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Related Questions
Derek owns a landscape business. He charges a fixed fee of $30 plus $1 per 1,000 square feet of lawn mowed. Derek's earnings (in dollars) in the past five weeks are {204, 344, 450, 482, 504}. To find the corresponding square footage of lawn mowed, construct a function that models the total area of lawn that Derek mows based on his earnings. Based on Derek's earnings, the corresponding square footage of the lawns he mowed in the past five weeks is
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then Derek earns 30 $+x $ =30+x ($)
Assume Derek earns y dollars, then
y= 30+x
to find x, the 1,000 sq feet area Derek mowed, we isolate x, that is we write x in terms of y, his earnings:
y= 30+x
x = y-30
Thus, the function A, which gives the area mowed in terms of the earnings y is :
x= A(y) = y-30
A(204)=204-30=174
A(344)=344-30=314
A(450)=450-30=420
A(482)=482-30=452
A(504)=504-30=474
Thus Derek earned 204, 344, 450, 482, 504 dollars for mowing correspondingly
174,000; 314,000; 420,000; 452,000 ; 474,000 square feet.
Answer: A(y) = y-30, is the function which gives the 1,000y square feet area mowed when earning y dollars.
Remark:
or A(x)=x-30, since x or y is a 'dummy variable', it doesn't make any difference in describing the function.
Answer:
{174,000, 134,000, 420,000, 452,000, 474,000}
Nicole Tobin receives a salary of $250 per week plus a commission of 15% on all sales over $1500. Find her earnings during a week in which sales totaled $3000.
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$3000 x 15% = $450
$450 + $250 = $700
Final answer:
To calculate Nicole Tobin's earnings for a week in which her sales totaled $3000, we first determine the total sales eligible for commission and then calculate 15% commission on that amount. Adding the resulting commission to her weekly salary of $250 gives us Nicole's total earnings for the week, which are $475.
Explanation:
Nicole Tobin receives a salary of $250 per week plus a commission of 15% on all sales over $1500. To calculate her earnings during a week in which her sales totaled $3000, we need to find out the commission on the sales exceeding $1500 and then add it to her weekly salary.
First, we calculate the amount eligible for commission:
Sales = $3000
Threshold for commission = $1500
Eligible amount for commission = Total sales - Threshold for commission = $3000 - $1500 = $1500
Next, we calculate the commission:
Commission rate = 15%
Commission = Eligible amount for commission × Commission rate = $1500 × 0.15 = $225
Finally, we find Nicole's total earnings:
Weekly salary = $250
Total earnings = Weekly salary + Commission = $250 + $225 = $475
Nicole's earnings for the week are $475.
-5/4x -5= -35 solve for x
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-5/4x = -30
x = -30 (-4/5)
x = 24
Selma uses a jogging trail that runs through a park near her home. The trail is a loop that is 3/4 of a mile long. On Monday, Selma ran the loop in 1/6 of an hour. What is Selma's unit rate in miles per hour for Monday's run?
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3/4 * 6/1 =
18/4 =
4.5 miles per hr <==
Tess and Dan have $24.00 each to spend at a book fair, where all students receive a 15% discount. They both want to purchase a copy of the same book, which normally sells for $24.50 plus 10% sales tax. To check if she has enough to purchase the book, Tess takes 15% of $24.50 and subtracts that amount from the normal price. She takes 10% of the discounted selling price and adds it back to find the purchase amount. Dan takes 85% of the normal purchase price and then computes 110% of the reduced price. Is Tess correct? Is Dan correct? Do they have enough money to purchase the book? Explain your answer using complete sentences, and show your work.
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Answer:
Tess is wrong and Dan is correct because the tax is calculated after discount.
Step-by-step explanation:
answer correctly for brainliest
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2. C
3. E
4. A
5. B
2) C
3) E
4) A
5) B
This is true because the phrases are simply defining what is going on in the equation.
is 3 sin(alpha)+4 cos(beta)=8 possible
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Answer:
No, it's not possible
Step-by-step explanation:
We know that for various values of x , [tex]-1\leq \sin x\leq 1[/tex]
and [tex]-1\leq \cos x \leq 1[/tex]
For values of [tex]\alpha[/tex], [tex]-1\leq \sin \alpha\leq 1[/tex]
On multiplying all sides by 3, we get
[tex]-3\leq 3\sin \alpha\leq 3[/tex]
For values of [tex]\beta[/tex], [tex]-1\leq\cos \beta\leq 1[/tex]
On multiplying all sides by 4, we get
[tex]-4\leq 4\cos \beta\leq 4[/tex]
On adding all sides of [tex]-3\leq 3\sin \alpha\leq 3\,\,,\,\,-4\leq 4\cos \beta\leq 4[/tex] , we get
[tex]-3-4\leq 3\sin \alpha+ 4\cos \beta\leq 3+4\\-7\leq 3\sin \alpha+ 4\cos \beta\leq 7[/tex]
Therefore, maximum value of [tex]3\sin \alpha+ 4\cos \beta[/tex] is 7.
So, it's not possible that [tex]3\sin \alpha+ 4\cos \beta=8[/tex]
There are two 6th grade classes one with 29 students and the other with 31 students. There are 26 male students between the two classes. What is the ratio of female students to total students?
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So, if the male ratio is 26/60, the remaining students are female. 60-26 Is 34, so the ratio of FEMALE students to total students is 34/60 which can be simplified to 17/30
Which statement best explains the value of 18 − (−5)?
The additive inverse of −5 is +5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 23.
The additive inverse of −5 is −5, so 18 − (−5) = 13.
The additive inverse of −5 is +5, so 18 − (−5) = 13.
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Pittsburgh international airport had approximately 714,587 passengers in august 2009. Write a number that is greater than 714,587.
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The ratio between the number of cats (c) and the number of dogs (d) in the shelter is 3. There are 27 cats in the shelter. How many dogs are in the shelter?
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Since the ratio is 3:1, that means for every 3 cats you get one dog.
Therefore your answer is 9
Can u help idk how to write it ?
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For part A, the inequality that we can form is x ≥ 2,450 because she needs more than $2,000 to survive after buying a $450 dollar worth laptop. Adding the two makes it 2,450.
For part B, if she has to withdraw $30 per week, then the inequality that we can form is x ≥ 2,450 - 30
For part C,
30x ≥ 2,000
x ≥ 66.67
For part D, the answer 66.67 means that Maggie can have 66 times to withdraw $30 per week worth of food from her balance $2000.
Given the following functions f(x) and g(x), solve for (f ⋅ g)(2) and select the correct answer below:
f(x) = 3x2 + 2
g(x) = x − 8 (1 point)
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Answer:
Given the functions:
[tex]f(x) = 3x^2+2[/tex]
[tex]g(x) = x-8[/tex]
we have to find [tex](f \cdot g)(2)[/tex]
[tex](f \cdot g)(2) = f(2) \cdot g(2)[/tex] ....[1]
Substitute the value of x = 2 in f(x) and g(x) we have;
[tex]f(2) = 3(2)^2+2 =12+2 = 14[/tex] and
[tex]g(2) = 2-8 = -6[/tex]
Substitute these in [1] we have;
[tex](f \cdot g)(2) = 14 \cdot -6 = -84[/tex]
Therefore, the value of [tex](f \cdot g)(2)[/tex] is, -84
Solve for x. Rs/x =1/4 A. X=rs/4 B. X=4/rs C. X=1/4rs D. X=4rs
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Answer:
The correct option is D.
Step-by-step explanation:
The given equation is
[tex]\frac{Rs}{x}=\frac{1}{4}[/tex]
We need to solve the given equation for x.
On cross multiplication we get
[tex]Rs\times 4=1\times x[/tex]
On further simplification we get
[tex]4Rs=x[/tex]
The value of x is 4 times of Rs. Only option D represents this situation.
Therefore, the correct option is D.
A professor teaches a small lecture class with 25 students. For a certain class, 22 students attend the lecture. What is the experimental probability that a student is absent?
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If you're looking for the fraction.. I'm not sure about that part.. all I know is the percentage..
:)
How to write x2+y2+2x-12y-9 in Standard form
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You run 6 miles in 1 hour. At this rate how long will it take you to run a marathon of 26 miles?
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Cross multiplication method.
1 hr*26 miles= 26
26/6= 4 1/3
4 1/3=x
Final answer: 4 1/3 hrs or 4 hrs and 20 minutes
During an 8 hour car ride to Georgia, my dog Pepper whined for 1/3 of the ride. How many hours did she whine
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multiply 8 by 1/3
8* 1/3 = 8/3 =2 2/3 hours
Which statement is false? A.The all them of a regular polygon is perpendicular to the side. B.the radius of a regular polygon is always greater than the all them. C.the perimeter of a regular hexagon is 6r. D.the perimeter of a regular n-gob is the area divided by the all them.
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What is the sum of 4.2•10^5 and 5.3• 10^5
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Write the linear inequality shown in the graph. The gray area represents the shaded region
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slope = (-1 - 2) / (2 - 1) = -3/1 = -3
y = mx + b
slope(m) = -3
(1,2)...x = 1 and y = 2
sub and find b
2 = -3(1) + b
2 = -3 + b
2 + 3 = b
5 = b
equation is : y = -3x + 5.......u have a solid line, so there is an equal sign in the problem...it is shaded below the line, so it is less then.
ur inequality is : y < = -3x + 5
The inequality from the given graph is y≤-3x+5.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
From the graph, the coordinate points are (2, -1) and (1, 2).
Here, slope (m)=(2+1)/(1-2)
m=-3
Substitute m=-3 and (x, y)=(2, -1) in y=mx+c, we get
-1=-3(2)+c
-1=-6+c
c=5
Substitute m=-3 and c=5 in y=mx+c, we get
y=-3x+5
So, the inequality is y≤-3x+5
Therefore, the inequality is y≤-3x+5.
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The best length of a triangle is 4 feet and the height is 2 feet. What is the area of the triangle?
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Plug it into the formula.
4*2=8
8/2=4
Final answer: 4 ft^2
given A = {a, e, i, o, u} and B = {a, l, g, e, b, r}, find A ∪ B.
{}
{a,e}
{a, b, e, g, i, l, o, r, u}
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Answer: the 3rd choice, {a, b, e, g, i, l, o, r, u}
A ∪ B = {a,e,i,o,u,l,g,b,r}
For any element ∈ A and B, you choose it once
Find two numbers that have 2,3 and 5 as factors. What other factors do the two numbers have in common?
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30 has 2,3, and 5 as factors....
60 has 2,3, and 5 as factors...
both 30 and 60 also have common factors of 1,6,10,15,and 30
Two numbers are 30 and 60 that have 2,3 and 5 as factors.
What is LCM ?LCM is the least common multiple of two or more that two given numbers which is exactly divisible by these given numbers.
According to the given question we have to find two numbers that have 2, 3 and 5 as common factors.
To find least such number which have common factor of 2, 3 and 5 we have to take LCM of 2, 3 and 5.
The LCM of 2, 3 and 5 is 30.
The next such possible higher numbers will be of the form 30k, where k is an integer.
At k = 2,
The number 30k will be 30(2) which is
= 60.
We can find any such form of numbers by putting different integer value of k.
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four times the square of a non-zero number is equal to twelve times the number.
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4x^2 - 12x = 0
4x(x - 3) = 0
4x = 0
x = 0...not this one
x - 3 = 0
x = 3 <== ur number
3 is the number whose four times the square is equal to twelve times 3.
What is equation?An equation is a relationship between two or more variables expressed in equal to sign. It is solved to find the value of variables. Equation of two variables will look like ax+ by=c.
How to find number?Let the required number be x.
According to question we have to form an equation which will be:
4[tex]x^{2}[/tex]=12x
[tex]4x^{2} -12x=0[/tex]
4x(x-3)=0
4x=0, x-3=0
x=0, x=3
Non negative number=3
Hence 3 is the number whose 4 times square is equal to 12*3.
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Please help answer this questionnnn
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y=5
5=1/4x^2+1
4=1/4x^2
16 = x^s
x = square root (16) = 4
x=3
y= 1/4(3)^2+1 = 3 1/4 = 13/4
Which of the following numbers has a value that is between 10% and 1/9? (a) 0.151 (b) 0.112 (c) 0.108 (d) 0.019
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10% = 0.10
1/9 = 0.11
So the answer has to be between 0.10 and 0.11.
A is more than 0.11.
B is more than 0.11.
C is between 0.10 and 0.11.
D is less than 0.10.
The answer is C. 0.108.
Among the given options, (c) 0.108 is the only number that lies between 0.10 (which is the decimal equivalent of 10%) and 0.111 (which is approximate decimal equivalent of 1/9).
Explanation:To answer the question "Which of the following numbers has a value that is between 10% and 1/9?", we first need to convert 10% and 1/9 into decimal form. 10% is equivalent to 0.10, and 1/9 is approximately 0.111. We are therefore looking for a number between 0.10 and 0.111.
Reviewing the options, (a) 0.151, (b) 0.112, (c) 0.108, and (d) 0.019, we see that only (c) 0.108 fits because it falls between 0.10 and 0.111.
Therefore, the correct answer is (c) 0.108.
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What is the value of z in the equation 5z − 9 = 36? 4 5 6 9
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5z = 36+9
5z = 45
Divide both terms by 5
5z/5 = 45/5
z = 9
add 9 to both sides
5z - 9 + 9 = 36 + 9
5z = 45
divide both sides by 5
5z / 5 = 45 / 5
z = 9
Emily made 75% of the baskets that she attempted if she may nine baskets how many attempts did you make?
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75/100= 9 baskets/ x attempts
The ratio of numerator to denominator should be 75/100 which simplifies to 3/4. 3/4= 9/x
3*3=9, 4*3=12
x=12
Final answer: 12 attempts
Julia wrote 14 letters to friends each month for y months in a row. Write an expression to show how many total letters she wrote.
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14y. In conclusion, 14y is an expression to show how many total letters she wrote. Have a nice day!
let S represents sum of letters that have been sent in y number of months
This simply means that we can write equation:
14*y = S
For any number of months we express it in equation above and we get total number of letters she wrote.