In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.

a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?

b. Roughly what proportion of vehicle speeds exceeded 57 mph?

Answer:

the probability that exactly 8 dentists in 10 samples recommend Colgate toothpaste is;

P(X) = 0.0043

P(X) = 0.43%

Step-by-step explanation:

The probability that a dentist recommend Colgate is;

P = 90% = 0.9

The probability that a dentist doesn't recommend Colgate is;

P' = 1 - P = 1 -0.9 = 0.1

Of 10 sample dentists, the probability that exactly 8 dentists recommend Colgate toothpaste is;

8 will recommend and two will not recommend it.

P(X) = P^8 × P'^2

P(X) = (0.9)^8 × (0.1)^2

P(X) = 0.0043

P(X) = 0.43%

The Probability of exactly 8 dentists in sample recommend Colgate toothpaste is 0.0043.

Since, Colgate claims that 90% of dentists recommend Colgate toothpaste.

Probability of dentist, who recommend Colgate toothpaste = 0.9

Probability of dentist, who does not recommend Colgate toothpaste,

                                       = 1 - 0.9 = 0.1

When 10 dentist randomly choose , out of which 8 dentists recommend Colgate toothpaste. It means that 8 recommend  Colgate toothpaste and 2 recommend other tooth paste.

Thus, The Probability of exactly 8 dentists in sample recommend Colgate ,

                  [tex]=(0.9)^{8}*(0.1)^{2} =0.0043[/tex]

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Step-by-step explanation:

in mathematics, a basic algebra corporation is there any one of the traditional operation of arithmetic, which are addition, subtraction, multiply, division, rising to an integer power, and taking root (fractional power ).

Answer:

  1.4

Step-by-step explanation:

The average rate of change is the "rise" divided by the "run".

  rise/run = (f(4) -f(-1))/(4 -(-1)) = (0 -(-7))/(4+1)

  rise/run = 7/5 = 1.4

The average rate of change on the interval [-1. 4] is 1.4.

We will see that the average rate of change in the given interval is 1.4

For a given function f(x), the average rate of change on an interval [a, b] is given by:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In this case the interval is [-1, 4], using the graph we can see that:

f(-1) = -7

f(4) = 0

replacing that in the formula we get:

[tex]r = \frac{0 - (-7)}{4 - (-1)} = \frac{7}{5} = 1.4[/tex]

If you want to learn more about rates of change, you can read:

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Answer: short answer

Just checked it’s False

Hope this helps :))

Step-by-step explanation:

Answer:

B. False

Step-by-step explanation:

A P E X

Answer:

Step-by-step explanation:

Rearranging the weights in ascending order, it becomes

5.4, 5.7, 5.7, 5.8, 6.0, 6.6, 7.1, 7.1, 7.5, 7.5, 8.1, 8.7, 9.3, 9.4, 9.4

The formula for determining the percentile is expressed as

n = (P/100)N

Where

n represents the value of the given percentile

P represents the given percentile

N represents the number of items(weights)

From the information given, the number of items, n is 15

P = 53

Therefore,

n = (53/100) × 15

n = 7.95

n = 8

Therefore, the weight that represents the 53rd percentile is the 8th value. It becomes 7.1

53rd percentile is 7.1

Answer: It’s to change the shape of a function

Step-by-step explanation:

To change the shape of a function, you need to stretch or compress it.

In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.

By definition, a function has one possible output for any given input. So if you want your function defined as some y=f(x), then not every shape can be written as a function. Any shape that has two points directly above each other (relative to the x-axis) cannot be written as a function, even a piecewise one.

Learn more about the shape of a function, here: https://brainly.com/question/1884491

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Answer:

yes the above is a function.

Answer:  [tex]y=4x-35[/tex]

y = Sidney’s weekly salary

x = Casey’s weekly salary

Answer: y=4x-35

x is Casey's salary

Y is Sidney's salary

Step-by-step explanation:

Sidney makes a quarter of Casey,

y=4x,

Then it also states that he makes 35 less than the first equation.

Therefore,

Y=4x-35

Answer:

x = 15

Step-by-step explanation:

3x = 45

x = 45/3

x = 15

Answer:

15

Step-by-step explanation:

3x = 45

Dividing 3 from both sides gives you

[tex]x = 45/3\\\\[/tex]

Now that isolated x.

[tex]45/3 = 15[/tex]

So x = 15

:D

Answer:

A sample size of at least 531 is required.

Step-by-step explanation:

We are lacking the confidence level to solve this question, so i am going to use a 90% confidence level.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Find the required sample size for the new study.

