Answer:
2000 kilograms
Step-by-step explanation:
Which of these pairs of functions are inverse functions?
Answer:
see below
Step-by-step explanation:
You can attack this several ways. One is to work through f(g(x)) in each case and see if the result is x.
Another is to use a graphing calculator to evaluate y=f(g(x)) to see if the result is the line y=x.
Yet another way to work this is to pick a convenient value for x and evaluate f(g(x)) or g(f(x)). Here, we'll show this last case.
A: f(1) = 2^0 +1 = 2; g(2) = log2(2-1) -1 = -1 . . . . g(f(1)) = -1, not 1 ⇒ not inverses
B: f(2) = 1/2(ln(1) -1) = -1/2; g(-1/2) = 2e^(0) = 2 . . . g(f(2)) = 2 ⇒ inverses
C: f(e) = 4ln(e^2)/e^2 = 8/e^2; g(8/e^2) = e^1 = e . . . g(f(e)) = e ⇒ inverses
D: f(10) = 10^0-10 = -9; g(-9) = log(1) -10 = -10 . . . g(f(10)) = -10, not 10
⇒ not inverses
_____
The second and third pairs of functions are inverses.
PRACTICE ANOTHER Calculate the standard deviation σ of X for the probability distribution. (Round your answer to two decimal places.) σ = (No Response) 1.00
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma = 1.17[/tex]
Step-by-step explanation:
From the question we are told that
The data is
x 1 2 3 4
P(X = x) 0.2 0.2 0.2 0.4
Generally the standard deviation is mathematically represented as
[tex]\sigma = \sqrt{ \sum x^2 P(x) - (\sum x P(x))^2 }[/tex]
Here [tex]x^2 = 1^2 \ \ 2^2 \ \ 3 ^2 \ \ 4^2[/tex]
=> [tex]x^2 = 1 \ \ 4 \ \ 9\ 16 \[/tex]
[tex]\sum x^2 * P(x) = (1 * 0.2) + (4 * 0.2 ) + (9 * 0.2 ) + (16 * 0.2 )[/tex]
[tex]\sum x^2 * P(x) = 9.4[/tex]
[tex]\sum x P(x) = (1 *0.2) + (2*0.2) + (3 * 0.2) + (4 * 0.2)[/tex]
[tex]\sum x P(x) = 2.8[/tex]
So
[tex]\sigma = \sqrt{ 9.2 - (2.8)^2 }[/tex]
[tex]\sigma = 1.17[/tex]
The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period.2 5 10 124 4 5 1711 8 9 812 21 6 87 13 18 3(a) Develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24.Class Frequency0-4 5-9 10-14 15-19 20-24 Total (b) Develop a relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places.Class Relative Frequency0-4 5-9 10-14 15-19 20-24 Total (c) Develop a cumulative frequency distribution using the classes in part (a).(c) Develop a cumulative frequency distribution using the classesClass Cumulative Frequency0-4 5-9 10-14 15-19 20-24 (d) Develop a cumulative relative frequency distribution using the classes in part (a). If required, round your answers to two decimal places.Class Cumulative Relative Frequency0-4 5-9 10-14 15-19 20-24 (e) What proportion of customers needing an oil change wait 9 minutes or less?%
Answer:
Kindly check explanation
Step-by-step explanation:
Waiting times collected over a one month period:
2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3
A)
Class(x) - - frequency(f)
0-4 - - - - - 4
5-9 - - - - - - 8
10-14 - - - - - 5
15-19 - - - - - 2
20-24 - - - - 1
B)
Class(x) - - frequency(f)- - relative frequency(rf)
0-4 - - - - - 4 - - - - - - - - - - 4/20 = 0.20
5-9 - - - - - - 8 - - - - - - - - - - 8/20 = 0.40
10-14 - - - - - 5 - - - - - - - - - - 5/20 = 0.25
15-19 - - - - - 2 - - - - - - - - - - 2/20 = 0.10
20-24 - - - - 1 - - - - - - - - - - - 1/20 = 0.05
C)
Class(x) - - frequency(f) - - cumulative frequency
0-4 - - - - - 4 - - - - - - - - - - - 4
5-9 - - - - - - 8 - - - - - - - - - - - 12
10-14 - - - - - 5 - - - - - - - - - - - 17
15-19 - - - - - 2 - - - - - - - - - - - 19
20-24 - - - - 1 - - - - - - - - - - - - 20
D)
Class(x) - - f - - cf - - - - rf - - - - - - crf
0-4 - - - - 4 - -- 4 - - - 0.20 - - - 0.20
5-9 - - - - - 8 - - 12 - - - 0.40 - - - 0.60
10-14 - - - 5 - - -17 - - - 0.25 - - - 0.85
15-19 - - - 2 - - - 19 - - - 0.10 - - - 0.95
20-24 - - 1 - - - 20 - - 0.05 - - - 1.00
crf - cumulative relative frequency
rf - relative frequency
cf - cumulative frequency
E) 0.6 (from the cumulative relative frequency column)
9 minutes or less :
Frequency = 12, total frequency = 20
12 / 20 = 0.6
The frequency distribution of the given data and frequency table for them would be presented as mentioned below.
Frequency Distribution
Given that,
Data
2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3
a). The use of classes to create a frequency distribution through classes would be as follows:
Class(X) frequency(f)
0-4 4
5-9 8
10-14 5
15-19 2
20-24 1
b). The relative frequency distribution would be as follows:
Class(X) frequency(f) relative frequency(rf)
0-4 4 4/20 = 0.20
5-9 8 8/20 = 0.40
10-14 5 5/20 = 0.25
15-19 2 2/20 = 0.10
20-24 1 1/20 = 0.05
c). The cumulative frequency distribution would be as follows:
Class(X) frequency(f) cumulative frequency(cf)
0-4 4 4
5-9 8 12
10-14 5 17
15-19 2 19
20-24 1 21
d). The cumulative frequency distribution employing classes in part a would be as follows:
Class(X) (f) (cf) rf crf
Frequency Cumulative Relative Cumulative Relative
Frequency Frequency Frequency
0-4 4 4 0.20 0.20
5-9 8 12 0.40 0.60
10-14 5 17 0.25 0.85
15-19 2 19 0.10 0.95
20-24 1 21 0.05 1
e). The proportion of customers requiring an oil change wait 9 minutes would be:
Frequency [tex]= 12[/tex]
Total Frequency [tex]= 20[/tex]
The Proportion of customers requiring an oil change wait 9 minutes or less
[tex]= 12/20\\= 0.6[/tex]
Learn more about "Frequency Distribution" here:
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Clara is growing her hair out and wants it to be no longer than 15 cm but more than 11 cm. Her hair is 7 cm right now and grows at a rate of 0.25 cm per week. The compound inequality 11 < 7 + 0.25t ≤ 15 models the scenario. How long will it take Clara to grow out her hair to the desired length? It will take Clara more than weeks and up to and including weeks to grow out her hair.
Answer:
It will take Clara more than
16
weeks and up to and including
32
weeks to grow out her hair.
Answer:
It will take Clara more than 16 weeks and up to and including 32 weeks to grow out her hair.
Step-by-step explanation:
Fraction that less then 5/6 dominater is 8
Answer:
1/8, 2/8, 3/8, 4/8, 5/8, 6/8
Step-by-step explanation:
If i have interpreted correct. You want to know a fraction with a denonminator of 8 that is less than 5/6
5/6=0.8333
Multiple Answers
1/8, 2/8, 3/8, 4/8, 5/8, 6/8
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answer:
[tex] y = 178.3 ft [/tex]
Step-by-step explanation:
y is opposite to the reference angle, 27°.
350 ft is adjacent to the reference angle, therefore:
[tex] tan(27) = \frac{y}{350} [/tex]
Multiply both sides by 350
[tex] tan(27)*350 = \frac{y}{350}*350 [/tex]
[tex] tan(27)*350 = y [/tex]
[tex] 178.3 = y [/tex] (to nearest tenth)
[tex] y = 178.3 ft [/tex]
A painter rented a wallpaper steamer at 9 a.m. and returned it at 4 p.m. He paid a total of $28.84. What was the rental cost per hour?
Greetings,
I hope you and your family are staying safe and healthy!
Answer: $4.12 per hour
Step-by-step explanation:
So, 9am to 4pm is 7 hours
Why? Because you go from 10am, 11am, 12pm, 1pm, 2pm, 3pm, and 4pm.
So now all we have to do is to divide the amount he paid by the number of hours.
Like this:
[tex]\frac{28.84}{7} = 4.12[/tex]
Therefore,
The rental cost per hour is $4.12
-----------------------------------
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What percent of 290 is 120?
Round your answer to the tenths place.
__________________ percent
Answer:
41.4%
Step-by-step explanation:
120/290 = x/100
290x = 120 * 100
x = 41.3793...
What is the correct relationship between events A and B: A: Laura participated in an out-of-town volleyball game at 11:00 AM last Friday. B: Laura met with her academic advisor on campus at 11:00 AM last Friday. A and B are mutually exclusive. A and B are complementary. A and B are not mutually exclusive. If B is true, A is trus
heplfdjnhkmxdjnhkml,;.
