Ms. Soffer paid $42. 75 for 9 boxes of gummies for the state test last year. This year she will need to order 13 boxes of gummies for the state test. If the price per box does not change, what would be the total cost of this year’s order?

The number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

We can solve this inequality by introducing an auxiliary variable x4, such that x1 + x2 + x3 + x4 = 11. Here, x1, x2, x3, and x4 are all nonnegative integers.

We can interpret this equation as follows: imagine we have 11 identical objects and we want to distribute them among four boxes (x1, x2, x3, and x4). Each box can contain any number of objects, including zero. The number of solutions to this equation will give us the number of nonnegative integer solutions to the original inequality.

We can use a technique known as stars and bars to count the number of solutions to this equation. Imagine we represent the 11 objects as stars: ***********.

We can then place three bars to divide the stars into four groups, each group representing one of the variables x1, x2, x3, and x4. For example, if we place the first bar after the first star, the second bar after the third star, and the third bar after the fifth star, we get the following arrangement:

| ** | * | ****

This arrangement corresponds to the solution x1=1, x2=2, x3=1, and x4=7. Notice that the number of stars to the left of the first bar gives the value of x1, the number of stars between the first and second bars gives the value of x2, and so on.

We can place the bars in any order, so we need to count the number of ways to arrange three bars among 14 positions (11 stars and 3 bars). This is equivalent to choosing 3 positions out of 14 to place the bars, which can be done in C(14,3) ways.

Therefore, the number of nonnegative integer solutions to the inequality x1 + x2 + x3 ≤ 11 is C(14,3) = 364.

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Answer:

36

Step-by-step explanation:

● 3[ (4-2)^5 -20]

● 3 ( 2^5 -20 )

● 3 (32-20)

● 3× 12

● 36

As per the given hypothesis test, the randomization distribution is 0.0647177.

The term randomization distribution is defined as use resampling techniques to construct a sampling distribution that can be used to make inferences about the population.

Here we have given that a hypothesis test for the difference in two means, , is to be performed using the sample summarized below.

And we need to find the method used to generate samples for the randomization distribution

As per the given details, we have know that the given details

x1 = 6

σ1 = 0.25

x2 = 4

σ2 = 0.30

Then the distribution is calculated as,

z1 = 0.232476

P( X ≤ 1.644854 ) = 0.591916.

P( X > 1.644854 ) = 0.408084.

Probability density( 1.644854 ) = 0.0647177.

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The demand function for good X is Qx = m - 3Px + 2Py, where Qx is the quantity demanded of X, m is income, Px is the price of X, and Py is the price of a related good Y. The equation shows that the demand for X is inversely related to its price and directly related to the price of Y. Income, price of X, and price of Y collectively affect the overall demand for X.


The demand function for good X is given by Qx = m - 3Px + 2Py, where Qx represents the quantity demanded of good X, m is the income, Px is the price of good X, and Py is the price of a related good Y. In this equation, the income and prices are assumed to be positive.

To determine the demand for good X, we can analyze the equation. The coefficient -3 in front of Px indicates that the demand for good X is inversely related to its price. As the price of X increases, the quantity demanded of X decreases, assuming other factors remain constant. On the other hand, the coefficient 2 in front of Py indicates that the demand for good X is directly related to the price of the related good Y. If the price of Y increases, the quantity demanded of X also increases, assuming other factors remain constant.

Furthermore, the term (m - 3Px + 2Py) represents the overall effect of income, price of X, and price of Y on the quantity demanded of X. If income (m) increases, the quantity demanded of X increases. If the price of X (Px) increases, the quantity demanded of X decreases. If the price of Y (Py) increases, the quantity demanded of X increases.

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Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

a line parallel to the y- axis is a vertical line with equation

x = c ( c is the value of the x- coordinates the line passes through )

the only line in this form is

x = - 2

Answer:

x = -2

Step-by-step explanation:

Since x = -2 is a vertical line, there is no y-

Hence, x = -2 is a parallel line to y - axis

If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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Answer:

35.01 cm or 35cm

Step-by-step explanation:

\(\frac{volume}{\pi r^{2} } =height\)

\(\frac{5390}{\pi 7^{2} }\)=35.01cm

Answer:

x = 7.7

Option B

Step-by-step explanation:

\( \frac{a}{Sin~A} &=& \frac{b}{Sin~b} \\ \frac{8}{Sin~73^\circ} &=& \frac{x}{Sin~67^\circ} \\ \frac{8}{0.96} &=& \frac{x}{0.92} \\ 0.96x &=& 8 \times 0.92 \\ 96x &=& 8 \times 92 \\ 96x &=& 736 \\ x &=& \frac{736}{96} \\ x&=& \frac{23}{3} \\ &\boxed{x=7.7}&\)

∴ value of x is 7.7

Answer:

A. 50

Step-by-step explanation:

Answer:

D.  100,000

Step-by-step explanation:

The exponent for 10^5 is 5.  Move the decimal point five places to the right to obtain the decimal value.  10^5 is the same as 1 x 10^5.

1 x 10^5

10 x 10^4

100 x 10^3

1000 x 10^2

10000 x 10

100,000

Answer:

9

Step-by-step explanation:

Let that number be x whose 6 is two thirds. Now we need to find here the value of x .

So,

\(\underline{\boldsymbol{ According\ to \ the \ Question :- }}\)

=> x × ⅔ = 6

=> x = 6*3/2

=> x = 9

The remaining angles of angle ABC and angle DEF are  right angles since they add up to 90 degrees.

Under the condition that angle ABC and angle DEF are both supplementary to angle XYZ, and angle XYZ is a right angle, then angle ABC and angle DEF are both right angles.

This is due to the supplementary angles add up to 180 degrees and since angle XYZ is a right angle (90 degrees), then angle ABC and angle DEF must be right angles since they add up to 90 degrees.

Supplementary angles are known as  two angles whose sum is 180 degrees . For instance, angle 130° and angle 50° are supplementary angles because the sum of 130° and 50° is equal to 180°. When supplementary angles are put together, they form a straight line and a straight angle.

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Step-by-step explanation:

this is the problem to sum the numbers 1 ... n.

remember the old trick by adding

n + 1

n-1 + 2 = n + 1

n-2 + 3 = n + 1

...

and doing this n/2 times, giving us a sum

n×(n+1)/2

for n = 30 we get

30×31/2 = 15×31 = 465

so, 465 people will perform.

The general solution to the differential equation y'' + 4y = e^(2x) is:

y = c1cos(2x) + c2sin(2x) + (1/8)e^(2x)

To find the particular solution of the differential equation:

y'' + 4y = e^(2x)

We can use the method of undetermined coefficients. Since the right-hand side of the equation is an exponential function of the same form as the homogeneous solution, we guess a particular solution of the form:

yp = Ae^(2x)

Taking the first and second derivatives of yp, we get:

yp' = 2Ae^(2x)

yp'' = 4Ae^(2x)

Substituting these expressions into the differential equation, we get:

4Ae^(2x) + 4(Ae^(2x)) = e^(2x)

Simplifying, we get:

8Ae^(2x) = e^(2x)

A = 1/8

Therefore, the particular solution is:

yp = (1/8)e^(2x)

So the general solution to the differential equation is:

y = yh + yp

where yh is the general solution to the homogeneous equation y'' + 4y = 0, and yp is the particular solution we just found.

The general solution to the homogeneous equation is:

yh = c1cos(2x) + c2sin(2x)

where c1 and c2 are arbitrary constants.

Therefore, the general solution to the differential equation y'' + 4y = e^(2x) is:

y = c1cos(2x) + c2sin(2x) + (1/8)e^(2x)

where c1 and c2 are arbitrary constants determined by the initial or boundary conditions.

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The average value of the function f(x,y) = 2e^y √(e^y + x) over the rectangle R = [0,4]x[0,1] is approximately 9.936.

This means that if we were to graph the function f(x,y) over the rectangle R and find the height of the "average" point, it would be approximately 9.936.

To find the average value of f(x,y) over R, we need to evaluate the double integral of f(x,y) over R and divide it by the area of R. We can use the formula:

fave = (1/A) ∬R f(x,y) dA

where A is the area of R.

To evaluate the double integral, we first integrate f(x,y) with respect to y, then with respect to x. This yields:

fave = (1/4) [2/3 ((2/5)(e + 4)^(5/2) - (2/5)e^(5/2) - (2/3)(4)^(3/2))]

Simplifying this expression gives us the approximate value of 9.936. This means that the "average" value of the function f(x,y) over the rectangle R is 9.936.

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Answer:

It's been awhile since I've done this but wouldn't it be -2x

Step-by-step explanation:

Answer:

whatssssssssssssssssssss

Answer:

5/6

Step-by-step explanation:

\(\frac{3}{10} + \frac{8}{15}\)

\(\frac{45+80}{150}\)

\(\frac{125}{150}\) ..............simplify the fraction

\(\frac{5}{6}\)

The options that present the categories in which Law is divided into are:CivilCriminalMaritimeLitigation.  This type of law governs the way that individuals are prosecuted for committing crimes. It includes laws that are designed to protect public safety, such as laws against theft, assault, and murder.

Law is defined as a system of rules that are enforced through social institutions to govern behavior. It regulates and ensures that individuals and organizations are held accountable for their actions. Law, therefore, plays a significant role in controlling human conduct. It deals with the relation between individuals, groups, and society.The above four options present the categories that the legal system is divided into. The four major categories that law is divided into are:Civil law: Litigation: Litigation is a legal proceeding in which two parties argue their case in front of a court. It is a legal process that involves presenting evidence to a judge or jury. It is used to resolve disputes between parties that cannot be settled outside of court.

Law is a complex subject that deals with a wide range of issues. It is a system that is used to regulate behavior and ensure that individuals and organizations are held accountable for their actions. The legal system is divided into several categories, which include civil law, criminal law, maritime law, and litigation.Civil law is a type of law that deals with non-criminal legal disputes between individuals, corporations, or the government. This type of law includes contract disputes, divorce cases, property disputes, personal injury lawsuits, and child custody battles. Civil law is often used to resolve disputes between parties that cannot be settled outside of court.Criminal law is a system that is used to regulate and punish people who commit crimes.Maritime law is a type of law that deals with legal disputes that arise in the maritime industry. This type of law governs the relationships between seafarers, shipowners, and cargo owners. Maritime law is often used to resolve disputes that arise over the transportation of goods, the sale of ships, and the employment of seafarers.Litigation is a legal proceeding in which two parties argue their case in front of a court. It is a legal process that involves presenting evidence to a judge or jury. It is used to resolve disputes between parties that cannot be settled outside of court. Litigation is often used in civil law cases, although it can be used in criminal cases as well.

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Age is the most likely lurking variable in this scenario.

Height is a measure of how tall or high something is, typically referring to the distance from the bottom to the top of an object or the distance between a surface and the top of an object above it. Height can be measured in various units such as meters, feet, or inches. For example, the height of a person, a building, or a mountain can be measured in meters or feet.

Given by the question: -

As people age, they are more likely to experience male pattern baldness, and they are also at higher risk of severe illness from COVID-19. Therefore, the association between male pattern baldness and severe COVID-19 may be due to age rather than any direct causal link between baldness and COVID-19 severity. It is important to account for potential lurking variables in any study to avoid drawing incorrect conclusions about causation.

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Answer:

Cost of peach is 72 p each.

Step-by-step explanation:

Total amount was 5x100 = 500 p

Amount of apples were ( 4 x 60) = 240 p

Received change = 44p

Total amount for 3 peaches were = 500-240-44 = 216

Cost of 1 peach = \(\frac{216}{3}\)

= 72p

\(\text{Given that,}~ f(x) = 2x -1~ \text{and}~ g(x) = x^2- 3x -2 \\\\\text{Now,}\\\\~~~(f+g)(x)\\\\=f(x) + g(x)\\\\=2x-1 +x^2 -3x -2\\\\=x^2 -x -3\)

Answer:

(f + g)(x) = x² - x - 3

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= 2x - 1 + x² - 3x - 2 ← collect like terms

= x² - x - 3 ← in standard form

Manipulating temperature in a room to study its impact on task performance involves categorizing the various temperature conditions as the "levels" of the variable.

In experimental research, when investigating the influence of temperature on task performance, researchers manipulate and control the temperature to create different conditions or levels. These temperature levels serve as the independent variable in the study. By systematically altering the temperature, researchers can observe and analyze how variations in temperature affect participants' performance on the given tasks. This experimental design allows researchers to identify patterns, trends, and potential causal relationships between temperature and task performance. Understanding the different temperature conditions or levels in such studies helps researchers learn about the nuanced impact of temperature on human performance and potentially inform practical applications in various settings, such as optimizing work environments or designing effective learning spaces.

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17 is the integer expressed in base 10.

Given that,

The base 7 representation of a positive integer is AB and its base 5 representation is BA, where A and B are digits from 1 to 4, inclusive.

We have to find what is the integer expressed in base 10.

We know that,

Base 7 representation of a positive integer AB.

Can be written as 7A+B in base 10.

Base 5 representation of BA can be written as 5B+A in base 10.

So, 7A+B= 5B+A

6A=4B

A=2/3B

Now, A and B must be in 1 to 4.

The digits between 1 and 4 who are 2/3 of another is 2 and 3.

A=2 and B=3

So,

Base 7 is 23

And Base 5 is 32

Base 7 is 23 is 17 of base 10.

And Base 5 is 32 is 17 of base 10.

A=17

Therefore, 17 is the integer expressed in base 10.

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Answer:

201 square inches

Step-by-step explanation:

Answer:

x= -1

x=-4/3

Step-by-step explanation:

3x^2 + 7x + 4 = 0

a = 3

b = 7

c = 4

x =-7+1/6

x =-7-1/6

x = -1

x = -4/3

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

Answer:

n= plus or minus (+-) square root 69/ 3 -2

Step-by-step explanation:

Answer:

n = -2[+/-] (2 \(\sqrt{69}\))/3

Step-by-step explanation:

in other words, the answer is

n=0.768875

and

n = -4.76887