HELP
Stained glass windows come in circles, semicircles, and quarter-circles. If Flo buys 2 circular windows, 5 semicircular windows, and 20 quarter-circular windows that all have a radius of 4 feet, what is the total area of the windows purchased by Flo? Round your final result to the nearest hundredth square foot.

Area of circle: _____
Area of semicircles: _____
Area of quarter-circles: _____
Total area of pattern: _____

Answers
Area of semicircles = 125.60

Area of quarter-circles=125.6

Area of circle=50.24

Total area of pattern=238.64

Area of quarter-circles = 251.20

Area of circle =100.48

Total area of pattern = 477.28
Area of semicircles=62.8

Answer:  x is equal to 9.

Step-by-step explanation: this can be solve  by multiplying both sides of the equation by 3/8:

24 = 8/3x

(3/8) * 24 = (3/8) * (8/3x)

9 = x

a) The lateral area of a rectangular prism is 360 square units. b) The total area of a rectangular prism is 6 square units. c) The volume of is 1200 cubic units.

A prism is a three-dimensional solid consisting of two bases that are parallel and congruent and are joined by a series of parallelograms. A prism's lateral faces are all parallelograms or rectangles. On the other hand, a pyramid is a three-dimensional solid with a polygonal base and an apex. A pyramid's lateral faces are triangles that converge at the top. The perpendicular distance between the bases of a prism determines its height, whereas the distance between the apex and base of a pyramid determines its height.

a) The lateral area of a rectangular prism is given by 2h(l+w):

Substituting the values we have:

2(6)(20+10) = 360 square units

b) The total area of a rectangular prism is given by 2lw + 2lh + 2wh:

Substituting the values we have:

2(20)(10) + 2(20)(6) + 2(10)(6) = 520 square units.

c) Volume is given as V = lwh substituting the values we have:

(20)(10)(6) = 1200 cubic units.

For Cube:

a) The lateral area is give as 4s(s)

Substituting the values:

LA = 4(1)(1) = 4

b) The total area is given as 6(s)(s):

Substituting the values:

TSA = 6(1)(1) = 6 square units.

c) The volume is given as s^3:

(1)^3 = 1 cubic unit.

For the triangular prism:

a) The lateral area is given as perimeter of base multiplied by height.

The perimeter of the base is (8 + 6 + 10) = 24, and h = 8.

LA = (24)(8) = 192 square units.

b) The total area is given by area of base + the lateral area:

Area of the base triangle is:

A = 1/2(6)(8) = 24

For two triangles at the base we have: 2(24) 48

Thus, total area of the prism is 176 + 48 = 224 square cm.

c) The volume of the triangular prism is given as:

1/2(base x height) x length = 1/2(6)(8)(8) = 192 cubic cm.

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Answer: $624.24.

Step-by-step explanation:

To find the total amount of interest paid on the loan, we first need to find the total amount of money repaid over the course of 36 months.

The total amount repaid is the monthly payment multiplied by the number of months:

Total amount repaid = Monthly payment x Number of months

Total amount repaid = $79.84 x 36 = $2,874.24

To find the total amount of interest paid, we need to subtract the original amount borrowed from the total amount repaid:

Total interest paid = Total amount repaid - Original amount borrowed

Total interest paid = $2,874.24 - $2,250 = $624.24

Therefore, the total amount of interest paid on the loan is $624.24.

Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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The fraction of the panel left after cutting the hole is 11/12.

The correct answer choice is option C

Fraction left = (area of panel) - (area of hole) / (area of panel

Area of panel = 3 feet × 2 feet

= 6 square feet

Area of hole = 1 foot × ½ foot

= ½ square foot

So,

Fraction left = (area of panel) - (area of hole) / (area of panel

= (6) - (½) / (6)

= (5½) / (6)

= 11/2 ÷ 6

multiply by the reciprocal of 6

= 11/2 × 1/6

= 11/12

Ultimately, the fraction left is 11/12

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Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

The origin is the location where the two axes meet. On both the x- and y-axes, the origin is at 0. The coordinate plane is divided into four portions by the intersection of the x- and y-axes. The term "quadrant" refers to these four divisions.

We can use the slope formula to get the slopes of the lines f(x) and g(x):

slope of f(x) = (change in y)/(change in x) = (1 - (-2))/(1 - 0) = 3/1 = 3

slope of g(x) = (change in y)/(change in x) = (2 - 0)/(0 - (-4)) = 2/4 = 1/2

The slope of g(x) is 1/2, which is less than the slope of f(x), which is 3.

