The amount of water left in the bathroom is 0.93 gallons
How to determine the amount of water left?From the question, the given parameters are:
Total amount of water in the bathroom = 7.2 gallonsAmount of eater drained out = 6.27 gallonsThe amount of water left is the difference between the total amount of water in the bathroom and the amount of eater drained out
This is represenetd as
Amount left = Total amount of water in the bathroom - Amount of eater drained out
Substitute the known values in the above equation
Amount left = 7.2 - 6.27
Evaluate
Amount left = 0.93
Hence, the amount left is 0.93 gallons
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The required measure of the volume of water left in the bathtub is 0.93 gallons.
As per the given data, There were 7.2 gallons of water in Sandra's bathtub. Then 6.27 gallons drained out. How much water is left in the bathtub is to be determined.
Here,
According to the question, the water left after the 6.27 gallons of draining out can be evaluated by the arithmetic subtraction of the initial volume to the volume that drained out, that is,
The volume of water left in the tub = 7.2 - 6.27 = 0.93.
Thus, the required measure of the volume of water left in the bathtub is 0.93 gallons.
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X=
//////////////////////////////
Answer: [tex]x=90[/tex]
Step-by-step explanation:
Using the alternate exterior angles theorem,
[tex]180-x=x\\\\180=2x\\\\x=90[/tex]
A square has approximately 300 square feet . The length of each side of the square is between which two whole numbers?
Area = 300 ft^2
Formula
Area = length of a side x length of a side
Substitution
300 = length of a side ^2
[tex]\sqrt{300}[/tex][tex]\sqrt{300}\text{ = 17.32}[/tex]The length of a side is between 17 and 18
Answer:
The length of the side of the square is approximately [tex]17.32[/tex] feet, which lies between the whole numbers [tex]17[/tex] and [tex]18[/tex].
Step-by-step explanation:
Step 1: Assume your variable
Since all the sides of a square are the same, let's consider the side to be the variable: [tex]x[/tex].
Step 2: Create an equation
The formula for the area of a square is:
[tex]\text{Area}=\text{Side}^{2}[/tex]
We have assumed the side to be [tex]x[/tex], and the area is said to be [tex]300[/tex], so substitute these values into the formula:
[tex]\text{Area}=\text{Side}^{2}\\300=x^{2}[/tex]
Step 3: Solve the equation
Using the formula for the area of a square, we came to find an equation:
[tex]x^{2}=300[/tex]
Now, let's find the value of [tex]x[/tex]:
[tex]x^{2}=300\\\\\text{Square root both sides of the equation:}\\\sqrt{x^{2}}=\sqrt{300}\\\\\text{Simplify:}\\x=\sqrt{300}\\\\\text{Calculate:}\\x\approx 17.32[/tex]
The length of the side of the square is approximately [tex]17.32[/tex] feet.
As we know, this number lies between [tex]17[/tex] and [tex]18[/tex].
3) A car can travel 442 miles on 26 gallons of gasoline. How much gasoline will it need to go 102 miles?
The car will need 6 gallons of gasoline to travel 102 miles
Explanation:Given that the car travels 442 miles on 26 gallons of gasoline.
Because the more the distance, the more the volume of gasoline used, this is a direct proportion.
So, we have:
[tex]\begin{gathered} V=\frac{102\times26}{442} \\ \\ =6 \end{gathered}[/tex]It will need 6 gallons.
2The shape shown is made up of three similar right-angled triangles.22The smallest triangle has two sides of side-length 2, as shown.What is the area of the shape?1412 + 12V22824 + 20V56Erase
The triangles are similar. The smaller is isosceles, so the 3 of them are as well.
Let's Start by finding the hypotenuse of the smaller one:
a² = 2
Write the equation of the line that passes through the points (3,1)(3,1) and (-7,-1)(−7,−1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:
[tex]\textsf{Point-slope form}: \quad y-1=\dfrac{1}{5}(x-3)[/tex]
Step-by-step explanation:
Define the given points:
(x₁, y₁) = (3, 1)(x₂, y₂) = (-7, -1)Substitute the defined points into the slope formula to find the slope of the line:
[tex]\implies \textsf{Slope $(m)$}=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-1-1}{-7-3}-\dfrac{-2}{-10}=\dfrac{1}{5}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=\dfrac{1}{5}(x-3)[/tex]
Simplify to slope-intercept form, if necessary:
[tex]\implies y-1=\dfrac{1}{5}x-\dfrac{3}{5}[/tex]
[tex]\implies y=\dfrac{1}{5}x+\dfrac{2}{5}[/tex]
the life of light bulbs is distributed normally. the variance of the lifetime is 225225 and the mean lifetime of a bulb is 520520 hours. find the probability of a bulb lasting for at most 533533 hours. round your answer to four decimal places.
The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.
Given that,
The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.
We have to calculate the probability that a light bulb will survive at most 533 hours.
We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,
z = (x - µ)/σ
Where
x = life of light bulbs.
µ = mean lifetime
σ = standard deviation
From the information given,
µ = 520 hours
Variance = 225
σ = √variance = √225
σ = 15
The probability that a light bulb will last for no more than 560 hours is given by
P(x ≤ 533)
For x = 533
z = (533 - 520)/15 = 0.86
According to the normal distribution table, 0.86 represents the probability for the z score.
Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.
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Bob is planning to start an it business, servicing computers that are infected with viruses. to start his new enterprise, bob estimates that he will need to spend $5,000 on equipment $6,000 on premises, $4,000 on advertising. all of these costs are fixed. he is planning on charging his customers $250 each to fix an infected computer. for each computer that he fixes, he must spend $25 on parts and software. suppose we let x be the number of computers that bob fixes. if bob only fixes 50 computers, what is his total loss?
If Bob only fixes 50 computers, his total loss is $3,750.
What is the total loss?The total loss results from the negative difference between the total revenue and the total costs.
The total costs consist of variable and fixed costs.
The result is a loss when the total costs exceed the total revenue. This result becomes a profit or income when the total revenue exceeds the total costs.
Fixed Costs:Equipment = $5,000
Premises = $6,000
Advertising = $4,000
Total fixed costs = $15,000
Variable cost per unit = $25
Selling price per unit = $250
Total number of computers fixed = 50
The total variable cost for 50 units = $1,250 (50 x $25)
The total costs (fixed and variable) = $16,250
The sales revenue for 50 units = $12,500 (50 x $250)
Loss = $3,750 ($12,500 - $16,250)
Thus, Bob will incur a total loss of $3,750 if he fixes only 50 computers based on his fixed and variable costs.
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-6+ (-3) how to find answer?
Answer:
-9
Step-by-step explanation:
−6 − 3
= −6 + −3
= -9
Answer:
-9!
Step-by-step explanation:
When you add negatives, it becomes more negative. Think of -6 getting 3 smaller.
You type 41 words per minute. How many minutes does it take you to type 615 words?
Given:
Type 41 words per min.
Find-:
How many min. take you to type 615 words
Explanation-:
1 min words type = 41
For 615 words,
41 words typed in 1 min.
For 1 words type it take min is:
[tex]1\text{ Words take time=}\frac{1}{41}\text{ min.}[/tex]For 615 words:
[tex]\begin{gathered} \text{ Time}=\frac{1}{41}\times615 \\ \\ =\frac{615}{41} \\ \\ =15 \end{gathered}[/tex]For type 615 words take time is 15 min.
Answer:
15 minutes.
Step-by-step explanation:
615 / 41
= 15
For a set of five numbers,
the mode is 8
the median is 12
Work out one possible set of five numbers.
Step-by-step explanation:
mode = the number appearing the most often in the list of data.
median = the middle number. half of the other numbers are smaller, and the other half is larger.
so, we know one number already : 12 in the middle.
that gives us
_ _ 12 _ _
a good mode is when it has a real majority (e.g. every other number appears only once, but the mode number appears twice).
so, 8 should appear twice.
as 8 is smaller than 12, it can only be on the left side of 12.
that gives us
8 8 12 _ _
note we need 2 numbers larger than 12, but each appearing only once.
so, e.g.
