Which two numbers multiply to 15 and add to -8

the measurement of the short side of the rectangle is approximately 8.09 cm.

Let's assume that the rectangle's sides are x and y, where x is the short side and y is the long side. We know that the area of the rectangle is 106.92 cm², so we can write:

x * y = 106.92

We also know that the long side measurement is 13.2 cm, so we can substitute y with 13.2 in the equation above:

x * 13.2 = 106.92

Solving for x, we get:

x = 106.92 / 13.2

x = 8.09

Therefore, the measurement of the short side of the rectangle is approximately 8.09 cm.

To explain this solution in 200 words, we can say that the area of a rectangle is equal to the product of its length and width. In this case, we are given the area and the length of the rectangle, but we need to find the width (short side). We use the formula for the area of a rectangle to write an equation in terms of the unknown width and the known length. Then, we substitute the known length with its value and solve for the unknown width. The resulting value is the measurement of the short side of the rectangle.

It's important to note that in some cases, there may be multiple possible solutions for the width of the rectangle, depending on the dimensions of the rectangle. However, in this particular case, there is only one possible solution, as the length and area of the rectangle are fixed.

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If the songs can be played in any order, there are 3,628,800 different ways for the DJ to play the 10 songs.

If the first song must be a slow song and the last song must be a slow song, there are 203,212,800 different ways for the DJ to play the 10 songs.

If the first two songs must be fast songs, there are 241,920 different ways for the DJ to play the 10 songs.

A) If the songs can be played in any order, the DJ has 10 songs to play, out of which 7 are slow songs and 3 are fast songs. This is a permutation problem since the order matters. The total number of ways to play the songs can be calculated using the formula for permutations:

Total number of ways = 10P10 = 10!

Here, "!" represents the factorial function. Evaluating the expression, we get:

Total number of ways = 10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 3,628,800 ways

Therefore, if the songs can be played in any order, there are 3,628,800 different ways for the DJ to play the 10 songs.

B) If the first song must be a slow song and the last song must be a slow song, we fix the positions of the first and last songs. The remaining 8 songs can be arranged in the middle in any order. This is a permutation problem with repetition since there are repeated elements (slow songs). The calculation is as follows:

Total number of ways = 7P1 * 8P8 = 7! * 8!

Here, 7P1 represents permuting the slow songs for the first position, and 8P8 represents permuting the remaining songs in the middle positions.

Simplifying the expression, we get:

Total number of ways = 7! * 8! = 5,040 * 40,320 = 203,212,800 ways

Therefore, if the first song must be a slow song and the last song must be a slow song, there are 203,212,800 different ways for the DJ to play the 10 songs.

C) If the first two songs must be fast songs, we fix the positions of the first two songs as fast songs. The remaining 8 songs can be arranged in the remaining positions in any order. This is again a permutation problem with repetition:

Total number of ways = 3P2 * 8P8 = 3! * 8!

Simplifying the expression, we get:

Total number of ways = 3! * 8! = 6 * 40,320 = 241,920 ways

Therefore, if the first two songs must be fast songs, there are 241,920 different ways for the DJ to play the 10 songs.

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B. 9/19

Step-by-step explanation:

there was 20 dogs in total he took 1 black dog now 19 in total, now 9 black dogs and 10 brown dogs so one less probability of black dogs so 9 black dogs and 10 brown dogs so 9/19

Answer:

The rate of change of the surface area of the sphere is;

-48π cm^2/s

Step-by-step explanation:

Here, we want to calculate dA/dt

Mathematically that will be;

dA/dt = dA/dr * dr/dt

From the question;

dr/dt = -2 cm/s

dA/dr = 8πr

So dA/dt will be;

-2cm/s * 8πr = -16 πr cm/s where r is 3 cm

So;

dA/dt = -48π cm^2/s

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere is of -151 square centimetres per second.

The surface area of an sphere of radius r is given by:

\(S = 4\pi r^2\)

Applying implicit differentiation, the rate of change is given by:

\(S = 8\pi r\frac{dr}{dt}\)

For this problem:

The rate of change is of:

\(S = 8\pi(3)(-2) = -48\pi = -151\)

The rate of change of the surface area of the sphere is of -151 square centimetres per second.

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The correlation coefficient is a number that measures the strength of the linear association between two numerical variables.

The correlation coefficient is a statistical measure used to determine the strength and direction of the linear relationship between two numerical variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger correlation, and values closer to 0 indicate a weaker correlation. A negative correlation means that as one variable increases, the other decreases, while a positive correlation means that both variables increase or decrease together. The correlation coefficient is an important tool in many fields, such as finance, economics, and healthcare, where it can help identify patterns and predict future outcomes based on past data.

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Answer:

The scale factor is 60

Step-by-step explanation:

The drawing is measured in inches and the billboard is measured in feet.  First, convert 15 feet to 180 inches.  Then use the ratio \(\frac{180}{3}\) to find that the scale factor is 60.  This means the length of the billboard will be 600 inches or 50 feet.

Answer:

B,C

Step-by-step explanation:

The sum of B is 1

The sum of C is -1/2

Let's try each option.

Option A:

-3 + 5 + (-1) = 2 + (-1) = 1

FALSE

Option B:

5 + (-8) + 4 = -3 + 4 = 1

TRUE

Option C:

-19/2 + 9 = -9.5 + 9 = -0.5

TRUE

Option D:

-17 + 36/2 = -17 + 18 = -1

FALSE

So, the correct answers are B and C

Best of Luck!

To test if there is a difference in two population means, a difference in sample mean should be used  , the correct option is (b) .

In the question ,

we have to find the what is used to test whether their is a difference in two population means or not .

For each hypothesis problem, there is test statistic .

This test statistic is compared to the critical value to make the decision about the hypothesis.

Hence choosing the appropriate test statistics matters a lot.

Here two samples are there. It is clearly given for which we have to test the hypothesis that is sample means .

Hence,  we can say that the test statistic is, the difference in sample mean .

Therefore , the difference in sample mean is used to test if there is a difference in two population means .

The given question is incomplete , the complete question is

To test if there is a difference in two population means, a ___ should be used.

(a) alpha

(b) the difference in sample means

(c) the degrees of freedom

(d) the difference in the population means

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The parameters needed to determine the sample size, denoted as 'n', are the desired level of confidence, the margin of error, and the population standard deviation. These parameters are essential in conducting a statistical analysis and obtaining reliable results.

The sample size is influenced by the desired level of confidence, which indicates the certainty of the results. A higher level of confidence requires a larger sample size. Similarly, a smaller margin of error, which represents the acceptable amount of deviation from the true population parameter, necessitates a larger sample size to achieve greater precision.

Additionally, the population standard deviation plays a crucial role in determining the sample size. If the standard deviation is known, it is used directly in the formula to calculate the sample size. However, if the standard deviation is unknown, a conservative estimate is often used, leading to a larger sample size.

Overall, determining the sample size involves considering the desired level of confidence, the margin of error, and the population standard deviation. By carefully selecting these parameters, researchers can ensure that their sample size is sufficient to provide accurate and reliable results for their analysis.

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

First find the slope

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

m = (-7-1)/(7-3)

m = -8/4

m = -2

The slope is -2.

Now pick either point for the (x,y) coordinate values. I'll pick the first point. So (x,y) = (3,1)

We'll plug m = -2, x = 3, y = 1 into the equation below to solve for b

y = mx+b

1 = -2*3+b

1 = -6+b

1+6 = b ... add 6 to both sides

7 = b

b = 7

The y intercept is 7.

Since m = -2 and b = 7, we go from y = mx+b to y = -2x+7

--------------------

As a check:

Plug in (x,y) = (3,1)

y = -2x+7

1 = -2(3)+7

1 = -6+7

1 = 1

So (3,1) is confirmed.

Let's check the other point

y = -2x+7

-7 = -2(7)+7

-7 = -14+7

-7 = -7

The other point (7,-7) is confirmed as well. Both points are on the line. This confirms the answer.

Answer:

Y=2x+1

Step-by-step explanation:

Slope= -7-1/7-3 =2

Point slope form:

y-y₁=m(x-x₁)

y-3=2(x-1)

  +3     +3

y=2x+1

The answer is 77520.

How many different (ordered) playlists are possible?

Number of possible playlists = 77520

Explanation:

Total number of songs = 20

Songs in the playlist = 7

So, we need to select 7 songs out of 20. This can be done using combinations.

n = 20 , r=7

C( n , r ) = ?

C( n , r ) = C (20 , 7)

              = 20! / ( 7! (20-7)!)

              =  20! / ( 7! × 13! )

              = 77520

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Answer:

D) y = -5x + 5

Step-by-step explanation:

If two lines are perpendicular to each other, they have opposite slopes.

The first line is y = 1/5x + 5. Its slope is 1/5. A line parallel/perpendicular to this one will have a slope of -5.

Plug this value (#) into your standard point-slope equation of y = mx + b.

y = -5x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (2, -5). Plug in the x and y values into the x and y of the standard equation.

-5 = -5(2) + b

To find b, multiply the slope and the input of x (2)

-5 = -10 + b

Now, add 10 to both sides to isolate b.

5 = b

Plug this into your standard equation.

y = -5x + 5

This equation is parallel/perpendicular to your given equation (y = 1/5x + 5) and contains point (2, -5)

Hope this helps!

Answer:

[(8x+6)=(20+6x) as M is the midpoint

8x-6x=20-6

2x=14

x=7

LN=(8x+6)+(20+6x)

LN= 8(7)+6+20+6(7)

LN= 56+6+20+42

LN= 124

LN =124 units

Given that for positive integers a and b, gcd(a, b) = d, we want to find gcd(a/d, b/d).
Since d is the greatest common divisor of a and b, it means that both a and b can be divided by d without leaving any remainder. Let a = d * m and b = d * n, where m and n are positive integers.
Now, gcd(a/d, b/d) can be written as gcd(d * m/d, d * n/d), which simplifies to gcd(m, n).
Since d is the greatest common divisor of a and b, m and n must be relatively prime, meaning their gcd is 1.
So, gcd(a/d, b/d) = gcd(m, n) = 1. This is justified because we have expressed a and b in terms of their greatest common divisor, d, and found that the resulting integers, m, and n, are relatively prime.

The gcd of two positive integers is always a positive integer. Therefore, since gcd(a,b) = d, we know that d is a positive integer.
Now, we can use the fact that if we divide two integers by a common factor, the resulting quotients will have no common factors (besides 1). In other words, if we divide a and b by d, the resulting numbers a/d and b/d will have no common factors (besides 1).
Therefore, the gcd of a/d and b/d must be 1.

To justify this, suppose there exists a positive integer k such that k is a common divisor of a/d and b/d. Then, we know that k must also be a divisor of a and b (since a/d and b/d are just a and b divided by d). But since gcd(a,b) = d, the only common divisor of a and b is d itself. Therefore, k must be equal to d.

But if k = d, then we have a common divisor of a/d and b/d that is larger than 1 (since d is a positive integer). This contradicts our assumption that a/d and b/d have no common factors (besides 1). Therefore, our original assumption must be false and the gcd of a/d and b/d is indeed 1.

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Answer:

84 in.

Step-by-step explanation:

6*6=36/2=18

6*11=66

18+66=84

Answer:

Step-by-step explanation:

can you post a better pic please

Answer:

Yes it is

Step-by-step explanation:

you're going up at a constant rate of 1.5 or down at a constant rate of 1.5

Research that provides data which can be expressed with numbers is called quantitative research.

Quantitative research is a type of research that focuses on gathering and analyzing numerical data. It involves collecting information or data that can be measured and quantified, such as numerical values, statistics, or counts. This research method aims to objectively study and understand phenomena by using mathematical and statistical techniques to analyze the data.

Quantitative research typically involves the use of structured surveys, experiments, observations, or existing data sources to gather information. Researchers often employ statistical methods to analyze the data and draw conclusions or make predictions based on the numerical findings.

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The correct order of the set of numbers from least to greatest is 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5 option (D) is correct.

To order the given set of numbers from least to greatest, we need to compare their values. We start by noticing that 2 and 3 over 4 are equivalent to 2.75. Next, we compare the values of the remaining numbers. Since the square root of 5 is approximately 2.236 and 5 over 2 is equivalent to 2.5, we have:

2, 3 over 4 < 2.71 repeating 71 < 2.5 < square root 5

Therefore, the set of numbers in order from least to greatest is 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5.

Ordering the set of numbers from least to greatest, we get:

2, 3 over 4, 2.71 repeating 71, square root 5, 5 over 2.

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The complete question is:

Order the set of numbers from least to greatest: (Group of answer choices)

A. 2.71 repeating 71, 2, and 3 over 4, square root 5, 5 over 2.

B. square root 5, 5 over 2, 2.71 repeating 71, 2 3 over 4

C. 5 over 2, square root 5, 2.71 repeating 71, 2 3 over 4

D. 2, 3 over 4, 2.71 repeating 71, 5 over 2, square root 5

Answer:

t = 3s

Step-by-step explanation:

The equation t = 3s can be used to calculate the total cost.

Answer:

D

Step-by-step explanation:

16m-(5+8m)

this expression change like

16m-5-8m

Answer:

v=ha^2/3

Step-by-step explanation:

Answer:

i think b

Step-by-step explanation:

Answer:

B. y = 2x + 8

Step-by-step explanation:

14x - 7y = 1

7y = 14x - 1

y = 2x - 1/7

If two lines are parallel, their slopes are equal.

With m = 2, x = -2, y = 4

y = mx + b

4 = 2(-2) + b

4 = -4 + b

b = 8

so y = 2x + 8

Answer:

3,266.53

Step-by-step explanation:

calculater

Answer:

E. X= 5+ (gcf)37/6

F. x= 5 - (gcf)37/6

Step-by-step explanation:

put in calculator MOD 5 3

write the values: -

                             a= 3    b= -5    c= -1

The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2/3x + 5/2y = 15

4x + 15y = 12

Multiply the first equation by 6, to eliminate the fractions.

6 * (2/3x + 5/2y = 15)

This gives

4x + 15y = 90

Subtract the equation 4x + 15y = 90 from 4x + 15y = 12

4x - 4x + 15y - 15y = 12 - 90

Evaluate the difference

0 + 0 = -78

Evaluate the sum

0 = -78

The above equation is the same equation as option (b) 0 = 26

This is so because they both represent that the system of equations have no solution

Hence, the equation that could represent a linear combination of the system is 0 = 26

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Complete question

The system of equations below has no solution.

2/3x + 5/2y = 15

4x + 15y = 12

Which equation could represent a linear combination of the system?

Answer:

250 pennies

Step-by-step explanation:

50 x 8 = 250

Answer:

y = 1/2x+5

Step-by-step explanation:

You have two points so you can find the slope

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

m = (8-3)/(6 - -4)

   (8-3)/(6+4)

    5/10

 1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1/2 x+b

Substitute a point into the equation

8 = 1/2(6)+b

8 = 3+b

b=8-3 = 5

y = 1/2x+5

The function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

A location where two or more straight lines or curves intersect is referred to as a vertex . A vertex in geometry is sometimes referred to as a corner or an intersection point. The phrase is frequently used to refer to the highest or lowest point on a curve or surface, the place where two lines intersect to make an angle, and the point where two sides of a polygon meet.

The vertex form of the equation of a parabola is given by:

\(y = a(x - h)^2 + k\)

where (h, k) represents the vertex of the parabola.

Using the given vertex and the point (6,0), we can find the value of "a" and plug it into the vertex form to get the equation of the parabolic path of the water stream.

Step 1: Find the value of "a"

Since the vertex is (3,5), we know that:

h = 3

k = 5

Using the point (6,0), we can find the value of "a" as follows:

\(0 = a(6 - 3)^2 + 5\)

\(0 = 9a + 5\)

\(9a = -5\)

\(a = -5/9\)

Step 2: Plug in the values of h, k, and a into the vertex form:

\(y = (-5/9)(x - 3)^2 + 5\)

Therefore, the function in vertex form that models the path of the stream is:

\(y = (-5/9)(x - 3)^2 + 5\)

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