Answer:
a. 0.87
b. The margin of error is of 0.0124.
c. The 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is (0.8576, 0.8824).
d. The 95% confidence interval for this population proportion is (0.8553, 0.8847).
Step-by-step explanation:
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].
The margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The confidence interval is:
[tex]\pi \pm M[/tex]
a. What is the point estimate of the population proportion of adults who think the future health of Social Security is a major economic concern.
The sample proportion, that is, 1740 out of n = 2000. So
[tex]\pi = \frac{1740}{2000} = 0.87[/tex]
0.87 is the point estimate.
b. At 90% confidence, what is the margin of error?
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
Then the margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.645\sqrt{\frac{0.87*0.13}{2000}}[/tex]
[tex]M = 0.0124[/tex]
The margin of error is of 0.0124.
c. Develop a 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern
[tex]\pi - M = 0.87 - 0.0124 = 0.8576[/tex]
[tex]\pi + M = 0.87 + 0.0124 = 0.8824[/tex]
The 90% confidence interval for the population proportion of adults who think the future health of Social Security is a major economic concern is (0.8576, 0.8824).
d.
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
Then the margin of error is of:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.87*0.13}{2000}}[/tex]
[tex]M = 0.0147[/tex]
The confidence interval will be of:
[tex]\pi - M = 0.87 - 0.0147 = 0.8553[/tex]
[tex]\pi + M = 0.87 + 0.0147 = 0.8847[/tex]
The 95% confidence interval for this population proportion is (0.8553, 0.8847).
The terminal side of in standard position contains the point (20, 21) . Find the exact values of the six trigonometric functions of? Please help
Answer:
27,29
Step-by-step explanation:
What 3 dimensional solid will be formed by rotating the given figure around the given line of symmetry?
Answer:
option D)
Step-by-step explanation:
when a equilateral triangle is rotated about x-axis
rotating equilateral triangle about x-axis will lead to the formation of cone in.
the height of the equilateral triangle will represent height of the cone.
the base of the equilateral triangle will represent the circular base of the cone
and the slant height of the cone will represented by the sides.
hence, the correct answer will cone which is option D)
If f(x)=x^3−5x^2−2x+24 and (x+2) is a factor, what are the remaining factors?
Factor 1:
Factor 2:
Factor 3:
Answer:
(x+2), (x-4), (x-3)
Step-by-step explanation:
Use the rational root theorem to get started, then factor the remaining quadratic to find:
x^3 − 5x^2 − 2x + 24 = (x + 2)(x − 4)(x − 3)
Explanation:
Let f(x) =x^3 − 5x^2 − 2x + 24
By the rational root theorem, any rational zeros of f(x) must be expressible in the for p/q for integers p, q with p a divisor of the constant term 24 and q a divisor of the coefficient 1 of the leading term.
That means that the only possible rational zeros are the factors of 24, namely:
± 1, ± 2, ± 3, ± 4, ± 6, ± 12, ± 24
Try each in turn:
f(1) = 1 − 5 − 2 + 24 = 18
f(−1) = −1 − 5 + 2 + 24 = 20
f(2) = 8 − 20 − 4 + 24 = 8
f(−2) = −8 − 20 + 4 + 24 = 0
So x = −2 is a zero and (x + 2) is a factor.
x^3 − 5x^2 − 2x + 24 = (x + 2)(x^2 − 7x + 12)
We can factor
x^2 − 7x + 12 by noting that 4 × 3 = 12 and 4 + 3 = 7, so:
x^2 − 7x + 12 = (x − 4)(x − 3)
Putting it all together:
x^3 − 5x^2 − 2x + 24 = (x + 2)(x − 4)(x − 3)
7m + 3mn
when m = 3 and n = -4
Answer:
-15
Step-by-step explanation:
When m=3 and n=-4
So, put the values
7(3)+3(3)(-4)
-> -15
Answer:
-15
Step-by-step explanation:
= 7(3) + 3(3)(-4)
= 21 + 3(3×-4)
= 21 + 3(-12)
= 21 + -36
= 21-36
= -15
What is the lead coefficient of the polynomial below?
3x^2+ 8x + 5
Answer:
The lead coefficient is 8
Step-by-step explanation:
This is because it is the biggest number that is right before the x or that is the coefficient.
The leading coefficient of the polynomial is given by C = 3
What is a polynomial?Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.
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 polynomial equation be represented as A
Now , the value of A is
A = 3x² + 8x + 5
On simplifying the equation , we get
The leading coefficient of a polynomial is the coefficient of the term with the highest degree. In this case, the polynomial 3x² + 8x + 5 has a term with degree 2 (the x² term) and the coefficient of that term is 3
Hence , the lead coefficient of this polynomial is 3
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factorise: 18x - 42y + 30z
Answer:
divide by 6
6 ( 3x - 7y + 5z )
Write an equation for the proportional relationship shown in the table
Answer:
y =74x
Step-by-step explanation:
A proportional relationship is represented by y = kx where x is the independent variable, or input, k is the constant of proportionality, and y is the dependent variable or output.
What do we do to the values in the row for x to get the values in the row of y?
It helps to have x = 1 in this table.
74 = (k)(1)
74 = k
A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey that attended college is randomly selected what is the probability that they also lived in 2 or more states during their life? P(2 state or more | College Degree)
This question is incomplete, the complete question is;
A study has been done to determine to see if the level of education determines how often people move between different states in America. If a person from the survey that attended college is randomly selected what is the probability that they also lived in 2 or more states during their life? P(2 state or more | College Degree)
Lived in just Lived in 2 or Total
1 state more states
No High School Diploma 6 2 8
High School Diploma 14 16 30
College Degree 2 18 20
Total 22 36 58
Options;
a) 0.111
b) 0.310
c) 0.500
d) 0.900
Answer:
The required probability is 0.9
Option d) 0.900 is the correct answer.
Step-by-step explanation:'
Given the data in the question;
Total number of people in the survey or sample size n = 58
Number of people with college degree who live in 2 or more state = 18
P(2 states or more and college degree) = Number of people with college degree who live in 2 or more state / Total number of people in the survey
P(2 states or more and college degree) = 18 / 58
Also, Total number of people with college degree = 2 + 18 = 20
so, P( College Degree ) = Total number of people with college degree / Total number of people in the survey
P( College Degree ) = 20 / 58
Therefore, P(2 state or more | College Degree) will be;
⇒ P(2 states or more and college degree) / P( College Degree )
⇒ ( 18 / 58 ) / ( 20 / 58 )
⇒ ( ( 18 / 58 )58 ) / 20
⇒ (( 18 × 58 ) / 58 ) / 20
⇒ 18 / 20
⇒ 0.9
Therefore, The required probability is 0.9
Option d) 0.900 is the correct answer.
Como se escribe el numeral 300,105,020 4to grado
please help me with this. will give brainliest due in 5 minutes
Answer:
A
Step-by-step explanation:
Michelle has 3/5 pounds of sugar. She gave her neighbor some sugar. Now she has 1/2 pounds of sugar left. How much sugar did she give to her neighbor?
Answer: 1/10
Step-by-step explanation:
Answer:
1/10 pound
Step-by-step explanation:
If you set up the equation as 3/5 - 1/2, you'll have to give them a common denominator. Multiply 3/5 by 2 and multiply 1/2 by 5, and now you can rewrite this equation as 6/10 - 5/10. From here, just subtract and you'll get 1/10.
Just help please need to pass
Answer: [tex]\frac{1}{10}[/tex]
Step-by-step explanation:
First, we need to find the common denominator
The easiest way to do this is by multiplying the two given denominators, which are 2 and 5.
2 × 5 = 10
So, our common denominator is 10. Then, multiply the numerators of the two fractions by 2 and 5. Here's why:
[tex]\frac{3*2}{5*2}[/tex] = [tex]\frac{6}{10}[/tex] We multiplied the top and bottom by 2 to make sure our new fraction stays equivalent to the original fraction.
Do the same thing for the other one:
[tex]\frac{1*5}{2*5}[/tex] = [tex]\frac{5}{10}[/tex]
Finally, subtract the two fractions to find the difference between the two times:
[tex]\frac{6}{10} -\frac{5}{10}[/tex] = [tex]\frac{1}{10}[/tex]
The reason we used the common denominator is because we can only add or subtract fractions if they have the same denominator.
la
You spend some time in the kitchen making sure the recipe is just right for
the cooking show. You spend 2 3/4 hours baking and half of an hour
cleaning up the kitchen. How much time were you in the kitchen?
Answer: 3¼ hours
Step-by-step explanation:
Number of hours used in baking = 2¾ hours
Number of hours used in cleaning up the kitchen = ½ hour
Therefore, the time used in the kitchen will be the addition of the time used in baking plus the time used in cleaning the kitchen which will be:
= 2¾ + ½
= 2 3/4 + 2/4
= 2 5/4
= 2 + 1¼
= 3¼ hours
Therefore, 3¼ hours was used in the kitchen.
f(x) = 3√4x
g(x) = 2x + 3
Find ( f/g) (x). Include any restrictions on the domain
Answer:
B
Step-by-step explanation:
To find [tex](\frac{f}{g} )(x)[/tex] you can write the expression as [tex]\frac{f(x)}{g(x)}[/tex]. We can substitute the f(x) and g(x) into the expression to get: [tex]\frac{\sqrt[3]{4x} }{2x+3}[/tex]. Now we need to find the domain. The numerator is fine, and the domain is all real numbers, but in a fraction, the denominator cannot equal 0. We can write: [tex]2x + 3\neq 0[/tex] and we can solve it:
[tex]2x\neq -3[/tex]
[tex]x\neq -\frac{3}{2}[/tex]
This is the same as option B.
The required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2. Option C is correct
Given the functions
f(x) = 3√4x
g(x) = 2x + 3
We are to find the resulting function (f/g)(x)
(f/g)(x) = f(x)/g(x)
(f/g)(x) = 3√4x/2x+3
Restriction to the function occurs at the point where the denominator is zero.
2x = 3 = 0
2x = -3
x = -3/2
Hence the required function (f/g)(x) is 3√4x/2x+3 where x ≠ -3/2
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You take Rocky to the Del Mar fair. His mom gives him $30 to spend. It costs $13 to get in and the $2 for every ride. How many rides can he ride?
Answe r with the system of equations. Please help me.
Answer:
8 rides
Step-by-step explanation:
$30-$13
=$17
1 ride= $2
x ride =$17
x= 17/2
= 8.5
= 8 rides
You take Rocky to the Del Mar Fair. His mom gives him $30 to spend.
It costs $13 to get in and $2 for every ride. he can ride 8 rides.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
You take Rocky to the Del Mar Fair. His mom gives him $30 to spend.
It costs $13 to get in and $2 for every ride.
$30 - $13
= $17
Let x be the ride he can rides.
1 ride = $2
x ride = $17
x = 17/2
= 8.5
= 8 rides
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Find the surface area of the prism.
s = 2b + PH
s = 4(3 * 4) + (8)(96) =
s = 4(12) + (8)(96)
s = 48 + (8)(96)
s = 48 + 768
s = 816
PLEASE HELP ME NOW!!!!!The television repair charge at "We Fix TVs" is $20 per hour plus a $60 flat fee charge. The television repair charge at "Electronic Depot" is $40 per
hour with no flat fee. Write a system of equations to model the charges for each repair shop.
Answer:
Step-by-step explanation:
we fix tvs
20h+60
electronic depot
40h+0
15. Solve for the specified variable:
-
х
+
7 8
- 10; for y.
Answer:
[tex]y=80-\frac{8x}{7}[/tex]
Step-by-step explanation:
15). Given equation is,
[tex]\frac{x}{7}+ \frac{y}{8}=10[/tex]
Multiply the equation by 8,
[tex]8(\frac{x}{7}+ \frac{y}{8})=10\times 8[/tex]
[tex]\frac{8x}{7}+y=80[/tex]
Subtract [tex]\frac{8x}{7}[/tex] from both the sides of the equation,
[tex]\frac{8x}{7}+y-\frac{8x}{7}=80-\frac{8x}{7}[/tex]
[tex]y=80-\frac{8x}{7}[/tex]
Therefore, value of the variable 'y' will be,
[tex]y=80-\frac{8x}{7}[/tex]
Simplify the expression
-2(5z -7)
fy: 143 +1.42 + 2.9°
Answer:
what does fy mean
Step-by-step explanation:
Step-by-step explanation:
I tell my friends about this and I found that FY means Fiscal year
Fid the cosine of angle Q. Round your answer to the nearest hundredth.
Which equations is parallel to y=4x+8?
Answer:
y=4x-8
hope this helps
have a good day :)
Step-by-step explanation:
The table shows the number of points Malik and Alexia scored while playing a video game together. Which equation relates Alexia’s score, a, to Malik’s score, m?
A. a=0.5m
B. a=1.5m
C. a= m+10
D. a=m+30
Answer:
D. a = m + 30
Step-by-step explanation:
It's not A, because that would be dividing Malik's score in half to get Alexia's score.
B only works for the first line.
C is adding 10 to Malik's score, and the difference is greater than that...it's 30 points.
Please Help if you can!! I also have more questions in my profile!
Answer:
(0, 9), (0, 0), (0, 1)
Step-by-step explanation:
Hope it helps you in your learning process.
The soup pot is 8 inches tall with a radius of 3 inches.
What is the volume of the soup pot?
150.8 cubic inches
anything
99+
Answer:
The volume of the soup pot is of 226.19 cubic inches.
Step-by-step explanation:
Format of a soup pot:
A soup pot has a cylindrical format.
Cylinder volume:
The volume of a cylinder, with radius r and height g is given by:
[tex]V = \pi r^2h[/tex]
The soup pot is 8 inches tall with a radius of 3 inches.
This means that [tex]h = 8, r = 3[/tex]
What is the volume of the soup pot?
[tex]V = \pi r^2h = \pi*3^2*8 = 72\pi = 72(3.1415...) = 226.19[/tex]
The volume of the soup pot is of 226.19 cubic inches.
what is 2476476263278x342234324
Answer:
8.4753518e+20
Step-by-step explanation:
I used calculator. You should've used a calculator too.
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Answer:
4/ 7-4
Step-by-step explanation:
The table shows the record low temperatures In Juneau, Alaska for each of the 12 months of the year in degrees F.
Record Low Temp
Month
Year
(in °F)
January
-22
1972
February
-22
1968
March
-15
1972
April
6
1963
May
25
1972
June
31
1971
July
18
1895
August
27
1948
September
23
1972
October
11
1984
November
-5
2006
December
-21
1941
According to the data, what is the range of the record low temperatures in Juneau, Alaska?
O A. -22°
OB. 4.67°
D. 31°
E. 539
O c. 8.50
Answer:
i think -22
Step-by-step explanation:
mrs.johnson is working on math with a group of students. she has a total of 15 students. 9 of them are girls. what is the ratio of boys to girls for mrs.johnsons math group?
make sure you simplify all ratios and fractions
Answer:
6
Step-by-step explanation:
the rest are boys
In Oklahoma the state sales tax rate is 7%. If
James purchases a lawn mower at $350.00, then
how much will James pay in state sales tax?
Write 7% as a decimal by dividing by 100:
7/100 = 0.07
Multiple the price of the mower by the decimal:
350 x 0.07 = 24.50
The tax = $24.50