Answer:
0.00420 is the answer
Step-by-step explanation:
The definition of sig figs is each of the digits of a number that are used to express it to the required degree of accuracy, starting from the first nonzero digit.
The rounding number of 0.004198223 to 3 significant figures is 0.0042
Here,
The number is 0.004198223.
We have to find, 0.004198223 to 3 significant figures.
What is Rounding number?
Rounding means making a number simpler but keeping its value close to what it was.
Here,
The number is 0.004198223.
To find 3 significant figures,
We round a number to three significant figures in the same way that we would round to three decimal places.
Then, We count from the first non-zero digit for three digits. We then round the last digit.
Here, the digit is 9 then it will be round.
We get, the number is;
0.0042
We fill in any remaining places to the right of the decimal point with zeros.
So, The rounding number of 0.004198223 to 3 significant figures is 0.00420
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Are the two terms on each tile like terms? Sort the tiles into the appropriate categories.
-7y^2and y^2
-4p and p^2
0.5kt and -10kt
6 and 9
5x and 5
3ad and 2bd
Answer:
LIKE TERMS: 6 and 9, 0.5kt and -10kt, and -7y2 and y2. UNLIKE TERMS: 3ad and 2bd, 5x and 5, and the last one is -4p and p2
Step-by-step explanation:
Answer: like terms: 6&9 , 0.5kt&-10kt , -7y^2&y^2
unlike terms 3ad&2bd, 5x&5, -4p&p^2
Step-by-step explanation:
passed
4. Dean Pelton wants to perform calculations to impress the accreditation consultants, but upon asking for information about GPAs at Greendale Community College, Chang only tells Pelton that the GPAs are distributed with a probability density function f(x) = D(2 + e −x ), 2 ≤ x ≤ 4 where D was some unknown "Duncan" constant. How many student records have to be retrieved so that the probability that the average GPA is less than 2.3 is less than 4 percent?
Answer:
the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Step-by-step explanation:
Let assume that n should represent the number of the students
SO, [tex]\bar x[/tex] can now be the sample mean of number of students in GPA's
To obtain n such that [tex]P( \bar x \leq 2.3 ) \leq .04[/tex]
⇒ [tex]P( \bar x \geq 2.3 ) \geq .96[/tex]
However ;
[tex]E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D[/tex]
[tex]E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D[/tex]
Similarly;
[tex]D\int\limits^4_2(2+ e^{-x}) dx = 1[/tex]
⇒ [tex]D*(2x-e^{-x} ) |^4_2 = 1[/tex]
⇒ [tex]D*4.117 = 1[/tex]
⇒ [tex]D= \dfrac{1}{4.117}[/tex]
[tex]\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103[/tex]
∴ [tex]Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711[/tex]
Now; [tex]P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)[/tex]
Using Chebysher one sided inequality ; we have:
[tex]P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}[/tex]
So; [tex](\omega = \bar x - \mu)[/tex]
⇒ [tex]E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}[/tex]
∴ [tex]P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}[/tex]
To determine n; such that ;
[tex]\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}[/tex]
⇒ [tex]n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}[/tex]
[tex]n \geq 16.83125[/tex]
Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.
Describe the solutions of the following system in parametric vector form,and provide a geometric comparison with the solution set .
x1 + 3x2- 5x3 = 4
x1+ 4x2 - 8x3 = 7
-3x1- 7x2 +9x3 =6
Answer:
The equations are linearly independent so there is no parametric vector form
Step-by-step explanation:
I attached the solution.
Round 1040 to the nearest hundred.enter your answer in the box below
Answer:
1000
Step-by-step explanation:
For rounding questions, you want to look at the place value to the right of the digit it wants you to round to. If that place value to the right of the digit you need to round is less than 5, you round down. If the place value to the right of the digit you need to round is 5 or greater, then you round up. In your situation, the place value you want to round is the hundreds place, so we need to look at the tens value. The tens value is 4, which is less than 5, so we round down. Therefore, the answer would be 1000.
A and b are similar shapes. B is an enlargement of a with scale factor 1.5 Work out the value of x, h and w
Answer:
x = 54°
h = 7.5cm
w= 6cm
Step-by-step explanation:
Find attached the diagrams as found at Maths made easy.
Similar shapes have same shapes but different sizes.
When two shapes are similar, the ratios of the lengths of their corresponding sides are equal.
B is an enlargement of A with scale factor 1.5. That is, each of the sides of B = 1.5 of each side of A
To determine the value of x, h and w, let's look at the relationship of A and B.
h = 1.5 × 5cm
h = 7.5cm
9cm = 1.5 × w
w = 9cm/1.5
w= 6cm
Since the angles do not change when a shape is enlarged, the value of x = 54°
x = 54°
Square A"B"C"D" is the final image after the rule was applied to square ABCD. On a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5). What are the coordinates of vertex A of square ABCD? (–1, –6) (–1, –2) (–1, 6) (–2, 1)
Answer:
The answer is (-2 , 1 ) or D on Edge
Step-by-step explanation:
The coordinates of vertex A of square ABCD is (-1, -2).
What are coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane.
Given:
A(-5, -3), B(-3, -1), C(-1, -3) and D(-3, -5)
By using the rule
T(-4, -1)
So, the coordinate of Vertex A will be
A( -5 + 4, -3 + 1)
=A(-1, -2)
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resuelve las siguientes ecuaciones tales que 0° ≤ x ≤ 360°
sen x=sen (π/2-x)
cos x + 2 sen x= 2
csc x = sec x
2 cos x * tan x -1 = 0
4 cos2 x = 3 - 4 cos x
Answer:
4cos=2X
X=3-4COS
X=-1
A supermarket is redesigning it’s checkout lanes. Design A has a sample size of 50, sample mean of 4.1 minutes, and sample standard deviation of 2.2 minutes. Design B has a sample size of 50, sample mean of 3.5 minutes, and sample standard deviation of 1.5 minutes. At the 0.05 level of significance, determine if their is evidence that the checkout times of the two systems differ.
Answer:
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
Null hypothesis is accepted at 5 % level of significance
There is no significance difference between Design A and Design B
Step-by-step explanation:
Given sample size of design A
n₁ = 50
sample mean of design A x⁻₁ = 4.1 minutes
Sample standard deviation S₁ = 2.2 minutes
Given sample size of design B
n₂ = 50
sample mean of design A x⁻₂ = 3.5 minutes
Sample standard deviation S₂ = 1.5 minutes
Null Hypothesis : H₀ : There is no significance difference between Design A and Design B
Alternative Hypothesis : H₁:There is significance difference between Design A and Design B
Level of significance ∝ = 0.05
Test statistic
[tex]t = \frac{x^{-} _{1}- x^{-} _{2} }{\sqrt{S^{2} (\frac{1}{n_{1} }+\frac{1}{n_{2} }) } }[/tex]
where
[tex]S^{2} = \frac{n_{1} S_{1} ^{2} +n_{2} S^2_{2} }{n_{1} +n_{2} -2}[/tex]
[tex]S^{2} = \frac{50 (2.2)^{2} +50(1.5)^2}{50+50-2}[/tex]
On calculation , we get
S² = 3.6173
Test statistic
[tex]t = \frac{4.1-3.5}{\sqrt{3.617(\frac{1}{50} +\frac{1}{50} }) }[/tex]
On calculation , we get
t = 1.57736
Degrees of freedom
ν = n₁ + n₂ -2 = 50 +50 -2 =98
t₀.₀₂₅ ,₉₈ = 1.9845
The calculated value t = 1.57736 < 1.9845 at 5 % level of significance
null hypothesis is accepted
What is the center of a circle represented by the equation (x+9)2+(y−6)2=102? Please Help
Answer:
(-9, 6)
Step-by-step explanation:
edgenuity 2020
hope this helps!
A machine produces 576 units in 18 hours at this rate how many will it produce in 28 hours
Answer: 896
Step-by-step explanation:
Let's use a rule of three here.
[tex]\frac{576}{x}=\frac{18}{28}[/tex]
Solve for x;
[tex]x=\frac{576*28}{18}[/tex]
[tex]x=896[/tex]
Please answer this correctly
Answer:
Step-by-step explanation:
George Fox university = 10,000,000 + 10,000,000
= full bag + full bag
( click 2 full bag}
Rockhurst university = 10,000,000 +10,000,000 +10,000,000 + 5,000,000
= full bag + full bag + full bag + half bag
(click 3 full bag and 1 half bag}
Lebanon Valley college = 10,000,000 +10,000,000 +10,000,000 +10,000,000+5,000,000
( click 4 full bag and 1 half bag)
Grand view college = 10,000,000
(click 1 full bag}
Given that it was less then 80degrees on a given day, what is the probability that it also rained that day?
The probability that it also rained that day would be 0.30
PEOPLE! THIS IS URGENT! PLEASE HELP ME!!!! If the product 3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9, what is the sum of a and b?
Answer:
35
Step-by-step explanation:
3/2 · 4/3 · 5/4 · 6/5 ·…· a/b =9
a+b=?
------
all numbers get cancelled apart from the first denominator and the last numerator:
1/2*a= 9
a= 18then
b= a-1= 18-1= 17a+b= 18+17= 35
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes. A random sample of twelve service calls is taken. What is the probability that exactly eight of them take more than 93.6 minutes
Answer:
The probability that exactly eight of them take more than 93.6 minutes is 5.6015 [tex]\times 10^{-6}[/tex] .
Step-by-step explanation:
We are given that it is known that times for service calls follow a normal distribution with a mean of 75 minutes and a standard deviation of 15 minutes.
A random sample of twelve service calls is taken.
So, firstly we will find the probability that service calls take more than 93.6 minutes.
Let X = times for service calls.
So, X ~ Normal([tex]\mu=75,\sigma^{2} =15^{2}[/tex])
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 75 minutes
[tex]\sigma[/tex] = standard deviation = 15 minutes
Now, the probability that service calls take more than 93.6 minutes is given by = P(X > 93.6 minutes)
P(X > 93.6 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{93.6-75}{15}[/tex] ) = P(Z > 1.24) = 1 - P(Z [tex]\leq[/tex] 1.24)
= 1 - 0.8925 = 0.1075
The above probability is calculated by looking at the value of x = 1.24 in the z table which has an area of 0.8925.
Now, we will use the binomial distribution to find the probability that exactly eight of them take more than 93.6 minutes, that is;
[tex]P(Y = y) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; y = 0,1,2,3,.........[/tex]
where, n = number of trials (samples) taken = 12 service calls
r = number of success = exactly 8
p = probability of success which in our question is probability that
it takes more than 93.6 minutes, i.e. p = 0.1075.
Let Y = Number of service calls which takes more than 93.6 minutes
So, Y ~ Binom(n = 12, p = 0.1075)
Now, the probability that exactly eight of them take more than 93.6 minutes is given by = P(Y = 8)
P(Y = 8) = [tex]\binom{12}{8}\times 0.1075^{8} \times (1-0.1075)^{12-8}[/tex]
= [tex]495 \times 0.1075^{8} \times 0.8925^{4}[/tex]
= 5.6015 [tex]\times 10^{-6}[/tex] .
Leila runs each lap in 6 minutes. She will run less than 9 laps today. What are the possible numbers of minutes she will run today? Use t for the number of minutes she will run today. Write your answer as an inequality solved for t.
Answer:
I'm not sure if Leila is allowed to run 0 laps.
6 ≤ t ≤ 48
Step-by-step explanation:
To find the number of possible laps, you just find the smallest possible number and the largest.
1 = smallest
8 = largest
But, you have to multiply by 6 to find the time.
6 ≤ t ≤ 48
You are rolling two dice. When the two numbers (1-6) come up, you multiply the numbers
together. What is the probability of getting a product that is NOT divisible by 2?*
Answer:
1/4 probability of getting a product that isn't divisible by 2.
Step-by-step explanation:
These are all the possible outcomes
1 x 1 = 1 2 x 1 = 2 3 x 1 = 3 4 x 1 = 4 5 x 1 = 5 6 x 1 = 6
1 x 2 = 2 2 x 2 = 4 3 x 2 = 6 4 x 2 = 8 5 x 2 = 10 6 x 2 = 12
1 x 3 = 3 2 x 3 = 6 3 x 3 = 9 4 x 3 = 12 5 x 3 = 15 6 x 3 = 18
1 x 4 = 4 2 x 4 = 8 3 x 4 = 12 4 x 4 = 16 5 x 4 = 20 6 x 4 = 24
1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25 6 x 5 = 30
1 x 6 = 6 2 x 6 = 12 3 x 6 = 18 4 x 6 = 24 5 x 6 = 30 6 x 6 = 36
All of the outcomes that aren't divisible by 2 are in bold
There are 9 out of 36 possible outcomes that aren't divisible by 2
9/36 = 1/4
Joana wants to buy a car. Her parents loan her $5,000 for 5 years at 5% simple interest. How much will Joana pay in interest?
Answer:
1250
Step-by-step explanation:
5% of $5000 is 250
250X5= 1250
Identify the predictor variable and the response variable. A farmer has data on the amount of precipitation crops received and the harvest of the crops. The farmer wants to determine the harvest of his crop based on the amount of precipitation his crop received.
Answer:
The Predictor variable is the amount of precipitation received while the Response variable is the crop harvest.
Step-by-step explanation:
The Response variable in an experiment is the factor being measured or studied. They are also known as the dependent variables. Predictor variables are those values that explain the changes in the Response variable. They are also known as the independent variables.
In the question above, the amount of precipitation provides an explanation for the harvest of his crops. Therefore, the amount of precipitation can be rightly described as the predictor or independent variable, while the harvest of his crops is described as the response or dependent variable.
Please help me with this problem I'm lost
Answer:
24
Step-by-step explanation:
Multiple (4)(2)= 8
-3(8) =24
please answer this correctly
Answer:
557
Step-by-step explanation:
l x w
13x24
13x7
22x7
557
Three spinners numbered 1 through 12 are spun. What is the probability of spinning a five on the first spinner, an even number on the second spinner, and a multiple of 4 on the third spinner?
1/96
1/72
7/12
5/6
Answer:
[tex]\frac{1}{96}[/tex]
Step-by-step explanation:
Spinning a 5 is [tex]\frac{1}{12}[/tex]
Spinning even is [tex]\frac{1}{2}[/tex]
Spinning multiple of 4 is [tex]\frac{1}{4}[/tex]
[tex]\frac{1}{12} *\frac{1}{2} *\frac{1}{4}[/tex][tex]=\frac{1}{96}[/tex]
Runners are always talking about minutes per mile. This is the inverse of distance divided by time. Like, on my morning jogs I shoot for 11 minutes per mile. Next month, I'm doing a 10k (that's 10 kilometer) run with my daughter. I'm going to average 11 minutes per mile. Calculate, in minutes how long it will take me to complete the run averaging 11 minutes per mile.
Answer:
around 68 minutes 31 seconds.
Step-by-step explanation:
10km = miles = 6.21x11 = 68.31
A research company desires to know the mean consumption of meat per week among people over age 27. A sample of 1179 people over age 27 was drawn and the mean meat consumption was 1.5 pounds. Assume that the population standard deviation is known to be 1.2 pounds. Construct the 99% confidence interval for the mean consumption of meat among people over age 27. Round your answers to one decimal place.
Answer:
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.575*\frac{1.2}{\sqrt{1179}} = 0.1[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 1.5 - 0.1 = 1.4 pounds
The upper end of the interval is the sample mean added to M. So it is 1.5 + 0.1 = 1.6 pounds
The 99% confidence interval for the mean consumption of meat among people over age 27 is between 1.4 pounds and 1.6 pounds.
PLEASE HELP
Which of the following is an arithmetic sequence?
A: -2, 4, -6, 8, ...
B: -8, -6, -4, -2, ...
C: 2, 4, 8, 16, ...
These items are taken from the financial statements of Sean McCann, CPA for 2019. Sean McCann, capital 1/1/19 $106,000 Sean McCann, Drawing 10,000 Equipment 130,000 Accumulated depreciation (equip) 32,000 Accounts payable 10,600 Cash 33,800 Supplies 7,000 Salaries payable 6,000 Fees earned 136,000 Salaries expense 66,000 Rent expense 14,200 Supplies expense 1,600 Depreciation expense 4,000 Utilities expense 2,400 Accounts receivable 28,000 Mortgage payable (due 12/31/35) 6,400 Instructions: 1. Prepare the journal entries to close your temporary accounts. (Hint: The temporary accounts are revenues, expenses and the drawing account) Date Description Debit Credit 2. Prepare an income statement and a statement of owner’s equity for the year ended December 31, 2019 and a classified balance sheet as of December 31, 2019. Sean McCann, CPA Income Statement For year ended 12/30/19 Sean McCann, CPA Statement of Owner’s Equity For Period Ended 12/31/19 Sean McCann, CPA Balance Sheet For Period Ended 12/30/19
Answer:
1. Prepare the journal entries to close your temporary accounts.
the journal entries required to close the temporary accounts are:
December 31, 2019, closing of temporary revenue accounts
Dr Fees earned 136,000
Cr Income summary 136,000
December 31, 2019, closing of temporary expense accounts
Dr Income summary 88,200
Cr Salaries expense 66,000
Cr Rent expense 14,200
Cr Supplies expense 1,600
Cr Depreciation expense 4,000
Cr Utilities expense 2,400
December 31, 2019, closing of temporary income summary account
Dr Income summary 88,200
Cr Retained earnings 88,200
December 31, 2019, closing of drawings account
Dr Retained earnings 10,000
Cr Sean McCann, Drawing 10,000
2. Prepare an income statement and a statement of owner’s equity for the year ended December 31, 2019 and a classified balance sheet as of December 31, 2019.
Sean McCann, CPA
Income Statement
For the Year Ended December 31, 2019
Fees earned $136,000
Salaries expense ($66,000)
Rent expense ($14,200)
Supplies expense ($1,600)
Depreciation expense ($4,000)
Utilities expense ($2,400)
Net income $47,800
retained earnings = net income - drawings = $47,800 - $10,000 = $37,800
Sean McCann, CPA
Balance Sheet
For the Year Ended December 31, 2019
Assets
Current assets:
Cash $33,800
Accounts receivable $28,000
Supplies $7,000
Total current assets $68,800
Non-current assets:
Equipment $130,000
Accumulated dep. (equip)-$32,000
Total non-current assets $98,000
Total assets $166,800
Liabilities and equity
Current liabilities:
Accounts payable $10,600
Salaries payable $6,000
Total current liabilities $16,600
Long term liabilities:
Mortgage payable $6,400
Total long term liabilities: $6,400
Equity
Sean McCann, capital $106,000
Retained earnings $37,800
Total equity $143,800
Total liabilities and equity $166,800
Sean McCann, CPA
Statement of Owner’s Equity
For the Year Ended December 31, 2019
Sean McCann, capital 1/1/19 $106,000
Net income $47,800
Subtotal $153,800
Drawings during the year -$10,000
Sean McCann, capital 1/1/19 $143,800
1. The mean of the data set{9,5,y,2,x} is twice the data set {8,x,4,1,3}. What is (y-x) squared.
2. How many alcohol must be added to480 grams of hand sanitizer that is 24% alcohol to make it a hand sanitizer that is 40% alcohol?
Answer:
1. (y - x)² = 256
2. 128g needed to be added
Step-by-step explanation:
1.
9 + 5 + 2 + y + x = 2(8 + 4 + 1 + 3 + x)
16 + y + x = 32 + 2x
y - x = 16
∴ (y - x)² = 256
2.
x = mass of alcohol to add
480 × 0.24 = 115.2 ← current mass of alcohol
0.4(480 + x) = 115.2 + x (×5)
2(480 + x) = 576 + 5x
960 + 2x = 576 + 5x
3x = 384
x = 128g
Making Friends Online
A survey conducted in March 2015 asked 1060 teens to estimate, on average, the number of friends they had made online. while 43% had not made any friends online, a small number of the teens had made many friends online.
(a) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left?
Skewed to the left.
Symmetric
Skewed to the right.
(b) Two measures of center for this distribution are 1 friend and 5.3 friends. Which is most likely to be the mean and which is most likely to be the median?
Mean=
Median=
1Lenhart A, "Teens, Technology, and Friendships", Pew Research Center, pewresearch.org, August 6, 2015. Value for the mean is estimated from information given.
Answer:
Step-by-step explanation:
) Do you expect the distribution of number of friends made online to be symmetric, skewed to the right, or skewed to the left?
Skewed to the left.
Symmetric
Skewed to the right.
(b) Two measures of center for this distribution are 1 friend and 5.3 friends. Which is most likely to be the mean and which is most likely to be the median?
Mean=
Median=
----------------------------------a)
as proportion of people with 0 friends is 43% whcih is on left side and maximum ; and % decrease with increasing number of friends
skewed to the right
b)
as it is skewed to the right ; therefore mean is greater than median
mean=5.3
median=1
[since for skwewed to the right distribution :mean is always greater than median, therefore higher value should be mean which is 5.3 and lower value is median which is 1]
Part(a): Skewed to the right
Part(b) The required values are,
mean=5.3
median=1
a)
As a proportion of people with 0 friends are 43% which is on the left side and maximum; and % decrease with an increasing number of friends
skewed to the right
b)
As it is skewed to the right; therefore mean is greater than the median
mean=5.3
median=1
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Bus A and Bus B leave the bus depot at 6 am.
Bus A takes 20 minutes to do its route and bus B takes 35 minutes to complete its route.
At what time are they both back at the bus depot together?
Give your answer as a 12-hour clock time
Answer:
8.20 am
Step-by-step explanation:
First, we have that Bus A will be back after 20 minutes, then after 40, then 60, 80, 100, 120, 140, 160 minutes, etc.
Then, we have that Bus B will be back after 35 minutes, then 70, then 105, then 140, 175....
From the list above we see that the first time they are both back at the station is after 140 minutes. (it's the MCM).
If we express this in terms of minutes, since one hour has 60 minutes, 2 hours have 120 minutes and thus, 140 minutes is 2 hours and 20 minutes.
Therefore, they will be both back at the station 2 hours and 20 minutes after they first departed at 6 am, so they will be back at the depot at 8.20 am
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line? (full problem attached)
Answer:
(0,34)
Step-by-step explanation:
For each rise of 14 in the x direction, this graph rises by -8 in the y direction. This means that, when x is 0, and the graph intersects the y axis, the y value will be 50-8-8=34. Therefore, the y intercept of this line is (0,34). Hope this helps!
Answer:
The answer is (0,34)
Quick Start Company makes a 12-volt car batteries. After many years of product testing, the company knows the average life of a Quick Start battery is normally distributed, with mean=45 months and a std. deviation = 8 months.
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearest month)
Answer:
The company will expect to replace 13.03% of batteries.
The company should guarantee the batteries for 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 45, \sigma = 8[/tex]
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 45}{8}[/tex]
[tex]Z = -1.125[/tex]
[tex]Z = -1.125[/tex] has a pvalue of 0.1303.
The company will expect to replace 13.03% of batteries.
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries
They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 45}{8}[/tex]
[tex]X - 45 = -1.28*8[/tex]
[tex]X = 34.76[/tex]
Rounding to the nearest month
The company should guarantee the batteries for 35 months.
