The simplest radical form of the expression is [tex]\mathbf{40 ^{2/3}x^{{10}/{3}}y^2}[/tex].
What is the simplification of power indices?When we have indices in the form [tex]\mathbf{ax^{2/3}}[/tex], we are going to find the cube root of the (ax)². This can be mathematically expressed as:
[tex]\mathbf{=(\sqrt[3]{ax})^2 }[/tex]
From the given information:
[tex]\mathbf{=(8x^55y^3)^{2/3}}[/tex]
[tex]\mathbf{=(\sqrt[3]{8x^55y^3} } )^2[/tex]
[tex]\mathbf{=(\sqrt[3]{40x^5y^3} } )^2[/tex]
[tex]= (\sqrt[3]{40x^5} \times \sqrt[3]{y}^3)^2[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{5*2}/{3}}y^2}[/tex]
[tex]\mathbf{= 40 ^{2/3}x^{{10}/{3}}y^2}[/tex]
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if jermeey has 9 apples, and sabrina has 10, how many apples do they have if erica takes 19 of them?
Answer:
0 apples
Step-by-step explanation:
Consider this function.
please help!
Solve this problem, and identify the percent, amount, and base. What percent 60 of 15 is ?
Answer:
Step-by-step explanation:
'
What is the mean of the data set below?
15, 5, 16, 9, 14, 3, 4, 18, 10, 4
Answer:
Mean = Sum of Values ÷ Total number of Values
Step-by-step explanation:
= 15+5+16+9+14+3+4+18+10+4 ÷ 10
= 98 ÷ 10
= 9.8 (Decimal point moves 1 place to the left when divided by 10)
Find the area of a regular polygon with 8 sides that has a perimeter of 96 inches and an apothem of 5 inches.
Area = [?]in2
Answer:
see the attachment photo!
Theo's friend made a display with dimensions that were each half as long as those theo used. what is the approximate mass of theo's friends display
Answer:
great question buddy and I wish you the most
Step-by-step explanation:
x-y=b^2/2=2
Which is the equation of the parabola with focus (6, 2) and vertex (6, –4)?
Based on the calculations, the equation of this parabola is equal to (x - 6)² = 16(y + 4).
How to determine the equation of this parabola?Mathematically, the standard equation with the vertex for a parabola is given by:
(y - k)² = 4a(x - h) for horizontal parabola.
(x - h)² = 4a(y - k) for vertical parabola.
where:
h and k are the vertex.a is a point.By critically observing the points, we can deduce that both the focus and vertex lie on the same vertical line x = 6.
Given the following data:
Focus with points = (6, 2).
Vertex (h, k) = (6, –4).
Note: a = 2 - (-4) = 2 + 4 = 6.
Substituting the given parameters into the formula, we have;
(x - 6)² = 4 × 4(y - (-4))
(x - 6)² = 16(y + 4).
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6x^2 + 2x-20/ 4x-2 simplify
Answer:
6x^2-3x-2
Step-by-step explanation:
6x^2 + 2x - 20 / 4 x x - 2
6x^2 + 2x - 5x - 2
6x^2 -3x - 2
Jillian is trying to determine what helium tank pressure she needs to fill balloons for the student council dance. Find the unknown numbers in the table until you find the best answer to the question. Which cylinder pressure will Jillian need if she plans to fill 90 balloons? Tank Pressure and Balloon Quantity Pressure in the helium cylinder (psi) Number of 9-inch balloons 100 30 150 ? 200 ? 250 ? 300 ?
Going by the standard Helium Cylinder/Balloon Chart, the amount of pressure she will require to fill 90 balloons is 300 per squared inch (PSI.)
How much pressure will each balloon take at 300 psi total?To get this amount, we simply divide the number of balloons with the total amount of PSI.
Thus:
90/300
= 0.3psi each.
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Answer: 300?
Step-by-step explanation:
tell me if i am wrong
Can 3×2×2×3 be written as a power with an exponent of 4? Explain your thinking.
84102 - 1052=?
pasagot po pls with solution
Answer:
83050
Step-by-step explanation:
that's the answer to the question
Seven x's and 3y's cost as much as 4z's. One z costs as much as 1x plus 1y together. How many x's cost as much as 1y?
Answer:
Step-by-step explanation:
Equations
7x + 3y = 4z
Second equation
x + y = z Multiply the entire equation by 4
4[x + y = z] Now distribute the 4 through the equation
4x + 4y = 4z Both equations = 4z. Equate the lefts.
Third equation
7x+3y = 4x + 4y Subtract 3y from both sides
7x + 3y -3y = 4x + 4y -3y
7x = y + 4x Subtract 4x from both sides
7x - 4x = y + 4x - 4x Combine
3x = y
Answer: 3x = y
Use the function below to find F(-2).
F(x) = 3x
A 1/6
B -9
C -6
D 1/9
Answer:
-6
Step-by-step explanation:
we can put the value of x as -2 cause f(-2) we can substitute the value...
f(-2)= 3*-2
-6
Difference of 8 Let's dig into this and find out for sure. First think of two numbers that have a difference of 8. Type the LARGER of these numbers below.
Answer:
16
Step-by-step explanation:
We need to find 2 numbers that have a difference of 8.
Let take's 16 and 8.
As we know :
⇒ 16 - 8
⇒ 8
The larger of these 2 numbers is 16
Choose the correct answer below:
A- A rate is just a different name for a ratio. The terms are interchangeable
B-a rate refers to the reduced form of a ratio
C-rates are a special type of ratio that always have a 1 in the denominator
D- rates are a special type of ratio used to compare different kinds of quantities
Answer:
C
Step-by-step explanation:
The answer would have to be C cus it can't be A or D
Let's suppose someone flips a fair coin three times. 1. How many outcomes are possible? [a] 2. What is the probability of getting exactly one tail? Give as a fraction [b] 3. What is the probability of getting at most two tails? Give asa fraction [c]
Probability helps us to know the chances of an event occurring. There are 8 outcomes.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Let's suppose someone flips a fair coin three times.
1. The outcomes of the coins are,
HHHHHTHTHHTTTTHTHTTTHTTTTherefore, there are 8 outcomes.
2. The probability of getting exactly one tail is,
P(X=1) = 2/8 = 1/4
3. The probability of getting at most two tails is,
P(X≤2) = P(X=1) + P(X+2) = 1/4 + 1/2 = 3/4
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Which expression is equivalent to the following complex fractions
1-(1/x)/2
Not D
The expression that is equivalent to complex fraction [tex]\frac{1 - \frac{1}{x}}{2}[/tex] is [tex]{\frac{x - 1}{2x}}[/tex]
To answer the question, we need to know what fractions are
What are fractions?Fractions are rational numbers written in the form a/b where
a and b are integers and b > 0.where
a is called the numerator and b the denominator.Expression similar to complex fractionTo find the expression similar to the complex fraction [tex]\frac{1 - \frac{1}{x}}{2}[/tex], we simplify the fraction.
So, [tex]\frac{1 - \frac{1}{x}}{2}[/tex]
Taking L.C.M of x in the numerator, we have
[tex]\frac{1 - \frac{1}{x}}{2} = \frac{\frac{x - 1}{x}}{2} \\[/tex]
Simplifying, we have
[tex]\frac{1 - \frac{1}{x}}{2} = \frac{\frac{x - 1}{x}}{2} \\= {\frac{x - 1}{2x}}[/tex]
So, the expression that is equivalent to the complex fraction [tex]\frac{1 - \frac{1}{x}}{2}[/tex] is [tex]{\frac{x - 1}{2x}}[/tex]
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factor this polynomial completely x2 - x - 20
Answer:
(x+4)(x-5)
Step-by-step explanation:
We can look at it by thinking of two numbers, that add up to -1 and multiply to -20. We can first do this by looking at factors of -20, which are 1, -20, -1, 20, 2, -10, -2, 10, and so on. After looking through it, we can notice that -5 and 4 added equal -1, and when multiplied equal to -20, so they work. So, we factor to (x+4)(x-5)
Answer:
(x +5) (x -4)
Step-by-step explanation:
Factors of 20:
1,20
2,10
4,5
4 and 5 combine to create 1
+5 -4 = 1
(x +5) (x -4)
The perimeter of a rectangle is 42 inches if the width of the rectangle is 6 inches what is the length
Answer:
The length would be 15 inches.
Step-by-step explanation:
Since we are solving for perimeter the first step would be doing 6+6 = 12 (covering 2 sides). The next thing we would do is subtract 12 from 42 getting 30 as our answer. We need to divide 30 by 2 to get an answer of 15. I hope this helps! :)
Answer:
15 inches
Step-by-step explanation:
Ajar has 20 marvels three green 12 blue five real what is the probability of randomly choosing a red and then a green marble
The answer is 3 I work it out
The table shows information about the meals
ordered at a restaurant.
Meal ordered
Frequency
Sandwich
11
Curry
12
Salad
7
If this information was shown on a pie chart,
how many degrees should the central angle of
the section that represents curry be?
Answer:
144°
Step-by-step explanation:
The central angle of a sector in a pie chart is proportional to the fraction the represented data is of the whole.
__
fractionThe total number of meals ordered at the restaurant was ...
11 +12 +7 = 30
The fraction of those that were Curry was ...
12/30 = 2/5
angleThen the central angle of the sector representing Curry will be 2/5 of the circle, or ...
2/5 × 360° = 144°
The central angle of the section representing Curry will be 144°.
A. 56
B. 154
C. 210
D. 252
Option A
Penelope’s 2000 kg new painted car accelerates from 50.0 m/s to 100.0 m/s. Calculate the impulse experienced by Penelope’s car.(Note: Include correct units and sign. Ex. "20 J" , "20 m" , "20 m/s")
The impulse that Penelope's car would experience is 100, 000 Kg. m/s
How to calculate the impulse
The formula for calculating the impulse is;
Impulse = m Δ v
Where m = mass = 2000kg
Δv = change in velocity = 100 - 50 = 50m/s
Substitute values into formula
Impulse = 2000 × 50 = 100, 000 Kg. m/s
Therefore, the impulse would be 100, 000 Kg. m/s
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please please help needs to be submitted in 15 minutes!!!
Answer:
Volume of prism 1: 104 cubic inches
Surface area of prism 2: 650 square inches
Step-by-step explanation:
To find the volume of prism 1, set up a proportion using the side lengths and the volume of prism 2.
The ratio of the side lengths will be your scale factor. When finding volume using scale factor, you need to cube the scale factor. The numerator in the proportion are from prism 1 and the denominator is prism 2. Prism 1 is the numerator since it is the new image and we are solving for it's volume.
[tex](\frac {4}{10}) ^{3} =\frac{x}{1625} \\\\\frac{64}{1000} =\frac{x}{1625} \\\\[/tex]
[tex]1000x=104000\\\frac{1000x}{1000} =\frac{104000}{1000} \\x = 104[/tex]
To find the surface area of Prism 2, we are going to setup another proportion, but this time we are going to square the scale factor since we are finding area. Prism 2 will be the numerator and prism 1 will be the denominator.
[tex](\frac{10}{4} )^2 = \frac{x}{104} \\\frac{100}{16} =\frac{x}{104} \\16x=10400\\\frac{16x}{16}=\frac{10400}{16}\\ x= 650[/tex]
Which shapes have the same volume at the given rectangular priam?
Som
base area-50 or
15 on
D
base area-50 cm
Son
base area-50 cm²
24 cm
base area- 50 cm
18 cm
4+-+-
base area-50 cm
Answer:
Cylinder
Step-by-step explanation:
Area of rectangular prism = base area * height
= 50 * 5
= 250 square cm
Area of cylinder = base area * height
= 50 * 5
= 250 square cm
Lines AB and CD are parallel. The coordinates of point A are (-2,5), the coordinates of point B are (6,3), and the coordinates of point D are (8,5).
The equation of line CD is y =
Equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].
What are parallel lines?" Parallel lines are defined as the lines in the same plane never intersect with each other. They are equidistant to each other in the same plane."
Formula used
[tex]Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
According to the question,
Given,
Coordinates of A [tex](x_{1},y_{1})[/tex] = ( -2 , 5)
Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 6 , 3)
Substitute the value to get the slope of line AB we get,
[tex]Slope of line AB 'm_{1}' =\frac{3-5}{6-(-2)}[/tex]
⇒ [tex]m_{1} = \frac{-2}{8}[/tex]
[tex]= \frac{-1}{4}[/tex]
Coordinates of C [tex](x_{1},y_{1})[/tex] = ( x ,y)
Coordinates of B [tex](x_{2},y_{2})[/tex] = ( 8,5)
Substitute the value to get the slope of line CD we get,
[tex]Slope of line CD 'm_{2}' =\frac{5-y}{8-x}[/tex]
Lines AB and CD are parallel.
Slope of parallel lines are equal.
Therefore,
[tex]m_{2} = m_{1}[/tex]
⇒ [tex]\frac{5-y}{8-x}[/tex] [tex]= \frac{-1}{4}[/tex]
⇒[tex]5-y = \frac{-1}{4} (8-x)[/tex]
⇒ [tex]y = \frac{-x}{4} +7[/tex]
Hence, equation of the line CD is equals to [tex]y = \frac{-x}{4} +7[/tex].
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rewrite this inequality so y is by itself:
3x − 4y ≥ 24.
Answer:
y [tex]\leq[/tex] 6 + [tex]\frac{3x}{4}[/tex]
Step-by-step explanation:
3x - 4y [tex]\geq[/tex] 24
-3x -3x
(-4y [tex]\geq[/tex] 24 - 3x ) / -4
y [tex]\leq[/tex] 6 + [tex]\frac{3x}{4}[/tex]
A bag contains 100 marbles which are red, green, and blue.
Suppose a student randomly selects a marble without looking,
records the color, and then places the marble back in the bag.
The student has recorded 7 red marbles, 2 green marbles and
11 blue marbles. Predict how many blue marbles are in the
bag.
Voir can earn 5 coins
Answer:
Step-by-step explanation:
Remark
The ratio you would use is 7 to 2 to 11
The question is what you you have to multiply these ratios by so the products when added come to 100?
Equation
7*x + 2*x + 11*x = 100 Combine the terms on the left
Solution
20x = 100 Divide both sides by 20
20x/20 = 100/20
x = 5
Red: 7 * 5 = 35Green: 2 * 5 = 10Blue: 11*5 = 55Total 100Answer: 55 blue marbles were in the bag.
Answer: 2
Step-by-step explanation:
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 16 subjects had a mean wake time of 100.0 min. After treatment, the 16 subjects had a mean wake time of 75.5 min and a standard deviation of 24.2 min. Assume that the 16 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 100.0 min before the treatment? Does the drug appear to be effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
The 95% confidence interval estimate of the mean wake time is equal to (62.61, 88.39).
Given the following data:
Mean wake time = 75.5 min.Standard deviation = 24.2 min. Number of sample, n = 16.How to construct a 95% confidence interval?Mathematically, a confidence interval of 95% is given by;
α = 1 - 0.95
α = 0.05.
α/2 = 0.05/2 = 0.025.
Also, the degrees of freedom (df) is given by:
Degrees of freedom (df) = n - 1
Degrees of freedom (df) = 16 - 1
Degrees of freedom (df) = 15.
From the Student's t-distribution table, a critical value at t₀.₀₂₅, ₁₅ = 2.131.
Mathematically, the confidence interval for mean is given by:
Mean ± (t-critical × (standard deviation/√(sample size)))
75.5 ± (2.131 × (24.2/√(16))
75.5 ± (2.131 × 6.05)
For the upper end, we have:
75.5 + 12.89 = 88.39
For the lower end, we have:
75.5 - 12.89 = 62.61.
In conclusion, we can deduce that there isn't a significant difference between the mean wake time before and after treatment and as such, this drug isn't effective at the significance level of 0.05.
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Which algebraic rule describes the translation of quadrilateral ABCD to quadrilateral A’B’C’D?
Answer:
A.
Step-by-step explanation:
The figure moves to the right 8 units which is positive and then up 7 units which is also positive.