Hampton ate 7 slices of fruit at lunch. after dinner, he ate some more, he ate a total of 15 pieces of fruit.

Hey there!

3x + 8x

= 3 + 8

= 11x

= 11

Therefore, your answer should be:

11x

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The corresponding growth factor of +70% is 1.7

The formula for the annual rate of change is

                    1 ± r             (1)

where r = rate of change

and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.

According to the question we have been given the growth that is +70%. Since there is plus sign therefore it is a growth factor.

Thus, r = + 0.7

Putting this value in equation (1) we get

= 1 + 0.7

= 1.7

Hence the corresponding growth factor of +70% is 1.7

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With the formula d=vt+1/2at², we can prove that the acceleration of an object can be calculated with a=2d-2v t/t²

To solve this problem we must establish the equation, isolate the variable (a) following the rules of clearance and solve the operations:

d=vt+1/2at²

1/2at² = d - vt

at² = (d - vt)*2

at² = 2d - 2vt

a= (2d - 2vt) / t² verified

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer: The value of the triangle = 3.

               The value of the square = -2,

               The value of the star = 7

               The value of the rhombus = 18.

               The value of the circle  = 4,

               The value of the right angle triangle  = -5

Step-by-step explanation:

Define Linear equation:

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

An equation that has the highest degree of 1 is known as a linear equation. This means that no variable in a linear equation has an exponent more than 1. The graph of a linear equation always forms a straight line.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Given that,

Let us assume the values is,

(Option 1) : A shape puzzle is given that,

Let's assume, the triangle shape represents = a

Let's assume, the square shape represents = b

Let's assume, the star shape represents = c

The equation becomes,

clue 1 : 2a-1 = 5

clue 2 : a + b = 1

clue 3 : a-2b = c

First take, clue 1 :         2a-1 = 5

                                       2a = 5+1

                                        2a = 6

                                         a = 6/2

                                          a = 3

Therefore,       triangle (a) = 3

Take, clue 2 :                      a + b = 1

Replace 'a' value in this equation,

                                            a + b = 1

                                            3+b = 1

                                              b = 1-3

                                              b = -2

 Therefore,         square (b) = -2

Take clue 3 :                     a-2b = c

Replace with 'a' and 'b' values in this equation,

                                          a-2b = c

                                           3-2(-2) = c

                                            3+4 = c

                                              c = 7

Therefore,             star (c) = 7

we can substitute these values,

Then,      clue 1 : 2(3) -1 = 6-1 = 5

               clue 2 : 3 + (-2) = 3-2 = 1

               clue 3 : 3-2(-2) = 3+4 = 7

Thus, The value of the triangle = 3.

         The value of the square is = -2,

          The value of the star = 7

after using the concept of linear equation in two variables.

(Option 2) : A shape puzzle is given that,

Let's assume, the rhombus shape represents = x

Let's assume, the circle shape represents = y

Let's assume, the right angle triangle shape represents = z

The equation becomes,

clue 1 : x+2 = 5y

clue 2 : 3y = 12

clue 3 : 2y = x+2z

Take, clue 2 :                     3y = 12

                                            y = 12/3 = 4

Therefore,      circle (y) = 4

First take, clue 1 :         x+2 = 5y

                                      x+2=5(4)

                                      x+2=20

                                      x = 20-2 = 18

Therefore,       rhombus (x) = 18

Take clue 3 :                      2y = x+2z                

Replace with 'x' and 'y' values in this equation,

                                         2y = x+2z

                                         2(4) = (18)+2z

                                          2(4) = (18)+2z

                                           8 = (18)+2z

                                            8-18 = 2z

                                             -10 = 2z

                                              z = -10/2

                                              z = -5

Therefore,         right angle triangle (z) = -5

we can substitute these values,

Then,      clue 1 : 18+2=5(4)

                            20 = 20

               clue 2 : 3(4) = 12

                             12 = 12

               clue 3 : 2(4) = 18+2(-5)

                             8 = 18-10

                             10+8 = 18

                              18 = 18  

Thus, The value of the rhombus = 18.

         The value of the circle  = 4,

          The value of the right angle triangle  = -5

after using the concept of linear equation in two variables.

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According to the solving this implies that the  1:3  ratio of 60 is 20.

A ratio expresses the number of times one number contains another. For example, if a dish of the fruit contains eight oranges and six lemons, the orange-to-lemon proportion is eight to six. Similarly, the lemonade and orange proportion is 6:8, while the orange to fruit weight ratio is 8:14.

Ratios are used to compare the two quantities by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Let us find 1/3 of 60.

We can write 1/3 of 60

= 1/3 × 60.

= 20.

According to the solving this implies that the  1:3  ratio of 60 is 20.

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Answer:

1/4

Step-by-step explanation:

the answer is in the question, but If that isn't what you meant to type, 2 3/4 - 1/4 is 2.5

Answer:

Oy-14=12(x+1)

Step-by-step explanation:

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The rational number between the square root of 7 and the square root of 8 is 27/10

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The features of the rational number are given as

Value = between the square root of 7 and the square root of 8

Rewrite the value properly

So, we have

Value = between √7 and √8

Evaluate the values of √7 and √8

So, we have

√7 = 2.65

√8 = 2.83

This means that the rational number is between 2.65 and 2.83

A number between 2.65 and 2.83 is 2.7

Express as fraction

value = 27/10

Hence, the rational number between the square root of 7 and the square root of 8 is 27/10

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The value of x = 45°

It is given that 3 cos² 2x / ( 1 - sin 2x) = 1

3cos² 2x / ( 1 - sin 2x) = 1

As we know sin²x + cos²x = 1

3 ( 1 - sin²2x) / ( 1 - sin 2x) = 1

3 - 3 sin²2x = 1 - sin 2x

3 sin²2x - sin2x - 2= 0

As we know sin2x = 2 sin x. cos x

3( 2 sin x. cos x)² + 2 sin x. cos x  - 2 = 0

Let's take sin x . cos  x = t

3 ( 2t)² - 2t - 2 = 0

12t² - 2t - 2 = 0

12t² - 6t + 4t - 2 = 0

6t( 2t - 1) + 2(2t - 1) = 0

(6t + 2)(2t - 1) = 0

t = -1/3 , 1/2

Now put the value of t we get

sin x . cos x = -1/3 , 1/2

2 sin x . cos x = -2/3 , 1

sin 2x = -2/3 , 1

It is given that x should be between 0° to 90°.

Therefore

sin 2x = 1

sin 2x = sin 90°

2x = 90°

x = 45°

Therefore the value of x is 45°

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The expected raise a union wage negotiator feels that   the union members will get is $1.22.

The probability of each pay raise is given below

P ($1.50 raise) = 0.40

P ($1.00 raise) = 0.30

P ($0.50 raise) = 0.20

P (no raise) = 0.10

The probability of each pay raise is then multiplied by the pay itself

Expected raise for each hour = $1.50(0.40) + $1.00(0.30) + $0.50(0.20) + $0.00(0.10)

E(x) = 0.6 + 0.52 + 0.1 + 0 (The probability of no pay at all gives 0 since the pay amount has no value)

E(x) = $1.22

Therefore, all together the union wage negotiator is able to predict a $1.22 pay raise for the workers for each time expected.

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Answer:

30 c + 100 m = 700

c+ m = 14

Step-by-step explanation:

The product of the number of movies where the song was played (m) multiplied by the earnings per movie (30) plus the product of the number of commercials where the song was played (m) multiplied by the earnings per commercial, must be equal to $700.

30 c + 100 m = 700

The number of movies (m) plus the number of commercials (c) is equal to 14.

c+ m = 14

The system is:

30 c + 100 m = 700

c+ m = 14

The equation of the line will be y = 2x - 2.

A linear equation with a degree of one is referred to as a line equation. Two variables, x, and y are present in the equation of the line. The third parameter is the line's slope, which indicates the line's elevation.

The general form of the equation of the line is given as:-

y = mx + c

Given that the equation of the line is passing through the point ( -2,0) and the slope of the line is 2.

The equation of the line will be calculated as:-

y = mx + c

-2 = 0 + c

c = -2

y = mx + c

y = 2x - 2

Therefore, the equation of the line will be y = 2x - 2.

