The probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).
What is Probability?
Probability is a mathematical concept used to measure the likelihood of a particular event occurring. It is a way of expressing the chance or possibility of an event happening, ranging from 0 (impossible) to 1 (certain).
In probability theory, an event is a subset of the possible outcomes of an experiment or a random process. Probability can be expressed in terms of fractions, percentages, or decimals.
The symbol for the event that a college student is female is A, as given in the statement. The symbol for the event that a college student has financial aid is B, as given in the statement.
So, A={A student is female} and B={A student has financial aid}.
These events are mutually exclusive because one does not necessarily affect the other. For example, a male student can have financial aid and a female student may not have financial aid. Hence, the occurrence of one event does not influence the occurrence of the other event.
Therefore, the probability of a college student being either female or having financial aid can be represented as the union of the events A and B. It can be denoted as P(A ∪ B) and is calculated as:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Where P(A ∩ B) represents the probability of a student having both characteristics, i.e., being female and having financial aid.
However, as these events are mutually exclusive, P(A ∩ B) = 0. So the probability of a college student being either female or having financial aid is simply the sum of their individual probabilities:
P(A ∪ B) = P(A) + P(B) - 0
P(A ∪ B) = P(A) + P(B)
Hence, the probability of a college student being either female or having financial aid can be expressed as P(A ∪ B) = P(A) + P(B).
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2 of 3
Some people took part in a game. The frequency shows information about their scores.
Score
1-7
8-10
11-15
16-20
21-35
36-50
Estimate the mean.
Give your answer rounded to 2 decimal places.
Frequency
13
1
19
20
19
20
The mean of the given data is 22.39.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Let us form a table by give data
Score Frequency Midpoint(x) fx
1-7 13 4 52
8-10 1 9 9
11-15 19 13 247
16-20 20 18 360
21-35 19 28 532
36-50 20 43 860
Mean=∑fx/N
=52+9+247+360+532+860/13+1+19+20+19+20
=2060/92
Mean=22.39
Hence, the mean of the given data is 22.39.
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plssss helppppp
Factor the polynomial.
x³+3x²-x-3
Answer:
(x-1)(x+1)(x+3)
Step-by-step explanation:
[tex]x^3+3x^2-x-3\\=x^2(x+3)-1(x+3)\\=(x^2-1)(x+3)\\=(x-1)(x+1)(x+3)[/tex]
A tank in the shape of a hemisphere has a radius of 5 feet. If the liquid that fills the tank has a density of 62. 7 pounds per cubic foot, what is the total weight of the liquid in the tank, to the nearest full pound?
The total weight of the liquid in the tank which is hemisphere in shape is 16,415 pounds.
The density and mass are related to each other with the formula -
Density = mass/volume
So, we have the density. We need to calculate the volume of hemisphere which will be accomodating the liquid. Then we will find the mass.
Volume of hemisphere = 2/3πr³, where r represents radius.
Volume = 2/3×π×5³
Performing multiplication, division and taking cube
Volume = 261.8 feet³
Now, mass = density × volume
Mass = 62.7 × 261.8
Performing multiplication
Mass = 16,414.86 pounds
Rounding off
Mass = 16,415 pounds
Thus, the mass of liquid will be 16,415 pounds.
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4. The table shows the number of beads used to make a necklace. Ginger wants to make a smaller necklace using the same ratio of pink to white beads. How many different necklaces could Ginger make? How do you know?
The number of different necklaces that Ginger can make, with the same ratio of pink to white beads is 5 necklaces.
How to find the number of necklaces ?To find the number of necklaces, find the smallest equivalent ratio of pink to white beats used to make the necklace.
Pink beads : White beads
30 : 35
( 30 / 5 ) : ( 35 / 5 )
6 : 7
To find the find the number of beads, divide the number of pink beads available by the number of pink beads in the ratio:
= 30 / 6
= 5 necklaces
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rulers are sold in boxes of 12
protractors are sold in boxes of 8
A teacher would want to buy the same number of rulers and protractors
work out the smallest number of boxes of each iteam he shoould by
ruler boxes?
protractor boxes?
