Answer:
A. 2x + 1
Step-by-step explanation:
f(x) = 2x + 7
g(x) = x - 3
To find f(g(x)), substitute x = x - 3 into f(x) = 2x + 7
Thus:
f(g(x)) = 2(x - 3) + 7
f(g(x)) = 2x - 6 + 7
Add like terms
f(g(x)) = 2x + 1
Write 6/7 as a decimal rounded to the nearest hundredth
Answer:
0.01
Step-by-step explanation:
6/7% = 6÷7÷100 = 0.0085714286 round to the nearest hundredth = 0.01
Each machine at a certain factory can produce 90 units per hour. The setup cost is 20 dollars for each machine and the operating cost is 26 dollars per hour (total, not 26 dollars per machine per hour). You would like to know how many machines should be used to produce 40000 units, with the goal of minimizing production costs.
First, find a formula for the total cost in terms of the number of machines, n:_______
TC = ______
machines for a total cost of The minimum total cost is achieved when using dollars.
Answer:
a) [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
b) [tex]n=24[/tex]
Step-by-step explanation:
From the question we are told that:
Rate r=90 units per hour
Setup cost =20
Operating Cost =26
Units=40000
Generally the equation for Total cost is mathematically given by
[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]
Differentiating
[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]
Equating equ 1 to zero
[tex]0=\frac{20n^2+11556}{n}[/tex]
[tex]n=24[/tex]
Therefore
Substituting n
For Equ 1
[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]
F(n)>0
For Equ 2
[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]
F(n)'<0
The age of Paul is 1/3 that of Kennedy. In four years time the age of Paul will be the same as Kennedy present age. How old is Paul now?
Answer:
Paul is 2 and Kennedy is 6
Step-by-step explanation:
6 × 1/3 = 2
2 + 4 =6
(-2x) (x-3) answer please
Answer:
−2x^2+6x
Explanation:
You just have to distribute meaning you have to multiply -2x to the equation.
Which equation is represented by the graph below?
A macaroni and cheese recipe calls for 2/5 of a 2 1/2 pound a block of cheese. How many pounds are needed?
I
2/5 of 2.5. = 2x2.5 / 5x1 = 5/5 = 1 pound
The principal amount of money for this loan is $9,500.00. If you deposit this into an account paying 4.2% annual interest compounded monthly. How much money will be in the account after 5 years? (also called Future value).
9514 1404 393
Answer:
$11,715.65
Step-by-step explanation:
The applicable formula is ...
FV = P(1 +r/n)^(nt)
where principal P earns interest at rate r compounded n times per year for t years.
FV = $9500(1 +0.042/12)^(12·5) = $9500(1.0035^60) ≈ $11,715.65
The account will hold $11,715.65 after 5 years.
Hello I'm new can anyone help me with this question?
Thank you so much! <3 xoxo
find the missing side length in the image below
Answer:
The missing side length is of 5.
Step-by-step explanation:
The sides are proportional, which means that the missing side can be found using a rule of three.
x - 10
3 - 6
Applying cross multiplication:
[tex]6x = 30[/tex]
[tex]x = \frac{30}{6} = 5[/tex]
The missing side length is of 5.
help with 27 please. thanks
Answer:
See Below.
Step-by-step explanation:
We are given the function:
[tex]\displaystyle y=\sqrt{\sin x}[/tex]
And we want to show that:
[tex]\displaystyle 4y^3\frac{d^2y}{dx^2}+y^4+1=0[/tex]
Find the first derivative of y using the chain rule:
[tex]\displaystyle \frac{dy}{dx} = \frac{1}{2\sqrt{\sin x}}\cdot \cos x = \frac{\cos x}{2\sqrt{\sin x}}[/tex]
And find the second derivative using the quotient and chain rules:
[tex]\displaystyle \begin{aligned} \frac{d^2y}{dx^2} &= \frac{1}{2}\left(\frac{(\cos x)'(\sqrt{\sin x})-(\cos x)(\sqrt{\sin x})'}{(\sqrt{\sin x})^2}\right) \\ \\ &=\frac{1}{2}\left(\frac{-\sin x\sqrt{\sin x} - \left(\cos x\right) \left (\dfrac{\cos x}{2\sqrt{\sin x}}\right)}{\sin x}\right) \\ \\ & = \frac{1}{2}\left(\frac{ -\sin x(2\sin x) -\cos x(\cos x) }{\sin x \left(2\sqrt{\sin x}\right) }\right) \\ \\ &= -\frac{1}{2} \left(\frac{2\sin^2 x + \cos^2 x}{2\sin^{{}^{3}\!/\! {}_{2}}x}\right)\end{aligned}[/tex]
Find y³:
[tex]\displaystyle y^3 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right) ^3= \sin^{{}^{3}\! / \! {}_{2} }x[/tex]
And find y⁴:
[tex]\displaystyle y^4 = \left((\sin x)^{{}^{1}\!/\!{}_{2}}\right)^4 = \sin^2 x[/tex]
Substitute:
[tex]\displaystyle 4\left( \sin^{{}^{3}\! / \! {}_{2} }x\right)\left(-\frac{1}{2}\left(\frac{2\sin ^2x + \cos ^2 x}{2\sin^{{}^{3}\!/ \! {}_{2}}x}\right)\right)+\left(\sin ^2 x\right) + 1= 0[/tex]
Simplify:
[tex]-\left(2\sin^2 x + \cos^2 x\right) + \sin ^2 x + 1=0[/tex]
Distribute:
[tex]-2\sin ^2 x - \cos^2 x + \sin ^2 x + 1=0[/tex]
Simplify:
[tex]-\sin ^2 x - \cos^2 x + 1= 0[/tex]
Factor:
[tex]-(\sin ^2 x + \cos^2 x ) + 1=0[/tex]
Pythagorean Identity:
[tex]-(1)+1=0\stackrel{\checkmark}{=}0[/tex]
Q.E.D.
