Answer:
The answer is below
Step-by-step explanation:
The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 270 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours b) What are the quartiles (the 25% and 75% values) of batterylife? c) c) What value of life in minutes is exceeded with 95% probability? (Roundthe answer to the nearest integer.)
Solution:
The z score is used to determine by how many standard deviations the mean is above or below the raw score. If the z score is positive then the raw score is above the mean while if the z score is negative then the raw score is below the mean. The z score is given by:
[tex]z=\frac{x-\mu}{\sigma}\\ \\\mu=mean, \sigma=standard\ deviation[/tex]
Given μ = 270 minutes, σ = 50 minutes
a)
P(x > 4 hours) = P(x > 240 minutes)
[tex]z=\frac{x-\mu}{\sigma}\\ \\z=\frac{240-270}{50} =-0.6[/tex]
From the distribution table, P(x > 240) = P(z > -0.6) = 1- P(z < 0.6) = 1 - 0.2743 = 0.7257
c) P(z > z*) = 0.95
1 - P(z < z*) = 0.95
P(z < z*) = 0.05
This corresponds to a z score of -1.645
[tex]z=\frac{x-\mu}{\sigma}\\ \\-1.645=\frac{x-270}{50} \\\\x=187.75 \ minutes[/tex]
For 75%, P(z < z*) = 0.75
This corresponds to a z score of 0.68
[tex]z=\frac{x-\mu}{\sigma}\\ \\0.68=\frac{x-270}{50} \\\\x=304 \ minutes[/tex]
c) For 25%, P(z < z*) = 0.25
This corresponds to a z score of -0.67
[tex]z=\frac{x-\mu}{\sigma}\\ \\-0.67=\frac{x-270}{50} \\\\x=236.5 \ minutes[/tex]
Estimating Sample Size: You want to obtain a sample to estimate a population proportion. Based on previous evidence, you believe the population proportion is approximately p ∗ = 54 % . You would like to be 90% confident that your esimate is within 1.5% of the true population proportion. How large of a sample size is required? (please do not do any intermediate rounding)
Answer:
The value is [tex]n = 2887[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.54[/tex]
The margin of error is [tex]E = 1.5 \% = 0.015[/tex]
From the question we are told the confidence level is 90% , hence the level of significance is
[tex]\alpha = (100 - 90 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]
Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} } }{E} ]^2 * p(1-p)[/tex]
=> [tex]n = [\frac{1.645 }{0.015} ]^2 * 0.54(1-0.54)[/tex]
=> [tex]n = 2887[/tex]
2) Christine, Odys, and Ariela decided to go to the movie. They got a discount of $10
dollars online. The total ticket price is $14. What is the price of the movie ticket without the
discount? Explain your answer and I will give you Brainliest
Answer:
4
Step-by-step explanation:
A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515.
Answer:
The value is [tex]P(\= X \ge 515 ) = 0.8944[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = 500[/tex]
The standard deviation is [tex]\sigma = 60[/tex]
The sample size is n = 25
Generally the standard error of mean is mathematically represented as
[tex]\sigma _{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]\sigma _{\= x } = \frac{60}{\sqrt{25} }[/tex]
=> [tex]\sigma _{\= x } = 12[/tex]
Generally the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 515 is mathematically represented as
[tex]P(\= X \ge 515 ) = 1 - P(\= X < 515)[/tex]
Here [tex]P(\= X < 515) = P(\frac{\= x - \mu }{\sigma_{\= x }} < \frac{515 - 500}{12} )[/tex]
[tex]\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )[/tex]
[tex]P(\= X < 515) = P(Z < 1.25 )[/tex]
From the z table the probability of (Z < 1.25 )
[tex]P(Z < 1.25 ) = 0.10565[/tex]
So
[tex]P(\= X < 515) = 0.10565[/tex]
So
[tex]P(\= X \ge 515 ) = 1 - 0.10565[/tex]
=> [tex]P(\= X \ge 515 ) = 0.8944[/tex]
Leanna has a rectangular piece of fabric. The fabric is 24 inches wide and 40 inches long. Leanna folds the piece of fabric along its diagonal to form a triangular scarf.
What is the area, in square inches, of the triangular scarf?
Given:
Length of a rectangular piece of fabric, l = 24 inches
Width, w = 40 inches
Leanna folds the piece of fabric along its diagonal to form a triangular scarf.
To find:
The area of the triangular scarf.
