The average rate of change of the function over the interval 2 < x < 10 is 5
How to determine the average rate?The function is given as:
h(x) = x^2 - 7x + 8
Calculate h(2) and h(10)
h(2) = 2^2 - 7 * 2 + 8
h(2) = -2
h(10) = 10^2 - 7 * 10 + 8
h(10) = 38
The average rate is then calculated as:
Rate = (h(10) - h(2))/(10 - 2)
This gives
Rate = (38 + 2)/(10 - 2)
Evaluate
Rate = 5
Hence, the average rate of change of the function over the interval 2 < x < 10 is 5
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The ratio of boys to girls in Ella's grade is 3 to 4. The ratio of boys to girls in Minh's grade is 4 to 5. Each grade has a total of 20 girls. How many boys are in each grade?
1. Michael deposited $500 in his bank account that pays 4% semi-annual compounded interest. If he does not touch the money for 5 years, how much money will be in the account?
Answer:
$609.50
Step-by-step explanation:
A = P(1 + r/n)^nt
= 500(1 + [tex]\frac{.04}{2}[/tex])^2(5)
= 500(1.02)¹⁰
= 500(1.218994)
= 609.497
Round answer up to $609.50
If you take -3/10 of a number and add 1, you get 10. Let x represent the original number. A. Write an equation that represents the situation. B. What is the original number
Answer:
A. -(3/10)x + 1 = 10
B. x = -30
Step-by-step explanation:
A. first, we know that we are multiplying a number (x) by -3/10 because that's the fraction of the number we are taking. Then, we add one to that number. After doing so, we are told that we get 10. Thus, -(3/10)x + 1 = 10
B. in solving this, first we subtract 1 from both sides, to get
-(3/10)x = 9
then, we divide both sides by -3/10 to get
x = -30
Tyler Invests $7900 in two different accounts. The first account paid 9 %, the second account paid 8
% in Interest. At the end of the first year he had earned $674 in interest. How much was in each
account?
$
at 9 %
$
at 8 %
Answer:
the dollar for 9 interstate is 16 rupees is and interest rate for 88 percentage is is 14 rupees
Isabella and Madeline share a bag of cherries. if isabella eats 25% of the cherries and there are 76 cherries in the bag, how many cherries did isabella eat?
Answer:
19
Step-by-step explanation:
Which relationships have the same constant of proportionality between Y and as the equation Y=5/2 X
Answer:
I'm pretty sure it's 10/4 but I'm not totally sure
Answer:
on Khan the answer is B,C,E
Jackson spent $3,472 on a new TV. If he paid it off in 16 equal payments, how much was each payment?
A $217
B $237
C $207
D $227
Answer:
A. 217
Step-by-step explanation:
3,472/16 = 217
I'm in my feelings again. Sad and Heartbroken. I guess those would be the same thing, but whatever.
Answer:
same here. i went through a breakup of 2 years, i'm super behind in school, and i've been grounded for the past 5 months and haven't spoken to any of my friends. i've learned that life is tough, but so are you. whatever is making you feel this way will pass. just try to find little things that make you happy. the most beautiful views come from the hardest climbs. you'e gotta make the most before the coffin.
Step-by-step explanation:
i hope this helps you, or at least encourages you. i don't know what is happening in your life but i know you can get through it. i'm here for you if you need me in the comments. i have super strict parents so i don't have any socials, but if you wanna talk or play together when i get ungrounded, my r0blox is adriii_rose and my pinterest is also adriii_rose. good luck and have a great day/night. best wishes! ❤️✨
Answer:
❤️❤️❤️
Step-by-step explanation:
Write the multiplicative comparison statement as an equation.
18 is 3 times as many as 6.
Answer:
18 = 3 × 6
Step-by-step explanation:
what is the solution of 7k+2=4k-10? (anwser asap plz)
1.- Divison property of Equality
2.- Simplify
3.-Subtraction Property of Equality
4.- Subtract
Answer:
3
Step-by-step explanation:
Answer:
k = -4
division property
Step-by-step explanation:
A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes.How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)
Answer:
Step-by-step explanation:
Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation [tex]^{n-k+1}C_k[/tex]
[tex]= \begin {pmatrix} ^{n-k+1}_{k} \end {pmatrix}[/tex]
where:
n = 26
k = 5
[tex]^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}[/tex]
[tex]^{n-k+1}C_k= \begin {pmatrix} ^{22}_{5} \end {pmatrix}[/tex]
[tex]^{n-k+1}C_k= \dfrac{22!}{5!(22-5)!}[/tex]
[tex]^{n-k+1}C_k= \dfrac{22!}{5!(17)!}[/tex]
[tex]\mathbf{^{n-k+1}C_k=26334}[/tex]
Therefore, there are 26334 selection of 5 episodes with no two consecutive episodes chosen
Megan deposits 4300 into an account that pays simple interest when she withdraws her money 6 months later she receives $4,536.50 what rate of interest did the account pay round to the nearest whole percent
Answer:
4500
Step-by-step explanation:
because if you round 4,536.50 you will get 4500 since 36 is before 50+
Answer:4500
Step-by-step explanation:
i will brainlist and give lots of points and stuff if you answer these 6 problems!!!!!!! PLEASE HELP MEEE btw i accidently click a answer botton on the first do but do thoes too pllllllsssssssssssss
ANSWER:
1.3/2
2.4/27
3.2/25
4.3/25
5.4
Answer:
1.3/2
2.4/27
3.2/25
4.3/25
Step-by-step explanation:
Write a positive or negative number for each situation.
a. you win $150 in a contest
b. a loss of 15 yards in a football game
c. 75 feet below sea level
d. 35 degrees above 0 degrees F
e, a debt of $24.75
Solve for x.
6(x – 1) = 9(x + 2)
Answer: -8
Step-by-step explanation:
Distribute 6 to x and -1
6x-6=9(x+2)
Distribute 9 to x and 2
6x-6=9x+18
Add 6 to both sides
6x=9x+24
Subtract 9x from both sides
-3x=24
Divide -3 from both sides
X=-8
write an equation that represent the table
Answer:
y equals 5x + 20
help with this immediately
Answer:
c
Step-by-step explanation:
%gggggyyhhttbu6gnmk8tg
A homogeneous 1300 kg bar AB is supported at either end by a cable. calculate the stress acting in bronze bar in N/mm² if stress should not exceed to 120MPa for steel and the area of the bronze bar and steel bar is 40.05 mm² and 36.33 mm² respectively.
Answer:
4553332 is the answer
Step-by-step explanation:
ayer 100% A company sells cases of tomato juice. Each case contains 24 cans of juice and sells for $18. The equation y = 18x represents the total price ( y), in dollars, when x number of cases are sold. Choose all statements about the situation that are correct based on the information. A. The cost per can is dependent on the number of cases sold. B. The number of cans sold is dependent on the price per can. C. The total price for a sale is dependent on the number of cases sold. D. The number of cases sold is independent from the number of cans in each case.
Answer:
c
Step-by-step explanation:
Answer:
C is the answer
pls help will give brainliest
Answer:3rd one
Step-by-step explanation:
in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)
Answer:
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
Step-by-step explanation:
Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:
[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)
Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)
If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:
[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]
[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:
[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)
If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:
[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]
[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]
The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].
2. Manny wants to rent a movie. Each movie costs $1 to rent. The function f(x) = X
represents this situation. Explain what x and f(x) represent in this situation."
PLEASE HELP!!!!! How do you turn 0.480 into a fraction???? PLEASE SHOW WORK IF YOU CAN?
Answer:
the answer is 48/100 im pretty sure .
Step-by-step explanation:
Answer:
12/25
Step-by-step explanation:
first you take your decimal and because it is a decmial the decimal is in a fraction, 48/100 don't pay attention to any 0's behind any other number.
once you have 48/100 divide the numerator(the top of the fraction) and the denominator(the bottom of the fraction) and divide it by 4
A population has standard deviation g = 17.2.
Part 1 of 2
(a) How large a sample must be drawn so that a 99.8% confidence interval for I will have a margin of error equal to 3.8?
Round the critical value to no less than three decimal places.
Round the sample size up to the nearest integer.
A sample size of is needed to be drawn in order to obtain a 99.8% confidence interval with a margin of error equal to
3.8.
Part 2 of 2
(b) If the required confidence level were 80%, would the necessary sample size be larger or smaller?
(Choose one) because the confidence level is (Choose one)
х
Answer:
idk
Step-by-step explanation:
Please I need some answers a few is fine
Lorie is using long division to find the quotient of x^3 + 6x^2 + 5 and x^2 + x -1, as shown at the bottom of this question.
What mistake did Lorie make?
A. She added an extra term to the dividend.
B. She combined the constants incorrectly in the last step.
C. The second term in the quotient should be 7.
D. The last term in the quotient has an incorrect denominator.
Answer:
Option (B)
Step-by-step explanation:
x² + x - 1) x³ + 6x² + 0x + 5 ( x + 5
- (x³ + x² - x)
5x² + x + 5
-(5x² + 5x - 5)
-4x + 10
Result : [tex]x+5+\frac{-4x+10}{(x^{2}+x-1)}[/tex]
By the comparing the result with the Lorie's solution,
She made a mistake in the last step in which she combined the constant incorrectly.
Therefore, Option (B) will be the answer.
What is m,y-intercept and the y
Answer: The slope is 500 and the y intercept is 0.
Step-by-step explanation:
To find the slope we need to find the rise and divide it by the run. The y intercept will be when x is equal to 0. And when x is 0 y is also zero because it cuts through the origin meaning that the y-intercept is 0.
The line rises up by 1000 and run by 2 to the right.
Slope : 1000/2 = 500
The slope is 500.
I think of two numbers.
When I add the numbers, the answer is 8.
When I subtract the numbers, the answer
Is less than 6.
What can the numbers be?
The two numbers can be _ and _ .
Answer:
There are a variety of possible answers, including the following:
4 and 4 (4 + 4 = 8........4 - 4 = 0.......... 6 > 0)
6 and 2 (6 + 2 = 8........6 - 2 = 4.......... 6 > 4)
5 and 3 (5 + 3 = 8.........5 - 3 = 2.......... 6 > 2)
And for the subtraction, each can be reversed (2 - 6 ...... 3 -5 ...... etc.)
Answer:
2 and 3 is the answer we know it right
Jumping makes a frog so tired, each successive jump is 2/3 the distance of the previous hump. If a frog jumps 24 cm on its first jump, how far will the frog travel after four jumps?
Find the measure of ZMLN
degrees. (Numbers only for your answer)