Answer:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex]
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex]
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex]
Step-by-step explanation:
Given
[tex]x^\frac{3}{5}[/tex]
Required
The equivalent expressions
We have:
[tex]x^\frac{3}{5}[/tex]
Expand the exponent
[tex]x^\frac{3}{5} = x^{ 3 * \frac{1}{5}}[/tex]
So, we have:
[tex]x^\frac{3}{5} = (x^3 )^\frac{1}{5}[/tex] ----- this is equivalent
Express 1/5 as roots (law of indices)
[tex]x^\frac{3}{5} = \sqrt[5]{x^3}[/tex] ------ this is equivalent
The above can be rewritten as:
[tex]x^\frac{3}{5} = (\sqrt[5]{x})^3[/tex] ------ this is equivalent
The thicknesses of 81 randomly selected aluminum sheets were found to have a variance of 3.23. Construct the 98% confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory. Round your answers to two decimal places
Answer:
The confidence interval for the population variance of the thicknesses of all aluminum sheets in this factory is Lower limit = 2.30, Upper limit = 4.83.
Step-by-step explanation:
The confidence interval for population variance is given as below:
[tex][(n - 1)\times S^{2} / X^{2} \alpha/2, n-1 ] < \alpha < [(n- 1)\times S^{2} / X^{2} 1- \alpha/2, n- 1 ][/tex]
We are given
Confidence level = 98%
Sample size = n = 81
Degrees of freedom = n – 1 = 80
Sample Variance = S^2 = 3.23
[tex]X^{2}_{[\alpha/2, n - 1]} = 112.3288\\\X^{2} _{1 -\alpha/2,n- 1} = 53.5401[/tex]
(By using chi-square table)
[(n – 1)*S^2 / X^2 α/2, n– 1 ] < σ^2 < [(n – 1)*S^2 / X^2 1 -α/2, n– 1 ]
[(81 – 1)* 3.23 / 112.3288] < σ^2 < [(81 – 1)* 3.23/ 53.5401]
2.3004 < σ^2 < 4.8263
Lower limit = 2.30
Upper limit = 4.83.
what shape is the 1st one? I already know the second one
the first one is a quadrilateral
Step-by-step explanation:
a quadrilateral have four side
Subtract the following polynomials.
(3.1x+2.8z)−(4.3x−1.2z)
Answer:
-2/5 (3x-10z)
Step-by-step explanation:
please help me with this on the image
Answer:
6ab
Step-by-step explanation:
how old is sherif now ? ahmed is eight years younger than sherif in seven years, the sum of their ages will be 7/10 th of 100
Answer:
32year
Step-by-step explanation:
let Ahmed be x years then sheriff will be x+8
in 7years time
sheriff will be x+8+7=x+15
Then Ahmed will be x+7
sum of their ages will be 7\10×100=70years
x+15+x+7=70
collect like terms
2x+22=70
2x=70-22
2x/2=48/2
x=24years
Sheriff=24+8
32years
Hi- how do we calculate the distance from C to D? Thanks so much!
Answer:
CD=20
Step-by-step explanation:
Use the pythagorean theorem: a²+b²=c²
(20√2)²-20²=a²
400(2)-400
800-400=400
√400=20
PLEASE HELP ASAP !!!! THANKS
Answer:
Its the first one
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- Blake bought a motorcycle for $550 last year and sold it for $330 this year. What is his sale
price as a percentage of his purchase price?
Answer:
The sale price was 60% of the purchase price.
Step-by-step explanation:
Given that Blake bought a motorcycle for $ 550 last year and sold it for $ 330 this year, to determine what is his sale price as a percentage of his purchase price, the following calculation must be performed:
550 = 100
330 = X
330 x 100/550 = X
33000/550 = X
60 = X
Therefore, the sale price was 60% of the purchase price.
Plz show steps for this
Answer: Choice D. 3 : r=3
Step-by-step explanation:
Easiest method and probably only method given the graph without knowing exact points besides an asymptote at x=-3.
Since we know there is an asymptote at x=-3, we just solve for the denominator and find r, when x=-3.
We are setting equation equal to 0, because when the denominator is 0, the graph has an asymptote at that point.
x+r=0
-3+r=0
r=3
Answer:
r=3
Step-by-step explanation:
The room numbers of two adjacent classrooms are two consecutive odd numbers. If their sum is 860, find the classroom numbers
Answer:
429 & 431
Step-by-step explanation:
Consecutive numbers are numbers that come right after the other.
Let x = first room number
[tex]x+x+2=860\\2x+2=860\\2x=858\\x=429\\\\(429) + 2 = 431[/tex]
Therefore, the two room numbers are 429 and 431.
The measurement of the radius of the end of a log is found to be 9 inches, with a possible error of 1/2 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.
Answer:
[tex]\pm 9in^2[/tex]
Step-by-step explanation:
We are given that
Radius of end of a log, r= 9 in
Error, [tex]\Delta r=\pm 1/2[/tex]in
We have to find the error in computing the area of the end of the log by using differential.
Area of end of the log, A=[tex]pi r^2[/tex]
[tex]\frac{dA}{dr}=2\pi r[/tex]
[tex]\frac{dA}{dr}=2\pi (9)=18\pi in^2[/tex]
Now,
Approximate error in area
[tex]dA=\frac{dA}{dr}(\Delta r)[/tex]
Using the values
[tex]dA=18\pi (\pm 1/2)[/tex]
[tex]\Delta A\approx dA=\pm 9in^2[/tex]
Hence, the possible propagated error in computing the area of the end of the log[tex]=\pm 9in^2[/tex]
Answer:
[tex]A = (254.34 \pm 28.26) in^2[/tex]
Step-by-step explanation:
radius, r = 9 inches
error = 0.5 inch
The area of the end is
A = 3.14 x r x r = 3.14 x 9 x 9 = 254.34 in^2
[tex]A = \pi r^2\\\\\frac{dA}{dr}=2\pi r\\dA = 2 pi r dr \\\\dA = 2 \times 3.14\times 9\times 0.5 = 28.26[/tex]
So, the area is given by
[tex]A = (254.34 \pm 28.26) in^2[/tex]
Which equation models the same quadratic relationship as function f? f(x) = 2x^2 - 12x + 11
A) y = 2(x + 6)^2 + 2
B) y = 2(x - 3)^2 -7
C) y = 2(x - 6)^2 + 5
D) y = 2(x + 3)^2 - 7
Answer:
im not sure but i think the answer is C) y = 2(x - 6)^2 + 5
The equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the function is,
f(x) = 2x^2 - 12x + 11
We have to find the equation models the same quadratic relationship as the given function,
⇒2x²-12x+11
Take common 2 in the complete equation,
⇒2(x²-6x+11/2)
Add and subtract 9 from the complete equation,
⇒2(x²-6x+9-9+11/2)
Rearrange the equation as,
⇒2[(x-3)²-(7/2)]
⇒2(x-3)²-7
Thus, the equation models the same quadratic relationship as function f(x) = 2x^2 - 12x + 11 will be 2(x-3)²-7.Option B is correct.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
Work out 45% of $200.00
Answer:
If you are using a calculator, simply enter 45÷100×200 which will give you 90 as the answer.
Mark me brainliest plz.
At the city museum, child admission is S5.80 and adult admission is $9.20. On Monday, twice as many adult tickets as child tickets
were sold, for a total sales of $895.40. How many child tickets were sold that day?
[tex]You can call c the number of children and a for adults; you get:5.20c+8.50a=1097.60anda=4c meaning that the number of adults was four times the children.Substituting this value of a into the first equation we get:5.2c+8.5(4c)=1097.65.2c+34c=1097.6rearranging:c=1097.639.2=28and so:a=4c=4⋅28=112[/tex]
I got: 28 children and 112 adults.
Please help me answer this question if you have time
Answer:
C: [tex]\frac{7x}{4} + 5y[/tex]
Step-by-step explanation:
1. Realize that 12 inches is 1 feet and 36 inches is 1 yard.
2. Multiply it so that both are inches.
[tex]\frac{5y}{12} * 12 = 5y[/tex]
[tex]\frac{7x}{144} * 36 = \frac{7x}{4}[/tex]
3. Add together [tex]\frac{7x}{4} + 5y[/tex]
Answer:
C.
Step-by-step explanation:
I also recommend to just search these things on the internet. it would be much faster.
1 ft = 12 in
1 yd = 3 ft = 3×12 = 36 in
so, we need to multiply a given number of ft by 12, and a given number of yards by 36 to get the inches.
5y/12 × 12 = 5y
7x/144 × 36 = 7x/4
that is all there is to it.
The volume of a boys' basketball is 434 cubic inches. Dan would like to get a ball
with half the volume for his son. What is be the diameter of the ball that Dan will buy
for his son?
A 9.4 inches
B 4.7 inches
C 3.7 inches
D 7.4 inches
Answer:
The correct answer is A. 9.4 inches.
Step-by-step explanation:
Given that the volume of a boys' basketball is 434 cubic inches, and Dan would like to get a ball with half the volume for his son, to determine what is the diameter of the ball that Dan will buy for his son, the following calculation has to be done, knowing that the volume of a sphere is four thirds multiplied by pi multiplied by the radius cubed:
4/3 x 3.14 x X ^ 3 = 434
4.186 x X ^ 3 = 434
X ^ 3 = 434 / 4.186
X = 3√ 103.662
X = 4.7
In turn, since the radius of a sphere is equal to half its diameter, the diameter of the basketball is 9.4 inches (4.7 x 2).
©/17
Correct
Question 1 of 17, Step 1 of 1
Write a mixed number to describe the length of the ribbon shown in the figure below.
Please enter your answer in the box below.
Inches
Answer
How to enter your answer
If your answer is a whole number, enter it in the left most box and leave the numerator and denominator boxes blank.
9514 1404 393
Answer:
3 3/8 inches
Step-by-step explanation:
If you spend a little time looking at the marks on the ruler, you see that the smallest marks divide each inch into 8 parts. The ribbon comes to the 3rd small mark* after the 3-inch mark, so the length of the ribbon is 3 3/8 inches.
_____
* Technically, it is the second small mark, as the marks are small, medium, small. It marks the end of the third space, where each space is 1/8 inch.
Economists have found that the amount of corruption in a country's government is correlated to the gross domestic product (GDP) per capita of that country. This can be modeled by y=507x−8030 where x is the corruption score and y is GDP per capita in dollars. Corruption scores range from 0 to 100 with 0 being highly corrupt and 100 being least corrupt.
Using this model, a country with a corruption score of 99 would have what GDP per capita? Round your answer to the nearest dollar.
A. $46,853
B. $36,444
C. $42,163
D. $50,546
Answer:
B i think
Step-by-step explanation:
A runner increases his velocity from 0 m/s to 20 m/s in 2.0 s. What was his average acceleration?
Answer:
[tex]a = \frac{dv}{dt } = \frac{20 - 0}{2} = 10[/tex]
Distance between two points
What is the length of the line?
Answer:
c
Step-by-step explanation:
that is the procedure above
Find the x- and y-intercepts of the following line: 4x − 3y = 12
Answer:
x-intercept: (3,0)
y-intercept: (0,-4)
Step-by-step explanation:
To find the x and y-intercepts, we first need to understand what they are. X and y-intercepts are points on the line that passes through the x-axis and y-axis. When a point is an x-intercept, it passes through the x-axis. This means the x-coordinate is an integer, while the y-coordinate is always 0. This can be denoted by (x,0). When a point is a y-intercept, it passes through the y-axis. This means the y-coordinate is an integer, while the x-coordinate is always 0. This can be denoted by (0,y).
