a bag contains 2 red crayons, 4 blue crayons, and 1 green crayon. A crayon is selected, kept out of the bag, and then another crayon is selected. What is P( blue, then green)?
The probability of drawing a blue crayon first and then a green crayon is 2/21.
Explanation:To find the probability of drawing a blue crayon first and then a green crayon, we need to consider the total number of crayons and the number of blue and green crayons in the bag.
There are a total of 7 crayons in the bag (2 red + 4 blue + 1 green).
The probability of drawing a blue crayon first is 4/7 because there are 4 blue crayons out of the total 7 crayons.
After drawing a blue crayon, there are 6 crayons left in the bag (1 blue + 2 red + 1 green + 2 blue). The probability of drawing a green crayon second is 1/6 because there is only 1 green crayon left out of the 6 crayons.
Therefore, P(blue, then green) = (4/7) * (1/6) = 4/42 = 2/21.
The probability of selecting a blue crayon followed by a green crayon from the bag is 1/10.5.
Explanation:The probability of selecting a blue crayon and then a green crayon from a bag containing 2 red crayons, 4 blue crayons, and 1 green crayon is calculated by multiplying the probability of each individual event. The probability of drawing a blue crayon first is 4 divided by the total number of crayons, which is 7 (4/7). After drawing a blue crayon, it is kept out of the bag, reducing the total number of crayons to 6. The probability of then drawing a green crayon is 1 divided by the remaining total, which is 6 (1/6). Multiplying these probabilities together gives us the compound probability: (4/7) × (1/6), which equals 4/42 or 1/10.5 after simplification.
Charlie rented a moving truck. He paid a daily fee plus a per-mile fee to rent the truck. The equation below represents the daily amount Charlie paid for the truck if he drives it x miles.
This question pertains to creating a linear equation for calculating the cost of renting a truck based on a daily fee plus a per-mile fee, an application of algebra in real-world scenarios such as vehicle rentals.
Explanation:The question provided involves creating or understanding a linear equation that models the cost associated with renting a truck based on a daily fee and a per-mile fee. A similar concept is seen in the provided examples like Aaron's Word Processing Service, where the cost depends on the number of hours and includes a one-time charge.
The equation to calculate the total cost for Charlie's truck rental would take the form y = mx + b, where y represents the total cost, m is the per-mile fee, x is the number of miles driven, and b is the daily fee. This type of problem utilizes basic algebra to model real-world scenarios such as vehicle rentals, which is an important aspect of personal finance and decision-making skills.
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Tiara has $2,000 in her savings account. David has one-tenth as much as Tara in his savings account. How much does David have
A landscaper uses 1225 lb of soil to complete a project. The soil comes in bags that weigh 40 lb each.
How many bags of soil does the landscaper use to complete the project?
(A) 30
(B) 30 5/8
(C) 32 1/8
(D) 35 1/5
Answer: The correct option is (B) [tex]30\dfrac{5}{8}.[/tex]
Step-by-step explanation: Given that a landscaper uses 1225 lb of soil to complete a project and the soil comes in bags that weigh 40 lb each.
We are to find the number of bags of soil that the landscaper use to complete the project.
We will be using the UNITARY method to solve the given problem.
Number of bags with weight 40 lb = 1.
So, the number of bags with weight 1 lb is
[tex]\dfrac{1}{40}.[/tex]
Therefore, the number of bags with weight 1225 lb is given by
[tex]\dfrac{1225}{40}=\dfrac{245}{8}=30\dfrac{5}{8}.[/tex]
Thus, the required number of bags is [tex]30\dfrac{5}{8}.[/tex]
Option (B) is CORRECT.
2x + 3y = 5x - y complete the missing value in the solution to the equation
Answer:
The missing value is(0,0)
Step-by-step explanation:
The complete question is:
2x+3y=5x-y
Complete the missing value in the solution to the equation.
( ,0)
Solution:
We have given:
2x + 3y = 5x - y
Combine the like terms:
2x-5x= -y-3y
-3x = -4y
Both negative signs will be cancelled out by each other.
So we have,
3x = 4y
We have given y = 0
Then
3x = 4*0
3x= 0
Divide both sides by 3
3x/3 = 0/3
x = 0
y=0
Therefore missing value is(0,0)
Answer:
The missing value is 0.
Step-by-step explanation:
Given : Expression [tex]2x + 3y = 5x - y[/tex]
To find : Complete the missing value in the solution to the equation (_,0) ?
Solution :
Write the expression,
[tex]2x + 3y = 5x - y[/tex]
Take like terms together,
[tex]3y+y = 5x-2x[/tex]
[tex]4y=3x[/tex]
Now substitute y=0,
[tex]4(0)=3x[/tex]
[tex]3x=0[/tex]
[tex]x=0[/tex]
So, The required point is (0,0).
Therefore, the missing value is 0.
Determine if the rates $168 raised for washing 24 cars and $280 raised for washing 40 cars are equivalent. Explain your reasoning.
