A correlation coefficient of 0.76 indicates a very strong positive linear relationship between the two variables.
What does the correlation coefficient mean?Correlation is a statistical measure used to measure the linear relationship that exists between two variables.
If the sign of the correlation coefficient is positive, it means that the two variables exhibits a positive correlation. The closer to 1, the correlation coefficient is, the stronger the linear relationship.
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Suppose C1;C2;C3 are three didifferent biased coins, whose probability of heads equals 0.4, 0.5, and 0.2 respectively. Suppose coins are placed together in a box and you randomly picked a coin from the box. Flip the coin 10 times. Let A denote the event you randomly chose coin C1. Let B denote the event that you got exactly 4 heads out of the 10 coin flips.
Compute the following probabilities:
P(A∩B)
P(B)
P(A|B)
Solution :
[tex]$ P(A \cap B) = P(\text{coin}\ C_1 \text{ chosen and 4 heads in 10 trails})$[/tex]
[tex]$= \frac{1}{3} \times ^{10}C_4 \times 0.4^4 \times 0.6^6$[/tex]
= 0.0836
P(B)= P(coin [tex]$C_1$[/tex] chosen and 4 heads in 10 trails) + P(coin [tex]$C_2$[/tex] chosen and 4 heads in 10 trail) + P(coin [tex]$C_3$[/tex] chosen and 4 heads in 10 trail)
[tex]$=\frac{1}{3}\times ^{10}C_4 \times 0.4^4 \times 0.6^6 + \frac{1}{3}\times ^{10}C_4 \times 0.5^4 \times 0.5^6 + \frac{1}{3}\times ^{10}C_4 \times 0.2^4 \times 0.8^6$[/tex]
[tex]$=0.0836+0.0684+0.0294$[/tex]
[tex]$=0.1813$[/tex]
P(A|B) = [tex]$\frac{P(A \cap B)}{P(B)}$[/tex]
[tex]$=\frac{0.0836}{0.1813}$[/tex]
[tex]$=0.4611$[/tex]
need help with this, ASAP
Pattern if decreasing perfect squares 121, 100, 81, __,49, 36 What number do you need to square to find missing term?
Answer:
8
Step-by-step explanation:
121 is 11^2, 100 is 10^2, 81 is 9^2, 49 is 7^2, and 36 is 6^2. 64 is missing in the pattern, and since each number is a perfect square, the number you'd need to square is 8.
The distance from Amy's house to Lake Ontario is 150 miles. On a map, it is 3 inches.
What is the scale used?
Answer:
50
Step-by-step explanation:
150 divided by 3 = 50
find the value of 2xy+3yz-xyz, when x=2, y=-2, z=4
Step-by-step explanation:
[tex]x = 2[/tex]
[tex]y = - 2[/tex]
[tex]z = 4[/tex]
[tex] \: [/tex]
[tex] = 2xy + 3yz - xyz[/tex]
[tex] = y.(2x + 3z - xz)[/tex]
[tex] = y.(2x + z.(3 - x))[/tex]
[tex] = - 2.(2.2 + 4.(3 - 2))[/tex]
[tex] = - 2.(4 + 4.1)[/tex]
[tex] = - 2.(4 + 4)[/tex]
[tex] = - 2.8[/tex]
[tex] = - 16[/tex]
Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 21% of the time, and roommate B chooses rock 61% of the time; roommate A selects paper 39% of the time, and roommate B selects paper 21% of the time; roommate A chooses scissors 40% of the time, and roommate B chooses scissors 18% of the time. (These choices are made randomly and independently of each other.) The probabilities were assigned using the . Define event A as the event that roommate A wins the game and thus does not have to wash the dishes.
Answer:
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.
Step-by-step explanation:
Independent events:
If two events are independent, the probability of both happening is the multiplication of their probabilities.
Rock-paper-scissors rules:
A player that choose rocks beats one who chooses scissors.
A player that choose paper beats one who chooses rocks.
A player that choose scissors beats one who chooses paper.
Probability that roommate A wins the game and thus does not have to wash the dishes.
3 possible events:
Roommate A - Rocks(21% of the time) and Roommate B - Scissors(18% of the time)
So
[tex]p_R = 0.21*0.18 = 0.0378[/tex]
Roommate A - Paper(39% of the time) and Roommate B - Rocks(61% of the time).
So
[tex]p_P = 0.39*0.61 = 0.2379[/tex]
Roommate A - Scissors(40% of the time) and Roommate B - Paper(21% of the time).
So
[tex]p_S = 0.4*0.21 = 0.084[/tex]
Probability of roommate A winning:
[tex]p = p_R + p_P + p_S = 0.0378 + 0.2379 + 0.084 = 0.3597[/tex]
0.3597 = 35.97% probability that roommate A wins the game and thus does not have to wash the dishes.
1) Which of the following are considered POLYNOMIALS according to the rules of polynomials? Check all that apply
Answer:
A polynomial is writen as:
p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x¹ + a₀
So we can only have positive integer exponents of x.
the coefficients "a" can be any real number.
Let's analyze the options:
1) Here we can see a term with "√x", remember that:
√x = (x)^(1/2)
This is not an integer exponent, then this is not a polynomial.
2) This is a polynomial.
3) Here we have the term "4/x"
This can be written as:
4/x = 4*x^(-1)
Then this is not a polynomial.
4) Here we have the term "5^x"
In a polynomial we must have powers of x, not x as a power, then this is not a polynomial.
5) This is a polynomial.
6) Here we have the term " 2/x^2"
This can be written as:
2/x^2 = 2*x^(-2)
We have a negative exponent of x, then this is not a polynomial.
Please answer for instant brainliest.
Answer:
5 T-shirts
or
35 T-shirts
Step-by-step explanation:
Alright so this question is a bit tricky but I will explain to you the steps. What you want to do is take every possible answer and multiply it by $15 (The price of an adult t shirt) and see if the answer you get can be added onto with the price of small t shirts ($10).
In other words you need a multiple of $10 as your answer so you can add $10 onto to that number until you get your total of $2,375.
Lets start with 185 t-shirts.
If we do 185 shirts x $15 per shirt we get $2775
That is way above the total of $2,375 so we know that this cant be the answer.
Next we can do 110 t-shirts.
If we do 110 shirts x $15 this time we get $1650.
Now while this is less than the total this is not a multiple of 10.
To prove this lets take the total amount of money earned ($2,375) and subtract this $1650 from it to see how much in youth shirts they sold.
$2,375 - $1650 = $725
Now we can divide $725 by the rest of the $10 youth shirts and you will see we get 72.5 which is not a whole number so it cant be answer. Since you cant sell someone 25% of a shirt or they probably would be upset.
Moving onto 35 t shirts lets take the same steps.
35 x $15 (price of adult t-shirt)
We then get $525 from this. Lets subtract this total again from the grand total earnings they made from selling both shirts ($2,375)
$2,375 - $525 = $1850.
Now this is a multiple of 10. Meaning you can add 10 into it go get that number and you wont have more or less than it. It will be spot on.
So we can do $1850 divided by $10 to find the total amount of youth shirts sold. We get 185 from this, which is a possible answer.
Lets do the last one.
5 t shirts multiplied by $15
We get $75 from this and now lets subtract again from the grand total.
$2,375 - $75 = $2,300
Now this would work too which is what kind of stumps me but we will go with it. Going off this either 5 t-shirts or 35 t-shirts would work as an answer cause you can have an even number of youth shirts sold with either answer. So I could have done something wrong but I believe based off of this either would be correct but I could be missing something. Someone correct me if I made a mistake.
Anyways I hope this helps :)\
EDIT :
I see what I did wrong here and failed to take into account the total of 220 t-shirts sold. But I believe this can help solve the last 2 answers.
what is the range of the function f(x) = -2|x+1|? QUICK PLEASE ITS A TIMED TEST
a) Dati cinci exemple de numere intregi mai mici ca zero.
Answer:
Numerele întregi pozitive sunt toate numerele întregi mai mari decât zero: 1, 2, 3, 4, 5, .... Numere întregi negative sunt toate opusele acestor numere întregi: -1, -2, -3, -4, -5, .... Nu considerăm că zero este un număr pozitiv sau negativ. Pentru fiecare număr întreg pozitiv, există un număr întreg negativ, iar acești numere întregi se numesc opuse. De exemplu, -3 este opusul lui 3, -21 este opusul lui 21 și 8 este opusul lui -8. Dacă un număr întreg este mai mare decât zero, spunem că semnul său este pozitiv. Dacă un număr întreg este mai mic decât zero, spunem că semnul său este negativ.
Step-by-step explanation:
Help me out plz geometry
Answer:
45°
Step-by-step explanation:
divide 90 by 2 see there is a right angle between them
During peak growing season, the kudzu vine can grow 6 inches in 12 hours. What is the growth
rate of kudzu in inches per hour?
А 0.25 inches
B
0.5 inches
С
2.0 inches
D
6.0 inches
Answer:
b
Step-by-step explanation:
Answer:
The answer is B. 0.5 inches.
simplify 7/341 and give step by step explanation! I will mark you a brainliest.
Answer:
it can't be simplified
Step-by-step explanation:
Linear equations -5(-5x+3)-5x+5=-50
Answer:
x=-30
Step-by-step explanation:
25x+15-5x+5=-50
20x+10=-50
20x+10-10=-50-10
2x=-60
x=60/2
x=-30
Hope it helps!
(I tired hard:))
Which of the following expressions represent a value greater than 4/5 ? A: 4/5 x 3/3. B: 4/5 x 1/2. C: 4/5 x 5/4 D: 4/5 x 4/5
Answer:
C = 1.
Step-by-step explanation:
A: 4/5 x 3/3 (1) = 4/5, Incase you didn't know, 3/3 means 1 whole because it is full. We can tell by just looking that this doesn't represent a value greater than 4/5, In fact, it's equal to 4/5.
B: 4/5 x 1/2 = 2/5 <--- By not using any calculator or math, we already know that 4/5 is greater than 2/5 and that 2/5 is less than 4/5. This is not the correct answer because it's less than 4/5.
C: 4/5 x 5/4 = 1. This could be a correct answer choice because one is greater than 4/5. If your confused, think of it like this, 5/5 is equal to one and then there's 4/5. Then you compare and contrast and see that 5/5 is greater than 4/5 so this is a correct answer choice.
D: 4/5 x 4/5 is equal to 16/25. In my opinion, I wouldn't choose this answer choice because though the numbers are bigger than 4/5, 4/5 IS equal to 16/25, so it wouldn't really be a correct answer choice.
Hope this helped!
7/8 − 1/3 =
i need help
Answer:
Step-by-step explanation:
7/8-1/3=13/24
Answer:
13/24
Step-by-step explanation:
7/8 = 21/24
1/3 = 8/24
21/24 - 8/24 = 13/24
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that a company wants to maximize its profit, or at least make a profit!
Part A: Answer the following questions about the cost function C(2) and the revenue function R(x).
1. What is the domain and range of C (x)?
2. What is the meaning of the slope and intercept of C(x)?
3. At what production level 2 will the company receive the most revenue?
Part B. Answer the following questions about the profit function P(x).
4. Assuming that the company sells all that it produces, what is the profit function?
5. Why is finding the range of P(x) important?
6. The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?
7. Can you explain, from our model, why the company makes less profit when producing 10 more units?
Solution :
a).
1. The domain of C(x)
[tex]$x \in [0, \infty)$[/tex]
Range of c(x) is [tex]$[0, \infty)$[/tex]
Since the negative value do not make any sense.
2. C(x) = Ax + b
Intercept here denotes the fixed cost (that is when x = 0)
The slope indicates the marginal cost (that is increase in cost per unit of quantity)
3. Revenue is maximum marginal revenue = 0
(that is when at the top of the parabola)
4. Profit = R(x) -C(x)
5. Range of P(x) is important so that we have the idea in mind about the maximum loss and the maximum profit for a particular quantity.
6 and 7 -- insufficient data.
Please answer!!!
y = Yolanda's height in inches
y + 7 = Linda's height in inches
2y + (y + 7) = 193
2. A 30-foot tree broke from its base and fell against a house. If the tree touches the house at a height of 21
feet, how far is the base of the tree from the house? Leave your answer in the simplest radical form.
A. 51 square root 3
B. 9 square root 17
C. 3 square root 51
D. 21.42
Answer:
C
Step-by-step explanation:
d Problems
The enrolment of our school is 800. If 35 % are girls
a. What fraction are girls?
b. What fraction are boys?
Answer:
Step-by-step explanation:
g=800(0.35)=280
a. 280/800=7/25
b. 520/800=13/20
Bjorn wants to save $1,680 so that he can buy the car he wants. If Bjorn can save $15 per day, how many days will it take him to save enough money?
How much would you need to deposit in an account each month in order to have $40,000 in the account in 8 years? Assume the account earns 3% annual interest compounded monthly.
Answer:
$166666.67Step-by-step explanation:
$40000 = amount after 8 years time = 8 years interest = 3%principle amount = ?? ( p )$40000 = (( p ) × 3 × 8 )÷100p = (40000 × 100) ÷ ( 3 × 8 )p = $166666.67MARK ME AS BRAINLISTPLEASE HELP MEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE PLEASEEEEEEEEEEEEEEEEEEEEEEEE WILL GIVE BRAINLIST
2. Hank used a semicircle, a rectangle, and a triangle to form the following composite figure. What is its area in square centimeters? Use 3.14 to approximate . Show your work.
Answer:
Step-by-step explanation:
The area of a circle is 3.14r^2
The area of the triangle is bh/2
The area of the rectangle is wh
A=3.14(5^2)/2+8(10)/2+5(20)
A=3.14(25)/2+40+100
A=179.25 cm^2
Answer:
Step-by-step explanation:
Area of rectangle = 5 × 20 = 100 cm²
Area of triangle = 0.5 × 10 × 8 = 40 cm²
Are of semicircle = 0.5 × area of circle = 0.5 × πr² = 0.5 × 25π = 12.5π cm²
Total area = 100+40+ 12.5π ≈ 179.25 cm²
Please help marking brainliest if correct, serious answers only, thank you.
GrumpyCorp drug tests all of the recent college graduates it hires each year. The drug test currently used correctly determines drug users 96% of the time(a Positive test) and correctly determines non-users 90% of the time(a Negative test). A recent study concluded that 36% of college students use drugs. A potential employee has been tested and the result was Negative for drug use.
a) Construct ALL necessary probabilities using proper notation(Example: P(D) for a "drug user"). (Hint: there should be 6 total)
b) Find the Probability of a Negative test, by showing use of the above Probabilities first, and then followed by the proper calculation.
c) Use Bayes' Theorem to find the probability that a person who tests Positive actually was not a Drug User. Set up using Conditional Probability Notation and then substitute in numeric values.
Solution :
Drug : Drug user
T : Test positive
a). [tex]P(D) =0.36[/tex]
[tex]$P\left(\frac{T}{D} \right) = 0.96$[/tex]
[tex]$P\left(\frac{T^c}{D^c} \right) = 0.90$[/tex]
b). [tex]$P(T^c)= P\left(\frac{T^c}{D^c}\right) \times P(D^c)+ P\left(\frac{T^c}{D}\right) \times P(D)$[/tex]
[tex]$=0.9 \times (1-0.36) + (1-0.96) \times 0.36$[/tex]
= 0.5904
c). [tex]$P\left(\frac{D^c}{T}\right) = \frac{P\left(\frac{T}{D^c}\right). P(D^c)}{P\left(\frac{T}{D^c}\right). P(D^c) + P\left(\frac{T}{D}\right). P(D)}$[/tex]
[tex]$=\frac{(1-0.90) \times (1-0.36)}{(1-0.90) \times (1-0.36)+(0.96 \times 0.36)}$[/tex]
[tex]$=0.15625$[/tex]
Ann's grade is the average of four scores: three chapter tests and a final
that counts as two chapter tests. She scored 72, 90, and 75 on the chapter
tests. What score does she need on the final to have a grade of at least 80?
Answer:
f = 81.5
Step-by-step explanation:
hello!
to be able to find the score she needs to have a final grade of at least 80, we use the following equation:
[tex]\frac{72+90+75+2f}{5}=80[/tex]
To get rid of the denominator, we multiply both sides of the equation by 5. Once we do, 5 gets canceled and 80 * 5 = 400. Therefore:
237 + 2f = 400.
Transpose, then simplify.
2f = 400 - 237
2f = 163
Divide both sides by 2 to isolate f:
f = 81.5
If it takes 30 apples to fill 2 boxes, how many apples are needed to fill 3 boxes?
Answer: 45 apples will be needed to fill 3 boxes
Step-by-step explanation: If there are an even amount of apples in each box, 15 times 2 is 30. So if there are 15 apples in each box, 15 times 3 is 45.
Answer:45 apples
Step-by-step explanation:
Since 15 apples are needed to fill 1 box, 45 apples are needed to fill 3 bboxes
Austin and Dale earn money by painting fences over the summer. Working alone, Austin takes 3 hours longer than Dale to paint a fence. Working together, the two of them can paint a fence in 2 hours. How many hours would it take each of them working alone?
Answer:
Austin will take 9 hours to paint a room and dale with take 3 hours to paint a room
Step-by-step explanation:
Ms. Rathman has 5 nickels, 3 dimes, and 2 quarter. In how many ways can she make change
for 50¢? Make a systematic list to answer this question
Answer:
I guess 5
Step-by-step explanation:
2 q 0 n 0 d
1 q 1 n 2 d
1 q 3 n 1 d
1 q 5 n 0 d
0 q 3 d 4 n
Solve x for -2x- 1 = -7
Answer:
x = 3
Step-by-step explanation:
Add 1 on both sides.
We get:
-2x = -6
Now divide -6 by -2...
-6/-2 = 3
-2x -1 = -7
add the "-1" on both sides, -2x -1 +1 = -7 +1
-2x = -6
divide "-2" on both sides, -2x/-2 = -6/-2
x = 3