Answer:
Approximately 201.06 in² of pizza sauce is needed
(if using the approximation π ≈ 3.14, then the answer is 200.96 in²)
Step-by-step explanation:
We assume that the pizza is perfectly circular and that we want to cover the entire surface. We need the formula for the surface area of a circle which is
A = πr²,
where r is the radius of the pizza.
By definition, the diameter is twice the radius. So the radius of this pizza is half of 16'' = 16 inches, which is 8 in.
Therefore, (using a calculator value for π instead of 3.14 approximation),
A = π(8 in)² = 64π in² ≈ 201.06 in².
Approximately 201.06 in² of pizza sauce is needed.
If you are need to use the approximation π ≈ 3.14, then the answer is 200.96 in²
Answer:
201.06 square inches
Step-by-step explanation:
We need to cover the whole surface area of the pizza so if the pizza is a circular one (using the typical shape), then we can use the formula of the area of a circle.
Area of a circle = pi * r^2
We are given the diameter of the circle to be 16 inches so its radius will be 8 inches.
Substituting this value of radius in the formula to get:
[tex]\pi r^2[/tex] = [tex]\pi (8)^2[/tex] = [tex]201.06[/tex]
Therefore, about 201.06 square inches of pizza sause is needed to cover the pizza.
1.Let x = 6.
What is the value of the expression 5x2+x−7 ? the x is x/2
Enter your answer in the box.
2.Which values from the specified set make up the solution set of the inequality?
4n<16 ; {1,2,3,4}
Select each correct answer.
3.Let m = 3.
Enter > , < , or = to compare the expressions.
4m−1______5m−4
4.Diana writes this inequality:
15>w
4.
Is the given value of w a solution to the inequality?
Select Yes or No for each value.
Solution? Yes No
w = 15
w = 21
w = 14
5.Which value in the replacement set is a solution to this equation?
2n + 5 = 27
Replacement set: {11, 12, 13}
Drag the solution into the box.
options 11,12,13
6.
Which situation can be represented by the inequality?
x<3
The ceiling is lower than 3 m.
The movie is longer than 3 h.
The child is 3 years old.
The backpack is heavier than 3 kg.
7.
Solve for g.
5.1g = 35.7
Enter your answer in the box.
g =
8.Solve for c.
36+c=54
Enter your answer in the box.
c =
9.Cassandra works at a bookstore. Yesterday, she sold 18 hardcover books. The rest of the books she sold were paperback books. She sold a total of 41 books. How many paperback books did she sell?
Use the variable p to represent the number of paperback books Cassandra sold yesterday.
Which equation represents this situation and its solution?
p + 18 = 41; p = 23
p + 41 = 18; p = 23
41p = 18; p = 23
18p = 41; p = 23
10.The table show the total distance d, in kilometers, a truck traveled after t hours.
Time in hours (t) Distance in kilometers (d)
0 0
1 100
2 200
3 300
Which equation shows the relationship between d and t?
d=t+300
d=t+100
d=100t
d=300t
Answer:
1: 6
2: 1,2,3
3: 4m-1>5m-4
4: Not enough data
5: n = 11
6: The ceiling is lower than 3m
7: G = 7
8: C = 18
9: p + 18 = 41; p = 23
10: D = 100t
Step-by-step explanation:
Question 1:
5*2+x/2-7
5*2+6/2-7
10+6/2-7
10+3-7
13-7
6
Question 2:
4*2<16
8<16 True
4*1<16
4<16 True
4*3<16
12<16 True
4*4<16
16<16 False
Question 3:
Let's plug in 1 for m
4*1-1____5*1-4
4-1_____5-4
3_____1
3>1
Question 4:
You did not give an equation, so I cannot answer.
Question 5:
2*11 + 5 =27
22 + 5 = 27
27 = 27
So n = 11
Question 6:
x<3
The ceiling is lower than 3m because x<3
Question 7:
5.1g = 35.7
5.1g/5.1=35.7/5.1
g = 7
Check: 5.1 * 7 = 35.7
Question 8:
36 + c = 54
36 + c -36 = 54 - 36
c = 18
Check: 36 + 18 = 54
Question 9:
p + 18 = 41; p = 23 is correct because the number of paperback books plus the number of hardcover books would equal the total number of books sold. Check: 23 + 18 = 41
Question 10:
d=100t is correct because each time t goes up one it goes up 100. Example: if it is at one hour, than it is 100, if it is at 3 hours, than d = 100*3 = 300, which is the same pattern as the table.
Hope this helps!
The expression 5x² + x - 7 is calculated by substituting x with 6. Inequality and equation solving techniques are used to find the solutions to 4n < 16, 4m - 1 compared to 5m - 4, and other given problems, resulting in specific numerical solutions and identifying suitable real-world scenarios like a ceiling height represented by x < 3.
To solve the expression 5x² + x
- 7 where x equals 6, we substitute and get 5(3)² + (3) - 7 = 45 + 3 - 7 = 41.
The solutions to the inequality 4n < 16 from the set {1,2,3,4} are 1, 2, and 3, since 4 times each of these is less than 16.
Comparing the expressions when m = 3, we get 4m - 1 and 5m - 4. Substituting we have 12 - 1 < 15 - 4, thus 11 < 11, which is false, so 4m - 1 = 5m - 4.
The inequality 15 > w is only true for w = 14. Values w = 15 and w = 21 do not satisfy the inequality.
In the equation 2n + 5 = 27, solving for n within the replacement set gives n = 11 as the correct solution.
The inequality x < 3 represents a situation where The ceiling is lower than 3 m.
To solve 5.1g = 35.7, divide both sides by 5.1 to find g = 7.
For the equation 36 + c = 54, subtract 36 from both sides to get c = 18.
Cassandra's situation is best represented by the equation p + 18 = 41, resulting in p = 23 paperback books sold.
The relationship between the distance d and time t from the truck table is d = 100t, since distance is increasing by 100 kilometers every hour.
Rachael’s patio has an area of 290 square feet. If the patio is shaped like a square, what is the approximate side length?
A. about 72.5 feet
B. about 145 feet
C. about 17 feet
D. about 24 feet
To find the side length of Rachael's square patio with an area of 290 square feet, you have to take the square root of the area. The square root of 290 is approximately 17. So, the side length of the patio is approximately 17 feet.
Explanation:The subject at hand pertains to the geometry and area calculation of a square. In a square, all sides are equal. Thus, to find the side length when only given the area, you can simply take the square root of the area. The square root of 290 is approximately 17. Therefore, Rachael's patio has a side length of approximately 17 feet, making option C the correct answer.
Learn more about Square Roots here:https://brainly.com/question/3120622
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solve the system of linear equations
-x=-6y+19
4=-4x-12y
(x, y) = (-7, 2)
Step-by-step explanation:Divide the second equation by 4 and add it to the first.
... (-x) +(4)/4 = (-6y+19) +(-4x -12y)/4
... -x +1 = -9y -x +19 . . . . simplify
... 9y = 18 . . . . . . . add 9y +x -1
... y = 2 . . . . . . . . . divide by 9
... -x = -6·2 +19 = 7
... x = -7
The solution is (x, y) = (-7, 2).
PLEASE HELP!!!!!!!! 100 POINTS!!!!! I need a step by step simple explanation and answer
A cylinder and a cone have the same diameter: 8 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.
Use π = 3.14.
What is the relationship between the volume of this cylinder and this cone? Explain your answer by determining the volume of each and comparing them. Show all your work.
The formula of a volume of a cylinder:
[tex]V_{cylinder}=\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in and height H = 9 in.
[tex]d=2r\to r=d:2\to r=8\ in:2=4in[/tex]
Substitute:
[tex]V_{cylinder}=\pi(4^2)(9)=\pi(16)(9)=144\pi\approx144\cdot3.14=452.16\ in^3[/tex]
The formula of a volume of a cone:
[tex]V_{cone}=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have the diameter d = 8 in → r = 4 in and the height H = 18 in.
Substitute:
[tex]V_{cone}=\dfrac{1}{3}\pi(4^2)(18)=\pi(16)(6)=96\pi\approx96\cdot3.14=301.44\ in^3[/tex]
[tex]\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{452.16}{301.44}=1.5[/tex]
The volume of the cylinder is one and a half times larger than the volume of the cone.
If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.
[tex]V_{cone}=\pi r^2H\\\\V_{cylinder}=\dfrac{1}{3}\pi r^2H\\\\\dfrac{V_{cylinder}}{V_{cone}}=\dfrac{\pi r^2H}{\frac{1}{3}\pi r^2H}=\dfrac{1}{\frac{1}{3}}=3[/tex]
The formula of a volume of a cylinder:
r - radius
H - height
We have the diameter d = 8 in and height H = 9 in.
Substitute:
The formula of a volume of a cone:
r - radius
H - height
We have the diameter d = 8 in → r = 4 in and the height H = 18 in.
Substitute:
The volume of the cylinder is one and a half times larger than the volume of the cone.
If the cylinder and the cone have equal radii and heights then the volume of the cylinder is three times greater than the volume of the cone.
Plz Mark me BRAINLIEST
Given the rectangle ABCD, AB has a slope of 2/3, what is the slope of BC?
Answer:
slope = - [tex]\frac{3}{2}[/tex]
Step-by-step explanation:
note that BC is perpendicular to AB, hence the slope of BC is the negative reciprocal of the slope of AB
[tex]m_{BC}[/tex] = - [tex]\frac{1}{2/3}[/tex] = - [tex]\frac{3}{2}[/tex]
20 POINTS PLEASE SOMEONE ANSWER What is the equation of the line with m = 3 and b = 8.25? a. y = 3x – 8.25 b. y = 3x 8.25 c. y = 3x 8.25 d. y = 3x 8.25
Answer:
Equation of the line with m=3 and b = 8.25 is y=3 x+8.25
Step-by-step explanation:
m = 3 and b = 8.25
To get equation of line we use y=mx+b
Where m represents the slope = 3
b represents the y intercept = 8.25
Plug in the values in y=mx+b
y= 3x + 8.25
Equation of the line with m=3 and b = 8.25 is y=3 x+8.25
Answer:
y = 3x + 8.25
Step-by-step explanation:
y = mx + b
y = 3x + 8.25
PLEASE HELP ME IM DESPERATE!!!!!!
1. 11x - 24 = -2
2. - 1/2x - 7 = 18
3. -4/5f + 1 = -13
4. - 6x + 4 = -2
5. kittens weigh about 100 grams when born and gain 7 to 15 grams per day. if a kitten weighed 100 grams at birth and gained 8 grams per day, in how many days will it take the kitten to triple its weight?
how to do 5,745 / 66
Answer:
1915/22
Step-by-step explanation:
5745 / 66
Factor the numbers:
5745 = 3 * 1915
66 = 3 * 22
(3 * 1915) / (3 * 22)
Cancel the common factor:
1915/22
To divide 5,745 by 66, first determine how many times 66 fits into 574, then bring down the next digit and repeat. The result is 87 with a remainder of 3 or 87.068 as a decimal. The answer to 5,745 ÷ 66 is 87.068.
To find the result of 5,745 ÷ 66, follow these steps:
Set up the division problem: 5745 ÷ 66.Determine how many times 66 can fit into the first part of 5745, which is 574. Perform the subtraction: 574 - 528 = 46.Bring down the next digit, which is 5, to make 465.Now see how many times 66 fits into 465. Perform the subtraction: 465 - 462 = 3.Since there are no more digits to bring down, the result of 5,745 ÷ 66 is 87 with a remainder of 3, or 87.068 when expressed as a decimal.The answer to 5,745 ÷ 66 is 87.068.
I NEED HELP someone plz help meh
Which input value produces the same output value for the two functions on the graph?x = x= –3
x = –1
x = 1
x = 3
Answer:
x=3
Step-by-step explanation:
Basically the question is asking what value of x gives the same value for y
(or where do the 2 lines cross)
the input is x=3, the out put is y =-1
Answer:
x = 3
Step-by-step explanation:
X - LINE: Horizontal
Y - LINE: VERTICAL
The reason why it's x = 3 is because it's where both line up to, where they both intersect.
Input (x) is 3 & output (y) is -1
Hope this helps you!!! :)
What are the solutions of x^2-2x+10=0
There are a few ways to solve this, the simplest of which is probably factoring. Start by finding factors of C (10) that add up to be B (-2).
fac(10) { -10, 1 ; -5, 2 }
Well, there are no factors of 10 that can add to b - so we will use the quadratic formula.
(-b +- sqrt(b^2 - 4ac)) / 2a
where a = 1, b = -2, c = 10
b^2 - 4ac = (-2)^2 - 4(1)(10) = 4 - 40 = -36
-b +- sqrt(-36) / 2a
(2 +- sqrt(-36)) / 2
sqrt(-36)
sqrt(-1 * 36)
sqrt(-1) * sqrt(36)
i * 6
6i
2 + 6i / 2 ; 1 + 3i
2 - 6i / 2 ; 1 - 3i
Solutions: 1 + 3i, 1 - 3i
Answer:
x = 1± 3i
Step-by-step explanation:
x^2-2x+10=0
We can complete the square to solve by subtracting 10 from each side
x^2-2x+10-10=-10
x^2 -2x = -10
We need to add (2/2) ^2 to each side or 1
x^2 -2x+1 = -10 +1
x^2 -2x+1 = -9
The left side factors into (x- (2/2) ) ^2
(x-1) ^2 = -9
Take the square root of each side
sqrt((x-1) ^2 =± sqrt(-9)
x-1 = ±sqrt(-1) sqrt(3)
Remember the sqrt(-1) = i
x-1 = ± 3i
Add 1 to each side
x-1+1 = 1± 3i
x = 1± 3i
Annie can make 18 baskets out of 30 attempts. Her younger brother Cameron can make half as many in the same number of attempts. How many baskets can Cameron make in 50?
Answer:
Cameron will make 15 baskets out of 50 tries.
Step-by-step explanation:
Since Annie can take out 18 baskets out of 30 and her brother can take out half as much, then we know that 18:2 is 9, so we know that Cameron can take out 9 baskets out of 30. Since this is our proportion( 9:30 ), we can simplify it which brings us to 3:10. And since we must find how much he will take out in 50 tries, We multiply the proportion by 5 which is 15:50, meaning he will make 15 baskets.
Final answer:
Cameron can make 15 baskets out of 50 attempts based on his success rate, which is half of his sister Annie's success rate of 60%.
Explanation:
Annie can make 18 baskets out of 30 attempts, which means her success rate is 60% (since 18 is 60% of 30). Her younger brother Cameron can make half as many baskets in the same number of attempts, so Cameron's success rate is 30% because half of 18 is 9, and 9 is 30% of 30. If Cameron were to attempt 50 shots, we would calculate the number of baskets he can make by applying his success rate to these 50 attempts. Therefore, 30% of 50 is 15. This means Cameron can make 15 baskets out of 50 attempts.
A steel company is making flat rectangular frames as a part of a new product they are launching. Each frame will be cut out of a piece of steel and will have a final area as close to 28 cm2 as possible. The width of the frame needs to be uniform throughout. The inside dimensions of the frame must be 11 cm by 6 cm. Complete the equation that models the above situation, and find the width of the frame, x
Answer:
[tex]4x^2+34x-28=0[/tex]
x = 0.76
Step-by-step explanation:
We can write the area of steel before it is cut as:
Area = [tex](11+2x)*(6+2x)cm^2[/tex]
Expanding it by multiplying the brackets to get:
Area = [tex]4x^2+22x+12x+66[/tex]
Area area of steel before cutting = [tex]4x^2+34x+66[/tex]
Then we need the area of steel after 11*6 inside dimensions are cut out:
[tex]4x^2+34x+66-(11*6)=4x^2+34x[/tex]
This area should be close to 28 cm[tex]^2[/tex], hence the equation becomes:
[tex]4x^2+34x-28=0[/tex]
Moreover, plotting the graph gives us a value of x = 0.76.
Answer:
Step-by-step explanation:
4x2+34x-28
0.76cm
plato
Three of the choices are ways to express 0.25. Which is NOT?
A. 25 hundredths
B. 2 tenths and 5 hundredths
C. 1 fourth
D. 25 tenths
Answer:the last one, 25 tenths
Step-by-step explanation:
What is the difference of (2x+5/x^2-3x)-(3x+5/x^3-9x)-(x+1/x^2-9)
Answer:
The difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].
Step-by-step explanation:
The given expression is
[tex]\frac{2x+5}{x^2-3x}-\frac{3x+5}{x^3-9x}-\frac{x+1}{x^2-9}[/tex]
Find factors of denominators.
[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x^2-9)}-\frac{x+1}{x^2-9}[/tex]
Use [tex]a^2-b^2=(a-b)(a+b)[/tex]
[tex]\frac{2x+5}{x(x-3)}-\frac{3x+5}{x(x-3)(x+3)}-\frac{x+1}{(x-3)(x+3)}[/tex]
Take [tex]x(x+3)(x-3)[/tex] as LCD.
[tex]\frac{(x+3)(2x+5)-(3x+5)-x(x+1)}{x(x+3)(x-3)}[/tex]
[tex]\frac{(2x^2+5x+6x+15)-3x-5-x^2-x}{x(x^2-3^2)}[/tex]
[tex]\frac{2x^2+5x+6x+15-4x-5-x^2}{x(x^2-9)}[/tex]
[tex]\frac{x^2+7x+10}{x^3-9x}[/tex]
Therefore the difference of given expressions is [tex]\frac{x^2+7x+10}{x^3-9x}[/tex].
Answer:
(x+5)(x+2)/x^3-9x
Step-by-step explanation:
For short if taking on edgen then option A is correct.
what is the median of this data set
Answer:
The median is four.
Step-by-step explanation:
First you put the numbers in order from least to greatest and write the number as many times as indicated.
2 2 2 3 4 4 4 4 6 6 7 7 7 8 9
then start from one side then go to the other crossing out numbers. So cross out a two, then nine, then another two, then eight, then the last two, then the first seven and so on. When your done you should be left with one middle number, in this case it's four.
Answer is provided in the image attached
Mrs.o’brien purchases 112 ounces of laundry detergent for $13.44. Mr. o’brien purchases a 17.5 pound container of laundry detergent for $19.60. What is the difference in the unit price per ounce for the laundry detergent mr. and mrs. o’brien Purchase?
Final Answer:
The difference in the unit price per ounce for the laundry detergent Mr. and Mrs. O’Brien purchased is $0.045 per ounce, with Mr. O’Brien's detergent being the more cost-effective option.
Explanation:
To find the unit price per ounce for each type of laundry detergent, we first determine the cost per ounce by dividing the total cost by the total weight. For Mrs. O’Brien's detergent, which is 112 ounces for $13.44, the unit price per ounce is $13.44/112 = $0.12 per ounce. For Mr. O’Brien's detergent, which is 17.5 pounds for $19.60, we convert pounds to ounces (1 pound = 16 ounces) and calculate the unit price per ounce as $19.60/(17.5 * 16) = $0.165 per ounce.
The difference in unit price per ounce is then found by subtracting Mrs. O’Brien's unit price from Mr. O’Brien's unit price, resulting in $0.165 - $0.12 = $0.045 per ounce. The positive value indicates that Mr. O’Brien's detergent is more cost-effective on a per-ounce basis.
This mathematical approach provides a clear comparison of the unit prices, allowing consumers to make informed decisions based on cost-effectiveness. The calculated difference highlights the savings per ounce associated with Mr. O’Brien's laundry detergent.
Consider the piecewise-defined function.
What is f(6)?
A 6
B 12
C 18
D 26
Answer:
B 12
Step-by-step explanation:
Since f(6) means we want to evaluate the function when x=6
We will want to use f(x) =2x because 5<= 6 <10
f(6) = 2*6
f(6)=12
f(x) = x when 2 ≤ x < 5
So you can use this function if "x" is greater than or equal to 2 and less than 5
f(x) = 2x when 5 ≤ x < 10
You can use this function if "x" is greater than or equal to 5 and less than 10
f(6) This means that x is 6, so you can plug in 6 for "x" in the equation.
You use the second function because 6 is greater than 5 and less than 10
f(x) = 2x
f(6) = 2(6)
f(6) = 12 Your answer is B
plz help 20 points!!! The length of the Titanic was 882 feet. Porter's history class is building a model of the Titanic. The model is 1/100(fraction) of the actual length of the ship. How long is the model?
8+1/82, 882/100 so you get 8 and 1/82
Diagonal AC divides the trapezoid ABCD (with bases AD and BC , AD>BC) into two similar triangles, △ABC and △DCA. Find AC if BC=4 cm and AD=9 cm.
Answer:
AC= 6 cm
Step-by-step explanation:
It is given that ABCD is a trapezoid
Also AC divides the trapezoid into two similar triangles
ΔABC≈ΔDCA
The ratio of corresponding sides of similar triangles are equal, so we have
[tex]\frac{AB}{CD} =\frac{BC}{AC} =\frac{AC}{AD}[/tex]
now we can take
[tex]\frac{BC}{AC} =\frac{AC}{AD}[/tex]
[tex]\frac{4}{AC} =\frac{AC}{9}[/tex] ( since BC=4 and AD= 9)
now we cross multiply
[tex]4(9)=AC^{2}[/tex]
[tex]AC^{2}=36[/tex]
[tex]AC=\sqrt{36}[/tex] (taking square root )
AC= 6 cm
what is the horizontal asymptote of f(x)= 3 / x-2
Answer: y = 0
Step-by-step explanation: Since the degree of the numerator is lower than the degree of the denominator, the horzontal asymptote is 0.
an object has a mass of 150 g and a volume of 30 ml what is the density?
Which pair of equations represents two perpendicular lines ? Please help !!
Slope-intercept form:
y = mx + b "m" is the slope, "b" is the y-intercept
For lines to be perpendicular, their slopes have to be the opposite/negative reciprocal (flipped sign and number)
For example:
slope is 2
perpendicular line's slope is -1/2
slope is -3/4
perpendicular line's slope is 4/3
#1: The slopes are the same, meaning they are parallel lines
#2: First isolate the "y" in the first equation
-4x + 5y = -5
5y = -5 + 4x
y = -1 + 4/5x They are not perpendicular because the slopes are 4/5 and -4/5
#3: Isolate "y" in the second equation
8y = 3x - 32
y = 3/8x - 4 They are perpendicular
#4: Isolate "y" is the 1st equation
10y = -9x
y = -9/10x They are parallel lines
The 3rd choice is your answer
Which equation in parallel to 3x-5y=10
3x-5y=n
3x-5y=1
----------------------------
Which of the following could be the equation of the function below?
Answer:
Correct answer is C.
Step-by-step explanation:
Note that graph in the diagram has period [tex]\pi.[/tex]
Consider the function [tex]y=-2\cos (2(x+\pi ))-1.[/tex]
This function has a period [tex]T=\dfrac{2\pi}{2}=\pi.[/tex] Functions in another options have period that differes from [tex]\pi.[/tex]
The graph of this function passes through the point (0,-3), because
[tex]y(0)=-2\cos (2(0+\pi ))-1=-2\cos 2\pi-1=-2\cdot 1-1=-3.[/tex]
Answer:
[tex]y=-2cos (2(x+\pi ))-1[/tex]
Step-by-step explanation:
We are a given a graph from which we can clearly see that y = -1 when x = 0.
Next, we will find out which of the options is the equation of the given graph and for that we need to set our calculator to the radian mode and then put the value of x to be 0.
1. y = -2 cos (4(x + pi)) - 1 = -2 cos (4(0 + pi)) - 1 = 3
2. y = 2 cos(x + pi) = 2 cos(0 + pi) = -1
3. y = -2 cos (2(x + pi)) - 1 = -2 cos (2(x + pi)) - 1 = -3
We get y = -1 when x = 0 in equation number 3, y = -2 cos (2(x + pi)) - 1, so that is the equation of the given graph.
−3 1/3÷9
PLEASE HELP ME!!!
Answer:
-.37
Step-by-step explanation:
PLZZZZ MARK BRANIEST I REALLY NEED IT!!!!
Answer:
-.37
Step-by-step explanation:
that 3 /1 is 3 that
A contractor has two choices for billing a completed job. · $500 flat rate, regardless of the number of hours worked · $20 per hour worked
Answer:
The solution (25, 20) tells the contractor the number of hours on a job where the hourly rate is the same for both billing options.
Step-by-step explanation:
The student's question involves choosing between a flat rate of $500 or an hourly rate of $20 for a contractor's job. The better option depends on the number of hours worked compared to the flat rate. Calculations must be made to determine which method yields a higher payment.
Explanation:The student's question is related to making a decision on a contractor's billing method.
The decision involves choosing between a flat rate of $500 or billing at an hourly rate of $20 per hour for a completed job. To determine which option is more advantageous, the contractor would need to calculate the total earnings based on the number of hours worked and compare it against the flat rate.
For instance, if the contractor works 10 hours, the payment at the hourly rate would be 10 hours × $20/hour = $200. Since $200 is less than the flat rate of $500, the hourly rate would be the better choice in this case. However, if the contractor works for 30 hours, the payment at the hourly rate would be 30 hours × $20/hour = $600, which is more than the flat rate, making the flat rate the better option.
one half gallon is equivalent to 4 pints.how many gallons are the equivalent of 72 pints
Answer: 9 gallons
Step-by-step explanation:
Set up the proportion, then multiply to solve for the variable.
[tex]\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=\dfrac{x}{72\ \text{pints}}[/tex]
[tex](72\ \text{pints})\dfrac{\frac{1}{2}\ \text{gallon}}{4\ \text{pints}}=(72\ \text{pints)}\dfrac{x}{72\ \text{pints}}[/tex]
[tex]\dfrac{36\ \text{gallons}}{4}=x}[/tex]
9 gallons = x
To convert pints to gallons, divide the number of pints (72) by the number of pints in a gallon (8), resulting in 9 gallons.
To determine how many gallons are the equivalent of 72 pints, we use the conversion factor that 1 gallon is equivalent to 8 pints.
First, we divide the given number of pints by the number of pints in a gallon:
Find the unit equivalence, which is 8 pints per gallon.Divide the number of pints (72) by the number of pints per gallon (8).Calculate: 72 / 8 = 9Therefore, 72 pints is equivalent to 9 gallons.
r + (-5r)
Please explain how it's done.
Answer:
-4r
Step-by-step explanation:
r + (-5r)
1r + (-5r)
Factor out an r
r( 1 -5)
One minus 5 is negative 4. If you have one dollar and you borrow five dollars, how much did you borrow? 4 but that 4 is borrowed so it is negative
r (-4)
-4r
A 16- fl oz bottle of juice cost $2.00. What is the unit cost ?
Answer:
$0.13 (this is a rounded answer)
Step-by-step explanation:
The unit cost is the cost of a 1 ounce bottle so you would divide the cost by the total number of ounces:
$2.00 divided by 16 is 0.125 but you would round because you need a cost not a decimal.
So your final answer would be $0.13 per ounce.
Answer:
$.13 per fl oz
Step-by-step explanation:
To find the unit cost, we take the cost and divide by the number of units
$2.00/16
$.125 per fl oz
Since this is money we round to the nearest cent.
$.13 per fl oz