Answers
The simplified form of the expression using the law of exponent is 5/a^9b^9
Exponential expressionGiven the exponential expression as shown:
\(\frac{25a^{-5}b^{-8}}{5a^4b}\)
According to product and quotient of exponents, multiplication will be addition and quotient will be difference.
\(\frac{25a^{-5}b^{-8}}{5a^4b}=\frac{25}{5}a^{-5-4}b^{-8-1}\\ \frac{25a^{-5}b^{-8}}{5a^4b}=5a^{-9}b^{-9}\)
Write the result as fraction
\(\frac{25a^{-5}b^{-8}}{5a^4b}=\frac{5}{a^9b^9}\)
Hence the simplified form of the expression using the law of exponent is 5/a^9b^9
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Related Questions
consider the grid of points shown here. suppose that, starting at the point labeled a, you can go one step up or one step to the right at each move. this procedure is continued until the point labeled b is reached. how many different paths from a to b are possible?
Answers
The following is an excerpt from A First Training in Probability by Sheldon Ross. (74) = 35 is the right response.
Total moves required are 7, as follows:
Three steps up as well as four steps right.
Remember that perhaps the number of paths equals the number of arranged 7-tuples with 3 U's and 4 R's. As instance, the word URRURRU indicates to travel up, right, up, right, right, up.
There are 7 ways to arrange these letters, 7 ways to arrange the corresponding Us, and 7 ways to arrange the comparable Rs, for a total of 7!3!4! (74).
For each NxN grid, we may write the following as a generalization of our formula: It should be noted that there's a simpler method of writing this: D = N! / (K! * (N-K))! additionally known as the binomial coefficient.
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how to do the first question?
Answers
Answer:
DUDE MAYBE SHOW THE GRAPH ????
PLSSSSS HELP MEEEE 24 POINTSSSS MATHHH
Answers
Answer:
the answer is equal to 6⁴
Step-by-step explanation:
by 6⁵/6¹
so 6^5-1
6^4
An article presents a method, based on a modal pushover analysis, of estimating the hysteretic energy demand placed on a structure by an earthquake. A sample of 18 measurements had a mean error of 457.7 kNm with a standard deviation of 317.7 kNm. An engineer claims that the method is unbiased, in other words, that the mean error is 0. Can you conclude that this claim is false
Answers
To determine whether the engineer's claim that the method is unbiased is false, we need to perform a hypothesis test.
The null hypothesis, denoted as H0, assumes that the method is unbiased, meaning that the mean error is zero. The alternative hypothesis, denoted as Ha, assumes that the method is biased, and the mean error is not zero.
Given a sample of 18 measurements with a mean error of 457.7 kNm and a standard deviation of 317.7 kNm, we can calculate the test statistic using a t-test. The test statistic is calculated by dividing the sample mean by the standard deviation divided by the square root of the sample size.
If the calculated test statistic falls within the rejection region defined by a chosen significance level, typically denoted as α, we can reject the null hypothesis and conclude that the engineer's claim of unbiasedness is false. The significance level determines the probability of making a Type I error, which is the probability of rejecting a true null hypothesis.
To make a definitive conclusion, we would compare the calculated test statistic to the critical value(s) from the t-distribution table or use statistical software to calculate the p-value associated with the test statistic. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the claim of unbiasedness is false. Conversely, if the p-value is greater than the significance level, we fail to reject the null hypothesis and cannot conclude that the claim is false.
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Jake is baking cookies for a bake sale. He needs 134 cups of flour for each batch of cookies, and he needs to make 323 batches.
How much flour does Jake need to make his cookies?
Answers
Answer:
He needs 43,282 cups of flour
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST !!!
If you have 3 points spread out randomly so that no 3 points are colinear, how many lines can you draw using 2 points? (Hint start at 1 dot and connect lines as you add each dot, you might notice a pattern)
Check more similar questions
Answers
Answer:
Step-by-step explanation:
i say 3 :I
cuz theres 3 dots spreed out and it said to connect the dots by starting off one and connect the others so i think its 3
how many soulutions are there to 8 (x-3) =8x-24
Answers
Answer:
Yes
Step-by-step explanation:
Answer:
infinitely many solutions.
Step-by-step explanation:
The given equation is 8(x-3)=8x-24
Distribute 8 over the parenthesis in the left hand side
8x-24 = 8x-24
Group the like terms
8x-8x=-24+24
Combine like term
0 = 0
We got a true result, 0 = 0.
Hence, the equations have infinitely many solutions.
Which value goes in the empty cell?
Answers
Answer:
[See Below]
Step-by-step explanation:
If you replace the x with -1 and evaluate the function you get -5.
Simplify. Keep your answer in exponent form.
