A fair six-sided die will be rolled fifteen times, and the numbers that land face up will be recorded. Let x¯1 represent the average of the numbers that land face up for the first five rolls, and let x¯2 represent the average of the numbers landing face up for the remaining ten rolls. The mean μ and variance σ2 of a single roll are 3. 5 and 2. 92, respectively. What is the standard deviation σ(x¯1−x¯2) of the sampling distribution of the difference in sample means x¯1−x¯2?

Jay has 7 $100 bills in his wallet.

Let's assume the number of $50 bills as x. So, in terms of x, the number of $100 notes can be represented as x - 5.

Now, the total amount contributed by $50 notes is $50x.

And the total amount contributed by $100 bills is $100*(x-5).

Since the total amount of money in his wallet is $1300, we can write an equation:

$50x + $100*(x-5) = $1300

Simplifying this equation, we get:

$50x + $100x - $500 = $1300

$150x = $1800

x = 12

So, Jay has 12 $50 bills in his wallet.

Using the earlier equation, the number of $100 bills can be found:

x - 5 = 12 - 5 = 7

Therefore, Jay has 7 $100 bills in his wallet.

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The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

Each element of a set (referred to as the domain) is mapped by a rule known as a function to a particular element of this other set (called the range). A function is, in other words, a connection between two subsets in which every member of the domain has a unique relationship to every element of the range. One popular approach to write a function is via function notation, which entails writing the function name surrounded by the incoming signal in parentheses, as in the following example: f (x). For instance, the formula f(x) = 2x + 1 takes the input x and produces the result 2x + 1.

given,

The fundamental quadratic function f(x) = x² serves as the parent function for g(x) = (x + 3)².

Since the argument of the function (x + 3) is x shifted left by 3 units, the graph of f(x) is horizontally displaced to the left by 3 units.

Given that the coefficient of the squared term is 1, the graph of the resulting function is shifted up by a factor of 1.

As a result, the transformation can be represented as a 3 unit horizontal shift and a 1 unit vertical stretch.

The resulting graph of g(x) will resemble the graph of f(x), but it will be stretched vertically and pushed leftward by three units.

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Unfortunately, there is no way to answer this question without more information.

We would need to know the amount of the ATM withdrawal, as well as the starting balance before the withdrawal, in order to calculate the ending balance.

For example, if the starting balance was $1500 and the withdrawal was for $50, the ending balance would be $1450.

However, if the starting balance was $1300 and the withdrawal was for $50, the ending balance would be $1250.

Without this information, we cannot determine the correct answer.

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Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment.

to find the business hours of work, Let's start by defining the variables given in the problem:

The initial cost of equipment is $175.

Stevie charges $12 per hour for cleanup.

Stevie wants to make at least $1200.

The number of hours worked is represented by h.

Now, we can set up an equation to solve for h:

Total earnings - Total cost = Desired profit

We can express the total earnings as the product of the hourly rate and the number of hours worked:

Total earnings = $12h

The total cost includes the initial cost of equipment plus any additional costs incurred during cleanup:

Total cost = $175 + additional costs

Since we don't know the value of the additional costs, we'll leave it as a variable.

Substituting these expressions into the equation, we get:

$12h - ($175 + additional costs) = $1200

Simplifying the equation, we get:

$12h - $175 - additional costs = $1200

$12h - $1375 = additional costs + $1200

$12h - $1375 = additional costs

Now we have an equation that relates the number of hours worked to the additional costs incurred during cleanup. We want to find the minimum value of h that satisfies this equation, since Stevie wants to make at least $1200.

To do this, we need to estimate the additional costs incurred during cleanup. Let's assume that Stevie spends an average of $4 per hour on additional costs (e.g., gasoline, trash bags, etc.). Then, the equation becomes:

$12h - $1375 = $4h + $175

Simplifying further, we get:

$8h = $1200

h = 150

Therefore, Stevie will need to work at least 150 hours to make at least $1200 after accounting for the initial cost of equipment and the estimated additional costs incurred during cleanup.

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Trapezoid 1. Has one pair of parallel sides.

Parallelogram 2. Has two pairs of parallel sides and its opposite sides are equal.

Square 3. Is a parallelogram and four right angles and four equal sides.

Rhombus 4. A parallelogram and four equal sides (a slanted square)

Rectangle 5. A parallelogram that has four right angles and it's opposite sides are parallel.

1. Trapezoid: A trapezoid has one pair of parallel sides, while the other two sides are non-parallel. The parallel sides are called bases, and the non-parallel sides are called legs.

2. Parallelogram: A parallelogram has two pairs of parallel sides and its opposite sides are equal. The opposite angles are also equal, and the consecutive angles are supplementary.

3. Square: A square is a parallelogram with four right angles and four equal sides. It is a special case of both a rectangle and a rhombus, as it has all their properties.

4. Rhombus: A rhombus is a parallelogram with four equal sides, which can be thought of as a slanted square. It has opposite equal angles, and its diagonals are perpendicular bisectors, dividing the rhombus into four congruent right-angled triangles.

5. Rectangle: A rectangle is a parallelogram that has four right angles, and its opposite sides are parallel. The opposite sides are also equal, and its diagonals are congruent, bisecting each other at right angles.

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Based on the cost and revenue function, if they want to make a profit, the range of pulp in tons per day that they should produce is between 152.6 and 152.8 tons per day.

To find the range of pulp in tons per day that will generate profit, we need to set the profit function equal to zero and solve for x. The profit function P(x) is given by:

P(x) = R(x) - C(x)

Substituting the given revenue and cost functions, we get:

P(x) = -3x^2 + 1000x - 400

Setting P(x) = 0, we can solve for x using the quadratic formula:

x = [-b ± sqrt(b^2 - 4ac)] / 2a

Plugging in the values from our profit function, we get:

x = [-(1000) ± sqrt((1000)^2 - 4(-3)(-400))] / 2(-3)

Simplifying, we get:

x = [1000 ± sqrt(1000000 + 4800)] / 6

x = [1000 ± sqrt(1004800)] / 6

x ≈ 152.7 or x ≈ 55.6

Since we're looking for the range of pulp in tons per day that will generate profit, we only want the positive solution, which is approximately 152.7 tons per day. Therefore, the company should produce between 152.6 and 152.8 tons per day to generate profit, rounded to the nearest tenth of a ton.

Note: The question is incomplete. The complete question probably is: A paper pulp company has discovered their cost and revenue functions for each day: C(x) = 2x^2 - 250x + 525 and R(x) = -3x^2 + 750x + 125, where x is the amount of pulp in tons. If they want to make a profit, what is the range of pulp in tons per day that they should produce? Round to the nearest tenth of a ton which would generate profit.

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Answer:

$1.01

Step-by-step explanation:

We Know

A 2-quart carton of pineapple juice costs $8.08

1 quart = 4 cups

2 quarts = 8 cups

So, 8 cups of pineapple juice cost $8.08.

What is the price per cup?

We Take

8.08 / 8 = $1.01

So, the price per cup is $1.01

The original price of the novel is $21.5

The first step is to write out the parameters given in the question

Last year, Gloria buys a novel for $18.70

This price is with a discount of 15% form the original price

The original price of the novel can be calculated as follows

15/100 × 18.70

= 0.15 × 18.70

= 2.805

The next step is to add 2.805 to the price of the novel last year($18.70)

= 18.70 + 2.805

= 21.5

Hence the original price of the novel before the addition of the discount is $21.5

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The house is currently 6 years old.

It is mentioned that when the mortgage is completely paid off for Mark and Lynne's house, it will be 3 times as old as it is now. They have 12 years left on the mortgage.

Let's denote the current age of the house as x. When the mortgage is paid off, the house will be x + 12 years old (since they have 12 years left on the mortgage). At that point, the house will be 3 times its current age, so we can write the equation:

x + 12 = 3x

Now we can solve for x:
12 = 2x
x = 6

So, the house is currently 6 years old.

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6d^2 - 51d + 24

that's it

...............................

[tex] \sf \longrightarrow \: \frac{2n - 1}{3} = \frac{n + 2}{2} \\ [/tex]

[tex] \sf \longrightarrow \: 2( 2n - 1) = 3(n + 2) \\ [/tex]

[tex] \sf \longrightarrow \: 4n - 2 = 3n +6 \\ [/tex]

[tex] \sf \longrightarrow \: 4n = 3n +6 + 2\\ [/tex]

[tex] \sf \longrightarrow \: 4n - 3n= 6 + 2\\ [/tex]

[tex] \sf \longrightarrow \: 1n= 6 + 2\\ [/tex]

[tex] \sf \longrightarrow \: n= 8\\ [/tex]

[tex] \longrightarrow { \underline{ \overline{ \boxed{ \sf{\: \: \: n= 8 \: \: \: }}}}} \: \: \bigstar\\ [/tex]

Answer:

Step-by-step explanation:

To determine the number of additional days that would make the cost equivalent for both Heather's Moving and Newton Rent-a-Truck, we can set up an equation:

Heather's Moving: 10 + 8x
Newton Rent-a-Truck: 80 + x

To find the point at which the costs are equal, we can set the equations equal to each other:

10 + 8x = 80 + x

Now, we can solve for x (additional days):

7x = 70
x = 10

So, the costs would be equivalent after 10 additional days. To find the total cost, we can plug the value of x back into either equation:

Total cost = 10 + 8(10) = 10 + 80 = $90.

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Both the chess and checkers group have the same range.

The box plots range for the ages of club members in the chess and checkers group are given. Based on the box plots, it appears that both groups have similar ranges, and it is difficult to determine which group has a greater range.

The range is a measure of variability that indicates the difference between the smallest and largest values in a dataset. In the chess group, the smallest value is 18, and the largest value is 20, which gives a range of 2. In the checkers group, the smallest value is 10, and the largest value is 20, which also gives a range of 10.

Although the difference between the smallest and largest values in the checkers group is greater than that in the chess group, the box plots suggest that the checkers group has more outliers than the chess group. An outlier is a data point that is significantly different from other observations in a dataset. The presence of outliers can increase the range of a dataset.

Therefore, despite the larger difference between the smallest and largest values in the checkers group, the presence of outliers makes it difficult to determine which group has a greater range. Overall, the box plots show that both groups have similar ranges, but the checkers group has more variability in the form of outliers.

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a. The slope and intercept of the least-squares line are -0.752 and 88.761, respectively.

b. The linear model may be useful for predicting ozone levels from relative humidity, but only to a limited extent. The R-squared value of 0.22 indicates that only 22% of the variation in ozone levels can be explained by relative humidity.

Additionally, the 95% prediction interval for a new observation (20.86, 66.37) is relatively wide, which suggests that the model may not be very precise in its predictions.

c. To predict the ozone level for a day when the relative humidity is 50%, we plug in x = 50 into the regression equation: Ozone = 88.8 - 0.752(50) = 53.8 ppb.

d. The correlation between relative humidity and ozone level can be found by taking the square root of the R-squared value, which gives us a correlation coefficient of 0.47.

This indicates a moderate positive correlation between relative humidity and ozone levels.

e. To find a 90% confidence interval for the mean ozone level for days where the relative humidity is 60%, we use the formula:

Mean ozone level ± (t-value)*(SE Fit)/sqrt(n), where the t-value is obtained from a t-distribution with n-2 degrees of freedom and a 90% confidence level.

For n = 120 and a 90% confidence level, the t-value is approximately 1.66. Plugging in the values, we get: 43.62 ± 1.66*(1.2)/sqrt(120), which simplifies to (42.39, 44.85).

f. To determine if a predicted ozone level of 80 ppb is reasonable when the relative humidity is 60%, we can calculate the 95% prediction interval for a new observation with x = 60: 43.62 ± 2.064*(11.43) = (21.18, 66.06).

Since the predicted value of 80 ppb falls outside of this range, it is not a reasonable prediction.

A more reasonable range of predicted values would be the 95% prediction interval, which gives us a range of (21.18, 66.06).

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The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

To determine the simple interest rate charged per monthly payment on the flat screen television, please follow these steps:

1. Calculate the total amount paid in monthly payments: 24 payments * $80 = $1920.
2. Subtract the down payment: $1920 - $100 = $1820.
3. Subtract the original cost from the total amount paid: $1820 - $1600 = $220. This is the total interest paid.
4. Divide the total interest by the number of monthly payments: $220 / 24 = $9.1667 interest per month.
5. Calculate the interest rate per monthly payment: ($9.1667 / $1600) * 100 = 0.5735% per month.

The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

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By increasing their recycling by 500 pounds per month, the school conserves 4,800 gallons of water in a year.

Determine the ratio of water conserved per pound of paper recycled:

8 gallons of water are saved for every 10 pounds of paper recycled.

Calculate the water saved for each pound of paper:

8 gallons/10 pounds = 0.8 gallons/pound.

Find the increase in paper recycled per month:

500 pounds/month.

Calculate the water saved per month:

[tex]500 $ pounds/month \times  0.8 $ gallons/pound = 400 $ gallons/month.[/tex]

Calculate the water saved in a year:

[tex]400 $ gallons/month \times  12 months = 4,800 $ gallons/year.[/tex]

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The approximate length of the base of the triangle is 5 units

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object. The area of a triangle is expressed as;

A = 1/2 bh

The hexagon is divided into six equal triangles.

The area of the hexagon is 65 units²

Therefore, the area of the triangle = 65/6

= 10.83

Area of a triangle = 1/2 b h

height = 4.3 units

10.83 = 1/2 × 4.3 × b

4.3b = 10.83 × 2

4.3b = 21.66

divide both side by 4.3

b = 21.66/4.3

b = 5.04

therefore the approximated value of the base is 5 units.

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The closest measurement to the circumference of the parachute in feet is 78.54 feet. The calculation was done by multiplying the radius by 2π (the constant pi, approximately equal to 3.14), which gives the circumference of a circle is 78.54 feet.

The circumference of the parachute can be calculated using the formula

C = 2πr

where r is the radius of the parachute.

Given that the radius of the parachute is 12.5 feet, we can substitute this value in the formula and calculate the circumference

C = 2πr

C = 2π(12.5)

C ≈ 78.54 feet

Therefore, the circumference of the parachute is closest to 78.54 feet.

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--The given question is incomplete, the complete question is given

" Which measurement is closest to the circumference of circumference of the parachute in feet if radius is 12.5.  "--

The vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

Since the directrix is a horizontal line, the axis of the parabola is vertical. Therefore, the vertex form of the equation of the parabola is:

r = a(y - k)^2 + h

where (h, k) is the vertex of the parabola and "a" is a constant that determines the shape and orientation of the parabola.

Since the focus is (3,-5), the vertex of the parabola is halfway between the focus and the directrix. The directrix is 6 units above the vertex, so the vertex is (3,1).

We can use this information to write the vertex form of the equation:

r = a(y - 1)^2 + 3

To find the value of "a", we need to use the distance formula between the vertex and the focus:

distance = |y-coordinate of focus - y-coordinate of vertex| = 6

| -5 - 1 | = |-6| = 6

Using the definition of the parabola, the distance from the vertex to the focus is also equal to 1/(4a). Therefore:

1/(4a) = 6

a = 1/(4*6) = 1/24

Substituting this value of "a" into the vertex form equation, we get:

r = (1/24)(y - 1)^2 + 3

Therefore, the vertex form of the equation of the parabola is:

r = (1/24)(y - 1)^2 + 3

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The remaining trigonometric functions are:

sin (θ) = 3/√34

cos (θ) = 5/√34

csc(θ) =  (√34)/3

sec (θ) = (√34)/5

cot(θ) = 5/3

Trigonometry is a branch of mathematics that deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

Since tan θ = 3 /5

Recall: tan = opposite/adjacent. Thus, opposite = 3, adjacent = 5

hypotenuse = √(3²+5²) = √34

Therefore, the remaining trigonometric functions are

sin (θ) = 3/√34

cos (θ) = 5/√34

csc(θ) =  (√34)/3     (csc (θ) = 1/sin (θ))

sec (θ) = (√34)/5     (sec(θ) = 1/cos (θ))

cot(θ) = 5/3       (cot(θ) = 1/tan (θ))

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Cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

We can use the trigonometric identity cos(180 - x) = -cos(x) to find cos(165) in terms of cosine of an acute angle.

Since 165 = 180 - 15, we have:

cos(165) = cos(180 - 15) = -cos(15)

To express cos(15) in terms of sine and cosine of an acute angle, we can use the following trigonometric identities:

sin(2x) = 2sin(x)cos(x) and cos(2x) = cos^2(x) - sin^2(x)

Let's take x = 7.5, which is half of 15 (the acute angle):

sin(15) = 2sin(7.5)cos(7.5)

cos(15) = cos^2(7.5) - sin^2(7.5)

Now, we can solve for cos(15):

cos(15) = cos^2(7.5) - sin^2(7.5)

= (1 - sin^2(7.5)) - sin^2(7.5)

= 1 - 2sin^2(7.5)

Therefore, we have:

cos(165) = -cos(15)

= -[1 - 2sin^2(7.5)]

= -1 + 2sin^2(7.5)

So, cos(165) in terms of sine and cosine of an acute angle is -1 + 2sin^2(7.5).

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Answer:Therefore, the total number of players on the team is 21.

Step-by-step explanation:Let's start by using algebra to represent the information given in the problem.

Let p be the total number of players on the team.

The number of players who chose water is given as 14.

This is also equal to 2/3 of the total number of players, so we can write:

14 = (2/3) * p

To solve for p, we can isolate it on one side of the equation by multiplying both sides by the reciprocal of 2/3, which is 3/2:

14 * (3/2) = (2/3) * p * (3/2)

21 = p

The value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.

∵ ΔJLM is a right triangle, as ∠MJL=90°

∴ tan(∠JML)= JL/JM            [∵ tan∅=perpendicular/hypotenuse]

⇒ tan(51°)=JL/14

⇒ JL=14×tan(51°)

       = 14×1.23

       = 17.29

∴ JL=17.29

Again, ΔJKL is a right triangle, with ∠JKL=90°

∴ cos(∠JLK)=KL/JL              [∵ cos∅=base/hypotenuse]

⇒cos(72°)= KL/17.29

⇒KL=17.29×cos(72°)

       = 17.29×0.309

        = 5.34

∴ KL=5.34

Hence, the value of KL is 5.34.

Also, tan(∠JLK)=KJ/KL

⇒tan(72°)=JK/5.34

⇒JK=5.34×tan(72°)

       = 5.34×3.077

       = 16.434

∴ JK=16.434

And, cos(∠JML)=JM/ML

⇒cos(51°)=14/ML

⇒ML=14/cos(51°)

        =14/.629

        =22.25

∴ ML=22.25

Hence, the value of sides are KL=5.34, JK=16.434, JL=17.29 and ML=22.25.

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The statements regarding the median and the quartiles are given as follows:

a. True.

b. True.

c. False.

The ordered data-set in this problem is given as follows:

7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 13.

Hence:

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The approximate value of x using the newton method is 0.7

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

[tex]\frac{x}{x^2+1}-\sqrt{1-x}[/tex]

Also, we have the function f(x) to be

[tex]f(x) = x(x^2+1)^{-1} -\sqrt{1-x}[/tex]

And we have the differentiated function to be

[tex]f'(x) = \frac{1}{x^2+1} - \frac{2x^2}{(x^2 + 1)^2} + \frac{1}{2\sqrt{1-x}}[/tex]

The value of x using the newton method is given as

[tex]x_n = x_{n-1} - \frac{f(x_{n-1})}{f'(x_{n-1})}[/tex]

Set [tex]x_{n-1}[/tex] = 0

So, we have

x₁ = 0 - -1/1.5 = 0.67

x₂ = 0.67 - undefined = undefined

So, we have

x₁ = 0.67

When approximated, we have

x = 0.7

This means that the value of x using the newton method is 0.7

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