Movies went on sale for $4 off the original price . Jacob bought 3 movies . He paid $24 . What was the original price of a movie?

Complete the sentences to show how to write and solve an equation to answer this question

Define a variable. Let x=_______

The equation that models the problem is ______

To solve the equation first _____ next _________.

Answer:

18

Step-by-step explanation:

Imagine the points on a coordinate plane

3,0 is 3 units above 0,0 and 0,6 is 6 units right of 0,0

since you know 2 sides, you can find the area, 3*6=18

Answer:

$12.50

Step-by-step explanation:

Let x = the cost of the food without the delivery fee.

The delivery fee can be represented as 0.10x.

Keep in mind that the cost of the food plus the delivery fee equals $13.75.

Therefore, your equation will look like: 13.75 = x + 0.10x

x + 0.1x = 1.10x

So, 13.75 = 1.10x

This means that x = 13.75/1.10

x = 12.5 = $12.50

Answer: Let's represent the cost of the food as "x".

We know that the delivery fee is 10% of the cost of the food, so it can be written as 0.1x.

The total cost that Carlos paid for lunch is the sum of the cost of the food and the delivery fee, which is:

Total cost = Cost of food + Delivery fee

$13.75 = x + 0.1x

Simplifying the equation, we get:

$13.75 = 1.1x

Dividing both sides by 1.1, we get:

x = $12.50

Therefore, the cost of Carlos' lunch before the delivery fee was $12.50.

YES 12.50 is correct I am a k12 student and I have proof. the quiz name is 2.09 Quiz: Multistep Percent Problems

Answer:

30

Step-by-step explanation:

3:7

30 students

3\10×30=9

7\10×30=21

9+21=30

Answer:

Step-by-step explanation:

The correct answer is decreasing the confidence level, increasing the sample size.

A narrower confidence interval means that the range of possible values for the true population parameter is smaller, indicating greater precision in the estimate.

Increasing the sample size will increase the precision of the estimate of the population parameter, thus resulting in a narrower confidence interval.

On the other hand, decreasing the confidence level will also result in a narrower interval. Since the confidence interval represents a range of values that are likely to contain the true population parameter, a lower confidence level means that there is less uncertainty in the estimate of the population parameter, which leads to a narrower interval.

Increasing the sample size and lowering the confidence level are the correct responses.

A narrower confidence interval denotes more accuracy in the estimate because it reduces the range of potential values for the true population parameter.

A narrower confidence interval will be produced by increasing the sample size because it will improve the estimate of the population parameter's precision.

On the other hand, a narrower interval will be produced by lowering the confidence level. A lower confidence level indicates that there is less uncertainty in the estimate of the population parameter, which results in a narrower interval. The confidence interval reflects a range of values that are likely to contain the true population parameter.

learn more about narrower confidence.

https://brainly.com/question/29664929

#SPJ4

If a dataset is generated with the model of polynomial regression of degree 3 then a polynomial regression model of degree 3 will have low bias and low variance.

The correct statement is d. A polynomial regression model of degree 3 will have low bias and low variance.

The given dataset is generated using a polynomial regression model of degree 3. Hence, a polynomial regression model of degree 3 will perfectly fit the data, leading to low bias and low variance. The degree 3 polynomial will have enough flexibility to capture the underlying non-linear relationships in the data. On the other hand, simple linear regression will not be able to capture the non-linear relationship between the predictor and response variables, resulting in high bias and low variance.

In summary, a polynomial regression model of degree 3 will have the best fit for this dataset, with low bias and low variance, whereas simple linear regression will have high bias and low variance.

Learn more about polynomial regression:

https://brainly.com/question/28490882

#SPJ11

Answer: A loss of 6 dollars

Step-by-step explanation:

Step 1 is to determine how many eggs she purchased:

3 dozen eggs * 12 eggs per dozen = 36 eggs purchased

Step 2 is to find the cost of the eggs purchased using the information you gave:

(36 eggs / 6) * 10 dollars = $60 purchase price

Step 3 is to find out how many eggs broke which is calculated like this:

36 total eggs * .25 = 9 broken eggs

Step 4 is to find how much money she made from selling the remaining eggs:

(36 total eggs - 9 broken eggs) * $2 per egg = $54 resale

Step 5 is finding the profit or loss:

$54 resale price - $60 purchase price = $ -6 (aka a 6 dollar loss)

Given:

Rolling a fair dice.

