What is the simplified form of the following expression?
4/7^3
A: 343/64
B: 21,952
C:407
D: 64/343
Answers
Evaluate the exponents
4³= 64
7³= 343
Final answer: 64/343
Answer:
The correct option is D.
Step-by-step explanation:
The given expression is
[tex](\frac{4}{7})^3[/tex]
According to the property of exponent.
[tex](\frac{a}{b})^n=\frac{a^n}{b^n}[/tex]
Using this property the given expression can be written as
[tex](\frac{4}{7})^3=\frac{4^3}{7^3}[/tex]
[tex](\frac{4}{7})^3=\frac{64}{343}[/tex]
The simplified form of the given expression is [tex]\frac{64}{343}[/tex].
Therefore the correct option is D.
Related Questions
If there are 12 boys in the class and 14 girls, what is the ratio of boys to all the students in the class?
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or 6:13 (simplified)
12:26
d=f+fx , solve for x
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To solve for x means we make x the subject of the formula. The value of x is:
[tex]x = \frac{d - f}{f}[/tex]
Given that:
[tex]d = f + fx[/tex]
To solve for x, we make use of the following steps
[tex]d = f + fx[/tex]
Subtract f from both sides
[tex]d - f =fx[/tex]
Isolate x: Divide both sides by f
[tex]\frac{d - f}{f} = x[/tex]
So, we have:
[tex]x = \frac{d - f}{f}[/tex]
Read more about subject of formula at:
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Students reported volunteering at the animal shelter during the last 6 months for 25, 36, 31, and 32 hours. What is the mean absolute deviation for the number of hours students volunteered? Round to the nearest tenth.
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(1) First get the mean: 25 + 36+ 31 + 32 / 4 = 31
(2) Find the distance of each value to the mean: 31-25= 6; 36-31=5; 31-31=0; 32-31=1
(3) Get the mean of the distance: 6 + 5 + 0 + 1 / 4 = 3
Answer: the answer is 3
How do u know if an inequality is sometime ,never , or always true ?
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Solve this equation for x round your answer to the nearest hundredth 0.43=log x
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Angie and Kenny play online video games. Angie buys 1 software package and 3 months of game play. Kenny buys 1 software package and 2 months of game play. Each software package costs $20. If their total is $115, what is the cost of one month of game play?
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75+40=115
A house worth 120,000 is in an area where real estate is increasing in value at the rate of 8% per year. How much will the house be worth in 1 year?
Answers
So we add that to get 129600
Hope that helped
P=21+2w the answer is w=p-21/2 I need the work to go along with it
Answers
P=21+2w
minus 21 both sides
P-21=2w
divide both sides by 2
[tex]\frac{P-21}{2}=w[/tex]
[tex]w=\frac{P-21}{2}[/tex]
plz help 50 points i am so confused
Answers
Answer: 15
Step-by-step explanation: 6*5*4*3*2 /2*4*3*2 = 720/48 = 15
question answered by
(jacemorris04)
Both 2 and 5 are common factors of a number. The number is between 101 and 118. What is the number
Answers
help me place tiles correctly geometry
Answers
BC = AD
6-x = x+2
6-2 = x+x
4 = 2x
2x = 4
x = 2
If x = 2, then
BC = 6-x = 6-2 = 4
AD = x+2 = 2+2 = 4
meaning that the top and bottom parallel sides are each 4 units long
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Similarly, the opposite angles are congruent as well
Angle A = Angle C
100-y = 12+y
100-12 = y+y
88 = 2y
2y = 88
y = 44
If y = 44, then
angle A = 100-y = 100-44 = 56
angle C = 12+y = 12+44 = 56
A professional baseball team will play 1 game Saturday and 1 game Sunday. A sportswriter estimates the team has a 60% chance of winning on Saturday but only a 35% chance of winning on Sunday. Using the sportswriter's estimates, what is the probability that the team will lose both games?
A) 14%
B) 21%
C) 25%
D) 26%
E) 39%
Answers
Final answer:
To find the probability of losing both games, multiply the probabilities of losing each game together. The probability is 26%.
Explanation:
To find the probability that the team will lose both games, we can multiply the probabilities of losing each game together.
The probability of losing on Saturday is 1 - 60%, or 40%. The probability of losing on Sunday is 1 - 35%, or 65%. Multiplying these probabilities gives us 40% × 65% = 26%.
Therefore, the correct answer is (D) 26%
Write the standard form of the equation of the circle with the given center and radius.center (0,0), requals=11
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Help please ! It’s practical math
Answers
the table shows the annual profits (in thousands of dollars) of a county fair from 2008 to 2012. What must the 2012 profit be (in hundreds of dollars) to break even over the five-year period?
Answers
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars = 4.5 hundred dollars to break even over the five-year period.
The 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
It is required to find the profit in 2012.
What is break even point?The break-even point is the point at which total cost and total revenue are equal, meaning there is no loss or gain for your small business. It tells an owner the amount of revenue needed to cover all expenses, including fixed costs.
Given:
The break-even point is the point in which a business makes no gain and no loss.
According to given question we have
Let the 2012 profit be x, then
2.5 + 1.75 + (-3.3) + (-1.4) + x = 0
4.25 - 3.3 - 1.4 + x = 0
-0.45 + x = 0
x = 0.45
Therefore, the 2012 profit must be 0.45 thousand dollars is equal to 4.5 hundred dollars to break even over the five-year period.
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The helvie family drinks 1 3/4 gallons of milk every 4 1/2 days. what is the unit rate of milk they drink per day?
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When can I apply the use of the cubic function (y= a( x - h ) ^3 + k) in a real life situation?
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Also, check out the topic of cubic splines -- curves that pass through a given set of "control points." One application of those is the design of typographic fonts.
How do you solve this equation: 3x+1/5y=7
Answers
3(2) + (1/5)5 = 7
6 + 5/5 = 7
6 + 1 = 7
7 = 7
Use foil method (8a - 8)(4a + 1)
Answers
__________________________________________________
Given:
__________________________________________________
(8a − 8)(4a + 1) ; Let us expand this expression using the: "FOIL" method.
___________________________________________________
"FOIL" stands for "First terms, Outer terms, Inner Terms, Last Terms" ;
in that order.
___________________________________________________
Basically:
_______________________________________________________
(a + b)(c + d) = ac + ad + bc + bd ;
in which the:
First term is: "ac" ;
Outer term is: "ad" ;
I nner term is: "bc" ;
Last term is: "bd " .
__________________________________
So; we have (given):
(8a − 8)(4a + 1) ;
__________________________________________________
Let's take the "First, Outer, Inner, and Last terms" ; as follows:
__________________________________________________
F: (8a)*(4a) = 32a² ;
__________________________________________________
O: (8a)*(1) = 8a ;
__________________________________________________
I : (-8)*(4a) = -32a ;
__________________________________________________
L: (-8)*(1) = -8
__________________________________________________
Now, let us write out these terms:
__________________________________________________
32a² + 8a − 32a - 8 ;
__________________________________________________
Now, combine the "like terms" in this expression; to simplify:
+ 8a − 32a = -24a ;
__________________________________________________
and rewrite the simplified expression ; which is:
__________________________________________________
32a² − 24a − 8 .
______________________________________________________
A dependent variable is a. directly changed by the experimenter. b. manipulated by changes to the independent variable. c. a variable that is kept constant. d. a variable that is used as a control.
Answers
A dependent variable is one that is changed, when the independent variable changes.
For example, if we wanted to calculate how many dollars we've earned in a given amount of time, time would be the independant variable, because it is a constant and is not affected by how much many we earn. The amount of money we earned is directly affected by the independent variable, time.
Your answer is b.
Hope I helped!
Be sure to leave a "Brainliest" if I was helpful. Or not lol. I really don't care tbh XD
Answer:- Option b. is the right answer. A dependent variable is manipulated by changes to the independent variable.
Explanation:-
In mathematical modelling or scientific research a variable is defined as a term that has a quantity that varies. There are two kinds of variables:- 1) dependent variables 2) independent variables.
A independent variable can be change by the experimenter to check the effects on dependent variables which is observed by the him in a scientific experiment.
Thus, A dependent variable is manipulated by changes to the independent variable.
Of the 30 girls who tried out for lacrosse team at euclid middle school ,12 were selected .of the 40 boys who tried out 16 were selected .and the ratio of the number of studets on the team to the number of students trying out the same for both boys and girls ? how do you know
Answers
boys :
on the team -- 16
trying out -- 40
ratio is : 16/40 which reduces to 2/5
girls :
on the team -- 12
trying out -- 30
ratio is : 12/30 which reduces to 2/5
so yes, the ratios are the same because in both boys and girls, the number of players selected was 2/5 of the total who tried out.
30 ÷6= 5
12 ÷6 =2
∴For Girls 2:5
Calculation for Boys
40 ÷ 4 = 10
16 ÷ 4 = 4
∴ For Boys 4:10---- which = 2:5
If u divided both 4 and 10 by 2
∴Both have the same ratio of 2:5
What is 4 pi cubed divided by 3
Answers
What is the equation of a horizontal line passing through the point (−3, 8)?
x = −3
y = 8
x = 5
y = −11
Answers
The equation of a horizontal line passing through the point (−3, 8) is y= 8
How to determine the equation of a horizontal line passing through the point (−3, 8)
From the question, we have the following parameters that can be used in our computation:
The point (−3, 8)
The equation of a horizontal line is of the form
y = c, where
c is a constant.
Since the line is horizontal, the value of y is constant for all points on the line.
In this case, the line passes through the point (−3,8), so the equation of the horizontal line is y = 8.
I don't know how to do this
Answers
2(6-7x) = -8(x+6)
multiply the numbers inside the parenthesis with the numbers outside of them:
12 -14x = -8x-48
add 12 to each side:
-14x =-8x -36
add 8x to both sides
-6x = -36
divide both sides by-6
x = 6
The area of a square is 18 sq in less than twice the area of a triangle. the base of the triangle is 3 in longer and the altitude is the same length as the side of the square
Answers
So, the altitude of the triangle = x
and it's base = x+3
2 (area of triangle) - 18 = area of the square
area of the triangle = (1/2)height× base
and
area of the square = side^2
{ (2)(1/2)(x)(x+3)} -18 = x^2
x^2 + 3 x -18 = x^2
3x -18 =0
3x = 18
x = 6
so, the length of one side of the square = 6 units = altitude of the triangle
and the base of the triangle = 6+ 3 = 9cm.
-4=g+1
A. g=-4
B. g=4
C. g=-5
D. g=-3
Answers
If f(x)=7x-3 and g(x)=x^2, what is (g•f)(1)
Answers
If f(x)=7x-3 and g(x)=x²,
(g•f)(1)= g(f(1))
bit : f(1) =7(1)-3 = 4
(g•f)(1)= g(f(1)) = g(4) = 1² = 16
Find two consecutive integers whose sum is 101
Answers
The coordinates of the endpoints of and are A(3, 6), B(8, 7), C(3, 3), and D(8, 4). Which statement describes how and are related?
a)AB//CD
b)AB//CD, and AB bisects CD
c)AB//CD, but AB does not bisect CD
d)AB is neither parallel nor perpendicular to CD
Answers
Answer:
The correct answer is option a.
Step-by-step explanation:
If a line passing through two points, then the slope of a line is defined as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The coordinates of the endpoints of are A(3, 6), B(8, 7), C(3, 3), and D(8, 4).
[tex]m_{AB}=\frac{7-6}{8-3}=\frac{1}{5}[/tex]
[tex]m_{CD}=\frac{4-3}{8-3}=\frac{1}{5}[/tex]
Since slope of AB and CD are same, therefore the line AB is parallel to CD because the slope of parallel lines are equal.
Two parallel lines never intersect each other, therefore AB does not intersect CD. Only option a is correct.
Find b given that p(b,2) is equidistant from a(5,4) and b(2,5)
Answers
PA = PB or PA² = PB²
(5-b)²+(4-2)² = (2-b)² + (5-2)²
(5-b)²+4 = (2-b)² + 9
25 -10b +b² + 4 = 4 -4b+b² +9
-6b = -16
b = 8/3