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Answer: 1 = e

Step-by-step explanation:

The values of g(x) are:

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

given:

g(x) = -2 |x + 5| + 2

so, x= -4

g(-4)= -2|-4 + 5| +2

g(-4) = -2 +2

g(-4) = 0

at,  x= -3

g(-3)= -2|-3 + 5| +2

g(-3) = -4 +2

g(-3) = -2

x= -1

g(-1)= -2|-1 + 5| +2

g(-1) = -8 +2

g(-1) = -6

and,  x= 0

g(-4)= -2| 0+ 5| +2

g(-4) = -10 +2

g(-4) = -8

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The height of the candle which is a linear function with respect to time after 12 hours was 25.2 centimeters.

A linear function has a graph of a straight line.

Given that height of a candle is a linear function of the amount of time in hours it has been burning.

The slope(m) is = - 0.4 which is = -(4/10) = - (2/5).

The height of the candle after 19 hours is 22.4 centimeters, which can be written as two points (x,y) = (19,22.4).

Now to obtain the height of the candle first we have to form an equation of a line in slope intercept form to find y-intercept(b), which is,

y = mx + b.

22.4 = -(2/5).19 + b.

22.4 = -7.6 + b.

b = 22.4 + 7.6.

b = 30.

∴ y = -(2/5)x + 30.

Now to obtain the height of the candle after 12 hours we have to substitute 12 in x.

So, y = -(2/5)(12) + 30.

y = 25.2 centimeters.

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The perimeter of rectangular classroom with its length five times its width is 108 ft.

The perimeter of rectangle is the sum of length of all its sides. Mathematically, it can be written as -

Perimeter = 2 (Length + Breadth)

Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -

Width [W] = 9 ft

Length [L] = 5W = 5 x 9 = 45 ft

The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -

[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft

Therefore, the perimeter of rectangle with its length five times its width is 108 ft.

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Answer:

10

Step-by-step explanation:

10 multiplied by 10 is 100. Therefore,the square root of 100 is 10

If he plans to spend 200 per month, then the number of months he can make withdrawals from his savings account until his balance is zero dollars is equal to 5.

First, we calculate the money earned by Nick in 6 months

Money earned per month = $400

Money earned in 6 months = 400 × 6 = 2400

If he spends $250 out of the money earned per month, then the money spent in these 6 months can be calculated as follows;

Money spent per month = 250

Money spent in 6 months = 250 × 6 = 1500

Now we calculate the money put in the saving account in 6 months by subtraction;

Money added to the saving account = 2400 - 1500 = $900

As he already had $100 in the saving account,

Total amount of money in the saving account = 900 + 100 = 1000

If he plans to spend 200 per month, then the number of months he can make withdrawals can be calculated by division

Number of months = total money in the account ÷ money spent per month

Number of months = 1000 ÷ 200 = 5

Therefore, Nick can make withdrawals for 5 months from his savings account.

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If a long run athlete can run 1/2 km in 3 minutes then he can run 10 km in an hour.

Given, a long distance athlete can run 1/2 kilometer in 3 minutes.

How much distance can he cover in an hour = ?

How quickly something or someone is moving is determined by their speed. If you know how far an object has traveled and how long it has taken, you can calculate its average speed. Speed equals distance times time, according to the speed formula. Knowing the units for distance and time will help you determine what the units are for speed.

Time = 60 minutes.

we know that 3 minutes = 1/2 km

therefore, distance covered in an hour = 1/2 ÷ 3/60

= 1/2 × 60/3

= 1/2 × 20

= 10

distance covered in an hour = 10 km.

hence we get the distance covered by the athlete in an hour as 10 km.

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Express 81 and 16 as a product of their prime factors. Apply the power rule for indices stating (a^m)^n = a^mn. Simplify the expression:

81=3x3x3x3 = 3^4

16 = 2x2x2x2 = 2^4

Thus, (3^4 x y^16 / 2^4 x X^12) ^ 1/2

3^4/2y^16/2 / 2^4/2 X^12/2

3^2 y^8 / 2^2 X^6 = 9y^8 / 4X^6

9y^8/4X^6 = (3/2)^2X^6y^8

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0.04, 3/11, 0.35, 3/5 would be the solution

If you buy 7 markers , each marker would cost 9.42 ( cents ) .

Given : The total cost ( in cents ) of x + 2 markers is x³ + 5 x ² + 2 x - 8 .

To find : cost of 1 marker

Cost of 1 marker = ( x³ + 5 x ² + 2 x - 8 ) / ( x + 2 )

                            = [tex]x^{2}[/tex] + 3 x - 4

Substituting value of 7 in cost function

   =  [tex]x^{2}[/tex] + 3 x - 4 at x = 7

= 49 + 21 - 4

Cost of 7 markers = 66

Cost of 1 marker = 66 / 7

                            = 9.42

Therefore , if you buy 7 markers , each marker would cost 9.42 ( cents ) .

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Answer:

-8

Step-by-step explanation:

(2)(-8)/2 convert it to a fraction and use fraction bar.

-16/2 = -8  Multiplication first then division

Note order of operations Division or multiplication which ever is first. also because the top of the fraction has parentherses do that first.

There are numerous videos and web sites that can show you the process of copying an angle. Some are animated. The best we can do here is show you a diagram with instructions. Of course, your curriculum materials already provide that

__

1. Set the compass to a convenient radius. Use that to draw an arc through rays ED and EF, using point E as the center.

2. Without changing the compass setting, draw a similar arc using S as the center, making sure it crosses the line containing S and extends far enough to accommodate the following steps. (In the attached, we show a full circle, because the tool we used won't draw an arc with a specific radius.)

3. Mark the points where the arc crosses ED as G, and where it crosses EF as H. Mark the point where the arc crosses the line containing S as I.

4. Set the compass radius to the distance GH. Using I as the center draw an arc with that radius so that it crosses the one made in step 2. Call that intersection point J. (Again, we have shown a circle because of the limitations of the tool being used for our diagram.)

5. Draw ray SJ to complete the angle copy.

Answer:

Step-by-step explanation: 23 is the median of the data set because it's the number in the middle.  

Median: 16, 18, 19,23, 24, 31, 32  

Mean: 16+18+19+23+24+31+32= 163 then divide by how many numbers you added by 163 divided by 7 equals 23.28571429. I'll just simplify it to 23.29 or rounding to tenths 23.3.

Answer:

Median = 23

Mean = 163/7 = 23.3 (1 d.p.)

Step-by-step explanation:

Given data set:

19, 18, 23, 24, 31, 32, 16

The middle value when all data values are placed in order of size.

Given data values in size order, from smallest to largest:

[tex]\sf 16, 18, 19, \boxed{\sf 23}, 24, 31, 32[/tex]

The middle value is 23, so the median of this data set is 23.

The sum of all data values divided by the total number of data values.

[tex]\begin{aligned}\implies \sf mean & =\sf \dfrac{19+18+23+24+31+32+16}{7}\\& = \sf \dfrac{163}{7}\\ & = \sf 23.28571429...\\ & = \sf 23.3\:(1\:d.p.)\end{aligned}[/tex]

Answer: Factor the expression

Factor

2(x+5)

Evaluate

2x+10

Solution

2(x+5)

Step-by-step explanation: hope this helps

0.03337327...   is expression to four decimal places. e⁻³.

The significance of an exponential function

e⁻³ in your calculator, which gives you 0.03337327...

Since you need 4 decimal places, you need to look at the 5th decimal place. If it's 5 or more, you add 1 to the 4th decimal place. If it's less than 5, you leave the 4th decimal as it is.

In this case, the 5th decimal place is 7 and the 4th is 3. Since 7>5, the 4th decimal place changes from 3 to 4.

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From the situation described in the problem, we have that:

a) The system of inequalities is given by: s + a ≤ 800, 4s + 7a ≥ 3400.

b) The solution is graphed at the end of the answer.

c) Yes, the club could meet it's goal.

A system of inequalities is when multiple variables are related in a described situation, and then inequalities are built to find the interval ranges of each variable, according to the relations built.

In the context of this problem, the variables are given as follows:

The auditorium has 800 seats, hence:

s + a ≤ 800.

They have a goal of making at least $3400, hence, considering the price of the tickets, we have that:

4s + 7a ≥ 3400.

The graphical solution of the inequality is given by the painted region on the graph, and since point (200, 475) is inside the region, the club could meet it's goal.

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