Given:
Total number of student = 40
Students who like Computer Science (group A) = 40
Students who like Philosophy (group B) = 30
Students who like both (group A∩B) = 20
To find:
If a student chosen randomly likes Computer Science, what is the probability that they also like Philosophy?
Solution:
Let the following events,
A: Student like Computer Science
B: Student like Philosophy
Now,
[tex]P(A)=\dfrac{40}{100}=0.4[/tex]
[tex]P(B)=\dfrac{30}{100}=0.3[/tex]
[tex]P(A\cap B)=\dfrac{20}{100}=0.2[/tex]
We need to find the probability that the student like Philosophy if it is given that he likes Computer science, i.e, [tex]P(\dfrac{B}{A})[/tex].
Using conditional probability, we get
[tex]P(\dfrac{B}{A})=\dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]P(\dfrac{B}{A})=\dfrac{0.2}{0.4}[/tex]
[tex]P(\dfrac{B}{A})=\dfrac{1}{2}[/tex]
[tex]P(\dfrac{B}{A})=0.5[/tex]
Therefore, the required probability is 0.5.
Subtract Integers
1. FOOTBALL A team gained 5 yards on
their first play of the game. Then they
lost 6 yards. Find the total change in
yardage.
total change is -1
The total change in yard is -1
By this question we can get
The football A team gained 5 yard on their first day of the game
Then they lost 6 yards
The total change in yard is
We all know
The formula of find change is
Total-loss
So,
5-6=-1
Gain 5 yards
Lost 6 yards
Total change 5-6=-1 (ans)
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Solve the linear inequality and express the solution in set-builder notation.
4(3-2x) + 3x < 6(4 + 2x)
...
The solution in set-builder notation is {x|
(Simplify your answer. Use integers or fractions for any numbers in the expression.)
Answer:
Step-by-step explanation:
Sales Application Statins are used to keep cholesterol in check and are a top-selling drug in the U.S. The equation: S = 1.7 x + 5.2 estimates the amount of sales, S , of statin (in billions of dollars) x years after January 1, 1998. Sales of statin on January 1, 2008 was billion dollars. Statin sales reached 25.6 billion dollars in the year .
Sales of Statin on January 1, 2008 was 22.2 billion dollars; and the year that the Statin sales reached 25.6 billion dollars was in 2010.
How do we calculate sales and the year it occurred?Given:
S = 1.7 x + 5.2 .............................. (1)
Sales of statin on January 1, 2008 can be calculated as follows:
x = 2008 - 1998 = 10
Substituting x = 10 into equation (1), we have:
S = (1.7 * 10) + 5.2
S = 17 + 5.2
S = 22.2
The answer above implies that sales of Statin on January 1, 2008 was 22.2 billion dollars.
The year that the Statin sales reached 25.6 billion dollars can be calculated as follows:
S = 25.6
Substituting S = 25.6 into equation (1) and solving for x, we have:
25.6 = 1.7x + 5.2
25.6 - 5.2 = 1.7x
20.4 = 1.7x
x = 20.4 / 1.7
x = 12
Therefore, we have:
The year Statin sales reached 25.6 billion = 1998 + x = 1998 + 12 = 2010
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The sales of Statin on January 1, 2008 is 22.2 billion dollars and the year statin sales reached 25.6 billion was in 2010
Linear functionsLinear functions are equations that has a leading degree of 1.
Given the expression that represents amount of sales, S , of statin (in billions of dollars) x years after January 1, 1998 as;
S = 1.7 x + 5.2
For the sales of statin on January 1, 2008, this is calculated as
x = 2008 - 1998 = 10years
Substitute x = 10 into the given equation to have;
S = 1.7(10) + 5.2
S = 17 + 5.2
S = 22.2
Therefore the sales of Statin on January 1, 2008 is 22.2 billion dollars.
For the year that the Statin sales reached 25.6 billion dollar;
S(x) = 25.6
Substituting S = 25.6 into the equation
25.6 = 1.7x + 5.2
1.7x = 25.6 - 5.2
1.7x = 20.4
x = 12
Hence the year statin sales reached 25.6 billion was in 2010
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Carol brought 4 pies to a party. Each serving of pie is 1/8 of an entire pie. How many servings of pie did Carol bring to the party?
Answer:
32
Step-by-step explanation:
do 4 divided by 1/8
if you flip the fraction it will become 4/1 × 8/1 = 32
Graph the image of the figure after a dilation with a scale factor of 3 centered at the origin.
Use the polygon tool to graph the dilated figure.
Answer: (3, 3), (3, 9), (-6, 9), (-6, 3)
Step-by-step explanation:
With a dilation of 3 centered about the origin-
the point (1, 1) would go to (3, 3)
the point (1, 3) would go to (3, 9)
the point (-2, 3) would go to (-6, 9)
the point (-2, 1) would go to (-6, 3)
simply multiply the original coordinates all by 3.
Find the slope of the regression line.
Shots on goal 22, 25, 28, 29, 33
Points scored 5, 7, 7, 9,8
A -0.561
B 0.283
C. 0.631
D. 0.794
Norm's electric bill for December 2013 was $149.32. In 2014 the electric bill was $194.31. Next year Norm expects the bill to be the 2013 amount plus $25.00 more than the difference between 2013 and 2014. What is the new bill expected to be?
A): 2013 = 149.32
Find difference of: 194.31
2014 = 194.31 149.32
= 44.99
2015 Total Will Be:
B):
149.32 + 25 = 174.32
(2013)
174.32 + 44.99 = 219.31(B) (A)
0.36 converted into a fraction
Answer:
9/25
Step-by-step explanation:
0.36 = 36/100
36 / 4 = 9
100 / 4 = 25
9/25
QUESTION : -137 +854-84+ 506 =
Answer: 1139
Step-by-step explanation:
-137+854=717
717-84=633
633+506=1139
If the average of 292, 305, 415, and x is 343, what is the value of x?
Of the 30 champions of the National Spelling Bee from 1974 to 2003, 16 are boys. Find the ratio of the number of champions who are girls to the number who are boys.
Answer:
14/16 or 7/8.
Step-by-step explanation:
We know the total champions is 30. There are 16 boys, so to find the number of girls we can do 30-16. This gives us 14. Now we know that there are 16 boys and 14 girls, and the question is asking for the ratio of champions who are girls to the number who are boys. This means the ratio would simply be 14 to 16, for every 14 girls there are 16 boys. You can simply this ratio to 7 to 8, meaning for every 7 girls there are 8 boys.
fraction numerator 8 over denominator 2.4 end fraction equals space 9 over x
Answer:
x = 2.7
Step-by-step explanation:
8/2.4 = 9/x
Cross multiply.
8x = 2.4 × 9
8x = 21.6
8x/8 = 21.6/8
x = 2.7
The length of a rectangle is two more than triple the width. If the perimeter is 84 inches, find the
dimensions.
The width is
The length is
Submit Question
inches.
inches.
Answer:
The length of rectangle seven more than triple the width. If the perimeter 126 inches, find the dimensions The width inches. The length inches.
"divide 9 by p, then multiply 2 by the result" i need the expression for this, thank you
Answer: The expression would look like this p/9 (2)
Step-by-step explanation: You should make it a fraction by putting the p on top and 9 on bottom and in parentheses you put in the 2!
Hope this helped! :D
Which personal expense did the Penders spend more on than they had budgeted? Refer to Figure 3.4 on page 165 of the ebook or at the back of the packet. Figure 3.4.pdf Download Figure 3.4.pdf
Group of answer choices
Credit Cards & Clothing
Clothing
Clothing & Pocket Money
Credit Cards & Pocket Money
The personal expense that the Penders spent more on than they had budgeted is:
Credit Cards & Pocket Money to the tune of $ 23.75 (Option C)
What is a budget?A budget is an estimate of revenue and costs for a given period of time that is generally created and re-evaluated on a regular basis. Budgets may be created for an individual, a group of individuals, a company, a government, or almost anything else that generates and spends money.
What is the justification for the above answer?The budgeted amount for Credit Card was $50. Total amount spent was $60. Hence the excess amount spent is $10.
The budgeted amount for Pocket money was $80. Total amount spent was $93.75. Hence the excess amount spent is $13.75.
Hence total amount spend over budget is $23.75
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If QS bisects PQR, m PQS = (10x-9), and m SQR= (4x+15), find x.
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
What is the numerical value of x?A bisector divides a segment or angle into two equal halves.
Given the data in the question;
QS bisects PQRm PQS = (10x-9)m SQR= (4x+15)Value of x = ?Since QS bisects PQR, m PQS is the same as m SQR.
Hence;
m SQR = m PQS
We plug in the values
(4x+15) = (10x-9)
Remove parenthesis and solve for x.
4x + 15 = 10x - 9
15 + 9 = 10x - 4x
24 = 6x
x = 24/6
x = 4
Given that QS bisects PQR making mPQS the same as the mSQR, the numerical value of x is 4
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Which of the following represents a function?
x -10 -9 0 5
y 19 17 25 19
A value 0 in x corresponds to 7 in y, and 52 in y. A value 1 in x corresponds to 4 in y. A value 2 in x corresponds to 16 in y. A value 3 in x corresponds to 7 in y.
{(0,0), (-4,3), (7,1), (-4,5), (3,2)}
A graph plots the points (negative 3, 4), (negative 3, negative 4), (negative 2, 3), (negative 2, negative 3), (negative 1, 0), (1, 0), (2, 3), (2, negative 3), (3, 4) and (3, negative 4) on the x y coordinate plane.
Paula pays $19.92 for 2.4 pounds of walnuts. What is the price per pound of walnuts?
Answer:
8.30
Step-by-step explanation:
19.92 / 2.40 = 8.30
8.30 is the amount per pound.
Answer: 8.30
Step-by-step explanation: We know that Paula Paid 19.92$ for 2.4 pounds
Price of 1 Walnut = 19.92 ÷ 2.4 = 8.30
Find the circumference of the circle with area 1÷4πd² cm²
Answer:C=3.54
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Write the least common multiple of 7 and 14.
Baljeet invested $5500 at a simple annual rate of 4.8% for 6 years. What is the total future value of the investment?
State your answer in terms of dollars rounded to the nearest cent, but do not include a $ sign or the word "dollars" with your response.
Answer:
[tex]a = p(1 + in) \\ = 5500(1 + 0.048 \times 6) \\ = 7084[/tex]
What is the coefficient of the x2-term of the algebraic expression 2 x 4 + x squared minus x + 7?
The Coefficient of x^2 in algebraic Expression 2x^4 + x^2 -x +7 will be 1.
What is Algebraic expression ?
Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.
Given algebraic Expression is :
2x^4 + x^2 -x +7
Now,
The coefficient is the constant term multiplied with the variable.
Therefore, here the Coefficient of of x^2 will be 1.
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Explain a method to find the area of triangle QRS given that RT is perpendicular QS. Then find the area. Show your work.
Applying the distance formula to find the base and height of the triangle, the area of the triangle is calculated as: 17.85 units².
How to Find the Area of a Triangle?Area of triangle = 1/2(base)(height).
The base of triangle QRS is QS.
The height of triangle QRS is RT.
Use the distance formula [tex]\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}[/tex] to find the length of QS and RT:
Q(2, 4) = (x1, y1)
S(8, -2) = (x2, y2)
QS = √[(8−2)² + (−2−4)²]
QS = √72
QS ≈ 8.5 units
R(6, 6) = (x1, y1)
T(3, 3) = (x2, y2)
RT = √[(3−6)² + (3−6)²]
RT = √18
RT ≈ 4.2 units
Area of triangle QRS = 1/2(8.5)(4.2)
Area of triangle QRS = 1/2(35.7)
The area of triangle QRS = 17.85 units²
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Please help me out here!!
The equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
How to Write an Equation in Point-slope Form?An equation can be written in point-slope form, where m represents the slope and (a, b) represents a point on the line, as: y - b = m(x - a).
From the given information describing Bray's distance from home after some time, we have the following parameters:
x = hours (time)y = distance (miles)Slope (m) = -6A point = (1/2, 4)Substitute m = -6 and (a, b) = (1/2, 4) into y - b = m(x - a):
y - 4 = -6(x - 1/2)
Therefore, the equation, in point-slope form, that represents the distance of Byron from home is: A. y - 4 = -6(x - 1/2).
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On the graph f(x)=cos x and the interval [-2pie,0] for what value of x does the function cross the x-axis?
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
For what values does the cosine function cross the x-axis?
Cosine function is a function bounded between - 1 and 1 and whose period is 2π, all the values of x such that the cosine function crosses the x-axis is described by the following expression:
cos x = 0 (1)
Then, by inverse trigonometric functions:
x = cos⁻¹ 0
x = 0.5π ± π · i, where i is a non-negative integer.
If we know that i = 1 and i = 2, then the values of x within the interval [- 2π, 0] are, respectively:
x₁ = - 0.5π, x₂ = - 1.5π
The function f(x) = cos x crosses the x-axis at x₁ = - 0.5π and x₂ = - 1.5π.
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One bar of candy A and two bars of candy B have 763 calories. Two bars of candy A and one bar of candy B contain 773 calories. Find the caloric
content of each candy bar
Candy bar A contains calories and candy bar B contains
(Simplify your answers.)
calories
Answer:
A = 261 calories. and B = 251 calories
Step-by-step explanation:
A + 2B = 763
2A + B = 773
---------------------------
-2(A + 2B = 763)
↓
-2A - 4B = - 1526
2A + B = 773
-----------------------------
-3B = - 753
B = 753/3
B = 251
Candy bar B has 251 calories
now let's find A
A + 2B = 763
A + 2 (251) = 763
A + 502 = 763
A = 763 - 502
A = 261
Candy bar A has 261 calories
Steve has 6 3/4 pounds of ground beef to make hamburgers for a party it takes 3/8 of ground beef to make a hamburger how many burgers can Steve make
The number of burgers Steve can make = 18
In this question, Steve has 6 3/4 pounds of ground beef to make hamburgers for a party.
It takes 3/8 of ground beef to make a hamburger.
We need to find the number of burgers Steve can make.
First we convert the improper fraction 6 3/4 into a proper fraction.
6 3/4 = 27/4
For 1 hamburger 3/8 of ground beef is required.
Let n be the number of burgers Steve can make.
n = (27 / 4) / (3 / 8)
n = 27/4 × 8/3
n = 9 × 2
n = 18
Therefore, the number of burgers Steve can make = 18
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Simplify the equation, [tex](x^{4})^{\frac{5}{6} }[/tex], to a simplified radical. Show work
The simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
The exponentiation is written as [tex]a^{n}[/tex], where a is the base and n is the exponent or power. We say as "a by n". Exponent means the number of times the base is used as a factor.
The expression = [tex](x^{4})^{\frac{5}{6} }[/tex]
Here we have to apply the exponent rule
We know,
The power rules for the exponent [tex](a^{m})^{n}=a^{mn}[/tex]
Here multiply the exponent times the power.
Simplify it
[tex](x^{4})^{\frac{5}{6} }=(x)^{4(\frac{5}{6}) }[/tex]
=[tex]x^{\frac{20}{6} }[/tex]
Divide both 20 and 6 by 2 to make it to simplest form, then the result
=[tex]x^{\frac{10}{3} }[/tex]
Hence, the simplified radical form of the equation [tex](x^{4})^{\frac{5}{6} }[/tex] is [tex]x^{\frac{10}{3} }[/tex]
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What is the domain of the graph below.
Answer:
acbs
Step-by-step explanation:
Why is adding two fractions different from multiplying the two fractions?
Answer:
Step-by-step: The reason we cross multiply fractions is to compare them. Cross multiplying fractions tells us if two fractions are equal or which one is greater. This is especially useful when you are working with larger fractions that you aren't sure how to reduce.
Answer:
adding two fractions is different than multiplying two fractions bc after adding the fractions, you have to simplify them and it is not easy but with multiplying, you multiply from left to right.
Step-by-step explanation:
example: 1/2+3/4
4/8+6/8=10/8=1 1/4
another example: 6/10*4/6=24/60