The solution explains how to find the number of bikes and tricycles in a garage based on the total number of wheels and the given combination.
Explanation:The question: A garage contains a combination of 20 bikes and tricycles. There are a total of 44 wheels.
Step-by-step solution:
Let's denote the number of bikes as B and the number of tricycles as T.
Each bike has 2 wheels, so the total number of wheels contributed by the bikes is 2B.
Each tricycle has 3 wheels, so the total number of wheels contributed by the tricycles is 3T.
Given that the total number of wheels is 44, we can form the equation: 2B + 3T = 44.
Since there are 20 bikes and tricycles in total, we have the equation: B + T = 20.
Solving the system of equations, we find that there are 12 bikes and 8 tricycles in the garage.
The measure of angle x is 25 more than 4 times the measure of its complement. find the measure of x. x= degrees
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Find the measure of “rst”
Answer: it is 110 bcs each section in 10° and there are 11 sections
A knife is 3 times the cost of the spoon 9 spoons and 12 knives costs £82.80 work out the cost of 1 knife
The cost of spoon is £1.84 and therefore the cost of one knife is £5.52.
Given :
A knife is 3 times the cost of the spoon.9 spoons and 12 knives costs £82.80.Solution :
This question is solve by creating a linear equation and linear equations are nothing but yet another subset of "equations". Linear calculations that requires more than one variable can be done with the help of linear equations.The standard form of a linear equation in one variable is ax + b = 0.Now let x be the cost of spoon. Than the cost knife is 3x. It is given that 9 spoons and 12 knives costs £82.80.
[tex]9x + 12\times(3x)= 82.80[/tex]
[tex]9x + 36x = 82.80[/tex]
[tex]45x =82.80[/tex]
[tex]x = 1.84[/tex]
Therefore the cost of 1 knife = [tex]1.84\times 3 = 5.52[/tex].
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Kana earns a $25,000 salary in the first year of her career. Each year, she gets a 4% raise. How much does Kana earn in the first 10 year of her career? (Round the final answer to the nearest dollar)
Eighty percent of the dogs have completed obedience classes. How many of the dogs have completed obedience classes? Five dogs of different breeds 4 dogs 3 dogs 2 dogs 1 dog
The table shows the percentage of students in each of three grade levels who list soccer as their favorite sport. Soccer Sophomores (35%) 50%
Juniors (33%) 45%
Seniors (32%) 30%
Total (100%) (0.5)(0.35) + (0.45)(0.33) + (0.32)(0.3) = 0.4195 or about 42%
Find the probability that the student is a junior, given that soccer is the favorite sport listed.
P(junior | soccer) = ???%
The probability that the student is a junior, given that soccer is the favorite sport listed is 0.354.
How to calculate the probability?The percentage of student on Junior level who like soccer will be:
= 33% × 45%
= 0.1485
The total percentage of students who like soccer is 42%. Therefore, probability that the student is a junior, given that soccer is the favorite sport listed will be:
= 0.1485/0.42
= 0.354
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Which properties of equality justify steps b and d?
1. Multiplication Property of Equality; Subtraction Property of Equality
2. Subtraction Property of Equality; Division Property of Equality
3. Subtraction Property of Equality; Multiplication Property of Equality
4. Subtraction Property of Equality; Subtraction Property of Equality
The properties that justify steps b and d, is 1. Multiplication Property of Equality; Subtraction Property of Equality.
Understanding these properties is crucial in solving equations properly.
Key Properties of Equality:
Multiplication Property of Equality: This property states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex], then [tex]a \times c = b \times c[/tex].
Subtraction Property of Equality: This property indicates that if you subtract the same number from both sides of an equation, the two sides will also remain equal.
Example: If [tex]a = b[/tex], then (a - c = b - c.
Division Property of Equality: Similar to multiplication, this property states that if you divide both sides of an equation by the same non-zero number, the two sides remain equal.
Example: If [tex]a = b[/tex] and [tex]c \neq 0[/tex], then [tex]\frac{a}{c} = \frac{b}{c}[/tex].
Justification Steps b and d:
Given the context, let's assume step b involves subtracting a term from both sides of an equation, and step d involves multiplying both sides by a number.
For step b (subtracting x):
This step is justified by the Subtraction Property of Equality because the same amount [tex]x[/tex] is subtracted from both sides, which keeps the equality balanced.
For step d (multiplying by a number):
This step is justified by the Multiplication Property of Equality as you are multiplying both sides of the equation by the same non-zero number, thus preserving the equality.
What is the probability that a point chosen at random in the rectangle is also in the blue triangle
Answer:
The probability that a point chosen at random in the rectangle is also in the blue triangle is:
1/2
Step-by-step explanation:
We are given a figure
We have to find the probability that a point chosen at random in the rectangle is also in the blue triangle.
Area of rectangle= 4×5 sq. in.
= 20 sq. in.
The area of blue triangle=[tex]\dfrac{1}{2}\times 4\times 5[/tex]
= 10 sq. in.
P(that a point chosen at random in the rectangle is also in the blue triangle)
= area of blue triangle/whole area of the rectangle
= 10/20
= 1/2
Answer: the answer is 1/2
Step-by-step explanation:
15p for an answer please
Simone is buying 10 bracelets for her friends. Each bracelet costs $8. Simone is also buying a necklace for her mother for $18. She believes that her total will be $98. Which expression could be used to estimate the reasonableness of Simone’s total? 8 × $8 + $10 8 × $8 + $18 10 × $8 + $20 10 × $10 + $10
How do I solve #21???? Please don't just give me the answer.... tell me how u got it... thanks!
z varies jointly with x and y. when x=2 and y=3, z=60. what is the value of z when x=4 and y=9?
A. 360
B. 60
C. 90
D. 40,
Select all of the potential solution(s) of the equation 2log5x=log54.
Given :[tex] 2log_{5} x^{2} =log_{5} 2^{2} [/tex]
To solve for x we use the logarithm rule for powers.
The log rule for powers states:
[tex] mlog_{a}n =log_{a} n^{m} [/tex]
We apply this rule to the left side of the equation.
[tex] log_{5} x^{2} =log_{5} 4
Both sides have log with same base so it can be eliminated.
Eliminating log from both sides we have:
[tex] x^{2} =4
To solve for x we take root of both sides
x=2,-2.
What is the domain of the given function? {(3, –2), (6, 1), (–1, 4), (5, 9), (–4, 0)}
{x | x = –4, –1, 3, 5, 6} {y | y = –2, 0, 1, 4, 9} {x | x = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9} {y | y = –4, –2, –1, 0, 1, 3, 4, 5, 6, 9}
What is the measure of
A. Cannot be determined
B. 74
C. 16
D. 32
This is embarrassing.. went to a Hobby Lobby job interview.. and flunked the math test.. ack! this involved percentages..how do you get 66% off of a total, and like tax % 7.5 we are not allowed to use a calculator
To get a percentage off of a total without a calculator, multiply the total by the percentage as a decimal. To calculate the total amount including tax, multiply the total by the tax percentage as a decimal and then add the result to the total.
Explanation:To calculate a percentage off a total without using a calculator, you can multiply the total by the percentage as a decimal. For example, to find 66% off of a total, multiply the total by 0.66. To calculate the total amount including tax, you can add the tax amount to the original total. For a 7.5% tax, multiply the total by 0.075 and then add the result to the total.
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Y= v^2/2a solve for v
Final answer:
To solve for v in the equation y = v²/2a, multiply both sides by 2a and then take the square root of both sides which gives v = √(2ay).
Explanation:
The question requires us to solve the equation y = v²/2a for the velocity v. To isolate v, we multiply both sides of the equation by 2a, then take the square root of both sides.
Multiply both sides of the equation by 2a: 2ay = v²Take the square root of both sides to solve for v: v = √(2ay)This mathematical process makes v the subject of the equation based on the given formula from kinematics. It's important to note that v will have two values, one positive and one negative, since taking the square root of a number yields both a positive and negative result.
if 7(t-4)-2t=4(t-3), what is the value of t?
The volumes of two similar solids are 53cm³ and 1113cm³. Which is the ratio of the corresponding sides?
A. 7
B. 21
C. √21
D. ³√21
Find the equation, f(x) = a(x-h)2 + k, for a parabola that passes through the point (2,4) and has the origin as its vertex. what is the standard form of the equation
Soybean meal is 14% protein; cornmeal is 7% protein. How many pounds of each should be mixed together in order to get 280lb mixture that is 8% protein?
How many pounds of the cornmeal should be in mixture?
How many pounds of the soybean meal should be in mixture? 50 POINTS!!!!
Three brothers have ages that are consecutive even integers. the product of the first and third boys' ages is 20 more than wice the second boy's age. find the age of each of the three boys.
Find the average rate of change of the function over the given interval. f(x) = 3x − 2; [0, 5]
The average rate of change of the function over the given interval is 3.
Explanation:To find the average rate of change of the function over the given interval, we need to calculate the change in the function values and divide it by the change in the input values.
Step 1: Calculate the function values for the two endpoints of the interval.
f(0) = 3(0) - 2 = -2
f(5) = 3(5) - 2 = 13
Step 2: Calculate the change in the function values.
Change in function values = f(5) - f(0) = 13 - (-2) = 15
Step 3: Calculate the change in the input values.
Change in input values = 5 - 0 = 5
Step 4: Divide the change in function values by the change in input values.
Average rate of change = (Change in function values) / (Change in input values) = 15 / 5 = 3
I need help ASAP. I don't understand how to solve this
3. Your fixed expenses are $1,500.45/month. Your emergency fund has 4 month’s worth of coverage. You invest half in a savings account with an interest rate of 3.15% APR and the other half in a 45 day CD with an interest rate of 4.65% APR. How much is your total interest in 45 days?
4. If you had invested only 1 month’s worth of the emergency fund in the saving account at a 3.15% APR and the remainder in the 45 day CD at a 4.65% APR, what is the difference in the interest earned in 45 days when compared with question #3?
The total interest earned in 45 days when the emergency fund is evenly split between a savings account and a CD is approximately $29.17. If 1 month's worth of emergency funds were in the savings account and the rest in a CD, the total interest would be approximately $38.05. The difference between the two scenarios is approximately $8.88.
Calculating Interest for Emergency Funds in Savings and CDs
To answer the student's question about the interest earned in 45 days on the emergency fund invested half in a savings account and half in a 45-day CD, as well as the comparison with an alternative investment scenario, we need to perform several calculations using the given interest rates and time periods.
Answer to Question 3
Firstly, the student's fixed expenses are $1,500.45/month, so for a 4-month emergency fund coverage, the total amount saved would be $1,500.45 x 4 = $6,001.80.
Half of this amount goes into the savings account and the other half into the CD, so each gets $3,000.90.
The interest in the savings account with an APR of 3.15% for 45 days (1.5 months) would be calculated using the formula for simple interest: Interest = Principal x Rate x Time.
So the interest earned on the savings account would be: $3,000.90 x (3.15% per year / 12 months) x 1.5 months ≈ $11.85.
The interest in the 45-day CD with an APR of 4.65% would be calculated similarly: $3,000.90 x (4.65% per year / 12 months) x 1.5 months ≈ $17.32.
Therefore, the total interest earned in 45 days would be approximately $11.85 + $17.32 = $29.17.
Answer to Question 4
If only 1 month's worth of emergency fund ($1,500.45) was invested in the savings account and the remainder in the CD, the interest from the savings account would not change, but the interest from the CD would, as it would be calculated on a larger principal of $4,501.35.
The new interest for the CD investment would be $4,501.35 x (4.65% per year / 12 months) x 1.5 months ≈ $26.20.
So the new total interest would be $11.85 (from savings) + $26.20 (from CD) = $38.05.
The difference in interest between the two scenarios would be $38.05 - $29.17 = $8.88.
o valor da expressão a=1,67 . 10 + 3,95 . 10
Rosen 15 how many solutions are there to the equation x1 x2 x3 x4 x5
Please help and show all work. 20 points.
The owners want to hire a contractor to build a porch along side the parlor. The parlor is rectangular with width Of 32 feet and length of 50 feet. The porch will have the same width that on each side of the house. See design plans.
The width of the porch will be 32 feet, the same as the parlor. However, to calculate the amount of building materials needed, additional specifics are required such as the porch's length, location of posts, and number of boards.
Explanation:To answer the question related to designing a porch that matches the width of the parlor, we first understand that the parlor is of a rectangular shape with a width of 32 feet. Considering that the porch will have the same width, it means the porch will also have a width of 32 feet.
From this point, specifics such as the desired length of the porch, location of posts, number of boards or rails, and other related factors would come into play in the calculating of building materials needed for the construction. There may also be the need to consider factors like the ratio of width to length in the design, akin to the mathematical relation mentioned in the statement 'X = Y x 2 + 1'.
So, while we know the width of the porch because it matches the parlor, the exact amount of materials that will be required would depend on further specifics of the porch design, similar to the steps in a stoichiometry problem in chemistry where one calculates the amount of reactants or products in a chemical reaction based on known ratios.
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