A moving company charges $840 plus$17 per hour. Another moving company charges$760 plus $22 per hour. How long is a job that costs the same no mater which company is used?
equation= 840+17x=760+22x
To find the length of the job that costs the same regardless of the moving company used, solve the equation 840 + 17x = 760 + 22x. The job would need to be 16 hours long.
Explanation:To determine the length of the job that costs the same regardless of the moving company used, we need to solve the equation 840 + 17x = 760 + 22x, where x represents the number of hours.
First, we subtract 760 from both sides: 840 + 17x - 760 = 760 + 22x - 760, which simplifies to 80 + 17x = 22x.
Next, we subtract 17x from both sides: 80 + 17x - 17x = 22x - 17x, resulting in 80 = 5x.
Finally, we divide both sides by 5 to solve for x: 80 ÷ 5 = 5x ÷ 5, giving us x = 16. Therefore, the job would need to be 16 hours long to cost the same regardless of the moving company used.
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what minus what equals 500
What are
the factor pairs for 60
The factor pairs are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10) of the number 60.
What is Number system?A number system is defined as a system of writing to express numbers.
To find the factor pairs of 60
we need to list all the possible pairs of two positive integers that can be multiplied to give 60.
1 x 60 = 60
2 x 30 = 60
3 x 20 = 60
4 x 15 = 60
5 x 12 = 60
6 x 10 = 60
Therefore, the factor pairs of 60 are (1, 60), (2, 30), (3, 20), (4, 15), (5, 12), and (6, 10).
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the product of 7 and p
Nu is designing a rectangular sandbox. The bottom is 16 square feet. Which dimensions require the least amount of material for the sides of the sandbox?
To minimize the amount of material needed for the sides of the sandbox, the sandbox should be square-shaped, with each side measuring 4 feet, resulting in a perimeter of 16 feet, which is the smallest perimeter for a 16-square-foot area.
The student is tasked with designing a rectangular sandbox such that the bottom has an area of 16 square feet and the dimensions of the sandbox require the least material for the sides. To achieve the least amount of material for the sides, we aim for a shape that has the smallest possible perimeter while maintaining the given area. This is achieved with a square-shaped sandbox.
Since the area is 16 square feet, we calculate the side length of the square by finding the square root of 16, which is 4 feet. Therefore, each side of the sandbox should be 4 feet long. This shape will have a perimeter of 16 feet (4 sides * 4 feet), which is the smallest perimeter possible for a rectangular shape with an area of 16 square feet.
In conclusion, the dimensions of the sandbox that will require the least amount of material for the sides are 4 feet by 4 feet.
What is the relationship between the 5s in the number 755,371
You've been hired to plan a New Year's Eve party at the Governor's Mansion. The Mansion Charges: $1, 250 plus $20 per person.
I. Write an equation that can be used to the determine the cost of the party. Define the variables.
II. What is the cost if there is 300 people attending the party?
III. Represent the previous answer in a graph. ( Count by intervals of 50)
IV. There are 750 people who attended the party. Daryl said the cost will be $16,500. Is he correct ? Explain why or why not. Prove your answer by showing your work and including detailed reasoning.
Kit bought a soft drink and a sandwich for $9.00. What was the price of each if the sandwich cost 3.5 times as much as the soft drink?
The required cost of the soft drink is given as $5.5 that Kit bought.
Given that,
Kit bought a soft drink and a sandwich for $9.00. What was the price of each if the sandwich cost 3.5 times as much as the soft drink is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Let the price of the soft drink be x,
total cost = 9
x + 3.5 = 9
x = 9 - 3.5
x = 5.5
Thus, the required cost of the soft drink is given as $5.5 that Kit bought.
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The cost of the soft drink is $2, and the cost of the sandwich is $7.
To solve the problem of determining the cost of both the soft drink and the sandwich that Kit bought for $9.00, we can set up an algebraic equation. If we let s represent the price of the soft drink, then the sandwich would cost 3.5 times as much, which can be represented as 3.5s. According to the information given, the total cost for both is $9.00, so our equation will be s + 3.5s = 9. Combining like terms, we have 4.5s = 9. To find the price of the soft drink (s), we divide both sides of the equation by 4.5, resulting in s = 2. Therefore, the soft drink costs $2, and the sandwich costs 3.5 times that, which means the sandwich costs $7.00.
what is 37493 decreased by 8,500
on Saturday 12 friends go ice skating altogether they pay $83.40 for admission they share the cost equally how much does each person pay
what is 1,864.29 rounded to the nearest one
olivia filled 6 baskets of strawberries. later she combined the fruit evenly into 3 larger boxes. if all 3 boxes sold for $42, how much did each box of strawberries cost?
The cost of each box of strawberries is $14.
What is division?Division is breaking a number up into an equal number of parts.
Given that, 3 boxes of strawberries sold for $42,
3 boxes = $42
1 box = $42/3 = $14
Hence, The cost of each box of strawberries is $14.
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Jakob is tiling a newly finished room.He estimates that he tiles about 9 square ft every 3/4 hour. About how many sq ft can he tile per hour
Can you translate a image however far you want it on a graph
What is the simplified form of this equation :
135(z^{0} )
The simplified from of expression; which is obtained by performing mathematical operations to the expression and convert it to its standard form. Hence, the simplified form of 135(z^{0} ) is 135.
What is simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression. Like, 5 + 2 is an expression whose simplified form can be obtained by doing the pending addition, which results in 7 as its simplified form. Simplification usually involves making the expression simple and easy to use later.
We need to find the simplified form of this equation :
135(z^{0} )
Since we know that any power of 0 is 1. So, z to the power of 0 is going to be one.
135(z^{0} ) = 135(1 )
135^1 = 135
The simplified from of expression; which is obtained by performing mathematical operations to the expression and convert it to its standard form. Hence, the simplified form of 135(z^{0} ) is 135.
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Thomas reads 2/9 of a book in Monday and 1/6 of it on Tuesday.He reads twice as many pages on Wednesday as on Tuesday.What fraction of the book is not read
The solution of the equation 2d - 6 = 5 is _____.
-1/2
1/2
5 1/2
1 1/2
Answer:
5 1/2
Step-by-step explanation:
the mass of a jar of sugar is 1.9 kg what is the total mass of 13 jars of sugar
J.D. opened a savings account with $425. After 2 years, the total interest he earned was $10.20. What was the annual interest rate?
The interest rate required to accumulate simple interest of $ 10.20 from a principal of $ 425.00 over 2 years is 1.2% per year.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given,
J.D. opened a savings account with $425
After 2 years, the total interest he earned was $10.20
We need to find the annual interest rate.
The rate of interest can be done by using below equation
r = 10.2 / ( 425 × 2 ) = 0.012
r = 0.012
convert r to the percentage by multiplying with 100
R = 0.012 × 100 = 1.2%year
Hence, the interest rate required to accumulate simple interest of $ 10.20 from a principal of $ 425.00 over 2 years is 1.2% per year.
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To calculate the annual interest rate, use the simple interest formula I = PRT, where I is the total interest earned ($10.20), P is the initial deposit ($425), and T is the time period in years (2). Solving for R gives us the annual interest rate, which in this case is 1.2%.
Explanation:The student is asking how to calculate the annual interest rate based on the total amount of interest earned over a specific period. In this question, J.D. earned a total interest of $10.20 over 2 years on an initial deposit of $425. To find the annual interest rate, we can use the formula for simple interest since compound interest is not mentioned.
To solve for the interest rate, we use the simple interest formula I = PRT, where I is the interest earned, P is the principal amount (initial deposit), R is the rate of interest per year, and T is the time in years. Based on the information provided:
Interest earned, I = $10.20Principal, P = $425Time, T = 2 yearsPlugging these values into the formula and solving for R, we get:
10.20 = 425 × R × 2
To isolate R, divide both sides by 850 (which is 425 × 2):
R = 10.20 ÷ 850
R = 0.012
The annual interest rate as a percentage is R × 100:
R × 100 = 0.012 × 100
R = 1.2%
Therefore, the annual interest rate was 1.2%.
54750 divided by 365
Which greater 9.28 or 9.3
A swimming pool holds 12,500 gallons of water at the start of the day. A valve at the bottom of the pool releases water into a cleaning tank at a constant rate of 20 gallons per hour. A hose is running water into the pool at a constant rate of 60 gallons per hour. On one day, the hose was running for 3 hours, and the valve was left open for 6 hours. How much water is in the pool at the end of the day?
The price of a pair of headphones is $39.99 before tax. Dalton bought the headphones for 30% off. He then paid 6% sales tax on the discounted price. Part A: How much did Dalton pay in sales tax? Show all work and steps in your solution. (5 points) Part B: What is the total amount that Dalton paid for the headphones? Show all work and steps in your solution. (5 points)
Answer
She paid 17.99 in sales tax
Step-by-step explanation:
A game room has a floor that is 400 feet by 90 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit:5 feet. What are the dimensions of the scale drawing? Enter your answer as length by width.
Answer:
80 units by 18 units
Step-by-step explanation:
Find the number of feet represented by 1 unit in the drawing.
1 unit ÷ 1
5 feet ÷ 1
=
1 unit
5 feet
1 unit in this model is about 5 feet in the actual room.
Find the width of the scale model represented by 90 feet in the actual room.
1 unit × 18
5 ft × 18
=
18 units
90 ft
The width of the scale model represented by 90 feet in the actual room is 18 units.
Find the length of the scale model represented by 400 feet in the actual room.
1 unit × 80
5 ft × 80
=
80 units
400 ft
The length of the scale model is 80 units.
The scale model is 80 units by 18 units.