60 engineering students are divided into 24 who take math and 29 who take physics. 10 students take statistics and physics together, 13 students take math and physics together. a) There are 26 students take statistics. b) P(A/B)=4/13.
The science of statistics is concerned with the research and advancement of methods for collecting, analyzing, interpreting, and presenting empirical data. The science of learning from data is called statistics, which is also possibly an art. The discipline's focus is on the gathering, analyzing, and interpretation of data as well as the efficient dissemination and presentation of findings that rely on data.
We can assume the following:
1). There are 13-8=5 pupils who study physics and math together but not statistics (green colour)
2). There are 10-8=2 pupils who study physics and statistics together but not math (grey colour)
3). Students who take algebra and statistics but not physics total 11-8=3. (yellow colour)
4). There are 14 pupils (29-5-8-2) who only take physics (pink colour)
We can now determine how many students solely take statistics by doing the following: The number of students enrolled in at least one course (60–7) less the number taking only math or just physics or just statistics but not math.
53-24-14-2=13 students take only statistics
There are 26 students who take statistics, or 13 + 2 + 3 + 8
b) Let's say A takes all three, and B takes statistics. Finding conditional probability is the goal.
P(A/B)= P(A⋂B)/P(B)
P(A⋂B)= 8/60, P(B)=26/60
So,
P(A/B)=P(A⋂B)/P(B)=8/26=4/13
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two friends who take metro to their jobs from the same station arrive to the station uniformly randomly between 7 and 7:20 in the morning. they are willing to wait for one another for 5 minutes, after which they take a train whether together or alone. what is the probability of their meeting at the station?
The probability of two friends meeting at the station 0.28.
To calculate the probability of the two friends meeting at the station, we need to find the overlap in their arrival times, which is between 7:00 and 7:05 in the morning. This overlap represents the time window where they both arrive at the station and can meet. Given that they both arrive between 7:00 and 7:20 in the morning with a uniform distribution, the probability of one of them arriving in the overlap time window is 5/20.
Thus, the probability of both friends arriving in this time window and meeting at the station is the product of these probabilities, which is (5/20) * (5/20) = 0.28.
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5x - (x + 3) = 3(2 - 2x) + x
X=
Step-by-step explanation:
To find the value of x, we need to solve the equation:
5x - (x + 3) = 3(2 - 2x) + x
Expanding the right-side expression:
5x - (x + 3) = 6 - 6x + x
Combining like terms on both sides:
6x - 3 = 6 - 5x
Adding 5x and 3 to both sides:
11x = 9
Dividing both sides by 11:
x = 9/11
So the value of x is approximately 0.818181818.
Half of the fish in a tank are rainbow fish.
20% are gouramis and the rest are corydoras.
Write the ratio of rainbow fish to gouramis to corydoras in the simplest form.
Originally there were 20fish. Three more rainbow fish are added.
What fraction of the fish in the tank are now rainbow fish?
The ratio of the rainbow fish to guoramis to corydoras is 5:2:3
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.
Rainbow fish is half, this means that the percentage of rainbow fish is 100×1/2 = 50%
percentage of guoramis is 20%
therefore the percentage corydoras = 100-(20+50) = 30%
therefore the ratio of rainbow fish to guoramis to corydoras = 50:20:30
divide through by 10 = 5:2:3
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If you were considering buying a stock, which time frame would you use to analyze its price history (1-day, 5-day, 1-month, etc)? Why?
Help me out please.
When considering buying a stock then the best time frame to use to analyze the price history depends on your investment goals but on average, 1 year to 5 years.
How to determine a time frame for analysis ?The time frame for analyzing a stock's price history depends on the investment horizon and the goals of the investor. If you are a short-term trader who seeks to make quick profits, you might use a 1-day or 5-day time frame to analyze the stock's price movements.
Medium-term investor with a horizon of a few months to a year, should use a 1-month or 3-month time frame. For long-term investors with a horizon of several years, use a 1-year or even longer time frame, such as 5 years or 10 years.
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Consider this right triangle.
7.5
4.
4.5
Determine whether each equation is correct. Select Yes or No for each equation.
sin (F) =
cos(F) = 6
7.5
sin (G) = 4.5
7.5
cos(G) =
6
7.5
Yes No
0
0
Step-by-step explanation:
Given
Opp=8
Adj=6
Hyp=10
Answer
1)Sin<A=Opp/Hyp
8/10=4/5... Yes
2)Cos<A=Opp/Adj
8/6=4/3... No
Given
Opp=6
Adj= 8
Hyp= 10
Answer
1)Sin<B= Opp/Hyp
6/10=3/5... No
2)Cos<B= Opp/Adj
6/8=3/4... No
Four boys have heights of 155155 centimeters, 156156 centimeters, 158158 centimeters, and 162162 centimeters.
What is the mean height of the four boys?
The mean height of the four boys is 157657.75 centimeters.
What are mean, median, and mode?The three main methods for identifying the average value of a set of integers are mean, median, and mode.
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean.
The middle value in a list that is arranged from smallest to greatest is called the median.
The value that appears the most frequently on the list is the mode.
Given, Four boys have heights of 155155cm, 156156cm, 158158cm, and 162162cm.
Therefore, The mean height of the boys is the sum of the heights of boys divided by the total number of boys which is,
= (155155 + 156156 + 158158 + 162162)/4.
= 630631/4.
= 157657.75 cm.
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the ratio of length to width f a rectangular garden is 6:7. if the permeter of the rectangle is 78 meters, what s the area of the garden in square meters
The area of the garden will be = 1512 square meters.
The formula for calculating the area of a rectangle.
Rectangle surface area. A = l × b.
Once the length and breadth of a rectangle are determined, the area is computed.
The area of a rectangle may be calculated by multiplying its length and width.
Let's assume the length of the garden is 6x meters and the width is 7x meters, where x is a positive value that we need to find.
From the given ratio, we have:
6x + 7x = 78
13x = 78
x = 6
So the length of the garden is 6 * 6 = 36 meters and the width is 7 * 6 = 42 meters.
The area of the garden can be calculated as: 36 * 42 = 1512 square meters.
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Which system of inequalities matches the graph?
A. y> 2x-4 and y > 2
B. y<2x-4 and y < 2
C. y <2x-4 and y ≤ -2
D. y <2x-4 and y < 2
Deadline: February 4 (Saturday)
The system of inequalities on the graph is:
y ≤ 2
y > 2x - 4
Which system of inequalities matches the graph?Here we have the graph of a system of inequalites.
First, we can see a solid horizontal line, such that the shaded region is below that line, then one of the two inequalities will be:
y ≤ 2
And then we have a dashed line with a slope of 2 and an y-intercept of -4, this time the region above the line is shaded.
y > 2x - 4
Then the system of inequalities on the graph is:
y ≤ 2
y > 2x - 4
I can notice that this system does not appear on the options, so there may be a mistake in the options.
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[tex]\frac{10}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}[/tex]
The value of the rationalization is 5√2
What are surds?Surds are described as the nth root of a number, say x and a number r which, when raised to the power n
Given that;
n is a positive integer or the degree of the root.
It is also seen as an expression that includes a square root, a cube root or other roots.
They are used to write irrational numbers only.
Given the surds;
10/√2 × √2/ √2
Multiply the values
10√2/2
Divide the values
5√2
Hence, the value is 5√2
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PLEASE HELP EASY MATH
The length PR is given as follows:
PR = 337.75 ft.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The similar triangles for this problem are given as follows:
PRE and POC.
Hence the equivalent side lengths are given as follows:
PR = x and 165 ft.x + 125 ft and 255 ft.Then the proportional relationship among the equivalent side lengths is given as follows:
x/165 = (x + 125)/255.
Applying cross multiplication, the length PR, represented by x, is obtained as follows:
255x = 165(x + 125).
225x = 165x + 20625
60x = 20265
x = 20265/60
x = 337.75 ft.
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A sphere has a volume of 2304πft3. What is the radius of the sphere?
The radius of the sphere is 42 feet.
The correct option is D.
What is volume?Space occupied by an object in three dimensional space is called as volume of an object. In simple words space is taken by object.
Given:
A sphere has a volume of 2304π cubic feet.
The volume of sphere = 4/3 π r³
4/3 π r³ = 2304π
r³ = 1728
r = 41.6
r ≈ 42 feet.
Thererfore, the radius is 42 feet.
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Simplify the expression (64)2.
Answer:16
Step-by-step explanation:
Answer:
128
Step-by-step explanation:
When dealing with those types of problems, that's just another way of saying it's multiplication.
(64)2=64×2
which in this case, if you multiply to those numbers
64×2
youll get 128
64×2=128
please help fill in each black so that the resulting statement is true.
Answer:
(x^2 + 4x) + (y^2 - 18 y) - 5, complete the square on on x by adding to both sides.
Step-by-step explanation:
Answer:
The 4th answer: ((x1+x2)/2 , (y1+y2)/2)
Step-by-step explanation:
To find the midpoint of a segment, you get the average of the x intercepts and y intercepts. So for the x-intercept, add the x-intercepts and divide by 2 and for the y-intercept, add the y-intercepts and divide by two.
((x1+x2)/2 , (y1+y2)/2)
Anni rode her bicycle on a trail for 80 minutes at an average speed of 12 miles per hour. How long will it take her to ride the same trail at a speed of 15 miles per hour?
Answer: 100 minutes
Step-by-step explanation:
Two boats were 400 miles apart at midnight and were both sailing to the same port on Honolulu. One boat was heading west and the other was heading east. If they both arrived at 8:00am, find the speed of each boat if one was 20MPH faster than the other.
The slower boat traveled at 15mph, and the faster boat traveled at 35mph.
How to determine the speed of each boatRepresent the speed of the slower boat with x.
So, the speed of the faster boat would be x + 20mph.
The time they took to meet is 8 hours, so the total distance they covered during that time is represented as
Distance = x * 8 + (x + 20) * 8
So, we have
Distance = 16x + 160
The distance between the two boats was 400 miles at midnight
So, we have the following distance equation
400 = 16x + 160
Evaluate the like terms
16x = 240
Divide by 16
x = 15
Recall that
Faster boat = x + 20mph.
So, we have
Faster boat = 15 + 20
Faster boat = 35
Hence, the slower boat was traveling at 15mph
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The function f(x) is invertible. Find the value of
�
(
−
43
)
f(−43).
The function f(x) has a value of 1929 for f(-43)
How to evaluate the invertible functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = x^2 - 2x - 6
An invertible function involves a function that have an inverse function or relation
The value of x in f(-43) is
x = -43
Substitute the known values in the above equation, so, we have the following representation
When the function f(-43) is calculated, we have
f(-43) = (-43)^2 - 2(-43) - 6
Evaluate the function
f(-43) = 1929
Hence, the value is 1929
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Complete question
The function f(x) is invertible. Find the value of
f(−43). if f(x) = x^2 - 2x - 6
suppose that 90% of all batteries from a certain supplier have acceptable voltages. a certain type of flashlight requires two type-d batteries, and the flashlight will work only if both its batteries have acceptable voltages. among ten randomly selected flashlights, what is the probability that at least nine will work? what assumptions did you make in the course of answering the question posed?
Suppose that 90% of batteries that are supplied from the certain supplier have acceptable voltages, probability that among all the batteries supplied least nine will work is 26 and 0.3076 .
M: Math
P: Physics
S: Statistic
n(Math) = 24
n(Physics) = 29
Formula:
Putting the values, we get,
Thus, 26 students took statistic.
Probability is basically based on the possible chances or the chances of happening of something. The theoretical probability is a type of probability that is mainly based on the reason behind that probability. For example, if a coin is tossed, the theoretical probability or the outcome of getting a head will be ½.
Probability is the branch of mathematics that basically concern about the occurrence of a random event or the chances of favorable outcome and there are mainly four types of probability exist: classical, empirical, subjective and axiomatic.
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Rewrite the following equation in slope-intercept form. 8x + 13y = -9
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Step-by-step explanation:
Rewrite the following equation in slope-intercept form. 8x + 13y = -9 Write your answer using integers, proper fractions, and improper fractions in simplest form.
Slope intercept form mean to solve for y:
8x + 13y = - 9
subtract 8x from both sides:
8x + 13y - 8x = - 9 - 8x
13y = - 9 - 8x
rearrange right side:
13y = - 9 - 8x becomes:
13y = - 8x - 9
divide both sides by 13:
13y/13 = (- 8x - 9)/13
Answer: y = [tex]\frac{-8}{13} x-\frac{9}{13}[/tex]
find the number of ways to seat n married couples around a table in each of the following cases: (a) men and women alternate. (b) every woman is next to her husband.
(a) In this case, the men and women alternate, so we can treat them as two separate groups. There are n! ways to seat the n men in the first n seats and n! ways to seat the n women in the next n seats.
So, there are a total of (n!) ^2 ways to seat the n married couples.
(b) In this case, every woman must be next to her husband. We can treat each married couple as a single entity and seat them in (n!) ways.
So, there are n! ways to seat the n married couples around the table in this case.
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What is the volume of this cylinder?
Use ≈ 3.14 and round your answer to the nearest hundredth.
The volume of the given cylinder would be = 4300 in³
How to calculate the volume of a cylinder?The formula that can be used to calculate the volume of a cylinder = V= πr²h
where,
π = 3.14
r = 14
h = 7
volume = 3.14× 14² × 7
= 3.14× 196× 7
= 4308.08
= 4300 in³
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*find x
26x-4=15x+24
with a side length of 10 feet. what will be the length of the path? round your answer to 2 decimal places.
The length of the path is determined by Pythagoras theorem and the length is equal to 14.14 feet.
The flower garden is in the shape of a square with a side length of 10 feet.
We have to find the length of the path at which Chi is paving the stones.
Since the length of the path is in the shape of the diagonal of the square.
Let, the length of the path be "L" feet.
By Pythagoras theorem,
[tex]10^{2} + 10^{2} =L^{2} \\100+100=L^{2} \\L^{2} = 200\\L=\sqrt{200} \\L=\sqrt[10]{2} = 14.142= 14.14 feet.[/tex]
Hence, the length (L) of the path is equal to 14.14 feet.
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Complete question:- ChiChi is planning to put a path of paving stones throughthrough her flower garden and the path is situated as a diagonal of her garden as the garden is a square with a side length of 10 feet. What will be the length of the path? Round your answer to 2 decimal places.
Lars bought a carton of
eggs for $2.19. He handed
the cashier $5.00. How
much change did Lars
receive?
Answer:
$2.81
Step-by-step explanation:
on the south side of the building, the first quartile is 43cm, the median is 46cm, and the third quartile is 48cm. if she goes to the south side and randomly selects three daffodils, what is the probability that none of them are between 46cm and 48cm?
Around 50% to 75% of the daffodils on the south side of the building are not between 46cm and 48cm.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
This question asks for the probability that none of the three daffodils selected from the south side of the building are between 46cm and 48cm.
Since the median of the data is 46cm
the third quartile is 48cm,
this means that about 50% to 75% of the daffodils on the south side of the building are between 46cm and 48cm.
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PLEASE answer this quickly
The true statement about b is b = p + q, and about c is c = p*q.
What is a quadratic function?A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. It is also known as the polynomial of degree 2 since the greatest degree term in a quadratic function is of the second degree.
Given a quadratic function, x² + bx + c
and factors of equation is (x + p)(x + q)
for any quadratic equation, the product of factors is equal to the product of a and c,
here a = 1 and c = c
c = p*q,
and the sum of factors is equal to b,
b = p + q.
Hence options A and C are correct.
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In baseball, each time a player attempts to hit the ball, it is recorded. The ratio of hits compared to total attempts is their batting average. Each player on the team wants to have the highest batting average to help their team the most. For the season so far, Jana has hit the ball 12 times out of 15 attempts. Tasha has hit the ball 9 times out of 10 attempts. Which player has a ratio that means they have a better batting average?
Tasha, because she has the lowest ratio since 0.9 > 0.8
Tasha, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Jana, because she has the lowest ratio since 0.9 > 0.8
Jana, because she has the highest ratio since 27 over 30 is greater than 24 over 30
Answer: Tasha
Step-by-step explanation:
9/10 = .900 avg
12/15 = .800 avg
If you standardize the ratios to 30, then:
27/30 = .900 avg
24/30 = .800 avg
Given m∠DBC=36°, m∠DBA=(3x+20)°, and m∠CBA=(8x+6)°and that ∠ABD and ∠CBD are adjacent angles.
The measure of the angle m∠DBA is equal to 50°
How to evaluate for the missing angle m∠DBAFrom the question, we observe that the larger angle m∠CBA consists of the two angles m∠DBC and m∠DBA, so we shall sum the two small angles and equate the result to the larger angle to solve for the value of x as follows:
36° + 3x + 20 = 8x + 6
8x - 3x = 36 + 20 - 6 {collect like terms}
5x = 50
x = 50/5 {divide through by 5}
x = 10
so we can evaluate for the angle m∠DBA as follows:
m∠DBA = 3(10) + 20
m∠DBA = 30 + 20
m∠DBA = 50°
In conclusion, the measure of the angle m∠DBA is equal to 50°.
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The blues band, Jonny and the Silver Toads, charges $25 per ticket at their performances. Their next venue charges them $800 for use of the venue. Based on the inequality below, how many tickets, t, do they need to sell in order to profit at least $1,725?
If they want to make a profit of $1,725 or more, then they need to sell at least 101 tickets.
How many tickets do they need to sell?We know that each ticket costs $25, then if they sell t tickets the revenue is:
R(t) = 25t
We know that the band has a cost of $800, and they want to make a profit of at least $1,725, then we can write the inequality below:
25t - 800 ≥ 1,725
(remember that the profit is the difference between the revenue and the cost).
Now we can solve that for t.
25t ≥ 1,725 + 800
25t ≥ 2,525
t ≥ 2,525/25
t ≥ 101
They need to sell at least 101 tickets.
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how to find the hypotenuse of a triangle with two sides?
The Pythagorean formula, c=√a²+b², can be used to get the required hypotenuse.
What is the hypotenuse?The hypotenuse is the longest side of a right-angled triangle or the side that faces away from the right angle.
The length of the hypotenuse can be calculated using the Pythagorean theorem, which states that the square of the hypotenuse's length equals the sum of the squares of the lengths of the other two sides.
If one of the other sides in this situation is 3 (when squared, this equals 9) and the other is 4, this equals 16, and the sum of their squares is 25.
The length of the hypotenuse is equal to the square root of 25, or 5.
The hypotenuse can be found using the Pythagorean formula, which is c=√a²+b².
Therefore, the Pythagorean formula, c=√a²+b², can be used to get the hypotenuse.
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simplify the ratio 14:8
Answer: 7:4
Step-by-step explanation:
To simplify the ratio 14:8, we find the greatest common divisor of 14 and 8, and then we divide 14 and 8 by the greatest common divisor.
The greatest common divisor that you can use to simplify 14:8 is 2. This means the answer to the ratio 14:8 simplified is:
7:4