-1/12 to the second power? Halp me plz
Answer:
1/144
Step-by-step explanation:
(-1/12)^2
(-1/12)*(-1/12)
1/144
Question 3 plz show ALL STEPS
Answer:
7,0, -1 and -2
Step-by-step explanation:
Just substitute the values,
a. f(g(7))=f(-1) [g(7)=-1 given]
=7 [f(-1)=7 given]
b.f(g(-1))=f(3)=0 [g(-1)=3 Given]
c.g(f(-1))=g(7)=-1 [f(-1)=7 given]
d.g(f(7))=g(5)=-2 [f(7)=g(5) given]
What is the expression and value of "six less than the quotient of a number and two, increased by ten" when n = 8?
Option 1 - StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.
Step-by-step explanation:
Given : Expression "six less than the quotient of a number and two, increased by ten".
To find : What is the expression and value of expression when n = 8?
Solution :
Let the number be 'n'.
The quotient of a number and two i.e. \frac{n}{2}2n
Six less than the quotient of a number and two i.e. \frac{n}{2}-62n−6
Six less than the quotient of a number and two, increased by ten i.e. \frac{n}{2}-6+102n−6+10
The required expression is \frac{n}{2}-6+102n−6+10 .
Now, when n=8,
\frac{n}{2}-6+10=\frac{8}{2}-6+102n−6+10=28−6+10
\frac{n}{2}-6+10=4-6+102n−6+10=4−6+10
\frac{n}{2}-6+10=82n−6+10=8
The value of the expression is 8.
Therefore, option 1 is correct.
StartFraction n Over 2 EndFraction minus 6 + 10; when n = 8, the value is 8.
How many times greater is
3.8 x 105
than
1.9 X 1022
2
20
200
2000
Step-by-step explanation:
there must be something wrong with your text.
what we can see is
3.8 × 105
and
1.9 × 1022
the true answer for these values has nothing to do with the 4 answer options.
maybe you meant
1.9 × 10.5 ?
because that answer would be 20.
but first working with the presented numbers :
3.8 × 105 = 399
1.9 × 1022 = 1941.8
so, the second number is actually much bigger than the first number.
but if it is
1.9 × 10.5 = 19.95
that works.
and we can either use the calculator to calculate
399 / 19.95 = 20
or we can simply look at the factor changes of the multiplication terms.
3.8 = 1.9 × 2
105 = 10.5 × 10
so, the multiplication product of the two larger numbers is then 2×10=20 times larger than the product of the 2 smaller numbers.
The sum of the interior angles of a regular nonagon (9-gon) is equal to
The sum of the interior angles is 1260°
Lena, Hong and David sent a total of 126 text messages over their cell phones during the weekend. David sent four times as many messages as Hong. sent six more messages than Lena. How many messages did they each send?
Step-by-step explanation:
Which is the first sincetist of world
A 7% acid solution will be mixed with a 15% acid solution. 20 L of a 12% acid solution needs to be made.
Identify the two variables in the problem by completing the following statements: * Let r represent: Let y represent:
Answer:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
r =7.5 L
y = 12.5 L
Step-by-step explanation:
Let r = amount of the 7% solution
y represent the amount of the 15 percent solution
.07r + .15 y = (r+y) .12
r+y = 20
y = 20-r
.07r + .15 (20-r) = (20) .12
0.07r+0.15(20-r)=2.4
.07r+ 3 - .15r = 2.4
-.08r = 2.4-3
-.08r = -.6
Divide by-.08
r =7.5
y = 20-7.5
y = 12.5
A poll of 400 people from Dobbs Ferry showed 250 preferred chocolate raspberry coffee while 170 out of 350 in Irvington preferred the same flavor. To test the hypothesis that there is no difference in preferences in the two villages, what is the alternate hypothesis
Answer: The alternate hypothesis would disprove the null hypothesis and state that there are a significant difference in preferences/proportions between the two villages.
For instance, let's say:
p₁ = proportion of preference from Dobbs Ferryp₂ = proportion of preference from IrvingtonThe null hypothesis would be that p₁ = p₂, while the alternative hypothesis would be that p₁ ≠ p₂.
Find the area of the region bounded by y=1/x^2,y=4, and x=5. Use dy to differentiate and/or integrate.
Step-by-step explanation:
Let [tex]f(x) = 4[/tex] and [tex]g(x) = \frac{1}{x^2}[/tex]. The area A of the region bounded by the given lines is
[tex]\displaystyle A = \int [f(x) - g(x)]dx[/tex]
Note that [tex]g(x) = \frac{1}{x^2}[/tex] intersects y = 4 at x = 1/2 so the limits of integration go from x = 1/2 to x = 5. The area integral can then be written as
[tex]\displaystyle A = \int_{\frac{1}{2}}^{5}\left(4 - \dfrac{1}{x^2}\right)dx[/tex]
[tex]\:\:\:\:= \left(4x + \dfrac{1}{x}\right)_{\frac{1}{2}}^5[/tex]
[tex]\:\:\:\:= (20 + \frac{1}{5}) - (2 + 2) = \dfrac{81}{5} = 16\frac{1}{5}[/tex]
Find the value of x in each case:
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Answer:
x = 45°
Step-by-step explanation:
The triangle interior angle at I will be the supplement of the angle marked 2x. The triangle interior angle at G will be equal to x, the alternate interior angle with respect to transversal GI crossing the parallel lines.
The angle marked 3x is the sum of these "remote" interior angles:
3x = 180 -2x +x
4x = 180 . . . . . . . . . add x; next, divide by 4
x = 180/4 = 45 . . . . . degrees
x = 45°
(A) The weight of cans of vegetables is normally distributed with a mean of 1380 grams and a standard deviation of 80 grams. What is the probability that the sample mean of weight for 15 randomly selected cans is more than 1410
Answer:
7.35%
Step-by-step explanation:
μ = 1380
σ = 80
n = 15
P(x>1410)
= (1410-1380)/((80)/(sqrt(15)))
= 1.4524
P(z>1.4524) = 0.4265 (from the graph)
P(z>1.4524) = 0.5 - 0.4265 = 0.0735
The profit earned by a hot dog stand is a linear function of the number of hot dogs sold. It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold. Which equation represents y, the profit earned by the hot dog stand for x hot dogs sold? y=48x−2 y=48x+2 y=2x−48 y=2x+48
Answer:
c. y=2x−48
Explanation:
It is telling us that it costs $48 each morning to buy the day's supply of hot dogs, so we must subtract that from our pay, and it will be our y intercept
It also says he earns $2 per hot dog, so that will be our slope (rate of change)
Hope it helps! :]
y = 2x - 48 equation represents the profit earned by the x hot dog sold.
What is linear equation?A linear equation is an algebraic expression in which highest power of the given variable is equals to one.
Given that, the profit earned by a hot dog stand is a linear function of the number of hot dogs sold.
It costs the owner $48 dollars each morning for the day’s supply of hot dogs, buns and mustard, but he earns $2 profit for each hot dog sold.
We need to establish an equation that represents the total profit,
According to the question,
x represents the number of hot dogs sold
y represents the total profit earned
Cost required for supply = $48
Profit on each hot dog sold = $2
As per the condition given, the required linear equation is =
y = 2x - 48
Hence, y = 2x - 48 equation represents the profit earned by the x hot dog sold.
Learn more about linear equation here :
brainly.com/question/11897796
#SPJ7
I want to know how to solve this equation
Answer:
the last two answers are the only correct ones
a bag contains 7 red chips and 11 blue chips. two chips are selected randomly without replacement from the bag. what is the probability that the two chips are NOT the same coler
Answer:
77/306 or around 25.2%
Step-by-step explanation:
[tex]\frac{7}{18} *\frac{11}{17}[/tex] section 1/total * section 2/(total-1) since there is no replacement
just solve and you get 77/306
Does the function ƒ(x) = (1∕2) + 25 represent exponential growth, decay, or neither?
A) Exponential growth
B) Impossible to determine with the information given.
C) Neither
D) Exponential decay
Answer:
A) Exponential growth
Step-by-step explanation:
What is the value of x?
2
3
6
7
Answer:
i think 3
Step-by-step explanation:
Answer: [A] 2
Step-by-step explanation:
100% on edge 2023
Find the length of the arc. Round your answer to the nearest tenth
Answer:
12.6 mi
Step-by-step explanation:
Arc length = 2πr (Θ/360)
2π(12) (60/360)
= 12.6 mi
Answered by g a u t h m a t h
What is 21 1/8 minus 14 1/8
Answer:
8.75
Step-by-step explanation:
211/8 = 26.375
141/8 = 17.625
now,
211/8-141/8
26.375-17.625
8.75
ACD = 30, Line segment AC = x + 1, Line segment CD = 2x + 2. What is x equal to? x =
Answer:
AC+ CD = ACD
X+1 + 2X + 2 = 30
3X+3 =30
3X=30–3
3X=27
X= 27/ 3
X= 9
I'm not sure of the solution, but I solved it according to a straight line (Line segment) .
I hope I helped you^_^
what’s the formula to find the shaded area?
shaded area = area of outer figure - area of inner figure........