Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $3000. What was the rate charged per hour by each mechanic if the sum of the two rates was $175 per hour?
Answers
Answer:
the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.
Step-by-step explanation:
A system of equations is a set of two or more equations in various unknowns in which you want to find a common solution.
So, first of all it is convenient to define the system variables:
x= the rate charged per hour by the first mechanicy= the rate charged per hour by the second mechanicIf the sum of the two rates were $ 175 per hour, then the mathematical expression that represents this situation is: x + y= 175
You know that the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Then the amount of money won by the first and second mechanic respectively is expressed by 20*x and 15*y. Together they charged a total of $3000, then 20*x + 15*y=3000
So, the system of equations to solve is:
\(\left \{ {{x+y=175} \atop {20*x+15*y=3000}} \right.\)
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied.
There are several methods for solving a system of equations. One of them is the substitution method, which consists of solving or isolating one of the unknowns (for example, x) and substituting its expression in the other equation. In this way, you obtain an equation of the first degree with the other unknown. Once solved, you must calculate the value of x by substituting the already known value of y.
In this case, you isolate the variable x from the first expression:
x= 175 - y
Replacing this expression in the second equation:
20*(175 - y)+15*y=3000
and solving you get:
20*175 -20*y +15*y=3000
3500 -20*y +15*y=3000
3500 -5*y=3000
-5*y=3000 -3500
-5*y= -500
y= (-500)÷(-5)
y= 100
So:
x=175 -y
x=175 -100
x=75
Then the rate charged per hour by the first mechanic is 75 $/hr and the rate charged per hour by the second mechanic is 100 $/hr.
Answer:
The rate charged by the first mechanic is $75/h and by the second is $100/h.
Step-by-step explanation:
We have that the two mechanics charged a total of $3000:
\( A + B = \$3000 \)
\( A = \$3000 - B \) (1)
The sum of the rate of the two mechanics was $175 per hour:
\( R_{A} + R_{B} = \$175/h \) (2)
The rate of the first (A) and second (B) mechanic is:
\( R_{A} = \frac{A}{t_{A}} = \frac{A}{20 h} \) (3)
\( R_{B} = \frac{B}{t_{B}} = \frac{B}{15 h} \) (4)
By entering equation (3) and (4) into (2):
\( \frac{A}{20 h} + \frac{B}{15 h} = \$175/h \) (5)
Now, by entering equation (1) into (5) we have:
\( \frac{\$3000 - B}{20 h} + \frac{B}{15 h} = \$175/h \)
\( \frac{-3B + 4B}{60 h} = \$175/h - \$150/h \)
\( B = \$25/h*60 h = \$1500 \)
Now, for the first mechanic we have:
\( A = \$3000 - B = \$3000 - \$1500 = \$1500 \)
Finally, from equation (3) and (4) we can find the rate charged per hour by each mechanic:
\( R_{A} = \frac{A}{20 h} = \frac{\$1500}{20 h} = \$75/h \)
\( R_{B} = \frac{B}{15 h} = \frac{\$1500}{15 h} = \$100/h \)
Therefore, the rate charged by the first mechanic is $75/h and by the second is $100/h.
I hope it helps you!
Related Questions
emma advertises a reward for the return of her lost dog. frank, who does not know of the reward, finds and returns the dog. frank cannot recover the reward because he
Answers
Frank cannot recover the reward because he was unaware of the reward being offered by Emma.
In order to claim the reward, one typically needs to have knowledge of the reward prior to finding and returning the lost item or fulfilling the specified condition. Since Frank was unaware of the reward, he would not have had the opportunity to intentionally seek the dog with the expectation of receiving the reward. As a result, Emma is not obligated to provide the reward to Frank in this situation.
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PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answers
Answer:
\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)
2x² + 12x + 16
what is it
Answers
Answer:
2(x+2)(x+4)
Step-by-step explanation:
There are 100 people in a sport centre. 67 people use the gym. 62 people use the swimming pool. 56 people use the track. 38 people use the gym and the pool. 31 people use the pool and the track. 33 people use the gym and the track. 16 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
Answers
Answer:
0.3 or 30%Step-by-step explanation:
Number of people using more than one sport facility:
38 - gym and pool31 - pool and track33 - gym and track16 - all threeSince 16 is counted for all three, total number of those using more than one facility is therefore:
38 + 31 + 33 - 16*2 = 70Number of people using exactly one facility is:
100 - 70 = 30Probability of the person using exactly one facility is:
30/100 = 0.3 or 30%riddle
What runs around the whole yard without moving?
Answers
Answer:
a yard stick, maybe I'm right
Answer:
a fence
Step-by-step explanation:
HAHAHA LOL
Dirk is going to send some flowers to his wife. Riverside Florist charges $3 per rose, plus $15 for the vase. Matthew's Flowers, in contrast, charges $2 per rose and $20 for the vase. If Dirk orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. How many roses would there be?
Answers
there would be 5 roses in the bouquet.
Let's assume the number of roses in the bouquet is 'x'.
The cost of the bouquet from Riverside Florist would be: $3 (cost per rose) * x (number of roses) + $15 (vase cost) = 3x + 15 dollars.
The cost of the bouquet from Matthew's Flowers would be: $2 (cost per rose) * x (number of roses) + $20 (vase cost) = 2x + 20 dollars.
Since the cost of the bouquet is the same at both flower shops, we can set up the equation:
3x + 15 = 2x + 20
Subtracting 2x from both sides:
3x - 2x + 15 = 2x - 2x + 20
x + 15 = 20
Subtracting 15 from both sides:
x + 15 - 15 = 20 - 15
x = 5
Therefore, there would be 5 roses in the bouquet.
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5x + 2y = 8 x + y = 4 if you want to solve the system of equations by addition which of the following could you do
Answers
Answer: x= 0, y = 4
Step-by-step explanation:
5x+2y=8
X+y=4 -> y=4-x
5x + 2(4-x)=8 -> 5x + 8-2x=8 -> 3x=0 -> x=0
y=4-x=4-0=4
For which of the following is the shape of the sampling distribution of the sample mean approximately normal? a random sample of size 5 from a population that is approximately normal a random sample of size 10 from a population that is strongly skewed to the right a random sample of size 60 from a population that is strongly skewed to the left.
Answers
Answer:
a random sample of size 5 from a population that is approximately normal
a random sample of size 60 from a population that is strongly skewed to the left.
Step-by-step explanation:
They are both correct
Answer:
D. Approximately Normal
The service manager for a new automobile dealership reviewed dealership records of the past 20 sales of new cars to determine the number of warranty repairs he will be called on to perform in the next 90 days. Corporate reports indicate that the probability any one of their new cars needs a warranty repair in the first 90 days is 0.05. The manager assumes that calls for warranty repair are independent of one another and is interested in predicting the number of warranty repairs he will be called on to perform in the next 90 days for this batch of 20 new cars sold. What type of probability distribution will most likely be used to analyze warranty repair needs on new cars?
a. binomial distribution
b. Poisson distribution
c. hypergeometric distribution
d. none of the above
Answers
The type of probability distribution that will most likely be used to analyze warranty repair needs on new cars is the binomial distribution. What is the binomial distribution? The binomial distribution is a statistical probability distribution used to determine the probability of a single successful outcome in a certain number of tests or experiments.
The correct option is-A
When two outcomes are possible (e.g. "yes" or "no"), it is used to analyze and predict their occurrence. A random variable X that is distributed binomially is known as a binomial variable, which is also known as a Bernoulli variable. Let the areas of the three rugs be a, b, and c.
Then according to the given information, a + b + c = 2200Also, area of overlap of the rugs (covered by exactly two layers of rug) = 24m²Hence, (a + b + c) – 2(area covered by two layers of rug) = area covered by three layers of rug (2200 – 2 × 24)m² = 2152m².
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Help me plz I would really appreciate it!
Answers
Hope you could get an idea from here.
Doubt clarification - use comment section.
I need help with this answer please
Answers
Answer:
Y= x+2
Step-by-step explanation:
The x value is always adding 2 to get the y value
1+2=3
2+2=4
3+2=5
4+2=6
5+2=7
Therefore your answer is y = x + 2
Hope this helps!
Answer:
2
Step-by-step explanation:
y = x + c
Put x as 1, and y as 3 and solve for c.
3 = 1 + c
3 - 1 = c
2 = c
When testing the differences between means, the _____ hypothesis suggests that population means are not equal.
Answers
Answer: Research
Step-by-step explanation:
A golf club manufacturer measures the impact elasticity of a new material. This is done by randomly selecting a driver head made from the new material, firing a golf ball at it from an air cannon (under carefully controlled conditions), and making certain measurements of the ball's motion. These measurements are used to calculate a number called the coefficient of restitution of the driver head. Engineers use this procedure 30 times. The sample mean coefficient of restitution is 0.835. Calculate a 99% confidence interval for the true mean coefficient of restitution, assuming the population standard deviation of such coefficients is 0.019. Round your answers to the fourth decimal digit.
Answers
The confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
Given sample mean coefficient of restitution 0.835,population standard deviation of 0.019 and the confidence level of 0.835.
We have to find the confidence interval for the true mean coefficient of restitution.
We can easily find the confidence interval through the formula of margin of error.
Margin of error is the difference between the calculated values and the real values.
Margin of error=z*σ/\(\sqrt{n}\)
where z is the z value of p value,
σ is population mean or sample mean,
n is the sample size.
In our problem the sample size is 30.
z value for the p value of 0.99 is 2.576.
Margin of error=2.576*0.019/\(\sqrt{30}\)
=0.048944/5.4772
=0.0089
Upper level=mean +margin of error
=30+0.0089
=30.0089
Lower level=Mean-margin of error
=30-0.0089
=29.9911.
Hence the confidence interval for the true mean coefficient of restitution is (29.9911,30.0089).
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Given: E is the midpoint of AB and CD little help please would be great
Answers
You need to prove that ΔAEC ≅ ΔBED
You know that point E is the midpoint of AB and CD
The midpoint divides a line segment into two congruent lines. This means that E divides AB into two congruent segments AE and EB, and it also divides CD into two congruent segments CE and ED, then we can conclude that:
1. AE=EB → Reason Midpoint Theorem
2. CE=ED → Reason Midpoint theorem
Both lines AB and CD intersect at point E, forming an X shape. The ingles formed inside the X are vertically opposite angles, this means that
3. ∠AEC= ∠BED → Reason Vertically opposite angles
Since E is the midpoint where both "diagonals of the parallelogram" AB and CD intersect, then sides AC and DB are parallel. If AB || CD, then ∠ACE and ∠BDE are alternate interiors angles as well as ∠CAE and ∠DBE. Alternate interior angles are congruent, so that:
4. ∠ACE=∠BDE → Reason alternate interior angles, AB || CD
5. ∠CAE=∠DBE → Reason alternate interior angles, AB || CD
Then → ΔAEC ≅ ΔBED by SAS and AAA
Lydia bought a shirt at 20% off its retail price of $40. She paid 5% tax on the price after the discount. How much did Lydia pay for the shirt?
make sure to look at the photo :) i hope you have a good day
Answers
Answer:
$33.60
Step-by-step explanation:
Original price of shirt: $40
Percent discount: 20%
Amount of discount: 20% of $40 = 0.2 × $40 = $8
Price after discount: $40 - $8 = $32
Percent of tax: 5%
Amount of tax: 5% of $32 = 0.05 × $32 = $1.60
Total paid after discount and tax: $32 + $1.60 = $33.60
Answer: Lydia paid the amount of 33.60 dollar
Step-by-step explanation:
Retail price of shirt = 40 dollar
Discount = 20%
Discount value:
=20% of 40 dollar [ 20/100 * 40 ⇒ 1/5 * 40 ⇒ 40/5 = 8 ]
= 8 dollar [ discount value]
Price of shirt after discount :
= 40 - 8
= 32 dollar
As she paid 5% discount on the discounted price ( 32 dollar )
So, 5% of 32 = 1.6 dollar [ 5/ 100 * 32 ⇒ 1/20 * 32 ⇒ 32/20 = 1.6]
Amount to pay = 32( price after discount) + 1.6 ( Tax)
= 33.60 dollar
PLS I NEED HELP ASAP I DONT HAVE TIME IT ALSO DETECTS IF IT RIGHT OR WRONG.
Answers
Answer:
2 1 2 1
Step-by-step explanation:
24+89
A.113
B.34
C.87
D.90
Answers
Answer:
answer is A 113 24+89=113
Answer:
A
Step-by-step expalanation:
24+89=113
Tìm hàm số bậc nhất,biết đồ thị đi qua điểm (3;−2), song song với đường thẳng
′:3−2+1=0
Answers
20234555446698382636
write down a sample distribution with n=20 so that the five
number summary of the distribution is 2,4,6,8,10
Answers
A sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10 can be generated by arranging the values in increasing order as follows: 2, 2, 3, 4, 4, 5, 6, 6, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10.
To construct a sample distribution with a specific five-number summary, we need to determine the arrangement of values within the dataset. The five-number summary consists of the minimum value (2), the first quartile (Q1, 4), the median (Q2, 6), the third quartile (Q3, 8), and the maximum value (10).
Since the dataset has 20 observations, we need to arrange these values in increasing order while ensuring that they match the given five-number summary. In this case, we can start by placing the minimum value of 2 at the beginning of the dataset. Next, we need to include additional values between 2 and 4 to represent the first quartile. We can add two 2's, a 3, and two 4's to achieve this.
Moving forward, we continue adding values to match the remaining quartiles. For Q2, we include values 5 and 6, and for Q3, we include three 8's and four 9's. Finally, we add four 10's to represent the maximum value.
By arranging the values in this manner, we obtain a sample distribution with n = 20 and a five-number summary of 2, 4, 6, 8, and 10.
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Daisy and Diesel play a game where Diesel's chance of winning is always 1/4. They play the game again and again until one of them wins 6 games. a. Find the probability that Diesel will win her 6th game on the 18th game (that is, Diesel will win the 18th game, at which point she will have a total of 6 wins). b. What's the expected number of games they'll play before Diesel wins six games?
Answers
The expected number of games they'll play before Diesel wins six games is 4.
a. The probability that Diesel will win her 6 th game on the 18th game is the probability that Diesel will win exactly 5 of the first 17 games and then win the 18 th game. The probability that Diesel wins any particular game is 1 / 4, so the probability that she wins 5 of the first 17 games is:
\($$\left(\begin{array}{c}17 \\5\end{array}\right)\left(\frac{1}{4}\right)^5\left(\frac{3}{4}\right)^{12} \approx 0.202$$\)
Then, the probability that Diesel wins the 18th game is 1 / 4. Therefore, the probability that Diesel will win her 6 th game on the 18th game is:
\($$0.202 \cdot \frac{1}{4}=0.0505$$\)
b. We can approach this problem using the concept of a geometric distribution. Let X be the number of games they play before Diesel wins 6 games. Then, X has a geometric distribution with parameter p=1 / 4, since the probability that Diesel wins any particular game is 1 / 4.
The expected value of a geometric distribution with parameter p is:
\(E(X)=\frac{1}{p}=\frac{1}{1 / 4}=4$$\)
Therefore, the expected number of games they'll play before Diesel wins six games is 4 .
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Mark and Dennis help their grandfather make rootbeer. They need 4 pounds of sassafras to make one barrel of rootbeer, but they only have 1 pound.
How much rootbeer can they make?
Answers
Answer:
the total is your denominator and how much they have is the numerator so the answer is 1/4 or one fourth
Step-by-step explanation:
how would you solve #81?
Answers
Find an equivalent ratio of 3:7 by filling the missing number.
3:7 = 12:
Enter the answer
Answers
3/7 = 12/x
x = (12*7)/3
x = 84/3
x = 28
a ________ is a type of chart that uses symbols instead of words or numbers to portray data.
Answers
Answer:
Step-by-step explanation:
Pictograph
Pictograms are a powerful tool for visualizing data and are widely used in a variety of different fields, from marketing and advertising to science and education.
A pictogram is a type of chart that uses symbols instead of words or numbers to portray data. Pictograms are often used in data visualization and are particularly useful for presenting complex information in a simple and easily understandable way. Pictograms can be used to represent a wide range of data, including statistical information, demographic data, and geographical information. They are also commonly used in advertising and marketing, as they are a powerful tool for communicating ideas and concepts quickly and effectively. Pictograms can be created using a variety of different techniques, including hand-drawn illustrations, computer-generated graphics, and photographs. They are typically presented in a grid format, with each symbol representing a single data point. Pictograms can be used to show trends, compare data sets, and highlight key points. They are also a great way to make data more engaging and interactive, as users can explore the data by clicking on individual symbols or groups of symbols.
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Which sequence of transformations will map figure H onto figure H'
-8
7
-6
-5
-4-
-3
-2
1
-5-4-3-2-10 1 2 3 4 5 6 7 8 9 10 11 12 13
-1
-2
3 4
587
H
-9
-10
H'
O
Rotation of 180° about the origin, translation of (x + 10, y − 2)
reflection across x = -6
Rotation of 180° about the origin, translation of (x + 10, y − 2).
reflection across y = -6
Rotation of 180° about the origin, translation of (x - 10, y + 2)
reflection across y = -6
Rotation of 180° about the origin, translation of (x - 10, y + 2)
reflection across x = -6
Answers
The sequence of transformations that will map figure H onto figure H' is: Option B: the rotation of 180° about the origin, translation of (x + 10, y − 2), and reflection across y = −6.
How to find the sequence of transformation?We are given the coordinates of the hexagon as:
Points of Hexagon H → (2,2), (2,6), (6,7), (8,6), (8,2), (6,1)
Points of Hexagon H' → (2,-8), (2,-4), (4,-3), (8,-4), (8,-8), (4,-9)
The steps that can be used to transform the hexagon H into hexagon H' are:
Step 1 - Translate the hexagon in the positive x-axis direction by a factor of 10.
Step 2 - Translate the graph obtained in the above step by factor 2 in the downward direction.
Step 3 - Rotate the graph obtained in the above step 180 degrees about the origin.
Step 4 - Then take the reflection of the graph obtained in the above step about y = -6. The resulting graph shows the graph of Hexagon H'.
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Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. k = -1; f(x) = 4x^3 - 2x^2 + 2x + 4; Lower bound? yes/no?
Answers
Answer:
Yes, k is lower bound for the real zeros of the function.
Step-by-step explanation:
Lower Bound Theorem:
If you divide a polynomial function f(x) by (x - k), where k < 0, using synthetic division and this yields alternating signs, then k is a lower bound to the real roots of the equation f(x) = 0.
Given;
4x³ - 2x² + 2x + 4
k = -1
synthetic division;
-1 ] 4 -2 2 4
↓ -4 6 -8
---------------------------------------------
4 -6 8 -4
(the result has alternating signs, hence k is lower bound)
Thus, k is lower bound for the real zeros of the function.
Please someone help!!!!
Answers
Tell me if u need more help :)
Answer this for me please
Answers
Answer:
-3
Step-by-step explanation:
You cant count the spaces up (9) and over (-3) between the two points and do up/over so it would be 9/-3 and simplified that is -3/1 or 3
Determine the slope through points (3,0) (-12,-15)
Answers
Answer:
The slope is 1.
Step-by-step explanation:
1. Which of the following does not represent perimeter ?
A. Border of a picture frame
B. Crust of slice of bread
C. Carpet size of a room
D. Fence around an object.
———————————————-
2. Which of the following statements is fire concerning the perimeter of a rectangular window?
A. You only need to measure the length of the window to calculate the perimeter .
B. You only need to measure the width of the window to calculate the perimeter.
C. You need to measure both the length and the width of the window to calculate perimeter
D. There is not enough information given about the window to calculate the perimeter.
————————————————
3. Sam is adding crown molding around the ceiling of his living room . He measures the perimeter of the room to be a total of 58ft. If molding planks are sold in 8-foot pieces, how many planks should he buy?
A. 10 planks
B. 8 planks
C. 6 planks
D. 9 planks
—————————————————-
4. Determine how far you will move in one turn of your wheel if the radius is 15 in.
_____inches.
Answers
C. Carpet size of a room does not represent perimeter.
C. You need to measure both the length and the width of the window to calculate perimeter.
What is perimeter ?
Perimeter is the total distance around the outside of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is measured in units such as inches, centimeters, meters, or feet, depending on the system of measurement being used.
The concept of perimeter is commonly used in geometry to calculate the distance around various shapes, such as squares, rectangles, triangles, circles, and polygons. It is an important measurement in many real-world applications, such as in construction, landscaping, and fencing.
According to the question:
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