Answer:
d
Step-by-step explanation:
im pretty sure the right answer would be 12 and 21 just doesn't look right
what is the answer?
Answer/Step-by-step explanation:
Given:
Data set for sandwich calories=> 242, 290, 290, 280, 390, 350
Mean: the mean is given as sum of all values in the data set ÷ total no. of data set given
[tex] \frac{242 + 290 + 290 + 280 + 390 + 350}{6} = \frac{1,842}{6} = 307 [/tex]
Mean Absolute Value:
Step 1: find the absolute value of the difference between each value and the mean
|242 - 307| = 65
|290 - 307| = 17
|290 - 307| = 17
|280 - 307| = 27
|390 - 307| = 83
|350 - 307| = 43
Step 2: find the sum of all values gotten in step 1
65 + 17 + 17 + 27 + 83 + 43 = 252
Step 3: divide the result you get in step 2 by 6 to get the M.A.D
[tex] M.A.D = \frac{252}{6} = 42 [/tex]
The Mean Absolute Value represents or gives us an idea how spread the data set for the number of sandwich calories are.
Thus, averagely, the number of calories of sandwich at the restaurant are far from the mean caloric value by 42 calories.
Jin tried to evaluate 5 + 2 x 9 step-by-step.
5+2 x 9
Step 1: =7 x 9
Step 2: =63
Find jin’s mistake
A: step 1
B: step 2
C: Jin did not make a mistake
Answer:
5 + 2 x 9
Step 1 = 7 x 9
Step 2 = 63
Step-by-step explanation:
= 5 + 2 x 9
= 5 + ( 2 x 9 )
= 5 + 18
= 23
Step 2 = 7 x 9
= 63
Step 3 = 63
C. jin did not make a mistake
Sorry i'm wrong :)
1/64, 1/16, 1/4, 1... What is the pattern and next term???
Answer:
[tex]\huge\boxed{\text{next term}=4}\\\boxed{f(n)=4^{n-4}}[/tex]
Step-by-step explanation:
[tex]\dfrac{1}{64},\ \dfrac{1}{16},\ \dfrac{1}{4},\ 1,\ ...[/tex]
It's the geometric sequence where
[tex]a_1=\dfrac{1}{64},\ q=4[/tex]
[tex]\dfrac{1}{16}=\dfrac{1}{64}\cdot4\\\\\dfrac{1}{4}=\dfrac{1}{16}\cdot4\\\\1=\dfrac{1}{4}\cdot4\\\\1\cdot4=4\to\text{next term}[/tex]
[tex]f(n)=\dfrac{1}{64}\cdot4^{n-1}=\dfrac{1}{4^3}\cdot4^{n-1}=\dfrac{4^{n-1}}{4^3}\\\\\text{use}\ \dfrac{a^n}{a^m}=a^{n-m}\\\\f(n)=4^{n-1-3}=4^{n-4}[/tex]
We are trying to come up with a regression model that predicts university GPA. Is high school GPA a significant predictor for university GPA?
Answer:
No.
Step-by-step explanation:
High school GPA is not a significant predictor of University GPA.
The Grade Point Average obtained at the end of high school education has almost nothing (in my opinion, it has nothing to do with) to do with grades that the scholar will obtain in college. Many scholars find it difficult adjusting to the social and academic life demands of tertiary institution.
A good predictor for university Grade Point Average would be:
The CGPA (Cumulative Grade Point Average) obtained by the student(s) in each year/session/level/part in the university.
This will be a significant predictor for university GPA.
Identify the center and radius for the equation y2 = -8x – x2 – 24 – 6y.
Answer:
Hey there!
This circle would have a center at (-4, -3) and a radius of 1.
Let me know if this helps :)
Solve for x 5x2-4x=6
Answer:
That would equal 36
Step-by-step explanation:
i added them up
Need help I don’t understand
Answer:
Complementary angles add up to 90 degrees, or a right angle.
In this case, it would be (c) AEF and FED, AEG and CEG
Step-by-step explanation:
The common ratio in a geometric series is 0.50.50, point, 5 and the first term is 256.
Find the sum of the first 6 terms in the series.
Answer:
504
Step-by-step explanation:
I think the correct question is like:The common ratio in a geometric series is 0.50 ( point 5) and the first term is 256.
Find the sum of the first 6 terms in the series.