A sample size of at least n is required.

n is found when [tex]M = 0.05[/tex]

We have that [tex]\sigma = 0.7[/tex]

So

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.05 = 1.645*\frac{0.7}{\sqrt{n}}[/tex]

[tex]0.05\sqrt{n} = 1.645*0.7[/tex]

[tex]\sqrt{n} = \frac{1.645*0.7}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.645*0.7}{0.05})^{2}[/tex]

[tex]n = 530.4[/tex]

Rounding up

A sample size of at least 531 is required.

Answer:

7x+6 = 6x-3

Step-by-step explanation:

2 (x + 3) + 5 x = 3 (2 x - 1)

Distribute

2x+6+5x = 6x-3

Combine like terms

7x+6 = 6x-3

Answer:

7x + 6 = 6x - 3                                  Option A

Step-by-step explanation:

Now Jalesa wants to simplify this equation.

Firstly applying the distributive property

Distribute the 2 over the parenthesis and distribute the over the parenthesis

that is,

2*x + 2*3 + 5x = 3*2x - 3*1

2x + 6 + 5x = 6x - 3

After that combine like terms

2x + 5x + 6 = 6x - 3

7x + 6 = 6x - 3

Result is:

7x + 6 = 6x - 3

That's the final answer.

Answer:

9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

Step-by-step explanation:

For each theft, there are only two possible outcomes. Either the need to buy drugs is the reason of the theft, or it is not. Each theft is independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

In a certain city district the need for money to buy drugs is stated as the reason for 70% of all thefts.

This means that [tex]p = 0.7[/tex]

Find the probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

This is P(X = 3) when n = 7. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{7,3}.(0.7)^{3}.(0.3)^{4} = 0.0972[/tex]

9.72% probability that among the next 7 theft cases reported in this district, exactly 3 of them resulted from the need to buy drugs.

Answer:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar x = 40, s =10[/tex]

And from these values we can estimate the sample variance like this:

[tex] s^2 = 10^2 =100[/tex]

And we can also estimate the coeffcient of variation given by:

[tex] \hat{CV} =\frac{s}{\bar x}[/tex]

And replacing we got:

[tex] \hat{CV} = \frac{10}{40}= 0.25[/tex]

And this coefficient is useful in order to see the variability in terms of the mean for this case since is lower than 1 we can conclude that this variation around the mean is low.

Answer:

Step-by-step explanation:

Consider the augments matrix (the right most column is  the extra vector).

[tex]\left[\begin{matrix} 1 & 4 & -2 \\3 & h & -6\end{matrix}\right][/tex]

By multypling the first row by 3 and substracting it from the second row and saving the result in the second row we get the matrix

[tex]\left[\begin{matrix} 1 & 4 & -2 \\0 & h-12 & 0\end{matrix}\right][/tex]

Note that since the value of the third column in the second row is 0, any value of h gives us a consistent system. An inconsistent system is when we get a row of zeros that is equal to a number different from 0.

Answer:

The undefined term which is used to define an angle is line i.e., . Further explanation: In geometry the three terms which are considered to be undefined are line, point and plane.

Answer:

Line

Step-by-step explanation:

A line is a undefined term used to define a angle. An angle is the corner that is created where two non-parallel lines meet/ intersect

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean GPA of night students and μ2 be the mean GPA of day students.

The random variable is μ1 - μ2 = difference in the mean GPA of night students and the mean GPA of day students.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 ≠ μ2 H1 : μ1 - μ2 ≠ 0

This is a two tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

μ1 = 2.35

μ2 = 2.58

s1 = 0.46

s2 = 0.47

n1 = 30

n2 = 25

t = (2.35 - 2.58)/√(0.46²/30 + 0.47²/25)

t = - 1.8246

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [0.46²/30 + 0.47²/25]²/[(1/30 - 1)(0.46²/30)² + (1/25 - 1)(0.47²/25)²] = 0.00025247091/0.00000496862

df = 51

We would determine the probability value from the t test calculator. It becomes

p value = 0.0746

Since alpha, 0.05 < than the p value, 0.0746, then we would fail to reject the null hypothesis.

Hey there!

First, let's take all of the expenses and change the ones that aren't monthly into monthly.

Groceries: $800/month

Car insurance: $87.5/month

Gasoline: $100/month

Now, let's add together all of our expenses

1090+800+125+87.5+100+200+50=2452.5

Now, we subtract that from her salary.

2300-2452.5=-152.5

Therefore, Rebecca's net monthly cash flow is -$152.5. She should spend a bit less on groceries, not do so much miscellaneous, find a place that charges less rent, drive less, etc. so she isn't spending more than she earns.

I hope that this helps! Have a wonderful day!

Answer:

a) 10.08 gallons and $32.66 of gas

b) gallons used = n/25

c)cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex]

Step-by-step explanation:

a) We know that Kimberly has traveled 252 miles and we also know that her car gets 25 miles per gallon. We can apply proportions and rule of three:

25 miles ------ 1 gallon

252 miles ----- x gallons

Solving for x:

x gallons = 252 miles(1 gallon)/25 miles= 10.08 gallons.

Thus, she has used 10.08 gallons since she started driving.

Now we need to know the cost of the gasoline that she has used.

We know that each gallon of gas costs $3.24 and she has used 10.08 gallons. Again, we can apply proportions and rule of three:

1 gallon ------ 3.24 dollars

10.08 gallons---- x dollars.

Solving for x we get:

[tex]x=(10.08)(3.24)[/tex]= 32.659=32.66 dollars.

Thus, she has used $32.66 of gas since she started driving.

b) Write an expression in terms of n that represents the number of gallons of gasoline she has used since she started driving.

If we know that n is the number of miles that she drives, from what we wrote above, an expression to know the number of gallons she has used would be:

Gallons used = n/25 (since her car gets 25 miles per gallon) where n is the number of miles.

c) Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.

Again, to know the cost of the gasoline we first need to know how many gallons she has used. From b) we know that the expression to know how many gallons she has used is n/25. Since each gallon costs $3.24 we will multiply this number by n/25 and we will get the cost (like we did in a))

Therefore, the cost of the gasoline = [tex]\frac{n}{25}(3.24)[/tex] where n is the number of miles.

Answer:

Isosceles right triangle

Answer:

It is a scalene triangle because 2 angles are equal and one angle is different .

Step-by-step explanation:

please mark as brainliest and follow me!!!!!...

Answer:47.1

Step-by-step explanation:6.28/4=x/30

                                             188.4=4x

                                              47.1=x

Answer:

47.1

Step-by-step explanation:

height of 1 book=6.28÷4=1.57

height of 30 books=1.57×30=47.1

Answer:

3u-2v = [tex]\sqrt{505\\}[/tex]

5u-v = [tex]\sqrt{1,157}[/tex]

2u-3v = [tex]\sqrt{1,300}[/tex]

u+4v = [tex]\sqrt{4,505}[/tex]

Step-by-step explanation:

I just started by doing the results for each of the operations given.

3u-2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u-2v and you get a resultant vector of (19, 12).

You calculate this by doing the square root of 19^2 + 12^2, which is the square root of 505.

5u-v:

5u = (-15, 40)       v = (-14, 6)

Do the operation of 5u-v and you get a resultant vector of (-1, 34).

You calculate this by doing the square root of (-1)^2 + 34^2, which is the square root of 1,157.

2u-3v:

2u = (-6, 16)   3v = (-42, 18)

Do the operation of 2u-3v and you get a resultant vector of (36, -2).

You calculate this by doing the square root of 36^2 + (-2)^2, which is the square root of 1,300.

3u+2v:

3u = (-9, 24)       2v = (-28, 12)

Do the operation of 3u+2v and you get a resultant vector of (-37, 36).

You calculate this by doing the square root of (-37)^2 + 36^2, which is the square root of 2,665. This is not a given tile, so we can just ignore this one.

u+4v:

u = (-3, 8)       4v = (-56, 24)

Do the operation of u+4v and you get a resultant vector of (-59, 32).

You calculate this by doing the square root of (-59)^2 + 32^2, which is the square root of 4,505.

Since this is a given tile, I didn't do 7u-2v, but you would use the same methodology.

Answer: [tex]y=\frac{3}{2} x - 3[/tex]

Step-by-step explanation:

Looking at the  graph we could locate the y intercept at point (0,-3)  and we can locate another point (4,3) which also passes through the line.  So using these coordinates we already know the the y-intercept as -3 but we need to find the slope to write it in slope intercept form.

To find the slope, we will need to find the difference in the y values and divide it by the difference in the x values.

(0,-3)

(4,3)

-3 - 3 = -6

0-4 =  -4  

-6 /-4 =  3/2   so now we know that the slope is 3 over 2  

so we could write the equation as   y = 3/2x -3  

Answer: Thank you (nermay7)

Step-by-step explanation: They are correct!!!!!!!

Answer:

Step-by-step

The null and the alternative hypothesis can be define as  follows,

Null Hypothesis; There is no significance difference between the proportions of non participating athletes in 1999 and 2000

[tex]H_0:(p_1-p_2)\neq 0[/tex]

Alternative Hypothesis: The proportion of non participating  athletes in  2000 will be more than the proportion of non participating athletes in 1999

[tex]H_1:(p_1-p_2)<0[/tex]

The proportion of nonparticipating athletes in 1999 is given by

[tex]\hat p_1 = \frac{x_1}{n_1} \\\\=\frac{159}{830} =0.1916[/tex]

The proportion of nonparticipating athletes in 2000 is given by

[tex]\hat p_2 =\frac{x_2}{n_1} \\\\=\frac{133}{825} =0.1612[/tex]

The pooled proportion can be calculated using the following formula

[tex]\hat p = \frac{x_1+x_2}{n_1+n_2} \\\\=\frac{159+133}{830+825} =0.1764[/tex]

under the null hypothesis, the test statistics can be calculated as follows

[tex]Z=\frac{\hat p_1 - \hat p_2}{\sqrt{\hat p \hat q(\frac{1}{n_1}+\frac{1}{n_2} ) } }[/tex]

[tex]=\frac{0.1916-0.1612}{\sqrt{(0.1764)(0.8236)(\frac{1}{830} +\frac{1}{825} )} } \\\\=1.6257[/tex]

Determine the P-value using the following formula

P-value = Normdist(1.6257)

=0.947993

Here, it can be observed that the P-value is greater than the level of the significance,

Hence, the null hypothesis fails to be rejected

Therefore it can be concluded that there is insufficient evidence to support that the proportions of non participating athletes in 2000 will be more than the proportions of non participating athletes in 1999

Answer:

Population = 34.27336

Step-by-step explanation:

Given:

Population function (t) = 34(1.00804)^t

Number of year = 2000

Find:

Number of citizen in year 2000

Computation:

We know that, base year is 2000

So, t = 1

Population function (t) = 34(1.00804)^t

Population function (1) = 34(1.00804)^1

Population = 34(1.00804)

Population = 34.27336

Therefore, Population is 34.273636 million

Answer:

(a) The probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b) The probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Step-by-step explanation:

The  cumulative distribution function of the random variable X, the waiting time, in hours, between successive speeders spotted by a radar unit is:

[tex]F(x)=\left \{ {{0;\ x<0} \atop {1-e^{-9x};\ x\geq 0}} \right.[/tex]

(a)

Compute the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function as follows:

[tex]12\ \text{minutes}=\frac{12}{60}=0.20\ \text{hours}[/tex]

The probability is:

[tex]P(X<0.20)=|F (x)|_{x=0.20}[/tex]

                  [tex]=(1-e^{-8x})|_{x=0.20}\\\\=1-e^{-8\times 0.20}\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the cumulative distribution function is 0.7981.

(b)

The probability density function of X is:

[tex]f_{X}(x)=\frac{d F (x)}{dx}=\left \{ {{0;\ x<0} \atop {8e^{-8x};\ x\geq 0}} \right.[/tex]

Compute the probability of waiting less than 12 minutes between successive speeders using the probability density function as follows:

[tex]P(X<0.20)=\int\limits^{0.20}_{0} {8e^{-8x}} \, dx[/tex]

                  [tex]=8\times [\frac{-e^{-8x}}{8}]^{0.20}_{0}\\\\=[-e^{-8x}]^{0.20}_{0}\\\\=(-e^{-8\times 0.20})-(-e^{-8\times 0})\\\\=-0.2019+1\\\\=0.7981[/tex]

Thus, the probability of waiting less than 12 minutes between successive speeders using the probability density function is 0.7981.

Answer:

A.

Step-by-step explanation:

Volume of cone = 1/3πr²h

= (1/3)(3.14)(1.5)²(5)

= (1/3)(3.14)(2.25)(5)

= (1/3)(35.3)

= 11.78

≈ 11.8 cubic inches

Answer:

The best data collection method or sampling method to provide an unbiased sample is the random sampling method.

Step-by-step explanation:

There are 5 popular known sampling methods or data collection methods.

1) Random Sampling

In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.

2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.

3) Convenience Sampling

This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.

4) Stratified Sampling

Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

5) Cluster sampling

Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.

Hope this Helps!!!

Answer:

9/16

Step-by-step explanation:

captain has a 3/4 probability of hitting the ship

pirate has a 1/4 probability of hitting the ship

This means he has a 3/4 probability of missing the ship

P (captain hitting and pirate missing) = 3/4*3/4 = 9/16