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There are seven elements in the set S, which represents the total number of distinct numbers we can form using one or more of the digits.

To find out how many distinct numbers we can form using these digits, we need to consider all possible combinations of digits. We can use one, two, or all three digits to form a number.

If we use only one digit, we can form three distinct numbers: 2, 3, and 5.

If we use two digits, we can form three distinct two-digit numbers: 23, 25, and 35. We cannot form the number 32 because we do not have the digit 2 available twice.

If we use all three digits, we can form only one three-digit number: 235.

Therefore, in total, we can form 7 distinct numbers using one or more of the digits 2, 3, and 5.

Mathematically, we can represent the solution as follows:

Let S be the set of all distinct numbers we can form using one or more of the digits 2, 3, and 5.

Then, S = {2, 3, 5, 23, 25, 35, 235} = 7

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Answer:

2/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\6.a_{n}=a_{1}+(n-1)d\\a_{1}=-\frac{1}{2} \\\\d=a_{2}-a_{1}\\d=\frac{1}{2} -(-\frac{1}{2} )\\d=\frac{1}{2} +\frac{1}{2} =\frac{1+1}{2} =\frac{2}{2} =1\\a_{n}=-\frac{1}{2} +(n-1)(1)\\a_{n}=-\frac{1}{2} +n-1\\a_{n}=\frac{-1-2}{2} +n\\a_{n}=n-\frac{3}{2}[/tex]

solve other questions  after finding d

First solve for the slope, m using the two points given. It doesn't matter which point you choose as point 1 or 2 as long as you're consistent.

m = (y2 - y1)/(x2 - x1)

point 1: (6.4, 2.6)

point 2:  (5.2, 9)

m = (9 + 2.6)/(5.2 + 6.4)

m = (9 + 2.6)/(5.2 + 6.4)

m = 11.6/11.6

m = 1

put the newly found slope into the linear equation for m

y = (1)x + b

y = x + b

Now solve for the y-intercept, b

by putting one of the given points

9 = 5.2 + b

b = 9 - 5.2

b = 3.8

final equation:

y = x + 3.8

The area of the shaded segement is approximately 1.68 square inches.

The complete question is:

What is the area of the shaded segment shown in O below?

Hints:

Area of shaded segment = Area of sector - Area of triangle

Area of sector = (θ/360) × πr²

Area triangle = 1/2 × b × c × sin(A)

Given that;

Area of segment = Area of sector - Area of triangle.

Area of sector = (θ/360) × πr²

Area triangle = 1/2 × b × c × sin(A)

From the diagram:

Plug the values into the above formula and simplify.

Area of segment = Area of sector - Area of triangle.

Area of segment = ( (θ/360) × πr² ) - ( 1/2 × b × c × sin(A) )

Area of segment = ( (30/360) × 3.14 × 12² ) - ( 1/2 × 12 × 12 × sin(30) )

Simplify

Area of segment = 37.68 - 36

Area of segment = 1.68 in²

Therefore, the area of the segment is 1.68 in².

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The given linear programming problem min 1x + 1y s.t. 5x + 3y < 30, 3x + 4y > 36, y < 7 , x , y > 0 exhibits infeasibility.

When constraints are inconsistent and  it is not possible to satisfy all the given constraints simultaneously then  a feasible solution is not possible for the linear programming problem.

Hence the solution of such a linear programming problem is said to be infeasible.

An infeasible solution violates at least one of the constraints of the given linear programming problem.

Here, the second constraint, that is 33x + 44y > 36 violates the linear programming problem. Therefore, the given linear programming problem exhibits   infeasibility (or, infeasible solution).

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The correct answer is A) 72÷14.

Divide the total number of cups of trail mix by the recommended serving size to determine how many servings are contained in the bag.

As a result, the expression that may be utilized is:

A) 72÷14

This expression represents dividing the total number of cups (312) by the suggested serving size (14):

312 ÷ 14 = 22.29

27 × 14

By multiplying the number of servings (27) by the recommended serving size (14), this expression shows the total number of cups. We are not informed of the bag's serving size.

72 × 14

By multiplying the number of servings (72) by the recommended serving size (14), this expression shows the total number of cups. We are not informed of the bag's serving size.

However, since we cannot have a fraction of a serving, the final result must be rounded to the nearest whole number:

22 portions

Therefore, the correct answer is A) 72÷14.

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Answer:

ok

Step-by-step explanation:

You took the picture and then wrote a sentence

Wow, I just happen to be learning this right now although...

The question provided is incomplete and unclear. It mentions a parabola with a focus at (-3,2) and directrix y = -3, and a point on the parabola at (a,5), and asks for the distance between the point and the focus. However, it does not specify what is the equation of the parabola or provide enough information to solve the problem.

The five number summary used to construct the box plot are

The interquartile range is 25

Statistical data based on the minimum, first quartile, median, third quartile, and maximum are shown graphically in a box plot.

The numbers are defined as follows

The interquartile range is

= top quartile - bottom quartile

= 120 - 95

= 25

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CB² + AC² = AB (BD + AD) ---------> segment addition postulate

BD + AD = AB -----------> substitution

CB² + AC² = AB(AB) ----------->  Factor

CB² + AC² = AB² ----------->  multiply

The statement that matches the steps of the proof is determined as follows;

The given options are;

The first proof and its correct statement is determined as;

CB² + AC² = AB (BD + AD) ---------> segment addition postulate

The second proof and its correct statement is determined as;

BD + AD = AB -----------> substitution

The third proof and its correct statement is determined as;

CB² + AC² = AB(AB) ----------->  Factor

The fourth proof and its correct statement is determined as;

CB² + AC² = AB² ----------->  multiply

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Answer: The value of the expression 1/7 divided by 5 is,

⇒ 1 / 35

Step-by-step explanation:

What is the Division method?

The division method is used to distribute a group of things into equal parts. The division is just the opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The expression is,

⇒ 1/7 divided by 5

Now, We can simplify as;

⇒ 1/7 divided by 5

⇒ 1 / 7 ÷ 5

⇒ 1 / 7×5

⇒ 1 / 35

Thus, The value of the expression 1/7 divided by 5 is,

⇒ 1 / 35

Answer:

B

Step-by-step explanation:

Using Pythagorean theorem and similar triangle theorem, the length of x is 1.123 units

Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other. Similar triangles look the same but the sizes can be different. In general, similar triangles are different from congruent triangles.

According to the SSS similarity theorem, two triangles will the similar to each other if the corresponding ratio of all the sides of the two triangles are equal. This criterion is commonly used when we only have the measure of the sides of the triangle and have less information about the angles of the triangle.

In this problem, we can use SAS or SSS theorem, however, we can decide to use the angle to find the length of the side;

Using SOHCAHTOA

we have hypothenuse and angle and we need to find the opposite side;

sin √8 = a / 4

a = 4sin√8

Let's find the hypothenuse side of the smaller triangle

using similarity theorem;

6√2 / 4 = b / 1

b = 6√2 / 4

But knowing that the ratio of the bigger triangle is 4 to 1 to the smaller triangle, we can easily find x

cos √8 = y / 4

y = 4cos√8

The length of the opposite side to the other triangle will be

6√2 - 4cos√8 = 4.49

Using this value, we can find the hypothenuse with Pythagorean theorem

c² = 4.49² + (4sin√8)²

c = 4.49

x = 4.49 / 4

x = 1.123

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Answer:

The line of reflection is the x-axis.

Answer:

0

Step-by-step explanation:

The limit of a sequence is the value that its terms approach.

We can present the limit of the terms in the sequence as:

[tex]\lim_{n \to \infty}\dfrac{1}{n^n}[/tex]

To evaluate this limit, we can plug infinity (the value that n is approaching) into the expression:

[tex]\lim_{n \to \infty}\dfrac{1}{n^n}[/tex]

[tex]= \dfrac{1}{\infty^\infty}[/tex]

We know that infinity to any positive power is still infinity. So, this expression simplifies to:

[tex]= \dfrac{1}{\infty}[/tex]

Any real number, no matter how large, is inconsequential (infinitely small) compared to infinity. Therefore, this expression evaluates to 0:

[tex]= 0[/tex]

So, the limit of the sequence [tex]\sum_{n=1}^{\infty} \dfrac{1}{n^n}[/tex] is 0.

__

Note: You could also deduce the limit of this sequence by plugging in larger and larger numbers:

[tex]\begin{array}{c | c | c}n & \text{seq. term} & \text{decimal} \\\cline{1-3} 2 & 1/4 & 0.25 \\3 & 1/81 & 0.012\\4 & 1/256 & 0.0039 \\5 & 1/3125 & 0.00032 \\... & ... & ... \\\infty & 1/\infty & 0\end{array}[/tex]

A situation that could follow a binomial distribution is the number of heads that occur when flipping a "fair-coin" multiple times.

A "Binomial-Distribution" is defined as a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success.

In this case, flipping a "fair-coin" is an independent trial with two possible outcomes (heads or tails), and the probability of getting a heads on any given flip is 0.5.

Each "coin-flip" is independent of the others, and the probability of getting a heads on any given flip is always the same which is "0.5",

So, this situation fits the requirements for a binomial distribution.

The "binomial-distribution" can then be used to calculate the probability of getting a certain number of heads out of a fixed number of flips. For example, if we flip a coin 10 times, the probability of getting exactly-5 heads can be calculated using the binomial distribution formula.

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Answer: 50

Step-by-step explanation:

Use pythagorean

c²=a²+b²   c is the hypotenuse which is across from the right angle or the longest side

x²=14²+48²

x²=2500

x=√2500

x=50

Answer:

The answer as follows

Step-by-step explanation:

Part I:

The graph of f(x) is a parabola with its vertex at the origin, opening upward.

To graph g(x), we can start by shifting f(x) 3 units to the right and 2 units up, according to the equation g(x) = (x - 3)² + 2. This means that the vertex of g(x) will be at the point (3, 2).

We can create a table of values for g(x) to plot some points and draw the graph:

| x  | g(x) |

|----|------|

| 0  | 11   |

| 1  | 8    |

| 2  | 5    |

| 3  | 2    |

| 4  | 5    |

| 5  | 8    |

| 6  | 11   |

Using these points, we can draw the graph of g(x) as a parabola that has the same shape as f(x), but is shifted to the right by 3 units and up by 2 units:

Part II:

The graph of g(x) is the graph of its parent function, f(x), shifted 3 units to the right and 2 units up. This means that every point on the graph of g(x) is 3 units to the right and 2 units up from the corresponding point on the graph of f(x).

In other words, the transformation that was applied to f(x) to get g(x) is a horizontal shift to the right by 3 units and a vertical shift up by 2 units. This is reflected in the equation g(x) = (x - 3)² + 2.

Answer: B

Step-by-step explanation:

For matrix addition to happen,

1) the 'number of rows' of all matricies have to be same.

2) the 'number of columns' of all matricies have to be same.

So the answer should be <B>.

The part of exponent, x, will have the value 7/4 according to the expression of exponent.

As we see the base on both sides is same, concerning this we can equate the exponents for equal values on Left Hand Side and Right Hand Side of the equation.

5x + 9 = 9x + 2

Rearranging the equation for like terms on each side

9x - 5x = 9 - 2

Subtracting the values in each side of the equation to find the value of x

4x = 7

Rearrange the formula

x = 7/4

Hence, the value of x will be 7/4.

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Answer:

8

Step-by-step explanation:

8*10+142=222

22*8+46=222

Answer:

D. 15

Step-by-step explanation:

Use the Fundamental Theorem of Calculus to solve this problem. Since f(x) is the derivative of 1/3 x^3 - 2x^2 + 3x - 5, you have:

f(x) = d/dx (1/3 x^3 - 2x^2 + 3x - 5) = x^2 - 4x + 3

To find f(-2), you substitute x = -2 into the expression for f(x):

f(-2) = (-2)^2 - 4(-2) + 3 = 4 + 8 + 3 = 15

The percentage of 8th grader that walk to school is 36.2%

The percentage of 8th grader that are female that walk to school is 20.8%

We have, 8 th grader’s school transportation survey.

1. The percentage of the 8th grader that walk to school is

= 80 / 221 x 100

= 36.2%

2. The percentage of female 8th grader that walk to school

= 46/ 221 x 100

= 20.8%

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The probability that the Yankees will win when they score fewer than 5 runs is about 0.102.

Let A be the event that the Yankees win, and let B be the event that the Yankees score 5 or more runs. We know that;

P(A) = 0.53

P(B) = 0.51

P(A and B) = 0.43

We want to find the probability that the Yankees win when they score fewer than 5 runs. This can be expressed as;

P(A and not B)

We can use the formula;

P(A and B)=P(B | A) × P(A)

to find;

P(B | A) = P(A and B) / P(A)

= 0.43 / 0.53

≈ 0.811

This means that given the Yankees win a game, the probability that they score 5 or more runs is about 0.811. Therefore, the probability that they win when they score fewer than 5 runs is;

P(A and not B) = P(A) - P(A and B)

= 0.53 - (0.811 × 0.53)

≈ 0.102

Therefore, the probability that the Yankees will win is 0.102.

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Answer:

276

Step-by-step explanation:

let x = the number

(2/3)x - 70 = 45 + (1/4)x

2/3x - 1/4x = 45 + 70

8/12x - 3/12x = 115

5/12x = 115

x = 115(12/5) = 276

Double check the answer:

(2/3()276) - 70 = 45 + (1/4)(276)

114 = 114    answer is correct!

After set s1.removeAll(s2), s1 is [1, 5].

After performing the operation s1.removeAll(s2) on sets s1 [1, 2, 5] and s2 [2, 3, 6], the set s1 would become [1, 5].

To determine the value of s1, the following steps has to be taken:

1. We have set s1 with elements [1, 2, 5] and set s2 with elements [2, 3, 6].
2. The removeAll() function is called on s1 with s2 as the argument: s1.removeAll(s2).
3. The removeAll() function will remove all elements from s1 that are also present in s2.
4. In our case, the number 2 is present in both sets, so it will be removed from s1.
5. After the operation, s1 will only contain the elements [1, 5].

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Step-by-step explanation:

The Key shows that 4 squares equals 8 games....so each single square is TWo games

tuesday = 22

wed = 10 games

Answer:

at all 32 or tue 22 and wed 10

Step-by-step explanation:

one equal 4 times separated square(quartered square) equals 8 video games then one part will be 2 because 8 divided by 4 is 2. back to the question,do it by your self

Answer:

y = -8x

Step-by-step explanation:

-2-6 = -8

the slope was -2 that decreased by 6 would be -8.

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