A server at a restaurant is hoping for a 15% tip from a large party. The
party's bill at the end of the night was $312.00. Write a proportion and
describe how you would solve it to calculate the amount of the tip the
server hopes to receive. Be sure to state your final answer as an amount of
money, rounded to the nearest cent.
*Use the "/" on your keyboard as a fraction bar for ratios when writing the
proportion. For example: I can show that one-half and two-fourths are
proportional by typing "1/2 = 2/4" for the proportion.

The equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

The first point = (3, 5)

The second point = (8, 10)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (10-5) / (8-3)
= 5 /5

= 1

The point slope form is

[tex]y-y_1=m(x-x_1)[/tex]

Where m is the slope of the line

Consider the point (3, 5)

Substitute the values in the equation

y-5 = 1(x-3)

Hence, the equation of the line passing through the points (3, 5) and (8, 10) is y - 5 = 1(x - 3)

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The amount of cell taxes on finn’s purchase is $5.94.

Since Finn wants to buy a sweater for $29.50 and jeans for $42.50, the total cost will be:

= $29.50 + $42.50

= $72

If the sales tax rate is 8.25%, the amount on tax will be:

= Tax rate × Total cost

= 8.25% × $72

= $5.94

The tax is $5.94.

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The measure of angle EBF is  80° .

In the question ,

it is given that ,

point A, B and C lie on a straight line .

and G , B and F lie on a different straight line .

angle GBA = 24° so ,

GBA + GBC = 180°   ...because linear pair

So , GBC = 180 - 24 = 156°

angle CBF = 24°          ......because vertically opposite angles are equal .

from the figure , we see that angle GBC and angle ABF are vertically opposite angles , so ,

156° = ABE + EBF         .....(1)

Since the line AC and DF are parallel and BE is the transversal

So  , angle DEB + angle ABE = 180°

104° + ABE = 180°

ABE = 180-104

ABE = 76°

Substituting ABE = 76° in the equation (1) ,

we get ,

156 = 76+ EBF

EBF = 156 - 76

EBF = 80°

Therefore , The measure of angle EBF is  80° .

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The equation that describing how x and y are related is y = 2x + 7

From the given table we have to choose two points

The first point = (1, 9)

The second point = (2, 11)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the values in the equation

The slope of the line = (11-9) / 2 - 1

= 2 / 1

= 2

From the table

At x = 0 the value of y = 7

Therefore the y intercept = 7

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Then,

y = 2x + 7

Hence, the equation that describing how x and y are related is y = 2x + 7

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For the given expression √3, its index form is written as ( 3 )¹/² .

As given in the question,

Given expression is equal to :

√3

Standard form of writing expression in index form is given by:

√  ( square root ) will express the value in index form as 1 / 2 in the exponent.

√x = ( x ) ¹/²

Here x = 3 substitute the value of x in the standard way of index form we have:

Index form of the given expression is written as :

√3

= ( 3 )¹/²

Therefore, for the given expression √3, its index  form is written as ( 3 )¹/² .

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Answer:

1

Step-by-step explanation:

To find the zero of an equation you set the equation equal to 0

That means you do this:

-5x+5=0

Then you solve for x

-5x=-5

x = -5/-5

x= 1

the factors of 28 are : 1, 2, 4, 7, 14, and 28.

the prime factors of 28 are : 2, 2, and 7.

The inequality is represented by the polynomial y ≥ 3.6 · (x - 11.5) · (x + 3.5).

What is the expression of the quadratic inequality?

Herein we must derive the quadratic expression within an inequality of the y ≥ f(x) based on its two roots and a known point on the curve. We can find the coefficients of the quadratic function by solving this system of linear equations:

(x₁, y₁) = (- 3.5, 0)

12.25 · a - 3.5 · b + c = 0       (1)

(x₂, y₂) = (11.5, 0)

132.25 · a + 11.5 · b + c = 0       (2)

(x₃, y₃) = (8.5, - 54)

72.25 · a + 8.5 · b + c = - 54     (3)

The solution of the system is a = 3.6, b = - 54, c = 144.9.

Thus, the inequality is represented by the polynomial y ≥ 3.6 · x² - 54 · x + 144.9, whose factored form is determined by the quadratic formula:

y ≥ 3.6 · (x² - 15 · x + 40.25)

y ≥ 3.6 · (x - 11.5) · (x + 3.5)

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20 times can you expect to land on yellow if you spin the spinner 100 times.

Given:

A spinner has 8 evenly spaced different colored sections. You spun the spinner 10 times and landed on yellow 2 times.

10 times spinning = landed on yellow 2 times.

divide by 10 on both sides

1 time spinning = landed on yellow 2/10 times

1 time = 1/5 times

multiply by 100 on both sides

1 time * 100 = 1/5*100 landed on yellow

100 times spinning = 20 times landed on yellow.

Therefore 20 times can you expect to land on yellow if you spin the spinner 100 times.

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Answer: 21

Step-by-step explanation:

If she makes 7 out of 10 shots she makes 70% of her shots (7/10 x 100 = 70%)

So if she makes 30 shots, 21 will go in the basket

(30)(0.70) = 21

The equation of the line through the point (-6,5) and parallel to the line is    y=[tex]\frac{1}{2}[/tex]x-7 is y=[tex]\frac{1}{2}[/tex]x+8.

What is equation of line ?

Any location with an x and y axis can have a line equation constructed using the slope of the line. To build a line with a certain point, one uses the equation for a straight line. Any two points can be used to find the slope. Slope is the part of a straight line that is steep.

Here the given equation is y=[tex]\frac{1}{2}[/tex]x-7

We know that equation of line is y=mx+c , where m = slope.

Then slope of given line is m= 1/2 . Now the line is parallel to given line so slope of the equation is also equal.

=> slope m=1/2.

Now the given point [tex](x_1,y_1)=(-6,5)[/tex] .

Using equation of the line is ,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-5 = 1/2(x+6)

=> 2y-10=x+6

=>2y=x+16

=>y=[tex]\frac{1}{2}[/tex]x+8

Hence the equation of the line is y=[tex]\frac{1}{2}[/tex]x+8.

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The value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

According to the question,

We have the following expression:

(2x − 12) + (1/2xy-10)

Now, the values of x and y are given to be 8 and 2 respectively.

So, we will put these values of x and y in the given expression:

(2*8-12)+(1/2*8*2-10)

First, we will use multiplication:

(16-12)+(8-10)

4+(-2)

(Note that when two integers are of different signs then the integers are subtracted but the sign in the result is of the larger integer.)

4-2

2

Hence, the value of the expression, (2x − 12) + (1/2xy-10), for x = 8 and y = 2 will be 2.

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The simplified expression is x² + 2x - 15.

We are given a mathematical expression. The expression has two terms. The first term is (x + 5) and the second  term is (x - 3). The terms are multiplied by each other to obtain the final expression. Let the resulting expression be represented by the variable "E". The expression has been solved below.

E = (x + 5)(x - 3)

We will use the distributive property.

E = x*(x - 3) + 5*(x - 3)

E = x*x - x*3 + 5*x - 5*3

E = x² - 3x + 5x - 15

E = x² + 2x - 15

Hence, the expanded and simplified form of the given expression is x² + 2x - 15.

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unable to see the graph

Answer:

[tex]y=-\frac{1}{5}x[/tex]

Step-by-step explanation:

Start by finding the slope of the line. Slope is defined as the RISE over the RUN. Find two points on the line with clear coordinate pairs. The line clearly passes through the origin, and the point (5,-1). To get from one point to the other, I have to go DOWN 1 unit. This is the RISE. The rise is -1 because I am going down. I also have to go RIGHT 5 units. This is the RUN. Slope is rise divided by run. Since a positive number divided by a negative number is a negative number, I move the negative sign outside the fraction: [tex]-\frac{1}{5}[/tex]. This is the slope!

The line crosses the y-axis at 0, so the y-intercept is 0.

Point-slope form is a way to write linear equations. It looks like this:

[tex]y=mx+b[/tex]

The letter m represents the slope, and the letter b represents the y-intercept. Let's plug in the values we found for those respectively:

[tex]y=-\frac{1}{5}x+0[/tex]

This simplifies to the equation below! This is the equation of the line!

[tex]y=-\frac{1}{5}x[/tex]

Daniel's purchasing power will decrease because the interest rate is lower than the historical rate of inflation.

Purchasing power can be portrayed as the quantity of labor and products that a unit of cash or an amount of cash can buy. The connection between financing cost and inflation rate influences the buying force of a saving record.

At the point when the loan cost is higher than the inflation rate, purchasing power increments. Yet, when the interest rate is lower than the expansion rate, buying power falls. For example, In the United States for the 12 months ending April 2022, the annual inflation rate was 8.3%. Since the 0.5% annual interest rate being earned by Daniel is lower than the 8.3% annual inflation rate, the most likely thing to happen to the purchasing power of his savings over time is to fall.

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The function for the transformation "The cubic function shifts 7 units right and 5 units up. is written as  f(x) = (x - 7)^3 + 5.

Let the cubic function be = f(x) = x^3

The transformation required include shifts 7 units right and 5 units up

shifting 7 units to the right is achieved by subtracting 7 units from x in the function hence f(x) = (x - 7)^3

moving 5 units up is achieved by adding 5 units to the function hence

f(x) = (x - 7)^3 + 5

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Answer:

Step-by-step explanation:

4x maybe

The given system of equations has solutions (-2, -1) and (-2, -1) respectively.

Calculating the unknown variables while keeping the equations balanced on both sides is the process of solving a system of equations.

Finding the value of the variable that makes the condition of all the given equations true is how we solve an equation system.

Given the system of equation below:

-2x² + y = -5

y = -3x² +5

Substitute equation 2 into 1 to have:

-2x² + (-3x+5) = -5

-2x²-3x² +5 = -5

-2x²-3x² +10=0
-5x² = -10

x²  = 10/5

x²  = 2

x = ±√2

If x = -√2

y = -3x² +5

y = -3(2) + 5

y = -1

If x = √2

y = -3x² +5

y = -3(2) + 5

y = -1

Hence the solutions to the given system of equations are (-√2, -1) and (√2, -1).

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Answer: 14

Explanation:

(3, -20)    (5, 8)

x1   y1       x2   y2

[tex]\frac{y2 - y1}{x2 -x1}[/tex]

[tex]\frac{8 - -20}{5-3}[/tex]  = [tex]\frac{8+20}{5-3} = \frac{28}{2} = 14[/tex]

The probability that the household contains 3 people must be 0.16

The probability of finding 3 people in a household is the same as the probability of finding 4 people.

The probability = Number of favorable outcomes / Total number of outcomes

The probability is the occurrence of the random event. The value of the probability varies from 0 to 1

Therefore if we add all the probability together, the result will be one

Also The probability of finding 3 people in a household is the same as the probability of finding 4 people.

Consider the probability of finding 3 people = Probability of finding 4 people = x

Then the equation will be

0.25 + 0.32 + x + x + 0.07 + 0.03 + 0.01 = 1

Add the terms

0.68 + 2x = 1

2x = 1 - 0.68

2x = 0.32

x = 0.32 / 2

x = 0.16

Hence, the probability that the household contains 3 people must be 0.16

The complete question is:

In government data, a household consists of all occupants of a dwelling unit. choose an American household at random and count the number of people it contains. here is the assignment of probabilities for the outcome. the probability of finding 3 people in a household is the same as the probability of finding 4 people. what is the probability of finding 3 people in the household ?

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Answer:

153.9 units squared

Step-by-step explanation:

A = pi*r^2

A = pi* 7^2

A = pi* 49

A = 153.9

Answer: 9 students will be on a bus that is not full

Step-by-step explanation:

123/38 = 3.23684210526 = 3 bus that is full.
38 x 3 = 114, 123 - 114 = 9

So, 9 students will be on a bus that is not full while the other 3 bus will be full of students.

Answer:

there will be nine students in the bus that is not full.

Step-by-step explanation:

if each bus holds 38 in your first bus you have 38 and then there are 85 students left so in the second bus there are also 38 and you should have 47 students left that need to go in a bus so then again in bus 3 there are also 38 which means in the fourth/last bus there are only 9 students left  

The probability that exactly two marbles are red, is 0.365.

In the given question we have to find the probability that exactly two marbles are red.

A bag contains 10 red marbles, 5 white marbles, and 6 blue marbles.

Total marbles is

10+5+6=21

We draw 5 marbles out at random, without replacement.

Marbles taken out =5

Total possibility of taking 5 marbles out of 21 marbles is [tex]^{21}C_{5}[/tex].

Using [tex]^{n}C_{r}=\frac{n!}{r!(n-r)!}[/tex]

So [tex]^{21}C_{5}=\frac{21!}{5!(21-5)!}[/tex]

[tex]^{21}C_{5}=\frac{21!}{5!16!}[/tex]

[tex]^{21}C_{5}=\frac{21\times20\times19\times18\times17\times16!}{5\times4\times3\times2\times1\times16!}[/tex]

Simplifying

[tex]^{21}C_{5}[/tex] =7×19×9×17

[tex]^{21}C_{5}[/tex] = 20,349

Probability of exactly two marbles are red is

Possible out comes of exactly two red marbles equal to 2 red and other color marble 3.

Total red marbles are 10. So [tex]^{10}C_{2}[/tex]

The remaining marble except red marble is 11. So [tex]^{11}C_{3}[/tex]

[tex]=^{10}C_{2}\times^{11}C_{3}[/tex]

Simplifying

[tex]=\frac{10!}{2!(10-2)!}\times\frac{11!}{3!(11-3)!}[/tex]

[tex]=\frac{10!}{2!8!}\times\frac{11!}{3!8!}[/tex]

[tex]=\frac{10\times9\times8!}{2\times1\times8!}\times\frac{11\times10\times9\times8!}{3\times2\times1\times8!}[/tex]

=5×9×11×5×3

=7,425

So the probability that exactly two marbles are red

P(R)=7,425/20,349

P(R)=0.365

Hence, the probability that exactly two marbles are red, is 0.365.

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Answer: Giuseppe is taller.

Step-by-step explanation:

Giuseppe is 74 inches tall, and we know that 12 inches is one foot, so 74/12 is ~6.1677777... versus 6.1.

Another way you can check this is by converting feet to inches. So 6 feet 1 inch would be (6 x 12) + 1 which is ~73.

The ratio of flower seeds to the total amount of seeds is 2/7 = 0.2857.

The greatest common divisor of two or more numbers that are not all equal to zero is the largest positive integer that divides each of the integers. This term is used in mathematics. The symbol represents the two integers x and y's greatest common factor. The GCF of two or more numbers is the greatest number among all the common factors of the given numbers.

Given that,

The local stores have donated 30 packets of flower seeds and 105 packets of vegetable seeds.

30/105

We have to find the GCF of 30 and 105=15

30/15=2

105/15=7

So, the answer is 2/7

The ratio of flower seeds to the total amount of seeds is 2/7.

By converting fractions as a decimal number we get,

2/7=0.2857

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Answer:

y = mx + b

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