Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
3.14 The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with cumulative distribution function F(x) = 0, x< 0, 1 − e−8x, x ≥ 0. Find the probability of waiting less than 12 minutes between successive speeders (a) using the cumulative distribution function of X; (b) using the probability density function of X.
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.
Classify the following triangle .check all that apply
Answer:
Isosceles right triangle
Answer:
It is a scalene triangle because 2 angles are equal and one angle is different .
Step-by-step explanation:
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Kimberly goes on a road trip; her car gets 25 miles per gallon (mpg) and gas costs $3.24 per gallon. Let n represent the number of miles Kimberly has traveled since she started driving.
a. Suppose Kimberly has traveled 252 miles (n 252) since she started driving. i. How many gallons of gasoline has she used since she started driving? gallons Preview i. What is the cost of the gasoline that she has used 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.
c. Write an expression in terms of n that represents the cost of the gasoline that she has used since she started driving.
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.
Observe the expression below and select the true statement(s).
3y(7 + 2x) + 9ry - 10
The "(7 + 2x)" in the first term is a factor.
The "9" in the second term is a coefficient.
The "By" in the first term is a factor.
The "10" in the third term is a coefficient.
The "2" in the first term is a constant.
The "x" in the second term is an exponent
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.
:)
PLEASE HELPPPPPPPPPP <3
Answer:
y = 1/2x + 4
Step-by-step explanation:
Slope intercept form is y = mx + b, where m is the slope and b is the y-intercept.
When we count rise over run, we find that the slope is 1/2
y = 1/2x + b
The line intersects the y-axis at 4, so the y-intercept is 4.
y = 1/2x + 4
I hope this helps :))
You are testing the claim that the mean GPA of night students is different from the mean GPA of day students. You sample 30 night students, and the sample mean GPA is 2.35 with a standard deviation of 0.46. You sample 25 day students, and the sample mean GPA is 2.58 with a standard deviation of 0.47. Test the claim using a 5% level of significance. Assume the sample standard deviations are unequal and that GPAs are normally distributed. Give answer to exactly 4 decimal places.Hypotheses:sub(H,0):sub(μ,1) = sub(μ,2)sub(H,1):sub(μ,1) ≠ sub(μ,2)**I'm not sure how to calculate this in excel***Enter the test statistic - round to 4 decimal places.A=Enter the p-value - round to 4 decimal places.A=
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.
To ______ a function, you need to stretch or compress it
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.
How to stretch or compress a function?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.
Is there a function for every shape?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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Which data collection method would provide an unbiased sample?
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!!!
Which operation is the default operation in algebra?
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 ).
A sinusoid is any function whose values repeat in a periodic manner.
A. True
B. False
SUBMIT
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
average of a data set was 40, and that standard deviation was 10, what else could you derive from that information.
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.
If the captain has a 3/4 probability of hitting the ship and the pirate has a 1/4 probably what is the probability the pirate hits and the captain misses
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
334% of what number is 33,400
Answer:
10000
Step-by-step explanation:
3.34x=33400
x=10000
The number is x=10000.
What is percentage?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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Given cot ø = 4/3. Find the other two reciprocal trigonometic ratios. 1) scs 2) sec
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
A fuel oil company claims that one-fifth of the homes in a certain city are heated by oil. Do we have reason to believe that fewer than one-fifth are heated by oil if, in a random sample of 1000 homes in this city, 136 are heated by oil? Please show all 4 steps of the classical approach clearly using α = 0.05.
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.
What is the average rate of change of f over the interval [-1, 4] Give an exact number.
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
How to find the average rate of change?
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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{(1,3),(2,5)(3,-4),(4-3),(5,1)} a function or not a function
Answer:
yes the above is a function.
maths
Ella mixes cordial and water in the ratio of 1:4 how much water should be mixed with 50ml or cordial
y=2x−4y=−12x+1 Question 1 options: a) (3, 2) b) (0, 2) c) (2, 0) d) (2, 3)
How do I explain this answer
Answer:
199
Step-by-step explanation:
i dont know
SOLVE THE EQUATION SHOW YOUR WORK 3x = 45
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
In order to solve for the variable in the equation 2 (x + 3) + 5 x = 3 (2 x minus 1), Jaleesa begins by applying the distributive property, then combines like terms. Which equation is the result of these steps?
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.
IQ levels: A study investigated whether there are differences between the mean IQ level of people who were reared by their biological parents and those who were reared by someone else. What is the null hypothesis in this case
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.
Colgate claims that 90% of dentists recommend Colgate toothpaste. Suppose you randomly choose 10 dentists and ask whether they recommend Colgate toothpaste. What is the probability that exactly 8 dentists in your sample recommend Colgate toothpaste
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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Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
PLEASE HELP
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!!!!!!!
is –68 + 90 positive or negative?
Answer:
22. positive
Step-by-step explanation:
–68 + 90
22
The radius of a circle is 2.6 in. Find the circumference
to the nearest tenth.
Answer:
16.
Step-by-step explanation:
since given the radius and the formula of the circumference of a circle is 2pie*r
A stack of 4 identical books is 6.28 high. What is the heigh of 30 of these books?
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
Find the mode for the following distribution.
Number Frequency
16
3
20
5
24
9
28
7
32
7
36
5
40
3
24
28
32
28 and 32
Answer:
28 and 32
Step-by-step explanation:
they have the most
Erythropoietin (EPO) is a banned drug used by athletes to increase the oxygen-carrying capacity of their blood. New tests for EPO were first introduced prior to the 2000 Olympic Games held in Sydney, Australia. Chance (Spring 2004) reported that of a sample of 830 world-class athletes, 159 did not compete in the 1999 World Championships (a year prior to the new EPO test). Similarly, 133 of 82:5 potential athletes did not compete in the 2000 Olympic Games. Was the new test effective in deterring an athlete's participation in the 2000 Olympics? If so, then the proportion of nonparticipating athletes in 2000 will be greater than the proportion of nonparticipating athletes in 1999, Use a 98% confidence interval to compare the two proportions and make the proper conclusion.
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