Suppose that a cylinder has a radius of r units, and that the height of the cylinder is also r units. The lateral area of the cylinder is 512π square units. Find the value of r.

The value of the smaller of the two missing sides (the second leg) is,

⇒ 144 units

We have to given that;

The length of one of the legs of a right triangle is 17.

And, The lengths of the other two sides are consecutive integers.

Hence, Let the smallest of the other legs be x,

And, the hypotenuse be x + 1.

So, By using the Pythagorean theorem as;

⇒ 17² + x² = (x + 1)²

⇒ 289 + x² = x² + 1 + 2x

⇒ 2x = 288

⇒ x = 144

Thus, The value of the smaller of the two missing sides (the second leg) is,

⇒ 144 units

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The 30th percentile in the uniform distribution is 2.4 min.

The correct option is (b)

The probability formula is defined as the ratio of favorable outcomes to the ratio of total outcomes. For any event (E), :

P(E)= Number of favorable outcomes/ Number of total outcomes

[tex]\mu=\frac{a +b}{2}[/tex]

[tex]\sigma=\sqrt{\frac{(b-a)^2}{12} }[/tex]

P(x) = 1/ b - a if a < x < b

P(X < a) = 0

and

P(X > b) = 0

In this case, a = 0 and b = 8

The 30th percentile in the uniform distribution, this means that the probability is 0.30. Therefore:

0.3 = [tex]\frac{1}{8-0}.x[/tex]

0.3 (8 -0) = x

2.4 = x

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The given question is incomplete, complete question is :

The Sky Train from the terminal to the rental-car and long-term parking center is supposed to arrive every eight minutes. The waiting times for the train are known to follow a uniform distribution. Find the 30th percentile for the waiting times (in minutes).

a. 2

b. 2.4

c. 2.75

d. 3

The percentage of boxes with green lamps is 60%, the correct option is C.

We are given that;

Number of boxes= 40

Green lamp boxes= 24

Now,

To calculate the percentage of boxes that contain green lamps, you need to divide the number of boxes with green lamps by the total number of boxes and then multiply by 100. This is according to the formula for finding a percentage of a number12.

=(24 / 40) x 100 = 60%

Therefore, by percentage the answer will be 60%.

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Answer: The IQR of this data set is 5.5

Step-by-step explanation: Ok so first you line the data set up in correct order.

Here's the correct order:

13, 15, 15, 16, 18, 19, 22, 28

Then you find the median and since there's even amount of numbers you add the two numbers in the middle which is 16 and 18 and divide that by 2 which is 17. So the median is 17. Then you split the data set into halves. The first quartile is 15 and the third quartile is 20.5. Then to find the IQR, you would minus 20.5 - 15 = 5.5. Hope this helps!

The value of the most expensive car loan that Cindy can afford is $13,712

We are given that;

Amount= $215

Percentage= 2.1%

PMT = 215 i = 0.021 / 12 = 0.00175 (the annual interest rate divided by 12 months) n = 6 × 12 = 72 (the number of months in 6 years)

Now,

The formula for the present value of an annuity is:

PV = PMT × (1 - 1/(1 + i)^n) / i

where:

PV = present value PMT = payment amount i = interest rate per period n = number of periods

Plugging these values into the formula, we get:

PV = 215 × (1 - 1/(1 + 0.00175)^72) / 0.00175 PV = 215 × (1 - 0.888) / 0.00175 PV = 215 × 0.112 / 0.00175 PV = 13,712

Therefore, by the percentage the answer will be $13,712.

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Answer:

how many or how much or what is the amount

Step-by-step explanation:

quantity means

the amount or number of a material or immaterial thing not usually estimated by spatial measurement.

if I were to ask you " How many apples are in that bag" Im basically asking what is the quantity of apples in that bag. So, in scatter plots it's asking you, how many points are on this graph of scatter points

The statement that correctly describes the expression |x^3|+5 is 5 more than the absolute value of the cube of a number.

