Step-by-step explanation:
The total number of students = 100
Let A represents calculus and B represents French
The no of students taking calculus = 32
The no of students taking French = 29
The no of students taking calculus and french = 13
the probability that the student is taking Calculus or French = ?
P (AUB) = P(A) + P(B) - P(A∩B)
= [tex]\frac{32}{100}[/tex] + [tex]\frac{29}{100}[/tex] - [tex]\frac{13}{100}[/tex]
= [tex]\frac{48}{100}[/tex]
Reducing to lowest fraction, it becomes [tex]\frac{12}{25}[/tex]
The probability that the student is taking Calculus or French = [tex]\frac{12}{25}[/tex]
The probability that a randomly selected student is taking Calculus or French is 12/25.
To find the probability that a randomly picked student is taking either Calculus or French, we use the principles of set theory, specifically the formula for the union of two sets:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
Here,
A = Students taking Calculus = 32
B = Students taking French = 29
A ∩ B = Students taking both Calculus and French = 13
Total students = 100
The formulas for the probabilities are:
P(A) = 32/100
P(B) = 29/100
P(A ∩ B) = 13/100
Now substitute these values into the union formula:
P(Calculus or French) = 32/100 + 29/100 - 13/100 = 48/100 = 12/25
Therefore, the probability that a randomly picked student is taking either Calculus or French is 12/25.
plzzz help 4^2 × 5^2 -30
Answer:
370
Step-by-step explanation:
4^2 = 16
5^2 = 25
25 x 16 = 400
400 - 30 = 370
Your welcome! :D
A bag contains 3 red marbles, 7 white marbles, and 5 blue marbles. You draw 3 marbles, replacing each one before drawing the next. What is the probability of drawing a red, then a blue, and then a white marble?
3 + 7 + 5 = 15 total marbles.
3 red, picking a red would be 3/15, reduced to 1/5
5 blue, picking a blue would be 5/15, reduced to 1/3
7 white, picking a white would be 7/15
Picking all 3 would be: 1/5 x 1/3 x 7/15 = 7/225
Answer:
7/225
Step-by-step explanation:
To find probability, we take the number of ways the specific event can occur and divide it by the number of ways any event can occur.
The probability of drawing a red marble is: (# of red marbles) / (total # of marbles) = 3/(3 + 7 + 5) = 3/15 = 1/5.
The probability of drawing a blue marble is: (# of blue marbles) / (total # of marbles) = 5/(3 + 7 + 5) = 5/15 = 1/3.
The probability of drawing a white marble is: (# of white marbles) / (total # of marbles) = 7/(3 + 7 + 5) = 7/15.
Now, we want these events to all occur for us. So, we must multiply them by each other: (1/5) * (1/3) * (7/15) = 7/225.
Thus, the probability is 7/225.
Hope this helps!
Solve by elimination 4x-8y=8 -5x-y=-21
Find the surface area of the figure, Please hurry and give an accurate answer
Given:
The base of the triangle = 5 mm
The other side of the of the triangle = 9 mm
The 3rd side of the triangle = 9 mm
The height of the triangle = 7 mm
The height of the prism = 12 mm
To find the surface area of the the prism.
Formula:
The surface area of a triangular prism is
[tex]SA = bh+(s_{1} +s_{2} +s_{3})H[/tex]
Where,
h be the height of the triangle
H be the side of the prism
b be the base of the triangle
[tex]s_{1} ,s_{2} ,s_{3}[/tex] are the sides of the triangle.
Now,
Putting, b=5, H= 12, h=7, [tex]s_{1} =5,s_{2} =9,s_{3} =9[/tex] we get,
[tex]SA = (5)(7)+(5+9+9)(12)[/tex]
or, [tex]SA = 35+276[/tex]
or, [tex]SA = 311[/tex] sq mm
Hence,
The surface area of the triangular prism is 311 sq mm.
Solve for x. x^2 +12x+27=0
Answer:
x= -3,-9
Step-by-step explanation:
Answer: 9,3
Step-by-step explanation:
What is the GCF for 84 and 90
Answer:
The GCF for 84 and 90 is 6.
Step-by-step explanation:
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Then the greatest common factor is 6.
Answer:
GCF=6
Step-by-step explanation:
In order to find the GCF of 84 and 90 you must find the prime factors of each term.
what is the value of f(x)=6
Answer:
f(x)=6
Step-by-step explanation:
By Substitution
f(x or coefficient of x)
=6 since X doesn't exist in question above
Final answer:
The value of f(x) is 6, indicating a constant function where the output is the same irrespective of the input. For constant functions, the total differential is zero as there is no change in the function value with varying x.
Explanation:
The question is asking for the value of f(x) when f(x) is equal to 6. This is a type of question that involves understanding how functions work. In this particular case, the question seems to be abstract, suggesting that f(x) = 6 for all x, indicating a constant function. A constant function is one where the output value is the same no matter what the input value is.
Considering this, without additional context or a specific function definition besides f(x) = 6, we presume that the student is being asked to recognize this as a constant function. Therefore, the value of f(x) is always 6, regardless of the value of x.
However, if we are considering a function that changes with respect to x, the total differential would be involved to find infinitesimal changes in f(x) as x changes. For a constant function like this one, the differential would be zero since the function's value does not change as x changes.
Jenny has a gift box shaped like a triangular prism. Each side of the base is 12 cm. The triangular base has a height of 10.4 cm. The prism is 68 cm tall. Find the amount of the gift wrap needed to cover the box
The total surface area will be 1360.2 square centimeters.
To find the amount of gift wrap needed to cover Jenny's gift box shaped like a triangular prism, we first need to calculate the surface area of the prism.
The box has two triangular bases and three rectangular sides.
Therefore,
Calculate the total surface area of the triangular prism: 2(base area) + (base perimeter * prism height)
Substitute the values:
= 2(1/2 * base side * base height) + (base side * 3base side + prism height)
Solve to find the total surface area:
= 2(1/2 * 12 cm * 10.4 cm) + (12 cm * 3 * 12 cm + 68 cm)
= 1360.2
After calculations, the total surface area will be 1360.2 square centimeters.
The amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.
To find the amount of gift wrap needed to cover a triangular prism, we need to calculate the total surface area of the prism.
Given information:
- Each side of the base is 12 cm.
- The triangular base has a height of 10.4 cm.
- The prism is 68 cm tall.
Calculate the area of the triangular base.
Area of a triangle = (1/2) × base × height
Area of the triangular base = (1/2) × 12 cm × 10.4 cm
Area of the triangular base = 62.4 cm²
Calculate the perimeter of the triangular base.
Perimeter of a triangle = sum of all sides
Perimeter of the triangular base = 12 cm + 12 cm + 12 cm = 36 cm
Calculate the area of the rectangular faces.
Area of a rectangle = length × width
Area of each rectangular face = 36 cm × 68 cm = 2,448 cm²
Total area of the rectangular faces = 2 × 2,448 cm² = 4,896 cm²
Calculate the total surface area of the triangular prism.
Total surface area = Area of the triangular base + Area of the rectangular faces
Total surface area = 62.4 cm² + 4,896 cm²
Total surface area = 4,958.4 cm²
Therefore, the amount of gift wrap needed to cover the box is 4,958.4 cm² or approximately 4.96 square meters.
Do you know the answers?
Answer:
In the picture above
Step-by-step explanation:
I hope that it's a clear solution and explanation.
Goodluck.
Which expression represents the approximate area of the circle in square inches?a.9.42 times 3 b.9.42 times 3 squared c.9.42 times 6 d.9.42 times 6 squared
Answer: The answer is B
Step-by-step explanation:
Answer:
A. 9.42
Step-by-step explanation:
Assume that 0
a. 16/63
b. -16/63
c. 63/16
d. -63/16
please help
Subtract: (6x – 3) - (11x – 8)
Answer:
-5x+5
Step-by-step explanation:
(6x-3)-(11x-8)=
6x-11x-3+8=
-5x+5
The subtraction of (6x -3) - (11x - 8) is 5(x - 1)
The subtraction method of algebraic terms takes a process whereby you first open the brackets, followed by rearranging variables with common-like terms.
Given that:
(6x -3) - (11x - 8)
Open brackets
= 6x - 3 - 11x + 8
Collecting like terms by rearrangement
= 6x - 11x - 3 + 8
= -5x + 5
Multiply through by (-)
= 5x - 5
Factorize out (5)
= 5(x - 1)
Therefore, we can conclude that the subtraction of (6x -3) - (11x - 8) is 5(x - 1)
Learn more about subtraction here:
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scientific notation for 1,424,600,000?
Answer: 1,424,600,000 = 1.4246 × 10^9
Step-by-step explanation: ten to the power of 9 =1000000000
1000000000 x 1.4246 = 1 ,424,600,000
PLS HELP Use elimination to solve each system of equations.
6x + 5y = 4]
6x - 7y = -20
Answer:
x = -1
y = 2
Step-by-step explanation:
6x + 5y = 4
6x - 7y = -20
__________ -
____12y = 24
______y = 24/12
______y = 2
6x + 5y = 4
6x + 5(2) = 4
6x + 10 = 4
6x = 4 - 10
6x = -6
x = -6/6
x = -1
Make as the brainliest answer
Answer:
x = -1
y = 2
Step-by-step explanation:
6x + 5y = 4
6x - 7y = -20
____________--
12y = 24
y = 24/12
y = 2
6x + 5y = 4 | ×7 |
6x - 7y = -20 | ×5 |
42x + 35y = 28
30x - 35y = -100
______________+
72x = -72
x = -72/72
x = -1
Given f (x )equals 5 x plus 9 and g (x )equals 3 x squared, first find f plus g, f minus g, fg, and StartFraction f Over g EndFraction . Then determine the domain for each function.
Answer with Step-by-step explanation:
We are given that
[tex]f(x)=5x+9[/tex]
[tex]g(x)=3x^2[/tex]
f(x) is linear function
Domain of f(x)=R
g(x) is a quadratic function
Domain of g(x)=R
[tex](f+g)(x)=f(x)+g(x)=5x+9+3x^2[/tex]
Domain of (f+g)=R
(f-g)(x)=f(x)-g(x)=[tex]5x+9-3x^2[/tex]
Domain of (f-g)=R
[tex]fg(x)=f(g(x))=f(3x^2)=5(3x^2)+9=15x^2+9[/tex]
Domain of fg=R
[tex]\frac{f}{g}=\frac{5x+9}{3x^2}[/tex]
The function is not defined where g(x)=0
[tex]3x^2=0[/tex]
[tex]x=0[/tex]
Domain of f/g=R-{0}
REWARD 50 POINTS
After stepping into a room with unusual lighting, Erick's pupil has a radius of 4 millimeters. What is the pupil's area?
Answer:
50.24 mm²
Step-by-step explanation:
Area = pi × r²
3.14 × 4²
50.24 mm²
Macy of New York sold LeeCo. of Chicago office equipment with a $7,600 list price. Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight. LeeCo. pays the invoice within the discount period. What does LeeCo. pay Macy?
Answer:
$7544 is the amount paid
Step-by-step explanation:
In this question, we are asked to calculate the amount Leeco pay Macy given the data in the question.
Firstly, we calculate the Discount amount.
That would be 1% ( from 1/10)
that is 7,600 * 1% = $76
Now, we proceed to subtract this value from cost of office equipment; 7,600 - 76 = $7,524
Afterwards, we can now add the freight charges = $7,524 + 20 = $7544
Answer: LeeCo. pay Macy 7544 dollars
Step-by-step explanation:
Given that the office equipment was sold at $7,600
And Sale terms were 1/10, n/30 FOB New York. Macy agreed to prepay the $20 freight.
Then,
7600 - 7600(0.01) + 20
= 7600 - 76 + 20
= 7544 dollars
LeeCo. pay Macy $7544
50 POINTS ANSWER FAST!!!!!!!!!!!
Answer:
d) 1/3
Step-by-step explanation:
fish = 3 + 2 + 1 = 6
bluegill = 2
p = 2/6 = 1/3
Answer:
1/3
Step-by-step explanation:
The total number of fish that were caught
3 trout + 2 bluegill + 1 bass = 6
P (bluegill) = number of bluegill/ total
=2/6
= 1/3
Describe fully the single transformation that maps triangle P onto triangle Q.
Answer: 3
P's coordinates are:
Y X
1, 4
1, 2
2, 2
Once we multiply it by 3 it's equal to Q's coordinates.
Y X
3, 12
3, 6
6, 6
Therefore, P was enlarged 3 times more.
The point P was enlarged by a factor of 3 in both the x and y directions to obtain point Q.
From the graph, the coordinates of point P are given as:
P:
(1, 4)
(1, 2)
(2, 2)
From the given coordinates, we can observe that the x-coordinates of Q are three times larger than the x-coordinates of P, and the y-coordinates of Q are also three times larger than the y-coordinates of P.
After multiplying each coordinate of P by 3, we obtain the coordinates of point Q:
Q:
(3, 12)
(3, 6)
(6, 6)
Learn more about Transformation here:
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A pumpkin is thrown horizontally off of a building at a speed of 2.5\,\dfrac{\text m}{\text s}2.5 s m 2, point, 5, start fraction, start text, m, end text, divided by, start text, s, end text, end fraction and travels a horizontal distance of 12\,\text m12m12, start text, m, end text before hitting the ground. We can ignore air resistance.
Answer:
-47.0
Step-by-step explanation:
The question pertains to Physics, specifically kinematics. The pumpkin's horizontal velocity and distance traveled are given, but without vertical distance, we can't compute the time of flight or height of the building. More information is needed.
Explanation:The subject of your question is Physics, specifically kinematics, which is the study of motion. Given that the pumpkin was thrown horizontally with a velocity of 2.5 m/s and it landed a horizontal distance of 12m from the base of the building, we could find the height of the building or the time the pumpkin was in the air.
The time it takes the pumpkin to hit the ground depends solely on the vertical motion. So we must find the time it takes for an object to fall from the height of the building. This time of flight can be calculated by using a kinematic formula: 2gh = v², where g is the gravitational acceleration (9.8 m/s² on Earth).
However, as the vertical distance travelled by the pumpkin isn't provided in this problem, we can't calculate the time using the given data. More information is needed to solve this problem appropriately.
Learn more about Kinematics here:https://brainly.com/question/7590442
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What is the total number of outcomes when choosing water, milk, juice,
or tea; with or without ice: served in a glass or plastic cup? *
The total possible outcomes of a serving would be 16.
Step-by-step explanation:
Given that,
The total number of beverages = b = 4 ( water, milk, juice,
or tea)
Ice options = i = 2 (with or without ice)
Serving options = s = 2 (glass or plastic cup)
We have to find the total possible outcome x, that can be calculated using
x = b x i x s
Putting the values in the equation, we get
x = 4 x 2 x 2
x = 16
Hence, the total possible outcomes of a serving would be 16.
Woodcut artist makes calendars by hand in one workday he can make approximately 4 calendars. If he works for nine weeks (working five days per week, how many calendars can he produce
Answer:
180 calendars
Step-by-step explanation:
Given that in one workday he can make 4 calendars
Nine weeks (working five days per week)
=> the total number of days he works is: 9*5 = 45 days
=> the total number of calendars he can make in nine weeks is:
the total number of days he works * the number of calendars he make in one day
= 45* 4 = 180 calendars
Hope it will find you well.
what’s the surface area of 5 inches and 7 inches
Answer:
Is the surface a rectangle?? If so, then the surface area would be 35
Step-by-step explanation:
5 * 7 = 35
Hope this helped!! :)
Answer:
35 inches
Step-by-step explanation:
6 11 of students at a school are girls. If there are 4741 students at the school, how many are boys?
Answer:
2155 or 5/11
Step-by-step explanation:
(5/11)4741=5×431=2155 boys
You need to put your reindeer, Bloopin, Balthazar, Bloopin, Prancer, and Quentin, in a single-file line to pull your sleigh. However, Prancer and Balthazar are best friends, so you have to put them next to each other, or they won't fly. How many ways can you arrange your reindeer?
Answer:
120 ways
Step-by-step explanation:
For the school fair, 3 English teachers, 8 math teachers, 5 science teachers, and 4 social studies teachers volunteered for the dunking booth. One of the teachers will be chosen at random for the dunking booth. Is it likely that a math teacher will be chosen for the dunking booth? Explain your answer.
Answer:
The likelihood that a math teacher is selected is 2 out of 5 possible cases or 40% chance.
Step-by-step explanation:
Please kindly check the attached files for explanation
Final answer:
It is likely that a math teacher will be chosen for the dunking booth since the probability is 8 out of 20 or 40%, which is close to a 50% chance.
Explanation:
To determine if it is likely that a math teacher will be chosen for the dunking booth, we need to look at the probability of selecting a math teacher from the total group of teachers. The total number of teachers is the sum of the English, math, science, and social studies teachers, which is 3 + 8 + 5 + 4 = 20. Since there are 8 math teachers, the probability of selecting a math teacher is 8 out of 20, or 40%.
This probability can be further simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 4, giving us 2 out of 5, or 40%. This indicates that there is a likelihood of 2 in 5 that a math teacher will be chosen, which can be considered likely since it is close to a 50% chance.
PLZ HELP ME ASAP What would coordinate d be
Answer:
Coordinate D would be (1,3)
Step-by-step explanation:
The difference between B and C is 2 up and 3 right, so that means the difference between A and D would be the same
D = -2+3, 1+2
D = 1, 3
HELP PLZ!!! Which of the following os the correct equation for this function?
Answer:
The correct answer is C! I just got it right:)
Write the equation in slope-intercept form.
- 4x + 2y = -8
Answer:
y=2x-4
Step-by-step explanation:
Slope intercept form is:
y=mx+b
We need to isolate y to be able to write the equation in slope intercept form
-4x+2y=-8
Add 4x to both sides
-4x+4x +2y= -8+4x
2y= 4x-8
Divide both sides by 2
2y/2=4x/2-8/2
y=2x-4
Now it is in y=mx+b or slope intercept form.
A picture frame is 9 inches long and 6 inches wide it can display pictures 6 inches long and 4 inches wide what is the area of the picture frame
Answer:
54
Step-by-step explanation:
multiply 9 x 6 to get the answer above
The area of the picture frame, after subtracting the area of the displayed picture, is 30 square inches.
To find the area of the picture frame, we need to subtract the area of the picture it displays from the area of the entire frame.
The area of the entire frame can be calculated by multiplying its length by its width:
[tex]\[ \text{Area of frame} = \text{Length} \times \text{Width} \][/tex]
Given that the frame is 9 inches long and 6 inches wide:
[tex]\[ \text{Area of frame} = 9 \times 6 = 54 \text{ square inches} \][/tex]
Now, we need to subtract the area of the picture it displays. Since the picture is 6 inches long and 4 inches wide:
[tex]\[ \text{Area of picture} = \text{Length} \times \text{Width} = 6 \times 4 = 24 \text{ square inches} \][/tex]
So, the area of the picture frame is:
[tex]\[ \text{Area of frame} - \text{Area of picture} = 54 - 24 = 30 \text{ square inches} \][/tex]
Therefore, the area of the picture frame is 30 square inches.