Express the following sum in sigma notation. Use 1 as the lower limit of summation and k for the index of summation. 1+4+9+16+25 +36 Express the sum in sigma notation. Σ" k 1

Answer:

12345678901234567890

In the given right-angled triangle, the sides are 21.3617 and 22.8815.

The given figure is a right-angled triangle. Hence, sides can be determined by using trigonometric function and/or the Pythagorean theorem. It is known that angle A = 69 and side b = 8.2. The side b is an adjacent side to angle A. Using the trigonometric function of tangent

tan Ɵ = opposite side/adjacent side

tan A = a/b

a = b tan A = 8.2 tan 69 ≈ 21.3617

As the two sides a and b are known, the remaining side c can be determined by using Pythagorean theorem,

Hypotenuse^2 = Opposite^2 + Adjacent^2

c^2 = a^2 + b^2

c^2 = (21.3617)^2 + (8.2)^2

c^2 = 523.3635

c =√523.3635

c ≈ 22.8815

Note: The question is incomplete. The complete question probably is: Use a calculator to find the length of each side to four decimal places. (Assume triangle ABC where side a is opposite angle A, side b is opposite angle B, and side c is the hypotenuse.) side length b = 8.2 and angle A = 69 degrees.

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The number of solutions for given three system of linear equations.

We can simply solve this numerical problem by using the following process.

3x - y = 4 ==> a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

What is meant by numerical?

Based on the formula is:

Let the system of equations be a₁x + b₁y = c₁ and  a₂x + b₂y = c₂ then

Condition for One solution: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

Condition for No Solution:  a₁/a₂ = b₁/b₂ ≠ c₁/c₂

Condition for infinitely many solutions:  a₁/a₂ = b₁/b₂ = c₁/c₂

Now in the given question:

a.) 3x - y = 4

6x - 2y = 8

⇒ a₁/a₂=3/6 = 1/2 ; b₁/b₂ = -1/-2 = 1/2 ; c₁/c₂ = 4/8 = 1/2

⇒  a₁/a₂ = b₁/b₂ = c₁/c₂ = 1/2

The given system of equations is coincident lines, hence has infinitely many solutions.

b.) -3x + y = 7

     2x - 4y = -8

⇒ a₁/a₂= -3/2 ; b₁/b₂ = 1/-4 ; c₁/c₂ = 7/-8

⇒ a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂

The given system of equations is intersecting lines, hence having a single solution.

c.) y = -4x - 5

y = -4x +1

⇒ a₁/a₂= -4/-4 = 1 ; b₁/b₂ = 1/1 = 1 ; c₁/c₂ = -5/1 = -5

⇒ a₁/a₂ = b₁/b₂ ≠ c₁/c₂

The given system of equations is parallel lines, hence having no solution.

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a. Taxpayer having a taxable income of $39,800 has $5,448 as the income tax.

b. The taxable income of taxpayer owing $21,197 is $102,800.

What is Income Tax?

Income tax is the tax which is levied on all individuals and businesses. The individual income taxes are calculated on the basis of the income received by the individual. Typically, it is categorized as a direct tax because the burden is thought to fall on the people who pay it. Net profits, calculated as the excess of receipts over permitted costs, are subject to corporate income tax.

We are given graph of a piecewise function with three equations which is attached below.

From the graph, it can be observed that the taxpayer who has the taxable income of $39,800 has to pay income tax of $5,448.

Also, a taxpayer owing $21,197 means that he has to pay income tax of $21,197.

His taxable income is $102,800 as shown in the graph  below.

Hence, taxpayer having a taxable income of $39,800 has $5,448 as the income tax and the taxable income of taxpayer owing $21,197 is $102,800.

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a) The percentage of pregnancies should last between 269 and 282 days is 18%

b) The days should the longest 10% of all pregnancies last is 291 days.

c) According to the Central Limit Theorem, the distribution of this sample mean is 265. The model is a Normal model, and standard deviation is 17/(√(67)).

d) The probability that the mean duration of these patients' pregnancies will be less than 258 days is 0.03 or 3%

a) To find the percentage of pregnancies that should last between 269 and 282 days, we need to find the proportion of the area under the normal distribution curve that falls between those two values. This can be done using a standard normal table or calculator. Using a calculator, we find that the proportion of the area under the curve between 269 and 282 days is approximately 0.18 (or 18%).

b) To find the longest 10% of all pregnancies, we need to find the duration that corresponds to the 90th percentile. We can use the standard normal table or calculator to find that the duration that corresponds to the 90th percentile is approximately 291 days.

c) According to the Central Limit Theorem, the distribution of the sample mean, y, is a normal distribution with a mean of 265 days (the population mean) and a standard deviation of 17/(√(67)) days. So the model is a Normal model with mean 265 and standard deviation 17/(√(67))

d) To find the probability that the mean duration of these patients' pregnancies will be less than 258 days, we need to find the proportion of the area under the normal distribution curve that falls to the left of 258 days. Using a calculator, we can find that the proportion of the area under the curve to the left of 258 days is approximately 0.03 (or 3%).

Therefore, the correct answers are as given above

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Answer:

(4,8) (0,2) (-6,-7)

Step-by-step explanation:

Perpendicular means it sort of makes a cross with 90º angle from the already existing line. Imagine it starts at (4,8) coordinate and comes falling to the left, passing through p(-4,-4) coordinate, the points it will go through will be (4,8) (0,2) and (-6,-7) respectively.

A sure way to do this is to mark every point that's on the table below and see which ones form a perpendicular line with the original.

Answer:

1650

Step-by-step explanation:

1732.5 / (1+5%) = 1732.5 / 1.05 = 1650

To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.

Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualization. These kinds of graphs are employed to visually represent particular data patterns or groups.

To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.

For the first question:

Scale on the number line from the first tick, 310 to 335.

For the second question:

Scale on the number line from the first tick, 18 to 31.

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=109

The distance between the xy, yz, and xz planes are 5, 3, and 7.

Multivariable Calculus

This question relates to multivariable calculus.

a) Distance of point (x, y, z) from the XY-plane

The |z co-ordinate of the point| = |z|

distance of the point (3, 7, -5) from xy plane

|-5|=5

b) Distance of point (x, y, z) from yz plane

The |x coordinate of the point| = |x|

Therefore, the distance of the point (3, 7, -5) from yz plane is

|3|=3

c) Distance of point (x, y, z) from xz plane

The |y coordinate of the point| = |y|.

The distance of the point (3, 7 -5) from the xz-plane is

|7|=7

d) Distance of point (x, y, z) from the x-axis

The distance of the points from the x-axis is

[tex]x^{2} =y^{2} +z^{2} \\\\x=\sqrt{y^{2} +z^{2} } \\\\x=\sqrt{7^{2}+(-5)^{2} } \\\\x=\sqrt{74}[/tex]

e) Distance of point (x, y, z) from the y-axis

[tex]y=\sqrt{x^{2} +z^{2} } \\\\y=\sqrt{3^{2}+(-5)^{2} } \\\\y=\sqrt{34}[/tex]

f) Distance of point (x, y, z) from the z-axis

[tex]z=\sqrt{x^{2} +y^{2} } \\\\z=\sqrt{3^{2}+7^{2} } \\\\z=\sqrt{58}[/tex]

From the calculations above,

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Answer:

Step-by-step explanation:

If we assume that the average rate of arrivals is 5 minutes, then this means that the Poisson distribution will have a mean of 5 customers/minutesThis means that the probability that a customer arrives in the next minute is 0.2 (1/5).

The exponential distribution will have a mean of 4 minutes, meaning that the probability that the customer is served in the next minute is 0.25 (1/4).

Therefore, the expected number of customers that the barber can serve in an hour is 15 (5*4). The expected number of customers served in a given minute is 0.2 (1/5) * 0.25 (1/4) = 0.05. This means that the barber can expect to serve an average of 3 customers per hour.

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The vertical scales for each type of vehicle are:

The rationale is to choose a vertical scale that represents the relative frequencies, or the proportion of each type of vehicle sold compared to the total number of vehicles sold. The calculation for each type of vehicle is as follows:

Here, the total number of vehicles sold (150) is calculated by adding up the sales for each type of vehicle. The relative frequency for each type of vehicle is then calculated by dividing the sales for that type of vehicle by the total number of vehicles sold.

This question should be provided as:

A car dealer is deciding what kind of vehicles he should order from the factory. he looks at his sales report for the preceding period. choose the vertical scale so that the relative frequencies are represented:

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As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.

The numeral is said to be in this simplest form when divided into its smallest equivalent fraction. How to do to find the most basic form. Find common factors in the denominator and numerators. Verify a fractional integer to verify if it passes as a prime number. A statement having two collinear and an equally sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The normal form of a linear function is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorised as identities or conditional equations. An identity holds true regardless of the value given to the variables.

given

Let the boat's speed in calm water be x km/h.

Boat speed downstream is equal to x plus 5.

Upstream boat speed is equal to x - 5

Distance x time speed

Time is therefore determined by speed and distance.

Boat travel time is equal to 30/km upstream (x – 5)

50/(x + 5) is the time it takes a boat to travel 50 kilometres downstream.

Since the boat takes the same amount of time in both scenarios, 30 (x + 5) = 50 (x -5), 30 x +150 = 50 (x -250), 20 (x = 400), and 20 (x = 20).

As a result, when a boat goes 30 km up a river in the same amount of time, its speed in still water is 20 km/h.

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Answer: she had 433 yards

Step-by-step explanation:

Answer:

absolutely

Step-by-step explanation:

Needs are for survival in life like food, rent or mortgage, utilities, and other expenses.  Transportation costs, insurance coverage, and any clothing and tools you need for work are included in this part of your budget.  A want includes expenses that you can comfortably live without and is not essential for survival.

There were 64 students who had taken a mathematics course. Of those 64, 28 had also taken a business course, and 26 had also taken a computer science course. This leaves 10 students who had taken only a mathematics course.

To calculate this, we start by subtracting the number of students who had taken all three courses (14) from the total number of students who had taken a mathematics course (64).

Then we subtract the number of students who had taken both a mathematics and a business course (28) and the number of students who had taken both a mathematics and a computer science course (26) from the result. This gives us 10 students who had taken only a mathematics course.

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Answer: -4(3y+4)

Step-by-step explanation:

First I found the Great common divisor (-4) and took that number and divided -12y and -16 with it getting 3y and 4 and then I set it up as if I was trying to get -12y and -16 so the best way to do that is to use the distributive property so I put 3y and 4 in parentheses like this (3y+4) then I added the -4 on to get the answer of -4(3y+4)

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{-12y - 16}[/tex]

[tex]\large\text{Let us look for the GCF for each of your numbers because it can}\\\large\text{make this equation somewhat easier to solve.}[/tex]

[tex]\mathsf{-12x \rightarrow -1, -2, -3, -4, -6, -12, \ \& \ -x}\\\\\mathsf{-16 \rightarrow -1, -2, -4, -8, \& -16}\\\\\large\text{Thus, your GCF for both of your numbers is: \boxed{- 4 }}\large\checkmark[/tex]

[tex]\large\text{So, let us put }\rm{-4}\large\text{ in front of your parentheses because we had to factor}\\\large\text{out the common like term they shared together.}[/tex]

[tex]\large\text{Now simplify it furthermore}[/tex]

[tex]\huge\text{This leaves your answer as:}[/tex]

[tex]\huge\boxed{\mathsf{-4(3y + 4)}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output.

The vector is a 1-dimensional array. The formula for this function is:

For i = 0 to length-1

   Print ( ptr[i] )

End

The calculation for this function is as follows:

The function starts with a for loop, where the initial value of i is set to 0, and the condition for the for loop is i < length, and the increment value of i is 1. The body of the for loop prints the value of ptr[i], which is the value at the i-th position in the vector. This loop is repeated until the condition i < length is false, at which point the function terminates.

In summary, the function void print int vector(int *ptr, int length) prints the values in the vector of integers indicated by ptr of length length to the standard output. The formula for this function is a for loop, where the initial value of i is set to 0 and the condition for the for loop is i < length. The body of the for loop prints the value of ptr[i], and the loop is repeated until the condition i < length is false.

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The solution to the given equation x² + 7x = 0 is x = 0, -7.

The quadratic equation is defined as a function containing the highest power of a variable is two.

The quadratic equation is given in the question, as follows:

x² + 7x = 0

We have to determine the solution to the given equation.

As per the question, we have

x² + 7x = 0

x(x + 7) = 0

Equating factors to zero, we get

x = 0 and (x + 7) = 0

x = 0 and x = -7

Thus, the solution to the given equation is x = 0, -7.

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Answer:

66

Step-by-step explanation:

32+44=66

32

+42

____

66

It will take 28 minutes for them to fill the tank.

Work done is defined as the amount of force needed to move and object a certain distance. In essence, it is a measure of an energy transferred to or from an object which allows it to be moved.

Given that, an aquarium tank can hold 6300 liters of water. There are two pipes that can be used to fill the tank. The first pipe alone can fill the tank in 84 minutes. The second pipe can fill the tank in 42 minutes by itself.

Work done by first pipe in 1 minute = 1/84

Work done by second pipe in 1 minute = 1/42

The time taken by both the pipes together =

1 / 84 + 1 / 42 = 3 / 84

= 1/28

Therefore, time taken by  both the pipe = 28 minutes.

Hence, it will take 28 minutes for them to fill the tank.

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x² + x² = 4

2x² = 4

x² = 2

x=√2

hope it helps

A discontinuity the left and right limits still need to exist but are different.

Since bounded, growing sequences of numbers have limits, a non-decreasing function can only have leap discontinuities, which means that at

Every leap indicates that one interval is missing from the function's range, and these intervals are all disconnected (since the function is non-decreasing, the skipped intervals march up the y-axis).

Since there are only a finite number of discontinuous intervals, there can only be a finite number of discontinuity sites (to see this last bit, just pick a rational number in each interval).

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Arithmetic operations on the directed numbers gives;

7) -7

8) +73

9) - 8

10) + 1

Any given number which has either a positive or negative sign is a directed number. Thus all numbers are directed in one way or the other. Some examples are: 8, +2, - 8.35, 10, 520 etc.

Performing an arithmetic operations on the given question, we have;

7) +9 - + 16 = +9 -(+16)

applying the rule of signs

+9 - (+16) = + 9 - 16

              = -7

8) +85 - + 12 = +85 - (+12)

applying the rule of signs

+85 - (+12) = +85 - 12

                 = +73

9) -6 - 2

applying the rule of signs

-6 -2 = -8

10) +13 - + 12 = +13 - (+12)

applying the rule of signs

+13 - (+12) = +13 - 12

                = +1

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The domain and range of the relation are { -2 } and { 4, 5, 6, 7 } respectively. The relation is not a function.

A function is simply a relationship that maps one input to one output, that is, each x-value can only have one y-value.

Given the relation in the question;

(-2,7), (-2,6), (-2,5), (-2,4)

For a relation to be a function, every x-value must have only one y-value mapped to it.

-2 appeared twice and its corresponding y-values are different.

Hence, the relation is Not a Function.

The Domains are the x-values and the Range are the y-values,

Domain: { -2 }

Range: { 4, 5, 6, 7 }

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