The table represents f(x), and the graph represents g(x). Which statements about the functions are true for the interval [4, 10]?
x f(x)
______
3 1.33
4 1
5 0.8
6 0.66
10 0.4
Select ALL that apply
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
2- The average rate of change of f(x) is less than the average rate of change of g(x).
3- Both functions have the same average rate of change.
4- The average rate of change of f(x) is 0.1, and the average rate of change of g(x) is 0.25.
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Answers
Answer:
1- The average rate of change of f(x) is greater than the average rate of change of g(x).
5- The average rate of change of f(x) is -0.1, and the average rate of change of g(x) is -0.25.
Step-by-step explanation:
average rate of change of a function h(x) in the interval [a, b] is computed as follows:
average rate of change = h(b) - h(a)/(b - a)
So, for f(x) (see table):
average rate of change = f(10) - f(4)/(10 - 4) = (0.4 - 1)/(10 - 4) = -0.1
And for g(x) (see figure):
average rate of change = g(10) - g(4)/(10 - 4) = (1 - 2.5)/(10 - 4) = -0.25
Related Questions
Sam intends to roll a six sided cube 100 times. What is the probability model he can use to predict whether or not each roll will give a result that is not a prime number?
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The outcomes of rolling fair six sided die is [tex] \{1,2,3,4,5,6\} [/tex]. The prime numbers in the above outcomes are [tex] \{2,3,5\} [/tex]. The probability of not rolling a prime number is [tex] p=\frac{3}{6}= 0.5 [/tex].
Each trial is independent.
In the given experiment of 100 trials, the binomial probability model can be used to predict the number of occurrence of non-prime numbers (X). The probability mass function is
[tex] P(X=x)=C(100,x)p^x(1-p)^{100-x},x=0,1,2,3,...,100 [/tex]. Since [tex] p=0.5,1-p=0.5 [/tex]
[tex] P(X=x)=C(100,x)0.5^x(0.5)^{100-x},x=0,1,2,3,...,100 \\
P(X=x)=C(100,x)(0.5)^{100},x=0,1,2,3,...,100 [/tex]
Find the variance and standard Deviation of the probability distribution of the random variable x, which can take the values 1,2,3 given that p(1) = 10/33 p(2) = 1/3 p(3) =12/33?
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42.5% of 59.2 is what number?
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Hope this helps.
Please mark as Brainliest:)
i needs help ........ .
Answers
3 3/4 + 5 1/4 = 9 inches ( 3/4 + 1/4 = 1, 3+5 = 8, 8+1 = 9 )
1/2 inch on the map = 4 miles
there are 2 1/2 inches to 1 inch so 4 miles x 2 = 8 miles to 1 inch
so now multiply 9 inches x 8 miles = 72 total miles
Please help me with these. You'll be respected forever. I really need help with these.
a) please write 5.(6) % as a common fraction or a mixed number. The (6) is repeated.
b) Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much. Which is more expensive and by how much?
c) Eight pounds of peanuts cost $24.00. Six pounds of walnuts cost half as much. How much will Jim pay for 3 lbs of peanuts and 6 lbs of walnuts?
d) Write “four hundred dollars and seventy two cents”... as a fraction (and then reduce).
I will give brainliest if correct. Thanks.
Answers
Answer:
b) Peanuts, $1 per lb
c) $21
Step-by-step explanation:
b)
Peanuts= 12*2=$24
Walnuts= 6*2=$12
1 lb of peanut= 3 lb
1 lb of walnut= 2 lb
24 is greater than 12
3-2=1
$1 greater per lb
c)
1 lb of peanut= 3 lb
1 lb of walnut= 2 lb
3*3=9
2*6=12
9+12= $21
Sorry I only figured out b and c :(
Will give brainliest. How long is this side?
Answers
Have questions? let me know (:
Good Luck!
Have a great day!!
If I'm correct give me 5 stars and brainliest.
Les drew the number line shown to add 2.5 + (–25). He says the sum is 22.5.
Which is a correct description of his work?
