a vertical cylinder is leaking water at a rate of ft3/sec. if the cylinder has a height of ft and a radius of ft, at what rate is the height of the water changing when the height is ft?

Answer:

9 1/6

Step-by-step explanation:

3 2/3 divided by 2/3

First convert 3 2/3 into a whole number

3 2/3 = 11/3

11/3 x 2/3 = 55/3

55/3 into a mixed number is 9 1/6

The equation of the line in slope intercept form is y = 4/5 x.

For the stated question-

The given points are-

(x1, y1) = (5,4)

(x2, y2) = (10,8)

Slope m = (y2 -y1)/ (x2 - x1)

m = (8 - 4)/(10 - 5)

m = 4/5

Equation of the line;

y - y1 = m(x - x1)

y - 4 = 4/5 (x - 5)

y = 4/5 x - 4 + 4

y = 4/5 x

Thus, the equation of the line in slope intercept form is y = 4/5 x.

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The longest possible length is 3 uints and the smallest square achieving this length is [tex]38^2[/tex] = 1444.

All squares end in the digit 0, 1, 4, 5, 6, or 9. A square ending in 11, 66, 55, 99 would be congruent to 3, 3, 2, 3 mod 4, but squares are congruent to 1 mod 4 or 0. So for a length > 1, the square should end in 4. For example, [tex]12^2[/tex] = 144.

A square ending in 4444 would be congruent to 12 mod 16, but squares are congruent to 0, 1 mod 16, 4 mod 16, or 9 mod 16. So, the maximum length should be 2 or 3.

If [tex]n^2[/tex] ends in 4, then n should end in 2 or 8. [tex](100a + 10b + 2) ^2[/tex]= 10000[tex]a^2[/tex] + 1000 (2ab) + 100 (4a + [tex]b^2[/tex]) + 10 (4b) + 4. So, if this ends in 44, then b = 6 or 1.

If b = 1, then 4a + [tex]b^2[/tex] is odd, so the square will not end in 444. If b = 6, then the square would be 1000k + (4a + 38) 100 + 44. This would end in 444 if we take, a= 9 or 4.

Thus the smallest numbers that end in  2 and whose square ends in 444 are 462 (square 213444) and 962 (square 925444).

[tex](100a + 10b + 8)^2[/tex] = 1000k + 100 ([tex]16a^2 + b^2[/tex]) + 10 (16b + 6) + 4.

Now, if this ends in 44, then b = 3 or 8.

let us take b=3, then [tex](100a + 38)^2[/tex] = 1000k + 100 (76a) + 1444, so this ends in 444 if a = 0. Hence, this should be the smallest solution.

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Answer:

b

Step-by-step explanation:

your answer is b to be precise

It will take 6 month to reach the same height for both maple tree and oak tree.

the country, region, or geographic area's yearly average rate of change in population size over a certain time period.

The given data is -

Let the number of months when both will have the same height be 'x'.

Thus,

For maple tree,the final height be-

125 + 3x

For oak tree,the final height be-

83 + 10x

Equating both

125 + 3x = 83 + 10x

7x = 125 - 83

7x = 42

x = 6 months

Thus, it will take 6 month to reach the same height for both maple tree and oak tree.

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Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Type I error is We conclude that the mean is not 34 years when it really is 34 years. The correct option to this question is C.

Rejecting the null hypothesis when it is in fact true is a Type I mistake. It entails drawing conclusions about outcomes that are statistically significant when, in fact, they were just the consequence of chance or unrelated causes.

The significance level you select (alpha or ) determines the likelihood that you will make this mistake. You determined that figure at the start of your research to determine the statistical likelihood of getting your results (p-value).

The typical significance level is 0.05 or 5%. If the null hypothesis is accurate, your results only have a 5% chance or less of occurring.

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Answer:

Step-by-step explanation:

The word ‘channel’ has multiple meanings which can be discerned based on the context.

What is the thesaurus entry for the channel?

According to the thesaurus, as a noun, the word channel has two meanings. They are-

A pathway that contains water - here the channel is a strait or a small stream of water. The synonyms of the word, in this case, would be - avenue, carrier, route, and tunnel.

A means to achieve something- The synonyms, in this case, are the instrument, medium, and vehicle.

As a verb, the word channel means to direct or to convey something. Thus the synonyms would be to carry and to transmit.

How is ‘channel’ used in the contexts above?

In the sentences above the word, 'channel' is used as follows

She was the first swimmer to cross the channel between the two countries.- Here, the channel is a water body.

If you want your complaint to be addressed, you need to go through the appropriate channel.- Here, the channel is a medium or a route.

Answer:

r = 0

Step-by-step explanation:

the first thing you can do to solve this equation is to remove the parenthesis

2r + 4 = r + 4

now subtract 4 from both sides

2r = r

subtract 4 from both sides

r = 0

that is your answer

By using the concept of confidence interval, it can be concluded that-

To reduce confidence interval, it is needed to increase sample size.

Option c is correct

What is confidence interval?

Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.

Formula for percentage confidence interval

[tex]\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}[/tex]

We have to reduce the size of the confidence interval

Confidence interval has no effect on  mean, directly proportional to  standard deviation and inversely proportional to sample size

So to reduce confidence interval, it is needed to increase sample size.

Option c is correct

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Complete Question

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:

Select one:

a. increase the population standard deviation

b. increase the level of confidence

c. increase the sample size

d. increase the sample mean

e. none of these would help

Answer:

Step-by-step explanation:  

$519.35 + $35

The original price of the iPhone 13 is $554.35

Answer:

Ava is running faster than Maura.

Step-by-step explanation:

We are finding the speed in miles/minute.

6/75=0.08miles/minute

5/45=0.(1)miles/minute

0.(1)is greater than 0/08

Ava is running faster than Maura.

240 people can seat in a row without restriction in an arrangement.

A permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.

Permutations differ from combinations, which are selections of some members of a set regardless of order. For example, written as tuples, there are six permutations of the set {1, 2, 3}, namely (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2), and (3, 2, 1). These are all the possible orderings of this three-element set. Anagrams of words whose letters are different are also permutations: the letters are already ordered in the original word, and the anagram is a reordering of the letters. The study of permutations of finite sets is an important topic in the fields of combinatorics and group theory.

According to the question:

Consider A and B being the people sitting next to each other, as one entity AB or BA.

There are now 5 entities (one of two persons A and B and five of one single person) that have to be placed in a row.

With AB, there are thus 5! possibilities. With BA, there are also 6! possibilities.

Considering both, there are thus 2× 5! = 240 ways to seat 6 people in a row of six seats if two people insist on sitting next to each other.

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Answer:

  4x +6

Step-by-step explanation:

You want the simplified form of 6x -2(x -3).

Generally, the first step in simplifying an expression is elimination of parentheses. This is done using the distributive property.

  6x -2(x -3) = 6x -2x -2(-3) = 6x -2x +6

Then, like terms can be combined:

  6x -2x +6 = (6 -2)x +6 = 4x +6

The simplified expression is 4x +6.

__

Additional comment

We notice the terms have a common factor of 2, so we can use the distributive property to factor that out:

  = 2(2x +3)

This form may be useful in some circumstances, but is generally not considered to be the simplified form.

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Answer: 86.8 dollars per month

Answer:

x = 2.5

Step-by-step explanation:

Answer:

[tex]\boxed{\boxed{\tt x=5}}[/tex]

Step-by-step explanation:

[tex]\tt \cfrac{3x+4}{2}=9.5[/tex]

Multiply both sides by 2:-

[tex]\tt \cfrac{2\left(3x+4\right)}{2}=9.5\times\:2[/tex]

[tex]\tt 3x+4=19[/tex]

Subtract 4 from both sides:-

[tex]\tt 3x=15[/tex]

Divide both sides by 3:-

[tex]\tt \cfrac{3x}{3}=\cfrac{15}{3}[/tex]

[tex]\tt x=5[/tex]

__

Hope this helps you!

Have a nice day!

The probability that a total of four tries will be necessary for both of you to get through is 0.1728.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty. A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

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The dimensions of the field that will allow for the maximum area are 200 meters by 400/3 meters

From the question, we have

Fencing available, Perimeter = 1600 meters

Number of sections, n = 3

Represent the dimensions with x and y

So, we have:

Area = Number of sections* x * y = 3xy

Perimeter = (Number of sections * 2x + 2(Number of sections) * y) = 6x + 4y

Recall that

Perimeter = 1600 meters

So, we have

6x + 4y = 1600

A = 3xy

Divide 6x + 4y = 1600 by 2

3x + 2y = 800

Make y the subject

y = (800 - 3x)/2

Substitute y = (800 - 3x)/2 in A = 3xy

A = 3x(800 - 3x)/2

So, we have

A = 1200x - 4.5x²

Differentiate and set to 0

1200 - 9x = 0

So, we have

9x = 1200

Divide by 9

x = 400/3

Recall that y = (800 - 3x)/2

So, we have

y = (800 - 3 x 400/3)/2

Evaluate

y = 200

Hence, the dimensions are 200 by 400/3

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Answer:

if he can run 1.5 miles in 12 min he can run 4 miles in 0.5

Answer:

1 1/3 or 4/3

Step-by-step explanation:

1/6 + 1/6 = 2/6

simplified, it would be 1/3 then you add the one, and you get 1 1/3 or (written as a mixed number,) 4/3

Answer:

2

Step-by-step explanation:

Since the denominator is the same, we can add the numerators.

11/6  +  1/6  =  12/6

We can simplify this to 2.

So, the answer is 2.

Answer:

Given,

Let's assume the maximum safe height of wall = h

angle formed between ladder and ground = 70°

length of ladder = 16 ft

From the given data, it can be seen that ladder will form a right angle triangle structure with the wall

So,from the concept of trigonometry,

Sin70^o\ =\ \dfrac{\textrm{maximum safe height of wall}}{\textrm{length of ladder}}Sin70

o

=

length of ladder

maximum safe height of wall

= > Sin70^o\ =\ \dfrac{h}{16\ ft}=>Sin70

o

=

16 ft

h

= > \ h\ =\ 16\times Sin70^o=> h = 16×Sin70

o

=> h = 16 x 0.9396

=> h = 15.03 ft

So, the maximum safe height that can be reached by the ladder will be 15.03 ft.

Here is the Correct asnwer.

The measures of central tendency from the given stem-and-leaf plot are given as follows:

The stem-and-leaf plot shows the measures of the data-set, in which:

For example:

4|7 = 47.

Hence all the measures of the data-set are given as follows:

47, 51, 56, 57, 62, 63, 63, 66, 66, 68, 68, 70, 71, 73, 73, 73, 73, 76, 76, 77, 77, 79, 80, 81, 82, 83, 86, 88, 88, 90, 91, 93, 93, 97.

The mean is given by the sum of all scores divided by the number of scores, hence it is given as follows:

Mean = 74.62.

The median is the middle value of the data-set. The data-set has 34 elements, which is an even cardinality, hence the median is given by the mean of the 17th and of the 18th element, as follows:

Median = (73 + 76)/2 = 74.5.

The mode is the value that appears the most times in the data-set, which is of 73, as it is the only score to appear four times in the data-set.

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the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

The following is a definition of the test's hypothesis:

H0: The actual average lifetime, which is > 750 hours, is not less than what is stated

Ha! The actual average lifespan, at 750 hours, is less than what is advertised.

The examination is left-tailed.

Making a decision:

The null hypothesis is rejected if the test's p-value is less than the significance level (), and vice versa.

The test's p-value is calculated as,

0.016 as the p-value

(a)

The level of significance is 0.05.

The p-value is equal to 0.016/0.05.

The null hypothesis was rejected since the test's p-value was lower than the threshold for significance.

Consequently, the test's finding at the 5% level of significance is that the genuine average lifetime is shorter than

(b)

The level of significance is = 0.01.

The p-value is equal to 0.016 > = 0.01.

The null hypothesis could not be rejected since the p-value of the test was greater than the level of significance.

Therefore, the test's finding at the 5% level of significance is that the true average longevity is not less than claimed.

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The thermometer relates with the rectangular coordinate system in the sense that both have

The idea behind how a thermometer works is that solids and liquids tend to expand as a function of temperature.

Mercury starts to rise when a thermometer lamp is submerged in a particular solution or material. On a temperature scale, this increase in mercury is investigated.

The mercury in the tube is similar to the y coordinate which gives the output while the object being measured  is similar to the x coordinate which is the input

The graduation in thermometers into units that rises and falls is a similar feature in the rectangular coordinate system

The functions from thermometer can be plotted on a graph in a rectangular coordinate system

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Answer:

−3 < −1

−3 ≤ −1

Step-by-step explanation:

Symbol explanation

A negative number is any number that is less than zero.

On the number line the negative numbers are to the left of the zero.

-3 is less than -1 because -3 lies to the left of -1 on the number line.

Therefore, the only given inequalities that are true statements are:

Answer:

if the first equation 3x - 3y = -2 is multiplication by 3

therefore, 3x - 3y = -2

multiplied by 3

:9x - 9y = -6

then the equations are added,

9x - 9y = -2 + 10x + 710x + 118x + 7

9x + 10x + 710x + 118x + 9y + 7

947x + 9y = 7