Kiki wants to rent a bounce house for her daughter's party. The cost, y, to rent a bounce house for a number of hours, x, is shown in the table. The initial set-up fee is included in the cost.
Answers
185 = 2(x) + y
X is the hours and y is the setup fee
315 = 4(x) + y
Now you solve the first
185 = 2x+y
185-y = 2x
(185-y)/2 = x
That means you can plug that value into the second equation where you see the x
315 = 4((185-y)/2) + y
315 = 370-2y + y
315 = 370 - y
-55 = - y
55 = y
So y is 55 (the setup fee)
Back to the original
185 = 2(x) + y
185 = 2(x) + 55
130 = 2x
65 = x
Now test it
575 = 8x + y
575 = 8(65) + 55
575 = 520 + 55
575 = 575
Answer:
The initial setup fee is $55.The hourly rate is $65.Step-by-step explanation:
First of all, we need to find the equation that models this situation.
Let's find the constant ratio of change using two pair of values from the given table.
[tex]m=\frac{575-185}{8-2}=\frac{390}{6}=65[/tex]
The ratio of change is 65.
In other words, the hourly rate is $65, that is, 65 dollars per hour.
Then, we use the point-slope form to find the equation
[tex]y-y_{1} =m(x-x_{1} )\\y-185=65(x-2)\\y=65x-130+185\\y=65x+55[/tex]
Where [tex]55[/tex] refers to the initial condition.
In other words, the initial setup fee is $55.
Related Questions
The largest number that rounds to 2,500 when rounded to the nearest ten?
Answers
Write an equation that represents this comparison sentence 32 is 8 times as many as 4
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32 = 8 × 4
32 "is" can stand for equal. 8 "times" (×) as many as 4.
Hope this helps! :)
Answer:
[tex]32=8\times 4[/tex]
Step-by-step explanation:
We have been given a word phrase. We are asked to write an equation for the given word phrase.
8 times 4 would be [tex]8\times 4[/tex].
We have been given that 32 is 8 times as many as 4. This means that 32 is equal to 8 times 4. We can represent this information in an equation as [tex]32=8\times 4[/tex]
Therefore, our required equation would be [tex]32=8\times 4[/tex].
find the coordinates of the missing endpoint if E is the midpoint of df. f=(5,8) E=(4,3)
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Coordinates of the midpoint [tex](h,k)[/tex] of a segment with endpoints [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,
[tex]h=\frac{x_1+x_2}{2}[/tex]
[tex]k=\frac{y_1+y_2}{2}[/tex]
If the coordinates of the endpoints D, F and midpoint E are [tex](x_1,y_1)[/tex], [tex](5,8)[/tex] and [tex](4,3)[/tex] respectively,
Coordinates of the endpoint D,
[tex]4=\frac{x_1+5}{2}[/tex]
[tex]x_1+5=8[/tex]
[tex]x_1=3[/tex]
[tex]3=\frac{8+y_1}{2}[/tex]
[tex]y_1+8=6[/tex]
[tex]y_1=-2[/tex]
Therefore, coordinates of the endpoint D are [tex](3,-2)[/tex].
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We have that the coordinates of the missing endpoint is
d=(13,14)
From the question we are told that
The coordinates of the missing endpointE is the midpoint of df. f=(5,8) E=(4,3)Generally the equation for the df is mathematically given as
For X
[tex]\frac{(x_1-x-2)}{2}= x_m\\\\\frac{(x_1-5)}{2}= 4[/tex]
x_1-5=8
x_1=13
For Y
[tex]\frac{(y_1-y-2)}{2}= y_m\\\\\frac{(y_1-8)}{2}= 3[/tex]
y_1-8=6
y_1=14
Therefore the coordinates of the missing endpoint
d=(13,14)
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4. This panel screen is an excellent example of how harmony is created in
artwork. What is the most obvious concept that has helped to create harmony
in this piece?
abstract shapes and themes
representation of historic scenes
realistic portraits
scenes of nature
Answers
Answer:
realistic portraits
Step-by-step explanation:
i did it
Consider a civilization broadcasting a signal with a power of 2.0×104 watts. The Arecibo radio telescope, which is about 300 meters in diameter, could detect this signal if it is coming from as far away as 141 light-years. Suppose instead that the signal is being broadcast from the other side of the Milky Way Galaxy, about 70000 light-years away.
Answers
For light: Inverse Square Law
The signal is weaken by the inverse square of the
difference of distances this means that one over the square of the
difference.
Therefore, 70000LY / 141 LY =496.45 and that squared =246462.602 times less signal, or 1/246462.602.
2 For a circular telescope like the
Arecibo radio telescope that equals Pi times the radius squared. Sensitivity
of the telescope depends on its area.
The new telescope needs 246462.60 times that area to have
enough sensitivity
(150 x 150 x Pi) = 70 685 sq m area for the Arecibo telescope
and that times 246462.60
= 1.74212 x 10^10
What is the diameter of a circle with that area?
1. Divide the area by Pi = 5.548156 x 10^9
2. Take the square root of the result to find the radius = 74485.94293
3. Multiply by 2 to find the diameter = 148971.886
Which transformations will produce similar, but not congruent, figures?
A) Triangle MNO is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle M"N"O".
B) Triangle MNO is reflected across the x-axis and then translated 9 units down to form triangle M"N"O".
C) Triangle MNO is reflected across the x-axis and then rotated 90° clockwise to form triangle M"N"O".
D) Triangle MNO is reflected across the y-axis and then rotated 180° clockwise to form triangle M"N"O".
Answers
Answer: A) Triangle MNO is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle M"N"O".
Step-by-step explanation:
We know that we prefer rigid motions to create congruent images.
There are four kinds of rigid motions:
1) translation 2) reflection 3) rotation 4) glide reflection.
But a dilation is a transformation that creates an image having similar shape as the original, but with a different size.
So it does not create congruent images.
Hence transformations will produce similar, but not congruent, figures is :
Triangle MNO is reflected across the y-axis and then dilated by a scale factor of 1.8 to form triangle M"N"O".
Round 0.078 to the nearest thousandths
Answers
Rounding 0.078 to the nearest thousandths gives us 0.078.
We have,
To round 0.078 to the nearest thousandths, we look at the digit in the thousandth place, which is the third decimal place.
The digit in the thousandth place is 8.
Now,
We will look at the digit preceding the digit in the thousandth place.
We see that,
The digit is zero which is less than 5.
So,
0.078 rounding to the nearest thousandth is 0.078 itself.
Therefore,
Rounding 0.078 to the nearest thousandths gives us 0.078.
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when would it be more useful to represent a proportional relationship with a graph rather than equation
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When you need to visually compare two things, that's when you would use a graph. (That is for qualitative data.) However, when you need quantitative data, nothing is better than using an equation.
Hope this helps! ^-^
how do you write 4.7 repeating as a fraction in simplest form
Answers
4.7 (repeating 7's) as a fraction would be 4 7/9
What is the product of any integer and –1?
A.The product is the opposite of the integer.
B.The product is the integer unchanged.
C.The product is positive.
D.The product is negative.
Answers
Find (7 × 106) − (4 × 104). A) 6.096 × 104 Eliminate B) 6.096 × 106 C) 6.96 × 104 D) 6.96 × 106
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D)6.96 × 106 is the right answer i hope this helps.
What does the ordered pair (2,16) represent
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Please vote my answer brainliest. thanks!
Which story represents the graph below?
A student slowly walks to a bus stop, waits, and then rides the bus.
A car accelerates, then maintains its speed before speeding up again.
both of the above
neither of the above
Answers
It's most likely the second option. The speed increases, stays constant, and increases again, which is exactly what's happening to the car's speed.
I'd choose the second choice.
Have an awesome day! :)
Your answer would be B: A car accelerates, then maintains its speed before speeding up again.
Graph y<1−3x .
A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.
Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.
Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
Answers
The correct answer is B. Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line. I took the test and this answer was correct, I'm 100% sure!
The correct option is (B) which represents the linear inequality y ≤ 1 - 3x as shown in the picture.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The inequality is:
y ≤ 1 - 3x
As we can see the above expression represents the linear inequality:
After plotting the linear inequality on the coordinate plane.
From the graph, a straight line is drawn and the shaded region represents the solution to the linear inequality.
Thus, the correct option (B) Number graph with an x-axis ranging from a negative one to five, and a y-axis ranging from negative four to two. A dotted line with arrows at both ends passes through the y-axis at one and the x-axis at point three. The graph is shaded below the line is correct.
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Ten students went to a pizza parlor together. They ordered 8 small pizzas. How much pizza will each student get if they share the pizzas equally? Express your answer as a fraction and a decimal.
Answers
Use rounding or compatible numbers to estimate each product or quotient.
5x2 3/5
about 10
about 10 3/5
about 12
about 15
2. use rounding or compatible numbers to estimate each product or quotient
25 7/8 divided by 2 8/9
about 9
about 10
about 11
about 12
3. Mr. Garcia's class at 3 2/3 pizzas, Mrs Rizzoli's class ate 4 1/8 pizzas, and Mrs. Tindal's class ate 3 1/4 pizzas. Use benchmarks to estimate the total number of pizzas eaten by all three classes.
about 9
about 10
about 11
about 12
Answers
Using rounding or compatible numbers, we estimate the product
[tex]5\times2 \frac{3}{5} [/tex]
to
[tex]5\times3[/tex]
Therefore, the estimate of the product [tex]5\times2 \frac{3}{5} [/tex], using rounding and compatible numbers is about 15.
Part 2
Using rounding or compatible numbers, we estimate the quotient
[tex]25\frac{7}{8}\div2 \frac{8}{9} [/tex]
to
[tex]27\div3[/tex]
Therefore, the estimate of the quotient [tex]25\frac{7}{8}\div2 \frac{8}{9} [/tex], using rounding and compatible numbers is about 9.
Part 3
Given that Mr. Garcia's class ate [tex]3\frac{2}{3}[/tex] pizzas, Mrs Rizzoli's class ate [tex]4\frac{1}{8}[/tex] pizzas, and Mrs. Tindal's class ate [tex]3\frac{1}{4}[/tex] pizzas.
Using benchmarks, we estimate the total number of pizzas eaten by all three classes as follows: [tex]3\frac{3}{4}[/tex], [tex]4[/tex] and [tex]3\frac{1}{4}[/tex]
Thus, the total number of pizzas eaten by all three classes is given by
[tex]3\frac{3}{4}+4+3\frac{1}{4}=11[/tex]
Therefore, the total number of pizzas eaten by all three classes is about 11.
To estimate the product or quotient, round numbers to the nearest whole or compatible number: 5 multiplied by 2 3/5 is about 15; 25 7/8 divided by 2 8/9 is about 9; and the total pizzas eaten by all classes is about 11.
Estimation with Rounding and Compatible Numbers
The estimation of products or quotients using rounding or compatible numbers involves adjusting values to simpler, more manageable numbers before performing the calculation. Here's how to estimate each of the provided examples:
For estimating the product of 5 by 2 3/5, you can round 2 3/5 to 3, which is a compatible number since 5 times 3 equals 15. Hence, the estimated product is about 15.To estimate the quotient of 25 7/8 divided by 2 8/9, round 25 7/8 to 26 (as 7/8 is close to a whole) and 2 8/9 to 3 (since 8/9 is close to 1), resulting in an estimated quotient of about 9 when you divide 26 by 3.For the total pizzas eaten by all three classes, use benchmarks: 3 2/3 rounds to 4, 4 1/8 rounds to 4, and 3 1/4 rounds to 3. Adding these gives 4+4+3 which equals 11. So, the total estimated number of pizzas is about 11.These estimations use the concept of rounding to the nearest whole number or to a fractions compatibility and demonstrate the importance of not over-representing the precision in your answer. Moreover, estimations are especially useful in mental math and when an approximate answer is sufficient.
Working together, two pumps can drain a certain pool in 4 hours. If it takes the older pump 9 hours to drain the pool by itself, how long will it take the newer pump to drain the pool on its own?
Answers
If it takes the older pump 15 hours to drain the pool by itself,
how long will it take the newer pump to drain the pool on its own?
:
you can do this in your head but here is an algebra equation way
:
Let t = time required by new pump to drain the pool
:
Let the completed job (drained pool) = 1
:
+ = 1
Multiply by 15t
t(5) + 15(5) = 15
5t + 75 = 15t
75 = 15t - 5t
75 = 10t
t = 75/10
t = 7.5 hrs new pump alone
;
:
Check this
5/15 + 5/7.5 =
.33 + .67 = 1
The ice-cream truck had 112 ice-cream bars when it went out on its afternoon route. The driver sold 76 ice cream bars at the first stop. At the next stop, the Smith family and the Allen family bought the remaining ice-cream bars, divided equally between the two families. Each ice-cream bar cost $1.50.
How much did the Smith family pay for their ice-cream bars?
Answers
Hope it helps,
The correct answer is $27.00
Hannah borrowed $2,000 from a bank. She agreed to pay back the bank $2,180 after 2 years. What was the simple interest rate of the loan? A. 9% B.4.5 % C.0.9% D. 5.45%
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Hope i helped and Good Luck on the quiz! :D
Does anyone know how to do this please help thank you
Answers
It is 1210 if rounded.
The independent variable of a function belongs to the domain or range?
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HELP ME PLS:( I don't understand
Answers
Hope this helped!
-7x= -56
Is the answer A or B
Answers
-7x = -56
then
x = 8
the result is positive due to the fact that dividing two negatives (-56 over -7) leads to a positive result. As a check, replace x with 8 to get...
-7x = -56
-7*x = -56
-7*8 = -56
-56 = -56
the fact that we get the same value on both sides confirms we have the right answer.
Jake got the expression 7x plus 1 and then wrote his answer as 1 plus 7x. Is his answer an equivalent expression? How do you know?
Answers
According to the commutative property of addition, it doesn't matter what order you add things in, you'll still get the same answer.
Hope this helps!
Is 81 in the sequence with the nth term 4n+1?
Explain
Answers
To justify that, it helps to think about ways we can represent numbers in terms of quotients and remainders. For example, if we take 10/3, we’ll obtain the quotient 3 with a remainder of 1, so another way of writing 10 would be 3(3)+1. If we replace that second three with any integer n, 3n+1 represents *every number* that leaves us with a remainder of 1 when we divide it by 3.
By the same logic, 4n+1 represents every number that leaves a remainder of 1 when we divide it by 4. 81 indeed meets this requirement, since can be written as 4(20)+1, so it would be a part of the sequence.
need help finding D=___
Answers
36+76+d= 180 D= 68
Simplify.
9y+11z+7y−4z
What is the answer?
Answers
[tex]16y + 7z[/tex]
A city ordinance in River City requires that there be a police officer for every 470 residents. If the population of River city is 410,300, what is the minimum number of police officers needed?
Answers
To meet the city ordinance's requirement, River City needs at least 874 police officers, determined by dividing the population of 410,300 by 470 and rounding up to the nearest whole number.
To determine the minimum number of police officers needed for the population of River City, we simply divide the city's population by the number of residents per officer as required by the ordinance. In this case, we divide 410,300 residents by the ordinance's requirement of one officer for every 470 residents.
Calculation: 410,300 residents / 470 residents per officer = approximately 873.19.
Since we cannot have a fraction of a police officer, we round up the number to the nearest whole number to ensure that we meet the minimum requirement. Therefore, River City needs at least 874 police officers.
Deon wants to make a mosaic using tiles. He will use 253 tiles in each of 4 different colors. He drew a diagram to help him find how many tiles he needs for his mosaic. (Plz show work)
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Item 2 Find the unit rate. 6 2/5 revolutions in 2 2/3 seconds The unit rate is revolutions per second.
Answers
(6 2/5) / (2 2/3) =
Rewrite each mixed numeral as a fraction.
= (32/5) / (8/3)
= 32/5 * 3/8
= 96/40
= 12/5
= 2 2/5
Answer: 2 2/5 revolutions per second