Answer:
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Step-by-step explanation:
Given
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Required
Find an equivalent expression
[tex]\frac{125^2}{125^\frac{4}{3}}[/tex]
Apply the following law of indices;
[tex]\frac{a^m}{a^n} a^{m-n}[/tex]
The expression becomes
[tex]125^{2-\frac{4}{3}}[/tex]
Solve the exponents
[tex]125^{\frac{6-4}{3}}[/tex]
[tex]125^{\frac{2}{3}}[/tex]
Express 125 as 5³
[tex]5^{3^*\frac{2}{3}}[/tex]
Solve the exponents
[tex]5^2[/tex]
[tex]25[/tex]
Hence;
[tex]\frac{125^2}{125^\frac{4}{3}} = 25[/tex]
Answer:
d
Step-by-step explanation:
i just took it! edgen
#6) Beth saved a total of $30 per month for her first car. Beth saved
money for 20 months and opened her account with $100. What is the
domain and range of the situation representing the amount of money
Beth saved in respect to time she saved? Write your answer in
interval notation.
D:
R:
Answer:
Domain = 0≤m≤20 for mEZ+
Range = $100≤A≤$700 for all values of m
Step-by-step explanation:
Initial amount in the account = $100
Amount saved by beth monthly = $30
Amount in the bank after X month = $100+$30X where X is the number of months beth intend to save up to.
The amount in her bank in her first month = $100+$30(1)
= $100+$30
= $130
Amount saved in the second month will be when X = 2
= $100+$30(2)
= $100+$60
= $160
The amount in the bank will keep increasing by $30 monthly until the 20month.
The amount he will have in her bank in the 20th month will be at when X = 20
= $100+30X
= $100+30(20)
= $100+$600
= $700
This means that her money will be $130 in the first month and will keep increasing until it reaches $700 in the 20th month.
The DOMAIN will be the interval of the time she used in saving. Since she saved for 20months, the domain will be expressed as 0≤m≤20 for mEZ+ where m is the number of month she uses to save.
The Range will represent the amount she saved within the specified time and will be expressed as $100≤A≤$700 for all values of m.
Where $100 is the amount in the account initially and $700 is the amount in the account after 20 months.
If 1/4 is 25% of 1, what percentage is 2/4?
Answer: 50%
Step-by-step explanation:
Add 25% to 25% : do this because 1/4+1/4=2/4, which is a half. If you add 25% to 25%, you get 50%, and 50% is also 1/2.
Answer:
Step-by-step explanation:
If 1/4 is 25% of 1, then 2/4 in its simplest form is 1/2 or 50%.
Fran’s store spent $64,000 on expenses last year. Rent of the store was 35% of those expenses .How much did Fran spend on rent.
Answer:
$22400
Step-by-step explanation:
multiply 64000 with 0.35 (35%)
Which of the following is correct based on this picture? A. tan M=38/63 B. sin M=38/63 C. none of these are correct D. cos M=38/63
Answer:
Option D. Cos M = 38/63
Step-by-step explanation:
Let the side opposite to angle M be y.
The value of y can be obtained by using the pythagoras theory as illustrated below:
y² = 63² – 38²
y² = 3969 – 1444
y² = 2525
Take the square root of both side
y = √2525
y = √(25 x 101)
y = √25 x √101
y = 5√101
Now, let us determine Tan M, Sine M and Cos M to know which of the options are correct.
This is illustrated below:
Tan M =?
Opposite = 5√101
Adjacent = 38
Tan M = Opposite /Adjacent
Tan M = 5√101 / 38
Sine M =.?
Opposite = 5√101
Hypothenus = 63
Sine M = Opposite /Hypothenus
Sine M = 5√101 / 63
Cos M =?
Adjacent = 38
Hypothenus = 63
Cos M = Adjacent /Hypothenus
Cos M = 38/63
From the calculations made above,
Tan M = 5√101 / 38
Sine M = 5√101 / 63
Cos M = 38/63
Therefore, Option D gives the correct answer.
correct
Ken's temperature prediction for February
is -3°C. By May, Ken predicts that the average
temperature will increase by 11°C.
Use the number line interactive tool to determine the
predicted temperature in May. What is Ken's
temperature prediction for May?
Answer:
Ken's prediction for May is 8 degrees centigrade : [tex]8\,C^o[/tex]
Step-by-step explanation:
Locate the starting point at the value -3 on the number line, and count (add) 11 units to the right of that point, ending at the point 8 on the number line.
Answer:8c
Step-by-step explanation:
Paul is planning a 303 mile road trip driving his truck that gets about 23 mpg. When he starts out, one gallon of gas costs $3.02. Using front-end estimation, choose which one of the following is the best estimate of the total cost of gas for this trip.
Answer:
45
Step-by-step explanation:
Help!!!!!!!!!!!!!!!!
Answer:
B
Step-by-step explanation:
To get x by itself, you have to divide each side by the number that x is attached with.
For the first one, divide each side by 3 so that x is by itself and 21/3 is 7 to get x<7
Do the same with the other side but with 5 to get x>11
Solve : - 43 - 4x = 3(1 - 9x)
Answer:
x = 2
Step-by-step explanation:
-43 - 4x = 3(1 - 9x)
Distribute the 3:
-43 - 4x = 3 * 1 - 3 * 9x
-43 - 4x = 3 - 27x
Add 27x to both sides:
-43 - 4x + 27x = 3 - 27x + 27x
-43 + 23x = 3
Add 43 to both sides:
-43 + 43 + 23x = 3 + 43
23x = 46
Divide both sides by 23:
23x / 23 = 46 / 23
x = 2
Answer:
The answer is
x = 2- 43 - 4x = 3(1 - 9x)
Expand the terms
That's
- 43 - 4x = 3 - 27x
Group like terms
Send the constants to the right side of the equation and those with variables to the left side
That's
- 4x + 27x = 43 + 3
Simplify
23x = 46
Divide both sides by 23
[tex] \frac{23x}{23} = \frac{46}{23} [/tex]
We have the final answer as
x = 2Hope this helps you
Find the smallest number which must be added to the following numbers so as to make them a perfect square 4931
Answer:
110.
Step-by-step explanation
4900 = 70^2
71^2 = 5041
5041- 4931 = 110
Answer is 110
How do I isolate the y variable?
[tex]x = \frac{2y + 4}{3} [/tex]
Answer:
y = [tex]\frac{3x}{2}[/tex] - 4
Step-by-step explanation:
first multiply by 3 on both sides
then subtract 4 on both sides
finally you have to divide by 2 on both sides to get
y = [tex]\frac{3x}{2}[/tex] - 4
What percent of one hour is 25 minutes?
Answer:
41.667% or 42%
Step-by-step explanation:
25/60
simplify
5/12 = 41.667
Number 51 is decreased to 26 what is the percentage by the numbers decrease
Answer:
about 49
Step-by-step explanation:
I basically estimated my way to the answer, you need to do a lot of calculations for this problem, but as long as you understand the concept, its fine by me to usr a calculator to get the percentage
Answer:49.0
Step-by-step explanation: First you subtract 26 from 51 and then divide that by the original number(51) and multiply that by 100
What is 825 rounded to the nearest ten?
Answer:
830
Step-by-step explanation:
In this case the tens place is where the 2 is at so 25 is close to 30 which is a solid ten
Use the position equation given below, where s represents the height of the object (in feet), v0 represents the initial velocity of the object (in feet per second), s0 represents the initial height of the object (in feet), and t represents the time (in seconds), as the model for the problem. s = −16t2 + v0t + s0 An aircraft flying at 900 feet over level terrain drops a supply package.
(a) How long does it take until the supply package to strike the ground? (Round your answer to three decimal places.) t = sec
(b) The aircraft is flying at 158 miles per hour. How far does the supply package travel horizontally during its descent? (Round your answer to one decimal place.) ft
Answer:
a) 17.667 s
b) 4094 feet
Step-by-step explanation:
a) The position equation of the model is given by:
[tex]s=-16t^2+v_ot+s_o\\\\v_o=initial \ velocity = 158\ miles/hour\\\\s_o=Initial\ height=900\ ft\\\\1 \ mile = 5280\ ft, 1\ hour= 3600\ s\\\\Therefore:\\\\v_o=158\ miles/hour = 158*\frac{5280}{3600}=231.733\ ft/s\\ \\Substituting:\\\\0=-16t^2+231.733t+900\\\\16t^2-231.733t=900\\\\\\16t^2-231.733-900=0\\\\Solving\ the\ quadratic\ equation\ gives:\\\\ t=17.667\ s\ or \ t=-3.184\ s\\\\Since\ the \ time\ cannot\ be\ negative\ therefore\ t=17.667\ s[/tex]
b) The horizontal distance = Initial velocity × time = 231.733 × 17.667 = 4094 feet
how can i get some awnser
Step-by-step explanation:
You need to ask a question about the problem/s you need help with
AB¯¯¯¯¯¯¯¯ plane CDE FG←→ HI−→ Question 2 Explain your reasoning. The one that does not belong is an undefined term. The one that does not belong uses a different kind of symbol. The one that does not belong contains fewer points. The one that does not belong has a different number of dimensions.
Answer:
The one that does not belong has a different number of dimensions.
Step-by-step explanation:
i did it and i got it right
Have a nice day
A. 569 x 102 = 569,000
B. 569 x 10 = 56.9
C. 103 x 569 = 569,000
D. 102 x 569 = 5,690
Answer:
A: False B: False C: False D: False
Step-by-step explanation:
569x 102 = 58038
569x 10 = 5690
103x 569 = 58607
102x 569 = 58038
In a recent year a baseball team paid seven times as much to their ace pitcher as they paid to their shortstop. If they paid $ 24 million for the two salaries, what did they pay each player?
Answer:
Shortstop =$3,000,000;
ace pitcher = $21,000,000
Step-by-step explanation:
Let amount earned by shortstop = s
Then, amount earned by ace pitcher = 7 times amount earned by shortstop = (7 × s) = 7s
Total amount Paid = $24,000,000
Amount earned by each player :
s + 7s = 24,000,000
8s = $24,000,000
s = 24,000,000 / 8
s = 3,000,000
Hence,
Salary earned by shortstop = $3,000,000
Salary earned by ace pitcher = (7 * 3,000,000) = $21,000,000
10) Gabe put up a fence around his rectangular vegetable garden this weekend.
The garden has a perimeter of 38 ft and an area of 48 ft? What is the length and
the width of the garden?
Answer:
The length is 16 ft, and the width is 3 ft.
Step-by-step explanation:
Let L = length & let W = width.
The perimeter of a rectangle is
P = 2(L + W)
The area of a rectangle is
A = LW
We know the perimeter and the area, so we substitute those values int he equations above and we switch sides in both equations.
Perimeter: 2(L + W) = 38
Divide both sides by 2:
L + W = 19
Area: LW = 48
We have a system of two equations in two unknowns:
L + W = 19
LW = 48
Solve the first equation for L and substitute it into the second equation.
L = 19 - W
(19 - W)W = 48
19W - W^2 - 48 = 0
Multiply both sides by -1, and rearrange the order of the terms.
W^2 - 19W + 48 = 0
(W - 16)(W - 3) = 0
W - 16 = 0 or W - 3 = 0
W = 16 or W = 3
Use W = 3 to find L
L = 19 - W
L = 19 - 3
L = 16
Answer: The length is 16 ft, and the width is 3 ft.
Nine years ago, Tarah opened a savings account with her bank. She started with a balance of $359 and has not made any withdrawals or deposits since then. If her interest rate is 8% each year, how much interest has accrued using simple interest?
Answer:
The interest accrued is $258.48.
Step-by-step explanation:
Given that:
Initial balance in the savings account = $359
Interest rate = 8%
Time for which no withdrawals or deposits were done = 9 years
To find:
Simple Interest accrued = ?
Solution:
First of all, let us have a look at the formula for simple interest.
[tex]SI = \dfrac{PRT}{100}[/tex]
Where P is the Principal Amount.
R is the annual rate of interest
T is the time in years.
Here, we are given:
P = $359
R = 8%
T = 9 years
Let us put all the values in the formula:
[tex]SI = \dfrac{359 \times 8 \times 9}{100}\\\Rightarrow SI = \dfrac{359 \times 72}{100}\\\Rightarrow SI = \dfrac{25848}{100}\\\Rightarrow \bold{SI = \$258.48}[/tex]
So, the interest accrued is $258.48.
In what ways are the steps for the long division of polynomials algorithm similar to the steps for the multiplying polynomials algorithm? In what ways are they different?
Answer:
Undermentioned explanation, similarity & dissimilarity between long division & multiplication of polynomials
Step-by-step explanation:
Long Division of Polynomial steps :
Complete missing terms in divisor with zero coefficients, sort terms in decreasing exponential order
Divide leading term, multiply divisor x quotient, subtract partial product & carry down remainder ............ (continue same)
Multiplication of Polynomial steps :
Multiply the 1st, 2nd, 3rd term(s) in the first polynomial with 1st, 2nd, 3rd consecutive term(s) in the second polynomial........... (go on)
Similarity (ies) : Both involve term by term treatment, multiplying monomial & polynomial
Dissimilarity (ies) : Division includes subtracting of exponential power. However, multiplication includes adding of exponential power
35 more than a number x is 73
Answer:
38
Step-by-step explanation:
X+35=73
x=73-35
x=38
Answer:
X=38
Step-by-step explanation:
x+35=73
-35 -35
Simplify each expression 6x + 4y + 5x
Explanation:
The like terms are 6x and 5x. They add to 11x since 6+5 = 11, and then we tack x onto each to get 6x+5x = 11x.
You can think 6x representing the idea we have 6 boxes. Then adding on 5x means we have 5 more boxes to get 6+5 = 11 boxes total.
Please help
Let a and b be positive integers. 23a×23b=?
Answer:
A) 23^(a+b)
Step-by-step explanation:
if you multiply a number with diferrent exponents, the exponents will always add.
The bases are the same, so we add the exponents
The answer is [tex]23^{a+b}[/tex] which is choice A============================================
Here's an example of why we add the exponents
Lets say we want to multiply 7^2 with 7^3
7^2 = 7*7
7^3 = 7*7*7
We have two copies of "7" being multiplied with 7^2, then we have an additional three copies of "7" with 7^3. Overall there are 2+3 = 5 copies of "7" that we multiply out.
So,
7^2*7^3 = (7^2) * (7^3)
7^2*7^3 = (7*7) * (7*7*7)
7^2*7^3 = 7*7*7*7*7
7^2*7^3 = 7^5
This example is fairly small in that we don't have that many copies of the base being multiplied. For larger examples, its best to use the formula mentioned
a^b*a^c = a^(b+c)
Which proportion could be used to solve
the following problem?
A recipe for sesame chicken calls for
cup of chopped carrots. If the recipe
2
is for 4 servings, how many cups of
carrots are needed for 9 servings?
Answer:
Cups of carrot needed for 9 servings = 4.5 cups
Step-by-step explanation:
A recipe for sesame chicken calls for cup of chopped carrots
recipe 2 is for 4 servings
That is
2 cups of carrot = 4 servings
2 : 4
= 1 : 2
1 cup of carrot = 2 servings
how many cups of
carrots are needed for 9 servings?
Let x= number of carrot needed for 9 servings
1 : 2 = x : 9
1 /2 = x/ 9
Cross product
1*9 = 2*x
9=2x
Divide both sides by 2
9/2 = x
x= 4.5 Or 4 1/2
Two drivers begin at point C simultaneously. One drives from C to B to A. The other drives directly to A at 50 mph. How fast must the first person dirve to get to A first? A) LESS THAN 50 MPH B) LESS THAN 60 MPH C) LESS THAN 70 MPH D) MORE THAN 70 MPH
Answer:
Option "D" is the correct answer to the following question.
Step-by-step explanation:
The first person drive "more than 70 mph " to get to A first.
It is given that average speed of second person is 50 mph, So to get A first , first diver must drive more than 50 mph.
So option "D" is the correct answer to the following question.
Which of the follwing equations has a quotient with a remainder?
Select the three that apply. A. 946/32
B. 1157/11
C.3524/44
D.37,392/82
B,C,D
A,B,C
A,C,D
A,B,D
Answer: Choice 2) A, B, C
====================================
Explanation:
Use a calculator to find that,
946/32 = 29.56251157/11 = 105.1818 approximately3524/44 = 80.0909 approximately37392/82 = 456The first three results have a decimal portion as the answer. So there is a remainder here. The remainder is the leftover bit that couldn't make another full value. Only choice D results in a whole number that isn't a decimal value, so this does not have a remainder.
As a smaller example, let's say we had 20 cookies and 3 people. If we want to divide the cookies evenly, then each person gets 20/3 = 6 full cookies and there would be 2 cookies left over (6*3 = 18 are eaten so 20-18 = 2 is left over). Notice that 20/3 = 6.67 approximately. The non-whole number decimal value indicates we have a remainder. If we had 21 cookies, then each person gets 21/3 = 7 full cookies with nothing left over, so there's no remainder here.
A line has a slope of 1/4 and passes through the point (4,8). Write the equation of the line in slope intercept form.
Answer:
y = 1/4x +7
Step-by-step explanation:
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = 1/4 x +b
Substitute the point into the equation
8 = 1/4(4) +b
8 = 1 +b
Subtract 1 from each side
8-1 =b
7 =b
y = 1/4x +7
true or false? Induction is a kind of thinking you use to form general ideas and rules based on mathematical formulas?
your answer is false
Your Teacher is wondering if the absolute value of a number can ever be negative. Is she correct? Why or Why not? Use specific examples and sound mathematical reasoning to support your answer