Name the figure as precisely as possible and solve for x.

Refer to the photos taken.

If a skid mark with a length of 82.5 feet was found, then the speed of the car is 13.59 miles per hour

The function is

l(s) = 0.46s^2 - 0.199s + 0.264

Where l is the length of a skid mark measured in feet at an accident scene

s is the speed of the car in miles per hour

Given that the skid mark length = 82.5 feet

Then the equation will be

0.46s^2 - 0.199s + 0.264 = 82.5

Rearrange the terms

0.46s^2 - 0.199s + 0.264 - 82.5 = 0

0.46s^2 - 0.199s - 82.236 = 0

Use the quadratic equation

= [tex]\frac{-b+/-\sqrt{b^2-4ac} }{2a}[/tex]

Substitute the values in the equation

= [tex]\frac{0.199+/-\sqrt{(-0.199)^2-4(0.46)(-82.236)} }{2(0.46)}[/tex]

= (0.199 ± 12.30) / 0.92

Then

(0.199 + 12.30) / 0.92 = 13.59

(0.199 - 12.30) / 0.92 = -13.15

Therefore, the speed of the car is 13.59 miles per hour

The complete question is:

The function l(s) = 0.46s^2 - 0.199s + 0.264 relates the length of a skid mark measured in feet at an accident scene to the speed of the car in miles per hour. that means an accident reconstructionist can measure the length of a skid mark and find the speed the car was traveling. if a skid mark with a length of 82.5 ft was found, find the speed of the car. round your answer to the nearest tenth.

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Answer:

m = [tex]\frac{rise}{run}[/tex]

Step-by-step explanation:

1. take any two points on the line

2. figure out the vertical change between both points, known as the rise

3. figure out the horizontal change between both points, known as the run

4. slope is defined as the variable m and is the [tex]\frac{rise}{run}[/tex]

Community colleges in the United States play an important role in higher education. In United States, everyone monitors they community colleges are primarily her two-year institutions of higher education that focus on teaching and learning and workforce preparation.

Community colleges are open access institutions that offer economically affordable entry into higher education. About half of first-time college-going students enroll in community colleges, which serve as her transition route to four-year colleges (Beach, 2011). However, despite the important role and primary focus of community colleges, students may view community college instruction as inferior and undesirable to her four-year college (Dougherty, Lahr, & Morest, 2017; Twombly, 2001; Twombly & Townsend, 2008). This general dissatisfied view of community college instruction has much to do with the historical legacy of community colleges, where most two-year schools are either officially called "junior colleges" or "junior colleges." is called Community colleges have reason to brag about progress. It tends to have a higher proportion of female and minority teachers compared to traditional her four-year colleges (Antonio, 2002; Marcotte, Bailey, Borkowski, & Kientz, 2005; Turner, 2001). While the high recruitment rate of minority teachers is laudable, most higher education institutions are still predominantly white and male dominated (with the exception of those serving minorities). Overall, despite the high proportion of women and minority teachers, empirical studies show that such teachers experience high levels of stress and frustration with the way students are treated in the classroom. (Allen et al., 2002; Pittman, 2010). For many teachers and teachers of color, the classroom environment serves as a reminder of the unfortunate social ills that plague our society (Harlow, 2003; Seo & Hinton, 2009).

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Answer:

1/6 r-1

Step-by-Step Explanation:

1/6(r-6)

1/6 * (r-6) - distribute 1/6

1/6 r - 1/6 * 6 - simplify the expression

SOLUTION 1/6 r-1

At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

The margin of error is a statistic that describes how much random sampling error there is in survey results. One should have less faith that a poll's findings would accurately reflect those of a population census the higher the margin of error. In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings.

Given,

Starting salaries of 150 college graduates who have taken a statistics course have a mean of $42,991. Suppose the distribution of this population is approximately normal and has a standard deviation of $9,166.

Margin of error:

At 85% confidence level

α = 1 - 85%  

α = 1 - 0.85 = 0.15

Zα/2 = 0.075

α/2 = Z0.075

Zα/2 = 1.44

At 85% confidence interval, the margin of error is 1.44 when the distribution of this population is approximately normal and has a standard deviation of $9,166.

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As per the margin of error, the value of n is 1068

Margin of error

In statistics, margin of error refers the statistic expressing the amount of random sampling error in the results of a survey.

Given

Kim wants to determine a 99 percent confidence interval for the true proportion pp of high school students in the area who attend their home basketball games. Out of n randomly selected students she finds that that exactly half attend their home basketball games.

Here we need to find  how large would n have to be to get a margin of error less than 0.01 for p.

Let us assume the worst case of the point estimate of 99% and n refers size of sample

Here the margin of error is calculated as,

=> Margin of error = z1 - α * standard error of worst case point estimate

=>  z x 99% x √(0.5(1-0.5)/n)

=> 1.96 * 0.5/√n

Now, we have to equate to given margin of error of 0.03, then

=> 0.03 = 1.96*0.5/√n

Then we have to solve for n

=> n = (1.96*0.5/0.03)²

=> n = 32.67²

=>  n = 1067.11

When we round off it, then  we get,

=> n = 1068

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Answer:

=5x2-(20-5)x-20

=5x2-20x+5x-20

=5x(x-4)+5(x-4)

=(x-4)(5x+5)

Answer:-5(2+3x)

Step-by-step explanation:

Answer:

853.15766421

Step-by-step explanation:

The square root of 727878 would be 853.15766421.

Answer:

= 853.157664

Step-by-step explanation:

√727878 = 853.157664

...

..

.

A .The canoe left the campsite did the motorboat catch up with it 3 hrs and 40 minutes

B . The motorboat travel at 1 hr 40 minutes

A group of campers and one group leader left a campsite in a canoe.

They traveled at an average rate of 10 km/h.

1st Group DATA:

rate = 10 km/h ; distance = x km ; time = d/r = x/10 hrs

Two hours later, the other group leader left the campsite in a motorboat.

He traveled at an average rate of 22 km/h.

Group Leader DATA:

rate = 22 km/h ; distance = x km ; time = d/r = x/22 hrs

A. How long after the canoe left the campsite did the motorboat catch up with it?

Group time - Leader time = 2 hr

x/10 - x/22 = 2

Multiply thru by 110 to get:

11x - 5x = 220

6x = 220

x = 110/3 = km

canoe total time = x/10 = (110/3)/(10) = 11/3 = 3 hrs and 40 minutes

B. How long did the motorboat travel?

motorboat time = x/22 = (110/3)/22 = 1 hr 40 minutes

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The diameter of the top of the trash ball is 5 inch.

The diameter is the distance along the circle's center that must travel in order to touch two points on its periphery.

solution:

Given that the diameter of top of the trash can is 20 inch.

And the diameter of trash ball is 1/4th of the diameter of trash can.

The diameter of trash ball = 1/4 ( the diameter of trash can )

The diameter of trash ball = 1/4 (20 inch)

The diameter of trash ball = 20/4

The diameter of trash ball = 5 inch.

Therefore, the diameter of the top of the trash ball is 5 inch.

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The exponent in the term 5x⁶ is of the expression 6

From the question, we have the following parameters that can be used in our computation:

Expression: 5x6+3yr-7yz2+2y/z

Rewrite the expression properly

So, we have the following representation

5x⁶ + 3yr - 7yz² + 2y/z

From the above expression, the spotlight is on the first term

i.e. 5x⁶

Considering an expression represented as axⁿ

Where x is a variable, the exponent is n

Using the above as a guide, we have the exponent of 5x⁶ to be 6

Hence, the exponent is 6

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As per the given question the median size of a new house and the values of different parts of the question will be as follows:

(a) We must locate the period when the rate of change is the smallest in order to establish the period during which the median house size increased the least quickly. Finding the derivative of the following equation will provide us with the rate of change of the house size with respect to time, which we can utilize to do this.

derivative of the function H(x) = 0.359x3 - 15.198x2 + 221.738x + 862.514 given by the equation for the rate of change of the house size with respect to time as

H'(x) = 3 (0.359) x2 - 2 (15.198) x + 221.738

(b) By setting the derivative to 0 and figuring out x, we may determine the moment at which the rate of change is the least. We have x = 3.904 as a result. The time where the rate of change is the smallest is 3.904 years after 1980, or 1984.904, because x denotes the number of years after 1980. This roughly corresponds to 1984, making 1984 the year in which the median house size increased at the slowest rate.

We may enter the value of x into the previous equation to obtain H(1984) = 0.359 x [tex](1984)^{3}[/tex] - 15.198 x [tex](1984)^{2}[/tex] + 221.738 ( 984) + 862.514

= 2,532,358 sq ft. as the comparable house size at this time. In 1984, this was the size of the typical home.

We may enter the value of x into the derivative equation to obtain H'(1984) = 3 (0.359) x [tex](1984)^{2}[/tex] - 2 (15.198 x 1984 + 221.738) = 606.696 sq ft per year, which corresponds to the rate of growth in house size. This represents the median house size's rate of change during the slowest period of growth.

(c) The biggest rate of change must be found in order to pinpoint the period in which the median house size increased most quickly. Finding the derivative equation's greatest value will help us do this. To accomplish this, one can solve for x while setting the derivative equal to 0, then determine the values of x that are either more or less than the answers we obtained. The derivative equation can then be used to solve for the maximum value using these x values.

Using the quadratic formula to solve for x. The quadratic formula is given by x =  [tex]\frac{(-b ± √(b^2 - 4ac))}{2a}[/tex], where a, b, and c are the coefficients of the quadratic equation. Here, a = 3 (0.359) = 1.077, b = -2 (15.198) = -30.396, and c = 221.738. Putting these values into the quadratic formula gives us x = [tex]\frac{(30.396 ± √(30.396^2 - 4 (1.077 X 221.738))}{2 (1.077)}[/tex]

=  [tex]\frac{(30.396 ± √(928.822 - 948.512))}{2.154}[/tex]

=  [tex]\frac{(30.396 ± √(-19.690))}{2.154}[/tex]

=  [tex]\frac{15.198}{2.154}[/tex]

= 7.096.

The derivative equation will have a maximum or lowest value at the value of x that we just discovered because it is a quadratic. We can enter this value of x into the derivative equation to obtain H'(7.096) = 3 x 0 and use this result to determine the derivative equation's maximum value.

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The p-value of the hypothesis test in this problem is given as follows:

0.075.

The first step in calculating the p-value of the test is obtaining the test statistic, which is given by the equation presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which the parameters are defined as follows:

The values of these parameters in this problem are given as follows:

[tex]p = 0.35, n = 500, \overline{p} = \frac{156}{500} = 0.312[/tex]

Hence the test statistic is of:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.312 - 0.35}{\sqrt{\frac{0.35(0.65)}{500}}}[/tex]

z = -1.78.

Now we have to consider that we have a two-tailed test, as we are testing if the mean is different of a value.

Using a z-distribution calculator, with a two-tailed test and z = -1.78, the p-value of the test is given as follows:

0.075.

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The solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

Any equation in algebra that can be rearranged in standard form as follows is known as a quadratic equation (from Latin quadratus, which means "square").

[tex]{\displaystyle ax^{2}+bx+c=0\,,}[/tex]

While a, b, and c are known values, x is an unknown value, and vice versa. The assumption is that a > 0; equations with a = 0 are thought to be degenerate because they become linear or even simpler. The terms "quadratic coefficient," "linear coefficient," and "constant or free term" can be used to distinguish the three values that make up the equation's coefficients, respectively.

Given,

4x²-9x-9=0

4x²-12x+3x-9=0

4x(x-3)+3(x-3)=0

(4x+3)(x-3)=0

4x+3=0, x-3=0

4x-3=0

4x=3

x= -3/4

x-3=0

x=3

Therefore, the solution sets for 4x²-9x-9=0 are -3/4, 3

Hence, the solution sets for the given quadratic equation 4x²-9x-9=0 are -3/4, 3

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The two consecutive positive integers as detailed in the question are;

15 and 16

Let the two consecutive integers be;

x and (x + 1).

We are told that the product of two consecutive positive integers is greater than their sum by 209.

Thus, the expression for this is;

x(x + 1) - 209 = x + x + 1

x² - x - 210 = 0

Using quadratic equation formula, we get;

x = -(-1) ± √((-1)² - 4(1 * -210))]/2(1)

x = (3 ± √(9 + 840)]/2

x = 15

Thus, the second number is; x + 1 = 15 + 1 = 16

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Answer:

14π in.

Step-by-step explanation:

First, we use the area to find the radius.

A = πr²

πr² = 49π in.²

r² = 49 in.²

r = √(49 in.²)

r = 7 in.

Now, we use the radius to fins the circumference.

C = 2πr

C = 2 × π × 7 in.

C = 14π in.

Bruce can be advised to correct his reasoning as the number divisible by six will also remain divisible to 3.

The factor of a number is any number that divides it completely.

In order to find the factors of a number keep dividing it with the known factors.

Given that,

A number is product of 6.

Then, 6 is the factor of that number.

But the factors of 6 are 2 and 3 which implies that 3 is also a factor of that number.

It implies that Bruce has not applied the correct reasoning to reach the conclusion.

