Answer: y = 4/3x -8
Step-by-step explanation:
(6,0) (0,-8)
0-(-8)/6-0 = 8/6 = 4/3
y intercept is given already
X+ 5
If m(x) =x-1 and n(x) = x-3, which function has the same domain as (mon)(x)?
X+5
O (x)=
11
11
o h(x)=
X-1
11
O (X)=
X-4
11
Oh(x) =
X-3
Answer:
third option
Step-by-step explanation:
m(n(x)) =
[tex] \frac{x - 3 + 5}{x - 3 - 1} = \frac{x + 2}{x - 4} [/tex]
the domain of this is R/(4)
so as the third option
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Option D is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
m(x) = (x + 5)/ (x - 1) and n(x) = x - 3,
Now,
(m o n)(x)
= m (n(x)
= m (x - 3)
= (x - 3 + 5) / (x - 3 - 1)
= (x + 2) / (x - 3)
We can not have x = 3.
So,
The domain can not have x = 3.
From the options,
h(x) = 11 / (x - 3) can not have x = 3.
Thus,
The function that has the same domain as (m o n)(x) is
h(x) = 11 / (x - 3)
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ7
DO THIS FAST PLEASE I WILL GIVE BRAINLY CROWN
Use a model to divide. 5 ÷ 1/2 10 4 2 20
5 ÷ 1/2 => 5 x 2/1 => 10/1 => 10
Answer:
10
Step-by-step explanation:
In the pic, it shows ten half squares.
In a sale, Ali buys a television for $195.80.
The original price was $220.
Calculate the percentage reduction on the original price.
11%
Hope this helps! :)
______________
Answer:
[tex] \frac{195.80}{220} \times 100 \% \\ = 0.89\%[/tex]
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2. (a) What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2
Answer:
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The fracture strength of tempered glass averages 14 (measured in thousands of pounds per square inch) and has standard deviation 2.
This means that [tex]\mu = 14, \sigma = 2[/tex]
Sample of 100:
This means that [tex]n = 100, s = \frac{2}{\sqrt{100}} = 0.2[/tex]
What is the probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2?
This is 1 subtracted by the p-value of Z when X = 14.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{14.2 - 14}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
1 - 0.8413 = 0.1587
0.1587 = 15.87% probability that the average fracture strength of 100 randomly selected pieces of this glass exceeds 14.2.
My sister’s house is 1 2/4 times as high as my house. My house is 5 feet high. How high is my sister’s house?
Answer:
Sister's house is 7.5 feet high
Step-by-step explanation:
Given :
My house = 5 feet
Sisters house = [tex]1\frac{2}{4}[/tex] [tex]times[/tex] [tex]my \ house[/tex]
= [tex]\frac{6}{4} \times 5[/tex]
[tex]=\frac{30}{4}\\\\=\frac{15}{2}\\\\= 7 . 5 \ feet[/tex]
What is the cube root of -1,000p12q3?
O-1004
O - 10pta
O 1004
O 10pta
Answer:
Your options are not clear
Step-by-step explanation:
[tex]\sqrt[3]{-1000 \times p^{12} \times q^3} \\\\(-1 \times 10^3 \times p^{12} \times q^3)^{\frac{1}{3} }\\\\(-1^3)^{\frac{1}{3} }\times 10^{3 \times \frac{1}{3} } \times p^{12 \times \frac{1}{3}} \times q^{3 \times \frac{1}{3}} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (-1)^3 = - 1 \ ] \\\\- 1 \times 10 \times p^4 \times q\\\\-10p^4q[/tex]
. A population of rabbits oscillates 25 above and below an average of 129 during the year, hitting the lowest value in January (t = 0). a. Find an equation for the population, P, in terms of the months since January, t. b. What if the lowest value of the rabbit population occurred in April instead?
Answer:
Because we know that here we have an oscillation, we can model this with a sine or cosine function.
P = A*cos(k*t) + M
where:
k is the frequency
A is the amplitude
M is the midline
We know that at t = 0, we have the lowest population.
We know that the mean is 129, so this is the midline.
We know that the population oscillates 25 above and below this midline,
And we know that for t = 0 we have the lowest population, so:
P = A*cos(k*0) + 129 = 129 - 25
P = A + 129 = 129 - 25
A = -25
So, for now, our equation is
P = -25*cos(k*t) + 129
Because this is a yearly period, we should expect to see the same thing for t = 12 (because there are 12 months in one year).