To find:

The theoretical probability of rolling a number less than 5.

Solution:

The possible numbers of rolling a dice are 1, 2, 3, 4, 5, 6.

Total outcomes = 6

Numbers less than 5 are 1, 2, 3, 4.

Favorable outcomes = 4

Now, the theoretical probability of rolling a number less than 5 is:

\(\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}\)

\(\text{Probability}=\dfrac{4}{6}\)

\(\text{Probability}=\dfrac{2}{3}\)

In decimal form, it can be written as:

\(\text{Probability}\approx 0.67\)

In percentage form, it can be written as:

\(\text{Probability}=\dfrac{2}{3}\times 100\)

\(\text{Probability}\approx 66.67%\)

Therefore, the theoretical probability of rolling a number less than 5 in the fraction, decimal and percent are \(\dfrac{2}{3}, 0.67\) and \(66.67\%\) respectively.

The marginal utility of coffee and pastry is found through the partial derivatives of the utility function. The partial derivatives of the function with respect to C and P are shown below:

∂U/∂C = 0.5 C^-0.5 P^0.5

∂U/∂P = 0.5 C^0.5 P^-0.5

In general, the marginal utility refers to the satisfaction or usefulness gained from consuming one more unit of a product. Since the function is a power function with exponent 0.5 for both coffee and pastry, it means that the marginal utility of each product depends on the quantity consumed. Let's consider the marginal utility of coffee and pastry. The marginal utility of coffee (MUc) is calculated as follows:

MUc = ∂U/∂C

= 0.5 C^-0.5 P^0.5

If John consumes more coffee and pastries, his overall utility may still increase, but at a decreasing rate. Marginal utility is the change in the total utility caused by an additional unit of the goods. The marginal utility of coffee and pastry is found through the partial derivatives of the utility function. The partial derivatives of the function with respect to C and P are shown below:

∂U/∂C = 0.5 C^-0.5 P^0.5

∂U/∂P = 0.5 C^0.5 P^-0.5

The marginal utility of coffee and pastry depends on the quantity consumed of each product. The more John consumes coffee and pastries, the lower the marginal utility becomes. However, if John decides to buy the coffee, he will receive 0.25P^0.5 marginal utility, and if he chooses to buy the pastry, he will receive 0.25C^0.5 marginal utility.

To know more about function visit:

https://brainly.com/question/30721594

#SPJ11

The value of x that makes the expressions equivalent is 8

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

4(x-5)= 32-20

Distribute the 4

4x-20=12

4x= 12+20 = 32

x= 32/4 = 8

To learn more about the solution of an equation from the given link

https://brainly.com/question/22688504

#SPJ1

Answer:

2. 13

Step-by-step explanation:

The least number of classes need for all of the students to be registered in a class is 13 since you want all of the stuednts to be registered so no one should be left out. If we do 12*12 (12 students in each class and there are 12 classes), that would only let 144 students take the swimming classes and 8 students would be left out. We don't want that though since we want all of the students to be registered. So let's go to 12*13 (12 students in each class and  there are 13 classes), that would let 156 students take the swimming class. 156>152 so therefore, 13 classes would allow for all 152 students to be registered and it is the least number of classes needed for all the students to be registered in a class (plus you would have 4 seats left for anyone who wants to register in the future but the remainder doesn't matter).  

The area of the triangle is 43.81 square units

The side a = 8 units

The side b = 11 units

The perimeter of the triangle = 32 units

First we have to find the third side of the triangle

a + b + c = 32

Substitute the values in the equation

8 + 11  + c = 32

19 + c = 32

c = 32 - 19

c = 13 units

Then the area of the triangle = \(\sqrt{s(s-a)(s-b)(s-c)}\)

The value of s = (a + b + c) / 2

= (8 + 11 + 13) / 2

= 32/2

= 16

Substitute the values in the equation

The area of the triangle = \(\sqrt{16(16-8)(16-11)(16-13)}\)

Subtract the terms

= \(\sqrt{(16)(8)(5)(3)}\)

= \(\sqrt{1920}\)

= 43.81 square units

Hence, the area of the triangle is 43.81 square units

The complete question is:

Find the area of a triangle , two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.

Learn more about area of triangle here

brainly.com/question/19305981

#SPJ9

Answer:

put them in desmos......

Answer:

can't see the question man take a different picture

The gambler's payoff has a standard deviation of $1. The gambler can expect to win or lose $1 on average for each coin flip, and there is a high degree of variability in the possible outcomes of the game.

The standard deviation of the gambler's payoff can be calculated using the following formula:

σ = √(Σ(xi - μ)^2 * P(xi))

where σ is the standard deviation, xi is the possible outcome of the game, μ is the expected value of the game, and P(xi) is the probability of each outcome.

In this case, there are two possible outcomes: winning $1 with probability 1/2 and losing $1 with probability 1/2. The expected value of the game is:

μ = (1/2 * $1) + (1/2 * -$1) = $0

To calculate the standard deviation, we need to determine the variance first. The variance can be calculated as:

σ^2 = Σ(xi - μ)^2 * P(xi)

= (1 - 0)^2 * 1/2 + (-1 - 0)^2 * 1/2

= 1

Therefore, the standard deviation is:

σ = √1 = 1

To learn more about click standard deviation on,

https://brainly.com/question/13720915

#SPJ4

The volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.


To find the volume of the solid, we can use the method of cylindrical shells. The region bounded by y = x^2 and y = 6 in the first quadrant is a parabolic shape above the x-axis.
To set up the integral for the volume, we consider an infinitesimally small vertical strip of thickness Δx at a distance x from the line x = -3. The height of the strip is given by the difference between the two curves: h = 6 – x^2. The circumference of the cylindrical shell is given by the formula 2πr, where r is the distance between x and the line x = -3, which is r = x + 3.

The volume of the infinitesimal shell is then given by dV = 2π(x + 3)(6 – x^2)Δx. Integrating this expression from x = 0 to x = 3, we obtain the volume V = ∫[0,3] 2π(x + 3)(6 – x^2)dx. Evaluating this integral, we find V ≈ 481.39 cubic units.
In summary, the volume of the solid obtained by rotating the region bounded by y = x^2 and y = 6 about the line x = -3 is approximately 481.39 cubic units.

Learn more about Method of cylindrical shells here: brainly.com/question/31259146
#SPJ11

Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

Learn more aboput the line segment visit:

https://brainly.com/question/280216

#SPJ1

The Fourier series for f(x) is f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...].

The square wave function can be defined as:

f(x) = {1 -π ≤ x < 0

-1 0 ≤ x < π

To find the Fourier series for this function, we first need to determine the coefficients a_n and b_n.

a_n = (1/π) ∫_0^π f(x) cos(nx) dx

= (1/π) ∫_0^π (-1) cos(nx) dx + (1/π) ∫_(-π)^0 cos(nx) dx

= (2/π) ∫_0^π cos(nx) dx

= (2/π) [sin(nπ) - sin(0)]

= 0

b_n = (1/π) ∫_0^π f(x) sin(nx) dx

= (1/π) ∫_0^π (-1) sin(nx) dx + (1/π) ∫_(-π)^0 sin(nx) dx

= -(2/π) ∫_0^π sin(nx) dx

= -(2/π) [cos(nπ) - cos(0)]

= (2/π) [1 - (-1)^n]

Therefore, the Fourier series for f(x) is:

f(x) = (4/π) [sin(x) + (1/3) sin(3x) + (1/5) sin(5x) + ...]

To find the first three Fourier approximations, we truncate this series at the third term.

F_1(x) = -(4/π) sin(x)

F_2(x) = (4/π) sin(x) + (4/3π) sin(3x)

F_3(x) = (4/π) sin(x) + (4/3π) sin(3x) - (4/5π) sin(5x)

These are the first three Fourier approximations of the square wave function f(x). The more terms we include in the Fourier series, the closer the approximations will be to the original function.

To learn more about the Fourier series

https://brainly.com/question/29672996

#SPJ4

Answer:

20³

(4.5)³

8000

Step-by-step explanation:

according to the question

(4.5)³

20³

20×20×20

8000

Answer:

8000 or (4*5)^3

Step-by-step explanation:

6m/s

calculate the number of balloon that can be filled up.

Step-by-step explanation:

speed =wavelength ×Frequency

=6×2 =12m/d

Answer:

the answer is B.

Step-by-step explanation:

hope this helps!

A coefficient is a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x).

The 2 and + are out since they don't have variables(and the + is just a +).

So 4 and x are left. x is a variable, not a coefficient, so the last(and correct) answer is 4.

---

hope it helps

The matrix A of T is given by A = [−4 2;1 -5].

Let T be a linear transformation from R² to R², such that T([1 0]) = [-4 1] and T([0 1]) = [2 -5].

We are to find the matrix A of T.

Linear transformations are functions that satisfy two properties.

These properties are additivity and homogeneity.

Additivity means that the sum of T(x + y) is equal to T(x) + T(y), while homogeneity means that T(cx) = cT(x).

Let A be the matrix of T.

Then, [T(x)] = A[x], where [T(x)] and [x] are column vectors.

This means that A[x] = T(x) for any vector x in R².

We can compute the first column of A by applying T to the standard basis vector [1 0] in R².

That is, [T([1 0])] = A[1 0].

Substituting T([1 0]) = [-4 1], we have -4 = a11 and 1 = a21.

We can compute the second column of A by applying T to the standard basis vector [0 1] in R².

That is, [T([0 1])] = A[0 1].

Substituting T([0 1]) = [2 -5], we have 2 = a12 and -5 = a22.

Therefore, the matrix A of T is given by A = [−4 2;1 -5].

Let us know more about linear transformation : https://brainly.com/question/24115917.

#SPJ11

The least sample size needed to assure with 90% confidence that the sample mean will not differ from the population mean by more than 5 minutes will be 416.16.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end. Data in a normal distribution are symmetrically distributed and have no skew. The majority of values cluster around a central location, with values decreasing as one moves out from the center. In a normal distribution, the measures of central tendency (mean, mode, and median) are all the same. The normal distribution, like any other probability distribution, defines how the values of a variable are distributed. Because it properly captures the distribution of values for many natural occurrences, it is the most important probability distribution in statistics.

Here,

The z value at the 90 percent confidence interval is 1.645.

t ≥ z*s/√n

5≥1.645*62/√n

√n≥20.398

√n≥20.4

n≥416.16

The smallest sample size required to ensure that the sample mean does not deviate from the population mean by more than 5 minutes with 90% confidence is 416.16.

To know more about normal distribution,

https://brainly.com/question/17199694

#SPJ4

Answer:

Distance ≈ 14.8

Step-by-step explanation:

Calculate the distance (d) using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = (- 4, 6) and (x₂, y₂ ) = (3, - 7)

Hope this helps!!!!

a) To calculate the annual demand, we need to use the last digit of your student number. Let's say your student number ends with the digit 5. In this case, the annual demand would be calculated as follows: 400 + 10 * 5 = 450.

b) To calculate the weekly demand forecast for 2021, we divide the annual demand by the number of weeks in a year. Since there are 52 weeks in a year, the weekly demand forecast would be 450 / 52 ≈ 8.65 (rounded to two decimal places).

c) The economic order quantity (EOQ) can be calculated using the formula EOQ = √(2DS/H), where D is the annual demand, S is the ordering cost, and H is the annual holding cost. Plugging in the values, we get EOQ = √(2 * 450 * 1000 / 500) ≈ 42.43 (rounded to two decimal places).

d) The reorder point can be calculated using the formula reorder point = demand during lead time + safety stock. The demand during lead time is the average weekly demand multiplied by the lead time. Assuming the lead time is 4 weeks, the demand during lead time would be 8.65 * 4 = 34.6 (rounded to one decimal place). The safety stock can be determined based on the desired cycle service level.

To calculate the safety stock, we can use the formula safety stock = z * σ * √(lead time), where z is the z-score corresponding to the desired cycle service level, σ is the standard deviation of the weekly demand, and lead time is the lead time in weeks.

Given that the targeted cycle service level is 90% and the standard deviation of the weekly demand is 10, the z-score is 1.28 (from the provided table). Plugging in the values, we get safety stock = 1.28 * 10 * √(4) ≈ 18.14 (rounded to two decimal places). Therefore, the reorder point would be 34.6 + 18.14 ≈ 52.74 (rounded to two decimal places).

e) The total annual cost of managing the inventory can be calculated using the formula TC = S * D / Q + H * (Q / 2 + SS), where S is the ordering cost, D is the annual demand, Q is the order quantity, H is the annual holding cost, and SS is the safety stock. Plugging in the values, we get TC = 1000 * 450 / 42.43 + 500 * (42.43 / 2 + 18.14) ≈ 49916.95 (rounded to two decimal places).

f) The pipeline inventory refers to the inventory that is in transit or being delivered. In this case, since the lead time is 4 weeks, the pipeline inventory would be the order quantity multiplied by the lead time. Assuming the order quantity is the economic order quantity calculated earlier (42.43), the pipeline inventory would be 42.43 * 4 = 169.72 (rounded to two decimal places).

g) If the manager would like to achieve a 95% cycle service level, we need to recalculate the safety stock and reorder point. Using the provided z-score for a 95% cycle service level (1.65), the new safety stock would be 1.65 * 10 * √(4) ≈ 23.39 (rounded to two decimal places). Therefore, the new reorder point would be 34.6 + 23.39 ≈ 57.99 (rounded to two decimal places).

To know more about annual demand here

https://brainly.com/question/32511271

#SPJ11

The correct match of each dilation to its function is: j(x) = (1/2x)^2: vertical stretch, k(x) = 2x²: vertical compression, h(x) = (2x)²: horizontal compression, and g(x) = x²: no dilation, it is the parent function.

Each of the given functions is a dilation of the parent function f(x) = x^2, which means that they are obtained by stretching or compressing the graph of the parent function either vertically or horizontally.

- j(x) = (1/2x)^2: This function is a vertical stretch of the parent function, because the constant factor of 1/2 in front of the x causes the function to be stretched vertically by a factor of 2.

- k(x) = 2x²: This function is a vertical compression of the parent function, because the constant factor of 2 in front of the x^2 causes the function to be compressed vertically by a factor of 1/2.

- h(x) = (2x)²: This function is a horizontal compression of the parent function, because the constant factor of 2 inside the x^2 causes the function to be compressed horizontally by a factor of 1/2.

- g(x) = x²: This is the parent function, and it is not dilated in any way. Its graph is a parabola that opens upwards and has a vertex at the origin.

Thus, this is the correct match for the given scenario.

For more details regarding dilation, visit:

https://brainly.com/question/13176891

#SPJ1

Answer: 4 left

Step-by-step explanation:

36 divided by 90% = 40

40-36=4

Answer:

-infinity < x < +infinity

Step-by-step explanation:

the domain of a cube root function is the set of all real numbers. unlike a square root function which is limited to non-negative numbers, a cube root can use all real numbers because it is possible for three negatives to equal a negative.

Answer:

A

Step-by-step explanation:

Edge 2021

The Probability that a randomly selected student who performed in the spring play, but did not perform in the spring concert is chosen is 26/53.

Now let A be the event of the student performing in Spring play

Let B be the event of students performing i the spring concert

Now according to what we know,

n(A) = 68

n(B) = 54

n(A ∩ B) = 16

Now total no. of students will be n(A U B) = 68 + 54 - 16

= 106

We need to find the number of people who performed in the spring play and not in the concert

Hence we need to find the Probability

P(A ∩ not B)

Now we can say that (A ∩ not B) will clearly be

A - (A ∩ B) Hence we get it to be

68 - 16 = 52

Hence, P(A ∩ notB) = 52/106

= 26/53

To learn more about Probability visit

https://brainly.com/question/29251004

#SPJ4