1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
What is expression ?
In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated to produce a value.
Yes, 1/3(r³) and (r³)/3 are equivalent expressions.
This is because division is commutative, meaning that it doesn't matter in which order we divide the numbers. So, we can write (r³)/3 as (1/3)(r³), which is equivalent to 1/3(r³).
In both cases, we are dividing r³ by 3, and the result is the same. Therefore, 1/3(r³) and (r³)/3 are equivalent expressions.
1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.
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for what values of a are the following expressions true 1/2a-5 1/2=5-a
The expression is only true for a = 5.
What is the expressions?An expression is a combination of numbers, variables, and operations that represents a quantity or a mathematical relationship. It can be a simple or complex representation of a value or function, and it can be evaluated or simplified using algebraic or numerical methods.
The given expression is:
(1/2)a - 5 (1/2) = (5 - a)
To find the values of 'a' that make this expression true, we can simplify and solve the equation:
(1/2)a - 2.5 = 5 - a
Adding 'a' to both sides:
(3/2)a - 2.5 = 5
Adding 2.5 to both sides:
(3/2)a = 7.5
Multiplying both sides by 2/3:
a = 5
Therefore, the expression is true when a = 5.
To verify, we can substitute a = 5 into the original expression:
(1/2)(5) - 5 (1/2) = (5 - 5)
2.5 - 2.5 = 0
The expression evaluates to 0, which is true.
Therefore, the expression is only true for a = 5.
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if anyone could help, would be much appreciated
Answer:
(√122 - √10)/112.
Step-by-step explanation:
The average rate of change of a function f(x) over an interval [a, b] is given by:
average rate of change = (f(b) - f(a))/(b - a)
Here, we have f(x) = √x - 1, a = 10, and b = 122. So, the average rate of change of f(x) from x = 10 to x = 122 is:
(f(122) - f(10))/(122 - 10)
= (√122 - 1 - √10 + 1)/(112)
= (√122 - √10)/112
Therefore, the exact, fully simplified answer for the average rate of change of f(x) from x = 10 to x = 122 is (√122 - √10)/112.
Assuming you can afford to spend 30% of your gross monthly income on housing, how much would you be able to afford on monthly rent if you make $34,000 per year?
Answer:
$850
Step-by-step explanation:
If you make $34,000 per year, then you make $2833.33 per month.
[tex]\frac{34000}{12} = 2833.333[/tex]
30% of your monthly income would go towards housing (every month)
(2833.33)(0.3) = $850
Use linear combination to solve the system of equations. Show your work.
Check your answer to show proof that the solution works in each equation.
[tex]2x+4y=6\\x-4y=-21[/tex]
The provided hypothesis, μ = 55, is the null. It is identifiable by the inclusion of the equality symbol (=). Hଵ: μ ≠ 55
The symbol μ represents the arithmetic mean of the population from which the sample
has been drawn
The given statemen is correct. The given hypothesis, μ = 55, is the null hypothesis, which is identified by the presence of the equality symbol.
The alternative hypothesis, Hଵ: μ ≠ 55, indicates that there is a difference between the population mean and the value specified in the null hypothesis. The symbol μ represents the population mean, which is the average of all the values in the population. In this case, the population from which the sample has been drawn is being referred to. Arithmetic mean is a mathematical term used to describe the average value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set.
The formula for the arithmetic mean of a set of numbers is:
Arithmetic Mean = (sum of all values) / (total number of values)
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To show that circle P Is similar to circle Q, circle P Is translated t units to the right. The Image Is then dilated about Its center by a scale factor of s.
What are the values of t and s?
T=
S=
Shelby is playing hide-and-seek with Dillon and Patty. Dillon is hiding 15 meters south of Shelby, and Patty is hiding due east of Dillon. If Shelby is 17 meters from Patty, how far apart are Dillon and Patty?
meters= ?
