The graph shows the total cost c of buying one large bucket of popcorn and d large drinks. Write an equation from the graph that could be used to find the total cost c if you buy one large bucket of popcorn and d large drinks.

The figure that has an area formula that is a linear function is the rectangle.

Area is the size or measurement of a two-dimensional space. It is usually expressed in square units such as feet, meters, or kilometers. Area is a fundamental concept in mathematics, and is used to measure the size of shapes and surfaces. Area is also used to calculate the amount of material or resources needed to cover a given space. In addition, it can be used to measure the cost or value of a piece of land.

The formula for the area of a rectangle is A=lw, where l is the length and w is the width. This formula is a linear equation because it is a product of two variables, where the relationship between the two variables is a constant. Thus, the area of a rectangle is a linear function of its dimensions.

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Grade R learners can be best taught using hands-on experience, thus use physical beads or objects to practically teach subtraction.

A manipulatives-based project can be a fantastic method to teach subtraction to grade R students, who frequently learn best via hands-on experiences. This activity can be modified to accommodate students who learn better visually, aurally, or kinesthetically.

The activity that can be used to teach grade R learners to subtract is by using physical objects, and asking them to count the initial number.

Remove some items and recount them.

The objects removed will denote the subtraction.

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Answer:

We can simplify the given expression using the rules of exponents and radicals:

4xy³√ 27x^2y^5

= 4xy * ³√(27x^2y^5) (since y and ³√(27) cannot be simplified further)

= 4xy * ³√(3^3 * x^2 * y^3 * y^2)

= 4xy * 3xy * ³√y^2

= 12x^2y^2 * ³√y^2

Therefore, the expression 4xy³√ 27x^2y^5 simplifies to 12x^2y^2 * ³√y^2.

Step-by-step explanation:

A. The probability that he'll win both seats is 0.48.

B. The probability he'll loose both seats is 0.52.

C. The probability he'll win one seat is 0.92.

The probability of an event is calculated using the mathematical notion of probability. We can only use it to determine the likelihood that an event will occur. On a scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.

We are given that a candidate is contesting for both national and provincial seats.

Event A = Winning national seat

Event B = Winning provincial seat

A. The probability that he'll win both seats is

P(A) × P(B) = 0.8 × 0.6 = 0.48

B. The probability he'll loose both seats is

1 - 0.48 = 0.52

C. The probability he'll win one seat is

Probability = 0.8 + 0.6 - 0.48

Probability = 0.92

Hence, the required probabilities have been obtained.

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Question: a candidate is consisting for both national and provincial assembly seats. the probability that he will win the national seat is 0.8 and will win the provincial seat is 0.6. what is the probability that

a) he will win both seats

b) he will lose both the seats

c) he will win at least one seat

Answer:

30 feet

So, 30 feet of ribbon is left on the roll

The positive solution is t = 8.

A quadratic equation is a polynomial which has variables in which one has the highest power of 2.

Considering the question, let the unknown number be represented by t. So that;

16 is subtracted from the square of a number = t^2 - 16;

the result is 6 times the number = 6t

So that;

t^2 - 16 = 6t

t^2 - 6t - 16 = 0

t^2 + 2t - 8t - 16 = 0

(t^2 + 2t)(-8t - 16) = 0

t(t + 2)-8(t + 2)

So that

(t + 2)(t - 8) =0

t + 2 = 0 or t - 8 = 0

t = -2 or t = 8

Thus the positive solution is t = 8.

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Answer:

Step-by-step explanation:

We can use the conditional probability formula to find the probability of a student taking a calculus class given that the student takes a statistics class:

P(calculus | statistics) = P(calculus and statistics) / P(statistics)

We are given that P(statistics) = 0.83 and P(calculus and statistics) = 0.66.

Substituting the values we have:

P(calculus | statistics) = 0.66 / 0.83

Simplifying the fraction:

P(calculus | statistics) = 0.795

Therefore, the probability of a student taking a calculus class given that the student takes a statistics class is 0.795. Rounded to three decimal places, the answer is 0.795.

Based on the information provided, the statement "Ricardo is half as likely to spin a 2 or 4 than an odd number" is false.

Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.

What is Probability ?

Probability can be defined as ratio of number of favourable outcomes, total number of outcomes

Let's start by assigning some variables to the probabilities of spinning each type of number. Let's say:

P(odd) is the probability of spinning an odd number

P(2 or 4) is the probability of spinning a 2 or a 4

According to the problem, we know that:

P(2 or 4) = 1/2 * P(odd)

We also know that the sum of the probabilities of spinning all possible numbers must equal 1. Since there are 5 odd numbers and 2 even numbers (2 and 4) on a standard six-sided die, we can write:

P(odd) + P(2 or 4) = 5/6 + 1/3 = 7/6

However, this equation doesn't make sense because the sum of probabilities should never exceed 1. This means that our assumption about P(2 or 4) being half as likely as P(odd) is incorrect.

To correct this, we can use the fact that P(odd) + P(even) = 1, where P(even) is the probability of spinning an even number (either 2 or 4). Since Ricardo is half as likely to spin a 2 or 4 than an odd number, we can write:

P(even) = 1/3 * P(odd)

Substituting this into the equation P(odd) + P(2 or 4) = 1, we get:

P(odd) + 1/2 * P(odd) = 1 - 1/3 * P(odd)

Simplifying this equation, we get:

3/2 * P(odd) = 1 - 1/3 * P(odd)

Multiplying both sides by 2/3, we get:

P(odd) = 2/9

Substituting this back into our equation for P(even), we get:

P(even) = 1/3 * P(odd) = 2/27

Therefore, Ricardo has a 2/27 chance of spinning either a 2 or a 4, and a 2/9 chance of spinning an odd number.

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Complete Question:

Use the information from the spinner to determine if the statement is True or False.

Ricardo is half as likely to spin a 2 or 4 than an odd number.

Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.

In mathematics, the first 10 integers are referred to as the fundamental numbers. From 0 to 9, these foundational numbers are listed. The 0 to 9 range of basic integers includes 0 through 1, 2, 3, 4, 5, 6, 7 and 8.

Let's start by defining some variables. Let:

We can write the equations for the total cost of each plan as:

T1 = 35 + 2x

T2 = 34 + 3x

Since we know that the two plans end up costing the same total amount when Josh attends a certain number of classes in a month, we can set T1 equal to T2 and solve for x:

35 + 2x = 34 + 3x

35 = 34 + x

1 = x

So if Josh attends 1 group class per month, the two membership plans will cost the same total amount. Let's substitute x = 1 into our equations for T1 and T2 to find out what that total amount is:

T1 = 35 + 2(1) = 37

T2 = 34 + 3(1) = 37

Therefore, if Josh attends 1 group class per month, both membership plans will cost him a total of $37 per month.

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Based on the information provided, it can be concluded the loan's simple interest is 4.01%.

The simple interest is the difference between the future value of the loan and the loan amount.

Simple interest = future value - loan amount $2762 - $2300 = $462

The simple interest rate is a linear function of the loan amount, the interest rate, and the duration of the loan. The simple interest that is paid is the same each year for each period of the duration of the loan.

Simple interest = loan amount x time x interest rate

Interest rate = simple interest / (loan amount x time) = 462 ÷ (6/12 x 2300) = 0.401= 4.01%

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[tex]12 + x = 12 + 6[/tex]

[tex]\implies 12 + x = 18[/tex]

NL would be 3.1 cm

What are similar triangles?

These are set of triangles which have some common relations on comparing their corresponding properties. But similarity of the triangles does not imply that they are congruent.

From triangle PQN, applying the trigonometric function. We have;

Tan θ = opposite/ adjacent

Tan 60 = 3.2/ y

1.7321 = 3.2/ y

y = 3.2/ 1.7321

 = 1.8475

y = 1.9 cm

To determine the value of NL,

NL + y = 5

NL = 5 - y

    = 5 - 1.9

    = 3.1

NL = 3.1 cm

The value of NL would be 3.1 cm.

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Answer:

3(3x−1)

Step-by-step explanation:

Answer:

The formula to calculate the minimum sample size required to estimate the population mean is given as:

n = (z^2 * σ^2) / E^2

Where,

z = the z-value for the given confidence level, which is 1.96 for c = 0.95

σ = the population standard deviation

E = the maximum error of estimate, also known as the margin of error

Plugging in the values, we get:

n = (1.96^2 * 9.1^2) / 1^2

n = 301.63

Rounding up to the nearest whole number, the minimum sample size required is 302.

