What is the decimal equivalent to the fraction 80/32

When the consumption schedule lies below the 45-degree reference line, it means that at every level of income, people are consuming less than their income.

The consumption schedule represents the relationship between income and consumption in an economy, while the 45-degree reference line represents the line where income and consumption are equal.

In this scenario, saving occurs because people are not spending all of their income. The difference between their income and consumption is their savings. Thus, the amount of saving in the economy will increase as the consumption schedule moves further below the 45-degree reference line.

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When the consumption schedule lies below the 45-degree reference line, saving what does it means?

Answer:

a = -3

Step-by-step explanation:

-3(a-6)=-(4a-6)-3a

-3a+18 = -4a+6-3a

-3a+18 = -4a-3a+6

-3a+18 = -7a+6

-3a+7a = 6-18

4a = -12

4a/4 = -12/4

a = -3

The probability of getting a sum of 9 when two dice are rolled is 1/9, the probability of getting an odd sum is 1/2, and the probability of rolling doubles is 1/6. These probabilities can be calculated by listing all possible outcomes and counting the number of outcomes that satisfy the given conditions, and then dividing by the total number of outcomes.

.

a. The probability of getting a sum of 9 when two fair dice are rolled can be found by listing all possible outcomes and counting the number of outcomes where the sum is 9. There are four such outcomes: (3, 6), (4, 5), (5, 4), and (6, 3). Since there are 36 equally likely outcomes when two dice are rolled, the probability of getting a sum of 9 is 4/36, or 1/9.

b. The probability of getting an odd sum when two fair dice are rolled can be found by counting the number of outcomes where the sum is odd and dividing by the total number of outcomes. An odd sum can be obtained in 18 of the 36 possible outcomes, since the only ways to obtain an even sum are by rolling either two even numbers or two odd numbers. Therefore, the probability of getting an odd sum is 18/36, or 1/2.

c. The probability of rolling doubles when two fair dice are rolled is 1/6, since there are six possible outcomes where the two dice show the same number (1-1, 2-2, 3-3, 4-4, 5-5, 6-6), and there are 36 equally likely outcomes in total. Therefore, the probability of rolling doubles is 1/6.

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Answer:

(9×3)+(4×2)

Step-by-step explanation:

Let a represent the price of books

Let b represent the price of magazines

Alicia purchase 3 books for $9

She also purchased 2 magazines for $4

(9×a) +(4×b)

= (9 ×3) + (4×2)

= 27+8

= 35

Answer:

you didnt give a clear question

Step-by-step explanation:

wth

\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)

Answer:

(x² - 9)(x² - 1)

Step-by-step explanation:

Using Quadratic trinomials

Factor x⁴ - 10x² + 9

Step 1: Find the two integers whose product of 9 and whose sum of -10

Product

-9 × -1 = 9

Sum

-9 + -1 = -10

Step 2: Use -1 and -9 to complete the factors

x⁴ - 10x² + 9 = (x² - 9)(x² - 1)

Step 3: Use the foil method to check the factors

(x² - 9)(x² - 1) = x⁴ - 1x² - 9x² + 9 = x⁴ - 10x² + 9

The answer is: \(10^5\) terms.

We know that the error bound for the nth partial sum of a series can be given by:

\(|E_n| < = S - S_n\)

where S is the sum of the infinite series, \(S_n\) is the sum of the first n terms, and \(E_n\) is the error in the approximation of S by \(S_n\).

For the given series, we have:

\(S = Σ(1/n^1.1)\)

We want to find the number of terms n such that the error\(|E_n|\) is at most 0.00001. In other words, we want to find the smallest value of n such that:

\(|E_n| < = 0.00001\)

Using the error bound formula, we have:

\(|E_n| < = S - S_n\)

Substituting the values, we get:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = 0.00001\)

where k is the number of terms we want to add.

We can simplify the left-hand side of this inequality using the reverse triangle inequality:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| < = |Σ(1/n^1.1)| + |Σ(1/k^1.1)|\)

Using the formula for the sum of a p-series, we have:

\(Σ(1/n^1.1) = Σ(1/n^(11/10)) = ∞\)

Therefore, we can ignore the second term on the right-hand side of the inequality, and focus on the first term. We want to find the smallest value of k such that:

\(|Σ(1/n^1.1)| < = 0.00001\)

We can approximate the sum of the series by an integral, using the integral test. Therefore, we have:

\(Σ(1/n^1.1) ≈ ∫[1,∞] dx/x^1.1 = [x^-0.1/-0.1]∞_1 = 10\)

Using this approximation, we get:

\(|Σ(1/n^1.1)| < = 10\)

Substituting this in the inequality, we have:

10 <= 0.00001

This is clearly not possible, so we need to increase the number of terms k. Let us try with k = 10000. Using a calculator or computer program, we can find that:

\(Σ(1/k^1.1) ≈ 9.986\)

Therefore, we have:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.986| ≈ 0.014\)

This is still greater than 0.00001, so we need to increase the value of k further. Let us try with k = 100000. Using a calculator or computer program, we can find that:

\(Σ(1/k^1.1) ≈ 9.9997\)

Therefore, we have:

\(|Σ(1/n^1.1) - Σ(1/k^1.1)| ≈ |∞ - 9.9997| ≈ 0.0003\)

This is less than 0.00001, so we can use k = 100000 terms to estimate the value of the series with error at most 0.00001.

Therefore, the answer is:

\(10^5\) terms.

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For, f(x) = 3x2 – 11x + 8 / (x + 5)(x - 1). (1) x = 1 is a vertical asymptote to the graph off. (II) y = 3 is a horizontal asymptote to the graph off. The correct answer is (II) ONLY.
To determine vertical asymptotes, we look for values of x that make the denominator of the fraction equal to zero. In this case, the denominator is (x + 5)(x - 1), which is equal to zero when x = -5 and x = 1. Therefore, x = -5 and x = 1 are vertical asymptotes of the graph of f(x).
To determine horizontal asymptotes, we look at the end behavior of the function as x approaches positive or negative infinity. In this case, the degree of the numerator (2) is less than the degree of the denominator (2), so we know that there is a horizontal asymptote at y = 0. We can confirm this by dividing the numerator by the denominator using long division or synthetic division. The result is:
f(x) = 3 - 26/(x + 5) + 9/(x - 1)
As x approaches infinity or negative infinity, the fractions with x in the denominator approach zero, leaving only 3 as the limit of the function. Therefore, y = 3 is a horizontal asymptote of the graph of f(x).
So the correct answer is (II) ONLY.

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Answer:

-19 and 3

Step-by-step explanation:

-19 x 3 = -57

-19 + 3 = -16

Answer:

Step-by-step explanation: To find the answer to "What two numbers have a product of 57 and a sum of 16?" we first state what we know. We are looking for x and y and we know that x • y = 57 and x + y = 16.

Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which This means that when we create one equation to solve the problem, we will have two answers.

To solve the problem, we take x + y = 16 and solve it for y to get y = 16 - x. Then, we replace y in x • y = 57 with 16 - x to get this:

x • (16 - x) = 57

Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of 57 and a sum of 16. The numbers are:

5.35425

10.64575

That's it! The two numbers that have a product of 57 and a sum of 16 are 5.35425 and 10.64575 as proven below:

5.35425 • 10.64575 = 57

5.35425 + 10.64575 = 16

HOPE THAT HELP YOU PLS MARK ME BRANLITS PLSSSS

Step-by-step explanation:

\(f(x) = \cot(x) \)

Can be written as

\(f(x) = \frac{ \cos(x) }{ \sin(x) } \)

So let's see these answers.

Part A is wrong, when x=0, the graph is undefined(infinite discontinuity), so (0,0) is not on the graph

B is correct,for every pi radians, the function is undefined for it.

C is incorrect, The function has a zero at pi/2

D is incorrect, the function is defined when cos(x)=0

E is correct, the range of cot(x) is all real numbers.

So B and E are correct.

The area of the rectangle ABCD is approximately 29.15 square units.

To find the area of the rectangle ABCD, we can use the formula for the area of a rectangle, which is given by the product of its length and width.

Let's first find the length and width of the rectangle using the coordinates of its vertices.

Length AB = distance between points A and B

= √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(1 - (-4))² + (4 - 4)²]

= √[5² + 0²]

= √25

= 5

Width BC = distance between points B and C

= √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - 1)² + (1 - 4)²]

= √[(-5)² + (-3)²]

= √[25 + 9]

= √34

Now that we have the length and width, we can calculate the area of the rectangle.

Area = Length × Width

= 5 × √34

≈ 5 × 5.83

≈ 29.15 square units

Therefore, the area of the rectangle ABCD is approximately 29.15 square units.

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Answer:

Your answer

43.8 %

Mark it as Brainlist. Follow me for more answer.

Step-by-step explanation:

Answer: Floor 8

Step-by-step explanation:

Starting on from the ground floor, the elevator goes up 7 floors. We are now on floor 7.

Then it goes down 3 floors, so 7 - 3 = 4, we are now on floor 4.

Finally, the elevator goes up 4 floors, 4 + 4 = 8, we are now on floor 8

Answer:

It is on the 8th floor.

Step-by-step explanation:

0 + 7 = 7

7 - 3 = 4

4 + 4 = 8

The two positive numbers are 36 and 72 which gives a sum equal to 108 and the product of 36 and the square of 72 is a maximum.

Any integer greater than zero is considered a positive number. A positive number can either be written as a number or with the "+" symbol in front of it.

Let us consider the two positive real numbers as x and y. Then, their sum is written as,

x+y=108

Then, y=108-x

And the product is written as,

P=xy²

Substitute value of y in the above equation, we get,

\(\begin{aligned}P&=x(108-x)^2\\&=x(11664-216x+x^2)\\&=11664x-216x^2+x^3\\&=x^3-216x^2+11664x\end{aligned}\)

Now, differentiate P with respect to x, and we get,

\(\begin{aligned}\frac{dP}{dx}&=3x^2-432x+11664\\&=x^2-144x+3888\end{aligned}\)

Solving the above equation to zero, we get,

\(\begin{aligned}x^2-144x+3888&=0\\x^2-36x-108x+3888&=0\\x(x-36)-108(x-36)&=0\\(x-108)(x-36)&=0\\x&=\text{108 or 36}\end{aligned}\)

Substitute values of x in y=108-x, to get values of y.

If we substitute x=108, we get the y value as zero which doesn't give the required solution.

But, if we substitute x=36, we get,

\(\begin{aligned}y&=108-36\\y&=72\end{aligned}\)

Thus, the two positive numbers are 36 and 72.

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Answer:

• Only Katie is correct

Step-by-step explanation:

A regular polygon is a polygon with equal and identical sides and angles

\(.\)

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

The values of f and g that has been worked out is given as 6 and 8

This is a question that would examine the combination of two shapes into one.

We have area of a triangle = base * height / 2

this would give

f * 4 / 2 = 60 - 48

2f = 12

divide through by 2

f = 12 / 2

f = 6

we have f * g = 48

given that the value of f = 6

g * 6 = 48

6g = 48

Divide through by 6 to get the value of f

6 g / 6 = 48 / 6

g = 8

Hence the value of f is given as 6 and the value of g is given as 8

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Answer: 46

Step-by-step explanation: 8 is closer to 10, so 45.8 would round to 46

Answer:

1.5

Step-by-step explanation:

it is 1 and it a half so... 1.5

Answer:

\(\sqrt{3}\)

Step-by-step explanation:

Using the pythagoras theorem,

\(a^2 = b^2 + c^2\)

Wherein a is the long side (2)

and b = 1

Hence,

\(2^2 = 1^2+c^2\\c^2 = 2^2 - 1^2\\c^2 = 4-1\\c^2 = 3\\c = \sqrt{3}\)

Hence,

c = x = \(\sqrt{3}\)

Answer:

2c²

Step-by-step explanation:

8c³d² / 4cd²

= 2 * c²

= 2c²

Polynomials are closed under the operation of addition, subtraction, and multiplication only. Here's why:

1. Addition: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we add these two polynomials, (x⁴ + 2x³ - 4) + (3x³ - 2x² + 6x), it will result to x⁴ + 5x³ - 2x² + 6x - 4 which is also a polynomial.

When adding polynomials, the variables and the exponents don't change. This guarantees that the sum of these variables with exponents will always be a polynomial.

2. Subtraction: (Closed)

Reason: Say we have two polynomials: (x⁴ + 2x³ - 4) and (3x³ - 2x² + 6x). If we subtract these two polynomials, (x⁴ + 2x³ - 4) - (3x³ - 2x² + 6x), it will result to x⁴ - x³ + 2x² - 6x - 4 which is also a polynomial.

When subtracting polynomials, the variables, and the exponents don't change. This guarantees that the difference of these variables with exponents will always be a polynomial.

3. Multiplication: (Closed)

Reason: Say we have two polynomials (x + 2) and (x - 4). If we multiply these two polynomials, (x + 2)(x - 4), it will result in x² - 2x - 8, which is also a polynomial.

When multiplying polynomials, the variables do not change but the exponents will be added to each other. In this case, we can guarantee that the new exponents will be positive whole numbers still and this guarantees that the answer will be a polynomial.

4. Division: (Not closed)

Reason: When dividing polynomials, exponents are being subtracted from each other, therefore, we might have a result of a negative exponent. Negative exponents are not allowed in a polynomial. Example, say we have two polynomials (x²) and (x⁴), if we divide (x²) by (x⁴), the resulting value would be:

The resulting value is x to the power of negative 2, and is not a polynomial.

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Answer:

  0.16

Step-by-step explanation:

You want the probability that team b will win 2 games in a row, given that the probability of team a winning is 0.6, and the probability of team b winning is 0.4.

After one win for team A, the series can have the possible outcomes ...

  A – team a wins with probability 0.6

  BA – team a wins with probability (0.4)(0.6) = 0.24

  BB – team b wins with probability (0.4)(0.4) = 0.16

The probability of team b winning the series is 0.16.

__

Additional comment

The probability team a wins the series after winning the first game is 0.6 +0.24 = 0.84 (= 1 -0.16). At the beginning of the series, the probability b wins is 0.352, dropping dramatically after a wins the first game.

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The probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.

What is probability?

Probability is a measure or quantification of the likelihood of an event occurring. It is a numerical value assigned to an event, indicating the degree of uncertainty or chance associated with that event. Probability is commonly expressed as a number between 0 and 1, where 0 represents an impossible event, 1 represents a certain event, and values in between indicate varying degrees of likelihood.

To determine the probability that Team B wins the series after Team A wins the first game, we need to consider the different possible outcomes of the remaining games.

Since the series continues until one team wins two games, there are three possible scenarios:

Team A wins the next game (Team A wins the series)

Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1)

Team B wins both the next and third games (Team B wins the series)

We'll calculate the probabilities of these scenarios and then determine the probability of Team B winning the series.

Scenario 1: Team A wins the next game (Team A wins the series):

The probability of Team A winning the next game is 0.6.

Scenario 2: Team B wins the next game, followed by Team A winning the third game (Series tied at 1-1):

The probability of Team B winning the next game is 0.4.

The probability of Team A winning the third game is 0.6.

To calculate the probability of this scenario, we multiply the individual probabilities:

Probability = 0.4 * 0.6 = 0.24

Scenario 3: Team B wins both the next and third games (Team B wins the series):

The probability of Team B winning the next game is 0.4.

The probability of Team B winning the third game is 0.4.

To calculate the probability of this scenario, we multiply the individual probabilities:

Probability = 0.4 * 0.4 = 0.16

To find the probability of Team B winning the series, we add the probabilities of Scenario 2 and Scenario 3 since both outcomes result in Team B winning the series:

Probability = 0.24 + 0.16 = 0.4

Therefore, the probability that Team B wins the series after Team A wins the first game is 0.4 or 40%.

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The number of $1, $5 and $10 are 49, 44 and 22 respectively.

There are 3 denominations of bills in a wallet: $1, $5, and $10.

There are 5 fewer $5-bills than $1-bills.

let

x = number of $1 bills

Hence,

number of $5 bills = x - 5

There are half as many $10-bills as $5-bills.

number of $10 bills = 1 / 2 (x - 5)

Therefore,

x + x - 5 + 1 / 2 (x - 5) = 115

2x - 5  + 1 / 2 x - 5 / 2 = 115

2x + 1 / 2 x - 5 - 5 / 2 = 115

5 / 2 x  - 7.5 = 115

2.5x  = 115 + 7.5

x = 122.5 / 2.5

x = 49

Number of $1 bills = 49

Number of $5 bills = 49 - 5 = 44

Number of $10 bills = 1 / 2 (49 - 5) = 22

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Answer:

40%

Step-by-step explanation:

Answer:

40%

Step-by-step explanation:

The star asterisk in the fraction 12*/23* is being replaced by all the possible values as outlined

1 to be 11/21

2 to be 61/116

4 to be 62/117

5 to be 25/47

6 to be 63/118

8 to be 64/119

0 to be 12/23

In mathematics, a fraction is represented by a number that identifies a portion of a whole. A fraction is a chunk or section taken from a whole, which can be any number, and can represent any amount.

The fractions with different numerators and denominators when compared with another fraction but the same value with the fraction are said to be equivalent fractions.

The asterisk value is replaced with digit in each case, and the fraction formed is reduced to their equivalent forms as below

12*/23* * replaced by 1 and reduced to be 11/21

12*/23* * replaced by 2 and reduced to be 61/116

12*/23* * replaced by 4 and reduced to be 62/117

12*/23* * replaced by 5 and reduced to be 25/47

12*/23* * replaced by 6 and reduced to be 63/118

12*/23* * replaced by 8 and reduced to be 64/119

12*/23* * replaced by 0 and reduced to be 12/23

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Answer:

-3 + 5 + 6 g = 11 - 3 g - 3 + 5 + 6 g = 11 - 3 g

6 g + 2 = 3 g + 13 = 11 - 3 g

{g = 11/3, g = 1, g = -1/3}

{3 g = 11, g = 1, 3 g + 1 = 0}

{3 g + 13 = 2 (3 g + 1), 11 - 3 g = 2 (3 g + 1), 11 - 3 g = 3 g + 13}

The radius of the Arctic Circle is approximately 6040.62 km.

To find the radius of the Arctic Circle, we can use the concept of trigonometry and the given information.

Let's consider the Earth as a sphere with a radius of 6400 km.

The Arctic Circle is located at an altitude of 66.6° North.

When we draw a line from the center of the Earth to the Arctic Circle, it will form a right triangle with the radius of the Earth as the hypotenuse and the radius of the Arctic Circle as one of the legs.

Using trigonometric functions, specifically the sine function, we can relate the angles and sides of a right triangle.

We have:

sin(66.6°) = Opposite/Hypotenuse

Let's solve for the Opposite side, which is the radius of the Arctic Circle:

sin(66.6°) = Opposite/6400 km

Opposite = sin(66.6°) × 6400 km

Using a calculator, we can find:

Opposite ≈ 6040.62 km

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The spin of the wheel by the contestant is an illustration of a sine function whose equation is \(\mathbf{y =-1.25 sin(0.8x) + 0.25}\)

The wheel is 1.5 m above the floor, and the peg reaches a maximum height of 2.75 m.

So, the amplitude is:

\(\mathbf{A = 1.5 - 2.75}\)

\(\mathbf{A = -1.25}\)

The vertical shift is the minimum height of the peg.

So, we have:

\(\mathbf{D = 0.25}\)

The period (T) equals one circumference.

So, we have:

\(\mathbf{T = (max-min)\pi}\)

This gives

\(\mathbf{T = (2.75-0.25)\pi}\)

\(\mathbf{T = 2.5\pi}\)

The frequency (B) is then calculated as:

\(\mathbf{B = \frac{2\pi}{T}}\)

This gives

\(\mathbf{B = \frac{2\pi}{2.5\pi}}\)

Divide

\(\mathbf{B = 0.8}\)

A sine function is represented as:

\(\mathbf{y =A sin(B(x + C)) + D}\)

Substitute the calculated values

\(\mathbf{y =-1.25 sin(0.8(x + C)) + 0.25}\)

The horizontal shift (C) is 0.

So, the function becomes

\(\mathbf{y =-1.25 sin(0.8x) + 0.25}\)

See attachment for the graph of the equation

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