The function would become an exponential decay function.
2^x - 3^x = √(6^x - 9^x)
[tex]2^x-3^x=\sqrt{6^x-9^x}\\\\D:6^x-9^x\geq0 \wedge 2^x-3^x\geq0\\D: 6^x\geq 9^x \wedge 2^x\geq3^x\\D:x\leq0 \wedge x\leq 0\qquad(\text{if }a < b \text{ then } a^x < b^x\text{ for } x > 0 \text{ and } a^x > b^x \text{ for } x < 0 )\\D:x\leq 0\\\\(2^x-3^x)^2=6^x-9^x\\(2^x-3^x)^2=3^x(2^x-3^x)\\\\\text{We divide both sides by } 2^x-3^x \text{ assuming }2^x-3^x\not=0\Leftrightarrow x\not=0.\\\\2^x-3^x=3^x\\2^x=2\cdot3^x\\\ln 2^x=\ln (2\cdot3^x )\\x\ln 2=\ln 2+\ln 3^x\\x\ln 2=\ln 2+x\ln 3[/tex]
[tex]x\ln 2-x\ln 3=\ln 2\\x(\ln 2-\ln 3)=\ln 2\\x=\dfrac{\ln 2}{\ln 2-\ln 3}=-\dfrac{\ln 2}{\ln 3-\ln 2}=-\dfrac{\ln 2}{\ln \frac{3}{2}}\approx-1.7[/tex]
For [tex]x=0[/tex], our initial equation is obviously true.
Therefore [tex]x\in\left\{-\dfrac{\ln 2}{\ln \frac{3}{2}},0\right\}[/tex].
Answer to the miscellaneous equation, is x=0 and x=-1.71
Miscellaneous equation are the equations which are not polynomial
The question can be solved by:
Factorising Splitting the terms to find the required solution
Completing the squares, etc
2ˣ - 3ˣ = √(6ˣ - 9ˣ)
Squaring both sides,
2²ˣ+3²ˣ -2.2ˣ.3ˣ=2ˣ.3ˣ - 3²ˣ
2²ˣ+2.3²ˣ -3.2ˣ.3ˣ=0
Factorising the terms,
2ˣ(2ˣ-3ˣ) -2.3ˣ(2ˣ-3ˣ)=0
(2ˣ-3ˣ)(2ˣ-2.3ˣ)=0
Equating the braces to zero,
Either,
2ˣ=3ˣ
x=0
or
2ˣ=2.3ˣ
Taking log on both sides
xln2=ln2+xln3
x=ln2/(ln2-ln3)
=-1.71
Therefore, x=0 and x=-1.71 is the only solution
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What is the square root of -1
Answer:
Step-by-step explanation:
Negative numbers don't have real square roots since a square is either positive or 0. so it doesn't exist
Answer:
i
Step-by-step explanation:
the square root of negative one is not real.
It is classed as an imaginary number denoted by i , that is
[tex]\sqrt{-1}[/tex] = i
Urgent!!……………………….. I NEED THE ANSWER!
Answer:
14 hours
Step-by-step explanation:
7h - 5(3h-8) = -72
7h - 15h + 40 = -72
-8h +40 = -72
-8h = -72 -40
-8h = -112
h = -112/ -8
h = 14
What is 108+259+301+405
Answer:
1073
Step-by-step explanation:
it's simple addition
Venn diagram ( attached image )
Assessing the given Venn diagram and the data related to it, we can answer the required question:
Q1. How many people were surveyed = 86.
Q2. What is the probability that a customer chosen at random:
a) takes salt P(S) = 46/85.
b) takes both salt and vinegar P(S ∩ V) = 13/85.
c) takes salt or vinegar or both P(S ∪ V) = 66/85.
The number of people who take salt chips n(S) = 46.
The number of people who take vinegar chips n(V) = 33.
The number of people who takes both n(S ∩ V) = 13.
The number of people who take neither n((S ∪ V)') = 19.
Therefore, the total number of people surveyed n(U) = n(S) + n(V) - n(S ∩ V) + n((S ∪ V)') = 46 + 33 - 13 + 19 = 85.
The number of people who takes salt or vinegar or both n(S ∪ V) = n(U) - n((S ∪ V)') = 85 - 19 = 66.
The probability that a customer chosen at random takes salt P(S) = n(S)/n(U) = 46/85.
The probability that a customer chosen at random takes both salt and vinegar P(S ∩ V) = n(S ∩ V)/n(U) = 13/85.
The probability that a customer chosen at random takes salt or vinegar or both P(S ∪ V) = n(S ∪ V)/n(U) = 66/85.
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I NEED HELP FAST Solve the following equation, and check your solution. Be sure to show all work in order to receive full credit.
Solve 24 - 3x = -27.
Which answer choice shows the decimal 23.476 written in expanded form?
Answer: 23.476 = 20+3+0.4+0.07+0.006
Step-by-step explanation:
I think you were supposed to write down the choices but I will guess the answer is this one:
23.476 = 20+3+0.4+0.07+0.006
Hope I helped!
Find the derivative of y = 4x^3.
Find the derivative of y = 2/x^4.
Find the derivative of y = 3√x.
Find the derivative of y = 3/√x.
Find the derivative of y = x^3/4.
Find the derivative of y = 3 x^5.
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
Question 1 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(4x^{3})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 4(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 12x^{2}}[/tex]
Question 2 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{2}{x^{4}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(2x^{-4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 2(-4)x^{-4-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -8x^{-5}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{8}{x^{5}}}[/tex]
Question 3 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3\sqrt{x})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3(x)^{\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(\frac{1}{2})x^{\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2}x^{-\frac{1}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{2\sqrt{x}}}[/tex]
Question 4 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{3}{\sqrt{x}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{-\frac{1}{2}})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(-\frac{1}{2})x^{-\frac{1}{2}-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2}x^{-\frac{3}{2}}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = -\frac{3}{2x\sqrt{x}}}[/tex]
Question 5 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(\frac{x^{3}}{4})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{1}{4}(3)x^{3-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = \frac{3}{4}x^{2}}[/tex]
Question 6 :
[tex]\mathsf {\frac{dy}{dx} = \frac{d}{dx}(3x^{5})}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 3(5)x^{5-1}}[/tex]
[tex]\mathsf {\frac{dy}{dx} = 15x^{4}}[/tex]
Define the face value. Choose the correct answer below.
A. The simple interest rate that the issuer promises to pay.
B. The status of the secondary bond market.
C. The date on which the issuer promises to repay the money.
D. The price that must be paid to the issuer to buy it at the time it is issued.
Option D is correct the face value is the price that must be paid to the issuer to buy it at the time it is issued.
What is face value?If the bond issuer doesn't default, face value, also known as par value, is the sum that is paid to a bondholder at the bond's maturity date. Bonds offered on the secondary market do, however, change in response to interest rates.
Therefore Option D is correct the face value is the price that must be paid to the issuer to buy it at the time it is issued.
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What is m∠M? I don't exactly remember how to do this type on problem...
Answer:
m∠M=98º
Step-by-step explanation
Sum of interior angles;
3x-16+x+6+x = 180
5x = 180-6+16
5x = 190
x = 38º
Angle M;
m<M= 3x - 16 = 3(38)-16= 98º
m∠M=98º
Answer:
<M = 98
Step-by-step explanation:
The sum of the angles of a triangle is 180 degrees
< M + < N + < O = 180
3x-16 + x + x+6 = 180
Combine like terms
5x - 10 = 180
Add 10 to each side
5x-10 + 10 = 180+10
5x = 190
Divide by 5
5x/5 = 190/5
x=38
We want to find <M
<M = 3x-16 = 3*38 -16 = 114-16 =98
which graph best represents -8x+2y=18
See the graph in the image.
Drag each response to the correct location on the table. Each response can be used more than once, but not all responses will be used.
Consider the two exponential equations shown. Identify the attributes for each equation to complete the table.
8.9%
250 89%
W
40 =
Decay
250 (0.89)
Initial Value::
Growth or Decay::
Growth/Decay Rate::
11%
F
40
Growth
250 =
111%
40(1.11)
Initial Value:
Growth or Decay:
Growth/Decay Rate::
The equation is y = 250(0.89)^x and the decay rate is 11%.
How to calculate the values?The initial value will be:
= 250(0.89)^x
= 250(0.89^0)
= 250
The decay rate will be:
= 1 - 0.89
= 0.11
= 11%
In conclusion, the equation is y = 250(0.89)^x and the decay rate is 11%.
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Match the circle equations in general form with their corresponding equations in standard form. x2 y2 − 4x 12y − 20 = 0 (x − 6)2 (y − 4)2 = 56 x2 y2 6x − 8y − 10 = 0 (x − 2)2 (y 6)2 = 60 3x2 3y2 12x 18y − 15 = 0 (x 2)2 (y 3)2 = 18 5x2 5y2 − 10x 20y − 30 = 0 (x 1)2 (y − 6)2 = 46 2x2 2y2 − 24x − 16y − 8 = 0 x2 y2 2x − 12y − 9 = 0
The equation given is matched with the respective vertex forms.
What is the standard Equation for a circle ?The standard equation for a circle is given by
(x-h)² + (y-k)² = r²
The equation given in the question are
x² + y² − 4x + 12y − 20 = 0
(x − 6)² + (y − 4)² = 56
x² + y² + 6x − 8y − 10 = 0
(x − 2)² + (y + 6)² = 60
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
5x² + 5y² − 10x + 20y − 30 = 0
(x+3)² + (y-4)² = 35
2x² + 2y² − 24x − 16y − 8 = 0
(x-1)² + (y+2)² = 11
The first equation is
x² + y² − 4x + 12y − 20 = 0
It can be written ad
x² -4x + 4 - 4 +y²+12y +36-36 -20 = 0
(x-2)² +(y+6)²= 60
The second equation is
x² + y² + 6x − 8y − 10 = 0
x² +6x +9-9 +y² -8y +16-16 -10 = 0
(x+3)² + (y-4)² = 35
The third equation is
3x² + 3y² + 12x + 18y − 15 = 0
(x + 2)² + (y + 3)² = 18
The fourth equation is
5x² + 5y² − 10x + 20y − 30 = 0
(x-1)² + (y+2)² = 11
The fifth equation is
2x² + 2y² − 24x − 16y − 8 = 0
(x − 6)² + (y − 4)² = 56
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Which of the following is equal to 5 1/3?
OA. 1/5
OB. 5 3
O C. √5.3
OD. √5
The correct answer is option B which is ( 5 / 3)
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division
The value will be calculated as:-
[tex]5\times \dfrac{1}{3}[/tex] = [tex]\dfrac{5}{3}[/tex]
1.67 = 1.67
Therefore the correct answer is option B which is ( 5 / 3)
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10 point to Help with this ?
All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.
What is congruence transformation?
A congruence transformation is defined as a movement of shape such that it can produce a shape that is congruent to the original.
There are three types of congruence transformation;
1. Translation
2. Reflection
3. Rotation
Given;
Shape B is made by applying a single transformation to shape A.
Hence, All the transformations for which A and B would be congruent are; Translation, Reflection, and Rotation.
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Write a product that converts 492 seconds into an equivalent time in minutes. Use division to find the answer.
(It will be a
decimal answer.)
Answer:
8.2 minutes
Step-by-step explanation:
[tex] \ \frac{492}{60} = 8.2[/tex]
492 seconds = 8.2 minutes
how much will you save if you buy an item listed at 17.50 at a 35 percent discount? savings = price x discount percentage
Answer:
17.50 × 0.35 = 6.13
Step-by-step explanation:
Answer:
That would be $11.37
Step-by-step explanation:
First Multiply the discount and the original price
17.50(0.35)= 6.125 = 6.13
Use that answer and subtract it from the original price
17.50 - 6.13 = 11.37
Two-Variable Systems of Inequalities
On a piece of paper, graph this system of inequalities. Then determine which
region contains the solution to the system.
ysx-2
y24x-4
O A. Region D
B. Region B
C. Region C
D. Region A
10
6
6
A 4
10 B 84
D
999
B
C
XA¹
10
Inequalities help us to compare two unequal expressions. The correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.
It is mostly denoted by the symbol <, >, ≤, and ≥.
The solution to two systems of inequalities in the region where the area of the two inequalities overlaps. As it can be observed in this case that the overlap area is B.
Hence, the correct option is B.
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Use separation of variables to solve the differential equation with initial condition y(1)=-2
Answer: A
Step-by-step explanation:
[tex]\frac{dy}{dx}=\frac{1+x}{xy} \\ \\ y \text{ } dy=\frac{1+x}{x} \text{ } dx \\ \\ y \text{ } dy= \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \int y \text{ } dy=\int \left(\frac{1}{x}+1 \right) \text{ } dx \\ \\ \frac{y^{2}}{2}=\ln \left| x \right|+x+C[/tex]
Substituting in the initial condition,
[tex]\frac{(-2)^{2}}{2}=\ln \left|1 \right|+1+C\\\\2=1+C\\\\C=1[/tex]
So,
[tex]\boxed{\frac{1}{2}y^{2}=\ln \left|x \right|+x+1}[/tex]
Answer:
[tex]\textsf{A.} \quad \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Step-by-step explanation:
To solve the differential equation:
Rearrange the given equation to get all the terms containing y on the left side, and all the terms containing x on the right side:
[tex]\dfrac{dy}{dx}=\dfrac{1+x}{xy}[/tex]
[tex]\implies y\dfrac{dy}{dx}=\dfrac{1+x}{x}[/tex]
[tex]\implies y\:dy=\dfrac{1+x}{x}\:dx[/tex]
[tex]\implies y\:dy=\dfrac{1}{x}+\dfrac{x}{x}\:dx[/tex]
[tex]\implies y\:dy=\left(\dfrac{1}{x}+1\right)\:dx[/tex]
Integrate both sides:
[tex]\displaystyle \implies \int y\:dy=\int \left(\dfrac{1}{x}+1\right)\:dx[/tex]
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+C[/tex]
Find the value of C using the given values of x and y:
when x = 1, y = -2
[tex]\implies \dfrac{1}{2}(-2)^2=\ln|1|+1+C[/tex]
[tex]\implies 2=0+1+C[/tex]
[tex]\implies C=1[/tex]
Substitute the found value of C:
[tex]\implies \dfrac{1}{2}y^2=\ln|x|+x+1[/tex]
Anyone knows how to do this please tell me how?
Step-by-step explanation:
0.000672, 6.72×10⁵, 67.2×10‐⁴, 672×10⁴
Scientific notation is a way of writing numbers that looks like the following:
[tex]a\times10^n[/tex]
a is any number between 1 and 10n is any integerFor instance, we can write 2930 in scientific notation.
First, move the decimal so that the number is between 1 and 10:First, write all the given values in scientific notation:
[tex]6.72\times10^5[/tex] ⇒ [tex]6.72\times10^5[/tex][tex]67.2\times 10^{-4}[/tex] ⇒ [tex]6.72\times 10^{-3}[/tex][tex]672\times 10^4[/tex] ⇒ [tex]6.72\times 10^6[/tex][tex]0.000672[/tex] ⇒ [tex]6.72\times10^{-4}[/tex]Now, let's compare the values of n, and organize the numbers from least to greatest:
[tex]6.72\times10^{-4}[/tex]
[tex]6.72\times 10^{-3}[/tex]
[tex]6.72\times10^5[/tex]
[tex]6.72\times 10^6[/tex]
Finally, rewrite all the numbers as their given format:
[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
Answer[tex]0.000672[/tex]
[tex]67.2\times 10^{-4}[/tex]
[tex]6.72\times10^5[/tex]
[tex]672\times 10^4[/tex]
In question 1, you found the cubes of both positive and negative numbers. Does x3 = 8 have two solutions as x2 = 4 does? Why or why not?
The cost of the fruit is given by the function y = 3x + 1, where x is the number of fruits and y is the total cost. Find the range of the function.
The range of the given function will lie from ( -0.333,0) to ( 0,1).
What is the range?A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Given that:-
The cost of the fruit is given by the function y = 3x + 1, where x is the number of fruits and y is the total cost.When we plot the graph of the function we will see that the straight line will cut the x-axis at point (-0.333 ) and the y-axis cut at ( 0,1 ) the points between the two points will be the solutions of the equation.
Therefore range of the given function will lie from ( -0.333,0) to ( 0,1).
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Answer:i think the answer is B
Step-by-step explanation:
The time it takes me to wash the dishes is uniformly distributed between 7 minutes and 15 minutes.
What is the probability that washing dishes tonight will take me between 13 and 14 minutes?
Give your answer accurate to two decimal places.
what is the slimpelst form for ratio 21:28
Answer:
3:4
Step-by-step explanation:
We know this because the GCD of 21 and 28 is 7
so we divide both numbers by 7 and get 3 and 4
so the answer is 3:4
Which ordered pair is the solution to the system of linear equations y =5x +8 and y= -4 x-1
Answer:
(-1,3)
y=5x+8 , y=-4x-1y=5x+8,y=−4x−1
Both sides have y on the left hand side so make the right hand side equal and solve for x
5x+8= -4x-15x+8=−4x−1
To solve for x , add 4x on both sides
9x+8=-19x+8=−1
Subtract 8 on both sides
9x=-99x=−9
Divide by 9 on both sides
x=-1x=−1
Now plug in -1 for x in the first equation and find out y
y=5x+8y=5x+8
y=5(-1)+8y=5(−1)+8
y=-5+8y=−5+8
y=3y=3
Ordered pair is (x,y) that is (-1,3)
Step-by-step explanation:
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An Amazon delivery driver receives a bonus if he delivers a package to a customer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus
[tex]15 \leq X \leq 25[/tex] is the equation represents the drivers allotted time (x) to receive a bonus.
