Answers
Answer:
[tex](u \circ w)(2) = -34[/tex]
[tex](w \circ u) = -49[/tex]
Step-by-step explanation:
We are given these following functions:
[tex]u(x) = 4x + 2[/tex]
[tex]w(x) = -5x + 1[/tex]
The first step to solve this question is finding the composite functions. So
[tex](u \circ w)(x) = u(w(x)) = u(-5x+1) = 4(-5x + 1) + 2 = -20x + 6[/tex]
[tex](w \circ u)(x) = w(u(x)) = w(4x + 2) = -5(4x+2) + 1 = -20x - 9[/tex]
At x = 2
Now we replace x by 2 in each of the functions. So
[tex](u \circ w)(2) = -20(2) + 6 = -40 + 6 = -34[/tex]
[tex](w \circ u)(2) = -20(2) - 9 = -40 - 9 = -49[/tex]
Related Questions
Let c be a positive number. A differential equation of the form dy/dt=ky^1+c where k is a positive constant, is called a doomsday equation because the exponent in the expression ky^1+c is larger than the exponent 1 for natural growth. An especially prolific breed of rabbits has the growth term My^1.01. If 2 such rabbits breed initially and the warren has 16 rabbits after three months, then when is doomsday?
Answers
Answer:
The doomsday is 146 days
Step-by-step explanation:
Given
[tex]\frac{dy}{dt} = ky^{1 +c}[/tex]
First, we calculate the solution that satisfies the initial solution
Multiply both sides by
[tex]\frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dt}{y^{1+c}} * \frac{dy}{dt} = ky^{1 +c} * \frac{dt}{y^{1+c}}[/tex]
[tex]\frac{dy}{y^{1+c}} = k\ dt[/tex]
Take integral of both sides
[tex]\int \frac{dy}{y^{1+c}} = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = \int k\ dt[/tex]
[tex]\int y^{-1-c}\ dy = k\int\ dt[/tex]
Integrate
[tex]\frac{y^{-1-c+1}}{-1-c+1} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
To find c; let t= 0
[tex]-\frac{y_0^{-c}}{c} = k*0+C[/tex]
[tex]-\frac{y_0^{-c}}{c} = C[/tex]
[tex]C =-\frac{y_0^{-c}}{c}[/tex]
Substitute [tex]C =-\frac{y_0^{-c}}{c}[/tex] in [tex]-\frac{y^{-c}}{c} = kt+C[/tex]
[tex]-\frac{y^{-c}}{c} = kt-\frac{y_0^{-c}}{c}[/tex]
Multiply through by -c
[tex]y^{-c} = -ckt+y_0^{-c}[/tex]
Take exponents of [tex]-c^{-1[/tex]
[tex]y^{-c*-c^{-1}} = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-c^{-1}[/tex]
[tex]y = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
i.e.
[tex]y(t) = [-ckt+y_0^{-c}]^{-\frac{1}{c}}[/tex]
Next:
[tex]t= 3[/tex] i.e. 3 months
[tex]y_0 = 2[/tex] --- initial number of breeds
So, we have:
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
-----------------------------------------------------------------------------
We have the growth term to be: [tex]ky^{1.01}[/tex]
This implies that:
[tex]ky^{1.01} = ky^{1+c}[/tex]
By comparison:
[tex]1.01 = 1 + c[/tex]
[tex]c = 1.01 - 1 = 0.01[/tex]
[tex]y(3) = 16[/tex] --- 16 rabbits after 3 months:
-----------------------------------------------------------------------------
[tex]y(3) = [-ck * 3+2^{-c}]^{-\frac{1}{c}}[/tex]
[tex]16 = [-0.01 * 3 * k + 2^{-0.01}]^{\frac{-1}{0.01}}[/tex]
[tex]16 = [-0.03 * k + 2^{-0.01}]^{-100}[/tex]
[tex]16 = [-0.03 k + 0.9931]^{-100}[/tex]
Take -1/100th root of both sides
[tex]16^{-1/100} = -0.03k + 0.9931[/tex]
[tex]0.9727 = -0.03k + 0.9931[/tex]
[tex]0.03k= - 0.9727 + 0.9931[/tex]
[tex]0.03k= 0.0204[/tex]
[tex]k= \frac{0.0204}{0.03}[/tex]
[tex]k= 0.68[/tex]
Recall that:
[tex]-\frac{y^{-c}}{c} = kt+C[/tex]
This implies that:
[tex]\frac{y_0^{-c}}{c} = kT[/tex]
Make T the subject
[tex]T = \frac{y_0^{-c}}{kc}[/tex]
Substitute: [tex]k= 0.68[/tex], [tex]c = 0.01[/tex] and [tex]y_0 = 2[/tex]
[tex]T = \frac{2^{-0.01}}{0.68 * 0.01}[/tex]
[tex]T = \frac{2^{-0.01}}{0.0068}[/tex]
[tex]T = \frac{0.9931}{0.0068}[/tex]
[tex]T = 146.04[/tex]
The doomsday is 146 days
Mariel says that a jewelry box that is 3 inches high, 4 1/2 inches wide, and 5 inches long has a volume of 67 1/2 inches. Katie says that answer is not quite correct. What is the error in Mariel's answer?
Answers
Answer: inside width, length and heights may be smaller
Step-by-step explanation. Walls of box have certain thickness, assume 0.1 inches. Then inner measures would be 2.8 in, 4.3 in and 4.8 in. You need to reduce thickness of wall from both sides.
3. $595 refrigerator; 22% discount.
Show the work
Answers
Answer:
Discount: $130.90
Total cost after discount: $464.10
Step-by-step explanation:
Since I don't know what the actual question is, I will solve for the discount:
595 × 22%
Convert percentage into decimal
595 × 0.22
130.9
Discount is 130.9
Now I'll solve for how much that will take off from the original price:
595 - 130.9
464.1
x
What is the angle of elevation of the sun when a 50-ft
mast casts an 18ft shadow? Round to the nearest
whole number.
Tano
50
Tan 0 =
18
0=
Opposite Leg
Adjacent Leg
Submit
50ft
How do I solve this please it’s the last problem
Answers
Answer:
[tex]\theta \approx 1.23^\circ[/tex]
Step-by-step explanation:
The expression has been given as:
[tex]tan(\theta) = \frac{50}{18}[/tex]
Required: Find [tex]\theta[/tex]
Simplify the fraction
[tex]tan(\theta) = 2.7778[/tex]
Take arc tan of both sides
[tex]\theta = tan^{-1}(2.7778)[/tex]
[tex]\theta \approx 1.23^\circ[/tex]
What is the probability of flipping a coin 85 times and getting tails 30 times or
fewer?
A. 99.8%
B. 33.2%
C. 95.9%
D. 0.4%
Answers
Answer:
C
Step-by-step explanation:
Answer:
0.4
Step-by-step explanation:
Is it a function yes or no
Answers
Answer:
no
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
²³√∛·×÷±≈≠≤≥βα∞∨∧∉∈⇔,⇒≅≡ΔπФω↑↓∵∴↔→←⇵∀⊅⊄⊇⊆⊃⊂∑∫⇆⇄⇅°∠∡⊥∪∩∅¬⊕║∦∝㏑㏒∞
What do all of these symbols stand for?
Answers
Answer:
Mathematical symbols used for different calculations?
What is the recursive formula for this sequence:
1,-1,-3, -5......
Answers
Answer:
d) A[n] = A[n=1] - 2 (Your selected answer is correct)
Step-by-step explanation:
Think of the formula as:
new number = previous number minus 2
The data is shown below:
91, 48, 86, 49, 77, 86, 64, 78
What is the median?
a. 72.37
b. 74
c. 86
Answers
Answer: 72
Step-by-step explanation: Its in the middle
Hello! I was trying to Do 69x24 but it is sadly not giving helpful tips so I was wondering if you can help me step by step?
Answers
Alexa uses the binomial theorem to correctly expand (x + 2)^4. Which is one of the terms in Alexa's
answer?
24x^2
6x^2
16x
2x^4
Answers
Answer:
24x^2
Step-by-step explanation:
When expanded (x+2)^4= x^4+8x^3+24x^2+32x+16
The only term that matches with these is 24x^2
Answer:
24x^2
Step-by-step explanation:
Which answer best describes the shape of this distribution?
uniform
skewed left
bell-shaped
skewed right
An untitled line plot from 35 to 49. The plot displays the following values as dots above the corresponding value on the number line. One dot at 36. One dot at 37. One dot at 38. One dot at 40. Two dots at 41. One dot at 42. Three dots at 43. Four dots at 44. Five dots at 45. Three dots at 46. Two dots at 47. One dot at 48.
Answers
Answer:
huh what am i looking at
Step-by-step explanation:
step-by-step explanation
Answer:
its skewed left if you are in k12
Step-by-step explanation:
HELPPP PLEASE YOU’LL GET 10 POINTS
Answers
Answer:
angle y and angle x
Step-by-step explanation:
Ralph opened up his checking account with $100. On Monday, he withdrew $45 to purchase a pair of jeans. On Wednesday, he deposited a $25 check he received for his birthday from his uncle. On Friday, he used his debit card to buy a $98 football ticket. What is the balance in Ralph's checking account?
Answers
Answer:
The answer is -18
Step-by-step explanation:
He starts off with $100 in his account. He then take so $45 to purchase a pair of jeans, so we have to subtract 45 from 100 and that gives us $55. He now has $55 in his account, he then adds another $25 to his account, so we have to add 25 to 55 and that will give us $80 in his account. Finally on Friday he takes out $98 of his checking account. He takes out more than he has in his checking account so we have to subtract $80 from $98 and we will get $18, but since he takes out more than what he has in his account the answer will be negative and we end up with -18 dollars in his checking account.
Answer:72
Step-by-step explanation:
What is the value of x in the equation 2/3x = 12
Answers
Answer:
x = 8
The value of 'x' is 8
Step-by-step explanation:
2/3(8)=12
2/(24)=12
Good luck!!
2. What is the solution to the inequality
--4x > 132? Show your work
Answers
Answer:
x < -33 ( mark me as the brainliest )
Step-by-step explanation:
1) -4x > 132
2) -4x/4 > 132/-4
3) x < -33
what is the answer to 1\2÷3
Answers
Answer:
0.16666666666
Step-by-step explanation:
1/2 ÷ 3
1/2/3
0.16666666666
Or
1/2 = 0.5
0.5 ÷ 3
0.16666666666
3/2 or 1.5. You have to multiply by the reciprocal.
there are 144 microscopes in boxes at a school. each box has 24 microscopes which equation could be used to find b, the number of boxes of microscopes at this school
A. 24+144= b
B. 144-b= 24
C. B divided by 24= 144
D. 24 x b= 144
Answers
The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.
Answers
Answer:
24.5
Step-by-step explanation:
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, of planted seeds will germinate. A random sample of seeds is chosen. If these seeds are planted according to the instructions, find the probability that of them germinate. Do not round your intermediate computations, and round your answer to three decimal places.
Answers
Complete question:
On the package for a certain brand of spinach seeds there is a guarantee that, if the printed instructions are followed, 63% of planted seeds will germinate. A random sample of 9 seeds is chosen. If these seeds are planted according to the instructions, find the probability that 4 of them germinate.
Answer:
[tex]P(x = 4) = 0.1376[/tex]
Step-by-step explanation:
Given
[tex]n = 9[/tex]
[tex]p = 63\%[/tex] --- proportion that germinates
[tex]p = 0.63[/tex]
Required
P(x = 4)
This question follows a binomial distribution:
[tex]P(x) = ^nC_x*p^x*(1-p)^{n-x[/tex]
When x = 4;
[tex]P(x = 4) = ^9C_4*0.63^4*(1-0.63)^{9-4[/tex]
[tex]P(x = 4) = ^9C_4*0.63^4*(0.37)^5[/tex]
[tex]P(x = 4) = 126*0.63^4*0.37^5[/tex]
[tex]P(x = 4) = 0.13763895392[/tex]
[tex]P(x = 4) = 0.1376[/tex]
Given that triangle ABC has angle ABC = 90 degrees, AB = 6 cm and BC = 9 cm. Calculate the length of AC in cm to 1 decimal place
Answers
Answer:
AC = 6.7
Step-by-step explanation:
If this is a 90 degree triangle which I am assuming it is you would the Pythagorean theorem c^2 = a^2 + b^2 since bc seems long I am using that as the hypotenuse.
9^2 = 6^2 + b^2
81 = 36 + b^2
81-36 = b^2
45 = b^2
6.7 = b
so AC = 6.7
Simplify the following expression completely, where x 20.
x5xy* + 405x’y* - 180x’y4
O xy2 5x + xy? V405x – xy2/80x
0 6xyV5x
-3xy 5x + xy? J405x
O 6xy ſ5x}
Answers
Answer:
Option B is your answer
Step-by-step explanation:
hope it helps
have a great day!!
Answer:
A.) -80X^8 + 40x^7 -5x^6 -3x^2
Its OPTION A
Step-by-step explanation:
please help sarie this is the rest of the questions and i need help
Answers
Well what's the question? I got a buncha graphs and no question!
A rectangle has vertices at P (16,16), Q(16,-16), R(-16,-16) and S(-16,16). The origin is the center of dilation and the rule of a dilation is (x,y)→(1/4x, 1/4y) What is P' of the dilated image, PQ’R’S’?
Answers
Answer:
(4, 4)
Step-by-step explanation:
So you're trying to find what P' is, and P' would be the dilation of P. This means that you apply the rule (x, y) --> (1/4x, 1/4y) with the coordinate point (16, 16). This would be:
(16, 16) --> (1/4 * 16, 1/4 * 16) = (4, 4)
Helpppp!!!!!! I need this nowwwww
Answers
I WILL GIVE BRAINLIEST!! PLEASE HURRY
Use the excerpt below taken from the Preamble of the United States Constitution to answer the following question:
"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."
—Public Domain
What aspect of Enlightenment influence on the early United States government does this excerpt of the U.S. Constitution illustrate? (5 points)
It gives power to the people rather than God, the Church, or the king.
It rejects the concept of social class in the American system.
It promotes the popular concept of the freedom of speech.
It encourages the development of the separation of church and state.
Answers
Answer:
B. It rejects the concept of social class in the American system.
Explanation:
The Enlightenment of the American Colonies was a period in time where the people were encouraged to become their own nation. This period was represented by many speeches and pieces of writing that boasted freedom of speech, equality, freedom of the press, and religious tolerance.
This specific piece of writing focuses on the aspect of all people in the nation of America having protected freedoms and rights to become their own people.
help me plz branniest to whoever is right
Answers
Answer:
x= -7, x=8
Step-by-step explanation:
factoring method..
f (x) = - x² + 12x - 20
= - x² + 10x + 2x - 20
= - x( x - 10 ) + 2( x - 10 )
= ( x - 10 ) ( -x + 2 )
=> x = 10, x = 2
A spinner has 3 equal sections that are purple, green, and blue. What is the probability of not landing on blue?
Answers
Answer:
P(not landing on blue section)=2/3
Step-by-step explanation:
Not landing on blue section = landing on one of the other sections
the remaining sections are 2 each one has a P=1/3
2 × 1/3 = 2/3
Answer:
66%
Step-by-step explanation:
2 divided by 3= 0.666666666 which is then converted to percent (66%)
Anybody can tell me How to solve |8|+|-6|?
Answers
2/6+1/4
Show work please
And no links
Answers
Answer:
7/12
Step-by-step explanation:
1/3+1/4
convert to twelfths
4/12+3/12
7/12
Answer:
7/12
Step-by-step explanation:
2/6 + 1/4
Change the denomintors to be alike (Change the denominators to 12) 4/12 + 3/12
Multipy the top and bottom
Add
Get 7/12
Brainliest?