Let A={A_α ∶α∈Δ} be a family of sets, Δ≠∅ and let B be an arbitrary set. Either prove the statement is true or give a counter example to show the statement is false.

Answer:

(-infinity, -2/3)u(-2/3,0)u(0, infinity)

Step-by-step explanation:

since it is asking for f(g(x)) we plug g into x which looks like:

f(2/x)

now we plug that into the f(x) equation for all of the x's because that is what replaced the x so:

1/(2/x)+3

we look at the denominator so we can pull the 2/x+3 out and set it equal to zero, therefore solving for x

this gives us -2/3

and we get the 0 from g(x) 's denominator

that should be correct and hope this helps!

Answer:

11x-5

Step-by-step explanation:

Answer:

positive 2...

Step-by-step explanation:

e is at -2 so the mirror number would be 2

Answer:

8 < x < 12

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is in the range

difference of sides < x < sum of sides , that is

10 - 2 < x < 10 + 2

8 < x < 12

Answer:

Step-by-step explanation:

It's gonna be true in just trust me when i say that im that guy

Answer:

true

Step-by-step explanation:

The answer is: \(10^5\) terms.

We know that the error bound for the nth partial sum of a series can be given by:

\(|E_n| < = S - S_n\)

where S is the sum of the infinite series, \(S_n\) is the sum of the first n terms, and \(E_n\) is the error in the approximation of S by \(S_n\).

For the given series, we have:

\(S = Σ(1/n^1.1)\)

We want to find the number of terms n such that the error\(|E_n|\) is at most 0.00001. In other words, we want to find the smallest value of n such that:

\(|E_n| < = 0.00001\)

Using the error bound formula, we have:

\(|E_n| < = S - S_n\)

Substituting the values, we get:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = 0.00001\)

where k is the number of terms we want to add.

We can simplify the left-hand side of this inequality using the reverse triangle inequality:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = |Σ(1/n^1.1)| + |Σ(1/k^1.1)|\)

Using the formula for the sum of a p-series, we have:

\(Σ(1/n^1.1) = Σ(1/n^(11/10)) = ∞\)

Therefore, we can ignore the second term on the right-hand side of the inequality, and focus on the first term. We want to find the smallest value of k such that:

\(|Σ(1/n^1.1)| < = 0.00001\)

We can approximate the sum of the series by an integral, using the integral test. Therefore, we have:

\(Σ(1/n^1.1) ≈ ∫[1,∞] dx/x^1.1 = [x^-0.1/-0.1]∞_1 = 10\)

Using this approximation, we get:

\(|Σ(1/n^1.1)| < = 10\)

Substituting this in the inequality, we have:

10 <= 0.00001

This is clearly not possible, so we need to increase the number of terms k. Let us try with k = 10000. Using a calculator or computer program, we can find that:

\(Σ(1/k^1.1) ≈ 9.986\)

Therefore, we have:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.986| ≈ 0.014\)

This is still greater than 0.00001, so we need to increase the value of k further. Let us try with k = 100000. Using a calculator or computer program, we can find that:

\(Σ(1/k^1.1) ≈ 9.9997\)

Therefore, we have:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.9997| ≈ 0.0003\)

This is less than 0.00001, so we can use k = 100000 terms to estimate the value of the series with error at most 0.00001.

Therefore, the answer is:

\(10^5\) terms.

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\((\stackrel{x_1}{8}~,~\stackrel{y_1}{6})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{ 7}(x-\stackrel{x_1}{8}) \\\\\\ y-6=7x-56\implies {\Large \begin{array}{llll} y=7x-50 \end{array}}\)

Step-by-step explanation:

that means the center of the circle is exactly in the middle between the 2 points.

and since both points have the same x value (so, the diameter here is a vertical line), it is ready to get the y value of the middle : (-7 - 0) / 2 = -3.5

so, the coordinates of the center are (3, -3.5).

and that makes the standard circle equation

(x - h)² + (y - k)² = r²

to

(x - 3)² + (y + 3.5)² = 3.5² = 12.25

as h, k are the coordinates of the center, and r is the radius (half the diameter).

Answer:

81.5

Step-by-step explanation:

<G and <H are congruent

<F and <I are congruent

so the last two angles in both triangles must also be congruent

this means that <K and <J are congruent

so we can create this equation: <K = <J

substitute the angles with what we know: 4\(y^{2}\) = 6\(y^{2}\) - 40

add 40 to both sides and subtract 4\(y^{2}\) from both sides: 40 = 2\(y^{2}\)

you get: 20 = \(y^{2}\)

root square on both sides: \(\sqrt{20}\) = \(\sqrt{y^{2} }\)

you get: y ≈ 4.5

substitute this into one of the equations for a missing variable:

6\(y^{2}\) -----> 6 (4.5 x 4.5) - 40

6 ( 20.25) - 40

121.5 - 40

81.5

Let f(x) = -2x³ - 7.The closed interval is [-3,2].To find the absolute maximum value of f(x) in the interval [-3,2], we need to evaluate f(x) at the critical numbers and at the endpoints of the interval [-3,2].

Step 1: The derivative of f(x) can be obtained by using the power rule of differentiation.f'(\(x) = d/dx [-2x³ - 7]= -6x\)²The critical numbers are the values of x where f'(x) = 0 or f'(x) does not exist.f'(x) = 0-6x² = 0x = 0

Step 2: We need to evaluate the value of f(x) at the critical number and at the endpoints of the interval \([-3,2].f(-3) = -2(-3)³ - 7 = -65f(2) = -2(2)³ - 7 = -15f(0) = -2(0)³ - 7 = -7\)

Step 3: We compare the values of f(x) to identify the absolute maximum value of f(x) in the interval [-3,2].f(-3) = -65f(0) = -7f(2) = -15The absolute maximum value of f(x) over the closed interval [-3,2] is -7.

The value of x that corresponds to the absolute maximum value of f(x) is 0.Therefore, the absolute maximum value of f over the closed interval [-3,2] occurs at x = 0.

Answer: x = 0.

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The simplified expression is 3.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

[ 5/(x - 3) - 5/(x + 3) ] / 10/(x² - 9)

= [ {5(x + 3) - 5(x - 3)} / (x + 3)(x - 3) ] x (x² - 9)/10

 Using [ (a² - b²) = (a + b) (a - b) ]

= [(5x + 15 - 5x + 15) / (x + 3)(x - 3)] x [(x - 3)(x + 3) / 10]

= (5x + 15 - 5x + 15) / 10

= 30/10

= 3

Thus,

The value of the expression is 3.

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Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right.

How to carry out Congruence Proofs?

We are told that both peter and Vivian were trying to prove from the attached diagram the statement that;

If ∠2 ≅ ∠3, then ∠1 is supplementary to ∠3.

Now, from the proofs of both of them, we can see that peter used a direct proof because he knew he could get it directly but Vivian utilized another means which was by starting with contradiction to reprove that the answer was correct.

Thus, we can conclude that Peter used direct proof method because he gets the answer directly whereas Vivian used direct proof method by contradiction because she first assumed that the answer was wrong and had to prove that the answer was right

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please branliest if correct

It is 0 (A)

16-4(3+2:2)

16-4(3+1)

16-4 x 4

16-16=0

To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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Answer: 16

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

To multiply powers of a variable, add the exponents:

\(x^m\cdot x^n = x^{m+n}\)

This rule works for all exponents, positive, negative, or zero.  Also, remember that \(x^0=1\).

Also, remember the definition of negative exponent:  \(x^{-n} = \frac{1}{x^n}\)

To multiply the two monomials, start by multiplying the coefficients, 14 and 4.  That gives 56, so your answer begins with 56.

Now for the powers of x,  \((x^3)(x^{-5}) = x^{3+(-5)} =x^{-2} = \frac{1}{x^2}\)

For the powers of y,  \((y^{-4})(y^4)=y^{4+(-4)} = y^0 = 1\)\((y^{-4})(y^4) = y^{-4+4} = y^0 =1\)

Your answer is

\(56 \cdot \frac{1}{x^2} \cdot 1 =\frac{56}{x^2}\)

Answer:

The distributive property

Step-by-step explanation:

When you have a number on the outside of a set of parenthesis, you can remove the parenthesis by multiplying the term on the outside by each of the terms on the inside. This is known as the distributive property.

To find the number of days it will take for Juliana's investment to grow, we can use the formula for simple interest

I = P * r * t.

I = interest earned
P = principal amount (initial investment)
r = interest rate per year (in decimal form)
t = time in years In this case,

Juliana's principal amount (P) is $3,300, the interest rate (r) is 6.25% or 0.0625, and she wants to reach $3,450. We need to solve for t. $3,450 = $3,300 * 0.0625 * t Divide both sides of the equation by ($3,300 * 0.0625) to isolate t:
t = $3,450 / ($3,300 * 0.0625)
t = 17 So it will take Juliana approximately 17 days for her investment to grow to $3,450.

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Answer:

680

Step-by-step explanation:

total percent=85%

total marks=800

obtain marks = total percent % 100 mutiply by total marks

The radius of the semi circle is 6 inches and the circumference of the semi circle is 18.84 inches.

A semi circle is half of a circle. The radius and circumference of the semi circle can be found as follows:

Therefore, radius is half of the diameter of a circle.

Hence,

radius of the semi circle  = 12 / 2

radius of the semi circle  =  6 inches

Therefore, let's find the circumference of the semi circle.

circumference of the semi circle = πr

circumference of the semi circle = 3.14 × 6

circumference of the semi circle =  18.84 inches

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

piggy bank:

quarters and dimes = $5.10

# quarters and dimes = 27

Step 02:

system of equations:

quarters = q

dimes = d

equation 1:

q + d = 27

equation 2:

0.25q + 0.10d = 5.10

The answer is:

q + d = 27 eq.1

0.25q + 0.10d = 5.10 eq.2

Answer:

-17

Step-by-step explanation:

-1 + (-16) =

-1 - 16 =

- (1 + 16) = -17

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Answer:

1cm = 60 miles

.5cm = 30 miles

Step-by-step explanation:

divide 270 by 4.5

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:

1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).

The area below z=1.04 is approximately 0.851, rounded to three decimal places.

(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:

1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.

The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.

(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:

1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.

The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.

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Answer:45 76 97 790 9786 99780 533455 6687878

Step-by-step explanation: