Answer:
[tex]h'(1) = 23[/tex]
Step-by-step explanation:
Let be [tex]h(x) = (x^{2}+8)\cdot g(x)[/tex], where [tex]r(x) = x^{2} + 8[/tex]. If both [tex]r(x)[/tex] and [tex]g(x)[/tex] are differentiable, then both are also continuous for all x. The derivative for the product of functions is obtained:
[tex]h'(x) = r'(x) \cdot g(x) + r(x) \cdot g'(x)[/tex]
[tex]r'(x) = 2\cdot x[/tex]
[tex]h'(x) = 2\cdot x \cdot g(x) + (x^{2}+8)\cdot g'(x)[/tex]
Given that [tex]x = 1[/tex], [tex]g (1) = -2[/tex] and [tex]g'(1) = 3[/tex], the derivative of [tex]h(x)[/tex] evaluated in [tex]x = 1[/tex] is:
[tex]h'(1) = 2\cdot (1) \cdot (-2) + (1^{2}+8)\cdot (3)[/tex]
[tex]h'(1) = 23[/tex]
Question 2 of 6
2 Points
The word problem below has too much information. Which facts are not
needed to solve the problem? Check all that apply.
On Tuesday, the wait to ride the roller coaster was 40 minutes. The roller
coaster is the fastest ride at the fair. The line of people waiting was 100
meters long. How long would you expect to wait if the line was 50 meters
long?
A. The wait to ride the roller coaster was 40 minutes.
B. The line of people was 100 meters long.
C. The roller coaster is the fastest ride at the fair.
D. It was Tuesday.
R
SUBMIT
fPREVIOUS
Answer:
C. and D.
Step-by-step explanation:
In the word problem, the two facts to solve the problem are:
A. The wait to ride the roller coaster was 40 minutes and
B. The line of people was 100 meters long
Because the length of waiters has an effect on the time. Thus, if the line is reduced to 50 meters, then the waiting time would reduce i.e 20 minutes.
Therefore, the facts that are not required to solve the word problem are:
C. The roller coaster is the fastest ride at the fair.
D. It was Tuesday.
what is the factorization of 2x^2+28+98
Answer:
[tex]2(x^2+63)[/tex]
Step 1:
To solve this, we have to add the terms without any variables together.
[tex]2x^2+28+98\\2x^2+126[/tex]
Step 2:
To factor this, we have to find the multiples of 2x^2 and 126.
[tex]2x^2 = 2x, x\\126 = 63, 2[/tex]
Now, we can factor these numbers like this:
[tex]2(x^2+63)[/tex]
When we multiply the numbers, we get 2x^2 + 126, and when we separate 126, we get our original question, so that means our factoring is correct.
Suppose that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%. Use a 0.10 significance level to test that claim.
A. What is the test statistic for the hypothesis test?
B. What is the p value?
C. Reject/fail to reject sufficient evidence.
Answer:
We conclude that the percentage of blue candies is equal to 29%.
Step-by-step explanation:
We are given that in a random selection of 100 colored candies, 28% of them are blue. The candy company claims that the percentage of blue candies is equal to 29%.
Let p = population percentage of blue candies
So, Null Hypothesis, [tex]H_0[/tex] : p = 29% {means that the percentage of blue candies is equal to 29%}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 29% {means that the percentage of blue candies is different from 29%}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of blue coloured candies = 28%
n = sample of colored candies = 100
So, the test statistics = [tex]\frac{0.28-0.29}{\sqrt{\frac{0.29(1-0.29)}{100} } }[/tex]
= -0.22
The value of the z-test statistics is -0.22.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -0.22) = 1 - P(Z [tex]\leq[/tex] 0.22)
= 1 - 0.5871 = 0.4129
Now, at a 0.10 level of significance, the z table gives a critical value of -1.645 and 1.645 for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of z, so we insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the percentage of blue candies is equal to 29%.
PLEASE HELP ANSWER A-B Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. A.) Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. B.) If Claire’s initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment? LOOK AT PICTURE BELOW
Answer:
Therefore, the volume V cyl is given by the equation: V cyl πr 2h (area of its circular base times its height) where r is the radius of the cylinder and h is its height. The volume of the cone (V cone) is one-third that of a cylinder that has the same base and height: .
Step-by-step explanation:
The owner of a shoe store wanted to determine whether the average customer bought more than $100 worth of shoes. She randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below.
Use a TI-83, TI-83 Plus, or TI-84 calculator to test whether the mean is greater than $100 and then draw a conclusion in the context of the problem. Use α=0.05.
125 99 219 65 109 89 79 119 95 135
Select the correct answer below:
A) Reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
B) Reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
C) Fail to reject the null hypothesis. There is sufficient evidence to conclude that the mean is greater than $100.
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Answer:
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Step-by-step explanation:
We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;
X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.
Let [tex]\mu[/tex] = average customer bought worth of shoes.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \leq[/tex] $100 {means that the mean is smaller than or equal to $100}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $100 {means that the mean is greater than $100}
The test statistics that will be used here is One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = $113.4
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $42.78
n = sample of receipts = 10
So, the test statistics = [tex]\frac{113.4-100}{\frac{42.78}{\sqrt{10} } }[/tex] ~ [tex]t_9[/tex]
= 0.991
The value of t-test statistics is 0.991.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that the mean is smaller than or equal to $100.
The shape in the figure is constructed from several identical squares. If the side of each square is 1 unit, what is the area and the perimeter of the shape?
Answer:
area: 7 units²perimeter: 14 unitsStep-by-step explanation:
You can count the unit squares to find the area. There are 7 of them, so the area is 7 square units.
__
There are 4 unit lengths along the bottom perimeter, 3 up each side (for a total of 6), and 4 more unit lengths across the tops of the squares in the figure. The perimeter is a total of 4+6+4 = 14 units.
At a museum cafe you can get a pre-made boxed lunch with a sandwich, fruit, and drink for only $3 . The sandwiches are made with either turkey or ham. The fruit is either an apple or an orange. The drink is either bottled water or juice. The number of boxes they make for every possible combination is the same. If you randomly choose one of the boxed lunches without knowing the contents, what is the probability you will get an orange and not get juice in your box?
Answer:
Step-by-step explanation:
Given that sandwiches are made with either turkey or ham.
Prob for turkey or ham = 1/2
The fruit can be either apple or orange. Hence p(apple) = p(orange) =12
Drinks can be either bottled water or juice
P(water) = P(juice) = 1/2
We find that sandwiches, fruits, and drinks are mutually independent of each other.
Hence the probability you will get an orange and not get juice in your box
Prob (you get an orange and bottled water)
= Prob (orange) *Prob (bottled water) (since the two are independent
= 1/2 (1/2)= 1/4
Hence answer is 0.25
6th grade math help me, please :))
Answer:
[tex]\sf a) \ 2.5\\b) \ 7.5[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{250}{100}[/tex]
[tex]\sf Express \ as \ a \ decimal.[/tex]
[tex]=2.5[/tex]
[tex]\sf Multiply \ 3\% \ with \ 250.[/tex]
[tex]\displaystyle 250 \times \frac{3}{100}[/tex]
[tex]\displaystyle \frac{750}{100}=7.5[/tex]
which of the following demonstrates how the first 21 on the left side of the triangle is calculated using the combination pattern?
Answer:
d
Step-by-step explanation:
I can't solve this problem, can anyone help me?
Answer:
x < 5
Step-by-step explanation:
The total amount is 595$ and the amount Helena want to leave for equipement is 420$
595-420 = 175The amount helena can use is 175$
each ticket costs 35$
175/35 = 5so Helena can oly buy 5 tickets or less
x < 5 with x the number of tickets
Help me find the equation and tell me if 22 or 12 is wrong
Answer:
your answer is correct.
