select the function that has a well-defined inverse 12. z to x 4

To show that 1^3 + 2^3 + ... + n^3 = [n(n+1)/2]^2 for any positive integer n, we can use the method of mathematical induction.

Step 1: Base Case
For n = 1, the left-hand side of the equation is 1^3 = 1, and the right-hand side is [(1)(1+1)/2]^2 = (1*2/2)^2 = 1^2 = 1. So the equation is true for n = 1.

Step 2: Inductive Step
Assume that the equation is true for some positive integer k, that is, 1^3 + 2^3 + ... + k^3 = [k(k+1)/2]^2. We need to show that the equation is also true for k+1, that is, 1^3 + 2^3 + ... + k^3 + (k+1)^3 = [(k+1)(k+2)/2]^2.

Step 3: Proof
Starting from the left-hand side of the equation for k+1, we can substitute the equation for k and simplify:
1^3 + 2^3 + ... + k^3 + (k+1)^3 = [k(k+1)/2]^2 + (k+1)^3 = (k^2+k)^2/4 + (k+1)^3 = (k^4+2k^3+k^2)/4 + (k^3+3k^2+3k+1) = (k^4+4k^3+6k^2+4k+1)/4 = [(k+1)(k+2)/2]^2

Thus, the equation is true for k+1. By the principle of mathematical induction, the equation is true for any positive integer n.

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The solutions of equations are x=7, y=1, z=8 and w=-2.

The given equations are 2w + x + 2y - 3z = -19

w - 2x - y + 4z = 15

x + 2y - z = 1

3w - 2x - 5z = -60

isolate x for x+2y-z=1, x=1-2y+z

Substitute x=1-2y+z:

3w-2(1-2y+z)-5y=-60...(1)

2w+1-2y+z+2y-3z=-19...(2)

w-2(1-2y+z)-y+4z=15..(3)

Simplify each equation

3w-2+4y-7z=-60

2w+1-2z=-19

3y+2z+w-2=15

Isolate z for -2z+1w+1=-19

z=w+10

Now substitute z=w+10

3w-2+4y-7w+70=-60

3y+3w+18=15

Isolate y for 4y-4w-72=-60, y=w+3.

substitute y=w+3

3(w+3)+3w+18=15

6w+27=15

w=-2

For y=w+3, substitute w=-2.

y=1

For z=w+10, substitute w=-2:

z=8

So x=7.

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Evaluate: 2w+x+2y−3z​ =−19

w−2x−y+4z=15

x+2y−z=1

3w−2x−5z=−60

The standard deviation measures how far the data are from the dataset mean. The lower the standard deviation is, the closest the data are to the mean.

In this case, the pilot strives for a mean equal to 0 (zero minutes late). Also, since the pilot needs the arrivals to be as close as possible to this mean of zero minutes late (on-time), they want the data of "minutes late" to be all close to this mean. And this is achieved with a lower standard deviation.

Therefore, they want a lower standard deviation.

Answer:

84 cm

Step-by-step explanation:

Area=a, length=l, width=w

\(A=lw\)

If area is 5376 cm², and width is 64 cm,

\(5376=64l\)

Divide each side by 64,

\(l=84\)

So, the length of the rectangle is 84 cm.

The set B in the expression AxB, where A={1, 2, 3}, is {a, b}. This is determined by observing the second elements in the resulting set AxB, which are 'a' and 'b'. Therefore, B={a, b}.

In the expression AxB, A represents the set {1, 2, 3}, and B represents an unknown set of elements. The notation AxB denotes the Cartesian product of sets A and B, which is the set of all possible ordered pairs where the first element is from set A and the second element is from set B.

The given expression AxB produces the following set of ordered pairs:

{(1.a), (2.a), (3.a), (1.b), (2.b), (3.b)}

From this set, we can observe that the second element of each ordered pair takes the values 'a' and 'b'. Therefore, we can deduce that the set B must contain these elements. Thus, B={a, b}.

In summary, the set B in the expression AxB is {a, b} as these are the values that appear as the second elements in the resulting set AxB.

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Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{60 \: meter}}}}}\)

Step-by-step explanation:

Area of a park = 3600 m

Length of one side of the park ( l ) = ?

Using the formula of area of square

\( \boxed{ \sf{area \: of \: square = {l}^{2} }}\)

\( \longrightarrow{ \sf{3600 = {l}^{2} }}\)

\( \longrightarrow{ \sf{ {l}^{2} = 3600}}\)

\( \longrightarrow{ \sf{ \sqrt{ {l}^{2} } = \sqrt{3600}}} \)

\( \longrightarrow{ \sf{l = 60 \: meter}}\)

Length of one side of the park = 60 meter

Hope I helped!

Best regards! :D

The duration of the race is 25 min which is completed by Amit,  

Arithmetic operations is a branch of mathematics, that involves the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.

These basic mathematical operations (+, -, ×, and ÷) we use in our everyday life. Whether we need to calculate the annual budget or distribute something equally to a number of people, for every such aspect of our life, we use arithmetic operations.

Amit Start the cycle race at 1:25,

He completed the race at 1:50,

So, the duration of the race is =1:50-1;25=25 min

Hence, The duration of the race is 25 min which is completed by Amit,

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To use the normal approximation for a test of two proportions, n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2) must all be greater than or equal to 5.

This is because the normal distribution assumes that the sample size is large enough to approximate the binomial distribution, and the rule of thumb is that each cell (n1 p1, n1 (1 - p1), n2 p2, and n2 (1 - p2)) should have at least 5 expected counts. If any of these cells have fewer than 5 expected counts, then the normal approximation is not reliable and a more appropriate test should be used. It is important to note that this is just a rule of thumb, and other factors such as the size of the effect and the desired level of significance should also be considered when deciding on a statistical test.

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Answer:

The bar over the 9 means that the nine is repeating itself

First page: D

Second page: The bar over 9 means that 9 goes on forever after the decimal point.

Third page: Point A

Fourth page: Greatest 3.1, 2, 2/3, 0.55, 0, -7/8, -4 Least

Fifth page: E is at the origin because the origin is the point (0,0), and point E's coordinates are (0,0)

hope this helps :)

The formula to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

The formula presented derived from the formula for the circumference of a circle, which is C = 2πr. By rearranging the equation and isolating the radius (r) on one side, we get r = C/(2π).

So, if the circumference (C) of a circle is 18 centimeters, you can use the formula r = C/(2π) to find the radius (r). Plugging in the given value for the circumference (C), we get:

r = 18/(2π)

Simplifying the equation gives:

r = 9/π

Therefore, the radius (r) of the circle is 9/π centimeters.

In conclusion, the formula you can use to find the radius (r) of a circle when you know the circumference (C) is r = C/(2π).

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The function fog(x) = √(4x - 2) has a domain of x ≥ 0, and the function gof(x) = 4√(x + 1) - 3 has a domain of x ≥ -1.

The function fog(x) is equal to f(g(x)) = √(4x - 3 + 1) = √(4x - 2). The domain of fog is the set of all x values for which 4x - 2 is greater than or equal to zero, since the square root function is only defined for non-negative values.

Thus, the domain of fog is x ≥ 0.

The function gof(x) is equal to g(f(x)) = 4√(x + 1) - 3. The domain of gof is the set of all x values for which x + 1 is greater than or equal to zero, since the square root function is only defined for non-negative values. Thus, the domain of gof is x ≥ -1.

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The calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

To determine the number of significant figures in the answer to the calculation (3.4876)/(4.11+1.2), we need to consider the number of significant figures in the given values and apply the rules for significant figures in mathematical operations.

First, let's analyze the number of significant figures in the given values:

- 3.4876 has five significant figures.

- 4.11 has three significant figures.

- 1.2 has two significant figures.

To perform the calculation, we divide 3.4876 by the sum of 4.11 and 1.2. Let's evaluate the sum:

4.11 + 1.2 = 5.31

Now, we divide 3.4876 by 5.31:

3.4876 / 5.31 = 0.6567037...

Now, let's determine the number of significant figures in the result.

Since division and multiplication retain the least number of significant figures from the original values, the result should be reported with the same number of significant figures as the value with the fewest significant figures involved in the calculation.

In this case, the value with the fewest significant figures is 5.31, which has three significant figures.

Therefore, the answer to the calculation (3.4876)/(4.11+1.2) should be reported with three significant figures: 0.657.

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If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

\(\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}\)

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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The derivative of of f(x) = 10 is 0

The derivative of a function is the measure of the rate of change of the function. They are fundamental to the solution of problems in calculus and differential equations.

Here the function is not changing as 10 is a constant. So, if f(x) = c where c is a constant then f'(x) = 0 as the derivative of a constant is always zero.

Mathematically:

           d(f(x))/dx = \(\lim_{h \to 0}\) (f(x+h) - f(x))/h

There  is no x to substitute for x + h so no difference is noticed:

             \(\lim_{h \to 0}\) (f(x+h) - f(x))/h =   \(\lim_{h \to 0}\) (10 - 10)/h = 0

Hence, the derivative of f(x) = 10 is 0

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Answer:

67

Step-by-step explanation:

we have a gap between 1st and 2nd terms of 4. a gap between 2nd and 3rd of 8. 16 for next gap. the gap doubles every time.

so we expect gap between 4th and 5th terms to be 2 X 16 = 32.

35 + 32 = 67. that is the next number in the sequence.

Answer:

A. (2,-1) i thought this is hard but its kind of easy actually

Step-by-step explanation:

so you just put the given options into the xs and ys.. so lets say we have (2,-1) 2=x -1=y

now put them into the equations.. y=x-3

-1=2-3( if this is true than this is the right answer)

y= -x +1

-1= -2 +1 (this is also correct)

Square root of 36 plus the square root of 125 cubed plus 8 to the power of 2" is 1,953,195 + 5√5

To find the square root of 36, we take the square root of 36, which is 6.

To find the square root of 125, we can break it down into its prime factors:

125 = 5 * 5 * 5.

Taking the square root of each factor, we get

√125 = √(5 * 5 * 5) = 5√5.

To find 125 cubed, we multiply 125 by itself three times:

125 * 125 * 125 = 1,953,125.

To find 8 raised to the power of 2, we multiply 8 by itself:

8 * 8 = 64.

So, the expression becomes:

6 + 5√5 + 1,953,125 + 64.

Therefore, the answer to the expression "square root of 36 plus the square root of 125 cubed plus 8 to the power of 2" is 1,953,195 + 5√5.

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Answer:

y = 2x - 3

Step-by-step explanation:

x + 2y = 4

2y = -x + 4

y = -1/2x + 2

1 = 2(2) + b

1 = 4 + b

-3 = b

y = 2x - 3

To calculate the probability of getting two numbers whose product is even when throwing two 4-sided dice simultaneously, we can use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening.

To start, we can determine the probability of getting two numbers whose product is odd. This can only happen if both dice show odd numbers, which occurs with a probability of 1/2 * 1/2 = 1/4. Therefore, the probability of getting two numbers whose product is even is:

Probability of even product = 1 - Probability of odd product

Probability of even product = 1 - 1/4

Probability of even product = 3/4

So, the probability of getting two numbers whose product is even when throwing two 4-sided dice simultaneously is 3/4 or 0.75. This means that in 75% of the cases when two 4-sided dice are thrown, the product of the two numbers will be even.

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Answer:

1. 4.5 oz in each container. 2. 27 divided by 6 = ? 3. the unknow quantity is 4.5 because if you take 27oz and divide that six ways into the six containers you get 4.5 oz  so it looks like this 27  * 6 = 4.5

Step-by-step explanation: just use that the  * means divided by but there isn't a real one on my laptop hope this helps

The solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have an equation:

x² – 4x + 4 = 2x + 1 + x²

After solving:

-4x + 4 = 2x + 1

6x = 3

x = 1/2 = 0.5

Thus, the solution to the equation x² – 4x + 4 = 2x + 1 + x² is x = 2.5 and the graph is shown in the picture.

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The probability that a person aged 40 or over has a master's degree is 6.15%

Given is table showing the educational qualification of a residential area, we need to find the probability that person aged 40 or over has a master's degree,

P(E) = favorable outcome / total outcome

P(person aged 40 or over has a master's degree) = 475+699 / 19076
= 1174 / 19076

= 0.06154

= 6.15%

Hence, the probability that a person aged 40 or over has a master's degree is 6.15%

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Answer:

the answer is A. 64:343.

Step-by-step explanation:

The ratio of the volumes of two similar figures is equal to the cube of the ratio of their corresponding side lengths. Since the scale factor of the two cylinders is 4:7, the ratio of their corresponding radii is 4:7 and the ratio of their heights is also 4:7.

So, the ratio of their volumes is (4/7)^3 = (64/ 343) = 64:343

So, the answer is A. 64:343.

The equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\\\)

As we can see in the graph the line goes from (-6, 0) and (0, 3)

Finding the slope:

\(\rm m =\dfrac{3-0}{0-(-6)}\\\)

m = 3/6 = 1/2

y = mx + c

y = (1/2)x + c

c is the y-intercept

c = 3

The equation:

y = (1/2)x + 3

Thus, the equation of the line in slope-intercept form is y = (1/2)x + 3 and the slope is 1/2.

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Answer:

\(h=30\)

Step-by-step explanation:

Volume of a cone=1540\(cm^{3}\), Radius=7cm.

The height of a cone=h

When we need to find the height of a cone, we can use the formula of the volume of a cone, which is \(\frac{1}{3} \pi r^{2} h\) to find the height of a cone.

\(1540cm^{3} =\frac{1}{3}\pi r^{2} h\)

Put the pi value=22/7 and the value of radius which is 7 cm into the formula.

\(1540cm^{3}=\frac{1}{3}*\frac{22}{7} 7^{2}h\)

\(1540cm^{3} =\frac{154}{3}h\)

Move \(\frac{154}{3}\) to another side. 1540 divided by  \(\frac{154}{3}\) to calculate what is the value of h, h is the height of a cone. Like this.

\(\frac{1540cm^{3} }{\frac{154}{3} } =h\)

\(30=h\)

Rearrange the h.

\(h=30\)

I hope you will understand my solution and explanation. If you still cannot get the point, you can ask me anytime! Thank you!

Answer:

The height of the cone is h = 30 cm.

Step-by-step explanation:

The formula for a cone is:

\( \\ V = \frac{1}{3}*\pi*r^2*h\)

We have (without using units) and using pi = 22/7:

\( \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)^2*h\)

Which is equals to:

\( \\ 1540 = \frac{1}{3}*\frac{22}{7}*(7)*h\)

\( \\ 1540 = \frac{1}{3}*22*7*h\)

Well, we have to solve the equation for h:

\( \\ \frac{1540*3}{22*7} = h\)

\( \\ 30 = h\)

Therefore, the height of the cone is 30 cm.

Answer:

7 hours

Step-by-step explanation:

20.00 + 10x = 90

10x = 70

x = 7

Answer:

20 + 10x = 90  (where x is the number of hours spent raking leaves)

7 hours

Step-by-step explanation:

let x = number of hours spent raking leaves

Given:

20 + 10x = 90

To solve:  20 + 10x = 90

Subtract 20 from both sides:

⇒ 10x = 70

Divide both sides by 10:

⇒ x = 7

Therefore he spent 7 hours raking the leaves.

Answer:

-24

Step-by-step explanation:

Answer:

−24

Step-by-step explanation:

Answer:

Remove parentheses.

y-10=-3\times -2y−10=−3×−2

2 Simplify 3\times -23×−2 to -6−6.

y-10=-(-6)y−10=−(−6)

3 Remove parentheses.

y-10=6y−10=6

4 Add 1010 to both sides.

y=6+10y=6+10

5 Simplify 6+106+10 to 1616.

y=16y=16

Answer:

  24.2% decrease

Step-by-step explanation:

The distance Javi must ride changed by ...

  1.25 -1.65 = -0.40 . . . miles

The ratio of that to the original distance is ...

  -0.40/1.65 × 100% ≈ -24.2%

The distance decreased by 24.2%.

Explanation

in this case we have a rule that says what the value is, for example for

n=1

then, to know the term number 30, we have to replace

so, the term number 30 is

I hope this helps you