Suppose that a storm front is traveling at 33 mph. When the storm is 13 miles away a storm chasing van starts pursuing an average speed of 54 mph. How long does it take for the van to catch up with the storm? How far have they driven? (Hint: we can let our two variables be x= distance and t= time. Additionally, [speed x time= distance]. Won’t the van catch up when the distances are equal?


Please make it easy to understand your answer :)

Answer:

28 and 32

Step-by-step explanation:

they have the most

Answer:

yes the above is a function.

Answer:

Yes, we have reason to believe that fewer than one-fifth are heated by oil.

Step-by-step explanation:

A one-sample proportion test is to be performed to determine whether fewer than one-fifth of the homes in a certain city are heated by oil.

The hypothesis can be defined as follows:

H₀: The proportion of homes in a certain city that are heated by oil is not less than one-fifth, i.e. p ≥ 0.20.  

Hₐ: The proportion of homes in a certain city that are heated by oil is less than one-fifth, i.e. p < 0.20.

The information provided is:

n = 1000

x = 136

α = 0.05

Compute the sample proportion as follows:

[tex]\hat p=\frac{x}{n}=\frac{136}{1000}=0.136[/tex]

Compute the test statistic as follows:

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

  [tex]=\frac{0.136-0.20}{\sqrt{\frac{0.136(1-0.136)}{1000}}}\\\\=-5.9041\\\\\approx -5.90[/tex]

The test statistic value is, -5.90.

Decision rule:

Reject the null hypothesis if the p-value of the test is less than the significance level.

Compute the p-value as follows:

[tex]p-value=P(Z<-5.90)\\\\=1-P(Z<5.90)\\\\=1-(\approx 1)\\\\=0[/tex]

The p-value of the test is, 0.

p-value = 0 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Conclusion:

The proportion of homes in a certain city that are heated by oil is less than one-fifth.

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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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:

10000

Step-by-step explanation:

3.34x=33400

x=10000

The number is x=10000.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

let, the number = x

now, we get,

3.34x=33400

x=10000

Hence, The number is x=10000.

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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:

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:

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:

(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: The 9 in the second term is a coefficient that is true. I think that is the only thing that is true. There may be one more thing that is true.

The 10 in the third term is not  a coefficient.

The 2 is not a constant

the x is not an exponent.

those are the ones that I'm sure about.

Please correct anything if i'm wrong.

:)

Answer:

csc ø = 5/3 ; sec ø = 5/4

Step-by-step explanation:

cot ø = adj/opp

adj = 4

opp = 3

after that, we must find the hypotenuse by using phytagoras theorem

hpy² = adj² + opp²

hpy² = 4² + 3²

hpy² = 25

hpy = 5

now let's find the other

csc ø (not scs) = hyp/opp = 5/3

sec ø = hyp/adj = 5/4

Answer:

The null hypothesis: there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.

Step-by-step explanation:The null hypothesis can be a general statement mostly in statistics that proposes no difference or no relationship between 2 phenomena etc

Researchers always carry out a study to test against the null hypothesis ie the opposite of the null hypothesis showing that there is a difference. In this study, the researchers aim is to establish that there is a difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. This goes against the null which states that

there is no difference between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else.

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:

16.

Step-by-step explanation:

since given the radius and the formula of the circumference of a circle is 2pie*r

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:

22. positive

Step-by-step explanation:

–68 + 90

22

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:

199

Step-by-step explanation:

i dont know

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:

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:

  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]

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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.

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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:

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

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: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:

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.