3.24 repeating as a mixed number in simplest form
A repeating mixed number is a mixed fraction, which after converted to decimal; the numbers after the decimal point repeat without end.
3.23 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
Given that
[tex]Number = 3.24[/tex]
First, we represent as a fraction
[tex]Number = \frac{324}{100}[/tex]
To represent the number as a repeating mixed number, we simply subtract 1 from the numerator
[tex]Number = \frac{324}{100 - 1}[/tex]
[tex]Number = \frac{324}{99}[/tex]
Represent as a mixed number
[tex]Number = 3\frac{23}{99}[/tex]
Hence, 1.12 as a repeating mixed number is [tex]3\frac{23}{99}[/tex]
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True or false: outliers "inflate" standard deviation.
A meteor crater is 4100 feet in diameter. Approximate the distance around the crater. Use 3.14 for piπ
Two buses are traveling to a state park. One bus leaves the terminal at 4:00 p.m. and travels at 40 miles per hour. The second bus leaves the terminal at 5:00 p.m. and travels at 60 miles per hour.
How much time passes until the second bus catches up with the first bus?
40t = 60(t-1)
distribute the right side
40t = 60t-60
subtract 60t from each side
-20t =-60
divide both sides by -20
t = -60 / -20 = 3
3 hours
what is the quotient of 6/7 and 3/14
Andrew has 10 more goldfish than Todd. Together, they have 50. goldfish. How many goldfish does each boy have?
If the population density of ocotillo in a desert is 15 per square kilometer, how many plants would be expected in an area that is 5 km by 3 km?
In an area that is 5 km by 3 km, with an ocotillo population density of 15 plants per square kilometer, we would expect to find 225 ocotillo plants.
The student's question pertains to calculating the expected number of ocotillo plants in a given area based on the known population density. First, we need to find the total area of the region in question, which in this case is a desert area that measures 5 km by 3 km. We calculate the area by multiplying the length by the width: 5 km x 3 km = 15 km2.
Since the population density of ocotillo is given as 15 plants per square kilometer, we can find the total number of ocotillos by multiplying the density by the total area:
15 plants/km2 x 15 km2 = 225 plants.
Therefore, in an area that is 5 km by 3 km, we would expect to find 225 ocotillo plants.
Which expression results in a product that is rational?
(a)square root of 7 times square root of 10
(b)square root of 8 times square root of 10
(c) square root of 9 times square root of 10
(d)square root of 10 times square root of 10
Final answer:
The expression that results in a rational product is √10 times √10, as this simplifies to the rational number 10.
Explanation:
To find which expression results in a product that is a rational number, we need to identify which pair of square roots can be multiplied to produce a non-radical number.
Multiplication of square roots is analogous to the multiplication of exponents. When the same base is multiplied, the exponents are added. Utilizing this property, we know:
√7 × √10 = √(7 × 10) = √70 (which is irrational since 70 is not a perfect square).
√8 × √10 = √(8 × 10) = √80 (which is irrational since 80 is not a perfect square).
√9 × √10 = √(9 × 10) = √90 (which is irrational since 90 is not a perfect square).
√10 × √10 = √(10 × 10) = √100 = 10 (which is rational since 100 is a perfect square).
Therefore, the expression that results in a rational product is √10 × √10, which simplifies to 10.
an engineering technician makes $25 for the first 40 hours she works during a week $32 an hour for each hour over 40 hours which piecewise equation models her total weekly pay
A piecewise equation to model the total weekly pay for an engineering technician who earns different rates for hours within and beyond 40 hours is P(h) = {25h if h ≤ 40, 1000 + 32(h - 40) if h > 40}.
Explanation:The question asks for a piecewise equation to model the total weekly pay of an engineering technician who makes $25 per hour for the first 40 hours and $32 an hour for each hour over 40 hours. The piecewise function is made up of two parts:
When written as a piecewise function, it will look something like this:
P(h) =
\{
\begin{array}{ll}
25h & \text{if } h ≤ 40,\\
1000 + 32(h - 40) & \text{if } h > 40.
\end{array}
\}
How can ΔWXY be mapped to ΔMNQ?
Which number is Not a rational number?
