The square root is a mathematical operation that determines a value which, when multiplied by itself, gives the original number. It is denoted by the symbol '√'. the equivalent expression for √(8x^7y^8) assuming x≥0 is option (c) 2x³y⁴√2x
The expression that is equivalent to √(8x^7y^8) assuming x≥0 is option (c) 2x³y⁴√2x.What is the meaning of √?√ is the symbol for square root. Square root refers to the reverse operation of squaring a quantity. A square root of a given number is another number that gives the original number when multiplied by itself.
What is the formula for simplifying the square root of any number?
The formula for simplifying the square root of any number is √(a*b) = √a * √b.
Using this formula, √(8x^7y^8) can be expressed as √(4x^6*2x*y^8)On simplifying further using the formula above,√(4x^6*2x*y^8) = 2x³y⁴√2x
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The given expression is `√(8x^7 y^8)`. The expression that is equivalent to `√(8x^7 y^8)` is option C: `2x^3y^4√2x`.
To find out which expression is equivalent to this expression.
We need to simplify this expression first.
Let's simplify the given expression:
Factor `8x^7 y^8` under the radical to obtain:
`√(8x^7 y^8) = √[(2^3)(x^3)(y^4)(xy^4)]`
We can now split the square root using the product property of radicals:
`√[(2^3)(x^3)(y^4)(xy^4)] = √(2^3) * √(x^3) * √(y^4) * √(xy^4)`
Evaluate each of the square roots:
`√(2^3) * √(x^3) * √(y^4) * √(xy^4) = 2√2 * x^(3/2) * y^2 * xy^2`
Simplify the expression to obtain: `2xy^2√(2x^3)`.
Thus, the expression that is equivalent to `√(8x^7 y^8)` is option C: `2x^3y^4√2x`.
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you welcome
Step-by-step explanation:
how many strings of length 5 are there over the alphabet {0, 1, 2}?
The length of the string is 5 and the alphabet is {0, 1, 2}.Therefore, the number of strings of length 5 that can be formed over the given alphabet is:$$3^5 = 243$$ Therefore, there are 243 strings of length 5 over the alphabet {0, 1, 2}.
To calculate the number of strings of length 5 over the alphabet {0, 1, 2}, we need to determine the number of choices for each position in the string. Since each position can be filled with one of three possible characters (0, 1, or 2), we have three choices for each position.
Therefore, the total number of strings of length 5 can be calculated as:
Number of strings = Number of choices for position 1 × Number of choices for position 2 × Number of choices for position 3 × Number of choices for position 4 × Number of choices for position 5
Number of strings = 3 × 3 × 3 × 3 × 3 = 3^5 = 243
So, there are 243 strings of length 5 over the alphabet {0, 1, 2}.
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The information given in question is that the length of the string is 5.
Alphabet {0,1,2}
Therefore, there are 243 strings of length 5 over the alphabet {0, 1, 2}.
To find the number of strings of length 5 over the alphabet {0, 1, 2}, we need to consider the number of choices we have for each position in the string.
There are three choices (0, 1, or 2) for each position, and since we have five positions, the total number of strings of length 5 is given by:
[tex]$$3^5 = \boxed{243}$$[/tex]
Therefore, there are 243 strings of length 5 over the alphabet {0, 1, 2}.
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5. use the integral representation of Jy(x) 1 XV Jv(x) = tixp (1 – p2)v-żdp (+1,0T ©) p VT(v-3): 1 - To show that the spherical Bessel functions in (x) are expressible in terms of trigonometric functions, that is, for example, sin x sin x j.(x) = x ji(x) х x2 COS X = = ) х
We are given a formula that uses the integral representation of Jy(x): $${x\over 2}\left[J_{v-1}(x) - J_{v+1}(x)\right] = v\int_0^\infty t^{v-1} J_{v-1}(xt)\,dt$$
We will use this formula to show that the spherical Bessel functions $j _v(x)$ are expressible in terms of trigonometric functions. Let $y=v-1$.
Substituting $v=y+1$, we have: $${x\over 2}\left[J_y(x) - J_{y+2}(x)\right] = (y+1)\int_0^\infty t^y J_y(xt)\,dt$$
This expression is known as a recurrence relation for spherical Bessel functions. Let us use this to derive the identity that was requested:
$${x\over 2}\left[J_{v-1}(x) - J_{v+1}(x)\right] = (v+1)\int_0^\infty t^v J_v(xt)\,dt - v\int_0^\infty t^v J_{v-1}(xt)\,dt$$
Rearranging and using the recurrence relation, we obtain:
$$J_{v+1}(x) = {2v\over x}J_v(x) - J_{v-1}(x)$$$$\begin{aligned}\sin x\,j_v(x) &= \sin x\left[{1\over x}J_v(x)\right]\\&= {1\over 2x}\left[J_{v-1}(x) - J_{v+1}(x)\right]\\&= {v+1\over x}\int_0^\infty t^v J_v(xt)\,dt - {v\over x}\int_0^\infty t^v J_{v-1}(xt)\,dt\end{aligned}$$
Similarly, $$x^2\cos x\,j_v(x) = {v\over x}\int_0^\infty t^v J_v(xt)\,dt + {v+1\over x}\int_0^\infty t^v J_{v-1}(xt)\,dt$$
Hence, we have shown that $j_v(x)$ can be expressed in terms of trigonometric functions as follows:$$\begin{aligned}\sin x\,j_v(x) &= {v+1\over x}\int_0^\infty t^v J_v(xt)\,dt - {v\over x}\int_0^\infty t^v J_{v-1}(xt)\,dt\\\cos x\,j_v(x) &= {v\over x}\int_0^\infty t^v J_v(xt)\,dt + {v+1\over x}\int_0^\infty t^v J_{v-1}(xt)\,dt\end{aligned}$$
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Rachel has 42 stickers she wants give to her friends. Rachel put the stickers in 7 equal groups. Then Rachel found more stickers and put 3 more in each pile. If Rachel gives 5 stickers to each of her 12 friends, how many stickers does she have left over?
Answer:
3 stamps
Step-by-step explanation: 42 stamps in equal groups would be 6 stickers/group.
6+3 = 9 stickers in each pile
there was 7 piles so multiply 7 by the 9 stickers in each pile
7· 9 = 63
5 · 12 = 60, so she gave her friends 60 stickers
63-60 = 3
What was different about the Yuan Dynasty? *
I’ll give brainiest answer to the person who gets it right.
Answer:
One big change during Kublai's reign was that foreigners became the rulers and administrators. Since they didn't trust the local people, they moved in a large number of Muslims and other people to help them rule the empire. The Mongols had their own religious belief called Shamanism.
Jenna works at a local sports bar and is interested in whether the percent tip she will receive is related to how many drinks people order. What test should she perform? O Correlation O ANOVA Independent samplest test O Single sample t test
She should perform a correlation test.
Jenna works at a local sports bar and is interested in whether the percent tip she will receive is related to how many drinks people order. What test should she perform?
She should perform a correlation test.
What is a correlation test?
A correlation test is a statistical method used to examine the relationship between two variables. It is used to determine the degree of association between two continuous variables.
How do you carry out a correlation test?
To perform a correlation test, follow these steps:
Step 1: Collect your data.
Step 2: Determine the level of measurement of each variable.
Step 3: Calculate the correlation coefficient.
Step 4: Determine the p-value.
Step 5: Interpret the results.
Therefore she should perform a correlation test
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x h(x)
-25 6
-13 0
-3 -5
0 -7
9 -11
11 -30
What is the average rate of change of h(x) over the interval -13 < x < 11 ?
Answer:
56
Step-by-step explanation:
Find all the first derivatives of the function f(x,y) = x^0.9y^1.8. Show all of your steps with explanations of what you are doing.
The first derivative of the given function with respect to x is 0.9x^(-0.1)y^1.8 and the first derivative of the given function with respect to y is 1.8x^0.9y^0.8.
The given function is f(x, y) = x^0.9y^1.8. The question is to find the first derivative of the given function with respect to x and y respectively.
Here are the solutions; The first derivative of the given function with respect to x is given by ∂f(x, y)/∂x:∂f(x, y)/∂x = 0.9x^(-0.1)y^1.8
On the other hand, the first derivative of the given function with respect to y is given by ∂f(x, y)/∂y:∂f(x, y)/∂y = 1.8x^0.9y^(1.8 - 1)∂f(x, y)/∂y = 1.8x^0.9y^0.8
Therefore, the first derivative of the given function with respect to x is 0.9x^(-0.1)y^1.8 and the first derivative of the given function with respect to y is 1.8x^0.9y^0.8.
The above steps use the concept of partial derivatives of a function with respect to a variable that can be applied in such types of questions.
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The given function is
[tex]f(x,y) = x⁰.⁹ y¹.⁸[/tex]
Now, let's find the first derivative of the function with respect to x and y.
First derivative of the function with respect to x:
We have to use the chain rule here.
According to the chain rule,
the derivative of the outer function is multiplied by the derivative of the inner function.
The inner function is [tex]y¹.⁸,[/tex]
whose derivative with respect to x is 0.
Therefore, we only have to differentiate the outer function with respect to x.
[tex]f(x,y) = x⁰.⁹ y¹.⁸∂f/∂x = ∂/∂x (x⁰.⁹ y¹.⁸)∂f/∂x = 0.⁹x^(-0.1) y¹.⁸∂f/∂x = 0.⁹y¹.⁸/x^0.1[/tex]
First derivative of the function with respect to y:
We have to use the chain rule here.
According to the chain rule, the derivative of the outer function is multiplied by the derivative of the inner function.
The inner function is [tex]x⁰.⁹,[/tex]
whose derivative with respect to y is 0.
Therefore, we only have to differentiate the outer function with respect to y.
[tex]f(x,y) = x⁰.⁹ y¹.⁸∂f/∂y = ∂/∂y (x⁰.⁹ y¹.⁸)∂f/∂y = 1.⁸ x⁰.⁹ y^(0.8)∂f/∂y = 1.⁸x^0.9 y^0.8[/tex]
Hence, the first derivative of the given function with respect to x is
[tex]0.⁹y¹.⁸/x^0.1[/tex]
and with respect to y is [tex]1.⁸x^0.9 y^0.8.[/tex]
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Determine the value of variables a, b, and c that make each equation true.
What is the value of a in this equation?
1
(14496
30
a
What is the value of b in this equation?
b=
What is the value of c in this equation?
(x2)° = 222
Answer:
77
Step-by-step explanation:
I got it right on my question
Solve for w. Make sure to use scrap paper to show your work. ( 36 ÷ 3 )( 2 x 6 ) = w
Answer:
your answer is w=144
Step-by-step explanation:
(36÷3=12)(2x6=12)
12x12=144Answer: 144
Step-by-step explanation:
Investigators performed a randomized experiment in which 411 juvenile delinquents were randomly assigned to either multisystemic therapy (MST) or just probation (control group). Of the 215 assigned to therapy, 87 had criminal convictions within 12 months. Of the 196 in the control group, 74 had criminal convictions within 12 months. Determine whether the therapy caused significantly fewer arrests at a 0.05 significance level. Start by comparing the sample percentages. Find and compare the sample percentages that were arrested for these two groups. The percentage of arrests for people who received MST was %.
The percentage of arrests for people who received Multisystemic Therapy (MST) can be calculated by dividing the number of individuals arrested in the MST group (87) by the total number of individuals.
Percentage of arrests for MST group = (87/215) * 100 ≈ 40.47%
To determine if therapy caused significantly fewer arrests at a 0.05 significance level, we need to compare this percentage with the percentage of arrests in the control group.
The percentage of arrests for the control group can be calculated in a similar manner by dividing the number of individuals arrested in the control group (74) by the total number of individuals in the control group (196), and multiplying by 100.
Percentage of arrests for control group = (74/196) * 100 ≈ 37.76%
Comparing the sample percentages, we find that the percentage of arrests for people who received MST (40.47%) is slightly higher than the percentage of arrests for the control group (37.76%).
