the test statistic of z is obtained when testing the claim that p. a. using a significance level of ​, find the critical​ value(s). b. should we reject or should we fail to reject ​?

The value of the F"(2) is √262.

What is the chain rule?

The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².

To find F"(2), we need to differentiate F(x) twice with respect to x.

First, we find F'(x):

F'(x) = f(x)

Next, we find F''(x):

F''(x) = f'(x)

To find f'(x), we need to apply the chain rule and the fundamental theorem of calculus. We have:

\(f(t) = \int\limits^{t^2}_1 \frac{\sqrt{6+u^4}}{u} , du\)

Let's define \(g(u) = \sqrt{6+u^4}/u\). Then, using the chain rule, we have:

\(f'(t) = g(t^2) \cdot 2t\)

Now, we can find F''(2) by evaluating f'(t) at t=2:

\(F''(2) = f'(2) = g(2^2) \cdot 2(2)\)

To find g(2²), we evaluate g(u) at u=2²=4:

\(g(4) = \sqrt{6+4^4}/4 = \sqrt{6+256}/4 = \sqrt{262}/4\)

Putting it all together, we have:

\(F''(2) = f'(2) = g(2^2) \cdot 2(2) = (\sqrt{262}/4) \cdot 4 = \sqrt{262}\)

Therefore, the value of the F"(2) is √262.

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Answer:

Multiply the divisor by a power of 10 to make it a whole number.

Multiply the dividend by the same power of 10. Place the decimal point in the quotient.

Divide the dividend by the whole-number divisor to find the quotient.

When 12.42 divided by (-4.8) then the quotient is -2.587.

To find the quotient when 12.42 divided by (-4.8).

Let us convert the dividend and divisor to whole number by multiplying each with 100:

12.42×100 = 1242

-4.8×100= -480

Now divide 1242 by 480 to find the quotient:

=  - 1242/480

= -2.5875

Hence, when 12.42 divided by (-4.8) then the quotient is -2.587.

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Answer:

17 + x <_ 26

Step-by-step explanation:

<_ means smaller than or equal to

Answer:

Divide 10 by 25 then multiply by 4 to get 40 / 100 which gives you the percentage: 40%

Answer:-

Step-by-step explanation:

-120 - 40- would be -160 because when negative you go up when subtracting.

(not sure if I'm right. take this answer at your own risk)

Answer:

21/24

Step-by-step explanation:

The 24 for the 24ths must be in the denominator.

What do you multiply 8 by to get 24? Answer: 3.

That means you must multiply both the 7 in the numerator and the 8 in the denominator to change the fraction to 24ths.

7/8 × 3/3 = 21/24

Answer:

C=h+k+p

Step-by-step explanation:

You just add all of the variables and it equals your total cost. if it was by hour the equation would be slightly different

The distributed computation (e, →) is said to be consistent if all computations lead to the same result, regardless of the order in which the steps are performed.

Let g and h be consistent cuts of a distributed computation (e, →).

We must demonstrate that g ∪ h and g ∩ h are also consistent cuts of (e, →).

Let R be the set of events that are in both g and h. If we remove R from either g or h, we get a consistent cut since the removed events cannot cause a change in the outcome.

By removing R from both g and h, we obtain two new consistent cuts: g − R and h − R.

Thus, we can write:g = (g − R) ∪ R and h = (h − R) ∪ R. Since (g − R) and (h − R) are consistent cuts, it follows that their union, g ∪ h, is also a consistent cut. I

f we let S be the set of events that are in both g and h, then we can write:g = (g ∩ h) ∪ (g − S) and h = (g ∩ h) ∪ (h − S).

Again, (g − S) and (h − S) are consistent cuts, so their intersection, g ∩ h, is also a consistent cut.

Therefore, if g and h are consistent cuts of a distributed computation (e, →), then so are g ∪ h and g ∩ h.

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Answer:

a) 60 times

b) 0.24

c) 150 times

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

divide 2 by 5 get 0

multiply the quotient (0) by the divisor 5

subtract 0 from 2

Add a decimal point to the solution Bring down the next number of the divided

divide 25 by 5 to get 5

Multiply the quotient digit (5) by the divisor 5

subtract 25 from 25

the solution for long of 2.5/5 is 0.5

The simplified value of 2.5/5 is 1/2

An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

Examples of expression includes; 5x +2 , 6y + 3 , 5/2 e.t.c

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible.

Simplifying 2.5/5

multiply all by 10

= 25/50

divide through by 5

5/10 = 1/2

Therefore 2.5/5 is thesame as 1/2

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Answer:

40 feet

Step-by-step explanation:

-10 -30

The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

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Answer:

23

Step-by-step explanation:

Raise 3 to the power of 3

27 - 4

Subtract 4 from 27

23

Hope this was correct

Answer:

23

Explanation:

step 1 - rewrite the expression with the value of x

\(x^3 - 4\)

\((3)^3 - 4\)

step 2 - solve the exponent

\((3)^3 - 4\)

\(27 - 4\)

step 3 - subtract

\(27 - 4\)

\(23\)

therefore, the value of the expression is 23.

Answer: 16

Step-by-step explanation: your welcome

Answer:

39

Step-by-step explanation:

15 students study Geography and 24 study history.

15+24=39

Answer:1/5?

Step-by-step explanation:

i think that is 4/5 x 1/4 so,  1/5?

Answer:

50cm

200cm

50cm^2

Step-by-step explanation:

The big square is divided into 4 with a side length of 25cm. 2 small square side lengths make up the big squares.

25 * 2 =

50cm

50 + 50 + 50 +50 =

200

15 +2

17

8 + 2

10

17 * 10 = 170

15 * 8 = 120

170-120 = 50

50cm^2

Answer: It will have to pay $36 in fees.

Step-by-step explanation: Hope this helps:) please mark me brainliest.

Answer:

Hi! The answer to your question is \(g = 0\)

Step-by-step explanation:

In the equation there is no g so g is nonexistant so it equals 0

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Hope this helps!!

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Answer:

$32,000 was the profit last year.

Step-by-step explanation:

Answer:

The answer is 32000 profit

Step-by-step explanation:

I just did quiz hope it helps :)

Answer:

The third one

Step-by-step explanation:

Answer:

6 hours

Step-by-step explanation:

Divide 3300 by 550, so it's 6.

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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(a) Using induction: n^7 ≤ 2^n for n ≥ 37. (b) Using leaping induction: n^7 ≤ 2^n for n ≥ 37.(a) Using induction, we can prove that n^7 ≤ 2^n for n ≥ 37.

Base Case: For n = 37, we have 37^7 = 69,343, while 2^37 ≈ 137,438,953,472. Since 69,343 ≤ 137,438,953,472, the base case holds.

Inductive Step: Assume that for some k ≥ 37, k^7 ≤ 2^k. We need to show that (k + 1)^7 ≤ 2^(k + 1).

Expanding (k + 1)^7 using the binomial theorem, we have:

(k + 1)^7 = C(7, 0)k^7 + C(7, 1)k^6 + C(7, 2)k^5 + C(7, 3)k^4 + C(7, 4)k^3 + C(7, 5)k^2 + C(7, 6)k + C(7, 7)

Since k ≥ 37, each term in the expansion is multiplied by a positive coefficient. Thus, we can rewrite the inequality as:

(k + 1)^7 ≤ 2k^7 + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2

By the induction hypothesis, k^7 ≤ 2^k, so we can substitute this in the inequality:

(k + 1)^7 ≤ 2^k + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2

Now, we need to prove that 2^k + 2k^6 + 2k^5 + 2k^4 + 2k^3 + 2k^2 + 2k + 2 ≤ 2^(k + 1).

Dividing both sides by 2, we have:

2^k + k^6 + k^5 + k^4 + k^3 + k^2 + k + 1 ≤ 2^k

Since k ≥ 37, each term on the left-hand side is positive, and the inequality holds.

Therefore, we have shown that if k^7 ≤ 2^k for some k ≥ 37, then (k + 1)^7 ≤ 2^(k + 1).

By the principle of mathematical induction, we can conclude that n^7 ≤ 2^n for n ≥ 37.

Keywords: induction, n^7, 2^n, base case, inductive step, binomial theorem, induction hypothesis.

(b) Using leaping induction, we can prove that n^7 ≤ 2^n for n ≥ 37.

For this approach, we'll use a different base case and an alternative inductive step.

Base Case: For n = 37, we have 37^7 = 69,343, while 2^37 ≈ 137,438,953,472. Since 69,343 ≤ 137,438,953,472, the base case holds.

Inductive Step: Instead of considering (k + 1), we'll consider (k + 7) in each step.

Assume that for some k ≥ 37, k^7 ≤ 2^k. We need to show that (k + 7)^7 ≤ 2^(k + 7).

Expanding (k + 7)^7 using the bin

omial theorem, we have:

(k + 7)^7 = C(7, 0)k^7 + C(7, 1)k^6(7) + C(7, 2)k^5(7^2) + ... + C(7, 6)k(7^6) + C(7, 7)(7^7)

Now, we can observe that each term in the expansion contains a factor of 7 raised to some power, while k^7 ≤ 2^k. Thus, we can rewrite the inequality as:

(k + 7)^7 ≤ 2^k + 7^1(7^6) + 7^2(7^5) + ... + 7^6(7^1) + 7^7

Simplifying further, we have:

(k + 7)^7 ≤ 2^k + 7^7(1 + 7 + 7^2 + ... + 7^5 + 7^6)

Since k ≥ 37, we know that k ≤ 7k. Therefore, we can rewrite the inequality as:

(k + 7)^7 ≤ 2^k + 7^7(1 + 7 + 7^2 + ... + 7^5 + 7^6) ≤ 2^k + 7^7(7^6 + 7^6 + ... + 7^6 + 7^6) = 2^k + 7^7(7^6 × 6)

By the induction hypothesis, k^7 ≤ 2^k, so we can substitute this in the inequality:

(k + 7)^7 ≤ 2^k + 7^7(7^6 × 6) ≤ 2^k + 7^7(2^k × 6)

Combining the terms, we have:

(k + 7)^7 ≤ (2^k + 7^7(2^k × 6)) = 2^k(1 + 7^7 × 6)

Since 1 + 7^7 × 6 is a constant, we can denote it as C. Therefore, we have:

(k + 7)^7 ≤ 2^k × C = 2^(k + 7)

Hence, we have shown that if k^7 ≤ 2^k for some k ≥ 37, then (k + 7)^7 ≤ 2^(k + 7).

By the principle of leaping induction, we can conclude that n^7 ≤ 2^n for n ≥ 37.

Keywords: leaping induction, n^7, 2^n, base case, inductive step, binomial theorem, induction hypothesis.

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Kristin will pay 21.20 for the jeans after the discount and sales tax are applied.

The first step is to calculate the discount Kristin will receive:

Discount = 20% of 25 = 0.20 x 25 = 5

Now subtract the discount from the original price to find the sale price:

Sale price = 25 - 5 = 20

Next, calculate the amount of sales tax Kristin will have to pay on the sale price:

Sales tax = 6% of 20 = 0.06 x 20 = 1.20

Finally, add the sale price and sales tax to find the total cost:

Total cost = 20 + 1.20 = 21.20

Therefore, Kristin will pay 21.20 for the jeans after the discount and sales tax are applied.

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To create a frequency distribution using the "2 to the power of k rule", we need to determine the value of k. The rule states that k should be equal to the largest value in the dataset. In this case, the largest value is 65.

Next, we calculate 2 to the power of k, which is 2^k. Since k = 6 (since 2^6 = 64), we have 2^6 = 64.

Now, we can create the frequency distribution. We start by dividing the range of the data (65 - 4 = 61) by 64 (2^k) to determine the interval size.

61 / 64 = 0.953125

Since the interval size is less than 1, we round it up to 1.

Now, we can start creating the frequency distribution table. We'll start with the lower limit of the first interval, which is 4. Then, we add the interval size to get the upper limit of the first interval, which is 4 + 1 = 5.

Now, we count how many values fall within this interval. From the given data, we have 4 values (4, 18, 19, 24). So, the frequency for this interval is 4.

We continue this process for the rest of the intervals until we reach the largest value in the data.

Here's the frequency distribution table:

Interval   Frequency
4-5           4
6-7           2
8-9           2
10-11       0
12-13       0
14-15       0
16-17       0
18-19       2
20-21       0
22-23       1
24-25       2
26-27       1
28-29       0
30-31       0
32-33       0
34-35       2
36-37       1
38-39       2
40-41       1
42-43       2
44-45       1
46-47       0
48-49       1
50-51       3
52-53       1
54-55       3
56-57       1
58-59       0
60-61       1
62-63       1
64-65       1

In conclusion, we used the "2 to the power of k rule" to create a frequency distribution for the number of families who used the tri-c day care service during a 30-day period. The frequency distribution table shows the intervals and the corresponding frequency of values falling within each interval.

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Answer:

{6, 7}

Step-by-step explanation:

Plug in each number for x

Plug in 2

2(2)-4≥8

4-4≥8

0≥8 (2 is wrong because 0 is not greater than or equal to 8)

So we can eliminate the middle ones because two are in both b and c

Plug in 6

2(6)-4≥8

12-4≥8

8≥8 (This is correct because 8 is greater than or equal to 8)

Plug in 7

2(7)-4≥8

14-4≥8

10≥8 (This is correct because 10 is greater than or equal to 8)

The old will Mr Lim be in 6 years time is 46 years old.

To make solving this problem easier, we need to consider the ages of Mr Lim and his son. For example by multiplying the number x.

Let:

Mr Lim's age = a

His son's age = b

So that,

The ratio of ages in the current year:

Mr Lim's age to his son's age = 5x : 2x

a : b = 5x : 2x

The ratio of ages in the four years ago:

Mr Lim's age to his son's age = 3x : x

(a - 4) : (b - 4) = 3x : x

\(\frac{a-4}{b -4} =\frac{3x}{x}\)

\(\frac{5x-4}{2x -4} =\frac{3x}{x}\)

\(\frac{5x-4}{2x -4} =\frac{3}{1}\)

5x - 4 = 6x - 12

5x - 6x = -12 + 4

-x = -8

x = 8

So that we know the age of Pak Lim's and the age of his son's this year.

Mr Lim's age = 5x

                     = 5 × 8

                     = 40 years old

His son's age = 2x

                     = 2 × 8

                     = 16 years old

After that, we find Mr Lim's age 6 years from now by adding 6 years to this year's age.

Mr Lim's age be in 6 years time = 40 + 6

                                                    = 46 years old

So, the old will Mr Lim be in 6 years time is 46 years old.

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