A.-5 4/11
B. sqrt of 31
C. 7.608
D. 18.46...
Answer:
[tex]\sqrt{31}[/tex]
Step-by-step explanation:
A.[tex]-5 \frac{4}{11} =\frac{-59}{11}[/tex]
Since it in in p/q form so it is a rational number
B. [tex]\sqrt{31} =5.5677643.......[/tex]
Since it cannot be represented in the form of p/q . So, it is irrational number .
C. 7.608
[tex]\frac{7608}{1000}[/tex]
Since it can be represented in p/q form . So, it is rational number.
D. 18.46...
18.4666.. Since 6 is repeating in decimal place . So, 18.46.. can be written in p/q form .
Hence Option B sqrt of 31 is not a rational number .
Jose is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $108 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? Use m for the number of miles driven, and solve your inequality for m .
Final answer:
Jose should rent a truck from Company A if he plans to drive more than 55 miles, as it will charge less than Company B beyond this mileage.
Explanation:
To determine for what mileages Company A will charge less than Company B, we set up an inequality comparing the total cost for each company and solve for m (the number of miles driven).
The cost for Company A is a flat rate of $108, so it does not depend on mileage. The cost for Company B includes an initial fee of $75 plus $0.60 per mile. We set up the inequality as follows:
Company A \< Company B
$108 < $75 + $0.60m
$108 - $75 < $0.60m
$33 < $0.60m
$33 / $0.60 < m
55 < m
Therefore, Company A will charge less than Company B for any number of miles greater than 55. So, if Jose plans to drive more than 55 miles, he should choose Company A for a cheaper rate.
The line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1. Please don't respond if you can't explain how to get out of an impossible square root. Thanks
To evaluate the line integral, calculate the arclength element and substitute it into the integral. Expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.
Explanation:To evaluate the line integral of (2x+9z) ds where the curve is given by the parametric equations x=t, y=t^2, z=t^3 for t between 0 and 1, we need to find the arclength element ds and substitute it into the integral. The arclength element ds can be calculated using the formula ds = sqrt(dx^2 + dy^2 + dz^2). In this case, dx = dt, dy = 2t dt, and dz = 3t^2 dt. Substituting these values into the arclength element formula, we get ds = sqrt(dt^2 + 4t^2 dt^2 + 9t^4 dt^2) = sqrt(1 + 4t^2 + 9t^4) dt.
Substituting ds into the line integral, we get the integral of (2x+9z) * sqrt(1 + 4t^2 + 9t^4) dt. To evaluate this integral, you can expand the expression inside the square root, multiply it by (2x+9z), and integrate term by term.
However, it seems that there might be a typo in the original question regarding the curve parametrization. The curve given by x=t, y=t^2, z=t^3 is actually a parabolic curve, not a line. If you need further clarification or assistance, please let me know.
a ramp has a height of 3 foot and a base of 12 feet what is the angle of elevation
Write an equation relating the length of the legs of an isosceles triangle, x, to the length of the hypotenuse of the triangle, h. g
An equation regarding the length of the sides of an isosceles right triangle is required.
The required equation is [tex]2x^2=h^2[/tex]
The length of the legs of triangle which are equal in length is [tex]x[/tex]
The length of the hypotenuse is [tex]h[/tex]
From the Pythagoras theorem we have
[tex]x^2+x^2=h^2\\\Rightarrow 2x^2=h^2[/tex]
Hence, in the above equation the length of the legs and the hypotenuse lengths are related.
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If 6 chocolates cost $0.93, how much do 22 chocolates cost?
I would be $3.41 first you figure out how much one cost by dividing 0.93 by 6 then you multiply your answer by 22
Which symbol makes the following statement true? 413,115 431,511
a painter charges $35 per hour for labor plus 40$ for a ladder rental when he paints a house.the costomer provides the paint.total charge to paint a costomer hoise was 950. how many hours did the painter spend painting this house
Anna wants to call Holly. Holly is on vacation in Asia. It is a time difference of ten hours. Holly's time is always later than Anna's time. If it is 7:35 P.M. where Anna lives, then what time is it where Holly is?
This was everything that was on paper I hope i gave enough
information!
