Answer:
The sampling distribution of [tex]\hat p[/tex] is: [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex].
Step-by-step explanation:
According to the Central limit theorem, if from an unknown population large samples of sizes n > 30, are selected and the sample proportion for each sample is computed then the sampling distribution of sample proportion follows a Normal distribution.
The mean of this sampling distribution of sample proportion is:
[tex]\mu_{\hat p}=p[/tex]
The standard deviation of this sampling distribution of sample proportion is:
[tex]\sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}[/tex]
The study was conducted using the data from 15,000 students.
Since the sample size is so large, i.e. n = 15000 > 30, the central limit theorem is applicable to approximate the sampling distribution of sample proportions.
So, the sampling distribution of [tex]\hat p[/tex] is: [tex]\hat p\sim N(p,\ \frac{p(1-p)}{n})[/tex].
Which property is illustrated by the equation 6+(4+x)=6+(x+4)?
1.) Associative property of addition 2.) Associative property of multiplication
3.) Distributive Property 4.) Commutative property of addition
The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.
The commutative property of addition states that the order in which numbers are added does not affect the result. In this equation, both sides of the equation involve adding numbers, and the numbers being added are the same: 6, 4, and x.
The equation shows that regardless of whether we add 4 and x first or x and 4 first within the parentheses, the final result will be the same. The commutative property of addition allows us to freely rearrange the order of the terms being added without changing the overall sum.
Therefore, The property illustrated by the equation 6 + (4 + x) = 6 + (x + 4) is the commutative property of addition.
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A 14 ft ladder is used to scale a 13 ft wall. At what angle of elevation must the laxder be situated in order to reach the top of the wall?
Answer:
The angle of elevation is equal to 68.2 degrees
Step-by-step explanation:
As you can see from the image below we are trying to find the angle on the bottom right.
We know that the hypotenuse is equal to 14 and we know that the opposite is equal to 14. This means that we will be using Sine.
sin x = 13/14
divide:
sin x = 0.9285714286
now we need to use sin^-1
sin^-1 (0.9285714286) = 68.21321071
Round 68.21321071 to the nearest tenth:
68.2
The angle of elevation is 68.2 degrees!
Answer:
[tex]\theta \approx 68^\circ[/tex]
Step-by-step explanation:
Trigonometry
The ladder, the wall, and the ground form a right triangle, where the ladder is the longest side (hypotenuse).
The trigonometric ratios stand on right triangles and can be used to relate side lengths with angles.
The angle of elevation, formed by the ladder and the ground has the height of the wall as the opposite side. Thus we can use the sine ratio, defined as:
[tex]\displaystyle \sin\theta=\frac{\text{opposite leg}}{\text{hypotenuse}}[/tex]
[tex]\displaystyle \sin\theta=\frac{13}{14}[/tex]
Solving:
[tex]\displaystyle \theta=\arcsin \frac{13}{14}[/tex]
Calculating:
[tex]\mathbf{\theta \approx 68^\circ}[/tex]
Kimberly is working in the mall. He is working making $12 an hour.
She wants to buy a bicycle that costs $192. How many hours does she need to work to
have enough money ?
Yesterday, between noon and midnight, the temperature went down by 32.1°F. If the temperature was -6.6°F at midnight, what was it at noon?
Answer:
25.5°F
Step-by-step explanation:
²3¹¹2.¹1
6.6 - Bold means that its supposed to have a strikethrough 2 5.5 meaning the number is being cancelled
just take 6.6 away from 32.1
if I burned 225 calories in 45 minutes how much will I burn in one minute
Answer:
5 calories per minute
Step-by-step explanation:
225÷45=5
HELP I DON'T WANNA GET THIS ONE WRONG
Which letter has rotational symmetry?
A. Q
B. H
C. G
D. A
Answer: (B). H
Step-by-step explanation:
Got it ?
jada mixed 8 cups of flour with 2 pints of water to make paste for an art project
Answer:
Let me check real quick
Step-by-step explanation:
Find the equation of the line through point (-2,-2)and parallel to 3x+4y=12
Find the measure of the angle which is double of its complement angle
Answer:
60°
Step-by-step explanation:
Complementary angles add to 90°, so if x is double its complement, then x + (1/2)x = 90. Doing the algebra gets you to x = 60. You know that answer is correct because 60 is double 30, which is its complement.
3. Fiona opened a retirement account that has an annual yield of 6%. She is planning on retiring in 20 years. How much must she deposit into that account each year so that she can have a total of $600,000 by the time she retires?
Fiona must deposit $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The present value of an annuity is:
PV = PMT x [(1 - (1 + r)⁻ⁿ) / r]
Where PV is the present value,
PMT is the periodic payment
r is the interest rate per period (6% per year), and
n is the number of periods (20 years).
We want to find PMT, so we can rearrange the formula to solve for it:
PMT = PV x [r / (1 - (1 + r)⁻ⁿ)]
We know that PV is $600,000, r is 6% or 0.06, and n is 20.
Plugging these values into the formula, we get:
PMT = $600,000 x [0.06 / (1 - (1 + 0.06)⁻²⁰)]
PMT ≈ $18,277.65
Therefore, Fiona must deposit $18,277.65 into her retirement account each year for the next 20 years in order to have a total of $600,000 by the time she retires.
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The equation of a horizontal line through (5,2) in slope-intercept form ?
Answer:
y=2 is the correct answer:)
Step-by-step explanation:
A chair cost $250 last year and $175 this year by what percent did the price decrease?
Answer:
I believe it is 50% decreased, not sure
Step-by-step explanation:
Answer:
30%
Step-by-step explanation:
in order to find the percentage of the price decrease,we must find the difference between the prices
250-175=75
the price has dropped 75$
to find the percentage, we do 75/250
which can be simplified to 3/10 or 30%
We can check this by finding 30% of 250 which is 75
75=75
Find the Slope and Y Intercept of the equation of a line: y = 14x + 21.
Write your answer without using variables, decimals, or exponents.
Nina works at Sweet Smoothies. She uses 3/4 of a cup of crushed ice in each smoothie. When Nina starts her
shift, there are 24 cups of crushed ice in the ice maker. How many smoothies can she make with thatice
Answer:
32
Step-by-step explanation:
The graph of which of the following equations contains the points (2,3) and (3,2)
Answer:
[tex] y = 5 - x [/tex]
Step-by-step explanation:
The graph of the equation that will contain the points (2, 3) and (3, 2) is the graph that has a slope value that is equivalent to the slope value of the line running through the two points.
Slope of the line running through (2, 3) and (3, 2):
[tex] slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 2} = \frac{-1}{1} = -1 [/tex].
Slope (m) = -1.
The equation, [tex] y = 5 - x [/tex] , is given in the slope-intercept form, which means it has a slope value of -1. I.e. the term "-x" is equivalent to -1x. So therefore, the graph of the equation that contains the points (2, 3) and (3, 2) is [tex] y = 5 - x [/tex].
Choose the function represented by the data.
O f(x) = h2 + 4h + 80
O f(x)=5h2 -5h + 13
O f(x) = h +50h2 - 120h
O f(x) = 5h3 - 50h2 + 130h
Answer:
Option (4)
Step-by-step explanation:
To solve this problem we will satisfy the polynomials given in the options with the input-output values given in the table.
Lets take a point (4, 40),
Option (1),
f(h) = h² + 4h + 80
40 = 4² + 4(4) + 80
40 = 16 + 16 + 80
40 = 112
False.
Therefore, table doesn't represent the polynomial given in option (1).
Option (2)
f(h) = 5h²- 5h + 13
40 = 5(4)² - 5(4) + 13
40 = 80 - 20 + 13
40 = 73
False.
Therefore, table doesn't represent the polynomial given in option (2).
Option (3)
f(h) = h³ + 50h² + 13
40 = 4³ + 50(4)²+ 13
40 = 64 + 800 + 13
40 = 873
False.
Therefore, table doesn't represent the polynomial given in option (3).
Option (4)
f(h) = 5h³- 50h²+ 13h
40 = 5(4)³ - 50(4)²+ 130(4)
40 = 320 - 800 + 520
40 = 840 - 800
40 = 40
True.
Therefore, given table represents this polynomial.
Option (4) will be the answer.
American football is a variation of what game?
Soccer
Speedball
Field Hockey
Rugby
Answer:
Rugby
Step-by-step explanation:
They're the most similar.
Soccer you play with only your feet
Speedball you kick the ball around
Field hockey uses a stick
can you explain this question please
Answer:
B
Step-by-step explanation:
θ and B are corresponding angles
Each is in the same position ( upper right hand corner ) in its group of four angles.
What numbers would be in the in the 4 sections of a 2 x 2 array that shows the problem 18 x 17? 100, 80, 70, 15 10, 80, 70, 56 100, 80, 70, 56 100, 80, 7, 56
Answer:
100, 70, 80, 56
Explanation:
Look at attached image!
In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.
The number in the 4 sections are 100, 80, 70, and 56.
A 2 x 2 array that shows the problem 18 x 17.
2 x 2 array has four blockers or magic quadrants, the matrix diagram is a simple square divided into four equal quadrants.
18 = 10 +8
17 = 10 +7
18 x 17 = 306
In the 2 x 2 array : 100+80+70+56 = 18 x 17 = 306
Therefore, In the 2 x 2 array, the sum of all squares is 18 x 17 = 306.
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can you answer this
Answer:
15
Step-by-step explanation:
HELP ASAP!!! determine how if possible the triangles are similar
Answer:
d not simlar just letting u know ur getting it wrong
Step-by-step explanation:
Answer:
I think A or C would be the answer! Hope this helped a little!!
Solve for x.
Please.
Write an equation of the line below
Answer:
I don't see the equation so when you put it I can answer
but I will help when you put the equation
Step-by-step explanation:
Find the GCF for the pair 4, 49.
please help me this is due soon!! ill mark brainiest :))
i also need a reason why please!!
Answer:
b
Step-by-step explanation:
One square = (2/5)/(3) Invert and multiply the 3
2 1
== == =
5 3
2/15
5 squares = 5 * 2/15 = 10 / 15 = 2/3
simplify 3square root 5 over 4square root of 5
Answer:
5[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
This is the answer because:
1) We have to do 5^1/3 x 5^-1/4
2) Next, we do 5^1/3 - 1/4 which is 5^1/12
Therefore the answer is 5^1/12
Hope this helps!
The simplified value of the given expression is 5¹/₁₂
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, [tex]\frac{\sqrt[3]{5} }{\sqrt[4]{5} }[/tex], we need to simplify it,
5¹/₃ / 5¹/₄
= 5⁽¹/₃-¹/₄⁾
= 5¹/₁₂
Hence, the simplified value of the given expression is 5¹/₁₂
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whats 5 1/2+2 5/6 ASAP PLEASE
Answer:
8 1/3 or 8.3 repeating
Step-by-step explanation:
you're welcome
If you were evaluating the expression (20 - 2^4)^4(20−24 )4 - 6, what would you do first?
Which statement is true regarding the functions on the
graph?
f(2) = g(2)
f(0) = g(0)
f(2) = g(0)
f(0) = g(2)
Answer:
Im pretty sure its f(0) = g(0)
Step-by-step explanation:
Explain the meaning of the point (1,1.5) in terms of the situation.
Answer:
there will be 1.5 table spoons of olive oil for every 1 tablespoon of vineagar
Step-by-step explanation: