Answers
Answer:
when we add all the angles.
=58+94+15=167
so it's a 180..
180_167
=13
round to nearest tenth.
=10..
Related Questions
Compute P7,2. (Enter an exact number.)
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Answers
Answer:
42
Step-by-step explanation:
The permutation formula is P(n, r) = n! / (n - r)!. We know that n = 7 and r = 2 so we can write:
7! / (7 - 2)!
= 7! / 5!
= 7 * 6 * 5 * 4 * 3 * 2 * 1 / 5 * 4 * 3 * 2 * 1
= 7 * 6 (5 * 4 * 3 * 2 * 1 cancels out)
= 42
Answer:
[tex]\boxed{42}[/tex]
Step-by-step explanation:
Apply the permutation formula.
[tex]P(n,r)=\frac{n!}{ (n-r)!}[/tex]
[tex]P=number \: of \: permutations\\n=total \: number \: of \: objects \: in \: the \: set\\r=number \: of \: choosing \: objects \: from \: the \: set\\[/tex]
[tex]n=7\\r=2[/tex]
Plug in the values and evaluate.
[tex]P(7,2)=\frac{7!}{ (7-2)!}[/tex]
[tex]P(7,2)=\frac{7!}{ (5)!}[/tex]
[tex]P(7,2)=\frac{5040}{120}[/tex]
[tex]P(7,2)=42[/tex]
In triangle abc what is the value of cos b A 5/13 B 12/13 C 5/12 D 13/12
Answers
Answer:
[tex]\boxed{Option \ B}[/tex]
Step-by-step explanation:
In the triangle,
Hypotenuse = 13
Opposite = Perpendicular = 5
Adjacent = Base = 12
Now,
Cos B = [tex]\frac{Adjacent}{Hypotenuse}[/tex]
Cos B = 12/13
If the triangle is just like in the attached file!
Answer:
B) 12/13
Step-by-step explanation:
In this exercise, we estimate the rate at which the total personal income is rising in a metropolitan area. In 1999, the population of this area was 924,900, and the population was increasing at roughly 9400 people per year. The average annual income was $30,388 per capita, and this average was increasing at about $1400 per year (a little above the national average of about $1225 yearly). Use the Product Rule and these figures to estimate the rate at which total personal income was rising in the area in 1999.
Answers
Answer:
the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
Step-by-step explanation:
From the given information:
Let consider y to represent the number of years after 1999
Then the population in time (y) can be expressed as:
P(y) = 9400y + 924900
The average annual income can be written as:
A(y) = 1400y + 30388
The total personal income = P(y) × A(y)
The rate at which the total personal income is rising is T'(y) :
T'(y) = P'(y) × A(y) + P(y) × A'(y)
T'(y) = (9400y + 924900)' (1400y + 30388) + (9400y + 924900) (1400y + 30388)'
T'(y) = 9400(1400y + 30388) + (9400y + 924900) 1400
Since in 1999 y =0
Then:
T'(0) = 9400(1400(0) + 30388) + (9400(0) + 924900) 1400
T'(0) = 9400(30388) + (924900)1400
T'(0) = $1,580,507,200 billion
Therefore; the rate at which total personal income was rising in the area in 1999 is $1,580,507,200 billion
what equals 1+1= Why can't I see any answers help i logged off etc is it just me?
Answers
Answer:
1 + 1 = 2
Step-by-step explanation:
^
Answer:
no , it's happening to everyone , even I can't see it .
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
Junk Bonds. 130%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answers
Answer:
(T, C, J) = (in dollars)
(10000, 10000, 0),
(15000, 4915.97, 84.03),
(18181.82, 1680.67, 137.51)
Step-by-step explanation:
There are a number of ways to approach this question. We have chosen an approach that determines the investments required to achieve interest rate targets.
__
For an overall interest rate of I, the proportion that must be invested at rate I1 < I < I2 is ...
proportion at I1 = (I2 -I)/(I2 -I1)
Similarly, the proportion that must be invested at I2 is what's left over. It can be computed similarly:
proportion at I2 = (I -I1)/(I2 -I1)
__
We want an overall interest rate of $2000/$20000 = 10%.
Given available interest rates of 9%, 11%, and 130%, we need to have investments at a rate lower than 10% and at a rate higher than 10%.
If we use only the options for 9% and 11% (no junk bonds), then we can compute ...
proportion at 9% = (11 -10)/(11 -9) = 1/2
proportion at 11% = (10 -9)/(11 -9) = 1/2
1st Option:
$10,000 in treasury bills; $10,000 in corporate bonds
__
Suppose we want to achieve a 13% return on our investments at 11% and 130%. Then the proportion invested at 9% will use this value for I2:
proportion at 9% = (13 -10)/(13 -9) = 3/4
Of the remaining 1/4 of the money, we can achieve a 13% return by mixing the investments like this:
proportion at 11% = (130 -13)/(130 -11) = 117/119
proportion at 130% = (13 -11)/(130 -11) = 2/119
2nd option:
$20,000 × 3/4 = $15,000 in treasury bills
$5000 × 117/119 = $4,915.97 in corporate bonds
The remaining amount, $84.03 in junk bonds
__
Let's suppose we want a 20% return on our investment in junk bonds and corporate bonds. Then the proportion of the money invested at 9% will be ...
proportion at 9% = (20 -10)/(20 -9) = 10/11
And the proportion at 11% will be ...
proportion at 11% = (130 -20)/(130 -11) = 110/119 . . . (of the remaining 1/11 of the funds)
3rd option:
$20,000 × 10/11 = $18,181.82 in treasury bills
$1,818.18 × 110/119 = $1,680.67 in corporate bonds
The remaining amount, $137.51 in junk bonds
_____
Additional comment
The most that could be invested in Junk Bonds is $165.29. If the remainder is invested in Treasury Bills, then the overall return will be $2000. (You could consider this to be a 4th option.)
using the horizontal line test, which of the following can be confused about the inverse of the graph?
Answers
Answer:
I think D
Step-by-step explanation:
Verticle or horizontal line test, it would be a function either way
Find the amount necessary to fund the given withdrawals. Semiannual withdrawals of 850 for 6 years,interest rate is 4.7% compounded semiannually.
Answers
Answer:
The amount necessary to fund the withdrawal is $8798.820
Step-by-step explanation:
Here, we are interested in calculating the necessary amount to fund the withdrawal given in the question.
From the question, we can identify the following;
Principal amount, P= $850
Here, Period rate, i = 0.047/ 2 =0.0235
n = 6*2 = 12
Mathematically;
Present Value of an annuity, Ao=P* [1-(1+i)^{-n}]/i
Ao=850* [1-(1+0.0235)^{-12}] /0.0235
Ao = $8798.820
What is the inverse of the function
Answers
Answer:
A
Step-by-step explanation:
let y = f(x) and rearrange making x the subject, that is
y = [tex]\frac{19}{x^3}[/tex] ( multiply both sides by x³ )
x³y = 19 ( divide both sides by y )
x³ = [tex]\frac{19}{y}[/tex] ( take the cube root of both sides )
x = [tex]\sqrt[3]{\frac{19}{y} }[/tex]
Change y back into terms of x, then
[tex]f^{-1}[/tex] (x) = [tex]\sqrt[3]{\frac{19}{x} }[/tex] = [tex]\frac{\sqrt[3]{19} }{\sqrt[3]{x} }[/tex] → A
Find a formula for an for the arithmetic sequence.
Answers
Answer:
a(n)= a(n+1)+4
Step-by-step explanation:
The first terms of this sequence are: 4,0, -4, -8, -12
Let 4 be a0 and 0 a1.
● a1-a0 = 0-4
●a1-a0 = -4
●a1 = -4+a0
So this relation links the first term with the second one.
replace 1 in a1 with n.
0 in a0 will be n-1
● an = -4+a(n-1)
Add one in n
● a(n+1) = a(n)-4
● a(n) = a(n+1)+4
9. A college financial advisor wants to estimate the mean cost of textbooks per quarter for students at the college. For the estimate to be useful, it should have a margin of error of 20 dollars or less. The standard deviation of prices is estimated to be around 100 dollars. How large of a sample size needs to be used to be 95% confident, with the given margin of error?
Answers
Answer: 97
Step-by-step explanation:
Formula to compute the required sample size :
[tex]n= (\dfrac{\sigma\times z_{\alpha/2}}{E})^2[/tex]
, where [tex]\sigma[/tex] = standard deviation
E= Margin of error
[tex]z_{\alpha/2}[/tex] = Two tailed z-value.
Here, E= 20
[tex]\sigma[/tex] = 100
For 95% confidence level: [tex]z_{\alpha/2}[/tex] =1.96
Required sample size:
[tex]n=(\dfrac{100\times1.96}{20})^2\\\\=(5\times1.96)^2\\\\=96.04\approx97[/tex]
Hence, the required sample size : 97
2.4.6.8. 10.... geometrical,arithmetic or neither?
Answers
Answer:
This is an arithmetic sequence.
Step-by-step explanation:
The difference between the consecutive terms is constant => sequence is arithmetic.
4-2 = 2
6-4= 2
8-6 = 2
10-8 = 2
Step-by-step explanation:
It's an arithmetic sequences.
Formed by the n th term 2n.
As the difference is 2 between them.
let's find it, by formulae.
n th term = 2n
t1= 2×1=2t2 = 2×2=4t3=2×3=6t4=2×4=8and so on.....
Therefore, it's an arithmetic sequence.
Hope it helps..
A bicycle tire has a radius of 5 inches. To the nearest inch, how far does the tire travel when it makes 8 revolutions?
Answers
Answer:
251 inches
Step-by-step explanation:
c = 2πr
c = 2(3.14)(5) = 31.4
31.4 x 8 rev. = 251 inches
The Escobar family and the Johnson family each used their sprinklers last month. The water output rate forthe Escobar family's sprinkler was 20 gallons per hour. The water output rate for the Johnson family's sprinkler was40 gallons per hour. The families used their sprinklers for a combined total of 32 hours, resulting in a total wateroutput of 960 gallons. How many hours was each family’s sprinkler used?
Answers
Answer:
J = 32
E = 0
Step-by-step explanation:
E is the number of hours for the Escobar family
J is the number of hours for the Johnson family
E + J = 32
E * 20 + J * 30 = 960
Multiply the first equation by -20 so we can use elimination
-20 E -20 J = -640
Add this to the second equation
E * 20 + J * 30 = 960
-20 E -20 J = -640
---------------------------------
10 J = 320
Divide by 10
J = 32
Now find E
E + J = 32
E + 32 = 32
E = 0
Mia agreed to borrow a 3 year loan with 4 percent interest to buy a motorcycle if Mia will pay a total of $444 in interest how much money did she borrow how much interest would Mia pay if the simple interest rate was 5 percent
Answers
Answer:
a) $3700
b) $555
Step-by-step explanation:
The length of the loan is 3 years.
The interest after 3 years is $444.
The rate of the Simple Interest is 4%.
Simple Interest is given as:
I = (P * R * T) / 100
where P = principal (amount borrowed)
R = rate
T = length of years
Therefore:
[tex]444 = (P * 3 * 4) / 100\\\\444 = 12P / 100\\\\12P = 444 * 100\\\\12P = 44400\\\\P = 44400 / 12\\[/tex]
P = $3700
She borrowed $3700
b) If the simple interest was 5%, then:
I = (3700 * 5 * 3) / 100 = $555
The interest would be $555.
Which statement is true about the function f(x)= -x?
O The domain of the graph is all real numbers.
The range of the graph is all real numbers.
O The domain of the graph is all real numbers less than or equal to 0.
The range of the graph is all real numbers less than or equal to 0.
Answers
Answer:
The domain of the graph is all real numbers less than or equal to 0.
Step-by-step explanation:
Hello,
We know that we cannot take square root of negative numbers, so we must have
[tex]-x\geq 0 \ \text{ ***multiply by -1, it changes the inequality, so*** } \\ \\\large \boxed{\sf \ \ x\leq0 \ \ }[/tex]
So the domain of the graph is all real numbers less than or equal to 0.