Therefore, a sample size of at least 302 is needed to estimate the population mean with a 95% confidence level, assuming a population standard deviation of 9.1 and a maximum error of estimate of 1.

Step-by-step explanation:

Answer: If a movie starts at 2:45 PM and has a duration of 2 hours and 10 minutes, what time does it end?

To solve this, we need to add the duration of the movie to the start time and convert it back to the 12-hour clock format.

Adding 2 hours and 10 minutes to 2:45 PM, we get:

2:45 PM + 2 hours + 10 minutes = 4:55 PM

So, the movie ends at 4:55 PM.

Step-by-step explanation:

The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is given as follows:

5/6.

The part-to-whole ratio that describes the location of point P(3, 1) on the directed line segment AB, with coordinates A(-2, 6) and B(4, 0) is obtained applying the proportions in the context of the problem.

We have that both the x-coordinate and the y-coordinate of A and B have a difference of 6 units.

We also have that both the x-coordinate and the y-coordinate of point P(3,1) have a difference of five units from the coordinates of the starting point of the segment A.

Then the ratio is given as follows:

5/6.

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The presence of these organic elements, according to scientists, is insufficient evidence for the existence of ancient life on Mars since the molecules been created via other non-living processes. This assertion true.

Everything that includes carbon compounds produced by living things is considered to be organic matter. Lawn trimmings, leaves, twigs, branches, moss, algae, lichens, any animal parts, sewage, dust, insects, earthworms, and bacteria are just a few examples of what it includes.

Carbohydrates, lipids, protein, and nucleic acids are the four main kinds of organic substances that are found in all living organisms.

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Answer:

3(x + 12)(x + 2)

Step-by-step explanation:

Given

3x² + 42x + 72 ← factor out 3 from each term

= 3(x² + 14x + 24) ← factor the quadratic

Consider the factors of the constant term (+ 24) which sum to give the coefficient of the x- term.

The factors are + 12 and + 2, since

12 × 2 = 24 and 12 + 2 = 14, thus

x² + 14x + 24 = (x + 12)(x + 2) and

3x² + 42x + 72

= 3(x + 12)(x + 2) ← in factored form

The exponential model for the data is y=0.646(1.087)ˣ.

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

From the table we have, (8, 1.26), (10, 1.49)

We know that, the general form of exponential model is y=abˣ.

Here, substitute (8, 1.26) in y=abˣ, we get

1.26=ab⁸ -------(i)

a=1.26/b⁸

Here, substitute (10, 1.49) in y=abˣ, we get

1.49=ab¹⁰ -------(ii)

a=1.49/b¹⁰

1.26/b⁸ = 1.49/b¹⁰

1.26=1.49/b²

b²=1.49/1.26

b=1.087

Substitute b=1.087 in equation (i), we get

1.26=a(1.087)⁸

1.26=a(1.95)

a=1.26/1.95

a=0.646

So, the equation is y=0.646(1.087)ˣ

Therefore, the exponential model for the data is y=0.646(1.087)ˣ.

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In a linear equation, The number of rest stops in the first 200 miles would be 8 or more.  

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                    Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

25x > 200

25       25

x > 8

The number of rest stops in the first 200 miles would be 8 or more.  

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Therefore , the solution of the given problem of interest comes out to be  $882.75 monthly affordable mortgage amount recommended by a lending organisation .

To determine simple interest, divide the sum by the cost of borrowing, the amount of time left, and other factors. Principal plus interest plus hours is the straightforward return strategy in marketing. The simplest approach to calculate interest is to use this method. The most popular method of calculating revenue is as a fraction of the principal amount.

Here,

We can use an internet mortgage calculator to determine the affordable monthly mortgage payment. With the provided data, we can determine the monthly mortgage payment to be $1,187.25 using a mortgage calculator.

Assume that Jamie Lee and Ross earn $8,000 per month in gross revenue.

Affordable debt amount

=>  $1,837.25 ($8,000 x 0.43)

=> $2,720 - $1,837.25

is an affordable mortgage sum.

=> $882.75 is an affordable mortgage sum.

This indicates that the $882.75 monthly affordable mortgage amount recommended by a lending organisation based on Jamie Lee and Ross's income.

