Use the Principle of Mathematical Induction to show that the given statement is true for all natural numbers 9+10+11+ (08) 3 (17) What two conditions must the given statement satisfy to prove that it is true for all natural numbers Select all that apply The statement is true for the natural number 1 of the statement is true for some natural numberk, it is also true for the next natural number + 1 The statomont is true for any two natural numbers and k1 at the statement is true for the natural number 1, it is also true for the next natural number

The value of side CA of the right angle triangle is 8.85.

Trigonometry is the branch of mathematics that set up a relationship between the sides and angles of right-angle triangles. The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths.

Given that △ABC has a right angle at C, BC=7.7 centimeters, and m∠A=41∘.

The value of side CA is calculated, from the right angle triangle applying the angle property,

tan41 = (7.7)/(CA)

CA = (7.7)/(tan41)

CA = 8.85

Therefore, the value of side CA of the right angle triangle is 8.85.

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By constructing these arcs and connecting the appropriate points, we ensure that the newly drawn line passing through point C is parallel to line AB. Remember to use a straightedge to draw the lines accurately and ensure that the arcs intersect correctly.

To construct a line that passes through point C and is parallel to line AB, the best next step is to use a compass to mark an arc centered at point C that intersects line AB at two distinct points.

Here are the steps:

1) Take a compass and set its width to a convenient distance.

2) Place the compass point on point C and draw an arc that intersects line AB at two different points, let's call them D and E.

3) With the compass width still set, place the compass point on point D and draw an arc that intersects the previously drawn arc.

4) Without changing the compass width, place the compass point on point E and draw another arc that intersects the previous arc.

5) Label the point where the two new arcs intersect as F.

6) Draw a straight line passing through point C and point F. This line will be parallel to line AB.

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Answer:

see below

Step-by-step explanation:

               15 x (12+2) = 210 square feet

The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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Answer:

Step-by-step explanation:

First, find the circumference

4.6 * \(\pi\) =14.4513

Then set up a proportion to find how far the wheel turns in the given angle let x be the distance the wheel has rolled

\(\frac{14.4513}{360} =\frac{x}{337}\)

solve for x

x=13.528

Round to nearest tenth

13.5

Answer:

The overlap is 40 - 30 = 10 which means 10 people like both. 65 - 40 = 25 people like tennis only and 25 + 10 = 35 people like tennis.

Answer:

P = 0.2517

Step-by-step explanation:

In this case we must calculate the probability of event, which would be the number of specific events (that is, at least one woman and the rest men, 4), then it would be to choose 1 of 6 women by 4 of 9 men divided by the number of total events, which would be to choose 5 (committee size) out of 15 (9 men + 6 women, total number of people)

P (at least one woman) = 6C1 * 9C4 / 15C5

we know that nCr = n! / (r! * (n-r)!)

replacing we have:

6C1 = 6! / (1! * (6-1)!) = 6

9C4 = 9! / (4! * (9-4)!) = 126

15C5 = 15! / (5! * (15-5)!) = 3003

Therefore it would be:

P (at least one woman) = 6 * 126/3003

P = 0.2517

That is, approximately 1 out of 4 women.

We are asked to determine the degree of the polynomial given its graph. To do that we can count the number of bumps in the graph. We notice that it has 4 bumps:

This type of behavior is usual of polynomials of degree 5.

The regular expression "10" matches any string that starts with zero or more ones followed by zero or more zeros. The regular expression "(10 u 0)(1 u 10)" matches any string that starts with zero or more occurrences of "10" or "0", followed by zero or more occurrences of "1" or "10".

The regular expression 10 matches any string that contains zero or more ones followed by zero or more zeros. This includes empty strings as well as strings containing only ones or only zeros, as well as any combination of ones and zeros.

The regular expression (10 u 0)(1 u 10) matches any string that starts with zero or more occurrences of the string "10" or "0", followed by zero or more occurrences of either "1" or "10".

This regular expression matches strings such as "10", "1010", "0101", "001110", and so on. It allows for any number of occurrences of "0" between any pair of "1" or "10".

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Answer:

x>-8

Step-by-step explanation:

7x+11>5x-5

2x+11>-5

2x>-16

x>-8

the > sign acts like an equal sign :)

Answer:

\( x > - 8\)

Step-by-step explanation:

\(7x + 11 > 5x - 5 \\ 7x - 5x > - 11 - 5 \\ 2x > - 16 \\ x > - 8\)

This is the Communative property of multiplication

Answer:

associative property, 5 can be an associate to both 12 and 25

Answer:

C) 8

Step-by-step explanation:

5x=2x+24

5x-2x=24

3x=24

x=8

The total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\) and the x-axis is 1/2.

Let the region bounded by the graph of y = x times the square root of\((1 - x^2)\) and the x-axis be the region R.

The total area of region R is given by A as;\(A = 2∫_0^1▒〖ydx〗\)

The boundary of the given region is given by y = x times the square root of\((1 - x^2)\) and the x-axis.

Thus, for any x in the interval [0, 1], the boundary of the region R can be represented as;\(∫_0^1▒〖x√(1-x^2)dx〗\)

Let \(u = 1 - x^2,\)

therefore, du/dx = -2x.

It implies that\(dx = -du/2x.\)

The integral becomes;\(∫_1^0▒〖(-du/2)√udu〗=-1/2 ∫_1^0▒√udu\)

=-1/2 2/3

= -1/3

Therefore the total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\)and the x-axis is 1/2. Hence, option B) 1/2 is the correct answer.

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It will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

To find the number of days it will take for $9500 to earn $800 at an annual interest rate of 8.25%, we need to use the formula for simple interest:

Interest = Principal * Rate * Time

In this case, we are given the interest ($800), the principal ($9500), and the annual interest rate (8.25%). We need to solve for time.

Let's denote the time in years as "t". Since we're looking for the number of days, we'll convert the time to a fraction of a year by dividing by 365 (assuming a standard 365-day year).

$800 = $9500 * 0.0825 * (t / 365)

Simplifying the equation:

800 = 9500 * 0.0825 * (t / 365)

Divide both sides by (9500 * 0.0825):

800 / (9500 * 0.0825) = t / 365

Simplify the left side:

800 / (9500 * 0.0825) ≈ 0.1083

Now, solve for t by multiplying both sides by 365:

0.1083 * 365 ≈ t

t ≈ 39.532

Therefore, it will take approximately 39.532 days for $9500 to earn $800 at an annual interest rate of 8.25%.

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Answer:

you need to give us the equation or we can't help you

Step-by-step explanation:

i'm sorry if this is not what you're looking for :(

Answer:

\({ \tt{2 {x}^{2} + 10x + 8 }} \\ { \tt{ = (x + 1)(x + 4)}}\)

Answer:

A. 2 ( x + 4 )( x + 1 )

Step-by-step explanation:

2x² + 10x + 8

factor out 2 from the equation

2 ( x² + 5 x + 4 )

write 5x as a sum and rewrite the expression

2 ( x² + 4x + x + 4 )

factor out x from the equation

2 ( x ( x + 4 ) + x + 4 )

factor out x + 4 from the equation

2 ( x + 4 ) ( x + 1 )

Answer:

A. X>-7

Step-by-step explanation:

So the equation is

X-5>-12

You add 5 on both sides to get the X by itself. You add it because you have to get rid of the -5 and to get to 0 you would add 5.

Which leaves you with X>-7

Answer:

A.) \(x>-7\)

Step-by-step explanation:

Solve this the way you would solve an equation: isolate the variable.

Use inverse operations. Add 5 to both sides:

\(x-5+5>-12+5\\\\x>-7\)

Since this can't be simplified further, x is greater than -7.

:Done

Answer:

E. y = 1/4x

Step-by-step explanation:

Using y = 1/4x. Do rise over run. The graph rises 1 on the y-axis for every 4 on the x-axis

Answer:

2235.71 ($)

Step-by-step explanation:

A (1 + increase) ^n = N

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

compounded twice a year. split the 2% into 2, so we have 1% for each half a year.

1661 X 1% (0.01) = 16.61.

1661 + 16.61 = 1677.61

for 2nd half of year: 1677.61 X 0.01 = 16.7761.

1677.61 + 16.7761 = 1694.39.

so A = 1694.39, increase = 2% (0.02), n = 14.

1694.39 (1 + 0.02)^14

= 1694.39 (1.02)^14

= 2235.71 ($).

Answer:

2480

Step-by-step explanation

this is 4 grade math

The value of the missing angle x is calculated as: 11°

The parallel lines depict the fact that the relationships involves angles and transversals. The angle marked as 33° and ∠CAB are seen as alternate interior angles and as such they are congruent. This tells us that:

∠CAB = 33°

5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:

5x = 2x + 33°

Subtract 2x from both sides to get:

3x = 33°

Divide both sides by 3 to get:

x = 11°

Therefore we conclude that is the value of the missing angle x.

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The optimal number of square feet of space to be added is approximately 101 square feet.

We have,

To determine the optimal number of square feet of space to maximize the restaurant's profit, we need to analyze the relationship between the additional square footage, the number of new customers, and the resulting profit.

Let's start by defining some variables:

Let "x" represent the number of additional square feet of space to be added beyond the initial 100 square feet.

Let "C(x)" represent the cost in dollars to add x square feet of space. In this case, C(x) = $100 * x.

Let "N(x)" represent the number of new customers attracted per month when x square feet of space is added.

Let "P(x)" represent the profit generated per month when x square feet of space is added. In this case, P(x) = $50 * N(x).

Given the information provided, we know that each additional square foot of space attracts 2 new customers per month.

So, N(x) = 2x.

However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

To incorporate this, we can modify our equation for N(x) as follows:

N(x) = 2x * (1 - 0.01 * (x - 100) / 10)

Now, we can express the profit function P(x) in terms of x:

P(x) = $50 * N(x)

= $50 * [2x * (1 - 0.01 * (x - 100) / 10)]

= $100x * (1 - 0.01 * (x - 100) / 10)

To find the optimal number of square feet of space that maximizes profit, we need to find the value of x that maximizes P(x).

We can do this by taking the derivative of P(x) with respect to x, setting it equal to zero, and solving for x.

dP(x)/dx = $100 * (1 - 0.01 * (x - 100) / 10) + $100x * (-0.01 / 10)

= $100 - $1 * (x - 100) + $100x * (-0.01 / 10)

= $100 - $1x + $100 * (-0.01 / 10) - $1x

= $100 - $2x - $0.01x + $10x

= $100 + $7x - $0.01x

Setting dP(x)/dx equal to zero:

$100 + $7x - $0.01x = 0

$7x - $0.01x = -$100

0.99x = $100

x ≈ $100 / 0.99

x ≈ 101.01

Since we're dealing with square footage, we can round the result to the nearest whole number.

Therefore,

The optimal number of square feet of space to be added is approximately 101 square feet.

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The complete question:

The manager of a restaurant is considering expanding the seating area. She wants to determine how many additional square feet of space should be added to maximize the restaurant's profit. The cost to add new space is $100 per square foot, and the profit generated per square foot is estimated to be $50 per month. The manager expects that each additional square foot of space will attract 2 new customers per month. However, the number of new customers per month is expected to decrease by 1% for every 10 square feet of additional space beyond the initial 100 square feet.

What is the optimal number of square feet of space that should be added to maximize the restaurant's profit?

The inverse of the function f(x) = (3√(x/7)) - 9 is f^(-1)(x) = 7x + 63.

To find the inverse of the function f(x) = (3√(x/7)) - 9, we need to interchange the roles of x and f(x) and solve for x.

Replace f(x) with y.

y = (3√(x/7)) - 9

Swap x and y.

x = (3√(y/7)) - 9

Solve the equation for y.

x + 9 = 3√(y/7)

Remove the cube root by cubing both sides.

(x + 9)^3 = [3√(y/7)]^3

Simplify.

(x + 9)^3 = (3√(y/7))^3

(x + 9)^3 = (y/7)^3

Remove the cube by taking the cube root of both sides.

∛((x + 9)^3) = ∛((y/7)^3)

Simplify.

x + 9 = y/7

Multiply both sides by 7.

7(x + 9) = y

Rewrite y as the inverse function.

f^(-1)(x) = 7x + 63

Therefore, the inverse of the function f(x) = (3√(x/7)) - 9 is f^(-1)(x) = 7x + 63.

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The permutations of four objects m, I, n, and k taken two at a time without repetition are: mn, mk, mi, nm, nk, ni, km, kn, ki, in, im, ik.

P is the total number of permutations, which is equal to 12.

The correct answer is OB, which lists all 12 permutations.

P2 is the number of permutations taken two at a time with repetition allowed. This means that we can repeat the same object in a permutation.

There are 16 possible permutations with repetition allowed: mm, ml, mn, mk, ll, ln, lk, nn, nk, kk, ii, ik, nn, ni, nk.

Therefore, P2 is equal to 16.

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Answer:

f = 10, g = 4.8 cm

Step-by-step explanation:

Area of ABCE = 60 cm²

Area of ABCD = 48 cm²

So,

Area of ADE = 60-48

=> 12 cm²

Area of ADE = \(\frac{1}{2} (Base)(Height)\)

Where Area = 12 cm², Base = 4 cm

12 = \(\frac{1}{2}(4)(Height)\)

Height = 12-2

Height = 10 cm

Where Height is AD

So, AD = 10 cm

Also, AD is parallel and equal to BC\((f)\)

So,

f = 10 cm

Now, Finding g

Area of ABCD = \(Base * Height\)

Where Area = 48 cm², Base = 10 cm

48 = 10 * Height

Height = 48/10

Height = 4.8 cm

Whereas, Height is g

So, g = 4.8 cm