A XYZ is an equilateral triangle.
X
2
3
Z
Y
What is the measure of Z 2?
HURRY AND NO LINKS

Value of  [tex]1^{3} + 10^{3} + 11^{3} +12^{3} +......+30^{3}[/tex] is "216225".therefore the correct option is C.

Natural Numbers are the counting numbers that start from 1 and go on till infinity. To find the sum of cube of first n natural numbers means to add the cube of a specific number of natural numbers starting from 1 and get the answer.

There are a lot of patterns in mathematics. One analogous pattern of numbers is the sum of cube of n natural numbers.

Given:  Equation  = [tex]1^{3} + 10^{3} + 11^{3} +12^{3} +......+30^{3}[/tex]

            Here  N=30  , We have given

solution:

                                              [tex]S=\frac{{n^{2} (n+1)^{2}}}{4} \\=\frac{30^{2} (30+1)^{2}}{4}\\=\frac{900 (31)^{2}}{4}\\=\frac{900 (961)}{4}\\=\frac{864900}{4}\\=216225[/tex]

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The rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

To find the rational roots of the polynomial, we can use the Rational Root Theorem. This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

In this case, the polynomial is

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

so a_0 = 12 and a_4 = 20. The divisors of 12 are 1, 2, 3, 4, 6, and 12. The divisors of 20 are 1, 2, 4, 5, 10, and 20. Therefore, the possible rational roots of the polynomial are

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

We can then test each of these values to see if they are actually roots of the polynomial. If a value is a root, then substituting it into the polynomial will result in a value of 0.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

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This theorem states that if a polynomial of the form a_n*x^n + a_{n-1}x^{n-1} + ... + a_1x + a_0 has a rational root, then that root must be of the form p/q, where p is a divisor of a_0 and q is a divisor of a_n.

f(x) = 20x^4 - 8x^3 - x^2 + 12x,

p/q = +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

Therefore, the rational roots of the given polynomial are +/- 1, +/- 2, +/- 3, +/- 4, +/- 6, +/- 12, +/- 1/2, +/- 1/4, +/- 1/5, +/- 1/10, and +/- 1/20.

360° is all the way around a circle. The length of the intercepted arc is equal to the circumference of the circle.

Arc Length of a Circle:

Length. A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement: measure of angle in degrees/360° = L/circumference.

Does arc length have to be in radians?

Arc length is a measurement of distance, so it cannot be in radians. The central angle, however, does not have to be in radians. It can be in any unit for angles you like, from degrees to arcsecs. Using radians, however, is much easier for calculations regarding arc length, as finding it is as easy as multiplying the angle by the radius.

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Answer:

B - 50

Step-by-step explanation:

the exterior angle is 105, and as it's on a straight line, the interior angle is 180-105=75

75+55=130

angles in a triangle are 180

180-130=50

Answer:50 degrees

Step-by-step explanation: The 105degrees angle forms a supplementary angle with the missing degrees in the triangle

so the missing value which is not requested is 180degrees-105 degrees=75 degrees

No we have two angles inside the triangle. We can now work out the missing angle for x

We know that a triangle adds up to 180 degrees

So x=180-55-75=50 degrees as the answer

There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 13, 16, 12, 14, 19, 12, 14, 13, 14. When we order this set from least to greatest, we get 12, 12, 13, 13, 14, 14, 14, 16, 19. There are nine numbers in this set, so the median is the fifth number. The fifth number in this set is 14, so the median is 14.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are nine numbers in the set, so the median is the middle number.

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The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

2x + y = 8             ...1

y = 3x - 2             ...2

From equations 1 and 2, then the value of the variable 'x' is calculated as,

2x + 3x - 2 = 8

5x = 10

x = 2

Then the value of the variable 'y' will be calculated as,

y = 3(2) - 2

y = 6 - 2

y = 4

The solution of the linear equations 2x + y = 8 and y = 3x - 2 will be (2, 4).

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Answer: -6

Step-by-step explanation:

If x:(x+3) = 2:3, we can set up the following equation:

x / (x+3) = 2/3

Next, we can multiply both sides of the equation by 3 to get rid of the fraction on the right side:

3 * (x / (x+3)) = 3 * (2/3)

This gives us:

x / (x+3) = 2

Finally, we can multiply both sides of the equation by (x+3) to get rid of the fraction on the left side:

x = 2 * (x+3)

We can then solve for x by rearranging the terms on the right side of the equation:

x = 2x + 6

Subtracting 2x from both sides gives us:

x - 2x = 6

This simplifies to:

-x = 6

Finally, we can divide both sides of the equation by -1 to solve for x:

x = -6

Therefore, x = -6.

Answer:

y= -1/3x+7

i graphed it so it should be right

The phone's cost that varies directly with time are given as follows:

Both Mark and Nikiya.

The variation of the functions can have two classifications, given as follows:

Mark's cost starts at (0, 20) and goes through (3, 40), meaning that when the input increases from zero to 3, the output increases from 20 to 40, hence it has a direct variation.

Nikiya's cost starts at (0, 0) and goes through (2, 30), meaning that when the input increases from zero to 2, the output increases from 0 to 30, hence it has a direct variation.

The problem asks for whom's function varies directly with time.

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Answer:

Based on the graph shown to the right, whose phone cost varies directly with the amount of time spent talking?  

✔ Nikiya’s only

Mark’s cost does not vary directly with time spent talking because

✔ the cost of 0 hours is not 0 dollars

For Nikiya’s plan, the value of the constant of variation is

15,

which represents Nikiya’s

✔ cost per hour

Step-by-step explanation:

Hope this helps :)

Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

Now, According to the question:

Python's Transform function returns a self-produced data frame with transformed values after applying the function specified in its parameter. This data frame has the same length as the passed data frame.

What does transform () do?

The transform CSS property lets you rotate, scale, skew, or translate an element. It modifies the coordinate space of the CSS visual formatting model.

The transform() function is used to call function on self producing a Series with transformed values and that has the same axis length as self. Function to use for transforming the data.

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An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.

Given that:

an employee earns $14 per hour.

constant rate of change :

When something has a constant rate of change, one quantity changes in relation to the other. For example, for every half hour the pigeon flies, he can cover a distance of 25 miles. We can write this constant rate as a ratio. For ratios, it's always a good idea to state both units in whole terms.

A). Let the number of hours be x and the total money earned be y

So, y = 14x

B). Let the money earn by an employee each year be a and total earning in a year be b.

So, b=a+3% of a

⇒ b = a + 0.03a

⇒ b = 1.03a

C) Let the number of months be m and the total charge be t

So, t=50+30m

D) Let cost of gym equipment be p, rate of change =8% and time period = 6 months

So,

E) Let the number of hour be x.

Here, 30 minutes = 1/2 hours

Total charge = 20 + 5x/2

An employee earns $14 per hour and a trainer charges $20 for every 30 minutes of training plus a $5 tip are a constant rate per unit interval. Therefore, options A and E are the correct answers.

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Full question :

For which situation does one quantity change at a constant rate per unit interval relative to another quantity? responses.

Select all that apply

A. An employee earns $14 per hour.

B. An employee earns a 3% raise each year.

C. A gym charges a $50 down payment plus $30 per month.

D. A piece of gym equipment decreases 8% in value every 6 months.

E. A trainer charges $20 for every 30 minutes of training plus a $5 tip.

The roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.

The quadratic equation is 2x² + 5x - 2 = 0.

We can solve this equation using the Quadratic Formula:

x = [-b ± Â√(b² - 4ac)] / 2a

Where a = 2, b = 5, and c = -2.

Substituting these values into the formula, we get:

x = [-5 ± Â√(5² - 4(2)(-2))] / 2(2)

x = [-5 ± Â√41] / 4

x = [-5 ± Â√41] / 4

x = [-5 ± 6.4] / 4

x = -2.7 or 1.3

Therefore, the roots of the quadratic equation 2x² + 5x - 2 = 0 are -2.7 and 1.3.

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The example of a rational function  is f ( x) = x 2 − 1 2 x + 21.  , we can represent this function in terms of ratio of p and q.

Other than than a real world example can be that , a cookie being divided among two children , the representation will be , 1 / 2.

A graph of a rational function has asymptotes which are of three types and that is what makes them different from the rest of the functions. Rational functions are the functions which can be represented in the ratio of two polynomials p and q. The solution of this equation is know as the roots of the equation.

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The value of  ZLMN is 58.

What is bisects?

Bisection in geometry is the division of an object into two equal or congruent halves, typically by a line, which is subsequently referred to as a bisector. The segment bisector and the angle bisector are the two forms of bisectors that are most frequently used. 

LMO+NMO = LMN,

x+34 + NMO = 6x-28

But, MO bisects LMN, so LMO=NMO

x+34 + x+34 = 6x-28

2x+68 = 6x-28

4x = 96

x = 24

That would makem it

24 + 34 =58 T NMO = 6(24)-28

58 + nmo = 144 - 28 = 119

116- 58 = 58

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Answer:

yes

Step-by-step explanation:

We require both to ascertain whether the findings are independent, this criterion is applied.

Statistics frequently employs the binomial distribution as a discrete distribution. When compared to a binomial distribution, the normal distribution is continuous. The chance for 'x' success of an investigation in 'n' trials is represented by the binomial distribution.

As per the given information in the question,

The normal distribution can be used to approximate the binomial distribution. The situation when performing a normal approximation is as follows:

np ≥ 10 and,

np(1 - p) ≥ 10

This criterion is used to determine whether the results are independent.

We are aware that when n and p are combined, the results are independent.

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The solution of the given system of equation is (3, 2).

In the given question we have to find the solution to the system of equations:

y = 4x − 10 and y = 2

We can solve the system of equation using the substitution method.

In substitution method we have to put the the value of one variable from one equation to the other equation.

We have to equations:

y = 4x − 10........................(1)

y = 2...................................(2)

Now putting the value of y from the equation 2 in equation 1

2 = 4x − 10

Add 10 on both side, we get

4x = 12

Divide by 4 on both side, we get

x = 3

Now putting the value of x in equation 1

y = 4(3) − 10

y = 12 − 10

y = 2

Hence, the solution of the given system of equation is (3, 2).

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The right question is:

What is the solution to the system of equations y = 4x − 10 and y = 2?

The percent that the average score on the test increased during the two months is 12.5%.

It should be noted that mean simply means the average of a set of numbers that are given. In this case, the average test score of RSM students in September increased by 10%. In October it increased by another 15%..

The average of the increase will be:

= (10% + 15%) / 2

= 25% / 2

= 12.5%

The average is 12.5%.

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Answer:

range

Step-by-step explanation:

the x values or inputs are called the domain

the y values or outputs are called the range

Answer:

29

Step-by-step explanation:

You have 1,500 Kilometers and 32 15- kilometer races.

Step 1: Divide 1,500 by 15

step 2: Multiply the answer by 10

step 3:  

Answer:

y=(2/3) x+7

Step-by-step explanation:

2/3 is the slope which would be parallel

The length of the side of the smaller box is 6 and the length of the side of the larger box is 20. The equation for the difference in volume of the boxes is, y3 - x3 = 7784 .

Let us consider the length of side of small box be x inch & length of large box be y inch.

Length of smallest box is 30% of the length of the side of the largest box 

x=30%*y

   = 30 * y / 100

x = 3y / 10

Volume of the smallest box is x3.

volume of the largest box is y3.

Volume of largest box is 7784 cubic inches more than the volume of smallest box. Therefore,

y3 =  x3 + 7784

     = (3y/ 10 )3 + 7784

     = 27y3 / 1000 + 7784

y3 - 27y3 / 1000 = 7784

973 y3  / 1000 = 7784

973 y3 = 7784 * 1000

y3 = 7784 * 1000 / 973

y3 = 8000

   y = 20

Now find the smaller side.

x = 3y / 10

putting the value of y  this we get,

x = 3 * 20 / 10

   x= 6    

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Answer:

2

Step-by-step explanation:

To solve this equation, use the distributive property to rewrite it as 4x - 2y = 12. Then, solve the equation using either addition or subtraction.

To solve the equation 4x 2y = -12, the first step is to use the distributive property to rewrite the equation as 4x - 2y = 12. This allows us to solve the equation using either addition or subtraction. If we choose to use addition, we can add 2y to both sides of the equation to get 4x + 2y = 12. We can then subtract 2y from both sides to get 4x = 12 - 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 - 2y)/4. If we choose to use subtraction, we can subtract 2y from both sides of the equation to get 4x - 2y = 12. We can then add 2y to both sides to get 4x = 12 + 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 + 2y)/4. In either case, the solution is x = (12 ± 2y)/4.

Addition:

4x + 2y = 12

4x = 12 - 2y

x = (12 - 2y)/4

Subtraction:

4x - 2y = 12

4x = 12 + 2y

x = (12 + 2y)/4

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The original amount is 10 and the new quantity is 14 percent increase  is 40%

An quantity or part that is contained in each hundred is known as a percentage. The symbol "%" signifies that it is a fraction with 100 as the denominator.

Here,

The increase in percentage is equal to (New quantity - Original quantity)/Original quantity 100

(14-10)/10* 100.

4/10 × 100

40%

A 40% increase from the original amount to the new quantity may be calculated as a result.

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The general formula for the variance varies according to the distribution, For the discrete and continuous probability distribution, The expected values formula varies. The variance is given by [tex]E(X^{2})-(E(X))^{2}[/tex] .

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

If distribution is discrete  , E(X) = x*P(x).

If distribution is continuous , E(x) = x *f(x).

Variance =  [tex]E(X^{2})-(E(X))^{2}[/tex]

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If in the past month Kaylynn rented one video game in for DVDs. the total amount that Kaitlyn spent on video game and DVD rentals in the past month. is : $7.60.

We would have to make use of this formula to find the total amount that Kaitlyn spent on video game and DVD rentals in the past month.

Total amount = (Number of video game × Video game rental price ) + Rental price for DVD

Let plug in the formula

Total amount = (1 × $3.30) + $4.30

Total amount = $3.30 + $4.30

Total amount = $7.60

Therefore we can conclude that the total amount is $7.60.

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Answer:

  6 inches

Step-by-step explanation:

You want to know the uniform width of border around a 3 ft square coffee table that would have an area of 7 square feet.

The area of the border is x feet wide by 3 feet long along each of the 4 sides, together with 4 corner squares that are x ft square.

  A = 7 = 4(3x +x²)

Completing the square, we have ...

  x² +3x +9/4 = 7/4 +9/4 . . . . . . divide by 4, add (3/2)² to both sides

  (x +3/2)² = 4 . . . . . . . . . . . . simplify

  x +3/2 = √4 = 2 . . . . . . square root

  x = 1/2 . . . . . . . . . foot

The width of the border should be 6 inches.