Evaluate ƒ(x) = 3|x – 2| + 1 for ƒ(–2) and ƒ(1).
Answer:
ƒ(x) = 3|x – 2| + 1
To find f(-2) substitute - 2 into f(x)
That's
f(-2) = 3| - 2 - 2 | + 1
= 3| - 4| + 1
But absolute value of any number is positive including negative numbers
That's
| - 4 | = 4
So we have
3(4) + 1
12 + 1
f(-2) = 13To find f(1) substitute 1 into f(x)
That's
f(1) = 3 | 1 - 2| + 1
= 3 | - 1| + 1
But | - 1| = 1
= 3(1) + 1
= 3 + 1
f(1) = 4Hope this helps you
Answer:
f(-2) =13
f(-1) = 4
Step-by-step explanation:
ƒ(x) = 3|x – 2| + 1
Let x = -2
ƒ(-2) = 3|-2 – 2| + 1
= 3 | -4| +1
Taking the absolute value
= 3*4 +1
= 12 +1 = 13
Let x = 1
ƒ(1) = 3|1 – 2| + 1
= 3 | -1| +1
Taking the absolute value
= 3*1 +1
= 3 +1 = 4
which point is a solution tot eh linear inequality y < -1/2x + 2?
(2,3)
(2,1)
(3,-2)
(-1,3)
Answer:
Step-by-step explanation:
(3,-2)
plug in 3 for x and -2 for y
-2< -1/2x3+2
-2<-1.5+2
-2<0.5
Help thanks !!!!!!!!!!!!!
Answer:
5:2
Step-by-step explanation:
There are 5 apples and 2 cherries. Put them together to get 5:2.
What is the length of leg s in the right triangle shown?
A.
B.
2
C.
D.
5
Answer:
5 units
Step-by-step explanation:
we can identify this as an isosceles triangle because both angles are equal (= 45 deg). Hence we can also conclude that the vertical leg of the triangle must also be "s"
We an also identify this as a right triangle because we have one angle that is 90 degrees. Hence we can use the Pythagorean formula to solve this (see attached for reference)
(5√2 )² = S² + S²
(5)²(√2 )² = 2S²
(25)(2) = 2S²
25 = S²
S = √25
S = 5 units
The length of leg s in the right triangle is 5 units. Therefore, the correct answer is option D.
In the given isosceles right triangle, hypotenuse is 5√2.
We know that, sinθ=Opposite/Hypotenuse
sin45°=s/5√2
1/√2 = s/5√2
1 = s/5
s = 5
Therefore, the correct answer is option D.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
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What is the value of the rate of change when we put a glass of water at room temperature in the freezer for 15 minutes, what is its temperature at 5 minutes and then at 10 minutes
Answer:
Step-by-step explanation:
I do not understand your question very well but I think that the state of the glass of the water would be liquid and solid at the same time since the water would not freeze 100% and would be with small pieces of solid and some parts liquid, in terms of temperature, I think that at 5 minutes it would be 5 ° C and at 10 it would be 3-4 ° C the longer it is in the freezer the less its temperature will be
(All of that is my point of view)
Average temperature 30 °
So :
30 ÷ 15 = 2 °
30 ÷ 10 = 3 °
30 ÷ 5 = 6 °
PLZ HURRY WILL MARK BRAINLIEST The stem and leaf plot shows the number of points a basketball team scored each game during its 15-game season. In how many games did the team score at least 70 points? 4 5 8 10
Answer:
5 games
Step-by-step explanation:
To find how many games the team scored at least 70 points, we need to look at the 7 on the stem side. The 7 means 70, and we add the digits on the leaf side. For example, 7 | 2 is 72. The numbers on the leaf side are: 1, 1, 2, and 3.
There are no points for the 8 on the stem side, but on 90, there is one digit on the leaf side: 1. So, the points they scored over 70 are 71, 71, 72, 73, and 91, which equals to five games.
Answer:
[tex]\boxed{\mathrm{5 \ games}}[/tex]
Step-by-step explanation:
At least 70 points makes it 70 and more. It should be at least 70 and at most anything above then 70.
So, In 5 games, the team scored at least 70. (71,71,72,73 and 91)
O A. lw= (x - 5)(x - 5); 49 square feet
O B. /w = x(x - 5); 84 square feet
O c. /w = (x + 5)(x + 5); 289 square feet
D. lw= (x + 5)(x - 5); 119 square feet
Answer:
D. [tex] lw = (x + 5)(x - 5) ; 119 ft^2 [/tex]
Step-by-step explanation:
Dimensions of the old square brick patio:
[tex] length (l) = x ft [/tex]
[tex] width (l) = x ft [/tex]
Note: a square has equal side measure
Dimensions of the new patio
[tex] length (l) = (x + 5) ft [/tex] ==> she increased length by 5 ft
[tex] width (l) = (x - 5) ft [/tex] she reduced width by 5 ft
Expression of the length and width of the new patio is: [tex] lw = (x + 5)(x - 5) [/tex]
Area of the new patio:
Dimension of original patio = x by x = 12 ft by 12 ft.
To find area of the new patio, replace x with 12 in the expression, [tex] lw = (x + 5)(x - 5) [/tex] , which gives you the area.
[tex] area = lw = (12 + 5)(12 - 5) [/tex]
[tex] area = (17)(7) [/tex]
[tex] area = 199 ft^2 [/tex]
Answer is D. [tex] lw = (x + 5)(x - 5) ; 119 ft^2 [/tex]
I NEED HELP ASAP!!!!!!! Find 2 numbers that multiply to make -24 and add to make -10
Answer:
Step-by-step explanation:
-8*3= -24+14=-10
Answer:
-12 and 2.
Step-by-step explanation:
-12*2= -24,
-12+2=-10
Please answer in the form of an angle or degree
Step-by-step explanation:
angle A = angle B( Corresponding angles)
so,
5x - 5 = 3x + 13
=> 5x - 3x = 13 + 5
=> 2x = 18
=> x = 9
angle B = 3x + 13 = (3×9) + 13 = 27 + 13 = 40
Answer:
x=9, ∠B=40
Step-by-step explanation:
In this case, ∠A≅∠B, as they are corresponding angles. Therefore, if you set up the equation to be 5x-5=3x+13,
2x=18, x=9
∠B=3(9)+13=27+13=40
Which of the following exponential functions represents the graph below
Answer:
Option (B)
Step-by-step explanation:
Let the equation of the exponential function give in the graph is,
f(x) = a(b)ˣ
Since the given graph passes through two points (0, 3) and (-1, 1.5)
For (0, 3),
f(0) = a(b)⁰
3 = a(1) [Since b⁰ = 1]
a = 3
For (-1, 1.5),
f(-1) = a(b)⁻¹
1.5 = 3(b)⁻¹
1.5 = [tex]\frac{3}{b}[/tex]
b = [tex]\frac{3}{1.5}[/tex]
b = 2
Therefore, equation of the given function will be,
f(x) = 3(2)ˣ
Option (B) will be the answer.
Please find the surface area of the cone (image attached) and reduce answer to nearest tenth, if necessary.
Answer:
[tex] S.A = 135.6 yd^2 [/tex] (
Step-by-step explanation:
Surface area of cone is given as:
Surface Area (S.A) = πr(r + l)
Where,
[tex] r = radius = 3 yd [/tex]
[tex] l = slant height = 11.4 yd [/tex]
Take π as 3.14
Plug the given values into the formula to find the surface area.
