The graph shows a vertical translation of y =[tex]\sqrt[3]{x}[/tex]
What is the range of the translated function?
{y|y < 0}
{y|y ≥ 0}
{y|y is a natural number}
{y|y is a real number}
![The Graph Shows A Vertical Translation Of Y =[tex]\sqrt[3]{x}[/tex] What Is The Range Of The Translated](https://i5t5.c14.e2-1.dev/c-qa-images/contents/attachments/c1vN4JC16XeBvYR0ddXcDy813IbxJdRS.png)
Answers
Answer:
Last option: {y|y is a real number}
Explanation:
The range of a real function is the set of the real numbers (values) that the function can return (the ouput of the function).
To figure out the range of a function, you first must figure out the domain.
The domain of the function [tex]y=\sqrt[3]{x}[/tex] is all real values, since the cube root function is defined for all the real numbers.
Since this function is continuous (which the translation of the function shows graphically), and the function is defined for all negative and positive values, the range of [tex]y=\sqrt[3]{x}[/tex] is all real numbers.
A vertical translation just slides the function vertically. Since the original function does not have either lower or upper bound, but the limits when x approaches ± ∞ are ± ∞, a translation will not modifiy the range.
Thus, the range of the translated function is (-∞, ∞).
That can also be written as {y|y is a real number}, which is read "y such that y is a real number", and is the last choice of the list.
Related Questions
The popcorn stand sells only soft drinks and popcorn, and only one size of each. In fact, the same cup is used for both products this is part of the stand's "sales pitch. "A soft drink cost $2.00 and a popcorn cost $4.00. On a certain day, 120 cups were used and $330.00 was collected. How many soft drinks and how many popcorns were sold on that day? Use a system of equations approach to find your answer. Show all work.
Answers
Answer:
On that day 75 soft drinks and 45 popcorn were sold.
Step-by-step explanation:
Given:
Let the number of soft drinks be 'x'.
Let the number of popcorn be 'y'.
Number of cups sold = 120
Now we know that;
Number of cups sold is equal to sum of the number of soft drinks and the the number of popcorn.
framing in equation form we get;
[tex]x+y=120 \ \ \ \ equation \ 1[/tex]
Also Given:
Cost of Soft drink = $2 .00
Cost of popcorn = $4.00
Total amount collected = $330.00
Now we know that;
Total amount collected is equal to sum of the number of soft drinks multiplied by Cost of Soft drink and the number of popcorn multiplied Cost of popcorn.
framing in equation form we get;
[tex]2x+4y = 330 \ \ \ \ eqaution \ 2[/tex]
Hence The System of equation to determine the number of softdrinks and cups sold is [tex]\left \{ {{x+y=120} \atop {2x+4y=330}} \right.[/tex].
Now to find the number of each type of cups sold we will solve the above equations.
First we will multiply equation 1 with 2 we get;
[tex]2(x+y)=120\times2\\\\2x+2y =240 \ \ \ \ equation \ 3[/tex]
Now we will subtract equation 3 from equation 2 we get;
[tex]2x+4y-(2x+2y)=330-240\\\\2x+4y-2x-2y=90\\\\2y = 90[/tex]
Now Dividing both side by 2 we get;
[tex]\frac{2y}{2}= \frac{90}{2}\\\\y=45[/tex]
Now we will substitute the value of 'y' in equation 1 we get;
[tex]x+y=120\\\\x+45 =120\\\\x=120-45 = 75[/tex]
Hence On that day 75 soft drinks and 45 popcorn were sold.
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice.
Answers
Answer:
22 yards
Step-by-step explanation:
Use a (+) sign for yards gained and a (-) sign for yards lost.
Geno gained 4 yards 3 times: (+4) × 3.
Geno lost 1 yard twice: (-1) × 2.
Geno gained 6 yards twice: (+6) × 2.
Net change
in field position
=
(4 × 3) + (-1 × 2) + (6 × 2)
=
12 − 2 + 12
=
10 + 12
=
22.
Geno gained 22 yards.
The net change in the position of Geno if In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice, is 22 yards.
What is addition?In math, addition is the process of adding two or more integers together. Addends are the numbers that are added, while the total refers to the outcome of the operation.
Given:
In the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice,
Calculate the net change in position as shown below,
The net change = Total gained - Total lost,
Total gained = 4 × 3 + 6 × 2
Total gained = 12 + 12
Total gained = 24
Total lost = 1 × 2
Total lost = 2
The net change = 24 - 2
The net change = 22
Thus, the net change in the Geno position is 22 yards.
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The complete question is:
Geno is a running back for the Bayside Barn Owls. During the final drive of his last football game, he gained 4 yards three times, lost 1 yard twice, and gained 6 yards twice. Find the net change in the position of Geno.
For a project on Egypt, Nick is building a paper model of a square based pyramid. The square base measures 8 inches by 8 inches. The slant height is 10 inches. Which measurement BEST describes the amount of construction paper needed to make this pyramid? (round to nearest whole number)
Answers
Answer:
Step-by-step explanation:
The square base measures 8 inches by 8 inches. The slant height is 10 inches.
The formula for determining the area of the square base of the pyramid is l^2. Therefore,
Area of the base = 8^2 = 64 inches^2
The formula for determining the perimeter of the square base is
4l. It becomes
4 × 8 = 32 inches
The amount of construction paper needed to make this pyramid is the total surface area of the pyramid. Therefore,
Total surface area = (1/2 × 32 × 10) + 64
= 160 + 64 = 224 inches^2
Nick will need approximately 224 square inches of construction paper for his square based pyramid project with a base measuring 8 inches by 8 inches and a slant height of 10 inches.
Explanation:To find the amount of construction paper needed for Nick's square based pyramid project, we need to calculate the surface area of the pyramid. The surface area of a pyramid includes the area of the base plus the area of the four triangular sides.
The area of the base (Abase) is the side length squared:
Abase = side × side = 8 inches × 8 inches = 64 square inches.
The area of one triangular side (Atriangular side) is given by the formula:
Atriangular side = 1/2 × base × slant height.
For Nick's project, the base of a triangular side is equal to the side of the square, so:
Atriangular side = 1/2 × 8 inches × 10 inches = 40 square inches.
Since there are four identical triangular sides:
Total area of triangular sides = 4 × 40 square inches = 160 square inches.
Adding the base and triangular sides areas together gives us the total construction paper needed:
Total construction paper needed = Abase + Total area of triangular sides = 64 square inches + 160 square inches = 224 square inches.
Therefore, Nick will need approximately 224 square inches of construction paper for his project. To get the nearest whole number, we round 224 to 224.
A study of voting chose 663 registered voters at random shortly after an election. Of these, 72% said they had voted in the election. Election records show that only 56% of registered voters voted in the election.
Which of the following statements is true about the percentages?
a. 72% is a sample; 56% is a population.
b. 72% and 56% are both statistics.
c. 72% is a statistic and 56% is a parameter.
d. 72% is a parameter and 56% is a statistic.
e. 72% and 56% are both parameters.
Answers
Answer: c. 72% is a statistic and 56% is a parameter.
Step-by-step explanation:
A population is a large group of all possible observations required for a study by the researcher's point of view.A Sample is a finite subset of population that is used by researcher to represent the entire population in an analysis.A parameter is a number that measure a characteristic for the entire population.A statistic is a number that measure a characteristic for the sample.A statistics given an estimate to the population parameter.Given : A study of voting chose 663 registered voters at random shortly after an election.
Population of interest : "registered voters"
Sample : " 663 registered voters "
72% of 663 registered voters said they had voted in the election.
⇒ Statistic = sample proportion registered voters voted in the election.= 72%
Election records show that only 56% of registered voters voted in the election.
⇒ Parameter = Population proportion of registered voters voted in the election = 56%
Hence, the correct answer is "c. 72% is a statistic and 56% is a parameter."
x2 - 2x - 24 = 0
Solve for X
Answers
Answer:
x = 6 or x = -4
Step-by-step explanation:
x^2 - 2x - 24 = 0
(x - 6)(x + 4) = 0
x - 6 =0 or x + 4 = 0
x = 6 or x = -4
Find f(-1) when f(x)=x^2-3x+6
Answers
Answer:
f(-1) = 10
Step-by-step explanation:
f(x)=x² - 3x + 6
when x = -1, substitute x=-1 into the equation above
f(-1) = (-1)² - 3(-1) + 6
= 1 + 3+6
= 10
At the end of the season, the coach took ten students to burger box.The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers. The total bill was $15.15. If a steak-in-a-bun cost $0.90 more than a queen-size burger, find the cost of one of each.
Answers
Answer:
Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.
Step-by-step explanation:
Let the cost of queen-size burger be 'q'.
Let the cost of steak-in-a-bun be 's'.
Given:
a steak-in-a-bun cost $0.90 more than a queen-size burger.
So we can say that;
[tex]s=0.9+q \ \ \ \ equation\ 1[/tex]
Given:
the coach took ten students to burger box.
Hence Number of person at burger box = 11
The coach and three students ordered steak-on-a-bun while the other students ordered queen-size burgers.
So we can say that;
Number of queen sized burger = 11 - 4 =7
Number of steak on a bun burger = 4
Also Given:
Total bill = $15.11
Now we can say that;
Total bill is equal to sum of Number of queen sized burger multiplied by Cost of queen sized burger and Number of steak on a bun burger multiplied by cost of steak on a bun burger.
framing in equation form we get;
[tex]4s+7q =15.15\ \ \ \ equation\ 2[/tex]
Substituting equation 1 in equation 2 we get;
[tex]4(0.9+q)+7q=15.15[/tex]
Applying distributive property we get;
[tex]3.6+4q+7q=15.15\\\\3.6+11q=15.15[/tex]
Subtracting both side by 3.6 we get;
[tex]3.6+11q-3.6 =15.15-3.6\\\\11q=11.55[/tex]
Dividing both side by 11 we get;
[tex]\frac{11q}{11}=\frac{11.55}{11}\\\\q=\$1.05[/tex]
Substituting the value of q in equation 1 we get;
[tex]s=0.9+q=0.9+1.05=\$1.95[/tex]
Hence Cost of steak-in-a-bun burger is $1.95 and cost of queen-size burger is $1.05.
Final answer:
The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.
Explanation:
The student's question involves finding the cost of one steak-on-a-bun and one queen-size burger given that the total bill for a group order at a restaurant was $15.15 and that a steak-on-a-bun costs $0.90 more than a queen-size burger.
Let's define Q as the price of a queen-size burger.
Therefore, the price of a steak-on-a-bun would be Q + $0.90. According to the problem, four people (the coach and three students) ordered steak-on-a-bun, and six students ordered queen-size burgers.
The equation representing the total cost is:
4(Q + $0.90) + 6Q = $15.15
Solving for Q, we first expand the equation:
4Q + $3.60 + 6Q = $15.15
Combining like terms, we get 10Q + $3.60 = $15.15.
Subtracting $3.60 from both sides, we get 10Q = $11.55.
Dividing both sides by 10, we find that Q = $1.155, which is the cost of a queen-size burger.
Finally, the cost of a steak-on-a-bun is Q + $0.90 = $1.155 + $0.90 = $2.055.
The cost of one steak-on-a-bun is $2.055, and the cost of one queen-size burger is $1.155.
Levi wants to order the fractions 1/3, 2/5, and 11/30 in descending order? How can you help him by using a common denominator? Explain and order the fractions in descending order.
Answers
Answer:
The correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
Step-by-step explanation:
Given fraction:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
To arrange them in descending order.
Solution:
In order to arrange the fractions in descending order, we will have to find the least common denominators.
To find the least common denominator, we will find the least common multiple of the denominators 3,5, and 30.
Since 30 is a common multiple of all 3 numbers, so it will be the least common denominator.
So, we multiply the numerators and denominators with same numbers in order to make the denominators = 30.
So, we have:
[tex]\frac{1}{3}, \frac{2}{5}, \frac{11}{30}[/tex]
⇒ [tex]\frac{1\times 10}{3\times 10}, \frac{2\times 6}{5\times 6}, \frac{11\times 1}{30\times 1}[/tex]
⇒ [tex]\frac{10}{30}, \frac{12}{30}, \frac{11}{30}[/tex]
Now, we compare the numerators and arrange them accordingly.
[tex]\frac{12}{30} > \frac{11}{30} > \frac{10}{30}[/tex]
So, the correct order of fractions in descending order will be:
[tex]\frac{2}{5}, \frac{11}{30}, \frac{1}{3}[/tex]
In May, the school store sells 80 erasers. In June, the store sells only 16 erasers. What is the percent of change in erasers sold from May to June?A) 80% B) 20% C) 64% D) 80%
Answers
Answer: 80%
Step-by-step explanation:
Since we have given that
Number of erasers sold in May = 80
Number of erasers sold in June = 16
Decrement in 1 month gap is given by
16-80=-64
So, Percentage of change in erasers sold from May to June is given by
[tex]\frac{-64}{80}[/tex] × 100
= -80% (Decreased 80%)
Answer:
80%
Step-by-step explanation:
I took a test with this question on it
Jaime claimes that when you multiply by 100, the decimal point moves to the right. Salome argue that the decimal point only moves when you multiply a whole number by 100. Salmon says that when you multiply a whole number by 100, product has 2 extra zeros. Which student got it correct? Justify your answer.
Answers
Answer:
Step-by-step explanation:
2.75×100=275.00
3=3.00×100=100.00
in either case decimal point moves to the right.
but in whole numbers 3=3
You are asked to draw a triangle with side lengths of 8 inches and 10 inches. What is the longest whole number length that your third side can be? Group of answer choices 18 20 16 21
Answers
Answer:
Correct number : c = 16
Step-by-step explanation:
The triangle theorem states that each side of the triangle is smaller than the sum of the other two and larger than their difference. We denote the three sides of a triangle as a, b, and c.
Suppose that a = 8 and b = 10 and as we see b is greater than a , b > a
b - a < c < b + a => 10 - 8 < c < 10 + 8 => 2 < c < 18
from the offered answers we choose number 16
c = 16
God is with you!!!
Answer:
Step-by-step explanation:
if a,b,c are three sides of a triangle,then a<b+c,b<c+a,c<a+b
or in general we can say any side < sum of other two sides.
third side<8+10
or third side <18
Here third side=16
if you are asked smallest side then any side >difference of other two sides.
third side >10-8 or>2
A 25-foot ladder rests against a building. The base of the ladder is 15 feet away from the base
of the building. At what height does the ladder rest on the building?
Answers
Answer: the top of the ladder is 20ft below the ground.
Step-by-step explanation:
The ladder makes an angle, θ with the ground thus forming a right angle triangle with the wall of the house.
The length of the ladder represents the hypotenuse of the right angle triangle.
The ground distance between the base of the house and the base of the ladder represents the adjacent side of the right angle triangle.
Therefore, to determine the height at which the ladder rest on the building, x, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
25² = x² + 15²
625 = x² + 225
x² = 625 - 225 = 400
x = √400 = 20 ft
if 12, 15, 18 and 16, 20, and x are the lengths of the corresponding sides of two similar triangles, what is the value of x?
Answers
To find the value of x for the corresponding sides of two similar triangles, we set up a proportion using the given sides.
Upon simplifying the ratio, x is calculated to be 24, which is the side length in the second triangle.
Explanation:To find the value of x in two similar triangles with side lengths 12, 15, 18 and 16, 20, x, we use the concept that corresponding sides in similar triangles have proportional lengths.
We start by setting up a proportion using the corresponding sides:
[tex]\(\frac{12}{16} = \frac{15}{20} = \frac{18}{x}\)[/tex]
We can simplify the first two ratios to find a single scale factor:
[tex]\(\frac{12}{16} = \frac{15}{20} \rightarrow \frac{3}{4} = \frac{3}{4}\)[/tex]
This confirms the triangles are indeed similar since the ratios are equal. We then use the third ratio to solve for x:
[tex]\(\frac{18}{x} = \frac{3}{4} \rightarrow x = \frac{4}{3} \cdot 18 = 24\)[/tex]
Therefore, the value of x is 24, which is the length of the corresponding side in the second triangle.
how to solve (-2/5x)(2/6y)=
Answers
Answer:
-2yx/15?
Step-by-step explanation:
The recommended angle for a wheel chair ramp is 5 degrees. If the rise of the ramp to go up the steps is 2 feet, find the horizantal run length that the ramp must start. (Round to one decimal place)
wheel chair ramp
Answers
Answer:
22.9 feet
Step-by-step explanation:
You are using Tangent because you have the opposite and adjacent sides
Tan 5 = 2/x
x Tan 5= 2
x= 2/Tan5
= 22.860
To find the horizontal run length of a wheelchair ramp with a 5-degree angle and a 2-foot rise, use the tangent function of trigonometry. Plug the given values into the tangent formula, rearrange to solve for 'Run', and calculate to get a run length of approximately 22.8 feet.
Explanation:The question is referring to the use of trigonometry to solve real-life problems. Here, we are going to use the tangent of the angle, which is defined as the ratio of the opposite side (the rise) to the adjacent side (the run). In this case, we know that the angle is 5 degrees and the rise is 2 feet.
In mathematical terms, this can be written as:
Tan(ρ) = Rise/Run
Substituting the values into the equation, we get:
Tan(5°) = 2/Run
Solving for Run, we get:
Run = 2/Tan(5°)
You can find this value using a calculator, rounding to the nearest tenth, to get the run as approximately 22.8 feet.
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Johnny must learn more than 10 New Pl. Before the big game you're already learned for writing and recording that represents how many more players he needs to learn to reach his goal
Answers
Question is Incomplete; Complete question is given below;
Johnny must learn more than 10 new plays before the big game. He has already learned 4. Write and solve the inequality that represents how many more plays he needs to learn to reach his goal?
Answer:
The Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].
Johnny should learn more than 6 games to reach his goals.
Step-by-step explanation:
Given:
Number of plays to be learn [tex]>[/tex] 10
Number of plays already learned = 4
we need to write an inequality that represents how many more plays he needs to learn to reach his goal.
Solution:
Let the number of plays needed to learn more be 'x'.
So we can say that;
Number of plays already learned plus number of plays needed to learn more should be greater than total Number of plays to be learn.
framing in equation form we get;
[tex]x+4>10[/tex]
Hence the Inequality representing the more plays he needs to learn to reach his goal is [tex]x+4>10[/tex].
On solving the equality we get;
Subtracting both side by 4 we get;
[tex]x+4-4>10-4\\\\x>6[/tex]
Hence Johnny should learn more than 6 games to reach his goals.
Susan and Jim each on a lawn care business the amount Susan charges for lawn care by the hour is shown in the table 2 hours $48.03 hours $72.07 hours $168.11 hours
Answers
Question is Incomplete;Complete question is given below;
Susan and Jim each own a lawn care business. The amount Susan charges for lawn care is shown in the table. The amount him charges for lawn care is shown in the table.
What is the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work ?
Susan
2 hrs $48
3 hrs $72
7 hrs $ 168
11 hrs $264
Jim
1 hr $20
2 hrs $40
3 hrs $60
4 hrs $80
5 hrs $100
6 hrs $120
A) $16
B) $20
C) $28
D) $40
Answer:
D) $40
Step-by-step explanation:
We need to find the DIFFERENCE between Susan's and Jim's lawn care business in the amounts they charge for 10 hours at work.
Solution:
First we will find the hourly charges of lawn care for both.
Given:
From the table of Jim we can see that
Charges of Jim for 1 hour = $20
So for 10 hour = Charges of Jim for 10 hour.
By using Unitary method we get;
Charges of Jim for 10 hour = [tex]10\times 20 =\$200[/tex]
Now From table of Susan we can see that;
for 2 hours = $48
So for 1 hour = Charges of Susan for 1 hour.
By Using Unitary method we get;
Charges of Susan for 1 hour = [tex]\frac{48}{2}= \$24[/tex]
Now we know that;
Charges of Susan for 1 hour = $24
So for 10 hour = Charges of Susan for 10 hour
again by using Unitary method we get;
Charges of Susan for 10 hour = [tex]24\times10 =\$240[/tex]
Now we need to find the difference between their charges.
Difference can be calculated by subtracting Charges of Jim for 10 hour from Charges of Susan for 10 hour.
framing in equation form we get;
Difference = [tex]\$240-\$200=\$40[/tex]
Hence The difference in the charges for 10 hour of work is $40.
The student council memebers are making decorative labels to cover 20 identical empty coffee cans for charity drive. Each label will cover the entire lateral surface area of a can. Which is the closest to the lateral surface coffee can
Answers
Answer:
127.48 in²Explanation:
The image attached shows the dimensions of the coffe cans considered for this question.
The figure is a cylinder with dimensions:
[tex]\text {radius }3\frac{1}{16}\text {inches and height }6\frac{5}{8}\text {inches}[/tex]Thus, to find the lateral surface of a coffe can, you use the formula for the lateral area of a cylinder:
[tex]LA=2\pi\times r\times h[/tex]Where, LA is the lateral area, r is the radius, and h is the height.
Substituting the dimensions given in the figure, you get:
[tex]LA=2\pi\times 3\frac{1}{16}\times 6\frac{5}{8}[/tex]To multiply, first convert the mixed numbers into improper fractions:
[tex]3\frac{1}{16}=3+\frac{1}{16}=\frac{3(16)+1}{16}=\frac{48+1}{16}=\frac{49}{16}\\ \\ 6\frac{5}{8}=6+\frac{5}{8}=\frac{6(8)+5}{8}=\frac{48+5}{8}=\frac{53}{8}[/tex]
Now, you can multiply:
[tex]LA=2\pi\times \frac{49}{16}\times \frac{53}{8}[/tex][tex]LA=127.48in^2[/tex]Alison bought jelly beans to share with her friends she bought 1 1/4 pounds of blueberry jelly beans and 2 1/3 pounds of Lemon Jelly Beans if she gave 1 and 2/3 pounds of jelly beans away to a friend how many pounds of jelly beans does she have left
Answers
After giving away 1 and 2/3 pounds of jelly beans, Alison has 4/3 pounds left.
Explanation:To find out how many pounds of jelly beans Alison has left after giving away 1 and 2/3 pounds, we need to subtract that amount from the total.
1 1/4 pounds + 2 1/3 pounds - 1 2/3 pounds = 2/4 + 7/3 - 5/3 = 8/12 + 28/12 - 20/12 = 16/12 = 4/3 pounds
Therefore, Alison has 4/3 pounds of jelly beans left.
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hi :) this lesson is about 30-60-90 triangles.
I need a formula to find the long side. I dont need the actual length if the long side, I just need the equation to find it. help would be much appreciated.
Answers
Answer:
5 times the square root of 3
Step-by-step explanation:
To get the longest side of a 30-60-90 triangle, you take the shortest side and multiply it by the square root of 3.
5*(square root of 3)
Tito receives a weekly salary of $350 at an appliance store. He also receives a 5% commission on a total dollar amount of all sales he makes. What must his total sales be in a week if he is to make a total of $675
Answers
Answer:his total sales be $6500 in a week if he is to make a total of $675
Step-by-step explanation:
The total amount of money that Tito receives as weekly salary at an appliance store is $350.
He also receives a 5% commission on a total dollar amount of all sales he makes.
Let x represent his total sales in a week.
The amount of commission that he receives would be
5/100 × x = 0.05x
if he is to make a total of $675 in a week, it means that
0.05x + 350 = 675
0.05x = 675 - 350 = 325
x = 325/0.05 = $6500
By setting up an equation to represent Tito's total earnings and solving for total sales, we find that Tito must make $6500 worth of sales to earn a total of $675 in a week.
Explanation:The subject of this question is Mathematics, specifically dealing with algebraic calculations to find the value of the variable. The variable in this case is the total sales Tito must make to earn a total of $675 in a week.
We know that Tito earns a fixed weekly salary of $350 and he also receives a 5% commission on his total sales. He wants to know how much he needs to sell to reach a total earning of $675.
To solve this, we set up an equation to represent the total earnings that Tito wishes to make: $350 (salary) + 0.05x (sales commissions) = $675.
Now we solve the equation for x (total sales). First, subtract $350 from both sides to get 0.05x = $675 - $350, which simplifies to 0.05x = $325.
Next, divide both sides of the equation by 0.05 to find x, so x = $325 / 0.05.
Therefore, Tito's total sales in a week must be $6500 for him to make a total of $675.
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Two cartons weigh 3x-2 and 2x-3 pounds, respectively. If the average weight of the cartons is 10 pounds, the heavier carton weights how many more pounds than the lighter carton
Answers
Final answer:
By setting up an equation using the average weight formula and solving for x, we find that x equals 5. Subsequently, the heavier carton weighs 13 pounds, and the lighter carton weighs 7 pounds, making the heavier carton weigh 6 pounds more than the lighter carton.
Explanation:
The question involves finding out how many more pounds the heavier carton weighs compared to the lighter carton when given their weights in terms of x and the average weight.
Firstly, we are given that the weights of the two cartons are 3x - 2 and 2x - 3 pounds, and their average weight is 10 pounds.
To find the value of x, we need to set up an equation using the average weight formula, which is:
(Weight of Carton 1 + Weight of Carton 2) / 2 = Average Weight
Substituting the given weights and average weight into the formula, we get:
((3x - 2) + (2x - 3)) / 2 = 10
Solving the equation by combining like terms and multiplying both sides by 2 to eliminate the fraction gives:
5x - 5 = 20
Adding 5 to both sides and then dividing by 5:
x = 5
Now, let's find the actual weight of each carton:
Weight of the first carton = 3x - 2 = 3(5) - 2 = 13 pounds
Weight of the second carton = 2x - 3 = 2(5) - 3 = 7 pounds
Lastly, we determine how many more pounds the heavier carton weighs compared to the lighter one:
13 pounds - 7 pounds = 6 pounds
Therefore, the heavier carton weighs 6 pounds more than the lighter carton.
Find the distance between the pair of points given on the graph
Answers
Answer: distance = 5
Step-by-step explanation:
The formula for determining the distance between two points on a straight line is expressed as
Distance = √(x2 - x1)² + (y2 - y1)²
Where
x2 represents final value of x on the horizontal axis
x1 represents initial value of x on the horizontal axis.
y2 represents final value of y on the vertical axis.
y1 represents initial value of y on the vertical axis.
From the graph given,
x2 = 1
x1 = - 2
y2 = 0
y1 = - 4
Therefore,
Distance = √(1 - - 2)² + (0 - - 4)²
Distance = √3² + 4² = √9 + 16 = √25
Distance = 5
Charlie has two dimes for Nichols and some quarters in his pocket if the probability of drawing a quarter out of his pocket is 1/2 how many quarters does he
Answers
Answer:
He has 2 quarters in his pocket.
A truck can be ready for company a 420 dayPlus $.30 per mile can we be charges $50 a day plus $.50 per mile to rent the same truck find the number of miles in a day at which the rental costs for a company a and Company B same
Answers
Answer:it will take 1850 miles
Step-by-step explanation:
Let x represent the number of miles in a day at which the rental costs for a company A and Company B same.
Let y represent the total cost of renting the truck for x miles with company A.
Let z represent the total cost of renting the truck for x miles with company A.
Company A charges $420 a day Plus $.30 per mile. This means that
y = 420 + 0.3x
Company B charges $50 a day plus $.50 per mile to rent the same truck. This means that
z = 50 + 0.5x
To determine the number of miles in a day at which the rental costs for a company A and Company B same, we will equate y to z. It becomes
420 + 0.3x = 50 + 0.5x
0.5x - 0.3x = 420 - 50
0.2x = 370
x = 370/0.2 = 1850 miles
The length of Martin's driveway, rounded to the nearest foot, is 121 ft. What is the minimum possible length of the driveway? A 121.0 ft B 120.5 ft C 120.9 ft D 120.3 ft
Answers
Answer:
B. 120.5 ft
Step-by-step explanation:
Given:
Length of Martins drive way = 121 ft
We need to find the minimum possible length of the driveway
Solution:
Now we know that ;
When a number is rounded to nearest whole number.
We can say that the number is in decimal format.
Also rounding techniques applies when the decimal number has digit 5 or more in ten's place after decimal then the number in increase by 1 as a whole number.
Here the number is rounded to nearest foot which is 121 ft.
So we an say that;
Number ranging from 120.50 to 120.99 can be made to 121 as nearest foot.
Hence the minimum possible length of the drive way could be 120.5 ft
The demand d for a companys product cost x is predicted by the function d(x) = 500-2x. The price p in dollars that the company can charge for the product is given by p(x)=x+5
Answers
The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function.
Explanation:The subject of this question is Mathematics. The student is given two functions, d(x) = 500-2x and p(x) = x+5, which represent the demand and price, respectively, of a company's product. To find the relationship between price and quantity, we can substitute the demand function into the price function:
p(x) = x + 5 = d(x) + 5 = (500 - 2x) + 5 = 505 - 2x
So the price can be represented by the equation p(x) = 505 - 2x.
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To earn an A in an algebra course, a student must have a test average of at least 90. Mary has grades of 95, 82, 88 on her first three algebra tests. What minimum score does Mary need to make on her fourth test to earn an A in her algebra course?
Answers
Answer: Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.
Step-by-step explanation:
Let x be the grades scored by Mary in the fourth algebra test.
Mary has grades of 95, 82, 88 on her first three algebra tests.
Then, the combined scores in four test will become = 95+82+88+x = 265+x
Average score = (Sum of all scores) ÷ (Number of tests)
[tex]=\dfrac{265+x}{4}[/tex]
As per given ,
To earn an A in an algebra course, a student must have a test average of at least 90.
i.e. Average score ≥ 90
[tex]\Rightarrow\ \dfrac{265+x}{4}\geq90\\\\\Rightarrow\ 265+x\geq 90\times4=360\\\\\Rightarrow\ x\geq360-265 =95\\\\\Rightarrow\ x\geq90[/tex]
Hence, Mary need to make at-least 95 on her fourth test to earn an A in her algebra course.
To receive a grade of A on 80 question test 90% of the questions must be answered correctly what is the maximum number of questions that can't be missed to still receive an A
Answers
Answer:
Step-by-step explanation:
Total number of questions in the test is 80.
To receive a grade of A on the 80 question test, 90% of the questions must be answered correctly. It means that the number if questions that must be answered correctly would be
90/100 × 80 = 0.9 × 80 = 72.
Therefore, the maximum number of questions that can't be missed to still receive an A is 72
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30 and you owe $59.50. How many text messages do you have?
Answers
Answer: you have 118 text messages.
Step-by-step explanation:
Let x represent the number of text messages that you have or sent.
A cell phone company charges a monthly fee plus $.25 for each text message. The monthly fee is $30. This means that the total cost of x sending x messages in a month would be
0.25x + 30
If you owe $59.50, then your total cost is $59.50
Therefore,
59.50 = 0.25x + 30
0.25x = 59.50 - 30
0.25x = 29.5
x = 29.5/0.25
x = 118