The total cost for a bucket of popcorn and 4 movie tickets is $56. The total cost for the same size bucket of popcorn and 6 movie tickets is $80. The cost of a bucket of popcorn is $8. Which equation represents the relationship between y, the total cost of the popcorn and movie tickets, and x, the number of movie tickets that are purchased?

y = 12x + 8
y = 12x − 8
y = 14x + 8
y = 14x − 8 Will give brainlliest

Answer:

Adding 4

Step-by-step explanation:

Pemdas

Answer:

Addition!

Step-by-step explanation:

Hope it helps <3

Step-by-step explanation:

please mark me as brainlest

Answer:

x = 51

Step-by-step explanation:

If the mean = 11.5, then that means all numbers added together divided by four = 11.5. Let's write this algebraically:

\(\frac{12.5+(-10)+(-7.5)+x}{4}=11.5\)

Now, let's solve for x:

\(12.5-10-7.5+x=11.5(4)\)

\(-5+x=46\)

\(x=51\)

I hope this helps!

Answer:

Step-by-step explanation:

sinx=.342

then x is just so simple

\(x=sin^{-1} (.342)\\\\\)

put that in a calculator or something

Answer:

The fourth one

Step-by-step explanation:

Surface area of a cylinder: \(SA=2\pi rh+2\pi r^2\)

where r = radius and h = height

We have a given height of 14cm and a given diameter of 6cm

We need the radius, not the diameter

To convert diameter to radius we simply divide by 2

6 / 2 = 3

so R = 3

We now plug in the given values into the formula

\(SA=2\pi (3)(14)+2\pi (3)^2\)

This equation matches with answer choice D

Answer:

349

Step-by-step explanation:

3141 divided by 9=349

The factor of ax²-49 is 1

Factoring an expression means writing a numerical or algebraic expression as a product of factors. To factor expressions, we can make use of the distributive property.

For example 2x +6 ha s a factor of 3, i.e 3(x+6)

In the expression ax²-49 , since there is no other r common factor , the factor of the expression will be 1.

i.e 1(ax²-49) = ax²-49

Therefore the factor of the expression ax²-49 is 1

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Answer:

The answer is SAS

The numbers ordered from least to greatest are 3.6, 3.621, 3.63, 3.702, 3.73, 3.785

The numbers are written in decimals. A decimal is a standard method used to write non-integers. A decimal is made up of integers and non-integers that are separated by a decimal point. An example of a decimal is 3.63.

In order to write decimals, from the least to the greatest, if the unit digit and tenth digit are the same, look at the hundredth digit, if the hundredth digit. Order the numbers on the basis of its hundredth digit. Based on this explanation, in the digits 3.6,  3.621, 3.63, 3.6 is the smallest and 3.63 is the largest.

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Answer:

in this diagram their are boxes.

on which 21 are shaded so the fraction is

Step-by-step explanation:

21/100

because their are total 100 boxes and 21 are shaded

hope you like the answer.

So to calculate 5 with an exponent of 3, you can write 5, 3 times with a multiplication symbol between them like so: 5 · 5 · 5 When we multiply them together, we get the answer to 5 with an exponent of 3.

The probability that he or she is a 12th Grade student is 0.1796

From the question, we have the following parameters that can be used in our computation:

The table of values

When a geometry student is selected, we have

12th geometry Grade student = 51

Geometry student = 74 + 47 + 112 + 51

So, we have

Geometry student = 284

The probability is then calculated as

P = 51/284

Evaluate

P = 0.1796

Hence, the probability that he or she is a 12th Grade student is 0.1796

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Answer:

The value of x is 2

Step-by-step explanation:

Now,

tan 27 = 1/x

0.5 = 1/x

x = 1/0.5

x = 2

Thus, The value of x is 2

-TheUnknownScientist 72

The equation of the line for the given point (-2,-5) and slope m=1/2

as y = (1/2)x - 4.

Given, the point = (-2,-5)

m = 1/2

we know that the equation of a line passing through the point and slope is:

y - y₁ = m(x-x₁)

y - (-5) = 1/2 (x-(-2))

y + 5 = 1/2 (x+2)

2y + 10 = x + 2

arrange the constants and variables on one side.

2y - x = 2 - 10

2y - x = -8

2y = x - 8

hence slope intercept form:

y = mx + c

y = x/2 - 8/2

y = (1/2)x - 4

hence m = 1/2 and c = 4

Hence we get the equation of the line as y = (1/2)x - 4.

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Step-by-step explanation:

15 / (1/3)  is equal to  15 x 3/1  = 15 x 3 = 45

Answer:12

Step-by-step explanation:

Therefore, a p-value less than 0.05 is considered statistically significant, which means that the observed result is unlikely to have occurred by chance and supports the rejection of the null hypothesis.

If your findings yield a 1 in 100 chance that differences were not due to the hypothesized reason, then the corresponding p-value would be 0.01. The p-value represents the probability of obtaining a result as extreme or more extreme than the observed result, assuming that the null hypothesis is true. In other words, a p-value of 0.01 indicates that there is a 1% chance of observing the data if the null hypothesis (the hypothesized reason) is true. Generally, a p-value less than 0.05 is considered statistically significant, which means that the observed result is unlikely to have occurred by chance and supports the rejection of the null hypothesis.

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The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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The relative rate of population change after seven years from now is a) 1.7 % (rounded off to 1 decimal place) b) Yes, the relative rate of population change will reach 2.3% in 19.21 years

The function for population t years from now is P(t)= 2+ 1.2e^(0.04t)

a) relative rate of change of population

= P'(t) / P(t)

= (0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(.04t) )

= 0.048 e ^(0.04t) / (2 + 1.2e^(0.04t) )

Relative rate of change of population 7 years from now

= 0.048 e ^(0.04 * 7) / (2+ 1.2e^(0.04*7))

=0.0177 = 0.177 * 100 = 1.7 % per year (rounded off to one decimal place

b) For the relative rate of change to reach 2.3 %

P'(t) / P(t) = 2.3 % = 0.023

⇒(0+1.2e^(0.04t) * 0.04 )/ ( 2+ 1.2e^(0.04t) ) = 0.023

⇒0.048e ^(0.04t) = 0.046 + 0.0267e^(0.04t)

⇒e ^(0.04t) = 0.958 + 0.556e ^(0.04t)

⇒e ^(0.04t) ( 1 - 0.556) = 0.958

⇒e ^(0.04t) ( 0.444) = 0.958

⇒e ^(0.04t) = 2.157

⇒0.04t = ln(2.157)           (applying ln on both sides)

⇒t = 19.21 years

The relative rate of population change is 2.3% in 19.21 years

Problem on the relative rate of change

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Answer:

This is a function because every input has its own output

Step-by-step explanation:

Answer:

What are we supposed to put in the boxes?!?!?!?

Step-by-step explanation:

Answer:

y = -3/8(x + 2)^2 + 8

Step-by-step explanation:

vertex form is

y = a(x - b)^2 + c     where a is a constant and (b,c) is the vertex.

The maximum is at (-2, 8)  because x 8 = height and x =-2 is equn. of symmetry

So here we have

y = a(x - (-2))^2 + 8

y = a(x + 2)^2 + 8

Now at the point (-6, 2):

2 = a(-6+2)^2 + 8

2 = 16a + 8

16a = -6

1 = -3/8.

So our equation is y = 3/8(x + 2)^2 + 8

the inequality that describes all the solutions is x > 16 or 16 < x.

To solve the inequality 4(5 - x) < -3x + 4, we first need to distribute the 4 on the left side of the inequality:

20 - 4x < -3x + 4

Next, we can isolate the variable on one side of the inequality by adding 4x to both sides:

20 < x + 4

Subtracting 4 from both sides gives:

16 < x

what is variable?

In mathematics, a variable is a symbol or letter that represents a value or a quantity that can vary or change in a given context. Variables are commonly used in equations and formulas to represent unknown values that need to be solved for or calculated. For example, in the equation y = 2x + 1, x is the variable, and its value can change depending on the situation or problem being considered. Variables can be used in a wide range of mathematical concepts, including algebra, geometry, calculus, and statistics, among others.

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Answer:

D) \(1 < x\leq 4\)

Step-by-step explanation:

1 is not included, but 4 is included, so we can say \(1 < x\leq 4\)

In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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Answer:

-3

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

that's just the correct answer, I know.

The interquartile range (IQR) formula is: IQR = Q3 - Q1, where Q1 is the first quartile and Q3 is the third quartile of a dataset.

The interquartile range (IQR) is a measure of variability in a dataset that represents the range between the first quartile (Q1) and the third quartile (Q3). The first quartile (Q1) is the value that separates the lowest 25% of the data from the rest of the dataset, and the third quartile (Q3) is the value that separates the highest 25% of the data from the rest of the dataset.

Therefore, the IQR formula is simply the difference between the third and first quartiles: IQR = Q3 - Q1. The IQR is commonly used to identify outliers in a dataset, where any data points that fall outside of the range Q1 - 1.5IQR to Q3 + 1.5IQR are considered outliers.

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