Answer:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Step-by-step explanation:
The Composite Function
Given f(x) and g(x) real functions, the composite function, named (g\circ f)(x) is defined as:
[tex](g\circ f)(x)=g(f(x))[/tex]
For practical purposes, it's found by substituting f into g.
Given the functions:
[tex]f(x) = 3x^2 - 4x - 1[/tex]
[tex]g(x) = -2x + 5[/tex]
We need to find
[tex](g\circ f)(x)=g(f(x))[/tex]
Replace f into g:
[tex](g\circ f)(x)=-2(3x^2 - 4x - 1) + 5[/tex]
Operating:
[tex](g\circ f)(x)=-6x^2 +8x +2 + 5[/tex]
Reducing:
[tex](g\circ f)(x)=-6x^2 +8x +7[/tex]
Thus,
[tex]\boxed{(g\circ f)(x)=-6x^2 +8x +7}[/tex]
You need to purchase supplies for building a backyard deck. Your boss gives you the supply list and asks that you get the best deal by buying from either True Builder or Quality Supplies. You call both stores, and they provide the price information that you put into the table below. Which store provides the lowest total cost, and what is the cost without sales tax?
Answer:
a) The store which provides the lowest total costs is:
True Builders
b) The cost without sales tax is:
$407.48
Step-by-step explanation:
Data and Calculations:
Product Quantity True Builders Quality Suppliers
Price Costs Price Costs
Bricks 120 $2.20 $264.00 $2.25 $270.00
2 x 4 boards 40 ft $0.75 30.00 $0.70 28.00
1 x 6 boards 120 ft $0.60 72.00 $0.65 78.00
2 x 6 boards 30 ft $0.80 24.00 $0.80 24.00
Paint 2 gal. $15.50 31.00 $11.25 22.50
Paint Brushes 2 $7.50 15.00 $9.75 19.50
Total costs $436.00 $442.00
Imputed Sales Tax of 7% 28.52 28.92
Without Sales Tax $407.48 $413.08
Answer:
Quality Supplies 442.00
Step-by-step explanation:
Using the following conversions between the metric and U.S. systems, convert the measurement. Round your answer to the nearest tenth as needed
There are 8 fluid ounces in a cup, 2 cups in a pint, 2 pints in a quart,
and 4 quarts in a gallon.
1L ~ 0.26 gallons
9 fl oz _____ mL
Answer:
266.162 ml
Step-by-step explanation:
Could you answer this please a lot of points to you
Answer:
Step-by-step explanation:
13/16 dived by 5/6 = 9/40
7 dived by 1/6 = 42
2 1/5 dived by 1 1/3 = 1 13/20
2 1/7 dived by 3/28 = 20
Eight individuals are candidates for positions of president, vice president, and treasurer of an organization. How many possibilities of selections exist
Answer:
336
Step-by-step explanation:
It is given that,
Total number of individuals are 8
They are candidates for positions of president, vice president, and treasurer of an organization.
It is a based on permutations. We need to find P(8,3). It can be calculated as follows :
[tex]P(n,r)=\dfrac{n!}{(n-r)!}[/tex]
So,
[tex]P(8,3)=\dfrac{8!}{(8-3)!}\\\\=\dfrac{8!}{5!}\\\\=\dfrac{8\times 7\times 6\times 5!}{5!}\ [\because n!=n(n-1)!]\\\\=8\times 7\times 6\\\\=336[/tex]
Hence, there are 336 possibilities of selections.
Your brother works for a company that cleans and paints the outside of houses at a rate of $35 per hour. The company charges a flat rate of $500 for their supplies. The equation f(x) = 500 + 35x represents this scenario. What does the variable "x" represent in this equation?
Answer:
The x represents the hours my bro will work for in that companyAnswer:
Step-by-step explanation:
Since it says 500+35x, then x is the number hours he will work
The answer is the number of hours.
Bro someone please help- i hate math -_-
Answer:
I can't see the image can you re upload
Step-by-step explanation:
Answer:Well I think the answer is 1/2 for the top because with mixed fractions the denominator has to be bigger then the numerator....And the bottom one is 2 because you put the bottom number on top. Hope it's right and it helps.
Step-by-step explanation:
Write the ratio in fractional notation in lowest terms.
5 megabytes to 22 megabytes
The ratio is (Type the ratio as a simplified fraction.)
Answer:
99999k
Step-by-step explanation:
kjjuhhhhhhhhhuurdghsex
If 6 pounds of apples cost $9, how much would 21 pounds of apples cost?
Answer:
$31.50
Step-by-step explanation:
divide 9 by 6 to get the price per pound ($1.50), then multiply that by 21 to get the close of 21 pounds of apples ($31.50)
Which representation has a constant of variation of –2.5?
A
x
–2
–3
–4
–5
y
–5
–7.5
–10
–12.5
B
5 x + 2 y = 0
C
y = negative 2.5 x + 1
D
On a coordinate plane, a line goes through points (negative 1, 0) and (0, negative 2).
A
B
C
D
Answer:
ez b no doubt
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Federico read the nutritional information on a package of gummi bears.
The points on the following coordinate plane show how many gummi bears there are in 2, 3, and 5 servings.
Answer:
80
gummi bears
Step-by-step explanation:
0.9 7/8 0.86 least to greatest work
Answer:
7/8, 0.86, 0.9
Step-by-step explanation:
Convert 7/8 to a decimal:
7 / 8 = .875
Solve:
.875, .86, .9
Or:
7/8, 0.86, 0.9
The ratio of boys to girls in homeroom is 2:3. If there are 8 boys, how many girls are there? Do not include units.
Answer:
12 girls
Step-by-step explanation:
boys girls
2:3
8 ÷ 2 = 4
4 × 3 = 12
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
3x-(-54x)=45= whats the sum
Answer:
x= 15/19 = 0.789
Step-by-step explanation:
Answer: 0.789 is the correct answer plz brainliest big brother
Math question please help
f(x)=x+3
g(x)=2x
its combining funtions please help
What is the area of a rectangle with sides measuring 2x+3 and 3x-1 feet
Rewrite the following using the GCF and Distributive properly ?
63 + 27
Ben drinks water everyday. He drinks 3 1/2 liters of water every 1/4 of an hour. Ben drinks water at a constant rate. How many liters of water can Ben drink in 3 hours?
Ben drinks 3 1/2 liters of tea every 40 minutes.
This means that he would drink 1 3/4 of tea every 20 minutes (divide both sides by 2).
Now, let's multiply each side by 3.
1.75 * 3 = 5.25 (aka 5 1/4)
20 * 3 = 60 minutes (an hour)
He drinks 5 1/4 liters of tea in one hour.
Answer:
42 liters
Step-by-step explanation:
3.5x4=14 in 1 hour
14x3=42liters in 3 hours
18. Leonardo lives in a 10-storey apartment
building. The building is 121 m tall.
All the storeys have the same height.
How high is each storey?
Answer:
12.1 m tall
Step-by-step explanation:
First you take 121 and divide it by 10 then you take the end number and add a m
HELP! WILL MARK BRAINLIEST!
Answer:
The answer to this question is C.
Step-by-step explanation:
All that you have to do is multiply the exponents.
x+2x+x+20=180 what is x
Answer: x=40
Step-by-step explanation:
x+2x+x+20=180
first you combine the like terms which are (x, 2x, x) and get 4x.
now you have 4x+20=180
next you subtract 20 on both sides:
4x+20=180
-20 -20
and get 4x=160
finally you divide 4 on both sides and get a final answers of x=40
A magazine includes a report on the energy costs per year for32-inch liquid crystal display (LCD) televisions. The article states that 14 randomly selected 32-inch LCD televisions have a sample standard deviation of $3.42 . Assume the sample is taken from a normally distributed population. Construct 98 % confidence intervals for (a) the population variance sigma squared and (b) the population standard deviation sigma .
Interpret the results. (a) The confidence interval for the population variance is (___,___ ). (Round to two decimal places as needed.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98 % confidence, you can say that the population variance is less than ___.
B. With 2 % confidence, you can say that the population variance is between nothing and ___ .
C. With 98 % confidence, you can say that the population variance is between ___ and ___ .
D. With 2 % confidence, you can say that the population variance is greater than ___
(b) The confidence interval for the population standard deviation is (n___,___). (Round to two decimal places asneeded.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to two decimal places as needed.)
A. With 98% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
B. With 98% confidence, you can say that the population standard deviation is greater than ___ dollars per year.
C. With 2% confidence, you can say that the population standard deviation is less than ___ dollars per year.
D. With 2% confidence, you can say that the population standard deviation is between ___ and ___ dollars per year.
Answer:
a
The confidence interval for the population variance is [tex] 5.49 < \sigma^2 < 37.02 [/tex]
The correct option is C
b
The confidence interval for the population standard deviation is [tex] 2.34 < \sigma < 6.08 [/tex]
The correct option is A
Step-by-step explanation:
From the question we are told that
The sample size is n = 14
The standard deviation is [tex]s = \$3.42[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = 14 -1[/tex]
=> [tex]df = 13 [/tex]
Given that the confidence level is 98% then that level of significance is
[tex]\alpha = (100 -98) \%[/tex]
=> [tex]\alpha = 0.02[/tex]
Generally the 98% confidence interval for the variance is mathematically represented as
[tex]\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}} < \sigma^2 < \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}[/tex]
=> [tex]\frac{(14- 1) (3.42)^2}{x^2 _{[\frac{0.02 }{2} , 13]}} < \sigma^2 < \frac{(14- 1) (3.42)^2}{x^2 _{[1- \frac{0.02 }{2} , 13]}}[/tex]
From the chi -distribution table
[tex]x^2 _{[1- \frac{0.02 }{2} , 13]} = 4.107[/tex]
and
[tex]x^2 _{[\frac{0.02 }{2} , 13]} = 27.689[/tex]
So
=> [tex]\frac{(14- 1) (3.42)^2}{27.689} < \sigma^2 < \frac{(14- 1) (3.42)^2}{4.107}[/tex]
=> [tex] 5.49 < \sigma^2 < 37.02 [/tex]
Generally the 98% confidence interval for the standard deviation is mathematically represented as
[tex]\sqrt{\frac{(n- 1) s^2}{x^2 _{[\frac{\alpha }{2} , df]}}} < \sigma <\sqrt{ \frac{(n- 1) s^2}{x^2 _{[1- \frac{\alpha }{2} , df]}}}[/tex]
=> [tex]\sqrt{5.49} < \sigma < \sqrt{37.02 }[/tex]
=> [tex] 2.34 < \sigma < 6.08 [/tex]
please help me!! i’ll love you forever
Answer:
Option A
Step-by-step explanation:
Rearrange and simplify them
First we simplify
5.78 , -5.9 , 58%(58/100) or 5.8 , -5.75
Now we rearrange
-5.9 , -5.75 , 5.78 , 5.8
The larger the number in negative is the smallest.
So option A is the answer
The points on a section of an exam is given by the function , f(x), where x is the number of questions answered correctly in that section. If f(12) = 18, then a test-taker receives 18 points for answering _____ questions in the section correctly. *
Answer:
12
Step-by-step explanation:
x is the number of questions answered correctly in that section
Zenzizenzicube is an obsolete word that represents the square of the square of a cube. In symbols, zenzizenzicube is written as
(((x^3)^2))^2
Required:
a. Use the chain rule twice to find the derivative.
b. Use the properties of exponents to first simplify the expression, and then find the derivative.
Answer:
Step-by-step explanation:
Given the expression (((x^3)^2))^2
a) Differentiating the function with respect to x using chain rule.
Given y = (((x^3)^2))^2
Let u = (x³)²
y = u²; dy/du = 2u
Let p = x³; dp/dx = 3x²
u = p²; du/dp = 2p
Applying the chain rule formula:
dy/dx = dy/du • du/dp • dp/dx
substitute in the formula
dy/dx = 2u•2p•3x²
Since u = (x³)² and p = x³
dy/dx = 2(x³)²(2x³)(3x²)
dy/dx = 12x^6•x^5
dy/dx = 12x¹¹
b) Using property of exponent
y = (((x^3)^2))^2
y = (x^6)²
y = x¹²
dy/dx = 12x^12-1
dy/dx = 12x^11
How much do you need to deposit into an account with 5.4% interest compound monthly of $200 for the next 10 years
Answer: $3703.70
Step-by-step explanation:
200x.054=$3703.70
apply the distrubtive property to simply the expression -3(6x+ 2)
Answer: -18x-6
Step-by-step explanation:
You're just multiplying the number outside of the parenthesis (-3) by the coefficients (number by X) and the constants (numbers without a variable by them).
-3 x 6 = -18
-3 x 2 = -6
(+ -6 can be written as -6)
AAAAAAAAAAAAAAAAAAHHHHHHHHHHHH
Answer:
-216
Step-by-step explanation:
I think
brainlist plz
13
In the figure shown below, if line mis parallel to line n, then find the value of x. (This is a 2 part question.)
m
(2x-10)
(65 - x)
Part A
Write the equation to find the value of x. (DO NOT find x, just write the equation.)
(2x - 10) (65 - x)
Part B
What is the value of x?
Y
Answer:
2x-10 = 65-xStep-by-step explanation:
just add up both alternate internal angles as they are both equal
so, the equation is: 2x-10 = 65-x
Answer:
The right equation will be 2x - 10 = 65 - x (you were wrong lol)
Step-by-step explanation:
We have: 2x - 10 = 65 - x
=> 2x - 10 + x = 65
=> 3x = 65 + 10 = 75
=> x = 75/3 = 25
P/S: After some little chats with the others, this might be wrong :(
Which best describes the solution set of the compound inequality below? 2 + x ≤ 3x – 6 ≤ 12 4 ≤ x ≤ 9 4 ≤ x ≤ 6 –2 ≤ x ≤ 2 –2 ≤ x ≤ 3
Answer:
Im sure you dont need this anymore but in case someone else does, im pretty sure the answer is B
Answer:
B is tha right answer
Step-by-step explanation: