a scale drawing of an office space uses a scale of 1 in. : 6 yd. the scale drawing has an area of 6 square inches. what is the area of the actual office space?

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:

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

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 statements are insufficient to answer the question.

What is measurement?

Measurement is the quantification of an object's or event's attributes for comparison with other objects or events. Measurement, in other words, is the process of determining how large or small a physical quantity is in comparison to a basic reference quantity of the same kind.

So we are given 2 lists, x and y and we are given the

1.  The total number of measurements is 30. x(n) + y(n) = 30.

2. Largest measurement - Smallest Measurement = 25

But we are not told the number of measurements in either x or y. We also don't know whether the largest of smallest measurement of the combined range belongs to x or y.

We need to find the largest measurement of x and the smallest measurement of x for our answer.

1)The range for the 12 measurements in list y is 20.

Okay so we know that y has 12 measurements, therefore x has 18. And we know the y(largest) - y(smallest) = 20 INSUFFICIENT

2) List x consists of 18 measurements.

We are told that x consists of 18 elements. We already figured this out in Statement 1 as well. It again does not tell us anything further. INSUFFICIENT DATA

Hence, the statements are insufficient to answer the question.

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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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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:

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

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:

a=3/4

Step-by-step explanation:

1) add 1/6 on both sides

-> 2/3a= 1/3+1/6

->2/3a = 1/2

2) isolate a by multiplying 3/2 on both sides

-> 2/3 x 3/2 a = 1/2 x 3/2

-> a=3/4

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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Step-by-step explanation:

it seems the questions 8., 9. and 10. demonstrate exactly what is the asked via variables in 11., 12. and 13.

you only need to apply the principles of equal angles of crossing lines again.

11.

to be parallel

50 + (x + 30) = 180

x + 80 = 180

x = 100.

12.

135 = 2y + 15

120 = 2y

y = 60

13.

70 = 4x - 10

4x = 80

x = 20

14.

yes, because

142 + 38 = 180°

15.

yes, because

112 + 68 = 180°

16.

no, because

146 + 44 = 190° <> 180°

17.

to be parallel, angle 1 = angle 2

88 = 2x

x = 44

18.

to be parallel, angle 1 = angle 3

88 = 2x + 10

2x = 78

x = 39

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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8 ounce of yellow color required.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two quantities of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol. As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

if you mix 3 ounces of blue paint and 2 ounces of yellow paint.

So, we have the composition ratio as 2:3

Then, to make 20 ounce paint 2/5 of the 20 ounces will be yellow paint, and the other 3/5 will be blue needed.

Thus, yellow = 2/5 x 20= 8 ounce

Blue= 3/5 x20 = 12 ounce

Hence, 8 ounce of yellow color required.

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Answer:

b

Step-by-step explanation:

your answer is b to be precise

The null and alternative hypotheses are-

The null and alternate hypothesis must be formulated as two opposed and mutually excluding hypotheses for hypothesis testing.

A specific laptop model's battery has a typical life of more than 9 hours, according to the claim.

For this assertion, we form:

Null hypothesis H₀; μ ≤ 9

Alternative hypothesis Hₐ: μ > 9

The assertion is represented by the alternative hypothesis in this right-tailed test.

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Answer: $7.5 tip

Step-by-step explanation:

divide 3 an 20 then get 0.15

then multiply 0.15 to 50 get 7.5

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:

0.36

0.26

0.16

0.06

the answers doesn't come in -

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!

Answer:

It would have a slope of a positive 6x

Step-by-step explanation:

Since the slope of the equation shown is -6x, we would just find the opposite which is -6x

Answer:

I would rather use Jane's bank because she earned more interest in a shorter amount of time. Jane's bank has a higher simple interest rate of 3.7%, which means she earned more money in a shorter amount of time than Tommy did with his 3.9% rate.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

A slope field, which displays the slope of a differential equation along specific vertical and horizontal axes of the x-y plane, can be used to estimate the tangent slope at a particular point on a curve, where the curve is one possible solution to the differential equation.

Here,

For figure 1 slope field=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}[/tex]

For figure 2 slope field=

[tex]\frac{dy}{dx} = xy-3\\[/tex]

For figure 1 a solution passing through the point (0,-1)

therefore,

slope=

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(0)-2(-1)}{-1}=-2[/tex]

so slope comes out to be negative

For figure 1 a solution passing through the point (-2,2)

[tex]\frac{dy}{dx}=\frac{-17x-2y}{y}\\\frac{dy}{dx}=\frac{-17(-2)-2(2)}{-1}=-30[/tex]

so slope comes out to be negative

For the slope field in figure 2. a solution passing through the point (1.-3)

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(1*-3)-3=-6[/tex]

so slope comes out to be negative

[tex]\frac{dy}{dx} = xy-3\\\\\frac{dy}{dx}=(0*4)-3=-3[/tex]

so slope comes out to be negative.

Therefore solution to this question is slope at (0,-1) is negative at (-2,2) is negative at (1,-3) is negative & (0,4) is also negative.

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Answer: 48%

Step-by-step explanation:

scale up,

24/50=x/100

multiply 24/50 by 2 to get 100

so you get 48/100 which is 48%

Answer:

57 I think I'm not entirely sure

Answer:

Step-by-step explanation:  

$519.35 + $35

The original price of the iPhone 13 is $554.35

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:

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 probability that he will miss is 25%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The odds in favor of Michael Jordan making a free throw were 21:4.

Total number of throw is 21+4 = 25

The number of time he will miss is 4

So the probability that he will miss is 4/25 = 0.25

Hence, the probability that he will miss is 25%.

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Answer: 86.8 dollars per month