10C5 use the formula for nCr to evaluate given expression.




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The average value of function can be calculated using the formula →

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex] and to find average rate of change of function can be calculated using → f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

We have a function (say f(x)).

We have to find the average value of a function and the average rate of change of function.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

PART - A → Finding the Average value of a function.

The average (or the mean) value of f (x) on [a, b] is defined by -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

PART - B → Finding the Average Rate of Change of a function.

The average rate of change of function f(x) is found out as follows -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex]

Hence, to find the average value of function -

[tex]$f(avg) =\frac{1}{b-a} \int\limits^a_b {f(x)} \, dx[/tex]

and to find average rate of change of function -

f '(x) =  [tex]$\frac{f(b)-f(a)}{b-a}[/tex].

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The company which has the absolute advantage when it comes to producing phones is: a. Gonzalez and Bros. Inc.

A comparative advantage can be defined as the ability of a business firm or country to produce goods and services at a lower opportunity cost than their rivals (competitors) or trade partners.

An absolute advantage can be defined as a measure of the ability of an individual or a business firm (manufacturer) to perform a specific economic activity such as the production of goods and services, more efficiently than another individual or business firm.

In this scenario, we can reasonably infer and logically deduce that the company which has the absolute advantage when it comes to producing phones is Gonzalez and Bros. Inc because it can produce 300 phones in comparison with the G company Inc.

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Answer: 24

Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

From the question, we are to solve the given system of linear equations

The given system of linear equation is

x + 2y -  z = 2       ----------- (1)

2x - 7y + 5z = 3    ----------- (2)

-4x + y + 2z = 4    ----------- (3)

From equations (1) and (2), eliminate z

5 × ( x + 2y -  z = 2      

1 × ( 2x - 7y + 5z = 3

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

5x + 10y -5z = 10

2x -7y + 5z = 3

Add the resulting equations

7x + 3y = 13 ----------- (4)

From equations (2) and (3), eliminate z

2 × ( 2x - 7y + 5z = 3    

5 × ( -4x + y + 2z = 4  

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

4x - 14y + 10z = 6

-20x + 5y + 10z = 20

Subtract the resulting equations

24x - 19y = -14 ---------- (5)

Now, solve equations (4) and (5) simultaneously

7x + 3y = 13

24x - 19y = -14

Eliminate y
19 × ( 7x + 3y = 13

3 × ( 24x - 19y = -14

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

133x + 57y = 247

72x - 57y = -42

Add the resulting equations

205x = 205

x = 205/205

x = 1

Substitute the value of x into equation (4)

7x + 3y = 13

7(1) + 3y = 13

7 + 3y = 13

3y = 13 - 7

3y = 6

c = 6/3

y = 2

Substitute the values of x and y into equation (1)

x + 2y -  z = 2

1 + 2(2) - z = 2

1 + 4 - z = 2

1 + 4 - 2 = z

3 = z

z =3

The solution to the given equation is x = 1, y = 2, z = 3. That is (1, 2, 3)

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The dimensions of the photograph are the length= 14 in  and the width= 5 in.

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.

A rectangle is a geometric figure that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).

The area of a rectangle is given by the multiplication between the base and the height.

The question gives:

Thenm

A= b * h

70 = (9 +w) * w

70= 9w +w²

w²+9w-70=0

[tex]w_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \left(-70\right)}}{2\cdot \:1}\\ \\ w_{1,\:2}=\frac{-9\pm \:19}{2\cdot \:1}[/tex]

Thus,  [tex]w_{1}=\frac{-9-\:19}{2\cdot \:1}=\frac{-28}{2}=-14[/tex] and [tex]w_{2}=\frac{-9+\:19}{2\cdot \:1}=\frac{10}{2}=5[/tex]

The dimensions should have positive values, then w=5.

If w=5, the length will be 5+9 = 14. With these dimensions, the area will be 14 * 5 = 70.

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Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

To determine if the ball will ever reach a hgeight of 30 ft, we need to determine the maximum height of the ball.

Using the equation of motion, v² = u² - 2gh where

So, making h subject of the formula, we have

h = (v² - u²)/-2g

Substituting the values of the variables into the equation, we have

h = (v² - u²)/-2g

h = ((0 ft/s)² - (40 ft/s)²)/-(2 × 32 ft/s²)

h = (0 ft²/s² - 1600 ft²/s²)/-(64 ft/s²)

h = - 1600 ft²/s²/-64 ft/s²

h = 25 ft

Since the ball is released from a height of 3 ft, its maximum height above the ground is H = 3 ft + h

= 3f + 25 ft

= 28 ft

So, we see that H = 28 ft < 30 ft.

Since the maximum height of the ball above the ground is 28 ft, the ball will never reach a height of 30 ft.

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Answer:you need to show the options at the bottom

Step-by-step explanation:

The slope of the line for which the line passes through the points (6, -5) and (-6, -5) is zero .

We have given two points  (6, -5) and (-6, -5) .

Using slope formula , we get

            m = - 5 - (-5) / - 6 - 6

            m = - 5 + 5 / -12

             m = 0 / 12

             m = 0

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The equation of the ellipse in standard form is equal to (y + 8)² / 25 + (x - 3)² / 16 = 1. (Correct choice: D)

In this problem we find the case of an ellipse whose center is located at a point distinct of the origin and whose major semiaxis is parallel to the y-axis. The standard form of the equation of the ellipse is:

(y - k)² / a² + (x - h)² / b² = 1

Where:

First, determine the coordinates of the center:

(h, k) = 0.5 · (3, - 3) + 0.5 · (3, - 13)

(h, k) = (3, - 8)

Second, calculate the length of the minor semiaxis:

a = 0.5 · [- 3 - (- 13)]

a = 5

c = 0.5 · [- 5 - (- 11)]

c = 3

b = √(a² - c²)

b = 4

Third, substitute all the parameters in the standard formula:

(y + 8)² / 25 + (x - 3)² / 16 = 1

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Using the z-distribution, it is found that since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.

At the null hypothesis, it is tested if the machine is calibrated correctly, that is, the mean is of 4 cm, hence:

[tex]H_0: \mu = 4[/tex]

At the alternative hypothesis, it is tested if the machine is not calibrated correctly, that is, the mean is different of 4 cm, hence:

[tex]H_1: \mu \neq 4[/tex]

The test statistic is:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

For this problem, the parameters are given as follows:

[tex]\overline{x} = 3.97, \mu = 4, \sigma = 0.14, n = 81[/tex]

Hence the test statistic is given by:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{3.97 - 4}{\frac{0.14}{\sqrt{81}}}[/tex]

z = -1.93.

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance value of 0.01, hence, using a z-distribution calculator, the critical value is given by:

|z| = 2.575 -> z < -2.575 or z > 2.575.

Hence:

Since the test statistic is less than the critical value, there is not enough evidence that the manufacturer needs to recalibrate the machines.

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Answer:

C

Step-by-step explanation:

For this problem you use the distributive property

the first expression should match the second

Answer:

Step-by-step explanation:

Because in your previous question the scale factor was 1:30 you would simply multiple 5 by 30 to get 150 inches

Using linear functions, it is found that 5 toppings would make the cost the same for all pizza.

A linear function is modeled by:

y = mx + b

In which:

For this problem, we have that:

Hence the cost functions are given as follows:

The costs will be the same when:

A(x) = B(x)

10 + 1.5x = 12.5 + x

0.5x = 2.5

x = 2.5/0.5

x = 5.

5 toppings would make the cost the same for all pizza.

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Answer:

a = 1

b = 5

Step-by-step explanation:

a + 2b = 11

(a - b = -4) × 2

2a - 2b = -8

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

a + 2b = 11

2a - 2b = -8

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

3a = 3

÷3   ÷3

-----------

a = 1

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

a - b = -4

1 - b = -4

-1         -1

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

-b = -5

÷-1   ÷-1

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

b = 5

I hope this helps!

The games that can be played for about places to cost the same is 3 games.

Let the number of games be represented by b.

The event charges $3 for bowling shoe rental and $10 per bowling. This can be represented as:

= 3 + 10b

MaxBowl charges $6 to run bowling shoes and $9 per bowling game. This will be:

= 6 + 9b

We will equate them together:

3 + 10b = 6 + 9b

Collect like terms

10b - 9b = 6 - 3

b = 3

Therefore, the games that can be played for about places to cost the same is 3 games.

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The Slope is [tex]\frac{4}{-5}[/tex].

    m = change in y/change in x = Δy/Δx

        = (y2 – y1)/(x2 – x1)

    Where “m” is the slope of a line.

As a result, using the formula above, we can quickly determine the slope of a line connecting two points.

Given points are (-5,6),(-10,10)​.

⇒ m = Δy / Δx

    = [tex]\frac{10 - 6}{-10 - (-5)}[/tex]

   = [tex]\frac{4}{-5}[/tex]

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Answer:

The total cost of the laptop including tax will be $952.43.

Step-by-step explanation:

885.98 x 7.5%= $66.45

885.98 + 66.45= $952.43

Hope this helps!

The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.

It should be noted that from the information, tje sophomore class is making blakets for the local animal shelter and the cost to make the blakets can be modeled by 0.2x² + 7.2x + 78.

Therefore, the number of blankets the sophomore class can make if they have $663 to spend on supplies will be illustrated as:

C = 0.2x² + 7.2x + 78.

0.2x² + 7.2x + 78 = 663

0.2x² + 7.2x = 663 - 78

0.2x² + 7.2x - 585 = 0

Using almighty formula, it should be noted that x will be 69.

The number of blankets the sophomore class can make if they have $663 to spend on supplies will be 69.

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Answer:

A

Step-by-step explanation:

Answer: A. 18

Step-by-step explanation:

Let the smallest number be x

Hence,

x+(x+2)+(x+4)+(x+6)=60

x+x+2+x+4+x+6=60

4x+12=60

4x+12-12=60-12

4x=48

Divide both parts of the equation by 4:

x=12

x+6=

12+6=

18

Yes, ∠2 and ∠3 are postulate or theorem that proves the condition is identified as supplementary.

∠1 and ∠2 are supplementary (Linear Pair Theorem)

m∠1 + m∠2 = 180◦ (Definition of supplementary ∠s)

∠1 ≈ ∠3 (Given)

m∠1 = m∠3 (Definition of ≈)

m∠3 + m∠2 = 180◦( Subst . prop . of ≈)

∠2 and ∠3 are supplements (Definition of supplementary ∠s)

An unsubstantiated claim that is assumed to be true is referred to as a postulate. A provable true assertion is referred to as a theorem. A line has at least two points, according to postulate 1. A plane has at least three noncollinear points, according to postulate 2.

Hence, postulate or theorem that proves j∥k and also ∠2 and ∠3 are supplementary.

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Using the weighted mean, it is found that Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

The complete problem is given as follows:

"Trent earns scores of 62, 86, and 80 on three chapter tests for a certain class.

His homework grade is 68 and his grade for a class project is 64.

The overall average for the course is computed as follows: the average of the three chapter tests makes up 50% of the course grade; homework accounts for 10% of the course grade; the project accounts for 20% of the course grade and the final exam accounts for 20% of the course grade.

What range of scores can Trent earn on the final exam to pass the course if he needs a "C" or better?

A "C" or better requires an overall course score of 70 or better, and 100 is the highest score that can be earned on the final exam."

The weighted mean is given by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.

For this problem, we have that:

Hence his weighted mean is given by:

76 x 0.5 + 68 x 0.1 + 64 x 0.2 + 0.2x = 57.6 + 0.2x.

For a grade C, he needs a score of at least 70, hence:

57.6 + 0.2x ≥ 70.

0.2x ≥ 12.4

x ≥ 12.4/0.2

x ≥ 62.

Hence Trent can earn scores of at least 62 on the final exam to pass the course if he needs a "C" or better.

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Answer:

28

Step-by-step explanation:

[tex]4(3)^{2}+2(-5)-(-2)=36-10+2= 28[/tex]

Hope this helps

if its solve then we can do it like above

Answer:

[tex]\frac{1}{2}[/tex] hour later

Step-by-step explanation:

Since Mr.A has already traveled 25 miles there are 53 miles left to person B's house. In half an hour, Mr. A will have traveled 25 miles, while person b will have traveled 28. 25 + 28 = 53.

The coordinates of G after it is reflected over the x-axis are (4, -3)

The graph represents the given parameter

On the graph, we have the following point

G = (4, 3)

The rule of reflection across the x-axis is

(x, y) = (x, -y)

This means that

G' = (x, -y)

So, we have

G' = (4, -3)

Hence, the coordinates of G after it is reflected over the x-axis are (4, -3)

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The number 1/2 is a rational number and the number 9/3 is an integer rational number.

They are referred to as rational numbers if the value of a numerical expression terminates, in which case they are a rational number, and as irrational numbers if the value of the expression does not terminate.

The numbers are given below.

1/2 and 9/3

The fraction numbers are converted into decimal numbers. Then we have

1/2 = 0.5

9/3 = 3

The number 1/2 is a rational number and the number 9/3 is an integer rational number.

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Perimeter of the parallelogram = 210 in.

Area of parallelogram = 2,484 in.²

Perimeter of parallelogram = 2(a + b), where a and b are its sides.

Area of parallelogram = (b)(h), where h is its height and b is the length of one of its bases.

Given:

a = 51 in.

b = 54 in.

h = 46 in.

Perimeter of the parallelogram = 2(54 + 51) = 210 in.

Area of parallelogram = (b)(h) = (54)(46) = 2,484 in.²

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