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The combination of  number of ways of groups of 3 customers are  19600 .

What is permutation and combination?

The number of store customer is N = 50

The number of customer that receive a special gift is r = 3

The expression for the number of possible ways to choose 3 customers is

                   = ⁿCr

                   = ⁵⁰C₃

                    = 50 * 49 * 48/3 * 2 * 1

                    = 19600

Thus, the number of ways of groups of 3 customers are  19600.

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Explanation:

We first need to find the slope

[tex](x_1,y_1) = (0,3) \text{ and } (x_2,y_2) = (4,11)\\\\m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}\\\\m = \frac{11 - 3}{4 - 0}\\\\m = \frac{8}{4}\\\\m = 2\\\\[/tex]

The y intercept is b = 3 due to the point (0,3). This is where the graph crosses the y axis. The y intercept always occurs when x = 0.

Since m = 2 and b = 3, we go from y = mx+b to y = 2x+3

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

Check:

I'll let you do these steps.

Another way to verify is to use graphing tools like GeoGebra, Desmos, or a TI83/TI84 graphing calculator.

⇒ Rounding off to the nearest 10 we look at the unit

⇒ for 0-4 we round down, and for  5-9 we round up.

⇒In this case the unit is 5, this means we will round up, the number in the tenth place will be affected.

∴ The answer is 1580

⇒Note 7 was rounded up to 8 due to the 5 in the unit place.

Any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the corresponding positive numbers are the negative numbers.

Here,

The n subsequent integers from -(n-1)/2 to (n+1)/2 have a sum of 0 if n is an odd number. Sum n is produced by translating the interval to the right by 1. Each positive sum is therefore a positive multiple of n.

If n is even, the sum of the next n even integers from -n/2-1 to +n/2 is n/2. Sum n+n/2 is produced by moving the interval to the right by 1. As a result, every positive sum is an odd multiple of n/2.

Therefore, any positive integer n that meets the three requirements is a multiple of 9 and 11, as well as an odd multiple of 5. Lcm(5,9,11)=5911=495 is the smallest such n.

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Answer:

Step-by-step explanation:

x=4

15-7=8

8/2=4

Answer: 2(4) + 7 = 15

Step-by-step explanation:

2 + 7 only equals 9

2 * 4 = 8

8 + 7 = 15

So x would be 4

The Equivalent equation using the Subtraction Property of Equality is y = 2.

If we have an expression as ( a + b ) = c

Then as per subtraction property of equality [ (a + b ) - b = c - b ]

Here given 9y = 4y + 10

Simplifying this equation, we get

⇒9y - 4y = 10

⇒( 9 - 4 )y = 10

⇒5y = 10

therefore, y = ( 10 ÷ 5 )

⇒y = 2

Therefore the equivalent equation is y = 2.

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A. The equations are given as follows:

B. The solutions are given as follows: x = 11, y = -5.

C. The angles are given as follows:

The two parallel lines, p and q, are cut by the transversal line, hence angles 2 and 3 are supplementary angles, and thus:

x - 9y + 1 + 11x + 2 = 180

12x - 9y = 177.

Angles 1 and 2 are alternate interior angles, meaning that they are congruent, hence:

6x + y - 4 = x - 9y + 1.

5x + 10y = 5.

x + 2y = 1.

x = 1 - 2y.

Replacing in the first equation, the value of y is given by:

12(1 - 2y) - 9y = 177

33y = -165

y = -165/33

y = -5.

Then the value of x is of:

x = 1 - 2y = 1 + 10 = 11.

The angle measures are given as follows:

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Answer:

B

Step-by-step explanation:

[tex] {x}^{6} \times {x}^{2} = {x}^{6 + 2} = {x}^{8} [/tex]

The volume of the cube with the given side length is 64x⁶ + 144x⁴ + 108x² + 27 , the correct option is (a) .

The Volume of the cube with side length "a" is given by the formula

Volume = a³ .

In the question ,

it is given that ,

the length of the side (s) of the cube is 4x² + 3 .

By using the formula for Volume of the cube ,

we get

Volume = (4x² + 3)³

using the identity (a + b)³ = a³ + b³ + 3a²b + 3ab²

we get ,

Volume = (4x²)³ + 3³ + 3*(4x)²*(3) + 3*4x*3²

Simplifying further ,

we get

= 64x⁶ + 27 + 9*16x⁴ + 27*4x²

= 64x⁶ + 27 + 144x⁴ + 108x²

= 64x⁶ + 144x⁴ +  108x² + 27

Therefore , The volume of the cube with the given side length is 64x⁶ + 144x⁴ + 108x² + 27 .

The given question is incomplete , the complete question is

The side length s , of a cube is 4x² + 3 . If V = s³ , what is the Volume of the cube ?

(a) 64x⁶ + 144x⁴ + 108x² + 27

(b) 64x⁶ + 48x⁴ + 12x² + 1

(c) 4x⁶ + 36x⁴ + 108x² + 27

(d) 4x⁶ + 12x⁴ +12x² + 1

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Answer:

Okay so for the first box the answer is, 116.85.

The second box is, 2,133.15

For the third box, 141

And the fourth and final box is, 2,109

Step-by-step explanation:

I really hope this helps!!

Answer:

38%

Step-by-step explanation:

[tex]\frac{1178}{3100}[/tex] x 100

Answer:

D

Step-by-step explanation:

if x = 0 or x = 3 the function doesn’t exist

If x = 1  Y = 0

The exponential function indicated will increase by 9.2%.

Given that,

y = 210(1. 092)^x

To find,

Determine the change's percentage rate of rise or reduction and decide if it shows growth or decay.

We have,

y = 210(1. 092)^x

Since the growth factor exceeds 1, the equation reflects exponential growth.

The general form equation is:

y(x)= a(1-r)^x such that r represents the growth rate.

1+r =1. 092

r = 0. 092= 9.2%

As a result, the exponential function will grow by 9.2%.

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Answer:

12

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

x=12

Step-by-step explanation:

x/6=2

x=(2)(6),

x=12

The measure of the angle coterminal to - 118° is equal to 242°. (Correct choice: A)

Two angles are coterminal when they have different measures and the same direction in the terminal side. Two consecutive coterminal angles differ their measures in 360°. Then, we can determine the value of the coterminal angle by using the following formula:

θ' = θ + 360°

Where:

If we know that θ = - 118°, then the coterminal angle between 0° and 360° is:

θ' = - 118° + 360°

θ' = 242°

The measure of the coterminal angle is 242°.

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Yes the acceptable move  that proves the two equation are equivalent.

What is equivalent equation?

Equivalent equation are algebraic equations that have identical solutions or roots. Adding or substracting the same number or expression to both side of an equation produce an equivalent equation.

Sol-

By observing both equation.

In equation A : -3(x+9)=18

Divide the equation A by -3

=> (x+9)=-6

And this result equals to equation B

Hence both equation are equivalent

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Answer: the answer is P (n,r)

To use the delta method to approximate the standard error for the square root of the sample average g, we first need to calculate the sample average g.

A variation from precision or correctness is called an error. An error, then, is a mistake or a failure to perform an action appropriately. Errors can take place  person commits a calculation error, an equipment breaks down, or a person interprets information incorrectly.

Various factors might lead to errors. For instance, a person may make a mathematical error because they misunderstood the problem or made an error when doing the computation. A machine may break down due to a design error, normal wear and tear, or an outside event like a power loss. A person's prejudice may cause them to interpret information incorrectly.

How to solve?

This can be done by summing all the values in the sample and dividing by the total number of values in the sample. Next, we need to find the derivative of the function that describes the square root of the sample average g. This derivative will be used to approximate the standard error. To find the standard error, we then multiply the derivative by the standard deviation of the sample average g. This will give us an approximation of the standard error for the square root of the sample average g. It is important to note that this approximation will only be accurate if the sample is normally distributed and the sample size is large. Additionally, the delta method is only one way to approximate the standard error, and other methods may be more appropriate in certain situations.

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Answer:

direct variation for both, 0.5x and -2.5x

Step-by-step explanation:

what you have is correct. it is linear lines on both plots and tables. and your equations are also correct because for example, -6 times -2.5 is equal to 15.

Answer:

y = 1/2x + 4

Step-by-step explanation:

slope-intercept form is: y = mx + b

- x and y are coordinates; if you plug the coordinates into your equation, you should receive a solution.

- m is the slope itself. this can be figured out by calculating the rise/run. look at the point (0,4). the line goes up by one, and right by two. therefore, the slope is 1/2. the line is also going up, so therefore it is a positively sloped line.

- b is the y-intercept, or where the line crosses the y-axis. in this specific example, the line crosses the y-axis at the point (0,4), and therefore the b would be + 4.

so when you put everything together and plug the m and the b into the slope formula, you get y = 1/2x + 4.

hope this helped!<3

Answer: x=-1

Step-by-step explanation:

1. -4(3x-7)=40

2. -12x+28=40

3. -12x=12

4. x=-1

The equation that could be used to find the length of the sign's base is 200 = 1*b(2b)/2 and the length of the sign's base is 10√2 feet..

According to the question,

We have the following information:

The sign will be in the shape of the store's logo: an isosceles triangle with a height that's double the length of its base.

Area of the sign is approximately 200 square feet.

Let's take the base of the triangle to be b feet.

Height of triangle = 2b

Now, we know that the following formula is used to find the area of triangle:

Area = 1/2 * base*height

200 = b*(2b)/2

[tex]2b^{2} /2 = 200[/tex]

[tex]b^{2} = 200\\[/tex]

b = 10√2 feet

Hence, the equation that could be used to find the length of the sign's base is 200 = 1*b(2b)/2 and the length of the sign's base is 10√2 feet.

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The required inequality is x ≥ 94.

What is average?

The middle number, which is determined by dividing the sum of all the numbers by the total number of numbers, is the average value in mathematics. When determining the average for a set of data, we add up all the values and divide this sum by the total number of values.

Add the scores with x and equate them to (82 times 4) as shown:

76 + 80 + 78 + x = (82 times 4)

234 + x = 328

Find x

x = 94

She needs x on the next exam so that her average is at least 82.

So, inequality is x ≥ 94.

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By using the concept of Pythagoras Theorem, the result obtained is

Distance between their tops is 13 ft.

What is Pythagoras Theorem?

Pythagoras Theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of perpendicular and base.

The figure has been attached

Let the poles be represented by CD and AE and let AC represents the distance between their tops

Construction

A line from C parallel to DE (shown by a dotted line) is drawn

CD = 10 ft.

AE = 15 ft.

BE = 10 ft.

AB = AE - BE

     = 15 - 10

     = 5 ft.

DE = 12 ft.

BC = 12 ft.

[tex]\angle AED = 90^{\circ}[/tex] [ Angle between pole and ground is 90°]

[tex]\angle ABC = 90^{\circ}[/tex] [ Corrosponding angles are equal]

By Pythagoras Theorem,

[tex]AC^2 = AB^2+BC^2\\AC^2 = 5^2 + 12^2\\AC^2 = 25 + 144\\AC^2 = 169\\AC =\sqrt{169}\\[/tex]

AC = 13 ft.

Distance between their tops is 13 ft.

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The Pythagorean Theorem could be represented mathematically as follows, Here, c represents the length of the hypotenuse (the longest side), or b or a are the lengths of the other 2 sides. From the equation, you can easily find the value of the 1 side if you have the values of the other 2

1) a2 = h2 + x2

Pythagorean theorem

2) h2 = a2 - x2

Rearrange the previous statement

3) c2 = h2 + (b-x)2

Pythagorean theorem

4) c2 = h2 + b2 -2bx + x2

Expand (b – x)2

What made Pythagoras think of the Pythagorean theorem?

   The number 1 : the number of reason.

   The number 2: the first even and female number, the number of opinion.

   The number 3: the first true male number, the number of harmony.

   The number 4: the number of justice or retribution.

   The number 5: marriage.

   The number 6: creation

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It will take 2.5 hours to make 32 1/2 cups of juice, in the fraction mode.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

Cye-Na is starting a juice stand. It takes her 15 minutes to prepare 3 1/4 cups of juice.

So in 15 minutes, she makes 13/4 cups of juice.

So for 1 cup she will take 15/ (13/4) minutes.

For 32 1/2 cup she will take 15 * (65/2)/ (13/4)

= 15*65*4/ 2*13

= 150 minutes.

Which is 2.5 hours

Hence, It will take 2.5 hours to make 32 1/2 cups of juice.

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