Complete Question
In a sample of 80 light bulbs, the mean lifetime was 1217 hours with a standard deviation of 52 hours. a. Find the 95% confidence interval for the mean lifetime of this type of bulb. Justify the reason you chose the distribution used to construct the confidence interval. b. How many light bulbs must be sampled so that a 95% confidence interval will specify the mean lifetime to within [tex]\pm 8 \ hours[/tex]?
Answer:
a
[tex]1206 < \mu < 1228 [/tex]
The reason why a normal distribution was chosen is because the sample size is large enough that is [tex]n > 30[/tex]
b
[tex]n =162 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 80
The sample mean is [tex]\= x = 1217[/tex]
The standard deviation is [tex]\sigma = 52[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 52}{\sqrt{80} }[/tex]
=> [tex]E = 11.395 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]1217 -11.395 < \mu < 1217 + 11.395[/tex]
=> [tex]1206 < \mu < 1228 [/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } * \sigma }{E} ] ^2[/tex]
Here E = 8
=> [tex]n = [\frac{1.96 * 52 }{8} ] ^2[/tex]
=> [tex]n =162 [/tex]
If the sum and product
of roots of a quadratic
equation are -7/2 and
5/2 respectively,then
the equation is :
Answer:
The equation is y = 2x² + 7x + 5
Step-by-step explanation:
In the quadratic equation y = ax² + bx + c
The roots of it are the values of x at y = 0The sum of the two roots = [tex]\frac{-b}{a}[/tex]The product of the two roots = [tex]\frac{c}{a}[/tex]∵ The sum of the roots is [tex]\frac{-7}{2}[/tex]
∵ The product of the roots is [tex]\frac{5}{2}[/tex]
→ By using the rules above
∴ [tex]\frac{-b}{a}[/tex] = [tex]\frac{-7}{2}[/tex]
∴ [tex]\frac{c}{a}[/tex] = [tex]\frac{5}{2}[/tex]
→ Compare between them
∴ a = 2
∴ -b = -7 ⇒ divide both sides by -1
∴ b = 7
∴ c = 5
∵ The form of the quadratic function is y = ax² + bx + c
→ Substitute the values of a, b, and c in it
∴ y = 2x² + 7x + 5
∴ The equation is y = 2x² + 7x + 5
Please explain as well how to do it. Thanks!
Answer:
The answer is B.
Step-by-step explanation:
Please refer to the attachment (ignore the horrible drawing, thank you).
Let the distance from P to T be red. The length of the red distance is x radians.
T’ is π-x. Thus, it is the red distance subtracted from the purple distance.
So, T’ is the reflection of T across the y-axis.
Therefore, we can simply multiply the x-coordinate of T to get T’.
T is (3/5, 4/5)
Then T’ must be (-3/5, 4/5).
Hence, our answer is B.
Jenny enjoys crocheting so she has decided to make and sell crocheted hats and crocheted scarves to make money for a trip she would like to take this coming summer. She is going to sell her scarves for $5 each and her hats for $10 each. In order to go on the trip, Jenny needs to make at least $200.
Answer:
Step-by-step explanation:
so the whole question is as follows
ian's car can go 99 miles on 3 gallons of gas During a drive last weekend,Ian used 7 gallons of gas.How far did he drive?Use pencil and paper. Explain how the problem changes if you were given the distance Ian drove last weekend instead of how much gas He used. He drove____ miles.
Answer:
The answer would be 231 miles.
Step-by-step explanation:
This is because you have to make this into the most common ratio, which would be 1/33. To get to 7 gallons, you must multiply 33 by 7, because you multiplied 1 by 7.
What fraction of this shape is shaded?
You must give your answer in its simplest form.
Type here
The fraction of the shape which is shaded in simplest form is 1/3.
The square in the diagram provided has a total of 12 boxes .
The number of shaded part is 4
To calculate the shaded fraction of the shape we have to use the formula:
Number of shaded part/ Total number of boxes present.
= 4/12
We can divide the numerator and denominator by 4 to get the simplest form.
= 1/3
The fraction of the shape which is shaded in simplest form is therefore
= 1/3.
Read more about Fraction here https://brainly.com/question/17743912
Les had $32.00 when he went to the city Market to buy some fresh fruits and vegetables. When he left, he had $23.05. How much money did he spend on food?
Answer:
$8.95
Step-by-step explanation:
Martinez bought 8 3/4 yd of fabric. She wants to make a skirt using 1 7/8 yd, pants using 2 3/8, and a vest using 1 2/3 yd. how much fabric will be left over?
Please help ASAP!!! :(
Answer:
The fabric left over will be [tex]2\frac{5}{6}[/tex]
Step-by-step explanation:
Total fabric bought= [tex]8\frac{3}{4} \ yd[/tex]
Fabric used for skirt = [tex]1\frac{7}{8} \ yd[/tex]
Fabric used for pants = [tex]2\frac{3}{8} \ yd[/tex]
Fabric used for vest = [tex]1\frac{2}{3} \ yd[/tex]
Total fabric used = Fabric used for skirt+Fabric used for pants+Fabric used for vest
Total fabric used=[tex]1\frac{7}{8}+2\frac{3}{8}+1\frac{2}{3}[/tex]
[tex]=\frac{15}{8}+\frac{19}{8}+\frac{5}{3}\\=\frac{15*3+19*3+5*8}{24}\\=\frac{45+57+40}{24}\\=\frac{142}{24} \\=\frac{71}{12}[/tex]
So, Total fabric used = [tex]\frac{71}{12}[/tex]
Total Fabric left= Total fabric bought-Total fabric used
Total Fabric left=[tex]8\frac{3}{4}-\frac{71}{12}[/tex]
[tex]=\frac{35}{4}-\frac{71}{12}\\=\frac{35*3-71}{12} \\=\frac{105-71}{12}\\=\frac{34}{12}\\=\frac{17}{6}\\=2\frac{5}{6}[/tex]
So, the fabric left over will be [tex]2\frac{5}{6}[/tex]
A school newspaper estimates that their academic team will win 25 out of 30 matches for the season. After 15 matches, they have won 12. If the team continues winning at this rate, what will be the percent error of the newspaper's estimate once the season is over? Round to the nearest percent
Answer:
4
Step-by-step explanation:
The percent error of the newspaper's estimate once the season is over will be 4%.
What is the percentage?The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A school newspaper estimates that their academic team will win 25 out of 30 matches for the season.
Then the percentage will be given as,
P = (25 / 30) x 100
P = 0.8333 x 10
P = 83.33%
After 15 matches, they won 12. Then the percentage will be given as,
P = (12 / 15) x 100
P = 0.80 x 100
P = 80%
If the team continues winning at this rate. Then the percent error of the newspaper's estimate once the season is over will be
P = [(83.33 - 80) / (83.33)] x 100
P = 0.04 x 100
P = 4%
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ5
First, write the fractions as decimals.
3
4
is
vand
11
1
2
IS
Next, plot the numbers on the number line.
The least number is
The greatest number is
The correct order from least to greatest is
Answer: d,d,a,,d,c,
Step-by-step explanation:
Answer:
ddadc
Step-by-step explanation:
Last year Jeremy weighed 70 bounds this year he weights 84 pounds by what percent did Jeremy weights increase from last year to this year
there are 4 circles and 16 squares. What is the simplest ratio of circles to total shapes?
Please help me. What’s the answer ?
Answer:
D
Step-by-step explanation:
D
61 meters = _____ feet
I'LL GIVE BRAINLIEST!
Answer:
200.131234
Step-by-step explanation:
The rate of 225 mi in 7 hr written as a unit rate
Answer:
32.14 an hour
Step-by-step explanation:
Answer:
32.142857 miles per hour
Step-by-step explanation:
This is the answer because:
This is a fraction equal to
225 miles ÷ 7 hours
We want a unit rate where 1 is in the denominator, so we divide top and bottom by 7 .
225/7 = 225/7 and 7/7 = 32.142857/1
Therefore, the answer is 32.142857 miles per hour.
Hope this helps!
If a decimal is only in the ____, you can move it up into the quotient
Answer:
Divident
Step-by-step explanation:
plz tell me 12 x 12 = and 12 x 13 =
Answer:
12 x 12 = 144, 12 x 13 = 156
Step-by-step explanation:
Which list shows the number in order from greatest to least? Help asap
Answer:
D
Step-by-step explanation:
Adam has joined a book club. The membership has an initial fee of $25.00 and each book rental costs $2.00. This table shows the linear relationship between the total cost, y, and the number of books Adam rents, x. Fill in each box to correctly model the relationship between x and y. Number of books rented, x 3 6 12 15 Total Cost, y $31.00 $ $43.00 $ $55.00
Answer:
Do you have a screenshot of the table? I’m struggling to visualise it with the data given.
Step-by-step explanation:
Answer:
$37.00 9 $49.00
Step-by-step explanation:
The equation of line j is y= -6/7x +7.Line k is perpendicular to j.What is the slope of line k?
Simplify your answer and write it as a proper fraction,improper fraction,or integer.
Answer:
y=7/6x
Step-by-step explanation:
When given an equation and asked to find the equation of a perpendicular line that intersects it, you know that the slope is the slope of the equation is the negative recipricoal of the given equation. i.e. y=2x+2 and y=-1/2x+2. The y-intercept does not matter.
I hope you understood and that this helps!
Guys I will mark brainliest if you get this right
Answer:
[tex]\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\frac{\frac{7}{8} - \frac{2}{3}}{\frac{5}{6}}\\\frac{7}{8}=\frac{21}{24}\\\frac{2}{3}=\frac{16}{24}\\\frac{21}{24}-\frac{16}{24}=\frac{5}{24}\\\frac{5}{24}*\frac{6}{5}=\frac{1}{4}[/tex]
alg 2 complex numbers in standard form! please help me :(
Answer:
B
Step-by-step explanation:
Refer to the picture that given
Write an equation for the line in the given form.
slope is 5 and (-3, 2) is on the line; point-slope form=
suma de fraccion 1/5 + 5/8
33/40
Step-by-step explanation:
you have to look for the lcm
1/5+5/8
8/40+25/40=33/40
Business math pls help
Solve.
1) A collection of dimes and quarters is worth S15.25. There are 103 coins in all.
How many of each is there?
2) A collection of half dollars and nickels is worth S13.40. There are 34 coins in
all. How many are there?
3) The attendance at a school concert was 578. Admission was S2.00 for adults
and S1.50 for children. The total receipts were S985.00. How many adults and
how many children attended?
4) A purse contains S3.90 made up of dimes and quarters. If there are 21 coins in
all, how many dimes and how many quarters were there?
5) A boy has S2.25 in nickels and dimes. If there are twice as many dimes as
nickels, how many of each kind has he?
can someone help me pls
Answer:use a calculator if you want since all you do is put in the calculator
Step-by-step explanation:
3/7 is 0.428571428
meanwhile 1/4 is 0.25...
which one do you think is bigger
3/7
so it is greater
12.
Question 19 (5 points)
2 - (-8) + (-3) =
15
OA) 1
18
B) 14
12
O
D) 7
Answer:
The answer is d because 10-3 is 7
Answer:
D)7
Step-by-step explanation:
2 - (-8) + (-3) =
10-3 =7
A line has a slope of - 3 and passes through the point (-3, 8). What is the equation of the line?
A. Y=-2/3x+6
B. Y=-2/3x+8
C. Y=6x-2/3
D. Y=8x-2/3
Answer:
y = -3x-1
Step-by-step explanation:
Point-slope equation of a line
y-y1=m(x-x1)
(x1,y1) are coordinates of a point in the line = (-3,8)
m is the slope of the line = -3
Fill in what you know and move constants to get y by itself (y=mx + b ... slope-intercept equation)
y-8=-3(x+3)
y-8=-3x-9
+8 +8
y = -3x-1
None of the options are correct
If you were to place $5,000 in a savings account that pays 6% interest compounded continuously, how much money will you have after 4 years? Assume you make no other deposits or withdrawals.
A.) $11,821.07
B.)$5,024
C.)$6,312.38
D.)$6,356.25
Answer: D
Step-by-step explanation: Use money chip calculator
HELP PLEASE!!!! It's overdue :(
1: y = 3x + 42
2: y = 3(40) + 42
y = 162
3: Bob put 657 in a bank account. He gained 2 times the amount per year. y = 2x + 657
Plz give brainliest.