For information, I attached the graph so that we can verify it.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Y+15<3 what is the solution
Answers
Answer:
y < -12
Step-by-step explanation:
Step 1: Subtract 15 on both sides
y + 15 - 15 < 3 - 15
y < -12
This inequality means the any number smaller than -12 would work. So:
-123415235 would work
-1234 would work
-46527 would work
2 would NOT work
6 would NOT work
Answer:
[tex]y < - 12[/tex]Step-by-step explanation:
[tex]y + 15 < 3[/tex]
Move constant to RHS and change its sign:
[tex]y < 3 - 15[/tex]
Calculate the difference
[tex]y < - 12[/tex]
Hope this helps..
Good luck on your assignment..
(1/6 + 3/7) + 2/7=
Answers
Answer:
37/42 or 0.88
Step-by-step explanation:
[tex]( \frac{1}{6} + \frac{3}{7} ) + \frac{2}{7} \\ ( \frac{1}{6} + \frac{3}{7} ) = \frac{25}{42} \\ [/tex]
[tex]\frac{25}{42} + \frac{2}{7} = \frac{37}{42} \\ \\ answer = \frac{37}{42} [/tex]
The following data was collected from the manufacturing of an auto component. It represents the diameter (in mm) of that component. What is the LCL for a control chart using this data (z=3)? Sample Obs 1 Obs 2 Obs 3 Obs 4 1 10 12 12 14 2 12 11 13 16 3 11 13 14 14 4 11 10 7 8 5 13 12 14 13
Answers
Answer:
14.6
Step-by-step explanation:
(A). STEP ONE: Calculate the mean
(1). Row one = (10 + 12 + 12 + 14 ) = 48/4 = 12.
(2). Row Two: (12 + 11 + 13 + 16 ) = 52/4 = 13.
(3). Row three : (11 + 13 + 14 + 14)/4 = 13.
(4). Row four: (11 + 10 + 7 + 8)/4 = 36/4 = 9.
(5). Row five: (13 +12 + 14 + 13)/4 = 52/4 = 13.
(B). STEP TWO:
- determine the maximum and minimum value for each row.
- for each row, maximum - minimum.
Maximum values for each row:
Row one = 14, row two= 16, row three = 14, row four = 11 and row five = 14.
Minimum value for each row:
Row one = 10, row two = 11, row three = 11, row four =7 and row five = 12.
DIFFERENCES in each row :
row one = 14 - 10 = 4, row two = 16 - 11 = 5, row three = 14 - 11 = 3, row four = 11 - 7 = 4 and row five = 14 -12 = 2.
(C). STEP THREE: Calculate the mean of all the rows = 60/5 = 12.
(D). STEP FOUR : Calculate the Average Range = 18/5 = 3.6.
(E). STEP FIVE : Calculate the UCL.
A = Average rage × 0.729 = 3.6 × 0.729.
B = overall mean = 12.
UCL = A + B = 14.6.
At a firm, ten entry-level employees earn $40,000 a year, 6 junior-level employees earn $60,000 a year, and 3 managers earn $80,000 a year per person respectively. Find the weighted average of the firm.
Answers
Answer: answer is: 1000000/19
Step-by-step explanation:
10/19 - 40k -> 10/19*40k= 400000/19
6/19- 60k -> 6/19*60k= 360000/19
3/19 - 80k -> 3/19*80k=240000/19
400000/19+360000/19+240000/19=1000000/19
answer is: 1000000/19
Given: △ABC, AB=5√2 m∠A=45°, m∠C=30° Find: BC and AC
Answers
Answer:
BC = 10, AC= approximately 13.66 OR 5+5 √3
Step-by-step explanation:
Law of Sines
Lengths of pregnancies (in humans) have a mean of 267.6 days and a standard deviation of 15.4 days. A woman tracked her pregnancy and found it to be 309 days. Find the z score for 309 days. Is such a length unusual?
Answers
Answer:
The z-score is [tex]z = 2.65[/tex]
The length of days is not unusual
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 267.6 \ days[/tex]
The standard deviation is [tex]\sigma = 15.4 \ days[/tex]
The value considered is [tex]x = 309 \ days[/tex]
The z-score is mathematically represented as
[tex]z = \frac{x - \mu}{\sigma }[/tex]
[tex]z = \frac{309 - 267.6}{15.6 }[/tex]
[tex]z = 2.65[/tex]
Now given that the z-score is not greater than 3 then we can say that the length of days is not unusual
(reference khan academy)
a test consists of 10 true false questions to pass a test a student must answer at least six questions correctly if a student guesses on each question what is the probability that the student will pass the test A. 0.172 B. 0.205 C. 0.828 D. 0.377
Answers
Answer:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=10, p=0.5)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
For this case in order to pass he needs to answer at leat 6 questions and we can rewrite this:
[tex] P(X \geq 6) = P(X=6) +P(X=7) +P(X=8) +P(X=9) +P(X=10)[/tex]
And using the probability mass function we got:
[tex]P(X=6)=(10C6)(0.5)^6 (1-0.5)^{10-6}=0.205[/tex]
[tex]P(X=7)=(10C7)(0.5)^7 (1-0.5)^{10-7}=0.117[/tex]
[tex]P(X=8)=(10C8)(0.5)^8 (1-0.5)^{10-8}=0.0439[/tex]
[tex]P(X=9)=(10C9)(0.5)^9 (1-0.5)^{10-9}=0.0098[/tex]
[tex]P(X=10)=(10C10)(0.5)^{10} (1-0.5)^{10-10}=0.000977[/tex]
And adding the values we got:
[tex] P(X\geq 6) = 0.377[/tex]
The best answer would be:
D. 0.377
If we assume that asset X has an expected return of 10 and a variance of 10, then its coefficient of variation is:
Answers
Answer: Its coefficient of variation = 0.316
Step-by-step explanation:
The formula to find the coefficient of variations:
Coefficient of variation: [tex](\dfrac{\sqrt{\text{variance}}}{\text{return}})[/tex]
Given: Asset X has
Variance = 10
Expected return = 10
then, coefficient of variation [tex]=\dfrac{\sqrt{10}}{10}=\dfrac{1}{\sqrt{10}}\approx0.316[/tex]
Hence, its coefficient of variation = 0.316
Lisa, a dentist, believes not enough teenagers floss daily. She would like to test the claim that the proportion of teenagers who floss twice a day is less than 40%. To test this claim, a group of 400 teenagers are randomly selected and its determined that 149 floss twice a day. The following is the setup for this hypothesis test: H0:p=0.40 H0:p<0.40 The p-value for this hypothesis test is 0.131. At the 5% significance level, should the dentist reject or fail to reject the null hypothesis?
Answers
Answer:
The dentist should fail to reject the Null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is n = 400
The sample mean is [tex]\= x = 149[/tex]
The level of significance is 5% = 0.05
The Null hypothesis is [tex]H_o : p = 0.40[/tex]
The Alternative hypothesis is [tex]H_a : p < 0.40[/tex]
The p-value is [tex]p-value = 0.131[/tex]
Looking at the given data we can see that the p-value is greater than the level of significance hence the dentist should fail to reject the Null hypothesis
Find one solution for the equation. Assume that all angles involved are acute angles. tangent (3 Upper B minus 32 degrees )equals cotangent (5 Upper B plus 10 degrees )
Answers
Answer:
Step-by-step explanation:
Equation given
tan(3B-32 ) = cot ( 5B +10 ) = tan [ 90 - ( 5B + 10 ) ]
tan(3B-32 ) = tan (90 - 5B - 10 )
(3B-32 ) = (90 - 5B - 10 )
8B = 32 + 80
B = 14° .
Find the solution(s) of the quadratic equation 2x2 – 3x – 35 = 0
Answers
Answer: x = 5, x = -7/2
Step-by-step explanation:
2x² - 3x - 35 = 0
Step 1: Find two values whose product = 2(-35) and sum = -3: -10 & 7
Step 2: Replace the b-value of -3x with -10x + 7x:
2x² - 10x + 7x - 35 = 0
Step 3: Factor the first two terms and the second two terms:
2x(x - 5) +7(x - 5) = 0
Step 4: Write the factored form:
Notice that the parenthesis are identical. This is one of the factors. The outside values are the other factor:
Parenthesis: (x - 5)
Outside: (2x + 7)
Factored form: (x - 5)(2x + 7) = 0
Step 5: Set each factor each to zero and solve for x:
x - 5 = 0 2x + 7 = 0
x - 5 [tex]x=-\dfrac{7}{2}[/tex]
The solutions of the quadratic equation given as 2x² - 3x - 35 = 0 are x=5 and x =-3.5.
Given that:
2x² - 3x - 35 = 0
This is a quadratic equation.
It is required to find the solutions of this equation.
The solution of the quadratic equation of the form ax² + bx + c = 0 can be found using the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
From the given equation:
a = 2
b = -3
c = -35
Substitute to the quadratic formula.
[tex]x=\frac{-(-3)\pm \sqrt{(-3)^2-4(2)(-35)}}{2(2)}[/tex]
[tex]=\frac{3\pm \sqrt{9+280}}{4}[/tex]
[tex]=\frac{3\pm \sqrt{289}}{4}[/tex]
[tex]=\frac{3\pm 17}{4}[/tex]
So, the solutions are:
[tex]x=\frac{3+ 17}{4}=5[/tex], and [tex]x=\frac{3-17}{4}=-3.5[/tex]
Hence, the solutions are x =5, -3.5.
Learn more about Quadratic Formula here :
https://brainly.com/question/22364785
#SPJ6
Please help, much needed. A lot of points
Answers
Answer:
A. -9
Step-by-step explanation:
If one of the variables were negative than, it would not be able to equal 2/7.
conditinal probability question. please help! :)
Answers
Answer:
P(A|B) = 1 / 6
Step-by-step explanation:
Assuming two fair sided dice with faces numbered 1 to 6.
By intuition, there can only be 6 possible outcomes, so probability is 1/6.
Illustration how to use conditional probability.
Given two events A, B, following is the equation of conditional probability
that A happens given B has already happened and observed.
P(A|B) = P( A intersect B ) / P(B)
In the given problem,
A = casting a double-six
B = casting a double
P(A) = (1 / 6) * (1 / 6) = 1/36
P(B) = (6/6) * (1/6) = 1/6
P(A|B) = 1/36 / (1/6) = 1/6
Plzzzzzzzzzzzzzzzzzzzzzz find the hcf of 15a²b² and -24ab
Answers
Let's take a look at each term separately.
15a^2b^2:
15 has factors 1, 3, 5, 15
a x a
b x b
-24ab
-24 has factors 1, 2, 3, 4, 6, 8, 12, 24
a
b
Now, we can see what each of these terms has in common. Both have a 3 in their factor lists, as well as one a and one b.
Therefore, the greatest common factor is 3ab.
Hope this helps!! :)
Answer:
3ab
Step-by-step explanation:
[tex]15a^{2} b^{2} - 24ab[/tex] is divided by 3
[tex]5a^{2} b^{2} - 8ab[/tex] take away a and b once
hope this helped!!!
[tex]5ab - 8[/tex]
= 3ab
15) In a recent study of 35 ninth-grade students, the mean number of hours per week that they played video games was 16.6. The standard deviation of the population was 2.8. Find the 95 % confidence interval of the mean of the time playing video games.
Answers
Answer:
The 95 % confidence interval of the mean of the time playing video games. is
[tex]15.67< \mu <17.52[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 35[/tex]
The sample mean is [tex]\= x = 16.6[/tex]
The standard deviation is [tex]\sigma = 2.8[/tex]
The confidence level is 95% hence the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Now the critical value of half of this level of significance obtained from the normal distribution table is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The reason for the half is that we are considering the two tails of the normal distribution curve which we use to obtain the interval
Now the standard error of the mean is mathematically evaluated as
[tex]\sigma _{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]\sigma _{\= x} = \frac{2.8 }{\sqrt{35} }[/tex]
[tex]\sigma _{\= x} = 0.473[/tex]
the 95 % confidence interval of the mean of the time playing video games.
is mathematically evaluated as
[tex]\= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x }) < \mu < \= x - (Z_{\frac{\alpha }{2} } * \sigma_{\= x })[/tex]
substituting values
[tex]16.6 - (1.96 * 0.473) < \mu < 16.6 + (1.96 * 0.473)[/tex]
[tex]15.67< \mu <17.52[/tex]