Use the definitions of expectation and variance.
Expectation[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]
Integrate by parts,
[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]
with
[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]
[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]
(since the integral of the PDF is 1, and this integral is 4 times that)
Variance[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]
Compute the so-called second moment.
[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]
Integrate by parts, with
[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]
[tex]E(X^2) = 8 E(X) = 32[/tex]
and the variance is
[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]
Comparing Fractions Choose the correct symbol to compare the fractions please see attached image
Answer:
>
Step-by-step explanation:
Given: [tex]\frac{1}{2} ? \frac{1}{3}[/tex]
Want: Which fraction is larger?
To identify the size of a fraction, converting it into a fraction is easier
[tex]\frac{1}{2}[/tex] = 0.5
[tex]\frac{1}{3}[/tex] = 0.33
where 0.5 is greater than 0.33
Choices:
< is less than symbol
> is greater than symbol
= is equal to
[tex]\frac{1}{2} > \frac{1}{3}[/tex]
Learn more about the Fractions at https://brainly.com/question/280013
Visual Representation:
Suppose you just purchased a digital music player and put 6 tracks on it. After listening to it you decide you only like 2 songs. With the random feature on the player, each of the 6 songs is played once in random order. Find the probability that among the first 2 songs played
A. You like both of them
B. You like neither of them
C. You like exactly 1
The probability that among the first 2 songs played ;a) 6% , not unusual b) 40% and c) 48.4%
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
We have the following information from the statement:
n = 6, r = 2
a)
P (like both of them) = P (like first song) x P (like second song)
P = 2/6 x 1/5
P = 0.06 = 6%
The probability that among the first 2 songs played and You like both of them is 6%.
b)
P (like neither) = P (not like first song) x P (not like second song)
P = 4/6 x 3/5
P = 0.4 = 40%
c) P (like exactly one of them) = P (first song liked) x P (second song not liked) + P (first song not liked) x P (second song liked)
P = ( 2/6 x 1/5) + (4/6 x 3/5)
P = 0.484 = 48.4%
Learn more about probability here;
https://brainly.com/question/11234923
#SPJ1
Help with this math problem
Answer:
The minimum cost of the X-ray machines is 12,197dollars.
Step-by-step explanation:
First, we check whether it’s a Quadratic Equation or not
The general form of the Quadratic equation [tex]f(x) =[/tex] [tex]ax^{2} + bx + c[/tex]
Let’s compare it with the given equation, we get
a = 1
b = -520
c = 79,79
Hence, it’s a quadratic equation.
Now, we will use the VERTEX FORMULA as we are asked to find the ‘minimum’ unit cost.
X = [tex]\frac{-b}\[2a[/tex] = [tex]\frac{-(-520)}\[2(1)[/tex] = [tex]260[/tex]
So , number of X-ray machines are = 260 (value of x)
To find the minimum unit cost, plug the value of x into the given equation, and we get
[tex]f(260) = (260)^{2} -520(260) + 79,797[/tex]
[tex]=12,197[/tex]
Learn more about quadratic equation here: https://brainly.com/question/23511870
#SPJ10
I need help with how to find x and y
The value of x and y from the given figure are 3 and 36
Similarity theorem of trianglesFrom the given similar triangles, the following expression is true
4/6 = x/54
Cross multiply
6x = 4 *54
x = 4 * 9
x = 36
Similarly
y/6 = 27/54
y/6 = 1/2
x =3
Hence the value of x and y from the given figure are 3 and 36
Learn more on similar triangle here; https://brainly.com/question/14285697
#SPJ1
Which statement about –2h2 – 15h – 7 is true?
One of the factors is (h + 2).
One of the factors is (3h – 2).
One of the factors is (2h + 1).
One of the factors is (h – 7).
Answer:One of the factors of the given expression is (2h + 1).
Step-by-step explanation:
ed
Answer:
C on edge 23
Step-by-step explanation:
because i said so
Rewrite the expression as a fraction.
Answer:
4/15
Step-by-step explanation:
in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.
I don’t understand this question can someone please help
Answer:
the second option listed
(A = 53 degrees)
(a = 13.3)
(c = 16.6)
Step-by-step explanation:
SOH CAH TOA
(sin = opposite / hypotenuse)
(cos = adjacent / hypotenuse)
(tan = opposite / adjacent)
For this question, you are provided an angle (37), and its opposite (10)
so, we can solve for either sin or tan first.
tan = opposite / adjacent
tan 37 = 0.7535540501
0.7535540501 = 10/a [multiply by a]
0.7535540501a = 10 [divide by [0.7535540501]
a = 13.2704482163
rounded to the nearest tenth, a = 13.3
we know that the three angles shown here must add up to 180
so,
90 + 37 + A = 180
127 + A = 180
- 127 - 127
A = 53
--this is enough information to answer, but I will also solve side c to prove my answer
c = hypotenuse
a²+ b²=c²
[13.3]² + [10]² = c²
176.89 + 100 = c²
276.89 = c²
√276.89 = √c²
16.6400120192 = c
c = 16.6 (rounded to the nearest tenth)
**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer
A photographer needs a frame for a 16 x 20 inch picture, such that the total area is 340 in^2. Calculate the width of the frame. Which of the following quadratic equations would be used when solving this?
2x^2 + 36x = 20
2x^2 + 72 = 20
4x^2 + 36x = 20
4x^2 + 72x = 20
How do i find the domain of F and write in interval notation??? I completely confused
Answer:
898
Step-by-step explanation:
898999
Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success. Round your answer to four decimal places. P(X≥14), n=18, p=0.8
The probability is 0.2153.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]^{n}C_x* P^{x}* (1-p)^{n-x}[/tex]
n=18, p=0.8
So,
[tex]^{18}C_{14}* 0.8^{14}* (1-0.8)^{18-14}[/tex]
=0.2153
Hence, the probability is 0.2153.
Learn more about probability here:
https://brainly.com/question/13708171
#SPJ1
Which of the following represents a geometric sequence with a common ratio r = 6?
1, 6, 36, 216, 1,296
3, 18, 24, 144, 864
7, 13, 19, 25, 31
648, 108, 18, 3, 0.5
Answer:
The first sequence is correct being (6)^k
Step-by-step explanation:
To find a ratio divide a term by its previous member such as 36/6 to give you r=6.
Mr. Tan, a manufacturer who produces
more medium-sized shirts than either
large-sized or small-sized T-shirts,
bases his decision on?
O A. Instinct
O B. Mean
O C. Median
O D. Mode
Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.
Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.
The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.
The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.
The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.
Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.
for such more question on Mode
https://brainly.com/question/14532771
#SPJ8
Fill in the blanks find P A And si
The answer will be Rs. 4330.
Step-by-step explanation:
Because if you subtract 340 from 4670, you will get the answer which is 4330.
What are the possible zeros for f(x) equals X to the third power minus 2X to the second power minus 4X +15
The roots of the polynomial are done by using a calculator will be -2.3671, 2.1835 + 1.2527i, and 2.1835 – 1.2527i.
What are the roots of the polynomial?The polynomial is given below.
[tex]\rm f(x) = a_0x^n + a_1 x^{n - 1}+ ....+ a_{n-2}x^2 + a_{n-1}x + a_nx^0[/tex]
The roots of the polynomial are equal to n or less than n.
And if one imaginary root is a + bi, then the other imaginary root will be a – bi.
The roots of the polynomial are done by using a calculator.
x = -2.3671, 2.1835 + 1.2527i, 2.1835 – 1.2527i
More about the roots of the polynomial link is given below.
https://brainly.com/question/1514617
#SPJ1
Ming drove to the lake and back. On the trip there she drove 30 km/h and on the return trip she went 24 km/h. How long did the trip there take if the return trip took five hours?
The trip to the lake took 4 hours.
How long did the trip to the lake take?The first step is to determine the distance of the trip.
Distance = average speed x time
24 km/h x 5 = 120 km
Time = distance / average speed
120 / 30 = 4 hours
To learn more about average speed, please check: https://brainly.com/question/21734785
#SPJ1
Tyrone paid $234.33 for a new watch, after-tax, and the tax rate is 7%. What was the original price of the watch?
the price of the watch plus tax = 100% + 7% = 107%
Divide the total cost by 107%:
234.33 / 1.07 = 219.00
The original price was $219.00
The Super 20 Hotel currently contracts out its cleaning service to Great Maids cleaners who charge $50 a room. They also charge an additional $185 no matter how many rooms they clean. Which equation could be used to determine the cost C of the Great Maids cleaning n rooms?
Answer:
a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from
When eighteen is reduced by two-thirds of a number, the result is 14. Find the number.
The number is
Step-by-step explanation:
ATTACHED IS THE SOLUTION!!!Please help me answer this question genius
(i) The Maclaurin's series is:
1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) Integral of limit o to 1∫ e^sinx is 0
Maclaurin's expansion is as follows:
y(x) = y₀ ₊ x y₁(0) ₊ x²/2! y₂(0) ₊ x³/3! y₃(0) ₊ ........
y = e^sinx
y(0) = e^sin0
y(0) = 1
Differentiate y with respect to x
y₁(x) = e^sinx . cos x
y₁(0) = 1 [i.e y₁ = cosx.y]
y₁(0) = 1
Differentiate y₁ with respect to x
y₂(x) = cosc . y₁ ₋ sinx . y
∴ y₂(0) = 1 ₋ 0 = 1
Differentiate y₂ with respect to x
y₃ = cosx . y₂ ₋ (2 sinx ₊ cosx)y₁
y₃(0) = 1 ₋(0 ₊ 1)1
y₃(0) = 0
Differentiate y₃ with respect to x
y₄ = cosx . y₃ sinx . y₃ ₋ (2sinx ₊ cosx)y₂ ₋ (2cos x ₋ sinx) y₁
y₄(0) = 0 ₋ (3 . 0 ₊ 1)1 ₋ (2 ₋ o) 1
y₄(0) = -3
∴ From maclaurin's equation we get:
e^sinx = 1 ₊ x . 1 ₊ x²/2! . 1 ₊ x³/3! (0) ₊ x⁴/4! (₋3) ₊ ....
=1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
Hence we get the the series expansion as 1 ₊ x ₊ x²/2! . 1 ₋ 3x⁴/4! ₊ ...........
(ii) limit 0 to 1∫e^sinx
integration formula ∫e^x dx = e^x + c
limit 0 to 1 ∫e^sinx = [e^sinx + c ]limit 0 to 1
= e^sin0 ₋ e^sin1
= 1 ₋ 1
= 0
Hence we get the answer as 0
Learn more about "Integration" here-
https://brainly.com/question/22008756
#SPJ10
A study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (the Wall Street Journal, May 5, 2010). Suppose a random sample of 100 teen drivers is taken. What is the probability that the sample proportion is within ± 0.02 of the population proportion?
The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
How to determine the probability?The given parameters are:
Sample size, n = 100Population proportion, p = 82%Start by calculating the mean:
[tex]\mu = np[/tex]
[tex]\mu = 100 * 82\%[/tex]
[tex]\mu = 82[/tex]
Calculate the standard deviation:
[tex]\sigma = \sqrt{\mu(1 - p)[/tex]
[tex]\sigma = \sqrt{82 * (1 - 82\%)[/tex]
[tex]\sigma = 3.84[/tex]
Within ± 0.02 of the population proportion are:
[tex]x_{min} = 82 * (1 - 0.02) = 80.38[/tex]
[tex]x_{max} = 82 * (1 + 0.02) = 83.64[/tex]
Calculate the z-scores at these points using:
[tex]z = \frac{x - \mu}{\sigma}[/tex]
So, we have:
[tex]z_1 = \frac{80.36 - 82}{3.84} = -0.43[/tex]
[tex]z_2 = \frac{83.64 - 82}{3.84} = 0.43[/tex]
The probability is then represented as:
P(x ± 0.02) = P(-0.43 < z < 0.43)
Using the z table of probabilities, we have:
P(x ± 0.02) = 0.3328
Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328
Read more about probability at:
https://brainly.com/question/25870256
#SPJ1
What is the simplified form of StartRoot StartFraction 72 x Superscript 16 Baseline Over 50 x Superscript 36 Baseline EndFraction EndRoot? Assume x ≠ 0.
StartFraction 6 Over 5 x Superscript 10 Baseline EndFraction
StartFraction 6 Over 5 x squared EndFraction
Six-fifths x Superscript 10
Six-fifths x squared
The simplification form of the provided expression is 6/5x¹⁰ option first is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have an expression:
[tex]\rm = \sqrt{\dfrac{72x^{16}}{50x^{36}}}[/tex]
[tex]\rm = \sqrt{\dfrac{72}{50}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm = \sqrt{\dfrac{36\times2}{25\times2}} \sqrt{\dfrac{x^{36}}{x^{16}}}[/tex]
[tex]\rm ={\dfrac{6x^{8}}{5x^{18}}}[/tex]
[tex]\rm ={\dfrac{6}{5x^{10}}}[/tex]
Thus, the simplification form of the provided expression is 6/5x¹⁰ option first is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ1
Answer:
6x3
Step-by-step explanation:
Edge 2023
I walked 280m of the road from the park to the station. This is equivalent to 9/10 of the total distance. How many meters is the total distance from the park to the station?
Answer:
311 1/9 or 311.11 mStep-by-step explanation:
Let the total distance be x.
We have:
9/10 of x is 280 m.Set this as equation and solve for x:
(9/10)x = 280x = 280 ÷ 9/10x = 280 × 10/9x = 2800/9 = 311 1/9 or 311.11 mTotal distance from the park to the station is approximately 311 m.
Let that be d
9/10 of d=2809/10d=280d=280(10/9)d=311.1mA sphere has a radius of 24 centimeters. What is its volume
Answer:
57905.8
Step-by-step explanation:
Use the formula:Plug in:
V = 4/3 * 24³π
= 4/3 * 13824π
= 18432π
= 57905.83579cm³
Rounded to nearest tenth:
57905.8
Answer: 18,432
Step-by-step explanation: ANSWER ON EDMENTUM/PLUTO
Question
Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were
weighed. What is the total weight of food donated?
Provide your answer below:
boz
FEEDBACK
MORE INSTRUCTION
SUBMIT
Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were weighed, the total weight of food donated is 65 ounces.
What is unit?Units are used to measure and express quantities. In the context of the given problem, units are used to indicate the weight of the donated food items.
Pounds (lb) and ounces (oz) are units of weight commonly used in the United States. One pound is equal to 16 ounces.
To add these weights together, we need to make sure they are all in the same units. Let's convert everything to ounces:
- 1 lb 6 oz = 22 oz (since 1 lb = 16 oz, and 6 oz + 16 oz = 22 oz)
- 2 lb 3 oz = 35 oz (since 2 lb = 32 oz, and 3 oz + 32 oz = 35 oz)
- 8 oz = 8 oz
Now we can add the weights:
22 oz + 35 oz + 8 oz = 65 oz
Therefore, the total weight of food donated is 65 ounces.
For more details regarding unit system, visit:
https://brainly.com/question/28579178
#SPJ2
Write the equation for the function graphed below.
Answer:
f(x) = (x + 1)^2 + 2
Step-by-step explanation:
A parabola function has different forms:
standard form: f(x) = ax + bx + c^2
vertex form: f(x) = a (x − h)^2 + k
Our equation that includes a horizontal translation is h
- negative h shifts right
- positive h shifts left
this graph shows a shift to the left by 1 so h = 1
Our equation that includes a vertical translation is k
- negative k shifts down
- positive k shifts up
this graph shows a shift to the up by 2 so k = 2
- a represents a compression / stretch which seems not to be in this graph
combine, f(x) = (x + 1)^2 + 2
Support her statements using scale factors of 5 and 6.
Reflection: Marissa wants to describe the relationship between the scale factor and perimeter of an image and its pre-image and between the scale factor and area of an image and its pre-image. What should she say about the relationship between the scale factor and perimeter of an image and its pre-image? What should she say about the relationship between the scale factor and area of an image and its pre-image? Support her statements using scale factors of 5 and 6.
Answer:
The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).
Step-by-step explanation:
Relationship between the scale factor and perimeter of an image and its pre-image.
Scale factor = k
Pre-image lengths: a, b = perimeter = 2a + 2b
Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.
She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.
What should she say about the relationship between the scale factor and area of an image and its pre-image?
area of the pre-image = ab
are of the image = (ka)(kb) = k^2 (ab)
The area of the image is the area of the preimage times the square of the scale factor.
Support her statements using scale factors of 5 and 6.
Scale factor 5
length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14
length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70
14 * 5 = 70 which shows the prediction
area of the pre-image = 3 * 4 = 12
area of the image = 15 * 20 = 300
12 * (5^2) = 12*25 = 300 which is the value predicted.
Now you can do the same using scale factor 6.
For more explanation, refer the following link:
https://brainly.com/question/4528070
#SPJ10
A number divided by 7
Select one:
a. 7+x
b. 7/x
c. x/7
d. 7x
Answer:
c. x/7
Step-by-step explanation:
seven is dividing something, and X is the placeholder in this equation.
So, since x is being divided by seven, that rules out B., because that's backwards.
A. and D. don't involve division, so they're both incorrect as well.
Thus we are left with C. x/7
Cancel tickets for his church is carnival for a total of 2820 children’s tickets cost three dollars each an adult tickets cost five dollars each the number of children so is 30 more than three times the number of adult tickets sold how many children tickets and how many adult tickets did he sell
Taking into account the definition of a system of linear equations, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.
Amount of children tickets and adult tickets soldIn this case, a system of linear equations must be proposed taking into account that
"x" is the amount of children tickets sold."y" is the amount of adult tickets sold.Galen sold tickets of his church’s carnival for a total of $2,820. Children’s tickets cost $3 each and adult tickets cost $5 each. The number of children’s tickets sold was 30 more than 3 times the number of adult tickets sold.
So, the system of equations to be solved is
[tex]\left \{ {{3x+5y=2820} \atop {x=3y+30}} \right.[/tex]
There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, substituting the second equation in the first you get:
3×(3y+30)+5y=2820
Solving:
3×3y+3×30+5y=2820
9y+90+5y=2820
9y+5y=2820 - 90
14y= 2730
y= 2730÷ 14
y= 195
Remembering that x=3y +30, then:
x= 3×195 + 30
Solving
x=585 +30
x=615
Finally, the number of adult tickets sold is 615 and the number of children's tickets sold is 195.
Learn more about system of equations:
brainly.com/question/14323743
brainly.com/question/1365672
brainly.com/question/20533585
brainly.com/question/20379472
#SPJ1
Line AB and line BC form a right angle at point B with points A (2,5) and B(8,3). what is the equation of line BC?
Answer:
y=3x-21
Step-by-step explanation:
General outlineFind equation for line ABFind equation for perpendicular line BCStep 1. Find equation for line ABGiven points A(2,5) and B(8,3), line AB must contain them.
To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]
[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]
[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]
Since the slope isn't undefined, line AB must cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]
[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]
Substituting values for a known point (point A) on line AB...
[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]
[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]
[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]
Finding a common denominator...
[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]
[tex]\frac{17}{3}=b_{\text{AB}}[/tex]
So, the equation for line AB is [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]
Step 2. Find equation for line BCSince line AB and line BC form a right angle, they are perpendicular. Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other. Stated another way, the slopes multiply to make negative 1.
[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]
[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]
[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]
[tex]m_{\text{BC}} =3[/tex]
Since the slope isn't undefined, line BC must also cross the y-axis somewhere. To find the y-intercept, build and equation in slope-intercept form:
[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]
[tex]y=(3) x+b_{\text{BC}}[/tex]
Substituting values for a known point (point B) on line BC...
[tex](3)=3 * (8)+b_{\text{BC}}[/tex]
[tex]3=24+b_{\text{BC}}[/tex]
[tex](3)-24=(24+b_{\text{BC}})-24[/tex]
[tex]-21=b_{\text{BC}}[/tex]
So, the equation for line BC is [tex]y=3 x -21[/tex]
NEED HELP ASAP !!!!
Which graphs represents the compound inequality x≤ 5 orx≥ 5?
Answer:
b
Step-by-step explanation:
