The area of a square is increasing at the constant rate of 16sq.ft./min. When the perimeter of the square is 36ft, how fast is the perimeter of the square increasing?

Answer:

5! = 120

Step-by-step explanation:

5! is basically 5(4)(3)(2)(1).

Answer:

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u >= 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u/ (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = -0.22 / (0.41/4.2426)

t = -0.22/ 0.0966

t = -2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.

Answer:

X = 2

Step-by-step explanation:

[tex]if \: {x}^{3} + {3}^{x} = 17 \: we \: can \: conclude \: that \: x \: is \: equal \: to \: two \\ {2}^{3} + {3}^{2} = 8 + 9 = 17[/tex]

Answer:

Ans) 42.7%

Step-by-step explanation:

For a continuous probability distribution, a curve known as probability density function contains information about these probabilities.

in the given range -

The probability that a continuous random variable = equal to the area under the probability density function curve

The probability that the value of a random variable is equal to 'something' is 1.

As per the diagram,

Weight of chocolate bar between 4 ounces and 7 ounces is highlighted in the blue part. That area is said to be 0.42739 and the total area under the curve is 1.

Hence required probability

=0.42739/1=0.42739

Ans) 42.7%

Round to nearest tenth of a percent

Answer:

y = -1/2x + 1/2

Step-by-step explanation:

Step 1: Write in known variables

y = -1/2x + b

Step 2: Find b

2 = -1/2(-3) + b

2 = 3/2 + b

b = 1/2

Step 3: Rewrite equation

y = -1/2x + 1/2

Answer:

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

(11,688.68 , 12,511.32)

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 17

mean of the sample x⁻ = 12,100

Standard deviation of the sample (S) = 800

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom ν =n-1 = 17-1 =16

[tex]t_{(16 , 0.05)} = 2.1199[/tex]

The 95​% confidence interval for the true mean resale value of a​ 5-year-old car of this​ model

[tex](x^{-} - t_{0.05} \frac{S}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S}{\sqrt{n} } )[/tex]

[tex](12,100 - 2.1199\frac{800}{\sqrt{17} } , 12,100 + 2.1199 \frac{800}{\sqrt{17} } )[/tex]

(12,100 - 411.32 , 12,100 + 411.32)

(11,688.68 , 12,511.32)

Answer:

18

Step-by-step explanation:

area of a triangle is length x base

so 6 x 6 = 36

36 divided by 2 = 18

I hope it helps :)

Answer: The area is about 15.59 and is round to the nearest hundredth.

Step-by-step explanation:

An equilateral triangle has three equal sides is just like an isosceles triangle.

So in this case, we know that the base is 6 and since the base is 6 all the other two sides is also 6 .But we do not know the height to find the area so we need to find the height.

The height is the distance of from the base to the tip or top which helps form two right triangles.. And if you divide as  an equilateral triangle into two parts you will form two right triangles. Imagine we have divide the isosceles triangle into two parts to form two right triangles. We will now have a base of 3 instead of 6 and and hypotenuse of 6 .  but we still don't know the height so we need to  find it.

Using the Pythagorean Theorem we could say that a^2 plus b^2 squared is equal to c^2 squared.

We know a as 3 and c the hypotenuse as 6.

so 3^2 + b^2 =6^2  solve for b

  9 + b^2 = 36

 -9               -9

   b^2 = 27

  b= [tex]\sqrt{27}[/tex]  

b= 5.196  

Now we know that b is about 5.196 which is the  height.Now we could find the area by  multiplying  the base by the height.

5.196 * 6 = 31.176  

31.176/2 = 15.588  

Now you could round it to the nearest hundredth to be 15.59  

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

[tex]Standard Form - \frac{\left(x-5\right)^2}{\left(\sqrt{7}\right)^2}-\frac{\left(y-\left(-5\right)\right)^2}{3^2}=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=\sqrt{7},\:b=3\\[/tex]

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!

Answer: a. 0.1031; fail to reject the null hypothesis

Step-by-step explanation:

Given: Significance level : [tex]\alpha=0.05[/tex]

The test statistic in a two-tailed test is z = -1.63.

The P-value for two-tailed test : [tex]2P(Z>|z|)=2P(Z>|-1.63|)=0.1031[/tex] [By p-value table]

Since, 0.1031 > 0.05

i.e. p-value > [tex]\alpha[/tex]

So, we fail to reject the null hypothesis. [When p<[tex]\alpha[/tex] then we reject null hypothesis  ]

So, the correct option is a. 0.1031; fail to reject the null hypothesis.

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

 [tex]\bar{x} = 1,465,752[/tex]

The standard deviation of mean salary is

 [tex]s = 1,346,046.2[/tex]

The confidence interval for the mean salary of all basketball coaches is given by

 [tex]$ CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]

Where [tex]\bar{x}[/tex] is the sample mean, n is the sample size, s is the sample standard deviation and  [tex]t_{\alpha/2}[/tex] is the t-score corresponding to a 95% confidence level.  

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is  

[tex]CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\[/tex]

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

[tex]\bar{x} = 1,371,191[/tex]

The standard deviation of the mean salary is

[tex]s = 1,130,666.5[/tex]

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is  

[tex]CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\[/tex]

Answer:

21900

Step-by-step explanation:

There are 12 months in a year, so multiply the yearly amount by 12

1825 * 12

21900

Answer:

Bob makes $21,000 in a year.

Step-by-step explanation:

There are 12 months in a year, so if he earns $1,825 every month to get his yearly pay you need to add 1,825 twelve times. Thus, 1,825×12=21,000. Hope this helps!

Answer:

7/2x

Step-by-step explanation:

Well first we need to put,

2x + 7y = 5,

into slope intercept

-2x

7y = -2x + 5

Divide y to all numbers

y = -2/7x + 5/7

So the slope for the given line is -2/7,

the slope of the line that is perpendicular to it is its reciprocal.

Meaning the slope of the perpendicular line is 7/2.

Thus,

the slope of the perpendicular line is 7/2x.

Hope this helps :)

Answer:

The slope of the perpendicular line is 7/2

Step-by-step explanation:

2x+7y=5

Solve for y to find the slope

2x-2x+7y=5-2x

7y = -2x+5

Divide by 7

7y/7 = -2/7 x +5/7

y = -2/7x + 5/7

The slope is -2/7

The slope of perpendicular lines multiply to -1

m * -2/7 = -1

Multiply each side by -7/2

m * -2/7 *-7/2 = -1 * -7/2

m = 7/2

The slope of the perpendicular line is 7/2

Answer: No there isn't

Explanation:

A score of 53.7% is quite close to 50% and this is a true or false exam. Charlie could have easily gotten this result by indeed guessing and not studying. This test mark is therefore not high enough to disregard the teachers's claim. Were the results to be significantly high enough above 50% then it could be said that indeed Charlie does study for his exams.

Answer:2/3

Step-by-step explanation:

Given that the length of the rectangle is described by the function y = 3x + 6, where x is the width of the rectangle. The domain of the function is (0, ∞).

The domain of a function is the set of all possible inputs for the function. In other words, domain is the set of all possible values of x. In this question, x is the width of the rectangle. Width of a rectangle existing in two dimensional space, cannot be negative or zero. Thus it is the set of all positive real numbers, or we say, (0, ∞).

Learn more about domain of a function here

https://brainly.com/question/13113489

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Answer:

[tex]\displaystyle AB \approx 8.39 \text{ inches} \text{ and } AC \approx 13.05 \text{ inches}[/tex]

Step-by-step explanation:

Note that we are given the measure of ∠C and the length of side BC.

To find AB, we can use the tangent ratio. Recall that:

[tex]\displaystyle \tan\theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \tan 40^\circ = \frac{AB}{BC} = \frac{AB}{10}[/tex]

Solve for AB:

[tex]\displaystyle AB = 10\tan 40^\circ \approx 8.39\text{ inches}[/tex]

For AC, we can use cosine ratio since we have an adjacent and need to find the hypotenuse. Recall that:

[tex]\displaystyle \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}}[/tex]

Substitute in appropriate values:

[tex]\displaystyle \cos 40^\circ = \frac{BC}{AC} = \frac{10}{AC}[/tex]

Solve for AC:

[tex]\displaystyle \begin{aligned} \frac{1}{\cos 40^\circ} & = \frac{AC}{10} \\ \\ AC & = 10\cos 40^\circ \approx 13.05\text{ inches} \end{aligned}[/tex]

In conclusion, AB is about 8.39 inches and AC is about 13.03 inches.

Answer:

[tex]153.86 \: {units}^{2} [/tex]

Step-by-step explanation:

[tex]area = \pi {r}^{2} \\ = 3.14 \times 7 \times 7 \\ = 3.14 \times 49 \\ = 153.86 \: {units}^{2} [/tex]

Answer:

153.86 [tex]units^{2}[/tex]

Step-by-step explanation:

Areaof a circle = πr^2

[tex]\pi = 3.14[/tex](in this case)

[tex]r^{2} =7[/tex]

A = πr^2

= 49(3.14)

= 153.86

Answer:

95891769

Step-by-step explanation:

This is extract from a brain teaser exercise in which sequence is formed to identify the numbers. In this brain teaser we have made combinations of different numbers which lead to the correct answer. The two correct forms of number are given which are used as a base for determining the correct answer.

Answer:

She makes conclusion about a population that is not well represented by the sample.

Step-by-step explanation:

The conclusion she is making is about a population that is not well represented by her sample: the population is the homeowners in the nation, but the sample is made of homeowners or only her state.

The population about which she can make conclusions with this sample is the homeowners of her state, given that the sampling is done right.

Answer: The sample is biased

Answer:

12, 1

Step-by-step explanation:

12- 6(1)=

12-6= 6

Answer:

1. A, C

2. A, D

Step-by-step explanation:

The mutually exclusive events are one which cannot happen together. The observation is made regarding with which students live. They live with either one of their biological parent or grandparent. The student have the option to live with two legally married couple this is mutually exclusive event. If the student is living with their one biological parent he cannot live with two legally married parents.

Answer:

[tex]n=(\frac{2.58(0.15)}{0.025})^2 =239.63 \approx 240[/tex]

So the answer for this case would be n=240 rounded up to the nearest integer

Step-by-step explanation:

We know the following info:

[tex]\sigma =0.15[/tex] represent the population deviation

[tex] ME= 0.025[/tex] the margin of error desired

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex]   (b)

The critical value for 99% of confidence interval now can be founded using the normal distribution. And we got [tex]z_{\alpha/2}=2.58[/tex], replacing into formula (b) we got:

[tex]n=(\frac{2.58(0.15)}{0.025})^2 =239.63 \approx 240[/tex]

So the answer for this case would be n=240 rounded up to the nearest integer

Answer:

1250,Rs

Step-by-step explanation:

Let Reetu paid for the watch x Rs. Then Reetu sold the watch to Reshmi having 20% profit => the selling price is 1.2*x

Then Teshmi sold the wathes with 10% loss (or 0.9 from purchase price 1.2x)   to Nikita, i.e. selling price is

1.2*x*0.9=1350

1.08*x=1350

x=1350:1.08

x=1250, Rs

Answer:

-6, -3

3, 8

Step-by-step explanation:

In order to find the number that are solutions to the compound inequalities, you first solve fr x on each inequality.

First inequality:

[tex]4(x+3)\leq 0\\\\4x+12\leq0\\\\4x\leq-12\\\\x\leq-3[/tex]  interval = (-∞ , -3]

Second inequality:

[tex]x+1>3\\\\x>2[/tex]   interval = (2 , ∞)

The interval solution is (-∞ , -3] U (2 , ∞)

The number that are included in the previous interval are:

-6, -3

or

3, 8

Answer: any except 0

Step-by-step explanation:

Step-by-step explanation:

pnotgrt8rthan4 = 3 ÷ 7 × 100

= 42.8571428571 / 43%

Answer:

8

Step-by-step explanation:

Because it is equal to the 4 side

Answer:

The rising tide gobbled up the sandcastle that the children had so carefully crafted.

Step-by-step explanation:

personification is when you use human characteristics to describe something non-human.

Answer:

Solved below.

Step-by-step explanation:

The data is provided for the starting salary (in $1,000) at some company and years of prior working experience in the same field for randomly selected 10 employees.

(a)

The formula to compute the correlation coefficient is:

[tex]r=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\[/tex]

The required values are computed in the Excel sheet below.

[tex]\begin{aligned}r~&=~\frac{n\cdot\sum{XY} - \sum{X}\cdot\sum{Y}} {\sqrt{\left[n \sum{X^2}-\left(\sum{X}\right)^2\right] \cdot \left[n \sum{Y^2}-\left(\sum{Y}\right)^2\right]}} \\r~&=~\frac{ 10 \cdot 7252 - 97 \cdot 661 } {\sqrt{\left[ 10 \cdot 1335 - 97^2 \right] \cdot \left[ 10 \cdot 45537 - 661^2 \right] }} \approx 0.9855\end{aligned}[/tex]

Thus, the sample correlation coefficient r is 0.9855.

(b)

The slope of the regression line is:

[tex]b_{1} &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 10 \cdot 7252 - 97 \cdot 661 }{ 10 \cdot 1335 - \left( 97 \right)^2} \\\\\approx 2.132[/tex]

Thus, the slope of the regression line is 2.132.

(c)

The y-intercept of the line is:

[tex]b_{0} &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} \\\\= \frac{ 661 \cdot 1335 - 97 \cdot 7252}{ 10 \cdot 1335 - 97^2} \\\\\approx 45.418[/tex]

Thus, the y-intercept of the line is 45.418.

(d)

The equation of the sample regression line is:

[tex]y=45.418+2.132x[/tex]

(e)

Compute the predicted starting salary for a person who spent 15 years working in the same field as follows:

[tex]y=45.418+2.132x\\\\=45.418+(2.132\times15)\\\\=45.418+31.98\\\\=77.398\\\\\approx 77.4[/tex]

Thus, the predicted starting salary for a person who spent 15 years working in the same field is $77.4 K.

Answer:

Yes correct

Step-by-step explanation:

I think this is correct becase: 2 50

5 55

7 62

etc

these are all correct

Answer:

Step-by-step explanation:

I'm not sure what are u asking exactly

Answer:

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

[tex]\mu = 13, \sigma = 0.2[/tex]

What percentage of players on the team run the 100-meter dash in 13.36 seconds or faster

We have to find the pvalue of Z when X = 13.36.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{13.36 - 13}{0.2}[/tex]

[tex]Z = 1.8[/tex]

[tex]Z = 1.8[/tex] has a pvalue of 0.9641

96.41% of players on the team run the 100-meter dash in 13.36 seconds or faster