Determine the value of the variables a, b, and c when simplifying and evaluating the expression. 3^8/3^4 = a^b = c
Answers
Answer:
3, 4, 81
Step-by-step explanation:
plz thank
The value of a is 3, value of b is 4 and value of c is 81.
To understand more, check below explanation.
Exponential identity:The exponential identity is,
\(\frac{a^{m} }{a^{n} } =a^{m-n}\)
We have to solve, \(\frac{3^{8} }{3^{4} }\)
\(\frac{3^{8} }{3^{4} } =3^{8-4} \\\\\frac{3^{8} }{3^{4} } =3^{4} \\\\\frac{3^{8} }{3^{4} } =3*3*3*3=81\)
Hence, the value of a is 3, value of b is 4 and value of c is 81.
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Related Questions
a box has 5 blue and 2 green jelly beans. a bag has 2 blue and 5 green jelly beans. a jelly bean is selected at random from the box and placed in the bag. then a jelly bean is selected at random from the bag. if a green jelly bean is selected from the bag, what is the probability that the transferred jelly bean was green?
Answers
Answer:
5/7
Step-by-step explanation:
because it is 5/(2+5)
The probability of A is 0.50, the probability of B is 0.45, and the probability of either (i.e. P(A?B)
is 0.80. What is the probability of both A and B?
Answers
The probability of both A and B occurring is 0.15.
The probability of both A and B occurring can be found using the formula P(A∩B) = P(A) + P(B) - P(A∪B), where P(A∩B) is the probability of both A and B occurring, P(A) is the probability of A occurring, P(B) is the probability of B occurring, and P(A∪B) is the probability of either A or B occurring.
Plugging in the given values, we get:
P(A∩B) = 0.50 + 0.45 - 0.80
P(A∩B) = 0.95 - 0.80
P(A∩B) = 0.15
Therefore, the probability of both A and B occurring is 0.15.
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2. Given f(x)=3x−1/3-3x. Find the value of (f^−1)′(−5/3).
Answers
Given f(x) = 3x − 1/3 − 3x, we found the inverse of the function to be f⁻¹(x) = −1/6x + 1/18. The derivative of the inverse of the function was found using the formula (f⁻¹)′(x) = 1/f′(f⁻¹(x)) and substituting x = −5/3. We found the derivative of the original function to be f′(x) = −1/2 and substituting this value into the formula, we got (f⁻¹)′(−5/3) = −2.
The given function is f(x) = 3x - 1/3 - 3x.The first step is to find the inverse of the function by swapping x and y, then solving for y. So, x = 3y - 1/3 - 3y becomes 1/3 = -2y or y = -1/6. Therefore, f⁻¹(x) = -1/6x + 1/18.Now, we need to find the derivative of f⁻¹(x) and substitute x = -5/3. The derivative of f⁻¹(x) is given by the formula: (f⁻¹)'(x) = 1 / f'(f⁻¹(x))Substituting f⁻¹(x) = -1/6x + 1/18 in f(x), we get:f(f⁻¹(x)) = f(-1/6x + 1/18) = 3(-1/6x + 1/18) - 1/3 - 3(-1/6x + 1/18)= -1/2x - 1/6Thus, f'(x) = d/dx [-1/2x - 1/6] = -1/2We substitute x = -5/3 to find (f⁻¹)'(-5/3) = 1/f'(-1/6 * (-5/3) + 1/18) = 1/f'(-1/4) = 1/(-1/2) = -2.Hence, (f⁻¹)'(-5/3) = -2.
Explanation: First, we must determine the inverse of the function: f(x) = 3x − 1/3 − 3x
We can do so by swapping x and y in the equation above and solving for y. This gives us: x = 3y − 1/3 − 3y → 1/3 = −2y → y = −1/6
Therefore, the inverse of the function is f⁻¹(x) = −1/6x + 1/18
Now we must find the derivative of the inverse of the function and substitute x = −5/3. The derivative is found using the formula: (f⁻¹)′(x) = 1/f′(f⁻¹(x))
Substituting the inverse of the function in the original equation gives us:f(f⁻¹(x)) = f(−1/6x + 1/18) = 3(−1/6x + 1/18) − 1/3 − 3(−1/6x + 1/18)= −1/2x − 1/6
The derivative of f(x) is: f′(x) = d/dx [−1/2x − 1/6] = −1/2
Thus, when we substitute x = −5/3 into the equation above, we get:(f⁻¹)′(−5/3) = 1/f′(−1/4) = 1/(−1/2) = −2Therefore, (f⁻¹)′(−5/3) = −2.
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Demand for park visits is Q =10,000 −100P. How many visitors will attend if the park charges a $20.00 admission fee?
A. 2,000
B. 4,000
C. 6,000
D. 8,000
2. Suppose the demand for vanilla ice cream was described by the equation Q = 20 – p, and the supply was described by Q = 10 + p. What are the equilibrium price (P*) and quantity(Q*)?
A. P* = -40, Q* = 20
B. P* = 5, Q* = 15
C. P* = 10, Q* = 50
D. P* = 25, Q* = -25
Answers
1. The number of visitors attending the park when the admission fee is $20.00 is 8,000.
2. The equilibrium price (P*) is $5 and the equilibrium quantity (Q*) is 15.
1. To find the number of visitors attending the park when the admission fee is $20.00, we substitute P = $20.00 into the demand equation Q = 10,000 - 100P:
Q = 10,000 - 100(20)
Q = 10,000 - 2,000
Q = 8,000
Therefore, the number of visitors attending the park when the admission fee is $20.00 is 8,000. The correct answer is option D.
2. To find the equilibrium price (P*) and quantity (Q*) for vanilla ice cream, we set the demand equation equal to the supply equation and solve for P:
20 - p = 10 + p
Combine like terms:
2p = 10
Divide both sides by 2:
p = 5
To find the equilibrium quantity, substitute the value of p into either the demand or supply equation:
Q = 20 - p
Q = 20 - 5
Q = 15
Therefore, the equilibrium price (P*) is $5 and the equilibrium quantity (Q*) is 15. The correct answer is option B.
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PLEASE HELP ASAP!!!!!!
IF NOT THEN I’LL FAIL!!!!!!
A. 90°
B. 60°
C. 120°
D. 180°
(Use the link/photo to help you)
Answers
7=6
6=4 (angle on a str line)
So 7 is 120
How would l solve this question???!!
Answers
Answer:
a = 6
Step-by-Step Explanation:
9 + 8a = 57
8a = 57 - 9 (subtract 9 from both sides)
8a = 48 (then divide 8 from both sides to get "a" alone)
a = 48/8
a = 6
Using suitable identity, find the value of 87^3+ 13^3/
87^2 −87 ×13 + 13^2
Answers
The value of the given expression [\(87^3+ 13^3/87^2 -87 * 13 + 13^2\)] by simplifying the numerator and denominator using suitable identities is 100.
We will first calculate the numerator:
As (\(a^3\) + \(b^3\)) = (a + b)(\(a^2\) - ab + \(b^2\)) :
\(87^3\) + \(13^3\) = (87 + 13)(\(87^2\) - \(87 * 13\) + \(13^2\))
= 100(\(87^2\) - 87 * 13 + \(13^2\))
Now, calculate the denominator:
\(87^2 - 87 * 13 + 13^2\)
As,(\(a^2 -2ab +b^2\)) =\((a - b)^2\):
\(87^2 - 87 * 13 + 13^2 = (87 - 13)^2\)
\(= 74^2\)
So by solving the equation further:
\((87^3+13^3) / (87^2- 87 * 13+13^2) = 100*(87^2- 87 *13 + 13^2)/(87^2 - 87 * 13 + 13^2)\)
As we can see the numerator and denominator are the same expressions (\(87^2 - 87 * 13 + 13^2\)). so, they cancel each other:
\((87^3 + 13^3) / (87^2 - 87 * 13 + 13^2) = 100\)
So, the value of the given expression is 100.
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according to the 1990 census, those states with an above-average number of people, x, who fail to complete high school tend to have an above average number of infant deaths, y. in other words, there is a positive association between x and y. the most plausible explanation for this is
Answers
There are certainly hidden variables, which is the most likely explanation for this correlation. (C) States with large populations, for instance, will also have a larger percentage of infant death and high school dropouts.
What is a positive association?When the values of one variable tend to rise as the values of the other rise, two variables are said to be positively correlated.
When the values of one variable tend to fall as the values of the other rise, two variables are said to be negatively correlated.
A favorable connection occurs when the graph's line is advancing, as in Problem 1.
In this illustration, we make the assumption that the number of years of schooling and the expected pay are positively correlated.
So, in the given situation the most likely explanation for this correlation is that there are likely lurking variables.
For instance, states with big populations will also have a higher proportion of neonatal mortality as well as high school dropouts.
Therefore, there are certainly hidden variables, which is the most likely explanation for this correlation. (C) States with large populations, for instance, will also have a larger percentage of infant death and high school dropouts.
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Complete question:
According to the 1990 census, those states with an above average number X of people who fail to complete high school tend to have an above average number Y of infant deaths. In other words, there is a positive association between X and Y. The most plausible explanation for this association is
a. X causes Y. Thus, programs to keep teens in school will help reduce the number of infant deaths.
b. Y causes X. Thus, programs that reduce infant deaths will ultimately reduce the number of high school dropouts.
c. lurking variables are probably present. For example, states with large populations will have both a larger number of people who fail to complete high school and a larger number of infant deaths.
d. the association between X and Y is purely coincidental. It is implausible to believe the observed association could be anything other than accidental.
Which table represents a linear relationship
Answers
Answer:
the answer is A or B if it is motebl choice
Step-by-step explanation:
Need help pls?!?!?! ASAP
Answers
Answer:
-15/16
Step-by-step explanation:
Both of the 7/16's cancel each other out.
Answer:
7/15
Step-by-step explanation:
easy as 1 2 3 na na naaaaaa he he he
Which word below means ¨to make as small as possible
Answers
Answer:
Minimize
Step-by-step explanation:
Hope this helps!
A square part of side 20 meters has a footpath along the boundary of width 10 meters . Find the area of path
Answers
Answer:
Answer: 84 meters squared. (i.e. 84m^2).
Step-by-step explanation:
Area of the path = total area of path and plot - plot area only
First, let’s find the area of the plot:
20m x 20m = 400m^2
The path is 1m wide and runs all the way around, so, it describes an ‘outer square’ of 22m x 22m (2 x 1m larger because there are 1m of the path on each side).
The area of this ‘outer square’ is equivalent to the ‘total area of path and plot’
22m x 22m = 484m^2
So:
Area of the path = total area of path and plot - plot area only
= 484 - 400 = 84m^2
jesse is putting a ribbon around a square frame. He uses 24 inches of ribbon. How long is each side of the frame
Answers
24÷4=6
So six
Find the volume of the figure. Round to the nearest tenth if necessary.
1 point
3.4 in
4.8 in
25
Answers
Answer: 34 in^3
Step-by-step explanation:
Surface area of triangle = 1/2 x 3.4 x 2.5 = 4.25
To find the volume of the prism, multiply the surface area of the triangle by length.
So 4.25 x 8 = 34 in^3
An art museum had 275,760 visitors last year. The museum was open every day of the year except for 5 holidays. How many visitors did the museum have each day, on average?
Answers
Answer:766 people on average because 275,760 divided 360 because 365=1 year 365-5=360 and 275760/360=766
Step-by-step explanation:
test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2)against the alternative that it is not (and assume equal variances). find the t-stat to 3 decimal places.
Answers
To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))
where:
x1 and x2 are the sample means of the two sheets,
s_p is the pooled standard deviation,
n1 and n2 are the sample sizes.
The pooled standard deviation (s_p) can be calculated using the following formula:
s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
where:
s1 and s2 are the sample standard deviations.
To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.
Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.
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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.
The t-statistic for a paired t-test is calculated as follows:
t = (X1 - X2) / (s / √n)
where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.
Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.
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Solve the equation for w.
w divided by 4.4 minus 2.8 equals 11.5
62.92
38.28
3.25
1.97
Answers
Answer:
62.92
Step-by-step explanation:
Erica brought $30.25 to the state fair. she bought a burger, a souvenir, and a pass. the burger was 1 6 as much as the souvenir, and the souvenir cost 3 4 the cost of the pass. erica had $4.00 left over after buying these items. what was the cost of each item?
Answers
Let's break down the given information and solve the problem step by step:
Let's assume:
The cost of the burger is 'b' dollars.
The cost of the souvenir is 's' dollars.
The cost of the pass is 'p' dollars.
According to the given information:
The burger was 1/6 as much as the souvenir. This can be expressed as: b = (1/6) * s.
The souvenir cost 3/4 the cost of the pass. This can be expressed as: s = (3/4) * p.
Erica had $4.00 left over after buying these items. This can be expressed as: b + s + p + 4 = 30.25.
Now, let's solve these equations to find the cost of each item.
Substituting the value of 's' from equation 2 into equation 1:
b = (1/6) * ((3/4) * p)
b = (3/24) * p
b = (1/8) * p
Substituting the values of 'b' and 's' into equation 3:
(1/8) * p + ((3/4) * p) + p + 4 = 30.25
Multiply through by 8 to eliminate the fraction:
p + 6p + 8p + 32 = 242
15p + 32 = 242
15p = 210
p = 210 / 15
p = 14
Substituting the value of 'p' into equation 2 to find 's':
s = (3/4) * 14
s = 10.50
Substituting the value of 'p' into equation 1 to find 'b':
b = (1/8) * 14
b = 1.75
Therefore, the cost of the burger is $1.75, the cost of the souvenir is $10.50, and the cost of the pass is $14.0
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Find the Area of this shape. 3in, 4in, 5in. PLS HELP ASAP
Answers
Answer:
I think it is 12 inches
Step-by-step explanation:
i hope this helped, if it didn't, i am sorry
NEED HELP ASAP PLEASE ON ALL OF THEM !!!!
Answers
Multiplying and Dividing by Powers of 10
~~~~~~~~~~~
which of these equivalent to 1,000,000?
A. 10(3)
B. 10(4)
C. 10(5)
D. 10 (6)
Answers
Answer:
10(6)
Step-by-step explanation:
Hope it's right.....
Find the value of x:
A. X = 41.0
B. X = 122.0
C. X = 61.0
D. X = 120.5
Answers
Step-by-step explanation:
hope this will help you..
On a coordinate grid, an island is located at (1,6). Another island is located at (4,9). What is the distance between the islands if the distance between consecutive grid lines represent 2 miles?
Answers
Answer:
6√2
Step-by-step explanation:
a can of soda is placed inside a cooler. as the soda cools, its temperature in degrees celsius is given by the following function, where is the number of minutes since the can was placed in the cooler. find the temperature of the soda after minutes and after minutes. round your answers to the nearest degree as necessary.
Answers
The temperature of the soda after 20 minutes is approximately -18 degrees Celsius. To find the initial temperature of the soda, we can evaluate the function T(x) at x = 0.
Substitute x = 0 into the function T(x):
T(0) = -19 + 39e^(-0.45*0).
Simplify the expression:
T(0) = -19 + 39e^0.
Since e^0 equals 1, the expression simplifies to:
T(0) = -19 + 39.
Calculate the sum:
T(0) = 20.
Therefore, the initial temperature of the soda is 20 degrees Celsius.
To find the temperature of the soda after 20 minutes, we substitute x = 20 into the function T(x):
Substitute x = 20 into the function T(x):
T(20) = -19 + 39e^(-0.45*20).
Simplify the expression:
T(20) = -19 + 39e^(-9).
Use a calculator to evaluate the exponential term:
T(20) = -19 + 39 * 0.00012341.
Calculate the sum:
T(20) ≈ -19 + 0.00480599.
Round the answer to the nearest degree:
T(20) ≈ -19 + 1.
Therefore, the temperature of the soda after 20 minutes is approximately -18 degrees Celsius.
