Answer:
a) 1.92
b) 3.25
c) 1.5
d) -5.23
Step-by-step explanation:
We are given the following in the question:
4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3
a) mean of score change
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{23}{12} = 1.92[/tex]
b) standard deviation for this population
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
Sum of squares of differences = 126.92
[tex]\sigma = \sqrt{\frac{126.92}{12}} = 3.25[/tex]
c) median change score
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
Sorted data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7
Median =
[tex]\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5[/tex]
d) change score that is 2.2 standard deviations below the mean.
[tex]x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23[/tex]
Rectangle N has an area of 5 square units. James drew a scaled version of Rectangle N and labeled it P. What scale factor did James use to go from Rectangle N to Rectangle P
Answer:3
Step-by-step explanation:
Answer:
3
Step-by-step explanation:
khan acadamy hope this helps
What is the equation of the circle with center (1, −1) that passes through the point (5, 7)?
A painting is drawn on a cardboard 22cm long and 12cm wide such that there is a margin of 2.5 meter cm along each side. Find the total are of the margin
Answer:
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Step-by-step explanation:
We have been given that a painting is drawn on a cardboard 22 cm long and 12 cm wide such that there is a margin of 2.5 meter cm along each side. We are asked to find the area of the margin.
The total area of the margin would be equal to area of whole cardboard minus area of painting.
[tex]\text{Area of whole cardboard}=22\text{ cm}\times 12\text{ cm}[/tex]
[tex]\text{Area of whole cardboard}=264\text{ cm}^2[/tex]
Since there is a margin of 2.5 meter cm along each side, so sides of painting would be 2,5 cm smaller on four sides. The sides painting would be [tex]22-5=17[/tex] and [tex]12-5=7[/tex].
[tex]\text{Area of painting}=17\text{ cm}\times 7\text{ cm}[/tex]
[tex]\text{Area of painting}=119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=264\text{ cm}^2-119\text{ cm}^2[/tex]
[tex]\text{Area of margin}=145\text{ cm}^2[/tex]
Therefore, the total area of the margin is 145 squared cm.
Half of Frank's weight added to Gary's weight equals 234. Half of Gary's weight added to Frank's weight is equal to 222 pounds. How much does Gary weigh?
Answer:
164 pounds
Step-by-step explanation:
Please see attached picture for full solution.
The idea in Exercise 3.51 generalizes to give a new formula for the expected value of any nonnegative integer-valued random variable. Show that if the random variable X takes only nonnegative integers as its values then E(X) = X[infinity] k=1 P(X ≥ k). This holds even when E(X) = [infinity], in which case the sum on the right-hand side is infinite. Hint. Write P(X ≥ k) as P[infinity] i=k P(X = i) in the sum, and then switch the order of the two summations.
Final answer:
The question asks to demonstrate that for a nonnegative integer-valued random variable X, the expected value E(X) equals the summation over all k of the probability P(X ≥ k). This is shown by expressing P(X ≥ k) as an infinite sum, switching the order of summation, and counting each probability P(X = i) exactly i times.
Explanation:
The student's question pertains to the calculation of the expected value (E(X)) of a nonnegative integer-valued random variable. Specifically, the question asks to show that for such a random variable X, the expected value can be expressed as E(X) = ∑₋∞ k=1 P(X ≥ k). To demonstrate this, we begin with the definition of expected value:
E(X) = μ = ∑ xP(x).
Next, we unpack P(X ≥ k) by writing it as an infinite sum of probabilities for all integers i starting from k:
P(X ≥ k) = ∑₋∞ i=k P(X = i).
To find the expected value, we consider the sum of all such probabilities over all k:
∑₋∞ k=1 P(X ≥ k) = ∑₋∞ k=1 ∑₋∞ i=k P(X = i).
We then switch the order of summation, so that we first sum over all possible values of i and then for each i, we sum over the corresponding k that contributes to P(X = i):
E(X) = ∑₋∞ i=1 P(X = i) ∑₉ i k=1.
By doing this, we count each P(X = i) exactly i times, which leads us to the initial definition of expected value, thus proving the given formula.
Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses but cannot work more than 30 hours per week in order to attend classes. Write a system of inequalities that models this situation where p represents the hours he works at the pizzeria and b represents the hours he works at the bookstore.
