Answer: E(X) = 4
V(X) = [tex]\frac{16}{3}[/tex]
Step-by-step explanation: An uniform distribution is a random variable X restricted to a finite interval [a,b] and has a constant function f(x) over this interval, i.e., the function is of form:
f(x) = [tex]\left \{ {{\frac{1}{b-a} } \atop {0}} \right.[/tex]
The mean or expectation of an unifrom distribution is:
E(X) = [tex]\int\limits^b_a {x.f(x)} \, dx[/tex]
For the density function in interval [0,8], expectation value is:
E(X) = [tex]\int\limits^8_0 {x.(\frac{1}{8-0} )} \, dx[/tex]
E(X) = [tex]\int\limits^8_0 {\frac{x}{8} } \, dx[/tex]
E(X) = [tex]\frac{1}{8}. \int\limits^8_0 {x} \, dx[/tex]
E(X) = [tex]\frac{1}{8}.(\frac{x^{2}}{2} )[/tex]
E(X) = [tex]\frac{1}{8} (\frac{8^{2}}{2} )[/tex]
E(X) = 4
Variance of a probability distribution can be written as:
V(X) = [tex]E(X^{2}) - [E(X)]^{2}[/tex]
For uniform distribution in interval [0,8]:
V(X) = [tex]\int\limits^b_a {x^{2}.\frac{1}{8-0} } \, dx - (\frac{8+0}{2})^{2}[/tex]
V(X) = [tex]\frac{1}{8} \int\limits^8_0 {x^{2}} \, dx - 4^{2}[/tex]
V(X) = [tex]\frac{1}{8} (\frac{x^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{1}{8} (\frac{8^{3}}{3} ) - 16[/tex]
V(X) = [tex]\frac{64}{3}[/tex] - 16
V(X) = [tex]\frac{16}{3}[/tex]
The mean and variance are 4 and 16/3, respectively
A line passes through the points ( – 4, – 2) and ( - 1, - 2). Determine the slope of the line.
Answer: -4/3
Step-by-step explanation:
Formula to find a slope of two given points is
y(sub2) - y(sub1) / x(sub2) - x(sub1)
Plug the values in to get the answer.
-2 - 2 / -1 - (-4)
-4/3
During a timed test, Alexander typed 742words in 14minutes. Assuming Alexander works at this rate for the next hour, which of the following best approximates the number of words he would type in that hour?
Answer:
3,180 words in the hourStep-by-step explanation:
First, you have to figure out how many words he types in one minute. Then, have to multiply by the number of minutes. So,
Number of words per minute:
742 = Total number of words in 14 min
14 = time given
742/14 = 53 words per minute
Number of Words in 1 hour:
53 = words per min
60 = number of minutes
53*60 = 3,180
3,180 words in one hour.Hope my answer helps,
Kavitha
Answer:
3180 words
Step-by-step explanation:
We can use a ratio to solve
742 words x words
--------------- = -----------------
14 minutes 60 minutes
Using cross products
742 * 60 = 14x
Divide each side by 14
742*60/14 = x
3180 words
Solve by factoring or find square root. x^2-3x-4=0
Answer:
x = -1 and x = 4.
Step-by-step explanation:
x^2 - 3x - 4 = 0
(x - 4)(x + 1) = 0
x - 4 = 0
x = 4
x + 1 = 0
x = -1
Check your work...
(4)^2 - 3(4) - 4
= 16 - 12 - 4
= 4 - 4
= 0
(-1)^2 - 3(-1) - 4
= 1 + 3 - 4
= 4 - 4
= 0
So, x = -1 and x = 4.
Hope this helps!
¿Qué escala se utilizó en un mapa, donde la distancia en la vida real es 45 km y en el plano es 5cm?please ayuda
Answer:
La escala utilizada en el mapa es 1 : 900000.
Step-by-step explanation:
El enunciado describe claramente una escala de reducción. El factor de escala se define como sigue:
[tex]n = \frac{s_{plano}}{s_{real}}[/tex]
Donde:
[tex]n[/tex] - Factor de escala, adimensional.
[tex]s_{plano}[/tex] - Distancia en el plano, medida en centímetros.
[tex]s_{real}[/tex] - Distancia real, medida en centímetros.