And remember that the period of a cosine function is 2*pi
Then:
k*12 = 2*pi
k = (2*pi)/12 = pi/6
Finally, the equation is:
P = -25*cos(t*pi/6) + 129
Now we want to find the lowest population was in April instead:
if January is t = 0, then:
February is t = 2
March is t = 3
April is t = 4
Then we would have that the minimum is at t = 4
If we want to still use a cosine equation, we need to use a phase p, such that now our equation is:
P = -25*cos(k*t + p) + 129
Such that:
cos(k*4 + p) = 1
Then:
k*4 + p = 0
p = -k*4
So our equation now is:
P = -25*cos(k*t - 4*k) + 129
And for the periodicity, after 12 months, in t = 4 + 12 = 16, we should have the same population.
Then, also remembering that the period of the cosine function is 2*pi:
k*12 - 4*k = 2*pi
k*8 = 2*pi
k = 2*pi/8 = pi/4
And remember that we got:
p = -4*k = -4*(pi/4) = -pi
Then the equation for the population in this case is:
P = -25*cos( t*pi/4 - pi) + 129
Stevens College plans to have 20 computers for every 100 students. How many computers are needed for 1,500 students?
Answer:
300 computers
Step-by-step explanation:
So I divided 1500 out of a 100 and got 15, then I multiply 15 to 20 and got 300.
(I am a high schooler so I hope this is 3rd grade math because I notice you are a college student and I hope this not some college tricky math, if you get this wrong I am truly sorry)
What is the sum of the series 18 E n=4 (n+1) ^2? 1,239 2,415 2,440 2,469
9514 1404 393
Answer:
(c) 2440
Step-by-step explanation:
The sum of the squares of numbers 1 .. n is ...
s(n) = n(n +1)(2n +1)/6
You want the sum of squares from 5 to 19. We can compute that from ...
s(19) -s(4) = (19(20)(39) -4(5)(9))/6 = (14820 -180)/6 = 2440
Answer:
C. 2440Step-by-step explanation:
hope it helps u too
2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)
Answer:
Step-by-step explanation:
How many numbers lie between the squares of 39 and 40
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
What’s the solution
Answer:
x ≥ 12
Step-by-step explanation:
-3/4x +2 ≤ -7
Subtract 2 from each side
-3/4x +2-2 ≤ -7-2
-3/4x ≤ -9
Multiply each side by -4/3, remembering to flip the inequality
-3/4x * -4/3 ≥ - 9 *(-4/3)
x ≥ 12
Answer:
x>=12
Step-by-step explanation:
-3/4x + 2<=-7
-3/4x <= -7 -2
-3/4x<=-9
cross multiply
-3x<=-36
dividing throughout by -3
x>=12
I am having a lot of difficulty in solving this question, so please help me..
Answer:
216
Step-by-step explanation:
=>log 36 = -2/3
m
=>36=(m)^-2/3
=>(root(-36))^3=m
=>m=(root(36))^3
=>m=6^3
=>m=216
HW HELP ASAP PLZZZZZ
Answer:
last step is (2x + 5)(2x + 1)
Step-by-step explanation:
4x^2 + 12x + 5
4x^2 + (10 + 2)x + 5
4x^2 + 10x + 2x + 5
2x(2x + 5) +1(2x + 5)
(2x + 5)(2x + 1)
Find(g-f)(x)
f(x)=1/x
g(x)=x^2+2x-5
a. 1/x-x^2-2x+5
b.1/x+x^2+2x-5
c.x^2+2x-5-1/x
d.1/x+x^2-5
Answer:
x^2+2x-5 - 1/x
Step-by-step explanation:
f(x)=1/x
g(x)=x^2+2x-5
(g-f)(x) = x^2+2x-5 - 1/x
Answer:
c. x² + 2x - 5 - 1 / x
Step-by-step explanation:
f ( x) = 1 / x.
g ( x) = x² + 2x - 5
so,
( g - f) ( x) = x² + 2x - 5 - 1 / x
If an average-sized man with a parachute jumps from an airplane, he will fall
12.5(0.2t − 1) + 21t feet
in t seconds. How long will it take him to fall 150 feet? (Round your answer to two decimal places.)
Answer:
It will take him 5.85 seconds.
Step-by-step explanation:
12.5 (0.2t - 1) + 21t = 150
Use Distributive Property:
2.5t - 12.5 + 21t = 150
Combine like terms:
23.5t - 12.5 = 150
Subtract 12.5 from both sides:
23.5t = 137.5
Divide both sides by 23.5 to isolate variable t:
5.851063.....
Round to two decimal places (hundredths place):
5.85
HELP ME PLEASE!!!
GIVEN sin0= √23/12
tan0= √23/11
Find cos0
Answer:
[tex]cos \theta = \frac{11}{12}[/tex]
Step-by-step explanation:
[tex]sin \theta = \frac{\sqrt{23}}{12} \ , \ tan \theta = \frac{\sqrt{23}}{11}\\\\tan \theta = \frac{sin \theta }{cos \theta }\\\\ \frac{\sqrt{23}}{11} = \frac{\frac{\sqrt{23}}{12} }{cos \theta}\\\\cos \theta = \frac{\frac{\sqrt{23}}{12} }{\frac{\sqrt{23}}{11} }\\\\cos \theta = \frac{\sqrt{23}}{12 } \times \frac{11}{\sqrt{23}}\\\\cos \theta = \frac{11}{12}[/tex]
PLEASEEEE HELP QUICKKKK
Given:
Line A goes through (0,y) and (-2,0).
Line B goes through (1,2) and (3,10).
To find:
The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.
Solution:
Two linear equation has no solutions if they are parallel line.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We know that the slopes of two parallel lines are the same.
So, the given system of given linear equation has no solutions if
Slope of line A = Slope of line B
[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]
[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]
[tex]\dfrac{y}{2}=4[/tex]
Multiply both sides by 2.
[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]
[tex]y=8[/tex]
Therefore, the required value of y is 8.
In a mathematics each correct answer gains 5 marks - However, 1 mark is deducted for each incorrect answer. Mary answered 30 questions for a total of 78 marks Determine the number of correct and incorrect questions Mary answered.
Answer:
Correct answers= 18
Incorrect answers=30-18= 12 answers
Step-by-step explanation:
total questions=30
correct answers= x
incorrect answers= 30-x
given: 5 marks for each correct answer
therefore, marks for correct answers = 5*x = 5x
Given: 1 mark deducted for every incorrect answer
therefore, marks deducted = 1(30-x) = 30-x
Total marks scored= 78
★ The Difference of Marks scored for Correct Answers and Marks deducted for Incorrect Answers should be equal to 78
5x- (30-x) =78
5x-30+x=78
5x+x=78+30
6x= 108
x=108/6 = 18
Correct answers= 18
Incorrect answers=30-18= 12 answers
Can someone help me simplify it more?
Answer:
8[tex]v^{-3}[/tex]z - [tex]\frac{5}{3}[/tex] vz
Step-by-step explanation:
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.
Clothes Food Toys
43 30 52
24 38 58
42 46 43
35 54 49
28 47 63
31 42 53
17 34 48
31 43 58
Required:
a. Find the values of mean and standard deviation.
b. Is there a difference in the mean attention span Of the children for the various commercials?
Answer:
(a)
Mean
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
Standard deviation
[tex]\sigma_1 = 8.73[/tex]
[tex]\sigma_2 = 7.65[/tex]
[tex]\sigma_3 = 6.04[/tex]
(b) Yes, there is a difference in the mean
Step-by-step explanation:
Solving (a): The mean and standard deviation of each commercial
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
For clothes:
[tex]\bar x_1 = \frac{43+24+42+35+28+31+17+31}{8}[/tex]
[tex]\bar x_1 = \frac{251}{8}[/tex]
[tex]\bar x_1 = 31.375[/tex]
For food:
[tex]\bar x_2 = \frac{30+38+46+54+47+42+34+43}{8}[/tex]
[tex]\bar x_2 = \frac{334}{8}[/tex]
[tex]\bar x_2 = 41.75[/tex]
For toys:
[tex]\bar x_3 = \frac{52+58+43+49+63+53+48+58}{8}[/tex]
[tex]\bar x_3 = \frac{424}{8}[/tex]
[tex]\bar x_3 = 53.00[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For clothes:
[tex]\sigma_1 = \sqrt{\frac{(43 - 31.375)^2 +.............+(31 - 31.375)^2}{8-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{533.875}{7}[/tex]
[tex]\sigma_1 = \sqrt{76.2678571429}[/tex]
[tex]\sigma_1 = 8.73[/tex]
For food:
[tex]\sigma_2 = \sqrt{\frac{(30 - 41.75)^2 +............+(43 - 41.75)^2}{8-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{409.5}{7}}[/tex]
[tex]\sigma_2 = \sqrt{58.5}[/tex]
[tex]\sigma_2 = 7.65[/tex]
For toys:
[tex]\sigma_3 = \sqrt{\frac{(52-53.00)^2+...................+(58-53.00)^2}{8}}[/tex]
[tex]\sigma_3 = \sqrt{\frac{292}{8}}[/tex]
[tex]\sigma_3 = \sqrt{36.5}[/tex]
[tex]\sigma_3 = 6.04[/tex]
Solving (b): Difference in mean in the commercials;
In (a), we have:
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
[tex]\bar x_1 \ne \bar x_2 \ne \bar x_3[/tex]
Hence, there is a difference in their means
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
Figure ABCD is a rectangle find the value of x
Answer:
Espanol la vecsu
Step-by-step explanation:
Answer:
x = 1
Step-by-step explanation:
The diagonals of a rectangle bisect each other , so
DE = EB , that is
7x - 1 = 2x + 4 ( subtract 2x from both sides )
5x - 1 = 4 ( add 1 to both sides )
5x = 5 ( divide both sides by 5 )
x = 1
Which statement correctly describes the end behavior of y = 3x8 + 5x2 +2x - 1
es
A)
The graph rises to the left and falls to the right.