Answer: The system of inequalities that models this situation are
p + b ≤ 30
12.5p + 9.5b ≥ 300
Step-by-step explanation:
Let p represent the number of hours he works at the pizzeria.
Let b represent the number of hours he works at the bookstore.
He cannot work more than 30 hours per week in order to attend classes. This means that
p + b ≤ 30
Marcus is working at a local pizzeria where he makes $12.50 per hour and is also working at the university bookstore where he makes $9.50 per hour. He must make at least $300 per week to cover his expenses. This means that
12.5p + 9.5b ≥ 300
You are dealt two cards successively without replacement from a standard deck of 52 playing cards. Find the probability that the first card is a two and the second card is a ten. Round your answer to three decimal places. A. 0.250 B. 0.994 C. 0.500 D. 0.006 Click to select your answer.
Answer:
(D) 0.006
Step-by-step explanation:
Total number of cards :52
Please note that, all cards have a the possibility of appearing 4 times.
Hence total possible number of a '2' is 4 cards and so it is also for a '10'
Having this Understanding, let's solve the question properly.
The probability that the FIRST CARD is 2 = 4/52
Probability that the second card without replacement is a 10 = 4 / 51
P( 1st two and 2nd four)
4/52 * 4/51 = 4/663
= 0.0060332
Rounding to 3 decimal places = 0.006
HRLP HELP HELP!!!!! nearest foot
The horizontal distance the plane has covered is 3940 feet
Explanation:
The plane makes an angle 10° with the ground when it took off from the field.
We need to find the horizontal distance the plane when it has flown 4000 feet.
The length of the hypotenuse is 4000 feet.
Let the horizontal distance be x.
We shall find the value of x using the cosine formula.
The formula is given by
[tex]cos \theta=\frac{adj}{hyp}[/tex]
Substituting the values, we have,
[tex]cos \ 10^{\circ}=\frac{x}{4000}[/tex]
Substituting the value for cos 10°, we get,
[tex]0.985=\frac{x}{4000}[/tex]
Multiplying both sides of the equation by 4000, we get,
[tex]0.985\times 4000=x[/tex]
Simplifying, we get,
[tex]3940=x[/tex]
Thus, the horizontal distance the plane has covered is 3940 feet
Find the derivative of f(x) = 5 divided by x at x = -1. (1 point)
Answer:
-5
Step-by-step explanation:
The power rule can be used.
f(x) = 5x^-1
f'(x) = 5(-1)x^(-1-1)
f'(x) = -5x^-2
Then ...
f'(-1) = -5(-1)^-2
f'(-1) = -5
_____
The attached graph shows the value of the derivative at x=-1, along with a tangent line having that slope at the point (-1, f(-1)).
An election with 8 candidates has a 2-stage voting process. In the first stage, voters choose 1 candidate from all 8 names on the ballot. The 3 candidates who receive the most votes in the first round will appear on the second ballot. Due to time constraints, a print shop must prepare ballots for the second ballot in advance of the first-stage results.
How many different ballots must the shop prepare?
Answer:
56
Step-by-step explanation:
8C3 = 56
What value of x satisfies the equation x + 3 = -(x + 1)? a. x = 8
b.x = 8/3
c.x=-8/3
d.x=-8
The solution to the equation x + 3 = -(x + 1) is x = -2, which is not listed among the provided options. There may be an error in the question or provided options.
Explanation:To find the value of x that satisfies the equation x + 3 = -(x + 1), we need to solve for x.
First, expand the right side of the equation: x + 3 = -x - 1. Then, add x to both sides of the equation to get 2x + 3 = -1. Finally, subtract 3 from both sides to obtain 2x = -4. Dividing both sides by 2 yields x = -2.
Upon examining the options provided, none of them match our solution. Therefore, there must be a mistake in the provided options or in the question as posed, because our correct solution is x = -2. This means the correct answer is not listed among the options a. x = 8, b. x = 8/3, c. x = -8/3, or d. x = -8.
The voters of the city passed an ordinance to increase their sales tax by ¼ percent. The proceeds of the sales tax are to be used for culture and recreation. In the governmental activities journal, how would the ¼ percent sales tax revenue be recorded?
Answer:
General Revenue Sales Tax
Step-by-step explanation:
The ¼ percent would be recorded as general revenue sales tax in government activities journal.
This is because the revenue from the tax are categorised as the revenues generated from payrolls (which are imposed on employers), income and profits taxes, social security contributions, taxes levied on goods and services.
Options:
Program Revenue-Culture and Recreation-Sales Tax.
Program Revenue-Culture and Recreation-Operating Grants and Contributions.
General Revenue-Sales Tax.
General Revenue-Culture and Recreation-Sales Tax.
Answer:
General Revenue - Sales Tax
Step-by-step explanation:
General revenue is the income that is generated by the state which may be used to serve any administrative purpose by the state, and tax revenue is the income that is generated by the state through taxation.
Since the sales tax is a way of generating income by the state, it should be recorded as sales tax under general revenue.
Use the value of the linear correlation coefficient r to find the coefficient of determination and the percentage ofthe total variation that can be explained by the linear relationship between the two variables. r = 0.885 (x = weight of male, y = waist size of male)
Answer:
Step-by-step explanation:
The coefficient of determination = [tex]r^{2}[/tex] = [tex]0.885^{2}[/tex] = 0.7832
It means about 78% variation in waist size of males can be explained by their weight and about 23% can not be explained.
On a coordinate plane, a curved line crosses the y-axis at (0, 1), crosses the x-axis at (.25, 0), turns at point (2, negative 3), and crosses the x-axis (3.75, 0).
What is the range of the function on the graph?
all the real numbers
all the real numbers greater than or equal to 0
all the real numbers greater than or equal to 2
all the real numbers greater than or equal to –3
Answer:
All numbers greater than or equal to -3.
Step-by-step explanation:
Just took the edge test.
Answer:
yeah. its d
Step-by-step explanation:
edge test 2020
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles how far is it from Chester to durbin
Answer:
It is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.
Step-by-step explanation:
Given:
Its 10 3/5 miles from Alston to Barton and 12 1/2 miles from Barton to Chester. The distance from Alston to Durbin, via barton and Chester, is 35 miles.
Now, to find the distance from Chester to durbin.
Distance from Alston to Barton = [tex]10\frac{3}{5} =\frac{53}{5} \ miles.[/tex]
Distance from Barton to Chester = [tex]12\frac{1}{2}\ miles =\frac{25}{2} \ miles.[/tex]
As, given the distance from Alston to Durbin, via barton and Chester, is 35 miles.
Thus, the total distance = 35 miles.
So, we add the distance of Alston to Barton and Barton to Chester and get the distance from Alston to Chester:
[tex]\frac{53}{5} +\frac{25}{2}[/tex]
[tex]=\frac{106+125}{10}[/tex]
[tex]=\frac{231}{10} \ miles.[/tex]
Distance from Alston to Chester [tex]=\frac{231}{10} \ miles.[/tex]
Now, to get the distance from Chester to durbin we subtract distance from Alston to Chester from the total distance:
[tex]35-\frac{231}{10} \\\\=\frac{350-231}{10} \\\\=\frac{119}{10} \\\\=11\frac{9}{10}\ miles.[/tex]
Therefore, it is [tex]11\frac{9}{10}[/tex] miles far from Chester to Durbin.
Which system of equations could be graphed to solve the equation below?
Answer:
B
Step-by-step explanation:
I think this is your full question and hope it is correct.
Which system of equations could be graphed to solve the equation below?
log(2x+1)=3x-2
A. y1=3x, y2=2x
B. y1=log(2x+1), y2=3x-2
C. y1=log2x+1, y2=3x-2
D. y1=log(2x+1+2), y2=3x
My answer:
We know that: log(2x+1)=3x-2 and they are a equation of log and linear so we need to make system of equation.
The left side is: [tex]y_{1}[/tex] => [tex]y_{1} = log( 2x+1)[/tex]
The right side is : [tex]y_{2} = 3x -2[/tex]
The system of equations are:
[tex]\left \{ {{y_{1} =log(3x+1)} \atop {y_{2} =3x -2}} \right.[/tex]
Now we have two new function with x and y.
I need help plz and I have to show work
This is a very simple and easy problem. I'm not sure why you need someone else to solve it, but I hope this helps
a. Linear equation:
Let x be amount of movies rented
$8 + ($2.50 * x)
b.
$8 + ($2.50 * 10)
= $8 + $25.0
= $33
A researcher selects a sample of 25 participants from a population with a mean of 20 and a standard deviation of 10. What is the range of values for the sample mean that fall within 1 standard error of the mean in a sampling distribution?
Answer:
The range of values for the sample mean is between a lower limit of 19 and an upper limit of 21.
Step-by-step explanation:
sample mean = 20
sd = 10
n = 25
standard error = 1
Lower limit of sample mean = sample mean - standard error = 20 - 1 = 19
Upper limit of sample mean = sample mean + standard error = 20 + 1 = 21
The range of values for the sample mean is between 19 and 21.
Please help. And show how you got your answer so I know how to do it.
Answer:
9. (x, y) = (6√3, 3)
10. (x, y) = (14, 14√2)
11. (x, y) = (2√6, 3√2)
12. (x, y) = (6, 2)
Step-by-step explanation:
Because you have memorized a short table of trig functions, you know that the ratio of side lengths of a 30°-60°-90° triangle is 1 : √3 : 2, and the ratio of side lengths of a 45°-45°-90° triangle is 1 : 1 : √2.
In each case, we compare the given side ratios to the known ratios for the kind of triangle we have. Then we multiply the triangle ratios by a scale factor that makes the given number match the corresponding ratio value. Matching the other ratio values, we can determine the values of the variables.
__
9. Using the side ratios for the 30-60-90 triangle, you have
6 : x : y+9 = 1 : √3 : 2
Multiplied by 6, the ratios on the right are ...
6 : x : y+9 = 6 : 6√3 : 12
x = 6√3
y +9 = 12
y = 3
__
10. Using the side ratios for the 45-45-90 triangle:
14 : x : y = 1 : 1 : √2
Multiplying the ratios on the right by 14, we have ...
14 : x : y = 14 : 14 : 14√2
x = 14
y = 14√2
__
11. Again using the 30-60-90 ratios:
√6 : y : x = 1 : √3 : 2
Multiplying the ratios on the right by √6, we have ...
√6 : y : x = √6 : 3√2 : 2√6
y = 3√2
x = 2√6
__
12. Again, using the 45-45-90 ratios:
x : 3y : 6√2 = 1 : 1 : √2
Multiplying the ratios on the right by 6, we have ...
x : 3y : 6√2 = 6 : 6 : 6√2
x = 6
3y = 6
y = 2
Prime numbers problem
Answer:
The answer to your question is 2² 3² or (4)(9)
Step-by-step explanation:
Data
factor 36
Process
1.- Divide 36 by prime numbers starting from 2, then 3, 5, 7, etc.
36 2
18 2
9 3
3 3
1
2.- Write 36 as a composition of prime numbers
36 = 2²3²
3.- The prime factors of 36 are 2² x 3²
A pool charges $4 each visit or you can buy a membership. Right and solve an inequality to find how many times a person should use a pool so that the membership is less expensive than paying each time. Interpret the solution
The inequality is:
[tex]n > \frac{m}{4}[/tex]
Membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
Solution:
Given that,
A pool charges $4 each visit or you can buy a membership
Let "n" be the number of times you visit the pool
Let the membership amount of the pool be "m"
A pool charges $4 each visit
Therefore, cost for "n" visit is: $ 4n
The inequality showing that a membership is less expensive than paying each visit to the pool is:
4n > m
Divide both sides by "4"
[tex]n > \frac{m}{4}[/tex]
Therefore, membership of the pool will be less expensive until number of visits to the pool is one fourth of the membership amount
If an object is shot upward with an initial velocity, v 0 v0 , in feet per second (ft/s), the velocity, v, in ft/s is given by the formula v= v 0 −32t v=v0−32t , where t is time in seconds. Find the initial velocity of an object if the velocity after 3 3 seconds is 28ft/s 28ft/s
We are given a velocity equation, and from that, we want to find the initial velocity such that we know the velocity for a given time.
We will see that the initial velocity is 124 ft/s
-------------------------------
Let's see how to solve this:
We have that the velocity equation:
v(t) = v₀ - (32 ft/s^2)*t
Where I added the units of the gravitational acceleration, which are in ft over seconds squared.
