Find the measure of two complementary 8. angles if one angle is four times the measure
of the other angle.

It has n-k basic variables. The basic variables are the variables that are not free variables, and they are the ones that can be solved for as part of the general solution.

The general solution of a system of m linear equations in n variables contains k free variables. This means that there are k variables that have no restrictions and can take on any value. The remaining n-k variables are the basic variables, which are the ones that can be solved for as part of the general solution. The basic variables are the ones that have restrictions and need to be solved for in order to determine the solution of the system. In other words, the number of basic variables is equal to the number of variables minus the number of free variables. Thus, the general solution of the system has n-k basic variables.

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Answer:

Step-by-step explanation:

P = k/Q where k is a constant.

P is 6 when Q is 24, so:

6 = k / 24

k = 6*24 = 144

so, the relation is P = 144/Q.

a. When P = 8,

8 = 144/Q

8Q = 144

Q = 144/8 = 18

b. When Q = 16

P = 144/16

  = 9.

The general solution of the differential equation is [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex], where C is an arbitrary constant.

To find the general solution, we can first try separating the variables by dividing both sides of the equation by x²:

The given differential equation is (x²)dy/dx + (x²)y = [tex]6xe^{-x[/tex]

[tex]\frac{dy}{y} = 6e^{-x} \frac{dx}{x^2}[/tex]

Integrating both sides with respect to their respective variables:

[tex]\int (dy/y) = \int 6e^{-x} \frac {dx}{x^2} + C[/tex]

ln [tex]|y| = \frac{-3e^{-x} - 1}{x} + C[/tex]

Exponentiating both sides:

[tex]|y| = \frac{Ce^{3e^{-x}} - 1}{x}[/tex]

where C is an arbitrary constant.

Since the solution for y is not unique, we need to determine the sign of y. To do this, we can analyze the initial conditions or the nature of the problem. If the initial conditions indicate that y is positive, then [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex]. If the initial conditions indicate that y is negative, then [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex].

Therefore, the general solution of the differential equation is [tex]y = \frac{\pm Ce^{3e^{-x}} + 1}{x}[/tex], where C is an arbitrary constant.

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If everyone shakes hands with everyone else in a group of 20, the number of handshakes take place is 210.

In a group of 20 people, if everyone shakes hands with everyone else, the number of handshakes that take place is equal to the sum of the first 20 positive integers, which can be found using the formula for the sum of an arithmetic series:

= n (n + 1)/ 2

= (20 * 21) / 2 = 210

To understand why this is the case, consider that each person shakes hands with 19 other people, so there are a total of 20 * 19 = 380 handshakes. However, each handshake is counted twice (once for each person involved), so we need to divide the total number of handshakes by 2 to get the actual number of unique handshakes. Hence, the answer is 380 / 2 = 210.

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If BC = 8 cm, ∠B = 60°and ∠C = 70° then the triangle is an acute triangle and the value of ∠A is 50.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

BC = 8 cm

∠B = 60° and ∠C = 70°.

Now,

The sum of all the angles is 180.

This means,

∠A + ∠B + ∠C = 180

∠A = 180 - 130

∠A = 50

Now,

The triangle is an acute triangle since all the angles are acute.

i.e less than 90.

Thus,

The triangle is an acute triangle.

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The coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down are B'(-14, -11).

In Mathematics, the translation of a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image.

On the other hand, the translation a geometric figure or graph downward simply means subtracting a digit from the value on the y-coordinate of the pre-image.

By translating the pre-image of quadrilateral ABCD vertically down by 3 units and horizontally left by 5 units, the coordinates of B in triangle A'B'C' include the following:

(x, y)                               →                  (x - 5, y - 3)

Coordinate B = (-9, -8)   →    Coordinate B' = (-9 - 5, -8 - 3) = (-14, -11)

In conclusion, the coordinates of B' are (-14, -11).

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Complete Question:

Determine the coordinates of the image of point B of quadrilateral ABCD after the translation of 5 units to the left and 3 units down.

The amount ethan payed is $31.992.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

The video game usually costs 39.99

Sale off= 20%

Now,

Let the 20% be x

x*100/39.99=20

x=20*39.99/100

x=799.8/100

x=7.998

After off;

=39.99-7.998

=31.992

Therefore, the value after 20 percent off will be $31.992

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There are 4 steps to build a VI to compute the variance of an array x.

Here is a VI in LabVIEW to compute the variance of an array x:

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The probability that the sample has one democrat, one republican and one independent is 0.1518.

Probability is a mathematical concept that describes the likelihood of an event occurring. It is a value between 0 and 1, where 0 indicates that an event is impossible, 1 indicates that an event is certain, and values between 0 and 1 indicate the degree of uncertainty or likelihood of an event occurring.

The total number of ways to select 3 voters out of 40 can be determined using the combination formula:

C(n, k) = n! / [k!(n - k)!]

where n is the total number of elements in the set and k is the number of elements to be selected.

C(40,3) = 40! / [3!(40 - 3)!] = 9880

The number of ways to select 1 Democrat, 1 Republican and 1 Independent is as follows:

C(20, 1) x C(15, 1) x C(5, 1) = 20 x 15 x 5 = 1500

So, the probability of selecting 1 Democrat, 1 Republican and 1 Independent in a sample of 3 voters is 1500 / 9880 = 0.151821, which rounded to four decimal places is 0.1518.

The problem seems incomplete, it must have been...

"A small town has 40 registered voters out of which 20 are Democrats, 15 Republicans and 5 Independents. A sample of 3 voters without replacement is to be selected. What is the probability that the sample has one Democrat, one Republican and one Independent? Express your final answer as a decimal and round to four decimal places. "

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The value (−1,7) is equal to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.

Since the limit of f(x,y) as (x,y) approaches (−1,7) is 4, that means that as (x,y) gets closer and closer to (−1,7) the value of f(x,y) gets closer and closer to 4. Therefore, when (x,y) is equal to (−1,7), the value of f(x,y) is 4.

The limit of the function f(x,y) as (x,y) approaches (−1,7) is 4, which means that as (x,y) gets closer and closer to (−1,7), the value of f(x,y) gets closer and closer to 4. In the limit, when (x,y) is equal to (−1,7), the value of f(x,y) is the same as the limit, which is 4. Therefore, the value of f(−1,7) is 4.

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Answer:

  Sn = (7 -(6n +7)3^-n)/4

Step-by-step explanation:

You want the sum of n terms of the series 2/3 +5/9 +8/27 +11/81 +....

The sums of n terms for n = 1 .. 5 are ...

  2/3, 11/9, 41/27, 134/81, 416/243

We recognize the denominators as powers of 3. The numerator sequence is ...

  2, 11, 41, 134, 416, ...

Differences are ...

  9, 30, 93, 282

And second differences are ...

  21, 63, 189

We note that these have a common ratio of 3, leading us to speculate that the numerator sequence can be written as the sum of a linear expression and a power of 3.

Assuming the sequence of numerator terms is of the form ...

  a·3^n +bn +c

We can write equations for a, b, c:

  a·3 +b·1 +c = 2 . . . . . . for n = 1

  a·9 +b·2 +c = 11 . . . . . .for n = 2

  a·27 +b·3 +c = 41 . . . . for n = 3

These equations can be solved for a, b, c using any of your favorite techniques. The attached calculator output shows the values to be ...

  a = 1.75 = 7/4

  b = -1.5 = -6/4

  c = -1.75 = -7/4

Then the sum of n terms can be written as ...

  [tex]\boxed{S_n=\dfrac{7\cdot3^n -6n-7}{4\cdot3^n}}[/tex]  

__

Additional comment

The n-th term of the series is (3n-1)/3^n. This can be decomposed into two sums: 3(n/3^n) -1/3^n. The latter is the well-known sum of a geometric series. The sum of the first term is less well-known: ∑(k/3^k) = (3(3^n-1)-2n)/(4·3^n).

Answer: See below

Step-by-step explanation:

A) The best way to estimate average speed is to make sure that each number is a whole number (with no decimals). This will make division much easier. The number of meters is already a whole number, but to make the number of minutes a whole number, we must round. Because the number after the decimal is greater than 5, that means we will round up, making the value of minutes 5. Now we can estimate 1500 metres/5 minutes = 300 metres/minute

As a little rounding tip, you can use this mnemonic: 4 and below, let it go (round down). 5 and above, give it a shove (round up)!

B) To do this part, we can simply plug the following into the calculator:

1500 metres/4.67 minutes = 321.2 metres per minute

Hope this helps!

The total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

The time Michelle and her family spend watching the movie in the visitor center is 14/60 of an hour or 14 minutes. We are told that this accounts for 15% of the total time they spend at Mount Rushmore, so to find the total amount of time they spent at Mount Rushmore, we need to divide the time spent watching the movie (14 minutes) by the percentage of the total time this accounts for (15%). This gives us the equation:

time = 14 / (15/100)

time = 14 × (100/15)

time = 14 × (6.67)

time = 93.38 minutes or 1 hour and 33.38 minutes.

So the total amount of time Michelle's family spends at Mount Rushmore is 93.38 minutes, which is equivalent to 1 hour and 33.38 minutes.

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If the price paid for a certain item is $40 and the consumer surplus is $4, then the maximum buying price for that item is $44 .

The Consumer's Surplus is defined as the difference between the maximum price a consumer is willing to pay for an item and the actual price paid for the item.

If the price paid for the item is $40 and the consumer's surplus is $4, then the maximum buying price for that item can be calculated as :

⇒ Maximum buying price = Price paid + Consumer's surplus

Substituting the values of Price paid and consumer surplus ,

we get ;

⇒ $40 + $4

⇒ $44

Therefore , the maximum buying price for that item is $44 .

The given question is incomplete , the complete question is

If the price paid for a certain item is $40 and the consumer surplus is $4, then what is the maximum buying price for that item ?

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Thomas lists all of the different arrangements of the letters in the word CABOOSE. How many of Thomas's arrangements begin with a C and end with an E?

(B) 120

If a b a♣︎b - a - b - 1, then what is the value of 284♣︎1001?

(A) 282435

What is the product of 4% of 112 and 61% of 375?

(D) 105

Josh rolls two standard six-sided dice. What is the probability that the product of the numbers shown on the dice is a multiple of six?

(C) 5/12

What is the remainder when the sum of the terms of the arithmetic series 101 108 + 115 + 290 is divided by 28?

(A) 7

Two right triangles have the same perimeter, and each triangle's side lengths are all whole numbers. One right triangle has legs of length 10 and 24. The other right triangle has a hypotenuse of length 25. What is the area of the second triangle?

(D) 144

A function f is defined for positive integers x as f(x) = 0 if x ≤ 2. Otherwise, f(x) = f(x - 1) if x is not divisible by 3, and f(x) = 2 + f (3) if x is divisible by 3. What is the value of f(2020)?

(B) 14

They sold 400 student tickets and 200 student tickets.

And at a certain performance, they sold 100 adult tickets and 200 student tickets.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

Given, Let 'x' represents the number of adult tickets and 'y' represent the number of student tickets.

So, The two equations can be formed as,

x + y = 600 and 7.5x + 4.5y = 3300.

Multiplying equation 1 by 7.5x we have 7.5x + 7.5y = 4500 and subtracting it from equation 2 we have,

- 3y = - 1200.

y = 400 and hence x = 200.

At a certain performance, they sold twice as many student tickets as adult tickets.

y = 2x.

x + y = 300.

x + 2x = 300.

3x = 300

x = 100 and hence y = 200.

100×7.5 + 200×4.5 = 750 + 900 = 1650.

So, they were 3300 - 1650 = $1650 short.

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At the haunted mansion, 6114 people were  scared by a group of 135 ghosts and 273 witches.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

According to the question each ghost must scare 19 people that means 135 ghost will scare:

135 ghosts x 19 people = 2,565 people......................(i)

And each witch must scare 13 people-no more and no less i.e 273 witches will scare:

273 witches x 13 people = 3,549 people.....................(ii)

Adding (i) and (ii) we get;

2,565 + 3,549 = 6114 people

Therefore, 6114 people were scared by a group of 135 ghosts and 273 witches.

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Step-by-step explanation:

it is a arithematuc sequence because it has a common difference of 5

so the general term is Tn = 1 + (n-1)5

also the 5th term is T(5) = 1 + (5-1)5 = 21

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

Complementary angles can be defined as the angles whose sum is 90 degrees.

The ‘c’ in complementary angle can be used to form 9 in 90 degrees. Supplementary angles are angles whose sum is 180 degrees. The ‘s’ in supplementary angle can be used to form 8 in 180 degrees

If the intersection of P and Q creates a 71 degree angle,

then 90 – 71 = 19 degrees is its complementary angle. Its supplementary angle is 180 – 71 = 109 degrees.

Therefore, The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

So, The answer is D)

The complementary angle is 19 degrees and the supplementary angle is 109 degrees.

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Answer: 5:8

Step-by-step explanation:

to reduce 250:400, simply start with common factors. Right now, it looks like both numbers have 10 in common, so we can divide 10 from both numbers, which will result in 25:40.

We still need to simplify, and now it looks like both numbers have 5 in common, so we can divide 5 from both numbers, resulting in 5:8.

I hope this helps!

Answer:

Step-by-step explanation:

y=mx+c

7=2*-4+c

7=-8+c

7+8=c

15=c

The y-intercept of the equation D = -30t + 300 is 300.

What is the y-intercept of the equation?

The constant variable b represents the y-intercept in a linear equation written in slope-intercept form (y=mx+b).

The given equation is D = -30t +300.

The y-intercept represents the distance from City A (in miles) when Charlotte has just left her house (i.e. when t = 0). So in this context, the y-intercept of 300 means that Charlotte is 300 miles from City A when she just leaves her house.

Hence, The y-intercept of the equation D = -30t + 300 is 300.

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The surface area of the right triangular prism is 108 ft²

An equation is an expression that shows the relationship between two or more numbers and variables.

The surface area of a three dimensional figure is gotten by individually adding each of their respective areas of the surfaces.

From the net and the diagram shown:

A = 5 feet, B = 4 feet, D = 3 feet and C = 8 feet

Surface area = area of triangle 1 + area of triangle 2 + area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Surface area = (0.5 * B * D) + (0.5 * B * D) + (A * C) + (C * B) + (D * C)

Substituting:

Surface area = (0.5 * 4 * 3) + (0.5 * 4 * 3) + (5 * 8) + (4 * 8) + (3 * 8) = 108 ft²

The surface area is 108 ft²

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The distance that Ann travelled is; 3.61 ft

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

Ann and Elena form the vertical leg of a right angle triangle of length = 3ft. Elena and Rob form the opposite side of the right angle triangle of length = 2 ft.

Using the Pythagorean theorem to find the distance that Anna traveled which is the length of the hypotenuse of the right angle triangle; let that length be x. Then:

x = √(3² + 2²)

x = √ 13

x = 3.61 ft

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The equation used to determine the value of the car ,v, after 5 years is V= 12500*4.5*5/100-D.

An equation represents equality of two or more mathematical expression.

When someone asks you to solve an equation, then they usually mean to find the values of the unknowns for which that equation would be true (the equality between expressions should hold true for those values).

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

Given;

A car depreciates ( loses value ) at a rate of 4.5% annually

Greg purchased a car for 12,500

Time= 5years

Here, the depreciation is equal to the simple interest but in depreciation

So, Let the depreciation be D

D=P*R*T/100

D=12500*4.5*5/100

=2812.5

Now, value of car v;

V= 12500*4.5*5/100-D

Therefore, the equation will be V= 12500*4.5*5/100-D

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Step-by-step explanation:

It's difficult for me to determine which recent decisions have been made using these strategies without more context about the specific situation. However, I can provide general information about how each strategy may be used and what factors may influence the decision-making process.

Spontaneity: This strategy may be used in situations where time is of the essence, and there is not enough time to weigh all options. The individual may also be impulsive or lack the ability to plan ahead.

Compliance: This strategy may be used in situations where the individual values the opinions of others over their own, or they may not want to upset their family, teachers, or friends.

Procrastination: This strategy may be used when the individual is overwhelmed by the decision-making process, and they are unsure of what choice to make. They may also be afraid of making the wrong choice.

Agonizing: This strategy may be used when the individual wants to make sure that they are making the best decision, and they want to gather as much information as possible. This can lead to paralysis by analysis, and they may not make a decision at all.

Desire: This strategy may be used when the individual wants to achieve a specific outcome, and they are willing to take a risk to do so. They may also be motivated by a sense of adventure.

Avoidance: This strategy may be used when the individual wants to avoid a negative outcome, and they are willing to make a decision based on that.

Security: This strategy may be used when the individual wants to make a decision that will not upset others or involve risk. They may also be motivated by a sense of stability.

Synthesis: This strategy may be used when the individual wants to choose an option that will probably be successful and which they like the best. They may also have a good sense of what they want and what is best for them.

These are general information, the hardest part of the decision-making process for an individual may vary depending on the situation, the options available, and their personal preferences. Furthermore, there may be more than one solution to a problem, and the best one depends on the individual's preferences, resources, and the context of the problem.

Shapes A and B are enlargements of x by a scale factor of -1 because they are mirror images of x. Shape C is not an enlargement of x by scale factor -1 because it is not a mirror image of x. Therefore, the option is A and B.

An enlargement by a scale factor of -1 means that the image is flipped and has the same size as the original.

Therefore, any shape that is a mirror image of x is an enlargement of x by scale factor -1. Looking at the shapes, we can see that shapes A and B are mirror images of x, so they are enlargements of x by scale factor -1.

Shape C is not a mirror image of x, so it is not an enlargement of x by scale factor -1. Therefore, the answer is A and B.

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Considering the Question G(x) = -x + 5 is the equation for such reflections at f(x) = x + 5 from across y-axis.

Similar to a vertical ruler is the y-axis. It displays the location of an object on a two-dimensional Cartesian graph with in y (vertical) plane. On a graph, it serves as the starting point, or "zero," from which to calculate how far a tip is from right or left (horizontally).

The sign of the x-coordinate is altered by reflection across the y-axis, while the y-coordinate remains constant. By changing the sign of x, we may represent f(x) = x + 5 from across y-axis as g(x) = -x + 5. G(x) = -x + 5 is the equation for the reflections for f(x) = x + 5 from across y-axis.

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