Now that we know what x and y-intercepts are, we can plug in x=0 and y=0 to find the intercepts.
x-intercept
4x-3y=12 [plug in y=0]
4x-3(0)=12 [multiply]
4x-0=12 [add both sides by 0]
4x=12 [divide both sides by 4]
x=3
---------------------------------------------------------------------------------------------------------
y-intercept
4x-3y=12 [plug in x=0]
4(0)-3y=12 [multiply]
0-3y=12 [subtract both sides by 0]
-3y=12 [divide both sides by -3]
y=-4
Therefore, the x-intercept is (3,0) and y-intercept is (0,-4).
What is the best interpretation of the y-intercept of the line
Answer:
vertical line
Step-by-step explanation:
because horizontal means horizon which goes left to right across a board
Hi there!
The y-intercept of a line represents its initial value. On a graph, the y-intercept would represent the value of y when the line crosses the y-axis.
For example, if an equation were to model the amount of money someone had in their bank account overtime starting from the day they opened their account, the y-intercept would represent the original amount of money they had.
I hope this helps!
Can I please get help it’s urgent . Find the lateral surface area and volume of the solid object.
Which diagram best shows how fraction bars can be used to evaluate One-half divided by one-fourth? A fraction bar labeled 1. Under the 1 are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing one-fourth. 2 one-fourths are circled. A fraction bar labeled one-fourth. Under the one-fourth are 2 boxes containing one-half. Under the 2 boxes are 4 boxes containing 1. 2 boxes containing 1 are circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 8 boxes containing one-half. One box containing one-half is circled. A fraction bar labeled 1. Under the 1 are 4 boxes containing one-fourth. Under the 4 boxes are 2 boxes containing one-half. One box containing one-half is circled.
Answer:
Step-by-step explanation:
The description is too ambiguous to reconstruct the diagram. You need to post the actual diagram.
That diagram is just one way to view division by a fraction. An easier way: DIVIDING by a fraction is the same as MULTIPLYING by the upside-down fraction. For example,
(1/2) ÷ (1/4) = (1/2) × (4/1) = 2
That doesn’t help you answer this particular question, though.
Answer:
C
Step-by-step explanation:
I need help ASAP!!!!
simplify
log(125) + log(625) / log(25) - log(5)
Answer:
3.39794000867
Step-by-step explanation:
first add log 125 and 625 and divide the answer by log 25 and minus the answer by 5
Answer:
The answer is 7.
the coefficients corresponding to k=0,1,2,5 in the expression (x+y)^5 are
Answer:
Step-by-step explanation: you got trolded
(2/5-1/2)+3/5 . [7/2-3/5÷(1/4-1/5)]
Answer: -8
Step-by-step explanation: So we after simplification we get
[(2/5) - (1/2) + (3/5)+ (7/2)] - [(3/5)/(1/4) - (1/5)]
After this I suppose it's just addition & subtraction, and can be easily done to get -8.
Suppose 5 men and 7 women are on a crowded elevator. At the next floor, four people get off the elevator. Find the probability that three are women.
0.010
0.354
0.424
0.25
Answer:
B. 0.354Step-by-step explanation:
Combination of 4 out of 5 + 7 = 12 is:
12C4 = 12!/8!4! = 495Combination of 1 man and 3 women is:
5C1*7C3 = 5*7!/4!3! = 5*35 = 175Required probability:
P(3W) = 175/495 ≈ 0.353Correct choice is B
simplify 2√3 x 3√8
i’ll give u brainiest pls
Answer:
[tex]12 \sqrt{6} [/tex]
Step-by-step explanation:
[tex]2 \sqrt{3} \times 3 \sqrt{8} \\ (2 \times 3) \sqrt{(3 \times 8)} \\ 6 \sqrt{24} \\( 6 \times 2) \sqrt{6 } \\ 12 \sqrt{6} [/tex]
