Complete Question
The proportion of adult women in the United States is 51% (p=0.51).What is the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p)?
Answer:
The probability is [tex]P( 0.48 < p < 0.54 ) = 0.77[/tex] or [tex]P( 0.48 < p < 0.54 ) = 77\%[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The population proportion is p = 0.51
Generally the standard deviation of this sampling distribution is mathematically represented as
[tex]\sigma = \sqrt{\frac{p(1-p)}{n} }[/tex]
=> [tex]\sigma = \sqrt{\frac{0.51(1-0.51)}{400} }[/tex]
=> [tex]\sigma = 0.02499[/tex]
Generally the lower limit for the range of the population proportion within 0.03 is
[tex]a = p - 0.03[/tex]
=>[tex]a = 0.51 - 0.03[/tex]
=>[tex]a = 0.48[/tex]
Generally the upper limit for the range of the population proportion within 0.03 is
[tex]b = p + 0.03[/tex]
=>[tex]a = 0.51 + 0.03[/tex]
=>[tex]a = 0.54[/tex]
Generally the probability that a random sample of 400 U.S. youth will provide a sample proportion (p¯) that is within 0.03 of the population proportion (p) is mathematically represented as
[tex]P( a < p < b) = P( \frac{a - p }{\sigma } < \frac{\^ p - p }{\sigma} < \frac{b - p}{\sigma } )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( \frac{0.48 - 0.51 }{0.02499 } < \frac{\^ p - p }{\sigma} < \frac{0.54 - 0.51}{0.02499 } )[/tex]
[tex]\frac{\^ p -p }{\sigma } = Z (The \ standardized \ value\ of \ \^ p )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( -1.2 < Z < 1.2 )[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = P( Z < 1.2) - P(Z < -1.2 )[/tex]
From the z table the area under the normal curve to the left corresponding to 1.2 and -1.2 is
[tex]P( Z < 1.2) =0.88493[/tex]
and
[tex]P( Z < -1.2) =0.11507[/tex]
So
[tex]P( 0.48 < p < 0.54 ) = 0.88493 - 0.11507[/tex]
=> [tex]P( 0.48 < p < 0.54 ) = 0.77[/tex]
If it took 8 hours to clean 12 houses how many houses could be cleaned in 12 hours
Answer:
18 houses
Step-by-step explanation:
12 houses / 8 hours = 1.5 houses an hour
We're given 12 hours, so:
1.5 houses/hour * 12 hours = 18 houses
A store buys lawnmowers from the manufacturer and marks
up the price by 40% to arrive at a retail price. Fill in the
blank: The wholesale price is times the retail price.
Answer:
0.7142857
Step-by-step explanation:
Let wholesale price = x
Retail price = 40% Markup of wholesale price
Retail price = (100 + 40)% of x
Retail price = 140% of x
Retail price = 140/100 * x
Retail price = 1.4x
Hence,
Wholesale price / retail price
x / 1.4x
= 0.7142857
Hence, wholesale price is 0.7142857 of the retailer price
f(x)=0.5-2xsquared find the value of f(x) when x=0
Answer:
f(0) = 0.5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 0.5 - 2x²
x = 0
Step 2: Evaluate
Substitute in x: f(0) = 0.5 - 2(0)²Exponents: f(0) = 0.5 - 2(0)Multiply: f(0) = 0.5 - 0Subtract: f(0) = 0.5Answer:
f ( 0 ) = 0.5
Step-by-step explanation:
Step 1:
f ( x ) = 0.5 - 2x² Function
Step 2:
x = 0 Given
Step 3:
f ( 0 ) = 0.5 - ( 2 ( 0 ) )² Multiply
Answer:
f ( 0 ) = 0.5
Hope This Helps :)
A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).
If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.
x = ______
Answer:
2/3
Step-by-step explanation:
cuz it is
Answer:
2/3
Step-by-step explanation:
If the radius r of a circle is decreasing at the rate of 5 cm per minute, find the rate of change of area when radius is 6 cm.
Answer:
-94.2 [tex]cm^2/min[/tex]
Step-by-step explanation:
Rate of change of radius = -5 cm per minute (as it is decreasing)
Radius of circle = 6 cm
Formula for area of Area:
[tex]A = \pi r^2[/tex]
Formula for differentiation of [tex]y = x^n[/tex]:
[tex]\dfrac{dy}{dt} = nx^{n-1}\dfrac{dx}{dt}[/tex]
Differentiating area w.r.to [tex]t[/tex]:
[tex]\dfrac{dA}{dt} = 2\pi r\dfrac{dr}{dt}[/tex]
Putting the values, [tex]r = 6, \frac{dr}{dt} = -5[/tex] cm per minute.
[tex]\dfrac{dA}{dt} = 6\pi \times (-5)\\\Rightarrow \dfrac{dA}{dt} = -30 \times 3.14\\\Rightarrow \dfrac{dA}{dt} = -94.2\ cm^2/min[/tex]
Negative sign indicates that area is decreasing.
Rate of change of area is -94.2 [tex]cm^2/min[/tex].
The area decreases at a rate of -188.4 square centimeter per minute
The area (A) of a circle of radius (r) is represented as:
[tex]A = \pi r^2[/tex]
Differentiate the area, with respect to r
[tex]A' = 2\pi r r'[/tex]
From the question, we have:
Radius (r) = 6cmRate of change of radius (r') = -5cm per minuteSo, the equation becomes
[tex]A' = 2\times 3.14 \times 6 \times (-5)[/tex]
[tex]A' =- 188.4[/tex]
Hence, the area decreases at a rate of -188.4 square centimeter per minute
Read more about rates of change at:
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what's 9x - 7i > 3 (3x - 7u) ?
Step-by-step explanation:
9x-7i>9x-21u
-7i>-21u
i<3u
The solution to the given inequality 9x - 7i > 3(3x - 7u) is i < 3u.
Given that:
Inequality: 9x - 7i > 3 (3x - 7u)
To solve the inequality 9x - 7i > 3(3x - 7u), follow these steps:
Step 1: Distribute the 3 on the right side of the inequality as:
9x - 7i > 9x - 21u.
Step 2: Simplify the inequality.
9x - 9x - 7i > - 21u.
Step 3: Rewrite the inequality.
After cancelling out the 9x terms, we are left with -7i > -21u.
Step 4: Divide both sides by -7.
i < 3u
Therefore, the solution to the inequality 9x - 7i > 3(3x - 7u) is i < 3u.
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The length of a rectangle exceeds its width by 1
inch and the area is 132 square inches. What
are the length and width of the rectangle?
Answer:
Width equals 11, and length equals 12.
Step-by-step explanation: It is helpful to memorize your multiplication tables up to 12. I personally couldn't figure out a formula for this, but I knew that 12 x 11 equals 132, and the length is greater than the width, so length is 12 and width is 11. Hopefully somebody else can figure it out. P.S. I meant the formula, not the answer, my answer is correct.
Answer:
[tex]l(l - 1) = 132[/tex]
[tex] {l }^{2} - l - 132 = 0 [/tex]
[tex](l - 12)(l + 11) = 0[/tex]
[tex]l = 12 \: or \: l = - 11[/tex]
[tex]length \: must \: be \: postive[/tex]
[tex]integers[/tex]
[tex]l = 12 \: and \: w = l - 1 = 11[/tex]
plato
For the state of Indiana, there are 181,560 businesses that are open during the pandemic. If this makes up only 68% of all businesses, how many total business are there in the state?
Answer:
267,000
Step-by-step explanation:
2d +4(d – 3) = 3, what is 9d+1
9514 1404 393
Answer:
9d +1 = 23.5
Step-by-step explanation:
=Simplifying, we have ...
2d +4d -12 = 3
6d = 15
d = 15/6 = 5/2
Then 9d+1 is ...
9(5/2) +1 = 45/2 +1 = 47/2
9d +1 = 23.5
when the Dixon family traded in their old car, it had 53,790 miles on it. they had the car for 8.25 years. on average, how many miles did they drive per year?
Answer:
6,520 miles per year
Step-by-step explanation:
53,790 divided by 8.25 equals 6,520
Hii I need the 7th and 8th question asap will mark brainliest 100% to who ever answers first and right thank you
Ryan feeds his chicken 1/ 3 cups of grain per day. The grain container has 6 cups of grain left. For how many days can Ryan feed the chicken?
Answer:
18 days
Step-by-step explanation:
1 cups=3 days
2 cups=6 days
3 cups=9 days
4 cups=12 days
5 cups=15 days
6 cups=18 days
Select a symbol to compare the numbers.
7/10
0.07
Answer:
7/10>0.07
Step-by-step explanation:
You can turn 7/10 into decimal and its 0.7.
0.7 is greater than 0.07 so you would put a > sign
so the answer is 7/10>0.07
pls mark brainliest
Find the ratio of red marbles to total marbles. Write the ratio in simplest form.
5/3
3/5
2/3
3/2
Answer:
3:5
Step-by-step explanation:
ratio is 4:6 so ratio equals 2:3
red marbles is 3/5
which of the following tables can be generated from the equation y equals 2x + 1
Answer: 2 the first one
Step-by-step explanation:
Answer: the first one
Step-by-step explanation:
4.9 divided by 3581.9
Just help me
Answer:
.00136799
Step-by-step explanation:
4.9/3581.9 into a calculator
Answer:
.00136798905
Step-by-step explanation:
Used a calculator!
Which situation cannot be represented by the equation 15 + x = 25?
Victor and Raul donated 25 cans of fruit to their local food bank. Victor donated 15 cans. What is, x, the number of cans Raul donated?
The day's low temperature read 15ºF. The day's high temperature read 25ºF. What is x, the amount of degrees the temperature increased throughout the day?
Jean has $25. She found $15 of the amount in her wallet and the rest in her coat pocket. What is x, the amount of money in her coat pocket?
Elizabeth worked 15 hours. Josh worked 25 hours. What is x, the amount of hours they worked together?
Answer:
the last answer about the jobs
Step-by-step explanation:
Students from Texas, New York, Washington, Florida, and Utah identified their area of concentration at various universities. The results are listed in the table.
One of these students is selected at random. What is the probability that the student is from the state of Washington under the condition that the student studies history?
Enter a number in the box.
The probability of a random student who is from Washington and studies history is [tex]\frac{5}{33}[/tex].
What is probability?Probability is the chance of happening an incident or event. A probability is calculated by the ratio of the possible outcomes to total number of outcomes.
Given, the total number of students of History
= (30 + 17 + 20 + 32 + 33) = 132
The number of students from Washington who studies history = 20.
Therefore, the probability that the student is from the state of Washington under the condition that the student studies history is = [tex]\frac{20}{132} = \frac{5}{33}[/tex] .
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May you please help ill give out brainlyist ..
Answer:
C. is your answer dear
Step-by-step explanation:
2^3 = 8
1 = 1
Find the Length of AC. Round answers to the nearest hundredth (2 decimal places)
Answer:
32.78
Step-by-step explanation:
Assuming that we have two right triangles joined together, with one having adjacent side a, with a side of 12 ft opposite reference angle 30°, and the other one having adjacent side b, with a side of 12 ft opposite reference angle 45°. Thus, a + b = length of AC.
Let's find a and b.
Finding a:
Reference angle = 30°
Opp = 12 ft
Adj = a
Using trigonometric ratio formula, we have:
tan(30) = 12/a
Multiply both sides by a
a*tan(30) = 12
Divide both sides by tan(30)
a = 12/tan(30)
a = 20.78 (nearest hundredth)
Finding b:
Reference angle = 45°
Opp = 12 ft
Adj = b
Using trigonometric ratio formula, we have:
tan(45) = 12/b
Multiply both sides by a
b*tan(45) = 12
Divide both sides by tan(45)
b = 12/tan(45)
a = 12
Length of AC = 20.78 + 12 = 32.78
1. Which equation represents the relationship shown in the table below? (1 point)
y = -x - 3
y=x-3
y = 2x - 3
y=-2x + 3
The equation representing the relationship in the table is y = 2x - 3. The correct option is C.
What is an equation?The equation in mathematics is the relationship between the variables and the number and establishes the relationship between two or more variables.
Given data in the table:-
x y
0 -3
1 -1
2 1
3 3
The equation satisfying the values of the table will be:-
y = 2x - 3
-3 = 2 x 0 - 3=-3
-1 = 2 x 1 - 3 =-1
1 = 2 x 2 - 3 = 1
3 = 2 x 3 - 3 = 3
Therefore, the equation representing the relationship in the table is y = 2x - 3. The correct option is C.
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Help help please I really need it
What is the step. some help
Answer:
Step-by-step explanation:
LM=2x+24
MN= x+28
LN=31
LN=(2x+24)+(x+28)
31=(2x+24)+(x+28)
solve
31=(2x+24)+(x+28)
31-24-28 = 2x +x
-21=3x
-7=x
Overdue! Please help me! Thank you.
Answer:
1. $79.5 for 10 pizzas
2. $107 for 20 pizzas
Step-by-step explanation:
all you have to do is plug in your numbers to the function! for question one, you would plug in 10 as p. the equation would be s=2.75(10)+52. simplify by multiplying 2.75 by 10 and adding 52. you should get $79.5. for the second one, the equation is s=2.75(20)+52. i encourage you to solve it yourself just to make sure you understand!
jack was 8 years older than priscilla. together their ages totaled 154 years. what were their ages?
Answer:
Jack is 81, Priscilla is 73
Step-by-step explanation:
Because their age difference is 8 years, we can subtract 8 from the total 154 years to get 146. Then we divide by 2 to get 73, so Priscilla is 73. Jack is 8 years older, so therefore he is 81. We can check this by adding 81 + 73 = 154.
Hamburger meat sells for $6 for every 3 pounds. If Alicia buys 10 pounds of hamburger meat, how much will she pay?
Answer:
20
Step-by-step explanation:
Generally those who are less active have no opportunities to exercise
Answer:
False
Step-by-step explanation:
Edge 2021
How do you say hi in chamoru?
Answer:
Step-by-step explanation:
To say Hi in Chamoru you say, "Håfa Adai" (Chamorro for "Hello").
Hope this helped!
In a company, the ratio of the number cashiers is 20:3. If there are 120 workers in the company,
how many cashiers are there ?
(A)17
(B)18
(C)21
(D) 23
9514 1404 393
Answer:
(B) 18
Step-by-step explanation:
Multiply each of the numbers in the ratio by 6.
workers : cashiers = 20 : 3 = 120 : 18
There are 18 cashiers for 120 workers.
5. A refrigerator is on sale for $1200. That is
25% off regular price. What was the original
price?
Answer: The original price is $4,800
Step-by-step explanation:
$1,200=25%
25%*4=100%
$1,200*4=$4,800=100%