If ( f ∘ g)(x) = x2 - 6x + 8 and g(x) = x - 3, what is f(x)?
Find the dimensions of the rectangle with area 120 square inches and smallest possible perimeter
If bethany earned $51,740 last year, how much did she earn per week?
Leo has 421 prize tickets. He can get 1 prize for every 100 tickets. How many prizes can Leo get? How many tickets will he have left over?
421 / 100 = 4.21
so he will win 4 prizes and have 21 tickets left over.
Show that for the same shear angle, there are two rake angles that give the same cutting ratio.
The time at which the mailman delivers the mail to ace bike shop follows a normal distribution with mean 2:00 pm and standard deviation of 15 minutes.
There are three questions related to this problem.
First, the probability of the mail will arrive after 2:30 PM
Find the z-score of 2:30 which is 30 minutes after 2:00.
z(2:30) = (2:30 – 2:00)/15 = -30/15 = -2
P(x < 2:30) = P(z<-2) = 0.0228
Second, the probability of the mail will arrive at 1:36 PM
Find the z-score of 1:36 which is 24 minutes before 2:00.
z(1:36) = (1:36 – 2:00)/15 = -24/15 = -1.6
P(x < 1:36) = P(z<-1.6) = 0.0548
Lastly, the probability of the mail will arrive between 1:48 PM and 2:09 PM
Find the z-score of 1:46 and 2:09 PM which will result to a z value of 0.034599
P(1:48 < x < 2:09) = P(z<0.034599) = 0.5138
a girl scout has (5x-12) boxes of cookies and sells (3x+18) of them. Write an expression to represent the amount of boxes she has left. Also can you show me the work that gets this answer not just the answer
Jessica is measuring two line segments. The first line segment is 30 cm long. The second line segment is 500 mm long. How long are the two line segments together? (answer in cm)
convert mm to cm
1mm = 0.1 cm
500 * 0.1 = 50cm
50 +30 = 80cm total length
chris has a bag of sweets. there are more than 20 sweets in the bag he shares his sweets equally between six people chris says, "the number of sweets in the packet was prime." is he correct? circle: yes or no, explain your answer below.
Divide.
3 5/9 ÷ -2 2/3
Enter your answer as a mixed number, in simplified form, in the box.
suppose someone tells you that she has a triangle with sides having lengths 2.6,8.1 and 8.6. Is this a right triangle? why or why not? Is there an angle in the triangle larger than 90 degree?
You are building a new house on a cartesian plane whose units are measured in miles. Your house is to be located at the point (2,0) . Unfortunately, the existing gas line follows the curve y= √(16 x^2 +5x+16). It costs 400 dollars per mile to install new pipe connecting your house to the existing line. What is the least amount of money you could pay to get hooked up to the system?
Emily bought a video game console and some games for $350. The video game console cost $200. Each game cost $25. How many games did Emily purchase?
Your Bank account balance was $235 and 24. After two checks were cashed (each for the same amount) your balance is now -45.58. What was the amount of each of those checks?
235.24 + 45.58 = 280.82
280.82/2 = 140.41
each check was for $140.41
Brandon bought a gallon of paint that covers 160 square feet. He wants to paint a wall that is 10 ft. high and 12 ft. wide. Explain whether he will need more than one gallon of paint. A. No, he won't need more paint. Brandon has enough paint to cover the 22-square-foot wall. B. Yes, he will need more paint. Brandon needs another gallon to cover the 240-square-foot wall. C. No, he won't need more paint. Brandon has enough paint to cover the 120-square-foot wall. D. Yes, he will need more paint. Brandon needs enough paint to cover the 1,200-square-foot wall.
How to find the width of a rectangular prim
n when the length is 6 cm height is 8 cm and surface area is 208 cm²
A bag contains 90 marbles some red and some transparent the ratio of red marbles to transparent ones is 1:4. how many red marbles are there? andwer
Is the expression 3x+2x−4 in simplest form
3x+2x-4 is not in simplest form.
What is Expression?An Expression is Combination of variables, numbers and operators.
The given expression is three x plus two x minus 4
i.e 3x+2x-4
It is not in simplest form because we have to add like terms.
In the above expression we have two terms of same variable.
We have to add 3x and 2x which gives 5x.
So 5x-4 is the simplest form.
Hence 3x+2x-4 is not in simplest form.
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9x-5y=-32 in slope intercept form
The slope intercept form of a linear equation has the following form where the equation is solved for y in terms of x:
y = a + bxb is the slopea is a constant term. It is the y intercept, the place where the line crosses the y axis.
Example 1
y = -13 + 7x
This equation is in slope intercept form. The y intercept is (0,-13) and the slope is 7.
Example 2
4x + 3y = 12
Rewrite this equation in slope intercept form.
3y = 12 - 4xThe equation is now in slope intercept form. The y intercept is (0,4) and the slope is
-4/3.
Example 3
5x - 3y - 15 = 0
Rewrite this equation in slope intercept form.
3y = -15 + 5xThe equation is now in slope intercept form. The y intercept is (0,-5) and the slope is
5/3.
Example 4
The equation is now in slope intercept form. The y intercept is (0,-7.5) and the slope is
1.5.
A carpenter has a 6-foot long board. He wants to cut the board into pieces that are 4/5 foot long. How many pieces of length 4/5 foot can the carpenter cut from the board? What length of the original board will be left after the carpenter has cut all the pieces that are 4/5 foot long?
Answer:
Number of pieces=7
Length of board remaining=[tex]\frac{2}{5}[/tex]
Step-by-step explanation:
We are given that a carpenter has board of length=6 foot
Length of each piece of board=[tex]\frac{4}{5}[/tex] foot
We have to find the number pieces of given length of piece can be made from given board.
In order to find the number of pieces we will divide the total length of board by the length of each piece.
Therefore, number of pieces =[tex]\frac{6}{\frac{4}{5}}[/tex]
Number of pieces=[tex]7\frac{1}{2}[/tex]
Length of each piece =[tex]\frac{4}{5}[/tex]
Therefore, number of pieces=7
Length used in 7 pieces =[tex]7\times\frac{4}{5}=\frac{28}{5}[/tex]
Length of board remaining=[tex]6-\frac{28}{5}=\frac{2}{5}[/tex]
The width of a rectangle is equal to m cm, but its length is five times greater than the width. Find the area of the rectangle.
The area will be 5m^2
At a school, 126 students play at least one sport. This is 40% of the students at the school. How many students are at the school?
Solve for x.
2/5≤x−4
At one university, the students are given z-scores at the end of the each semester, rather than the traditional gpas. the mean and standard deviation of all students' cumulative gpas, on which the z-scores are based, are 2.7 and 0.5, respectively
The students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is 1.9.
Given data:
To translate z-scores to corresponding GPAs, you can use the formula:
GPA = (z * standard deviation) + mean
Given:
Mean (μ) = 2.7
Standard Deviation (σ) = 0.5
Let's calculate the corresponding GPAs for the given z-scores:
For z = 2.0:
GPA = (2.0 * 0.5) + 2.7
= 1.0 + 2.7
= 3.7
For z = -1.0:
GPA = (-1.0 * 0.5) + 2.7
= -0.5 + 2.7
= 2.2
For z = 0.5:
GPA = (0.5 * 0.5) + 2.7
= 0.25 + 2.7
= 2.95
For z = -2.5:
GPA = (-2.5 * 0.5) + 2.7
= -1.25 + 2.7
= 1.45
Now, to determine the corresponding probationary GPA for z = -1.6:
GPA = (-1.6 * 0.5) + 2.7
= -0.8 + 2.7
= 1.9
Hence, students with z-scores below -1.6 would be put on probation, and the corresponding probationary GPA is approximately 1.9.
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The complete question is attached below:
At one university, the students are given z-scores at the end of each semester rather than the traditional GPAs. The mean and standard deviation of all students’ cumulative GPAs, on which the z-scores are based, are 2.7 and .5, respectively.
- translate each of the following z-scores to corresponding GPA: z=2.0, z=-1.0, z=.5, z =-2.5.
- Students with z-scores below -1.6 are put on probation. What is the corresponding probationary GPA?
Charlie's father is 41 years old. His age is two years more than three times Charlie's age. What is Charlie's age?
Final answer:
By setting up a linear equation, it is determined that Charlie is 13 years old based on the given information that his father is two years more than three times Charlie's age and is 41 years old.
Explanation:
The problem presented is a classic example of a linear equation in the subject of mathematics. We are given that Charlie's father is 41 years old, and his age is two years more than three times Charlie's age.
To determine Charlie's age, we can set up the equation as follows: Let x represent Charlie's age. The father's age is then described by the expression 3x + 2.
Since we know the father is 41 years old, we have:
3x + 2 = 41
Subtract 2 from both sides of the equation to isolate the terms with x:
3x = 39
Now, divide both sides by 3 to solve for x:
x = 39 / 3
x = 13
Therefore, Charlie is 13 years old.
There are 5 slots, each containing the letters w, r, l, d or o. one letter is picked at random from each slot. what are the odds that the letters stored in these slots read the word world?
The probability of the 5 letter slots randomly making the word 'world' is calculated by finding the product of the probability of choosing each letter correctly, which for this problem, is (1/3125).
Explanation:To calculate the probability of picking the letters 'w', 'o', 'r', 'l', 'd' in that order, we understand that we are dealing with a probability problem regarding independent events. This scenario means that the outcome of each selection does not affect the others.
Here, each slot contains 5 distinct letters. The probability of picking a specific letter correctly is 1/5 (1 way to pick a correct letter divided by 5 total letters). So, the probability of picking each letter correctly and in the order of 'world' is the product of the probabilities of choosing each letter correctly i.e P(choosing all five correct letters) = P(choosing 1st correctly) X P(choosing 2nd correctly) X P(choosing 3rd correctly) X P(choosing 4th correctly) X P(choosing 5th correctly) = (1/5) X (1/5) X (1/5) X (1/5) X (1/5) = (1/3125).
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All real numbers at least 3 units from -2
How did you calculate the price of each nickel to begin with? Thanks
What is the quotient?
-5 1/4 ÷ 2 3/4
Enter your answer as a mixed number, in simplified form, in the box.
To divide -5 1/4 by 2 3/4, convert both numbers to improper fractions, multiply the first fraction by the reciprocal of the second fraction, and simplify the result. The quotient is -1 10/11.
Explanation:To divide -5 1/4 by 2 3/4, first convert both mixed numbers to improper fractions. -5 1/4 can be written as -21/4, and 2 3/4 can be written as 11/4. Next, divide -21/4 by 11/4. To divide fractions, multiply the first fraction by the reciprocal of the second fraction. So, (-21/4) * (4/11) = -21/11. This quotient can be written in mixed number form as -1 10/11, which is the simplified answer.
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The soccer team voted on what they wanted to eat. There are 20 members on the team. Six members voted for pizza, 10 voted for chicken, and the rest voted for hot dogs. Which ratio represents the number of votes for hot dogs to chicken? 1/5 2/5 3/5 5/2
The answer is 2/5 because hot dogs to chicken is 2/5