Therefore, the correct answer is: The slope of g(x) is less than the slope of f(x).

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A spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

To solve the question :

The volume of a sphere = 4/3 πr³

Where,

π = mathematical constant pi and

r = radius of the sphere.

Given,

radius (r) = 8 cm and

π = 3.14,

Substituting the values of π and r to the volume equation

V = (4/3) x 3.14 x 8³

V = (4/3) x 3.14 x 512

V = 2688.53 cm³ (rounding off to the nearest hundredth)

Hence, a spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.

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The correct matches for the probability of falling below the z-score are:

-0.08: 0.4681

0.63: 0.7357

-2.7: 0.0035

1.95: 0.9744

Explain probability

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability is calculated by dividing the number of favourable outcomes by the total number of possible outcomes. Probability is used in many fields, including mathematics, statistics, science, economics, and finance, to make predictions and decisions based on uncertain events.

According to the given information

To match the probability of falling below a given z-score, we need to use a standard normal distribution table or a calculator with a built-in normal distribution function. Here are the probabilities for each z-score:

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The perimeter of the figure is 37 m.

Explain perimeter

Perimeter is the distance around the edge of a two-dimensional shape, such as a polygon or a circle. It is calculated by adding the length of all the sides of the shape. Perimeter is a fundamental measure in geometry and is used to determine the amount of material needed to enclose a shape, such as fencing or paving. It is also used to compare the size of different shapes with the same perimeter.

According to the given information

The perimeter of the figure is

12+12+7.75+2+3.25 = 37m

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Answer:

-5

Step-by-step explanation:

subtract 25 by 25 and do it to the other side than the last thing to do is just divided 15 by -3 and we get -5.

PLS GIVE BRAINLIST
have a nice day

Answer:

-3x=40-25

resta los términos

-3x=15

multiplica ambos lados

3x( -1/3)=15 (-1/3)

3x(-1/3)=-5

x=-5

Answer:

To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction.

So, 7/10 divided by 1/3 can be written as:

(7/10) ÷ (1/3) = (7/10) x (3/1)

Multiplying the numerators and denominators, we get:

(7 x 3) / (10 x 1) = 21/10

Therefore, the answer is 21/10, which is an improper fraction. We can simplify it to a mixed number by dividing the denominator into the numerator.

21 ÷ 10 = 2 with a remainder of 1, so the mixed number is:

= 1 1/10

Hence, the answer is 1 1/10 or 11/10.

Step-by-step explanation:

7/10  /  (1/3)   is equal to   7/10  *  3/1   =  (7*3) / (10*1) = 21/10 = 2  1/10

The probability of picking a blue marble or a marble with an odd number is 7/9.

We can use set theory to calculate the probability of picking a blue marble or a marble with an odd number. Let B be the set of blue marbles and O be the set of marbles with odd numbers. Then, we need to calculate the probability of the union of B and O.

P(B or O) = P(B U O) = P(B) + P(O) - P(B and O)

We know that P(B) = 4/9 and P(O) = 5/9. To calculate P(B and O), we need to count the number of marbles that satisfy both conditions, i.e., they are blue and have an odd number. There are two such marbles: B1 and B3.

Therefore, P(B and O) = 2/9, and the probability of picking a blue marble or a marble with an odd number is:

P(B or O) = P(B U O) = P(B) + P(O) - P(B and O) = 4/9 + 5/9 - 2/9 = 7/9

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Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

A prism having a pentagonal base is referred to as a pentagonal prism. It has two hexagonal bases, five parallelogram faces, and seven faces. Seven faces, fifteen edges, and ten vertices make up a pentagonal prism.

The two bases of each of the seven faces—two pentagons—and the remaining five faces—parallelograms—connect the bases of the pentagons.

Given data:

surface area of pentagonal prism = 2* base area + 5*rectangle area

surface area of pentagonal prism = 2* B + 5*L*w

surface area of pentagonal prism = 2* 84.3 + 5*7*4

surface area of pentagonal prism = 168.6 + 140

surface area of pentagonal prism = 308.6 sq. ft

Thus, the total surface area of pentagonal prism is found to be 308.6 sq. ft.

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The variance of the population according to the given table is option B 41.

The spread or dispersion of a set of data around its mean is measured by variance. It has the same units as the original data and is calculated as the average of the squared deviations from the mean. Variance is a frequently used statistical term to describe the diversity or variability of a population or sample. When the variance is modest, the data points are closely grouped around the mean, whereas when the variance is great, the data points are widely dispersed.