B)
The graph falls to the left and rises to the right.
C)
The graph rises to the left and rises to the right.
D)
The graph falls to the left and falls to the right.
I need help with this last question plz
Answer:
C) The graph rises to the left and rises to the right.
Step-by-step explanation:
The highest expone tis even and it's coefficient is positive
therefor
The graph rises to the left and rises to the right.
62.5% of a number is 25. What is half of the same number.
let the number be b
62.5/100 x b = 25
0.625 x b = 25
b =25/0.625
b=40
half of b= 40/2 = 20
Neglecting air resistance and the weight of the propellant, determine the work done in propelling a five-ton satellite to a height of (a) 100 miles above Earth and (b) 300 miles above Earth.
Answer:
a) the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Step-by-step explanation:
Given the data in the question;
We know that the weight of a body varies inversely as the square of its distance from the center of the earth.
⇒F(x) = c / x²
given that; F(x) = five-ton = 5 tons
we know that the radius of earth is approximately 4000 miles
so we substitute
5 = c / (4000)²
c = 5 × ( 4000 )²
c = 8 × 10⁷
∴ Increment of work is;
Δw = [ ( 8 × 10⁷ ) / x² ] Δx
a) For 100 miles above Earth;
W = ₄₀₀₀∫⁴¹⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4100}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4100}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 6.09756 × 10⁻⁶ ]
= 487.8 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 100 miles above Earth is 487.8 mile-tons
b) For 300 miles above Earth.
W = ₄₀₀₀∫⁴³⁰⁰ [ ( 8 × 10⁷ ) / x² ] Δx
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{x}[/tex] [tex]]^{4300}_{4000[/tex]
= (8 × 10⁷) [tex][[/tex] [tex]-\frac{1}{4300}[/tex] [tex]+\frac{1}{4000}[/tex] [tex]][/tex]
= (8 × 10⁷ ) [ 1.744186 × 10⁻⁵ ]
= 1395.3 mile-tons
Therefore, the work done in propelling a five-ton satellite to a height of 300 miles above Earth is 1395.3 mile-tons
Which statement best describes the areas and perimeters of the figures?
Answer:
The last one!
Step-by-step explanation:
find the equation of the line passing through points A(3,4) and B(1,10)
Answer:
y = -3x + 13
Step-by-step explanation:
First, find the slope:
[tex]m=\frac{y_1-y_2}{x_1-x_2}\\\\m=\frac{4-10}{3-1}\\\\m=\frac{-6}{2}\\\\m=-3[/tex]
Finally, find the equation:
[tex]y-y_1=m(x-x_1)\\\\y-4=-3(x-3)\\\\y-4=-3x+9\\\\y=-3x+13[/tex]
Antiderivative of Acceleration is???
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
Step-by-step explanation:
Answer:
Since acceleration is the derivative of velocity, velocity is the antiderivative of acceleration. If you know the acceleration for all time, and if you know the starting velocity, you can figure out the velocity for all time.
Trong một lớp học có 50 sinh viên. Hỏi có bao nhiêu cách bầu ra một ban cán sự lớp gồm 3 người: 1 lớp trưởng, 1 lớp phó, 1 bí thư và không kiêm nhiệm chức vụ.
Answe
SI Si olla amigo lel just spammin here
Step-by-step explanation:
