refer to the above table. if the consumer buys both product x and product y, how much will the consumer buy of each in order to maximize utility?

Answer:

With work shown...

Answer: 2^23 + 12 / 2

Step-by-step explanation:

WORK:

(1) -A negative base raised to an odd power equals a negative.

4^7 x (-8^3) + 12 / 2

(2) -Multiplying two negatives equals a positive: (-) x (-) = (+)

2^14 x 2^9 + 12 / 2

(3) -Calculate the product

2^23 + 12 / 2

The solution is located at the top.

Hope this helped <3

Answer:

Solution in attached photo.

Step-by-step explanation:

To expand the brackets, we will use the rainbow expansion method.

Answer:

f(3) = 14

Step-by-step explanation:

f(x) = 3x +5

Let x = 3

f(3) = 3*3 +5

      = 9 + 5

      = 14

Answer:

Step-by-step explanation:

fș

The degree measure of angle BCD is 130.

What is the measure of angle?

An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given:  the diameter EB is parallel to DC, and AB is parallel to ED. The angles AEB and ABE are in the ratio 4: 5.

We can let  ∠AEB be 4x and  ∠ABE be 5x because they are in the ratio 4: 5.

When an inscribed angle contains the diameter, the inscribed angle is a right angle. Therefore by the triangle sum theorem,

= 4x+5x+90 = 180

x = 10 and

∠ABE = 50.

∠ABE =∠BED because they are alternate interior angles and AB||ED.

Opposite angles in a cyclic quadrilateral are supplementary,

so ∠BED + ∠BCD = 180

Use substitution to get ∠ABE + ∠BCD = 180

50 + ∠BCD = 180

∠BCD = 130

Hence, the degree measure of angle BCD is 130.

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a) There is a 60% probability that the boy picks up a blue pen and recognizes it as blue.

b) There is a 62.5% probability that the boy chooses a pen and thinks it is blue.

c) Given that the boy thinks he chose a blue pen, there is a 96% probability that he actually chose a blue pen.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The following probabilities are given -

A 75% probability that a pen is blue.

A 25% probability that a pen is green.

If a pen is blue, an 80% probability that the boy thinks it is a blue pen.

If a pen is blue, a 20% probability that the boy thinks it is a green pen.

If a pen is green, a 90% probability that the boy thinks it is a green pen.

If a pen is green, a 10% probability that that the boy thinks it is a blue pen.

a) The probability that the boy picks up a blue pen and recognizes it as blue.

There is a 75% probability that he picks up a blue pen.

There is a 80% probability that he recognizes a blue pen as blue.

So, the equation will be -

P = 0.75 × 0.8

P = 0.6

Therefore, there is a 60% probability.

b) The probability that the boy chooses a pen and thinks it is blue.

There is a 75% probability that he picks up a blue pen.

There is a 80% probability that he recognizes a blue pen as blue.

There is a 25% probability that he picks up a green pen

There is a 10% probability that he thinks a green pen is blue.

So, the equation will be -

P = (0.75 × 0.80) + (0.25 × 0.10)

P = 0.6 + 0.025

P = 0.625

Therefore, there is a 62.5% probability.

c) Given that he thinks he chose a blue pen, the probability that he actually chose a blue pen.

There is a 62.5% probability that he thinks that he choose a blue pen.

There is a 60% probability that he chooses a blue pen and think that it is blue.

So, the equation will be -

P = 0.6/0.625

P = 0.96

Therefore, there is a 96% probability.

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A boy has color blindness and has trouble distinguishing blue and green. There are 75 blue pens and 25 green pens mixed together in a box. Given that he picks up a blue pen, there is a 80% chance that he thinks it is a blue pen and a 20% chance that he thinks it is a green pen. Given that he picks a green pen, there is an 90% chance that he thinks it is a green pen and a 10% chance that he thinks it is a blue pen. Assume that the boy randomly selects one of the pens from the box.

a) What is the probability that he picks up a blue pen and recognizes it as blue?

b) What is the probability that he chooses a pen and thinks it is blue?

c) (Given that he thinks he chose a blue pen, what is the probability that he actually chose a blue pen?

According to the information, the concentration of sugar in this solution is 62.5%.

To calculate the concentration of sugar we have to divide the mass of the solute by the mass of the solution and then multiply it for 100.

Equation:

The sugar concentration = 50g/80g x 100 = 62.5%

Therefore, the sugar concentration is 62.5%.

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A circle is formed by all points on a plane equidistant from a given point

The possible x-coordinates of Q are -134.71 and +134.71

Known parameters are;

The radius of the golf course, r = 30 feet

Point the ball exits the green = The right-most edge

Speed of the ball = 8 ft./sec

Location of the cup = The origin (0, 0)

Location the ball starts = (-40. -50)

Required:

To find the possible x-coordinates of Q, the point where the line L parallel to the path of the ball is tangent to the circle

The coordinates of the rightmost edge of the golf course = (30, 0)

[tex]slope,m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} }[/tex]

the slope of the path: [tex]m=\frac{-50-0}{-40-30}[/tex]

m=-50/-70

m=5/7

The equation of a circle is (x - h)² + (y - k)² = r²

The center of the circular green, (h, k) = (0, 0)

The equation of the given circle is (x - 0)² + (y - 0)² = x² + y² = 30²

the slope of the radius at the tangent Point [tex]m_{r} =-\frac{1}{m}[/tex]

The equation of the radius at a tangent point is therefore;

[tex]y=-\frac{7}{5} .x[/tex]

Which gives the equation of the circle as follows;

[tex]x^{2} +(-\frac{7}{5} .x)^2=30^2\\\\\frac{31.x^2}{25} =30^2\\\\x=\frac{\sqrt{30^2*25} }{31} \\\\x=\frac{750}{31}*\sqrt{31}[/tex]

x=±134.70

The possible x-coordinates of point Q are -134.70 and +134.70

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The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable  sum range of .05 fluid ounces or less.

The simulation did not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces, indicating that the variability of the juice dispensed was within the acceptable sum of range

The result of the simulation does not provide evidence that the standard deviation of the juice dispensed exceeds .05 fluid ounces because the simulation does not indicate any instances where the standard deviation of the juice dispensed was greater than .05 fluid ounces. This indicates that the variability of the juice dispensed was within the acceptable range of .05 fluid ounces or less.

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We got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

Therefore, x³+2x² +x-7=0 is correct answer.

An a non real solution uses non real numbers to solve the equation, which cannot be solved with real numbers. Back to the school answer: A non-real solution to a math equation is a solution that has “imaginary numbers” (also called “complex numbers”) in it because it cannot be solved with real numbers.

Step1

We need to find equation that has exactly two real and two non real solutions

2 real  and 2 non real solution means 4 solutions

x³ equation has maximum of 3 solutions

So we ignore equation that has largest exponent x³

We ignore options B  and D

Let check option A

x⁴ 36x² =0

factor the left hand side

Factor out x^2

x² (x² -36)=0

WE set each factor =0  and solve for x

x² =0  so x=0

x²  - 36 =0 so x= +-6

So solutions are x=0, x=6 , x= -6. Only 3 real solutions we got

LETS check with option C

x⁴  - 5x² -36=0

Factor left hand side

(x² -9)(x² +4)=0

set each factor =0  and solve for x

x² -9 =0  so x= -3, + 3

x² + 4 =0 , x² = -4, so x= +2i, -2i

So we got two real solutions (-3,+3) and two non real solutions (-2i,+2i)

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Answer:

Q9:
[tex]\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]

Q10

[tex]\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]

Step-by-step explanation:

For a rectangular prism, the volume = length x width x height

Given these 3 dimensions simply multiply them to get the volume

Q9

[tex]V = \dfrac{7}{8} \cdot \dfrac{2}{3} \cdot \dfrac{1}{8}\\\\[/tex]

[tex]V = \dfrac{7\cdot 2\cdot 1}{8\cdot 3 \cdot 8}\\\\V = \dfrac{14}{192}\\\\[/tex]

Divide numerator and denominator to reduce to lowest fraction

[tex]V = \dfrac{14 \div 2}{192\div 2}\\\\\boxed{V = \dfrac{7}{96}\;cubic\;feet}}[/tex]

Q10

This is a cube since each side is the same length

For a cube of side a, the volume = a³

So for this particular cube

[tex]V = \left(\dfrac{4}{5}\right)^3\\\\\\\boxed{V = \dfrac{64}{125}\;cubic\;yards}[/tex]

The determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1

The determinant of an n-by-n tridiagonal matrix containing only 1s as nonzero elements is given by the formula:

det(A) = 1^n-2 + 1^n-3 + ... + 1^2 + 1

For example, consider the 3x3 matrix:

A = [1 1 0; 1 1 1; 0 1 1]

Using the formula above, the determinant of A can be calculated as:

det(A) = 1^2 + 1 = 2

More generally, the determinant of an n-by-n tridiagonal matrix containing only 1s can be calculated by iterating over the diagonal elements and summing the products of each element and its corresponding power of 1. This sum can then be taken to the power of 1 to obtain the determinant of the matrix.

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Box1: x = -9 Box2: x = 7

For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.

The two numbers are -9 and +7.

So, the factored equation is (x - 9)(x + 7) = 0.

For this equation, we need to factor the left side of the equation to solve it. To do this, we need to find two numbers that multiply to give us 63 and add to give us 16.

To solve the equation, we set each factor equal to zero and solve for x.

x - 9 = 0  -> x = 9

x + 7 = 0  -> x = -7

Therefore, the larger solution is x = -9, and the smaller solution is x = 7.

Therefore, the answer is Box1: x = -9 and Box2: x = 7.

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The correct expression is a) [tex]x^2-6x+9[/tex].

What is expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given expression is ,

=> [tex](x-3)^2[/tex]

Now using formula [tex](a-b)^2=a^2-2ab+b^2[/tex] then

=> [tex]x^2-2.x.3+3^2[/tex]

=> [tex]x^2-6x+9[/tex]

Hence the correct answer is a) [tex]x^2-6x+9[/tex].

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The method of moments estimate and the maximum likelihood estimate are the same.

The method of moments estimate is the sample mean, which can be calculated by adding the numbers together and dividing by 5. In this example, the mean is 52. The maximum likelihood estimate is the mean of the population distribution, which can be estimated by maximizing the likelihood function. This involves taking the partial derivatives with respect to the parameters and solving for the values that make the derivative equal to zero. In this example, the maximum likelihood estimate will also be 52. Thus, the method of moments estimate and the maximum likelihood estimate are the same.

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The value of the company after 5 years is given as follows:

$75,631.5.

The value will decline below $140,000 when:

3.27 years.

The exponential function for this problem is defined as follows:

V(x) = 450000(0.7)^x.

The value after 5 years is found replacing the lone instance of x by 5, hence:

V(5) = 450000(0.7)^5

V(5) = $75,631.5.

The value will decline below $140,000 when at x for which V(x) = 140000, hence:

140000 = 450000(0.7)^x.

(0.7)^x = 140000/450000

(0.7)^x = 0.311111

xlog(0.7) = log(0.311111)

x = log(0.311111)/log(0.7)

x = 3.27 years.

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36.714 x 98.77 = 3627.7198

36.714 + 98.77 = 135.484 (4 decimal places)

The solution set is {x | x < -35/2} and {x | x > -40/7}.

To find the solution set of these two inequalities, first we need to solve them.

The first inequality is x < -40/7. To solve this inequality, we need to divide both sides of the inequality by -7. This gives us x > -40/7.

The second inequality is x > -35/2. To solve this inequality, we need to divide both sides of the inequality by 2. This gives us x < -35/2.

Therefore, the solution set is {x | x < -35/2} and {x | x > -40/7}.

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The unit value should Royal Decking use for each of its products,

Product A: $8 (loss),

Product B:  $16 (loss),

Product C: $10 (profit),

Product D: $9 (profit),

Product E: $8 (profit).

The sum of the quantities divided by the total value of purchases and sales yields the unit value of a group of similar goods. As a result, it represents a quantity-weighted average of the various prices at which the good is bought and sold.

Given inventory,

                      Product Cost               Selling Price

A                            $130                          $150

B                             $170                         $190

C                             $130                         $170

D                              $90                         $120

E                               $50                         $70

a sales commission equal to 10% of the selling price and shipping costs equal to 10%,

Product A :

the unit value is given by,

Value = selling price - (product cost + sales commission + shipping cost)

= $150 - ($130 + 10% x selling price + 10% x product cost)

= $150 - ($130 + 10% x $150 + 10% x $130)

= $150 - ($130 + $15 + $13)

= -$8 = $8 (loss)

Product B :

Value = selling price - (product cost + sales commission + shipping cost)

= $190 - ($170 + 10% x selling price + 10% x product cost)

= $190 - ($170 + 10% x $190 + 10% x $170)

= $190 - ($170 + $19 + $17)

= -$16 = $16 (loss)

Product C :

Value = selling price - (product cost + sales commission + shipping cost)

= $170 - ($130 + 10% x selling price + 10% x product cost)

= $170 - ($130 + 10% x $170 + 10% x $130)

= $170 - ($130 + $17 + $13)

= $10 = $10 (profit)

Product D :

Value = selling price - (product cost + sales commission + shipping cost)

= $120 - ($90 + 10% x selling price + 10% x product cost)

= $120 - ($90 + 10% x $120 + 10% x $90)

= $120 - ($90 + $12 + $9)

= $9 = $9 (profit)

Product E :

Value = selling price - (product cost + sales commission + shipping cost)

= $70 - ($50 + 10% x selling price + 10% x product cost)

= $70 - ($50 + 10% x $70 + 10% x $50)

= $70 - ($50 + $7 + $5)

= $8 = $8 (profit)

Hence unit value for each product is -$8, -$16, $10, $9, and $8.

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First, we translate b and place the tail at the tip of a, being careful to draw a copy of b that has the same length and direction. then we draw the vector a+b (see the middle figure) starting at the initial point of a and ending at the terminal point of the copy of b.

Alternatively, we could place b so it starts where a start and construct a+b by the parallelogram law as in the bottom figure.

The parallelogram law says that if we place two vectors so they have the same initial point, and then complete the vectors into a parallelogram, then the sum of the vectors is the directed diagonal that initiates at the same point as the vectors.

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The dot plot consists of ten dots, each representing the data value of a single person at the talk. The data values are spread out as far as possible, resulting in the largest possible standard deviation.

A dot plot is a graph that is used to represent the distribution of data. It consists of dots, each of which represents a single data value. In this case, the dot plot represents the distribution of possible data values from a talk with ten people. To achieve the largest possible standard deviation, the data points should be spread out as far as possible. Each dot should be placed on the graph in such a way that the difference between any two adjacent data points is maximized. This is done by placing the highest and lowest values at opposite ends of the graph, and then evenly spacing out the remaining data points in between. All of this should result in the largest possible standard deviation of the data set.

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The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.

Let the function f is given as

y = m(x + a) + c

Then the inverse function of the function f will be given by swapping x with y and y with x.

The function is given below.

f(x) = √(x - 2) / 6

Replace x with y and f(x) with x. Then the inverse function is given as,

x = √(y - 2) / 6

6x = √(y - 2)

36x² = y - 2

y = 36x² + 2

f⁻¹(x) = 36x² + 2

The inverse function of the function f(x) will be f⁻¹(x) = 36x² + 2. Then the correct option is A.

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The complete question is given below.

To solve the radical equation √4z²-13z+9+3=3z, we need to get rid of the radical sign in order to isolate the variable.

First, we can add 9 to both sides to get:

√4z²-13z+12=3z+9

Then we can square both sides of the equation:

4z²-13z+12 = 9z²+27z+81

Now, we can rearrange the equation to get:

9z²-40z+69 = 0

Now we can use the quadratic formula to find the solutions for z:

z = (40 ± √(40²-4969)) / 2*9

z = (40 ± √(1600-2772)) / 18

z = (40 ± √(-1172)) / 18

Since the square root of a negative number is an imaginary number, this equation has no real solutions, which means that there are no values of z that will make the equation true.

So the radical equation √4z²-13z+9+3=3z doesn't have any solution.

Answer: 272 miles

Step-by-step explanation:

The scale factor is [tex]\frac{816}{1.5}=544[/tex] inches per mile.

So, the distance from Chicago to STL is [tex]544(0.5)=272[/tex] miles.

These events would be considered as: Subjective, Independent, Dependent, Classical

Subjective event: An event that is based on individual opinion or belief. This event would not be represented by a formula or calculation.

Independent event: An event that is not influenced by other events. This event can be represented by a formula such as P(A) = P(A) which calculates the probability of an event occurring on its own.

Dependent event: An event that is influenced by other events. This event can be represented by a formula such as P(A|B) = P(A ∩ B) / P(B) which calculates the probability of an event occurring given that another event has already occurred.

Classical event: An event that is determined by predetermined probabilities or odds. This event can be represented by a formula such as P(A) = n(A) / n(S) which calculates the probability of an event occurring based on the number of favorable outcomes divided by the total number of outcomes.

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The value of the missing number will be 3.

A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."

It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.

The equation for the missing number is given as x + (-4) = -1. the missing number will be calculated as:-

x + (-4) = -1

x -4 = -1

x = 4 - 1

x = 3

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Reason:

c = Craig's score

c+12 = twelve more than Craig's score

c+12 = 70 because the key term "is" translates to "equals". As an example, saying "x is 5" means "x = 5".

Number of 7 students have both a dog and a cat, out of the 39 eighth grade students at Lincoln Middle School.

Total number of 8th grade students: 39

Number of students with a dog: 20

Number of students with a cat: 26

Number of students with both a dog and a cat: 20 + 26 - 39 = 7. Therefore, 7 have both a dog and a cat.

There are 39 students in the 8th grade at Lincoln Middle School. Of those students, 20 have a dog, 26 have a cat, and 7 have both a dog and a cat. To calculate this number, we added the number of students with a dog (20) and the number of students with a cat (26) and then subtracted the total number of students (39). The result of this calculation, 7, is the number of students who have both a dog and a cat. This means that 7 out of 39 8th grade students at Lincoln Middle School have a dog and a cat.

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It is a sample size proportion. 0.16 is the proportion of the 1,000 college students that reported using Ecstasy, which is a measure of the sample.

The number 0.16 is a sample proportion. This means that it is the proportion of the sample of 1,000 college students that reported using the drug Ecstasy. A sample proportion is a measure of the sample, not of the population. It is not a randomly chosen number and it is not a margin of error. A margin of error is a measure of how accurate a sample statistic is likely to be, usually expressed as a percentage or a number of standard deviations. A population proportion is the proportion of the total population that holds a certain characteristic or has had a certain experience. Thus, 0.16 is a sample proportion and not a population proportion, margin of error, or randomly chosen number

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[tex]\bold{n + (n+1)^{2}}[/tex]

An unknown number can be interpreted with any letter of the alphabet, they will be our unknowns to be able to form an algebraic expression.

Well, in this case, I will use the variable n, to name the unknown number.

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

(grouping the data the following algebraic expression is obtained):

[tex]\bold{n + (n+1)^{2}}[/tex]

Answer:

(n + 1 )

Let "n" be the number, the square of it is; n² and the following number results from adding the unit; then (n + 1) will be the next of the number.

Answer: (-1, 5)

Step-by-step explanation:   I wrote down all the explanations refer to the image please