Answer:
8 meters
Step-by-step explanation:
their formation creates a triangle
Shelby to Dillon =15
Shelby to Patty =17
Dillon to Patty =?
a^2 + 15^2 = 17^2
a^2 + 225 = 289
a^2 = 64
a = 8
Please follow directions
Answer:
Step-by-step explanation:
__________ will produce an irrational answer when added to 7/8 , because __________.
The square root of 2, or any other irrational number, will produce an irrational answer when added to 7/8.
Why is the number √ 2 irrational?Ancient mathematicians understood that a square with one-unit-long sides has a diagonal whose length is irrational. The Pythagorean Theorem states that the length of the diagonal is equal to the square root of two. Thus, it is absurd to use the square root of 2!
When added to 7/8, the square root of 2 or any other irrational number will result in an absurd result.
This is so that irrational numbers can be expanded indefinitely without repeating, since they cannot be stated as a fraction of two integers.
The consequence of adding an irrational number to a rational one, such as 7/8, will also be irrational since the irrational number cannot be reduced to a fraction of two integers because its decimal expansion will go on indefinitely without repeating.
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Answer:
√7 irrational number
Step-by-step explanation:
Select the true statement. Group of answer choices For any real number x, x > 5 implies that x ≥ 5. For any real number x, x ≥ 5 implies that x ≥ 6. For any real number x, x > 5 implies that x ≥ 6. For any real number x, x ≥ 5 implies that x > 5
For any real number x, x > 5 implies that x ≥ 5 is the true statement.
For any real number x, x > 5 implies that x ≥ 5 is the true statement. This can be expressed with the following inequality:
x > 5 implies x ≥ 5
This means that if x is greater than 5, then x must be greater than or equal to 5. We can demonstrate this with an example calculation. Let x = 6.
6 > 5
We can see that 6 is greater than 5, so the inequality is true.
6 ≥ 5
We can see that 6 is also greater than or equal to 5, so the inequality is also true. Therefore, for any real number x, x > 5 implies that x ≥ 5.
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The students in Mrs. Holbrook’s class are growing plants. One day they measured the heights of the plants in inches. Make a line plot to represent the data
Based on the information in the table, we can infer that the graph would be as shown in the attached image.
How to graph the information in the table?To graph the information in the table we must analyze the information in the table. In this case we must take into account that to locate the fractions we can perform the division and convert it into a decimal number to locate them more easily on the number line.
In accordance with the above, we can establish that the height that is repeated the most times is 1 7/8 with a frequency of 4 times.
Note: This question is incomplete. Here is the complete information:
Attached image
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What is the slope of the line that passes through the points
(
−
4
,
−
10
)
(−4,−10) and
(
−
7
,
−
19
)
(−7,−19)?
Answer:
3
Step-by-step explanation:
slope of the line, m = (y2 - y1 ) / ( x2 - x1 )
= (-19 + 10 ) / (-7 + 4)
= -9 / -3
= 3
Quick Loans will loan you $500 with the understanding that you will pay them $3.98 in interest for every day you have the loan out. What is the APR for this loan?
The APR on the loan, given the amount you are to pay in interest every day, can be found to be 190. 54 %
How to find the APR ?To calculate the APR (Annual Percentage Rate) for this loan, we need to know the total interest paid over the course of a year, as a percentage of the loan amount.
First, we need to determine the total interest paid over the course of one year. Since the interest rate is $3.98 per day, we can multiply that by the number of days in a year (365) to get the total interest paid per year:
$3.98 x 365 = $1, 452.70
The APR would therefore be :
= ( 1, 452. 70 - 500 ) / 500
= 1. 9054
= 190. 54 %
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30 dollars to spend on 3 gifts. She spent 8 9/10 dollars on gift A and 6 3/5 dollars on gift B. How much money did she have left for gift C?
From the given information provided, she has 14.50 dollars money left to spend on gift C.
