Option c is the correct answer. Sam's total earning for the day is equal to
E(n) = 2.5n + 24
Given data
Sam earning per hour = $6
Sam earning on tips per person = $2.5
Sam's total hour per day =4
How to find the function for Sam's total earningsSam's daily earning excluding tips = Sam earning per hour * Sam's total hour per day
= $6 * 4 hours = $24
If n represents the number of people Sam serves that day, then Sam's earnings on tips in a day = $2.5 * n = $2.5n
The function for Sam's total earning is given by E(n)
E(n) = Sam's daily earning excluding tips + Sam's earnings on tips in a day
E(n) = $24 + $2.5n
this is re arranged as
E(n) = 2.5n + 24
Therefore we can say that Sam's total earning for the day is equal to
E(n) = 2.5n + 24
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Complete question
Sam is a waiter at a local restaurant where he earns wages of $6 per hour. Sam figures that he also earns about $2.50 in tips for each person he serves. Sam works 4 hours on a particular day. If n represents the number of people Sam serves that day, which of the following functions could Sam use to figure E, his total earnings for the day?
A. E(n) = 2.5n
B. E(n) = 4n + 10
C. E(n) = 2.5n + 24
Solve each equation. (m-2)-5=8-2(m-4)
The solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
According to the given question.
We have a linear equation in one variable
(m-2)-5=8-2(m-4)
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable (m-2)-5=8-2(m-4) is given by
(m -2) -5 = 8 -2(m -4)
⇒ m -2 - 5 = 8 -2m + 8 (by distributive rule)
⇒ m -7 = 16 - 2m (adding and subtracting the line terms)
⇒ m + 2m = 16 + 7
⇒ 3m = 23
⇒ m = 23/3
Hence, the solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.
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→
List all the 4-digit even numbers
that can be created by
rearranging
these number tiles.
3472
A refrigerator that originally costs $ 1,200 it's on sale for 15% off. Tax is 8%. What would be the sale price of this refrigerator be including tax
The sale price of this refrigerator be including tax $1101.6 .
The value on the label of associate article/product is termed the marked price or asking price. this is often the worth at that product is meant to be sold-out. However, there will be some discount given on this value and therefore the actualof the merchandise could also be but the marked price. it's typically denoted by MP.When Discount is obtainable, M.P. > S.P.When Discount isn't offered, M.P. < S.P.Discount is outlined because the quantity of rebate given on the label value (marked price) of a piece. it's given by merchants/shopkeepers for attracting customers for increasing their sales.Discount = Marked value – priceIt is given that a refrigerator that originally costs $ 1,200 it's on sale for 15% off.
Discount percentage = [(Discount)/(Marked price)]× 100
15 = Discount / 1200 × 100
15 = Discount / 12
Discount = 15 × 12
= $ 180
Selling price = marked price - discount
= 1200 - 180
= $ 1020
The selling tax is given by = 8% 1020
= 8 / 100 ×1020
= $ 81.6
The total amount one has to pay to buy a refrigerator is = 1020 + 81.6
= $ 1101.6
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can someone please help me I don’t understand and it’s a really important homework
Answer: Large number: 36
Smaller number: 9
Step-by-step explanation:
Can someone provide a justification?
The piecewise function that best models her weekly pay h(t) is given by:
h(t) = 12t, 0 ≤ t ≤ 40.h(t) = 480 + 18t.What is a piecewise-defined function?A piecewise-defined function is a function that has different definitions, depending on the input of the function.
For this problem, we have that:
The input is the number of hours worked.The output is the weekly pay.Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:
Standard hours: t ≤ 40.Overtime hours: t > 40.For up to 40 hours, she receives the standard wage of $12, hence:
h(t) = 12t, 0 ≤ t ≤ 40.
For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:
h(t) = 480 + 18t.
Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:
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Determine if 21 is rational or irrational and give a reason for your answer.
Suppose you pull a card from a standard 52-card deck. Find the probability of following event. The card is a face card.
3/13 is the probability of following event. The card is a face card.
In statistics, what does a probability mean?
The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Total no.of cards = 52
Let A be the event of taking face card.
No.of face cards = 4×3 = 12
Now n(S)= 52C1 = 52, n(A) = 12C1 = 12
So P(A) = n(A)/n(S) = 12/52 = 3/13
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Write an algebraic expression that models each situation.
The piggy bank contained 25 , and 1.50 is added each day.
The algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x
Given,
The piggy bank contained = $25
The amount added in each day = $1.50
Consider number of days as x
Then the algebraic expression = 25+1.50x
Hence, the algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x
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Determine whether the following statement is true or false. If false, give a counterexample. If true, give an argument to support your conclusion.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
The statement given is true.
If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.
What is acute angle ?The acute angle can be defined as the angle less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.
According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.
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In a bag, the ratio of purple counters to green counters was 3:4. 8 more purple counters were then added to the bag, and the ratio of purple counters to green counters became 5 : 4. How many green counters are in the bag?
Answer:16
Step-by-step explanation:
since the increase is 2 units for purple counters
8 ÷ 2 = 4
4×4=16
Solve the following problem for x. If there is more than one solution include all solutions in your answer.
|3z-6|=9
X=
X=
Answer:
z = - 1 , z = 5
Step-by-step explanation:
| 3z - 6 | = 9
the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is
3z - 6 = 9 ( add 6 to both sides )
3z = 15 ( divide both sides by 3 )
z = 5
or
- (3z - 6) = 9
- 3z + 6 = 9 ( subtract 6 from both sides )
- 3z = 3 ( divide both sides by - 3 )
z = - 1
As a check
substitute these values into the left side of the equation and if equal to the right side then they are the solutions.
x = 5
| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side
x = - 1
| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side
then solutions are z = - 1 , z = 5
name all the sets of numbers to which each real number belongs.
1. 12
2. -15
3. 1 1/2
4. 3.18
5. square root 48
6. 9.3
7. -2 7/9
8. square root 25
9. square root 3
10. negative square root 64
11. negative square root 12
12. 8/4
These are the description of the real numbers.
According to the statement
We have to explain all about the real numbers.
So, For this purpose, we know that the
Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.
From the given information:
Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.
• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.
• Whole numbers include all positive integer values including 0.
• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)
• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)
Using the definitions above :
• 12 = Natural, integer , integer and rational (12/1)
• -15 = Integer, rational (-15/1)
• 1 1/2 = 3/2 = Rational
• 3.18 = rational (terminating decimal)
• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)
• 9.3 = rational (terminating decimal)
• -2 7/9 = -25/9 = rational (a/b)
• root 25 = √25 = ±5 = integer, rational (5/1)
• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .
• negative root 64 = - √64 = - 8 = integer, rational (-8/1)
• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)
• 8/4 = 2 = natural, number, rational, integer
So, These are the description of the real numbers.
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Find the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi. (PLEASE SHOW WORK IF POSSIBLE)
The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
Volume of a coneThe formula for calculating the volume of a cone is expressed according to the formula
V = 1/3 pir²h
where
r is the radius of the cone = 10/2 = 5in
h is the height = 2in
Substitute to have;
V = 1/3pi(5)² × 2
V = 50/3pi
Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches
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Three integers have a mean of 8, a median of 8 and a range of 4.
Answer:
The 3 integers are 6 8 and 10
Step-by-step explanation:
Comment
Start with the median. That's the middle number of an ordered set of numbers.
a 8 b is what you have so far.
Now the range between a and b is 4 which means that a and b differ by 4.
a + 4 = b
The mean will solve this quickly. Put a + 4 for b
[(a + 8 + a + 4)]/3 = 8 Combine like terms
(2a + 12)/3 = 8 Multiply both sides by 3
3 (2a + 12)/3 = 8 *3
2a+12 = 24 Subtract 12 from both sides
2a + 12 - 12 = 24-12 Combine
2a = 12
a = 6
but we know that the range between a (which is 6 ) and b is a + 4 = 10
So b must equal 10
i need 3.234 minus 3.234 written out
If each student in the class drinks
1 cups of juice during the party
and there are 9 students in the
class, how many cups of juice will
be needed?
Answer:9
Step-by-step explanation:
Use summation notation to write each arithmetic series for the specified number of terms. Then evaluate the sum. 21+19+17+ . . . ; n=8
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
The given series is 21+19+17+ . . .
On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.
So the formula will be (-2n +/- something).
Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.
So if n=0, our first term is 21
If n=1, our second term is 19
If n=2, our third term is 17
and so on.
So, we have the expression (21 - 2n).
The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.
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Evaluate each algebraic expression for x=3 and (y=-2).
2x-3y
The result of the algebraic expression 2x-3y for x=3 and y=-2 is 12
Given,
The algebraic expression = 2x-3y
x= 3
y= -2
Substitute the values in the expression
2x-3y= 2(3)-3(-2)
=6+6
=12
Hence, the result of the algebraic expression 2x-3y for x=3 and y=-2 is 12.
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A diver is 7.5 meters above water. she takes her dive 1.7 meters below the surface. how far does the dive take her.
The diver take her at a distance of 9.2 meters.
What is distance?A resultant displacement can be used to quantify distance. It involves measuring the coordinate values of the beginning and ending positions. The distance is measured in quantities like meters, centimeters, kilometers, etc.
A diver descends 1.7 meters below the surface of the water while suspended 7.5 meters above it, according to the question.
According to fundamental mathematics, values that are less than zero can be represented as negative values.
She will thus descend (-1.7) meters as she dives below the surface.
The formula may now be expressed as follows: Total Distance = 7.5 - (-1.7) = 9.2 meters.
As a result, the diver descends 9.2 meters below the surface with her.
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Simplify the expression.
16-12 / 15-11
The simplified expression for (16-12 / 15-11) is 1 .
The given expression is,
( 16-12 / 15-11 )
First we need to solve the numerator which is (16-12) and on simplifying the numerator we can write,
Numerator = ( 16 - 12 ) = 4 equation 1
Similarly, now we can proceed to solve the denominator which is (15 - 11) and on simplifying the denominator we write,
Denominator = (15 - 11) = 4 equation 2
Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 16-12 / 15-11 ) as,
(Numerator / Denominator) = (16-12 / 15-11) = (4/4) = 1
The simplified expression for (16-12 / 15-11) is 1 .
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Enter the rational number as a decimal. Then tell whether the decimal is a terminating or a repeating
decimal.
4/5
how can changing fractions to decimals make them easier to compare?
Answer:
They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.
Step-by-step explanation:
find the interest rate if $13400 has a final value of $17829 in 4 years give your answer to 1dp
Answer: It is $4429 (interest combined) or $1107.25 (interest annually)
Step-by-step explanation:
1. Subtract 13400 from 17829:
17829 - 13400 = 4429
2. Now, we know that 4429 is the accumulated interest in 4 years, now divide 4429 by 4:
4429/4 = 1107.25
3. Now we know that 1107.25 is the interest accumulated every year.
5
y≥--x-3
2
how do i graph this?
The given inequality can be graphed by solving the inequation first.
What is an inequality?
Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.
The given inequality can be solved as
[tex]5y\geq -x-32[/tex]
[tex]for, x=1, 5y\geq -1-32[/tex]
[tex]or, 5y\geq -33[/tex]
[tex]or, y=\frac{33}{5}[/tex]
Solve for two more values of x and then plot the inequality on the graph
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Which expression is equal to this expression, according to the associative property? 5+(3-1)
Answer:7
Step-by-step explanation:
3-1= 2
5+2=7
Which is an equivalent expression for (5^2 • 3^4)^3?
15^18
5^6 • 3^12
5^2 • 3^12
5^5 • 3^7
Answer:
answer 2
Step-by-step explanation:
3*4=12
Answer:
B. 5^6 x 3^12
Step-by-step explanation:
(5^2 x 3^4)^3 =
5 x 5 x 3 x 3 x 3 x 3 =
25 x 81 =
2025
2025^3 =
8,303,765,625
Option B is correct because,
5^6 x 3^12 =
5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =
15,625 x 531,441 =
8,303,765,625
The path is 8,000 meters. How long
is the path in kilometers?
kilometers
Answer:
8 kilometers
Step-by-step explanation:
8000/1000
= 8 kilometers.
2.
lons that are made of more than
one atom are called
A ionic compounds
B crystals
C polyatomic atoms
D ionic bonds
Answer:
C polyatomic atoms
Step-by-step explanation:
Kevin needs to order some new supplies for the restraunt where he works. the restraunt needs at least 492 glasses. there are currently 333 glasses. if each set on sale contains 18 glasses
Answer:
Step-by-step explanation:492 is needed right,and Kevin has 333 glass.So you need 159 glasses,but you need to find out how many sets you need to get 492 glasses.If 18 glasses comes in a set you'll need to divide 159 by 18 and get 8.83333333333. Then simplefiy the number to 8.8
PLS HELP I NEED TO FINISH THES IN ORDER TO PASS MY GRADE
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 2, 3 comma 3, 2 comma negative 5
Determine the coordinates of triangle A′B′C′ if triangle ABC is rotated 270° clockwise.
A′(−2, 2), B′(3, −3), C′(−5, −2)
A′(2, −2), B′(−3, 3), C′(5, 2)
A′(2, 2), B′(−3, −3), C′(5, −2)
A′(2, −2), B′(−3, 3), C′(2, 5)
Answer:
A′(2, −2), B′(−3, 3), C′(5, 2) (2nd choice)
Step-by-step explanation:
Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°
In either case, the coordinates of any point (x, y) become new coordinates (-y, x)
I will summarize the original and rotated points,.
Original Rotated
Point(x, y) Point(-y, x) Remarks
-------------- -------------- -------------
A(-2, -2) A'(2, -2) eliminates 1st and 3rd choices
B( 3, 3) B'(-3, 3) no luck, both 2nd and 4th choices have this
C(2, -5) C'( 5, -2) only the 2nd choice fits all three
Answer: A′(2, −2), B′(−3, 3), C′(5, 2)
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
The correct answer is (A).
What are coordinates in a graph?The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
To rotate a point (x,y) 270° clockwise about the origin,
We can use the formulas:
x' = y and y' = -x.
So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:
A' = (-2, 2) rotated 270° = (2, -2)
B' = (3, 3) rotated 270° = (-3, 3)
C' = (2, -5) rotated 270° = (5, 2)
Therefore,
The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).
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