Answer:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
Step-by-step explanation:
Information given
n=100 represent the random sample taken
[tex]\hat p=0.21[/tex] estimated proportion of the readers owned a particular make of car
[tex]p_o=0.31[/tex] is the value that we want to test
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We need to conduct a hypothesis in order to test if the true proportion is 0.31 or no.:
Null hypothesis:[tex]p=0.31[/tex]
Alternative hypothesis:[tex]p \neq 0.31[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
And replacing we got:
[tex]z=\frac{0.21 -0.31}{\sqrt{\frac{0.31(1-0.31)}{100}}}=-2.162[/tex]
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.162)=0.0306[/tex]
Kylie and miranda began arguing about who did better on their tests, but they couln't decide who did better given that they took different tests, kylie took a test in Art History and earned a 77.3, and Tan took a test in English and earned a 62.9. Use the fact that all the students' test grades in the Art History class had a mean of 73 and a standard deviation of 10.7, and all the students' test grades in English had a mean of 66.8 and a standard deviation of 10.8 to answer the following questions.
a) Calculate the Z-score for Isaac's test grade.
b) Calculate the 2-score for lan's test grade.
c) Which person did relatively better?
A. Kylie
B. miranda
C. They did equally well.
Answer:
a) 77.3-73/10.7= 0.40187
b) 62.9-66.8/10.8= -0.36111
c) Kylie did relatively better
Step-by-step explanation:
In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats
Answer: probability = 0.506
Step-by-step explanation:
The data we have is:
Total people: 205 + 160 + 40 = 405
prefer cats: 205
prefer dogs: 160
neither: 40
The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:
p = 205/405 = 0.506
in percent form, this is 50.6%
Unfortunately, the bus broke down at the distance of 50 km continue the story
Answer:
the driver tried to fix it by lighting up the engine thinking it would start again. it didnt and the entire engine set on fire. the bus doors were closed and everyone was trapped inside. everybody inside burnt to a crisp as the fire spread and local residents heard their screams as their skin melted. the end...
Use the equation Y = 3/27x - 54 +5.
Which is an equivalent equation of the form
y=aVx-h+k
y=-273x +2 +5
y=-3x + 2 + 5
y=33x-2+5
y=27*X-2 +5
Answer:
In the picture below for both parts
Step-by-step explanation:
Edge 2021
The solution is Option C.
The value of the equation is y = 3∛ ( x - 2 ) + 5
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
y = ∛ ( 27x - 54 ) + 5 be equation (1)
On simplifying the equation , we get
y = ∛27 ( x - 2 ) + 5
The cube root of 27 is ∛27 = 3
So , the equation will be
y = 3∛ ( x - 2 ) + 5
Therefore , the value of y is 3∛ ( x - 2 ) + 5
Hence , the equation is y = 3∛ ( x - 2 ) + 5
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Can someone divide this using long division please :)
(4x^3– 2x^2 – 3) divide by (2x^2 - 1)
Answer:
The quotient is 2x+1. The remainder is 2x-2
Step-by-step explanation:
A college student is taking two courses. The probability she passes the first course is 0.7. The probability she passes the second course is 0.67. The probability she passes at least one of the courses is 0.79. Give your answer to four decimal places. a. What is the probability she passes both courses
Answer:
0.58 = 58% probability she passes both courses
Step-by-step explanation:
We have two events, A and B.
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In which:
[tex]P(A \cup B)[/tex] is the probability of at least one of these events happening.
P(A) is the probability of A happening.
P(B) is the probability of B happening.
[tex]P(A \cap B)[/tex] is the probability of both happening.
In this question:
Event A: Passes the first course.
Event B: Passes the second course.
The probability she passes the first course is 0.7.
This means that [tex]P(A) = 0.7[/tex]
The probability she passes the second course is 0.67.
This means that [tex]P(B) = 0.67[/tex]
The probability she passes at least one of the courses is 0.79.
This means that [tex]P(A \cup B) = 0.79[/tex]
What is the probability she passes both courses
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
[tex]0.79 = 0.70 + 0.67 - P(A \cap B)[/tex]
[tex]P(A \cap B) = 0.58[/tex]
0.58 = 58% probability she passes both courses
What percent of the area underneath
this normal curve is shaded?
the answer is not 36%
Answer:
95%
Step-by-step explanation:
Answer:
99.7
Step-by-step explanation:
hope this helps !
7. The mean age at first marriage for respondents in a survey is 23.33,
with a standard deviation of 6.13. For an age at first marriage of 33.44,
the proportion of area beyond the Z score associated with this age is
.05. What is the percentile rank for this score?
Answer:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
Step-by-step explanation:
For this case we have the following parameters:
[tex] \mu = 23.33, \sigma =6.13[/tex]
And for this case we are analyzing the value os 33.44 and we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z=\frac{33.44 -23.33}{6.13}= 1.649[/tex]
We know that the proportion of area beyond the Z score associated with this age is .05 so then the percentile would be: 95
will give brainliest Evaluate 15/k when k is 3
Answer:
Hey there!
15/k, when k=3
15/3=5
Answer:
5
Step-by-step explanation:
its a simple as 15/3 = 5
have fun
Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).
Answer:
√17
Step-by-step explanation:
The Pythagorean theorem can be used for the purpose.
hypotenuse² = base² +height²
(√26)² = 3² +height²
26 -9 = height²
height = √17
The length of the other leg is √17.
Find the z-score corresponding to the given area. Remember, z is distributed as the standard normal distribution with mean of and standard deviation .
Answer:
Step-by-step explanation:
The z-score corresponding to a given area of a distribution, is the number of standard deviations that the values in that area have/are from the mean.
In this case, we have a STANDARD normal distribution. In a standard normal distribution, the mean is 0 and the standard deviation is 1.
The Z-score corresponding to a given area, say the 30th percentile is
X = 0 + (-0.524)(1)
Hence, the X (number of values in the given percentile - in this case, 30th) is same as the z-table or z-calculator value for the 30th percentile in ANY normal distribution.
For a certain salesman, the probability of selling a car today is 0.30. Find the odds in favor of him selling a car today.
Answer:
The odds in favor of him selling a car today are 3 to 10
Step-by-step explanation:
Probability and odds:
Suppose we have a probability p.
The odds are of: 10p to 10
In this question:
Probability of selling a car is 0.3.
10*0.3 = 3
So the odds in favor of him selling a car today are 3 to 10
An auto race consists of 15 laps. Jon Kimm completes the first 3 laps at an average speed of 195 mph, and the remaining laps at an average speed of 205 miles per hour. Let d represent the length of one lap. Choose the time in terms of d that it takes the driver to complete the race.
Answer:
equation is inconclusive
Step-by-step explanation:
you average the two speeds getting 200 mph. then you need to know the time is took to fully complete the race to get the unit rate which you would multiply to find yiur time.
The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?
Which point is on the graph of f(x)=3.4x
Answer: The answer is (1, 12).
12 = 3 x 4^{1}
Step-by-step explanation: Hope it helps!
Answer:
Hi! The answer to your question is (1,12)
Step-by-step explanation:
The steps are:
I attached a picture to make sure if that’s the same problem as yours.
So in the picture you can see that there is option A, B, C, D
When we do A and B we will know that it is wrong
When we try C let’s see what we get!
When I did C I got 3.4₁ which equals to 12
Work:
Y=F [1] which equals to 3.4
3.4=12
So the answer will be C. (1,12)
Hope this helps! :)
What is a15 of the sequence −7,2,11,…
?
Step-by-step explanation:
a=-7
d=9
n=15
we have to find a15
a(n)= a+(n-1)d
a(15)= -7+(15-1)9
a(15)= -7+126
a(15)=119
so 15 term of the sequence is 119
The 15th term in the given sequence is 119.
The given sequence is −7,2,11,…
Here, a=-7, d=9
What is the formula to find the nth term of the sequence?The formula to find the nth term of the sequence is [tex]a_{n} =a+(n-1)d[/tex].
Now, [tex]a_{15} =-7+(15-1) \times9=119[/tex].
Therefore, the 15th term in the sequence is 119.
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A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 2 divided by ft for the legs and $ 4 divided by ft for the hypotenuse, write the total cost C of construction as a function of h.
Answer
(4h/√2)+4h
Explanation:
the side length as a function of h will be needed, so we will compute it first,
Let x be the side length of the right isosceles triangle, then using Pythagorean theorem.
CHECK THE ATTACHMENT FOR DETAILED EXPLANATION
Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters
Answer:
Length = 29 m
Width = 29 m
Step-by-step explanation:
Let x and y be the length and width of the rectangle, respectively.
The area and perimeter are given by:
[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]
Rewriting the area as a function of x:
[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]
The value of x for which the derivate of the area function is zero, is the length that maximizes the area:
[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]
The value of y is:
[tex]y = 58-29\\y=29\ m[/tex]
Length = 29 m
Width = 29 m
If -5(x+8) =-25, then x=-3
Answer:
Correct!
Step-by-step explanation:
-5(x+8)=-25
x+8=5
x=-3
Answer:
here, -5(x+8)=-25
or, -5x +(-40)= -25
or, -5x=-25+40
or, x= 15/-5
therefore the value of x is -3....ans..
hope u understood..
The following data represent the miles per gallon for a particular make and model car for six randomly selected vehicles. Compute the mean, median, and mode miles per gallon 24.2. 22.2. 37.8, 22.7. 35 4. 31.61. Compute the mean miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mean mileage per gallon is _______B. The mean does not exist 2. Compute the median miles per gallon. Select the correct choice below and, if necessary, fill in the answer box to complete your choice A. The median mileage per gallon is __________B. The median does not exist. 3. Compute the mode miles per gallon. Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The mode is _________B. The mode does not exist.
Answer:
A. The mean mileage per gallon is _____ 28.99__
A. The median mileage per gallon is _____27.905_____
B. The mode does not exist.
Step-by-step explanation:
Mean= Sum of values/ No of Values
Mean = 24.2 + 22.2+ 37.8+ 22.7 + 35.4 +31.61/ 6
Mean = 173.91/6= 28.985 ≅ 28.99
The median is the middle value of an ordered data which divides the data into two equal halves. For an even data the median is the average of n/2 and n+1/2 value where n is the number of values.
Rearranging the above data
22.2 , 22.7 , 24.2 , 31.61 , 35.4, 37.8
Third and fourth values are =24.2 + 31.61 = 55.81
Average of third and fourth values is = 55.81/2= 27.905
Mode is the values which is occurs repeatedly.
In this data there is no mode.
Please help. !!!!! Only if you are good at college algebra
I the horizontal change between two points on a line.
Answer:
m = rise /run = (y2-y1)/(x2-x1)
Step-by-step explanation:
In math, slope is the ratio of the vertical and horizontal changes between two points on a surface or a line. The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run.
Answer: Run is the horizontal change between two points on a line.
Step-by-step explanation:
i am stuck on this please help!
Answer:
[tex]20 {x}^{3} - 36 {x}^{2} + 7x + 3[/tex]Solution,
[tex](5x + 1)(2x - 1)(2x - 3)[/tex]
[tex] = 5x(2x - 1) + 1(2x - 1) \times (2x - 3) \\ = (10 {x}^{2} - 5x + 2x - 1)(2x - 3) \\ = (10 {x}^{2} - 3x - 1)(2 x - 3) \\ = 10 {x}^{2} (2x - 3) - 3x(2 x - 3) - 1(2x - 3) \\ = 20 {x}^{3} - 30 {x}^{2} - 6 {x }^{2} + 9x - 2x + 3 \\ = 20 {x}^{3} - 36 {x}^{2} + 7x + 3[/tex]
Hope this helps..
Good luck on your assignment...
Stats A simple random sample of FICO scores is listed below. The mean FICO score is reported to be 678. Assuming that the standard deviation of all FICO scores is known to be 58.3, use a 0.01 significance level to test the claim that these sample FICO scores come from a population with a mean equal to 678. DATA: 714, 751, 664, 789, 818 , 779, 698, 836, 753, 834, 693, 802.
Step-by-step explanation:
The sample mean is:
(714+751+664+789+818+779+698+836+753+834+693+802) / 12
≈ 760.9
At 0.01 significance level and 11 degrees of freedom, the critical value is t = 3.106.
The standard error is 58.3 / √12 = 16.8.
The confidence interval is:
760.9 ± 3.106 × 16.8
(708.6, 813.2)
678 is outside of the confidence interval, so we can conclude with 99% confidence that the sample does not come from a population with a mean of 678.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
What is t-test?A t-test is a statistical test used to determine if there is a significant difference between the means of two groups.
It is often used when the sample size is small or when the population standard deviation is unknown.
To test the claim that the sample FICO scores come from a population with a mean equal to 678, we can use a one-sample t-test.
First, we need to calculate the t-value using the following formula:
t = (x - μ) / (s / sqrt(n))
We are given that x = 678, μ = 678, s = 58.3, and n = 12. Substituting these values into the formula, we get:
t = (678 - 678) / (58.3 / sqrt(12))
t = 0
Next, we need to find the critical t-value using a t-distribution table or calculator with 11 degrees of freedom (df = n - 1) and a 0.01 significance level. The critical t-value is 3.106.
Since the calculated t-value of 0 is less than the critical t-value of 3.106, we fail to reject the null hypothesis that the sample FICO scores come from a population with a mean equal to 678.
Thus, in other words, there is not enough evidence to support the claim that the sample FICO scores have a different mean than the population mean of 678.
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Evaluate the expression (image provided). A.) 1.5 B.) 6 C.) 6^15 D.) 1.5^6
Answer:
1.5
Step-by-step explanation:
6 to the log base of 6 will be one (they essentially cancel each other out, log is the opposite of exponents) and we are left with 1.5.
Fill in the table using this function rule.
Answer:
1, 2.2, 5.5, 10.2.
Step-by-step explanation: these are simplified to the nearest tenth
Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)
Answer:
Monthly: $4,821
Weekly: $1112.54
Step-by-step explanation:
Monthly
A monthly salary can be found by dividing the yearly salary by the number of months.
salary / months
His salary is $57,852 and there are 12 months in a year.
$57,852/ 12 months
Divide
$4,821 / month
Jeremy makes $4,821 per month.
Weekly
To find the weekly salary, divide the yearly salary by the number of weeks.
salary / weeks
He makes $57,852 each year and there are 52 weeks in one year.
$57,852 / 52 weeks
Divide
$1112.53846 / week
Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.
$1112.54 / week
Jeremy makes $1112.54 per week
Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be to find the amount of money you can expect to win or lose if you play this game 100 times. How many times would you win? how many times would you lose?
Answer:
(a)$67
(b)You are expected to win 56 Times
(c)You are expected to lose 44 Times
Step-by-step explanation:
The sample space for the event of rolling two dice is presented below
[tex](1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]
Total number of outcomes =36
The event of rolling a 5 or a 6 are:
[tex](5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)[/tex]
Number of outcomes =20
Therefore:
P(rolling a 5 or a 6) [tex]=\dfrac{20}{36}[/tex]
The probability distribution of this event is given as follows.
[tex]\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|[/tex]
First, we determine the expected Value of this event.
Expected Value
[tex]=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67[/tex]
Therefore, if the game is played 100 times,
Expected Profit =$0.67 X 100 =$67
If you play the game 100 times, you can expect to win $67.
(b)
Probability of Winning [tex]=\dfrac{20}{36}[/tex]
If the game is played 100 times
Number of times expected to win
[tex]=\dfrac{20}{36} \times 100\\=56$ times[/tex]
Therefore, number of times expected to loose
= 100-56
=44 times
Determine the logarithmic regression of the data below using either a calculator or spreadsheet program. Then, estimate the x−value when the y−value is 5.2. Round your answer to one decimal place. (4.7,10.7),(7.8,20.6),(10.5,30.2),(15.6,41),(20.8,56.1),(22,65.1). Please help right away! Thank you so much!
Answer:
y ≈ 33.7·ln(x) -45.94.6Step-by-step explanation:
A graphing calculator can perform logarithmic regression, as can a spreadsheet. The least-squares best fit log curve is about ...
y ≈ 33.7·ln(x) -45.9
The value of x estimated to make y = 5.2 is about 4.6.
The mean MCAT score 29.5. Suppose that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2. Test the claim that the students that took the Kaplan tutoring have a mean score greater than 29.5 at a 0.05 level of significance.
Answer:
We conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.
Step-by-step explanation:
We are given that the Kaplan tutoring company obtains a sample of 40 students with a mean MCAT score of 32.2 with a standard deviation of 4.2.
Let [tex]\mu[/tex] = population mean score
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] 29.5 {means that the students that took the Kaplan tutoring have a mean score less than or equal to 29.5}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 29.5 {means that the students that took the Kaplan tutoring have a mean score greater than 29.5}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean MCAT score = 32.2
s = sample standard deviation = 4.2
n = sample of students = 40
So, the test statistics = [tex]\frac{32.2-29.5}{\frac{4.2}{\sqrt{40} } }[/tex] ~ [tex]t_3_9[/tex]
= 4.066
The value of t-test statistics is 4.066.
Now, at 0.05 level of significance, the t table gives a critical value of 1.685 at 39 degrees of freedom for the right-tailed test.
Since the value of our test statistics is more than the critical value of t as 4.066 > 1.685, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the students that took the Kaplan tutoring have a mean score greater than 29.5.