If it's right, then
Sₙ = (a₁ × (1 - rⁿ)) / (1 - r)
S₆ = (256 × ( 1 - 0.5⁶)) / (1 - 0.5)
= (256 × 0.984375) / 0.5
= 504
hope it will help :)
Water flows through a pipe at a rate of 6300 liters every 8.5 months. Express this rate of flow in cubic feet per hour. Round your answer to the nearest hundredth.
Answer:
0.04
Step-by-step explanation:
[tex] \dfrac{6300~L}{8.5~month} \times \dfrac{1000~cm^3}{1~Liter} \times \dfrac{1~ft^3}{(30.48~cm)^3} \times \dfrac{12~months}{1~year} \times \dfrac{1~year}{365.25~days} \times \dfrac{1~day}{24~hours} \times \dfrac{1~day}{24~hours} = [/tex]
[tex]= 0.04 \dfrac{ft^3}{hour}[/tex]
The value of the flow rate in cubic feet per hour is 0.04.
What is the rate of flow?The rate of the flow of the fluid is defined as the volume of the fluid flowing through the cross-section per unit of time. The unit of the flow rate is cubic feet per hour or cubic meter per hour etc.
Given that water flows through a pipe at a rate of 6300 liters every 8.5 months. Then the flow rate in cubic feet per hour will be calculated as below:-
1 litre = 0.0353 cubic feet
6300 litres = 6300 x 0.0353
6300 litres = 222.4 cubic feet
1 month = 730 hours
8.5 months = 6205 hours
The rate of flow in cubic per hour will be:-
Rate of flow = 222.4 / 6205 = 0.04 cubic feet per hour
Therefore, the value of the flow rate in cubic feet per hour is 0.04.
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The area of a rectangular piece of land J is 220 square metres.Its width is 12.5.what is the perimeter of the land ?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{ {60.2 \: m}}}}}}[/tex]
Step-by-step explanation:
Given,
Area of rectangular piece of land ( l ) = 220 m²
Width ( w ) = 12.5 m
Finding length of the rectangular piece of land
[tex] \boxed{ \sf{area \: of \: rectangle = l \times w}}[/tex]
plug the values
⇒[tex] \sf{220 = l \times 12.5}[/tex]
Swap the sides of the equation
⇒[tex] \sf{12.5 \: l = 220}[/tex]
Divide both sides of the equation by 12.5
⇒[tex] \sf{ \frac{12.5 \: l}{12.5} = \frac{220}{12.5} }[/tex]
Calculate
⇒[tex] \sf{l = 17.6 \: m}[/tex]
Length of rectangular piece of land ( l )= 17.6 m
Finding perimeter of rectangular piece of land
[tex] \boxed{ \sf{perimeter \: of \: rectangle = 2(l + b)}}[/tex]
plug the values of length and breadth
⇒[tex] \sf{2(17.6 + 12.5) }[/tex]
Add the numbers
⇒[tex] \sf{2 \times 30.1}[/tex]
Multiply the numbers
⇒[tex] \sf{60.2 \: m}[/tex]
Therefore, Perimeter of rectangular piece of land is 60.2 m
Hope I helped!
Best regards!!
Enter the correct value so that each expression is a perfect square trinomial
Answer:
Step-by-step explanation:
1). x² - 10x + a²
By using the formula of (a - b)² = a² - 2ab + b²
x² - 2(5)x + a²
Therefore, for a perfect square of the expression a should be equal to 5.
Therefore, (x² - 10x + 25) will be the answer.
2). x² + 2ax + 36
= x² + 2(a)x + 6²
For a perfect square of the given expression value of a should be 6.
x² + 2(a)x + 6² = x² + 2(6)x + 6²
= (x + 6)²
Therefore, x² + 12x + 36 will be the answer.
3). [tex]x^{2}+\frac{1}{2}x+a^2[/tex]
[tex]x^{2}+2(\frac{1}{4})x+a^2[/tex]
To make this expression a perfect square,
a² = [tex](\frac{1}{4})^2[/tex]
[tex]x^{2}+2(\frac{1}{4})x+(\frac{1}{4})^2[/tex] = [tex](x+\frac{1}{4})^2[/tex]
Therefore, the missing number will be [tex]\frac{1}{16}[/tex].
Answer:
it's 1/16 you're welcome!
Step-by-step explanation:
is 6 a solution of 2x+7=3x
Answer:
No
Step-by-step explanation:
because the answer is 7
2x + 7 = 3x
2x + 7 - 7 = 3x - 7
2x = 3x - 7
2x - 3x = 3x - 7 - 3x
-x = -7
x = 7
witch number produces a rational number when multipled by 0.25
Answer:
1
Step-by-step explanation:
.25 is already a rational number as it equals 25/100 and 1/4 simplified
What is the slope of the line that passes through the points (-3, -3)(−3,−3) and (-9, 5) ?(−9,5)? Write your answer in simplest form.
Answer:
Slope= -4/3
Step-by-step explanation:
The points are (−3,−3) and (-9, 5)
Slope= gradient between the two points
Slope= (y2-y1)/(x2-x1)
Where y2= 5
Y1= -3
X2= -9
X1= -3
Slope= (y2-y1)/(x2-x1)
Slope= (5-(-3))/(-9-(-3))
Slope= (5+3)/(-9+3)
Slope= 8/-6
Slope= -4/3
Find the interval in which f(x)=sinx−cosx is increasing or decreasing?
Answer:
There is no short answer.
Step-by-step explanation:
To find to intervals which f(x) increases or decreases, we first need to find it's derivative.
[tex]f(x) = sinx - cosx\\f'(x) = cosx - (-sinx) = cosx + sinx[/tex]
The function is increasing when it's value is > 0 and decreasing when it's value is < 0.
If we take a look at this graph, cosx+sinx is positive when they are both positive or when cosx is greater then sinx on the negative part.
I hope this answer helps.
Please help I dont understand
Answer:
X+Y=8W^2-7W+7
Step-by-step explanation:
HEY,... HERES YOUR ANSWER ! I HOPE I HELPED! BRAINLIEST WOULD BE APPRECIATED :)
THE QUESTION-->
X=7W^2+4W-6
Y=W^2-11W+13
X+Y=?
THE EXPLANATION-->
SO LETS JUST ADD BOTH EQUATIONS!
SO...
X+Y=7W^2+4W-6+W^2-11W+13
SIMPLIFY LIKE TERMS..
7W^2+W^2+4W-11W-6+13
SIMPLIFY EVEN FURTHER..
X+Y=8W^2-7W+7
THE ANSWER-->
X+Y=8W^2-7W+7
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
JUST A RANDOM GIRL WANTING TO HELP PEOPLE!
PEACE!
Change $35,000 per year to dollars per hours
The revenue, in dollars, of a company that produces video game systems can be modeled by the expression 5x2 + 2x – 80. The cost, in dollars, of producing the video game systems can be modeled by 5x2 – x + 100, where x is the number of video game systems sold. If profit is the difference between the revenue and the cost, what expression represents the profit?
Answer: 3x-180
Step-by-step explanation:
Given: Expression for Revenue = [tex]5x^2 + 2x - 80[/tex]
Expression for Cost = [tex]5x^2- x + 100[/tex]
If profit is the difference between the revenue and the cost then the expression for profit will be:
Profit = Revenue - cost
[tex]=5x^2 + 2x - 80-(5x^2- x + 100)\\\\=5x^2 + 2x - 80-5x^2+x-100\ \ [\text{Multiply ' - ' sign inside the bracket}]\\\\=2x+x-80-100\\\\=3x-180[/tex]
Hence, the expression represents the profit is 3x-180 .
Answer:
its 3x-180 and for the seond one its $2,820
Step-by-step explanation:
got it right on edge
the total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m +5. After a policy change, five more dollars are added on and then the total reimbursement amount is multiplied by 1.25 describe how to transform the graph of f. what is the total reimbursement for a trip of 95 miles?
Answer:
The slope becomes 0.5625 and y intercept becomes 12.5.
$65.9375
Step-by-step explanation:
Given that
the total reimbursement function in terms of [tex]m[/tex] miles:
[tex]f(x) = 0.45m +5[/tex]
After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.
To find:
How to transform the graph of f.
Total reimbursement for a trip of 95 miles?
Solution:
[tex]f(x) = 0.45m +5[/tex] can also be written as:
[tex]y = 0.45m +5[/tex]
It is nothing but slope intercept form, comparing with [tex]Y = M X+ C[/tex]
M is the slope and C is the y intercept.
Slope of the graph is 0.45.
Y intercept is 5.
After change in the function, first of all add $5.
[tex]0.45m + 5+5 = 0.45m+10[/tex]
Now, multiply with 1.25
Resulting function becomes:
[tex]f(x) =1.25\times (0.45m+10)\\\Rightarrow f(x) =0.5625m+12.5[/tex]
Kindly refer to the attached image for the graph of the two functions.
Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.
To find the reimbursement for a trip of 95 miles:
Put m = 95
[tex]f(95) =0.5625\times 95+12.5 = \bold{\$65.9375 }[/tex]
If 512+14=x then x=23 Question 10 options: True False