Evaluate |2x+y-3z| for x=-2, y=10, and z=3
How to solve?
Carl Cornfield took up bowling. He paid a $15.00 entry fee plus $8.00 a week for 16 weeks. He purchased a bowling ball for $94, a bag for $49.95, glove for $10.00, and a pair of shoes for $38.99. What was his cost before taxes?
Jan’s pencil is 8.5 cm long. Ted’s pencil is longer. Write a decimal that could represent the length of Tex’s pencil?
1. which expression is equal to (f+g) (×) f (x)=x^2+3;g (x)=x-1
A. x^3-3
B.x^2-2x+4
C. x^2+x+2
D. x^3-x^2+3x-3
2. which expression is equal to (fog)(x)
f (x)=3x; g (x)=4x^2+1
A. 12x^3+3x
B. 4x^2+3x+1
C.12x^2+3
D. 36x^2+1
3. f (x)= 2x-8; g (x) = x-5
what is the value of (gof)(6)
a. -6
b. -1
c. 1
d. 6
4. f(x) =5x-10 what is the value of f^-1 (-3)
a. -5
b. 1.4
c. 9.4
d. -25
one afternoon 1,656 people rode the ferris wheel at one time. the passengers were equally distributed among the cars. all chairs were taken. how many passengers were standing in each car ?
A satellite 200 miles above the earth is orbiting the earth once every 4 hrs. How far does the satellite travel in 1 hr
Assume the radius of the the earth is ~4000 miles.
radius of orbit = 4000 +200 = 4200 miles
In 4 hrs it orbits 2Pi*r =2pi*4200= 8400pi miles
In 1 hr it would travel (8400pi/4 )
= 2100pi = 6597.3445 miles (exact value)
= 6597 miles ( approximate)
Ken watches a marching band. He sees 2 rows of flute players. Six people are in each row . He sees 8 trombone players. How many flute players and trombone players does Ken see?
What is 7√27+5√48 in simplified radical form?
The expression 7√27+5√48 in simplified radical form is [tex]41 \sqrt{3}[/tex] and this can be determined by using the arithmetic operations.
Given :
Expression -- 7√27+5√48
The following steps can be used in order to determine the simplified radical form of the given expression:
Step 1 - The arithmetic operations can be used in order to determine the simplified radical form of the given expression.
Step 2 - Write the given expression.
= 7√27+5√48
Step 3 - Rewrite [tex]\sqrt{27}[/tex] as [tex]3\sqrt{3}[/tex] in the above expression.
[tex]= 7 \times 3 \sqrt{3}+ 5 \sqrt{48}[/tex]
Step 4 - Rewrite [tex]\sqrt{48}[/tex] as [tex]4\sqrt{3}[/tex] in the above expression.
[tex]= 21 \sqrt{3}+ 20\sqrt{3}[/tex]
Step 5 - Simplify the above expression.
[tex]= 41 \sqrt{3}[/tex]
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Julie is selling candy bars to raise money for new band uniforms. Candy bar X sells for $2 and candy bar Y sells for $3. Julie needs to sell at least three times more Y candy bars than X candy bars. She has at most 36 candy bars to sell. Which objective function can be used to find the profit P that Julie makes from selling the candy bars?
A) P = x + y
B) P = 36xy
C) P = 2x + 3y
D) P = 3x + 2y
Answer:
Answer is C [tex]P = 2x + 3y[/tex]
Step-by-step explanation:
Selling price of candy bar X =$2
Selling price of candy bar Y =$3
So if Julie sells x from X candy bars and y bars from Y candy bars,
Profit made from selling X candy bars = [tex]2\times x[/tex]
Profit made from selling Y candy bars = [tex]3\times y[/tex]
Therefore, assuming that there is no cost for the candy bars the profit by selling candy bars can be represented by the following objective function:
[tex]P = 2x + 3y[/tex]
Therefore, answer is C
The sum of two numbers is with a ratio of 15:10. Find the larger number.
What is the most specific name that can be given to a figure with the following coordinates? (–10, 8), (–7, 13), (3, 7), and (0, 2)
It takes Joey 1/16 of an hour to write one thank you card. How many cards can he write in 3/4 of an hour?
A rectangular floor is 6 yards long and 4 yards wide. What is the area of the floor in square feet? Please help!
The area of rectangle is 24 yards² or 216 square feet..
What is area of rectangle?The area of rectangle is the product if its length to its width.
i.e., Area of Rectangle= length x width
Given:
length= 6 yards
width= 4 yards
So, the area of rectangle
= l x w
= 6 x 4
= 24 yards²
= 24 x 9
= 216 square feet.
Hence, the area of rectangle is 24 yards².
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Sean, a freelance editor, charges the rates shown in the table below to edit manuscripts. The cost per page increases as the quality of editing improves. Sean also gives a 5% discount if the entire amount is paid up front. A 2 column table with Type of Editing and Cost per page as the column headings. Express Proofreading costs 2 dollars, Basic Proofreading 2.95 dollars, Extended Proofreading 3.95 dollars, and Deep Editing 11 dollars Michelle has an 85-page manuscript. The equation below shows the relationship between the total cost of editing 85 pages, T, and the cost per page, c, if she gets the 5% discount: 85c − 0.05(85c) = T Using the equation, what is the best quality of editing that Michelle can get done for a maximum of $161.50? Express proofreading Basic proofreading Extended proofreading Deep editing
We bought five 3 3/4 pound bags of bird seed. A. What is the total weight of the birdseed they bought? B. If each smaller bag contains 1 1/2 pounds, how many bags can they make? C. Will there be any birdseed
Left over? .
Answer:
We bought five 3 3/4 pound bags of bird seed.
A :
Total weight is = [tex]3\times(\frac{3}{4} )=\frac{9}{4}[/tex] pounds of bird seed.
In mixed fraction it is : [tex]2\frac{1}{4}[/tex] pounds
B :
As given, each smaller bag contains 1 1/2 pounds, so 9/4 pounds can make:
=[tex]\frac{\frac{9}{4}}{\frac{3}{2}}[/tex]= 18/12 = 3/2 bags
C :
We can make 1 full bag and will have left out enough for half of another bag. Half of a 3/2 pound is :
[tex]1/2(3/2)[/tex] = 3/4 of a pound.
A contiguous subsequence of a list s is a subsequence made up of consecutive elements of s. for instance, if s is
A contiguous subsequence of a list is a subsequence made up of consecutive elements.
Explanation:A contiguous subsequence of a list s is a subsequence made up of consecutive elements of s. For example, if s is [1, 2, 3, 4, 5], a contiguous subsequence could be [2, 3, 4].
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A car travels 2 1/3 miles in 3 1/2 minutes at a constant speed. Write an equation to represent the car travels in miles and minutes
Answer:
x = [tex]\frac{2}{3}\times t[/tex]
Step-by-step explanation:
We know the formula to represent the speed is,
Speed = [tex]\frac{\text{Distance}}{\text{Time}}[/tex]
If a car travels the distance = [tex]\frac{7}{3}[/tex] miles in [tex]\frac{7}{2}[/tex] minutes then the speed will be
Speed = [tex]\frac{\frac{7}{3}}{\frac{7}{2}}[/tex]
= [tex]\frac{7}{3}\times \frac{2}{7}[/tex]
= [tex]\frac{2}{3}[/tex] miles per minute
If the car travels x miles in t minutes then the equation to calculate the distance will be
[tex]\frac{2}{3}=\frac{x}{t}[/tex]
x = [tex]\frac{2}{3}\times t[/tex]
Therefore, the equation that represents the distance in terms of time will be
x = [tex]\frac{2}{3}\times t[/tex]
The volume of a cone is 62.8 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the nearest inch? Use pi = 3.14
2 inches
4 inches
8 inches
9 inches
Answer: 2inches
Step-by-step explanation:
Ms. Banerjee bought a car for $22,500. The amount she paid for her new car was twice the amount she paid for her previous car, which she bought 8 years ago. Which equation shows p, the price in dollars that she paid for her previous car?
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What is the equation of the line that is parallel to the line y − 1 = 4(x + 3) and passes through the point (4, 32)?
A)y = –x + 33
B)y = –x + 36
C)y = 4x − 16
D)y = 4x + 16
The equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
Further explanation:
It is given that the equation of line is [tex]y-1=4\left({x+3}\right)[/tex] and passes through point [tex]\left({4,32}\right)[/tex] .
Rewrite the given equation [tex]y-1=4\left({x+3}\right)[/tex] as follows:
[tex]\begin{aligned}y-1&=4\left({x+3}\right)\\y-1&=4x+12\\y&=4x+12+1\\y&=4x+13\\\end{aligned}[/tex]
Now, compare the obtained equation of line [tex]y=4x+13[/tex] with the standard equation of line [tex]y=mx+b[/tex] .
[tex]\begin{aligned}m&=4\\b&=13\\\end{aligned}[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that both lines are parallel to each other so the product of slope must be equal.
[tex]{m_1}={m_2}[/tex] …… (1)
Substitute [tex]4[/tex] for [tex]{m_1}[/tex] in equation (1) to obtain the value of slope [tex]{m_2}[/tex] .
[tex]{m_2}=4[/tex]
Therefore, the slope is [tex]4[/tex] .
It is given that the line passes through point [tex]\left({4,32}\right)[/tex] .
The point-slope form of the equation of a line with slope [tex]m[/tex] passes through point [tex]\left({{x_1},{y_1}}\right)[/tex] is represented as follows:
[tex]y-{y_1}=m\left({x-{x_1}}\right)[/tex] …… (2)
Substitute [tex]4[/tex] for [tex]{x_1}[/tex] , [tex]32[/tex] for [tex]{y_1}[/tex] and [tex]4[/tex] for [tex]m[/tex] in equation (2) to obtain the equation of line.
[tex]\begin{aligned}y-32&=4\left({x-4}\right)\\y-32&=4x-16\\y&=4x-16+32\\y&=4x+16\\\end{aligned}[/tex]
Therefore, the equation of line is [tex]y=4x+16[/tex] .
Now, the four options are given below.
[tex]\begin{gathered}{\text{OPTION A}}\to y=-x+33\hfill\\{\text{OPTION B}}\to y=-x+36\hfill\\{\text{OPTION C}}\to y=4x-16\hfill\\{\text{OPTION D}}\to y=4x+16\hfill\\\end{gathered}[/tex]
Since OPTION D matches the solution that is [tex]y=4x+16[/tex] .
Thus, the equation of line that is parallel to the line [tex]y-1=4\left({x+3}\right)[/tex] and passes through the point [tex]\left({4,32}\right)[/tex] is [tex]\boxed{{\mathbf{y=4x+16}}}[/tex] and it matches with [tex]\boxed{{\mathbf{OPTION}}\,{\mathbf{D}}}[/tex] .
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Answer Details:
Grade: Junior High School
Subject: Mathematics
Chapter: Coordinate Geometry
Keywords: Coordinate Geometry, linear equation, system of linear equations in two variables, variables, mathematics, equation of line, line, passes through point.
Miguel Rodriguez borrow 200 from his brother Julio to pay for books and tuition . He agreed to pay Julio 6!months with simple annual interest at 6.2% A)how much with the interest amount to ? B) what amount must Miguel pay Julio at the end of 6 months ?
To answer the problem, you must the formula in finding the interest and after that we will add it to the principal to get the future value.
The formula is: I = Prt
Interest = Principal x rate x time
= 200 x 0.062 x 6/12
= $6.2 is the interest for 6 six months.
Future Value = Principal + Interest
FV = 200 + 6.20
FV = $206.20 is the amount to be paid at the end of 6 months.
A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to
Final answer:
The normal distribution in question behaves according to the Empirical Rule, which states that about 68% of the data falls within one standard deviation of the mean in a bell-shaped, symmetric distribution. This percentage changes to about 95% within two standard deviations and over 99% within three standard deviations.
Explanation:
A normal distribution in which approximately 68% of the data values fall within one standard deviation of the mean behaves according to the Empirical Rule. This is a key concept of descriptive statistics that applies specifically to bell-shaped, symmetric distributions. According to the rule, about 68 percent of the data lies within one standard deviation of the mean, about 95 percent lies within two standard deviations, and over 99 percent lies within three standard deviations.
For example, if a distribution has a mean (μ) of 50 and a standard deviation (σ) of 6, then approximately 68 percent of the values (x) would lie between 44 (50 - 6) and 56 (50 + 6). These points are one standard deviation away from the mean and correspond to the z-scores of -1 and +1, respectively. It is important to remember that this rule only applies when the distribution is perfectly bell-shaped and symmetric.
Ralph has 957 race car stickers. He gave 10 to ken. He gave 100 to Matt. How many stickers does Ralph have left?
Use compatible numbers to find two estimates 336 divided by 12
Determine whether the given equation has one solution, no solution, or infinitely many solutions. 2 - 3(x + 4) = 3(3 - x) one solution no solution infinitely many solutions cannot be determined
The given equation 2-3(x+4)=3(3-x) has no solution.
What is equation?An equation is relationship between two or more variables that are expressed in equal to form. Equation of two variables look like ax+by=c.
It can be a linear equation, quadratic equation, cubic equation.
How to solve equation?We have been given an equation 2-3(x+4)=3(3-x) and we have to find the number of solution that equation posses. The easiest way of finding the number of solutions is that we will solve the equation.
Equation is as under:
2-3(x+4)=3(3-x)
2-3x-12=9-3x
-3x-10=9-3x
-3x+3x=9+10
Next step is cancelling of 3x and after that no variable will present in the equation. It shows that there are no solutions of the equation.
Hence there are no solutions for the equation 2-3(x+4)=3(3-x).
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4 3/4 minus 5/8 in simplest form
Which of the following expressions is in simplified form?
A) 1 1/2n + 2.9n
B) 4w - 5
C) -2 + 1.4m + 0.5
D) 9j - 3 - j
Answer:
B. Is the Answer Because its the only one that is simplified.
Step-by-step explanation:
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What value of n will make (-5) × (-8) = n × (-5) a TRUE statement?
A) (-8)
B) 8
C) (-3)
D) 3
to make the statement true, n need to equal the same as what is on the left side, so n = -8
correct answer is A
Which problem can be solved using this inequality?
x + 5 ≤ 20
A) Beth is purchasing school supplies. She knows that the price for her pencil case is $5. She only has $20 to spend. How much money will she have left after buying the pencil case?
B) Beth is purchasing school supplies. She knows that the price for her pencil case is $5. She only has $20 to spend. What is the most amount of money she can spend on the remaining supplies?
C) Beth is purchasing school supplies. She knows that the price for her pencil case is less than $5. She only has $20 to spend. How much money will she have left to spend after buying the pencil case?
D) Beth is purchasing school supplies. She knows that the price for her pencil case is $5 more than the cost of a book bag. She only has $20 to spend. Does Beth have enough money to buy the pencil case and book bag?
Answer:
The answer would be b.
Step-by-step explanation:
Dan bought 5 1/4 gallons of gas on Friday and 6 1/2 gallons of gas on Saturday. How many liters of gas did he buy? Assume 1 gallon = 3.8 liters.
Answer:
Dan bought 44.65 liters of gas.
Step-by-step explanation:
The gas Dan bought on Friday and Saturday in gallons is
[tex]5\frac{1}{4}+6\frac{1}{2}[/tex]
[tex]=\frac{21}{4} +\frac{13}{2}[/tex]
We collect LCM for the denominators,
[tex]=\frac{21+26}{4}[/tex]
[tex]=\frac{47}{4}[/tex]gallons
We now convert to liters using the relation,
[tex]1\:gallon=3.8\: liters[/tex]
Let [tex]\frac{47}{4}\:gallons=x\:liters[/tex]
Then,
[tex]x=3.8\times \frac{47}{4}[/tex]
[tex]x=\frac{38}{10}\times \frac{47}{4}[/tex]
[tex]x=\frac{19}{5}\times \frac{47}{4}[/tex]
[tex]x=\frac{893}{20}=44.65[/tex]
Therefore Dan bought 44.65 liters of gas.