A. His number line is correct, and the correct sum is 22.5.
B. Les should have started at 0, moved right to 2.5, and then moved left to –25. The correct sum is –23.5.
C. Les should have started at 0, moved right to 2.5, and then moved left 25 units. The correct sum is –22.5.
D. The correct sum is 22.5, but his number line is incorrect. Les should have started at 0, moved left to –2.5, and then moved right 25 units.
Answers
Answer:
Answer = c
Step-by-step explanation:
Evaluate the expression 7x2y, when x = 4 and y = 2. 112 224 542 718
Answers
Keep in mind that all the terms are just being multiplied together, like this:
7 * x * 2 * y
When we plug in 4 for x and 2 for y, we end up with this:
7 * 4 * 2 * 2 =
28 * 4 =
112
Your answer should be 112.
224 will be your answer
7 x^2 y
7 (4 ^2) 2=?
4x4=16
16x 7= 112
112x2 =224
Helpppp plzzz Maddie is packing for a trip. in her closet,there are 3 red, 4 black, 2 green, and 2 yellow blouses. She randomly selects 2 blouses. Find each probability. 1. P(black and yellow) 2. P(green and green
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Calculate the probabilities of selecting specific pairs of blouses from Maddie's closet with different colors.
Explanation:1. P(black and yellow):
Number of ways to select 1 black blouse out of 4 black blouses = 4Number of ways to select 1 yellow blouse out of 2 yellow blouses = 2Total number of ways to select 2 blouses out of 11 blouses = 11C2 = 55Therefore, P(black and yellow) = (4/55) * (2/11) = 8/605
2. P(green and green):
Number of ways to select 2 green blouses out of 2 green blouses = 1Total number of ways to select 2 blouses out of 11 blouses = 11C2 = 55Therefore, P(green and green) = (1/55) * (1/11) = 1/605
Karen spends 450 on monthly bills.of this total amount,12% is for phone service,1/10 is internet service,2/9 is for utilities.id the rest of the amount is for food ,how much does Karen have for
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how much does Karen have for food?
For this case, we have that the full amount of money is:
12/100 + 1/10 + 2/9 + x = 1
Where,
x: fraction of money for food
Clearing x we have:
x = 1 - (12/100 + 1/10 + 2/9)
Rewriting:
x = 251/450
Thus, the amount of money for food is:
450 * x = 450 * (251/450) = 251
Answer:
Karen has for food about:
$ 251
Which rule matches the function graphed below?
y = x + 3
y = x - 4
y = x - 3
y = x + 4
Answers
Because if the coordinates are 0,-3 it's 0 (which equals x) -3 = -3
And 2 - 3 = -1
Hope this makes sense (sorry I’m really bad at explaining things)
11499 round to the nearest thousand
Answers
How many cubic centimeters of water can this paper cone cup hold?
Answers
To determine the number of cubic centimeters of water that the paper cone cup can hold, calculate the volume using the formula for the volume of a cone, and then convert it to cubic centimeters.
Explanation:To calculate the number of cubic centimeters of water the paper cone cup can hold, we need to first determine its volume. The volume of a cone can be calculated using the formula V = (1/3) π r² h, where V is the volume, π is the mathematical constant pi, r is the radius of the base of the cone, and h is the height of the cone.
Once we have the volume of the cone, we can convert it to cubic centimeters since the dimensions given are in centimeters. Finally, we can determine the number of cubic centimeters of water the paper cone cup can hold.
For example, if the cone has a radius of 5 cm and a height of 10 cm, the volume would be:
V = (1/3) π (5 cm)² (10 cm)
V = (1/3) π (25 cm²) (10 cm)
V = (1/3) π (250 cm³)
V ≈ 261.79 cm³
Therefore, the paper cone cup can hold approximately 261.79 cubic centimeters of water.
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Which decimal has the greatest value0.0005, 0.5 or 0.05 ?
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48 pounds are equal to approximately _______ kg.
Answers
1 pound = 0.453592kg
48 x 0.453592 = 21.7724
Answer : 21.7724 kg, rounding off would be 22kg.
Hope this helps. - M
You need to convert pounds to kg, first. The closest that number 21.7724 relates to is 21. So it is about 22 kg.
Hope this helps,
-DJ-
The weather report says there is an 85% chance it will be very hot tomorrow. Should you get ready to use the air conditioner? Explain.
Answers
Based on the 85% chance of very hot weather, it is reasonable to prepare to use the air conditioner. Weather forecasts with high probabilities can guide us in making practical preparation decisions for comfort and safety.
The weather report indicates there is an 85% chance that it will be very hot tomorrow. Given this high probability, it would be reasonable for you to prepare to use the air conditioner. Decisions based on weather forecasts often involve considering the likelihood of different outcomes and planning accordingly.
Weather is the atmospheric conditions at a particular place over a short period of time, and preparing for it helps us manage daily activities and comfort levels. When the probability of a specific weather event, such as extreme heat, is high, it is generally wise to prepare for that scenario. By planning to use the air conditioner, you can ensure you're able to maintain a comfortable environment during the hot weather.
When Sally went bowling her scores were 108, 72, and 95. If she bowls a 4th game, what will her score need to be to give her an average of 91?
Answers
Add the 4 scores, divide by 4 and set it equal to 91
(108 + 72 + 95 + x)/ 4= 91
multiply both sides by 4 to eliminate fraction
108 + 72 + 95 + x= 364
275 + x= 364
subtract both sides by 275
x= 89
ANSWER: The scored needed for the fourth game is 89.
Hope this helps! :)
To achieve an average score of 91, Sally needs to bowl an 89 in her fourth game, calculated by subtracting her current total score of 275 from the desired total of 364 points.
To calculate the score Sally needs in her fourth game to achieve an average of 91, we first need to determine the total points she needs after four games. We can calculate the required total points by multiplying the desired average score by the number of games:
91 × 4 = 364 total points
Next, we add up the scores from Sally's first three games:
108 + 72 + 95 = 275 points
Finally, we subtract the sum of her first three games from the total required points to find the score Sally needs in her fourth game:
364 - 275 = 89 points
Therefore, Sally needs to bowl a score of 89 in her fourth game to achieve an average of 91.
Jack is trying to figure out a rule for this table. He comes to the conclusion that the rule is f(x)= 3x. Why is Jack's rule incorrect?
Answers
how many times greater is one hour than one minutes
Answers
Sorry If I’m wrong
What is the size of the obtuse angle CBA
Answers
Answer:
[tex]m<CBA=102\°[/tex]
Step-by-step explanation:
we know that
The internal angle of an equilateral triangle is equal to [tex]60\°[/tex]
The internal angle of a square is equal to [tex]90\°[/tex]
To find the internal angle of a regular pentagon, apply the formula
[tex]S=[(n-2)180\°]/n[/tex]
where
n is the number of sides (n=5)
substitute
[tex]S=[(5-2)180\°]/5=108\°[/tex]
therefore
In this problem
[tex]m<CBA+60\°+90\°+108\°=360\°[/tex]
[tex]m<CBA+258\°=360\°[/tex]
[tex]m<CBA=360\°-258\°=102\°[/tex]
Which system of equation can represent the equation?
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log(x+3)
y₁ = --------------
log(4)
log(2 + x)
y₂ = ----------------
log(2)
Explanation:
1) Here you must use the property named change of base of the logarithm.
That rule is:
[tex]log_{a}b= \frac{log_c{b}}{log_ca} [/tex]
2) Changing to base 10 that is:
[tex]log_{b}a= \frac{loga}{logb} [/tex]
3) Using it with the given equation, you get:
[tex]log_4(x+3)= \frac{log_(x+3)}{log(4)} log_2(2+x)= \frac{log(2+x)}{log(2)}[/tex]
4) Now, to set your system you can make the left side of the equation equal to y₁ and the right side equal to y₂
log(x+3)
y₁ = -------------
log(4)
log(2 + x)
y₂ = ---------------
log(2)
And that is your system which is the first choice of the list.
Answer:
A on edge 2021
Step-by-step explanation:
which expression gives the length of pq in the triangle shown below?
