Given the following sample: 7, 9, 18, 22, 27, 29, 32, 40
1. Find the range of this data.
2. Find the interquartile range.
3. Compute the variance and the standard deviation of the data. 4. Compute the mean deviation.
5. Compute the median deviation.

Answer:

V=418.67 ft³

Step-by-step explanation:

Answer:

418.67 ft³

Step-by-step explanation:

This question is really just asking you to solve for the volume of the object.

Let's identify some shapes that we recognize.

I see a sphere and a cylinder.

First, let's find the volume of a sphere!

V = (4/3) π r³

V = (4/3) π (r=8ft / 2 = 4ft)³

V= 267.95 ft³

Then, let's find the volume of the cylinder!

V= h π r²

V = (12ft) π (r=4ft / 2 = 2ft)²

V= 150.72 ft³

Finally, let's add the two volumes together.

267.95 ft³ + 150.72 ft³ = 418.67 ft³

By answering the presented question, we may conclude that As a result,  linear equation Deshaun spent $2.40 on each movie and $6.20 on each video game.

In algebra, a linear equation has the form y=mx+b. The slope is denoted by B, while the y-intercept is denoted by m. Because y and x are variables, the preceding sentence is sometimes referred to as a "linear equation with two variables." Bivariate linear equations are two-variable linear equations. Linear equations may be found in various places: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When an equation has the form y=mx+b, where m represents the slope and b represents the y-intercept, it is said to be linear. A linear equation is one that contains the formula y=mx+b, with m signifying the slope and b denoting the y-intercept.

Let us denote the cost of renting a movie as "m" and the cost of renting a video game as "v."

We may deduce the following from the problem:

3m + 2v = 16

5m + 6v = 42

Using the elimination approach, we can solve this system of equations. To begin, multiply equation 1 by 3 to remove the variable "m":

[tex]9m + 6v = 48 \\-10m - 12v = -84 \\-1m - 6v = -36\\m = 6v - 36 \\3(6v - 36) + 2v = 16\\20v = 124\\v = 6.2\\m = 6(6.2) - 36\\m = 2.4[/tex]

Thus the cost of renting a movie is $2.40.

As a result, Deshaun spent $2.40 on each movie and $6.20 on each video game.

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The interest rate is approximately 15.14%.

The interest yοu earn οn interest is knοwn as cοmpοund interest. Simple maths can be used tο demοnstrate this: if yοu have $100 and it earns 5% interest annually, yοu will have $105 at the end οf the first year.

We can use the fοrmula fοr cοmpοund interest:

[tex]A = P (1 + r/n)^{(nt)[/tex]

where:

A = final amount

P = initial principal (starting balance)

r = interest rate (in decimal form)

n = number of times interest is compounded per year

t = time (in years)

Using the information given in the problem, we have:

P = $312.50

A = $1250

t = 9 years

Substituting these values into the formula, we get:

[tex]1250 = 312.50 (1 + r/n)^{(n*9)[/tex]

Dividing both sides by 312.50, we get:

[tex]4 = (1 + r/n)^{(n*9)[/tex]

Taking the ninth root of both sides, we get:

[tex](1 + r/n)^n = 1.167[/tex]

As n approaches infinity (continuous compounding), the left side of the equation approaches [tex]e^r[/tex], where e is the mathematical constant approximately equal to 2.71828. Therefore, we can rewrite the equation as:

[tex]e^r = 1.167[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(e^r) = ln(1.167)[/tex]

Using the property that [tex]ln(e^x) = x[/tex], we simplify the left side to:

r = ln(1.167)

Using a calculator, we find:

r ≈ 0.1514

Therefore, the interest rate is approximately 15.14%.

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Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

To write a quadratic function to represent the height h of the acrobat t seconds after the jump, we can use the following formula:

[tex]h(t) = -16t^2 + vt + h0[/tex]

Where h0 is the initial height of the acrobat, which is 25 feet, and v is the initial vertical velocity, which is 4 ft/s. Plugging in these values, we get:

[tex]h(t) = -16t^2 + 4t + 25[/tex]

To find how long it will take for her to land safely on the net, we need to find the time at which h(t) = 5. In other words, we need to solve the equation:

[tex]-16t^2 + 4t + 25 = 5[/tex]

Simplifying this equation, we get:

[tex]-16t^2 + 4t + 20 = 0[/tex]

Dividing both sides by -4, we get:

[tex]4t^2 - t - 5 = 0[/tex]

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

[tex]t = (-b ± \sqrt(b^2 - 4ac)) / 2a[/tex]

Where a = 4, b = -1, and c = -5. Plugging in these values, we get:

[tex]t = (1 ± \sqrt(1 + 4(4)(5))) / 8[/tex]

Simplifying this equation, we get:

[tex]t = (1 ± 9) / 8[/tex]

So, the two solutions are:

[tex]t = 1 and t = -5/4[/tex]

Since we are only interested in the positive solution, the time it will take for her to land safely on the net is:

t = 1 second.

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The statement that is not true about perpendicular lines is:

"Perpendicular lines are rotated 90° clockwise around the origin into lines that are parallel."

What are perpendicular lines?

Perpendicular lines are lines that intersect at a right angle (90 degrees).

A 90° clockwise rotation around the origin interchanges the x and y-coordinates and changes the sign of the new x-coordinate. So, if a point (x,y) is rotated 90° clockwise around the origin, it becomes the point (y,-x).

Now, let's consider the statement about perpendicular lines:

"Perpendicular lines are rotated 90° clockwise around the origin into lines that are still perpendicular."

This statement is actually true. A 90° clockwise rotation around the origin preserves the angle between two lines, so if two lines are perpendicular before the rotation, they will still be perpendicular after the rotation.

Therefore, the statement that is not true about perpendicular lines is:

"Perpendicular lines are rotated 90° clockwise around the origin into lines that are parallel."

This statement is false because a 90° clockwise rotation around the origin does not turn perpendicular lines into parallel lines. Instead, perpendicular lines are still perpendicular after the rotation, as mentioned above.

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Answer:

The measure of the angle is 22 degrees.

Answer: Kate's video game costs $38.40.

Step-by-step explanation: Kate's video game costs 20% more than Lori's game, which means Kate's game costs $32 + (20% of $32) = $32 + $6.40 = $38.40. Therefore Kate's video game costs $38.40.

Kate's video game costs $38.40.

To find out, we can first calculate 20% of $32 to get the amount of the increase:

20% of $32 = 0.20 x $32 = $6.40

Then we can add that amount to the original cost of $32 to get Kate's total cost:

$32 + $6.40 = $38.40

May I please have a Brainliest? I put a lot of thought and effort into my answers, so I would really appreciate it!

Answer:

56.552 m²

Step-by-step explanation:

Recall the equation for the area of a circle;

A = πr²

r of smaller circles = 3m

r of larger circle = 3m x 2 = 6m

Area of each smaller circle: 28.274 m²

Area of the larger circle: 113.1 m²

To find the area of the shaded region, take the area of the larger circle - the area of the smaller circle(s).

113.1 m² - 2(28.274 m²) = 56.552 m²

Answer:

The area of the shaded region is 56.55 m² rounded to the nearest hundredth.

Step-by-step explanation:

From inspection of the given diagram, the radius of the two congruent unshaded circles is 3 m.

As the two congruent unshaded circles touch each other and touch the circumference of the larger circle, the radius of the larger circle is the diameter of one of the unshaded circles, i.e. 6 m.

To calculate the area of the shaded region, subtract the areas of the congruent unshaded circles from the area of the larger circle.

The formula for the area of a circle is πr², where r is the radius.

Therefore:

[tex]\begin{aligned}\textsf{Area of shaded region}&=\textsf{Area of larger circle}-2(\textsf{Area of unshaded circle})\\&=\pi \cdot 6^2-2(\pi \cdot 3^2)\\&=36\pi-2(9\pi)\\&=36\pi-18\pi\\&=18\pi\\&=56.5486677...\\&=56.55\;\sf m^2\;(nearest\;hundredth)\end{aligned}[/tex]

Therefore, the area of the shaded region is 56.55 m² rounded to the nearest hundredth.

By answering the presented question, we may conclude that As a result, equation the area above the x-axis and below the curve t2 + 4t + 2, y = e-t with 0 t 2 is roughly 18.49 square units.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.

[tex]t = (-4 ± √(4^2 - 412))/2*1\st = (-4 + √12)/2\st = (-4 + 2√3)/2\\t = (-4 + 2√3)/2 = -2 + √3\\[/tex]

We can now integrate the difference between the curve and the x-axis as t increases from 0 to 2:

[tex]Area = ∫[0,2] (e^-t - (t^2 + 4t + 2)) dt[/tex]

For the first term, we may use integration by parts to get:

[tex]Area equals [-e-t - 1/2(t2 + 4t + 2)2 + 2(t2 + 4t + 2)]\\Area = (-e^-2 - 1/2(18 + 16√3)^2 + 2(18 + 16√3)) - (-1 - 2) (-1 - 2)\\Area = -e^-2 + 17 + 16√3 ≈ 18.49[/tex]

As a result, the area above the x-axis and below the curve t2 + 4t + 2, y = e-t with 0 t 2 is roughly 18.49 square units.

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All the conditions for inference are met, and we can proceed with constructing a confidence interval for the difference in proportions.

The technique of assessing the outcome and drawing conclusions from data with random variation is known as statistical inference. Additionally known as inferential statistics. Applications of statistical inference include hypothesis testing and confidence intervals.

To check the conditions for inference, we need to verify the following:

1. Randomness condition: The problem states that both samples were selected randomly, so this condition is met.

2. Independence condition: Since each household is sampled independently from each other, this condition is met.

3. Large Counts Condition: We need to check if the sample sizes are large enough to use normal approximation. The expected counts for each category should be at least 10.

For households with school-aged children:

For households without school-aged children:

Since both expected counts are greater than 10, the Large Counts Condition is met.

Therefore, all the conditions for inference are met, and we can proceed with constructing a confidence interval for the difference in proportions.

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Answer:

$1,620

Step-by-step explanation:

If you are looking for a way to make some money, you might be tempted by the offer of a purchase that has a positive expectation. But before you jump into it, you should know what expectation really means and how to calculate it. Expectation is not the same as the actual outcome of a purchase. It is just an average of what you can expect to get in the long run, based on the probabilities of different outcomes. Sometimes you might get more than the expectation, sometimes less, and sometimes nothing at all. For example, suppose you have a chance to buy a lottery ticket that costs $7,200 and has a 50% chance of winning $9,000, a 10% chance of winning nothing, and a 40% chance of losing your money. How do you know if this is a good deal or not? You can use the formula for expectation to find out:

Expectation = (50% x $9,000) + (10% x $0) + (40% x -$7,200)

Expectation = (0.5 x 9,000) + (0.1 x 0) + (0.4 x -7,200)

Expectation = 4,500 + 0 - 2,880

Expectation = 1,620

The expectation of this purchase is $1,620. This means that on average, you can expect to make $1,620 from this purchase in the long run. But this does not mean that you will always make $1,620 every time you buy the ticket. Sometimes you might win $9,000 and be very happy. Sometimes you might lose $7,200 and be very sad. And sometimes you might win nothing and be very bored. The expectation is just an average of all these possible outcomes.

So what does this mean for your decision? Well, it depends on how much you value risk and reward. If you are a risk-taker who likes to gamble and doesn't mind losing money sometimes, then you might go for the purchase with a positive expectation. After all, you have a chance to make more money than you spend in the long run. But if you are a risk-averse person who prefers to play it safe and avoid losses, then you might stay away from the purchase with a positive expectation. After all, you have a chance to lose money or break even in the short term.

The choice is yours. But remember: expectation is not reality. It is just a mathematical tool to help you evaluate your options. Don't let it fool you into thinking that you know what will happen in the future. The only thing that is certain is uncertainty, and luckily this is just Mathematics!

✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧

Answer:

Step-by-step explanation:

38,704.29

i hope its right

The water bill for the given service period is: $384.30

Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations. and a single variable. Usually, the variable we will use represents an unknown quantity especially in a real-life scenario.

We are given the parameters as:

Jack's previous meter reading = 34,765 ccf

Jack's  present water reading = 36,900 ccf

Cost per ccf of water

Difference in water reading = 36900 - 34765

Difference = 2135 ccf

Thus:

Water bill for service period = 0.18 * 2135

= $384.30

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The original cost of the deck chair is equal to $34.

In Economics and Mathematics, a tax can be defined as the involuntary fees that are levied on individuals or business organizations (companies or firms) by the government of a particular country, in order to generate revenues that can be used to fund public projects, institutions and activities.

Assuming the original cost is denoted by the variable x.

Next, we would determine the original cost of the deck chair by using the following mathematical equation (formula);

Original cost + sales tax rate = total cost

x + 0.08x = 36.72

x + 0.08x = 36.72

1.08x = 36.72

x = 36.72/1.08

x = $34.

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Answer:

cos 30° = 9√3 / d

d = 18 cm

r = d/2 = 18/2 = 9 cm

A = πr² = π•9² = 81π cm² or 254.47 cm²

To serve two chocolate-dipped strawberries to each of the 350 guests, you should buy about 21.875 pounds of strawberries.

There are some straightforward adjustments you need to make if your recipe calls for a pint  of fresh strawberries. A pint weighs around 3/4 pounds . So, you would require about 525 pounds of strawberries to feed 700 visitors.

Assume that two strawberries covered in chocolate weigh 1 ounce each. One strawberry therefore weighs 1/2 ounce.

By dividing the weight of one strawberry by the total quantity of strawberries required, we can calculate the total weight of strawberries required:

Strawberries' total weight = (one strawberry's weight) x. (total number of strawberries needed)

Total strawberries required = (number of guests) x (number of strawberries per guest)

The total quantity of strawberries required is: Assuming that there will be 350 guests and that everyone will receive two chocolate-dipped strawberries:

350 multiplied by two equals 700 strawberries in total.

The total amount of strawberries required is thus:

350 ounces of strawberries total weight is (half an ounce each strawberry) multiplied by 700 strawberries.

Since there are 16 ounces in a pound, the total weight of strawberries must be divided by 16 to convert to pounds:

strawberries weigh 21.875 pounds total (350 ounces divided by 16 ounces per pound).

For each of the 350 guests to receive two chocolate-covered strawberries, you should buy about 21.875 pounds of strawberries.

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The table of values of the equation y = 4x + 2 is added below

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

y = 4x + 2

To create a table for the line y = 4x + 2 where x is between 1 and 3, we simply substitute values for x within the given range and solve for y.

x y

1 6

2 10

3 14

Therefore, when x is between 1 and 3, the corresponding values of y for the line y = 4x + 2 are 6, 10, and 14.

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Answer:

6 ft 9 ins and 7 ft 3 ins.

Step-by-step explanation:

If one piece is x feet long the the other is x + 0.5 feet long. So:

x + x + 0.5 = 14

2x = 13.5

x = 6.75 ft.

So the 2 pieces are 6.75 and 7.25 ft long

= 6 ft 9 ins and 7 ft 3 ins,

The standard deviation of the sampling distribution of sample means is 4.5.

What is standard deviation?

Standard deviation is a statistical measure that is used to quantify the amount of variability or dispersion of a set of data values around their mean or average. It is calculated as the square root of the variance, which is the average of the squared differences from the mean.

The standard deviation of the sampling distribution of sample means (also known as standard error) is given by:

σ/√n

where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get:

9/√4 = 4.5

Therefore, the standard deviation of the sampling distribution of sample means is 4.5.

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The required volume of the container to the nearest cubic centimeter with a radius of 5 centimeters and a height of 5 centimeters is approximately 131 cubic centimeters.

We are given that the volume of the container varies jointly with the square of its radius, r, and its height, h. This can be expressed mathematically as:

[tex]V = k * r^2 * h[/tex]

where V is the volume of the container, r is the radius, h is the height, and k is a constant of proportionality.

To find the value of k, we can use the given values for the height, radius, and volume of the container:

[tex]V = k * r^2 * h\\616 = k * 7^2 * 12\\k = 616 / (7^2 * 12)\\k = 1.047[/tex]

Now we can use this value of k to find the volume of a container with a radius of 5 cm and a height of 5 cm:

[tex]V = k * r^2 * hV = 0.708 * 5^2 * 5V = 130.875[/tex]

Therefore, the volume of the container to the nearest cubic centimeter with a radius of 5 centimeters and a height of 5 centimeters is approximately 131 cubic centimeters.

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Answer/Solution

x is x = 1/432.

Step-by-step explanation:

Hope This Helps!

The probability that a randomly selected car is silver and has air conditioning is 23.81%.

The probability that a car is silver and has air conditioning will take the form :

P( Silver ∩ Air conditioning ) = P(Silver ) + P(Air conditioning) - P(Silver ∪ Air conditioning)

The individual probabilities would be:

P (Silver ) = 18/63

P ( Air conditioning ) = 57/63

P (Silver ∪ Air conditioning) = 60/63

So then the probability is:

P( Silver ∩ Air conditioning ) = (18/63) + (57/63) - (60/63)

= (18 + 57 - 60)/63

= 15/63

= 5/21

= 23.81%

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Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

A bookstore had 90 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 1/6 of what remained. The bookstore now has 50 copies left.

The problem involves figuring out how many copies of a magazine a bookshop still has after selling a certain percentage of its initial stock over two days. We can deal with the issue by taking the following actions:

Take into account the problem's estimate of the bookshop's initial stock of 90 copies.

Multiply the starting amount by 1/3 to get the number of copies sold yesterday by the bookshop, which is 30.

To determine the number of copies still available at the bookshop, which is 60, subtract the total number of copies sold from the number of copies sold yesterday.

Increase the excess number of duplicates by 1/6 to get the quantity of duplicates sold today at the bookshop.

The final number of copies available at the bookshop, 50, can be determined by subtracting the number of copies sold today from the number of copies that are still available.

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The parametrization of C, given the line segment would be r(t) = (3t, 4t).

Using the parametrization to evaluate the expression gives 41.67.

To find the parametrization of the line segment from (0, 0) to (3, 4). We can use the following formula:

r(t) = (1 - t)A + tB, where A and B are the endpoints of the line segment, and t is the parameter ranging from 0 to 1.

A = (0, 0)

B = (3, 4)

r(t) = (1 - t)(0, 0) + t(3, 4)

r(t) = (3t, 4t)

Now, we have the parametrization of the line segment C: r(t) = (3t, 4t).

To evaluate the integral ∫_{C} (x² + y²) ds. We will need to calculate the derivative of r(t) with respect to t:

dr(t)/dt = (3, 4)

Now, find the magnitude of the derivative:

||dr(t)/dt|| = √(3² + 4²) = √(9 + 16) = √25 = 5

x² + y² = (3t)² + (4t)² = 9t² + 16t² = 25t²

Set up the integral:

∫_{C} (x² + y²) ds = ∫_{0}^{1} 25t²(5) dt = 125 ∫_{0}^{1} t² dt

Integrate with respect to t:

125 [t^3/3] |_{0}^{1} = 125(1/3 - 0) = 125/3

The value of the integral ∫_{C} (x² + y²) ds is 125/3.

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Answer:

Step-by-step explanation:

200.00 division ➗️ 66

a 5 line ad costs $32. Expressing this as an ordered pair, we have (5, 32).

What is an Equations?

Equations are mathematical statements with two algebraic expressions on either side of equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.

We are given that the cost of placing an ad x lines long is given by y = 4x + 12.

To find the cost of a 5 line ad, we can substitute x = 5 into the equation:

y = 4x + 12

y = 4(5) + 12

y = 20 + 12

y = 32

Therefore, a 5 line ad costs $32. Expressing this as an ordered pair, we have (5, 32).

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Answer:

Step-by-step explanation:

A because its graph

The inequality 6 > 5n + 5 + 4 is equivalent to n < -3/5.

What is inequality?

Inequality in math refers to a relationship between two values that are not equal. Inequality is typically represented using mathematical symbols, such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

For example, if we have two numbers, a and b, we can say that a is greater than b by writing a > b. Conversely, we can say that b is less than a by writing b < a. We can also express that a is greater than or equal to b by writing a ≥ b, or that b is less than or equal to a by writing b ≤ a.

The inequality 6 > 5n + 5 + 4 can be simplified by combining like terms on the right side of the inequality:

6 > 5n + 9

We can further simplify this inequality by subtracting 9 from both sides:

-3 > 5n

Finally, we can divide both sides by 5 to solve for n:

-3/5 > n

Therefore, the inequality 6 > 5n + 5 + 4 is equivalent to n < -3/5.

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Answer:

None of these answers are correct

Step-by-step explanation:

arc length =0/360×2pir

38pi=34/360×2×pi×r

38=1496r/2520

cross multiply

1496r=38×2520

1496r=95760

divide both sides by 1496

1496r/1496=95760/1496

r=64.01

C=2pir

C=2×22/7×64.01

C=402.35in