Find the equation of the line passing through the point (8, -4) and slope -4.
A. y + 4x = 22
B y + 4x = 28
C y - 4x = 28
D y + x = 36

Therefore , using  pigeonhole principle we get 101 students must be present to guarantee that at least three students.

According to the pigeonhole principle, which is used in discrete mathematics, some pigeonholes must contain two or more pigeons if we must fit expression N + 1 or more pigeons into N Pigeon Holes. An illustration would be if there were Kn+ 1 pigeons dispersed across n holes, where K is a positive variable, and at least K + 1 pigeons were present in each hole.

Here,

You must do the math first. Add one to the result after (n-1)/m.

Now, if you compare this question, you will see that students (pigeons) and states are holes, and given that at least three students must originate from the same state, the answer is three. Divide (n-1)/m and add 1 to the result if you looked at the previous example.

Now, if you go through the process backwards, you must first subtract 1 from the results

(it is 3-1 = 2), multiply by 50 (m = 50), which becomes

(m*2 = 100), and then add 1 again (n-1 makes 1 go to the right side, making it Plus)...

N = 101 is the result.

Therefore , the 101 students must be present to guarantee that at least three students.

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By observation or by inspection, 7.40 appears the most, thus mode.

The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.

Data can be disseminated in statistics in a number of different ways. The traditional normal (bell-curve) distribution is the one that is referenced the most. The midpoint of this distribution, as well as some others, coincides with the peak frequency of observed values and is where the mean (average) value is located.

The mean, median, and mode all have the same values for such a distribution. This indicates that this value—the one that appears the most frequently in the data—is the average value, the middle value, and the mode.

When analyzing categorical data, such as automobile models or soda taste varieties, where a mathematical average median value based on ordering cannot be computed, mode is most helpful as a gauge of central tendency.

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Based on the calculations we have rejected the null hypothesis .

Given,

Standard deviation = $ 45

Random sample = 20

Now,

Part 1

Set the null hypothesis and alternative hypothesis,

\(H_{0} : u = 0\\ H_{0} : u > 606.40\)

Part 2

The value of z critical signifies 5% level of significance .

\(Z_{0.05} = 1.65\)

According to critical value if z after calculation is greater than or equal to 1.65 we reject the null hypothesis .

Part 3

The value of Z can be calculated by the formula,

Z = X - µ/σ/√n

Substitute the values ,

Z = 628.85 - 606.40/45/√20

Z = 1.93

Part 4

From the above calculation the value of Z is greater than the critical value .

Thus we reject the null hypothesis .

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Answer:B

Step-by-step explanation:

The number of men on the sight-seeing tour was 22.

What is the proportion?

A unique class of ratio called a percentage has the numerator and denominator combined. An illustration is the ratio of deaths to men, which is calculated by dividing deaths to men by deaths to men and women (i.e. the total population).

We have,

w/c = 5/2

w/c = 5/2

w = 5x  

and c=2x

for some integer x. Q : m =?

(1) on the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11

c/m = 5/11cm

c=5y and m = 11y,

for some integer y. Not sufficient to calculate m.

(2) the number of women on the sight-seeing tour was less than 30 --> w<30. Not sufficient to calculate m.

(1) + (2)

w = 5x < 30w --> x<6x.

c=2x and as c=5y,

c is a multiple of 5 --> x=5x  

c = 10 = 5y --> y = 2

m = 11y = 22.

Hence, the number of men on the sight-seeing tour was 22.

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Answer:

5a-40=-2b

5a-40/-2=-2b/-2

-5a/2+20=b

Answer:

first box is 18 second is 32 and third is 8

Step-by-step explanation:

Answer:

Step-by-step explanation:

3   6     8

18   36   48

your ratio is 1:6, so  however many boxes you have, just multiply by 6 to get the candle number

Answer:108

Step-by-step explanation:

12+12+42+42

A) The annual growth rate between 1993 and 2004, is approximately 5.68%.  B) Converting the growth rate from part A to percentage form, is approximately 5.68%.  C) Assuming the house value continues to grow at the same annual growth rate, the estimated value in the year 2009 would be approximately $215,000

A) The annual growth rate between 1993 and 2004, assuming exponential growth, can be calculated using the formula: growth rate = (final value / initial value) ^ (1 / number of years) - 1. In this case, the initial value is $95,000, and the final value is $165,000. The number of years is 2004 - 1993 = 11. Plugging these values into the formula, we get: growth rate = (165,000 / 95,000) ^ (1 / 11) - 1 ≈ 0.0568.

B) Converting the growth rate from part A to percentage form, we multiply it by 100. Therefore, the correct answer in percentage form is approximately 5.68%.

Now let's move on to part C. Assuming the house value continues to grow at the same percentage, we can calculate the value in the year 2009. We know that the value in 2004 was $165,000. To find the value in 2009, we need to calculate the growth over a period of 5 years. Using the growth rate of 5.68% (or 0.0568 as a decimal), we can calculate the value in 2009 as follows: value in 2009 = value in 2004 (1 + growth rate) ^ number of years = 165,000 (1 + 0.0568) ^ 5 ≈ $215,291.

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No triangle can be constructed with the given angles of 90 degrees, 60 degrees, and 60 degrees, as the sum of the angles exceeds the total of 180 degrees required for a valid triangle.

To determine the number of triangles that can be constructed with angles measuring 90 degrees, 60 degrees, and 60 degrees, we need to consider the conditions for triangle construction.

In a triangle, the sum of all angles must be equal to 180 degrees. Since we already have two angles of 60 degrees each, the sum of these angles is 60 + 60 = 120 degrees.

To form a valid triangle, the sum of all three angles must be equal to 180 degrees. However, in this case, the sum of the given angles (90 + 60 + 60 = 210 degrees) exceeds 180 degrees. Therefore, it is not possible to construct a triangle with angles measuring 90 degrees, 60 degrees, and 60 degrees.

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Answer:

  n < 2

Step-by-step explanation:

This inequality can be solved the same way the corresponding 3-step linear equation would be solved.

  8n +20 < 6n +24 . . . . . given

  2n +20 < 24 . . . . . . . . step 1, subtract 6n to isolate the variable on the left

  2n < 4 . . . . . . . . . . . . step 2, subtract 20 to separate constants and variable terms

  n < 2 . . . . . . . . . . . divide by the coefficient of the variable

The curve of intersection between the cylinder x^2 + y^2 = 1 and the plane y + z = 2 is a circle lying on the plane y + z = 2. The parametric equations for this curve are x = cos(θ), y = sin(θ), and z = 2 - sin(θ), where θ is the parameter representing points on the circle.

To find the parametric equations for the curve of intersection between the cylinder and the plane, we can start by parameterizing the cylinder using the angle θ. Since the equation x^2 + y^2 = 1 represents a circle in the x-y plane with radius 1, we can use θ as a parameter to represent points on this circle.

The parametric equations for the cylinder are:

x = cos(θ)

y = sin(θ)

z = 2 - y

Next, we substitute these equations into the plane equation y + z = 2 to determine the intersection points. By substituting y and z, we have sin(θ) + 2 - sin(θ) = 2, which simplifies to sin(θ) - sin(θ) = 0. This implies that the plane equation is satisfied for any value of θ.

Therefore, the intersection between the cylinder and the plane is the entire cylinder itself, lying on the plane y + z = 2. The parametric equations for the curve of intersection are x = cos(θ), y = sin(θ), and z = 2 - sin(θ).

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Answer:

its A

Step-by-step explanation:

asymptotes:=-1 and hole:x=4

Answer:

It should be -5, 5 to the power of -1, 0.5, 5 to the power of 0 in least to greatest form.

Step-by-step explanation:

Answer:

60°, 60°, and 60° is the set of interior angles of triangle.

Step-by-step explanation:

Given:

Set of interior angles

Find:

Set of interior angles of triangle

Computation:

We know that, sum of  interior angles of triangle is 180°

So,

90° + 42° + 58° = 190°

60° + 60° + 60° = 180°

100° + 48° + 42° = 190°

31° + 75° + 70° = 176°

So,

60°, 60°, and 60° is the set of interior angles of triangle.

Answer:

60°, 60°, and 60°

Step-by-step explanation: I took the quiz

Answer:

-5   and   1

Step-by-step explanation:

Answer:

-5×1 = -5 so , -5 plus 1 = -4

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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Your answer is a, 2 chairs per 3 tables.

Notice you need 12 chairs for 3 tables.

D says 3 tables per chair, this cannot be the answer.

C says 12 chairs for each table, this cannot be the right answer neither.

B says 3 chairs for every 12 tables, this cannot be the answer.

A says 12 chair per 3 tables, this is the answer it is just worded differently.

If this helped may i have brainliest?

a. The vector from (2, -7, 0) to (1, -3, -5)  is (-1, 4, -5).

b.  The vector from (1, -3, -5) to (2, -7, 0) is (1, -4, 5).

c. The position vector for (-90, 4) is (-90, 4).

(a) The vector from (2, -7, 0) to (1, -3, -5):

To find the vector between two points, we subtract the coordinates of the initial point from the coordinates of the final point. Therefore, the vector can be calculated as follows:

(1 - 2, -3 - (-7), -5 - 0) = (-1, 4, -5)

So, the vector from (2, -7, 0) to (1, -3, -5) is (-1, 4, -5).

(b) The vector from (1, -3, -5) to (2, -7, 0):

Similarly, we subtract the coordinates of the initial point from the coordinates of the final point to find the vector:

(2 - 1, -7 - (-3), 0 - (-5)) = (1, -4, 5)

Therefore, the vector from (1, -3, -5) to (2, -7, 0) is (1, -4, 5).

(c) The position vector for (-90, 4):

The position vector describes the vector from the origin (0, 0, 0) to a specific point. In this case, the position vector for (-90, 4) can be found as follows:

(-90, 4) - (0, 0) = (-90, 4)

Thus, the position vector for (-90, 4) is (-90, 4). This vector represents the displacement from the origin to the point (-90, 4) and can be used to describe the location or direction from the origin to that specific point in space.

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The total number of tickets is 200 tickets.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given;

On Monday,

the theater club sells 30 tickets for the school play.

On Tuesday,

they sell 20 tickets.

On those two days,

they sell 30 + 20 tickets and that is 25% of total tickets.

So, total number of tickets,

here, 25%  = 50

So, 25 x 4 = 100% = 50 x 4 = 200 tickets.

Therefore, 200 tickets are the total number of tickets.

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A different combination of models and colors available is 18.

Combination:

the act of combining or the state of being combined. a number of things combined: a combination of ideas. something formed by combining: A chord is a combination of notes. an alliance of persons or parties: a combination in restraint of trade.

Here it is given 6 different colors. Harley Davidson offers 3 different motorcycle models.

We have to find the number of different combinations of models and colors available.

Based on the above-given data we get the:

Different combination = 3 × 6

= 18

Therefore the number of combinations is 18.

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The amount in the account at the end of ten years, after the $200 for that year has been added is given by Amount in account after 10 years= $6539.81 (nearest cent).

The given expression for the amount in the account at the end of 1 year, Amount in account at end of

1 yr= $4000 × 1.08 + $200 + T,

and that for the amount in the account at the end of 2 years, Amount in account at end of

2 yrs= ($4000 × 1.08 + $200) × 1.08 + $200 + T2

can be generalized as follows: Amount in account at end of n years, where n is a positive integer,

we have

In= $4000 × 1.0810−1 + $200 {13.9332 + T[1 − (1.08)9/0.08]}.

Now, substituting T=0, we obtain, Amount in account after

10 years= $4000 × 1.0810−1 + $200 {13.9332 + 0[1 − (1.08)9/0.08]}.

Thus, the amount in the account at the end of ten years, after the $200 for that year has been added is given by Amount in account after 10 years= $6539.81 (nearest cent).

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Answer: D) Reflect over x-axis

=======================================================

Explanation:

When we do this type of reflection, a point like (1,2) moves to (1,-2).

As another example, something like (5,-7) moves to (5,7)

The x coordinate stays the same but the y coordinate flips in sign from positive to negative, or vice versa.

We can say that \((x,y) \to (x,-y)\) as a general way to represent the transformation. Note how y = f(x), so when we make f(x) negative, then we're really making y negative.

If we apply this transformation to every point on f(x), then it will flip the f(x) curve over the horizontal x axis.

There's an example below in the graph. The point A(2,8) moves to B(2,-8) after applying that reflection rule.

There are 13 teams in the softball league, so there are 13 options for the first-place team. Once the first-place team is determined, there are 12 remaining teams for the second-place spot. Finally, there are 11 remaining teams for the third-place spot. Therefore, the number of different end-of-the-season rankings of first, second, and third place is possible is:

13 x 12 x 11 = 1,716

So there are 1,716 possible rankings.

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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Answer:

Real numbers

Step-by-step explanation:

Answer:

The answer is C

I turned it in and it was correct

Step-by-step explanation:

Please mark brainliest

Answer:

c

Step-by-step explanation:

Answer:

55 feet

Step-by-step explanation:

40+15 feet

Answer:

The equation in point-slope form is: y - 5 = 4(x - 2).

The equation in standard form is: 4x - y + 3 = 0.

Answer:

Standard form

4x - y = 3

Step-by-step explanation:

Point slope form of a line equation is:
y - y1 = m(x - x1)

where
(x1, y1) is a point on the line and m is the slope

The standard form of a line equation is:
Ax + Bc = C
where
A, B, C are integers

Slope Point Form

Given
(x1, y1) = (2, 5)
m = 4

The slope-point equation is
y - y1 = m(x - x1)

which is

y - 5 = 4(x - 2)

Expanding the bracket on the right side:
y - 5 = 4x  - 8

Move constant -5 to the right to become +5
y = 4x - 8 + 5 = 4x - 3

Move 4x to left becoming -4x

y - 4x = -3

or

-4x + y = -3

same as

4x - y = 3

This is the standard form with A = -4, B = 1 and C = 13