Answers
We have then:
PQ ^ 2 = 15 ^ 2 + 19 ^ 2
Clearing we have:
PQ = root (15 ^ 2 + 19 ^ 2)
Answer:
The expression used to find PQ is given by:
PQ = root (15 ^ 2 + 19 ^ 2)
option C
So it will be:
PQ ^ 2 = 15 ^ 2 + 19 ^ 2
PQ = root (15 ^ 2 + 19 ^ 2)
So the expression used to find PQ is given by:
PQ = root (15 ^ 2 + 19 ^ 2)
So the answer would be letter C.
Two classes have a total of 50 students. One of the classes has 6 more students than the other. How many students are in the larger class?
Answers
class 2 = x
total= 50
so you need to find the x
50=6+x+x
50=2x+6
50-6=2x
44=2x
22=x
22+6
28 is the larger class
The Lin family has a fish tank
Answers
Answer: And... what about the fish tank can you give more detail?
Step-by-step explanation:
A new patio will be an irregular hexagon. The patio will have two long parallel sides and an area of 360 square feet. The area of a geometrically similar patio is 250 square feet, and it’s long parallel sides are 12.5 feet apart. What is the corresponding distance on the new patio
Answers
The area scale factor=(area of new patio)/(area of original patio)
=360/250
=36/25
but
Linear scale factor=√(area scale factor)
Linear scale factor=√(36/25)=6/5
thus the length of the patio will be:
length=(linear scale factor)*(length of the original patio)
=6/5×12.5=15 ft
A nurse has an annual income of $48,752 the income taxes to 20% rate what is the amount of the nurses income tax in dollars and cents
Answers
20/100 = .20 + 1 = 1.20
Then multiply the rate with the annual income.
48,752(1.20) = 58502.4
Which expression represents the multiplicative inverse of -9/7
A. -7/9
B. 9/7
C. 7/9
D. -9/7
Answers
Answer:
-7/9Step-by-step explanation:
To find a multiplicative inverse, switch the numerator and denominator in the fraction. The sign stays the same. In this problem, we have -9/7. Switching the numerator and denominator, we get -7/9.
I am always happy to help :)
What is the quotient in polynomial form?
Answers
Completing the synthetic division, first bring down the leading coefficient:
-1| 2 7 5
2
Now multiply this by the divisor, -1, and write it under the 7:
-1| 2 7 5
-2
2
Now add the two values in the middle, 7 and -2:
-1| 2 7 5
-2
2 5
Multiply the 5 by the -1:
-1| 2 7 5
-2 -5
2 5
Add the 5 and -5:
-1| 2 7 5
-2 -5
2 5 0
This corresponds with an answer of 2x+5 and remainder of 0.
17 is the sum of a number and 6 write this in an equation for the word sentence.
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A number plus 6 is equal to 17.
x + 6= 17
ANSWER: x + 6= 17
Hope this helps! :)
17 is the sum of a number and 6
⇒ x + 6 = 17
Answer: Equation: x + 6 = 17
To solve x:
x+ 6 = 17
x = 17 - 6
x = 11
Answer: x = 11
The table shows the results of spinning a spinner several times. (Don’t mind my answer)
Answers
The experimental probability of spinning a B or a C is [tex]\( \frac{1}{4} \)[/tex].
To find the experimental probability of spinning a B or a C, we need to sum up the frequencies of outcomes B and C and then divide that by the total number of spins.
Given frequencies:
Outcome A: 3
Outcome B: 2
Outcome C: 1
Outcome D: 4
Outcome E: 2
Total frequency of B and C: 2 (from outcome B) + 1 (from outcome C) = 3
Total number of spins: Sum of all frequencies = 3 + 2 + 1 + 4 + 2 = 12
Experimental probability of spinning a B or a C: [tex]\(\frac{\text{Total frequency of B and C}}{\text{Total number of spins}} = \frac{3}{12} = \frac{1}{4}\)[/tex]
So, the experimental probability of spinning a B or a C is [tex]\(\frac{1}{4}\)[/tex].
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