Given this expression: |x^3|+5

| | = This sign means Absolute value,

x^3 = x³ = x × x × x

Hence, the statement that correctly describes the expression |x^3|+5 is : 5 more than the absolute value of the cube of a number.

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Answer:

correct answer is D

Step-by-step explanation:

Answer:

80%

Step-by-step explanation:

After all the trade he got 50 stickers

40 Big

10 small

50 stickers is 100%

40B stickers is ??

WE multiply 40 by 100 then divide by 50

so 80%

Answer:proving that EFGH is a square: points E,F,G,H

separate the sides of the square ABCD into two lines. if AE=BF=CG=DH then

AH=DG=EB=FC and it shows that if we connect the points E,F,G,H to each other with line we will have a square

HAE~EBF~FCG

Thus the numbers that we are looking for are 8 and -6.

We would have to use a method in which we would call the  numbers that we want to find x and y.

We know that we have to solve the problem as a simultaneous equation so that we can be able to obtain the numbers that we seek.

If

xy = -48 ---(1)

x + y =2 --- (2)

y = -48/x ---(3)

Substitute (3) into (2)

x - 48/x = 2

x^2 - 48 = 2x

x^2 -2x - 48 = 0

x = 8 and x = -6

Thus;

8 + y = 2

y = -6

Or

-6 + y = 2

y = 8

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Missing parts:

What numbers multiply to -48 and add to 2 at the same time

Answer:

The answer would be option A

Step-by-step explanation:

-14 times 8=-122

Victoria's statement that her running speed is faster an elephant's does not make sense because it is based on the comparison of unlike units of measurement.

Elephant's running speed = 100 yards in 20 seconds

= 5 yards per second (100 ÷ 20)

1 yard = 3 feet

5 yards = 15 feet (5 x 3)

The elephant's running speed = 15 feet per second.

Victoria's running speed = 60 feet in 10 seconds

= 6 feet per second (60  ÷ 10)

Thus, we conclude that the elephant's running speed is 15 feet per second, while Victoria does 6 feet per second, making her claim untrue.

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Answer:

There would be a 38% or 8/21 probability of picking a red jelly bean on the first draw and a 20% or 4/20 probability of picking a blue jelly bean on the second.

Step-by-step explanation:

There are 21 jelly beans in total. So on the first draw, there is an 8/21 chance you will get a red jelly bean. If you turn this fraction into a percentage, it is 38%.

Now that a jelly bean is missing, there are 20 jelly beans. There are four blue ones still, so there is a 4/20 chance of getting a blue jelly bean. Turning this ratio into a percent gets you 20%.

I would love a brainliest. I haven't had one yet and it would make my day. Hope this helped you!

The  probability of selecting a red jelly bean on the first draw and a blue jelly bean on the second draw is 32/441.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

We have,

The jar contains 8 red, 2 green, 4 blue, and 7 pink, jelly beans.

total beans = 8 + 2 + 4 + 7 = 21

So, the probability of selecting a red jelly bean on the first draw and a blue jelly bean on the second draw

= 8/21 x 4 / 21

= 32 /441

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The range of the function f(x) = |x| + 5 include the following; B. R: {f(x) ∈ ℝ | f(x) ≥ 5}.

In Mathematics and Geometry, a domain is the set of all real numbers for which a particular function is defined.

Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or -∞ ≤ x ≤ ∞.

Range = {5, ∞} or 5 ≤ f(x) ≤ ∞.

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The distinct orders of light bulbs are there if two light bulbs of the same color are considered identical = 4,620

Here, the total number of bulbs = 11

The number of red light bulbs = 3

The number of yellow light bulbs = 2

and the number of  pink light bulbs = 6

We know that the formula for the permutation with repetition is:

n! / (n1! × n2! x ... × nk!)

We use this formula to find the required number of light bulbs.

Here, two light bulbs of the same color are considered identical

We divide by 3! in order to adjust for overcounting, because we have 3 red light bulbs.

simmilarly for the 2 yellow light bulbs, we divide with 2!.

and for the 6 pink light bulbs, we divide by 6!

Thus, the total number of distinct orders of bulbs will be:

11! / (3! × 2! × 6!) = 4,620

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Length of board should Jessica buy is 4.4 feets.

Step-by-step explanation:

Height of the ramp =

Distance of the porch from the ground = x

Inclination of the ramp,θ = 35°

In triangle ABC,

AB =

AC = x

θ = 35°

According trigonometric ratios:

Length of board should Jessica buy is 4.4 feets.

The surface area of the cylinder in terms of pi is:

S = pi*301 cm²

We know that for a cylinder of radius R and height H the surface area is:

S = pi*( 2RH + R²)

Here the height is 18 cm and the diameter is 14cm, then the radius is.

R = 14cm/2 = 7cm

Then the surface area will be:

S = pi*(2*7cm*18cm + (7cm)*7cm)

S = pi*301 cm²

That is the surface area in terms of pi.

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The Venn diagram for (D ⋃ E) ⋃ F will be the ovarlapped region of D,E and F.

To represent the sets D, E, and F in the Venn diagram, we first construct three overlapping circles. Then, beginning with the innermost operation and moving outward, we shade the regions corresponding to the set operations in the expression.

We shade the area where the circles for D and E overlap because the equation (D ⋃ E)  denotes the union of the sets D and E. All the elements in D, E, or both are represented by this area.

The union of (D ⋃ E) with F is the next step. This indicates that we darken the area where the circle for F crosses over into the area that we shaded earlier. All the components found in sets D, E, F, or any combination of these sets are represented in this region.

The final Venn diagram should include three overlapping circles, with (D ⋃ E) ⋃ F shaded in the area where all three circles overlap.

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The pineapple has 1097g more mass than the apples.

We have,

The difference between two values is the result of subtracting one value from the other.

In this case, we want to find the difference between the mass of the pineapple and the mass of the apples.

To do this, we subtract the mass of the apples from the mass of the pineapple.

The equation for this is:

Pineapple mass - Apple mass = Difference

Substituting the given values:

3547g - 2450g = 1097g

Therefore,

The pineapple has 1097g more mass than the apples.

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The number of scoops of birdseed Sarah puts in the feeder n = 2

Given data ,

Let the number of scoops of birdseed Sarah puts in the feeder be n

While utilizing a scoop that can contain 1/4 cup of birdseed, Sarah's bird feeder holds 1/2 cup of birdseed. We must divide the capacity of the bird feeder by the capacity of the scoop to determine how many scoops Sarah will add to the feeder.

On simplifying the equation , we get

1/2 ÷ 1/4 = n

n = 1/2 x 4/1

n = 4/2

n = 2 scoops

Hence , the equation is solved and n = 2

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The slope of the line perpendicular to the line is m = ( 7/2 )

Given data ,

The equation of the given line is y = -2/7x + 3/7.

Now , it is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The slope of the given line is -2/7, which means that for any line perpendicular to this line, the slope would be the negative reciprocal of -2/7.

So , m = ( 7/2 )

Hence , the slope of the perpendicular line is = 7/2

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The meaning of the absolute value of -5.5 is given as follows:

The temperature decreases 5.5 degrees.

The absolute value of a number is the number without the signal, for example:

|-2| = |2| = 2.

The number in this problem is given as follows:

-5.5.

Hence:

Hence the second option is the correct option in the context of this problem.

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Question 11 seems to have strange typos in it. Please double-check to make sure it has been typed correctly.

I'm not sure how to answer that one.

----------

I'll focus on Question 12.

The long division scratch work is shown in the image attachment below.

The answer to problem 12 is  x+9 remainder -7x-7

Please let me know if you have questions about any step of the polynomial long division process.