Alicia bought two slices of pizza and a bottle of juice for $4.95. The juice was $1.65. How much is one slice of pizza?

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

To know more about probability visit:

https://brainly.com/question/31828911

#SPJ11

Answer:

Point Y

Step-by-step explanation:

This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.

What is a pre-image?

Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

What is an Image?

The new position of a point, a line, a line segment, or a figure after a transformation is called its image.

Center of Dilation:

The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

I hope this helps! :)

The consumption next year for Ms. Anderson will be approximately $56,363.64 which is not in options, and the debt-equity ratio, based on a total debt ratio of 0.5, so the answer is option d.

To answer the first question, we need to calculate the consumption next year based on the given information. We can use the concept of present value to determine the amount.

The present value formula is:

Present Value = Future Value / (1 + Interest Rate)^n

Where:

Future Value is the amount to be received in the future

Interest Rate is the rate of return or interest rate per period

n is the number of periods

Given that Ms. Anderson has an income of $40,000 next year and the market interest rate is 10 percent, we can calculate the present value of $40,000:

Present Value = $40,000 / (1 + 0.10)^1

Present Value = $40,000 / 1.10

Present Value ≈ $36,363.64

Since Ms. Anderson consumes $80,000 this year and her present income next year is approximately $36,363.64, her consumption next year will be the sum of her present income and the remaining amount:

Consumption next year = Present income + Remaining amount

Consumption next year = $36,363.64 + ($80,000 - $60,000)

Consumption next year = $36,363.64 + $20,000

Consumption next year = $56,363.64

Therefore, the consumption next year will be approximately $56,363.64. None of the provided options match this amount, so it seems there might be an error in the answer choices.

Given that the total debt ratio is 0.5, it implies that the total debt is half of the total equity.

The debt-equity ratio is calculated by dividing the total debt by the total equity:

Debt-Equity Ratio = Total Debt / Total Equity

Substituting the given information, we have:

Debt-Equity Ratio = 0.5 * Total Equity / Total Equity

The term "Total Equity" cancels out, resulting in:

Debt-Equity Ratio = 0.5

Therefore, the correct answer is option d. 0.5.

Learn more about present value at:

brainly.com/question/30390056

#SPJ11

Answer:

c hope this helps

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

hdjxjdbdjdnekzneisbd

Answer:

1+1=2

Step-by-step explanation:

lol, i hope this helped.

brainliest please? :)

Answer:

it the first one cause you adding so it 8b plus 2

Answer:

C

Step-by-step explanation:

The area (A) of a triangle is calculated as

A = \(\frac{1}{2}\) bh ( b is the base and h the perpendicular height )

Here b = 14 and h = 8 , then

A = \(\frac{1}{2}\) × 14 × 8 = 7 × 8 = 56 in² → C

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

Similar question here:

https://brainly.com/question/29181688?referrer=searchResults

#SPJ11

Answer:

720

Step-by-step explanation:

Answer:

Survey every student participating in after-school sports.

Step-by-step explanation:

Answer:

1. 6x+18 2. 5y-20 3. -7m+7

Step-by-step explanation:

1. 6(x+3) 2. 5(y-4) 3. -7(m-1)

6x+24. 5y-20. -7m+7 <--- - times - = +

Answer:

81

Step-by-step explanation:

9 x 3 x 3 is 81

Answer:

18

Step-by-step explanation:

Area=3x3=9 units

9+9=18

The slope- intercept form of the equation of a line is : y = mx + b

The slope is represented by m and the y-intercept is represented by b.

You can use the coordinates of the two points to find the slope:

m = (y 2 - y 1)

 (x 2 - x 1)

For this problem:

m =   (4 - 2 ) =   2  

(1 - 2)     -1

To determine the y-intercept , substitute the coordinates of either point into the slope-intercept equation using a slope of -2:

y = mx + b

y = -2 • x + b

Using (1,4):

4 = -2 • 1 + b

4 = -2 + b

b = 6

The equation of the line will be :  y = -2•x + 6

Answer:

Goku died you I just started watching

An unnormalized relation refers to a table in a relational database that contains more than one row. This means that there are duplicate rows in the table, which violates the rules of normalization.

Normalization is a process in database design that aims to eliminate data redundancy and ensure data integrity. It involves breaking down a database into multiple tables and defining relationships between them. By doing so, we can efficiently store and retrieve data while minimizing inconsistencies.

In an unnormalized relation, duplicate rows can lead to various problems. For example, it can result in data inconsistencies, as updating one instance of a row may not reflect changes in other duplicate rows. Additionally, it can cause unnecessary storage and maintenance overhead.

To normalize an unnormalized relation, we need to identify the functional dependencies in the table and create separate tables for related data. This helps organize the data and reduces redundancy.

In summary, an unnormalized relation is a table in a relational database that has duplicate rows. It is important to normalize such relations to ensure data integrity and efficiency.

To know more about unnormalized relation click this link -

brainly.com/question/30888382

#SPJ11

The caramel topping demand curve will not change:

The cost of caramel topping is falling; there will be an increase in demand for caramel topping:

Butterscotch topping costs more money;

There will be less demand for caramel topping:

Ice cream now costs more money.

The quantity of caramel topping demanded would increase if the price of the topping dropped. Consequently, the demand curve for caramel topping would go lower.

Ice cream and caramel toppings are complementary products.

Products that are consumed together are said to be complementary.

The amount of ice cream demanded would drop if the price went up. There would be a drop in the number of caramel toppings needed as a result of the fall in demand.

a decline in the popularity of caramel toppings. With less demand, the demand curve for caramel toppings would move inward.

Butterscotch and caramel ice cream toppings serve as stand-ins.

Products that can be used in place of one another are known as substitute goods.

The quantity demanded for butterscotch topping would decline if the price of butterscotch topping rose, making it more expensive overall. Customers might switch to caramel topping. As a result, demand for caramel topping would rise and the demand curve would move outward.

Demand curve: what is it?

The demand curve is a graphical representation of how the cost of an item or service relates to how much is demanded over a given period of time.

To know more about the demand curve visit:

https://brainly.com/question/13131242

#SPJ4

(a) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.

(b) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.

(c) we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.

a. If α is assigned the value 0.001, we are setting a very low significance level for the hypothesis test. This means that we are willing to accept only a very small probability of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.001 or 0.1%.

b. If α is assigned the value 0.05, we are setting a standard significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.05 or 5% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.05 or 5%.

c. If α is assigned the value 0.10, we are setting a relatively high significance level for the hypothesis test. This means that we are willing to accept a probability of up to 0.10 or 10% of making a Type I error. Specifically, we are saying that the probability of rejecting a null hypothesis that is actually true is 0.10 or 10%.

Learn more about hypothesis test

brainly.com/question/30588452

#SPJ11

Each number should be classified as follows:

In Mathematics, there are six (6) common types of numbers and these include the following:

A rational number simply refers to a type of number which consist of integers, fractions, terminating or repeating decimals such as -3, 3, 1/2, -3 3/4, etc.

Additionally, an integer is a whole number that may either be positive, negative, or zero such as, -3, -2, -1, 0, 1, 2, 3, 4 etc.

Read more on rational number here: brainly.com/question/12088221

#SPJ1

Hi there!  

»»————-　★　————-««

I believe your answer is:  

\(\huge\boxed{2\sqrt{3}}\)

»»————-　★　————-««  

Here’s why:  

\(\boxed{\text{Simplifying the square root of 12}}\\\\\rightarrow\sqrt{12}\\\\\text{4 can be factored out of 12.}\\\\\rightarrow\sqrt{4(3)}\\\\\text{Two '2's can be factored out of 4.}\\\\\rightarrow\sqrt{2*2*3}\\\\\rightarrow\sqrt{2^2(3)}\\\\\text{Pulling out the terms from under the radical...}\\\\\rightarrow\boxed{2\sqrt{3}}\)

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The value for $\frac{0.\overline{72}}{0.\overline{27}}$ as a common fraction in lowest terms is 2.666

To convert repeating decimals to fractions, we can use the following method:

Let's call the repeating decimal 0.72... = x, and the repeating decimal 0.27... = y.

Then 10x = 7.2... and 10y = 2.7...

Subtracting the original expressions from the above:

10x - x = 7.2... - 0.72...

=> 9x = 7

=> x = 7/9

And similarly,

10y - y = 2.7... - 0.27...

=> 9y = 2

=> y = 2/9

Therefore,

0.72... / 0.27... = x / y = (7/9) / (2/9) = 7/2 = 3.5

A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. To convert a repeating decimal to a fraction, we need to identify the repeating pattern and convert it to a fraction. This is done by multiplying both the numerator and denominator by a power of 10 that makes the repeating part an integer.

Then, the resulting fraction can be simplified to its lowest terms. In this case, the repeating decimals 0.72... and 0.27... can be converted to the fractions 7/9 and 2/9 respectively, and dividing the two results in a fraction of 7/2 can be simplified to 3.5.

Learn more about common fractions here:

https://brainly.com/question/16937911

#SPJ4

Answer:

The answer is 5.1 from my calculator but the price should be about 14.62

Step-by-step explanation:

I put it into a calculator

Answer:

x = (59/16)

y = (-65/32)

Step-by-step explanation:

2x + 12y = −17

3x + 2y = 7

--------------------------

(2x + 12y = −17) × 3

6x + 36y = -51

(3x + 2y = 7) × -2

-6x - 4y = -14

----------------------------------

6x + 36y = -51

-6x - 4y = -14

-----------------------

32y = -65

÷32 ÷32

--------------------------

y = (-65/32)

3x + 2y = 7

3x + 2(-65/32) = 7

3x - (65/16) = 7

+(65/16) +(65/16)

-------------------------------

3x = (177/16)

÷3 ÷3

---------------------------

x = (59/16)

I hope this helps!

Answer:

so not submit yet, i cant see the digits in the sphere.

Using the four-step process,  f'(1) = 10, f'(2) = 12, and f'(3) = 14.

To identify f'(x), the derivative of f(x), using the four-step process, we can follow these steps:

1: Identify the function.
The given function is f(x) = x^2 + 8x - 6.

2: Apply the power rule.
Differentiate each term of the function separately.
The derivative of x^2 is 2x.
The derivative of 8x is 8.
The derivative of -6 is 0 (constant term).

3: Simplify.
Combine the derivatives obtained in step 2.
So, f'(x) = 2x + 8.

4: Evaluate f'(1), f'(2), and f'(3).
Substitute x = 1, 2, and 3 into the derived equation to identify the respective values.
f'(1) = 2(1) + 8 = 10.
f'(2) = 2(2) + 8 = 12.
f'(3) = 2(3) + 8 = 14.

You can learn more about derivatives at: brainly.com/question/29144258

#SPJ11

The process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.

We can use a mass balance approach to solve this problem. Let's start by calculating the amount of salt in the tank at any given time. We know that initially there are 5 grams of salt in 20 liters of water, so the concentration of salt is:

c1 = 5 g / 20 L = 0.25 g/L

As brine with a concentration of 2 grams per liter is added at a rate of 3 liters a minute, the concentration of salt in the tank increases at a rate of:

dc/dt = 2 g/L * 3 L/min = 6 g/min

At the same time, the tank is being drained at 3 liters a minute, so the volume of the tank remains constant. This means that the total amount of salt in the tank is changing at a rate of:

dm/dt = dc/dt * V = (6 g/min) * (20 L) = 120 g/min

We want to know how long the process has to continue until there are 20 grams of salt in the tank, which means we need to solve for the time t when the total amount of salt in the tank reaches 20 grams:

m = 5 g + (6 g/min) * t - (3 L/min) * t * (0.25 g/L) = 20 g

Simplifying this equation, we get:

6t - 0.75t = 15

5.25t = 15

t = 2.86 minutes

Therefore, the process has to continue for approximately 2.86 minutes until there are 20 grams of salt in the tank.

To know more about mass balance approach  click here:

brainly.com/question/14301365

#SPJ4

Answer:

Point form: (-2,3)

Equation form: x= -2, y=3

Step-by-step explanation:

Hope it helps!