Phillip invested $6000 compounded continuously at 7.5% interest. How long will it take him to reach $10000
identify the number in the hundreth(1/100)position 15.386
rewrite 3/8 and 5/14 to have a common denominator
Travis wants to collect 20% more than Jessica. Robin wants to collect 35% more than Travis. If Travis collects $43, how much was collected in all?
Help Yaya ASAP Please
Jessica and Marcus each earn the same amount of money every week mowing lawns. Jessica saves 50% of her money and Marcus saves 1/4 of his money.
Which statement is correct?
A. Marcus saves 4/5 as much money as Jessica.
B. Jessica saves 4/5 as much money as Marcus.
C. Marcus saves twice as much money as Jessica.
D. Jessica saves twice as much money as Marcus.
If you need to cut 5 pieces of glass from a 14 feet length, how long should each piece be?
14 / 5 = 2.8 feet each
2.8 feet = 2 feet 9.6 inches
2 feet 9 3/5 inches
(3x6÷2)v+10=3²v+9 (Need work)
The student's equation simplifies to 9v + 10 = 9v + 9. Upon further simplification, it becomes apparent that the equation is a contradiction and has no solution.
Explanation:The student is asking about the solution to the equation (3x6÷2)v+10=3²v+9. The first step in solving this equation is to simplify the terms. We start by simplifying the multiplication and division in the first part of the equation (3x6÷2), which equals 9 since 3 times 6 is 18 and 18 divided by 2 is 9. Therefore, the equation simplifies to 9v + 10 = 3²v + 9. Next, we simplify 3², which is 3 raised to the power of 2, meaning 3 times itself, which results in 9. The equation now reads 9v + 10 = 9v + 9.
With the equation simplified, we notice that the terms containing v are equal on both sides of the equation. This indicates that we may be dealing with an identity or a contradiction depending on the constants. Subtracting 9v from both sides yields 10 = 9, which is clearly not true. Therefore, we conclude that the equation is a contradiction, and there is no solution for v that would make the equation true.
Final answer:
To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. However, the equation is inconsistent and has no solution.
Explanation:
To solve the equation (3x6÷2)v+10=3²v+9, we need to follow the order of operations and solve for the variable v. Let's break it down step by step:
Start by performing the division 3x6÷2 = 18÷2 = 9.
Now rewrite the equation as 9v+10=9v+9.
Subtract 9v from both sides of the equation to isolate the constants: 10 = 9.
Since 10 is not equal to 9, the equation is inconsistent and has no solution.
Therefore, there is no value of v that satisfies the equation.
Suppose one bakery oven at a cookie manufacturer is being used to bake chocolate cookies and vanilla cookies. A batch of chocolate cookies bakes in 8 minutes, and a batch of vanilla cookies bakes in 10 minutes. Let x represent the number of batches of chocolate cookies and y represent the number of batches of vanilla cookies. Write a linear inequality for the number of batches of each type of cookie that could be baked in one oven in an 8-hour shift.
Answer:
The answer is .......D
Step-by-step explanation:
d. 480
You have to remember that The answer is D
One integer is 2 times another. If the product of the two integers is 32, then find the integers
Final answer:
The two integers that satisfy the conditions of being twice of each other and having a product of 32 are either (4, 8) or (-4, -8).
Explanation:
The two integers as x and y, with y being 2 times x (y = 2x). According to the problem, the product of these two integers is 32 (x * y = 32). If we substitute y in the equation with 2x, we obtain the following: x * 2x = 32. Simplifying this equation gives us a quadratic equation, x² = 16.
To find x, we take the square root of both sides. The square root of 16 is 4, so x can be either 4 or -4. Consequently, y can be either 8 or -8, depending on whether x is positive or negative.
Therefore, the two sets of integers that satisfy the equation x*y = 32 are (4, 8) and (-4, -8), as both pairs have a product of 32 and one integer is exactly twice the other.
A Chinese restaurant offers buffet takeout for $4.99 per pound. How much does your takeout meal cost?
Answer:
1.99
Step-by-step explanation:
Dave rented a limousine for his wife's birthday. The hourly rate is $60. They used the limousine for 4 hours, plus Dave gave the driver a 10% tip. How much did he spend in total for the hourly charges plus tip?