The equivalent expression to the 4th root of 16x^11y^8/81x^7y^6 is (2x/3)^4, assuming x > 0 and y = 0. The expression simplifies to x because the y terms become 0 and the exponents on x reduce to 1 when the fourth root is taken into account.
Explanation:The question asks for an expression equivalent to 4th root of the fraction 16x^11y^8/81x^7y^6 assuming that x > 0 and y = 0. First, we need to deal with the fourth root and exponents separately. To find the fourth root of a number, you can raise that number to the 0.25 power. This rule simplifies finding roots, as a full calculation is not always needed with modern calculators that have a y* button or equivalent.
The fourth root of 16 is 2 because (2^4) = 16. We can address the exponents of x and y by subtracting the exponents in the denominator from those in the numerator for each variable: x^(11-7) = x^4 and y^(8-6) = y^2. Now, considering y = 0, any term with y to any power will be 0, so we can omit y terms. For x, we have x^4.
Regarding the numbers, we have (2/3)^4 because the fourth root of 81 is 3, and this is in the denominator. Finally, because y = 0, our expression reduces to just concerning x, which is (2x)^4/(3)^4, or (2x/3)^4. This simplifies to x raised to the power of 1 because (2/3)^4 * x^4 with x^4 raised to the 1/4th power cancels out the fourth power.
To simplify the given expression, we can find the fourth roots of the numbers inside the radical and then simplify the variables using exponent rules.
Explanation:To simplify the expression ^4√16x^11y^8/81x^7y^6, we can first simplify the numbers inside the radical by finding their fourth roots. The fourth root of 16 is 2, and the fourth root of 81 is 3. So, the expression becomes 2x^(11/4)y^2 / 3x^(7/4)y^6.
Next, we can simplify the variables inside the expression by subtracting the exponents. So, x^(11/4) / x^(7/4) simplifies to x^((11/4)-(7/4)) = x^(4/4) = x^1 = x, and y^2 / y^6 simplifies to y^(2-6) = y^(-4).
Combining the simplified numbers and variables, the expression becomes 2x * y^(-4) / 3 = (2x)/(3y^4).
Round off 1563385 to the nearest million?
To round 1,563,385 to the nearest million, we look at the hundred-thousands digit (5), and since it's 5 or greater, we round up to 2,000,000.
To round off 1,563,385 to the nearest million, look at the hundred-thousands digit, which is 5 in this case.
If it is 5 or greater, we round up; if it is less than 5, we round down.
Since our hundred-thousands digit is 5, we round up, so 1,563,385 rounded to the nearest million is 2,000,000.
Factor completely.
3x squared + 2xy - y squared
37% of a certain country's voters think that it is too easy to vote in their country. you randomly select 12 likely voters. find the probability that the number of likely voters who think that it is too easy to vote is (a) exactly three, (b) at least four, (c) less than eight.
The probability that the number of likely voters who think that it is too easy to vote is:
a) exactly three = 0.17422
(b) at least 4 = 0.70533
(c) less than eight = 0.96406
How to use binomial probability theorem?
The general formula for binomial probability theorem is:
P(X = x) = ⁿCₓ * pˣ * (1 - p)⁽ⁿ ⁻ ˣ⁾
Where:
n = 12
p = 0.37
(a) exactly three,
P(x = 3) = ¹²C₃ * 0.37³ * 0.93⁹
= 0.17422
(b) at least 4,
P(4 ≤ x ≤ 12) = P(4) + P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12)
= 0.70533
(c) less than eight.
P(x < 8) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
= 0.96406
the snowfall in year 1 was 2.03 meters .the snowfall in year 2 was 1.6 meters .how many total meters of snow fell in years 1 and 2
340 students went to the first dance but only 306 went to the second. What is the percent decrease in the attendance from the first to the second dance
Please help me with coordinates. IT'S DO IN 3 HOURS
What are the values of the variable in 37=30-x^2
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A farmer wishes to build a rectangular plot with 800 meters of wire fencing. use calculus to find the maximum area that can be enclosed by the fence
Answer:
40,000 meters squared
Step-by-step explanation:
Find the optimum and constraint equations. (They are just fancy terms for the two equations you need).
The Constraint is 2x + 2y= 800 (As the plot is a normal rectangle and there is 800 m to make a fence, you would use the perimeter formula for a rectangle)
The optimum is xy= A. The area equals length times width (or in this case) xy.
You will need to plug in the simplified constraint into the optimum.
2y= -2x + 800 (divide by two next)
y= -x + 400
Plug in this to the Optimum
x(-x + 400)
this equals -xsquared + 400x
Find the derivative of it
-2x plus 400
Set it equal to )
x=200, this is only one of the lengths of the side.
In order to find the other, plug in x=200 to the constraint
-x + 400
-200 + 400
y = 200 also
So, going back to the Optimum 200 times 200 equals 40,000.
This means that the maximum area is in fact 40,000 meters squared.
Patrick's favorite shade of purple paint is made with 4 ounces of blue paint for every 3ounces of red paint.
Which of the following paint mixtures will create the same shade of purple?
Choose 2 answer
Blue : 4x2=8
Red : 3x2=6
Blue :4x5=20
Red:3x5=15
The following mixtures will create Patrick's favorite shade of purple:
:8ounces of blue paint mixed with 6ounces of red paint
:20 ounces of blue paint mixed with 15 ounces of red paint
Answer:
actually its b and d
Step-by-step explanation:
according to khan academy
simplify the expression (-5)2. -10 10 -25 25
The population standard deviation of the numbers 3, 8, 12, 17, and 25 is 7.563 correct to 3 decimal places. what happens if each of the five numbers is multiplied by 3
A piece of cardboard has two circles punched out of it. What is the approximate area of the remaining cardboard? Use 3.14 for pie and round to the nearest whole number.
227 cm2
246 cm2
258 cm2
276 cm2
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Mr Walton ordered 12 pizzas,for the art class celebration one fourth of the pizza had only mushrooms. how many of the pizza has only mushrooms
A brother and a sister are in the same math class. There are 8 boys and 10 girls in the class. One boy and one girl are randomly chosen. What is the probability that the brother and sister are chosen? Write your answer as a fraction in simplest form.
[tex] |\Omega|=8\cdot10=80\\ |A|=1\\\\ P(A)=\dfrac{1}{80} [/tex]
Name the pattern block used to cover 1 third of the hexagon
What percent of 7 is 2?
Anna plans a business model to compete with two video stores, where she hopes to draw in customers from one store but not lose money on the deal. Movie Mania charges a subscription fee of $30 and an additional $5 per movie, x. Movie Time charges a subscription fee of $25 and an additional $6 per movie, x. Based on this information, which system of inequalities could be used to determine how many movies need to be rented for a customer on Anna’s plan, y, to pay her more than they would at Movie Time, but less than they would at Movie Mania?
Answer:D. y<5x+30/x
y>6x+25/x
Step-by-step explanation:
got right on edmentum
Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month. Which equation can be used to find the number of months it would take him to reach a balance of $500? Let m = number of months.
Answer:
[tex]150+25m = 500[/tex]
Step-by-step explanation:
Given : Carlos has $50 in his savings account. He deposits $100 on his birthday, and then another $25 every month.
To Find: Which equation can be used to find the number of months it would take him to reach a balance of $500?
Solution:
Carlos has $50 in his savings account.
He deposits $100 on his birthday.
Let m be the number of months
He save $25 every month
So, he saves in x months = 25 m
Now wants to reach a balance of $500.
So, equation becomes:[tex]50+100+25m = 500[/tex]
:[tex]150+25m = 500[/tex]
Hence Equation can be used to find the number of months it would take him to reach a balance of $500 is [tex]150+25m = 500[/tex]
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if a circle has a radius of 13 and a sector defined by a 7.4 degree arc, what is the area, in cm2, of the sector? round your answer to the nearest tenth.
Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100. what is the probability that in a randomly selected hour the number of watches produced is greater than 500
Answer: 0.5
Step-by-step explanation:
Given : The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.
i.e. [tex]\mu = 500\text{ and } \sigma= 100[/tex]
Let x be the number of watches produced every hour.
Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :
[tex]P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5[/tex]
Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.
27 33 34 35 37 39 40 41 54 84,75,90,87,99,91,85,88,76,92,94 median: first quartile: third quartile: interquartile range:
Final answer:
For the given data, the median is 85, the first quartile is 37, the third quartile is 90.5, the interquartile range (IQR) is 53.5, and the range is 72.
Explanation:
The median in a dataset is the middle value when the values are arranged in numerical order. For the given data 27, 33, 34, 35, 37, 39, 40, 41, 54, 75, 84, 75, 90, 87, 99, 91, 85, 88, 76, 92, 94, after arranging them in ascending order, the median (Q2) is the value positioned at the center of the dataset. Since there are 21 values, the median is the 11th value, which is 85. The first quartile (Q1) is the median of the first half (lower half) of the dataset, which is the value in the 5.5th position, so we average the 5th and 6th values to get 37. Similarly, the third quartile (Q3) is the median of the second half (upper half) of the dataset, which would be the average of the 16th and 17th values, yielding 90.5. The interquartile range (IQR) is the difference between the third quartile and the first quartile, so IQR = Q3 - Q1 = 90.5 - 37 = 53.5. The range of the dataset is the difference between the maximum and minimum value which is 99 - 27 = 72.
1. A line passes through the ordered pairs (7,2) and (5,4). What is the slope? please show work
2. A sphere has a diameter od 20 cm. What would be the volume of sphere?
Which polynomial represents the difference below?
The difference between given two polynomials is [tex](- x^{2} + 12x + 3)[/tex].
What is a polynomial?"A polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables."
Given two polynomials are [tex](5x^{2} + 9x + 3)[/tex] and [tex](6x^{2} - 3x)[/tex].
Therefore, the difference between these two polynomials
[tex]= (5x^{2} + 9x + 3) - (6x^{2} - 3x)\\= (5x^{2} - 6x^{2}) + (9x + 3x) + 3\\= - x^{2} + 12x + 3[/tex]
Learn more about polynomial here:
https://brainly.com/question/21610884
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Which values are outliers?
5.8, 6.1, 4.9, 10.9, 0.8, 6.1, 7.4, 10.2, 1.1, 5.2, 5.9
Select Outlier or Not Outlier for each data point.
Data Outlier Not Outlier
0.8
1.1
10.2
10.9
The outliers are 0.8, 1.1, 10.2, and 10.9. The rest are not outliers.
A value is typically considered an outlier if it is less than Q1 - 1.5 [tex]\times[/tex] IQR or greater than Q3 + 1.5 [tex]\times[/tex] IQR.
First, we need to arrange the data in ascending order:
0.8, 1.1, 4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4, 10.2, 10.9
Next, we find the first quartile (Q1), which is the median of the first half of the data:
(4.9 + 5.2) / 2 = 5.05
We find the third quartile (Q3), which is the median of the second half of the data:
(6.1 + 7.4) / 2 = 6.75
Now, we calculate the interquartile range (IQR):
IQR = Q3 - Q1 = 6.75 - 5.05 = 1.7
The lower bound for outliers is:
Q1 - 1.5 [tex]\times[/tex] IQR = 5.05 - 1.5 [tex]\times[/tex] 1.7 = 5.05 - 2.55 = 2.5
The upper bound for outliers is:
Q3 + 1.5 [tex]\times[/tex] IQR = 6.75 + 1.5 [tex]\times[/tex] 1.7 = 6.75 + 2.55 = 9.3
Now we can determine which values are outliers:
0.8 is less than the lower bound (2.5), so it is an outlier.
1.1 is less than the lower bound (2.5), so it is an outlier.
10.2 is greater than the upper bound (9.3), so it is an outlier.
10.9 is greater than the upper bound (9.3), so it is an outlier.
The remaining values (4.9, 5.2, 5.8, 5.9, 6.1, 6.1, 7.4) are not outliers as they fall within the range of Q1 - 1.5 [tex]\times[/tex] IQR and Q3 + 1.5 [tex]\times[/tex] IQR.
Can someone help me with this problem? please explain.
Value of m varies directly as value of n and n=5 when m=12. What is n when m=18?