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INCOMPLETE QUESTION
A can of soda is placed inside a cooler. As the soda cools, its temperature Tx in degrees Celsius is given by the following function, where x is the number of minutes since the can was placed in the cooler. T(x)= -19 +39e-0.45x. Find the initial temperature of the soda and its temperature after 20 minutes. Round your answers to the nearest degree as necessary.
I NEED HELP ASAP
A triangle with sides 3, 4 and 6 is ___________
Select one:
a. obtuse
b. acute
c. right
Answers
Answer:
obtuse
Step-by-step explanation:
A triangle with sides of 3,4and6 is NOT a Right triangle.
Slove for x ,
:2x + 3=11 ??
Answers
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\(2x + 3 = 11\)
Subtract sides 3
\(2x + 3 - 3 = 11 - 3\)
\(2x = 8\)
Divide sides by 2
\( \frac{2}{2} x = \frac{8}{2} \\ \)
\(x = 4\)
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If you have an independent group design and ordinal data, which test do you use?
Answers
The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test
Given: Independent group and ordinal data. To find which test to use.
What's the Kruskal Wallis test?
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.
The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.
How to calculate the Kruskal Wallis test?
The computation of the Kruskal- Wallis statistic requires
Combine the individualities from all the separate samples and rank order the entire group.Regroup the individualities into the original samples and cipher the sum of the species( T) for each sample. A formula is used to cipher the Kruskal- Wallis statistic which is distributed as a ki-square statistic with degrees of freedom equal to the number of samples minus one. The attained value must be lesser than the critical value for ki- forecourt to reject H0 and conclude that there are significant differences among the treatments.Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.
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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.
We are given an independent group design and ordinate data.
We need to tell which test to use on them.
The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.
The null hypothesis for the Kruskal- Wallis test tells us that:
There are no methodical or harmonious differences among the treatments being compared.
Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.
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how to find the distance between 1.5 and any point,n,on a numberline
Answers
The distance between 1.5 and any point,n,on a number line is |1.5 - n|
How to determine the distanceFrom the question, we have the following parameters that can be used in our computation:
Points = n and 1.5
The distance between these points is the absolute difference between them
This is represented with the following equation
Distance = |1.5 - n|
Hence, the distance is |1.5 - n|
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a professor writes 20 multiple-choice questions, each with the possible answer a, b, c, or d, for a discrete mathematics test. if the number of questions with a, b, c, and d as their answer is 8, 3, 4, and 5, respectively, how many different answer keys are possible, if the questions can be placed in any order?
Answers
Considering that the professor writes 20 multiple-choice questions with the possible answers a, b, c, and d, and the number of questions with each answer option is given, there are 25,200 different answer keys possible.
To calculate the number of different answer keys possible, we need to determine the number of ways to arrange the questions with the given answer options.
First, let's consider the number of ways to arrange the questions themselves. Since there are 20 questions, there are 20 factorial (20!) ways to arrange them.
Next, let's consider the number of ways to assign the answer options to each question. For each question, there are 4 possible answer options (a, b, c, and d). So, for each of the 20 questions, there are 4 possibilities. Therefore, the total number of ways to assign the answer options is 4 raised to the power of \(20 (4^20).\)
To obtain the total number of different answer keys possible, we multiply the number of ways to arrange the questions by the number of ways to assign the answer options:
Total number of different answer keys = \(20! * 4^20\)= 25,200.
Therefore, there are 25,200 different answer keys possible for the test when considering the given conditions.
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which of the following outliers would most likely be the easiest to correct? a. a typographical error in data transfer b. a measurement error in instrument calibration c. a heavily skewed distribution d. a correctly measured anomalous result
Answers
a. a typographical error in data transfer outliers would most likely be the easiest to correct.
What is typographical error?Typo, often known as a misprint, is short for a typographical error. Typos are mistakes created during the typing process that editors and proofreaders failed to catch.
When the writer means to enter the wrong term, the error is referred to be a typo. The majority of the time it is spelt wrongly. It's possible for a word to be incomplete, to have an extra letter, or to be missing a letter, which can occasionally result in the creation of a new term with a completely different meaning. A typographical error in material that has been written or printed.
Thus, correct option is: a
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