in a school of 330 students 85 of them...

it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

What is Integers?

A whole number is a number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, 5+, and √2 are not. The set of integers consists of zero, positive natural numbers, also called integers or counting numbers, and their additive inverses.

To prove that there are no integers x, y, z such that x² + y² = 8z + 3, we can use the concept of modulo arithmetic.

First, let's consider the possible values of x² and y² modulo 8:

For any integer n, n² modulo 8 can only be 0, 1, or 4.

Now, let's examine the possible values of 8z + 3 modulo 8:

8z modulo 8 is always 0.

3 modulo 8 is equal to 3.

Therefore, the possible values of x² + y² modulo 8 can only be 0, 1, or 4, while 8z + 3 modulo 8 is equal to 3. Since 0, 1, and 4 are not equal to 3 modulo 8, there are no integers x, y, z that satisfy the equation x² + y² = 8z + 3.

Hence, it is proven that there are no integers x, y, z such that x² + y² = 8z + 3.

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The average rate of change in the number of bacteria from t = 4 to t = 6 is best described as an increase of 320 bacteria per hour.

To find the average rate of change in the number of bacteria from t = 4 to t = 6, we need to calculate the difference in the number of bacteria at these two times and divide it by the time interval.

Given the growth model N(t) = 200(1.8), we can substitute the values of t = 4 and t = 6 to find the number of bacteria at these times.

N(4) = 200(1.8)^4 = 200(3.24) = 648

N(6) = 200(1.8)^6 = 200(5.83) = 1166

Now, we can calculate the difference in the number of bacteria:

1166 - 648 = 518

Next, we divide this difference by the time interval:

518 / (6 - 4) = 518 / 2 = 259

Therefore, the average rate of change in the number of bacteria from t = 4 to t = 6 is an increase of 259 bacteria per hour.

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Taxpayers in California may need to calculate the itemized deduction limitation when filing their state income taxes. This limitation sets a cap on the amount of itemized deductions that can be claimed, based on the taxpayer's federal adjusted gross income (AGI) and other factors.

Calculating the California itemized deduction limitation involves several steps and considerations to ensure compliance with the state tax regulations. To calculate the California itemized deduction limitation, taxpayers should first determine their federal AGI. This can be found on their federal tax return. Next, they need to identify any federal deductions that are not allowed for California state tax purposes, as these will be excluded from the calculation. Once the applicable deductions are determined, taxpayers must compare their federal AGI to the threshold specified by the California Franchise Tax Board (FTB). The limitation is typically a percentage of the federal AGI, and the percentage may vary depending on the taxpayer's filing status. If the federal AGI exceeds the threshold, the itemized deductions will be limited to the specified percentage. Taxpayers should consult the official guidelines and instructions provided by the California FTB or seek professional tax advice to ensure accurate calculation and compliance with the state tax regulations. Calculating the California itemized deduction limitation is an important step in accurately reporting and calculating state income taxes. It helps determine the maximum amount of itemized deductions that can be claimed, ensuring that taxpayers adhere to the tax laws and regulations of the state.

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The equation to be solved on the interval [0, 2) is 2cos²(x) + 3cos(x) + 1 = 0. To solve this equation, we can substitute u = cos(x) and rewrite the equation as a quadratic equation in u.

Replacing cos²(x) with u², we have 2u² + 3u + 1 = 0.

Next, we can factorize the quadratic equation as (2u + 1)(u + 1) = 0.

Setting each factor equal to zero, we get two possible solutions: u = -1/2 and u = -1.

Now we substitute back u = cos(x) and solve for x.

For u = -1/2, we have cos(x) = -1/2. Taking the inverse cosine or arccosine function, we find x = π/3 and x = 5π/3.

For u = -1, we have cos(x) = -1. This occurs when x = π.

Therefore, the solutions on the interval [0, 2) are x = π/3, x = 5π/3, and x = π.

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The function which is used to represent the graphed geometric sequence is

\(f(x) = 80{( \frac{1}{4}) }^{x - 1} \)

Let a be first term and r common ratio of the Geometric progression.

The Geometric sequence is of the form a,ar,ar^2, ...

The common ratio will be ar/a.

From the graph, we can find out the sequence as 80,20,5, ...

Here we can see that the sequence is in Geometric Progression.

First term a=80

Common ratio r= ar/a

= 20/80

=1/4

General term of Geometric sequence is

\(f(x) = a {r}^{x - 1} \)

Substituting the value a = 80 and r = 1/4,

we get,

\(f(x) =80 { (\frac{1}{4} )}^{x - 1} \)

Hence, the correct answer is

\(f(x) =80 { (\frac{1}{4} )}^{x - 1} \)

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Answer:

I got the answer 234/23

i hope this helps

Answer:

m<B=74°

Step-by-step explanation:

3x-23+2x-12=180

5x-35=180

5x=180+35

5x=215

x=215÷5

x=43

m<B=2x-12=2(43)-12=86-12=74

answer:

b= 10x i pretty sure

Step-by-step explanation:

Answer:

g=-4/5

Step-by-step explanation:

-25/32g=5/8

-200g=160

g=-4/5

Answer:

the answer is g= -4/5 if u want decimal form its g=-0.8

A conversion of this equation in point-slope form into standard form is y = x/2 + 1.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

y - 3 = -1/2(x + 4)

Making y the subject of formula in the above equation, we have the following:

y = x/2 - 2 + 3

y = x/2 + 1

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Answer:

Add 5 to both sides.

Step-by-step explanation:

3.7 = x + (-5)

3.7 + 5 = x + ( -5) + 5

5 cancels on the right

8.7 = x

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 3.7=x+(-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 3.7=x-5

Add 5 to both sides of an equation, we get

3.7+5=x-5+5

x=8.7

The correct step to solve an equation is add 5 to both sides. Therefore, option B is the correct answer.

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(a) Therefore, the range of possible values for "x" is 1 to 5. (b) Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.  Therefore, there are 31 different ways this can happen

To find the number of different ways this can happen, we can consider the number of internet friends each person can have. Since each person has the same number of internet friends, let's denote that number as "x". We can then create equations based on the given information:

1. Some, but not all, of them are internet friends with each other: This means that at least two people are internet friends with each other, but not everyone is friends with each other. This implies that the minimum number of internet friends any person can have is 1, and the maximum number is 5 (since there are 6 people in total).

Therefore, the range of possible values for "x" is 1 to 5.

2. None of them has an internet friend outside this group: This means that each person's internet friends must be within this group of 6 people. So, the number of internet friends each person can have is limited to the remaining 5 people.

To find the number of different ways this can happen, we need to sum up the possible values of "x" and calculate the corresponding combinations. For "x = 1", we choose 1 person out of 5 remaining people, giving us C(5, 1) = 5. For "x = 2", we choose 2 people out of 5 remaining people, giving us C(5, 2) = 10.

Similarly, for "x = 3", "x = 4", and "x = 5", we have C(5, 3) = 10, C(5, 4) = 5, and C(5, 5) = 1 respectively. Summing up these values, we get 5 + 10 + 10 + 5 + 1 = 31.

Therefore, there are 31 different ways this can happen

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The integral ˆ«(1 to [infinity]) xe^-x2 dx, is  E) divergent, that is, an indefinite integral with an upper limit of infinity.

Let's use the following steps to evaluate indefinite integral:

ˆ«(1 to [infinity]) xe^-x2 dx

We can start by making a substitution to simplify the integral.

We substitute u = -x^2, du = -2x dx. When x approaches infinity, u approaches negative infinity, and when x is 1, u is -1.

Now we can rewrite the integral with the substitution:

ˆ«(-1 to -infinity) e^(u/2) du

Next, we can use the limit property of integrals to evaluate the integral as u approaches negative infinity:

lim[u->-infinity] ˆ«(-1 to u) e^(u/2) du

As u approaches negative infinity, e^(u/2) approaches zero, so the integral becomes zero or the integral converges to zero.

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The above statement can be represented as :

value of x = 20

hence, the required number is 20

Answer: in mathematics, an extraneous solution is a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem. A missing solution is a solution that is a valid solution to the problem, but disappeared during the process of solving the problem.

Step-by-step explanation:

The standard form of linear equation is written as ax + by = c, where a, b, and c are real numbers and a and b are not both zero.

In this form, the coefficients a and b are the slopes of the line and c is the y-intercept.

In the equation x = -5, the coefficient of x is 1 and the constant is -5. This equation can be written as 1x + 0y = -5, which is the standard form of the equation.

To solve this equation, we can first subtract 5 from both sides:

1x + 0y - 5 = -5 - 5

1x + 0y = 0

This is the simplest form of the equation and can be used to find the x-intercept of the line. By setting y = 0 and solving for x, we get x = 0. This means that the x-intercept of the line is (0, -5). We can also use this equation to find the slope of the line. The slope of the line is equal to the coefficient of x, which is 1. This means that the slope of the line is 1.

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Answer:

26505/16

Step-by-step explanation:

4/9 + 1/5x = 589

Subtract x from both sides: 4/9x + 1/5 = 589 + x

Simplify: - 16/45x = 589

Multiply both sides by 45: 45 ( - 16/45x )  = 589 x 45

Simplify again: - 16/-16 = 26505/-16

x= 26505/-16

Yes the graph of the function represents a linear piecewise function of x.

From the graph we can see that the function can be broken down into 3 distinct parts.

Let us take the first part of the graph which represents the function:

For values of x ranging from negative infinity to 0, the value of y is 2 .

So the function is of the form y = 2.

Now for the second slanting part of the function.

The function passes through the points (0,2) and (2,-2)

Slope of the line = (-2-2)/(2-0) = -2

Equation of the line :

y-2 = -2(x)

or, y + 2x = 2.

Now for the third part of the function is y = -2 for all x>2

Hence the piecewise function can be represented as for the domain of x:

     {2 , x < -2 }

y = {2-2x , -2 ≤ x ≤ 2}

     {-2 , x > 2}

Hence all parts are linear so the function is linear in nature.

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The activity that is not associated with the purchase and payments business process is Selling products and services.

therefore d. Selling products and services is correct.

Business process is a set of activities carried out in a systematic manner, aimed at achieving specific results.

The purchase and payment process are important in businesses as it involves the payment of vendors for goods and services bought.

The activities associated with the purchase and payment business process includes buying products and services, receiving goods, recording payments to vendors, and verifying and approving invoices.

The sales of goods and services, on the other hand, are part of the sales process, not the purchase and payment process.

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The cost price of pawpaw is 40 and the cost if the basket of mangoes is 1250.

Based on the information given, the equations to solve the question will be:

30p + 100m = 2450 .... i

1.3 × 40p - 30 p + 1.3 × 100m = 855 ..... ii

30p + 100m = 2450

12p + 30m = 855

Solving simultaneously, the price of pawpaw is 40 and the price of mango is 12.5.

Therefore, the cost of 100 basket of mangoes will be:

= 12.5 × 100

= 1250

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Answer:

  28.5 m/s

Step-by-step explanation:

Given that power is 1400 W when speed is 25 m/s, and power is proportional to the square of speed, you want the speed when the power is 1820 W.

Since power is proportional to the square of speed, the ratio of speed squared to power is a constant:

  s²/P = 25²/1400 = x²/1820

where x is the unknown speed.

We can find the value of x by multiplying by 1820 and taking the square root:

  x² = 25²(1820/1400)

  x = 25√(1820/1400) = 25√1.3 ≈ 28.5 . . . . m/s

The speed is 28.5 m/s when the power is 1820 watts.

Answer:

n=-7

Step-by-step explanation:

-234=-38+28

-28n=-38+28n

-28n=196

As per the square ABCD, the scale factor r is 7/9

Square:

According to geometry, square is a two-dimensional plane figure with four equal sides and all the four angles are equal to 90 degrees.

Given,

Square A′B′C′D′ is the image of square ABCD under a dilation from center O1 by scale factor r . Square A′′B′′C′′D′′ is the image of square A′B′C′D′ under a dilation from center O2 by scale factor 14 . The side lengths of square A′′B′′C′′D′′ are 18 of the corresponding side lengths of square ABCD.

Here we need to find the scale factor r.

AS per the given details we know that,

Side length of square = 18.

Scale factor of square A′′B′′C′′D′′ = 14

So,

Side lengths of square A''B''C''D'' = 18 × Side lengths of square ABCD

Noe, we have to apply the known values on these formula, then we get,

14 = 18 x r

r = 14/18

When we simplify it, then we get,

r = 7/9

Therefore, the value of the scale factor r is 7/9.

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Answer:



Step-by-step explanation:

Answer:

15-inch times 11 =165

Step-by-step explanation:

The greatest number of 15-inch pieces the carpenter can cut from 6 of these wood boards is 52.

Given that, cut 15-inch pieces of wood from a board of wood that is 11 feet in length.

We need to find the greatest number of 15-inch pieces the carpenter can cut from 6 of these wood boards.

Converting an inch length measurement to feet is as simple as dividing the number of inches by 12 because there are 12 inches in a foot.

Now, 11×6×12/15=52.8

Therefore, the greatest number of 15-inch pieces the carpenter can cut from 6 of these wood boards is 52.

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Answer:ik i am late but it is 4.4 for the people that need it now

Step-by-step explanation:

Answer:

the answer is 80

Step-by-step explanation:

QR=ST: 7x+3=5x+25

2x=22

x=11

7(11)+3=80      5(11)+25=80

Answer:

4

Step-by-step explanation:

3r = 10 + 5s

r = 10

3(10) = 10 + 5s

30 = 10 + 5r

20 = 5r

r = 4

we can conclude that the probability for the first apple than the peach fruit is 10/39.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here, we have

Given that there are 8 apples and 5 peaches in a basket.

Total Fruits = 13

For the first event, the probability of getting an apple is,

P(A) = 8/13

Now, Total Fruits = 12

For the second event, the probability of getting peach is,

P(B) = 5/12

The probability for both events is given below.

P = P(A)×P(B)

P = 8/13 ×  5/12

P = 40/156 = 10/39

Hence we can conclude that the probability for the first apple than the peach fruit is 10/39.

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