The required linear equation that represents the table is y = -x + 4.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
Given that,
The values of x are 0, 1, 2, 3,
And values of y are 4, 3, 2, 1.
The linear equation that represents the values, can be written as,
y = -x + 4
When the values of x are substitute in the above equation, the values of y are,
At x = 0, the value of y = 4
At x = 1, the value of y = 3
At x = 2, the value of y = 3
And at x = 3 the value of y = 1
Hence, the required linear equation is y = -x + 4.
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Let f(x) = cxe−x2 if x ≥ 0 and f(x) = 0 if x < 0.
(a) For what value of c is f a probability density function?
(b) For that value of c, find P(1 < X < 3).
(a) If f(x) is to be a proper density function, then its integral over the given support must evaulate to 1:
[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx = \int_0^\infty cxe^{-x^2}\,\mathrm dx=1[/tex]
For the integral, substitute u = x ² and du = 2x dx. Then as x → 0, u → 0; as x → ∞, u → ∞:
[tex]\displaystyle\frac12\int_0^\infty ce^{-u}\,\mathrm du=\frac c2\left(\lim_{u\to\infty}(-e^{-u})-(-1)\right)=1[/tex]
which reduces to
c / 2 (0 + 1) = 1 → c = 2
(b) Find the probability P(1 < X < 3) by integrating the density function over [1, 3] (I'll omit the steps because it's the same process as in (a)):
[tex]\displaystyle\int_1^3 2xe^{-x^2}\,\mathrm dx = \boxed{\frac{e^8-1}{e^9}} \approx 0.3678[/tex]
Ms.Thompsons english class has 24 students. As a reward for their hard, she would like to give each student 4 pieces of candy since she only has 75 pieces of candy, she will need to buy more.. which of the following equations should she use to find p, the number of pieces she needs to buy (no websites)
Which expression is equivalent to
(5^-2) (5^-1)?
A. -1/125
B. -1/5
C. 1/125
D. 1/5
Answer:
Step-by-step explanation:
C
Please help me thank youuuu!
answer.......pls NOW
Answer:
3. 224 cm3
4. 35 cm3
5. 60 cm3
Step-by-step explanation:
To find the volume you need to multiple the base times the height times the length.
F(x)=8x sqrt(x-x^2) Find the exact maximum
First take note of the domain of f(x) ; the square root term is defined as long as x - x ² ≥ 0, or 0 ≤ x ≤ 1.
Check the value of f(x) at these endpoints:
f (0) = 0
f (1) = 0
Take the derivative of f(x) :
[tex]f(x)=8x\sqrt{x-x^2}=8x\left(x-x^2\right)^{\frac12}[/tex]
[tex]\implies f'(x)=8\left(x-x^2\right)^{\frac12}+4x\left(x-x^2\right)^{-\frac12}(1-2x)=4\left(x-x^2\right)^{-\frac12}\left(2\left(x-x^2)\right)+x(1-2x)\right)=\dfrac{4(3x-4x^2)}{\sqrt{x-x^2}}[/tex]
For x ≠ 0, we can eliminate the √x term in the denominator:
[tex]x\neq0\implies f'(x)=\dfrac{4\sqrt x (3-4x)}{\sqrt{1-x}}[/tex]
f(x) has critical points where f '(x) is zero or undefined. We know about the undefined case, which occurs at the boundary of the domain of f(x). Check where f '(x) = 0 :
√x (3 - 4x) = 0
√x = 0 or 3 - 4x = 0
The first case gives x = 0, which we ignore. The second leaves us with x = 3/4, at which point we get a maximum of max{f(x) } = 3√3 / 2.
Hannah signs on a $148,500 mortgage at a 4.5% annual interest rate for 20 years. This results in a monthly payment is
$938.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her
balance?
First let's find the amount of interest she paid in month 1, then find the amount toward reducing the balance.
Round to the nearest cent.
Answer:
Interest in one month= 556.88
Her balance is reduced by= 381.6
Step-by-step explanation:
3
Delete
12
4
EVAN
8
15
Drag one value into each box to
make each expression equivalent
to 4x + 20.
20
(x + 5)
x + 3x + 5+
x + 40
2
7x -x + 25 - 5
Answer:
the answer to the problem is 4,15,8,3
What is the measure of A?
А [?] degrees
B 87
C 35
Answer:
B 87
Step-by-step explanation:
Answer: 58
explanation: Acellus
Express using algebra A stick l feet long is broken into 2 parts one of which is twice as long as the other. How long is the shorter piece
Answer:
20 is the longer piece, and 9 is the shorter piece
Step-by-step explanation:
9*2=18
18+2=20
20+9
Find the ratio of the areas.
9514 1404 393
Answer:
3 -2√2
Step-by-step explanation:
For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...
small area / large area = (1/(1+√2))^2 = 1/(3+2√2)
small area/large area = 3 -2√2
_____
The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.
What’s the slope ?
Please help I’ll mark u as Brainliest
9514 1404 393
Answer:
5/2 = 2.5
Step-by-step explanation:
The slope is given by ...
m = (y2 -y1)/(x2 -x1)
Using the first two lines in the table, this is ...
m = (10 -5)/(2 -0) = 5/2
The slope of the line is 5/2.
__
As a decimal, that is 2.5.
What is the ratio of the wavelengths of these two notes?
a. 5 to 4
b. 3 to 2
c. 6 to 5
d. 2 to 1
Answer:
d
Step-by-step explanation:
edge 2021
The ratio of the wavelength of the red note and blue note is 2 : 1.
What is wavelength?Wavelength is the distance between two consecutive crest and troughs.
Mathematically, we can write wavelength as -
λ = c/ν
where -
λ : wavelength
ν : frequency
Given are the two notes as shown in the image.
For the red note, the distance between the consecutive crests is twice to that of the distance between the consecutive crests in case of blue note. We can write the ratio of the wavelengths as -
λ(R)/λ(B) = 2/1
Therefore, the ratio of the wavelength of the red note and blue note is 2 : 1.
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A scale drawing of a rectangle is made by using a scale factor of StartFraction 5 over 8 EndFraction. The original and the scale drawing are shown below. A rectangle has a length of 18 inches and width of 12 inches. [Not drawn to scale] Which method can be used to find the dimensions of the original rectangle? 18 minus StartFraction 5 over 8 EndFraction = 17 and StartFraction 3 over 8 EndFraction inches and 12 minus StartFraction 5 over 8 EndFraction = 11 and StartFraction 3 over 8 EndFraction inches StartFraction 5 over 8 EndFraction divided by 18 = StartFraction 5 over 144 EndFraction inches and StartFraction 5 over 8 EndFraction divided by 12 = StartFraction 5 over 96 EndFraction inches 18 times StartFraction 5 over 8 EndFraction = 11 and one-fourth inches and 12 times StartFraction 5 over 8 EndFraction = 7 and one-half inches 18 divided by StartFraction 5 over 8 EndFraction = 28 and four-fifths inches and 12 divided by StartFraction 5 over 8 EndFraction = 19 and one-fifth inches
Answer:
its dddddddddddddddddddddddd
Step-by-step explanation:
The method that can be used to determine the dimensions of the orginal rectangle is multiply the length and the width of the scale drawing of rectangle by 8/5.
What is a scale drawing?
A scale drawing is smalleer image of a bigger diagram.The scale drawing is usually reduced at a constant dimension
The orginal dimensions can be determined by multiplyinf the dimensions of the scale drawing by 8/5
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67 1/2% of what number of people is 135 people
Answer:
go to omnicalculator.com they have all sorts of calculators including one called a percent changer calculator
Step-by-step explanation:
A certain type of legal proceeding has three possible outcomes: in favor of party A, in favor of party B, or not in favor of either party. The outcomes are expected to be 40 percent, 20 percent, and 40 percent, respectively. A random sample of 40 cases is selected from a certain judge to investigate whether the judgeâs outcomes are consistent with the expected outcomes. A chi-square goodness-of-fit test is conducted, and the value of the chi-square test statistic is Ï2=9.19 with a corresponding pâvalue of 0.01. Assuming the conditions for inference were met, which of the following is the correct interpretation of the pâvalue?
a. There is a 1 percent chance that the company's claim is correct.
b. If the null hypothesis is true, there is a 1 percent chance that the company's claim is correct.
c. If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of 9.19.
d. If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of at least 9.19.
e. There is a 1 percent chance of obtaining a chi-square value of at least 9.19.
The basically it tells us the chances of the claim being true
If we assume the null hypothesis is correct.
What is the method of chi-square test?The Chi-Square Test of Independence determines whether there is an association between categorical variables.
We have given that,
The outcomes are expected to be 40 percent, 20 percent, and 40 percent, respectively.
If the null hypothesis is true, there is a 1 percent chance that the company’s claim is correct.
The p-value tells us the likeliness of our data occurring under the null hypothesis.
Therefore ,basically it tells us the chances of the claim being true
If we assume the null hypothesis is correct.
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А Campus athletics is interested in the proportion of registered students living on campus who play basketball recreationally during the semester. They take a random sample of 198 registered students listed as living in campus housing and ask each whether or not they do so. A 95% confidence interval is correctly calculated from this data as (0.12, 0.18). Which of the following is the correct interpretation of this confidence interval ?
a. None of these are correct.
b. We are 95% confident that the proportion of the 198 sampled students that actually play basketball is between 0.12 and 0.18
c. We are 95% confident that, among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18.
d. The sample proportion of on-campus students that play basketball will be between 0.12 and 0.18 in 95% of samples of size 198
Answer:
c. We are 95% confident that, among the population of students that play basketball recreationally, the proportion who live on campus is between 0.12 and 0.18.
Step-by-step explanation:
According to the question, it is mentioned that there is 95% confidence interval and it is calculated (0.12,0.18)
So the correct interpretation is that they are 95% confident that the students who play basketballs the proportion should lies between 0.12 and 0.12
So, the option C is correct
The rest of the options are wrong
2a^2 + 7 + 5b^3
when a = 2 and b= 3
Answer:
150
Step-by-step explanation:
2(2^2)+7+5(3^3)
2(4)+7+5(27)
8 + 7 + 135= 150
Find the greatest common factor of 9n3 and 8n4.
Answer:
9 and 3 GCF is 3
8 and 4 GCF is 4
the GCF of 8,3,4,9 = 1
Step-by-step explanation:
A basket contains 5 purple pencils and 9 brown pencils. If two pencils are picked at random
one after the other without replacement, then what is the probability that both the pencils
are purple?
5/182
10/91
2/91
9/182
please state reasoning as to why it is what ever answer you provide..
Answer:
sorry id.k this im so sorry
Step-by-step explanation:
Answer:
10/91
Step-by-step explanation:
The given spinner has equal sectors. If you spin the spinner, what is the sample space?
A. {3}
B. {1, 2, 3, 4
C. {1, 2, 3, 4, 5)
What is the measure of angle X? Enter your answer as a decimal in the box. (Units are degrees - please only enter numbers in the box.) Round only your final answer to the nearest hundredth.
Answer:
81.20
Step-by-step explanation:
I took the test and got it right
The volume of this rectangular prism is 240 cubic centimeters. What is the surface area?
Please help, anything would be very much appreciated
Answer:
answer is 5.50
Step-by-step explanation:
multiply 2.75 times two because 3 by 5 is half of 9 by 15
Help I need answers now
Answer:
The Answer in Exact Form:
-3/22
In Decimal Form:
-0.136
Step-by-step explanation:
-[tex]\frac{3}{2}[/tex]÷5[tex]\frac{1}{2}[/tex]=-3/22
Which two values of xare roots of the polynomial below?
5x^2-5x+1
Answer:
Step-by-step explanation:
Apply the quadratic formula. The coefficients are {5, -5, 1}. The discriminant is b^2 - 4ac, which here works out to 25 - 4(5)(1), or 5. This positive result tells us that this quadratic has two unequal, real roots. These roots are:
-(-5) ± √5 5 ± √5
x = --------------- = -------------
10 10
Step-by-step explanation:
can't factor so can use quadratic
5 +/- √(25-20)/10
(5+√5)/10
(5-√5)/10
someone please help with this question!! i will give you brainly if it’s right
Answer:
2000 ft
x= 175/ tan5 which is approximately 2000.
Which algebraic expression best represents the following verbal
description: Four more than the price, p?
Answer: I think it is 4+$p
Step-by-step explanation:
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answer:
Let x be the number of 3- point questions and y be the number of 5-points questions.
Step-by-step explanation:
Jayda is watching a movie that lasts 1 hour and 37 minutes. She has watched 52 minutes so far. How many minutes are left in the movie? *
Answer:
45 minutes
Step-by-step explanation:
97-52 = 45