Answers
The average rate of change of g(x) over the interval [2, 8] is given by
(g (8) - g (2)) / (8 - 2)
In other words, it's the slope of the line through the points (2, g (2)) and (8, g (8)).
Use the definition of the function to evaluate it at the points in the numerator:
• 8 ≥ 4, so using the second piece, g (8) = -0.5(8) + 8 = 4
• 2 < 4, so g (2) = 5(2) + 1 = 11
Then the average rate of change is
(g (8) - g (2)) / (8 - 2) = (4 - 11) / 6 = -7/6
Related Questions
sana is senior to Mona by 18 years after 6 years.Sana will be twice as old as Mona. find Mona,s percentage
Answers
Present age of Sana = s
Present age of Mona = m
Sana is senior to Mona by 18 years
s=m+18............(1)
After 6 years
Sana will be = s+6
Mona will be = m+6
Then
Sana will be twice as old as Mona
(s+6)=2(m+6)
s+6=2m+12
s=2m+12-6
s=2m+6.............(2)
Put the value of s from (2) to (1)
2m+6=m+18
2m-m=18-6
m=12
Put the value of m in (1)
s=m+18
s=12+18
s=30
Present age of Sana = s = 30 years old
Present age of Mona = m = 12 years old
A city planner is considering adding a pedestrian crossing signal to a particular intersection. They know that on average 11.5 cars go through the intersection each minute. It takes an average person 10 seconds to walk across the intersection. Name the distribution appropriate to model the time to the next car crossing this intersection (in minutes). Use the proper notation, and include the value of the distribution parameter (s).
Answers
Answer:
The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5
and the PMF of X is;
P (X = x) = e^-λ ( λˣ / x! ); where x = 0, 1, 2, 3, , , , , ,
Step-by-step explanation:
Given that;
on average eleven and a half cars go through the intersection each minute and It takes an average person ten seconds to walk across the intersection.
Therefore
The number of cars that go through the intersection each minute X has Poisson distribution with parameter λ = 11.5
and the PMF of X is;
P ( X = x ) = e^-λ ( λˣ / x! ) ;
where x = 0, 1, 2, 3, , , , , ,
We need to find the homeownership proportion in Southern California. The homeownership proportion is believed to be around 50%. How many householders would you survey for a 93% CI where the maximum likely sampling error is 1.5%?
Answers
Answer:
The value is [tex]n = 3648 [/tex]
Step-by-step explanation:
From the question we are told that
The sample proportion is [tex]\^ p = 0.5[/tex]
The margin of error is [tex]E = 0.015[/tex]
From the question we are told the confidence level is 93% , hence the level of significance is
[tex]\alpha = (100 - 93 ) \%[/tex]
=> [tex]\alpha = 0.07[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.812[/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{ 1.812 }{ 0.015} ]^2 *0.5 (1 - 0.5 ) [/tex]
=> [tex]n = 3648 [/tex]
A large aquarium has 6 more fish than a small aquarium. There are 19 fish in the large aquarium. How many fish are in the small aquarium
Answers
Answer: 13
Step-by-step explanation:
An experienced carpenter can panel a room 3 times faster than an apprentice can. Working together, they can panel the room in 6 hours. How long would it take each one working alone to do the job
Answers
Answer:
experienced carpenter would need 1 and 1/2 hours
apprentice would need 4 1/2 hours
Step-by-step explanation:
experienced = e
apprentice = 3e
3e + e = 6
4e = 6
e = 6/4 or 3/2
6 - 3/2 = 9/2
Considering the 5th slab of tax structure of Pakistan for 2020-2021, Where the taxable salary income exceeds Rs. 2,500,000 but does not exceed Rs. 3,500,000 the rate of income tax is Rs. 195,000 + 17.5% of the amount exceeding Rs. 2,500,000. If we create a mathematical Model of the tax structure, the function for this particular slab will be:
0.175x-195000
0.175x+195000
0.175x-445000
0.175x-242500
Answers
Answer:
it is the answer A
Step-by-step explanation:
simplify solution
[tex]6 \sqrt{4 \sqrt{2} } [/tex]
Answers
Answer:
16.97
Step-by-step explanation:
Type the correct answer in each box
Answers
Answer:
(-1,0) these two points have the same x-value
(x,y)
Step-by-step explanation:
help algebra 1 !! help me with this question
Answers
mark me brainliest
why can you use fraction multiplication to check the answer to a fraction division problem? How do you use multiplication to check a division problem
Answers
Answer:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.i hope this helps:)
Use the linear equations to answer the questi
y= -3
y= x+2
Which statement about the lines is true?
Answers
Answer: Though no choices of statements are shown, you can predict that x+2=-3, since both numbers are equal to y. (This isn't really an answer but I hope it'll at least help you in some way!)
-By subtracting 2 on both sides, you end up with x=-5. So in both equations, y is -3 and x is -5.
-The point where they intersect is (5,-3)
TARGET SELLS 24 BOTTELS OF WATER FOR 3 DOLARS AND 36 DOLARS WHICH IS THE BETTER BUY AND BY HOW MUCH
Answers
Answer:
The 36-pack is a better buy by $0.50 per 36 bottles.
Step-by-step explanation:
24 bottles for $3 compared to 36 bottles for $4
Unit rates:
$3/24 = $0.125/bottle
$4/36 = $0.111/bottle
The 36-pack is a better buy since the unit price is lower.
$0.125 - $0.111 = $0.013888...
$0.01388888... * 36 = $0.50
Answer: The 36-pack is a better buy by $0.50 per 36 bottles.
A neighborhood was given a vacant lot in the shape of a rectangle on which to build a park. The base of the lot is 72.2 feet and the width is 50 feet. Complete the following statements about the park they can build on the lot.What size will the park be?
If the neighborhood wants to know the amount of fencing needed to go around the park, it will need to find the _______.
What is the exact amount of fencing they will need?
(will mark brainliest to best answer).
Answers
area
i took the test and got a 100
Answer:
area, 244.4
Step-by-step explanation:
sorry it late
PLZ Help!!! Best answer gets Brainliest!!!
Answers
Answer:
Yes
Step-by-step explanation:
There is a steady increase (non-changing) between both the x and y columns, so I know this is a proportional relationship.I hope this helps!
Graph: y = 3/4 x + 5
Click or tap the graph to plot a point.
Answers
Answer:
Put the dot on the 5 on the Y-axis
Step-by-step explanation:
Put the initial dot on the 5 on the y-axis (vertical), then it's rise over run if plotting a line. Since it's 3/4 you would go up 3 and over to the right four. You can get the rest of the line by going down 3 from the initial point on five, down left 3.
What is the are of parallelogram ABDC?
Answers
Answer:
9 cm2
Step-by-step explanation:
area=3×3=9cm2
.....
Answer:
9 cm^2
Step-by-step explanation:
inside the parallelogram, two right angled triangles form.
Use the formula, A = [tex]\frac{1}{2}[/tex] x base x height (Area of a triangle) and multiply by 2 as there are two triangles. So,
A = ([tex]\frac{1}{2}[/tex] x base x height) x 2
= ([tex]\frac{1}{2}[/tex] x 3 x 3 ) x 2
= 9 cm^2
Solve the equation. Then check your solution.
-8p =-3 1/4
a. 4 3/4
b. - 13/32
c. 13/32
d. 26
Answers
Answer: C
Step-by-step explanation:
-8p = -3 1/4 The first think you want to do is convert the mixed fraction into an improper fraction.
-8p = -13/4 Now multiply both sides of the equation by 4.
-32p = -13 Divide both sides by -32
p = 13/32
Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = xe^−x^2/32, [−2, 8]
Answers
The question is missing parts. Here is the complete question.
Find the absolute maximum and absolute minimum values of f on the given interval.
[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex] , [ -2,8]
Answer: Absolute maximum: f(4) = 2.42;
Absolute minimum: f(-2) = -1.76;
Step-by-step explanation: Some functions have absolute extrema: maxima and/or minima.
Absolute maximum is a point where the function has its greatest possible value.
Absolute minimum is a point where the function has its least possible value.
The method for finding absolute extrema points is
1) Derivate the function;
2) Find the values of x that makes f'(x) = 0;
3) Using the interval boundary values and the x found above, determine the function value of each of those points;
4) The highest value is maximum, while the lowest value is minimum;
For the function given, absolute maximum and minimum points are:
[tex]f(x)=xe^{-\frac{x^{2}}{32} }[/tex]
Using the product rule, first derivative will be:
[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex]
[tex]f'(x)=e^{-\frac{x^{2}}{32} }(1-\frac{x^{2}}{16} )[/tex] = 0
[tex]1-\frac{x^{2}}{16}=0[/tex]
[tex]\frac{x^{2}}{16}=1[/tex]
[tex]x^{2}=16[/tex]
x = ±4
x can't be -4 because it is not in the interval [-2,8].
[tex]f(-2)=-2e^{-\frac{(-2)^{2}}{32} }=-1.76[/tex]
[tex]f(4)=4e^{-\frac{4^{2}}{32} }=2.42[/tex]
[tex]f(8)=8e^{-\frac{8^{2}}{32} }=1.08[/tex]
Analysing each f(x), we noted when x = -2, f(-2) is minimum and when x = 4, f(4) is maximum.
Therefore, absolute maximum is f(4) = 2.42 and
absolute minimum is f(-2) = -1.76
The absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
The function is given as:
[tex]\mathbf{f(x) = xe^{-\frac{x^2}{32}}}[/tex]
Start by differentiating the function
[tex]\mathbf{f'(x) = e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}}}[/tex]
Set to 0
[tex]\mathbf{ e^{-\frac{x^2}{32}} - \frac{x^2}{16}e^{-\frac{x^2}{32}} = 0}[/tex]
Rewrite as:
[tex]\mathbf{ \frac{x^2}{16}e^{-\frac{x^2}{32}} = e^{-\frac{x^2}{32}}}[/tex]
Cancel out common factors
[tex]\mathbf{ \frac{x^2}{16}=1}[/tex]
Multiply both sides by 16
[tex]\mathbf{ x^2=16}[/tex]
Take square roots of both sides
[tex]\mathbf{ x=\pm 4}[/tex]
The interval is given as: [-2,8]
This means that the value of x = -4, is out of the interval.
So, we have the following critical points:
x = (-2, 4, 8)
Calculate f(x) at the these points
[tex]\mathbf{f(-2) = -2 \times e^{-\frac{(-2)^2}{32}}}[/tex]
[tex]\mathbf{f(-2) = -2 \times e^{-\frac{4}{32}}}[/tex]
[tex]\mathbf{f(-2) = -1.765}[/tex]
[tex]\mathbf{f(4) = 4 \times e^{-\frac{(4)^2}{32}}}[/tex]
[tex]\mathbf{f(4) = 4 \times e^{-\frac{16}{32}}}[/tex]
[tex]\mathbf{f(4) = 2.426}[/tex]
[tex]\mathbf{f(8) = 8 \times e^{-\frac{(8)^2}{32}}}[/tex]
[tex]\mathbf{f(8) = 8 \times e^{-\frac{64}{32}}}[/tex]
[tex]\mathbf{f(8) = 1.083}[/tex]
By comparison, the absolute maximum and absolute minimum values of f(x) are 2.426 and -1.765, respectively.
Read more about absolute maximum and absolute minimum values at:
https://brainly.com/question/12752779
You earn 3% each year on your initial investment amount of $2000. How much interest do you earn after 2 years?
Answers
Answer: You earn 6% interest on that the next year.
Which one is it? Please answer
Answers
Answer:
b
24 ÷ 5 = x
X × 8 = 44
15. At a football match, 10 men bought either a pie or a cup of
coffee. A pie costs 60p and a coffee costs 50p. The total
amount spent on pies and cups of coffee was £5.80. How many
of each must have been bought?
Answers
Answer:
8 pies and 2 coffees must have been bought.
Step-by-step explanation:
Given that:
10 men bought either a pie or a cup of coffee.
Cost per pie = 60p
Cost per coffee = 50p
Total amount spent = £5.80 * 100 = 580p
Let,
x be the number of pies
y be the number of coffees
According to given statement;
x+y = 10 Eqn 1
60x+50y=580 Eqn 2
Multiplying Eqn 1 by 50
50(x+y=10)
50x+50y=500 Eqn 3
Subtracting Eqn 2 from Eqn 3
(60x+50y)-(50x+50y) = 580-500
60x+50y-50x-50y=80
10x=80
Dividing both sides by 10
[tex]\frac{10x}{10}=\frac{80}{10}\\x=8[/tex]
Putting x=8 in Eqn 1
8+y=10
y=10-8
y=2
Hence,
8 pies and 2 coffees must have been bought.
Please help do right don't do just for points please
Answers
Answer:
-100
75
Step-by-step explanation:
Find the slope using the points (0, -2) and (3, 4)
Answers
(18 POINTS!!!) When Katie installed a fence along the 200-
fixed perimeter of her rectangular backyard,
she left an op an opening for a gate. What is
the value of x, if the equation
2(x+ 60) + 2(300) = 200
Answers
Answer:
-260
Step-by-step explanation:
Answer:
x = -260
Step-by-step explanation:
A Hulu subscription cost $55 a month. If 5 people wanted to split this cost each month how much would eat person pay ?
Answers
Answer:
each person would pay $11
Step-by-step explanation:
u have to do 55 divided by 5 and that would give you the $11
Answer: 11
Step-by-step explanation: 55/5=11
Alison can swim 75 feert in 12 seconds. What is he rate to the nearest mile per hour?.
Answers
Answer:
in an hour she can swim around 22,500 feet which is about 4.26 miles
Step-by-step explanation:
Answer:
22,500 miles per hour
Step-by-step explanation:
60 seconds in a minute times 60 minutes in one hour. 3600
Divide that by 12 then multiply by 75 to get your answer
PLZ MARK BRAINLIEST
a line passeses through the ponts (2, a) and (4a,5) and has a slope of 1/2 find the value of a
Answers
Answer:
a=2
Step-by-step explanation:
Slope is found by (y2-y1)/(x2-x1)
Using the points, that is (5-a)/(4a-2) = 1/2
multiply both sides by the denominator 4a-2
5-a = (1/2)(4a-2)
5-a=2a-1
put like terms on opposite sides by adding a to both sides so a terms on the right, adding 1 on both sides so numbers are on the left
6=3a
divide both sides by 3
a=2
please give thanks :)
The sum of two numbers is -10.5. Can one of these addens be positive and the other negative? Provide an example to prove your answer.
Answers
Step-by-step explanation:
In order for the solution of a problem to be negative, you need one negative number and one positive number. Same goes for when having a positive sum, you know that the equation has an even number of negative numbers.
-6 + 3 = -3
You get -3 because you have both a positive and negative number in the equation.
00:00
What is the number of terms in this expression?
m
5
+4x6
5
Enter your answer in the box.
Answers
Answer:
40
Step-by-step explanation:
Which operation is NOT closed for polynomials?
es )
A)
add a trinomial to a trinomial
B)
divide a binomial by a trinomial
multiply a binomial by a binomial
D)
subtract a binomial from a trinomial
Answers
Answer:
B) divide a binomial by a trinomial
Step-by-step explanation:
We know that the polynomials are very nearest to the addition, subtraction and the multiplication part but the same cannot happen under the division part since the division of two polynomials could not become a polynomial it is not necessary condition that it could become a polynomial
So if we divide the binomial by a trinomial therefore it would provides a rational expression and have a negative exponent and a negative exponent is not permitted under the polynomial
Therefore the option B is correct