Complete Question
According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. Suppose a random sample of 100 Americans is asked "Are you satisfied with the way things are going in your life?"
What is the probability the sample proportion who are satisfied with the way things are going in their life is greater than 0.85
Answer:
The probability is [tex]P(X > 0.85 ) = 0.21745[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.82[/tex]
The value considered is x = 0.85
The sample size is n = 100
The standard deviation for this population proportion is evaluated as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
substituting values
[tex]\sigma = \sqrt{\frac{0.82(1-0.82)}{100} }[/tex]
[tex]\sigma = 0.03842[/tex]
Generally the probability that probability the sample proportion who are satisfied with the way things are going in their life is greater than x is mathematically represented as
[tex]P(X > x ) = P( \frac{X - p }{ \sigma } > \frac{x - p }{ \sigma } )[/tex]
Where [tex]\frac{X - p }{ \sigma }[/tex] is equal to Z (the standardized value of X ) so
[tex]P(X > x ) = P( Z> \frac{x - p }{ \sigma } )[/tex]
substituting values
[tex]P(X > 0.85 ) = P( Z> \frac{ 0.85 - 0.82 }{ 0.03842 } )[/tex]
[tex]P(X > 0.85 ) = P( Z> 0.78084)[/tex]
from the standardized normal distribution table [tex]P( Z> 0.78084)[/tex] is 0.21745
So
[tex]P(X > 0.85 ) = 0.21745[/tex]
when using the rational root theorem, which of the following is a possible root of the polynomial function below f(x)=x^3-5x^2-12x+14
A.9
B.3
C.7
D.5
Answer:
[tex]\Large \boxed{\sf \ \ 7 \ \ }[/tex]
Step-by-step explanation:
Hello, please consider the following.
The polynomial function is
[tex]x^3-5x^2-12x+14[/tex]
The rational root theorem states that each rational solution
[tex]x=\dfrac{p}{q}[/tex]
, written in irreducible fraction, satisfies the two following:
p is a factor of the constant term
q is a factor of the leading coefficient
In this example, the constant term is 14 and the leading coefficient is 1. It means that p is a factor of 14 and q a factor of 1.
Let's proceed with the prime factorisation of 14:
14 = 2 * 7
Finally, the possible rational roots of this expression are :
1
2
7
14
and we need to test for negative ones too
-1
-2
-7
-14
From your list, the correct answer is 7.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
the answer is C.) 7
0.25 multiplied by 15 = ?
What is ?
Answer:
Your correct answer is 3.75
Step-by-step explanation:
0.25 x 15 = 3.75
Answer:
3.75
Step-by-step explanation:
You can do this many ways. Write a table that looks like this:
0.25
15
--------
Ignore all decimal points. Multiply the 5's together and carry the 2 to the next column. Multiply 2 x 5 + 2, write the second digit (which is 2) and carry the 1. Multiply 0 by 5 + 1 = 1, so your top number should be 125. Then, multiply all the numbers by the 1. 5 x 1 = 5; 2 x 1 = 2; 0 x 1 = 0. We now have something that looks like:
0.25
15
--------
1 2 5
0 2 5
Add these numbers together and add the decimal point 2 numbers from the right, since that's what was in the original decimal.
1 2 5
0 2 5
---------------
3.75
What the answer now fast
sine(X) = opposite side / hypotenuse
sine(X) = (2√11) / (4√11)
sine(X) = (2/4)
sine(X) = 0.5
X = arcsine(0.5)
X = 30°
Answer: m∠x = 30°
Step-by-step explanation:
In a right triangle, if the short side of the right angle is Half the length of the hypotenuse, the triangle has angles of 30°, 60° and 90°
∠x is the smallest one, so m∠x = 30°
It is possible to figure the sine and get the angle from that, but in this case it might not be necessary. ;-)
Using the quadratic formula y=4x ²-81
Answer:
[tex]\huge\boxed{x=\pm4.5}[/tex]
Step-by-step explanation:
The quadratic formula of
[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]
We have:
[tex]y=4x^2-81\to 4x^2-81=0\\\\a=4;\ b=0;\ c=-81[/tex]
substitute
[tex]x=\dfrac{-0\pm\sqrt{0^2-4(4)(-81)}}{2(4)}=\dfrac{\pm\sqrt{1296}}{8}=\dfrac{\pm36}{8}=\pm4.5[/tex]
help please winth this will give bralienst
Answer:
1rst way they give is CORRECT WAY
The rest of the options are the INCORRECT WAY.
Step-by-step explanation:
When you do 620*7 + 6 = 4376 is the answer you get.
When you do the other math - you do not get the same initial value.
a.Find the L.C.M of 18, 40, and 75.
Answer:
1800
Step-by-step explanation:
Hello,
First of all we need to find the prime factorisation of the numbers.
18 = 2 * 3 * 3
40 = 2 * 2 * 2 * 5
75 = 3 * 5 * 5
It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3
Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
1800
Step-by-step explanation:
→ First of all we need to find the prime factorisation of the numbers.
18 = 2 × 3 × 3 or 2 × 3²
40 = 2 × 2 × 2 × 5 or 2³ × 5
75 = 3 × 5 × 5 or 5² × 3
→ Now find the number that appear twice or more and write them down
3 and 3 from 18
2, 2 and 2 from 40
5 and 5 from 75
→ Now multiply all of these numbers together
3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800
A bike tire just ran over a nail, and it is losing pressure at a rate of 5% every minute. The tire pressure is currently 1,300 kilopascals. What will it be in 3 minutes? If necessary, round your answer to the nearest tenth.
Answer:
1,114.6 kPa
Step-by-step explanation:
P(t) = 1300 (0.95)^t
P(3) = 1300 (0.95)^3
P(3) = 1114.6
A box contains 100 marbles, some of which are red and the rest blue. A sample of 10 marbles is taken randomly (with replacement) from the box and the statistic: number of red marbles in the sample is calculated. The probability model for this statistic is shown below. (Note: the probabilities should add to 1 - any difference from 1 is due to round-off errors.)
values probability
(%)
0 0.6047
1 4.0311
2 12.0932
3 21.4991
4 25.0823
5 20.0658
6 11.1477
7 4.2467
8 1.0617
9 0.1573
10 0.0105
a. Roughly, what is the shape of the probability model? Write the shape in a complete sentence
b. Calculate the center (mean) of the probability model. Use R as a calculator to calculate the mean. Write the mean in a complete sentence
c. Argue that 1.5 is a good guess for the standard deviation of the probability model. Write a brief answer
d. Suppose you repeat the experiment of sampling 10 randomly with replacement n times. Each time, you calculate the number of red marbles in your sample. Suppose you were to make a plot of the running means of the results, what would happen as n increases?
Step-by-step explanation:
a) The Roughly shape of the probability model is bell shaped or symmetric
( normal )
(b) Roughly, guess the center (mean) of the probability model
The mean is 5/10 =0.5
Because the symmetric distribution mean is middle bar and here we see using histogram 5/10 is mean .
(c) Argue that 1.5 is a good guess for the standard deviation of the probability model.
Yes 1.5 is very good guess because then it follow normal distribution it is exactly correct .
#if a sum become rs 6480 in 3 years and rs 7776 in 4 years interest being compounded annually, find the sum and rate of interest.
solve it
it's urgent
Answer:
The rate of interest is 20% and the sum is $3,750
Step-by-step explanation:
In order to calculate the sum and rate of interest we would have to make the following calculation:
rate of interest= (sum in 4 years-sum in 3 years)*100/sum in 3 years*1
According to the given data we have the following:
sum in 4 years=$7,776
sum in 3 years=$6,480
Therefore, sum in 4 years-sum in 3 years=$7,776-$6,480=$1,296
Therefore, rate of interest=$1,296*100/$6,480*1
rate of interest=20%
To calculate the sum we would have to make the following calculation:
FV=PV(1+20%)∧3
$6,480=PV(1,20)∧3
PV=$3,750
Sum is $3,750
In △ABC,c=9, m∠B=65°, and a=105. Find b.
Answer:
b ≈ 101.52
Step-by-step explanation:
Given two sides and the angle between, the Law of Cosines is useful.
b^2 = a^2 +c^2 -2ac·cos(B)
b^2 = 105^2 +9^2 -2·105·9·cos(65°) ≈ 10307.251
b ≈ √10307.251
b ≈ 101.52
1. What is the length of the shortest side if the perimeter of the rectangle is
56 inches?
3х
5х – 4
Answer:
Length of Shortest Side = 12 inches
Step-by-step explanation:
Length of Shortest Side = L = 3x
Length of Longest Side = W = 5x-4
Condition:
2L+2W = Perimeter
2(3x)+2(5x-4) = 56
6x+10x-8 = 56
16x-8 = 56
Adding 8 to both sides
16x = 56+8
16x = 64
Dividing both sides by 14
=> x = 4
Now,
Length of the Shortest Side = L = 3(4) = 12 inches
Length of the Longest Side = W = 5(4)-4 = 16 inches
Answer:
12 inches
Step-by-step explanation:
The length is the longest side.
The width is the shortest side.
Length : [tex]l=5x-4[/tex]
Width : [tex]w=3x[/tex]
Apply formula for the perimeter of a rectangle.
[tex]P=2l+2w[/tex]
[tex]P=perimeter\\l=length\\w=width[/tex]
Plug in the values.
[tex]56=2(5x-4)+2(3x)[/tex]
[tex]56=10x-8+6x[/tex]
[tex]56=16x-8[/tex]
[tex]64=16x[/tex]
[tex]4=x[/tex]
The shortest side is the width.
[tex]w=3x[/tex]
Plug in the value for x.
[tex]w=3(4)[/tex]
[tex]w=12[/tex]
Two angles are supplementary. Angle A is twice as large as angle B. What is the measure of each angle ?
Yesterday a car rental agency rented 237 vehicles, of which 51 were sport utility vehicles.
What is the experimental probability that the first vehicle rented today will be a sport utility
vehicle?
Write your answer as a fraction or whole number.
P(sport utility vehicle)
Submit
Next up
Dong for now? Try these next:
Answer:
21.5%
Step-by-step explanation:
51 divided by 237 to get percentage (237*.215% = 51)
Expedia would like to test the hypothesis that the average round-trip airfare between Philadelphia and Paris is higher for a flight originating in Philadelphia when compared to a flight originating in Paris. The following data summarizes the sample statistics for round-trip flights originating in both cities. Assume that the population variances are equal.
Originating City
Philadelphia Paris
Sample mean $1,240 $1,060
Sample size 15 19
Sample standard
deviation $270 $240
If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris, the degrees of freedom for this hypothesis test are _____
(a) 33
(b) 32
(c) 34
(d) 28
Answer:
(b) 32
Step-by-step explanation:
From the information given :
sample mean of Philadelphia μ₁ = $1240
Sample size of Philadelphia n₁ = 15
Sample Standard deviation σ₁ = $270
sample mean of Paris μ₂ = $1,060
Sample size of Paris n₂ = 19
Sample Standard deviation of Paris σ₂ = $240
If Population 1 is defined as flights originating in Philadelphia and Population 2 is defined as flights originating in Paris;
the degrees of freedom for this hypothesis test can be calculated as;
degree of freedom df = n - 1
degree of freedom for both hypothesis test = (n₁ - 1 + n₂ -1)
degree of freedom for both hypothesis test = (n₁ + n₂ - 2)
degree of freedom for both hypothesis test = ( 15 + 19 - 2)
degree of freedom for both hypothesis test are 32
The data found below measure the amounts of greenhouse gas emissions from three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicle have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gasemissions?
Type A Type B Type C
7.6 6.2 6.4
6.1 7.6 7.5
6.1 6.7 7.4
6.7 7.5 6.6
7.4 7.7 6.1
7.4 7.5 7.5
5.9 5.8 6.6
5.9 6.8 6.3
6.2 7.3
7.4
What are the hypotheses for this test?
A. H0: μ1 = μ2 = μ3
H1: μ1 ≠ 2μ ≠ μ3
B. H0: μ1 = μ2 = μ3
H1: At least one of the means is different from the others.
C. H0: μ1 ≠ μ2 ≠ μ3
H1: μ1 = μ2 = μ3
D. H0: At least one of the means is different from the others.
H1: μ1 = μ2 = u3
Determine the test statistic.
F = ________
What is the critical F value?
F = _________
Identify the P-value.
P-value = __________
What is the conclusion of the test?
_________ the null hypothesis. Conclude that the type of vehicle ______________ appear to affect the amount of greenhouse gas emissions for these three types.
Answer:
1.
A. H0 : μ1 = μ2 = μ3
Ha : μ1 ≠ 2μ ≠ μ3
2. Test Statistics = 95%
3. Critical F-Value = 3.76
4. P-Value = 2.32
5. Conclusion : Reject the null hypothesis
6. Type of vehicle does effect the amount of green house gas emissions.
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
A. H 0 μ1 = μ2 = μ3
Ha μ1 ≠ 2μ ≠ μ3
2. Test Statistics is 95%
3. Critical F-Value is 3.76.
4. P-Value is 2.32.
5. Conclusion Reject the null hypothesis.
6. Type of vehicle does effect the amount of green house gas emissions.
The correct order of the steps of a hypothesis test is given below.
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the critical value F-test for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
All steps are performed in the given sequence to test a hypothesis.
The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.
For more details on hypothesis test follow the link:
https://brainly.com/question/10758924
1. Draw the multiplication table on the set P= {3,5,7,9) in modulo twelve.
(b) From your table, evaluate;
(0 (305) (509)
() (589)®(789)
3*5 ≡ 15 ≡ 3 (mod 12)
3*7 ≡ 21 ≡ 9 (mod 12)
3*9 ≡ 27 ≡ 3 (mod 12)
5*7 ≡ 35 ≡ 11 (mod 12)
5*9 ≡ 45 ≡ 9 (mod 12)
7*9 ≡ 63 ≡ 3 (mod 12)
Your table should look like the attached.
It's unclear what you're supposed to evaluate for part (b)...
When using the Distance Formula, the solution is the perimeter of a polygon.
true or false?
Answer:
false
Step-by-step explanation:
When solving the distance formula it is the distance from one point to another. If you had a rectangle and used the distance formula from each point then you would have a perimeter
What is the length of in the right triangle below?
A.
150
B.
25
C.
D.
625
Answer:
25
Step-by-step explanation:
We can use the Pythagorean theorem to solve
a^2 + b^2 = c^2
We know the two legs and want to find the hypotenuse
15^2+ 20 ^2 = c^2
225 + 400 = c^2
625 = c^2
Taking the square root of each side
sqrt(625) = c^2
25 = c
Thank you for the help!!
Answer:
B. 5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5
A storage basin is 1240 ft by 637 ft. It’s 15.63 ft deep. How many gallons of water is in the basin
Answer:
12345824.4
Step-by-step explanation:
I'm not really sure. I just did 1240x637x15.63=12345824.4
answer:
53,445.1 gallons of water
Step-by-step explanation:
im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps
HELP! EASY! WILL GIVE BRAINLIEST!
Answer:
c
Step-by-step explanation:
The lengths, in order, of four consecutive sides of an equiangular hexagon are 1, 7, 2 and 4 units, respectively. What is the sum of the lengths of the two remaining sides?
Answer:
9
Step-by-step explanation:
Extend every other side of the hexagon so that a triangle is formed. Since the hexagon is equiangular, the overall triangle is an equilateral triangle, as well as the smaller triangles in the corners.
The length of the sides of the overall triangle is 7 + 2 + 4 = 13.
Therefore, the other two sides of the hexagon are 5 and 4.
The sum is 5 + 4 = 9.
what is the slope of the line described by the equation below? Y=-x+8
Answer:
The slope of line is -1.
Step-by-step explanation:
This equation is in the form Y=mx+b form, where m is the slope of the line. in this equation, -1 is m.
Solve the System of equations.
Answer:
x=9y=12Step-by-step explanation:
Plug x as 2y-15 in the first equation and solve for y.
-5(2y-15)+4y=3
-10y+75+4y=3
-6y+75=3
-6y=-72
y=12
Plug y as 12 in the second equation and solve for x.
x=2(12)-15
x=24-15
x=9
The hypotenuse of an isosceles triangles measures 10 inches long. What is the length of one leg of the triangle?
For any isosceles right triangle (aka 45-45-90 triangle), the hypotenuse is always equal to sqrt(2) times the leg. If x is the leg and y is the hypotenuse, then
[tex]y = x*\sqrt{2}[/tex]
which solves to
[tex]x = \frac{y}{\sqrt{2}}[/tex]
from here we plug in the given hypotenuse y = 10 to get the final answer. Optionally we could rationalize the denominator, but your teacher has chosen not to.
Answer:b
On edge
Step-by-step explanation:
In order to estimate the difference between the average Miles per Gallon of two different models of automobiles, samples are taken, and the following information is collected. Model A Model B Sample Size 50 55 Sample Mean 32 35 Sample Variance 9 10 a) At 95% confidence develop an interval estimate for the difference between the average Miles per Gallon for the two models. b) Is there conclusive evidence to indicate that one model gets a higher MPG than the other
Answer:
At 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
Step-by-step explanation:
Model A Model B
Sample Size 50 55
Sample Mean x` 32 35
Sample Variance s² 9 10
At 95 % confidence limits are given by
x1`-x2` ± 1.96 [tex]\sqrt{\frac{s^{2} }{n1} +\frac{s^{2}}{n2} }[/tex]
Putting the values
32-35 ± 1.96 [tex]\sqrt\frac{9}{50}+\frac{10}{55}[/tex] ( the variance is the square of standard deviation)
-3 ± 1.96 [tex]\sqrt{ \frac{495+500}{2750}[/tex]
-3 ± 1.96( 0.6015)
-3 ± 1.17896
-1.8210; 4.1789
Thus the 95% confidence limits for the true difference between the average Miles per Gallon for the two models is -1.8210 to 4.1789.
Yes 95 % confidence means that there's conclusive evidence to indicate that one model gets a higher MPG than the other.
Simplify the expression:
(4k – 4) + ( –9k – 5)
Answer:
The answer is
- 5k - 9Step-by-step explanation:
(4k – 4) + ( –9k – 5)
Remove the bracket and simplify
That's
4k - 4 + - 9k - 5
4k - 4 - 9k - 5
Group like terms
4k - 9k - 4 - 5
We have the final answer as
- 5k - 9
Hope this helps you
We can use FOIL to solve:
(4k - 4) + (-9k - 5)
(4k * -9k) + (4k * -5) + (-4 * -9k) + (-4 * -5)
-36k - 20k + 36k + 20
-20k + 20
Best of Luck!
6.3.67 x 10-3 is equivalent to:
A. 0.03267
B. 3.35.7
C. 0.003267
D. 3267
What is the product of the polynomials below? (4x^2-2x-4)(2x+4)
Answer: 8x³ + 12x² - 16x - 16
Step-by-step explanation:
(4x² - 2x - 4)(2x + 4)
= (2x + 4)(4x² - 2x - 4)
= 2x(4x² - 2x - 4) + 4(4x² - 2x - 4)
= 8x³ - 4x² - 8x + 16x² - 8x - 16
= 8x³ + (-4x² + 16x²) + (-8x - 8x) - 16
= 8x³ + 12x² - 16x - 16
If the sum of the first n terms of an AP is 1/2 (3n^2+7n),then find its nth term.Hence write its 20th term.
Answer:
62
Step-by-step explanation:
Sn=1/2(3n^2+7n)
S1=1/2(3+7)=5
S2=1/2(3*4+7*2)=26/2=13
We know
S1=a1=5
S2=a1+a2=13
S2-s1=a1+a2-a1
13-5=a2
a2=8
We know d=a2-a1
d=8-5=3
nth term of AP =an=5+(n-1)3
an= 2+3n
Therefore 20th term =
a20= 2+3(20)=62
Hence 20th term of AP is 62
I hope this helps