Prove that if a is any well-ordered set of real numbers and b is a nonempty subset of $a$, then $b$ is also well-ordered.

The Mistake made by Shane is shown below.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. Typically, these functions are identified by letters like f, g, and h. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(1)=4 and f(n)=2f(n-1)+1

f(2)= 2f(1)+1

f(2) = 9

and, f(3)= 2f(2) + 1

f(3) = 19

and, f(4)= 2f(3)+1

f(4) = 37

so, for finding the 5th term of the function

f(5) = 2 f(4) + 1

So, we need f(4) and then value of f(4) is multiplied by 2.

As, f(5) = 2(37)+1 = 75

and, according to Shane f(5)= (4*2*2*2*2)+1 = 65

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The expression equivalent to 11 - 9(-2x - 3) is 18x + 38 after applying the distributive property and rules for multiplying numbers with different signs. This corresponds to option A.

To find which expression is equivalent to 11 − 9(−2x − 3), we need to apply the distributive property and the rules for multiplying numbers with different signs. The distributive property tells us to multiply the number outside the parentheses by each term inside the parentheses. So, let’s apply this to the expression:

Therefore, the expression equivalent to 11 − 9(−2x − 3) is 18x + 38, which corresponds to option A.

Answer: 48

Step-by-step explanation:

Do 12 divided by 1.5 = 8

8 * 6 = 48

so 48 is your answer

:3

The best estimate for the division of 5 3/4 by -3 3/8 is 6 divided by -3 because rounding each number to the nearest whole provides the most accurate estimation.

To estimate an answer for 5 3/4 divided by -3 3/8, we should round each number to the nearest whole number. The number 5 3/4 rounds up to 6 because the fractional part (3/4) is more than half. The number -3 3/8 rounds to -3 because the fractional part (3/8) is less than half. Therefore, the closest estimation of the original division problem using whole numbers is 6 divided by (-3).

Answer:

the answer is B

Step-by-step explanation:

The model would be most helpful in solving the problem 'How many 1/6s are in 2/3?'. This is found by dividing 2/3 by 1/6 through fractional division, giving a result of 4.

The model would be most helpful in solving the question 'How many 1/6s are in 2/3?'. Let me explain why:

To solve this, you simply need to divide 2/3 by 1/6. When we say 'how many 1/6s are in 2/3', it means how many times can 1/6 fit into 2/3. Division is the process of finding out how many times one number (the divisor) is contained within another (the dividend).

So we divide 2/3 by 1/6. But rather than directly divide, in fractional division we multiply the first fraction by the reciprocal of the second. The reciprocal of 1/6 is 6/1.

So, 2/3 * 6/1 = 4.

That means, there are 4 1/6s in 2/3.

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The amount of Janet's interest cost from a loan of $50,000 at an interest rate of 8% from March 19 to July 8, 2015 is $1,160. The calculation is done using the simple interest formula, with time approximated as 0.29 years.

The problem asking for the simple interest incurred on a loan taken by Janet can be solved using the formula of simple interest, which is I=PRT in financial mathematics. I is interest, P is the principal amount (initial loan), R is the interest rate, and T is the time.

Substituting these values into the formula, we get:

I = 50000 * 0.08 * 0.29

Calculating this out will give you the total interest, $1160.

So, the amount of Janet's interest cost is $1,160.

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Function transformation involves changing the form of a function

The function that represents the transformation is: g(x) = 1/2(5^(x -3))

The parent function is given as:

f(x) = 5^x

When the function is vertically compressed by a factor of one-half, the function becomes

f'(x) = 1/2(5^x)

When the function is shifted 3 units right, it becomes

f"(x) = 1/2(5^(x -3))

Rewrite the function as:

g(x) = 1/2(5^(x -3))

Hence, the function that represents the transformation is: g(x) = 1/2(5^(x -3))

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The correct function representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]

1. **Vertical Compression by a Factor of One-Half:**

  To vertically compress the function by a factor of one-half, we multiply the function by [tex]\( \frac{1}{2} \)[/tex]. This affects the [tex]\( y \)[/tex]-coordinates of all points on the graph. So, the function becomes: [tex]\( \frac{1}{2} \cdot 5^x = \left(\frac{1}{2}\right)5^x \).[/tex]

2. **Shifted to the Left Three Units:**

  To shift the function to the left three units, we add 3 to the [tex]\( x \)[/tex] -coordinate. This affects the input values. So, the function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} \).[/tex]

3. **Shifted Down Two Units:**

  To shift the function down two units, we subtract 2 from the [tex]\( y \)-[/tex]coordinate. This affects the output values. So, the final transformed function becomes: [tex]\( \left(\frac{1}{2}\right)5^{x+3} - 2 \).[/tex]

Now, let's compare this transformation with the provided options:

A) [tex]\( g(x) = 5^{\left(\frac{n}{2}\right)+3} - 2 \)[/tex]

  This option doesn't match the transformation. It introduces a variable [tex]\( n \)[/tex] and doesn't involve the original function [tex]\( 5^x \)[/tex].

B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \)[/tex]

  This option matches the transformation. It has the vertical compression by [tex]\( \frac{1}{2} \)[/tex], shifting to the left by three units, and shifting down by two units.

C) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x+5} - 2 \)[/tex]

  This option doesn't match the transformation. It shifts the function to the right by five units instead of to the left.

D) [tex]\( g(x) = 5^{\left(\frac{1}{2}\right)^{x-3}} - 2 \)[/tex]

  This option introduces a fractional exponent, which doesn't correspond to the given transformations. It also has an incorrect shift to the right by three units.

Therefore, the correct option representing the transformation is B) [tex]\( g(x) = \left(\frac{1}{2}\right)5^{x-2} - 2 \).[/tex]

Complete Question :

The parent function, f(x)=5^x has been vertically compressed by a factor of one-half shifted to the right three units and down two units.

Choose the correct function to represent the transformation

A) g(X)=5^(((n)/(2))+3)-2  

B) g(x)=((1)/(2))5^(x-2)-2  

C) g(x)=((1)/(2))5^(x+5)-2

D) g(x)=5^(((1)/(2))^(x-3))-2

For a 95% confidence interval with ±0.0001 margin of error, sample size[tex]\( n \approx 385 \)[/tex] measurements are needed.

To determine the sample size [tex]\( n \)[/tex] needed to achieve a margin of error of [tex]\( \pm 0.0001 \)[/tex] for a 95% confidence interval for the mean [tex]\( \mu \)[/tex], we can use the formula for the margin of error of a confidence interval:

[tex]\[\text{Margin of Error} = Z \times \frac{\sigma}{\sqrt{n}}\][/tex]

Where:

[tex]- \( Z \) is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to \( Z = 1.96 \)).\\- \( \sigma \) is the standard deviation of the measurements (given as \( 0.001 \) g).\\- \( n \) is the sample size.[/tex]

Given that the margin of error [tex](\( \text{MOE} \)) is \( 0.0001 \)[/tex], we can rearrange the formula to solve for \( n \):

[tex]\[n = \left(\frac{Z \times \sigma}{\text{MOE}}\right)^2\][/tex]

Substituting the given values:

[tex]\[n = \left(\frac{1.96 \times 0.001}{0.0001}\right)^2\]\[n = \left(\frac{0.00196}{0.0001}\right)^2\]\[n = \left(19.6\right)^2\]\[n = 384.16\][/tex]

Since [tex]\( n \)[/tex] must be a whole number (you can't have a fraction of a measurement), we round up to the nearest whole number. So, [tex]\( n = 385 \).[/tex]

Therefore, you would need to take at least 385 measurements to ensure that the margin of error for the 95% confidence interval of the mean [tex]\( \mu \) is \( \pm 0.0001 \) g.[/tex]

As per linear equation, total price is directly proportional to the number of tickets I buy.

A linear equation is an equation that has the highest power of the variable as 1.

Given, a movie theater charges $10.50 per ticket and $5 per bucket of popcorn.

I never buy the popcorn because I think it's too expensive.

Let, I buy 'n' number of tickets.

Therefore, the total price for the tickets is

[tex]P = 10.50n[/tex]

⇒ P∝ n

Therefore, total price is directly proportional to the number of tickets I buy.

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Answer:

[tex](x-12)[/tex] is a factor

Step-by-step explanation:

[tex]x^2-14x+24[/tex]

The product is 24 and sum is  [tex]-14[/tex]

To factor it we need to find out two factors whose product is 24 and sum is  [tex]-14[/tex]

[tex]-12 \cdot -2= 24[/tex]

[tex]-12 +(-2)= -14[/tex]

Two factors are [tex]-12 , -2[/tex]

[tex]x^2-14x+24[/tex]

[tex](x-12)(x-2)[/tex]

[tex](x-12)[/tex] is a factor

Answer:

5∧5

Step-by-step explanation:

Answer:

D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.

Step-by-step explanation:

All sides of a square has to be equal.

Here it is given that X an Y are 2 of the vertices of the square. We can say that XY is the length of one side of the square.

So e should make sure that a length of the square on the YZ line is same as the XY line.

So,

Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.

Answer:

D. Place the point of the compass on point Y and draw an arc that intersects YZ¯¯¯¯¯ , using XY as the width of the opening of the compass.

Step-by-step explanation:

Verified by test results

Hope this helps:)

The expression p(11,7) is evaluated by calculating the permutation of 11 items taken 7 at a time, resulting in a value of 55440.

The expression p(11,7) is a notation used in mathematics to represent a permutation.

To evaluate the permutation p(n, k), where n is the total number of items and k is the number of items to be arranged, we use the formula n! / (n-k)!.

Let's calculate the permutation for p(11, 7):

First, we find the factorial of 11, which is 11!, or 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

Then, we find the factorial of (11-7), which is 4!, or 4 x 3 x 2 x 1.

The permutation is calculated as follows:

p(11, 7) = 11! / 4!

After cancelling out the common terms in the numerator and the denominator, we have:

p(11, 7) = 11 x 10 x 9 x 8 x 7, which is equal to 55440.

Therefore, the value of the expression p(11,7) is 55440.

Final answer:

To find the finance charge for an unpaid balance of $246.07, apply 1.5% on the first $100 and 1% on the remainder. The total charge is $2.9607, which rounds to $2.96, matching answer D.

Explanation:

To calculate Larry's finance charge for the unpaid balance of $246.07, we'll first divide the balance into the portions that are charged at different rates as per the bank's policy. So, the first $100 is charged at a higher rate of 1.5%, and the remaining balance ($146.07) is charged at a lower rate of 1%.

Calculate 1.5% on the first $100: $100 × 0.015 = $1.50

Calculate 1% on the remaining $146.07: $146.07 × 0.01 = $1.4607

Sum both charges to find the total finance charge: $1.50 + $1.4607 = $2.9607

After rounding to the nearest cent, Larry's total finance charge is $2.96, which corresponds to answer choice D.

Answer: Is D.

Step-by-step explanation:

Using the Pythagorean theorem: After applying the theorem, the hypotenuse, which represents the distance between the two points, is approximately 6.1 miles when rounded to the nearest tenth of a mile.

To solve the problem of determining the distance from Frostburg Mall to Sojourner Truth Park, we can employ the Pythagorean theorem, which is used to find the length of the hypotenuse of a right-angled triangle.

Given that the mall is located 3 miles west and 4 miles south of the City Center, while the park is 3 miles east and 5 miles north, we can calculate the total east-west distance and the total north-south distance.

First, we add the east-west distances: 3 miles west of City Center to Mall plus 3 miles east from City Center to Park, which equals 6 miles in total.

Next, we calculate the north-south distance: 5 miles north from City Center to Park minus 4 miles south from City Center to Mall, resulting in 1 mile to the north.

We now have a right triangle where one leg is 6 miles and the other leg is 1 mile. Applying the Pythagorean theorem (a² + b² = c²), where 'a' and 'b' are the legs and 'c' is the hypotenuse:

c² = 6² + 1²
c² = 36 + 1
c² = 37

Finding the square root of 37, c ≈ 6.08 miles.

Therefore, the distance from the Frostburg Mall to the Sojourner Truth Park is approximately 6.1 miles to the nearest tenth.

Answer:.344 if you have to round to the third decimal

Step-by-step explanation:

Final answer:

The probability of drawing an odd number between 24 and 33 is 50%, as there are 5 odd numbers (25, 27, 29, 31, 33) within the 10 numbers in this range.

Explanation:

The probability of randomly drawing an odd number between 24 and 33 is calculated by identifying all the odd numbers in that range and dividing by the total number of possibilities.

The odd numbers between 24 and 33 are 25, 27, 29, 31, and 33. Since there are 10 total numbers (24 through 33), and 5 of these are odd, the probability is 5 out of 10, which simplifies to ½ or 50%.