a gasoline tank is in the shape of a right circular cylinder (lying on its side) of length 10 ft and radius 4 ft. set up an integral that represents the volume of the gas in the tank if it is filled to a depth of 6 ft

A 99% confidence interval for the ratio of two population standard deviations (sigma_1/sigma_2) ranges from 1.06 to 2.22. Based on this confidence interval, we can conclude that sigma_1 is larger than sigma_2. (Option B).

A confidence interval (CI) refers to a range of estimates for an unknown parameter. A confidence interval for a standard deviation refers to the range of values that is likely to contain a population standard deviation with a certain level of confidence. In the given situation, when sigma 1 is divided by sigma 2, the result lies within the range from 1.06 to 2.22. When a number x is divided by number y, the result would be less than 1 if x < y, greater than 1 if x > y, and equal to 1 if x = y. Since the ratio of sigma 1 and sigma 2 is more than 1, sigma 1 is greater than sigma 2.

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Answer:

The percentage of area increased is 56.25%

Step-by-step explanation:

Area is the total amount of space occupied by a flat (2-D) surface or an object's shape.

Length of the garden = 20 feet

Breadth of the garden = 15 feet

Area of Original rectangular garden  = 20 × 15 = 300 [tex]feet^{2}[/tex]

If each side is increased by 25%

Then,

Length of new garden = 20 + [tex]\frac{25}{100}[/tex]×20 = 25 feet

Breadth of new garden = 15 +[tex]\frac{25}{100}[/tex]×15  =18.75 feet

Area of new rectangular garden = 25×18.75 =468.75[tex]feet^{2}[/tex]

Increase in Area = (468.75-300) [tex]feet^{2}[/tex]

                            =  168.75 [tex]feet^{2}[/tex]

Percentage of area increased = [tex]\frac{168.75}{300}[/tex]×100= 56.25%

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Answer: Maximum amount of people who can go to the amusement park is 6

Step-by-step explanation:

Answer:

Just add 15.50+19.25 several times until you reach 150 or 150+

therefore, The max amount of friends would be 4. This is because 15.50x4= 62 and 19.25x4=77. 77+62=139. If you went any farther up you would get more than 150, passing the budget.

The figure H''B''G''P'' created following the transformations applied to HBGP such that HBGP is larger than  H''B''G''P'', inverted and on the other side of the y-axis indicates;

The completed table is presented as follows;

[tex]\begin{array}{|c|c|c|c|c|\pi \pi }\text{Preimage} &\text{Side Length} & \text{Image} &\text{Side Length}&\text{Ratio of Preimage to Image Lengths } \\GB & 5 &G''P'' &2.5&2:1 \\PH &3 & P''H'' &1.5&2:1 \\HB & 5 & H''B'' &2.5&2:1 \\BG &3 & B''G'' & 1.5& 2:1 \\\end{vmatrix}[/tex]

A geometric transformation involves making changes to a geometric figure.

The coordinates if the vertices of the quadrilateral HBGP are;

H(-1, -2), B(-6, -2), G(-6, 1), and P(-1, 1)

The approximate coordinates of the vertices of the quadrilateral H''B''G''P'' are;

H''(0.5, 1), B''(3, 1), G''(3, -0.5), P''(0.5, -0.5)

The length of the side GP in quadrilateral HBGP = -1 - (-6_) = -1 + 6 = 5

Length of the side PH in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

Length of the side HB in quadrilateral HBGP = -1 - (-6) = -1 + 6 = 5

Length of the side BG in quadrilateral HBGP = 1 - (-2) = 1 + 2 = 3

The possible transformations applied to HBGP to create H''B''G''P'' includes;

A dilation, a rotation of 180° and a translation

The length of the side G''P'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side P''H'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

The length of the side H''B'' in quadrilateral H''B''G''P'' = 3 - 0.5 = 2.5

The length of the side B''G'' in quadrilateral H''B''G''P'' = 1 - (-0.5) = 1 + 0.5 = 1.5

Ratio of the side length of GP to the side length of G''P'' = 5:2.5 = 2:1

Ratio of the side length of PH to the side length of P''H'' = 3:1.5 = 2:1

Ratio of the side length of HB to the side length of H''B'' = 5:2.5 = 2:1

Ratio of the side length of BG to the side length of B''G'' = 3:1.5 = 2:1

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If the exam is quite easy then the shape of the histogram would be negatively skewed.

What is a histogram?

A histogram is a statistical information display that uses rectangles to show the frequency of data items in equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most common form of a histogram.

a) If the exam is quite easy, it is expected that the majority of the students score well on the test, and since most of the data is closer to the maximum value rather than the minimum, the histogram has a negatively skewed shape.

Hence, if the exam is quite easy then the shape of the histogram would be negatively skewed.

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(C) The standard deviation is 100 and the mean is 22.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers.

While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

So, using the concepts of expected value and variance of random variables, this issue can be resolved.

By the expected value principle:

E(Y) = E(2+4X) = E(2) + E(4X) = 2 + 4E(X) = 2 + 4(5) = 22

[tex]\mathrm{E}(\mathrm{Y})=\mathrm{E}(2+4 \mathrm{X})=\mathrm{E}(2)+\mathrm{E}(4 \mathrm{X})=2+4 \mathrm{E}(\mathrm{X})=2+4(5)=22[/tex]

Then, μy = 22

In terms of variance concept:
Var(Y) = Var(2 + 4x) = Var(2) + Var(4x) + 2Cov(2, 4x)

Cov(2, 4x) = 0

Var(2) = 0

Hence:
Var(Y) = Var(4x) = 4²Var(X) = 16σ²ₓ = 16(25²) = 10000

Standard deviation(Y) = √10000 = 100

Therefore, (C) the standard deviation is 100 and the mean is 22.

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Complete question:
The random variable X is normally distributed with a mean of 5 and a standard deviation of 25. The random variable Y is defined by Y = 2 + 4X. What are the mean and the standard deviation of Y? The mean is 20 and the standard deviation is 102.

A) The mean is 20 and the standard deviation is 50.

B) The mean is 22 and the standard deviation is 102.

C) The mean is 22 and the standard deviation is 100.

D) The mean is 22 and the standard deviation is 50.

If I drove at the speed of a light year it would take me 1.152×10⁻⁴ seconds.

In scientific notations numbers are written in the form of a base that is

0  ≤ b < 10 and multiplied by 10ⁿ where n represents integers.

We write large standard numbers in the scientific form in a compact manner.

We know 1 meter is 0.000621371 miles.

∴  34700 meters is (34700× 0.000621371) = 21.56 = 2.156×10¹ miles.

Given, A light year is equivalent to 6.7x10^8 miles/hour.

∴ It would take (2.156×10¹/6.7x10^8) = 0.32×10⁻⁷ miles per hour.

Or (0.32×10⁻⁷×3600) = 1.152×10⁻⁴ seconds.

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Answer:THE ANSWER IS C) 9.947, graph A

;)

Step-by-step explanation:

An arrangement of bars joined at the ends to create a two- or three-dimensional structure is called a truss.

External forces and responses to those forces are thought to act only at the nodes and cause either tensile or compressive forces in the members.

A planar truss is a two-dimensional truss that has all of its members and forces in the same plane. A space truss is another name for a three-dimensional truss. A member is said to be in traction when it is being pulled or pushed. When a member is being pushed or pulled, it is said to be in compression, and when it is in tension.

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Answer:

coffee table = 380

couch = 760

Step-by-step explanation:

1140÷3=380

table= 380×1=380

couch = 380×2=760

Answer:

[tex]\huge\boxed{\sf P = 42 \ cm}[/tex]

Step-by-step explanation:

Finding length:

Area = Length × Width

104 = Length × 8

Divide 8 to both sides

104/8 = Length

13 cm = Length

Finding Perimeter:

P = 2Length + 2Width

P = 2(13) + 2(8)

P = 26 + 16

[tex]\rule[225]{225}{2}[/tex]

Point A will lie at the point 15 on the number line.

Dilation is a transformation, which is used to resize the object. Dilation is used to make the objects larger or smaller. This transformation produces an image that is the same as the original shape. But there is a difference in the size of the shape. A dilation should either stretch or shrink the original shape. This transformation is expressed by the term “scale factor.”

If point A is at 6 and it is dilated by the factor 5/2 which means extension then the new location of point A is 5/2 x 6 which is 15

In conclusion the new location of point A on the number line is 15

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The p-value will be 0.9457

Sample size = 49

Meantime = 19 minutes

Standard deviation = 3.9 mins

Calculating the z-score for test statistic -

z = (x - μ) / (s / √n)

z = (19 - 18) / (3.9 / √49)

= 1 / 0.63

= 1.58

To find the p-value, we can use a standard normal table to find area under the normal curve of the z-score.

The p-value will be the area under the curve to the right of 1.58.

This value is 0.9457, which means that there is a 94.57% chance.

Now,

Since the p-value is greater than the significance level (0.9457 > 0.05),  the null hypothesis can not be rejected. Therefore, the mean time parents spend posting pictures of their children per week is not significantly different from 18 minutes at the 5% significance level.

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Answer:

15 is a composite number.

In basic Mathematics, the numbers that have more than two factors are known as composite numbers. For example, factors of 6 are 1, 2, 3 and 6. Thus, there are four factors in total, and 6 is a composite number. The first ten composite numbers are 4, 6, 8, 9, 10, 12, 14, 15, 16, 18. To understand better, have a look at the following examples.

Therefore, your answer is 15

Answer:

n = 1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction

2. Find common denominator

3. Combine fractions with common denominator

4. Combine multiplied terms into a single fraction

5. Multiply by 1

6. Multiply the numbers

7. Rearrange Terms

8. Add n to both sides

9. Simplify

10. Multiply all terms by the same value to eliminate fraction denominators

11. Cancel multiplied terms that are in the denominator

12. Subtract 2 from both sides

13. Simplify

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So the answer here is approximately 95% of housing prices are between a low price of  $143000 and a high price of $171000.

The empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, is a statistical principle that asserts that, with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).

The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.

The Empirical Rule indicates that 99.7% of data that are seen to have a normal distribution fall within 3 standard deviations of the mean.

According to this criteria, 68% of the data falls within one standard deviation, 95% within two standard deviations, and 99.7% within  three standard deviations of the mean.

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The statements that correctly describes the points of discontinuity of the function include the following;

A. There is an infinite discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

E. There is a jump discontinuity at x = 1.

In Mathematics, there are three (3) main types of discontinuity in a function and these include the following:

A jump discontinuity can be defined as a point on the graph of a function at which the left-hand limit [tex]\lim_{x \to x^-_0} f(x) = A_2[/tex] and right-hand limits [tex]\lim_{x \to x^+_0} f(x) = A_2[/tex] are not equal (A₁ ≠ A₂).

By critically observing the graph representing this function, we can logically deduce that there is a jump discontinuity at x is equal to 1 (x = 1).

A removable discontinuity can be defined as a point on the graph of a function at which it is not connected. This ultimately implies that, a removable discontinuity refers to a point on the graph of a function that is considered to be undefined or doesn't accurately fit the other part of a graph.

By critically observing the graph representing this function, we can logically deduce that there is a removable discontinuity at x is equal to negative 1 (x = -1) while there is an infinite discontinuity on the vertical asymptote at negative 2 (x = -2).

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Complete Question:

Which correctly describes the points of discontinuity of the function? Select all that apply.

A. There is an infinite discontinuity at x = -2.

B. There is a jump discontinuity at x = -2.

C. There is a removable discontinuity at x = -1.

D. There is an infinite discontinuity at x = 1.

E. There is a jump discontinuity at x = 1

Answer:

Your friend jogs faster and he will finish a 5 km race in 27.5 minutes

You jog 1km every 6 minutes and your friend jogs 1km in 5.5 minutes

Step-by-step explanation:

Answer:

the weight of a male: G+M

total weight of females: A

weight of child: G

total weight of adults: M+A

Step-by-step explanation:

i mean... u got it right

The player with the greater final score is of:

Barry.

Barry's final score is given as follows:

45.

Then we have to obtain Lee's score, from the description given in the missing information section.

Lee's scored is obtained as follows:

Thus Lee's final score is given as follows:

-55.

The classifications of the final scores according to the signals are given as follows:

A positive score will always be greater than a negative score, hence Barry had the greater final score.

Lee and Barry play a trivia game in which questions are worth different numbers of points. If a question is answered correctly, a player earns points. If a question is answered incorrectly, the player loses points. Lee currently has -350 points.

a. Before the game ends, Lee answers a 275 -point question correctly, a 70 -point question correctly, and a 50 -polnt question incorrectly. Write and find the value of an expression to find Lee's final score.

b. Barry's final score is 45. Which player had the greater final score?

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After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

Here, we are given that a sheet of paper is cut into 6 ​same-size parts. Each of the parts is then cut into 6 ​same-size parts and so on.

Thus, after one cut we will have 6 pieces

After second cut, we will have 6*6 = 36 pieces

After the third cut, we will have 36*6 = 216 pieces

After the fourth cut, we will have 216*6 = 1,296 pieces

Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.

Thus, after the nth cut, the number of pieces will be-

a[tex]r^{n-1}[/tex]

where a = first term which is 6

and r = common ratio which is also 6

⇒ 6*[tex]6^{n-1}[/tex]

= [tex]6^{n}[/tex]

Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.

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Answer:7 sry if this is not correct but that is the answer

Step-by-step explanation:

x=7-y             y-x=7

2y-7=7          x= 7-y

y=7              x=7-y

x=0              y=7

x= 7

here is  your answer

Answer: One solution

Step-by-step explanation:

6x+16=2x+30

4x=14

x=7/2

The measure of the given sides and angles are,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

What is congruent triangles?

If the three sides and the three angles of both angles are equal in any orientation, two triangles are said to be congruent.

Given: ΔXYZ ≅ ΔEGF

Because the triangles are assumed to be congruent, their corresponding angles and sides must have similar measurements and lengths.

a. ZX = _ in

ZX's length is the same as FE's length. Therefore, the length should be 1.3 inches.

b. EG = _ in

EG's length is the same as XY's length. The figure indicates that the answer should be 3.0 in.

c. m ∠X = _ °

Angle E and angle x should both have the same measure. This is stated to be 48 degrees.

d. m ∠G

Angle Z's measurement is the same as angle F's measurement.

In that case, 107° should be the value assigned to angle F.

Angle E in the triangle to the right measures 48°, while angle F measures 107°.

the sum of these angles is subtracted from 180°.

The angle G's measure, which is equal to 25°.

Hence,

1) ZX = 1.3 inch

2) EG = 3.0 inch

3) m ∠ X = 48°

4) m ∠G = 25°

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Complete question:

Complete question is attached below.

Answer:

Your answer is 7 rentals, at the cost of $22.75.

Step-by-step explanation:

First, let's make an equation

[tex]y =[/tex] total cost while [tex]x=[/tex] amount of rentals

[tex]y = 3.25x[/tex]

[tex]y = 2x + 8.75[/tex]

After graphing the two, we find that they intersect and 7, 22.75

Hence, the answer is 7 rentals, at the cost of $22.75

Answers to both subparts are shown:

(A) Only 1 prime number is in the multiples of 5 which is number 5 itself.

(B) No prime numbers are in the multiples of 8.

Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number.

A composite number is a natural number greater than one that is not prime.

For instance, the number 5 is prime because there are only two ways to write it as a product, 1 × 5 and 5 × 1.

(A) Prime numbers that are multiples of 5:

All numbers that come in the table of 5 are multiples of 5.

Only the number 5 is the number that comes in the table of 5 is a prime number.

As 5 is only divisible by 1 and 5 itself.

(B) Prime numbers that are multiples of 8:

All numbers that come in the table of 8 are multiples of 8.

No number that comes in the table of 8 is a prime number.

As all the numbers are divided by also as 8 is an even number.

Therefore, answers to both subparts are shown:

(A) Only 1 prime number is in the multiples of 5 which is number 5 itself.

(B) No prime numbers are in the multiples of 8.

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Answer:

ASA

Step-by-step explanation:

angle side angle because, due to vertical angles, the outer angles of both triangles are congruent, and the middle side is reflexive property

hope this helps :3

Answer:

70%

Step-by-step explanation:

the percentage of both single stranded RNA molecule which are adenine and thymine is 100%

the Perce of the adenine is 30

therefore, 100 - 30=70

Answer: 16

Step-by-step explanation:

its 16 because if you do 3/7 times 2/15 it gives you 16

Answer: x = 37

Step-by-step explanation: (3/7)*(x-2) = 15 // - 15

(3/7)*(x-2)-15 =

0 3/7*(x-2)-15 = 0

3/7*(x-2)-15 = 0

3/7*x-111/7 = 0

3/7*x-111/7 = 0 // + 111/7

3/7*x = 111/7 // : 3/7

x = 111/7/3/7

therefore the answer is x =37