The variance is given by the formula:

variance = (sum of squared deviations from the mean) / (number of observations)

Using the table we have sum of squared deviations from the mean:

81 + 1 + 1 + 81 = 164

variance = 164 / 4 = 41

Hence, the variance of the population according to the given table is option B 41.

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x = -3 is the vertical asymptote of the function.

A vertical asymptote of a function is a vertical line on the graph where the function approaches positive or negative infinity as the input (x-value) approaches a certain value.

To identify the vertical asymptote(s) of the rational function f(x) = (x + 4)/(2x + 6), we need to look for the values of x that make the denominator equal to zero.

So, we solve the equation 2x + 6 = 0 for x:

2x = -6

x = -3

Therefore, x = -3 is the vertical asymptote of the function.

The other answer choices (B) x = -4 and (C) y = 1/2 are not correct as they do not make the denominator of the function equal to zero. And (D) is also not correct as this function has a vertical asymptote at x = -3.

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Answer:

[tex]f(x) = \frac{(x - 1)(x - 2)(x - 6)}{(x - 1)(x - 3)(x - 5)} [/tex]

Answer: 3,45

Step-by-step explanation:

Answer:

3.45

Step-by-step explanation:

Mean is the average of the data set. To find the mean, we need to add all the numbers and divide by the amount of numbers.

{4.2, 3.5, 4.55, 2.75, 2.25}

4.2 + 3.5 + 4.55 + 2.75 + 2.25 = 17.25

17.25/5 = 3.45

The two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

What is the quadratic equation?

The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.

The zero product property can be used to solve equations that can be factored into the product of two or more expressions, where one or more of those expressions is equal to zero.

Therefore, the two equations that can be solved using the zero product property are:

3x² - 6x = 0

This equation can be factored as:

3x(x - 2) = 0

Using the zero product property, we get:

3x = 0 or x - 2 = 0

Solving for x, we get:

x = 0 or x = 2

-(x - 1)(x + 9) = 0

This equation can be factored using the difference of squares:

-(x - 1)(x + 9) = -(x² - 1² - 9x + 1x) = -(x² - 8x - 9) = 0

Using the zero product property, we get:

x - 1 = 0 or x + 9 = 0

Solving for x, we get:

x = 1 or x = -9

Therefore, the two equations that can be most appropriately solved by using the zero product property are:

3x² - 6x = 0 and -(x - 1)(x + 9) = 0.

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1. We can see that brainstorming, we discover that sports the graph represents is 100-yard dash. This is because athletes start from a stationary position and accelerate to their maximum speed, which is usually reached halfway through the race, and then slow down to a stop at the finish line.

2. The vocabulary and properties of graphs and functions do you see represented in the graph are:

A graph is a mathematical representation of a set of data or a relationship between two or more variables. It typically consists of a set of points, or vertices, connected by lines or curves, known as edges or arcs. Graphs are used to visualize and analyze data, and to model and solve real-world problems in a variety of fields, including mathematics, science, engineering, economics, and social sciences.

We see here that the vocabulary and properties of the graph shows the choice of sports as it tells us how the speed decreases as time increases.

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The complete question is:

Portfolio Option 1: Sports Graph

This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.

Brainstorm: Which of the above sports do you think the graph could represent? Why?

Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?

Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.

Answer: x2 - 4 = 0 and 4x2 = 16

Step-by-step explanation:

The income tax payable can be calculated as follows:

Taxable income = $500,000

Tax rate = 40%

Income tax payable = $500,000 x 40% = $200,000

The DTA (Deferred Tax Asset) year-end balance can be calculated as follows:

Beginning balance DTA = $20,000

Future deductible amounts = $55,000

DTA year-end balance = $20,000 + $55,000 = $75,000

The DTL (Deferred Tax Liability) year-end balance can be calculated as follows:

Beginning balance DTL = $50,000

Future taxable amounts = $45,000

DTL year-end balance = $50,000 - $45,000 = $5,000

The income tax expense can be calculated as follows:

Income tax payable = $200,000

Add: Increase in DTL = $5,000

Less: Increase in DTA = $55,000 - $20,000 = $35,000

Income tax expense = $200,000 + $5,000 - $35,000 = $170,000

The originating/reversing amount for the future taxable amount and for the deductible amount of the current year can be calculated as follows:

Future taxable amount:

Origination amount = $45,000 x 40% = $18,000

Reversing amount = $18,000

Future deductible amount:

Origination amount = $55,000 x 40% = $22,000

Reversing amount = $22,000 - $20,000 = $2,000 (since the beginning balance of DTA was $20,000)

