A student randomly selects a marble from a bag with 3 red marbles , 4 blue marbles, 2 green marbles, and 5 yellow marbles. How many outcomes are in the sample space?

Answer:

We can use the formula for compound interest to solve this problem:

A = P(1 + r/n)^(nt)

where A is the future value, P is the present value, r is the interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

(a) To find the present value of the money, we need to solve for P in the formula above. We are given that A = $3000 and t = 18/12 = 1.5 years. The interest rate is 6% per year, compounded monthly, which means n = 12. Substituting these values into the formula, we get:

3000 = P(1 + 0.06/12)^(12*1.5)

Simplifying and solving for P, we get:

P = 3000 / (1 + 0.06/12)^(12*1.5)

P = $2,572.39

Therefore, the equivalent value of the money now is $2,572.39.

(b) To find the equivalent value of the money one year from now, we need to calculate the future value of $1 after one year, and then multiply it by the present value we found in part (a). The future value of $1 after one year, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*1)

FV = $1.06168

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.06168 = $2,735.92

Therefore, the equivalent value of the money one year from now is $2,735.92.

(c) To find the equivalent value of the money three years from now, we need to calculate the future value of $1 after three years, and then multiply it by the present value we found in part (a). The future value of $1 after three years, at 6% per year, compounded monthly, is:

FV = 1*(1 + 0.06/12)^(12*3)

FV = $1.19102

Multiplying this by the present value we found in part (a), we get:

$2,572.39 * $1.19102 = $3,066.63

Therefore, the equivalent value of the money three years from now is $3,066.63.

x2−1x5=(x−a)2+b2−15=(−)2+

The probability of picking a prime number is 2/3 or approximately 0.667.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Out of the given options of 2, 3, and 4, only 2 and 3 are prime numbers. Therefore, the probability of picking a prime number is:

P(prime) = number of prime options / total number of options

P(prime) = 2/3

So the probability of picking a prime number is 2/3 or approximately 0.667.

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Therefore, the volume of Prism B is 727/4 ft³ or 181 3/4 ft³ in mixed number form.

Subtract the denominator from the numerator. The quotient should be expressed as a whole number in step 2. Step 3: Enter the denominator and numerator, respectively, as the remainder and the divisor.

We can write: Using the formula for a prism's volume (V = Bh, where B is the base area):

We must determine Prism B's cross-sectional area in order to get the volume of Prism B. By dividing the height equation of prism A by its volume equation, the following result is obtained:

cross-sectional area of Prism A = (Volume of Prism A) / (height of Prism A) = (872/1 ft³) / (6 ft) = 218/3 ft²

Using the scale factor equation for height, we get:

k = (height of Prism A) / (height of Prism B) = (6 ft) / (31/12 ft) = 24/31

Using the scale factor equation for cross-sectional area, we get:

k² = (cross-sectional area of Prism A) / (cross-sectional area of Prism B) = (218/3 ft²) / (cross-sectional area of Prism B)

Solving for the cross-sectional area of Prism B, we get:

cross-sectional area of Prism B = [tex](218/3 ft^2) / k^2 = (218/3 ft^2) / (24/31)^2 = 59/3 ft^2[/tex]

Finally, substituting the height and cross-sectional area of Prism B into the volume equation of Prism B, we get:

Volume of Prism B = (cross-sectional area of Prism B) * (height of Prism B) = [tex](59/3 ft^2) * (31/12 ft) = 727/4 ft^3.[/tex]

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The value after solving mixed fraction is 32/10=3.2

A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.

The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.

according to question,

=51/10 - 19/10

=32/10

=3.2

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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.

To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.

5 1/10 can be converted to an improper fraction as follows:

5 1/10 = (5 x 10 + 1)/10 = 51/10

1 9/10 can be converted to an improper fraction as follows:

1 9/10 = (1 x 10 + 9)/10 = 19/10

Now we can subtract the two fractions:

51/10 - 19/10 = (51 - 19)/10 = 32/10

32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.

So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.

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Answer:

2/15 litre

Step-by-step explanation:

There is 1 litre in total. Max used 1/5 litre.

1 - 1/5 = 4/5 litre

Then he used 5/6 of the remaining 4/5 litre. He would have 1/6 of 4/5 litre left.

1/6 * 4/5 = 2/15 litre

or

You could do 5/6 * 4/5 to find out how much syrup he used on Sunday and then subtract that from 4/5 litre. It will give you the same answer

Answer: there is no solution

Step-by-step explanation:

The solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.

The general form of the quadratic equation is: ax² + bx + c = 0

Given that, a quadratic equation (x-5)² + 3(x-5) + 9 = 0, we need to solve it,

So, put x-5 = u

Therefore,

u² + 3u + 9 = 0

Solving using quadratic formula,

[tex]x=\frac{-b \pm \sqrt{b^2-4ac}} {2a}[/tex]

Here a = 1, b = 3 and c = 9

Therefore,

[tex]u=\frac{-3 \pm \sqrt{3^2-4(9)}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{9-36}} {2}[/tex]

[tex]u=\frac{-3 \pm \sqrt{-27}} {2}[/tex]

[tex]u=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

Put u = x-5,

Therefore,

[tex]x-5=\frac{-3 \pm 3\sqrt{3}i} {2}[/tex]

[tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

Hence, the solution of the equation is [tex]x=\frac{-7 \pm 3\sqrt{3}i} {2}[/tex]

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The  polynomial with integer coefficients and a leading coefficient of 1  is (x-6) (x-3)²  which in turn will be: f(x) = x³ - 12x² + 45x - 54

Based on the question, If the zeros of a polynomial are said to be 6, 3, and 3, one can say that the polynomial can be written in factored form such as

f(x) = (x - 6)(x - 3)(x - 3)

The to solve this, we have to multiply it:

f(x) = (x - 6) (x² - 6x + 9)

f(x) = x³ - 6x² + 9x - 6x² + 36x - 54

f(x) = x³ - 12x² + 45x - 54

Therefore, the polynomial with integer coefficients and a leading coefficient of 1  will be f(x) = x³ - 12x² + 45x - 54

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The possible rule of the polynomial function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

From the question, we have the following zeros and multiplicities that can be used to derive the rule of the function

The possible rule of the function is represented as

f(x) = a(x - zero)^multiplicity

So, we have

f(x) = a(x + 2)(x + 1)²(x - 1)²

The graph passes through (0, 1)

So, we have

a(0 + 2)(0 + 1)²(0 - 1)² = 1

This gives

2a = 1

Divide

a = 1/2

Recall that

f(x) = a(x + 2)(x + 1)²(x - 1)²

So, we have

f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

Hence, the function is f(x) = 1/2(x + 2)(x + 1)²(x - 1)²

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Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

To represent a+b using the parallelogram method,

we must draw vectors representing a and b.

The initial point of vector a is (1, 3), and its terminal point is (-4, -2). The initial point of vector b is (-4, -2), and its terminal point is (1, 3).

Using the vector tool, we then  draw the vectors a and b. We start at the initial point of each vector and select the terminal point.

Vector a: start at (1, 3) and end at (-4, -2)

Vector b: start at (-4, -2) and end at (1, 3)

We the diagonal, we start at the initial point of vector a, (1, 3), and draw a line parallel to vector b that passes through the initial point of vector b, (-4, -2). This line intersects the line parallel to vector a that passes through the initial point of vector b at point (2, 7). This point is the terminal point of the diagonal vector, which is a+b.

We use the vector tool, we can draw vector a in blue, vector b in red, and vector a+b in green.

Vector a: start at (1, 3) and end at (-4, -2) in blue.

Vector b: start at (-4, -2) and end at (1, 3) in red.

Vector a+b: start at (1, 3) and end at (2, 7) in green.

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Emilee will spend around $3,726 for her wrist surgery once her insurance company pays 70% and she meets the $371 deductible.

Calculating out-of-pocket costs for a medical expense after insurance coverage and deductibles often requires simple arithmetic.

To begin, deduct the deductible from the overall cost of the surgery: $12,791 - $371 = $12,420.

70% of the remaining cost after the deductible is calculated as follows: 70% of $12,420 = $8,694.

Total cost after insurance coverage: $12,420 - $8,694 = $3,726

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Generally, it is better to use a Line Graph if your raw data includes non-numeric values. If your raw data only has numeric values, use a Scatter Plot. You can use a Line Graph if you want to label your horizontal axis with text labels. These labels can represent evenly spaced values as days, weeks, and years.

Answer:

38 inches

Step-by-step explanation:

We can use the Law of Sines to solve for the length of side g:

sin(66°)/67 = sin(30°)/g

Cross-multiplying, we get:

g*sin(66°) = 67*sin(30°)

Dividing both sides by sin(66°), we get:

g = 67*sin(30°)/sin(66°) ≈ 38 inches (rounded to the nearest inch)

Therefore, the length of side g is approximately 38 inches.

Using limits the value of k is c √2

The limit of a function is the valuer the function tends to as the dependent variable tends to a particular value.

Given that the limit lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1, we desirte to find the value of k.

So, we proceed as follows

lim n → ∞ [x√(x + 1)[1 - √(2x + 3)]/(7 - 6x + kx²) = - 1

Factorizing out √2x, we have that

lim n → ∞ [x√(x + 1)[1 - √(2x√(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√(x + 1)√(2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Also, factorizing out √x, we have that

lim n → ∞ [x√x√(1 + 1/√x)√2x[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [x√2x√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7 - 6x + kx²) = - 1

Factorizing x² from the denominator, we have that

lim n → ∞ [√2x²√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/x²(7/x² - 6/x + k) = - 1

lim n → ∞ [√2√(1 + 1/√x)[1/√(2x - √(1 + 3/√(2x)]/(7/x² - 6/x + k) = - 1

Now substituting x = ∞ into the equation, we have that

[√2√(1 + 1/√∞)[1/√(2∞ - √(1 + 3/√(2∞)]/(7/∞² - 6/∞ + k) = - 1

[√2√(1 + 0)[0 - √(1 + 0]/(0 - 0 + k) = - 1

[√2√(1)[- √1]/k = - 1

[√2(1)[- 1]/k = - 1

-√2/k = - 1

k = -√2/-1

k = √2

So, the value of k is c √2

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When the block is cut into smaller pieces, 512 pieces of cheese remain.

A cube is a solid three-dimensional shape with 6 square faces, 8 vertices and 12 edges. It is also said to be a regular hexahedral.

The volume V of a cube  is given by the formula V = a^3, where a = the length of one side of the cube. V = 4 ^ 3 = 64 cubic meters or inches ^ 3. The volume of a cube is 64 cubic meters

The total volume of the cheese block is obtained as follows:

V = edge length³ = 8³ = 512 cubic meters

Since the volume of each piece is 1 cubic inch, the total number of pieces is obtained by dividing the total volume by the volume of each piece:

Number of pieces = V / volume per piece = 512 / 1 = 512 pieces

Therefore, when the block is cut into smaller pieces, 512 pieces of cheese remain.

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1. A  back-to-back stem-and-leaf plot for the data would be

Mowed by you          stem           mowed by your friend

       8   7   5  4            0              

       7   2   2  0            1                  9

            5   1   0           2                  7    8    9

                      0           3                  0    1     2     2   5   5   8

                                    4                  4

KEY: 3 | 1 ⇒ 31

2.  The mean for you = 14.25 and your friend 31.3. This means that your friend has a higher mean than you. The median for you is 11 and your friend is 30.5. Given that both the mean and median of your friend is higher than yours, it means that your friend mowed more lawns than you

3. The range of data for you is 26 and for your friend is 21.

To find the mean for each data set, add all the number together and divide it by the set number. For example;

4 + 5 + 7 + 8 + 10 + 12 + 12 + 17 + 20 + 21 + 25 + 30

= 171 / 12

= 14.25

To find the range for the data set, simply take the highest number of a set and minus it by the lowest number. For Example;

For your data set, it is 30 - 4 = 26

To find the median for the data sets, simply look for the number in the middle. However, in your data set, there are two middle numbers. take the sum of the two numbers and divide it by 2.

            (10 + 12) / 2 = 11

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Answer:

To calculate how much is deducted from Scott’s paycheck, we need to first find out how much his employer pays for his health insurance premium.

55% of the annual premium is covered by the employer, so we can calculate this as:

0.55 x $20,969 = $11,532.95

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium.

To find out how much is deducted from Scott’s paycheck, we need to divide the remaining 45% of the premium by the number of pay periods in a year. Since Scott is paid biweekly, he receives 26 paychecks in a year.

45% of the annual premium is not covered by the employer, so we can calculate this as:

0.45 x $20,969 = $9,437.55

To find out how much is deducted from each biweekly paycheck, we can divide $9,437.55 by 26:

$9,437.55 ÷ 26 = $363.75 (rounded to the nearest cent)

Therefore, Scott’s employer pays $11,532.95 towards his health insurance premium and $363.75 is deducted from each of his biweekly paychecks for health insurance.

Psychologist requires a sample size of at least 126 SI scores.

We may use the following calculation to get the minimal sample size required to estimate the mean SI score of smokers with a margin of error of 12 and a 90% confidence level:

[tex]n = [Z * (\sigma / E)]^2[/tex]

Where:

Z = the z-score associated with the confidence level (90%), which can be found using a z-score table or calculator.

For a 90% confidence level, Z is approximately 1.645.

σ = the population standard deviation (82)

E = the desired margin of error (12)

Plugging in the values, we get:

n = [1.645 * (82 / 12)]^2

n = 126.2

We round up to the closest integer as the sample size must be a whole number in order to guarantee that the sample size is sufficient to fulfill the required confidence level and margin of error.

Thus, n = 126 is the required minimum sample size.

In order to estimate the mean SI score of smokers with 90% confidence that the estimate is within 12 of the actual population mean, the psychologist requires a sample size of at least 126 SI scores.

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A statistical question would be:  What is the average salary of teachers in this school district?

When a question can be answered statistically, it can be done so by gathering and analysing data, for example. This particular question aims to comprehend a population or a phenomenon by using numerical data. In contrast to non-statistical questions, which are more concerned with acquiring information or opinions, statistical questions are more concerned with getting and analysing data. Statistical procedures including sampling, data analysis, and inference are frequently used to answer statistical issues.

A statistical question would be:  What is the average salary of teachers in this school district?

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The variables are as follows:

x = 4

y = 4.8

The lengths of the sides of the kites are 4.5 and 6.8 units.

A kite is a quadrilateral with 2 pairs of consecutive congruent sides. The diagonals are perpendicular in a kite.

The non vertex angles are congruent.

Therefore,

x + 0.5 = 2x - 3.5

2x - x = 0.5 + 3.5

x = 4

y + 2 = 2y - 2.8

2y - y = 2 + 2.8

y = 4.8

Hence,

length of one pair = 4 + 0.5 = 4.5 units

length of the other pair = 4.8 + 2 = 6.8 units

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A linear equation that models the relationship shown in the table is: D. y = 0.8x + 9.75

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) = (10.55 - 9.75)/(1 - 0)

Slope (m) = 0.8/1

Slope (m) = 0.8

At data point (0, 9.75) and a slope of 0.8, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 9.75 = 0.8(x - 0)  

y = 0.8x + 9.75

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

We can use the formula for compound interest to calculate the amount of interest Brian will earn:

A = P (1 + r/n)^(nt)

where:

A = the total amount after 7 years

P = the principal amount ($9,411)

r = the annual interest rate (3.48%)

n = the number of times the interest is compounded per year (52 weeks in a year, so n = 52)

t = the number of years (7)

Plugging in the values, we get:

A = $9,411 (1 + 0.0348/52)^(52*7)

A = $9,411 (1.0006692302021135)^364

A = $12,471.36

To find the amount of interest earned, we can subtract the principal amount from the total amount:

Interest = $12,471.36 - $9,411 = $3,060.36

Therefore, Brian will earn $3,060.36 in interest after 7 years. Rounded to the nearest cent, this is $3,060.37.

Based on the given data, the age of Mr. Wright currently is 30 years

If Micah is 3 years old, then Lilly is twice as old, which means that

Lilly is 2 * 3 = 6 years old.

Now we know that Mr. Wright is five times as old as his daughter, Lilly, so Mr. Wright's age is:

5 * 6 = 30 years old.

Therefore, Mr. Wright is 30 years old.

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The value of the expression when x = -1 and y = 4 is 41.

Evaluating the expression [tex]x^2[/tex]+7y+12 when x = -1 and y = 4, we get:

[tex]x^2[/tex]+7y+12 = [tex](-1)^2[/tex] + 7(4) + 12 = 1 + 28 + 12 = 41

Therefore, the value of the expression when x = -1 and y = 4 is 41.

Here is the step-by-step solution:

Substitute x = -1 and y = 4 into the expression.

Evaluate the exponent.

Multiply 7 by 4.

Add 1, 28, and 12.

The answer is 41.

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Answer:

Her rate of mowing lawns per hour is 4 lawns to one hour

Step-by-step explanation:so on a table you divide 4÷4=1 then you do the same thing for the 16÷4=4. So Oliva can mow 4 lawns per hour

The horizontal asymptote   of  the given function is 0

Given the function y = 19800/x

Vertical asymptote occurs at when f(x) = 0 where;

f(x) is the denominator of the given function.

From the expression given: f(x) = x

Since f(x) => 0, hence x = 0

To get the horizontal asymptote, we will look at the degree of the numerator and denominator.

If the degree of numerator is less than the denominator,

the horizontal asymptote will be zero. From the function, we can see that the degree of the numerator is zero (being a constant) and that of the denominator is 1.

Since 0<1, hence the horizontal asymptote is 0

x = 0, y = 0

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Answer:

Let's call the unknown number "x". According to the problem, we know that:

x * (x - 6) = 27

Expanding the left side of the equation, we get:

x^2 - 6x = 27

Subtracting 27 from both sides, we get:

x^2 - 6x - 27 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = -6, and c = -27, so:

x = (-(-6) ± sqrt((-6)^2 - 4(1)(-27))) / 2(1)

x = (6 ± sqrt(180)) / 2

x = (6 ± 6sqrt(5)) / 2

x = 3 ± 3sqrt(5)

So the two possible solutions are:

x = 3 + 3sqrt(5) ≈ 8.746

x = 3 - 3sqrt(5) ≈ -2.746

Since the problem statement doesn't specify whether the number should be positive or not, both solutions are valid.

Answer: The answer could be 9 or -3.

Step-by-step explanation: The product(multiply) of a number(x) and 6 less than a number(x-6) is 27.

x(x-6)=27

x^2-6x-27=0

(x-9) (x+3)=0

x=9 or x=-3

The number is 9 or -3.

The probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

To find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m., we need to calculate the proportion of the total possible time range between 8:00 a.m. and 8:50 a.m. that falls within the specified time interval.

The total time range between 8:00 a.m. and 8:50 a.m. is 50 minutes (8:50 - 8:00 = 50). The time interval between 8:05 a.m. and 8:45 a.m. is 40 minutes (8:45 - 8:05 = 40).

So, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is:

Probability = (Time interval between 8:05 a.m. and 8:45 a.m.) / (Total time range between 8:00 a.m. and 8:50 a.m.)

Probability = 40 minutes / 50 minutes

Probability = 0.8

Therefore, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

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