Answer:
Decreased by 20%
Step-by-step explanation:
0.5 x ? = 0.4
? = 0.4/0.5
? = 0.8
1 - 0.8 = 0.2
0.2 = 20%
To check, 20% of 0.5 is 0.1. 0.5 - 0.1 is 0.4. So the answer is correct.
Suppose that a local TV station conducts a survey of a random sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
Required:
a. Construct and interpret a 99% CI for the true proportion of voters who prefer the Republican candidate.
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
Answer:
a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.
So 120 - 62 = 58 favored the Republican candidate, so:
[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]
The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).
b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.
The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.
From the figure, the cylinder glass has a height of 6 inches and a radius of the mouth of the glass 1.25 inches. Find the length of SK in inches.
Answer:
D. 6.5
Step-by-step explanation:
The diameter of the cylinder is 1.25 x 2 = 2.5
SK = √1.25² + 6² = √42.25 = 6.5
Each Friday, the sixth grade students in Mr. Shin's physical education class spend the first five minutes doing crunches. Instead of keeping track of the weekly total number of crunches, Mr. Shin keeps track of how they do compared to the week before, and then records the result as a positive or negative number. Record the number for each of the following:
Ben did 10 more crunches this week than last week. What number would Mr. Shin record?
Gail did 8 less crunches this week than last week. What number would Mr. Shin record?
Nathaniel did the same number of crunches this week as last week. What number would Mr. Shin record?
awnser asap
Answer:
Mr. Shim would record the number +10 or 10 for Ben because of the word "more".
For Gail, Mr. Shin would record the number -8 because of the word, "less''.
Since Nathaniel did not improve or decrease the number of crunches, Mr. Shin would record the number 0.
I hope this helps better
Mila wants to buy a scooter for Rs 62,000 . She has only Rs 19,000 with her, so she decides to take a loan from a bank for the remaining amount. The bank offers Mini three loan schemes as shown below. Mini has to return the loan amount with interest in equal monthly instalments
1) How much money does mila take as loan from the bank?
a) Rs 62,000
b) Rs 44,000
c) Rs 45,000
d) Rs 43,000
Answer:
Scheme a 45000 is the answer
The range is the set of________
A) First Coordinates
B) Ordered Pairs
C) Second coordinates
Answer:
The range is the set of first coordinates
Working for a car company, you have been assigned to find the average miles per gallon (mpg) for acertain model of car. you take a random sample of 15 cars of the assigned model. based on previous evidence and a qq plot, you have reason to believe that the gas mileage is normally distributed. you find that the sample average miles per gallon is around 26.7 with a standard deviation of 6.2 mpg.
a. Construct and interpret a 95% condence interval for the mean mpg, , for the certain model of car.
b. What would happen to the interval if you increased the condence level from 95% to 99%? Explain
c. The lead engineer is not happy with the interval you contructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Answer:
a) The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b) Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c) 37 cars would have to be sampled.
Step-by-step explanation:
Question a:
We have the sample standard deviation, and thus, the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 15 - 1 = 14
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 14 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.1448
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.1448\frac{6.2}{\sqrt{15}} = 3.4[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 26.7 - 3.4 = 23.3 mpg.
The upper end of the interval is the sample mean added to M. So it is 26.7 + 3.4 = 30.1 mpg.
The 95% confidence interval for the mean mpg, for the certain model of car is (23.3, 30.1). This means that we are 95% sure that the true mean mpg of the model of the car is between 23.3 mpg and 30.1 mpg.
b. What would happen to the interval if you increased the confidence level from 95% to 99%? Explain
Increasing the confidence level, the value of T would increase, thus increasing the margin of error and making the interval wider.
c. The lead engineer is not happy with the interval you constructed and would like to keep the width of the whole interval to be less than 4 mpg wide. How many cars would you have to sample to create the interval the engineer is requesting?
Width is twice the margin of error, so a margin of error of 2 would be need. To solve this, we have to consider the population standard deviation as [tex]\sigma = 6.2[/tex], and then use the z-distribution.
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 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
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.
How many cars would you have to sample to create the interval the engineer is requesting?
This is n for which M = 2. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]2 = 1.96\frac{6.2}{\sqrt{n}}[/tex]
[tex]2\sqrt{n} = 1.96*6.2[/tex]
[tex]\sqrt{n} = \frac{1.96*6.2}{2}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*6.2}{2})^2[/tex]
[tex]n = 36.9[/tex]
Rounding up:
37 cars would have to be sampled.
Give the domain and range of G={(6.0),(-9,-3),(1,-3)}
Answer:
Step-by-step explanation:
D={ 6 , -9 , 1 }
R={ 0 ,-3 }
Please help me determine the general equation for the graph above as well as solve for a. Thank you.
Observe that the x coords of the roots of a polynomial are,
[tex]x_{1,2,3,4}=\{-3,0,1,4\}[/tex]
Which can be put into form,
[tex]y=a(x-x_1)(x-x_2)(x-x_3)(x-x_4)[/tex]
with data
[tex]y=a(x-(-3))(x-0)(x-1)(x-4)=ax(x+3)(x-1)(x-4)[/tex]
Now if I take any root point and insert it into the equation I won't be able to solve for y because they will always multiply to zero (ie. when I pick [tex]x=-3[/tex] the right hand side will multiply to zero,
[tex]y=-3a(-3+3)(-3-1)(-3-4)=0[/tex]
and a will be "lost" in the process.
If we observed a non-root point that we could substitute with x and y and result in a non-loss process then you could find a. But since there is no such point (I don't think you can read it of the graph) there is no other viable way to find a.
Hope this helps :)
Factor.
64x^12 + 27y^3
Answer:
answer is (4x^4+3y)(16x^8-12x^4y+9y^2)
Step-by-step explanation:
Most brainiest for the right answer on this problem!
Answer:
82.8
Step-by-step explanation:
mean = sum of all points, over the total given number of points
84 * 26 = 2184
2184 + 69 + 66 = 2319
Now the total number of tests is 26 + 2 or 28
So divide 2319 by 28
2319/28 = 82.82142
rounded to the nearest tenth is 82.8
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
In the figure above, AABC is an equilateral
triangle and each circle is tangent to the other
two circles. If each circle has diameter 10, what
is the distance h?
(A) 103
(B) 1513
(C) 15+513
(D) 10+1013
(E) 10+5/5
Answer:
B
Step-by-step explanation:
Suppose you choose a marble from a bag containing 4 red marbles, 2 white marbles, and 3 blue marbles. You return the first marble to the bag and then choose again. Find P(red then blue).
Answer:
4/27
Step-by-step explanation:
total number of marbles=9
probability of red=4/9
since you returned the first marble, the total number of marbles remains the same
prob(Blue)=(3/9)=1/3
P(red then blue)=(4/9)*(1/3)
=4/27
Carmen Martinez
What is the slope of the line that passes through the point 4,4 and 10,7 write your answer in simplest form
[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto m\approx0.5[/tex]
Answer:
[tex]m=\frac{1}{2}[/tex]
Step-by-step explanation:
The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{7-4}{10-4}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m=\frac{1}{2}[/tex]
[tex]m=0.5[/tex]
1. (02.01)
Solve -4(x + 10) - 6 = -3(x - 2). (1 point)
-40
-46
-52
52
Answer:
-52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Answer: -52
Step-by-step explanation:
-4(x + 10) - 6 = -3(x - 2)
Distribute the left side to get:
(-4x + -40) - 6
Now distribute the right side to get:
-3x + 6
Arrange the equation as the following:
-4x - 40 - 6 = -3x + 6
Add the like terms on each side:
-4x - 46 = -3x + 6
Do the inverse operation of each term:
-x = 52
Now we need to get x to become a positive, so we just divide -x by -1 to get x.
And 52/-1 to get our final answer of -52.
Question 6 of 10
Which situation shows a constant rate of change?
A. The number of tickets sold compared with the number of minutes
before a football game
B. The height of a bird over time
C. The cost of a bunch of grapes compared with its weight
D. The outside temperature compared with the time of day
SUBMI
a) the cost of a bunch of grapes compared with its weight
GRAAAAAAAAAAAAAAAAAAAAAAAAAAAAPES!!!!!
14 cm 8 cm 10cm 5 cm.
find the area and the perimeter of the above figures
Perimeter = Sum of all sides
Perimeter = 14cm + 8cm + 10cm + 5cm
Perimeter = 22cm + 15cm
Perimeter = 37cm
Step-by-step explanation:
hope it helps you
...
........
I need help ASAP please please please
Answer:
n=39/5
Step-by-step explanation:
24=5(n-3)
24=5n-15
-5n= -15-24
-5n=39
n= 39/5
i need help figuring it out
Which of the following is NOT a requirement for testing a claim about two population standard deviations or variances? A. The populations are independent. B. One of the populations is normally distributed. C. The two samples are simple random samples. D. This test requires that both populations have normal distributions.
Answer:
B. One of the populations is normally distributed.
Step-by-step explanation:
To test a claim about two population standard deviation or variance, it is imperative that the data meets certain requirements which include :
Randomness : Data must not be biased as such it must be drawn as a random sample from a larger group.
The data must be independent. That is not related to one another, the outcome of one should not rely on the outcome or value of another.
Both groups must be drawn From a population which is normally distributed.
One group being normally distributed by stribuyed while the other isn't a requirement for hypothesis testing in this scenario.
Can anyone please help me out?
Please help me with 9 I really need it
Answer:
605 boys.
Step-by-step explanation:
5:7 means 5 parts consists of boys and 7 parts consist of girls.
Since 7 parts = 847, 1 part = 121 and 5 parts = 605
Hence there are 605 boys.
Hope you have a nice day :)
solve for x please help (show ur work)
Answer:
x = -3
Step-by-step explanation:
12 -4x-5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from each side
12-9x-12 = 39-12
-9x = 27
Divide by -9
-9x/-9 = 27/-9
x = -3
Answer:
x = -3
Step-by-step explanation:
12 - 4x - 5x = 39
Combine like terms
12 - 9x = 39
Subtract 12 from both sides
12 - 12 - 9x = 39 - 12
-9x = 27
Divide both sides by -9
-9x/-9 = 27/-9
x = -3
5^3×25=
Simplify as much as possible
I add 7 to a certain number. I double the result. My final answer is 34. What was my number?
Answer:
answer is 10
explanation
when u add 7 with 10 u get 17 then double of 17 is 34
I hope It helps
It is found that the unknown number was 10.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. The addition is one of the mathematical operations. then the addition of two numbers results in the total amount of the combined value.
Given that "I add 7 to a certain number. I double the result. My final answer is 34".
Let consider the number be 10.
When we add 7 with 10 we get;
7 + 10 = 17
then double the result of 17 = 34
Hence, the unknown number was 10.
Learn more about equations here;
https://brainly.com/question/25180086
#SPJ2
A solid is formed by rotating the region bounded by y = x − x^2 and y = 0 about the line x = 2 . Use the shell method to find the volume of the solid.
Answer:
The volume of the resulting solid is π/2 cubic units.
Step-by-step explanation:
Please refer to the diagram below.
The shell method is given by:
[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]
Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.
From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:
[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]
Evaluate:
[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]
The volume of the resulting solid is π/2 cubic units.
Answer:
pi/2
Step-by-step explanation:
I always like to draw an illustration for these problems.
For shells method think volume of cylinder=2pi×r×h
Integrate(2pi(2-x)(x-x^2) ,x=0...1)
Multiply
Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)
Combine like terms
Integrate(2pi(2x-3x^2+x^3) ,x=0...1)
Begin to evaluate
2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1
2pi(x^2-x^3+x^4/4), x=0...1
2pi(1-1+1/4)
2pi/4
pi/2
The distribution of widgets from a production line is known to be approximately normal with mean 2.7 inches and standard deviation 0.25 inches. About 95% of the distribution lies between what two values?
A. 2.45 inches and 3.2 inches
B. 2.45 inches and 2.95 inches
C. 2.2 inches and 3.2 inches
D. 1.95 inches and 3.45 inches
Option D is correct. 95% of the distribution lies between 1.9975inches and 3.4025inches.
To get the required range of values, we will have to first get the z-score for the two-tailed probability at a 95% confidence interval. According to the normal table, the required range is between -2.81 and 2.81
The formula for calculating the z-score is expressed as;
[tex]z=\frac{x-\overline x}{s}[/tex] where:
[tex]\overline x[/tex] is the mean
s is the standard deviation
z is the z-scores
Given the following
[tex]\overline x[/tex]=2.7 in
s = 0.25
if z = -2.81
[tex]-2.81=\frac{x-2.7}{0.25}\\x-2.7=-2.81*0.25\\x-2.7=-0.7025\\x=-0.7025+2.7\\x=1.9975[/tex]
Similarly:
[tex]2.81=\frac{x_2-2.7}{0.25}\\x_2-2.7=2.81*0.25\\x_2-2.7=0.7025\\x_2=0.7025+2.7\\x_2=3.4025[/tex]
Hence the 95% of the distribution lies between 1.9975inches and 3.4025inches.
Learn more on normal distribution here: https://brainly.com/question/23418254
Students at a virtual school are allowed to sign up for one math class each year. The numbers of students signing up for various math classes for the next school
year are given in the following table:
Grade Geometry Algebra II Pre-Calculus AP Statistics Total
10th
150
75
25
5
255
11th
50
100
75
20
245
12th
10
50
100
65
225
Total 210
225
200
90
725
Part A: What is the probability that a student will take AP Statistics? (2 points)
Part B: What is the probability that a 12th-grader will take either Pre-Calculus or AP Statistics? (2 points)
Part C: What is the probability that a student will take Algebra II given that he or she is in the 11th grade? (2 points)
Part D: Consider the events "A student takes Algebra II and "A student is a 10th-grader. Are these events independent? Justify your answer. (4 points)
A well formatted table of the distribution is attached below :
Answer:
0.124
0.733
0.408
Step-by-step explanation:
Using the table Given :
1.) P(AP Statistics) = 90 / 725 = 0.124
2.) P(12th grade ; Precalculus or AP Statistics) = (100 + 65) / 225 = 165 /225 = 0.733
3.) P(Algebra 11 | 11th grade) = P(Algebara11 n 11th grade) / P(11th grade) = 100 / 245 = 0.408
Yooooo HELPPP
with this question plz
Answer:
Step-by-step explanation:
(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0
Answer:
A
Step-by-step explanation:
Stuck on this problem
9514 1404 393
Answer:
-8,257,536·u^5·v^10
Step-by-step explanation:
The expansion of (a +b)^n is ...
(c0)a^nb^0 +(c1)a^(n-1)b^1 +(c2)a^(n-2)b^2 +... +(ck)a^(n-k)b^k +... +(cn)a^0b^n
Then the k-th term is (ck)a^(n-k)b^k, where k is counted from 0 to n.
The value of ck can be found using Pascal's triangle, or by the formula ...
ck = n!/(k!(n-k)!) . . . . where x! is the factorial of x, the product of all positive integers less than or equal to x.
This expansion has 11 terms, so the middle one is the one for k=5. That term will be ...
5th term = (10!/(5!(10-5)!)(2u)^(10-5)(-4v^2)^5
= (252)(32u^5)(-1024v^10) = -8,257,536·u^5·v^10
PLSSS HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
I believe its EG and NE but i might be wrong
Step-by-step explanation:
