Answers
Answer:
[tex] {( \sqrt{ {x}^{ - 3} }) }^{5} = ({( {x}^{ - 3}) }^{ \frac{1}{2} } ) ^{5} \\ \\ = {x}^{ - 3 \times \frac{1}{2} \times 5} = {x}^{ - \frac{15}{2} } = \frac{1}{ {x}^{ \frac{15}{2} } } [/tex]
Or ;
[tex] {( \sqrt{ {x}^{ - 3} } )}^{5} = {( \sqrt{ \frac{1}{ {x}^{3} }} })^{5} = ( { \frac{ \sqrt{1} }{ \sqrt{ {x}^{3} } } })^{5} \\ \\ = ( { \frac{1}{ \sqrt{x} \sqrt{ {x}^{2} } } })^{5} = ({ \frac{1}{ x\sqrt{x} }})^{5} \\ \\ = ( \frac{ {(1)}^{5} }{ {x}^{5} ( \sqrt{x} )^{5} } ) = \frac{1}{ {x}^{5} \times {x}^{ \frac{1}{2} \times 5 } } \\ \\ = \frac{1}{ {x}^{5} \times {x}^{ \frac{5}{2} } } = \frac{1}{ {x}^{5} \sqrt{ {x}^{5} } } \\ \\ = \frac{1}{ {x}^{5} \sqrt{ {x}^{4} {x}^{1} } } = \frac{1}{ {x}^{5} \sqrt{x} \sqrt{( { {x}^{2} })^{2} } } \\ \\ = \frac{1}{ {x}^{5} {x}^{2} \sqrt{x} } = \frac{1}{ {x}^{7} \sqrt{x} } = \frac{ \sqrt{x} }{ {x}^{8} } [/tex]
Related Questions
A fingernail grows about 0.1 mm, day. How much does a fingermail grow in 45 days ? 90 days?
Answers
Answer:
- In 45 days = 4,5mm ; In 90 days = 9mm
Step-by-step explanation:
in 45 days = 0,1 * 45 = 4,5 mm ; in 90 days = 0,1 * 90 = 9mm
Which table has greater constant of proportionality?
Answers
The table with greater proportionality is table 3.
What is constant proportionality?The constant of proportionality is the ratio between two directly proportional quantities.
As, the constant proportionality is
k= y/x
For table 1,
k = 1/1 = 2/2 =1
For table 2,
k = 6/1= 12/2 = 2
For table 3,
k = 5/1 = 10/2 = 5
For table 4,
k = 4/1 = 8/2 = 4
Hence, table 3 is with greater proportionality.
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Help please I need it now!
Answers
Answer: [tex]\sum^{7}_{n=1} (-2+9n)[/tex]
Step-by-step explanation:
This is an arithmetic series with first term 7 and common difference 9, so the general formula for the nth term of the sequence is [tex]7+9(n-1)=7+9n-9=-2+9n[/tex].
The sequence has 7 terms, so the sigma notation is:
[tex]\sum^{7}_{n=1} (-2+9n)[/tex]
What is the vertex of the absolute value function defined by f(x) =3|x+7|-2
Answers
The vertex of the absolute value function is (-7,-2)
How to determine the vertex?The function is given as:
f(x) = 3|x + 7| - 2
The above function is an absolute value function.
An absolute value function is represented as:
f(x) = a|x - h| + k
Where:
Vertex = (h,k)
By comparison, we have:
(h,k) = (-7,-2)
Hence, the vertex of the absolute value function is (-7,-2)
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Dwayne is selling hamburgers and cheeseburgers. he has 100 burger buns. each hamburger sells for $3, and each cheeseburger sells for $3.50. which system of inequalities represents the number of hamburgers, h, and the number of cheeseburgers, c, he must sell to have sales of at least $80? h c ≤ 80 3h 3.5c ≤ 100 h c ≤ 80 3h 3.5c ≥ 100 h c ≤ 100 3h 3.5c ≤ 80 h c ≤ 100 3h 3.5c ≥ 80
Answers
Let h represent hamburgers and c represent cheeseburgers
h + c ≤ 100 - The number of burgers sold
3h + 3.5c ≥ 80 - Amount that each burger sells for
Find the domain and range of the function.
f(x) = 9x² + 3
domain
range
Answers
Answer:
Domain: all real numbers, or (-oo, oo)
Range: (3, oo).
Step-by-step explanation:
The domain is the set of x-values that work when plugged into a function. Here, all values when plugged in produce a real answer, so the answer is all real numbers, or (-oo, oo).
The range is the result of the domain, or the y-values. Since the x^2 will only produce positive numbers, the lowest y-value we can get is 3, and the highest y-value we can get is infinity. So, the answer is (3, oo).
Brainliest, please :)
Find x. Round to the nearest 10th
Answers
Answer:
[tex]\boxed{\bf x = 23.5}[/tex]
Step-by-step explanation:
Using the law of sines.
[tex] \bf \cfrac{ \sin(A) }{a} = \cfrac{ \sin(B) }{b} [/tex]
A = 42B = x a = 22a = 12[tex]\bf \cfrac{ \sin(42) }{22} = \cfrac{ \sin(x) }{12} [/tex]
[tex]\bf \cfrac{12}{22} \sin(42) = \sin(x) [/tex]
[tex] \bf \sin(x) = 0.4[/tex]
[tex]\bf x = 23.5[/tex]
_______________________Select all the correct answers. Function g is a transformation of the parent exponential function. Which statements are true about function g? A Linear graph function where red line g intercepts y-axis at (0, 4) and passes through (minus 10, 3) and (3, 10) Function g is positive over the interval . The domain of function g is . Function g has a y-intercept of . Function g decreasing over the interval . Function g is 4 units above function f. The range of function g is .
Answers
The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
The parent function i.e. exponential function is defined by:
y=f(x)=aˣ
From the graph given below,
1. The graph of the function g is 3 units above the graph of the parent exponential function. as the parent exponential function aˣ cuts the y-axis at (0,1) and the child transformed function cut at (0,4) for which g is 4-1=3 units above the parent function
2. The domain of the function is set of all the inputs for which function is defined. From the graph of function g, it is clear tha the domain of the function is (-∞ , ∞ ) as the domain of the parent exponential function is also (-∞ , ∞ ).
3. The y-intercept is the point at which function cut the y-axis. Graph of function g cut the y-axis at (0, 4). Therefore, Function g has the y-intercept at (0,4).
4. From the graph it is clear that Function g increases over the interval (-∞, 0) .
5. The range of the function is the output values of the function. From the graph, it is observed that the range of function g is (3, ∞). as its minimum value is 3 then the maximum value is ∞.
6. As, the graph of function g is drawn above the x-axis. Therefore, Function g lies completely on +ve y-axis, so function g is positive over the interval (-∞ , ∞ ).
Therefore The correct statements are:
Function g has a y-intercept of (0,4)
The range of the function g is (3, ∞).
The function g is positive over the interval (-∞ , ∞ ).
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find 7x +y when x=7 and y=1
Answers
Answer:
7x+y
7(7)+1
49+1
50
Step-by-step explanation:
please mark me as brainlest
Answer:
7x + y
x=7 y=1
7(7) + 1
49 + 1
= 50
My supersonic jet burns 4 gallons of jet fuel in 3 seconds. How many gallons of jet fuel do I need to fly for an hour?
Answers
The number of gallons of Jet fuel that is needed to fly for an hour is; 14400 gallons
How to solve simple Algebra?We are given;
Number of gallons burned = 4 gallons
Time to burn 4 gallons = 3 seconds
Now, for 1 hour there are 3600 seconds and so;
Number of gallons that is burnt in 3600 seconds = 3600 * 4
Number of gallons that is burnt in 3600 seconds = 14400 gallons
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PLease simplify this!!!
show all work!
Answers
The simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].
The given expression is [tex]\frac{4(3x^{2} y^{4} )^{3} }{(2x^{3} y^{5} )^{4} }[/tex].
What are exponents?Exponentiation is a mathematical operation, written as bⁿ, involving two numbers, the base b and the exponent or power n, and pronounced as "b raised to the power of n".
We need to simplify the given expression.
Now, [tex]\frac{4(3^{3}x^{6} y^{12} )}{2^{4} x^{12}y^{20} }[/tex]
⇒[tex]\frac{108x^{6}y^{12} }{16x^{12} y^{20} }[/tex]
⇒[tex]\frac{27}{4x^{12} y^{8} }[/tex]
Therefore, the simplified form of the given expression is [tex]\frac{27}{4x^{12} y^{8} }[/tex].
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Express 10/4 as a mixed fraction
Answers
Hey there!
10/4
≈ 10 ÷ 2 / 4 ÷ 2
≈ 5/2
≈ 2 1/2
Therefore, your answer should be:
2 1/2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
A carpet installer charges a flat rate of $40 + $1.50 per square foot for labor so the total cost for the labor depends on the amount of carpet installed the relationship between the total cost for labor and the amount of corporate installed is the domain of the relation is the range of the relation is
Answers
The domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
What are domain and range?The domain means all the possible values of x and the range means all the possible values of y.
A carpet installer charges a flat rate of $40 and $1.50 per square foot for labor.
So the total cost for the labor depends on the amount of carpet installed, the relationship between the total cost for labor and the amount of corporate installed.
Then the domain of the relation is the range of the relation will be
Let y be the total amount and x be the number of square foot.
y = 1.5x + 40
Then the domain of the linear function is (1.5, ∞) and the range of the linear function will be (40, ∞).
The graph is given below.
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what is the measure of < ABC ?
Answers
Answer:
I believe its A. 37
Step-by-step explanation:
That seems to be the measure of B
The number of wrecks at a certain intersection varies directly as the number of cars that travel through the intersection. If there are 31 wrecks when 1,085 cars have traveled through the intersection, how many cars have passed through the intersection after 7 wrecks?
Answers
The number of cars that have passed through the intersection after 7 wrecks is 1/5 cars
Direct variationNumber of wrecks = wNumber of cars = cw = k × c
31 = k × 1,085
31 = 1,085k
k = 1085/31
k = 35
If w = 7
w = k × c
7 = 35 × c
7 = 35c
c = 7/35
c = 1/5 car
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Evaluate 21 + (-3c) when c=-2
Answers
27
Solution:
Substitute c with -221 + ( -3 ) ( -2 )
Simplify21 + 6
27
Therefore, The answer is 27.
What would the slope of a line be if it were parallel to the line: y = 1 / 3x - 5 ?
Answers
Answer:
Parallel lines have the same slope, so the slope would be 1/3. It would need a different y intercept though or it would be the same line.
What is the base area of Box 3? x2 + x
edge
Answers
The expression of base area of box will be 4x + x²
The area of a a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. Basically, the area formula is the product of the rectangle's length and width.
Given,
Length = 4+x
width = x
height = x²+1
We have to find the expression of base area of box
Given the length, width, and height
The formula for area of rectangle is as follow:
Area of rectangle = length x width
Area of rectangle = (4+x) x (x)
Area of rectangle = 4x + x²
Hence the expression of base area of box will be 4x + x²
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Transform each graph as specified below.
Answers
Answer:
Transcribed image text: Transform each graph as specified below. (a) The graph of y=f(x) is shown. Graph y=2f(x). (b) the graph of y=g(x) is shown. Graph y=g(2x).
Americans receive an average of 20 Christmas cards each year. Suppose the number of Christmas cards is normally distributed with a standard deviation of 6. Let X be the number of Christmas cards received by a randomly selected American. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N( 20 , 6 ) b. If an American is randomly chosen, find the probability that this American will receive no more than 24 Christmas cards this year. 0.7486 c. If an American is randomly chosen, find the probability that this American will receive between 21 and 26 Christmas cards this year. d. 66% of all Americans receive at most how many Christmas cards? (Please enter a whole number)
Answers
The distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
Probabilitya. Distribution
X ~ N (20 , 6)
b. P(x ≤24)
= P[(x - μ ) / σ (24 - 20) / 6]
= P(z ≤0.67)
= 0.74857
=0.7486
Hence:
Probability = 0.7486
c. P(21 < x < 26)
= P[(21 - 26)/ 6) < (x - μ ) / σ < (24 - 20) / 6) ]
= P(-0.83 < z < 0.67)
= P(z < 0.67) - P(z < -0.)
= 0.74857- 0.2033
= 0.54527
Hence:
Probability =0.54527
d. Using standard normal table ,
P(Z < z) = 66%
P(Z < 0.50) = 0.66
z = 0.50
Using z-score formula,
x = z× σ + μ
x = 0.50 × 6 + 20 = 23
23 Christmas cards
Therefore the distribution of X is X ~ N (20 , 6) and the probability that this American will receive no more than 24 Christmas cards this year is 0.7486.
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A swiming pool has a length of 12meters width of 6 meter and a height of a 5 meter how much water is needed to fill the swiming pool?
Answers
Answer:
[tex]\boxed {360 m^{3}}[/tex]
Step-by-step explanation:
Water needed to fill the pool = volume of pool
Volume :
Volume = Length × Width × HeightVolume = 12 m × 6 m × 5 mVolume = 12 m x 30 m²Volume = 360 m³Hence, 360 m³ of water has to be filled.
Answer:
360 m³
Step-by-step explanation:
The swimming pool can be modeled as a rectangular prism with the following dimensions:
length = 12 mwidth = 6 mheight = 5 mTo find how much water is needed to fill the pool, calculate the volume of the rectangular prism using the given dimensions:
[tex]\begin{aligned}\textsf{Volume of a rectangular prism} & = \sf length \times width \times height\\\implies \textsf{Volume of pool} & = \sf 12 \times 6 \times 5 \\& = \sf 72 \times 5\\& = \sf 360 \:\: m^3\end{aligned}[/tex]
Therefore, 360 m³ of water is needed to fill the swimming pool.
Which is the correct classification of StartRoot 18 EndRoot?
irrational number, non-repeating decimal
irrational number, terminating decimal
rational number, terminating decimal
rational number, non-repeating decimal
Answers
The correct classification for √18 is an irrational number, non-repeating decimal.
The correct classification of √18 is an irrational number.An irrational number is a number that cannot be expressed as a fraction (ratio) of two integers and cannot be written as a terminating or repeating decimal.
√18 cannot be simplified to a fraction, and when expressed as a decimal, it is a non-repeating decimal that continues indefinitely without a pattern.
Therefore, the correct classification for √18 is an irrational number, non-repeating decimal.The number √18 is the square root of 18. An irrational number is a number that cannot be expressed as a fraction of two integers (a/b) where a and b are integers and b is not equal to zero.
When we calculate the square root of 18, we find that it is approximately 4.24264. However, this decimal representation continues indefinitely without repeating or terminating. It does not settle into a pattern of digits that repeats infinitely like a rational number or terminate after a finite number of decimal places.
Since √18 cannot be expressed as a fraction and its decimal representation is non-repeating and non-terminating, it falls under the category of an irrational number.
Therefore, the correct classification of √18 is an irrational number, specifically a non-repeating decimal.
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Help I’m stuck on this question! Please help.
Answers
Answer: 20
Step-by-step explanation:
A and B have 57+79-42=94 distinct elements in total.
This means that 114-94=20 elements are in neither A nor B.
Suntract (7x-3x)-(5x-6).
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: final \:\:value = -x + 6 \degree[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: (7x - 3x) - (5x - 6)[/tex]
[tex]\qquad \tt \rightarrow \: (4x) - 5x - ( - 6)[/tex]
[tex]\qquad \tt \rightarrow \: 4x - 5x + 6[/tex]
[tex]\qquad \tt \rightarrow \: - x + 6[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:6-x
Step-by-step explanation:
The solution is in the image
Similar Polygons
Not quite sure how to get this question.
Answers
Answer:
No
Step-by-step explanation:
We know that the 3-4-5 and 9-12-15 right triangles are similar. If you add 6 units to the length of each side of both of these triangles, you obtain 9-10-11 and 15-18-21 triangles, which are not similar since 9/15 is not equal to 10/18.
Attached is a document that I need help on, please help!!!
Answers
The ratio of the median weekly earnings is 3 : 5
The ratio of the median weekly earningsFrom the graph, we have the median weekly earnings to be:
High school diploma = $750Bachelor's degree = $1250So, the ratio is:
Ratio = $750 : $1250
Simplify
Ratio = 3 : 5
Hence, the ratio of the median weekly earnings is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph A?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
Both rectangles have a width of 1 unit.
So, we have:
Ratio = 3 * 1: 5 * 1
Simplify
Ratio = 3 : 5
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5
The ratio of the area of the red rectangle to the blue rectangle in graph B?In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width
So, we have:
Ratio = 3 * 3 : 5 * 5
Simplify
Ratio = 9 : 25
Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25
The ratio of the volume of the red cube to the blue cube in graph C?
In (a), we have:
Ratio = 3 : 5
The scale on the horizontal axis is given as:
1 unit per grid mark
The red rectangle has a width of 3 units, while the blue has 5 units as its width.
Since the base are squares, we have:
Ratio = 3 * 3 * 3 : 5 * 5 * 5
Simplify
Ratio = 27 : 125
Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125
The most misleading graph
The most misleading graph is graph B.
This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale
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An avid traveler is investigating whether travel websites differ in their pricing. She chooses a random sample of 32 hotel rooms from across the state and notes the price of each room from site A and site B. The mean difference (site A – site B) in the prices for the rooms is $5.49 with a standard deviation of $18.65.
Assuming the conditions for inference have been met, is there evidence that the prices of hotel rooms from site A and site B are different, on average? Use a significance level of a = 0.05.
A. Because the P-value is less than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
B. Because the P-value is greater than α, there is evidence that the prices of hotel rooms from site A and site B are different, on average.
C. Because the P-value is less than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
D. Because the P-value is greater than α, there is not sufficient evidence that the prices of hotel rooms from site A and site B are different, on average.
Answers
Consider the following loan. Complete parts (a)-(c) below
An individual borrowed $88,000 at an APR of 6%, which will be paid off with monthly payments of $667 for 18 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $, the annual interest rate is%, the number of payments per year is the loan term is years, and the payment amount is $
Answers
The complete statements are mathematically given as
the amount borrowed= 88000the annual interest rate= 6%the number of payments per year= 12The loan term= 18the payment amount.=8004What is the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.?Generally, The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."
In conclusion, the amount borrowed= 88000
the annual interest rate= 6%
the number of payments per year= 12
The loan term= 18
the payment amount.=667*12
the payment amount.=8004
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A woman when working with her takes 2 hours to complete the housework, and takes 3 hours when working alone How long would it take the daughter to complete the housework if working alone?
A) 6 hours
B) 2 hours
C) 4 hours
D) 9 hours
E) 0 hours
Answers
Answer:
6 hours for daughter alone Answer A
Step-by-step explanation:
Rate of mom to clean one house = 1 house /3 hrs = 1/3
rate of daughter = 1/x
Now find the time to clean one house with their combined rates for one house
1 / (1/3 + 1/x ) = 2 hrs
1/3 + 1/x = 1/ 2
x + 3 = 3/2 x
3 = 1/2 x
x = 6 hrs daughter alone
Covert 3/7into a percent
Answers
Answer:
42.86%
Step-by-step explanation:
Our percent fraction is 42.857142857143/100, which means that 37 as a percentage is 42.86%
Here we are going to show you step by step how to convert the fraction 3/7 to a percentage.
In the fraction 3/7, 3 is the numerator and 7 is the denominator.
First, we are going to divide the numerator by the denominator. Therefore, we are going to divide 3 by 7.
3 ÷ 7 = 0.428571A percentage shows a number as a proportion of one hundred.
Now we are going to multiply 0.72 by 100 to get the percentage.
0.428571 x 100 = 42.86Therefore, the answer to 3/7 percent is
42.86%Note: If necessary, we round to the nearest hundred.
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