We want to get the value of the initial velocity, v₀, given that after 3 seconds the velocity is 28ft/s.
This means that:
v(3s) = 28 ft/s = v₀ - (32 ft/s^2)*3s
We can solve this for v₀:
28 ft/s = v₀ - (32 ft/s^2)*3s
28 ft/s + (32 ft/s^2)*3s = v₀
124 ft/s = v₀
So we can see that the initial velocity is 124 ft/s
If you want to learn more, you can read:
https://brainly.com/question/9163788
Brenda invests $4500 in a savings account earning 5.5% interest compounded quarterly. What will the account balance be after 7 years?
Answer: The account balance will be $6596 after 7 years.
Step-by-step explanation:
We would apply the formula for determining compound interest which is expressed as
A = P(1+r/n)^nt
Where
A = total amount in the account at the end of t years
r represents the interest rate.
n represents the periodic interval at which it was compounded.
P represents the principal or initial amount deposited
From the information given,
P = $4500
r = 5.5% = 5.5/100 = 0.055
n = 4 because it was compounded 4 times in a year.
t = 7 years
Therefore,.
A = 4500(1 + 0.055/4)^4 × 7
A = 4500(1 + 0.01375)^28
A = 4500(1.01375)^28
A = $6596
Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. 1 4 of this amount is blue paint, and the rest is white paint. How many paints of white paint did she use to paint her bedroom walls
Answer: she used 6.525 pints of white paint.
Step-by-step explanation:
Kelly uses 8.7 paints of blue paint and white paint to paint her bedroom walls. If 1/4 of this amount is blue paint, it means that the amount of blue paint that she used in painting her bedroom walls is
1/4 × 8.7 = 2.175 pints of blue paint.
Since the rest of the paint is white, it means that the pints of white paint that she used to paint her bedroom walls is
8.7 - 2.175 = 6.525 pints of white paint
Answer:
she uses 6.525 pints of paint
Step-by-step explanation:
Find v × w if v = 3i + 8j – 6k and w = –4i – 2j – 3k.
Answer:
[tex]vXw =-36i+33j+26k[/tex]
Step-by-step explanation:
v = 3i + 8j – 6k
w = –4i – 2j – 3k
The cross product
[tex]v X w=\left|\begin{array}{ccc}i&j&k\\3&8&-6\\-4&-2&-3\end{array}\right|[/tex]
[tex]=i\left|\begin{array}{cc}8&-6\\-2&-3\end{array}\right|-j\left|\begin{array}{cc}3&-6\\-4&-3\end{array}\right|+k\left|\begin{array}{cc}3&8\\-4&-2\end{array}\right|\\[/tex]
[tex]=i(-24-12)-j(-9-24)+k(-6+32)\\vXw =-36i+33j+26k[/tex]
plz help i really need it
Answer:
y=\frac{1}{8}x+4
Step-by-step explanation:
first, we can quickly get rid of options 1 and 2, since the y-intercept is not -4, but +4.
this leaves us with options 3 and 4.
we can rule out option3, since the slope is not 4, but 1/8.
hope this helps :)
Can someone help me on this?? I'm stuck!
Find the total area for the regular pyramid.
T. A. =
Answer:
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]
Step-by-step explanation:
we know that
The total area or surface area of the regular pyramid is equal to the area of the triangular base plus the area of its three lateral triangular faces
so
step 1
Find the area of the triangular base B
Is an equilateral triangle
Applying the law of sines
[tex]B=\frac{1}{2}(12^2)sin(60^o)[/tex]
[tex]B=\frac{1}{2}(144)\frac{\sqrt{3}}{2}[/tex]
[tex]B=36\sqrt{3}\ units^2[/tex]
step 2
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)h][/tex]
Find the height
Applying the Pythagorean Theorem
[tex]10^2=6^2+h^2[/tex]
[tex]h^2=100-36\\h^2=64\\h=8\ units[/tex]
Find the area of the lateral triangular faces
[tex]A=3[\frac{1}{2}(12)8]=144\ units^2[/tex]
therefore
The total area is
[tex]TA=(144+36\sqrt{3})\ units^2[/tex]
Suppose that 4 fair coins are tossed. Let Equals The event that exactly 2 coins show tails and Equal The event that at least 2 coins show tails. Find Upper P (Upper E | Upper F )and Upper P (Upper E | Upper F prime ).
Answer:
a) P ( E | F ) = 0.54545
b) P ( E | F' ) = 0
Step-by-step explanation:
Given:
- 4 Coins are tossed
- Event E exactly 2 coins shows tail
- Event F at-least two coins show tail
Find:
- Find P ( E | F )
- Find P ( E | F prime )
Solution:
- The probability of head H and tail T = 0.5, and all events are independent
So,
P ( Exactly 2 T ) = ( TTHH ) + ( THHT ) + ( THTH ) + ( HTTH ) + ( HHTT) + ( HTHT) = 6*(1/2)^4 = 0.375
P ( At-least 2 T ) = P ( Exactly 2 T ) + P ( Exactly 3 T ) + P ( Exactly 4 T) = 0.375 + ( HTTT) + (THTT) + (TTHT) + (TTTH) + ( TTTT)
= 0.375 + 5*(1/2)^4 = 0.375 + 0.3125 = 0.6875
- The probabilities for each events are:
P ( E ) = 0.375
P ( F ) = 0.6875
- The Probability to get exactly two tails given that at-least 2 tails were achieved:
P ( E | F ) = P ( E & F ) / P ( F )
P ( E | F ) = 0.375 / 0.6875
P ( E | F ) = 0.54545
- The Probability to get exactly two tails given that less than 2 tails were achieved:
P ( E | F' ) = P ( E & F' ) / P ( F )
P ( E | F' ) = 0 / 0.6875
P ( E | F' ) = 0
There are 5 blue chips, 4 red chips and 3 yellow chips in a bag. One chip is drawn from the bag. That chip is placed back into the bag, and a second chip is drawn. What is the probability that the two selected chips are of different colors? Express your answer as a common fraction.
The probability of drawing two chips of different colors from the bag is 35/33.
The probability of drawing the chips:
Calculate the total number of ways to draw 2 chips: 12 chips total, so 12C2 = 66 ways.
Calculate the number of ways to draw 2 chips of different colors: (5 blue chips × 7 non-blue chips) + (7 non-blue chips × 5 blue chips) = 70 ways.
Probability = Number of favorable outcomes / Total outcomes = 70/66 = 35/33.
the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
To find the probability that the two selected chips are of different colors, we can use the concept of complementary probability.
The complementary event of selecting two chips of different colors is selecting two chips of the same color.
Let's calculate the probability of selecting two chips of the same color and then subtract that from 1 to find the probability of selecting two chips of different colors.
1. Probability of selecting two blue chips:
[tex]\[ P(\text{blue, blue}) = \frac{5}{12} \times \frac{5}{12} = \frac{25}{144} \][/tex]
2. Probability of selecting two red chips:
[tex]\[ P(\text{red, red}) = \frac{4}{12} \times \frac{4}{12} = \frac{16}{144} \][/tex]
3. Probability of selecting two yellow chips:
[tex]\[ P(\text{yellow, yellow}) = \frac{3}{12} \times \frac{3}{12} = \frac{9}{144} \][/tex]
Now, let's add these probabilities together because any of these scenarios results in two chips of the same color:
[tex]\[ P(\text{same color}) = P(\text{blue, blue}) + P(\text{red, red}) + P(\text{yellow, yellow}) \]\[ P(\text{same color}) = \frac{25}{144} + \frac{16}{144} + \frac{9}{144} = \frac{50}{144} \][/tex]
Finally, we subtract this probability from 1 to find the probability of selecting two chips of different colors:
[tex]\[ P(\text{different colors}) = 1 - P(\text{same color}) \]\[ P(\text{different colors}) = 1 - \frac{50}{144} = \frac{144}{144} - \frac{50}{144} = \frac{94}{144} \][/tex]
So, the probability that the two selected chips are of different colors is [tex]\( \frac{94}{144} \), which simplifies to \( \frac{47}{72} \).[/tex]
Christopher's back yard is in the shape of a trapezoid. The bases of his back yard are 30 and 40 feet long. The area of his back yard is 525 square feet. Write and solve an equation to find the height of Christopher's back yard.
Answer:
15 feet
Step-by-step explanation:
525 = ½(30+40)h
525 = 35h
h = 525/35
h = 15 feet