Answer:
a) 0.5447
b) 0.0228
c) 0.4325
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Normal distribution with a mean of 9.6 minutes and a standard deviation of 2.3 minutes.
This means that [tex]\mu = 9.6, \sigma = 2.3[/tex]
a. between 5 and 10 min
This is the p-value of Z when X = 10 subtracted by the p-value of Z when X = 5. So
X = 10
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 9.6}{2.3}[/tex]
[tex]Z = 0.17[/tex]
[tex]Z = 0.17[/tex] has a p-value of 0.5675
X = 5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 9.6}{2.3}[/tex]
[tex]Z = -2[/tex]
[tex]Z = -2[/tex] has a p-value of 0.0228
0.5675 - 0.0228 = 0.5447 probability that a randomly received emergency call is between 5 and 10 minutes.
b. less than 5 min
p-value of Z when X = 5, which from item a), is 0.0228, so 0.0228 probability that a randomly received emergency call is of less than 5 minutes.
c. more than 10 min
1 subtracted by the p-value of Z when X = 10, which, from item a), is of 0.5675.
1 - 0.5675 = 0.4325
0.4325 probability that a randomly received emergency call is of more than 10 minutes.
help me moderate helping me
Problem 1
It's not clear if the person deposits at the start of the quarter, or at the end of the quarter. I'm going to assume they deposit at the end of the quarter. This means we go with an ordinary future value of annuity.
The formula we use is
F = P*( (1+i)^n - 1)/i
where,
F = future value of the accountP = payment per periodi = interest rate per periodn = number of periodsIn this case,
F = 300,000P = unknown, what we want to solve fori = 0.08/4 = 0.02n = 25*4 = 100 quarters (equivalent to 25 years)So,
F = P*( (1+i)^n - 1)/i
300,000 = P*( (1+0.02)^100 - 1)/0.02
300,000 = P*(312.232305912618)
P = (300,000)/(312.232305912618)
P = 960.823061288088
P = 960.82
You must deposit $960.82 per quarter
If you deposit that amount of money per quarter, for 100 quarters, then you deposited a total of 960.82*100 = 96,082 dollars in total.
The amount of interest is 300,000 - 96,082 = 203,918 dollars
============================================================
Problem 2
We use the same formula from problem 1. This time we know the periodic payment ($250 per month) and we want to find the value of F
More specifically, we have this given info:
P = 250i = 0.072/12 = 0.006n = 30*12 = 360 months (aka 30 years)So,
F = P*( (1+i)^n - 1)/i
F = 250*( (1+0.006)^360 - 1)/0.006
F = 317,306.360545277
F = 317,306.36
If you deposit $250 per month, for 360 months, then you'll have $317,306.36 in the account.
This includes interest. The total amount deposited, without interest involved, is 250*360 = 90,000 dollars.
Therefore, the amount of interest earned is 317,306.36 - 90,000 = 227,306.36 dollars.
PLEASEEEEE HELPPPPPPPP
Answer:
f(-5) = -195
Step-by-step explanation:
Given that,
[tex]f(x)=x^3-2x^2+3x-5[/tex] ....(1)
and
[tex]g(x)=x^2+x-1[/tex]
We need to find the value of f(-5).
Put x = -5 in equation (1).
[tex]f(-5)=(-5)^3-2(-5)^2+3(-5)-5\\\\=-195[/tex]
So, the value of f(-5) is equal to (-195).
What is the left-hand limit of this function as x approaches 2? f(x)=x/x-2
9514 1404 393
Answer:
B. -∞
Step-by-step explanation:
There is a vertical asymptote at x=2. Left of that line, the denominator is negative. As x approaches 2 from the left, the function approaches negative infinity.
find the area of irregular figures
Answer:
I believe it is 90
Step-by-step explanation:
I'm not so sure but when finding the area of a shape you times all those lengths together.
Answer: There is NO answer because there is some missing information!
Step-by-step explanation:
Write equation could use to find number of centimeters in 1 inch.
Answer:
0.393701 cm = 1 in
Step-by-step explanation:
We want to find the number of centimeters in 1 inch.
First, the two conversion rates we need to use:
1m = 100 cm
1m = 39.3701 in
From these two equations, we can conclude that:
100cm = 1m = 39.3701 in
100cm = 39.3701 in
Because we want to find the total number of centimeters in 1 inch, we need to divide both sides by 39.3701
We will get:
(100cm)/39.3701 = (39.3701 in)/39.3701
0.393701 cm = 1 in
This equation gives us the number of centimeters in one inch.
1. There are 2 schools. Each school has 3 buildings. Each building has 4 floors. Each floor has 5 classrooms. Each classroom has 6 rows of desks. Each row has 7 desks. How many desks are there in the two schools?
Charlie weighed 8 lbs. 11 oz. at birth given that 1 pound is equivalent to 16 ounces what is Charlie’s birthweight expressed in ounces
Answer:
139 oz.
Step-by-step explanation:
If 1 pound equals 16 ounces, multiply 8 by 16 and you will get 128, then add the original 11 ounces to get 139.
solve the question
Answer:
40*40=1600
PLS MARK BRAINLIEST
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
Compare the rules of two games:
Game A: Two six-sided dice are thrown.The numbers on the dice determine which player gets a point.Player 1 gets a point if the product of the numbers on the dice is even.Player 2 gets a point if the product is odd.
Game B: Two six - sided dice are thrown.The numbers on the dice determine which player gets a point.Player 1 gets a point if the sum of the numbers on the dice is even.Player 2 gets a point if the sum is odd.
Which statement accurately describes whether these games are fair?
A: Both Game A and Game B are fair.
B: Game A is not fair,and Game B is fair.
C: Neither Game A nor Game B is fair.
D: Game A is fair,and Game B is not fair.
Answer: Choice B
Game A is not fair, and game B is fair.
==============================================================
We'll start with game A.
The sides of the dice are {1,2,3,4,5,6}
There are 6*6 = 36 ways to roll two dice.
If we roll two odd numbers, say 3 and 5, the product is odd because 3*5 = 15.
If any of the numbers are even, then the product is even. Eg: 4*5 = 20 or 2*6 = 12.
To be an even number, 2 must be a factor.
So you can probably see that it's more likely to get an even number product considering that in order to get an odd product, both values must be odd (which narrows the selection pool). We can say that game A is not fair. It favors player 1 more. If you're sure about this, then I recommend looking at a multiplication table but only focus on the first 6 rows and 6 columns. Ignore the row and column that has 0s in it.
------------------------------
Now onto game B
The rules are nearly the same, except now instead of multiplying the dice values, we add them up.
We still have 6*6 = 36 outcomes.
Here are some handy rules we'll take into account
even+even = eveneven+odd = oddodd+odd = evenIf the first dice rolls to '1', then there are 3 ways to get an even number (rolling either 1,3,or 5 on the second dice) and there are 3 ways to get an odd number (rolling either 2,4,or 6 on the second dice). We can see that there are the same number of ways to get an even sum or an odd sum. Apply this in general to any result that the first dice shows, and this basically leads to the conclusion that half of the 36 sums are even, and the other half are odd. We have a fair game now. Refer to a sum of dice chart if you need more convincing.
Answer:
Game A is not fair, and game B is fair.
Step-by-step explanation:
test on iready
How many times bigger is a group of 20 coins than a group of 5 coins
Answer:
It is there difference:
20-5
15
The circle shown has a radius of 4 cm.
What is the area of the circle to 1 decimal place?
Answer:
A = 50.2 cm^2
Step-by-step explanation:
The area of a circle is given by
A = pi r^2 where r is the radius
A = (3.14) * 4^2
A =50.24
To 1 decimal place
A = 50.2 cm^2
Answer:
50.3 cm^2 to 1 dec. place.
Step-by-step explanation:
Area = pi r^2
= pi * 4^2
= 16 * pi
= 50.265
The Boffo Product Company sells a waffle iron on which they have done product testing. They have determined that the amount of time the product will last can be described by a normal distribution. In particular, the average waffle iron lasts for 12 years and one standard deviation is 8 months. How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time
Answer:
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
The average waffle iron lasts for 12 years and one standard deviation is 8 months.
Measuring the time in months, we have that [tex]\mu = 12*8 = 96[/tex] and [tex]\sigma = 8[/tex]
How long should they warranty the product for if they want no more than 6.7% of the waffle irons to fail within that time?
This is X when Z has a p-value of 0.067, so X when Z = -1.5. Then
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.5 = \frac{X - 96}{8}[/tex]
[tex]X - 96 = -1.5*8[/tex]
[tex]X = 84[/tex]
84 months = 7 years.
They should warranty the product for 7 years if they want no more than 6.7% of the waffle irons to fail within that time.
Determine whether the following event is mutually exclusive or not mutually exclusive.
Choosing a student who is a history major or a business major from a nearby university to participate in a research study. (Assume that each student only has one major.)
Answer:
Following are the solution to the given points:
Step-by-step explanation:
Both A and B are exclusive to each other because of P(A and B) = 0.
Therefore, Let A be the major in mathematics and B be the major in philosophy.
Each student is required to only have one major.
No student does have two significant students.
Therefore, the likelihood of both the major pupils being zero.
This is P(A and B) = zero
Therefore, The events are exclusive to each other.
The ratio between boys and girls in a class is 3 : 1. Find the number of boys in the class is the total number of students is 40.
Answer: 30 boys
Step-by-step explanation:
Boys:Girls
3 : 1
Let no. of girls =x
⇒ no. of boys =3x.
⇒ no. of students in class =4x
= 4/3×3x
= 4 /3 ×no. of boys
40=4/3* no.of boys
40* (3/4)=no.of boys
30=no of boys
A museum has a model of an Egyptian pyramid. It has a rectangular base that is 10 feet by 8 feet, with a height of 12 feet.
What is the volume of the pyramid?
Answer: 320ft^3
Step-by-step explanation:
Assuming the pyramid is just a normal rectangular pyramid and isn't made of stairs...
10x8x12/3 = 320 ft^3
Please can someone help quick and now 115 students choose to attend one of three after school activities: football, tennis or running.
There are 54 boys.
52 students choose football, of which 25 are girls.
43 students choose tennis.
10 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
Answer:
only 20 students would
Step-by-step explanation:
the probability would be very since it is 20 out of 115. i hope this helped
which equation is correctly rewritten to solve for x?
Use the piecewise function below to evaluate the points f(–3), f(0), and f(–1).
{9x,x−4,x<−1x≥−1
Question 17 options:
f(–3) = –7, f(0) = –0, and f(–1) = 5
f(–3) = –27, f(0) = –4, and f(–1) = 5
f(–3) = –7, f(0) = –4, and f(–1) = –1
f(–3) = –27, f(0) = –4, and f(–1) = –5
Given:
The piecewise function is:
[tex]f(x)=\begin{cases}9x & \text{ if } x<-1 \\ x-4 & \text{ if } x\geq -1 \end{cases}[/tex]
To find:
The values of [tex]f(-3),f(0), f(-1)[/tex].
Solution:
In the given piecewise function,
[tex]f(x)=9x[/tex] for [tex]x<-1[/tex] and [tex]f(x)=x-4[/tex] for [tex]x\geq -1[/tex].
Putting [tex]x=-3[/tex] in [tex]f(x)=9x[/tex], we get
[tex]f(-3)=9(-3)[/tex]
[tex]f(-3)=27[/tex]
Putting [tex]x=0[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(0)=0-4[/tex]
[tex]f(0)=-4[/tex]
Putting [tex]x=-1[/tex] in [tex]f(x)=x-4[/tex], we get
[tex]f(-1)=-1-4[/tex]
[tex]f(-1)=-5[/tex]
The required values are [tex]f(-3)=27,f(0)=-4,f(-1)=-5[/tex].
Therefore, the correct option is D.
Crhistine paid $633.68 for a handbag the sales tax in her state is 6.5% what was the price of the hand bag before the sales tax was added
Answer:
Step-by-step explanation:
X * (1.065) = $633.68
X = $633.68/1.065
X= $595.00
The price of the handbag before the sales tax was added is $595
What is sale tax?A sales tax is a tax paid to a governing body for the sales of certain goods and services. Usually laws allow the seller to collect funds for the tax from the consumer at the point of purchase.
Given that, Christine paid $633.68 for a handbag the sales tax in her state is 6.5%
Let the cost of the handbag before sales tax be x,
Therefore,
x + 6.5% of x = 633.68
x + 6.5 / 100 × x = 633.68
x(1 + 6.5 / 100) = 633.68
x(106.5 / 100) = 633.68
x = 633.68 × 100 / 106.5
x = 595
Hence, the price of the handbag before the sales tax was added is $595
Learn more about sales tax, click;
https://brainly.com/question/29751934
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Common ration of 54 and 72
Answer:
answer is 18 54 an 72 is 18
Calculate the remaining values: de a y b
Step-by-step explanation:
of what ? there is nothing here to work with.
be a little bit more careful to at least understand the meaning of the problem, Ame what is given to you written with to solve the problem. because we here also need that information. we would need to read in a Crystal ball what your teacher wants from you, if you don't give us that information.
and I am good but not that good ...
John made this model to show 4/7 * 13/9
Using John's model, what is 4/7 * 13/9? (has to be in fractions)
Answer:
52/63
Step-by-step explanation:
Given the expression
4/7 * 13/9
Taking the product
= (4*13)/(7*9)
= 52/63
Hence the product of both fractions is 52/63
what is a bank statement
Answer:
A statement that shows current balance of an account and all transactions that occurred on that account since the last statement.
Transactions such as deposits, withdrawals, checks written, debt card uses...
There are other examples of bank statements for things like home loans, business loans, and investments.
What is the measure of AngleCAB?
Answer:
52
Step-by-step explanation:
answer is in photo above
Answer:
52
Step-by-step explanation:
step-by-step explanation is a c and b is 52
Angles measuring 8x – 3 and 7x + 18 are supplementary. Find the measure of each angle. (5 points)
Answer:
The measures of the angles are 85 and 95 degrees each.
Step-by-step explanation:
Two angles are supplementary when they add up to 180 degrees.
Therefore, set up an equation and solve for the variable x in the first place.
(8x-3)+(7x+18)=180
8x-3+7x+18=180
8x+7x-3+18=180
15x-3+18=180
15x+15=180
15x=165
x=165/15
x=11
Angle 8x-3=8(11)-3=88-3=85.
Angle 7x+18=7(11)+18=77+18=95.
Answer:
85⁰ and 95⁰
Step-by-step explanation:
Supplementary angle add up to 180⁰
8x-3+7x+18=180
8x+7x-3+18=180
15x+15=180
15x=180-15
15x=165
15x/15=165/15
x=165/15
x=11⁰
measure of first angle=8(11⁰)-3
=88⁰-3
=85⁰
measure of second angle=7(11⁰)+18
=77⁰+18
=95⁰
The radius of a circle is 12.4 cm. Find the circumference to the nearest tenth.
an electric guitar costs $790 with a 235 full replacement warranty if the manufacturer sells 500 and 98,274 warranties and has to honor 11% of them, how much profit did the manufacturer gain from the warrenties
Answer:
i got Profit = $125,129,007.1
Step-by-step explanation:
As a manager of a company you are given 2 estimates for the annual firm’s profits: 1) Estimate A predicting that the mean profit would be between $1mil and $1.5 mil which is a 95% confidence interval; 2) Estimate B that the annual profits are between $1.2 mil and $1.4 mil, a 93% confidence interval. Which of the two estimates is more accurate and why?
Answer and Explanation:
A confidence interval determines the probability that a range of values(e.g-given a large data set )has the true parameter. Example, to find mean of height of 30+ men, our confidence interval will say that there is 96% confidence that the mean height of 30+ men is between 5ft and 6ft. While confidence intervals, narrow or broad with high or low significance levels may not be akin to accuracy, it will only help to determine the precision or otherwise of our estimate. For example, if confidence interval is narrow as in second option and confidence level is lower, it only narrows down our options to ascertain the true mean or parameter we are investigating and doesn't exactly affect accuracy since we are still not 100% confident our true mean lies in this interval.
*PLEASE HELP ASAP I WILL MARK BRAINLIST*
(Questions and Answers pictured)
Answer:
The first equation, sorry can’t explain.
Answer:
g(x)=3f(2x)
I think
please helppppppppppppppp
Answer:
10 units
Step-by-step explanation:
Given that,
The area is modeled by the equation as follows :
[tex]A=-l^2-10l+300[/tex]
Where
l is the linear dimensions of the frame.
Put A = 100
So,
[tex]-l^2-10l+300=100\\\\-l^2-10l+200=0\\\\l=10,-20[/tex]
So, the linear dimension of the frame is equal to 10 units.