[tex] S.A = 3.14*3(3 + 11.4) [/tex]
[tex] S.A = 9.42(14.4) [/tex]
[tex] S.A = 135.6 yd^2 [/tex] (rounded to the nearest tenth)
At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 8 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 22 feet high
Answer:
(11π/9 )ft/s
Step by step Explanation
Let us denote the height as h ft
But we were told that The diameter of the base of the cone is approximately three times the altitude, then
Let us denote the diameter = 3h ft, and the radius is 3h/2
The volume of the cone is
V = (1/3)π r^2 h
Then if we substitute the values we have
= (1/3)π (9h^2/4)(h) = (3/4)π h^3
dV/dt = (9/4)π h^2 dh/dt
We were given as 22feet and rate of 8 cubic feet per minute
h = 22
dV/dt = 8
8= (9/4)π (22) dh/dt
= 11π/9ft/s
Therefore, the rate is the height of the pile changing when the pile is 22 feet is
11π/9ft/s
A 4 foot wide painting should be centered on a 14 foot wide wall. How many feet (x) should be on each side of the painting?
Answer:
5 feet
Step-by-step explanation:
To find x, we can write:
x + 4 + x = 14
2x + 4 = 14
2x = 10
x = 5 feet
Bobby has $27 to spend on ice cream for the month. The ice cream he likes is $2 each. How many ice creams can he buy this month?
Answer:
13
Step-by-step explanation:
Divide:
27 ÷ 2 = 13 r1
So, he can buy 13 but has a dollar left.
Hope this helps you out! : )
find the arithmetic
mean median and mode
Step-by-step explanation:
The formulae to find them are:
arithmetic mean in individual series = sum x/Narithmetic mean in discrete data= sum fx/Narithmetic mean in continuous data= sum fm/N[tex]median = \frac{n + 1}{2} th[/tex]and mode= number of greatest frequency.
(note; f is frequency, N is number of data and x is x is the raw data)
hope it helps..
What Is The Prime Factor Of 4275 ?
Answer:
[tex]5^2[/tex]·[tex]3^2[/tex]·[tex]19[/tex]
Step-by-step explanation:
Well to find the prime factor we make the prime factorization tree.
Look at the image below↓
Thus,
the prime factorization of 4275 is [tex]5^2[/tex]·[tex]3^2[/tex]·[tex]19[/tex]
Hope this helps :)
Yesterday a car rental agency rented 237 vehicles, of which 51 were sport utility vehicles.
What is the experimental probability that the first vehicle rented today will be a sport utility
vehicle?
Write your answer as a fraction or whole number.
P(sport utility vehicle)
Submit
Next up
Dong for now? Try these next:
Answer:
21.5%
Step-by-step explanation:
51 divided by 237 to get percentage (237*.215% = 51)
what is the ratios 3/4 in it simplest form
Answer:
3/4
Step-by-step explanation:
3/4 is already in it's simplest form as you already know that consecutive numbers don't have anything in common to multiply.So, it is in it's simplest form.
Hope it helps u : )
The equivalent and the percentage form of 3/4 are 12/16 and 75% respectively.
What is the ratio?
The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.
Given, the ratio of 3/4
Percentage of 3:4 = 34×100%=75%
the equivalent ratio of 3:4 is 12:16.
A ratio is a fraction that may compare part to whole or part to part. For example, suppose in a class, the ratio of boys to girls is 3 to 4. It means that the number of boys divided by the number of girls is a fraction that, in its simplest form, equals 3 over 4.
Learn more about ratios here:
https://brainly.com/question/13419413
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The population of fruit flies in a laboratory grows geometrically and is checked everyday at noon. If the population began with 80 fruit flies and reached 125 in two days, what is the population after 4 days?
Answer:
[tex]\boxed{195}[/tex]
Step-by-step explanation:
The fruit flies grows geometrically.
[tex]125=80k^2[/tex]
Find the value of k.
[tex]\sqrt{\frac{125}{80} } =k[/tex]
[tex]1.25=k[/tex]
[tex]P=80(1.25)^t[/tex]
[tex]t[/tex] is number of days.
[tex]P=80(1.25)^4[/tex]
[tex]P=195[/tex]