What us the absolute value of inequality?An absolute value inequality is an expression with absolute functions as well as inequality signs.
According to the question:
Mathematically absolute value inequality is represented as :
|X -20|≤ 5
Solving the equation using
|z| ≤ a→ -a ≤ z ≤ a :
here, z = X- 20 and a = 5:
[tex]| X-20| \leq 5\\\\ - 5\leq X-20 \leq 5[/tex]
By Solving X adding 20 on the three sides of the inequality
[tex]-5 + 20 \leq X -20 +20 \leq 5 + 20[/tex]
By simplifying it:
[tex]15 \leq X \leq 25[/tex]
Therefore the equation or inequality which represents the drivers allotted time (x) to receive a bonus [tex]15 \leq X \leq 25[/tex]
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Jose rides his bike for 5 minutes to travel 8 blocks he rides for 10 minutes to travel 16 blocks which value will complete the table
Using the unit rate, the missing values that completes the table are:
A = 5; B = 15; C = 40
How to Find Unit Rate?Unit rate (m) = change in y/change in x.
5 minutes for 8 Blocks (5, 8) and 10 minutes for 16 blocks (10, 16)are given.
Unit rate (m) = (16 - 8)/(10 - 5) = 8/5
An equation that will define the function is, y = 8/5x. Use it to complete the table.
Find A (y) when x is 5:
y = 8/5(5) = 8
The value of A is: 5
Find B (x) when y is 24:
24 = 8/5(x)
5(24) = 8x
120 = 8x
120/8 = x
15 = x
The value of B is: 15
Find A (y) when x is 25:
y = 8/5(25) = 40
The value of C is: 40
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Micah is keeping track of how much he spends this month on gas. In the first week, he bought x gallons of gas at $2.39 per gallon. In the second week, he bought 3 fewer gallons of gas than the first week at $2.49 per gallon. So far this month, he has spent a total $46.21 on gas.
In the first week, Micah bought
x gallons of gas.
In the second week, Micah bought
x gallons of gas.
Answer: In the first week, Micah bought 11 gallons of gas,
and in the second week, he bought 8 gallons of gas
Step-by-step explanation:
In the first week, Micah bought x gallons of fuel at $2.39/gallon
In the second week, he bought (x - 3) gallons at $2.49/gallon
Formulating an equation and solving for x gallons of fuel:
x × 2.39 + (x - 3) × 2.49 = 46.21
2.39x + x × 2.49 − 3 × 2.49 = 46.21
2.39x + 2.49x − 7.47 = 46.21
4.88x − 7.47 = 46.21
4.88x = 53.68
[tex]\frac{4.88x}{4.88} = \frac{53.68}{4.88}[/tex]
x = 11
Therefore,
In the first week, Micah bought 11 gallons of gas
In the second week, he bought (11 - 3) = 8 gallons of gas
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime. During store inventory she worked 48.5h. Her gross earnings were $1,471.88. What is Gracie’s overtime rate of pay? show work please
Gracie’s overtime rate of pay would be $635.06.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.
For one hour she earns $17.25
For 37.5h she earns = 37.5h x 17.25
= $646.87
The total money she earns = $646.87 + overtime pay
During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.
= 48.5h x 17.25
= $836.625
So, $836.625 + overtime pay = $1,471.88
overtime pay = $1,471.88 - $836.625 = $635.06
Hence, Gracie’s overtime rate of pay would be $635.06.
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A bottle holds
5
55 milliliters of perfume.
How many bottles can we fill with
2
22 milliliters of perfume?
Answer:
0.4 bottles can be filled
Step-by-step explanation:
divide the amount that is present by the max amount
the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.
the amount that is present is 2.22 millimeters.
[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]
0.4 bottles
if the given values are 555 and 222 then the answer is still .4
Answer:
0.4 bottles can be filled