Answer:
Step-by-step explanation:
Find the GCF:
12, 24, 36
8, 16, 24, 32
GCF is 24
The lowest amount of boxes the teacher could buy would be 2 boxes of Rulers and 3 boxes of Protractors. I hope this helped
Evaluate the expression when x= -7 and y=2 .
X - 2y
Answer:-3
Step-by-step explanation: -7 -4
Which additional fact would prove that quadrilateral WXYZ is a parallelogram?
here is a quadrilateral WXYZ in which side XY is parallel to side WZ.
A. XY = YZ
B. m∠X + m∠Y = 180°
C. YZ = WX
D. m∠Y ≅ m∠W
The extra information "XY = YZ" would demonstrate that the parallelogram WXYZ is a parallelogram.
The parallelogram theorem is what?Theorem: The area of a triangle is roughly half the area of a parallelogram if they share a base and are situated between the same parallels.
These bisectors meet at a 90-degree angle.
And it indicates that they are parallel.
We discover that there are four congruent triangles, with XY parallel to WZ and WX parallel to YZ even though they are perpendicular to one another.
In addition, contrasting angles are equal.
The properties of the parallelogram are these two latter results.
Therefore, the additional fact "XY = YZ" would demonstrate that the triangular WXYZ is a parallelogram.
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HELP will give BRAINLYST
Luke sells 386 dollars worth of candy bars as part of a school club fundraiser. If the candy bars cost 297 dollars, what equation can we make to find out how much money Luke raised as the variable x ?
Which equations for the measures of the unknown
angles x and y are correct? Check all that apply.
x = costa
x= sin" E)
x= tan'a
y= sin "(a)
y = cos-'
The correct equations for the measures of the unknown angles x and y are:
x = cos(a), y = sin(a).
The trigonometric functions (sin, cos, tan) are mathematical functions that describe the relationships between the sides and angles of a right triangle. Given an angle a in a right triangle, we can use these functions to find the values of the side ratios for that angle. For example:
sin(a) = opposite side / hypotenuse
cos(a) = adjacent side / hypotenuse
tan(a) = opposite side / adjacent side
In these expressions, "opposite side" refers to the side opposite the angle a, "adjacent side" refers to the side adjacent to the angle a, and "hypotenuse" refers to the longest side in the right triangle (the one opposite the right angle).
The inverse trigonometric functions[tex](sin^-1, cos^-1, tan^-1)[/tex] are the reverse of the trigonometric functions. Given a value of a trigonometric function, the inverse function returns the measure of the angle (in radians) for which that value is the result. For example:
[tex]sin^-1(y) = a (where y = sin(a))cos^-1(x) = a (where x = cos(a))tan^-1(t) = a (where t = tan(a))[/tex]
So, the correct equations for the measures of the unknown angles x and y are:
[tex]x = cos^-1(x)y = sin^-1(y)[/tex]
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A ladder 50m long is placed on the ground in such a way that it touches the top of vertical wall 30m high. Find the distance of the foot of the ladder from the bottom of the wall
The distance between the foot of the ladder from the bottom of the wall is 40 meters.
What is the Pythagorean theorem?The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Here,
The distance between the foot of the ladder from the bottom of the wall can be found by using the Pythagorean theorem.
The ladder is the hypotenuse, with a length of 50m
The distance from the wall to the ground is 30m
The distance from the wall to the foot of the ladder is x
Using the Pythagorean theorem:
x² + 30² = 50²
x² + 900 = 2500
x² = 1600
x = 40
So, the distance between the foot of the ladder from the bottom of the wall is 40 meters.
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in a group of 8 students, 5 are first-year students, while 3 are second-year students.in how many unique ways can we form three groups comprising 3, 3, and 2 students? (within group order does not matter)
The total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.
The formula for calculating the number of unique ways to form three groups comprising of 3, 3, and 2 students is given by:
Number of ways = Number of ways to select 3 first-year students from 5 first-year students x Number of ways to select 3 second-year students from 3 second-year students x Number of ways to select 2 students from 8 students
=[tex]5C3 x 3C3 x 8C2[/tex]
= 10 x 1 x 28
= 280
Therefore, there are 280 unique ways to form three groups comprising 3, 3, and 2 students. This can be seen by considering the total number of possible arrangements of the 8 students into 3 groups of 3, 3 and 2. First, we need to select 3 students from 5 first-year students in 5C3 ways, which is equal to 10. Second, we need to select 3 students from 3 second-year students in 3C3 ways, which is equal to 1. Finally, we need to select 2 students from 8 students in 8C2 ways, which is equal to 28. Therefore, the total number of ways to form 3 groups comprising of 3, 3 and 2 students is calculated by multiplying the individual numbers of ways, which results in 280.
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relationship btw three set( in a market survey 100traders sell fruit, 40sell Apple, 46 sell Orange, 50 mango, 15sell Apple and Mango, 10 sell the three
fruit draw a venn diagram
Number of student that sell mango and orange
Answer:
7 traders sell oranges and mangoes alone.
Step-by-step explanation:
(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)
(107 – x = 100)
(x = 107 – 100 = 7)
Therefore, 7 traders sell oranges and mangoes alone.
(b) (312_{four} + 52_{x} = 96_{ten})
(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})
= (48 + 4 + 2 = 54_{10})
(52_{x} = 5 times x^{1} + 2 times x^{0})
= ((5x + 2)_{10})
(therefore 54 + (5x + 2) = 96)
(56 + 5x = 96 implies 5x = 96 – 56 = 40)
(x = 8)
(therefore 312_{4} + 52_{8} = 96_{10})
The binomial (x+5) is a factor of x² + 8x + 15. What is the
other factor?
O (x+3)
O (x + 7)
(x+12)
O (x+13)
4X
Factor 2
Product
Factor 1
Reset
The binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .
Given that binomial (x+5) is a factor of x² + 8x + 15.
We need to find the other factor.
Let us solve x² + 8x + 15=0
x² + 5x +3x+ 15=0
x(x+5)+3(x+5)=0
(x+3)(x+5)
So the other binomial factor is x+3.
Hence, the binomial (x+5) is a factor of x² + 8x + 15 then the other factor is x+3.
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3 ways a relationship is proportianl
Determine if events A and B are independent.
P(A)=1/5, P(B)=7/20, P(A and B)= 7/100. The events A and B are independent.
What is independent probability?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B).
1) P(A)=1/5, P(B)=7/20, P(A and B)= 7/100
Here, P(A and B)= P(A)×P(B)
= 1/5 × 7/20
= 7/100
So, the events A and B are independent.
2) P(A)=13/20, P(B)=13/20, P(A and B)= 169/400
Here, P(A and B)= P(A)×P(B)
= 13/20 × 13/20
= 169/400
So, the events A and B are independent.
3) P(A)=7/10, P(B)=2/5, P(A and B)= 21/100
Here, P(A and B)= P(A)×P(B)
= 7/10 × 2/5
= 14/50
So, the events A and B are not independent.
2) P(A)=1/5, P(B)=1/5, P(A and B)= 1/25
Here, P(A and B)= P(A)×P(B)
= 1/5 × 1/5
= 1/25
So, the events A and B are independent.
Therefore, options 1, 2 and 4 are correct answers.
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Solve for x questions in picture
Answer: x = 22
Step-by-step explanation:
Subtract 34 from both sides.
x + 34 - 34 = 56-34 --> x = 22
A 13-foot ladder is leaning up against a building. The top of the ladder reaches the wall at a height of 12 feet. How far is the
bottom of the ladder from the building? Find the angle (2B) that the ladder makes with the ground?
A
12
C
building
13
ladder
X
ground
B
How far is the ladder from the building? Find x = ?
Keep the results to the nearest whole number.
feet
Find the angle that the ladder makes with the ground? LB =
Keep the results to the nearest whole number.
The angle that the ladder makes with the ground is ∠B = 67.38°.
The distance between the ladder from the building is 5 feet.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
Given that a 13-foot ladder is placed up against a wall.
The ladder's top touches the wall at a height of 12 feet.
As per the given question, we have the right triangle ΔABC
Using sine ratio to find angle ∠B as:
sin ∠B = AC/ AB
sin ∠B = 12/13
∠B = sin ⁻¹(12/13)
∠B = 67.38°
Now, using Pythagoras's theorem to find distance x as:
AC² + BC² = AB²
12² + x² = 13²
144 + x² = 169
x² = 169 - 144
x² = 25
x = 5
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A survey was done that asked employees to indicate whether they ride a bicycle or drive to work, and whether they live up to 5 miles or more than 5 miles from work. What is the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle? Enter your answer, rounded to the nearest whole percent, in the box
The probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we need to use the data from the survey. Let's assume that the survey results are summarized in the following table (attached) :
From this table, we can see that the probability of a worker living more than 5 miles from work is 35%. We can also see that the probability of a worker riding their bicycle is 50%, and the probability of a worker living more than 5 miles from work and riding their bicycle is 20%.
To calculate the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle, we can multiply the probabilities of these two events:
P(Lives > 5 miles and Rides Bicycle) = P(Lives > 5 miles) x P(Rides Bicycle | Lives > 5 miles)
= 35% x (20%/35%)
= 0.5714 or 57% (rounded to the nearest whole percent)
Therefore, the probability that a randomly selected worker lives more than 5 miles from work and rides their bicycle is 57%.
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the riverton high rockets won their regional basketball tournament and were awarded this trophy. what is the approximate volume of the trophy?
V Prism is V = B × h=9.5*4=38
the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47
V=10.47+38=48.476
A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.
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The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet. 2 0, 1, 4 3 1, 2, 6 4 1, 3, 7 5 1, 1 6 5key: 3|2 means 3.2 what is the mean, and what does it tell you in terms of the problem? a. 3.85 feet; the value means that a typical throw of the ball results in 3.85 feet. b. 3.2 feet; the value means the furthest the ball went. c. 5.1 feet; the value means this measurement had the most occurrences. d. 4.62 feet; the value means that a typical throw of the ball results in 4.62 feet.
The mean, also known as the average, is a central value that represents the typical value of a set of data.
To calculate the mean, you add up all the values in the data set and divide by the number of values. The mean provides a general sense of the distribution of the data and helps to identify any patterns or trends. In the stem-and-leaf plot, the mean can be calculated by adding up all the values and dividing by the number of throws. The mean in this case is 4.62 feet, which indicates that a typical throw of the ball results in 4.62 feet. This value can be used to gain a better understanding of the overall performance of the ball thrower and provide insight into how far the ball is typically thrown.
It is important to note that the mean is sensitive to outliers or extreme values, so it may not accurately reflect the typical value of the data in all cases. However, in this particular case, the mean provides a useful representation of the typical performance of the ball thrower.
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Answer:d
Step-by-step explanation:
PLSSS HELP!!
Which cross-sections are possible in BOTH cylinders and cones? Choose ALL that apply.
A. circle
B. oval
C. half-oval
D. rectangle
E. triangle
A. Circle
B. Ellipse (which can resemble an oval)
PLEEASSE HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
John and Mary are building towers out of lego bricks. John used fewer than 18 bricks for his
tower. Mary used twice as many bricks as John. What is the greatest number of bricks Mary
could have used?
Answer:
34 bricks is the greatest amount Mary could have used
Step-by-step explanation:
1.1 write down the loan term of the truck in years
Answer:
if its 50,000k for example it is gonna be Loan term in years is 7 it depends on the price
Step-by-step explanation:
A linear equation in one variable can have solution(s).
a. only 1
b. 2
c. 3
d. any number of
do you believe that this conjectures "all numbers coming from the question p=n²-n+41 are prime numbers"?
Answer: No
Step-by-step explanation:
Valid only for numbers less than 40.
P(40) = 412 which is not a prime number
Mav is working two summer jobs, making
$15 per hour lifeguarding and making $10
per hour landscaping. In a given week, she
can work at most 12 total hours and must
earn no less than $140. If x represents the
number of hours lifeguarding and y
represents the number of hours
landscaping, write and solve a system of
inequalities graphically and determine
one possible solution.
Inequality 1: y ≥û
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
y
Inequality 2: y ≥û
0 1 2 3
4
5
switch shade
plot
6
switch shade
plot
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Xx
This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
What is inequality?
In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
We can write the first inequality as x + y <= 12
This inequality represents the constraint that Mav can work at most 12 hours in total between both jobs.
The second inequality represents the constraint that Mav must earn no less than $140 in a given week, which can be written as:
15x + 10y >= 140
To graph the system of inequalities, we can plot the lines corresponding to x + y = 12 and 15x + 10y = 140 on the coordinate plane and shade the region that satisfies both inequalities.
The solution to the system of inequalities will be the values of x and y that lie in the shaded region.
One possible solution is x = 4 and y = 8, which means that Mav works 4 hours of lifeguarding and 8 hours of landscaping in a given week, earning a total of 15 * 4 + 10 * 8 = $120.
Hence, This solution satisfies both constraints, as x + y = 4 + 8 = 12, which is less than or equal to 12, and 15x + 10y = 15 * 4 + 10 * 8 = 120, which is greater than or equal to 140.
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Answer:
y ≤ 12 -xy ≥ 14 -1.5x(x, y) = (4, 8) — 4 hours lifeguarding, 8 hours landscapingStep-by-step explanation:
You want inequalities, their graph, and a possible solution satisfying Mav's requirement for at most 12 total hours spent lifeguarding at $15 per hour and landscaping at $10 per hour, with an income of at least $140.
SetupThe required relations can be written ...
x + y ≤ 12 . . . . . . . total hours
15x +10y ≥ 140 . . . . total earnings
InequalitiesThe inequalities need to be solved for y to match the answer format requirements.
inequality 1: y ≤ 12 -x . . . . . . . . . . subtract x
inequality 2: y ≥ 14 -1.5x . . . . . . divide by 10, subtract 1.5x
SolutionThe attached graph shows a couple of possible solutions. The solution space is the doubly-shaded area bounded by vertices ...
(4, 8), (12, 0), and (9 1/3, 0)
Mav will make the most money working 12 hours lifeguarding (x, y) = (12, 0).
She can just meet her income requirements by working 8 hours lifeguarding and 2 hours landscaping (x, y) = (8, 2).
One possible solution is 4 hours lifeguarding and 8 hours landscaping.
The cost of fuel per litre is calculated using the following formula. (1 + 100) X + X 160 C = cost of oil per barrel. F = rate of fuel duty tax in %. P = percentage profit the petrol station wants to make. Fuel duty is 50%, and oil costs £128 per barrel. A petrol station wants to make 100% profit. Work out the cost of fuel per litre at this petrol station.
If a petrol station wants to make 100% profit. the cost of fuel per litre at this petrol station is 1.4 pence.
How to find the cost?Given, the formula to calculate the cost of fuel per litre:
(1 + 100) X + X 160 C = cost of oil per barrel.
Where :
X = cost of oil per litre
C= rate of fuel duty tax in %.
We know that fuel duty is 50% and oil costs £128 per barrel, so we can substitute these values into the equation:
(1 + 100) X + X 160 * 0.5 = 128
Expanding the equation:
100 X + 80 X = 128
180 X = 128
Dividing both sides by 180:
X = 128/180 = 7/10 = 0.7
So, the cost of oil per litre is 0.7 pence.
The petrol station wants to make 100% profit, so we add the profit to the cost of oil per litre:
0.7 + 0.7 * (100/100) = 1.4 pence
Therefore, the cost of fuel per litre at this petrol station is 1.4 pence.
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anyone knows the answer for this?
The blank in the statement should be filled in with "ΔVYZ." which is proven by the definition of congruence.
What is a Triangle?Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbolΔ.
Since S, T, and U are midpoints in ΔVYZ, it follows that:
ST is a median of ΔVYZ, meaning it bisects the side VZ into two equal parts.
TU is a median of ΔVYZ, meaning it bisects the side VY into two equal parts.
SV is a median of ΔVYZ, meaning it bisects the side YZ into two equal parts.
Using the definition of congruence, two triangles are congruent if their corresponding sides are equal in length and their corresponding angles are equal in measure. Since medians bisect their corresponding sides, it follows that all three pairs of corresponding sides in ΔYST, ΔTUZ, and ΔSVU are equal in length.
Furthermore, since the medians divide the triangle into two smaller triangles that are similar to the original triangle, it follows that the corresponding angles in ΔYST, ΔTUZ, and ΔSVU are equal in measure.
Therefore, ΔYST ≅ ΔTUZ ≅ ΔSVU ≅ ΔVYZ.
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