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Expressions for the square footage of the tile Dining area, Considering only the tile floor, and not the cabinets shown in black will be (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11)

The area of a rectangle is a measure of the amount of space it occupies in two-dimensional (2D) space. It is calculated by multiplying the length of the rectangle by its width. Mathmatically,

                                     [tex]Area=length*width[/tex]

Now, Solving given problem,

The total area of the grid will be:Length of grid = 16 ft, Width of grid = 13 ft

Total area of grid = Length x Width = 16 ft x 13 ft = 208 sq ft

The area of the rectangle in the top right :Length of rectangle = 12 ft, Width of rectangle = 2 ft

Area of rectangle = Length x Width = 12 ft x 2 ft = 24 sq ft

To remove the top right rectangle from the tile dining area, subtract its area from the total area of the grid:

(Total area of grid) - (Area of rectangle in top right) = (208 sq ft -24 sq ft )= 184 sq ft

So, the expression for this calculation will be: (16 x 13) - (12 x 2) = 184 sq ft

The area of the vertical rectangles on the far left and right sides is calculated as follows:Width of vertical rectangles = 4 ft, Length of grid = 13 ft

Area of vertical rectangles = Width of vertical rectangles x Length of grid = 4 ft x 13 ft = 52 sq ft

The area of the rectangle in the top right:Length of rectangle = 12 ft, Width of rectangle = 11 ft

Area of rectangle = Length x Width = 12 ft x 11 ft = 132 sq ft

Add the areas of the vertical rectangles and the rectangle in the top right to get the total area of the tile dining area:

Area of vertical rectangles + Area of rectangle in top right = 52 sq ft + 132 sq ft = 184 sq ft

So, the expression for this calculation is: (4 x 13) + (12 x 11) = 184 sq ft

Hence, both of these expressions- (16 x 13) - (12 x 2) and (4 x 13) + (12 x 11) gives the square footage of the tile dining area based on the given information.

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The exponential function of the population is P(x) = 15000 * 1.046^x

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

Initial, a = 15000

Rate, r = 4.6%

The equation of the function is represented as

P(x) = a * (1 + r)^x

Substitute the known values in the above equation, so, we have the following representation

P(x) = 15000 * (1 + 4.6%)^x

Evaluate

P(x) = 15000 * 1.046^x

Hence, the function is P(x) = 15000 * 1.046^x

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The sample variance ratio, denoted by [tex]$\frac{S_x^2}{S_y^2}$[/tex], which follows an F-distribution.

The sample variance for a random sample of size (m) from a normal distribution with mean [tex]$\mu_X$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{x} ^2 =\frac{1}{m-1}\sum_{i=1}^{m}($X_i$-$\overline{X}$)^2[/tex]

where [tex]$X_i$[/tex] are the individual observations from the sample, and [tex]$\overline{X}$[/tex] is the sample mean.

Similarly, the sample variance for a random sample of size (n) from a normal distribution with mean [tex]$\mu_{Y} _$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:

[tex]S_{y} ^2 =\frac{1}{n-1}\sum_{i=1}^{n}($Y_i$-$\overline{Y}$)^2[/tex]

where [tex]$Y_i$[/tex] are the individual observations from the sample, and [tex]$\overline{Y}$[/tex] is the sample mean.

Provided that both samples have normal distributions with the same variance [tex]$\sigma^2$[/tex], the ratio of sample variances [tex]\frac{Sx^2}{Sy^2}[/tex] follows an F-distribution with degrees of freedom [tex]m-1$ and $n-1$[/tex], respectively.

Thus,

[tex]\frac{S_x^2}{S_y^2} $\sim$ $F(m-1,n-1)$[/tex]

where [tex]$\sim$[/tex] denotes "follows the distribution of"

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In this Venn  diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.

Let's use T to represent the set of people who like tea, M to represent the set of people who like milk, and U to represent the universal set of all 180 people. We know that:

|T| = 95 (the number of people who like tea)

|M| = 80 (the number of people who like milk)

|T ∪ M| = 180 - |T ∩ M| = 180 - 35 = 145 (the number of people who like either tea or milk)

To find the number of people who like both tea and milk, we can use the formula:

|T ∩ M| = |T| + |M| - |T ∪ M|

Substituting in the values we know, we get:

|T ∩ M| = 95 + 80 - 145 = 30

Therefore, 30 people like both tea and milk.

To represent this information in a Venn diagram, we can draw two overlapping circles to represent the sets T and M. The circle for T should contain 95 elements, and the circle for M should contain 80 elements. The overlap region between the circles should contain 30 elements. The region outside of both circles should contain 35 elements, since 35 people do not like either tea or milk. The Venn diagram would look like this:

         _______________

        /               \

       /                 \

      /         T         \

      \                   /

       \_________________/

              |

              |     30

              |

       ______/ \______

      /               \

     /                 \

    /         M         \

    \                   /

     \_________________/

In this diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.

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Answer: The type of probability illustrated here is theoretical probability, and option A correctly identifies it as such.

Theoretical probability is based on mathematical reasoning and analysis of possible outcomes. In this case, we know that there are 52 cards in a deck, and 13 of them are hearts. So, the probability of drawing a heart on the first card is 13/52. After the first card is drawn, there are 51 cards remaining in the deck, including 12 hearts. So, the probability of drawing a heart on the second card is 12/51. Continuing this process, we find the probability of drawing five hearts in a row to be:

P(heart) = (13/52) x (12/51) x (11/50) x (10/49) x (9/48) = 0.0104 or about 1.04%

This probability is based purely on mathematical reasoning and analysis of possible outcomes, and does not involve any actual experimentation. Therefore, it is an example of theoretical probability.

Step-by-step explanation:

The 95% confidence interval for the mean number of books people read is (9.403, 11.397).

A confidence interval is a range of values that is likely to contain an unknown population parameter with a certain degree of confidence, based on a sample of data.

To construct a 95% confidence interval for the mean number of books people read, we can use the formula:

CI = x ± t*(s/sqrt(n))

where x = 10.4 is the sample mean, s = 16.6 is the sample standard deviation, n = 1012 is the sample size, and t is the critical value from the t-distribution with 1011 degrees of freedom and a 95% confidence level.

Looking up the critical value from the t-distribution table with 1011 degrees of freedom and a 95% confidence level, we get t = 1.962.

Substituting the values into the formula, we get:

CI = 10.4 ± 1.962*(16.6/sqrt(1012))

Simplifying the expression, we get:

CI = 10.4 ± 0.997

Therefore, the 95% confidence interval for the mean number of books people read is (9.403, 11.397).

Interpretation: We are 95% confident that the true mean number of books people read in the population lies between 9.403 and 11.397 books. This means that if we were to repeat the survey many times and calculate the confidence interval each time, approximately 95% of the intervals would contain the true population mean.

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The 95% confidence interval for the mean number of books people read is (9.403, 11.397).

What is confidence interval?

A confidence interval is a range of values that is likely to contain an unknown population parameter with a certain degree of confidence, based on a sample of data.

According to question:

To construct a 95% confidence interval for the mean number of books people read, we can use the formula:

[tex]CI = x \pm t\times(\frac{s}{\sqrt n})[/tex]

where x = 10.4 is the sample mean, s = 16.6 is the sample standard deviation, n = 1012 is the sample size, and t is the critical value from the t-distribution with 1011 degrees of freedom and a 95% confidence level.

Looking up the critical value from the t-distribution table with 1011 degrees of freedom and a 95% confidence level, we get t = 1.962.

Substituting the values into the formula, we get:

[tex]CI = 10.4 \pm( 1.962\times\frac{16.6}{\sqrt1012})[/tex]

Simplifying the expression, we get:

CI = 10.4 ± 0.997

Therefore, the 95% confidence interval for the mean number of books people read is (9.403, 11.397).

Interpretation: We are 95% confident that the true mean number of books people read in the population lies between 9.403 and 11.397 books. This means that if we were to repeat the survey many times and calculate the confidence interval each time, approximately 95% of the intervals would contain the true population mean.

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In order to calculate the time that Charlotte took we just first have to calculate the time that Terrence took to finish the word search, that is done by multiplying the 32 minutes that Frank took by the three quartes that it took Terrence:

[tex]\text{Time}=\huge \text(\dfrac{3}{4} \huge \text)(32)[/tex]

[tex]\text{Time}=\huge \text(\dfrac{96}{4} \huge \text)[/tex]

[tex]\text{Time}=24[/tex]

So now we know that It took Terrence 24 minutes, and that Charlotte took two thirds of that time so we now just multiply that:

[tex]\text{Time}=\huge \text(\dfrac{2}{3} \huge \text)(24)[/tex]

[tex]\text{Time}=\huge \text(\dfrac{48}{3} \huge \text)[/tex]

[tex]\boxed{\underline{\bold{Time=16}}}[/tex]