Answer: B. f(x - 3) = 6x - 16
Concept:
When encountering a question that gives you a function and the evaluation value, then basically plug the given value into the function.
Solve:
Given function and value
f(x) = 6x + 2
f(x - 3)
Substitute the value into the given expression
f(x - 3) = 6 (x - 3) + 2
f(x - 3) = 6x - 18 + 2
f(x - 3) = 6x - 16
Hope this helps!! :)
Please let me know if you have any questions
I need help.
You are interested in finding a 95% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 12 randomly selected non-residential college students. Round answers to 3 decimal places where possible.
Answer:
(11.847 ; 15.813)
Step-by-step explanation:
We are given 12 samples which are :
8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25
We use a T-distribution to find the confidence interval since the sample size. is small, n < 30
Using a calculator :
The sample mean, xbar = 13.83
Sample standard deviation, s = 6.87
The confidence interval, C.I
C.I = xbar ± Tcritical * s/√n)
Tcritical at 95%, df = n - 1, 12 - 1 = 11
Tcritical(0.05, 11) = 2.20
Hence,
C.I = 13.83 ± 2.20(6.87/√12)
C.I = 13.83 ± 1.9831981
C. I = (13.83 - 1.983 ; 13.83 + 1.983)
C. I = (11.847 ; 15.813)
Solve for x Solve for x Solve for x
9514 1404 393
Answer:
x = 3
Step-by-step explanation:
The two right triangles share angle A, so the similarity statement can be written ...
ΔABC ~ ΔADE
Corresponding sides are proportional, so we have ...
BC/DE = AB/AD
x/12 = 3/(3+9)
x = 3 . . . . . . . . . . multiply by 12
Answer:
x=3
this is correct!!!
The hypotenuse of a right triangle is 16 units and the length of one of the legs is 12 units. What is the length of the other leg in simplest radical form?
A. 2√13
B. 4√11
C. 2√17
D. 4√7
Answer:
D, 4√7
Step-by-step explanation:
Answer:
Step-by-step explanation:
c = 16
a = 12
b = ?
a^2 + b^2 = c^2
12^2 + b^2 = 16^2
144 + b^2 = 256
b^2 = 256 - 144
b^2 = 112
b^2 = 16 * 7
sqrt(b^2) = sqrt(16)*sqrt(7)
b = 4 * sqrt(7)
Below, the two-way table is given for a
class of students.
Freshmen Sophomore
Juniors
Seniors
Total
Male
4
6
2
2
Female 3
4
6
3
Total
If a student is selected at random, find the
probability the student is a male given that it's
a sophomore. Round to the nearest whole
percent.
[?]%
Answer:
20%
Step-by-step explanation:
The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)
The probability is: 6/30 = 1/5 = 0.2 = 20%
The probability that the student is a male given that he's a sophomore is approximately 60%.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The probability that the student is a male given that it's a sophomore can be calculated using the formula:
P(male | sophomore) = P(male and sophomore) / P(sophomore)
The number of male sophomores is 6, and the total number of sophomores is 6+4=10.
So, the probability of selecting a sophomore is:
P(sophomore)
= (number of sophomores) / (total number of students)
= 10 / 23
The number of male sophomores is 6.
So,
The probability of selecting a male sophomore is:
P(male and sophomore) = 6 / 23
Therefore,
The probability that the student is a male given that it's a sophomore is:
P(male | sophomore)
= (6 / 23) / (10 / 23)
= 6 / 10
= 3 / 5
Rounding to the nearest whole percent, we get:
P(male | sophomore) ≈ 60%
Thus,
The probability that the student is a male given that he's a sophomore is approximately 60%.
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Anthony steps on a bathroom scale that records his weight at 195 pounds. He immediately steps back onto the same scale, which records his weight at 205 pounds. It is MOST accurate to describe these scales as:
Answer:
Moving upwards with an acceleration.
Step-by-step explanation:
weight of the person = 195 pounds
Apparent weight = 205 pounds
As the weight increases so the scale is moving upwards with some acceleration.
The scale is in elevator which is moving upwards.
I need to know the answer and the work it asks for
Answer:
b 25x6 = 150
25 decreases every month so
150 decreses every 6 month
800-150
650 are the bees remaining after 6 month
Subtract 7 pounds 3 ounces from 10 pounds
(c³d)a(cd⁷)a
Simplify
Answer:
= c^4 d^8 a^2
Step-by-step explanation:
Apply exponent rule: aa= a^2
= c^3 da^2 cd^7
= c^4 da^2 d^7
= c^4 d^8 a^2
I really need help please
Answer:
first question is D
second question is D .875
Step-by-step explanation:
35*2.5= 87.5
7 divided by 8= .875
Answer:
D 87.5 miles
D 0.875 = 7/8 so it is a decimal that terminates after 3 dp.
Step-by-step explanation:
We write;
Scale Inch x Miles
2.5 x 35 = 87.5 miles
Why??
87.5 miles is found when we use the scale of 35 miles = 1inch
Answer = D 87.5 miles
The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;
1/ 1/8 = 0.125
1-0.125 = 0.875
please help, will give brainliest!!!
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
y = x^2 -4
Exchange x and y
x = y^2 -4
Add 4 to each side
x+4 = y^2
Take the square root of each side
sqrt(x+4) = y
f^-1(x) = sqrt(x+4)
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
Someone help please
66 because you have to solve the problem next time
Find m These questions getting hard
Answer:
the
Step-by-step explanation:
it's fairly easy actually. You just have to use sin
Engineers are designing a large elevator that will accommodate 44 people. The maximum weight the elevator can hold safely is 8228 pounds. According to the National Health Statistics Reports, the weights of adult U.S. men have mean 186 pounds and standard deviation 60 pounds, and the weights of adult U.S. women have mean 157 pounds and standard deviation 69 pounds.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
Answer:
a) Their average weight is of 187 pounds.
b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?
8228/44 = 187
Their average weight is of 187 pounds.
b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For men, we have that [tex]\mu = 186, \sigma = 60[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]
This probability is 1 subtracted by the p-value of Z when X = 187. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]
[tex]Z = 0.11[/tex]
[tex]Z = 0.11[/tex] has a p-value of 0.5438.
1 - 0.5438 = 0.4562
0.4562 = 45.62% probability that the maximum safe weight will be exceeded.
c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?
For women, we have that [tex]\mu = 157, \sigma = 69[/tex]
Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]
[tex]Z = 2.88[/tex]
[tex]Z = 2.88[/tex] has a p-value of 0.998.
1 - 0.998 = 0.002.
0.002 = 0.2% probability that the maximum safe weight will be exceeded
Matthew Travels 42/50 Meters In 26/30 Minutes. Find The Speed of Mathew In Meters Per Second.
Answer:
Matthew travels 0.0161 meters per second.
Step-by-step explanation:
Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:
42/50 = 0.84
26/30 = 0.86
0.86 x 60 = 52
0.84 meters in 52 seconds
0.84 / 52 = 0.01615
Therefore, Matthew travels 0.0161 meters per second.
How many gallons each of 25% alcohol and 5% alcohol should be mixed to obtain 20 gal of 16% alcohol?
Answer:
✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.
Step-by-step explanation:
Hope this helps~ ;D
find the area of this unusual shape.
Answer:
104 m^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w = 10*8 = 80
Then find the area of the triangle
A = 1/2 bh = 1/2 (8) * 6 = 24
Add the areas together
80+24 = 104 m^2
Given m = 1/2 and the point (3, 2), which of the following is the point-slope form of the equation?
Answer:
The point-slope form is y - 2 = 1/2 (x - 3)
Step-by-step explanation:
The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.
I need help with this
Answer: D
Step-by-step explanation:
When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)
The three coordinates of ΔCDE are
C = (-8, -1)D = (-6, -5)E = (-2, -4)After the y-axis reflection, they'll become:
C' = (-(-8), -1) = (8, -1)D' = (-(-6), -5) = (6, -5)E' = (-(-2), -4) = (2, -4)I hope this is correct :\
Find the percentile rank for each test score in the data set. 12, 28, 35, 42, 47, 49, 50 What value corresponds to the 60th percentile
Answer:
Percentile rank:
12 = 7th
28 = 21st
35 = 36th
42 = 50th
47 = 64th
49 = 79th
50 = 93rd
- Vth number i.e. 47 is the value that corresponds to the 60th percentile.
Step-by-step explanation:
As we know,
Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100
For 12,
Percentile rank = [0 + 0.5]/7 * 100
= 7th
For 28,
Percentile rank = [1 + 0.5]/7 * 100
= 21st
For 35,
Percentile rank = [2 + 0.5]/7 * 100
= 36th
For 42,
Percentile rank = [3 + 0.5]/7 * 100
= 50th
For 47,
Percentile rank = [4 + 0.5]/7 * 100
= 64th
For 49,
Percentile rank = [5 + 0.5]/7 * 100
= 79th
For 50,
Percentile rank = [6 + 0.5]/7 * 100
= 93rd
Now,
n = 7
60th percentile = 60% of n
So,
60% of n = 60/100 * 7
= 0.6 * 7
= 4.2
After rounding it off,
5th value is the 60th percentile i.e. 47.
HELP ASAP!!!!!!!PLEASE SHOW WORK!!!!!!
Answer:
Area = 72.62 m²
Step-by-step explanation:
Area of a triangle with the given three sides is given by,
Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
Here, s = [tex]\frac{a+b+c}{2}[/tex]
And a, b, c are the sides of the triangle.
From the question,
a = 20 m, b = 10 m and c = 15 m
s = [tex]\frac{20+10+15}{2}[/tex]
s = 22.5
Substitute these values in the formula,
Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]
= [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]
= [tex]\sqrt{5273.4375}[/tex]
= 72.62 m²
James, Aimee and Zack have
weighed their suitcases. Each
weighs a prime number of
kilograms and the total weight
is 40kg.
an
What's the difference between
the lightest and heaviest
suitcase?
Answer:
29Kg
Step-by-step explanation:
P1=2Kg
P2=7Kg
P3=31Kg
P3-P1=29Kg
To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.
I was lucky and I got the result after few steps :-)
Under which transformation can the image be a different size than the original
figure?
A. translation
B. rotation
C. dilation
D. reflection
C. Dilation.
Dilation can resize the image.
Translation will shift the imagine's position but won't change its actual size.
Rotation will mangle with image's orientation but also won't change its size.
Reflection is just a type of rotation which as established, also won't change its size.
Hope this helps.
Refer to the values described below, then identify which of the following is most appropriate: discrete random variable, a. Responses to the survey question "How many pets do you have?" b. Exact heights of the next 100 babies born in a region c. Responses to the survey question "What is your eye color?" d. Exact foot length of humans e. Number of people in families a. Since the outcomes are b. Since the outcomes are countable, this is this is a discrete random variable. random variable.
Answer:
Exact heights of the next 100 babies born in a region.
Step-by-step explanation:
A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.
F(x) = 4x^3 + 7x^2-2x-1
G(x) = 4x-2
Find (f-g)(x)
Find the length of the missing side. triangle with an 8 inch side and 12 inch side with a right angle 8.9 in. 104 in. 4 in 14.4 in
Given:
In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.
To find:
The length of the missing side.
Solution:
In a right angle triangle,
[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]
Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.
Substituting Perpendicular = 8 inches and Base = 12 inches, we get
[tex]Hypotenuse^2=8^2+12^2[/tex]
[tex]Hypotenuse^2=64+144[/tex]
[tex]Hypotenuse^2=208[/tex]
Taking square root on both sides, we get
[tex]Hypotenuse=\sqrt{208}[/tex]
[tex]Hypotenuse=14.422205[/tex]
[tex]Hypotenuse\approx 14.4[/tex]
The length of the missing side is 14.4 inches. Therefore, the correct option is D.
From a random sample of 20 bars selected at random from those produced, calculations gave a mean weight of = 52.46 grams and standard deviation of s = 0.42 grams. Assuming t distribution is followed, construct a 90% confidence interval for the mean weight of bars produced, giving the limits to two decimal places.
Answer:
(52.30 ; 52.62)
Step-by-step explanation:
Given :
Sample size, n = 20
Mean, xbar = 52.46
Standard deviation, s = 0.42
We assume a t - distribution
The 90% confidence interval
The confidence interval relation :
C.I = xbar ± Tcritical * s/√n
To obtain the Tcritical value :
Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05
Using the T-distribution table, Tcritical = 1.729
We now have :
C.I = 52.46 ± (1.729 * 0.42/√20)
C. I = 52.46 ± 0.1624
C.I = (52.30 ; 52.62)
.
Bob wants to install a
solar panel on his roof to
heat water for his family. The
power company advertises a
35% savings to electric bills
with the installation of a solar
panel. If Bob's average
electric bill is $132.50 how
much could he save if he had
a solar panel?
a. $35.00
b. $46.38
c. $62.14
d. $100.35
Answer:
46.38
Step-by-step explanation:
all the answer are not same but buy calculating its the right answer
Which recursive formula can be used to generate the sequence below, where f(1) = 3 and n ≥ 1?
3, –6, 12, –24, 48,
Answer:
f (n + 1) = -2 f(n)
Step-by-step explanation:
The graph below shows a company's profit f(x), in dollars, depending on the price of pencils x, in dollars, sold by the company.
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x = 2 to x = 5, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
Answer:
Step-by-step explanation:
Part A
The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)
The given parameters are;
The values of the function, f(x) = The company's profit
The values of the independent variable, "x" = The price of erasers
Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)
2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4
3) The intervals where the function is increasing is 0 ≤ x ≤ 4
At the interval where the function is increasing, the sale price is increasing and the profits are increasing
The intervals where the function is decreasing is 4 ≤ x ≤ 8
At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing
Part B
The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows
Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50
The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00
THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!
During a certain 9-year period, the Consumer Price Index (CPI) decreased by
45%, but during the next 9-year period, it decreased by only 5%. Which of
these conditions must have existed during the second 9-year period?
A. Deflation
B. Stagnation
C. Conflation
D. Inflation
Answer:
deflation ,,,,
Step-by-step explanation:
I hope it's helpful for you ☺️Deflation must have existed during the second 9-year period.
What is deflation?Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.
The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.
Given data ,
Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.
In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.
Hence , the process is deflation in the second year
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