If a linear function passes through two points (x1, y1) and (x2, y2), what is the average value of the function on the interval from x1 to x2

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

205

Step-by-step explanation:

Step-by-step explanation:

-11-7-3+1+225

-21+1+225

-20+225

205

Answer: 18

Step-by-step explanation:

Multiply number of each item possible

3*2*3=18

Answer:

Step-by-step explanation:

slope intercept form is

y=mx+b

where m is the slope and b is the y-intercept.

In your equation m = 5/4 so this is your answer.

Hello.

In your question, we can see that the points Q, P, and R can be assumed that they are in a straight line, meaning that the angle measures will add up to 180 (think of half a circle, which is 360 degrees).

This means that every angle added up will add up to 180 degrees.

Meaning we can set up the below equation:

\((8b-12)+(b)+(2b+5)=180\)

\(8b-12+b+2b+5=180\)

\(11b-7=180\)

\(11b=187\)

\(b=17\)

After finding \(b\), we can plug it back in to each expression for each angle measure.

∠QPS = \(8b-12=8(17)-12=124\)

∠SPT = \(b=17\)

∠TPR = \(2b+5=2(17)+5=39\)

Hope this helps!

Answer:

x=2

Step-by-step explanation:

To solve this equation combine like terms and move all like terms to the same side. Then, isolate the variable.

First, combine like terms that are on the same side,

-10x+4=-2x-12

Next, move -10x to the other side by adding it to both sides,

4=8x-12

Then, add 12 to both sides as well,

16=8x

Finally, isolate x by dividing the whole equation by 8,

2=x

Answer:

x=2

Step-by-step explanation:

I know the answer is x=2.

First, I set up the equation.

-7x+4-3x=-2x-12

Next, I added like values on each side.

-10x+4=-2x-12

Then, I added 10x to both sides.

4=8x-12

Then, I added 12 to both sides.

16=8x

Next, I divided 8 on both sides.

2=x

To make sure 2 is the true value of x, I inserted 2 to all values of x in the equation. -7(2)+4-3(2)=-2(2)-12. Both sides of the equation are -16. So, 2 is the real value of x in this equation.

Answer:

Thirty two thousand five hundred and six

Step-by-step explanation:

Answer:

Thirty - Two Thousand Five Hundred and Six

Answer:

a) The degrees of freedom are given by:

\(df = 15\)

And the rejection region is \(t_{\alpha}<3.733\)

And the significance level would be:

\(P(t_{15} >3.733) =0.001\)

b) The degrees of freedom are given by:

\(df = 24-1=23\)

And the rejection region is \(t_{\alpha} <-2.5\)

And the significance level would be:

\(P(t_{23} <-2.5) =0.0099 \approx 0.01\)

c) The degrees of freedom are given by:

\(df = 31-1=30\)

And the rejection region is \(t_{\alpha} <-1.697\) or \(t_{\alpha} >1.697\)

And the significance level would be:

\(2*P(t_{30} <-1.697) =0.10\)

Step-by-step explanation:

Part a

We have the following system of hypothesis:

Null hypothesis: \(\mu \leq \mu_0 \)

Alternative hypothesis: \(\mu > \mu_0 \)

The degrees of freedom are given by:

\(df = 15\)

And the rejection region is \(t_{\alpha}<3.733\)

And the significance level would be:

\(P(t_{15} >3.733) =0.001\)

Part b

We have the following system of hypothesis:

Null hypothesis: \(\mu \geq \mu_0 \)

Alternative hypothesis: \(\mu < \mu_0 \)

The degrees of freedom are given by:

\(df = 24-1=23\)

And the rejection region is \(t_{\alpha} <-2.5\)

And the significance level would be:

\(P(t_{23} <-2.5) =0.0099 \approx 0.01\)

Part c

We have the following system of hypothesis:

Null hypothesis: \(\mu = \mu_0 \)

Alternative hypothesis: \(\mu \neq \mu_o\)

The degrees of freedom are given by:

\(df = 31-1=30\)

And the rejection region is \(t_{\alpha} <-1.697\) or \(t_{\alpha} >1.697\)

And the significance level would be:

\(2*P(t_{30} <-1.697) =0.10\)

Answer:

y = \(\frac{-1}{6}\)x - \(\frac{7}{3}\)

Step-by-step explanation:

1. Find the slope -3- -2 / 4 - -2  so -3+2/4+2, -1/6 so m = -1/6

2.  Find y intercept (b)   y = mx + b so -2 = -1/6(-2) + b, -2 = 1/3 + b

b = -2-1/3, b = -6/3 - 1/3, so b = -7/3

3.  Put it all together y = mx + b so y = -1/6x -7/3

Answer:

None are equal.

Step-by-step explanation:

None.

First lets find the total number of cookies

12*4=48

48 cookies

Number of cookies eaten

5*2=10

10 were eaten

Cookies left

48-10=38

38/48=19/24

19/24 of the cookies are left

Answer:

38 are left

Step-by-step explanation:

The equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute

Average speed is defined as the rate of change in distance of a body. Mathematically;

Given the distance of the runner in miles to be;

To express t in terms of the average speed s and distance of 6.2miles, we will substitute the values into the formula;

Substituting D = 6.2miles into the formula;

Cross multiply

Divide both sides by 's'

st/s = 6.2/s

t = 6.2/s

Hence, the equation that could be used to determine the time, t, it takes to run 10,000 meters as a function of the average speed, s, of the runner where t is in minutes and s in miles per minute is t = 6.2/s miles/minute

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Answer:

{x,y,z}={5,−3,3}

Step-by-step explanation:

  [1]    2x + 4y + z = 1

  [2]    x - 2y - 3z = 2

  [3]    x + y - z = -1

// Solve equation [3] for the variable  y  

 [3]    y = -x + z - 1

// Plug this in for variable  y  in equation [1]

  [1]    2x + 4•(-x +z -1) + z = 1

  [1]    -2x + 5z = 5

// Plug this in for variable  y  in equation [2]

  [2]    x - 2•(-x +z -1) - 3z = 2

  [2]    3x - 5z = 0

// Solve equation [2] for the variable  x  

 [2]    3x = 5z

 [2]    x = 5z/3

// Plug this in for variable  x  in equation [1]

  [1]    -2•(5z/3) + 5z = 5

  [1]    5z/3 = 5

  [1]    5z = 15

// Solve equation [1] for the variable  z  

  [1]    5z = 15

  [1]    z = 3

// By now we know this much :

   x = 5z/3

   y = -x+z-1

   z = 3

// Use the  z  value to solve for  x  

   x = (5/3)(3) = 5

// Use the  x  and  z  values to solve for  y  

 y = -(5)+(3)-1 = -3

Solution :

{x,y,z} = {5,-3,3}

A quadrilateral is a shape with four sides

The indicated measures are A = 56, B = 128, C = 100 and D = 76

The angles in a quadrilateral add up to 360 degrees.

So, we have:

4n + 5n + 6 + 9n + 2 + 8n - 12 = 360

Collect like terms

4n + 5n + 9n + 8n = 360 - 6 - 2 + 12

Evaluate the like terms

26n = 364

Divide through by 26

n = 14

From the figure, we have:

A = 4n

B = 9n + 2

C = 8n - 12

D = 5n + 6

So, we have:

A = 4 * 14 = 56

B = 9*14 + 2 = 128

C = 8*14 - 12 = 100

D = 5*14 + 6 = 76

Hence, the indicated measures are

A = 56, B = 128, C = 100 and D = 76

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The speed of the person in miles per hour is S = 3 mph

Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude

Speed = Distance / Time

Given data ,

Let the speed of the person in miles per hour be S

Now , the distance traveled by the person D = 1/4 miles

The time taken by the person to travel ( 1/4 ) miles = 1/12 of an hour

Now , speed of the person in miles per hour S = distance traveled by the person D / time taken by the person to travel ( 1/4 ) miles

On simplifying , we get

The speed of the person in miles per hour S = ( 1/4 ) / ( 1/12 )

The speed of the person in miles per hour S = ( 1/4 ) x 12

The speed of the person in miles per hour S = 3 miles per hour

Hence , the speed is 3 mph

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Answer: $74.75

Step-by-step explanation:

Answer:

74.75 dolors i take test

Step-by-step explanation:

The calculated bill for a person who uses 600kWh in a month is $80

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

b(x) = 0.10x, x ≤ 200

b(x) = 0.15(x - 200) + 20, x > 200

For a person that uses 600kWh per month, we make use of the function

b(x) = 0.15(x - 200) + 20

This is because it is valid for x > 200

Substitute the known values in the above equation, so, we have the following representation

b(600) = 0.15(600 - 200) + 20

Evaluate

b(600) = 80

Hence, the bill for a person who uses 600kWh in a month is $80

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Answer:

360°

Step-by-step explanation:

The sum of the exterior angles of any n-gon is 360°

Option A) is correct

There is only one solution: x = 1. The solution x = 3 is an extraneous solution.  

Solution :

Given Equations:

\(\frac{1}{x} +\frac{1}{1-x} =\frac{x-2}{y-3}\)

solving The given Equation have :

\(\frac{1}{x}+ \frac{1}{x-3} =\frac{x-2}{y-3}\)

\(\frac{2x-3}{x(x-3)} =\frac{x-2}{y-3}\)

\(2x-3=x^{2} -2x\)

\(x^{2} -4x+3=0\)

\(x^{2} -x-x3+3=0\)

\(x(x-1)-3(x-3)=0\\x-3)(x-1)=0\\x=1,x=3\)

Extraneous solutions:

Due to its exclusion from the original equation's domain, an auxiliary solution is not a root of the original equation.

We may get this conclusion, but we cannot accept it as a conclusion since it is insufficient.

However, x = 3 cannot be a solution to the preceding equation because it produces a denominator of zero when used in the provided equation.

As a result, the following equation's solution is x = 1, while its superfluous solution is x = 3.

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Answer:

DEON is awesome at swimming

Step-by-step explanation:

good job deon

Answer:

\(y = 1.67x\)

Step-by-step explanation:

Function A:

x  || 3  ||  6  ||  9  ||  12  ||  15

y  || 5  ||  10 ||  15 ||  20 || 25

See attachment for Function B

First, we need to determine the equation of function A using linear interpolation

As follows:

\(y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}\)

Take any two corresponding values of x and y to be:

\((x_1,y_1) = (3,5)\)

\((x_2,y_2) = (15,25)\)

The equation becomes:

\(y = y_1 + (x - x_1)\frac{y_2 - y_1}{x_2 - x_1}\)

\(y = 5 + (x - 3)\frac{25 - 5}{15 - 3}\)

\(y = 5 + (x - 3)\frac{20}{12}\)

\(y = 5 + (x - 3)\frac{5}{3}\)

Open bracket

\(y = 5 + \frac{5x}{3} - \frac{5*3}{3}\)

\(y = 5 + \frac{5x}{3} - 5\)

Collect Like Terms

\(y = \frac{5x}{3} - 5 + 5\)

\(y = \frac{5x}{3}\)

\(y = 1.67x\)

This function is linear and there is no need to check for function B

The value of x is 13 in the equation x+8=2x-5.

Two or more expressions with an Equal sign is called as Equation.

The given equation is x+8=2x-5

x plus eight equal to two times of x minus five.

Subtract 2x from both the sides

x+8-2x=-5

-x+8=-5

Subtract 8 on both sides

-x=-5-8

-x=-13

x=13

Hence, the value of x is 13 in the equation x+8=2x-5.

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B is a 2 by 2 matrix, and the determinant of B written as |B| is equal to -1.

We can find |B|, the determinant of the matrix B by subtracting the multiple of row column and row 2 column 1 from the multiple of row column 1 and row 2 column 2 as follows:

|B| = (-2 × -2) - (1 × 5)

|B| = 4 - 5

|B| = -1.

Therefore, the determinant of the 2 by 2 matrix B written as |B| is equal to -1.

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Answer:

Step-by-step explanation:

Volume of a cylinder is given by

\(V = \pi {r}^{2} h \\ \)

where

r is the radius

h is the height of the cylinder

From the question

r = 4 ft

h = 12 ft

π = 3.14

So we have

\(V = (3.14) ({4})^{2} (12) \\ = (3.14)(16)(12) \\ = 602.88\)

We have the final answer as

603 ft³ to the nearest whole number

Hope this helps you

Answer:

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

Explanation:

If 60% of the sample are pink salmon, then an estimate of the number of salmon in the population (aka the entire pond) is:

60% of 44 = 0.60*44 = 26.4 which rounds to 26 pink salmon

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

If 20% are yellowfin tuna, then we estimate there are 0.20*44 = 8.8 = 9 yellowfin tuna in the pond.

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

If 20% are bluegill, then we predict there are 0.20*44 = 8.8 = 9 bluegill

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

As a check:

salmon + tuna + bluegill = 26+9+9 = 44 fish total

Answer:

The answer is 1000

Step-by-step explanation:

10x10=100

100x10=1000

1000+1=1001

1001-2=999

999+1=1000

Answer:

1000

Step-by-step explanation:

10x10=100

100x10=1000

1000+1=1001

1001+1=1002

1002-2=1000.

therefore the answer is 1000

Answer:

48.37 degrees

Step-by-step explanation:

c = AB = sqrt((9-7)² + (2-7)²) = sqrt(4+25) = sqrt(29)

b = AC = sqrt((5-7)² + (3-7)²) = sqrt(4+16) = sqrt(20)

a = BC = sqrt((5-9)² + (3-2)²) = sqrt(16+1) = sqrt(17)

A = angle at A

B = angle at B

C = angle at C

cos(A) = (b²+c²-a²)/(2bc) = (20+29-17)/2sqrt(20)sqrt(29) =

= 32/48.16637832... = 0.664363839...

A = acos(0.664363839...) = 48.366461... degrees

Given:

In triangle ABC, D is incenter m∠ACB = 3x + 54 and m∠ACD = x + 31.

To find:

m∠ACD.

Solution:

We know that,

Incenter of a triangle is the intersection point of all angle bisectors.

\(\angle ACD=\angle BCD\)      ...(i)

Now,

\(\angle ACB=\angle ACD+\angle BCD\)

\(\angle ACB=\angle ACD+\angle ACD\)       [Using (i)]

\(\angle ACB=2\angle ACD\)

Substitute the values, we get

\(3x+54=2(x+31)\)

\(3x+54=2x+62\)

\(3x-2x=62-54\)

\(x=8\)

The value of x is 8.

\(m\angle ACD=x+31\)

\(m\angle ACD=8+31\)

\(m\angle ACD=39\)

Therefore, the measure of angle ACD is 39 degrees.