Each of your eight friends owes you 10$. use integer multiplaction to represent the total amount your friends owe you

Answer:

Rational.

Step-by-step explanation:

The product of two rational numbers is always rational. This means that if you multiply two numbers that can be made into a fraction, their product can also become a fraction.

~

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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The probability that X is between 134.4 and 140.1 is approximately 0.4076, which is closest to the option 0.4069.

To calculate this probability, we need to standardize the values using the standard normal distribution. First, we find the z-scores for the lower and upper bounds:

z1 = (134.4 - 137.0) / 5.3 ≈ -0.4906

z2 = (140.1 - 137.0) / 5.3 ≈ 0.5849

Next, we use a standard normal distribution table or a calculator to find the probabilities associated with these z-scores. The probability corresponding to z1 is P(Z < -0.4906) ≈ 0.3131, and the probability corresponding to z2 is P(Z < 0.5849) ≈ 0.7207.

To find the probability that X is between 134.4 and 140.1, we subtract the probability associated with the lower bound from the probability associated with the upper bound:

P(134.4 < X < 140.1) = P(Z < 0.5849) - P(Z < -0.4906) ≈ 0.7207 - 0.3131 = 0.4076.

As a result, the chance that X lies between 134.4 and 140.1 is roughly 0.4076, which is closest to the value of 0.4069 for the option.

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Answer:

\(\huge \colorbox{blue}{B}\)

Step-by-step explanation:

we are given the formula,Mass and volume

to find density we just need to substitute the value of mass and value and simplify it

\( \sf substitute \: the \: value \: of \: mass \: and \: volume : \)

\( \quad \: \sf \dfrac{7.0 \times {10}^{24} \: kg }{3.5 \times {10}^{12} \: {km}^{3} } \)

now we will use \(\dfrac{x^m}{x^n}=x^{m-n}\) to simplify division

\( \sf simplify \: division : \\ \quad \: \sf 2 \times {10}^{24 - 12} \times \frac{kg}{ {km}^{3} } \\ \quad \tt 2 \times {10}^{12} \frac{kg}{ {km}^{3} } \)

hence, our choice is \(B\)

___________________________________

\(\huge\underline{\tt{\red{Formula:}}}\)

\(\quad\quad\quad\quad\tt{density = \frac{mass}{volume} }\)

\(\huge\underline{\tt{\red{Solution:}}}\)

\(\quad\quad\quad\quad\tt{density = \frac{7.0 \times {10}^{24} \: kg}{3.5 \times {10}^{12} \: k {m}^{3} } }\)

\(\quad\quad\quad\quad\tt{density = (\frac{7.0}{3.5 } = 2.0)}\)

\(\quad\quad\quad\quad\tt{\:\:and\:\:({10}^{24 -12})}\)

\(\quad\quad\quad\quad \boxed{\tt{density = 2.0 \times {10}^{12} \: \frac{kg}{k {m}^{3} }} }\)

\(\huge\underline{\tt{\red{Answer:}}}\)

\(\quad\quad \underline{\boxed{\tt{ \red{B.) \: \: 2.0 \times {10}^{12} \: \frac{kg}{k {m}^{3} }}}} }\)

\(\huge\underline{\tt{\red{Explanation:}}}\)

Given that the formula for density is equal to mass all over the volume.

We use this formula:

\(\boxed{\tt{density = \frac{mass}{volume} }}\).

We substitute it like this:

\(\boxed{\tt{density = \frac{7.0 \times {10}^{24} \: kg}{3.5 \times {10}^{12} \: k {m}^{3} } }}\)

Then, hence we got:

\(\boxed{\tt{density = 2.0 \times {10}^{12} \: \frac{kg}{k {m}^{3} }} }\)

___________________________________

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✍︎ C.Rose❀

The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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Answer:

\(m = \frac{ - 5 - 1}{2 - ( - 3)} = - \frac{6}{5} \)

Answer: May not be the exact answer you're looking for, but the explanation below should make sense.

Step-by-step explanation:

To shift the graph of y=2x+5 up, there is no need for a seperate equation. When you notice is that 5 is the y-intercept. Since the slope of the equation is still the same, all you do is increase the y-intercept to shift it up and decrease to shift it down. This may be a little hard, but if you graph it, and mess around with the y-intercept, you will see that the graph goes up as the y-intercept increases. As you decrease the y-intercept, the graph will travel down.

I hope this answers your question. Let me know if you have any questions.

Answer:

hink of sea level as 0 , and the elevation above sea level as positive, while the elevation below sea level is negative. Then determine the distance between them as if the two values are on a number line.

20617 feet

Step-by-step explanation:

Answer:

i would have to go with b or c i would choose one of those

Step-by-step explanation:

Hοmοzygous means both letters are uppercase, or both are lowercase.

Heterozygous means one is uppercase and the other is lower case.

Dominant is represented by uppercase.  Recessive is represented by lowercase.

"Hοmοzygous dominant" is NN.

"Heterozygous" is Nn.

"Hοmοzygous recessive" is nn.

Shade NN red, and shade Nn green.  Leave nn unshaded.

Answer:

suppose 2^2 + b^2 = c^2 with 2 < b < c (it should be clear that this assumption is fine, 12 + 22 = 5 and sqrt(5) is not an integer; 22 + 22 = 8 and sqrt(8) is not an integer). Then c^2 - 4 = b^2 so (c+2)(c-2) = b^2. As b is prime, this means c-2=b or c-2=1 (since c+2 > 1). So either c=b+2 or c=3. The c=3 case can't happen since that would make b^2 = 5 so we are left with c=b+2. Then we have 4 + b^2 = (b+2)2 = b2 + 4b + 4 meaning that b=0. So there are no triples involving 2.

Step-by-step explanation:

A Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.

The given function:

\((x^2-y^2) + (2xy)^2 = (x^2 + y^2)^2\)

This function is expanded as follows;

\((x^2-y^2)^2 + (2xy)^2 = (x^2 + y^2)^2\\\\x^4 + y^4 -2x^2y^2 + 4x^2y^2 = x^4 +y^4 + 2x^2y^2\\\\add \ \ (+2x^2y^2) \ to \ both \ sides \\\\x^4 +y^4 +4x^2y^2 = x^4 +y^4 +4x^2y^2\)

In this expanded form of the given function, it is clear that non of the coefficients of x and y contains integer 2 and the supposed coefficient value of xy increase to 4 because of the extra 2x²y² added to the function.

Thus, we can conclude that a Pythagorean triple of this form cannot contain integer 2 if we add extra 2x²y² because it will increase the value of the coefficient of xy to 4.

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De acuerdo con las definiciones de precio a pagar, porcentaje de descuento y porcentaje remanente, el precio a pagar por el celular es $ 1080.

En esta situación una persona recibe un descuento por la compra de su celular, el precio a pagar es el producto de multiplicar el coste sin descuento y el porcentaje remanente en forma fraccionaria. El porcentaje remanente se calcula al restar el descuento del cien por ciento. A continuación, procedemos al cálculo requerido:

x = 4500 × (1 - 76/100)

x = 1080

De acuerdo con las definiciones de precio a pagar, porcentaje de descuento y porcentaje remanente, el precio a pagar por el celular es $ 1080.

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Answer:

2.438

Step-by-step explanation:

1=0.305m

x=8m

( do cross multiplication)

8=0.305x

x=2.438 or 2.44

The given boundary-value problem can be solved using the method of variation of parameters. the solution to the given boundary-value problem is у(x) = -e2x + 2e4x.

First, we need to find a particular solution of the homogeneous equation y" - 8y' + 16y = 0, which is yp(x) = c1e2x + c2e4x, where c1 and c2 are constants.

To find the particular solution, we can use the given boundary conditions y(0) = 1 and y(1) = 0. We solve for c1 and c2, and we get c1 = -1 and c2 = 2.

So, the particular solution is yp(x) = -e2x + 2e4x. The general solution of the boundary-value problem is then:
у(x) = c1e2x + c2e4x -e2x + 2e4x
= c1e2x + (c2 + 2)e4x.

By using the boundary conditions, we can find the value of c1 and c2:
у(0) = c1 + c2 + 2 = 1
у(1) = c1e2 + (c2 + 2)e4 = 0

Solving these two equations, we get c1 = -1 and c2 = 2.
Therefore, the solution to the given boundary-value problem is
у(x) = -e2x + 2e4x.

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Answer:

Step-by-step explanation:

Sorry I can't explain how it is done. It is very difficult to explain on paper.

Answer: The eldest, Colin, is 41 years old

Step-by-step explanation:

The area of the rectangle is \($\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$\) square units. Thus, the answer is option D: 10 square units.

What is area of rectangle?

The area of a rectangle is the measure of the region enclosed by its sides, and is calculated by multiplying the length and the width of the rectangle. The unit of area is typically expressed in square units, such as square meters (m²) or square feet (ft²).

The area of rectangle can be calculated using the distance formula to find the length and width of the rectangle, and then multiplying them. Let A(2,1), B(1,3), C(5,5), and D(6,3) be the coordinates of the rectangle's vertices.

The distance between A and B is \(\sqrt{(1-2)^2 + (3-1)^2} = \sqrt{1+4} = \sqrt{5}$.\)

The distance between B and C is \(\sqrt{(5-1)^2 + (5-3)^2} = \sqrt{16+4} = \sqrt{20}$.\)

So, the length of the rectangle is \(\sqrt{20}$ units.\)

The distance between A and D is \(\sqrt{(6-2)^2 + (3-1)^2} = \sqrt{16+4} = \sqrt{20}$.\)

The distance between C and D is \(\sqrt{(6-5)^2 + (3-5)^2} = \sqrt{1+4} = \sqrt{5}$.\)

Therefore, the width of the rectangle is \(\sqrt{5}$ units.\)

Hence, the area of the rectangle is \($\sqrt{20} \times \sqrt{5} = \sqrt{100} = 10$\) square units. Thus, the answer is option D: 10 square units.

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Answer:

24

Step-by-step explanation:

3*8 = 24

Answer: A 3(5x-8)

Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24

You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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The values of g(x) for the given values of x are g(0) = 4, g(-7) = 3, g(-4) = 0

Functions can be used to model a wide range of real-world phenomena, such as physical laws, economic relationships, or biological processes. They are a fundamental concept in mathematics and play a central role in many fields, including engineering, physics, computer science, and statistics.

Functions can be represented graphically, algebraically, or numerically, and can be manipulated and analyzed using a variety of mathematical tools and techniques. By understanding how functions work and how to use them, people can solve problems, make predictions, and gain insights into a wide range of mathematical and real-world phenomena.

To evaluate the piecewise function at each value of the independent variable, we need to substitute the given value of x into the appropriate expression for g(x):

a. To find g(0), we use the first expression since 0 is greater than or equal to -4:

g(0) = 0 + 4

g(0) = 4

b. To find g(-7), we use the second expression since -7 is less than -4:

g(-7) = -(-7 + 4)

g(-7) = -(-3)

g(-7) = 3

c. To find g(-4), we need to consider both expressions since -4 is exactly equal to -4:

g(-4) = -(-4 + 4) (using the second expression)

g(-4) = 0 (simplifying)

or

g(-4) = -4 + 4 (using the first expression)

g(-4) = 0 (simplifying)

So, g(-4) is equal to 0 using both expressions.

Therefore, the values of g(x) for the given values of x are:

g(0) = 4

g(-7) = 3

g(-4) = 0

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After the partitioning algorithm has completed, the low partition would be (27, 56, 46, 57) and the high partition would be (99, 77, 90).

Explanation: In the quicksort algorithm, partitioning is an important step. The partition algorithm in quicksort chooses an element as a pivot element and partition the given array around it.

In this way, we will get a left sub-array that consists of all elements less than the pivot, and the right sub-array consists of all elements greater than the pivot. If the pivot element is selected randomly, then quicksort performance would be O(n log n) in the average case.

In the given question, the given numbers are (27, 56, 46, 57, 99, 77, 90), and the pivot element is 77.To partition this array, the following steps are followed.

1. The left pointer will point at 27, and the right pointer will point at 90.

2. Increment the left pointer until it finds an element that is greater than or equal to the pivot element.

3. Decrement the right pointer until it finds an element that is less than or equal to the pivot element.

4. If the left pointer is less than or equal to the right pointer, swap the elements of both pointers.

5. Repeat steps 2 to 4 until left is greater than right.

In the given question, the left pointer will point at 27, and the right pointer will point at 90. Incrementing the left pointer will find the element 56, and the decrementing the right pointer will find the element 77.

As 56 < 77, swap the elements of both pointers. In this way, partitioning continues until left is greater than right. Now, the array will be partitioned into two sub-arrays.

The left sub-array will be (27, 56, 46, 57), and the right sub-array will be (99, 77, 90).

So the low partition is (27, 56, 46, 57), and the high partition is (99, 77, 90).

Therefore, the answer is: low partition (27, 56, 46, 57) and high partition (99, 77, 90).

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The cash price of the refrigerator is $408.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, a new refrigerator has a price of $480.00.

The store will discount the price by 15% if the purchaser pays in cash.

Now, the discount is

15% of 480

= 15/100 ×480

= 0.15×480

= 72

Now, 480-72

= $408

Therefore, the cash price of the refrigerator is $408.

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firm 2's quantity at the Cournot equilibrium is q2=5/3.the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. firm 2's quantity at the new Cournot equilibrium is q2=4/5.

The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the following diagram:
At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.

Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=q2=5/3
Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.
The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function. The new best response function is illustrated below:

At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect. Therefore, solving the two best response functions simultaneously for q1 and q2 gives:
q1=11/5
q2=4/5
Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5.

To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function:
p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4
Therefore, the market price at the new Cournot equilibrium is p=4.

In this exercise, we consider a market with two firms, 1 and 2, facing the inverse demand p()=10− p(Q)=10-Q where =1+2Q=q1+q2.

The two firms incur a marginal cost of production c1=c2=2c1=c2=2, produce a homogeneous good, and are Cournot competitors. The best response of firm 1 is given by 1q1=5−0.5q21+q2, and the best response of firm 2 is given by 2q2=5−0.5q12+q1. These best response functions are illustrated in the diagram below:

At the Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect

. Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=q2=5/3. Therefore, firm 2's quantity at the Cournot equilibrium is q2=5/3.The new best response function for firm 2 is given by 2q2=5−q1+2q22. This is obtained by replacing c2=2 with c2=4 in firm 2's profit function.

The new best response function is illustrated in the following diagram:At the new Cournot equilibrium, the two firms' quantities will be such that they are both choosing the best response to the other's quantity, which means that they will be producing where the two functions intersect.

Therefore, solving the two best response functions simultaneously for q1 and q2 gives q1=11/5 and q2=4/5. Therefore, firm 2's quantity at the new Cournot equilibrium is q2=4/5

To determine the market price at the new Cournot equilibrium, we substitute the new equilibrium quantities into the inverse demand function: p=10−Q=10−(q1+q2)=10−(11/5+4/5)=4. Therefore, the market price at the new Cournot equilibrium is p=4.

In conclusion, we have analyzed the effect of a raising rival's cost strategy on a Cournot duopoly. We have shown that the strategy reduces firm 2's quantity and increases the market price, but does not affect firm 1's quantity.

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Answer:

nope

Step-by-step explanation:

sorry about not knowing how to

Answer:

08

16

24

32

40

48

56

64

72

80

Step-by-step explanation:

From 1-10 You can see the numbers going from 0-8 on the left side except you repeat the number 4 twice then proceed. Then on the right side you do it backwards but instead you use the 2 times tables and you’re going to want to work your way from bottom to top and then when you reach to 0 which is the number 10 you repeat the 2 times tables again.

Answer:

It is the first answer y=- x + 5 and y = x - 3

Step-by-step explanation:

y=-x+5 and y=x-3 is the system of linear equations for the given table values.

Two or more expressions with an Equal sign is called as Equation.

A system of linear equations is usually a set of two linear equations with two variables.

x       y

0      5

5      0

2      3

4       1

Let us find equation of these values by considering any two points.

Slope: m=1-3/4-2=-2/2=-1

1=-1(4)+b

1+4=b

b=5

So y=-x+5 is the linear equation for first table.

x        y

0       -3

3       0

5       2

-1       -4

Slope m=-4-2/-1-5=-6/-6=1

Now find the y intercept

-4=1(-1)+b

-4+1=b

-3=b

y=x-3 is the equation of second table.

Hence,  y=-x+5 and y=x-3 is the system of linear equations for the given table values.

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