Answer:
Sample size n [tex]\simeq[/tex] 1269.15
Step-by-step explanation:
From the information given ,
At 99% of confidence interval,
the level of significance ∝ = 1 - 0.99
the level of significance ∝ = 0.01
the critical value for 99% of confidence interval is:
[tex]\mathtt{\dfrac{\alpha }{2} = \dfrac{0.01}{2}}[/tex]
= 0.005
[tex]\mathtt {z_{\alpha/2} = z_{0.005/2} }[/tex]
The value for z from the standard normal tables
= 2.58
The Margin of error E= 3% = 0.03
The formula to determine the sample size n used can be expressed as follows:
[tex]\mathtt { n = (\dfrac{z_{\alpha/2}}{E})^2 \ \hat p (1 - \hat p) }[/tex]
where;
[tex]\mathtt{\hat p }[/tex] = 22% = 0.22
Then:
[tex]\mathtt { n = (\dfrac{2.58}{0.03})^2 \ \times 0.22 \times (1 - 0.22) }[/tex]
[tex]\mathtt { n = (86)^2 \ \times 0.22 \times (0.78) }[/tex]
[tex]\mathtt { n = 7396 \ \times 0.22 \times (0.78) }[/tex]
n = 1269.1536
Sample size n [tex]\simeq[/tex] 1269.15
A researcher surveys middle-school students on their study habits. She finds that in a random sample of 28 middle-school students, the mean amount of time that they spend working on the computer each night is 2.4 hours with a standard deviation of 0.92 hours. She uses the sample statistics to compute a 95% confidence interval for the population mean - the the mean amount of time that all middle-school students spend working on the computer each night. What is the margin of error for this confidence interval
Answer:
The margin of error is [tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 28[/tex]
The sample mean is [tex]\= x = 2.4 \ hr[/tex]
The standard deviation is [tex]\sigma = 0.92 \ hr[/tex]
Given that the confidence level is 95% the the level of significance can be evaluated as
[tex]\alpha = 100 -95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table,the value is [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.05}{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 0.92}{\sqrt{28 } }[/tex]
[tex]E = 0.3408[/tex]
In the adjoining figure, in ΔABC, D is the midpoint of the side BC.Hence a) AD is ___________ A b) AM is ____________ c) Is BD = DC please help!!!!!!!!!!!!!!
Answer:
a) AD is Median
b) AM is Perpendicular Bisector
Step-by-step explanation:
c) Yes because the Median divides the line into two equal parts
Do not use spaces in your answer. Solve for x. -5x + 12x - 8x = -24 x = ___ a0
Answer:
[tex]\Huge \boxed{x=24}[/tex]
Step-by-step explanation:
[tex]-5x + 12x - 8x = -24[/tex]
Combine all like terms.
[tex](-5+ 12- 8)x = -24[/tex]
[tex]-x=-24[/tex]
Multiply both sides by -1.
[tex]x=24[/tex]
Answer:
x must be 24
Step-by-step explanation:
I assume you meant " -5x + 12x - 8x = -24
Combine the x terms on the left side, obtaining -x = -24.
Then x must be 24
Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?
Answer:
The state can issue 456,976,000 license plates.
Step-by-step explanation:
For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.
For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.
For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:
[tex]\frac{10}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{26}[/tex] [tex]\frac{10}[/tex] [tex]\frac{10}[/tex]
= 10*26*26*26*26*10*10
=456,976,000.
Therefore, the state can issue 456,976,000 license plates.
- -
X+y=3 and x+y=-2 find the value of x and y
Answer:
no solutions.
Step-by-step explanation:
the given lines are parallel, then they can not have intersection points.
Today only, a suit is being sold at a 26% discount. The sale price is $259.
What was the price yesterday?
Answer:
$350
Step-by-step explanation:
1. Set up the equation. The sale price of $259 is 74% of the original price.
[tex]\frac{74}{100}[/tex] = [tex]\frac{259}{x}[/tex]
2. Cross multiply
74x = 25900
3. Solve
x = 350
Credit card companies lose money on cardholders who fail to pay their minimum payments. They use a variety of methods to encourage their delinquent cardholders to pay their credit card balances, such as letters, phone calls and eventually the hiring of a collection agency. To justify the cost of using the collection agency, the agency must collect an average of at least $200 per customer. After a trial period during which the agency attempted to collect from a random sample of 100 delinquent cardholders, the 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75). Given this, what recommendation(s) would you make to the credit card company about using the collection agency
Answer with explanation:
A x% confidence interval interprets that a person can be x% confident thatthe true mean lies in it.
Here, Credit card companies is using the collection agency to justify the cost of , the agency must collect an average of at least $200 per customer.
i.e. [tex]H_0:\mu \geq200,\ \ \ H_a:\mu<200[/tex]
The 90% confidence interval on the mean collected amount was reported as ($190.25, $250.75) .
I recommend that we can be 90% sure that the true mean collected amount lies in ($190.25, $250.75).
Also, $200 lies in it such that it is more far from $250.75 than $190.25, that means there are large chances of having an average is at least $200 per customer.
Use AABC shown below to answer the question that follows:
Which of the following is a step towards proving the similarity of triangle so AABC and ADBA? (5 points)
Segment BC is a hypotenuse.
Angle B is congruent to itself.
Segment BA is shorter than segment BC.
Segment BC is intersected by segment AD.
Answer:
Bc is intersected by segment AD
Answer:
Bc is intersected by segment AD
Step-by-step explanation:
Convert 6 feet to miles ( round five decimal places
Answer:
0.00114
Step-by-step explanation:
Divide length value by 5280
QUESTION 6 . 1 POINT
$12,000 is invested at 6.8% compounded continuously. After how many years, to the nearest hundredth, will it be worth
$36,230?
Provide your answer holom
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Answer:
16.25
Step-by-step explanation:
The value of principal P compounded continuously at annual rate r for t years is ...
A = Pe^(rt)
Then t is ...
t = ln(A/P)/r
t = ln(36230/12000)/0.068 ≈ 16.2497
The investment will be worth $36,230 after 16.25 years.
The table below shows the values of f(x) and g(x) for different values of x. One of the functions is a quadratic function, and the other is an exponential function. Which function is most likely increasing quadratically? x f(x) g(x) 1 3 3 2 6 9 3 11 27 4 18 81 5 27 243 f(x), because it grows faster than g(x) g(x), because it will not intersect f(x) g(x), because it grows slower than f(x) f(x), because it grows slower than g(x)
Answer:
D
Step-by-step explanation:
Exponential functions always will end up being bigger than quadratic functions and since g(x) is probably the exponential it makes f(x) the quadratic because it is growing slower than the function g(x)
The function g(x) increases faster than the function f(x). Then the correct option is D.
What is a function?The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
The table below shows the values of f(x) and g(x) for different values of x.
One of the functions is a quadratic function, and the other is an exponential function.
The quadratic function f(x) will be
f(x) = ax² + bx + c
At x = 1, f(x) will be 3
a + b + c = 3 ...1
At x = 2, f(x) will be 6
4a + 2b + c = 6 ...2
At x = 3, f(x) will be 11
9a + 3b + c = 11 ...3
On solving equations 1, 2, and 3, we have
a = 1, b = 0, and c = 2
Then the quadratic function will be
f(x) = x² + 2
The exponential function g(x) will be given as
g(x) = abˣ
At x = 1, g(x) will be 3
ab = 3 ...4
At x = 2, g(x) will be 9
ab² = 9 ...5
From equations 4 and 5, we have
a = 1 and b = 3
Then the exponential function will be
[tex]\rm g(x) = 3^x[/tex]
More about the function link is given below.
https://brainly.com/question/5245372
5 people cleared a plot of land in 15 days. How many people would I need to hire to clear three times that plot in 5 days?
Convert 4.206 m into mm
Answer:
4206 is the answer of this question
Answer:
I think it will help you a lot.
A B means:
A is an element of B
B is a subset of A
B is an element of B
A is a subset of B
none of the above
Answer:
A is a subset of B i believe that's the answer
Subtract these polynomials.
(3x2 – 2x + 5) – (x2 + 3) =
Answer:
D. 2x^2 - 2x + 2
Step-by-step explanation:
(3x2 – 2x + 5) – (x2 + 3) add or subtract like terms
3x^2 - x^2 - 2x - 3 + 5 = 2x^2 - 2x + 2
Answer:
2x^2 - 2x + 2
Step-by-step explanation:
Ape-x
Write as an equation: The sum of a number and 12 is 78.
Answer:
x+12=78
Step-by-step explanation:
like that? x because its an unknown number but if you actually want to know the number just subtract 78-12 equals 66.
Answer:
n + 12 = 78
Step-by-step explanation:
Let n = number.
n + 12 = 78
look at the image below
Answer:
117.8
Step-by-step explanation:
Surface area = πr²+πrl (whee r = radius and l = slant height)
= π×3²+π×3×9.5
= 75π/2
= 117.8
Help me I’m stuck please
Answer:
choice 1,2,4,5 from top to bottom
Step-by-step explanation:
1:the points given are in the line where both planes intersect
2:point H is not on any plane
3:in the diagram point F is on plane R so false
4:if you connect the points given they will intersect so not collinear
5:the points F and G are on the plane R
6:so F is on plane R but H is not on any do false
What is the measure of ∠x?
Angles are not necessarily drawn to scale.
∠x= ____∘
Please help me!
Answer:
hey mate ...
105 + JID = 180 ( STRAIGHT LINE )
JID = 75
NOW APPLY ANGLE SUM IN TRIANGLE JID
75 + 39 + IJD = 180
IJD = 66
x = IJD by vertically opposite angles
x = 66
Use technology to find the P-value for the hypothesis test described below. The claim is that for 12 AM body temperatures, the mean is F. The sample size is n and the test statistic is t.
Answer:
P value = 0.1575
Step-by-step explanation:
Data provided in the question
t = 1.021
n = 33
[tex]\mu[/tex] = 98.6° F
Based on the above information, the P-value could be determined by using the excel spreadsheet i.e. shown in the attachment
So, the P value is 0.1575
The 1.021 denotes the test statistic
32 denotes degrees of freedom
And,
1 denotes one tailed alternative hypothesis.
a is less than or equal to 10
Lmk
Answer:
[tex]a \leqslant 10[/tex]
Step-by-step explanation:
a is less than or equal to 10
less than: <
equal: =
less than or equal to: ≤
Hope this helps ;) ❤❤❤
hope it helps you
imp=draw dark shaded point in thqt line and point towards left
Which best describes the relationship between the lines with equations -36x + 8y = 16 and
-9x + 2y = 4?
Hi there! :)
Answer:
The lines are the same.
Step-by-step explanation:
Begin by converting each equation into its simplest form in slope-intercept form:
-36x + 8y = 16
Move the "x" variable to the right side of the equation:
8y = 36x + 16
Divide all terms by 8:
y = 36/8x + 16/8
y = 9/2x + 2
-------------------------------
-9x + 2y = 4
Move "x" variable:
2y = 9x + 4
Divide both sides by 2:
y = 9/2x + 2
Both of the equations are equivalent, meaning both of the lines are the same.
Which equation would represent 30 kittens divided into groups of 4
Answer:
30÷4
Step-by-step explanation:
What is the critical F value when the sample size for the numerator is seven and the sample size for the denominator is six
Answer:
Critical F value = 4.9503
Step-by-step explanation:
Given that:
The sample size of the numerator = 7
The sample size of the denominator = 6
The degree of freedom for the numerator df = n -1
The degree of freedom for the numerator df = 7 - 1
The degree of freedom for the numerator df = 6
The degree of freedom for the denominator df = n - 1
The degree of freedom for the denominator df = 6 - 1
The degree of freedom for the denominator df = 5
The assume that the test is two tailed and using a level of significance of ∝ = 0.10
The significance level for the two tailed test = 0.10/2 = 0.05
From the standard normal F table at the level of significance of 0.05
Critical F value = 4.9503
which of the following illustrates commutative property of addition? 17+4=4+17
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Answer:
17 +4 = 4 +17
Step-by-step explanation:
The only expression shown here illustrates that property.
a golfer hits the golf ball. the quadratic y = -14x^2+84x gives the time x seconds when the golf ball is at height 0 feet. In total, how long is the golf ball in the air?
Answer: 6 seconds
Step-by-step explanation:
x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)
0 = -14x² + 84x
0 = -14x(x - 6)
0 = -14x 0 = x - 6
0 = x 6 = x
x = 0 seconds is when the ball was hit
x = 6 seconds is when the ball landed on the ground
A city council consists of seven Democrats and six Republicans. If a committee of five people is selected, find the probability of selecting two Democrats and three Republicans.
Answer:
solution,
let d and r denote democrats and republicans respectively.
given,
no. of total sample space n(s) =7+6=13
no. of total democrats n(d)=7
no. of total republicans n(r)=6
no. of democrats events n(D1)=2
no. of republicans events n(R1)=3
it is a mutually exclusive event. so the probability of selecting two democrats and three republicans= {n(D1)/n(s)} * {n(r1)/n(s)}
=(2/13)*(3/13)
=6/169
Answer:
6/169
Step-by-step explanation:
Find the slope of the line tangent to the graph of x²+2xy² +3y=31 at the point (2, -3)
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Answer:
22/21
Step-by-step explanation:
Taking the derivative, we have ...
2x·dx +2y²·dx +4xy·dy +3·dy = 0
dx(2x +2y²) +dy(4xy+3) = 0
At the given point, this is ...
dx(2·2 +2·(-3)²) +dy(4·2·(-3) +3) = 0
22dx -21dy = 0
dy/dx = 22/21
The slope of the tangent at the point of interest is 22/21.
(2f-1)^2, please help, also tell me how to give you brainlyist, or what ever it’s called
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Answer:
4f^2 -4f +1
Step-by-step explanation:
It can be useful to memorize the form of the square of a binomial:
(a +b)^2 = a^2 +2ab +b^2
Here, you have a=2f and b=-1. Then the square is ...
(2f)^2 +2(2f)(-1) +(-1)^2 = 4f^2 -4f +1
__
More generally, the distributive property applies.
(2f -1)^2 = (2f -1)(2f -1) = 2f(2f -1) -1(2f -1)
= (2f)(2f) +(2f)(-1) +(-1)(2f) +(-1)(-1) = 4f^2 -2f -2f +1 = 4f^2 -4f +1
Su Jean is driving from phoenix to houston. A distance of 1185 miles. After driving for 4 hours she calculates that she has driven 237 miles. What portion of the distance does she have left to drive?
Answer:
4/5
Step-by-step explanation:
237/1185 = .2 = 1/5
meaning there's 4/5 left