the sum of three numbers is 56. the difference of the larges and smallest is 44 and the sum of the two smaller numbers is 16. what are the numbers?

The given statement "there is some k∈I such that [tex]D_{i}[/tex]⊆[tex]D_{k}[/tex] and [tex]D_{j}[/tex]⊆[tex]D_{k}[/tex]means that there is a set [tex]D_{k}[/tex] in a collection of sets I that contains all the elements of both sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex].

For example, let's say we have a collection of sets I that includes sets A, B, C, D, E, and F. If we have two sets [tex]D_{i}[/tex] and [tex]D_{j}[/tex], where [tex]D_{i}[/tex] is the set of all even numbers, and [tex]D_{j}[/tex] is the set of all positive integers less than or equal to 10, then we can say that there exists a set [tex]D_{k}[/tex] in I that contains both [tex]D_{i}[/tex]and [tex]D_{j}[/tex] as subsets.

In this case, the set [tex]D_{k}[/tex] could be the set of all even positive integers less than or equal to 10. This set contains all the elements of [tex]D_{i}[/tex] and [tex]D_{j}[/tex], making them both subsets of [tex]D_{k}[/tex]. The statement "there is some k belongs I such that [tex]D_{i}[/tex] is a subset of [tex]D_{k}[/tex] and [tex]D_{j}[/tex] is a subset of [tex]D_{k}[/tex]" is a way to express this relationship between the sets.

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The calculated value of x if ∠A and ∠B are vertical angles is 13 degrees

From the question, we have the following parameters that can be used in our computation:

∠A = (2x − 2)

∠B = (3x − 15)

Since the ∠A and ∠B are vertical angles, then they are congruent angles

So, we have

3x - 15 = 2x - 2

Evaluate the like terms

So, we have

x = 13

Hence, the solution is x = 13

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Using trigonometric identities, the given expression, tan(x) × cos(x), simplified to a single trigonometry is sin(x)

From the question, we are to simplify the given trigonometric expression

From the given information

The given expression is

tan(x) × cos(x)

From trigonometric identities, we know that

tan(x) = sin(x) / cos(x)

Now,

Substituting this value in the given expression

tan(x) × cos(x)

We get

sin(x) / cos(x) × cos(x)

Simplifying further

sin(x) / cos(x) × cos(x) = sin(x)

Hence,

The simplified expression is sin(x)

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Answer:

Molly has four choices for which shirt to wear on the first day, and one of those choices is the black shirt. So the probability that she will wear the black shirt on the first day is 1/4. Therefore, the answer is 1/4.

Step-by-step explanation:

The probability of getting two numbers whose sum is greater than 9 = 5/36

We know that the probability is nothing but the number of favourable outcomes divided by the total number of outcomes.

Here, a single die is rolled twice.

and we get the set of 36 equally likely outcomes.

so, the total number of outcomes n(S) = 36

Let us assume that event A: getting two numbers whose sum is greater than 9

A = {(4, 6), (5,5), (5, 6), (6, 4), (6, 5)}

n(A) = 5

Using above formula of probability,

P(A) = n(A)/n(S)

P(A) = 5/36

Thus the required probability = 5/36

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107 over 103 times 101 over 100 would result in 10807/10300.

In order to multiply the fractions 107/103 and 101/100, we can simply multiply their numerators together and their denominators together:

(107/103) x (101/100) = (107 x 101) / (103 x 100)

Now we can simplify this fraction by finding the greatest common factor of the numerator and denominator and dividing both by it:

(107 x 101) / (103 x 100) = 10807 / 10300

Therefore, 107/103 times 101/100 simplifies to 10807/10300.

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The equation of line of reflection of the coordinates is

y = x

Mathematics gives the concept of a line of reflection, otherwise known as a line of symmetry. This line acts as a mirror for any figure, where when shown through its reflection, the image becomes congruent to the initial shape.

In simpler words, the line of reflection is like an invisible partition that accurately segments a figure into two identical halves, each resembling the other in more ways than one.

The image is attached and upon investigation shows that the equation of y = x matches the equation of line of reflection

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Monthly you should deposit approximately $241 to accumulate ​$ 85,000 in 18 ​years.

Given that,

f = 85000

r = 6% = 0.06/12 = 0.005

n = 17×12 = 204

We know that, a = (f×r)/((1+r)ⁿ⁻¹)

a is the annuity.

f is the future amount.

r is the interest rate per time period.

n is the number of time periods.

Here,

a = (85000×0.005)/((1.005)²⁰⁴⁻¹)

a = 240.6356536

a ≈ $241

Therefore, monthly you should deposit approximately $241 to accumulate ​$ 85,000 in 18 ​years.

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Answer:

The total cost per month is $190.76 to the nearest cent.

Step-by-step explanation:

From the given table, the monthly service plan costing $52.00 is:

The base calling plan includes two lines.

Therefore, for 4 lines, we will need to pay for 2 additional lines per month:

⇒ $21.99 × 2 = $43.98 per month

If 3,487 minutes are used per month, then the overage of minutes is:

⇒ 3487 - 2000 = 1487 minutes per month

As the overage rate is $0.06 per minute, then the cost of the additional minutes is:

⇒ 1487 × $0.06 = $89.22 per month

Therefore, the total cost per month before tax is:

⇒ $52.00 + $43.98 + $89.22 = $185.20

To apply the federal tax of 3%, multiply the total cost by 1.03:

⇒ $185.20 × 1.03 = $190.756 = $190.76 (nearest cent)

Therefore, the total cost per month is $190.76 to the nearest cent.

Answer: n>5

Step-by-step explanation:

The line is a vertical line, then the correct option is D, the slope is undefined.

A general linear equation can be written as:

y = a*x + b

Where a is the slope, b is the y-intercept, and x is the variable.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope of that line is given by the formula:

a = (y₂ - y₁)/(x₂ - x₁)

Here we know that the two points are (2, -4) and (2, 4)

Replacing that we would have a problem, that is because we have the same x-value in both points.

Then we have a vertical line at x = 2.

That line has no defined slope, thus, the correct option is D.

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The new vertices of the triangle after moving the triangle 5 units down, are A(1,-7), B(9,-7), and C(5,-3). So, correct option is B.

To determine the coordinates of the triangle after it is translated 5 units down, we need to subtract 5 from the y-coordinates of each vertex.

Let's start with vertex A(1,-2). If we subtract 5 from -2, we get -7. Therefore, the new coordinates of vertex A are (1,-7).

Next, let's look at vertex B(9,-2). Again, if we subtract 5 from -2, we get -7. So the new coordinates of vertex B are (9,-7).

Finally, let's consider vertex C(5,2). If we subtract 5 from 2, we get -3. So the new coordinates of vertex C are (5,-3).

In this case, we are moving the triangle 5 units down, which means that we are subtracting 5 from the y-coordinates of each vertex. This is a common transformation in geometry, and it's important to be familiar with it when working with shapes and figures in the Cartesian plane.

So, correct option is B.

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Answer: B. 4

Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.

The dragging of the tiles to the appropriate places is given below.

1. 5.83 m/s > magnitude 4.5 m/s, direction angle 55˚ magnitude 3m/s, direction angle 135°

2. 4.05 m/s > magnitude 3.5 m/s, direction angle 35˚ magnitude 4 m/s, direction angle 150˚

3. 5.29 m/s > magnitude 6 m/s, direction angle 120˚ magnitude 2 m/s, direction angle 240˚

4. 3.32 m/s > magnitude 3 m/s, direction angle 70° magnitude 5 m/s, direction angle 210˚

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The area of the forest after 11 years will be 298 km².

To calculate the area of the forest after 11 years, we need to decrease the initial area of 1700 km² by 7.5% each year for 11 years.

First, let's calculate the decrease in area for one year:

Decrease in area for one year = 7.5% of 1700 km²

7.5% of 1700 km² = (7.5/100) × 1700 km²

= 127.5 km²

Now, we can calculate the total decrease in area over 11 years:

Total decrease in area over 11 years = 11 × 127.5 km² = 1402.5 km²

Finally, we can subtract the total decrease in area from the initial area to get the area of the forest after 11 years;

Area of the forest after 11 years = Initial area - Total decrease in area

= 1700 km² - 1402.5 km²

= 297.5 km²

Therefore, Rounding to the nearest square kilometer, the area of the forest after 11 years will be approximately 298 km².

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The recipe will need 21 cups of sauce and three and a half teaspoons of oregano for 7 servings. The correct option is C.

The sauce to oregano ratio for five servings is equal to 15 cups and 2.5 teaspoons, respectively. For a single portion of the recipe, this computes to 3 cups and 0.5 teaspoons.

It should be noted that to attain the correct amount needed for seven servings, simply multiply each part of the ratio by seven. Consequently, you should use 21 cups of sauce and three and one-half teaspoons of oregano. All together, this recipe requires 21 cups of sauce and three and a half teaspoons of oregano for 7 servings.

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Answer: 17/24 for both jobs

Step-by-step explanation:

The match to A line that has a slope of 5/3 and a y-intercept of 4 is 2y - x = -4.

We are given that;

The four equations to match from

Now,

Using the slope-intercept form, we can plug in m = 3/2 and b = -8:

y = (3/2)x - 8

This equation matches with y = 3/2x - 5 if we multiply both sides by 2:

2y = 3x - 16

Therefore, the correct equation is 2y - x = -16.

A line that contains the points (0,-2) and (4,0)

m = (0 - (-2)) / (4 - 0) m = 2 / 4 m = 1/2

Then we can plug in m = 1/2 and any of the given points to find b. For example, using (0, -2), we have:

-2 = (1/2)(0) + b -2 = b

Therefore, the equation is:

y = (1/2)x - 2

This equation matches with -5x - 3y = -12 if we multiply both sides by -6:

6y = -3x + 12

Therefore, the correct equation is -5x - 3y = -12.

A line that contains the y-intercept (0-2) and the slope of -3/4

Using the slope-intercept form, we can plug in m = -3/4 and b = -2:

y = (-3/4)x - 2

This equation matches with y = -3/4x - 2.

A line that has a slope of 5/3 and a y-intercept of 4

Using the slope-intercept form, we can plug in m = 5/3 and b = 4:

y = (5/3)x + 4

This equation matches with 2y - x = -4 if we multiply both sides by 3:

3y = (5/3)x + 12

Therefore, the correct equation is 2y - x = -4.

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Answer:(6, −2), (6, 0.5) I’m pretty sure

The students error is in step 3 and the correct solution is g(x) = 2x² + 4x - 4

From the question, we have the following parameters that can be used in our computation:

The steps to solve the expression

From step 2 to step 3, we have

g(x) = 2(x + 1)(x + 1) - 6

g(x) = 2(x² + 1x + 1) - 6

The step 3 is incorrect

Because when the expression is expanded, we have

g(x) = 2(x² + 2x + 1) - 6

This gives a solution of

g(x) = 2x² + 4x - 4

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A graph of triangle TOW is shown below.

A graph of triangle T'O'W, the image of ΔTOW after a reflection in the y-axis is shown below.

The coordinates of ΔT'O'W are: T' (5, 6), O' (-1, 8), and W' (4, -2).

In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y). This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

Next, we would apply a reflection over or across the x-axis;

(x, y)                →      (-x, y)

T (-5, 6)       →      (-(-5), 6) = T' (5, 6)

O (1, 8)       →      (-(-1), 8) = O' (-1, 8)

W (-4, -2)       →      (-(-4), -2) = W' (4, -2)

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Answer:

  h(x) = 3·2^x

Step-by-step explanation:

You want the equation of the exponential curve h(x) = a·b^x when it goes through the points (0, 3) and (1, 6).

When x=0, the equation is ...

  h(0) = a·b^0 = a

We know that h(0) = 3, so a = 3.

When x=1, the equation is ...

  h(1) = 3·b^1 = 3b

We know that h(1) = 6, so 3b = 6, or b = 2.

The equation is h(x) = 3·2^x.

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Answer:

Step-by-step explanation:

down 1

compress 1/2

Answer:

The correct function is y = 4(.25^x).

Answer: C: 144

Step-by-step explanation:

First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.

Next subtract this from 180 to find the exterior angle.

180- 36 = 144 degrees

thats the meaure of the exterior angle!

Answer:144

First find the measure of the unknown interior angle of the triangle. That is 180 - 100 - 44 = 36 degrees.

Next subtract this from 180 to find the exterior angle.

180- 36 = 144 degrees

The amount of sales tax he collected from the office services would be =$658.43

To calculate the amount of sales tax,the percentage tax amount should be determined as follows.

The total receipts from the office services = $1861.16

The amount that is for labor = $1240

The amount for parts = 1861.16-1240

= $621.16

The tax amount = 6/100 × 621.16

= 3726.96/100

= $37.27

Therefore the amount sale tax = 621.16+37.27 = $658.43

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Answer:

3t^2i + 2tj is the correct answer.