8 8 12 13 14
Which of the following represents the dimensions of the room
Given:
The length of the rectangular room is 6 more than the width.
The area of the room, A = 27 square units.
Required:
We need to find the dimensions of the given rectangular room.
Explanation:
Let w be the width of the rectangle.
6 more than means add 6.
The length of the rectangle, l= w+6.
Consider the area of the rectangle formula.
[tex]A=lw[/tex]Substitute A = 27, and l=w+6 in the formula.
[tex]27=(w+6)w[/tex][tex]27=w^2+6w[/tex]Subtract 27 from both sides of the equation.
[tex]27-27=w^2+6w-27[/tex][tex]0=w^2+6w-27[/tex][tex]w^2+6w-27=0[/tex][tex]Use\text{ }6w=9w-3w.[/tex][tex]w^2+9w-3w-27=0[/tex]Take out the common multiple.
[tex]w(w+9)-3(w+9)=0[/tex][tex](w+9)(w-3)=0[/tex][tex](w+9)=0,(w-3)=0[/tex][tex]w=-9,3[/tex]The measure is always positive.
[tex]w=3\text{ units,}[/tex]Substitute w =3 in the equation l =w+6.
[tex]l=3+6=9\text{ units.}[/tex]We get l =9 units and w =3 units.
Final answer:
The dimensions of the room are 3 and 9.
Rewrite x4y2 − 3x3y3 using a common factor. 3xy(x3y − x2y) 3xy2(x2 − x2y) x2y(xy − 3xy2) x2y2(x2 − 3xy)
Answer:
(d) x²y²(x² − 3xy)
Step-by-step explanation:
You want to identify a rewrite of x⁴y² − 3x³y³ using a common factor among ...
3xy(x³y − x²y) 3xy²(x² − x²y) x²y(xy − 3xy²) x²y²(x² − 3xy)SimplifiedHere, we write the expanded form of the answer choices to see if any is a fit for the given expression.
3xy(x³y − x²y) = 3x⁴y² -3x³y²3xy²(x² − x²y) = 3x³y² -3x³y³x²y(xy − 3xy²) = x³y² -3x³y³x²y²(x² − 3xy) = x⁴y² -3x³y³ . . . . . . . matches the given expression__
Additional comment
The relevant rule of exponents is ...
(a^b)(a^c) = a^(b+c)
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Mr. Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long. If each DVD is 11⁄20 inches wide, how many DVDs can he put side-by-side on the shelf?
DVDs
The number of DVDs that he can put side-by-side on the shelf is 19.
How to calculate the value?From the information, Mr Washington is putting his DVDs on a shelf that is 10 2⁄3 inches long and each DVD is 11⁄20 inches wide.
The number of DVDs that can be put will be the division of the numbers that are given. This will be:
= Length of shelf / Width of each DVD
= 10 2/3 ÷ 11/20
= 32/3 ÷ 11/20
= 32/3 × 20/11
= 640 / 33
= 19 13/33
= 19 approximately
He can put 19 DVD.
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a recipe uses 1 aubergine for every 3 people. how many aubergines should you buy for 10 people
Answer:
3 1/3 I am assuming that you cannot by 1/3 of an aubergines, so you would need to buy 4. if you can buy a partial one then it would be 3 1/3
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] = [tex]\frac{a}{10}[/tex] Set up a proportion and then cross multiply and solve for a
3a = 10 Divide both sides by 3
a = [tex]\frac{10}{3}[/tex] = 3 1/3
5. Which expression does not have a value of 3?
å
O
O
-16-(-11)
19-16
-13-(-16)
1-(-2)
The ratios in an equivalent ratio and 3:12 , 4:16 and 5:20 if frost number is 10 what is the second number ?
WHATS THE ANSWER PLSZ HELP
Answer:
a. 0.8 = 0.5 + 0.3
b. 30.9 = 2.7 + 28.2
c. 15.4 = 3.1 + 2.4 + 9.9
d. 17.4 = 15.2 + 1.4 + 0.8
e. 42.5 = 39.2 + 2.5 + 0.8
f. 8 = 4 + 4
g. 35 = 23 + 8 + 4
h. 84 = 53 + 3 + 28
i. 121 = 11 + 17 + 93
j. 35 = 24 + 8 + 3
7 ft
9 ft
26 ft
What is the area?
The total area of the figure is 298.17 ft².
What is termed as the area of the figure?The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area.Sketch a square on a paper piece with a pencil. It is a two-dimensional figure. The area of the shape just on paper is referred to as its Area.For the given question;
Let divide the given the figure in three parts;
RectangleTrianglesemi circleThe dimensions of the rectangle is;
Length = 26 - 9 = 15 ft
Breadth = 9 ft
Area = length x breadth
Area = 15 x 9
Area = 135 ft²
The dimension of the triangle is-
Base = 9 ft
Height = 15 - 7 = 8 cm
Area = (1/2) base x height
Area = (1/2) x 9 x 8
Area = 36 ft²
The dimension of semi circle is -
Radius = 9 ft
Area = πr²/2
Area = 3.14 x 9² / 2
Area = 127.17 ft²
Total area = rectangle +triangle + semicircle
Total area = 135 + 36 + 127.17
Total area = 298.17 ft²
Thus, the total area of the figure is 298.17 ft².
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Determine the relationship between lines a, b, and c line a y=5x -3 line b X + 5y=2 line c -10y - 2x =0
Among the given lines line a y = 5x - 3, line b x + 5y = 2, and line c -10y - 2x =0, lines a and line b are intersecting, lines a and c are intersecting whereas lines b and c are parallel to each other.
Write the given lines in standard form
Line a -5x + y = -3
Line b x + 5y = 2
Line c -2x - 10y = 0
a1 = -5, b1 = 1, c1 = -3
a2 = 1, b2 = 5, c2 = 2
a3 = -2, b3 = -10, c3 = 0
a1/a2 = -5/1
b1/b2 = 1/5
c1/c2 = -3/2
As we see that
a1/a2 ≠ b1/b2
Hence, lines a and b are intersecting.
a1/a3 = -5/-2
b1/b3 = 1/-10
As we see that
a1/a3 ≠ b1/b3
Hence, lines a and c are intersecting.
a2/a3 = 1/-2
b2/b3 = 5/-10 = 1/-2
c2/c3 = 2/0
As we see that
a2/a3 = b2/b3 ≠ c2/c3
Hence, lines b and c are parallel.
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0.9(x+1.4)−2.3+0.1x=1.6
please help, I'm really not sure how to do this.
Answer:
x = 2.64
Step-by-step explanation:
Do the distributive property first.
0.9(x + 1.4)
0.9(x) + 0.9(1.4)
0.9x + 1.26 - 2.3 + 0.1x = 1.6
Simplify the left side by adding like terms. I'm going rewrite the equation and group the like terms together.
0.9x + 0.1x + 1.26 - 2.3 = 1.6
1x - 1.04 = 1.6
1x is the same as x, so I am going to remove the 1. Solve for x.
x - 1.04 + 1.04 = 1.6 +1.04
x = 2.64
find a number of ways in which 4 algebra books, 5 geometry and 2 chemistry books can be placed on a shelf so that the arrangement begins and ends with a chemistry book
4 algebra books, 5 geometry and 2 chemistry books can be arranged in 5760 ways.
What is permutation?A permutation of a set is a loosely defined arrangement of its members into a sequence or linear order, or a rearrangement of its elements if the set is already ordered. The act or process of changing the linear order of an ordered set is also referred to as "permutation." A permutation is a specific arrangement of objects. Set members or elements are arranged in a sequence or linear order here. For example, the permutation of set A=1,6 is 2, as in 1,6,1. There are no other ways to arrange the elements of set A, as you can see.Given ,
4 algebra books , 5 geometry , 2 chemistry books,
The number of permutations =
2! x 5! x 4!
= (1 x 2) x (5 x 4 x 3 x 2) x (4 x 3 x 2)
= 2 x (120) x (24)
= 5760 ways.
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Solve 2x + 32 + x = 17.
x = 5
x = 0.2
x = −0.2
x = −5
Please and thank you.
2x+32+x = 17
Combine 2x and X to get 3x.
3x+32 = 17
Subtract 32 on both sides.
3x = 17−32
Remains 32 of 17 to obtain −15.
3x = −15
Divide both sides by 3.
x = -15/3
Divide −15 by 3 to get −5.
x = −5
The last option is correct.The value of x after solving the given equation 2x + 32 + x = 17, is x = -5, which is the last option.
Given an equation:
2x + 32 + x = 17
It is required to find the value of x after solving or simplifying the equation.
In order to get the value of x, the equation has to be solved in such a way that the terms with the variable have to be placed on one side and the constant terms on the other side.
Consider:
2x + 32 + x = 17
Add x and 2x since they are like terms in variables.
3x + 32 = 17
Subtract 32 from both sides of the equation.
3x = 17 - 32
3x = -15
Divide both sides of the equation by 3.
x = -5
Hence, the value of x is -5.
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How far up a wall will an 11-meter ladder reach, if the foot of the ladder is 4 meters away from the base of the wall?
A. 11 m
B. 4 m
C.
D.
Answer:
√105 meters, or about 10.25 meters
Step-by-step explanation:
[tex] {x}^{2} + {4}^{2} = {11}^{2} [/tex]
[tex] {x}^{2} + 16 = 121[/tex]
[tex] {x}^{2} = 105[/tex]
[tex]x = \sqrt{105} = 10.25[/tex]
Answer:
10.246 or sqrt(105)
Step-by-step explanation:
Given,
length of the ladder = 11 m
distance of the foot of the ladder from the base of the wall = 4 m
According to Pythagoras' theorem,
(hypotenuse)^2 = (side1)^2 + (side2)^2
As per the problem,
hypotenuse = 11m
side1 = distance from wall = 4 m
side2 = height reached by the ladder on the wall
that is, (11)^2 = (4)^2 + (side2)^2
121 = 16 + (side2)^2
121 - 16 = (side2)^2
(side2)^2 = 105
(side2) = sqrt(105) = 10.246 m
Hence, the ladder can reach up to 10.246 m height on the wall.
In Exercises 1-3, graph AABC and its image after a reflection in the given line.
1. A(0, 2), B(1, -3), C(2, 4); x-axis
1.
2. A(-2,-4), B(6,2), C(3. – 5); y-axis
3. A(4, -1), B(3, 8), C(-1, 1); y = -2
The figures after each reflection are given at the end of the answer.
Reflection over the x-axis
The rule for the reflection over the x-axis is:
(x,y) -> (x, -y)
Hence the signal of the y-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(0,-2), B'(1,3) and C(2,-4)
Reflection over the y-axis
The rule for the reflection over the x-axis is:
(x,y) -> (-x, y)
Hence the signal of the x-coordinate is changed.
Then the coordinates of the image of triangle ABC are given as follows:
A'(2,-4), B'(-6,2) and C'(-3,-5)
Reflection over y = -2The rule for the reflection over the line y = -2 is:
(x,y) -> (x, y +/- constant)
The constants for each point are given as follows:
A': -3, hence point (4,-3), as -1 is one unit above y = -2, hence the reflected coordinate will be one unit below.B': -12, hence point (3,-12), as 8 is 10 units above y = -2, hence the reflected coordinate will be ten units below.C': -5, hence point (-1, -5), as 1 is 3 units above y = -2, hence the reflected coordinate will be three units below at y = -5.More can be learned about reflections at https://brainly.com/question/27224272
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At a high school, students can choose between three art electives, four history electives, and five computer electives.
Fach student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
O
7C2
1202
С
.?
122
O (G) 4401)
12Cz
12P2
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Expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
As given in the question,
Number of art electives students = 3
Number of history electives students = 4
Number of computer electives students = 5
Choosing an art electives students = ³C₁
Choosing an history electives students = ⁴C₁
Expression represents the probability that a student chooses an art elective and a history elective
= (³C₁⁴C₁) / ¹²C₂
Therefore, expression represents the probability that a student chooses an art elective and a history elective is equal to (³C₁⁴C₁) / ¹²C₂.
The complete question is:
At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives.
Which expression represents the probability that a student chooses an art elective and a history elective?
a. ⁷C₂ / ¹²C₂
b. ⁷P₂ / ¹²P₂
c. (³C₁⁴C₁) / ¹²C₂
d. (³P₁⁴P₁) / ¹²P₂
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A tree initially measured 18 feet tall. Over the next 3½ years, it grew to a final height of 35½ feet. During those 3½ years, what was the average yearly growth rate of the height of the tree?
Answer:
The average yearly growth o
Explanation:
Given that the tree grew from 18 ft 35 1/2 feet in 3 1/2 years.
The growth within these years is:
35 1/2 - 18
= 35.5 - 18
= 17.5
Now, this averages:
17.5/3.5 (3.5 is the number of years)
= 5
The average is 5 ft per year
first answer will be brainliest
You decide to use a scale of 1 in: 7 ft to make a scale drawing of your classroom. If the actual length of your classroom is 49 feet, what should the length of the classroom in the drawing be?
The dimension of the length of the classroom in the drawing is calculated to be 7 ft
What is scale of a map?The scale of a map represents by how much a map is reduced or increased. Most of the times the map is smaller than what is being represented hence the scale is usually a reduction.
How to find the length of the classroom in the drawingGive that
1 in in drawing represent 7 ft in actual length
If the actual length of your classroom is 49 feet then we solve as follows to get the dimension in the drawing:
1 in = 7 ft
? in = 49 ft
cross multiplying gives
7 * ? = 49 * 1
? = 49 / 7
? = 7 in
Hence, the conclusion is that the unknown dimension in the drawing represented as ? is equal to 7 in.
This implies that 7 in in the drawing represents actual distance of 49 ft and this is a reduction
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Jake has a 8 pounds of lunch meat to serve for a picnic lunch. He plans to serve each adult 2/3 of a pound. Part B: The price of lunch meat is $7.36 per pound. Which equation can be used to determine the total cost, c, for lunch meat that weighs a total p pounds? Then find the cost of the lunch meat. •p/7.36=c •p=7.36c, the cost is $1.09 •c=7.36p, the cost is $58.88 •p+7.36-c, the cost is $15.36
Part B
The most appropriate choice for linear equation will be given by -
Third option is correct
c = 7.36p is the required equation for total cost of p pounds of meat
The cost is $58.88
What is linear equation?
At first it is important to know about equation
Equation shows the equality between two algebraic expressions by connecting the two algerbraic expressions by an equal to sign.
A one degree equation is known as linear equation.
Here,
Price of one pound of meat = $7.36
Cost of p pounds of meat = $7.36p
By the problem,
c = 7.36p
This is the required equation for total cost of p pounds of meat
Putting p = 8
c = [tex]7.36 \times 8\\[/tex]
c = $58.88
Third option is correct
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Solve. (−7x−14)−(x−5)
Step-by-step explanation:
-7x(x-5)-(-14)(x-5)
-7x²+35+14x-70
-7x²-14x-35
Hope this is correct
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Which of the following describes the graph of y 3 -3 in a coordinate plane?
ANSWER
The boundary line is a solid horizontal line that passes through (0, -3). The half-plane that does not contan the origin is shaded.
(the answer is the second option)
EXPLANATION
The graph is