Solution:
Area of the rectangular piece of fabric is
[tex]Area=length\times width[/tex]
[tex]Area=24\times 40[/tex]
[tex]Area=960[/tex]
Area of rectangular piece of fabric is 96 sq. inches.
We know that diagonal of a rectangle divides the rectangle in two equal parts.
Leanna folds the piece of fabric along its diagonal to form a triangular scarf. So, area of triangular scarf is half of area of rectangular piece of fabric.
[tex]\text{Area of triangular scarf}=\dfrac{1}{2}\times 960[/tex]
[tex]\text{Area of triangular scarf}=480[/tex]
Therefore, the area of triangular scarf is 480 sq. inches.
3. Chan Hee is paid $25 for tutoring.
Then he spends $4 on a sandwich
and $2 on a drink. Write an
equation to show the amount of
money Chan Hee has now. Solve
the equation.
Answer: x + 2 + 4 = 25
x = 19
Step-by-step explanation:
First, you would solve The word problem with the equation 25 - 2 - 4, which equals 19, then you essentially flip the equation around, but instead of 19, you have x. when you do this it’s important to flip the operation you use too, so if the original equation uses subtraction, switch it to addition, and vise versa. The end result would be x + 2 + 4 = 25.
What is the slope of the line given by the equation below?
y+ 2 = -3(x-5)
O A. 2
O B.-3
O c.3
O D.-5
Answer:
B. -3
Step-by-step explanation:
y + 2 = -3(x - 5)
y + 2 = -3x - 15
y = -3x - 15 - 2
y = -3x - 17
y = mx + b
m = -3
can i get brainliest please?
What is an equation to 3,
509
Answer:
3000+509
Step-by-step explanation:
Is 2.967 and 9.974 grater than 3???
Answer:
2.967 isn't greater but 9.974 is greater than 3
Hope this was helpful
A middle school sold 673 student tickets and staff tickets for the end of year carnival.
The tickets for the carnival were $2.50 for students and $4.00 for staff. The school made
$1,924.00 from student and staff ticket sales. Which equation will help to determine the
number of student tickets (s) and the number of staff tickets (1) sold?
OA
45 + 2.5f = 673
OB. suf = 1,924
• C. 2.5s + 4f = 673 + 1,924
OD. 2.5s + 4f = 1,924
Suppose that, on average, 1 person in 1000 makes a numerical error in preparing his or her income tax return. If 10,000 returns are selected at random and examined, find the probability that 6, 7, or 8 of them contain an error.
Answer:
0.2657
Step-by-step explanation:
Given that:
Probability of Error (p) = 1/ 1000 = 0.001
Number of trials (n) = 10000
μ = (n * p) = 10000 * 0.001 = 10
Using the binomial distribution :
P(x, μ) = e^-μ (μ^x) / x!
for x = 6
P(6, 10) = e^-10 (10^6) / 6!
P(6, 10) = 0.0000453999 (1388.8888) = 0.06305541263112
for x = 7
P(7, 10) = e^-10 (10^7) / 7!
P(7, 10) = 0.0000453999 (1984.1269) = 0.09007916284731
for x = 8
P(8, 10) = e^-10 (10^8) / 8!
P(8, 10) = 0.0000453999 (2480.1587) = 0.11259895696413
P(6) + P(7) + P(8)
0.06305541263112 + 0.09007916284731+ 0.11259895696413
= 0.26573353244256
= 0.2657
Identify the angle pair as congruent or supplementary. Give your reasoning.
Answer:
Step-by-step explanation:
a). ∠3 and ∠5 [Alternate exterior angles]
b). ∠1 and ∠8 [Consecutive exterior angles]
c). ∠2 and ∠6 [Corresponding angles]
d). ∠1 and ∠7 [Alternate exterior angles]
e). ∠4 and ∠5 [Consecutive interior angles]
f). ∠3 and ∠7 [Alternate angles]
g). ∠5 and ∠6 [Supplementary angles]
h). ∠2 and ∠4 [Vertically opposite angles]
Using the constant if proportionality, write an equation that represents this proportional relationship. Let x be the number of kilograms, and let y be the number of inches.
Answer:
the question 55 and 66
Step-by-step explanation:
Answer:
x: weight in kilograms
y: distance stretched in inches
proportionality constant: k = 1/3
Step-by-step explanation:
Write 640000 in standard form.
Answer:
6.4 ×10raise to power 5
Step-by-step explanation:
it is times 10 raise to power 5 because the moved the decimal point 5 times
6.4 ×10000= 6.4×10⁴×10¹
=6.4×10 raise to power 4+1
=6.4×10 raise to power of 5
can u help me
How many groups of 2/3 are in 3/5
Answer:
9/10
Step-by-step explanation:
(3/5)/(2/3) = 9/10
Which product is modeled by the number line below?
O (-3/4)
O (-24)
O (214)
O (3)(4)
Answer:
D
Step-by-step explanation:
there are 4 jumps. and 3 numbers between the jumps
The distance between Dallas and Houston is 136 kilomenters. There are approximately 8 kilometers in 5
miles. What is the measurement that is closest to the number of miles between these two?
Help out please ASAP!
Jan needs $20 to buy her radio. She has saved $15. What percent of the cost of the radio has she saved?
Answer:
75%
Step-by-step explanation:
10 is half and 5 is half of 10 its 75%
-4x - 2y - z = 15
12x + 6y + 3z = 45
2x + 5y + 72 = -29
I Need help
Which of the following responsibilities are held by federal government. choose all that apply
1. protecting national parks
2.administering healthcare
3.providing social security
4.managing intercity traffic
5.creating garbage collection services
6.chartering city governments into existence
there are two answers
Answer:
I thinks it's 2 an 3 sorry if I'm wrong btw have a nice day
Gail has 2 gallons of milk. About how many liters of milk does Gail have?(1 quart =0.94 liters)
Answer:
It should be about 7 liters
Step-by-step explanation:
Basically you would multiply 3.785 by 2 and that would equal 7.57 but if you want to round you can.
Which list correctly orders A, B, and C from least to greatest when A=17, B = -6, and C = -5/?
0 A, B, C
0 B, C, A
C, BA
A, C, B
vJuan purchased 16 lemons and used 5 on the first day of making lemonade. On the second day, he purchased 12 lemons and used 11. Juan wrote this expression to find how many lemons he should have left.
(16 – 5) + (12 – 11)
Which expression correctly uses the additive inverse and properties of operations to show the same value?
Answer:12 Left
Step-by-step explanation:
Answer: He should have 12 lemos left
Step-by-step explanation:
what is the solution of
Answer:A
Step-by-step explanation:
Answer: D (12)
Step-by-step explanation: I put both equations into desmos and the coordinates are (12,23) and x=12. It's not 6!
maurice has 20 strips of leather that are each 4 1/2 feet long. maurice wants to punch holes in each strip of leather that are 3/8 of a foot apart. maurice will use the expression shown to determine the number of hles to punch in each strip of leather.
4 1/2 ÷3/8
which expression will also give the number of holes that maurice will punch into each strip of leather?
2/9 ÷8/3
2/9÷3\8
9/2 . 8/3
9/2 . 3/8
Answer:
A
Step-by-step explanation:
Answer:
9/2 . 8/3
Step-by-step explanation: Both equations equal 12
........................................................................
Answer:
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PLEASE SOMEONE HELP QUICK I WILL GIVE BRAINLIEST
Answer:
134 deg
Step-by-step explanation:
x + 46 = 180
v + 46 = 180
Solve
Please answer !!!!!!!!!!!!!!!!!!!
Answer:
the answer is < 98
Step-by-step explanation:
means first the sum of every degree of triangle is must be <180 so at the angle of A is straight line so it measure 180° - 143° =37°
So the formula form of 61°+37°+x =180°
x+61°+37°-37°=180°-37°...subtract by 37°
x+61°=143°...simplifying
x+61°-61°=143°-61°.....subtract by 61°
x=82°......simplifying
Please help me with this I really need the help
Answer:
16(1 + 2)
Step-by-step explanation:
16 needs to stay the same as the first number, so the number you'd select is 1, because 16 × 1 is 16.To find out the second number in parentheses, do 32 ÷ 16. 32 ÷ 16 = 2, so the number you'd select is 2.I hope this helps!
A Store makes a profit of 18 on a blanket after a markup of 30% what was the selling price
Answer:
78
Step-by-step explanation:
% profit= profit/CP ×100/1
Profit= selling price (S.P) - cost price(C.P)
%profit= 30
profit= 18
% profit= profit / CP×100/1
30= 18/CP ×100/1
30 = 1800 /CP
CP= 1800/30
CP =60
Recall that:
Profit= SP- CP
SP= Profit +CP
= 18+60
=78
