Answer:
The possible values of the number of hours clearing tables are 2 , 3 , 4 , 5 hours
Step-by-step explanation:
* Lets explain how to solve the problem
- Madelyn is making $20 per hour life guarding
- She is making $12 per hour clearing tables
- She can work no more than 13 total hours
∴ The greatest time she can work is 13 hours (≤)
- She must earn no less than $180
∴ The least money she wants to earn is $180 (≥)
- If Madelyn worked 8 hours life guarding and assume that she
worked x hours clearing tables
∵ She can work no more than 13 hours
∴ 8 + x ≤ 13
- Subtract 8 from both sides
∴ x ≤ 5 ⇒ (1)
∵ She must earn no less than $180
∴ 8 × 20 + x × 12 ≥ 180
∴ 160 + 12x ≥ 180
- Subtract 60 from both sides
∴ 12x ≥ 20 ⇒ (2)
- From equation (1) ⇒ x = 1 , 2 , 3 , 4 , 5
- Substitute x in equation (2) by these values to find the right values
of x
# If x = 1
∴ 12(1) ≥ 20
- But 12 is less than 20
∴ x can not be 1
# x = 2
∴ 12(2) ≥ 20
∴ 24 ≥ 20
- 24 is greater than 20 then x can be 2
∵ 3 , 4 , 5 greater than 2
∴ All of them give answers greater than 20
∴ x can be 3 , 4, 5
∵ x represents the number of hours for clearing tables
∴ The possible values of the number of hours clearing tables are
2 , 3 , 4 , 5 hours
Madelyn can work 2, 3, 4, or 5 hours clearing tables to meet her requirements. This ensures she earns at least $180 while working no more than 13 total hours. The calculations consider her earnings from both jobs and time constraints.
Let's determine the possible values for the number of hours Madelyn must work clearing tables to meet her requirements. We know the following:
Madelyn earns $20 per hour lifeguarding.Madelyn earns $12 per hour clearing tables.She can work no more than 13 total hours.She must earn no less than $180.She worked 8 hours lifeguarding.First, calculate the earnings from lifeguarding:
[tex]\[8 \times \$20/hour = \$160\][/tex]Now, let x be the number of hours she works clearing tables. To meet the requirement of earning no less than $180, we set up the following inequality:
[tex]\[160 + 12x \geq 180\][/tex]Subtract 160 from both sides:
[tex]\[12x \geq 20\][/tex]Divide both sides by 12:
[tex]\[x \geq \frac{20}{12}\][/tex]Which simplifies to:
[tex]\[x \geq 1.67\][/tex]Since x must be a whole number, the minimum value for x is 2. Now, considering the total hours she can work (no more than 13), calculate the maximum value for x:
[tex]\[8 \text{ hours lifeguarding} + x \text{ clearing tables} \leq 13 \text{ hours}\][/tex]This gives us:
[tex]\[8 + x \leq 13\][/tex]Subtract 8 from both sides:
[tex]\[x \leq 5\][/tex]So, the possible values for the number of hours she could work clearing tables are:
2, 3, 4, or 51. Is Pi a rational number?
2. Is 7 squared a rational number?
3. Is 7.1234... rational?
The classification of the numbers into rational and irrational are:
1. Pi is irrational
2. 7 squared is irrational
3. 7.1234... is irrational
How to identify a rational number?1) π is a mathematical expression whose approximate value is 3.14159365…
The given value of π is expressed in decimal which is non-terminating and non-repeating. As the value is non-terminating it shows the nature of irrational numbers. Hence, π is not a rational number
2) 7 squared is not a perfect square and as such it will have non-terminating and non-repeating decimal and so it is irrational.
3) 7.1234... is an irrational number because it is non-terminating and non-repeating decimal.
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A lawyer has an annual income of $173,482 and will pay a 5.5% income tax rate. What is the amount of income tax in dollars and cents that the lawyer will have to pay?
Answer:
173,482-5.5=173,476.5
Answer:
$9,541.51
Step-by-step explanation:
$35+0.50()=52 what does this equal
Answer:
[tex](34)[/tex]
Step-by-step explanation:
We are looking for what number times .50 makes the equation true.
So, just do backwards equation:
[tex]52 - 35[/tex]
[tex]==> 17[/tex]
Thus, meaning that what multiplied by 0.50 is equal to 17?
[tex]0.50 * 34[tex]
[tex]==> 17[tex]
Put any Variable in between the parentheses, for example x.
Step-by-step explanation:
1. Move the Constant 35 to the other side of the problem, and flip it's sign.
0.5(×)=52-35
2. Subtract the numbers
0.5×=17
3. Divide both sides of the equation by 0.5
×=34
7.4x + 5) = 32
Help me please
Answer:
x = 3.65
Step-by-step explanation:
7.4x + 5 = 32
-5 -5
7.4x = 27
----- -----
7.4 7.4
x = 3.64864865
This rounds to 3.65
x = 3.65
What 21 over 40 divided by
I’m
Answer:
if you're asking what 21 divided by 40 is then it's 0.525
Step-by-step explanation:
How many solutions for x does the following equation have?
3(X + 8) - 1 = 3x + 4
A. 4
B. O
c.1
D. infinite
Answer:
B. No solutions.
Step-by-step explanation:
Let's try solving it:
3(x + 8) = 3x + 4
3x + 8 = 3x + 4.
There are no solutions because if we simplify we get an absurd result. Subtract 3x from both sides of the equation:
3x - 3x + 8 = 3x - 3x + 4
8 = 4.
There are no solutions for x in this equation.
Explanation:To solve this equation, we need to combine like terms and isolate the variable. Here are the steps:
Expand the brackets: 3(x + 8) - 1 = 3x + 4 becomes 3x + 24 - 1 = 3x + 4.Combine like terms: 3x + 24 - 1 = 3x + 4 becomes 3x + 23 = 3x + 4.Isolate the variable: Subtract 3x from both sides to get 23 = 4.Since 23 does not equal 4, these two sides are not equal. Therefore, there are no solutions for x in this equation.
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40 seconds to 3 minutes | 3 dollars to 65 cents
Ratios simplified
Answer:
2 : 9, 60 : 13Step-by-step explanation:
We know:
1min = 60s → 3min = (3)(60s) = 180s
40s : 3min = 40s : 180s = (40/20) : (180/20) = 2 : 9
$1 = ¢100 → $3 = (3)(¢100) = ¢300
$3 : ¢65 = ¢300 : ¢65 = (300/5) : (65/5) = 60 : 13
How do you simplify 5 (3t) - 7 (2t)
Answer:
3t-2
Step-by-step explanation:
Multiply the terms 3t and 2t. You should get 5t.Subtract 7 from 5; you should get -2.Now, your equation is 3t-2, you're done!What is a reasonable height for a doorway? NEEDS TO BE ANSWERED ASAP
A. 2 cm
B. 2 m
C. 2 mm
D. 2 km
Answer:
B. 2 m
Step-by-step explanation:
cm are centimeters and mm means millimeters and these a both smaller than an inch, and km kilometers is a distance like miles. Whilst m stands for meters.
How can 4.17 be written as a whole number with a fraction?
Final answer:
4.17 can be written as 4 17/100.
Explanation:
The number 4.17 can be written as a whole number with a fraction by separating it into the whole number part and the fractional part.
To write 4.17 as a whole number with a fraction, we need to separate the whole number part and the fractional part. The whole number part is 4, and the fractional part is 0.17. Since 0.17 is already expressed as a decimal, we can convert it to a fraction by considering the place value of each digit. The 7 is in the hundredths place, so it can be expressed as a fraction with the denominator 100.Thus, 4.17 can be written as 4 17/100.
What is 18/27 simplify?
Answer:
The answer is 2/3 okay? Pls thx me!
Paulo ran a marathon in about 1.56 × 10^4 s. A) Write Paulo's time in standard notation. B) Miguel ran a marathon in 4 h and 16 min. Who ran the race in the shorter amount of time? Show your work. (Question 2) Solve each given equation and show your work. Tell whether each equation has one solution, an Infinite number of solutions, or no solution. Explain your answers. A) 2x+4(x-1)=2+4x , (B) 25-x=15-(3x+10) , (C) 4x=2x+2x+5(x-x). (I posted a picture of question 3).
Paulo's time in standard notation is 15,600 seconds. Miguel ran the marathon in a shorter time of 15,360 seconds. For the given equations, A) and B) each have one solution (x=3 and x=10, respectively), while C) has an infinite number of solutions.
Explanation:To convert Paulo's time from scientific to standard notation, we multiply 1.56 by 10 to the power of 4. This equals 15,600 seconds. Next, we need to convert Miguel's time to seconds to directly compare the two durations. Miguel ran for 4 hours and 16 minutes, which is equal to (4 × 3600) + (16 × 60) = 14,400 + 960 = 15,360 seconds. Therefore, Miguel ran the race in a shorter amount of time by 240 seconds.
For question 2, we solve the following equations:
For equation A) 2x + 4(x - 1) = 2 + 4x, after simplifying we get 2x + 4x - 4 = 2 + 4x. The 4x terms cancel out and we are left with 2x - 4 = 2. Solving for x gives x = 3. This equation has one solution.
For equation B) 25 - x = 15 - (3x + 10), simplifying gives 25 - x = 5 - 3x. Solving for x yields x = 10, so this equation also has one solution.
For equation C) 4x = 2x + 2x + 5(x - x), simplifying results in 4x = 4x, which is true for all values of x. Therefore, this equation has an infinite number of solutions.
As question 3 involves an image that we cannot see here, this part of the student's question has been left unanswered.
Solve for y.
-38 = 7v+17 – 12v
Answer:
v = 11Step-by-step explanation:
[tex]-38=7v+17-12v\qquad\text{subtract 17 from both sides}\\\\-38-17=7v+17-17-12v\qquad\text{combine like terms}\\\\-55=-5v\qquad\text{divide both sides by (-5)}\\\\\dfrac{-55}{-5}=\dfrac{-5v}{-5}\\\\11=v\to v=11[/tex]
Find the greatest comman factor of 15 and 20
Answer:
GCF(15,20) = 5
Step-by-step explanation:
Prime Factorization of 15
Prime factors of 15 are 3, 5. Prime factorization of 15 in exponential form is:
15 = 31 × 51
Prime Factorization of 20
Prime factors of 20 are 2, 5. Prime factorization of 20 in exponential form is:
20 = 22 × 51
Factors of 15
List of positive integer factors of 15 that divides 15 without a remainder.
1, 3, 5
Factors of 20
List of positive integer factors of 20 that divides 15 without a remainder.
1, 2, 4, 5, 10
Greatest Common Factor
We found the factors and prime factorization of 15 and 20. The biggest common factor number is the GCF number.
So the greatest common factor 15 and 20 is 5.
How do you solve -4.46•11
Answer:
Step-by-step explanation:
(−4.46)(11)=−49.06
Dave is driving to Gilmore to visit his friend. If he wants to stop for lunch when he is about halfway there, in which town should he plan to stop?
Answer:
Dave should stop at Springfield.
Step-by-step explanation:
As shown, Gilmore is 26 miles away.
And Dave is driving to Gilmore but he wants to stop for lunch when he is about halfway there.
That means he wants to stop around [tex]\frac{26}{2}=13[/tex] miles.
And Springfield is 15 miles away that is nearest to 13 miles.
Hence, Dave should stop at Springfield.
Evaluate ab for a = -2 3/4 and b= - 4/6
Answer:
1 5/6
Step-by-step explanation:
ab = (-2 3/4) * (-4/6)
= ( -11/4) * ( -4/6)
= (11 * 4) / (4 * 6 )
= 11/6
= 1 5/6
How do i explain 5×23×2
Answer:
Step-by-step explanation:
Jsjxjxkd jfjfjfel
Jabari is thinking of three numbers. The greatest number is twice as large as the least number. The middle number is three more than the least number. The sum of the three numbers is
75
. Find the numbers.
Answer:
18,21,36
Step-by-step explanation:
You can use Algebra to solve it x+x+3+2x=75 or 4x+3=75 will give you the answer 1818 then plus 3 is 21so 18 plus 21 is 39Then the greatest number is 18x2=3639+36=75IIIIIII NNNNNNEEEDDDDD AAAANNNNSSSWWEERR NNNNOOOOOWWWW plz
James wants to carpet the room shown in the diagram. If he uses 12 ft wide carpet strips, how many linear feet will he need to buy?
A) 11
B) 12
C) 20
D) 60
The area of the room = (40 x 24) - (20 x 12)
Area = 960 - 240 = 720 square feet
Divide square feet by width of a strip:
720 / 12 = 60 linear feet.
The answer is D.
Answer : The correct option is, (D) 60
Step-by-step explanation :
First we have to calculate the area of room.
Area of room = Area of big rectangle + Area of small rectangle
Area of rectangle = Length × Width
Area of room = (40 × 12) + (20 × 12)
Area of room = 720 square feet
Now we have to calculate the number of linear feet will he need to buy.
Number of linear feet = [tex]\frac{\text{Area of room}}{\text{Width of carpet strips}}[/tex]
Number of linear feet = [tex]\frac{720}{12}=60[/tex]
Thus, the number of linear feet will he need to buy is, 60
A nurse mixes 60cc of a 50% saline solution with a 30% saline solution to produce a 35% saline solution. How much of the 30% solution should he use?
Final answer:
To create a 35% saline solution by mixing a 50% and a 30% solution, the nurse needs to use 6000cc of the 30% solution.
Explanation:
The question asks how much of a 30% saline solution a nurse needs to mix with 60cc of a 50% saline solution to achieve a final solution concentration of 35%. To solve this problem, let's denote the volume of the 30% solution needed as x cc. Using the concept of weighted averages for concentrations, we can set up the following equation:
(60cc × 50%) + (x cc × 30%) = (60cc + x cc) × 35%
Solving this equation, we get:
3000 + 0.3x = 0.35(60 + x)
3000 + 0.3x = 21 + 0.35x
Subtracting 0.3x from both sides:
3000 = 21 + 0.05x
Subtracting 21 from both sides and dividing by 0.05:
x = 6000 cc
Therefore, the nurse should use 6000cc of the 30% saline solution to achieve the desired concentration.
I need help simplifying this
Answer:
x^(1/12).
Step-by-step explanation:
By the laws of indices:
(x ^ 1/2)^1/6)
= x ^(1/2*1/6)
= x^(1/12).
Eight years from now , Bianca will be 50% older than she is now . How old is Bianca
Answer:
16
Step-by-step explanation:
because eight is 50% of 16
Answer: She will be 16
Step-by-step explanation:
Emma's final grade in her math class is the average (mean) of her 5 chapter tests she took throughout the year. If she received a 92%, 85%, 78%, 97%, and 88% on the five tests, what is her final grade?
Answer:
Step-by-step explanation:
The mean (or average) of a set of numbers can be found with the following formula:
[tex]Mean = \frac{A_{1} + A_{2} + ... + A_{N}}{N}[/tex]
For this problem, we have five numbers, so we add them together and divide by 5:
[tex]Mean = \frac{92 + 85 + 78 + 97 + 88}{5}[/tex]
[tex]Mean = \frac{440}{5}[/tex]
[tex]Mean = 88[/tex]
Answer:
88%
Step-by-step explanation:
Emma took tests of her 5 chapters throughout the year.
She received the score on the five tests
92%, 85%, 78%, 97% and 88%
We have to calculate the average (mean) of her final grade.
average = [tex]\frac{\text{addition of all grades}}{\text{total number of tests}}[/tex]
= [tex]\frac{92+85+78+97+88}{5}[/tex]
= [tex]\frac{440}{5}[/tex]
= 88%
Her final grade would be 88%.
If m∠EBD = 36° and m∠DBC = 108° find m∠EBC
Check the picture below.
The measure of m∠EBC if m∠EBD = 36° and m∠DBC = 108° is 144degrees
The point where two lines intersect is known as the angle.
From the diagram shown:
m∠EBC = m∠EBD + m∠DBC
Given the following:
m∠EBD = 36degrees
m∠DBC = 108degrees
Substitute the given values into the expression as shown:
m∠EBC = 36 + 108
m∠EBC = 144degrees
Hence the measure of m∠EBC is 144degrees
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3/10 + 1/4 in simplest form
Answer:
0.55 or 55/100 or 11/20
Step-by-step explanation:
Hey there!
3/10 + 1/4
≈ 6/20 + 5/20
= 6 + 5 / 20 - 0
= 11 / 20
Thus, your answer is: 11/20
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Question is provided in the image attached.
25 points!
Hey!
-------------------------------
Find the zero term:
Plug in 0 for n.
a = 8 + 3(0 - 1)
a = 8 + 3(-1)
a = 8 + (-3)
a = 5
Answer: 5
-------------------------------
Find the first term:
Plug in 1 for n.
a = 8 + 3(1 - 1)
a = 8 + 3(0)
a = 8 + 0
a = 8
Answer: 8
-------------------------------
Find the 40th term:
Plug in 40 for n.
a = 8 + 3(40 - 1)
a = 8 + 3(39)
a = 8 + 117
a = 125
Answer: 125
-------------------------------
Hope This Helped! Good Luck!
Rob purchased a rug for his apartment the rug is 72 inches by 96 inches . Calculate the area of the rug in square inches
Answer:
Area of the rug will be 6912 square inches.
Step-by-step explanation:
Rob has purchased a rug having measurement 72 inches by 98 inches for his apartment.
Since the rug will be in the shape of a rectangle, area will be represented by the formula,
Area = Length × width
= 72 × 96
= 6912 square inches.
Therefore, area of the rug will be 6912 square inches.
To calculate the area of Rob's rug, multiply the length of 96 inches by the width of 72 inches, resulting in an area of 6,912 square inches. Thus, the area of the rug is 6,912 square inches.
To find the area of Rob's rug, you need to multiply the length and the width of the rug.
Length = 96 inchesWidth = 72 inchesThe formula for area is:
Area = Length × Width
Using the given dimensions:
Area = 96 inches × 72 inches = 6,912 square inches
Therefore, the area of the rug is 6,912 square inches.
i need the answers for 11-13 please and thank you is you can only do one of them that’s okay with me
Answer:
Step-by-step explanation:
11. I can't see the full problem statement, so I'm unable to answer the question.
12. Answer below:
"one half" = [tex]\frac{1}{2}[/tex]
"negative five eighths" = [tex]\frac{-5}{8}[/tex]
To evaluate the expression, you multiply the two numbers together:
[tex]\frac{1}{2} * \frac{-5}{8} = \frac{1 * -5}{2 * 8} = \frac{-5}{16}[/tex]
13. Answer below:
"one third" = [tex]\frac{1}{3}[/tex]
"eleven sixteenths" = [tex]\frac{11}{16}[/tex]
To evaluate the expression, you multiply the two numbers together
[tex]\frac{1}{3} * \frac{11}{16} = \frac{1 * 11}{3 * 16} = \frac{11}{48}[/tex]
Gabby’s goal is to save more than $400. She saves $20 per week plus $50 initially. Let we b the number of week.
1. Write an inequality that represents this situation.
2. What is the least number of weeks she must have?
Answer: 17
Step-by-step explanation:
Gabby's savings over 'b' weeks can be written as an inequality 50 + 20b > 400. Simplifying this, we find that Gabby has to save up for at least 18 weeks to save more than $400.
Explanation:Gabby's savings can be represented as 50 + 20b, with 'b' being the number of weeks. For her to save more than $400, we can write this inequality 50 + 20b > 400. Subtract 50 from both sides to simplify the inequality and we get 20b > 350. To find the least number of weeks, divide both sides by 20 to solve for b and we get b > 17.5. However, since 'b' must be a whole number (because you can't have half a week), the least number of weeks Gabby must save is 18 weeks.
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