Recursively define each of the following sets: (3 points each) (a) The set of powers of 2 . (b) The set of integers congruent to 4 modulo 5 . (c) The set of bit-strings with an even number of 1's

Hence, 15 people out of 3 people can be chosen in 35 ways.

It is given that:

The total number of people in a race, n = 15

The number of finalists, r = 3.

Hence, the number of ways in which 3 people out of the 15 people can be finishers are:

\(^{15}C_{3} }\) = \(\frac{15!}{(15-3)!3!}\) = \(\frac{15!}{12!3!}\) = 35.

Hence, 15 people out of 3 people can be chosen in 35 ways.

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Answer:

25

Step-by-step explanation:

Segment XY = 10

Segment XZ = 15

Since the lenght of segment WX is said to be congruent to the lenght of segment XY, therefore:

WX = XY = 10

Segment WX + Segment XZ = Segment WZ (segment addition postulate)

\( 10 + 15 = WZ \) (substitution)

\( 25 = WZ \)

\( WZ = 25 \)

Length of segment WX = 25

The probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.

There are a total of 6 x 6 = 36 possible outcomes when rolling a pair of dice, assuming the dice are fair and unbiased.

The probability of rolling double ones or double sixes on any one roll is 2/36 = 1/18. So, the probability of NOT rolling double ones or double sixes on any one roll is 1 - 1/18 = 17/18.

The probability of not rolling double ones or double sixes on all three rolls is \((17/18) \times (17/18) \times (17/18) = (17/18)^3 = 0.701.\)

Therefore, the probability of rolling double ones or double sixes at least once in three rolls is 1 - 0.701 = 0.299, or approximately 29.9%.

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Answer:

If the length of x is less than 200, then add <.

If the length of x is more than 200, then add >.

If the length of x is 200, then add =.

Step-by-step explanation:

The recursive rule for the number of acres at the beginning of the nth day in a forest fire that grows by 20% each day and is battled by firefighters who can put out 15 acres per day is given by: A(n) = 1.2 * A(n-1) - 15, where A(n) represents the number of acres at the beginning of the nth day. Using this rule, we can calculate that there are 89.6 acres burning at the beginning of the 8th day.

Explanation: To determine the recursive rule for the number of acres at the beginning of the nth day, we need to consider the given information. The forest fire initially covers 60 acres and grows by 20% each day. This means that the number of acres at the beginning of the next day (n+1) is 1.2 times the number of acres at the beginning of the current day (n). However, the firefighters are able to put out 15 acres of fire per day.

Therefore, to calculate A(n), we start with the initial number of acres, which is 60, and apply the recursive rule. A(n) = 1.2 * A(n-1) - 15. This formula takes into account the growth of the fire by 20% and the reduction of 15 acres due to the firefighters' efforts. By substituting the values, we can calculate the number of acres at the beginning of each day.

To find the number of acres burning at the 8th day, we substitute n = 8 into the recursive rule. A(8) = 1.2 * A(7) - 15. We need to determine A(7) first by substituting n = 7, and so on, until we reach the initial value A(1) = 60. Once we have calculated A(8), we can determine that there are 89.6 acres burning at the beginning of the 8th day

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Answer:

12 goes into 53 4 times

Step-by-step explanation:

Answer:

4 times

Step-by-step explanation:

Answer:

98 units.

Step-by-step explanation:

Circumference = 2 * pi * radius

615.44 = 2 * 3.14 * r

r = 615.44 / (2 * 3.14)

 =2 * 3.14

 = 98 units.

The number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

The permutation is a way of finding the number of ways of selecting a set of articles from a larger set of articles, with the order of selection being significant.

If we want to choose r items from n items, where the order of selection is significant, then we can find the number of ways of doing this using the permutation as follows:

nPr = n!/{(n - r)!}.

In the question, we are asked to find the number of ways Kristen can rank her favorite four investments from the 8 potential investments that her financial advisor has given her.

Thus, using permutations, we need to select 4 items from 8 items, with order of selection being significant.

Substituting n = 8, and r = 4 in the formula, we get:

8P4 = 8!/{(8 - 4)!}

= 8!/4!

= 5 * 6 * 7 * 8

= 1680.

Thus, the number of ways in which Kristen can rank her favorite four from 8 using permutations is 1680.

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Answer:

Step-by-step explanation:

The loop will run an infinite number of times

Answer: CD = 10

Step-by-step explanation:

Subtract the smaller one from the larger one.

D(14, 2) - C(4, 2)

First, you subtract the x-values:

14 - 4 = 10

Then, you subtract your y-values:

2 - 2 = 0

Since the y-value is 0 (since it is a straight line), your distance of CD is 10.

Hope this helps!

Step-by-step explanation:

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

On taking LHS

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

We know that

Tan θ = 1/ Cot θ

and

Cot θ = 1/Tan θ

=> (1+Cot²θ)(1+Tan²θ)

=> (Cosec² θ) (Sec²θ)

Since Cosec²θ - Cot²θ = 1 and

Sec²θ - Tan²θ = 1

=> (1/Sin² θ)(1/Cos² θ)

Since , Cosec θ = 1/Sinθ

and Sec θ = 1/Cosθ

=> 1/(Sin²θ Cos²θ)

We know that Sin²θ+Cos²θ = 1

=> 1/[(Sin²θ)(1-Sin²θ)]

=> 1/(Sin²θ-Sin²θ Sin²θ)

=> 1/(Sin²θ - Sin⁴θ)

=> RHS

=> LHS = RHS

Hence, Proved.

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

→ Tan θ = 1/ Cot θ

→ Cot θ = 1/Tan θ

→ Cosec θ = 1/Sinθ

→ Sec θ = 1/Cosθ

→ Cosec²θ - Cot²θ = 1

→ Sec²θ - Tan²θ = 1

→ Sin²θ+Cos²θ = 1

Hope this helps!!

Any variable that can be placed into either of two discrete and mutually exclusive categories is called dichotomous.

A dichotomous variable is one in which, as a result of said variability, there are only two possible outcomes. That is, there is a dichotomy or mutual exclusion between both results of the variable, in such a way that the presence of one result makes the presence of the other null.

An example of dichotomous variables is one in which a certain situation exists or not, that is, where the result varies between 0 and a positive integer.

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The value of Sin(P) = Sin(30°) = 1/2

It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.

Triangle PQR is given.

Angle QRP is a right angle.

∠QRP = 90°

And the other two angle measures are,

∠RPQ = 30°, and ∠PQR = 60°.

The value of Sin(P) = Sin(30°) = 1/2

Therefore, SinP = 1/2.

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Answer:

I put the answers in order.

True

False

True

False

(Hope this helped☺️! )

For the given scatter plot, line C fits the best to represent the data represented as the line is as close as possible to all of the points, so it better represents the trend between them.

A scatterplot is known to be a series of points plotted on horizontal and vertical axes. Scatter plots are crucial in statistics because they can represent the degree, if any, of correlation between the values ​​of observed quantities or phenomena (called variables). If case of no correlation between the variables, the points will appear randomly scattered all over  the coordinate plane. If the correlation is high, the points will be clustered around the straight line.

A scatter chart is a type of data visualization tool that aids to show trends. A best-fit line is defined as a line that more accurately represents the various points on the scatterplot.

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Answer:

y + 10 =2( x +1)

or

y -2 + 2( x -5)

These both name the same line.

Step-by-step explanation:

First we need to find the slope.  The slope is the change in y over the change in x.  In the point (-1,-10)

-1 is the x and -10 is the y.

In the point (5,2)  

5 is the x and 2 is the y.

\(\frac{2- -10)}{5 - -1)}\)  Subtracting a negative is the same as adding a positive.

\(\frac{2+ 10}{5+1}\) = \(\frac{12}{6}\) = 2

We know know the slope.  We will use the form

y - \(y_{1}\) = m (x-\(x_{1}\))  we will plug in the numbers that we know.  

If we use point (-1, -10)

y -- -10 = 2(x - -1)

y + 10 = 2( x+1)

If we use the point (5,2)

y -2 = 2(x -5)

Both equations mean the same thing.

Answer:

35

Step-by-step explanation:

1,8 is 7 numbers apart 8,16 is 8 numbers apart, 16,25 is 9 numbers apart so with that information we should get 35 as the next number.

The specific name of the quadrilateral is kite

The measures of the missing angles are 75 degrees each

To determine the measure of the angle, we need to know the different properties of a kite.

The properties of a kite includes;

Since the adjacent angles are equal, we have that;

105+ x = 180

collect the like terms, we have;

x = 180 - 105

x = 75 degrees

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The quadrilateral is a kite and the missing angles are 105° and 45°

A kite is a quadrilateral that has 2 pairs of equal-length sides and these sides are adjacent to each other.

A kite has a pair of equal angle and the diagonals of a kite meets at 90°.

In a kite , there are two pairs of congruent or equal sides.

This means that the missing angles are

The opposite angle to 105 is also 105°

The fourth angle is calculated as;

105+105+105+x = 360

= 315 +x = 360

x = 360- 315

x = 45°

Therefore the quadrilateral is a kite and the missing angles are 105° and 45°

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Answer:

250

Step-by-step explanation:

20% of 250 is 50. 100% of 250 is 250, therefore 20 percent of 250 equals 50.

More simplified explanation: The question is asking if 50 is 20% of a number, what is the number? So we know that 20% is 1/5 of 100%; if we know that 50 is 20% of something, then we would multiply 50 by 5 to get the answer. We would have to multiply 50 by 5 because if 50 is 20% of a number that would mean that 50 is 1/5 of the number we need to find, so to find the number, you to multiply 50 by 5.

Hope this helps!

Answer:

36 trust me I'm good at math

Step-by-step explanation:

add 19 and 17

Answer:

No, they are not similar to each other because they are not proportional to each other.

Step-by-step explanation:

A proportional statement with both of these triangles would look like this :

8/16 = 12/12

That is not a true statement, so the triangles aren't similar :)

Answer:

No, they are not similar because are not proportional

Step-by-step explanation:

Set up proportion and simplify to check:

8/12 = 16/12

Left side is 0.6, right side is 1.3

These are not the same so no this would not work.

Answer:

6

Step-by-step explanation:

yw;)

The correct value of the integral equation, considering the constant of integration \(\sqrt({x^2}+14x)\) will be equal to\(1/2(x+7)\sqrt({x^2}+14x)-[49/2ln(1/7\sqrt({x^2}+14x) + (x+7)] + C\).

Integration is a mathematical operation in which adding or summing up of some parts of an equation is done. It is opposite of differentiation. To solve the equation, first the knowledge about various trigonometric equations is very important. These are given below:

cosh²θ−sinh²θ = 1

cosh2θ = 2sinh²θ+1

sinh²θ = 1/2 (cosh2θ - 1)

sinh2θ = 2 sinhθcoshθ

arc cosh\(x\) = ln (\(\sqrt{x^2-1}\) + \(x\))

Substituting the values to simplify the equation:

\(x^{2} +14x = x^{2} +14x-49+49\\x^{2} +14x = (x+7)^{2} - 49\)

Now putting, x+7 = 7coshθ

dx = 7sinhθdθ

\(\sqrt{(x+7)^2-49} = \sqrt{49cosh^2\theta-49}\)

dx = \(7\sqrt{cosh^2\theta-1} = 7sinh\theta\)

\(sinh^2\theta=cosh^2\theta-1 = (\frac{x+7}{7})^2 - 1\)

\(\frac{x^2+14x-49+49}{49} = \frac{x^2+14x}{49}\\ sinh\theta = \frac{1}{7} \sqrt{x^2+14x}\)

\(\int\limits {\sqrt{x^2+14x} } \, dx =\int\limits {7sinh\theta*7sinh\theta} \, d\theta\)

\(= 49\int\limits {sinh^2\theta } \, d\theta\\=\frac{49}{2}\int\limits {(cosh2\theta -1)} \, d\theta\\= \frac{49}{2} (\frac{sinh2\theta}{2} -\theta)\\=\frac{49}{2}(sinh\theta cosh\theta - arc cosh(\frac{x+7}{7}))\)

Thus, on further solving, the final answer will be equal to \(1/2(x+7)\sqrt({x^2}+14x)-[49/2ln(1/7\sqrt({x^2}+14x) + (x+7)] + C.\)

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Answer:

y^2(3+4)

7y^2

BTW isn't it too much to ask for high school level question?

Step 1: The test statistic z is approximately 1.54.
Step 2: The P-value for Ha: μ > 19 is approximately 0.0620.
Step 3: The P-value for Ha: μ ≠ 19 is approximately 0.1240.

step-1 To perform a significance test of H0: μ = 19 based on an SRS of n = 25, and assuming that σ = 13, follow these steps:

Calculate the test statistic z for x = 23 to 2 decimal places.

z = (x - μ) / (σ / √n)
z = (23 - 19) / (13 / √25)
z = (4) / (13 / 5)
z = 4 / 2.6
z ≈ 1.54

step-2 Determine the P-value for Ha: μ > 19 to 4 decimal places.

To find the P-value, use a z-table or an online calculator to find the probability that z > 1.54. The P-value = 1 - P(z ≤ 1.54).

P-value ≈ 1 - 0.9380

P-value ≈ 0.0620

step-3 Determine the P-value for Ha: μ ≠ 19 to 4 decimal places.

For a two-tailed test, double the P-value calculated in Step 2:

P-value (two-tailed) ≈ 2 × 0.0620

P-value (two-tailed) ≈ 0.1240

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Answer: 6a^3b^3

Step-by-step explanation:

Answer:

6a³b³

Step-by-step explanation:

-0.6a^2b*(-10ab^2) =

= -0.6 × (-10) × a² × a × b × b²

= 6a³b³

The answer is option B: $8,014,195.

We can use the formula for the future value of an annuity to solve this problem:

FV = PMT x [(1 + r)^n - 1] / r

Where:

PMT = $12,000 (annual payment)

r = 11.5% (annual interest rate)

n = 40 (number of years)

Plugging in the values, we get:

FV = $12,000 x [(1 + 0.115)^40 - 1] / 0.115

FV ≈ $8,014,195

Therefore, the answer is option B: $8,014,195.

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Answer:

The expression x⁴ + 8x³ + 34x² + 72x + 81 cannot be factored further using simple integer coefficients. It does not have any rational roots or easy factorizations. Therefore, it remains as an irreducible polynomial.