Si [tex]s_{plano} = 5\,cm[/tex] y [tex]s_{real} = 4500000\,cm[/tex], entonces el factor de escala es:
[tex]n = \frac{5\,cm}{4500000\,cm}[/tex]
[tex]n = \frac{1}{900000}[/tex]
La escala utilizada en el mapa es 1 : 900000.
3
Easton mixed
kg of flour with
kg of sugar.
6
Determine a reasonable estimate for the amount of flour and sugar combined.
Choose 1 answer:
1
Less than
2
kg
B
More than
1
kg but less than 1 kg
2
More than 1 kg
A system of equations is shown below: Equation A: 3c = d − 8 Equation B: c = 4d + 8 Which of the following steps should be performed to eliminate variable d first?
Answer:
multiplying the equation A
Step-by-step explanation:
3c=d-8 ####### *4
+ c=4d + 8
After that you will get the value of c and d.
Answer:
Multiply equation A by -4
Step-by-step explanation:
3c = d - 8
c = 4d + 8
Multiply equation A by -4.
-12c = -4d + 32
c = 4d + 8
Add the equations.
-11c = 40
Variable d is eliminated.
solve for the inequality ᵏ⁄₄ ≥ 6
Answer:
k ≥ 24
Step-by-step explanation:
ᵏ⁄₄ ≥ 6
Multiply each side by 4
ᵏ⁄₄ *4 ≥ 6*4
k ≥ 24
Answer:
k≥24
Step-by-step explanation:
k/4≥6
Use the multiplication property of equality by multiplying both sides by 4 to get
k≥24
If this is wrong or if I did something wrong, please tell me so I can learn the proper way, I am just treating this like a normal problem
Thank you
Graph y less than or equal to 3x
Answer:
See Image Below.
Step-by-step explanation:
The Shaded region is the area of numbers that this equation satisfies.
Answer:
Please see attached image
Step-by-step explanation:
In order to graph the inequality, start from plotting the boundary line defined by the equality;
y = 3 x
You just need two points to accomplish such. so let's use two simple values for x and find what the y-values are:
for x = 0 then y = 3 (0) = 0
for x = 1 then y = 3 (1) = 3
Then use the points (0, 0) and (1, 3) to plot the boundary line.
After this, grab any point on the plane either clearly above the boundary line, or clearly below it and check if the inequality satisfies. For example, you can pick the point (3, 0) which is on the x line, 3 units to the right of the origin, and clearly below the boundary line we just plot.
When you use it in the inequality, you get:
(0) [tex]\leq[/tex] 3 (3)
0 [tex]\leq[/tex] 9
which is a true statement, therefore, the points below the boundary lie are also solutions of the inequality.
Then the solution consists of all the points in the boundary line we just plotted (and indicated by drawing a solid line), plus all the points below the line, as depicted in the attached image.
Tensile strength tests were performed on two different grades of aluminum spars used in manufacturing the wing of a commercial transport aircraft. From past experience with the spar manufacturing process and the testing procedure, the standard deviations of tensile strengths are assumed to be known. The data obtained are as follows:
n_1 = 10
x_1 = 87.6
σ_1 = 1
n_2 = 12
x^2 = 74.5
σ_2 = 1.5.
Required:
If μ _1 and μ _2 denote the true mean tensile strengths for the two grades of spars. Construct a 90 percentage confidence interval on the difference in mean strength.
Answer:
(12.141, 14.059)
Step-by-step explanation:
Explanation is provided in the attached document.
A researcher predicts that the proportion of people over 65 years of age in a certain city is 11%. To test this, a sample of 1000 people is taken. Of this sample population, 126 people are over 65 years of age.
The following is the setup for this hypothesis test:
H0:p=0.11
Ha:p≠0.11
The p-value was determined to be 0.106.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select all that apply:
a. Reject the H0.
b. Fail to reject the H0.
c. There is NOT sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%.
d. There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%.
Answer:
Option b and d
Step-by-step explanation:
With the following data,
H0:p=0.11
Ha:p≠0.11
The p-value was determined to be 0.106 and significance level of 0.05.
Since the p value (0.106) is great than 0.05, then we will fail to reject the null hypothesis and conclude that There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%
Raven has a bag of 33 red and black marbles. The number of red marbles is 6 more than double the number of black marbles. Let r represent the number of red marbles and b represent the number of black marbles. Which statements about the marbles are true? Check all that apply. The equation r + b = 33 represents the total number of marbles. The equation r = 2 b + 6 can be used to find the number of red marbles. The equation r = 2 b + 6 represents the total number of marbles. The equation r + b = 33 can be used to find the number of red marbles. There are 9 red marbles in the bag. There are 9 black marbles in the bag. There are 24 black marbles in the bag. There are 24 red marbles in the bag.
Hey there! I'm happy to help!
If the number of red marbles is 6 more than double the number of black marbles, we can create this equation, with r representing the red marbles and b representing the black marbles.
r=2b+6
We also know that r+b=33, and if we know that r is equal to 2b+6, we can just replace r with that and then solve for b.
2b+6+b=33
We combine like terms.
3b+6=33
We subtract six from both sides.
3b=27
We divide both sides by 3.
b=9
Now we just subtract 9 from 33 to see how many red ones there are.
33-9=24
So, there are 24 red marbles and 9 black marbles.
Now, let's see which of these options are correct.
The equation r+b=33 represents the total number of marbles.
This is true because r plus b is equal to the total, which is 33.
The equation r=2b+6 can be used to find the number of red marbles.
This is true because it we used this r-value to find how many black marbles there were.
The equation r=2b+6 represents the total number of marbles.
This is false because it does not have the total number, which is 33.
The equation r=b=33 can be used to find the number of red marbles.
This is true because we plugged in the r-value to solve for b with this equation.
There are 9 red marbles in the bag.
This is false. There are 24 red marbles.
There are 9 black marbles in the bag.
This is true.
There are 24 black marbles in the bag.
This is false. There are 9 black marbles.
There are 24 red marbles in the bag.
This is true.
Have a wonderful day! :D
Answer:
1,2,4,6,8
Step-by-step explanation:
A certain forest covers an area of 2100 km². Suppose that each year this area decreases by 3.5%. What will the area be after 5 years
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.
At the beginning the area is 2100
After one year the area will be
2100*(1-3.5%)=2100*0.965
After n years the area will be
[tex]2100\cdot0.965^n[/tex]
So after 5 years the area will be
[tex]2100\cdot0.965^5=1757.34027...[/tex]
So rounded to the nearest square kilometer is 1757
Hope this helps
Answer: 1757 km²
Step-by-step explanation:
Because 3.5% = 0.035, first do 1-.035 to get .965. Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.
NEED URGENT HELP ON 5 QUESTIONS SIMILAR TO THIS!!!!! WILL GIBE BRAINLIEST AND 5 STARS IF CORRECT QUICKLY! - 50 POINT - also, no wrong answers just for the points please.
Answer:
As X → - ∞ , y → ∞ and as x→ ∞ , y → ∞
option c is the correct option.Step-by-step explanation:
let f(x) = y = 3x² - 5x + 2
y = 3x² - 5x + 2
= x ( 3x - 5 ) + 2
y = ∞ ( 3 ( ∞ - 5 ) ) + 2
= ∞ (∞ ) + 2
y = ∞
y → ∞ as x → ∞
Now,
as x → - ∞
y = x ( 3x - 5 ) + 2
= ∞ ( 3 ( - ∞ ) - 5 ) + 2
= - ∞ ( - ∞ ) + 2
∞² + 2 = ∞
Hence , Option C is the correct answer.
Answer:
Mathematically you can use the following V = ⁴⁄₃πr³
π = pi
r = radius
To do this you would need a set of scales, a jug, some water, a pen, a ruler and some paper.
ωα√
9 less than twice a number is 13. What is the number?
Answer:
11
Step-by-step explanation:
Answer:
x = 11.
Step-by-step explanation:
9 less than twice a number is the same thing as twice a number minus 9. Let's say that the number is x.
2x - 9 = 13
2x = 22
x = 11
Hope this helps!
Suppose you are climbing a hill whose shape is given by the equation z = 1600 − 0.005x2 − 0.01y2, where x, y, and z are measured in meters, and you are standing at a point with coordinates (120, 80, 1464). The positive x-axis points east and the positive y-axis points north. (a) If you walk due south, will you start to ascend or descend?
Answer:
you will start to ascend at the rate of 1.6
Step-by-step explanation:
Walking south, it's the negative part of a coordinate, so the unit vector at this point is; u = (0,-1)
We are told that the equation z = 1600 − 0.005x² − 0.01y²
Therefore, we have;
∇z = ((δ/δx)i + (δ/δx)j)(1600 − 0.005x² − 0.01y²)
This gives;
∇z = -0.005(2x)i - 0.01(2y)j
∇z = <-0.01x - 0.02y>
coordinates are (120, 80, 1464).
Thus;
∇z(120, 80, 1464) = <-0.01(120), - 0.02(80)> = <-1.20, -1.60>
D_uf = <-1.20, -1.60> × <0, - 1>
D_uf = 0 + 1.6
D_uf = 1.6
So, you will start to ascend at the rate of 1.6
If the sample size is nequals9, what is the standard deviation of the population from which the sample was drawn?
Answer:
13.33
Step-by-step explanation:
As in the attached diagram, we can see that the points belong to [tex]\mu\pm \sigma[/tex] interval
Data provided in the question as per the details below:
[tex]\mu_{\bar x}[/tex] = 440
[tex]\mu_{\bar x} + \sigma_{\bar x}[/tex] = 480
So,
[tex]\sigma_{\bar x}[/tex] = 480 - 440
= 40
Now the standard deviation of the population is
[tex]V(\bar{x}) = \frac{\sigma}{\sqrt n} \\\\ = \frac{40}{\sqrt 9}[/tex]
= 13.33
Hence, the standard deviation of the population for which the sample is drawn is 13.33
Given the graph of the circle find the equation
Answer:
[tex](x+4)^2+(y-4)^2=9[/tex]
Step-by-step explanation:
From the graph, we need to identify two things: the center of the circle and the radius of the circle.
From this graph, we find that the center of the circle is at (-4,4) and the radius of the circle is 3.
Recall that the format for the equation of a circle is [tex](x-x_1)^2+(y-y_1)^2=r^2[/tex]
Now, we can put our know information into this equation and simplify to get our answer
[tex](x-(-4))^2+(y-4)^2=3^2\\\\(x+4)^2+(y-4)^2=9[/tex]
what is improper sampling in statistical analysis and how can i use it in day-to-day life
Answer:
Statistical concepts are used in quality testing. Companies make many products on a daily basis and every company should make sure that they sold the best quality items.
Step-by-step explanation:
pls keep brainly questions only school related thank you!
please help me, i will give you brainliest
Answer:
3rd
Step-by-step explanation:
i got it right on khan academy
solve for x in the diagram below
Answer:
45
Step-by-step explanation:
Both angles (2x+45) and x together form a straight angle which measures 180 degrees.
Together should make you think of adding the angle measurements.
So we have that (2x+45)+x should be 180 degrees.
The equation we want to solve is:
(2x+45)+x=180
2x+45+x=180
(2x+x)+45=180
3x+45=180
3x=180-45
3x=135
x=135/3
x=45
Let's confirm that x is 45.
(2x+45) with x=45:
(2*45+45)
(3*45)
135
So (2x+45)+x at x=45 gives us:
135+45
180
Answer has been confirmed.
Answer:
[tex]\boxed{x = 45}[/tex]
Step-by-step explanation:
=> [tex]x+2x+45 = 180[/tex] (Angles on a straight line add up to 180 degrees)
=> [tex]3x+45 = 180[/tex]
Subtracting 45 to both sides
=> 3x = 180-45
=> 3x = 135
Dividing both sides by 3
=> x = 45
Chapter Reference
b
A board 65 inches long is sawed into two pieces, so that one piece is 7 inches shorter than twice the length of the other piece ? Find the length of the two pieces .
Step-by-step explanation:
It is given that,
Total length of a board is 65 inches
It is sawed into two pieces such that one piece is 7 inches shorter than twice the length of the other piece.
Let x is the length of other piece and y is the length of first piece such that,
y = 2x-7 ....(1)
Also,
x+y = 65 .....(2)
Put the value of y from equation (1) to equation (2) such that,
x+2x-7 = 65
3x=65+7
3x=72
x = 24 inches
Put the value of x in equation (1)
y = 2(24)-7
y = 41 inches
So, the length of first piece is 41 inches while the length of other piece is 24 inches.
What percentage of babies born in the United States are classified as having a low birthweight (<2500g)? explain how you got your answer?
Answer:
2.28% of babies born in the United States having a low birth weight.
Step-by-step explanation:
The complete question is: In the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g. What percent of babies born in the United States are classified as having a low birth weight (< 2,500 g)? Explain how you got your answer.
We are given that in the United States, birth weights of newborn babies are approximately normally distributed with a mean of μ = 3,500 g and a standard deviation of σ = 500 g.
Let X = birth weights of newborn babies
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 3,500 g
[tex]\sigma[/tex] = standard deviation = 500 g
So, X ~ N([tex]\mu=3500, \sigma^{2} = 500[/tex])
Now, the percent of babies born in the United States having a low birth weight is given by = P(X < 2500 mg)
P(X < 2500 mg) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{2500-3500}{500}[/tex] ) = P(Z < -2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275 or 2.28%
The above probability is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
Answer:
The z-score for 2,500 is -2. According to the empirical rule, 95% of babies have a birth weight of between 2,500 g and 4,500 g. 5% of babies have a birth weight of less than 2,500 g or greater than 4,500 g. Normal distributions are symmetric, so 2.5% of babies weigh less than 2,500 g.
Step-by-step explanation:
did the assignment on edge:)
please help!! shirley is drawing triangle that have the same area
Answer:
12 and 7
Step-by-step explanation:
The area of the first triangle is
A = 1/2 bh
A = 1/2 ( 14*6)
A = 42
The area of the second triangle must equal 42
Varying inversely means as the height increases, the base must decrease at the same rate
Lets try 12 and 7
A = 1/2 (12*7)
A = 42
The height of the new triangle increased and the base decreased
Answer:
[tex]\boxed{12 \: \mathrm{and} \: 7}[/tex]
Step-by-step explanation:
Solve for the area of first triangle.
[tex]\frac{bh}{2}[/tex]
[tex]b=base\\h=height[/tex]
[tex]\frac{14 \times 6}{2}[/tex]
[tex]\frac{84}{2} =42[/tex]
The area of second triangle is same as the first triangle.
The area of second triangle is 42 units².
The base varies inversely with the height.
[tex]b \propto \frac{1}{h}[/tex]
As the value of b increases, the value of h decreases.
[tex]\frac{12 \times 7}{2}=42[/tex]
The answer is b = 12 and h = 7.
A coin is tossed and an eight-sided die numbered 1 through 8 is rolled. Find the probability of tossing a tail and then rolling a number greater than 3. The probability of tossing a tail and then rolling a number greater than 3 is
Answer:
5/16
Step-by-step explanation:
P(tails) = 1/2
P(>3) = 5/8
P(tails AND >3) = 1/2 × 5/8 = 5/16
Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
The answer is below
Step-by-step explanation:
Twenty-five blood samples were selected by taking every seventh blood sample from racks holding 187 blood samples from the morning draw at a medical center. The white blood count (WBC) was measured using a Coulter Counter Model S. The mean WBC was 8.636 with a standard deviation of 3.9265. (a) Construct a 90% confidence interval for the true mean using the FPCF. (Round your answers to 4 decimal places.) The 90% confidence interval is from to
Answer:
Given:
Mean (μ) = 8.636, standard deviation (σ) = 3.9265, Confidence (C) = 90% = 0.9, sample size (n) = 25
α = 1 - C = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05
From the normal distribution table, The z score of α/2 (0.05) corresponds to the z score of 0.45 (0.5 - 0.05) which is 1.645
The margin of error (E) is given by:
[tex]E=z_{\frac{\alpha}{2} }*\frac{\sigma}{\sqrt{n} }\\ \\E=1.645*\frac{3.9265}{\sqrt{25} }=1.2918[/tex]
The confidence interval = μ ± E = 8.636 ± 1.2918 = (7.3442, 9.9278)
The 90% confidence interval is from 7.3442 to 9.9278
A subcommittee is randomly selected from a committee of eight men and seven women. What is the probability that all three people on the subcommittee are men
Answer:
The probability that all three people on the subcommittee are men
= 20%
Step-by-step explanation:
Number of members in the committee = 15
= 8 men + 7 women
The probability of selecting a man in the committee
= 8/15
= 53%
The probability of selecting three men from eight men
= 3/8
= 37.5%
The probability that all three people on the subcommittee are men
= probability of selecting a man multiplied by the probability of selecting three men from eight men
= 53% x 37.5%
= 19.875%
= 20% approx.
This is the same as:
The probability of selecting 3 men from the 15 member-committee
= 3/15
= 20%
What is the equation of the line that passes through the point (3,6) and has a slope of 4/3
Answer:
y = 4/3x+2
Step-by-step explanation:
We can use the slope intercept form of the equation
y = mx+b
Where m is the slope and b is the y intercept
y= 4/3 x +b
Substitute the point into the equation
6 = 4/3(3) +b
6 = 4 +b
Subtract 4 from each side
2 = b
y = 4/3x+2
A special tool manufacturer has 50 customer orders to fulfill. Each order requires one special part that is purchased from a supplier. However, typically there are 2% defective parts. The components can be assumed to be independent. If the manufacturer stocks 52 parts, what is the probability that all orders can be filled without reordering parts
Answer:
0.65463
Step-by-step explanation:
From the given question:
It is stated that 2% of the parts are defective (D) out of 50 parts
Therefore the probability of the defectives;
i.e p(defectives) = [tex]\dfrac{N(D)}{N(S)}[/tex]
p(defectives) = [tex]\dfrac{2}{50}[/tex]
p(defectives) = 0.04
The probability of the failure is the P(Non-defectives)
p(Non-defectives) = 1 - P(defectives)
p(Non-defectives) = 1 - 0.04
p(Non-defectives) = 0.96
Also , Let Y be the number of non -defective out of the 52 stock parts.
and we need Y ≥ 50
P( Y ≥ 50) , n = 52 , p = 0.96
P( Y ≥ 50) = P(50 ≤ Y ≤ 52) = P(Y = 50, 51, 52)
= P(Y = 50) + P(Y =51) + P(Y=52) (disjoint events)
P(Y = 50) = [tex](^{52}_{50}) ( 0.96)^{50}(1-0.96)^2[/tex]
[tex]P(Y = 50) = 1326 (0.96)^{50}(0.04)^2[/tex]
P(Y = 50) = 0.27557
P(Y = 51) =[tex](^{52}_{51}) ( 0.96)^{51}(1-0.96)^1[/tex]
[tex]P(Y = 51) = 52(0.96)^{51}(0.04)^1[/tex]
P(Y = 51) = 0.25936
(Y = 52) =[tex](^{52}_{52}) ( 0.96)^{52}(1-0.96)^0[/tex]
[tex]P(Y = 52) = 1*(0.96)^{52}(0.04)^0[/tex]
P(Y = 52) = 0.1197
∴
P(Y = 50) + P(Y =51) + P(Y=52) = 0.27557 + 0.25936 + 0.1197
P(Y = 50) + P(Y =51) + P(Y=52) = 0.65463
Select a committee of 3 people from your staff of 9. How many different ways can this be accomplished when one person will be the lead, one will be the record keeper, and one will be the researcher
Answer:
504 ways.
Step-by-step explanation:
In this case, order matters. If Amy were lead, Bob were record keeper, and Charles were researcher, that would be different than if Bob were lead, Charles were record keeper, and Amy were researcher. So, we will be using a permutation formula to compute.
The formula is n! / (n - k)!, where n is the total number of people (9), and k is the number you are selecting (3).
9! / (9 - 3)! = 9! / 6! = (9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (6 * 5 * 4 * 3 * 2 * 1) = 9 * 8 * 7 = 72 * 7 = 504 ways.
Hope this helps!
Find the measure of each unknown angle
Answer:
1. 55 degrees, 2. 316 degrees
Step-by-step explanation:
When it shows interior angles on a triangle it adds up to 180 degrees
When it shows exterior angles on a triangle it adds up to 360 degrees
1. ? = 55 degrees
85 + 40 = 125
180 - 125 = 55
2. ? = 316 degrees
Inside of triangle:
14 + 30 = 44
180 - 44 = 136 degrees
Exterior of triangle:
360 - 14 = 346 degrees
360 - 30 = 330 degrees
360 - 44 = 316 degrees