately 1091.

Where:
- n = sample size
- Z = Z-score for the desired confidence level (98% confidence level corresponds to a Z-score of 2.33)
- p = estimated proportion (based on the information given, p = 0.8)
- q = 1 - p
- E = desired margin of error (3 percentage points)

Plugging in the values:

n = (2.33^2 * 0.8 * 0.2) / 0.03^2
n = 806.67

Rounding up to the nearest whole number, we get a sample size of 807. Therefore, the researcher needs to survey at least 807 women to be 98% confident that the proportion of women who wear shoes that are too small is within 3 percentage points of the true proportion.

To determine the necessary sample size for this study, we can use the formula for sample size calculation in proportion estimation:

n = (Z^2 * p * q) / E^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, p is the estimated proportion, q is the complement of the proportion (1 - p), and E is the margin of error.

In this case, we have:
- Confidence level: 98%, which corresponds to a Z-score of 2.33 (from the standard normal distribution table)
- Estimated proportion (p): 80% or 0.80
- Complement of the proportion (q): 1 - 0.80 = 0.20
- Margin of error (E): 3 percentage points or 0.03

Now, we can plug these values into the formula:

n = (2.33^2 * 0.80 * 0.20) / 0.03^2
n ≈ 1090.65

Since we need to round to the nearest whole number, the necessary sample size is approximately 1091.

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Answer:

Step-by-step explanation:

Square Area = l × l or l²

we use the inverse formula

l = √A

l = √240000

l = 489.8 cm ( you can round to 490cm)

Given the volume of the box is 100 cm^3

And to made the box we need to cut a square measuring 4 centimeters on a side from a square piece of cardboard.

so, the height of the box = 4 cm

so, the volume = height * area of the base

100 = 4 * area of the base

Area of the base = 100/4 = 25 cm^2

so, the side length of the base of the box =

so, the lenght of the a side of the original square = 5 + 2*4 = 5 + 8 = 13 cm

Answer:

121cm −25πcm ≈42.46cm

Step-by-step explanation:

First, calculate the area of the whole figure, including the unshaded area.

(The area of a rectangle is the length times the width.)

Next, calculate the area of the inner figure.

π×5cm×5cm=25πcm

Finally, subtract the area of the inner circle from the area of the outer rectangle.

Answer: The range of the function is

Consider the provided information.

The plumber charges a fixed cost of $80 plus an additional cost of $45 per hour.

Let plumber works for x hours, then the required linear function will be:

The plumber works a maximum of 8 hours per day.

That means the minimum value of x is 0 and maximum value of x is 8.

We need to find the range of the function.

Range of the function is the set of y values.

Substitute x=0 in above function,

Now substitute x=8 in above function.

Hence, the range of the function is

An equation that describes this function in slope-intercept form is y = -6x - 1.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (-7 - 5)/(1 + 1)

Slope (m) = -12/2

Slope (m) = -6

At data point (-1, 5) and a slope of -6, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -6(x + 1)

y - 5 = -6x - 6

y = -6x - 1

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The terms with "x" cancel out, and we're left with:

0 = 12

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

Let's denote the number of slices with both pepperoni and mushrooms as $x$. We are given that there are 6 slices with pepperoni and 10 slices with mushrooms.

Since every slice has at least one topping, the total number of slices is 12. We can break down the slices into the following categories:

Slices with only pepperoni: 6 slices

Slices with only mushrooms: 10 slices

Slices with both pepperoni and mushrooms: $x$ slices

Slices with neither pepperoni nor mushrooms: 12 - (6 + 10 + x) slices

We know that the total number of slices is 12, so we can write an equation:

6 + 10 + x + (12 - (6 + 10 + x)) = 12

Simplifying the equation, we have:

16 + x - (16 + x) = 12

The terms with "x" cancel out, and we're left with:

0 = 12

This equation is not possible to satisfy. Therefore, there must be an error or inconsistency in the given information. Please check the information provided again.

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Given the picture attached, we can use the Pythagorean Theorem to solve it:

Where a and b are the legs on the right triangle and c hypotenuse.

Hence:

ANSWER

b = 24

we have

Simplify

Group terms

therefore

Step-by-step explanation:

This equation does not describe the situation.

Let x be the number of donuts I made.

x-25= 40

(because there is 25 lesser cookies than donuts.

Answer: No; x-25=40

Step-by-step explanation:

40=x-25

cookies equals 25 less than donuts

because donuts is 25 less than cookies

donuts = 65

total = 40 + 40+65=145

Answer:

n-5

 2

Steps:

subtract n ny 5 and then hind half of the difference.

Answer:

13, 14, 15

Step-by-step explanation:

Let x = age of one of the siblings

Since the age of the siblings are consecutive integers, the age of the next sibling would be x + 1 and the age of the third sibling would be x + 2

x +( x +1) + (x +2) = 42

3x + 3 = 42

collect like terms and solve for x

x = 13

The age of the first sibling is 13

The age of the second sibling is x + 1 = 13 + 1 = 14

The age of the third sibling is x + 2 = 13 + 2 = 15

\(\quad \huge \quad \quad \boxed{ \tt \:Answer }\)

\(\qquad \tt \rightarrow \:y-6 = 3(x + 2) \)

____________________________________

\( \large \tt Solution \: : \)

Equation of line in point - slope form :

\(\qquad \tt \rightarrow \:y-y_1 = m(x - x_1)\)

Here :

\(\qquad \tt \rightarrow \:y - 6 = 3(x - ( - 2))\)

\(\qquad \tt \rightarrow \:y - 6 = 3(x + 2)\)