Topic 6 Performance Task
Tomas and Emilio have a budget of $200 to plan their party at a movie theater. The party room at the theater costs $45.99 to rent and includes a free cake. Movie tickets cost $12.50
each, and a small bag of popcorn costs $4.50.
Seven friends accept the invitation to the twins' birthday party. At the last minute, Tomas and Emilio learn that their neighbor also wants to attend. The twins realize that they can stay
within their budget by buying different amounts of popcorn.
Small Popcorn
(serves 1)
$4.50
Medium Popcorn
(serves 2)
$5.75
Large Popcorn
(serves 2-3)
$6.50
Describe a different popcorn scenario that will allow the twins to bring 8 friends, including their neighbor, and still stay within their budget.

The amount he earned last week in commission is $994.

The commission he earned in 2011 is $51,688

The commission earned is a fraction of the total sales of stocks.

Commission earned = amount of sales x percentage commission

14% x $7,100

= 14/100 x $7,100

= 0.14 x $7,100

= $994

Amount she earned in commission in a year = number of weeks in a year x commission earned per week

= $994 x 52 = $51,688

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The assertion that both zeros of the quadratic polynomial x² - 2kx +2 in magnitude but opposite in sign then value of k is 1/2 is false.

The standard definition of a quadratic function is given as follows:

y = ax² + bx + c.

The sum of the roots of a quadratic function is given as follows:

S = -b/a.

The equation in this problem is given as follows:

x² - 2kx +2

Hence the parameters are:

a = 1, b = -2k.

If the roots are equal in magnitude but the opposite sign, the sum of the roots is of:

0.

Hence:

-b/a = 0.

b = 0.

Meaning that the value of k is obtained as follows:

-2k = 0.

k = 0.

And the statement is false.

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Answer:

Answer in attached photo.

Step-by-step explanation:

Steps are in the attached photo, this question is testing on the concept of Similar Triangles.

Formula:

[tex]\frac{Shorter \ Length \ of \ line \ segment \ A}{Longer \ Length \ of \ line \ segment \ A} = \frac{Shorter \ Length \ of \ line \ segment \ B}{Longer \ Length \ of \ line \ segment \ B}[/tex]

The number of commercials in which Avery's songs were played is 5.

The number of movies in which Avery's songs were played is 5.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 9 is an equation.

We have,

The number of times the song played in commercials = x

The number of times the song played in a movie = y

Now,

Avery will earn $40 every time one of her songs is played in a commercial and earn $140 every time one of her songs is played in a movie.

We can make two equations.

x + y = 7 ____(1)

x = 7 - y _____(2)

40x + 140y = 480 _____(3)

Substituting (2) in (3) we get,

40(7 - y) + 140y = 480

280 - 40y + 140y = 480

100y = 480 - 280

100y = 200

y = 2

Now,

x = 7 - 2

x = 5

Thus,'

The number of commercials and the number of movies in which Avery's songs were played are 5 and 2.

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Answer:

[tex]8^{9}[/tex]

Step-by-step explanation:

[tex]8^{5}[/tex] x [tex]8^{4}[/tex]

In expanded form this would be

8·8·8·8·8·8·8·8·8

The product of power principle tells us that when we are multiplying powers with the same bases, we add the exponents.

Answer:

3x-5y

Step-by-step explanation:

⇒13x+2y-10x-7y

arrange the like terms together

⇒13x-10x-7y+2y

⇒3x-5y ...answer

hope that helps...

Yes, 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) is an example of distributive law.

The distributive property is also known as the distributive law of multiplication over addition and subtraction. The name itself implies that the operation involves dividing or distributing something. The distributive law applies to addition and subtraction. The formula for the distributive property is expressed as:

Over addition : a( b + c ) = ab + ac

and subtraction : a( b - c) = ab - ac

Example: Solve the expression 7(20 + 3)

Multiplication of 7(20) and 7(3) is done before addition. This leads to 7(20) + 7(3) = 140 + 21 = 161.We have, an expression 3×(5 - 2) =(3 × 5 ) - (3× 2 ).

Consider the left hand side, 3×(5 - 2)

=> 3× 5 - 3× 2 = 15 - 6 = 9

Now, the right hand side, (3 × 5 ) - (3× 2 ) => 15 - 6 = 9 = LHS

Hence, it is an example of distributive law.

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Complete question:

Is 3 * ( 5 - 2 ) = ( 3 * 5 ) - ( 3 * 2 ) an example of distributive law *?.

You have to distribute it. To do this, multiply x^2 to (7x^2-5x-5) and do the same to 9 times (7x^2-5x-5). Add like variables. The attached image is your answer.

I hope this was able to help you :D

The product of 2x2x2 is 8.

A product is the outcome of multiplication in mathematics, or an expression that specifies the factors (numbers or variables) to be multiplied. For instance, the sum of 6 and 5 is 30. (the result of multiplication).

So 2x2x2 = 4x2= 8

Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.

In linear algebra, there are numerous different types of products. Some of them have names that sound confusingly close but have very distinct meanings (outside product, external product), while others have names that sound completely different but basically imply the same thing (outer product, tensor product, Kronecker product). These are briefly discussed in the sections that follow.

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If the perimeter of the train ticket is 60 centimeters and it's length is 17 centimeter long it's height is 13 centimeter

A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length.

To find the perimeter of a rectangle we add all this sides together. This means that the perimeter of a rectangle is given as ;

P = l+l+w+w

P= 2(l+w)

60 = 2( 17+w)

60 = 2( 17+w)

17+w= 60/2

17+ w = 30

w = 30-17

w = 13cm

Therefore the height of the train ticket is 13cm

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The density is 12.5 grams per cubic centimeter and 80 grams per cubic centimeter.

What is the density?

Density is a measure of how much mass is contained in a given volume. It is defined as the ratio of mass to volume and is typically measured in units of grams per cubic centimeter (g/cm^3) or kilograms per liter (kg/L).

The mass is 500 grams and the volume is 40 cubic centimeters, therefore the density is:

density = mass / volume = 500 grams / 40 cubic centimeters = 12.5 grams per cubic centimeter

The mass is 125 grams and the volume is v cubic centimeters. To find the value of v, you can use the equation:

density = mass / volume = 125 grams / v cubic centimeters

so v = mass / density = 125 grams / 12.5 grams per cubic centimeter = 10 cubic centimeters

The volume is 1.4 cubic centimeters and the density is 80 grams per cubic centimeter. To find the mass you can use the equation:

mass = density x volume = 80 grams per cubic centimeter x 1.4 cubic centimeters = 112 grams

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The total amount of money which Trevor's family spend, in total, on shower water in the past month is equal to $86.4.

Based on the information provided about the house Trevor's family lives in, we have the following important parameters;

Next, we would calculate the total volume of water that is used to shower by six (6) persons as follows;

Total volume of water for 6 persons = 72 × 6

Total volume of water for 6 persons = 432 liters.

Furthermore, the total amount of money that was spent on shower water by Trevor's family in the previous month is given by;

Total amount of money = total volume of water used for shower × cost per liter of water

Total amount of money = 432 × 0.2

Total amount of money = $86.4.

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An angle has a length of 166.7°. The extra degree at 166.7 is 13.3

Given,

The measure of an angle is 166.7°.

The supplement of 166.7 degrees is 180 - 166.7  = 13.3

Therefore the answer is 13.3°

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Answer:50.00

Step-by-step explanation:

First you need to find what 15% of 39.62 is 5.94 or 6 so you would add 6 to 39.62 and get 34.62 then you round it all and get 35 and it is closer to 50 than 40.

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

(3x + 1)(x + 7)

Step-by-step explanation:

3x² + 22x + 7 =

3x² must factor into 3x and x.

= (3x +    )(x +     )

7 factors into 7 and 1. We can place 7 and 1, or 1 and 7.

= (3x + 7)(x + 1)

or

= (3x + 1)(x + 7)

Now we multiply both possibilities out to see which one produces the middle term 22x that we need.

= (3x + 7)(x + 1) = 3x² + 10x + 7     No what we need

or

= (3x + 1)(x + 7) = 3x² + 2x + 7      Exactly what we need

Answer: (3x + 1)(x + 7)

When the coin is tossed and then dice is rolled, the possible outcomes are 12.

For the stated question.

Sample space for tossing coin. { H, T}.

Sample space for rolling dice. { 1, 2, 3, 4, 5, 6 }

Then,

Total sample = { H1, H2, H3,H4, H5, H6, T1, T2, T3, T4, T5, T6}

Thus, the total possible outcomes for tossing coin and rolling dice is 12.

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Answer:

$700

Step-by-step explanation:

1. We see the original price is $1,000.

2. Change 30% to a decimal

3. 30/100=0.30

4. Multiply the original cost of the item(mattress) by the percentage.

5. 0.3×1,000=300

6. $300 is the amount discounted.

7. For final price with discount: Take its original price($1,000) and subtract the discount from the original price

8. $1,000-$300=$700

Answer:

$300

Step-by-step explanation:

The inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex] is [tex]e^{x}[/tex].

In the given question, we have to find the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex].

The given function is f(x) = [tex]\log_{e}x[/tex].

The features of logarithms will simply follow from our understanding of exponents if the logarithm is viewed as the inverse of the exponential function.

Now let, y = [tex]\log_{e}x[/tex]

Now x = log y

Then, y = [tex]e^{x}[/tex]

So, f(x) = [tex]e^{x}[/tex]

As a result, [tex]e^{x}[/tex] is the logarithmic function's inverse, where f(x) = [tex]\log_{e}x[/tex].

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The complete question is:

What is the inverse of the logarithmic function f(x) = [tex]\log_{e}x[/tex]?

Raul's distance from Main street decreases in the interval,

0 ≤ t ≤ 0.75. And Raul walks 6 miles to get to school.

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by d=√{(x₂-x₁)² + (y₂-y₁)²}.

Given:

Raul crosses Main Street when he walks home from school.

The graph of the function d(t)=4I(t-0.75)I shows Raul's distance, in miles, from Main Street after t hours.

The domain of the function is 0 ≤ x ≤ 1.5.

The graph shows his entire trip.

From the graph;

Raul's distance from Main street decreases in the interval,

0 ≤ t ≤ 0.75.

And to get to school,

Raul walks,

distance = (distance when t = 1.5) - (distance when t = 0)

Distance = (4 x 0.75) - (4 x -0.75)

Distance = 3 -(-3)

Raul walks = 6 miles.

Therefore, Raul walks 6 miles to get to school.

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The complete question is given on the attached image,

The credit utilisation ratio to the nearest percentage is found as 17%.

Steps:

For the stated question:

Balance = $180 + $230 = $410.

credit limits = $1500 + $1000 = $2500.

Credit utilisation ratio = Balance / credit limits

Credit utilisation ratio = 410 / 2500 * 100 = 16.4%

Thus, the credit utilisation ratio to the nearest percentage is found as 17%.

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The next operation that should be done when evaluating this expression is -12

The rules that specify the order in which we should perform several operations to solve an expression are known as the order of operations. Parentheses, Exponents, Multiplication, Division (from left to right), Addition, and Subtraction are the sequence in which the operations are performed (from left to right).

The next operation that should be done when evaluating this expression is

9-12+6/-3+3(-3)

Addition or Subtraction (from left to right)

9-12=-5

Multiplication or Division (from left to right)

6 /-3 = -2

-5 + -2+3(-3) = -12

The next operation that should be done when evaluating this expression is -12

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Answer:

The answer is c which is=5605

Answer:

C.

Step-by-step explanation:

Since there's no sequence of numbers, we assume that the number that lies between 5,595 and 5,610 is the mean of the 2 numbers.

However, if we calculate its mean, we can have 5,602.5 and it doesn't appear on any options. Thus, we will choose the nearest value from those options.

The given equation's answer is [tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]

[tex]$z+5=55\left(5^z\right):$[/tex] [tex]$z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex], [tex]$z=-\frac{\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}$[/tex]

[tex](Decimal: $z=-1.75934 \ldots, z=-4.98187 \ldots$ )[/tex]

[tex]$$z+5=55\left(5^z\right)$$[/tex]

Prepare [tex]$z+5=55\left(5^z\right)$[/tex] Lambert form: [tex]$(z+5) e^{-\ln (5) z}=55$[/tex]

the equation once more using [tex]$(-z-5) \ln (5)=u$[/tex] and [tex]z=-\frac{u+5 \ln (5)}{\ln (5)}$[/tex]

[tex]$$\left(\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)+5\right) e^{-\ln (5)\left(-\frac{u+5 \ln (5)}{\ln (5)}\right)}=55$$[/tex]

[tex]$$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$$[/tex]

