Answer:
1/5³ = 1/125 = 5⁻³
Step-by-step explanation:
It can be useful to remember that an exponent signifies repeated multiplication.
5^3 = 5×5×5
5^6 = 5×5×5×5×5×5
Then the ratio is ...
[tex]\dfrac{5^3}{5^6}=\dfrac{5\times5\times5}{5\times5\times5\times5\times5\times5}=\dfrac{1}{5\times5\times5}=\boxed{\dfrac{1}{125}}[/tex]
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If you want to leave this in terms of exponents, you can see that factors in the denominator cancel (subtract from) those in the numerator. That is ...
[tex]\dfrac{5^3}{5^6}=\dfrac{5^{3-3}}{5^{6-3}}=\dfrac{5^0}{5^3}=\boxed{\dfrac{1}{5^3}}[/tex]
The same sort of exponent arithmetic works to leave a numerator value with a negative exponent:
[tex]\dfrac{5^3}{5^6}=\dfrac{5^{3-6}}{5^{6-6}}=\dfrac{5^{-3}}{5^0}=\dfrac{5^{-3}}{1}=\boxed{5^{-3}}[/tex]
_____
Additional comment
These ideas are formulated as the rules of exponents:
(a^b)/(a^c) = a^(b-c)1/(a^b) = a^-bAl and Betty want to create a playlist of songs for their drive back and forth to school. Since Al and Betty have different tastes in music, they decide to compromise by only playing Al’s favorite rap and Betty’s favorite pop music that they can both agree upon.
Betty wants to include at least as many pop songs as rap songs. Al, in return, wants to include at least five rap songs. To provide enough variety to make the playlist interesting, they decide to include at least 20 songs altogether.
To create the playlist, Al and Betty will need to purchase the songs. They will have to pay $1.50 for each rap song and $1.00 for each pop song. How many of each type should they put on their playlist to minimize their cost?
Consider the expression (1.0045)^4t that represents the interest earned on a money
market account, where t is the time In years. What is the approximate yearly interest rate? Round your percent to the nearest tenth. INCLUDE THE % SYMBOL IN YOUR ANSWER
The approximate yearly interest rate is 1.02%
Exponential equationsGiven the expression that represents the interest earned on a money given as (1.0045)^4t
In order to calculate the approximate yearly percent, we will substitute t = 1 into the expression as shown:
f(t) = (1.0045)^4t
f(1) = (1.0045)^4(1)
f(1) = (1.0045)^4
f(1) = 1.018
Hence the approximate yearly interest rate is 1.02%
Learn more on interest rate here: https://brainly.com/question/25545513
A book costs $10 at one book store. About how much more does the book cost when the book store increases its prices 18%?
$11.80
Step-by-step explanation:
Summary What is an example of a sequence of transformations that, if performed in a different order-would result in a different image?
Answer:
an architect used the same floor plans in different locations and orientations to complete the layout of a housing complex.
Step-by-step explanation:
uwu
i will give brainliest
Find n.
35n/35 = 700/35
Answer:
20
Step-by-step explanation:
[tex]\frac{35n}{35} =\frac{700}{35} \\[/tex]
multiply both sides by 35
[tex]35*\frac{35n}{35} = 700 * 35\\35n = 700[/tex]
divide both sides by 35
[tex]n = 20[/tex]
Answer:
N = 20
Step-by-step explanation:
Move all terms to the left
35n/35-(700/35)=0
Add all of the numbers together, and all of the variables
35n/35-20=0
Multiply all of the terms by the denominator
35n-20*35=0
Add all of the numbers together, and all of the variables
35n-700=0
Move all of the terms containing N to the left, all other terms to the right
35n=700
n=700/35
n=20
The equation f = v + at represent the final velocity of an object f with an initial velocity v and an acceleration rate a overtime t. which is an equivalent equation solved for t
Answer:
t = f-v/a (First choice)
Explanation:
step by step:
1) f = v + at
2) f - v = v - v + at
3) f - v = at
4) f - v / a = at / a
5) f - v / a = t
6) t = f - v / a
pls answer i will mark u brainlist
Explain how to solve the equation.
g/4=24
Part 1
Select the correct choice below and fill in the answer box within your choice.
(Type a whole number.)
A.Divide both sides by
B.Subtract from both sides.
C.Multiply both sides by
D.Add to both sides.
Answer:
C. Multiply both sides by 4.
Step-by-step explanation:
You are isolating the variable, g, and so you will do the opposite of all operations that occurs with the variable, g.
Note the equal sign, what you do to one side, you would do to the other. Isolate the variable, g, by multiplying 4 to both sides of the equation:
[tex]\frac{g}{4} * 4 = 24 * 4[/tex]
[tex]g = 24 * 4[/tex]
[tex]g = 96[/tex]
~
Solve for x
3(x-a)+2b=4x+a
Find the equation of the axis of symmetry of the following parabola algebraically.
y=3x^2+18
Answer:do you have a picture
Step-by-step explanation:
i need it to solve
solve the inequality and tell weather it has infinite or no solutions
[tex]0.5x+8\ \textless \ 2x-4[/tex]
The first to answer will be named brainlest
Answer:
Id say 1st and 3rd answer.
Step-by-step explanation:
Answer:
First Third and Fourth Statements are true.
Step-by-step explanation:
all four sides of the baseball diamond are 90 ft long.
if you ran in a straight line from first base to third base, what would the distance be rounded to the nearest whole number?
a. 13 feet
b. 16,200 feet
c. 127 feet
d. 180 ft
Answer:
d. 180 ft
Step-by-step explanation:
Answer:
well that will be 180ft
Step-by-step explanation:
POINTS AND BRAINLY
PLEASE HELP MEEEE
Answer:
the answer would be A a pure sound
Answer:
I think it is A pure Sound
Step-by-step explanation:
Find the total amount given the original price, tax rate and tip rate. Round to the nearest hundredth if necessary.
Original price: $90.34
Tax rate: 3.5%
Tip: 20%
Enter the correct answer in the box.
Answer:
$111.5699. Round to hundredths $111.57
Step-by-step explanation:
First identify the %
20% =.20 20/100= .20
3.5% = .035 3.5/100= .035
Then Find the tax rate and tip
Tax Rate .035 × 90.34
= $3.1619 (tax rate)
Tip. is .20× 90.34
= $18.068 (tip)
Final Add all it up tax rate+ tip + original price
$90.34. Don't forget to line up your demicals
$3.1619. or use a calculator
+ $18.068
Total = $111.5699
round to the nearest hundredth
$111.57 is your total
1. In the computer lab, there
are 14 desktops and 16
laptops. Approximately what
percent of the computers are
laptops?
Answer:
53.3333333%
Step-by-step explanation:
Given the following question:
14 desktops
16 laptops
14 + 16 = 30
To find the answer use the formula to calculate percentages.
[tex]\frac{16}{30}\times100[/tex]
[tex]16\div30=0.533333333[/tex]
[tex]0.533333333\times100=53.3333333[/tex]
[tex]=53.3333333[/tex]
16 of 30 as a percentage is "53.3333333%."
Hope this helps.
Cesar y Ana reciben uuna cuerda de igual longitud.Cesar corta 40/100 de su cuerda para jalar un paquete mientras que Ana corta 9/25 para amarrar dos maletas¿quien usa mayor longitud de cuerda?,justifica
César ha cortado el segmento de cuerda de mayor longitud para amarrar una maleta.
Cómo determinar el segmento más largo utilizado de cuerdas
Una fracción es un número real formado por dos números enteros, un numerador y un denominador, respectivamente.
En esta pregunta debemos determinar quien tiene la mayor longitud de cuerda y para ello debemos aplicar propiedades tal que ambas fracciones tengan el mismo denominador. En consecuencia, la persona que tendría la mayor fracción tendría además el mayor numerador. A continuación, procedemos a realizar las siguientes operaciones:
40/100, 9/25
Al dividir cada término de la primera fracción por 4, tenemos lo siguiente:
10/25, 9/25
Por tanto, César ha cortado el segmento de cuerda de mayor longitud para amarrar una maleta. [tex]\blacksquare[/tex]
Para aprender más sobre fracciones, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/24570029
4. What is the value of b in the triangle shown below?
(1 point)
3b
24 in.?
b
0-4 in
04 in
0 =4 in
O no solution
Answer:
4 inches
Step-by-step explanation:
[tex]24 = \frac{1}{2} (b)(3b) \\ \\ \implies \: 24(2) = 3 {b}^{2} \\ \\ \implies \: 48 = 3 {b}^{2} \\ \\ \implies \: \frac{48}{3} = {b}^{2} \\ \\ \implies \: {b}^{2} = 16 \\ \\ \implies \: {b} = \pm\sqrt{16} \\ \\ \implies \: {b} = \pm \: 4 \\ \because \: b \: is \: side \: length \\ so \: its \: value \: cant \: be \: negative. \\ \implies \: b = 4 \: in[/tex]
Hey I really need help with metric conversions test is tomorrow.
I would appreciate a lot if y’all help me!
Answer:
Deductive reasoning
Step-by-step explanation:
Owen measured a line to be 17.9 inches long. If the actual length of the line is 17.8 inches, then what was the percent error of the measurement, to the nearest tenth of a percent?
Answer:
0.6%
Step-by-step explanation:
Percent Error = the absolute value of (actual value observed-expected value)/(expected value) x100%
(17.8-17.9)/(17.9) = -0.006
Absolute value is 0.006
0.006 times 100% equals 0.6%
The percent error of the measurement in the length is 10%.
What is percent error in measurement?Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.Given is that Owen measured a line to be 17.9 inches long. The actual length of the line is 17.8 inches.
We can calculate the percentage error as -
%e = {(A.V. - E.V.)/(A.V.)} x 100
%e = (17.9 - 17.8) x 100
%e = 0.1 x 100
%e = 10%
Therefore, the percent error of the measurement in the length is 10%.
To solve more questions on functions, expressions and polynomials, visit the link below -
brainly.com/question/17421223
#SPJ2
Can anyone solve this please? ASAP
Answer:
5a) 4
5b) 4
Step-by-step explanation:
You'll use Pythagorean theorem throughout this problem a lot. So, to find X, You have a right triangle with one leg of 6, and one leg of 2. 2 squared plus 6 squared equals c squared. 4 + 36 = c squared then you get 40 = c squared.
To get c by itself you'd square root both sides. So that leaves you with X = the square root of 40.
Now, to get Y, you have another triangle with a leg of 4, and another leg of the square root of 40. 4 squared = 16, and the square root of 40 squared is just 40. So, 16 + 40 = c squared. 56 = c squared, then again, to get the c value by itself you need to square root both sides, leaving you with Y = the square root of 56.
70200 NC)
Demarcus will be 21 years old when he graduates. It is mean weekly wage over his career is $1.258.00 what will his lifetime earnings be when he retires at the age of 62? (1 point)
$1371 532.00
$287779200
$3.572132.00
$4049344.00
Step-by-step explanation:
Her life term earnings will be 4049344.00 dollars
Is (6, 1) a solution to the equation y = 5x?
Answer:
False, but depends on…
Step-by-step explanation:
If you are dealing with x and y-intercepts, or slopes, then no. The answers wouldn't be in the given format. If you're looking for a coincidence, then it could be a solution. Hope this helps!
PlS can anyone help me ASAP
Answer:
yo what is that
Step-by-step explanation:
The mean of 3 numbers is 4. 2 of the numbers are 1 and 9
What is the third number
Answer:
2
Step-by-step explanation:
[tex]\frac{a+b+c}3}= 4\\[/tex]
multiply both sides by 3
a+b+c=12
substitute the values we have
1+9+c=12
10+c=12
-10 -10
c=2
so the third number is 2
hope this helped you !
x-85=156 what is x equal to? or supposed to be. whichever. what is x? pls help me:))
Answer:
X would equal 241
Step-by-step explanation:
Hope this helps and have a wonderful day~
Anthony resells shoes that he purchases. He bought a pair for $210, and then applied a 43% markup. How much will the shoes be sold for?
The area of the triangle below is 4.14 square inches. What is the length of the buse?
Answer:
3.6
Given:
are of triangle=4.14
height=2.3
Step-by-step explanation:
area of the triangle=1/2 × base × height
4.14 = 1/2 × base × 2.3
4.14 = 2.3/2 × base
by cross multiplying,
4.14 × 2 = 2.3 × base
8.28 = 2.3 × base
8.28/2.3 =base
To remove the decimal point, multiply with 100 in both numerator and denominator
8.28×100 / 2.3×100 = base
828/230 = base
base = 3.6
hope it helps you!
Answer:
3.6 inches.
Step-by-step explanation:
Area = 1/2 * base * height
4.14 = 1/2 * base * 2.3
1/2 * base = 4.14 / 2.3
base = 4.14 * 2 / 2.3
= 3.6.
Which of these descriptions would NOT guarantee that the figure is a parallelogram?
A) A quadrilateral with consecutive angles supplementary.
B) A quadrilateral with diagonals bisecting each other.
C) A quadrilateral with both pairs of opposite sides congruent.
D) A quadrilateral with one pair of opposite sides parallel
Answer:
D) A quadrilateral with one pair of opposite sides parallel
Step-by-step explanation:
Choice D matches the description of a trapezoid, not a parallelogram. That description will not guarantee the figure is a parallelogram.