15. Suppose an economy's marginal propensity to consume (MPC) is 0.6. Then, the multiplier must be

a. 1.96.

b. 3.

c. 1.67.

d. 2.5.

Step-by-step explanation:

So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.

First, multiply both sides by 40

5/8*40=x

Express 5/8 * 40 as a single fraction.

5*40/8=x

Multiply 5 40 to get 200.

200/8=x

Divide 200 by 8 to get 25.

25=x

Swap sides so that all variable terms are on the left-hand side.

x=25

Answer:

58

Step-by-step explanation:

There are 5 lines between 50 and 60

60 - 50 = 10

10 / 5 = 2

This means that each increment is 2.

We see the end of the box plot is above the fourth increment above 50.

4 x 2 = 8

50 + 8 = 58

Since the function f(x) = 9.25x + 3 represents the amount of money that Radda earns dog walking for x hours, Radda's earnings would increase by $12.25 each hour.

In Mathematics, a linear function is sometimes referred to as an expression or the slope-intercept form of a straight line and it can be used to model (represent) the total amount of money that is being earned by Radda for dog walking;

T = mx + b

Where:

Therefore, the required linear function that represents the total amount of money that is being earned by Radda for dog walking per hour is given by this mathematical expression;

f(x) = T = 9.25x + 3

When the number of hours Radda spend dog walking is equal to 1 (x = 1), the rate of change(slope) can be calculated as follows;

f(1) = T = 9.25(1) + 3

f(1) = T = 9.25 + 3

f(1) = T = $12.25.

In this context, we can reasonably infer and logically conclude that Radda's earnings increases each hour by $12.25.

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Complete Question:

The function f(x) = 9.25x + 3 represents the amount Radda earns dog walking for x hours. How much does Radda's earnings increase each hour?

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.

We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08.  The unit price for each bottle will be: The bottle having the lower price will be:-

30-ounce bottle = $6.00

One ounce bottle = 30 / 6.00 = $5.00

and

24-ounce bottle = $4.08

One ounce bottle = $24/ 4.08 = $5.88

30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.

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The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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The degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

What is an isosceles triangle?

In an isosceles triangle, the two base angles are congruent, or equal in measure.

In addition, the sum of the measures of the angles in any triangle is always 180 degrees. Therefore, we can set up an equation to find the measure of each angle in the triangle:

m∠D + m∠F + m∠E = 180 degrees

Substituting the given values for the measures of angles D and F, we get:

(5x+26) + (3x+63) + m∠E = 180

Combining like terms and solving for m∠E, we find that:

m∠E = 180 - (5x+26) - (3x+63)

= 180 - 8x - 89

= 91 - 8x

Therefore, the measure of angle E is 91 - 8x degrees.

To find the measure of angles D and F, we can substitute this value back into the equation:

m∠D + m∠F + m∠E = 180

(5x+26) + (3x+63) + (91-8x) = 180

Solving for x, we find that x = 6.

m∠D =5(6) + 26 = 30 + 25 = 56°

m∠F = 3(6) + 63 = 18 + 63 = 81°

m∠E = 91 - 8(6) = 91 - 48= 43°

Therefore, the degree measure of each angle in the triangle would be

m∠D = 56°

m∠F = 81°

m∠E = 43°

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The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

The well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, [tex]a^{2}+b^{2} =c^{2}[/tex]

Given that,

Length of the ladder is, [tex]l=9ft[/tex]

Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.

Now, from triangle ABC,

[tex]AB^{2} +BC^{2} =AC^{2}[/tex]

[tex]h^{2} +b^{2} =l^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = [tex]9^{2}[/tex]

[tex]h^{2} +b^{2}[/tex] = 81               (Equation-1)

Differentiating the above equation with respect to time, 't'.

So,

We can write,

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = [tex]\frac{d}{dt}[/tex] (81)

[tex]\frac{d}{dt} (h^{2}+b^{2} )[/tex] = 0

[tex]2h\frac{dh}{dt} +2b\frac{db}{dt}[/tex] = 0

[tex]h\frac{dh}{dt} +b\frac{db}{dt}[/tex] = 0                (Equation-2)

In the above equation the term [tex]\frac{dh}{dt}[/tex] is the rate at which top of ladder slides down and [tex]\frac{db}{dt}[/tex] is the rate at which bottom of ladder slides away.

Let us assume,

h = 3 ft and db/dt = 3 ft/s

We can substitute values in equation-1,

[tex]3^{2} +b^{2}[/tex] = 81

9 + [tex]b^{2}[/tex] = 81

[tex]b^{2}[/tex] = 81-9

[tex]b^{2}[/tex] = 72

b = [tex]\sqrt{72}[/tex]

b = 8.48 ft

Now, plug in all the given values in equation (2) and solve for [tex]\frac{dh}{dt}[/tex]

3*[tex]\frac{dh}{dt}[/tex] + 8.48 * 3 = 0

3*[tex]\frac{dh}{dt}[/tex] + 25.44 = 0

3*[tex]\frac{dh}{dt}[/tex] = - 25.44

[tex]\frac{dh}{dt}[/tex] = -25.44/3

[tex]\frac{dh}{dt}[/tex] = - 8.48 ft/s

Therefore,

The rate at which the top of ladder slide down is 8.48 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.

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Option D is the correct answer, Universal Instantiation is The implicational rule of inference that permits us to derive a specific instance from a universal statement.

It is the process of deriving an individual statement from a general one by replacing the variable with a name or another referring expression called Instantiation.

Universal Instantiation is also called universal specification or universal elimination, it is a valid rule of inference from the truth about each member of a class of individuals to the truth about a particular individual of that class.

Example: "No humans can fly. John Doe is human. Therefore John Doe can not fly."

∀xA⇒A(x↔a}

for every formula A and every term a, where A(x↔a}  is the result of substituting a for each free occurrence of x in A. A(x↔a} is an instance of

∀xA.

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The binary representation of each of these hexadecimal numbers is given as follows:

a) 80E = 100000001110

b) 135AB = 00010011010110101011

c) ABBA = 1010101110111010

d) DEFACED = 1101111011111010110011101101

To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:

Then, for example:

80E hexadecimal = 100000001110.

As:

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Answer:

x=5

Step-by-step explanation:

If p and q are parallel, then the two angles in question should be equal to one another.

So,

(3x+15)°=(8x-10)°

(3x+15)°+10°=(8x-10)°+10°

(3x+25)°=(8x)°

(3x+25)°-(3x)°=(8x)°-(3x)°

25°=5x°

5=x

So, the two angles should be (8(5)-10)° and (3(5)+15)°.  Both of these expressions equal 30°.  This makes sense, as the illustration shows that the two angles are acute.

According to the given questions the answer is for 3 hour $560, for 8 hour cost $685 and for 12 hour cost $785.

A crucial concept that time and labour have in common with some other mathematical topics is the concept of proportionality. Because efficiency grows inversely linked to the amount of time needed when the quantity of work is constant.

The fundamental equation for solving is 1/r+1/s=1/h. Let's choose Hrithik as our example. Let's assume that Hrithik completes 1/20 of something like the work in a day and Dhoni completes 1/30 of the work in a day. They will accomplish 1/20 + 1/30 = 5/60 = 1/12th of something like the work in a day if they collaborate.

Given that John paid $485 to build a deck.

And he will pay $25 per hour to his brother for building the deck.

one hour of work costs John $25 + $485 .

Total cost of building deck = $25 × h number of hours + $485

3 hour of work costs $25 × 3 = $75 + $485 = $560

8 hour of work costs = $25 × 8 = $200 + $485 = $685

12 hour of work costs = $25 × 12 = $300 + $485 = $785

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The complete question is-

John is having a new deck built. He paid $485 for the required materials, and he will pay his brother $25 an hour to build the deck. Which table shows the relationship between h, the number of hours John’s brother works, and c, the total cost of the project?

h c

0 485

3 510

8 535

12 560

h c

0 510

3 535

8 560

12 585

h c

0 485

3 560

8 685

12 785

h c

0 510

3 585

8 710

12 810

Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306

Degree of freedom {df}=18

We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t

It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]

As we know, t distribution provides the cumulative probability

As the value of the total area under the t distribution will 1

So, we can write it as:

[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]

Now, using excel, we can easily calculate the t-critical value as follows

=T. INV ( Probability, DF)

Where Probability is the area and DF is the degree of freedom,

Now we will enter these values in excel:

=T. INV (0.95,18)

t-critical value can also be found using t table

Look up for df = 18, in very first column

Now look up for 0.05 in one tail row

Now intersect both of them to get the t-critical value

We will get it as: 2.306

So t-critical value will be =2.306

[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]

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The graph shows that Becca walks five dogs at the end of the third month.

We know that we can be able to read off the graph of an function that has been shown such as the one that we have in the image that has been attached to this answer.

We can see that the graph of the function agrees that Becca's dog-walking business started with 1 dog. By the end of the first month , she was walking 2 additional dogs per month .  We would now read off the graph to know the number of dogs that he walks after three months.

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Answer:

The number of degrees Celsius goes down 6 every week. (-6)

Step-by-step explanation:

If the city's temperature changed the same every week, and over the period of 2 weeks it changed -12 degrees Celsius, we need to figure out how much it changed every week (c). We can do this by dividing the number of weeks (w), by the total number of Celsius it changed (t).

The equation will look something like this:

w ÷ t = c

Fitting the numbers into this equation will look something like this:

2 ÷ -12 = -6

Every week, it changed -6 degrees Celsius.

Simplifying the expression, every week it changed -6 degrees Celsius. We know this because the temperature changes the same amount every week. So if the total amount is -12, we have to divide that by 2 to get -6.

From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-or-no question and having its own Boolean-valued outcome: success (with probability p) or failure (with probabilitq=1-pq=1-p).

This distribution is used in probability theory and statistics.

A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results. For a single trial, or n = 1, the binomial distribution is a Bernoulli distribution.

The popular binomial test of statistical significance is based on the binomial distribution.

A sample of size n drawn with replacement from is widely used to model the number of successes using the binomial distribution.

Hence, From the directory for her state, Haylee randomly chooses 10 small firms. Assume that the binomial variable BBBB represents the number of the firms she chooses that have websites.

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The correct option is b) ii only

From the given data we can construct confidence interval. So, the statement that we are 95% confident that the average rent for students at the university is between $ 564 and $664 is true.

What is meant by distribution?

The methodical effort to account for how the owners of the labor, capital, and land inputs divide the country's income. Rent, wages, and profit margins have historically been the focus of economists' research into how these expenses and margins are set.

What are the 3 types of distribution?

The Three Types of Distribution

What are the 5 factors of distribution?

Market, Product, Company, Channel, and Environment Related Factors are 5 Important Factors Affecting Distribution Channel Selection. The distribution of goods can be done through a variety of routes.

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(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389.

Below table showing calculation of Point Estimate of Mean and Standard Deviation:

Score                                  X-X’                                  (X-X’)^2

87                                         5                                         25

91                                         9                                         81

86                                         4                                         16

82                                         0                                         0

72                                        -10                                       100

91                                         9                                         81

60                                        -22                                       484

77                                        -5                                         25

80                                        -2                                         4

79                                        -3                                         9

83                                         1                                         1

96                                         14                                       196

984                                                                                   1022

Mean(X’) = Total Score/n

n = Total number = 12

X’ = 984/12 = 82

Standard Deviation (σ) = √∑(X-X’)^2/(n-1)

σ = √1022/(12-1)

σ = √1022/ 11

σ = 9.6389

(a) The point estimate of mean wine score for this pinot noir is 82.

(b) The point estimate of standard deviation wine score for this pinot noir is 9.6389

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Answer:

listed below

Step-by-step explanation:

5.) x=77 and y=63

6.)y=60 and x= 1230

7.)y=65 and x=92

8.)y=69 and x=175

Answer:

Some points that are on this line are:

(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)

Answer:

Step-by-step explanation:

Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7

Answer: B & A

Step-by-step explanation: I think?

The cost of the carpentering of the floor at the rate 12 rupees per square meter is 60 rupees.

A cuboid is a solid in three dimensions with six rectangular faces, eight vertices, and twelve edges. Three dimensions, including length, breadth, and height, define a cuboid. A cuboid with integer edges is referred described as being perfect.

We have the room as a cuboid.

And its length is 6 meters and height is 3 meters.

The volume of the cuboid = length x height x width

90 = 6 x 3 x width

width = 90 / 18

width = 5 meter.

To find the cost of carpentering the floor, the rate of Rs. 12 per square meter.:

12 x width = 12 x 5 = 60 rupees.

Therefore, at the rate of 12 rupees per square meter, the cost of the carpentering of the floor is 60 rupees.

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Step-by-step explanation:

x = second number

first number = x - 6

third number = 4x

x - 6 + x + 4x = 96

6x - 6 = 96

6x = 102

x = 102/6 = 17

first number = x - 6 = 17 - 6 = 11

second number = x = 17

third number = 4x = 4×17 = 68

The expression that could be used to determine the length of segment AB in the triangles given is: A. AB = AX * AC/AY.

When two triangles are stated to be similar to one another, it means both triangles have equal corresponding angles, but their corresponding sides have proportional lengths or have ratios that are equal.

This means similar triangles have the same shape but different sizes, since their corresponding side lengths have proportional length.

Given that triangle AXY is similar to triangle ABC, it means that:

m<A = m<A

m<X = m<B

m<Y = m<C

AX/AB = AY/AC = XY/BC

To find the length of AB, we could use the following expression derived from the ratios stated above:

AX/AB = AY/AC

Cross multiply:

(AB) * (AY) = (AX) * (AC)

Divide both sides by AY

(AB) * (AY) / AY = (AX) * (AC) / AY

AB = AX * AC/AY

The expression to use is: A. AB = AX * AC/AY

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280 is the number which is 16 2/3% more than 240

What is the percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We would receive 16 times 3 plus 2 if we converted 16 2/3 to an improper fraction. Then, we would divide this number by 3, getting 50/3, which is equal to 50/3 divided by 100, or 1/6.

(1/6) th of 240 = 240/6 = 40

40 more than 240 = 280

So, 280 is the number which is 16 2/3% more than 240

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Answer:

[tex]27x^6y^6[/tex]

Step-by-step explanation:

The formatting of the question is a bit confusing, but if the expression is [tex](3x^2y^2)^3[/tex], use the power of a product exponent rule [tex](ab)^m=(a)^m(b)^m[/tex].  So,

[tex](3x^2y^2)^3=(3)^3(x^2)^3(y^2)^3[/tex].

Next, use the power of a power exponent rule [tex](a^m)^n=a^{m*n}[/tex].  So,

[tex](3)^3(x^2)^3(y^2)^3=27(x^{2*3})(y^{2*3})=27x^6y^6[/tex]

Answer:

B

Step-by-step explanation:

2x + 2 + 5x + 3 = 180

7x + 5 = 180

7x = 180 - 5

7x = 175

x = 175/7

x = 25°

Interest is the price you pay to borrow money or the cost you charge to lend money.

To find the difference of 310 and 285, subtract 310 from 285. This will give you the added interest cost.

310-285 = 25

So, Polly will pay $25 in interest.

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Inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

What do you mean by inequality?

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size.

The notation a < b means that a is less than b.

The notation a > b means that a is greater than b.

Let the number be x

According to the question:

a) The sum of a number and 12 is at most -8.

inequality become:

x + 12 ≤ -8

b) A number increased by -8 is greater than 12

inequality become:

x + (-8) > 12

⇒ x - 8 > 12

c)  -8 less than a number is no more than 12

x - (-8) < 12

⇒ x + 8 < 12

Therefore, inequality for each part be

a) x + 12 ≤ -8

b)  x - 8 > 12

c) x + 8 < 12

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