Rewrite [tex]$e^{u+5 \ln (5)}\left(-\frac{u+5 \ln (5)}{\ln (5)}+5\right)=55$[/tex]in Lambert form: [tex]$e^u u=-\frac{11 \ln (5)}{625}$[/tex]

Solve [tex]$e^u u=-\frac{11 \ln (5)}{625}: \quad u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{W}_0\left(-\frac{11 \ln (5)}{625}\right)$$$u=\mathrm{W}_{-1}\left(-\frac{11 \ln (5)}{625}\right), u=\mathrm{w}_0\left(-\frac{11 \ln (5)}{625}\right)$$[/tex]

Substitute back [tex]$u=(-z-5) \ln (5)$[/tex] , solve for z

[tex]$$\begin{aligned}& \text { Solve }(-z-5) \ln (5)=W_{-1}\left(-\frac{11 \ln (5)}{625}\right): \quad z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& \text { Solve }(-z-5) \ln (5)=W_0\left(-\frac{11 \ln (5)}{625}\right): z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)} \\& z=-\frac{W_{-1}\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}, z=-\frac{W_0\left(-\frac{11 \ln (5)}{625}\right)+5 \ln (5)}{\ln (5)}\end{aligned}$$[/tex]

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The Solution to the system of linear equations given as "y = -5x+3" and "y= 1" is that x = 2/5   and y = 1  .

Linear equations are the equations that are made up of Variables and Constants which are joined by mathematical operators .

The system of linear equations is given to us is: "y = -5x+3" and "y= 1"

Substituting the values of y=1 in y = -5x+3 ,

we get ;

⇒ 1 = -5x + 3 ;

⇒ -5x = 1 - 3  ;

⇒ -5x = -2 ;

⇒ x = (-2)/(-5) ⇒ x = 2/5 .

Therefore , solution can be written as : x = 2/5 and y = 1 .

The given question is incomplete , the complete question is

What is the solution to the system of linear equations y = -5x+3 and y = 1 ?

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To plot more equivalent ratios on the coordinate plane, move up one and right one and half.

Equivalent ratios are the ratios that are the same when we compare them. Two or more ratios can be compared with each other to check whether they are equivalent or not.

Given that, Three equivalent ratios are shown on the graph. On a coordinate plane, points (1, 0.5), (2, 1), and (5, 2.5) are plotted.

As we see, the x-coordinates are 1, 2, 5 and y-coordinates are 0.5, 1, 2.5

We see that, x-coordinates are increasing by 1, and y-coordinates are increasing by a half,

Therefore, to plot more equivalent coordinates, we will move up 1 on y-axis and a half right on x-axis,

Hence, to plot more equivalent ratios on the coordinate plane, move up one and right one and half.

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The 1/10 gradient means  6 degrees is the angle of 1 in 10 slopes.

The gradient is the inclination of a line. The gradient is often referred to as the slope (m) of the line. The gradient or slope of a line inclined at an angle θ is equal to the tangent of the angle θ.

In geometry, 1 in 10 means for every ten units of horizontal distance crosses there is 1 unit of vertical drop or rise. The angle of tan is used to measure this value of the slope. Let x be the angle to be used for tan.

[tex]tanx=\frac{horixontal distance}{vertical distance}[/tex]

[tex]tanx= \frac{1}{10}=0.1[/tex]

[tex]x=tan^{-1}(0.1)\\x=5.71'[/tex]

By rounding to the nearest digit, the degree value will be 6.

Hence, 6 degrees is the angle of 1 in 10 slopes.

Hence, the 1/10 gradient means  6 degrees is the angle of 1 in 10 slopes.

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Yes , the graphing calculator can be used as a scientific calculator.

As given in the question,

Scientific calculator can not be used as a graphing calculator.

But graphing calculator can be used as a scientific calculator.

Therefore, yes the graphing calculator can be used in place of scientific calculator.

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Answer:

the answer is option A

Step-by-step explanation:

Distance between two points

/XY/ = √((X2-X1)²+(Y2-Y1)²)

Therefore

/XY/= √((7-(-5)²+(15-4)²)

Answer:

First a farl we should know,

Distance (d) = √(x2-x1)^2+ (y2-y1)^2

x(-5,4) = (x1, y1)

y(7,15) = (x2, y2)

Now,

Distance (d) = √(x2-x1) + (y2-y1)

Ans = √(7-5)^2 + (15-4)^2

Answred by : - ||Ziddiboy||