Hence, a number which is a product of 6 can also be a product of 3.

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The value of standard deviation is 88,389.

The Normal distribution id the contionuouse distribution with unimodal and symmetric shaped, it is widely used to approximated discrete distribution and sample mean and a total sum of the random variable, the approximation depends on the concept og the Central limit theorem.

The Central limit theorem states that the sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough.

We have given that,

average = 2.500,000

standard deviation σ = 625,000

sample n = 50.

Therefore S = σ / √n

                    = 625000 / √50

                    = 625000 / 7.071

                 S = 88,389

Hence the standard deviation will be 88,389.

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Answer:

a+k =7

Step-by-step explanation:

In the given system of equations, ax + 3y = 10 and kx - 3y = 6, we are told that the solution to the system is (2,1). This means that when we plug the values x = 2 and y = 1 into the equations, we get two true statements.

To find the value of a + k, we can start by plugging the values x = 2 and y = 1 into the first equation to get:

a(2) + 3(1) = 10

Next, we can solve for a by dividing both sides of the equation by 2:

a + 3/2 = 5

a = 5 - 3/2 = 5/2

Next, we can plug the values x = 2 and y = 1 into the second equation to get:

k(2) - 3(1) = 6

Next, we can solve for k by dividing both sides of the equation by 2:

k - 3/2 = 3

k = 3 + 3/2 = 9/2

Finally, we can add the values of a and k to find the value of a + k:

a + k = (5/2) + (9/2) = 14/2 = 7

Therefore, the value of a + k is 7.

The number of hours to operate the mines to minimize cost are Mine 1 hour = 30 hours and Mine 2 hour = 10 hours

The given parameters can be represented using the following table of values

                             Mine 1 (x)              Mine 2 (y)   Available

Regular grade          5                            20             350

Low grade               17                             10              610

Operating cost      7000                     29000

Time                        54                              27

From the table, we understand that we are to minimize cost

This means that:

Objective function: C = 7000x + 29000y

Subject to:

5x + 20y ≥ 350

17x + 10y ≥ 610

Next, we plot the constraints on a graph (see attachment)

From the graph, we have

(x, y) = (30, 10)

This means that

Mine 1 hour = 30 hours

Mine 2 hour = 10 hours

Hence, the number of hours are 30 and 10 hours

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The method for finding the instantaneous rate of change of the depth of the water; in feet per hour; at 6 AM is B. D' ( 6 ) = 0 .

Given :

The function D ( t ) = 10 + 4.9 cos ( pi/6 * t )

D is defined above models the depth, in feet, of the water t hours after 12 am. Which of he following shows the method for finding the instantaneous rate of change of the depth of the water, in feet per hour, at 6 am .

Differentiate :

D'( t )  = -4.9 sin ( πt / 6 ) ( π / 6 )

D'( 6 ) = -4.9 sin ( π ) ( π / 6 )

we know that

sin ( π ) = 0

so D'( 6 ) = 0

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Answer:

10mph

keeping it short so you can ace your quiz :D

if this helps you, it would help me a lot if you could mark this as brainliest :)

P-value is equal to 0.0206 and the significance levels at which there is sufficient evidence to reject H0 are at = 0.05 and [tex]\alpha[/tex]=0.1  and value of 99% CI = 7.132, 10.218.

Here we have,

n= 36

e= 9.06

S.E. = 4.256

Hypothesis

H0: μD = 0

Ha: μD > 0

This a right-tailed test

Test statistics,

t = 2.12

P-value at t= 2.12 and degree of freedom(df) = n-1 =36-1 = 35

P-value = t-dist(t, df, tails)

            = t-dist(2.12, 35, L)

= 0.020585

= 0.0206 Round to 4  decimals

If pvalue>[tex]\alpha[/tex], then we reject the null hypothesis.

So, [tex]\alpha[/tex]= 0.05 and [tex]\alpha[/tex]=0.1 we reject the H0.

For sample of n=45 df will be= 45 -1 =44

t0.025 = 2.015

Mean weight = (7.520 + 9.830)/2 = 8.675

Margin of error = 9.830 - 8.675 = 1.155

SE = 1.155/2.015 = 0.573

99%tc = 2.692

Margin of error = 2.692 x 0.573 = 1.543

99% CI =  8.675 ± 1.543

           = 7.132, 10.218

99% CI = 7.132, 10.218.

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The conclusion the residuals have an increasing variance as the dependent variable increases is correct.

What is scatter chart?

Charts that depict the relationship between two variables are known as scatter charts, also known as scatter plots. They are a very effective type of chart because they enable viewers to see relationships or trends right away that are difficult to see in almost any other form.

In order to observe and visually display the relationship between variables, a scatter plot is a common type of chart. Other names for it include scatter gram, scatter graph, and scatter chart.

The conclusion can be drawn from the scatter chart is,

The residuals have an increasing variance as the dependent variable increases.

There is a violation of the homoskedasticity (homogeneity of variance for residuals) assumption.

The given plot is used to check the assumption for homoskedasticity (homogeneity of variances) of data points.

Hence if the homoskedasticity assumption hold, the spread of data points should be along the line and the line should be approximately horizontal.

From the given plot we can see that spread is centered at the middle not equally distributed along the line which is a violation of the homoskedasticity assumption

Hence, the conclusion the residuals have an increasing variance as the dependent variable increases is correct.

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The scatter chart is attached below.

The option which describes a situation in which reduction occurs Cl2 becoming Cl–. (Option B)

Reduction refers to the type of chemical reactions in which the number of electrons in an atom, or a group of atoms increases. The electrons taken up by the substance reduced are supplied by another substance, which is thereby oxidized. Hence, oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a decrease in the oxidation state. In the given situation, Cl2 becoming Cl- represents reduction as the oxidation state is decreased from 0 to -1.

Note: The question is incomplete. The complete question probably is: Which option describes a situation in which reduction occurs? A) S2– becoming S. B) Cl2 becoming Cl–. C) Al becoming Al3+. D) Xe2+ becoming Xe6+.

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The logarithm of base 7 of t, as a logarithm of base 2 is given as follows:

log2(t)/log2(7).

A logarithm is defined as follows:

log_a(b).

In which:

To change the logarithm to a new base c, the logarithm is written by the fraction presented as follows:

log_c(b)/log_c(a).

In this problem, the logarithm is defined as follows:

log_7 t.

The new base is given as follows:

2.

(as stated in the problem, since we want the logarithm as a logarithm of base 2).

Hence, applying the change of base, the logarithm of base 2 will be given as follows:

log2(t)/log2(7).

As the term log2 represents the logarithm of base 2 of the term.

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The probability that such cuts would be supported by at least 155 persons in a survey of 250 people is 0.62.

Probability is a branch of mathematics that deals with numerical descriptions of the likelihood of an event occurring or a statement being true. The probability of an occurrence is represented by a number between 0 and 1, where 0 signifies the event's impossibility and 1 denotes its certainty.

Assume 60% of the public favors huge government budget cutbacks.

We must determine the likelihood that, in a poll of 250 persons, at most 155 respondents approve such reduction.

As a result, the chance is 155/250 = 0.62.

Hence, probability in that a survey of 250 people ,at most 155 people support such cuts is 0.62.

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The required value of PE is given as 22. The correct option is (B).

The PE ratio can be calculated by taking the ratio of the price of stock to the earning of the company per share.

The given question can be solved as,

The earning per share is $1.80.

And, the closing price i s $40.

Thus, the PE ratio can be calculated as follows,

PE = 40/1.80

     = 22.2

Which is equivalent to 22, rounding to the nearest whole number.

Hence, the PE ratio is given as 22.

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Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

Item a:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 11 - 1 = 10 df and t = 1.91, hence it is of 0.0426.

The p-value is of 0.0426, which is less than 0.05, thus the null hypothesis is rejected.

Item b:

We have a left-tailed test, as it is being tested if the mean is less than a value.

The p-value is found using a t-distribution calculator, with 17 - 1 = 16 df and t = -3.45, hence it is of 0.0016.

The p-value is of 0.0016, which is less than 0.05, thus the null hypothesis is rejected.

Item c:

We have a two-tailed test, as it is being tested if the mean is different than a value.

The p-value is found using a t-distribution calculator, with 7 - 1 = 6 df and t = 0.83, hence it is of 0.4383.

The p-value is of 0.4383, which is more than 0.05, thus the null hypothesis is not rejected.

Item d:

We have a right-tailed test, as it is being tested if the mean is more than a value.

The p-value is found using a t-distribution calculator, with 28 - 1 = 27 df and t = 1.91, hence it is of 0.0195.

The p-value is of 0.0195, which is less than 0.05, thus the null hypothesis is rejected.

Therefore, in an independent random sample is selected from an approximately normal population with an unknown standard deviation. Using the t-distribution, it is found that the null hypothesis is rejected for a, b, c

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