Building Bonds puts on team-building events. The company charges a base rate of $45 per event, plus $7.50 per participant. Write an equation showing how the cost of an event, y, depends on the number of participants, x.

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Answer

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Hint: We will write the first ten odd natural numbers and then add them to find their sum. We will then substitute the values in the formula of arithmetic mean , a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.

Complete step-by-step answer:

We have to find the arithmetic mean of first ten odd natural numbers .

Natural numbers are counting numbers and starts from 1.

Odd numbers are not multiples of 2.

The first ten odd natural numbers are 1,3,5,7,9,11,13,15,17,19.

Arithmetic mean is calculated by adding all the observations by the total number of observations.

Arithmetic mean is given by a1+a2...+ann, where n is the number of terms and a1,a2,..an are n observations.

Therefore, we will calculate the sum of the first ten odd natural numbers.

⇒1+3+5+7+9+11+13+15+17+19⇒100

Now, we will divide this by 10 as there are a total 10 numbers.

10010=10

Hence, the arithmetic mean of first ten odd natural numbers is 10.

Note: Arithmetic mean is also known as average or simply mean. Odd numbers are not divisible by 2. The sum of n odd natural numbers is also given by n2

Answer:

[tex]2.\bar{81}mm[/tex]

Step-by-step explanation:

First the formula for find the are of a trapezoid is:

[tex]A = \frac{h(a+b)}{2}[/tex]

Where [tex]a[/tex] is the top, [tex]h[/tex] the height and [tex]b[/tex] the base measures.

Then we need to know what is the base ([tex]b[/tex]), for that isolate [tex]b[/tex] from the equation

[tex]2A = h(a+b)\\\frac{2A}{h} = a+b\\\frac{2A}{h} - a = b[/tex]

Then in the new equation replace the given values:

[tex]A = 65mm^2\\a = 9mm\\h = 11mm[/tex]

[tex]\frac{2 \cdot 65mm^2}{11mm} -9mm = b\\\frac{130mm^2}{11mm} -9mm = b\\11.\bar{81}mm -9mm = b\\2.\bar{81}mm = b[/tex]

So the final answer is [tex]2.\bar{81}mm[/tex]

Answer:

It is a horizontal line through y-coordinate 6.

Step-by-step explanation:

Because 10*3/5=6.

Answer:

The slope is: (y1 - y2)/(x1 - x2) = [(-1) - (-10)] / [0 - 3] = 9/-3 = -3. So the slope is -3. To plug the values into the point slope form

Step-by-step explanation:

For this, you are just looking for x and y coordinates

Answer:

letter D

Step-by-step explanation:

it's my guess I think it's correct

Answer:

Step-by-step explanation:

y - 4 = -2(x - 6)          It might be easier to do if we removed the brackets and collect like terms.

y - 4 = -2x + 12          Add 4 to both sides

y = - 2x + 4 + 12        Combine

y = - 2x + 16

It's not one because -6*-2 + 16 = 28 for y.

It's B

y = -2 * 6 + 16

y = - 12 + 16

y = 4

(6,4) is the answer.

c: doesn't appear to be right. Any minus sign is going to make the number in front of x  + which only adds to 16 making bigger.

d: -2*4 + 16 = - 8 + 16 = 8 which is incorrect. The answer should by 6 not 8

Answer:

-4x + 2

Step-by-step explanation:

The outputs are decreasing by 4, so -4 is the slope, the coefficient for x.

The y- intercept is 2 because when x is zero, y is 2. You can find the y-intercept by adding 4 to -2, the output for when x is 1.

Answer:

y = -4x + 2

Step-by-step explanation:

First find the slope using this equation ....

y2 - y1/x2 - x2 =

plug in two ordered pairs (doesn't matter which one) ....

-2 - (-6)/1 - 2 =

-2 + 6/-1 =

4/-1 = -4

The slope is -4. The next blank is the y-intercept (0,y) ....

y = -4x + b

plug in any ordered pair ....

-2 = -4(1) + b

-2 = -4 + b

+4   +4

2 = b

Put it all together ....

y = -4x + 2

Answer:

It is 0.6 miles

Step-by-step explanation:

Answer:

The answer is A (-2)^3 * 6^3

Answer:

g(x)o(x) = -6x²-4x+16

Answer:

91°

Step-by-step explanation:

The angles are consecutive interior angles (CIA) which add up to 180°.

180 - 89 = 91

Answer: $2

Step-by-step explanation:

just do 4 divided by 2 and your answer is 2

Answer:

$2 for 1 Amy's Organic Soup

Step-by-step explanation:

Since 2 of Amy's Organic Soup is = $4

Divide to find the Unit Rate for the cost of 1 soup.

Let x = Cost of Amy's Organic Soup

$4 = 2x

$4/2 = 2x/2

$2 = x

Answer:

The student is correct.

Step-by-step explanation:

Given that 5x² = 20:

It is true that the value of x = 2 because 2² = 4, and when you multiply 4 with 5, you'll get a product of 20:

5x² = 20

5(2)² = 20

5(4) = 20

20 = 20

Therefore, the student is correct that x = 2.

Answer:52

Step-by-step explanation:.

By using the concept of the point-slope form of an equation,

The initial number of party favor bags Razi had to fill would be 52.

In this situation, the independent variable (x) is the amount of time in minutes.  

The dependent variable (y) is the number of bags remaining.

Since he is working at a constant rate, this makes it a linear function.  

In a linear function, the amount he had to fill, to begin with, is the y-intercept.  

Since The point-slope form of the equation is,

y - y₁ = m(x - x₁)

First, we find the slope using the formula

m = (y₂-y₁)/(x₂-x₁)

m = (32-36)/(5-4)

m = -4/1

m = -4

Using this and the first point, we have

y - 36 = - 4(x - 4)

Using the distributive property, we have

y - 36 = -4(x)- 4(-4)

y - 36 = -4x--16

y - 36 = -4x + 16

Add 36 to each side:

y - 36 + 36 = -4x + 16 + 36

y = -4x + 52

So, for the initial number of party favor bags Razi had to fill;

Substitute x = 0;

y = - 4 (0)+ 52

y = 52

Hence,

The required initial number is 52.

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The missing table in the question is attached below.

Answer:

y=4

Step-by-step explanation:

84=30y-9y, first you collect like terms.

84=21y, swap the sides

21y=84, devide both sides and you get y =4

Answer:

4(7+6)

Step-by-step explanation:

first find GCF

prime factorize

28= 2*2*7 24=2*2*2*3

only common factor is 2

there are at least 2 2s in each

apply

4(7+6)

Answer:

6$

Step-by-step explanation:

2+4=6

20%+40%=60%

The new price after the increase is $2.8 .

Percentage increase is the difference between the final value and the initial value, expressed in the form of a percentage. In other words, it is the difference between the final value and the initial value which is divided by the initial value and then multiplied by 100.

According to the question

The price of chocolate bar = $2

The price of a particular chocolate bar is increased by 40%,

i.e

The percent increase in the price of chocolate bar = 40%

Now,

increase prize :

= [tex]2*\frac{40}{100}[/tex]

= $0.8  

The new price after the increase

= $2.8

Hence, the new price after the increase is $2.8 .

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Answer:

7. The area should be 32. Multiply 5 by 4 to get 20. Find the missing length to multiply by 3, which is 4, and multiply. 3 * 4 = 12. Add 20 + 12 and get 32 cm.

8. The area should be 70. You did pretty well, but when finding the area of a triangle, divide the product by 2, or multiply by 0.5. 5 * 8 = 40/2 or 40 * 0.5 which both equal 20. 50, plus the area of the triangle, 20, will get you 70.

Answer:

x = -5

Step-by-step explanation:

f(x) = [tex]\frac{x+5}{4}[/tex]

Okay, so in order to find the zeroes of the equation, we need to find the values of x for which f(x) = 0.

[tex]\frac{x+5}{4}[/tex] = 0

We can start by multiplying both sides by 4.  Anything multiplied by 0 equals 0, so we have the following:

x + 5 = 0

Now, subtracting 5 from both sides in order to isolate x, we have:

x = -5

To check our work, let's substitute -5 into our equation:

f(-5) = [tex]\frac{-5+5}{4}[/tex] = [tex]\frac{0}{4}[/tex]

0 divided by anything equals 0, so f(-5) = 0.

Answer:

  a) interior angle: 156°

  b) exterior angle: 24°

Step-by-step explanation:

The sum of the exterior angles of a convex polygon is 360°. Then the exterior angle of a regular 15-gon will be ...

  360°/15 = 24°

__

The interior angle of a convex polygon is the supplement of the exterior angle at that vertex. For an exterior angle of 24°, a regular 15-gon will have an interior angle of ...

  180° -24° = 156°

_____

Additional comment

We find it easier to work this problem by finding the exterior angle first. Note that the results only apply to a 15-gon in which all interior angles are congruent.

Answer:

x=23

Step-by-step explanation:

3x+4x+19=180 is the equation you would set up because the two angles added up would be 180 degrees.

:))

Answer:

5/8

Step-by-step explanation:

the answer is 5/8 hope you get answer right.

Answer:

45

Step-by-step explanation:

-5(-12)+(-15)

--> Multiply -5 and -12 to get 60

60-15

--> Subtract 15 from 60 to get 45

Hope this helps you!

Answer:

12

Step-by-step explanation:

There is a right angle formed, hence this triangle is a right-angled triangle.

Using Pythagoras Theorem,

[tex]a^2+b^2=c^2[/tex]

[tex]16^2+b^2=20^2[/tex]

[tex]256+b^2=400[/tex]

[tex]b^2=400-256=144[/tex]

[tex]b=12[/tex]

The missing length is 12

Answer:

m = 8

Step-by-step explanation:

2m + m = 24 ( collect like terms on left side )

3m = 24 ( divide both sides by 3 )

m = 8

Answer:

m = 8

Step-by-step explanation:

2m + m = 24

3m = 24

(3m)/3 = (24/3)

m = 8

Check:

2*8 + 8 = 24

16 + 8 = 24

Answer:

[tex]6.56\times10^{-7}[/tex]

Step-by-step explanation:

[tex]1nm[/tex] is equal to [tex]1\times 10^{-9}m[/tex] so you have the next relation

[tex]\frac{1nm}{1\times 10^{-9}m} = \frac{656nm}{x}[/tex]

Then isolating [tex]x[/tex] you have

[tex]x = \frac{6.56\times 10^{2}nm \cdot 1\times 10^{-9}m}{1nm} = 6.56\times 10^{-7}m[/tex]