The box plot below represents some data set. What is the interquartile range (IQR) of the data? 20 40 E 60 80 E 100​

The percentile for each z-score is solved

a) z = -0.47 , P₁ = 32.84%

b) z = 2.24 , P₂ = 98.89%

Given data ,

To find the percentile corresponding to a given z-score, we can use a standard normal distribution table or a calculator that can compute the cumulative distribution function (CDF) of the standard normal distribution.

The CDF gives the probability that a value from a standard normal distribution is less than or equal to a given z-score.

a) For z = -0.47, we can use a standard normal distribution table or a calculator to find the percentile. Let's assume that the percentile corresponding to z = -0.47 is P₁

P₁ = Percentile for z = -0.47

Using a standard normal distribution table or a calculator, we find that P₁ is approximately 32.84%. This means that about 32.84% of individuals scored at or below a z-score of -0.47.

b) For z = 2.24, we can use a standard normal distribution table or a calculator to find the percentile. Let's assume that the percentile corresponding to z = 2.24 is P₂

P₂ = Percentile for z = 2.24

Using a standard normal distribution table or a calculator, we find that P₂ is approximately 98.89%. This means that about 98.89% of individuals scored at or below a z-score of 2.24.

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Hence ,the sphere does not fill up 230.92 cubic centimeters of space inside the cylinder.

Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

The volume of the sphere can be calculated as Volume of sphere = [tex]\frac{4}{3} \pi r^3,[/tex]

where r is the radius of the sphere.

According to question, r = 6 cm,

so,Volume of sphere = [tex]\frac{4}{3} \pi 6^3,[/tex] = 904.78 [tex]cm^3[/tex] (rounded to two decimal places).

The volume of the cylinder can be calculated as

Volume of cylinder =[tex]\pi r^2 h[/tex] , where r is the radius of the cylinder and h is its height.

According to question,r = 6 cm and h = 12 cm, so V of cylinder = [tex]\pi(6 cm)^2(12 cm)[/tex] = 1,135.70 [tex]cm^3[/tex] (rounded to two decimal places).

The sphere is placed inside the cylinder, so it will take up some space. The amount of space it does not fill up is equal to the volume of the cylinder minus the volume of the sphere:

Volume of  sphere not filled = Volume of cylinder - V of sphere = 1,135.70 [tex]cm^3[/tex] - 904.78[tex]cm^3[/tex] = 230.92 [tex]cm^3[/tex] (rounded to two decimal places).

Therefore, the sphere does not fill up 230.92 cubic centimeters of space inside the cylinder.

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Answer:

61.0

Step-by-step explanation:

I searched it for you

Answer:

Step-by-step explanation:

[tex]\frac{4(x+9)(x-4)^{2}(x+2) }{(x-3)(x+5)^{2} (x+2)}[/tex]

The only think i'm unsure of is the square on bottom. I know the exponents need to add up because there is a horizontal asymptote vs. slant. Everything else is right

4 on top is for the HA

x+9 is for going through x

x-4 touches

x+2 on top and bottom is hole

x-3 and x+5 is VA

Answer: the additional discount amount is $61.56 and the additional discount rate is approximately 41%.

Step-by-step explanation: The following text has been given for academic rewriting. Provided:

The identified monetary value assigned to a particular item or service, commonly referred to as the list price, is reported to be $152.

Discount 1 involves a reduction of thirty percent.

The second discount availed equals a fifteen percent reduction in price.

The objective of this study is to determine.

The currency amount specified in the document indicating the seller's listed cost for goods or services rendered is referred to as the present invoice price.

The supplementary reduction in price value and percentage.

The proposed resolution to the given problem is as follows:

Initially, we shall ascertain the cost subsequent to the initial reduction:

The equation to determine the price after a discount is expressed as Price after Discount 1 = List price - Discount 1 multiplied by the List price.

The modified pricing display, following the application of a discount, can be computed using the formula: Price after Discount 1 = $152 - 0.3 x $152.

The price subsequent to the application of a discount, denoted as discount type 1, may be expressed as the difference between the initial price of $152 and the discount amount of $45.6.

The residual cost subsequent to the implementation of a discount of 1 amounts to $106.4 in this instance.

Subsequently, the subsequent step involves determining the price subsequent to the application of the second discount.

The mathematical formula for calculating the price after the second discount, denoted as "Price after Discount 2," is derived by deducting the product of the discount amount represented by "Discount 2" and the initial price after the first discount, "Price after Discount 1," from the latter. This can be represented as: Price after Discount 2 = Price after Discount 1 - (Discount 2 x Price after Discount 1)

The post-discount price can be expressed as $106.4 minus 15% of $106.4.

The discounted price, denoted as Price after Discount 2, may be represented as the difference between $106.4 and $15.96, yielding a value of $90.44.

The cost subsequent to deduction 2 is equivalent to $90.44.

Consequently, the extant amount on the invoice stands at $90.44.

To determine the supplementary discount value, it is possible to deduct the cost subsequent to Discount 2 from the catalogue price.

The formula utilized to determine the additional discount amount involves the calculation of the difference between the list price and the price following Discount 2.

The reduction in price can be computed as the difference between the initial amount and the discounted amount, where the former is represented by $152 and the latter is computed to be $90.44. Therefore, the additional discount amount is equivalent to $61.56.

The supplementary reduction amount has been tabulated at $61.56.

Ultimately, the supplementary reduction rate may be derived as a proportion of the published cost:

The formula for calculating the additional discount rate is expressed as the ratio between the additional discount amount and the list price multiplied by 100%.

The supplementary discount rate can be calculated by taking the quotient of $61.56 and $152, and then multiplying the result by 100%.

The discount rate is estimated to be approximately 41% higher than the original cost in academic writing.

Answer:

D

Step-by-step explanation:

using the cosine ratio in the right triangle

cos ? = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{27}{40}[/tex] , then

? = [tex]cos^{-1}[/tex] ( [tex]\frac{27}{40}[/tex] ) ≈ 48° ( to the nearest degree )

Answer: [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

     In a slope-intercept equation written in the form as y = mx + b, the slope is equal to m

                 y = 3/4x

     The slope is [tex]\frac{3}{4}[/tex]

The correct interpretation of the standard error of the mean is that :

If we select many random samples of adults who do not currently run and assign them to this training program, the sample mean amount of time needed to adjust to this workout would typically vary by about 2.2 days from the population mean.

Given that,

A trainer would like to estimate the number of runs of the same length and same speed it takes for an individual’s body to adjust to the activity.

trainer selects a random sample of 30 adults who do not currently run and assigns them to run 1 mile at a 12-minute pace every day until they can do so easily.

Standard error of the mean = 2.2 days

Standard error is the deviation by which the sample mean deviates from the population mean.

So if we select as many samples as the sample type of people for the same activity, the sample mean vary by about 2.2 days from the population mean.

Hence the correct option is B.

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The interval of systolic blood pressure that represents the middle 95% of males is [94, 126].

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

According to the empirical rule (also known as the 68-95-99.7 rule), for a normal distribution, approximately 68% of the observations fall within one standard deviation of the mean, approximately 95% of the observations fall within two standard deviations of the mean, and approximately 99.7% of the observations fall within three standard deviations of the mean.

In this case, we want to find the interval that contains the middle 95% of observations. Since the distribution is normal, we know that approximately 95% of the observations will be within two standard deviations of the mean. Therefore, we need to find the values that are two standard deviations away from the mean in both directions.

Using the formula for z-scores, we can find the z-score corresponding to the upper and lower endpoints of this interval:

z_lower = (x_lower - mu) / sigma = (x_lower - 110) / 8 = -2

z_upper = (x_upper - mu) / sigma = (x_upper - 110) / 8 = 2

Solving for x_lower and x_upper, we get:

x_lower = mu + z_lower * sigma = 110 + (-2) * 8 = 94

x_upper = mu + z_upper * sigma = 110 + 2 * 8 = 126

Therefore, the interval of systolic blood pressure that represents the middle 95% of males is [94, 126].

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In the quadrant III, all except tangent and cotangent have negative values.

Given,

sinθ = -3/5

sinθ = opposite/hypotenuse

So, adjacent = √5² - 3²

Adjacent = 4

So, cosθ = -4/5

tanθ = sinθ/cosθ

tanθ = 3/4

cosecθ = 1/sinθ = -5/3

secθ = 1/cosθ = -4/5

cotθ = 1/tanθ = 4/3

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Your question was incomplete, but most probably your question will be:

If sin(theta) = -3/5, and theta is in quadrant 111, then find cosθ, tanθ, cosecθ, secθ and cotθ.

Answer:

The volume of the sphere is 217.2995490ft

Step-by-step explanation:

Volume = 4/3πr³

The dimeter is 16 and to find the radius of the sphere you divide by 1/2

V = 4/3π(8)³

= 217.2995490

Answer:

exact form: x=21/4

decimal form: 5.25.

mixed number form: x=5 1/4

Step-by-step explanation:

have a good day :)

Answer:

x = 5.25 or 21/4 or 5 1/4

Step-by-step explanation:

3x : 9 = 7 : 4

3x = 9 x 7 : 4

3x = 63 : 4

3x = 15.75

x = 15.75 : 3

x = 5.25 or 21/4 or 5 1/4

-----------------

check

(3 × 5.25) : 9 = 7 : 4

15.75 : 9 = 7 : 4

1.75 = 1.75

same value, the answer is good

The expanded and simplified form of the expression (x + 5)(x - 1) is  x² - x + 5x - 5.

Given the expression in the question;

(x + 5)(x - 1)

To expand and simplify the expression (x+5)(x-1),

we use the distributive property:

(x + 5)(x - 1)

x(x - 1) + 5(x - 1)

Now we can simplify each term by using the distributive property again:

x(x - 1) = x² - x

5(x - 1) = 5x - 5

Putting these terms back together, we have:

(x+5)(x-1) = x² - x + 5x - 5

Combining like terms, we get:

(x+5)(x-1) = x² + 4x - 5

Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.

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Answer:

mark me brilliant

Step-by-step explanation:

To determine whose purple paint will be bluer, we need to compare the ratios of blue to red in their mixes.

Justin's ratio of blue to red is 7:6 or 7/6.

Latanya's ratio of blue to red is 4:3 or 4/3.

To compare which ratio has more blue, we can simplify each ratio so that they have the same denominator:

- Justin's ratio: 7/6

- Latanya's ratio: 4/3 = 8/6

Now we can see that Justin's mix has a slightly higher ratio of blue to red than Latanya's mix. Therefore, Justin's purple paint will be bluer.

Answer:

Step-by-step explanation:

For Justin, the ratio is 7 cups of blue paint to 6 cups of red paint. For Latanya, the ratio is 4 cups of blue paint to 3 cups of red paint.

To compare the blueness of their purple paint, we must simplify these ratios. Justin's ratio simplifies to 7/6, while Latanya's ratio simplifies to 4/3. Now, let's convert these fractions to decimals for easier comparison:

Justin: 7 ÷ 6 ≈ 1.167

Latanya: 4 ÷ 3 ≈ 1.333

As you can see, Latanya's ratio (1.333) is greater than Justin's (1.167), which means her purple paint will be bluer.

Answer:

[tex]\left[d(A,C)\right]^2=\boxed{178}[/tex]

[tex]\left[d(A,B)\right]^2+\left[d(B,C)\right]^2=\boxed{128+50=178}[/tex]

[tex]\text{Area of the triangle}=\boxed{40}\; \text{units}^2[/tex]

Step-by-step explanation:

From inspection of the given triangle, the coordinates of vertices A, B and C are:

We can use the distance formula to find the lengths of the sides of triangle ABC.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}d(A, C) & =\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\& =\sqrt{(-4-9)^2+(1-4)^2}\\& =\sqrt{(-13)^2+(-3)^2}\\& =\sqrt{169+9}\\& =\sqrt{178}\end{aligned}[/tex]

[tex]\begin{aligned}d(A, B) & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(1-9)^2+(-4-4)^2}\\& =\sqrt{(-8)^2+(-8)^2}\\& =\sqrt{64+64}\\& =\sqrt{128}\end{aligned}[/tex]

[tex]\begin{aligned}d(B, C) & =\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\& =\sqrt{(-4-1)^2+(1-(-4))^2}\\& =\sqrt{(-5)^2+(5)^2}\\& =\sqrt{25+25}\\& =\sqrt{50}\end{aligned}[/tex]

Pythagoras Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Therefore, to determine if triangle ABC is a right triangle, substitute the found side lengths into the Pythagoras Theorem:

[tex]\begin{aligned}\implies \left[d(A, B)\right]^2 + \left[d(B, C)\right]^2 &= \left[d(A, C)\right]^2\\\left[\sqrt{128}\right]^2+\left[\sqrt{50}\right]^2&=\left[\sqrt{178}\right]^2\\128+50&=178\\178&=178\end{aligned}[/tex]

As the equation is true, this proves that triangle ABC is a right triangle.

The area of a right triangle is half the product of the lengths of its legs.

The legs of triangle ABC are AB and BC.

Therefore, the area of triangle ABC is:

[tex]\begin{aligned}\text{Area\;of\;triangle\;$ABC$}&=\dfrac{1}{2} \cdot d(A,B) \cdot d(B,C)\\\\&=\dfrac{1}{2} \cdot \sqrt{128} \cdot \sqrt{50}\\\\&=\dfrac{1}{2} \cdot \sqrt{128 \cdot 50}\\\\&=\dfrac{1}{2} \cdot \sqrt{6400}\\\\&=\dfrac{1}{2} \cdot \sqrt{80^2}\\\\&=\dfrac{1}{2} \cdot 80\\\\&=40\; \text{square\;units}\end{aligned}[/tex]

Therefore, the area of the triangle is 40 square units.

Answer:

The first set of data is not proportional because the ratio between the input and output values is not constant. For example, when x decreases from -4 to -2, y increases by 2 (from 0 to 2), which is a ratio of 1:1. When x decreases from -2 to 0, y increases by 2 (from 2 to 4), which is a ratio of 1:2.

The second set of data is proportional because the ratio between the input and output values is constant. For example, when x decreases from 3 to 1, y increases by 2 (from -2 to 0), which is a ratio of 1:1. When x decreases from 1 to -1, y increases by 2 (from 0 to 2), which is also a ratio of 1:1.

The third set of data is proportional because the ratio between the input and output values is constant. For example, when x increases from 0 to 1, y increases by 1 (from -1 to 0), which is a ratio of 1:1. When x increases from 1 to 2, y increases by 1 (from 0 to 1), which is also a ratio of 1:1.

The fourth set of data is not proportional because the ratio between the input and output values is not constant. For example, when x decreases from 6 to 3, y decreases by 1 (from -2 to -1), which is a ratio of 1:3. When x decreases from 3 to 0, y decreases by 1 (from -1 to 0), which is a ratio of 1:3, but from x=0 to x=-3, y does not decrease by 1, meaning that the ratio among changes varies.

To solve for x in the equation 8.88 = 4.44(x+7), we need to isolate x on one side of the equation. Here are the steps:

   Distribute the 4.44 on the right side of the equation:

8.88 = 4.44x + 31.08

   Subtract 31.08 from both sides of the equation:

-22.2 = 4.44x

   Divide both sides by 4.44:

x = -5

Therefore, the solution for x in the equation 8.88 = 4.44(x+7) is x = -5.

Answer:

We can start by substituting y from the first equation into the second equation:

y = x^2 - 6x

x + y = -4

x + (x^2 - 6x) = -4

x^2 - 5x - 4 = 0

We can solve for x by factoring:

(x - 4)(x + 1) = 0

So x = 4 or x = -1.

If x = 4, then y = -8 from the first equation, and y = 4^2 - 6(4) = -8 from the second equation, so (x,y) = (4,-8) is a solution.

If x = -1, then y = 3 from the first equation, and y = (-1)^2 - 6(-1) = 7 from the second equation, so (x,y) = (-1,3) is another solution.

Therefore, the system of equations has two solutions: (4,-8) and (-1,3).

The density of the wooden cube is 0.6 g/cm³ when length is 8cm and has a  mass of 307.2g.

To find the density of the wooden cube, we use the formula:

Density = Mass / Volume

Given that the length of the cube is 8 cm, all sides are equal in length.

The volume of a cube is given by the formula:

Volume = side length³

Substituting the given values:

Volume = 8 cm × 8 cm × 8 cm = 512 cm³

Now we can calculate the density:

Density = Mass / Volume = 307.2 g / 512 cm³

Simplifying:

Density = 0.6 g/cm³

Therefore, the density of the wooden cube is 0.6 g/cm³

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The equations that can be used to find the length of the base are a and d

The formula for the volume of a rectangular prism is V = lwh

V = volume, l = length

w = width

h = height

In this problem, the volume of the rectangular prism is given as 1,392 cubic centimeters, the height is given as 12 centimeters, and the width is given as 8 centimeters. We can use the formula to find the length of the base as:

l = V / wh

Substituting the given values, we get:

l = 1,392 / (8 x 12)

Simplifying, we get:

l = 14.5

Therefore, the length of the base of the rectangular prism is 14.5 centimeters.

The two equations that can be used to find the length of the base are:

a. 1392 = 96l (multiplying both sides of the equation by 8 x 12)

d. 12 x 8 x l = 1392 (rearranging the formula V = lwh to solve for l)

Therefore, the equations that can be used to find the length of the base are a and d

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The answer will be $68 and Here's Why:

Samantha received $59 for her birthday. That will be the base of the equation. She spent $25 on a charm bracelet so that will be the number being subtracted.

$59 - $25 = $34

We also know that he brother has twice as much money as she does. So that means he has 2x more money than her.

So: $34 x 2 = $68.

So here brother has $68 more than her.

Answer:

6 teaspoons!

Step-by-step explanation:

if he is doubling the recipe (4 divided by 2 = 2) then 3 * 2 would give you 6!

Answer:

g(x) = x^2 -3

Step-by-step explanation:

First of all we see that the graph is shifted downward (f(0)=0^2=0)

let g(x) = f(x) + c = x^2 + c

where c is a constant

from the graph we know that:

g(0) = -3

0^2 + c = -3

c = -3    

so g(x) = x^2 -3

then plug in some points to see if its true:

g(2) = 2^2 - 3 = 1         ### correct

g(3) = 3^2 - 3 = 6        ### correct

Answer: 2.1

Step-by-step explanation:

Use this property: log(ab)=log(a)+log(b)

log(180)=log(6*6*5)=log(6)+log(6)+log(5)=0.7+0.7+0.7=2.1

In order to simulate the amount of bullseyes that Grace will strike during her upcoming turn, we can carry out the following steps:

Within each loop cycle, generate 5 random integers between 0 and 1 to represent the likelihood of hitting a bullseye with each missile.

Accumulate the total number of bullseyes achieved for each round by adding the number of times the generated figure is less than or equal to 2/3.

After successfully running the simulation through 10,000 rounds, divide the total number of bullseyes hit by 10,000 to get the average number of bullseyes struck every round.

Finally, state the expected number of bullseyes that Grace will hit on her next turn by saying the average from step 4.

As a result, by prudently repeating numerous rounds, our algorithm can factor in the differential element instinctive throughout this process and eventually obtain a more precise tally of the predicted number of bullseyes Grace may potentially hit during her upcoming turn.

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The condensed form of the expression is  log [(a⁵¹× c²⁵) / b²⁷

We can use the logarithmic identities:

log aˣ = x log a

to simplify the expression:

51 log a - 27 log b + 25 log c

= log a⁵¹- log b²⁷ + log c²⁵

using the identity log (a/b) = log a - log b

= log [(a⁵¹× c²⁵) / b²⁷

Therefore, the condensed form of the expression is  log [(a⁵¹× c²⁵) / b²⁷

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Answer:

Picture one - Reflection on the y axis

Picture two - 180 degree counterclockwise rotation

Step-by-step explanation:

Answer: Question 1 is: Reflection across the y-axis

Question 2 is: 180° counterclockwise rotation