In a certain Algebra 2 class of 28 students, 7 of them play basketball and 5 of them play baseball. There are 18 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball?
Answer:
2 students play both
Step-by-step explanation:n(u)=28
n(b)=7,n(b)=5,n(who play neither sport)=18
HERE,
n(u)=n(b)+n(b)-n(BnB)+n(who play neither sport)
28=7+5-n(BnB)+18
28=30-n(BnB)
n(BnB)=30-28
=2 answer
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A regional survey found that 60% of all families who indicated an intention to buy a new car bought a new car within 3 months, that 10% of families who did not indicate an intention to buy a new car bought one within 3 months, and that 26% indicated an intention to buy a new car. If a family chosen at random bought a car, find the probability (as a percent) that the family had not previously indicated an intention to buy a car. (Round your answer to two decimal places.)
Let A be the event that a family chose at random indicated an intention to buy a new car and let B be the event that a family chose at random bought a new car within 3 months.
We are asked to find P(A'), which is the probability that a family chosen at random had not previously indicated an intention to buy a car.
We can use the given information to write the following conditional probabilities:
P(B | A) = 60%
P(B | A') = 10%
P(A) = 26%
We can use these probabilities to apply Bayes' theorem to find P(A' | B), which is:
P(A' | B) = P(B | A') * P(A') / P(B)
Substituting the values from the problem, we have:
P(A' | B) = (10%) * (100% - 26%) / (60% * 26% + 10% * (100% - 26%))
= (10%) * (74%) / (60% * 26% + 10% * 74%)
= (10%) * (74%) / (15.4% + 7.4%)
= (10%) * (74%) / (22.8%)
= 43.86%
Therefore, the probability that a family chosen at random had not previously indicated an intention to buy a car is 43.86%.
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Who knows how to do this
Answer:
144 \( {cm}^{2} \)Step-by-step explanation:
Given,
As we know that the all sides of the square are equal.
Length of a square paper = 12 cm
Area of square = ?
Now, let's find the area of square
\( = {l}^{2} \)
plugging the value of length,
\( {(12)}^{2} \)
Evaluate the power
\( = 144\) square cm
Hope this helps...
Best regards!!
a tank truck holds 33.8 kl of oil. How many gallons does it hold
30% of apples in a bag are red and the rest are green there are 24 red apples how many are in the bag
Answer:
80 apples are in the bag
Step-by-step explanation:
24/n=30/100
24x100=2400
2400/30=80
80 apples in total
Evaluate each expression.
Answer:
THIS DESERVES A BRAINLIEST BECAUSE I PUT ALL OF THE ANSWERS AND THE WORK TO IT
1: 6
2: 3
3: 5
4: 1
5: 3
6: -1
7: 8
8: 4
9: 3
10: 16
Step-by-step explanation:
Use PEMDAS
1. (2x2)+2
You do 2x2 first which is 4 so then you do 4+2 which is 6
2. 6 divided by (5-3)
You do 5-3 first which is 2 then 6/2 (that's 6 divided by 2) which is 3
3. 6/6 x5
so you do 6 divided by 6 which is 1 then you get 1x5 which is 5.
4. 2-(5-4)
5-4 is 1 and 2-1 is 1
5. 2+6/6
6 divided by 6 is 1 and 2+1 is 3
6. (-6)+5 is -1
7. 1-(-7) is the same as 1+7 which is 8
8. (-3)-7 is the same as -3+7 which is the same as 7-3 which is 4
9. 5+(-2) is the same as 5-2 which is 3
10. 8-(-8) is the same as 8+8 which is 16
Helppp please on this question
Answer:
Answer h = 34 i hope it is helpful have a nice day
Answer:
h = 34
Step-by-step explanation:
64 = h + 30
64-30 = h
34 = h
h = 34
Find the range of the function f(n) = n² - 2n for the domain (1, 3, 5).
Range:
Answer: {-1, 3, 15}
Step-by-step explanation:
\(f(1)=-1\\\\f(3)=3\\\\f(5)=15\)
So, the range is {-1, 3, 15}.
What statement is true for a square with an area of 44 in²? A. Each side is 11 inches long. B. Each side is exactly 6.5 inches long. C. Each side is more than 7 inches long. D. Each side is more than 6 inches long.
Answer:D
Step-by-step explanation: The sides should be 6.633 to have an area of 44in squared so that cancels out 11 and 7 and 6.5 because 11 and 7 are higher than 6 and 6.633 and they said exactly 6.5 which is obviously wrong.
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Suppose that the Blood Alcohol Content (BAC) of students who drink five beers varies from student to student according to a Normal distribution with mean 0.07 ans standard deviation 0.01.
1. The middle 95% of students who drink five beers have a BAC between
a. 0.06 and 0.08 b. 0.05 and 0.09 c. 0.04 and 0.10 d. 0.03 and 0.11
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
a. 0.15% b. 0.3% c. 2.5% d. 16% e. 32%
Answer:
1. b. 0.05 and 0.09
2. d. 16%
3. a. 0.15%
Step-by-step explanation:
Given that :
mean = 0.07
standard deviation = 0.01
Confidence interval = 95%
The level of significance ∝= 1 - 0.95 = 0.05
At 0.05 level of significance,
critical value for \(z_{\alpha/2} = z_{0.05/2}\)
critical value for \(z_{0.025}\) = 1.96
Confidence interval = \(\mathtt{\mu \pm ( {z} \times{\sigma})}\)
Lower limit = \(\mathtt{\mu -( {z} \times{\sigma})}\)
Upper Limit = \(\mathtt{\mu +( {z} \times{\sigma})}\)
Lower limit = \(\mathtt{0.07 - ({1.96} \times {0.01})}\)
Upper limit = \(\mathtt{0.07 + ({1.96} \times {0.01})}\)
Lower limit = 0.07 - 0.0196
Upper limit = 0.07 + 0.0196
Lower limit = 0.0504 \(\simeq\) 0.05
Upper limit = 0.0896 \(\simeq\) 0.09
The confidence interval of 95% is ( 0.05, 0.09)
2. What percent of students who drink five beers have a BAC above 0.08 (the legal limit for driving in most states)?
\(P(X> 0.08) = P(\dfrac{0.08 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )\)
\(P(X > 0.08) = P(z > \dfrac{0.08 - 0.07}{0.01} )\)
\(P(X > 0.08) = P(z > \dfrac{0.01}{0.01} )\)
\(P(X > 0.08) = P(z > 1 )\)
\(P(X> 0.08) = 1- P(z < 1 )\)
P(X > 0.08) = 1 - 0.8413
P(X > 0.08) = 0.1587
P(X > 0.08) \(\simeq\) 16%
3. What percent of students who drink five beers have a BAC above 0.10 (the legal limit for driving in most states)?
\(P(X> 0.10) = P(\dfrac{0.10 - \mu}{\sigma} > \dfrac{X - \mu}{\sigma} )\)
\(P(X > 0.10) = P(z > \dfrac{0.10 - 0.07}{0.01} )\)
\(P(X > 0.10) = P(z > \dfrac{0.03}{0.01} )\)
\(P(X > 0.10) = P(z > 3)\)
\(P(X> 0.10) = 1- P(z < 3 )\)
P(X > 0.10) = 1 - 0.9987
P(X > 0.08) = 0.0013
P(X > 0.08) \(\simeq\) 0.15% which is the closet value to 0.0013
A health and fitness club surveys 40 randomly selected members and found that the average weight of those questioned is 157lb. Is this a statistic or a parameter?
This average will be an example of statistics.
Let’s look at our question:
An example of a statistic is the average weight of those surveyed, which was 157 lbs., from a survey of 40 randomly chosen members of a health and fitness club. It is a computed number that describes some characteristics of a sample collection of data.
What is Statistic?
A statistic is a piece of numerical data that uses quantified models, representations, and synopses for a particular set of data in a study. Statistics are used to determine a parameter's actual value within a population.
Therefore our question will be an example of statistics.
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Which decimal is equivalent to 0.75?
Answer:
Fracción
3/4
Fracciones equivalentes
6/8
Decimal
0,75
Answer:
3/4.
Step-by-step explanation:
0.75 = 75/100
= 3/4
Which option best shows X ≤ -3
Step-by-step explanation:
the answer is b because the circle is filled with color as it should be and shows that x is equally to number 3 too
Answer:
yep, it's b.
Step-by-step explanation:
a line with a closed circle means that it's less than or equal to.
Use the image to determine the direction and angle of rotation. Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1. 90° clockwise rotation 180° clockwise rotation 180° counterclockwise rotation 90° counterclockwise rotation
For the function: y = Sqrt X-7-1
The domain is : x > =
The range is: y > =
Answer:
7
-1
Step-by-step explanation:
Answer:
The domain is 7.
The range is -1.
Step-by-step explanation:
Got it right on EDGE2022
The following data are the acity scar of all student in a history class complete the frequency distribution for the data
For the given data, we will count every score to complete the frequency distribution for the data.
ACT score Frequency
1 - 6
Karen Gaines invested $10,000 in a money market account with an interest rate of 3.25% compounded semiannually. Three years later, Karen withdrew the full amount to put toward the down payment on a new house. How much did Karen withdraw from the account?
The total amount of money that Karen withdrew from her account three years later is $11,015.48.
How much did Karen withdraw?When an amount earns a compound interest seminannually, it means that the amount invested and interest accured increases in value twice a year.
The formula for calculating future value:
FV = P (1 + r)^nm
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of years$10,000 x (1 + 0.0325/2)^6 = $11,015.48
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Please help ASAP
Compare -2.3 and -8/3 using symbols <, >, or =
Answer:
to compare -2.3 and -8/3, we need to put them in the same form. We can convert -8/3 to a decimal by dividing -8 by 3, which gives us -2.66667.
Now we can see that -2.3 is greater than -2.66667, so we can write -2.3 > -8/3.
Step-by-step explanation:
Don't worry I can help.
Mathmetics isn't easy. so study
Please Hurry and Answer this
Answer:
5x + 20 = 5(x+4)
5(2x+8) = 10x + 40
5(x+8) =5 + 5 x 8
Step-by-step explanation:
solve and graph the inequality 3x < 13
The solution of the inequality 3x < 13 is x < 4.33.
None of the given option is correct.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
An inequality,
3x < 13.
Simplifying,
x < 4.33
The graph is given in the attached image.
Therefore, the solution is x < 4.33.
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what is the domain and range and determine if the given relation is a function.
Answer:
+-3 x2
Step-by-step explanation:
Ann's car can go 210 miles on 6 gallons of gas. During a drive last weekend, Ann used 7 gallons of gas. How far did she drive?
Answer:
245 miles
Step-by-step explanation:
210 = 6 gallons
210/6 = how far you can travel with one gallon
210/6 = 35
7*35 = how far you can travel with 7 gallons
7*35 = 245
Answer:
Ann drove 245 miles during her drive last weekend.
Step-by-step explanation:
If Ann used 7 gallons of gas during her drive last weekend, we can use the car's MPG to find out how far she drove by multiplying the number of gallons used by the MPG:
7 gallons * 35 miles/gallon = 245 miles
What is the length of FH in the right triangle below?
Answer:
7
Step-by-step explanation:
apply the Pythagorean theorem
\(10 {}^{2} = ( \sqrt{51} ) {}^{2} + x {}^{2} \\ 100 = 51 + x {}^{2} \\ 100 - 51 = x {}^{2} \\ 49 = x {}^{2} \\ x = 7\)
I select two cards from a deck of 52 cards and observe the color of each (26 cards in the deck are red and 26 are black). Which of the following is the most appropriate sample space S for the possible outcomes?
a. S={red, black}
b. S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."
c. S={0,1, 2}
d. All of the above
Answer:
b. S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."
Step-by-step explanation:
The sample space S for the possible outcomes reflects all possible cmobinations linked to the event of selecting the two cars.In any case, you have to take into account all possible scenarios from te event of selecting two cars. Because there are two possible alternatives of color for the cars, when picking two cars, you can face the situations: S={(red, red), (red, black), (black, red), (black, black)}.The most appropriate sample space S for the possible outcomes will be S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."
Option B is correct.
Sample space is defined as the total number of outcomes in an eventGiven that two cards are selected from a pack of 52 cards card where 26 cards in the deck are red and 26 are blackNote that the colors are being observed, hence the combination of colors we can select will be (red, red), (red, black), (black, red), (black, black)The most appropriate sample space S for the possible outcomes will be S={(red, red), (red, black), (black, red), (black, black)} where, for example, (red, red) stands for the event "the first card is red and the second card is red."
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What is the value of y^2−x 2 when y =6 and x=5
Answer:
11
Step-by-step explanation:
y²−x²
6² - 5²
36 - 25
= 11
Please help with segments
50 points for 3 questions. solve and explain please.
(1) The value of x is determined as 16.8.
(2) The measure of length VX is calculated as 4.1.
(3) The measure of angle UWV is 69.5⁰.
What is the value of the missing lengths of the triangle?
The value of the missing lengths of the triangle is calculated by applying the following formula;
(1) For the two similar triangles, the value of x is calculated as follows;
20 / (28 - x) = 30 / x
20x = 30 (28 - x )
20x = 840 - 30x
20x + 30x = 840
50x = 840
x = 840 / 50
x = 16.8
(2) The measure of length VX is calculated by applying trig ratios.
tan 63 = 8 / VX
VX = 8 / tan 63
VX = 4.1
(3) The measure of angle UWV is calculated as follows;
angle T = 360 - (94 + 127) = 139
angle UWV = ¹/₂ x 139 (angle at circumference is half of angle at center)
angle UWV = 69.5⁰
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Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594 Division I male athletes in the survey, 3547 reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1% margin of error. The confidence level was not stated in the report. Use what you have learned to find the confidence level, assuming that the NCAA took an SRS.
The confidence level in this report of survey of student atheletes concerning their gambling-related behaviors is equals to 87.88%.
The confidence interval when calculated with the two tails methods then it can be used to test the two tail hypothesis for the same parameter provided that the confidence level. We have, National Collegiate Athletic Association (NCAA) take a survey of randomly selected student athletes concerning their gambling-related behaviors.
repoted participation of students, x = 3547
Sample size,n = 5594
Margin of error, E = 1% = 0.01
The sample proportion is a number of successes divided by the sample size, p-cap = 3547/5594
= 0.6341
The margin of error is for a confidence interval for a proportion, which is determined by using the following formula is
\(CL = Zα/₂ \sqrt{ \frac{ \hat{p} \: (1- \hat{p})}{n} }\)
= Zα/₂√(1 - 0.6341)0.6341/5594
= 0.0064 Zα/₂
This margin of error also has to be equal to 1% or
0.0064 Zα/₂ = 0.01
=> Zα/₂ = 0.01/0.0064 ~ 1.55
The confidence level is the probability of obtaining this value or less extreme, determine the probability using z- table,
P(-1.55< Z < 1.55) = P(Z < 1.55) - P(Z < -1.55)
= 0.9394 - 0.0606 = 0.8788 = 87.8
Thus the confidence level is 87.88%.
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What is the area of triangle UVW?
Answer:
30 units²
Step-by-step explanation:
Triangle Area = 1/2bxh
Base (b) = 12 units
Height (h) = 5 units
let's apply the formula1/2 × 12 × 5 =
6 × 5 =
30 units²