Hervenson is working two summer jobs, making $12 per hour at Mcdonald's and making $8 per hour washing cars. In a given week, he can work at most 20 totalhours and must eam a minimum of $200. If Hervenson works 15 hours at McDonalds, determine the minimum number of whole hours washing cars that he mustwork to meet his requirements. Write a system of inequalities to describe Hervenson's situation.
Answers
Data:
McDonalds: m
Washing cars: w
$12 per hour in m
$8 ér hour in w
m and w are the corresponding number of hours in each work
he can work at most 20 hours in total:
\(m+w\le20\)must earn a minimum of $200:
\(12m+8w\ge200\)If he works 15 hours at macdonalds (m=15) find the number of hours w:
You have the next system of inequalities:
\(\begin{gathered} m+w\le20 \\ 12m+8w\ge200 \end{gathered}\)Substitute the m in both equations for 15 and find the minimum number of whole hours washing cars (w):
\(\begin{gathered} 15+w\le20 \\ 15-15+w\le20-15 \\ w\le5 \\ \\ 12(15)+8w\ge200 \\ 180+8w\ge200 \\ 180-180+8w\ge200-180 \\ 8w\ge20 \\ w\ge\frac{20}{8} \\ w\ge2.5 \end{gathered}\)As you can see if he works 15 hours in mcdonalds, he needs to work a minimum of 3 whole hours (2.5 ≤ w ≤ 5) washing cars to meet his requirements (work at most 20 hours and earn minimum $200)
Answer: he needs to work a minimum of 3 whole hours washing cars
Related Questions
Which expression is equivalent to (2x^4y)^3?
Answers
Answer:
8x^{12}yx^{3}
Step-by-step explanation:
Simplify the expression.
Hopefully this helps you
- Matthew
A vitamin C tablet contains 1/4
of a gram of vitamin C. You take 1 1/2
tablets every day. In simplest form, how many grams of vitamin C do you take every day?
Answers
Answer:
3/8 gramsStep-by-step explanation:
1 tablet ⇒ 1/4 gramsMultiply the amount of tablets by 1/4 to find the answer
1 1/2 tablet ⇒ 1 1/2 *1/4 = 3/2 * 1/4 = 3/8 gramsy=1/2x+2 y=1/3x+2 solve for graphing
Answers
Answer:
I plotted it out on the graph and here it is:
6 years ago, Bernie won some money in the lottery and put it in a bank account that earns
8% interest compounded annually. If Bernie currently has $1,000.00 in the bank account,
how much interest has he earned?
Round your answer to the nearest cent.
Answers
The earned interest on given principal amount of $1000 is $1587.
What is compound interest?Compound interest is defined as the interest on the both initial principal amount and interest amount of previous period.
According to given data:We have initial saving of $1000 in bank which gives 8% interest compounded annually.
Formula to find interest , P(1 + r/100)^n
p is principal, r is rate of interest , n is time period.
Interest for 6 years = $1000(1 + 8/100)^6
⇒$1000(108/100)
⇒ $1000×1.59
⇒ $1587 approx
Thus, required answer is $1587 approx.
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Solve the simultaneous equations using elimination method= x+2y-3z=0 3x+3y-z = 5 x-2y = 2z=1
Answers
Answer:
[1;1;1]
Step-by-step explanation:
try this option; all the details are in the attachment.
Why do we choose 5% as a risk of making error and not 1%
Answers
In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.
The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.
In general, the choice of significance level depends on the specific application and context of the statistical analysis.
The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.
The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.
A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.
A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.
For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.
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What is the volume of the sphere below
Answers
Answer:
A.) \(\frac{500}{3} \pi units^3\)
Step-by-step explanation:
To find the volume of the sphere, you need to use the following equation:
\(V= \frac{4}{3} \pi r^3\)
In this equation, "V" represents the volume (units³) and "r" represents the radius (units). Since you have been given the value of the radius (r = 5 units), you can use it to solve the equation.
\(V= \frac{4}{3} \pi r^3\) <----- Volume equation
\(V= \frac{4}{3} \pi (5)^3\) <----- Plug 5 into "r"
\(V= \frac{4}{3} \pi (125)\) <----- Solve 5³
\(V= \frac{500}{3} \pi\) <----- Multiply \(\frac{4}{3}\) and 125
Answer:
\(\sf A. \quad \dfrac{500}{3} \pi \:\:units^2\)
Step-by-step explanation:
Volume of a sphere
\(\sf V=\dfrac{4}{3} \pi r^3\)
(where r is the radius)
From inspection of the given diagram:
r = 5 unitsSubstitute the value of r into the equation and solve for V:
\(\begin{aligned}\sf V & = \sf \dfrac{4}{3} \pi r^3\\\\\implies \sf V & = \sf \dfrac{4}{3} \pi (5)^3\\\\& = \sf \dfrac{4}{3} \pi (125)\\\\ & = \sf \dfrac{4 \cdot 125}{3} \pi\\\\& = \sf \dfrac{500}{3} \pi \:\:units^2\end{aligned}\)
the container that holds the water for the football team is 2/5 full. After pouring in 8 gallons of water, it is 2/3 full. How many gallons can the container hold?
Answers
Answer:
30 gallons
Step-by-step explanation:
Let c represent the capacity of the container in gallons.
2/5c +8 = 2/3c . . . . adding 8 gallons to 2/5 full gives 2/3 full
8 = (2/3-2/5)c = 4/15c . . . . subtract 2/5c
8(15/4) = c = 30 . . . . . . . . . multiply by 15/4
The container can hold 30 gallons.
Isaiah brought two dozen donuts to a class party. Half of the donuts had vanilla frosting with sprinkles, 2 had strawberry frosting with cream filling, and the rest had chocolate frosting with sprinkles. what fraction of the donuts had sprinkles?
Answers
Answer: 22
Step-by-step explanation:
Two dozen equals 24, divide it in half leaves 12 vanilla sprinkle doughnuts
the remaining 12 minus the 2 strawberry cream equals 10 chocolate sprinkles
add the 10 chocolate plus 12 vanilla to get 22
You have been asked to set up chairs for the school concert. The first row will have 10 seats, and each additional row has 4 seats more than the previous row. How many seats are there in row 20?
Answers
Hello!
This is a question about an arithmetic sequence. We can solve it using the formula:
\(a_n=a_1+(n-1)\cdot r\)Let's replace them with the values mentioned in the exercise:
\(\begin{gathered} a_{20}=10+(20-1)\cdot4 \\ a_{20}=10+19\cdot4 \\ a_{20}=10+76 \\ a_{20}=86 \end{gathered}\)Answer:86 seats in row 20.
Use the diagram to find the angle measuresof the triangle. Recall that the sum of theangle measures of a triangle is 180°3x(x+5)*Xº =(x+5)° = Dº3xº =
Answers
Answer:
x = 35 degrees
x + 5 = 40 degrees
3x = 15 degrees
Explanation:
Given that the angle measures of a triangle is 180 degrees, we have
3x + (x + 5) + x = 180
3x + x + 5 + x = 180
5x + 5 = 180
Subtract 5 from both sides
5x + 5 - 5 = 180 - 5
5x = 175
Divide both sides by 5
5x/5 = 175/5
x = 35 degrees
x + 5 = 35 + 5 = 40 degrees
3x = 3(5) = 15 degrees
what is the average allowance for each student?
$7,$12,$8.50,$10,$7,$8,$10.50,$11
Answers
The average allowance for each student is $9.25.
What is the average allowance for each student?To find the average allowance for each student, we need to add up all the allowances and divide by the total number of students.
Adding up the allowances:
$7 + $12 + $8.50 + $10 + $7 + $8 + $10.50 + $11 = $74
There are 8 students, so we divide the total allowance by 8 to get:
$74 / 8 = $9.25
Therefore, the average allowance for each student is $9.25.
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PLEASE HELP ME
An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.
According to this data, what is wrong with the article's statement?
Answers
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
How to determine what is wrong with the data?The prices from 5 gas stations surveyed are given as:
$2.79, $2.99, $2.69, $2.89, and $2.69.
There are no outliers in the dataset
So, the dataset can be summarized by the mean
The mean is
Mean = Sum/Count
So, we have
Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5
Evaluate
Mean = 2.81
The article quoted $2.69 as the typical price
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
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Find the slope and the -intercept of the line -8x-4y=-5
Answers
Answer:
The slope is -2 and y-intercept is (0, 5/4).
Step-by-step explanation:
-8x-4y=-5
4y=-8x-(-5)
4y=-8x+5
y=-8/4x+5/4
y=-2x+5/4
y=mx+b where m=slope and b=y-intercept.
Thus, m=-2 and b=5/4.
Hi, really need help on this last question for the night, heeeeelp pls.
Answers
Answer:
Move it 2 places to the right.
Step-by-step explanation:
The magnitude of the exponent of 10 tell you how many places to move
The sign of the exponent of 10 tells you the direction.
Positive, decimal moves right.
Negative, decimal moves left.
The sum of three consecutive odd integers is 255. Find the integers.
Answers
Step-by-step explanation:
X+x+1+x+2=225
3x+3=225
3x+3-3=225-3
3x=222
3x÷3=222÷3
X=74
Which means the first number is 74, the second number is 74+1 and the third number is 74+2. Therfore the consecutive integers that add up to 225 are 74, 75,and 76
Check answer
74+75+76=225
225=225
On a map, 12 inch represents 45 mile.
What distance on the map represents 1 mile?
25 in.
58 in.
135 in.
212 in.
I'll give brainlyest.
Answers
Answer: 5/8 inch represents 1 mile
Step-by-step explanation:
to get 1, multiply 4/5 by its reciprocal, 5/4
Then multiply 1/2 by 5/4
1/2 × 5/4 = 5/8
Answer: The correct answer is 5/8
Step-by-step explanation: Answer verified as correct on test
What is the image of (-9,12)(−9,12) after a dilation by a scale factor of \frac{1}{3} 3 1 centered at the origin?
Answers
The image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
In the given question,
We have to find the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin.
Since we have to find the image after a dilation.
So we learn about it now,
Any scale factor will dilate the image of any coordinate. A specific scale factor can be used to scale the coordinate up or down. To determine the answer, consider the scale factor in the equation and multiply or divide the coordinates of dilation by the appropriate scale factor.
So the given point is (-9,12).
Scale factor is 1/3.
So the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is define as
=(-9×1/3,12×1/3)
Simplifying
=(-3,4)
Hence, the image of (-9,12) after a dilation by a scale factor of 1/3 centered at the origin is (-3,4).
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Part (C) Cup B has a diameter of 20 cm. and a height of 20 cm. Find the volume of Cup B.
Answers
Answer:
V=6280cm²
Step-by-step explanation:
V=pi r²h
V=3.14 x 10²cm×20cm
V=6280cm²
fill in the mission numbers to make the fractions equivalent. 1/2 and /8= 4/12 and /60= 2/3 and /12= 4/4 and /8=
Answers
To make the fractions equivalent, we need to find the missing numerators that would make them equal. Let's fill in the missing numerators:
1/2 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
1/2 and 4/8
Now, the fractions are equivalent.
---
4/12 and __/60
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 5:
4/12 and 20/60
Now, the fractions are equivalent.
---
2/3 and __/12
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 4:
2/3 and 8/12
Now, the fractions are equivalent.
---
4/4 and __/8
To make the fractions equivalent, we can multiply both the numerator and denominator of the first fraction by 2:
4/4 and 8/8
Now, the fractions are equivalent.
What is the common ratio of the following geometric sequence? 6, 9, 27/2, 81/4,...
Answers
Answer:
1.5
Step-by-step explanation:
To find the common ratio of a geometric sequence, you divide two consecutive terms together. You can start by dividing 9/6, or 1.5. To confirm this is the common ratio, you can divide 27/2 ÷ 9, which is indeed 1.5. The common ratio is the multiplier of the sequence, so it is consecutive and does not change throughout the function.
Answer:
r = 3/2
Step-by-step explanation:
1.5 written as a fraction is 3/2
What is the smallest positive integer which when divided by 5 leaves a remainder of 3?
Answers
The smallest positive integer which when divided by 5 leaves a remainder of 3 is 8
How to determine the smallest positive integerFrom the question, we have the following parameters that can be used in our computation:
Divisor = 5
Remainder = 3
Using the above as a guide, we have the following:
Smallest integer = Divisor + Remainder
So, we have
Smallest integer = 5 + 3
Evaluate
Smallest integer = 8
Hence, the smallest is 8
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5a+4b=65 elimination substitute and check
Answers
Answer:
a=13 - 4b/5
b=65/4-5a/4
Step-by-step explanation:
Solve for x and graph the answer on a number line
2
Answers
The solution to the system of inequalities in interval notation is [-2, 1].
How to solve the system of inequalities?Based on the information provided in the image below, we have the following system of inequalities;
-12 < 3x - 6
-3 ≥ 3x - 6
By adding 6 to both sides of the equation (inequality), we have;
-12 < 3x - 6
-12 + 6 < 3x - 6 + 6
-6 < 3x
-2 < x
x > -2 (flip)
-3 ≥ 3x - 6
-3 + 6 ≥ 3x - 6 + 6
3 ≥ 3x
1 ≥ x
x ≤ 1
Therefore, the solution to the system of inequalities is given by:
-2 < x ≤ 1
In interval notation, we have [-2, 1].
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Which expressions simplify to a rational answer?
Select each correct answer.
Responses
9√⋅16−−√
, root 9 times root 16
3√⋅2√
root 3 end root times root 2 end root
11−−√⋅5√
root 11 times root 5
52⋅−√2√
5 root 2 end root times root 2
Answers
√9 × √16 and 5√2 × √2 simplify to a rational answer
How to find the expressions that simplify to a rational answer?A rational number is a number that can be written in the form of a/b, where a and b are integers, and b is not equal to 0. e.g 1/3, 2/3, √4 = 4/1, etc.
The opposite of a rational number is called an irrational or non-rational number. They are mostly in the form of square roots, which when evaluated can be expressed in the form a/b e.g √7, π, 2/√5, 3√11, etc.
Given:
For √9 × √16:
√9 × √16 = 3× 4 = 12
This is a rational answer
For √3 × √2:
√3 × √2 = √(3×2) = √6
This is not a rational answer
For √11 × √5:
√11 × √5 = √(11×5) = √55
This is not a rational answer
For 5√2 × √2:
5√2 × √2 = 5√(2×2) = 5√4 = 5×2 = 10
This is a rational answer
Therefore, √9 × √16 and 5√2 × √2 simplify to a rational answer. Select the 1st and 4th options
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I neeed help guyssssss...
Answers
Answer: 7
Step-by-step explanation:
15 + 5x = 50
5x = 35
x = 7
Answer:
10 years old is the answer
how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
Find the unit vector in the direction of (-2, -1).Write your answer in component form.Do not approximate any numbers in your answer. ( , )
Answers
A unit vector has a module of 1.
We can calculate the coordinates of a unit vector in the direction of an specific vector by dividing the coordinates of that vector by the module.
Then, first we will calculate the module of the vector:
\(\begin{gathered} |r|=\sqrt[]{x^2+y^2} \\ |r|=\sqrt[]{(-2)^2+(-1)^2} \\ |r|=\sqrt[]{4+1} \\ |r|=\sqrt[]{5} \end{gathered}\)We then can write the unit vector as:
\(r=(-\frac{2}{\sqrt[]{5}},-\frac{1}{\sqrt[]{5}})=(-\frac{2\sqrt[]{5}}{5},-\frac{\sqrt[]{5}}{5})\)Answer: (-2√5/5, -√5/5)
Enter the ratio as a fraction in lowest terms.
5 ft to 70 in.
Answers
Answer:
1/14
Step-by-step explanation:
The ratio is 5:70. The fraction form of that is 5/70. To get the lowest terms, I divided both numbers by 5. So it is 1/14
The ratio of Wei Ling's age to Wei Xuan's age 5 years ago was 2: 5. In 9 years
time, the ratio of Welling's age to Wel Xuan's age will be 3:4 How old is Wei
Xuan now?
Answers
Answer:
15 years old
Step-by-step explanation:
Start by defining the variables that we are going to use throughout our working:
Let the current age of Wei Ling and Wei Xuan be L and X years old respectively.
Next, form equations using the given information.
5 years ago
Wei Ling: (L -5) years old
Wei Xuan: (X -5) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan's is 2: 5,
\( \frac{ L - 5}{X - 5} = \frac{2}{5} \)
Cross multiply:
2(X -5)= 5(L -5)
Expand:
2X -10= 5L -25
2X= 5L -25 +10
2X= 5L -15 -----(1)
9 years time
Wei Ling: (L +9) years old
Wei Xuan: (X +9) years old
Given that the ratio of Wei Ling's age to that of Wei Xuan is 3: 4,
\( \frac{L + 9}{X + 9} = \frac{3}{4} \)
Cross multiply:
3(X +9)= 4(L +9)
Expand:
3X +27= 4L +36
3X= 4L +36 -27
3X= 4L +9 -----(2)
Let's solve using the elimination method.
(1) ×3:
6X= 15L -45 -----(3)
(2) ×2:
6X= 8L +18 -----(4)
(3) -(4):
6X -6X= 15L -45 -(8L +18)
0= 15L -45 -8L -18
0= 7L -63
7L= 63
L= 63 ÷7
L= 9
Substitute L= 9 into (1):
2X= 5(9) -15
2X= 45 -15
2X= 30
X= 30 ÷2
X= 15
Thus, Wei Xuan is 15 years old now.