Suppose 43% of the population has a retirement account. If a random sample of size 774 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3%?
Answer:
the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
Step-by-step explanation:
Given that:
sample size n = 774
Let P be the population proportion for having a retirement account = 0.43
Also
Let consider [tex]\hat p[/tex] be the sample proportion of having a retirement account.
However; as n is > 30 ; we can say:
[tex]\mathbf{\mu_{\hat p} = 0.43}[/tex] ;
[tex]\mathbf{\sigma_{\hat p^2} = \dfrac{p(1-p)}{n}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(1-0.43)}{774}}[/tex]
⇒ [tex]\mathbf{\sigma_{\hat p^2} = \dfrac{0.43(0.57)}{774}}[/tex]
So; we need P( the sample proportion will differ from 'p' by less than 3% i.e 0.03)
[tex]=P(| \hat p- p|< 0.03)[/tex]
[tex]=P(| \hat p- \mu _p|< 0.03)[/tex]
[tex]= P ( |\dfrac{\hat P - \mu_p}{\sigma_{\hat p}}|< \dfrac{0.03}{\sqrt{ \dfrac{0.43*0.57}{774} }})[/tex]
[tex]= P(|Z|<1.6859)\ \ \ \ [Z=(\dfrac{\hat P - \mu_{\hat P}}{\sigma_{\hat P}}) \sim N(0,1)][/tex]
[tex]= P(-1.6859 <Z<1.6859) \\ \\ = \Phi(1.6859)- \Phi (-1.6859) \\ \\ = \Phi (1.6859) - (1- \Phi(1.6859) \\ \\ = 2 \Phi (1.6859)-1[/tex]
From Normal Cumulative Distribution Function Table
[tex]= 2*0.9541 -1[/tex]
= 1.9082 - 1
= 0.9082
Thus; the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 3% is 0.9082
Fill in the following for a possible study with one independent variable (IV) with two conditions/treatments and a dependent variable (DV) that is measured on a continuous scale (interval or ratio): • Independent variable = ______________ • Condition A = ______________ • Condition B = ______________ • Dependent variable = _______________ • How do you know this DV is measured on a continuous scale? • How would you word the null hypothesis for your sample study? • How would you word the alternative hypothesis for your sample study? • What alpha level would you set to test your hypothesis? Why?
Answer:
Step-by-step explanation:
A possible study is to compare the prices of items in a two different online auction platform: the Dutch auction and the first-priced sealed auction.
Independent variable = the two types of auction
• Condition A = Dutch auction
• Condition B = First-price sealed auction
The Dependent variable in my case study is the prices for each pair of identical items I place in each auction using a known pair sample. The depends variable is measured in the continuous scale because prices are in numbers and these numbers vary continuously, it is not fixed.
The null hypothesis for my study would be: there is no difference in the prices of identical items in the two different auction.
The alternative hypothesis for my study would be: there is a difference in the prices of identical items in the two different auction.
I would set it to the 0.05 level of significance because this is the standard level of significance normally set in a study although this varies.
you will get alot of points if you answer this explain your answer
Answer:
The surface area of stand is 46 feet.
First
taking the upper rectangular prism only.
so we get
l=3
w=1
h=3
surface area of rectangular prism = 2lw+2lh+2hw
= 2×3×1+2×3×3+2×3×1
= 30
taking the lower rectangular prism only.
surface area of rectangular prism = 2lw+2lh+2hw
=2×7×2+2×1×7+2×2×1
=46
add both the rectangular prism.
we get,
30+46
76
Yes, $15 is enough
Taking out the square of all the rectangle the total would be 52m²
52/25×6.79 ( as 6.79 dollars for 25 m²)
$14.1232
Answer:
freecoins
Step-by-step explanation:
A fraction with a zero in the numerator equals
Answer:Any legal fraction (denominator not equal to zero) with a numerator equal to zero has an overall value of zero. all have a fraction value of zero because the numerators are equal to zero.
What’s the correct answer for this?
Answer:
B.
Step-by-step explanation:
Using the formula
S = r∅
Where s is Arc length,l
R is radius
∅ is radian measure for angle RAD
Substituting
L = R∅
So
∅ = L/R
The total sales made by a salesperson was $25,000 after 3 months and $68,000 after 23 months. Predict the total
sales after 39 months. A) $102,400 B) $102,370 C) $102,500 D) $102,442
Answer:
A) $102,400
Step-by-step explanation:
For these answers, we must assume the increase is linear.
The two-point form of the equation for a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Filling in the given (x, y) values of (3, 25000) and (23, 68000), we have ...
y = (68000 -25000)/(23 -3)(x -3) +25000
y = 2150x +18,550
Then for x = 39, we find the predicted sales to be ...
y = (2150)(39) +18,550 = 102,400
The predicted sales after 39 months is $102,400.
_____
The graph shows sales in thousands of dollars.
find the area of the triangle. ? square units
Answer:
54 square units
Step-by-step explanation:
The formula for the area of a triangle is:
[tex]\frac{1}{2}[/tex] x base x height
The base is 12
The height is 9
So 1/2 x 12 x 9 = 54 square units
Find w and y, will give brainliest for the correct answer
Answer: w=12, y=6√3
Step-by-step explanation:
Looking at the figure, we can split the triangle into 2 separate triangles. One on the left and one on the left. The triangle on the right is a 30-60-90 triangle. For this triangle, the hypotenuse is 2x in length. This is directly opposite of the right angle. The leg opposite to 30° is x in length. The leg opposite 60° is x√3 in length. Once you know the length of one side, you can plug in x to find the length of the other legs.
In this case, w and y are located on the same 30-60-90 triangle. Normally we would focus on that triangle to find our values, but in this instance, we don't have any values. We have to use the left triangle to find the leg that both triangles share.
The left triangle is a 45-45-90 triangle. For this triangle, the legs opposite of 45° is x in length. The hypotenuse is x√2. Since we know the hypotenuse, we can use it to find x.
x√2=8
x=8/√2
x=5.7 or 6 [Let's use 6 so that it is easier to work with a whole number]
Now that we know x, we can find w and y. Going back to the right triangle, we know the hypotenuse is 2x. We plug in 6 to find the length.
w=2x
w=2(6)
w=12
We know the leg opposite of 60° is x√3. We can plug in x.
y=6√3
Increase £130 by 15%
Answer:
£149.5
Step-by-step explanation:
[tex]100 + 15 = 115\\115/100 = 1.15\\130 * 1.15 = 149.5[/tex]
From a barrel of colored marbles, you randomly select 1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles. Find the experimental probability of randomly selecting a marble that is NOT yellow.
A: 8/9
B: 9/10
C: 11/18
D: 7/9
Answer:
8/9
Step-by-step explanation:
1 blue, 2 yellow, 7 red, 6 green, and 2 purple marbles = 18 marbles
The number that are not yellow = total - yellow
P( not yellow) = number that are not yellow / total
= (18-2) / 18
= 16/18
=8/9
Carole's age is five times Joe's age. The sum of their ages is 18. How old are Carole and Joe?
Answer:
Carole is 15
Joe is 3
Step-by-step explanation:
Carole's age is 15
Joes age is 3
3*5=15
15+3=18
Answer:
Carole = 15 Yrs
Joe = 3 Yrs
Step-by-step explanation:
15/5 =3
15+3 =18
Sry for the short explanation. Hope this helps!
The cost of 4kg of Apple and 6kg of orange is Rs620.If the cost of orange is the same as the cost of 5 kg Apple find the cost of per kg of Apple and orange?
Answer:
The apple cost RS 18.24 per kg, while
the orange cost RS 91.18 per kg.
Step-by-step explanation:
Let the cost of 1kg if apple and orange be RS A and RS O respectively.
From the first line:
4A +6O= 620
2A +3O= 310 -----(1) (÷2 throughout)
From the information given in second line:
O= 5A -----(2)
subst. (2) into (1):
2A +3(5A)= 310
2A +15A= 310 (expand)
17A= 310 (simplify)
A= 310 ÷17 (÷17 on both sides)
A= 18.235 (5 s.f.)
A= 18.24 (2 d.p.)
Subst. into (2):
O= 5(18.235)
O= 91.18 (2 d.p.)
What is the distance between the following points?
Answer:
square root of 72
Step-by-step explanation:
Answer:
(c) square root of 72
Step-by-step explanation:
khan academy answer :)
What is the volume of the rectangular prism?
Answer:
10ft[tex]{3}[/tex]
Step-by-step explanation:
One face has 15 blocks of 1/3 ft. You can clearly see 2 sets of blocks.
15 x 2 = 30
30 ÷ 3 or 30 x 1/3
= 10 ft cubed
Which ratio is less than StartFraction 7 Over 15 EndFraction? StartFraction 9 Over 15 EndFraction Two-fifths Three-fifths StartFraction 24 Over 45 EndFraction
Answer:
2/5
Step-by-step explanation:
First you want to find the least common denominator, which in this case would be 15. If you multiply 2/5 by 3, you get 6/15 which is less than 7/15
Answer:
2/5
Step-by-step explanation:
Find the length of Line segment A C . Use that length to find the length of Line segment C D . Triangle A B C is shown. A perpendicular bisector is drawn from point A to point C on side B D. Angle A B C is 30 degrees and angle A D C is 25 degrees. The length of A B is 10 centimeters. What is the length of Line segment C D? Round to the nearest tenth. 2.3 cm 4.0 cm 10.7 cm 18.6 cm
Answer:
10.7 CM
Step-by-step explanation:
Correct on Edge 2020
Answer:
answer is C 10.7 cm
Step-by-step explanation:
got it right on edg 2020-2021
How many commuters must be randomly selected to estimate the mean driving time of Chicago commuters? We want 98% confidence that the sample mean is within 4 minutes of the population mean, and the population standard deviation is known to be 12 minutes. 25 35 49 60
Answer:
49
Step-by-step explanation:
Margin of error = critical value × standard error
ME = CV × SE
The critical value at 98% confidence is z = 2.326.
Standard error is SE = σ / √n.
4 = 2.326 × 12 / √n
n = 49
It is known that 50% of adult workers have a high school diploma. If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma
Answer:
85.56% probability that less than 6 of them have a high school diploma
Step-by-step explanation:
For each adult, there are only two possible outcomes. Either they have a high school diploma, or they do not. The probability of an adult having a high school diploma is independent of other adults. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
50% of adult workers have a high school diploma.
This means that [tex]p = 0.5[/tex]
If a random sample of 8 adult workers is selected, what is the probability that less than 6 of them have a high school diploma
This is P(X < 6) when n = 8.
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.5)^{0}.(0.5)^{8} = 0.0039[/tex]
[tex]P(X = 1) = C_{8,1}.(0.5)^{1}.(0.5)^{7} = 0.0313[/tex]
[tex]P(X = 2) = C_{8,2}.(0.5)^{2}.(0.5)^{6} = 0.1094[/tex]
[tex]P(X = 3) = C_{8,3}.(0.5)^{3}.(0.5)^{5} = 0.2188[/tex]
[tex]P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734[/tex]
[tex]P(X = 5) = C_{8,5}.(0.5)^{5}.(0.5)^{3} = 0.2188[/tex]
[tex]P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) = 0.0039 + 0.0313 + 0.1094 + 0.2188 + 0.2734 + 0.2188 = 0.8556[/tex]
85.56% probability that less than 6 of them have a high school diploma
Write a quadratic function f whose zeros are −6 and −1.
Answer:
y = (x+6) (x+1) or in quadratic form: y = x² + 7x + 6
Step-by-step explanation:
Which point is coplanar with B , C , H ?
Answer:
G
Step-by-step explanation:
Point G is coplanar with points B, C, H.
The following stem-and-leaf plots compare the ages of 30 actors and 30 actresses at the time they won the Oscar award for Best Actor or Actress. Actors Stems Actresses 2 146667 98753221 3 00113344455778 88776543322100 4 11129 6651 5 210 6 011 6 7 4 8 0 (a) What is the age of the youngest actor to win an Oscar? years (b) What is the age difference between the oldest and the youngest actress to win an Oscar? years (c) What is the oldest age shared by two actors to win an Oscar?
The image of the stem-and-leaf plots is in the attachment.
Answer: (a) 31 years; (b) 59 years; (c) 56 years
Step-by-step explanation: Steam and leaf is a table that shows the digits of the data value split into a "stem", which represents the first digit, and a "leaf", which is the last digit.
For example, the first row of the table in the attachment, indicate a "stem" 2 and the first number of a "leaf" is 1, so the actress has 21 years.
(a) According to the table, the youngest actor to win an Oscar has a "stem" 3 and the first "leaf" from the right is 1, so the actor has 31 years.
(b) The oldest actress is 80 and the youngest is 21, so difference is:
80 - 21 = 59
The difference is 59 years.
(c) The oldest age shared by 2 actors is 56 years.
Which linear function has initial value 4?
a. y = 3x - 4
b. y = - 3x + 4
c. y = 4x - 3
d. y = 4x + 3
Answer:
y = -3x+4
Step-by-step explanation:
An initial value of 4 would be the y intercept
The only function with a y intercept of 4
(y = mx+b where b is the y intercept)
is y = -3x+4
Directions and Analysis
Task 1: Completing the Square
Look at the quadratic equation below.
2x^2-12x-16=0
This is not an equation that could be easily solved by factoring. Instead, you are going to use the method of completing the square to solve this equation. Follow each step in this task to complete the square and solve the equation.
a. To complete the square, the coefficient of the x2 term must be 1. Divide both sides of the equation by a value and rewrite the equation to meet this criteria.
Type your response here:
b. Rewrite the resulting equation so the constant term is on the right side of the equation and the variable terms are on the left.
Type your response here:
c. Identify the coefficient of the x term in the previous equation. Then divide it by half and square the result. What is the result?
Type your response here:
d. Add the value you identified in part c to both sides of the equation from part b and simplify the right side. Remember that when solving equations, whatever is done to one side of the equation must also be done to the other side the equation: that is why you must add the value to both sides.
Type your response here:
e. Notice that the left side of the equation now represents a perfect square quadratic expression. Use this fact to rewrite the left side of the previous equation as the square of a linear term and create a new equation.
Type your response here:
f. You have now completed the square. Starting with the result from part e, solve the equation for x. Show your work.
Type your response here:
g. Now that you know how to complete the square to solve a quadratic equation, solve the equation 3x^2 – 3x − 6 = 0. Show your work.
Type your response here:
Answer:
a. [tex]x^2-6x-8=0[/tex]
b. [tex]x^2-6x=8[/tex]
c.
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d. [tex]x^2-6x+9=17[/tex]
e. [tex](x-3)^2=17[/tex]
f, g. [tex]x=3\pm \sqrt{17}[/tex]
Step-by-step explanation:
Given: [tex]2x^2-12x-16=0[/tex]
To solve: the given equation
Solution:
a.
[tex]2x^2-12x-16=0[/tex]
Coefficient of [tex]x^2=2[/tex]
Divide both sides by 2
[tex]x^2-6x-8=0[/tex]
b.
[tex]x^2-6x=8[/tex]
c.
Coefficient of x = -6
[tex]\frac{1}{2}[/tex] (Coefficient of x) = [tex]\frac{-6}{2}=-3[/tex]
Also, [tex](-3)^2=9[/tex]
d.
Add 9 to both sides of the equation: [tex]x^2-6x=8[/tex]
[tex]x^2-6x+9=8+9\\x^2-6x+9=17[/tex]
e.
[tex]x^2-6x+9=17\\x^2-2(3)x+3^2=17\\(x-3)^2=17\,\,\left \{ \because (a-b)^2=a^2+b^2-2ab \right \}[/tex]
f.
[tex](x-3)^2=17\\x-3=\pm \sqrt{17}\\x=3\pm \sqrt{17}[/tex]
g.
[tex]x=3\pm \sqrt{17}[/tex]
Please help. I’ll mark you as brainliest if correct!
These are 2 math problems .
Answer:
-4 503/12 ≈ 41.91667Step-by-step explanation:
To find the average rate of change, find the change in function value, and divide that by the length of the interval.
1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4
The average rate of change of g(x) on [-1, 1] is -4.
__
2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5
= (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5
= 503/12 = 41 11/12
The average rate of change of g(x) on [-2, 3] is 41 11/12.
Mathematics: The graph below have the same shape. What is the equation of the blue graph?
Answer:
Since the blue graph is the red graph translated 3 units to the left the answer is D.
Estimate the quotient 241 ÷ 5. A. 40 B. 250 C. 50 D. 60
Answer:
The quotient of 241 ÷ 5 is 48.
Step-by-step explanation:
Division is splitting into equal parts or groups.
The quotient is the answer after we divide one number by another.
To find the quotient 241 ÷ 5 you must:
Write the problem in long division format
[tex]5\overline{|\smallspace241}[/tex]
Divide 24 by 5 to get 4
Multiply the quotient digit 4 by the divisor 5
Subtract 20 from 24
Bring down the next number of the dividend
Divide 41 by 5 to get 8
Multiply the quotient digit 8 by the divisor 5
Subtract 40 from 41
[tex]\mathrm{The\:solution\:for\:Long\:Division\:of}\:\frac{241}{5}\:\mathrm{is}\:48\:\mathrm{with\:remainder\:of}\:1\\\\48\quad \mathrm{Remainder}\quad \:1[/tex]
What is the simplified value of the exponential expression 27 1/3 ?
1/3
1/9
3
9
Answer:
3
Step-by-step explanation:
27^1/3 = cuberoot(27) = 3
Classify the following triangle check all that apply. 98,41,41
Answer:
B. Isosceles triangle
Answer: obtuse and isosceles <3
Step-by-step explanation:
If 3^2+1 =3^x+5. What is the value of x?
Answer:
[tex]x=1.464974[/tex]
Step-by-step explanation:
[tex]3^2+1 =3^x+5[/tex]
[tex]9+1 =3^x+5[/tex]
[tex]10 =3^x+5[/tex]
[tex]10-5 =3^x[/tex]
[tex]5=3^x[/tex]
[tex]log(3x)=log(5)[/tex]
[tex]x \times (log(3))=log(5)[/tex]
[tex]x=\frac{log(5)}{log(3)}[/tex]
[tex]x=1.464974[/tex]
Answer: 1.46497352 or 1.5
Step-by-step explanation:
Complete 3^2 to get 9, then add 1 to get 10
Then subtract 5 from both sides to get [tex]5=3^x[/tex]
Youre gonna have to apply a log rule here to get:
[tex]log_{3}5=x[/tex]
You get 1.46497352 or approximately 1.5
if p=7,q=5,r=3 find value of p2+q2-r2
Answer: The value is 18.
Step-by-step explanation:
Since we already know what p, q, and r equal, we can use what we know and plug in the numbers:
p=7, q=5, and r=3,
p2=7*2=14
q2=5*2=10
r2=3*2=6
In conclusion, 14+10-6=18
The value of p2+q2-r2 is 18.
Answer:
Just simply change the variables with their values
7 x 2 + 5 x 2 - 3 x 2
14 + 10 - 6
24 - 6 = 18
18 is the answer
Hope this helps
Step-by-step explanation:
Use the augmented matrix to determine if the linear system is consistent. Is the linear system represented by the augmented matrix consistent? A. Yes, because the rightmost column of the augmented matrix is a pivot column. B. Yes, because the rightmost column of the augmented matrix is not a pivot column. C. No, because the rightmost column of the augmented matrix is a pivot column. D. No, because the rightmost column of the augmented matrix is not a pivot column.
Answer:
The correct option is (A).
Step-by-step explanation:
If the reduced row echelon form of the coefficient matrix of a linear system of equations in four different variables has a pivot, i.e. 1, in each column, then the reduced row echelon form of the coefficient matrix is say A is an identity matrix, here I₄, since there are 4 variables.
[tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]
Then the corresponding augmented matrix [ A|B] , where the matrix is the representation of the linear system is AX = B, must be:
[tex]\left[\begin{array}{ccccc}1&0&0&0&a\\0&1&0&0&b\\0&0&1&0&c\\0&0&0&1&d\end{array}\right][/tex]
Now the given linear system is consistent as the right most column of the augmented matrix is a linear combination of the columns of A as the reduced row echelon form of A has a pivot in each column.
Thus, the correct option is (A).