3. Assume that there are only 2 commodities and that the utility function is multiplication of the form U = 1÷4qxqy.Find the demand function of the commodity x and y and explain the relationship between price and income in relation to the demand.​

For the given triangular prism, the volume value is obtained as Option B: 31.5 in³.

What is a triangular prism?

The pentahedron Triangular Prism contains nine different nets. The bases' vertices and edges are connected by means of their three rectangular sides. The rectangular sides of the triangular prism are joined to one another side by side. Every cross-section that is perpendicular to the base faces is a triangle.

The height of the triangular prism is given as 2 inches.

The base of the triangular prism is given as 7 inches.

The length of the triangular prism is given as 4.5 inches.

The volume of a triangular prism is given by the formula -

V = (1/2) × b × h × l

where b is the base of the triangle, h is the height of the triangle, and l is the length of the prism.

Substituting these values into the equation, we get -

V = (1/2) × 7 inches × 2 inches × 4.5 inches

V = 7 inches × 1 inch × 4.5 inches

V = 31.5 cubic inches

Therefore, the volume of the triangular prism is 31.5 cubic inches.

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The missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

What is the quadratic equation?

A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus," which means "square."

First, let Xa, Xb, Xc, Xd = each factor

Xd = each factor which shows In the graph

Then, we can know that

Xa, Xb are the roots of x² + ___x + 14

Xb, Xd are the roots of x²= 3x - __

Xc, Xd are the roots of x² - __x - 15

Xa, Xc are the roots of x² + 10x + __

Xa * Xb = 14           Xd = 15/10 +Xa

Xb+ Xd = 3            14/Xa + 15/10 +Xa = 3

Xc* Xd = - 15          140 + 29Xa/Xa(10+Xa)

Xa + Xc = -10x        140 + 29Xa = 30Xₐ + 3Xₐ²

Xb = 14/Xa             3Xₐ² + Xₐ² - 140 = 0

14/Xa + Xd = 3       Xa1 = -7   Xa2 = 20/3

Xd = -15/-3             Xb1 = -2   Xb2 = 21/10

Xc = -10 -X1            Xc1 = -3    Xc2 = -30/3

Xc1 = -3     Xc2 = -30/3

Xd1 = 5         Xd2=9/10

There are two kinds of answers.

1) x² + 9x + 1x           Xa1 + Xb1 = -9

x² - 3x + 10           Xb1 * Xd1 = -10

x² - 2x - 15           Xc1 + Xd1 = 2

x² + 10x + 21           Xa1 * Xc1 = 21

2)

x² - (263/30)x + 14           Xa2 * Xb2 = 263/30

x² - 3x - (-189/100)           Xb2 * Xd2 = 189/100

x² - (413/30)x - 15           Xc2 + Xd2 = 413/30

x² + 10x + (1000/9)           Xa2 * Xc2 = 1000/9

Hence, the missing values that make this statement true are as

x² + 9x + 14,  x² - 3x - 10

x² - 2x - 15,   x² + 10x + 21

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Therefore , the solution of the given problem of matrix comes out to be  V = (4/3)π(1³) = (4/3)π.

A matrix is a collection of integers set up in a rectangular array with rows and columns. The elements or components of the matrix are the integers. Numerous areas of mathematics as well as the fields of economics, physics, statistics, and architecture all make extensive use of matrix algebra.

Here,

(a)

Let (x1, x2, x3) be any point in the set {(x1, x2, x3) e IR³ | x1²/a² + x2²/b² + x3²/c² ≤ 1}, on the other hand. Next, we have

(x1²/a²) + (x2²/b²) + (x3²/c²) ≤ 1

When we multiply both parts by 3, we obtain:

a²x1² + b²x2² + c²x3² ≤ 3

The condition for T(S) is satisfied by (x1, x2, x3), indicating that (x1, x2, x3) is in T.(S).

T(S) is the collection ({(x1, x2, x3) e IR³ | x1²/a² + x2²/b² + x3²/c² ≤ 1}.a result.

(b) The following formula determines the volume of the spheroid with semiaxes of lengths(1/√(a))(1/√(b)) and (1/√(c))

=>V = (4/3)π (1/√(a))(1/√(b))(1/√(c))

If we replace a = b = c = 1, we get:

=> V = (4/3)π (1)(1)(1) = (4/3)π

The following algorithm determines the unit ball's volume in IR3:

=> V = (4/3)π(1³) = (4/3)π

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The provided remark indicates that option (A) is accurate for 2.5 inches.

The measurement or size of something to end to end is referred to as its length. To put it another way, it is the bigger of the upper two or three dimensions of a geometric form or object. For instance, the length and width of a parallelogram define its measurements.

Using the given equation:

Arc Length / 20π = 45/360

Cross multiply:

Arc length × 360 = 20π x 45

Arc length x 360 = 900π

Divide both sides by 360:

Arc length = 900π / 360

Arc Length = 2.5 π inches.

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Answer:

Dan eat 2 2/3 of a pizza

Step-by-step explanation:

the answer is above

Let

x-----> amount of pizza Jay ate

y-----> amount of pizza Dan ate

we know that

----> equation A

-----> equation B

substitute equation A in the equation B and solve for y

Convert to mixed number

Answer:

y = 3x - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 and c = - [tex]\frac{1}{2}[/tex] , then

y = 3x - [tex]\frac{1}{2}[/tex] ← equation of line

Answer:

     6.75 inches.

Step-by-step explanation:

[tex]183.69 = 2*3.14*3^2 + 2*3.14*3*h[/tex]

[tex]= 56.52 + 18.84h[/tex]

[tex]183.69 - 56.52 = 18.84h[/tex]

[tex]127.17 = 18.84h[/tex]

[tex]=\frac{127.17}{18.84}[/tex]

[tex]=6.75[/tex]

Answer:

Step-by-step explanation:

To calculate the equal monthly payments under this loan, we can use the formula for the present value of an annuity due, since the payments are due at the end of each period. The present value of the equal monthly payments can then be set equal to the loan amount of R250,000, and we can solve for the payment amount.

First, we need to calculate the present value factor for an annuity due with 12 payments per year over a four-year period, using a nominal annual rate of 6%.

PVIFA(due) = (1 - (1 + r/n)^(-nt))/((r/n)(1 + r/n))

Where:

r = nominal annual rate = 6%

n = number of compounding periods per year = 12

t = number of years = 4

PVIFA(due) = (1 - (1 + 0.06/12)^(-12*4))/((0.06/12)(1 + 0.06/12)) = 43.232

Next, we can use the formula for the present value of an annuity due to calculate the equal monthly payments:

PMT = PV / PVIFA(due)

Where:

PV = present value of the loan = R250,000

PMT = 250000 / 43.232 = R5,785.97

Therefore, your equal monthly payments will be R5,785.97. At the end of the four-year period, you will also need to make a final balloon payment of R50,000 to fully pay off the loan.

The scaling factor for given transformation is 3.

What exactly is scaling factor?

The scaling factor, also known as the scale factor, is a value that indicates how much a geometric figure is enlarged or reduced. It is the ratio of the length of a side or dimension of the original figure to the length of the corresponding side or dimension of the new figure. The scaling factor can be greater than 1, which indicates an enlargement, or less than 1, which indicates a reduction. When the scaling factor is 1, the two figures are congruent, which means they have the same shape and size.

Now,

We can find the scale factor by comparing the corresponding side lengths of the two polygons. Let's start by finding the side lengths of the original polygon:

HI: √[(4-0)² + (-5+3)²] = √20

IJ: √[(6-4)² + (0-0)²] = 2

JK: √[(4-6)² + (5-0)²] = √41

KL: √[(0-4)² + (3-5)²] = √20

LH: √[(0-0)² + (-3+5)²] = 2

Now let's find the corresponding side lengths of the dilated polygon:

H'I': √[(12-0)² + (-15+9)²] = √600

I'J': √[(18-12)² + (0-0)²] = 6

J'K': √[(12-18)² + (15-0)²] = √600

K'L': √[(0-12)² + (9-0)²] = √600

L'H': √[(0-0)² + (-9+3)²] = 6

We can see that the side lengths of the dilated polygon are all 3 times as long as the corresponding side lengths of the original polygon. Therefore, the scale factor is 3.

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Hi!

Okay, lets make this quick for you :)
1 Inch = 16 feet
2.25 (=1/4 as a decimal) x 16 is 36.
3 x 16 is 48.
4 x 16 is 64.
1.75 (= 3/4 as a decimal) x 16 is 28.

Add all of them together!
36 + 48 + 64 + 28 = 176.

So, your answer is 176.

Hope this helps!
~~~PicklePoppers~~~

Answer:

2512 ft^2

Step-by-step explanation:

Consider the whole figure as ABCD.

Law used: Opposite sides are equal.

Soln: For rectangle ABCD,

= L*B

= 4*3 = 12 inches

And,For extended area, BFEL:

Area: L*B = 7/4*5/4 = 35/16

So,Area of given region:

=12-35/16

= 192-35/16 = 157/16 inches.

In Feet,we have:

Given 1in = 16 ft.

1 in^2 = 16*16 ft^t

in ^2 = 256 ft^t

157/16 in^2 = 256*157/16 = 2512 ft^2 (ans)

In linear equation, “Yes.” This is the example of bias.

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.

The question asked by the soft drink company is leading and suggestive in nature as it implies that their product is better than their rival's product. This can influence the respondent's answer and lead to biased results. Additionally, the sample size of 500 people may not be representative of the entire population, and the respondents may not be randomly selected.

Therefore, the results of this survey may not accurately reflect the true opinions of the population regarding the superiority of the soft drink company's product over its rival's product. To obtain more accurate and reliable results, the question should be more neutral and the sample should be randomly selected and representative of the population.

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The value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

Mathematical statements called expressions must have a minimum of two words with either numbers, variables, or both, joined by an operator. The four different types of mathematical operators are addition, subtraction, multiplication, and division. For instance, the expression x + y is an expression where x and y are words with an addition operator between them. Mathematical expressions may be divided into two categories: algebraic expressions, which include both numbers and variables, and numerical expressions, which solely contain numbers.

The given expression is tan(arcsin (2/7)).

The value of arcsin(2/7) = 16.60

Now substitute the value:

tan(16.60) = 0.29

Hence, the value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

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The trigonometric expression tan(arcsin (2/7)) has a value of 0.29.

What are trigonometric expressions?

Mathematical statements called expressions must have a minimum of two words with either numbers, variables, or both, joined by an operator.

The addition, subtraction, multiplication, and division operations are the four distinct categories of arithmetic operators.

For instance, the expression x + y is an expression where x and y are words with an addition operator between them.

Mathematical expressions may be divided into two categories: algebraic expressions, which include both numbers and variables and numerical expressions, which solely contain numbers.

The given expression is tan(arcsin (2/7)).

The value of arcsin(2/7) = 16.60

Now substitute the value:

tan(16.60) = 0.29

Hence, the value of the given trigonometric expression tan(arcsin (2/7)) is 0.29.

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Answer:51,000

Step-by-step explanation:

ther is 1000 grams every kilogram so 17x3 is 51 and 51x1000 is 51,000

Answer:

The integers are 5 and 7.

Step-by-step explanation:

im 99% sure that is right! hope i helped!

Therefore, the cost per yard of wool carpet is $52.

When two expressions are joined by the equal sign, a mathematical statement is referred to as an equation. 3x - 5 = 16 is an illustration of an equation.

Let x be the cost per yard of nylon carpet, and let y be the cost per yard of wool carpet.

From the information given in the problem, we can set up two equations based on the two purchases:

18x + 20y = 1922 (equation 1)

18x + 27y = 2286 (equation 2)

We want to find the cost per yard of wool carpet, y. We can solve for y by subtracting equation 1 from equation 2:

7y = 364

y = 52

Therefore, the cost per yard of wool carpet is $52.

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Answer:

Step-by-step explanation:

Here's a step-by-step explanation of how to calculate the p-value for the hypothesis test:

Step 1: State the null and alternative hypotheses

The null hypothesis is that the true population mean weight of stoaches is 308 g, and the alternative hypothesis is that the true population mean weight is not 308 g.

H0: µ = 308 g (null hypothesis)

Ha: µ ≠ 308 g (alternative hypothesis)

Step 2: Determine the test statistic

We can use a t-test to determine the test statistic for this hypothesis test. The test statistic is given by:

t = (sample mean - hypothesized mean) / (standard error of the mean)

where the sample mean is 313.8 g, the hypothesized mean is 308 g, and the standard error of the mean is calculated as:

standard error of the mean = standard deviation / sqrt(sample size)

Substituting the given values, we get:

t = (313.8 - 308) / (58 / sqrt(54))

t = 1.547

Step 3: Determine the p-value

To determine the p-value, we need to find the probability of obtaining a test statistic as extreme or more extreme than our observed t-value, assuming the null hypothesis is true. Since we have a two-sided alternative hypothesis, we need to find the area in both tails of the t-distribution that is more extreme than our observed t-value.

Using a t-distribution table or calculator with 53 degrees of freedom (since we have a sample size of 54), we find that the probability of obtaining a t-value of 1.547 or greater is 0.0722 in the right tail, and the probability of obtaining a t-value of -1.547 or less is also 0.0722 in the left tail. Therefore, the p-value for the two-sided test is the sum of these two probabilities:

p-value = 0.0722 + 0.0722

p-value = 0.1444

Step 4: Compare the p-value to the significance level

The significance level is typically set to 0.05 for hypothesis tests. Since our calculated p-value (0.1444) is greater than the significance level of 0.05, we fail to reject the null hypothesis. This means that we do not have sufficient evidence to suggest that the true population mean weight of stoaches is different from 308 g.

In summary, the p-value for the two-sided hypothesis test is 0.1444, and since this value is greater than the significance level of 0.05, we do not reject the null hypothesis.

Answer:

(2x)(4x)= 8x^22x + 4x = 6x(x+1)+ 2x = 3x + 1(x+1)(2x) = 2x^2 + 2x3x + (2x) = 5x(3x)(2x) = 6x^2

Step-by-step explanation:

hope this helped

The missing coordinate of line is r = 8.

A straight line is a geometrical object that extends infinitely in both directions and has no curvature or bending. It is a one-dimensional object that is defined by two points on the line, called its endpoints, or by its slope and a point on the line.

the slope formula to find the slope of the line given two points:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Plugging in the coordinates we have:

-4 = (-16 - r) / (1 - (-5))

Simplifying:

-4 = (-16 - r) / 6

Multiplying both sides by 6:

-24 = -16 - r

Adding 16 to both sides:

-8 = -r

Dividing both sides by -1:

r = 8

Therefore, the missing coordinate is r = 8.

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Because the x2 term's coefficient is positive, the function will rise without  equation bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the number "9".

The y-intercept of the equation y = (0,0) is the point on the line where it meets the y-axis and corresponds to the value of y when x equals 0. As a result, the equation y = 0's y-intercept is (0,0).

An equation's domain is the set of all possible values of x for which the equation is defined.

a) Because there are no constraints on the potential values of x, the domain of the equation y = x2 - 4x is all real integers.

b) The domain of the equation y = 1/(x-4) includes all real numbers except x = 4, which is undefined since division by zero is undefined.

c) Because the term within the square root must be non-negative, the domain of the equation y = sqrt(x-3)(x-4) is x >= 3.

As x approaches a specific value, the graph of the function approaches but never reaches vertical asymptotes. As the denominator of a rational function hits 0, they arise.

Because y = (x-3)(x-4) is not a rational function, it lacks vertical asymptotes.

A function's horizontal asymptote is a horizontal line that it approaches when x approaches infinity or negative infinity.

The dominant term in the formula as x gets extremely large or very tiny is x2, thus we can rewrite the equation as [tex]y = x2 - 7x + 12[/tex]  .

Therefore, Because the x2 term's coefficient is positive, the function will rise without bound as x approaches infinity or negative infinity. As a result, no horizontal asymptote exists.

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Using the product rule of logarithms, we can condense the expression as follows:

log(x/3 * y/3 * z/3)

= log((xyz) / 27)

So, the condensed form of the given expression is log((xyz) / 27).

a. The shape οf the distributiοn οf the sample mean time is nοrmal.

b. The standard error is 0.5345.

Standard deviatiοn is: It is a measure οf hοw spread οut numbers are. It is the square rοοt οf the Variance, and the Variance is the average οf the squared differences frοm the Mean.

Given that:

μ =35

σ = 2

n = 14

a. The shape of the distribution of the sample mean time is normal.

b. To calculate the standard error of the mean time, we would apply this formula,

Standard error :

[tex]$ \rm SE = \frac{ \sigma}{\sqrt{(n)} }[/tex]

[tex]$ \rm SE = \frac{ 2}{\sqrt{(14)} }[/tex]

SE = 0.5345

Thus, the standard error is 0.5345.

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Complete question:

Majesty Videο Prοductiοn Inc. wants the mean length οf its advertisements tο be 30 secοnds. Assume the distributiοn οf ad length fοllοws the nοrmal distributiοn with a pοpulatiοn standard deviatiοn οf 2 secοnds. Suppοse we select a sample οf 16 ads prοduced by Majesty.

a. What can we say abοut the shape οf the distributiοn οf the sample mean time?

b. What is the standard error of the mean time?

The table that represents the function for a lawn being mowed more quickly than by Killian's rate is given as follows:

Second table.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

Killian can cut grass at a rate of 1000 square feet each 10 minutes, hence his average rate of change is given as follows:

1000/10 = 100 square feet per minute.

For the second table, in 7 minutes, 1100 square feet of lawn is mowed, hence the rate is given as follows:

1100/7 = 157 square feet per minute.

It is more quickly than Killian's as the rate of change is greater.

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Answer:0

Step-by-step explanation: just like you did on my question and stole the points :) xx

Answer:

Alright

Step-by-step explanation:

50/1.428

Multiply the numerator by the denominator to get 50000/1428

Set equation up in long division format

Divide 50000 by 1428 to get 3

Divide 7160 by 1428 to get 5

Divide 200 by 1428 to get 0

Divide 2000 by 1428 to get 1

Divide 5720 by 1428 to get 4

Divide 80 by 1428 to get 0

Divide 800 by 1428 to get 0

35.014

Answer:

8 feet.

Step-by-step explanation:

Let's denote the width of the sandbox as "w".

We know that the perimeter of a rectangle is given by the formula:

Perimeter = 2(length + width)

So, we can plug in the given values:

46 = 2(15 + w)

Now, we can solve for "w":

46 = 30 + 2w

Subtracting 30 from both sides:

16 = 2w

Dividing by 2:

w = 8

Therefore, the width of the sandbox is 8 feet.

Answer:

Step-by-step explanation:

5/9 + (-4/9) - (-2)

5/9 - 4/9 + 2

[tex]5-4+18/9[/tex]

19/9 or 2.1, 2 1/9

Answer:

168 cm^2

Step-by-step explanation:

This rhombus is made up of two triangles. To find triangle area, base x height/2 (but bc there are two triangles we don’t need to divide by 2). To do this, 14 x 12 to get 168cm^2

Answer: yes, no, yes, no

Step-by-step explanation: