Answer:
The sample size required is 289.
Step-by-step explanation:
Let p be population proportion of people that would buy the product.
It is provided that the nationwide poll on this type of product and price was run earlier this year, with percentages running from 75% to 80%.
Assume that the sample proportion of people that would buy the product is, [tex]\hat p=0.75[/tex].
A 95% Confidence Interval is to be constructed with a margin of error of 5%.
We need to determine the sample size required for the 95% Confidence Interval to be within 5% of the actual value.
The formula to compute the margin of error for a (1 - α)% confidence interval of population proportion is:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
The critical value of z for 95% confidence interval is,
z = 1.96.
Compute the sample size required as follows:
[tex]MOE=z_{\alpha/2}\times\sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
[tex]n=[\frac{z_{\alpha/2}\ \sqrt{\hat p(1-\hat p)} }{MOE}]^{2}[/tex]
[tex]=[\frac{1.96\cdot \sqrt{0.75(1-0.75)} }{0.05}]^{2}\\\\=(16.9741)^{2}\\\\=288.12007081\\\\\approx 289[/tex]
Thus, the sample size required is 289.
Florian ran 1.2 miles and walked 4.8 laps around the path at the park for a total distance of 3.6 miles. Which shows the correct equation and value of x, the distance of 1 lap around the path at the park? 3.6 x + 1.2 = 4.8; x = 1 mile 4.8 x + 1.2 = 3.6; x = 1 mile 3.6 x + 1.2 = 4.8; x = 0.5 mile 4.8 x + 1.2 = 3.6; x = 0.5 mile
Answer:
The correct answer would be D) 4.8x + 1.2 = 3.6; x = 0.5 mile
Step-by-step explanation:
This is because laps would be the dependent variable, so we know the number of them (4.8) would be multiplied by the variable (x). We also know that 1.2 is the constant. Now we can solve to make sure this is the right equation.
4.8x + 1.2 = 3.6
4.8x = 2.4
x = 0.5
Answer:
D) 4.8x + 1.2 = 3.6; x = 0.5 miles
Prove the Triangle Proportinality Theorem
Answer:
Step-by-step explanation:
Given: DE║BC
To prove: [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex]
Statements Reasons
1). DE║BC 1). Given
2). ∠1 ≅ ∠4, ∠3 ≅ ∠4 2). Corresponding angles theorem
3). ΔADE ~ ΔABC 3). AA Similarity theorem
4). [tex]\frac{\text{AB}}{\text{AD}}=\frac{\text{AC}}{\text{AE}}[/tex] 4). Corresponding sides are proportional
5). [tex]\frac{\text{AD+DB}}{\text{AD}}=\frac{\text{AE+EC}}{AE}[/tex] 5). Segment addition postulate
6). [tex]1+\frac{\text{DB}}{\text{AD}}=1+\frac{\text{EC}}{\text{AE}}[/tex] 6). [tex]\frac{a+b}{c}=\frac{a}{c}+\frac{b}{c}[/tex]
7). [tex]\frac{\text{DB}}{\text{AD}}=\frac{\text{EC}}{\text{AE}}[/tex] 7). Subtract 1 from both sides
8). [tex]\frac{\text{AD}}{\text{DB}}=\frac{\text{AE}}{\text{EC}}[/tex] 8). Take the reciprocal of both sides
A sample of carbon-12 has a mass of 6.00 g. How many atoms of carbon-12 are in the sample?
3.01 x 10^23
6.02 x 10^23
1.20 x 10^24
3.60 x 10^24
Answer:
The answer is 3.01 x 10’23
Step-by-step explanation:
I got the answer to wrong and guessed the first one and it was correct
Please answer this correctly
Answer:
Height of this missing bar would be 1
Step-by-step explanation:
Since there is 1 and only 1 quantity between 80-99.
Answer:
1
There is 1 number that is between 80 and 99 which is 99 so there should be 1 bar.
Step-by-step explanation:
What is the image of (-4,12) after a dilation by a scale factor of 1/4 centered at the origin
Answer:
(-1,4)
Step-by-step explanation:
Divide each imput by 4
The required image of the given point (-4, 12) dilation by a scale factor of 1/4 and centered at the origin is (1, -3).
Given that,
To determine the image of (-4,12) after dilation by a scale factor of 1/4 centered at the origin.
The graph is a demonstration of curves that gives the relationship between the x and y-axis.
What is coordinate?Coordinate, is represented as the values on the x-axis and y-axis of the graph
Here,
For the point, we have a dilation factor of 1/4,
So dilated coordinate,
= (1/4 * - 4 , 1/4 * 12)
= (-1 , 3)
To form the image across the origin
= - (-1, 3)
= (1, -3)
Thus, the required image of the given point (-4, 12) with a scale factor of 1/4 and centered at the origin is (1, -3).
Learn more about coordinate here:
brainly.com/question/13498438
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The sum of one and the product of 4 and a number x
Answer:
1 + 4x
Step-by-step explanation:
Let's break this down.
"The sum of one" means that something is being added to the number one:
1 +
"and" whatever comes after the word 'and' will be added to the number one
"the product of 4 and a number x" this means that the number four and the variable x are being multiplied:
4x
Put it together:
1 + 4x
Therefore, the expression is 1 + 4x.
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Calculate simple interest
Question
Carolyn makes a deposit of $2,800 into a savings account. The bank calculates simple interest annually at a rate of 7.5%.
Interest is added every year on the anniversary of the initial deposit. How many years must Carolyn wait before her
investment exceeds $3,500? Give your answer in years. Do not include units in your answer.
Provide your answer below:
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Answer:
4
Step-by-step explanation:
A=P0(1+rt).
We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:
A=P0(1+rt)⟹t=A−P0P0r,
and substituting the known quantities gives
r=$3,500−$2,800$2,800×0.075=3.33,
which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.
A bag contains 4 green, 5 red, and 6 purple balls. The probability that all of them are red is?
Answer:
The percentage would be 20% (5x20=100)
Step-by-step explanation:
