Working his way through school, Joe works two part-time jobs for a total of 30 hours a week. Job A pays $5.90 per hour, and Job B pays $7.20 per hour. How many hours did he work at each job the week that he made $197.80? (Round to two decimal places if necessary.)
Joe worked for 14 hours at Job A and for 16 hours at Job B.
What are simultaneous equation?In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Now it is given that,
Joe works two part-time jobs for a total of 30 hours a week.
Let x be the number hours that Joe worked at job A in a week.
and y be the number hours that Joe worked at job B in a week.
⇒ x + y = 30 ...(i)
Now Job A pays $5.90 per hour,
Therefore,
Amount receive from Job A = 5.9x
And Job B pays $7.20 per hour
Therefore,
Amount receive from Job B = 7.20y
Also it is given that, he work at each job the week that he made $197.80
Therefore,
5.90x + 7.20y = 197.8 ....(ii)
Now multiplying equation (i) by 5.9 we get,
5.90x + 5.90y = 177 ....(iii)
Subtracting equation (ii) and equation (iii) we get,
1.3y = 20.8
Dividing both the side by 1.3 we get,
1.3y/1.3 = 20.8/1.3
Solving we get,
y = 16
Putting the value of y in equation (i) we get,
x + 16 = 30
Subtracting both the side by 16 we get,
x + 16 - 16 = 30 - 16
Solving we get,
x = 14
Thus, we get
x = 14
y = 16
Hence,
Number hours that Joe worked at job A in a week = 14 hours
and,
Number hours that Joe worked at job B in a week = 16 hours
Thus, Joe worked for 14 hours at Job A and for 16 hours at Job B.
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Gavin and Jim are marking exam
papers.
Each set takes Gavin 41
minutes and Jim 1 hour. Express the
times Gavin and Jim take as a ratio in its
simplest form.
Answer:
41:60
Step-by-step explanation:
Time taken by Gavin takes = 41 minutes
Time taken by Jim takes = 1 hour
We know that 1 hour = 60 minutes
So, the ratio of times that Gavin and Jim take as a ratio would be
Gavin:Jim
41:60
Find the quadratic function (0,7)(2,15)(3,10)
The quadratic equation that contains (0, 7), (2, 15) and (3, 10) is y = - 3 · x² + 10 · x + 7.
What is the quadratic equation associated with a given set of points?
Quadratic functions are polynomials of the form y = a · x² + b · x + c, where a, b, c are real coefficients. To determine the coefficients, we need at least three distinct points on Cartesian plane. A solution that is algebraic exact only need three points, then we must resolve this system of linear equations:
c = 7 (1)
4 · a + 2 · b + c = 15 (2)
9 · a + 3 · b + c = 10 (3)
The solution to this system of linear equations is (a, b, c) = (- 3, 10, 7).
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Margaret uses 1 3/4 teaspoons of key lime zest to make 12 like cupcakes. She wants to make 30 cupcakes. How much key lime zest will margaret use?
The number of teaspoons of key lime zest to make 30 cupcakes is
35/8 or 4 3/8
Given,
Margaret uses 1 3/4 teaspoon of key lime zest to make 12 cupcakes.
She wants to make 30 cupcakes.
We need to find how much key lime zest will Margaret use.
How to compare given two units?Example:
1 bag = N mango
Then to find the number of mangoes in 5 bags we need to multiply 5 on both sides.
5 bags = 5 x N mangoes.
We have,
1 3/4 teaspoons of key lime zest = 12 cupcakes
7/4 teaspoons of key lime zest = 12 cupcakes
7/4 = 12 cupcakes
Multiply 30 on both sides.
7/4 x 30 = 30 x 12 cupcakes
Divide both sides by 12.
7/4 x 30/12 = 30 cupcakes
35 / 8 = 30 cupcakes
or
4 3/8 = 30 cupcakes
This means,
35/8 or 4 3/8 teaspoons of key lime zest to make 30 cupcakes.
Thus the number of teaspoons of key lime zest to make 30 cupcakes is
35/8 or 4 3/8.
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HELP ME OUT PLEASE!!!!
Answer:
b
Step-by-step explanation:
To find the average of a student's test scores, add the scores and divide by the number of tests. Suppose George scored 83, 91, 82, and 95 on four
tests. Write a numerical expression to describe Chase's average test score.
Please use the test scores in order of the question to earn full credit.
Answer: (83 + 91 + 82 + 95) / 4
Step-by-step explanation:
The information given tells us how to complete the question. We will be finding the average.
Add all the scores together, and divide by the number of tests.
(83 + 91 + 82 + 95) / 4
Since this question asks for an expression, we will end here. If it asked us to solve, we would do the following;
(83 + 91 + 82 + 95) / 4
(351) / 4
87.75
Do the following calculation according to correct significant figures:
2.9/1.3 +4.0=
Answer: 6.2
Step-by-step explanation:
2.9/1.3 +4.0=
2.23 + 4.0=
2.2 + 4.0=6.2
The given information is,
→ (2.9/1.3) + 4.0
Let's solve the problem,
→ (2.9/1.3) + 4.0
→ 2.23 + 4 = 6.23
Thus, the answer is 6.23.
Y varies jointly with X y=16 when x=4 and z= 1/2 find y when x= 2 and z= 1/4
The value of y when x= 2 and z= 1/4 is y = 4
In this question, we have been given y varies jointly with x and z.
This means y is directly proportional to x and z.
y = 16 when x = 4 and z = 1/2
We need to find the value of y when x= 2 and z= 1/4
From y = 16 when x = 4 and z = 1/2 we can compute the equation as,
y = 8xz
16 = 8(4)(1/2)
16 = 8 × 2
16 = 16
So, the equation is y = 8xz
Now for x= 2 and z= 1/4,
y = 8xz
y = 8 × 2 × (1/4)
y = 2 × 2
y = 4
Therefore, the value of y when x= 2 and z= 1/4 is y = 4
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PLEASE HELP ME!!! DUE TODAY, I WILL GIVE 20 POINTS!!!! NO EXPLAINATION NEEDED!!!! FIRST PERSON TO ANSWER GETS BRAINLIEST AWARD!!!!
Answer:
The weight of gold in the alloy is 32 g.
Answer:
The weight is 32 grams
Step-by-step explanation:
3 1/3 (y plus 1 1/8) = 6 11/12
HELp
The value of y in the given equation is 19/20
Solving linear equationsFrom the question, we are to determine the value of y in the given equation
The given equation is
3 1/3(y + 1 1/8) = 6 11/12
First, convert the the fractions into improper fractions
10/3(y + 9/8) = 83/12
Multiply both sides of the equation by 3/10
3/10× 10/3(y + 9/8) = 3/10× 83/12
y + 9/8 = 3/10× 83/12
y + 9/8 = 83/40
y = 83/40 - 9/8
y = (83 - 45)/40
y = 38/40
y = 19/20
Hence, the value of y in the given equation is 19/20
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Translate to an equation. Then solve the equation.
Seven times the difference of some number and 2 amounts to the quotient of 112 and 8.
Answer: 7(x-2(112/8))= 7(x-28)= 7x - 28*7
7x = 28*7
x=28
Halp me
Vtxtvdcvdtcgdtgcgdtcgcvfg
Answer: 5578
Step-by-step explanation:
1058 + 4520 = 5578
what is the answer to
8-(4*2)/2=
can someone help me with this question? :)
Thank you so much for the help
For the given function, we have that:
The domain is [-4,4].The function has no zeros.The function is positive for x ≤ 0.The function is negative for x > 0.What is the domain of a function?The domain of a function is the set that contains all possible input values for the function. In a graph, it is the set that contains all the values of x of the function.
Hence, the domain is [-4,4] for the given function.
What are the zeros of a function?The zeros of a function are the values of x for which f(x) = 0, on the graph they are the values of x when the function crosses the x-axis.
For this problem, the function does not cross the x-axis, hence it has no zeros.
When a function is negative and when it is positive?Looking at the graph of the function, we have that:
It is positive if it is above the x-axis.It is negative if it is below the x-axis.Hence, for the function in the given graph:
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At Acme Supermarket there are 12 full-time employees; 10 of them earn $12 per hour each, and the assistant manager and manager make $18 and $20 per hour respectively. What is the average rate of pay for the 12 employees? What is the median rate of pay? Which do you think is the better summary model to represent the pay rate of Acme’s employees?
Answer:
Average salary 13.16 120 + 18 + 20/12
Alex makes $20 an hour as a dental assistant. She works 8 hours per day, and 80 hours on each paycheck. How much does Alex make, before
taxes, on each paycheck?
Answer:
give the amount of tax please
Answer: 160
Step-by-step explanation:
20 per hour 8h a day
160 per day
20x8
7. After testing for COVID-19 at Mulago Hospital, the ratio of positive to negative to asymptomatic cases was 4:5:7 respectively. If the total number of negative and positive cases was 63, (a) find the number of negative cases tested at the hospital. (03 Marks)
Answer:
7. After testing for COVID-19 at Mulago Hospital, the ratio of positive to negative to asymptomatic cases was 4:5:7
Step-by-step explanation:
ve and positive cases was 63, (a) find the number of negative cases tested at the hospital. (03 Marks)
the table shows that the total cost of buying and running a small heater
The following trial balance of Reese Corp. at December 31, 2014 has been properly adjusted except for the income tax expense adjustment. Reese Corp. Trial Balance December 31, 2014 Dr. Cr. Cash $ 775,000 Accounts receivable (net) 2,695,000 Inventory 2,085,000 Property, plant, and equipment (net) 7,566,000 Accounts payable and accrued liabilities $ 1,701,000 Income taxes payable 654,000 Deferred income tax liability 85,000 Common stock 2,350,000 Additional paid-in capital 3,680,000 Retained earnings, 1/1/14 3,450,000 Net sales and other revenues 13,560,000 Costs and expenses 11,180,000 Income tax expenses 1,179,000 $25,480,000 $25,480,000 07. The current assets total is: A. $6,080,000 C. $5,405,000 B. $5,555,000 D. $4,955,000
The current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.
What are the current assets?The current assets are Cash and Cash Equivalents (Marketable Securities), Accounts Receivable, Inventory, and Prepaid Liabilities (Expenses).
The current assets are the short-term portion of the total assets.
The current assets show Reese Corp.'s short-term liquidity and the company's ability to meet its short-term obligations (current liabilities), especially to suppliers, vendors, and other short-term creditors.
Data and Calculations:Reese Corp.
Trial Balance
December 31, 2014
Dr. Cr.
Cash $ 775,000
Accounts receivable (net) 2,695,000
Inventory 2,085,000
Property, plant, and equipment (net) 7,566,000
Accounts payable and accrued liabilities $ 1,701,000
Income taxes payable 654,000
Deferred income tax liability 85,000
Common stock 2,350,000
Additional paid-in capital 3,680,000
Retained earnings, 1/1/14 3,450,000
Net sales and other revenues 13,560,000
Costs and expenses 11,180,000
Income tax expenses 1,179,000
$25,480,000 $25,480,000
Current Assets:Cash $ 775,000
Accounts receivable (net) 2,695,000
Inventory 2,085,000
Total current assets = $5,555,000
Thus, the current assets total for Reese Corp. on December 31, 2014, is B. $5,555,000.
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If you ask Megan how many dogs she has, she answers with a riddle: "Four-sevenths of my dogs plus 9." How many dogs does she have?
Step-by-step explanation:
This is a simple system of equations problem, with our equation being:
[tex]\frac{4}{7}x+9=x[/tex]
We know this as her dogs (x) is equal to 4/7 of her dogs (x) plus 9. Now all we must do is solve for x:
[tex]\frac{4}{7}x+9=x\\\\\frac{4}{7}x=x-9\\\\\frac{4}{7}x=\frac{7}{7}x-9\\\\\frac{-3}{7}x=-9\\\\x=21[/tex]
2 + 3 * 5 – 1 + (3 – 5)
Answer:
14
Step-by-step explanation:
PEMDAS
parathesis first
3-5=-2
2+3*5-1-2
next multiply
3*5=15
2+15-1-2
go in order of subtracting and adding
2+15=17
17-1-2
17-1=16
16-2
14
The diameter of Mars is 6.794 × 106 m.
The diameter of Earth is 1.2756 × 107 m.
Jo says, ‘Earth is more than ten times the diameter of Mars.’ Is Jo right? You must show how you get your answer.
Mars is half as big as Earth and that they each have an equal amount of dry land surface to determine by how much the circumference of the Earth is larger than that of Mars.
we need D(Earth) / D(Mars).
D(Earth) / D(Mars) = 1.2763 x 10⁴km/6.8 x 10³ km ≈ 1.9
D(Earth) / D(Mars) ≈ 1.9
The fifth-largest planet in our solar system by radius, the Earth has a circumference of 3,959 miles.
The other seven planets are joined by Earth and Mars. These two planets in our solar system share some geological characteristics, such as the fact that Mars, the seventh-largest planet in our solar system, has a radius of 2,106 miles. There are a few distinctions between Mars and Earth, though.
Hence, these planets differ in terms of their sizes, atmospheres, and temperatures.
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Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $35 and same-day tickets cost $20. For one performance, there were 45 tickets sold in all, and the total amount paid for them was $1125. How many tickets of each type were sold?
By solving a system of equations, we conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.
How many tickets of each type were sold?Let's define the variables that we will be using:
x = number of advance tickets sold.y = number of same-day tickets sold.We can write the system of equations:
x + y = 45
x*35 + y*20 = 1125
Isolating x on the first equation we get:
x = 45 - y
Repacing that in the other equation we get:
(45 - y)*35 + y*20 = 1125
1,575 - y*15 = 1125
1,575 - 1125 = y*15
(1,575 - 1125)/15 = y = 30
Then:
x = 45 - y = 45 - 30 = 15
We conclude that they sold 30 of the same-day tickets and 15 of the advance tickets.
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Andy has 20 coins made up of quarters and half dollars, and their total value is $9.25. How many quarters does he have?
Using simple linear equations, we can calculate that Andy has 3 quarters.
What is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) component are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.
Let the number of quarters Andy has = x
number of dollars Andy has = 20 - x
value of quarter = 0.25x
value of dollars = 0.5(20 - x)
Total value = $9.25
⇒ 0.25x + 0.5(20 - x) = 9.25
⇒ 0.25x + 10 - 0.5x = 9.25
⇒ - 0.25x = 9.25 - 10
⇒ - 0.25x = - 0.75
⇒ x = 3
Andy has quarter = 3
He has dollars = 20 - 3 = 17
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What is the equation of the linear function in slope intercept form described by this table?
The equation of the linear function in slope intercept form is given as y = -2x + 1
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
From the table, the linear function contains the points (0, 1) and (2, -3), hence:
y - 1 = [(-3 - 1)/(2 - 0)](x - 0)
y = -2x + 1
The equation of the linear function in slope intercept form is given as y = -2x + 1
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A farmer looks over a field and sees 34 heads and 94 feet. Some are goats, some are geese. How many of each animal are there?
Answer: 13 goats and 21 geese
Step-by-step explanation:
Since we know some are goats, which have four feet, and some are geese, which have two feet, we will set up an equation.
Let x be goats and y be geese.
4x + 2y = 94
Next, we know both animals [usually] only have one head.
x + y = 34
Lastly, we will solve this as a system of equations.
➜ I graphed the equations, see attached, but you can also solve by substitution or other methods.
➜ When graphing, the point of intersection is the solution. This means there are 13 goats and 21 geese.
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Yolanda opened a retirement account earning 5.5% interest per year, compounded monthly. She deposited $100 each month. Assume that no other deposits or withdrawals were made. Answer the following, writing your answers to the nearest dollar.
The balance in dollars and cents in Yolanda's account at the end of 4 years is $5,355.29
What is the future value of an ordinary?
An ordinary annuity is the one where the monthly deposit occurs at the end of each month rather than at the beginning of the months such its future value based on 5.5% annual interest rate can be determined thus:
FV=PMT*(1+r)^N-1/r
FV=balance in dollars and cents in Yolanda's account at the end of 4 years=unknown
PMT=monthly deposit=$100
r=monthly interest rate=5.5%/12=0.00458333333333333
N=number of monthly deposits in 4 years=4*12=48
FV=$100*(1+0.00458333333333333)^48-1/0.00458333333333333
FV=$5,355.29
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Missing question:
What was the balance in dollars and cents in Yolanda's account at the end of 4 years?
Misses Ali owns a business. She assigns two of her employees their shifts. She assigns the first employee 6 hour shift and the second employee 15 hours shift. If both workers recieved same number of hours what is the mininum number of hours each employee will be assigned.
Based on the fact that both workers received the same number of hours, the minimum number of hours that each employee will be assigned is 60 hours.
What is the minimum assigned hours?One worker gets 15 hours shifts and the other gets 6 hour shifts.
If they will have the same number of working hours, the minimum number of hours for these workers will be the lowest common multiple of 6 and 15.
Multiples of 15:
15, 30, 45, 60, 75Multiples of 6:
6, 18, 30, 42, 60, 72The minimum number of hours is therefore 60 hours.
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Answer: 60
Step-by-step explanation:
LCM of 6 & 15
15
-------------
15
30
45
60
75
90
105
6
---------
6
12
18
24
30
36
42
48
54
60
LCM of 6 & 15 is 60
A child’s pool is filled to the top. On Day 1, the level of the water in the pool decreases by 1
1
3
inches. On Day 2, the level of the water decreases by
3
8
inch. What number represents the water level after 2 days?
Answer:
this makes no sense but I think the answer is 38 inches
Step-by-step explanation:
SOMEONE HELP PLS ILL MARK BRAINLIEST
Based on the linear pair postulate, the value of x is proven to be 11.
See proof below.
What is a Linear pair?A linear pair is formed by two adjacent angles that lie on a straight line, thus, they have a sum that is equal to 180 degrees.
We know that angle 1 and angle 2 are a linear pair, the complete proof would be stated as follows:
Statement Reason
1. Angle 1 and angle 2 are a linear pair 1. Given
2. Angle 1 and angle 2 are supplementary 2. Linear pair postulate
3. m<1 + m<2 = 180° 3. Supplementary angles
4. 11x - 6 + 4x + 21 = 180 4. substitution
5. 15x + 15 = 180 5. Combine like terms
6. 15x = 165 6. Subtraction property
7. x = 11 7. Division property
Thus, based on the linear pair postulate, the value of x is proven to be 11.
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