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Answer:

7withax2

Step-by-step explanation:

There are 10⁹(1 billion) possible Social Security numbers that can be formed. The probability of correctly guessing the Social Security number of the president of the United States is practically zero. This is because there are so many possible combinations, and it is highly unlikely that anyone would guess the correct number.

Number is a mathematical object used to count, measure, and label. It is used to express amounts, or magnitude of a quantity. Numbers are used in almost every field of life, such as science, engineering, economics, finance, and many other areas. Numbers are used in a wide range of contexts and are essential to modern life. They are used to communicate information, to measure time, and to represent values. Furthermore, numbers are used to represent abstract ideas, such as the probability of an event occurring. Numbers are also used to create patterns, which are essential to understanding complex systems. Without numbers, it would be impossible to measure anything, make estimates, or draw conclusions.

(a) There are a total of 10^9 (1 billion) possible Social Security numbers. This is calculated by multiplying the 10 possible digits (0-9) for each of the nine positions in the number, which gives 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10⁹.

(b) The probability of correctly guessing the Social Security number of the president of the United States is 1 in 10⁹. This is because there are a total of 10^9 possible Social Security numbers, and the president's number is only one of those.

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la surface de l'écharpe est de 1 1 56 cm² car la formule pour calculer l'air d'un carré est A= coté * coté soit coté²

donc :  Aécharpe=34²=1156

The first step to calculate the indicated x value using synthetic division is to assemble the synthetic division table, which will be:

The first number on the top line, 1, is the coefficient of the highest degree term in the polynomial. The remaining coefficients are written in order, with 0 placeholders for any missing terms. The divisor, -4, is written to the left of the table.

Therefore, we find ƒ(-4) = -51.

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The value given that cannot be an r ² value is A. - 0.75.

The r² value, also known as the coefficient of determination, is a statistical measure that represents the proportion of variance in the dependent variable that can be explained by the independent variable(s). It is a value between 0 and 1, with higher values indicating a better fit of the regression model to the data.

It is not possible for the r² value to be negative because it is the square of the correlation coefficient.  - 0.75 cannot possibly be a value of r ² as a result.

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a) The finance charge for the financing of the company airplane priced at $250,000 with 15% down payment is $66,308.

b) The monthly payments Vista's aircraft loan are $4,646.80.

The finance charge and the monthly payments can be determined using an online finance calculator as follows:

The finance charge represents the total interest and other fees that the financier charges for the loan.

The monthly payments are the periodic payments that must be made to settle the loan and compounded interest with the installment period of 60 months.

Company Airplane Price = $250,000

Down Payment = 15%

Loan Term = 60 months (5 years x 12)

Interest Rate = 11.25%

Results:  

Monthly Payment (PMT):  $4,646.80

House Price = $250,000

Down Payment = $37,500 ($250,000 X 15%)

Loan Amount = $212,500 ($250,000 - $37,500)

Total of 60 Mortgage Payments = $278,808

Total Interest (Finance Charge) = $66,308 ($278,808 - $212,500)

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Answer:

[tex]x[/tex] = 67 , [tex]y[/tex] = 113 , [tex]z[/tex] = 67

Step-by-step explanation:

What we need to know:

A parallelogram has two pairs of equal angles

Opposite angles are equal

Angles in a quadrilateral add up to 360

1) Find out as many angles we can

We know that the opposite angles are equal, this means that y would be equal to 113

2) Find the remaining angles

We already know that two of our angles are 113, this means that our total is 226 for now. We have two angles left which are equal so to find them we have to subtract 226 by 360 then divide by 2

Hope this helps, have a lovely day! :)

Answer:

x = 67

y = 113

z = 67

Step-by-step explanation:

The properties of a parallelogram are:

Two angles are said to be adjacent when they share a common vertex.

Therefore, both angle x and angle z are adjacent to the angle that measures 113°.

Since adjacent angles in a parallelogram are supplementary:

⇒ x° + 113° = 180°

⇒ x° = 67°

⇒ x = 67

Similarly:

⇒ z° + 113° = 180°

⇒ z° = 67°

⇒ z = 67

As opposite angles in a parallelogram are equal:

⇒ y° = 113°

⇒ y = 113

Answer:

1/2

Step-by-step explanation:

42/84=1/2