To find out how much money is left for gift C, we first need to add up the amounts spent on gift A and gift B:
8 9/10 dollars + 6 3/5 dollars = (8 + 6) + (9/10 + 3/5) dollars
= 14 + (9/10 + 6/10) dollars
= 14 + 15/10 dollars
= 15 5/10 dollars
= 15.50 dollars
So the total amount spent on gift A and gift B is 15.50 dollars. To find out how much money is left for gift C, we need to subtract this amount from the total amount she has to spend:
30 dollars - 15.50 dollars = 14.50 dollars
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In a group of 15 children, 5 said they are an only child, 3 said they have 1 sibling only, 4 said they have exactly 2 siblings, and 3 said they have exactly 3 siblings.
What is the average number of siblings for this group?
Enter your answer as a decimal, rounded to the nearest tenth, in the blank.
Answer:
Step-by-step explanation:
1.3
2
1 point
Find the value x:
12
Type your answer...
+
6
Answer:
Step-by-step explanation:
1
If the volume of the cube is 1 ft cubed each side of this cube is
If the volume of the cube is 1 ft cubed each side of this cube is 1 cube.
How to calculate the volume of a cube?In Mathematics, the volume of a cube is calculated by using this following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.Substituting the given points into the volume of a cube formula, we have the following;
1 = m³
By taking the cubic root of both sides of the equation, we have the following:
Side length, m = ∛1
Side length, m = 1
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Which set of transformations is needed to graph f(x) = –2sin(x) + 3 from the parent sine function?
vertical compression by a factor of 2, vertical translation 3 units up, reflection across the y-axis
vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axis
reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down
The main function is given by:
f (x) = sine (x)
We then have the following transformations:
Reflections:
Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.
To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)
f (x) = - sine (x)
Expansions and vertical compressions:
To graph y = a*f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
f (x) = - 2 * sine (x)
Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = - 2 * sine (x) + 3
Answer:
C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
The set of transformations which is needed to graph f(x) = –2sin(x) + 3 is reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up, the correct option is C.
What is rigid transformation?A rigid transformation (also called an isometry) is a transformation of the plane that preserves length. In a rigid transformation the pre-image and image are congruent (have the same shape and sizes).
We are given that;
The function= f(x) = –2sin(x) + 3
Now,
To graph f(x) = –2sin(x) + 3 from the parent sine function y = sin(x), we need to apply the following transformations:
A reflection across the x-axis, because of the negative sign in front of the 2.
A vertical stretching by a factor of 2, because of the absolute value of the coefficient of sin(x), which is 2.
A vertical translation 3 units up, because of the constant term 3.
Therefore, by transformations answer will be Reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up.
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What Percent of Cedric's gross pay is his net pay. Round to the nearest tenth of a percent. Gross=$2,195 Net=$1,714. 74
we know that we must add 29.8% more, in decimal form, to the net income in order to get the gross income.
Let's see the facts:
Income = $3,788
Withheld:
6.2% for social security
1.45% for medicare
16% for federal income tax
6.15% for state income tax
Now, with this given data, we can asseverate that the gross income is obtained by multiplying the net income by the sum of percentages as follows:
The sum of contributions: 6.2+1.45+16+6.15 = 29.8 %
So, we know that we must add 29.8% more,in decimal form, to the net income in order to get the gross income.
The gross income is:
Gross income= 3,788x 1.298
[Because 1 represents 100% and 0.298 represents %29.8]
Gross income = $4,916.82
The complete question is-
Cedric's monthly net income is $3,788. The following is withheld from him monthly gross income: 6.2% for social security • 1.45% for Medicare 16% for federal income tax 6.15% for state income tax Determine Cedric's monthly gross income. Round your answer to the nearest cent.
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solve for x : 17-1/6x=23 ?
Answer:
x = -36
hope it helps
Answer:36
Step-by-step explanation:
-1/6x=23-17
-1/6x=-6
1/6x=6
x=36
What is the end behavior of the function f(x) = 3x?
As x
O As x
-00, f(x) → -00, and as x
→ -∞, f(x) → ∞, and as x
->
O As x 0, f(x)
∞o, f(x) → ∞0.
co, f(x) -18.
O As x-00, f(x) → 0, and as x → ∞, f(x) → 0.
-00, and as x → ∞, f(x) - 0.
Answer:
As x goes negative infinity, f(x) goes negative infinity and as x goes to infinity, f(x) goes to infinity
Step-by-step explanation:
If you put the function on a graphing calculator you can see how they work
may I get brainliest thanks
What is the average of the given set of numbers? *
23, 18, 35, 27, 19, 22, 25
• 22.6
• 24.1
• 7
• 169
Answer:
24.1
Step-by-step explanation:
23+18+35+27+19+22+25=169:7=24.1
I need the answer please I will give you 44 points!
The number of hours it would take 3, 5, 6 and 15 bakers to make 30 loaves is :
3 bakers - 2 / 3 hours 5 bakers - 2 / 5 hours 6 bakers - 1 / 3 hours 15 bakers - 2 / 15 hoursHow to find the number of bakers ?Time taken per baker in hours :
= 30 / 2
= 15 loaves per hour per baker
The number of hours it would take 3 bakers to make 30 loaves is :
= ( 30 loaves / ( 15 / 60 minutes x 3 bakers ) ) / 60 minutes per hour
= 2 / 3 hours
5 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 5 bakers ) ) / 60 minutes per hour
= 2 / 5 hours
6 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 6 bakers ) ) / 60 minutes per hour
= 1 / 3 hours
15 bakers :
= ( 30 loaves / ( 15 / 60 minutes x 15 bakers ) ) / 60 minutes per hour
= 2 / 15 hours
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Given the geometric sequence an with the following information, find a9.
a2= −24, a5=8/9
The ninth term of the given geometric sequence is 8/2187.
Now, let's apply this concept to solve the problem. We are given two terms of a geometric sequence: a₂ = -24 and a₅ = 8/9. We need to find a₉.
First, let's find the common ratio (r) of the sequence. To do this, we can use the formula for the nth term of a geometric sequence:
an = a1 x rⁿ⁻¹
We can use this formula for two different terms of the sequence to find the common ratio. Let's use a₂ and a₅:
a₂ = a₁ x r²⁻¹ --> -24 = a₁ x r
a₅ = a₁ x r⁵⁻¹ --> 8/9 = a₁ x r⁴
Now, let's divide these two equations to eliminate a1:
(-24) / (8/9) = r / r⁴
Simplifying, we get:
-27 = 1/r³
Taking the cube root of both sides, we get:
r = -1/3
Now that we know the common ratio, we can use the formula for the nth term of a geometric sequence to find a₉:
a₉ = a₁ x r⁹⁻¹
We don't know a1, but we can use the fact that a₂ = -24 to find it:
a₂ = a₁ x r²⁻¹ --> -24 = a₁ x (-1/3)
Simplifying, we get:
a₁ = 72
Now we can substitute the values we found for a1 and r into the formula for a₉:
a₉ = a₁ x r⁹⁻¹ --> a₉ = 72 x (-1/3)⁸
Simplifying, we get:
a9 = 8/2187
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The Picture and Sound electronics store has hired Trevor to work in the warehouse. He uses a pulley with a hand crank to lift heavy boxes. There is a proportional relationship between the number of times Trevor turns the crank to lift a box, x, and the height the box has been lifted (in feet), y. The equation that models this relationship is y=0.6x.
How high does Trevor lift a box by turning the crank 10 times? Write your answer as a whole number or decimal.
Trevor lifts a box to a height of 6 feet by turning the crank 10 times.
What is equation?In mathematics, an equatiοn is a fοrmula that uses the equals sign (=) tο express hοw twο expressiοns are equal. In οther languages, the wοrd equatiοn and its cοgnates may have slightly different meanings. Fοr instance, in French, an equatiοn is defined as having οne οr mοre variables, while in English, an equatiοn is any prοperly fοrmed fοrmula that cοnsists οf twο expressiοns linked by the equals sign.
Using the equation y = 0.6x, we can calculate the height Trevor lifts a box by turning the crank 10 times:
y = 0.6x
y = 0.6(10)
y = 6
Therefore, Trevor lifts a box to a height of 6 feet by turning the crank 10 times.
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One number is less than the other number by 10. The sum of there two number is 50. Find them
Answer:100
Step-by-step explanation:
Find the values of x where the tangent line is horizontal for
f(x)=3x^3−2x^2−9.
A. x=0, x = −2/3
B. x=0, x = 2/3
C. x=0, x = − 4/9
D. x=0, x = 4/9
answer is D but don't know workin
The values of x where the tangent line is horizontal for f(x)=3x³−2x²−9. is D, x = 0 and x = 4/9.
What is the Derivative οf a Functiοn?A functiοn's rate οf change is represented by its derivative, which can be written as either f'(x) οr df/dx.
The derivative οf the functiοn f(x) = 3x³ − 2x² − 9 is:
f'(x) = 9x² − 4x
Setting f'(x) = 0 tο find the critical pοints:
9x² − 4x = 0
x(9x − 4) = 0
x = 0 οr x = 4/9
Sο, the critical pοints are x = 0 and x = 4/9.
The secοnd derivative οf f(x) is:
f''(x) = 18x − 4
f''(0) = -4 < 0, sο x = 0 is a lοcal maximum.
f''(4/9) = 2 > 0, sο x = 4/9 is a lοcal minimum.
Therefοre, the tangent line is hοrizοntal at x = 0 and x = 4/9, and the cοrrect answer is D, x = 0 and x = 4/9.
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Angie is x years old.
Mandy is 22 years older than Angie.
In 2 years’ time, Mandy will be twice Angie’s age.
Calculate Angie and Mandy’s current age.
The Angie and Mandy’s current age are 22 and 44 years respectively.
Explain about the term linear equations?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as this same denominator of either a fraction in a linear equation.The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.Angie is x years old.
Mandy = 22 + x
After 2 years:
22 + x = 2x
Solving linear equation:
22 = 2x - x
22 = x (Angie’s current age)
Mandy’s current age.
x + 22 = 22 + 22
x = 44
Thus, the Angie and Mandy’s current age are 22 and 44 years respectively.
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Please ASAP Help
Will mark brainlest due at 12:00
Answer:
(2,3)
Step-by-step explanation:
22. Which of the following are the possible lengths to complete a triangle with side lengths of 9 in. and 11 in.? A greater than 2 in., less than 19 in. B greater than 2 in., less than 20 in. C greater than 4 in., less than 19 in. D greater than 4 in., less than 20 in.
The possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.
How to determine the length of the triangle ?
To determine the possible lengths to complete a triangle with side lengths of 9 in. and 11 in., we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Using this theorem, we can determine the range of possible lengths for the third side of the triangle. We start by adding the two given side lengths:
9 + 11 = 20
The third side must be less than the sum of the other two sides, so the third side must be less than 20 in.
Next, we subtract the two given side lengths:
11 - 9 = 2
The third side must be greater than the difference of the other two sides, so the third side must be greater than 2 in.
Therefore, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are between 2 in. and 20 in. This eliminates options A and C from the choices given.
Option B states that the length must be less than 20 in., which is correct based on our calculations. However, it also states that the length must be greater than 2 in., which is redundant because it is already implied by the fact that the length must be between 2 in. and 20 in. Therefore, option B is also correct.
Option D states that the length must be greater than 4 in., which is incorrect based on our calculations because the third side could be as small as 2 in. Therefore, option D is not correct.
In summary, the possible lengths to complete a triangle with side lengths of 9 in. and 11 in. are greater than 2 in. and less than 20 in., which is correctly represented by options B.
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