To determine if this difference is statistically significant at a 0.05 significance level, we would need to perform a hypothesis test, such as a chi-square test, to compare the observed frequencies with the expected frequencies under the assumption that therapy has no effect on reducing arrests.
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4. Write neatly and legibly.
QUESTION 1
1.1
Find the sum:
1.1.1 2+6+(-7) + 10 = 11
Find the sum:
1.1.1 2+6+(-7) + 10 = 11
11=11
Use the distributive property to rewrite each algebraic expression 7(y+2) + (8+r) + 8(x + 9)
Answer:
7y+r+8x+94
Explanation
Given the algebraic expression 7(y+2) + (8+r) + 8(x + 9)
Given A, B and C. According to distributive law;
A(B+C) = AB + AC
A is distributed over C. In the same vein
On expanding the expression;
7(y+2) + (8+r) + 8(x + 9)
7y+7(2) + 8 + r + 8(x)+ 8(9)
7y+14+8+r+8x+72
Bringing the variables and constants together
7y+r+8x+14+8+72
7y+r+8x+94
Identify if they are function or not
Answer:
1=function
2=not function
3=function
4=function
5=function
6=not function
7=not function
8=function
plss help answer true or false
Answer:
"false" I believe if wrong srry
PLEASE HURRY!! I need help!!!
Calculate the IQR given in the box: 
Based on the two data sets represented below, complete the following sentences.
\text{DATA SET B}
DATA SET B
0
0
23
24
25
26
27
28
29
30
31
32
33
\text{DATA SET C}
DATA SET C
0
0
23
24
25
26
27
28
29
30
31
32
33
The median of Data Set B is
than the median of Data Set C. The minimum of Data Set B is
than the minimum of Data Set C.
Sarah practices the piano 1/3 hour in the morning, 5/6 hour in the afternoon, and 4/5 hour in the evening.
How many hours did Sarah practice in all?
I’ll give brainless too who ever respond fast and correctly.
Is 9.90 equal to greater than or less than 9.9
Answer:
Equal to.
Step-by-step explanation:
The 0 at the end of 9.90 does not add any value to the number because its 0.
Answer:
It is equal.
Step-by-step explanation:
9.90 = 9.9 , it's the same as the 0 does not count on it.
PLS ANSWER THIS AND GET BRAINLIEST !!!
A grocery store collected sales data. It found that when customers buy less bread, they tend to purchase more rice. What can we conclude?
A. There is no correlation between amount of bread bought and amount of rice purchased.
B. There is a correlation between amount of bread bought and amount of rice purchased. However, there is no causation. This is because there is an increase in the amount of rice purchased with a decrease in the amount of bread bought.
C. There is a correlation between amount of bread bought and amount of rice purchased. There may or may not be causation. Further studies would have to be done to determine this.
Answer: C
Step-by-step explanation: C because there is obviously a correlation yet we cannot determine if there is causation or not.
How long will it take for quarterly deposits of $625 to accumulate to be $20,440 at an interest rate of 8.48% compounded quarterly?
It will take approximately 9 years and 2 months for quarterly deposits of $625, with an interest rate of 8.48% compounded quarterly, to accumulate to $20,440.
To calculate the time it takes for the deposits to accumulate to the desired amount, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = the accumulated amount
P = the principal amount (initial deposit)
r = the annual interest rate (converted to a decimal)
n = the number of times interest is compounded per year
t = the number of years
In this case, the principal amount (P) is $625, the interest rate (r) is 8.48% (or 0.0848 as a decimal), the number of times interest is compounded per year (n) is 4 (quarterly compounded), and the desired accumulated amount (A) is $20,440.
We need to solve for t, the number of years. Rearranging the formula, we have:
t = (log(A/P)) / (n * log(1 + r/n))
Plugging in the values, we get:
t = (log(20440/625)) / (4 * log(1 + 0.0848/4))
Calculating this, we find that t is approximately 9.18 years. Converting this to years and months, we get approximately 9 years and 2 months. Therefore, it will take around 9 years and 2 months for the quarterly deposits of $625 to accumulate to $20,440 at an interest rate of 8.48% compounded quarterly.
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if 1-3(y+2)=-32 find the value of y/3
Answer:
7.6
Step-by-step explanation:
-3 multiple by y and -3 multiple by 2 resolve to 7.6....
Suppose your favorite coffee machine oder 14 ounce cup of coffee the actual amount of coffee pot in the cup by the machine vanes according to a normal distribution with mean equal to 15 ounces and standard deviation equal to 0.65 ounces. What percentage of cups will be filled with less than 14 ounces?
Approximately 6.3% of cups will be filled with less than 14 ounces is the answer.
Given, mean = 15 ounces and standard deviation = 0.65 ounces
The actual amount of coffee in the cup by the machine vanes according to a normal distribution.
For this, we need to calculate the z-score as z=(X-μ)/σ
We need to find the percentage of cups that will be filled with less than 14 ounces of coffee.
For this, we will calculate the probability that X < 14. So, we need to find P(X<14).
For this, we will first calculate the z-score as z = (X - μ) / σ= (14 - 15) / 0.65= -1.538
Now, we will find the area to the left of the z-score using the standard normal distribution table or calculator:
Using the standard normal distribution table, we get the area as 0.0630.
The percentage of cups that will be filled with less than 14 ounces is 6.3%.
Thus, approximately 6.3% of cups will be filled with less than 14 ounces.
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Slove the system of linear equations by graphing y=-x+7 y=x-1
Answer: Point Form: ( 4 , 3 ) Equation Form: x = 4 , y = 3
Step-by-step explanation: Solve for the first variable in one of the equations, then substitute the result into the other equation.
Brainliest or a thank you please? :))
hey lol pls help <3
Ms. Philor is going on a trip to Hawaii. The function A(d)=0.80d+200 models the amount A, in dollars, that Ms.Philor's company pays her based on the round trip distance d, in miles that Ms. Philor travels to do a job.
Ms. Philor's pay increases by $
A)80.200
B) 0.80
C)200.80
Write the equation of the given line in slope-intercept form:
(-1,2) and (1,-4)
answer is y=-3x+(-1/3)
how do I graph this linear equation?
4x+6y=-12
Answer: Simplifying
Step-by-step explanation:
Simplifying
4x + 6y = 12
Solving
4x + 6y = 12
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-6y' to each side of the equation.
4x + 6y + -6y = 12 + -6y
Combine like terms: 6y + -6y = 0
4x + 0 = 12 + -6y
4x = 12 + -6y
Divide each side by '4'.
x = 3 + -1.5y
Simplifying
x = 3 + -1.5y
Then you get your answer I think or hopeful get your answer. I hoped this helped!
data analysts use one-sample hypothesis tests to ______. a. frustrate students b. manage random sampling error c. justify their jobs d. make bad decisions e. all of the choices above f. none of the choices
Data analysts use one-sample hypothesis tests to manage random sampling error. The correct answer is (b).
Data analysts use one-sample hypothesis tests to manage random sampling error. Random sampling error refers to the variability or differences that can occur between a sample and the population it represents.
By conducting hypothesis tests, analysts can determine if the observed data from a sample is statistically significant and can be generalized to the larger population.
Hypothesis tests help analysts assess whether an observed effect or relationship in the sample is likely to be a true effect or relationship in the population or if it is simply due to random chance.
By testing a hypothesis and comparing the sample data to a null hypothesis, analysts can evaluate the validity of their findings and make informed decisions based on the results.
The purpose of hypothesis tests is not to frustrate students, justify their jobs, or make bad decisions. Instead, they serve as a statistical tool to manage random sampling error and provide reliable and valid conclusions based on data analysis.
The correct answer is (b)
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Of all the animals admitted to the local pet hospital, 10 of them are dogs. They represent 25% of all the animals at the hospital. How many animals are at the hospital in total? A. 20 B. 30 C. 40 D. 50
Answer:
C. 40
Step-by-step explanation:
[tex]\frac{25}{100} = \frac{10}{y}[/tex]
[tex]\frac{1}{4} = \frac{10}{y}[/tex] (cross multiply)
40 = 1y (rewrite)
y = 40