**You should not need to round on this problem, no %'s decimals only**
At Houston Community College 60% of the students who take English will pass. Of those who pass English, 70% will also pass Accounting. Of those that do not pass English, 45% will still pass accounting.
Answers
a) Probability of student passed in English and Accounting [tex]= \frac{21}{50}[/tex]
b) Probability of Number of Student passed Accounting [tex]=\frac{3}{5}[/tex]
c) Given that student passed Accounting. Probability that they passed English = [tex]\frac{9}{125}[/tex]
What is Probability?The ratio of favorable outcomes to all possible outcomes of an event is known as the probability.
Here let us assume the Total Number of students is 100.
Students who passes in English = 60% of total number of students
= [tex]60*100/100=60[/tex]
Students who passes in English = 60.
Out of 60 students , 70% of 60 pass in Accounting = [tex]70/100*60=42[/tex]
So Student who passed in both English and Accounting = 42.
Also Number of student that do not passed in English = 100 - 60 = 40.
Out of these 40 students , 45% passes in Accounting = [tex]45/100*40=18[/tex]
So Number of student pass in Accounting but not in English = 18.
Total Number of student pass in Accounting = 42 + 18 = 60.
A) Number of student passed in English and Accounting = 42
Total Number of student = 100
Probability of student passed in English and Accounting= [tex]\frac{42}{100} = \frac{21}{50}[/tex]
B) Total Number of Student passed Accounting = 60
Total Number of student = 100
Probability of Number of Student passed Accounting = [tex]\frac{60}{100} = \frac{3}{5}[/tex]
C) Probability that student passed Accounting = 60/100.
Probability that student passed English = 60/100.
Given that student passed Accounting. Probability that they passed
English = [tex]\frac{60}{100} * \frac{60}{100} = \frac{3600}{10000} = \frac{9}{125}[/tex]
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Related Questions
The function f(x)= -3x^3 + x^2 +2x rises as x grows very small.
A. True
B. False
Answers
When x is very small (close to 0), the term -3x^3 is much smaller in magnitude than the term x^2. Therefore, the overall value of the function will be dominated by the x^2 term, which is positive. This means that the function will decrease as x becomes very small.
False, the function f(x)=[tex]-3x^3 + x^2 +2x[/tex] does not rises as x grows very small.
How to determine the statementFirst, we need to know that functions are described as laws, expressions or rules that are used to show the relationship between two variables in an equation.
These variables are known as;
The independent variableThe dependent variableThe function f(x) =[tex]-3x^3 + x^2 + 2x[/tex] does not rise as x grows very small. When x approaches negative infinity, the dominant term is [tex]-3x^3[/tex], which becomes increasingly negative.
Therefore, the function decreases as x grows very small in the negative direction.
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156x2.2=?????Help fast
Answers
Answer:
343.2
Step-by-step explanation:
156 × 2.2
= (156 × 22)/10
= 3432/10
= 343.2
BRAINLIEST FOR ANSWER UNDER 10 MINUTES The table shown represents a linear relationship.
x 0 1
3
4
y-8-6-20
Based on the table, what is the equation of the linear relationship in slope-intercept form?
Oy=2x-8
Oy = 2x+8
Oy = -2x + 4
Oy=-2x - 4
Answers
Answer: y = 2x-8
Step-by-step explanation:
Let's try to determine by substitution method. Starting from the first equation:
y = 2x-8
2·0-8 = -8
2·1-8 = -6
2·3-8 = -2
2·4-8 = 0
The first equation satisfies the conditions of the table.
Solve for -10 - 9/2 x <80
Answers
Answer:
X > -20
Step-by-step explanation:
-10 - 9/2 x < 80
Move 10 to the other side
- 9/2 x < 80 + 10
Simplify
-9/2 x < 90
-9 x < 180
x > -20
(We switch the inequality sign if we are dividing with negatives)
Find the length of AB.
Answers
The length of AB in the line segment is 21 units.
How to find the length of a line segment?A line segment is bounded by two distinct points on a line. In other words, a line segment is a part of a line that connects two points which are considered to be its endpoints.
Therefore, let's find the length AB, in the line segment AC.
Hence,
AC = AB + BC
AC = 23
AB = 2x + 7
BC = 3x - 19
Therefore,
23 = 2x + 7 + 3x - 19
23 = 5x - 12
23 + 12 = 5x
35 = 5x
divide both sides by 5
x = 35 / 5
x = 7
Therefore,
AB = 2x + 7 = 2(7) + 7 = 14 + 7 = 21
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draw and divide a rectangle to show each product use a distributive property to find the product 5×14
Answers
The product of 5 and 14 using the distributive property is 70.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
For three numbers a, b and c, Distributive property states that,
a (b + c) = a b + a c
We have to find the product 5 × 14 using distributive property.
5 × 14 = 5 (12 + 2)
Using distributive property,
5 × 14 = (5 × 12) + (5 × 2)
= 60 + 10
= 70
Hence using distributive property, we can find the product of 5 and 14 as 70.
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Why is the discriminant a useful tool to use when solving quadratic equations?
Answers
If d>0, the the quadratic has 2 real solutions
If d=0, the quadratic has one (repeated) solution
If d<0, the quadratic has no real roots.
You must plug d in for these inequalities to determine which one is true, and that will tell you how many solutions a quadratic contains.
A student is graduating from college in 12 months but will need a loan in the amount of $10,958 for the last two semester. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are:
Unsubsidized Stafford Loan: annual interest rate of 3.85%, compounded monthly, and a grace period of six months from time of graduation
PLUS loan: annual interest rate of 4.15%, compounded monthly, with a balance of $11,421.51 at the time of repayment
Which loan will have a higher balance, and by how much at the time of repayment?
Answers
Answer:
To determine which loan will have a higher balance at the time of repayment, we need to calculate the balance of each loan after the interest has been compounded over the repayment period.
The unsubsidized Stafford Loan has an annual interest rate of 3.85% and a grace period of six months from the time of graduation. This means that the loan will accrue interest for a total of 12 months - 6 months = 6 months.
The balance of the unsubsidized Stafford Loan at the time of repayment can be calculated using the following formula:
Balance = Principal * (1 + Interest rate / Number of compounding periods per year)^(Number of compounding periods)
Plugging in the given values, we have:
Balance = $10,958 * (1 + 0.0385 / 12)^(6) = $10,958 * (1.003125)^(6) = $11,283.16
The PLUS loan has an annual interest rate of 4.15% and a balance of $11,421.51 at the time of repayment.
The balance of the PLUS loan at the time of repayment can be calculated using the same formula:
Balance = $11,421.51 * (1 + 0.0415 / 12)^(6) = $11,421.51 * (1.003479)^(6) = $11,973.54
Therefore, the PLUS loan will have a higher balance at the time of repayment, by $11,973.54 - $11,283.16 = $690.38.
Step-by-step explanation:
please help fast for my math project and its due today !!!!!!! fasttttb pleaseeee
Answers
1) Note that in the problem above, the complete table is given as:
Team Number: 1 2 3 4 5
Best Jump (ft) 20.6 21.5 20.9 19.4 20.2
2) If Best Jump is denoted as y and Team number as x then, Best Jump is the Range while Team Number is the Domain.
3) For each element of the domain, there is a corresponding element of the range. So this relation is a function.
Why are the Domain and Range Important?Domain and range are crucial characteristics that aid in the definition of a relationship. The domain is a collection of input values.
The independent variable represents these values, which are graphed on the axis of a coordinate graph. A function's range is its collection of output values.
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Which is a rational function?
A. Y= 2/x
B. Y=x^2 - x + 4
C. Y= x-3^x/x^2
D. Y= x-5/2
Answers
A rational function is the algebraic expression y = 2 / x. (Correct choice: A)
What function is a rational function?
Rational functions are algebraic expressions, whose form is described below:
R(x) = P(x) / Q(x)
Where:
P(x) - Numerator polynomic function.Q(x) - Denominator polynomic function.Please notice that Q(x) must be a polynomial whose grade is greater than zero.
Polynomials are algebraic expressions of the form:
P(x) = ∑ cₙ · xⁿ, for n = {0, 1, 2, 3, ..., n, ..., m}, where m is the grade of the polynomial.
Therefore, by direct inspection, we conclude that algebraic expression y = 2 / x is a rational expression.
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You deposit $250 in an account that earns simple interest at an annual rate of 2.2%.
How much money is in the account after 4 years?
Answers
Answer: $272
Step-by-step explanation: you would multiply 250 * 0.022 = 5.5
then you would multiply 5.5 * 4 = 22 then you would add 22 + 250 = 272
Which of the following functions describes the graph of g(x)? (5 points)
Rational function with one piece decreasing from the left asymptotic to the line y equals 2 and going through a hole at the point negative 2 comma eight-fifths and going down through the point 2 comma 0 asymptotic to the line x equals 3 and another piece decreasing from the left asymptotic to the line x equals 3 and going through the point 5 comma 3 going up to the right asymptotic to the line y equals 2
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus x minus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared plus 5 x plus 6 end quantity
g of x is equal to the quantity 2 x squared minus 8 end quantity over the quantity x squared minus 5 x plus 6 end quantity
Answers
The equation of rational function is (c) g(x) = (2x + 4)/(x + 1).
What is a function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that,
The function g(x).
The graph of a function never touches the x = 1 line
At x = -1 there will be a vertical asymptote.
At x = -2 there will be a horizontal asymptote.
The equation of the function g(x) will be:
g(x) = (2x + 4)/(x + 1)
The equation of rational function is g(x) = (2x + 4)/(x + 1)
Therefore, g(x) = (2x + 4)/(x + 1) is correct.
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24.
-2
2
NO
2
y-int=
slope =
equation:
y
2
X
Answers
Answer:
y-int = 0
slope = -1
equation: y = -x
Step-by-step explanation:
The line crosses the y-axis at y = 0, so the y-intercept is 0.
Go from (0, 0) to (-1, 1).
slope = m = rise/run = 1/(-1) = -1
y = mx + b
y = -x
y-int = 0
slope = -1
equation: y = -x
Rahquez and Francesca both leave the coffee shop at the same time, but in opposite directions. If
Francesca travels 5 mph faster than Rahquez and after 3 hours they are 105 miles apart, how fast is each
traveling?
Answers
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.
Define acceleration.Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.
What is velocity?Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).
Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:
F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)
We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:
105 = (R + F) * 3
Now we can substitute the first equation into the second equation:
105 = (R + (R + 5)) * 3
Simplifying and solving for R, we get:
R = 20 mph
So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).
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which is the highest 4,16,77 and lowest
Answers
Answer:
highest 77 and lowest is 4
Five student government officers want to go to the state convention. It will cost them $115 for registration, $365 for transportation and food, and $55 per person for the hotel. There is $485 budgeted for the convention in the student government savings account. They can earn the rest of the money they need by having a car wash. If they charge $6 per car, how many cars must they wash in order to have enough money to pay for the trip?
Answers
Answer:
45 cars
Step-by-step explanation:
115+365+(55*5) = 755
755 - 485 =270
270/6 = 45
What is a b c d and e?
Answers
Answer:
Step-by-step explanation:
[tex]if \: x = 1 - \sin( \alpha ) \: and \: y = 1 + \cos( \alpha ) \\ [/tex]
Express y in terms of x and alpha only
Answers
Answer:
A sample of helium was compressed at 35 °C from a volume of 0.5 L
to 0.25 L where the pressure is 500 mmHg. What was the original pressure?
Step-by-step explanation:
It is industry norms and key business ratios Dunn and Bradstreet reported that Q1 Q2 and Q3 were 2037 gasoline service stations sales to inventory ratios or 24 833.4 and 53.8 respectively from this we can conclude that what percentage of these service stations have sales to inventory ratio
Answers
From the inventory ratios of 24 8, 33.4 and 53.8 of Dunn and Bradstreet report. It can be concluded that
50% of these service station had sales to inventory ratios of 53.8 or moreHow to find the correct statement about the reportsThe problem is seeking expression of ratios in percentage
Ratios represents part or share of a whole while percentage refers to a fraction of hundred
Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up
= 24 8 + 33.4 + 53.8
= 108
Expressing as ratio 53.8 a percentage, we have
= 53.8/108 * 100
= 0.4981 * 100
= 49.81%
approximately 50%
We can therefore say that inventory of 53.8 or more is 50%
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1.2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
whats the answer?
Answers
Answer:
3(y^2 + 1) + 2(y+4)
Step-by-step explanation:
2y^2 + 8.9 + 6y - 8.6 - 4y + y^2
= 2y^2 + y^2 + 6y - 4y + 8.9 - 8.6
= 3y^2 + 2y + 8(9-6)
= 3y^2 + 2y + 24
= 3y^2 + 2y + 3.2.2.2
= 3(y^2 + 1) + 2(y+4)
Given f(x)+3f(-x) = 2x+6, find f(x)
Answers
The function f(x) = -x-3.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain.
Given function:
f(x)+3f(-x) = 2x+6.
Let the function is an even function.
So, f(-x) = f(x)
To solve for f(x):
Substituting the property of an even function,
f(x) - 3f(x) = 2x + 6
-2f(x) = 2x + 6
f(x) = -x-3
Therefore, f(x) = -x-3 is the function.
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In Circle O, mAB = 72. Find m
Answers
Check the picture below.
Carlos measures an angle x. He then finds that the complement of the angle is 35 degrees. A. What is the measure of angle x? B. What is the supplement of angle x?
Answers
Therefore , the solution of the given problem of complementary angles comes out to be x = 55° and y =125°.
Describe complimentary angles.A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The angles of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplementary triangle tilt is two possible approaches combined to create a 180 degree angle. If the sum of two angles is 90 degrees, they are said to be complementary. A straight angle, to put it another way
Here,
Given : complementary angle one of the angle is 35°
=> x+ 35° = 90°
=> x = 55°
Let y be the supplement of angle x
=> x+ y = 180°
=>55° + y =180°
=>y =125°
Therefore , the solution of the given problem of angle comes out to be
x = 55° and y =125°.
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please help with geometry proof
Answers
Answer:
a and c are both congruent to each other i just learned about rhombuses the other day so if a and c are congruent then b and d are congruent too
if (x+A)^2 -3 = x^2 + 4x + B. Find the value of A and B
Answers
The values of A and B are 2 and 4 respectively.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is the equation as -
(x + A)² - 3 = x² + 4x + B
We can write the given equation as -
(x + A)² - 3 = x² + 4x + B
x² + A² + 2Ax = x² + 4x + B
A² + 2Ax = 4x + B
A² + 2Ax = B + 4x
Equating both sides, we get -
A² = B
and
2A = 4
A = 2
Then B will be equivalent to 4.
B = 4
Therefore, the values of A and B are 2 and 4 respectively.
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A case of tomato cans weighs 563 dekagrams. A case of soup cans weighs 458 dekagrams. How much do the two cases weigh together in decigrams? Use the metric table to help answer the question.
Metric Table
kilo-
hecto-
deka-
unit
deci-
centi-
milli-
1,000
100
10
1
0.1
0.01
0.001
1,021 decigrams
10,210 decigrams
102,100 decigrams
1,021,000 decigrams
Answers
Answer:
102200
Step-by-step explanation:
564+458= 1022
1 decagram=100 decigram
So multiply the sum by 100
1022*100=102200
The temperature during the night was -4. In the morning the temperature increased by 3. What is the temperature in the morning
Answers
Answer:
-1
Step-by-step explanation:
Night: -4
Morning: -4 + 3 = -1
Solve each equation for both variables help please 15 points
Answers
Answer:
I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!
Latisha plans to purchase her school pictures. The prints cost $108 plus any add-ons she wants to purchase. If she saves $18 per week, which solution represents how many weeks, w, it will take Latisha before she can purchase her school pictures?
Answers
The number of weeks w is given by the equation w = 6 weeks
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the number of weeks be represented as w
The prints cost $108 plus any add-ons she wants to purchase
The amount saved by Latisha per week = $ 18
So , the total amount saved by Latisha for w weeks = 18w
Now , the equation will be
18w = 108 be equation (1)
On simplifying the equation , we get
Divide both sides of the equation by 18 , we get
w = 108 / 18
w = 6 weeks
Therefore , the value of w is 6
Hence , the number of weeks is 6 weeks
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evaluate 5² + 7 - 3 +4
Answers
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
The expression is given below.
⇒ 5² + 7 - 3 + 4
Simplify the expression, then we have
⇒ 5² + 7 - 3 + 4
⇒ 25 + 7 - 3 + 4
⇒ 36 - 3
⇒ 33
The value of the numerical expression 5² + 7 - 3 + 4 will be 33.
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