:) help
Answers
((-6)³)^6
3×6=18
power=18
(-6)^18
Carlos is playing a dice game with Elena. Carlos will roll 222 six-sided dice, and if the sum is greater than 777, he will win \$5$5dollar sign, 5. If the sum is 777, they will tie and he will break even. If the sum is less than 777, he will lose \$4$4dollar sign, 4. What is Carlos's expected value of playing this game? Round your answer to the nearest cent.
Answers
Answer:
Step-by-step explanation:
The expected value of one six-sided dice is (1 + 2 + 3 + 4 + 5 + 6)/6 = 3.5.
So, the expected value of the sum of 222 dice is 3.5 * 222 = 777.
This means that the expected value of playing this game is 0, since the expected outcome is to break even.
Thus, Carlos's expected value of playing this game is 0, rounded to the nearest cent.
Answer:
Step-by-step explanation:
The expected value of Carlos playing this dice game is
$0.42
Kaya’s family spends $105 to rent a boat for 7 days. The total cost, c, of the boat rental is proportional to the number of days, d, the family rents the boat.
How much does it cost, in dollars, to rent the boat for one day?
Answers
Answer:
$15/day
Step-by-step explanation:
If the rent is proportional to the number of days, the dividing the total cost by the number of days will tell you the price of each day:
105/7=15
!30 POINTS! How can I use this trapezoid to prove the Pythagorean Theorem?
Answers
Answer:
a
Step-by-step explanation:
Which of the following is a function rule for the sequence 3, 8, 13, 18, 23, ...? A(n) = 5 + (n - 1)(3)A(n)= 3 + (n - 1)(5) A(n) = 1 + (n = 115) A(n) = 1 + (n - 1)(3)
Answers
Solution:
Given:
\(\begin{gathered} \text{The sequence;} \\ 3,8,13,18,23,\ldots \end{gathered}\)The sequence given is an arithmetic progression because it increases by a common difference.
Hence, the function rule for the sequence will follow that of an arithmetic progression (A.P).
The nth term of an A.P is given by;
\(\begin{gathered} a_n=a+(n-1)d_{} \\ \text{where;} \\ a_n\text{ is the nth term} \\ a\text{ is the first term} \\ n\text{ is the number of terms} \\ d\text{ is the co}mmon\text{ difference} \end{gathered}\)For the sequence given;
\(\begin{gathered} 3,8,13,18,23,\ldots \\ \\ a=3 \\ d=8-3\text{ or 13-8 or 18-13 or 23-18} \\ d=5 \\ \\ \text{Hence, substituting these values into the nth term of an A.P to get the rule,} \\ a_n=a+(n-1)d_{} \\ A(n)=3+(n-1)(5) \end{gathered}\)Therefore, the function rule for the sequence is;
\(A(n)=3+(n-1)(5)\)Press all of the equations that are correct. 271 divided by 3 equals 93. 6 thousand 438 divided by 6 equals 1 thousand 73. 953 divided by 7 equals 136 R 1. 5 thousand 608 divided by 8 equals 71. 2 thousand 683 divided by 4 equals 67 R 3.
Answers
Answer:
6 thousand 438 divided by 6 equals 1 thousand 73
953 divided by 7 equals 136 R 1
Step-by-step explanation:
Calculation for the equations that are correct
The equations that are correct are:
6 thousand 438 divided by 6 equals 1 thousand 73 which is written as 6,438/6=1073 will be calculated using this formula
Numerator/Denominator
Where,
Numerator=6,438
Denominator=6
Let plug in the formula
6,438/6
=1,083
953 divided by 7 equals 136 R 1 which is written as 953/7= 136.1 is calculated using this formula
Numerator/Denominator
Where,
Numerator=953
Denominator=7
Let plug in the formula
953/7
=136.1
Therefore the equations that are correct are :
6 thousand 438 divided by 6 equals 1 thousand 73 and 953 divided by 7 equals 136 R 1
Sarah's bill at the restaurant was $39. She left a tip of 20%.
What was the tip amount? Round your answer to the nearest
hundredth.
Answers
Answer:
The tip amount is $7.80.
Step-by-step explanation:
To calculate the tip amount, you can multiply the bill amount by the tip percentage.
Tip amount = Bill amount * Tip percentage
In this case, the bill amount is $39 and the tip percentage is 20%.
Tip amount = $39 * 0.20 = $7.80
Rounding the answer to the nearest hundredth, the tip amount is $7.80.
Answer:
$7.80
Step-by-step explanation:
$39 x 0.2 = $7.80
solve for x: 2x-10 and 2x+50
Answers
Answer:
2(-5 + x) and 2(25 + x)
Step-by-step explanation:
“add the product of 3 and 8 to 17”
what is the expression
Answers
Answer:
41
Step-by-step explanation:
3x8=24
24+17=41
Arik invested $500 in a savings account that earns 6.25% interest compounded monthly. Assuming there are no other deposits or withdrawals, what is the total amount in his account after 4 years?
Answers
The total amount that would be found in the account after 4 years, would be $ 641. 69
How to find the total amount ?The total amount after 4 years in Arik's account can be found by the formula :
= A = Amount invested x ( 1 + r /n )ⁿ
The variables are:
Amount invested = $ 500
r = 6.25% = 0. 0625
n = 12
t = 4 years
The total amount is then :
A = 500 x ( 1 + 0. 0625 / 12 ) ^ ⁽¹² ˣ ⁴ ⁾
A = $ 641. 69
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State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).t(45) = ________ p= ________
Answers
Degrees of freedom (df) refers to the number of independent pieces of information that can be used to estimate a parameter. The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from your sample data, assuming the null hypothesis is true.
However, I can still help you understand the terms and how they relate to your question.
1. Test Statistic Name: In this case, the test statistic is the t-statistic, which is used for hypothesis testing in statistics when the population standard deviation is unknown.
2. Degrees of Freedom: Degrees of freedom (df) refers to the number of independent pieces of information that can be used to estimate a parameter. In a t-test, the degrees of freedom are typically represented as "t(df)". In your example, the degrees of freedom are 45 (t(45)).
3. Test Statistic Value: This is the calculated value of the t-statistic, which you will need to compute based on the data provided. It is used to compare against the critical value or to find the p-value. You need to provide the data or information about the test to calculate this value.
4. P-value: The p-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from your sample data, assuming the null hypothesis is true. You will need to compute the p-value using the t-statistic value.
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There are four groups of 20 people walking on a shrew each person walks 3 miles how many total miles do all of the people walk
Answers
All the peoples in a group walk 240 miles.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
There are 4 groups of 20 peoples.
And, Each person walk 3 miles.
Now,
Since, There are 4 groups of 20 peoples.
So, Total number of peoples in 4 groups = 4 x 20
= 80
And, Each person walk 3 miles.
So, The distance cover by 80 peoples = 80 x 3
= 240 miles.
Thus, All the peoples in a group walk 240 miles.
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Test your PEMDAS
6+8/2(2+2)
This one is tricky
Answers
Then, do the division 8/2 = 4
Then multiply 4 and 4 which will be 16
Add 6 to 16 and you get 22
Solve the equation below
Answers
Answer:
(5, -9)
Step-by-step explanation:
y = -9
5x + 3y = -2
5x + 3y = -2
5x + (3) (−9) = -2
5x - 27 = -2
5x = 25
x = 5
y = -9, x = 5
Question 1
A. Given the following: A = 0 1
2 −3
, B = −2 1
2 3 ,
C = −2 −1
1 1 . Find the value of 3 – 2. (5 marks)
B. Using the matrix method or otherwise, solve the following system of simultaneous equations.
x + 2y – z = 6
3x + 5y – z = 2
– 2x – y – 2z = 4
Answers
A. To find the value of 3 - 2, we simply subtract 2 from 3, which equals 1.
B. To solve the system of simultaneous equations, let's represent the given equations in matrix form:
[A | B] * [x; y; z] = [C]
where A is the coefficient matrix, B is the constant matrix, and C is the solution matrix.
Substituting the given values, we have:
A = 0 1 -2
2 -3 1
B = -2 1
2 3
C = -2 -1
1 1
Now, let's solve for [x; y; z] using the matrix method. We need to find the inverse of matrix A:
A^-1 = 1/((0*(-3)) - (1*2)) * (-3 2)
(-2 0)
Calculating the inverse, we get:
A^-1 = 1/6 * (-3 2)
(-2 0)
A^-1 = (-1/2 1/3)
(-1/3 0)
Now, multiply A^-1 by matrix C to find the solution [x; y; z]:
[x; y; z] = A^-1 * C
[x; y; z] = (-1/2 1/3) * (-2 -1)
(1 1)
[x; y; z] = (3/2)
(-1/3)
Therefore, the solution to the system of simultaneous equations is x = 3/2, y = -1/3, and z is arbitrary.
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How many packages of military dynamite (m1) are required to create a relieved-face crater that is 120 feet long?
Answers
The number of packages that are required to create a relieved-face crater of the given length would be = 37 packages.
How to calculate the number of packages needed?To calculate the number of packages that are required to create a relieved-face crater of the given length, the length is converted to meters.
To convert 120 feet to meters divide the value by 3.281. That is, = 120/3.281 = 36.6m
But if 1 m = package
36.6 m = 36.6
= 37 packages
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!!!!PLEASE HELP!!!!!
Answers
Answer:
inverse = ( log(x+4) + log(4) ) / (2log(4)), or
c. y = ( log_4(x+4) + 1 ) / 2
Step-by-step explanation:
Find inverse of
y = 4^(-6x+5) / 4^(-8x+6) - 4
Exchange x and y and solve for y.
1. exchange x, y
x = 4^(-6y+5) / 4^(-8y+6) - 4
2. solve for y
x = 4^(-6y+5) / 4^(-8y+6) - 4
transpose
x+4 = 4^(-6y+5) / 4^(-8y+6)
using the law of exponents
x+4 = 4^( (-6y+5) - (-8y+6) )
simplify
x+4 = 4^( 2y - 1 )
take log on both sides
log(x+4) = log(4^( 2y - 1 ))
apply power property of logarithm
log(x+4) = (2y-1) log(4)
Transpose
2y - 1 = log(x+4) / log(4)
transpose
2y = log(x+4) / log(4) + 1 = ( log(x+4) + log(4) ) / log(4)
y = ( log(x+4) + log(4) ) / (2log(4))
Note: if we take log to the base 4, then log_4(4) =1, which simplifies the answer to
y = ( log_4(x+4) + 1 ) / 2
which corresponds to the third answer.
5 ≤ 12 - m, if m = 8
Answers
Answer:
5 ≤ 12 - m
5 ≤ 12 - 8
5 ≤ 4
Therefore, it is false statement
Step-by-step explanation:
If you than please mark me brainliest thanks
The given statement is false.
The given statement is 5 ≤ 12 - m, if m = 8.
What is a inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Now, replacing m by 8 in the given inequality, we get
5 ≤ 4
Therefore, the given statement is false.
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Officials at Dipstick College are interested in the relationship between participation in interscholastic sports and graduation rate. The following table summarizes the probabilities of several events when a male Dipstick student is randomly selected.
Event Probability Student participates in sports 0.20 Student participates in sports and graduates 0.18 Student graduates, given no participation in sports 0.82 a. Draw a tree diagram to summarize the given probabilities and those you determined above. b. Find the probability that the individual does not participate in sports, given that he graduates.
Answers
a. The tree diagram that summarizes the given probabilities is attached.
b. The probability that the individual does not participate in sports, given that he graduate sis 0.2 = 20%.
How do we calculate?We apply Bayes' theorem to calculate:
Probability (Does not participate in sports if graduates) = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)
The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating = 0.18
Probability (Does not participate in sports if graduates) = (0.02 * 0.82) / 0.18 = 0.036 / 0.18= 0.2
The Tree Diagram| Sports | No Sports |
|-------|--------|
Student participates | 0.18 | 0.62 |
|-------|--------|
Student does not participate | 0.02 | 0.78 |
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-6 1/3 what is true
A. -6 + -1/3
B.6 + 1/3
c.-6 1/3
D.6 + -1/3
Answers
Answer:
c is true which is the answer
Consider the system of inequalities and its graph. y ≤ –0.75x y ≤ 3x – 2 On a coordinate plane, 2 solid straight lines are shown. The first line has a negative slope and goes through (negative 8, 6) and (0, 0). Everything below the line is shaded. The second line has a positive slope and goes through (negative 2, negative 8) and (2, 4). Everything to the right of the line is shaded. The section in quadrant 1 is labeled 3, the section in quadrant 2 is labeled 2, the section in quadrant 3 is labeled 1, and the section in quadrant 4 is labeled 4. In which section of the graph does the actual solution to the system lie? 1 2 3 4
Answers
Answer:
4
Step-by-step explanation:
the answer is 4 so d on edge .
Based on the information given regarding the graph, it should be noted that the correct option is graph 4.
What is a graph?
It should be noted that a graph is a diagram that shows the relationship between two or more sets of numbers.
From the information given, the system of inequalities and its graph is given is y ≤ –0.75x y ≤ 3x – 2 and the first line has a negative slope and goes through (negative 8, 6) and (0, 0).
Therefore, the section of the graph where the actual solution to the system lie is in graph 4.
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A group of people were asked whether they prefer soup or salad for lunch.
The table shows the probabilities of the results
Let A represent having soup and B represent having salad for lunch.
Which statement is true?
A. Having soup and salad for lunch are independent events because P(A]B) = P(A) and P(BA) = P(B)
B. Having soup and salad for lunch are independent events because P(A]B) + P(A) and P(BA) + P(B)
C. Having soup and salad are not independent events because P(A]B) + P(A) and P(BA) + P(B)
D. Having soup and salad for lunch are not independent events because P(A]B) = P(A) and P(BA) = P(B)
Answers
Answer:
Having soup and salad for lunch are independent events because P(A/B)=P(A) and P(B/A) = P(B)
Step-by-step explanation: