To convert a fraction to a decimal, divide the numerator by the denominator. For example, 1/2 converted to a decimal is 0.5.
Explanation:To convert a fraction to a decimal, you use the method defined by option B: Numerator divided by Denominator (Numerator / Denominator). This will give you the decimal equivalent of the fraction. For example, if you have the fraction 1/2, you divide the numerator (1) by the denominator (2) to get 0.5, which is the decimal equivalent of the fraction 1/2.
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characteristics of the graph of the absolute value parent function
Explain why rational number is either a terminating or repeating decimal?
Part A: If (72)x = 1, what is the value of x? Explain your answer.
Part B: If (70)x = 1, what are the possible values of x? Explain your answer.
The solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.
The equation is given below.
72x = 1
Simplify the equation, then the value of x will be
72x = 1
x = 1/72
The equation is given below.
70x = 1
Simplify the equation, then the value of x will be
70x = 1
x = 1/70
Then the solution of the equation 72x = 1 is 1/72 and 70x = 1 is 1/70.
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What is the simplest form of the expression 6x(x − 4) − 16x2 − (9x − 1)?
Suppose Lisa places $8500 in an account that pays 16% interest compounded each year. Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
(a) Find the amount in the account at the end of 1 year.
(b) Find the amount in the account at the end of 2 years.
At the end of 1 year, the amount in the account will be $9860. At the end of 2 years, the amount in the account will be $11437.6. This is calculated using the formula for compound interest.
Explanation:Lisa is placing $8500 in an account that pays 16% interest compounded annually. To solve for part (a) and part (b) which ask for the amount in the account at the end of 1 year and 2 years respectively, we use the formula for compound interest: A = P *(1 + r/n)^(nt).
Here, P is the principal amount ($8500), r is the annual interest rate (16% or 0.16 as decimal), n is the number of times that interest is compounded per unit t (n = 1 as it's compounded annually), and t is the time the money is invested for.
For (a), t = 1 year. Inserting these values into the formula, we get:
A = $8500 * (1 + 0.16/1)^(1*1) = $8500 * 1.16 = $9860.
Therefore, at the end of 1 year, the amount in the account will be $9860.
For (b), t = 2 years. Using the same formula, we get:
A = $8500 * (1 + 0.16/1)^(1*2) = $8500 * 1.16^2 = $11437.6.
Therefore, at the end of 2 years, the amount in the account will be $11437.6.
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It says to find each product
A regulation soccer goal net is 24 ft wide by 8 ft high. A soccer net for children is 6 ft wide. If the manufacturer wishes to keep the children's soccer net to scale, how tall should the children's net be? What is the scale factor? (round answer to two decimal places)
To maintain the scale of a children's soccer net to that of a regulation net, the height should be 2 feet, given that the child-size net is 6 feet wide. The scale factor used is 0.25.
Explanation:The question asks us to find the scaled dimensions for a children's soccer net based on the dimensions of a regulation soccer goal net. The original dimensions are 24 ft in width and 8 ft in height. If a children's soccer net is 6 ft wide and we want to keep the same scale, we need to calculate the height of the net in proportion to the regulation net's dimensions.
Height Calculation:
The scale factor is the ratio of the width of the children's net to the width of the regulation net. To find the height of the children's net, we multiply the height of the regulation net by the scale factor:
Scale Factor = Width of Children's Net / Width of Regulation Net
Scale Factor = 6 ft / 24 ft = 0.25
Height of Children's Net = Scale Factor × Height of Regulation Net
Height of Children's Net = 0.25 × 8 ft = 2 ft
Therefore, to maintain the scale, the height of the children's soccer net should be 2 feet, and the scale factor is 0.25.
I dont understamd this problem please help------!
A work crew has a new pump and an old pump. The new pump can fill a tank in 5 hours, and the old pump can fill the same tank in 7 hours. Write and solve and equation for the time it will take both pumps to fill one tank of the pumps are used together.
Cd tower is shaped like a cylinder and holds CDs in a diameter of 4.7 inches . If the cd tower is 12 inches tall what is the volume in cubic inches. Use 3.14 for pi. Round your answer to the nearest hundredth
A street that is 351ft long is covered in snow. City workers are using a snowplow to clear the street. The snowplow has tires that are 3.5ft in diameter. How many times does a tire have to turn in traveling the length of the street?
common ratio of fraction in geometric sequence?
5/12,-1/6,1/15,-2/75,4/375
The common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
Explanation:A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a constant factor called the common ratio. To find the common ratio in a geometric sequence of fractions, we divide each term by the previous term. Let's calculate the common ratios for the given sequence:
Common ratio between 5/12 and -1/6 = (-1/6) / (5/12) = -1/6 * 12/5 = -2/5Common ratio between -1/6 and 1/15 = (1/15) / (-1/6) = 1/15 * (-6/1) = -2/5Common ratio between 1/15 and -2/75 = (-2/75) / (1/15) = -2/75 * 15/1 = -2/5Common ratio between -2/75 and 4/375 = (4/375) / (-2/75) = 4/375 * (-75/2) = -2/5As we can see, the common ratio between each pair of terms in the given geometric sequence of fractions is -2/5.
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Is 7.6 repeating greater or less than square root 55
Which of the following describes the graph of a linear function?
It is V shaped and passes through the origin.
Its y-values increase at a constant rate as its x-value increases.
It is a straight line in one portion and a curve in another portion.
Its y-values increase at a nonconstant rate as its x-value increases.
Answer:
Option B is the correct option.
Step-by-step explanation:
The Linear function is always in the form of y = mx + c
Where m defines the slope which is rate of change of y-values or change in y-values with the change in x-values.
Therefore, Option B is the correct option.
Which line has the following intercepts?
x intercept = (3/7, 0)
y intercept = (0, -1.2)
A) 7x+6y = 3
B) 7x-6y = 3
C) 7x+6y = (-3)
D) 7x-6y = (-3)
How to work with negative exponents
Final answer:
Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. When multiplying or dividing with negative exponents, add or subtract them accordingly. In scientific notation, divide the coefficients and subtract the exponents to divide numbers.
Explanation:
Working with negative exponents is an essential skill in mathematics, where a negative exponent indicates the inverse or reciprocal of the base raised to the corresponding positive exponent. For example, 2-1 equals 1/2, which means that we are finding the reciprocal of 2. In operations involving exponents, such as multiplication and division, we follow certain rules with negative exponents:
When multiplying numbers, add the exponents (negative exponents included).
When dividing numbers, subtract the exponents (again, include negative exponents).
To convert a negative exponent into a positive one, take the reciprocal of the base with the corresponding positive exponent.
Here's an example of division in scientific notation: 106 ÷ 103 = 10(6-3) = 103. If you need to divide two numbers using scientific notation, you divide the coefficients and subtract the exponents.
Remember, a number like 3-4 is equivalent to 1/34, or 1 divided by 3 multiplied by itself four times. In general, negative exponents flip the base to the denominator, signifying a division rather than multiplication.
3 litters were born last year and each litter had 7 puppies how many puppies were born last year
Write the relatioship between the values of the given digits
The 6s in 6,600
Leo spent the same amount of time working on each of 5 different weight machines and then spent 2/3 of an hour on the treadmill. If he spent a total of 1 3/4 hours at the gym, which shows the correct equation and solution for x, the number of hours Leo spent at each of the weight machines?
Let's break this down. We know that there are 5 weight machines, and Leo spent an equal amount of time on all of them. Since we don't know how long he spent on each, we'll use x. Our equation so far is 5x. Then, we know that he spent 2/3 hour on the treadmill, which we will just add to the 5x. So, now our equation is 5x + 2/3. Lastly, we know that the total time Leo spent at the gym is 1 3/4 hours, which we set the last equation equal to. Our final equation is 5x + 2/3 = 1 3/4. Then, all we have to do is solve for x. What we can do to make this easier is to change all of the fractions into numbers. After changing everything, here is our equation: 5x + 40 = 105. Then, we will subtract 40 from each side and divide both sides by 5. Therefore, Leo spent 13 minutes on each weight machine.
ANSWER:
A) 5x + 2/3 = 1 3/4 ; Leo spent 13 minutes at each machine
Hope this helps!! :)
If there's anything else that I can help you with, please let me know!
Final answer:
Solving for the time Leo spent on each weight machine involves setting up an equation based on the total gym time and subtracting the time spent on the treadmill, resulting in Leo spending about 13 minutes at each weight machine.
Explanation:
To solve for the amount of time Leo spent at each weight machine, we need to set up an equation based on the total time spent at the gym. First, we know that Leo spent 2/3 of an hour on the treadmill. With a total gym time of 1 3/4 hours (which is the same as 7/4 hours), we can subtract the treadmill time to find the time spent on the weight machines. Thus, the equation can be set up as follows:
5x + 2/3 = 7/4
To solve for x, the hours Leo spent at each weight machine, follow these steps:
Subtract 2/3 from both sides of the equation: 5x = 7/4 - 2/3
Find a common denominator for the fractions and subtract: 5x = 21/12 - 8/12
Simplify the right side: 5x = 13/12
Divide both sides by 5 to solve for x: x = 13/60 hours
This means Leo spent 13/60 hours, or about 13 minutes, at each of the 5 weight machines.
55 divided by 2044 i need help for my summer packets
Final answer:
To divide 55 by 2044, use long division. The quotient is 0.027.
Explanation:
To divide 55 by 2044, you can use long division. Here is the step-by-step process:
Start by dividing 55 by the first digit of 2044, which is 2. The quotient is 27 and the remainder is 1.Bring down the next digit of 2044, which is 0.Divide 10 by 2044. The quotient is 0 and the remainder is 10.Bring down the next digit of 2044, which is 4.Divide 104 by 2044. The quotient is 0 and the remainder is 104.Bring down the next digit of 2044, which is 4.Divide 1044 by 2044. The quotient is 0 and the remainder is 1044.At this point, you have reached the end of the division process. The final quotient is 0.027 and there is no remainder. Therefore, 55 divided by 2044 is approximately 0.027.
Triangle PQR is formed by the three squares A, B, and C:
Which statement best explains the relationship between the sides of triangle PQR?
(PQ)2 + (QR)2 = (PR)2, because 9 + 16 = 25
PQ + QR = PR, because 9 + 16 = 25
(PQ)2 + (QR)2 = (PR)2, because 52 + 32 = 42
PQ + QR = PR, because 52 + 32 = 42
Answer:
A.[tex]PR^2=PQ^2+QR^2[/tex]
Because [tex]25=9+16[/tex]
Step-by-step explanation:
We are given that
Area of square A=[tex]9[/tex] square units
Are of square B=[tex]16[/tex] square units
Area of square C=[tex]25[/tex] square units
We have to find the relationship between sides of triangle PQR.
Side of square=[tex]\sqrt{Area\;of\;square}[/tex]
Using the formula
Side of square A=[tex]\sqrt{9}[/tex]=3 units
Side of square B=[tex]\sqrt{16}=4[/tex] units
Side of square C=[tex]\sqrt{25}=5[/tex] units
Pythagoras theorem
[tex](hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2[/tex]
Using Pythagoras theorem
[tex]PR^2=PQ^2+QR^2[/tex]
[tex]5^2=3^2+4^2[/tex]
[tex]25=9+16[/tex]
Option A is true
NEED HELP FAST!
13.
(08.06 LC)
Variable g is 8 more than variable w. Variable g is also 2 less than w. Which pair of equations best models the relationship between g and w? (1 point)
g= 8w
g = w + 2
w = g + 8
w = g – 2
w = 8g
w = g + 2
g= w + 8
g = w – 2
The two equations are:
g= w +8
g= w +2
^_^
Plz someone help me
Greg bought 2 boxes of balloons he used half of them to decorate his yard he used 40 to decorate his porch he used the rest inside his house how many balloons did he use
Angle DAB measures ( 2x4 )°− and angle BCD measures 47°. Find x.
How many 2/3- cup servings are in 6 cups of yogurt
Answer: The required number of servings in 6 cups of yogurt is 9.
Step-by-step explanation: We are given to find the number of [tex]\dfrac{2}{3}[/tex] cup servings in 6 cups of yogurt.
We will be using the UNITARY method to solve the given problem.
We have
Number of servings in [tex]\dfrac{2}{3}[/tex] cups of yogurt = 1.
So, the number of servings in 1 cup of yogurt will be
[tex]\dfrac{1}{\frac{2}{3}}=\dfrac{3}{2}.[/tex]
Therefore, the number of servings in 6 cups of yogurt is given by
[tex]\dfrac{3}{2}\times6=9.[/tex]
Thus, the required number of servings in 6 cups of yogurt is 9.
Jacob wants to use an elevator to carry identical packages having the same weight. Each package weighs 3 pounds and Jacob weighs 99 pounds. If the elevator can carry a maximum of 300 pounds at a time, which inequality shows the maximum number of packages, n, that Jacob can carry with himself in the elevator if he is the only passenger?
Answer:
The required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
Step-by-step explanation:
Consider the provided information.
Each package weighs 3 pounds and Jacob weighs 99 pounds.
let n is the maximum number of package that Jacob can carry with himself in the elevator.
Thus, the total weight of Jacob while having n packages on the elevator is:
[tex]3n+99[/tex]
The elevator can carry a maximum of 300 pounds at a time, therefore.
[tex]3n+99\leq 300[/tex]
Now, subtract 99 from both sides and divide the obtained inequality with 3.
[tex]3n+99-99\leq 300-99[/tex]
[tex]3n\leq 201[/tex]
[tex]\frac{3n}{3}\leq \frac{201}{3}[/tex]
[tex]n\leq 67[/tex]
Thus, the Jacob can carry maximum 67 packages.
Hence, the required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].
A skydiver is falling at about q42 feet per second.How many feet per minute is she falling?
compare the values of the underlined digets 6035 and 530 the digit is 3
is 113,724 divisible by 3,5,6,or9
Which line has an undefined slope? A y = 0 B y = 2 C x = y D x = 2
Line x =2 has undefined slope.
What is slope?" Slope is defined as the ratio of the difference in the increase of y-coordinates to the difference in the increase of x-coordinates."
Formula used
Equation of the line
y = mx + c
c = y-intercept
m = slope
m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
According to the question,
1. y = 0
Compare it with standard equation of the line
y = 0x + 0
slope = 0
It is not a correct answer.
2. y =2
Compare it with standard equation of the line
y = 0x + 2
slope = 0
It is not a correct answer.
3. x= y
Compare it with standard equation of the line
y = 1x + 0
slope = 1
It is not a correct answer.
4. x=2
It is vertical line , x value remain constant.
Therefore,
[tex]x_{1}=2\\x_{2}=2[/tex]
Slope = [tex]\frac{y_{2}-y_{1}}{2-2}[/tex]
= [tex]\frac{y_{2}-y_{1}}{0}[/tex]
Zero in the denominator therefore, undefined slope
Hence, line x =2 has undefined slope.
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Final answer:
The line with an undefined slope is D. x = 2, which is a vertical line with a constant x-value for all points on the line.
Explanation:
The question asks which line has an undefined slope. An undefined slope occurs when a line is vertical since slope is defined as the change in y over the change in x, and in a vertical line the change in x is zero. Looking at the options given, the equation representing a vertical line is D. x = 2. This line is vertical because it has the same x-value for all points on the line, meaning there is no change in x as you move along the line, thus creating an undefined slope.