When the sun is at a certain angle in the sky, a 50-foot building will cast a 20-foot shadow. What is the length of the shadow in feet cast by a 20-foot pole at the same time? Enter only the number.

Answer:

x=3.25

Step-by-step explanation:

To solve this you would have to distribute the 3 to both numbers in the parenthesis and then you'd combine like terms. Once you combine like terms it'll be a bit easier to solve. When I distributed and combined like terms I got 3x-12-10=4-11x and then I solved and got x=3.25

Not sure if this is how your supposed to solve this problem for your assignment but for us it's usually like this...if it happens to be wrong then I'm sorry.

For the given function 3x + 2y = 10 the slope of the function is equal to -3/2.

As given in the question,

Given function is equal to 3x + 2y = 10

Standard form  of the equation representing slope intercept form is given by :

y = mx  + c

'm' is the slope of the given function

'c' is the value of y-intercept of the given function.

Now simplify the given function 3x + 2y = 10  in standard form ,

3x + 2y = 10

⇒2y = -3x + 10

⇒ y = 1/ 2(-3x + 10 )

⇒ y = -3/2x + 5

Compare with the standard form of the equation ,

Slope of the given function is m = -3/2.

Therefore, for the given function 3x + 2y = 10 the slope of is given by

m = -3/2.

The given question is incomplete , the complete question is:

What is the slope of the function 3x + 2y =  10?

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The point of intersection of these two lines is (2,1)

Point of intersection means the point at which two lines intersect.

These two lines are represented by the equation a1x + b1y + c1= 0 and    a2x + b2y + c2 = 0, respectively.

When the graphs of y = f(x) and y = g(x) intersect, both graphs have exactly the same x and y values.

So we can find the point or points of intersection by solving the equation f(x) = g(x)

We have been given that line l1  is horizontal and passes through the point (1,1). The line l2 is vertical and passes through points (2,2). We are asked to find a point of intersection between line l1 and line l2.  

Line l1 is a horizontal line so the y-coordinate will be 1 for any value of x. Line l2  is a vertical line, so the x-coordinate will be 2 for any value of y.

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Answer: 3,385.00

Step-by-step explanation: To find the number of student tickets sold, we need to first figure out the total number of tickets sold at the football game. We can do this by dividing the total amount of money collected by the cost of each ticket. In this case, we have:

Total number of tickets = 8,816.00 / (5.00 + 8.00)

                      = 8,816.00 / 13.00

                      = 677.5

Since the total number of tickets sold must be an integer, we can round this number down to 677. This means that 677 student tickets were sold at the football game.

We can verify this answer by calculating the total amount of money collected from the student tickets and checking that it is equal to the total amount collected at the game:

Total amount collected from student tickets = 677 * 5.00

                                          = 3,385.00

Since the total amount collected from the student tickets is less than the total amount collected at the game, we know that this is the correct answer.

Answer:

a) 27.9069767442

b} 75.439%

Step-by-step explanation:

The circumcenter of a triangle is the point in the plane equidistant from the three vertices of the triangle.

In geometry, the circumscribed circle or circumcircle of a polygon is a circle that passes through all the vertices of the polygon. The center of this circle is called the circumcenter and its radius is called the circumradius.

Not every polygon has a circumscribed circle. A polygon that does have one is called a cyclic polygon, or sometimes a concyclic polygon because its vertices are concyclic. All triangles, all regular simple polygons, all rectangles, all isosceles trapezoids, and all right kites are cyclic.

A related notion is the one of a minimum bounding circle, which is the smallest circle that completely contains the polygon within it, if the circle's center is within the polygon. Every polygon has a unique minimum bounding circle, which may be constructed by a linear time algorithm.

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The answer is 40, by using addition.

Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.

Here, what we can do is use addition to find the number one more than 39.

= 39 + 1

= 40

Hence, the number one more than 39 is 40.

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Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").

Here, what we can do is use addition to find the number one more than 39.

= 39 + 1

= 40

The required sample interval in the given situation is 10.

The sampling interval is the space or period of time in which measurements or data collection occur.

This is known as the "nth selection" in research and occurs when we choose the nth participant (or sample unit) from the list; this sampling interval results in a random selection from the entire population.

Calculating the sampling interval involves dividing the population size by the desired sample size to arrive at the predetermined periodic interval.

So, have a population size of 500 people.

The number of members to be selected is only 50.

We already know that to find the sample interval, we should divide the population size bu the required sample size.

Now, calculate the sample interval as follows:

= 500/50

= 50/5

= 10

Therefore, the required sample interval in the given situation is 10.

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Answer:

-6r+48

Step-by-step explanation:

The answer above is what you end up when you use distributive property.

The lines y = - 4x + 5 and y = x + 4y = - 40 is neither parallel nor perpendicular.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, Are two lines y = - 4x + 5 and y = x + 4y = - 40.

Now,

x + 4y = 40

4y = - x + 40.

y = - (1/4)x + 10.

We know lines parallel to each other have the same slope and lines perpendicular to each other have a slope that is negative reciprocal of each other.

So, Line 1 is neither parallel nor perpendicular to line 2.

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The roots of this quadratic equation are real and equal.

given equation:

[tex]x^{2}[/tex] - 6x + 9 =0

now we need to find discriminant

discriminant = D = [tex]b^{2}[/tex] - 4ac

from the given equation

a = 1

b = -6

c = 9

D = [tex](-6)^{2}[/tex] - 4(1)(9)

  = 36 - 36

D = 0

1.  [tex]b^{2}[/tex] - 4ac < 0 there roots are imaginary

2.  [tex]b^{2}[/tex] - 4ac = 0 there roots are real and equal

3. [tex]b^{2}[/tex] - 4ac >0  there roots are real and  distinct

The roots of this quadratic equation are real and equal.

A quadratic equation is graphically represented by a parabola with vertex located at the origin , below the x-axis , or above the x-axis . Therefore , a quadratic function may have one ,two or zero roots.

If the quadratic function is always more than zero that means, when graphed on coordinate system, the function never have intersects the

x-axis. That means that quadratic equation has no real roots.

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Answer:

  c. $350.24, the april balance plus the late fee

Step-by-step explanation:

You want to know the required total payment when the balance being repaid is $325.24 and a late fee of $25 is charged.

Arthur must pay both the balance due and the late fee. The total amount he must pay is ...

  balance + late fee = $325.24 +25.00 = $350.24

Total surface area = 2(lb+bh+hl)

TSA = 2(25×20+20×15+15×25)

TSA= 2(500+300+375)

TSA= 2(1175)

TSA= 2350 cm²

Lateral surface area = 2(l+b)h

LSA= 2(25+20)15

LSA,= 2(45)15

LSA= 1350 cm²

h=25 cm

l=20 cm

b=15 cm

Total surface area is 2(lb+bh+hl)

2(20×15+15×25+25×20)

2(300+375+500)

2(1175)=2350 cm 2

Based on Paul's batting scores for cricket in a season, his mean score to the nearest whole number is equal to 13.

In Mathematics, a mean is sometimes referred to as an average and it can be defined as a ratio of the sum of the total number in a data set (population) to the frequency of the data set.

Mathematically, the mean for this set of scores can be calculated by using the following formula:

Mean = [F(x)]/n

For the total scores, we have;

F(x) = 17 + 23 + 9 + 0 + 8 + 21 + 12

F(x) = 90.

Now, we can determine the mean score as follows;

Mean score = 90/7

Mean score = 12.86 ≈ 13.

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The difference between transform and fit_transform is that transform() method is used to perform scaling whereas fit_transform does both the fitting and the transforming in one step.

In this question we need to describe the difference between methods transform() and fit_transform()

We know that the methods like transform(), and fit_transform() provided by the scikit-learn package.

Both are the methods of class sklearn.preprocessing.StandardScaler()

The transform() method is used to perform scaling using mean and standard deviation which is calculated using the .fit() method.

The fit_transform() method does both fits and transform i.e., fit_transform() calculates the mean and standard deviation for a given feature and also perform scaling.

Therefore, transform() changes the data and fit_transform does both the fitting and the transforming in one step.

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The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

What is rational function ?

A rational function is one that can be written as a polynomial divided by a polynomial. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. Example 1. f(x) = [tex]\frac{x}{x - 2}[/tex].

Rational functions are typically identified by the degrees of the numerator and denominator. For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. A rational function model is a generalization of the polynomial model.

The formula of rational function is [tex]R(x) = \frac{P(x)}{Q(x)}[/tex] , where P(x) and Q(x) are polynomial functions.

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If the spheres are connected by a long thin wire, then the two spheres are at the same potential.

In math, the term sphere refers a three dimensional solid, that has all its surface points at equal distances from the center.

Here we have given that the two conducting spheres, here one having twice the diameter of the other, that are separated by a distance large compared to their diameters. Then the smaller sphere (1) has charge q and the larger sphere (2) is uncharged.

And we need to find If the spheres are connected by a long thin wire.

While we looking into the given question when these two conducting spheres are connected together through a thin wire then charge from the smaller sphere will travel through the wire.

Therefore, here this charge will continue to travel towards the neutral sphere until the charge on both the spheres will become equal to each other.

Therefore, their potential will also become equal.

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Answer:

  C.) The only extreme point is (-1, 18).

Step-by-step explanation:

You want the local and global extrema of f(x) = -2x² - 4x + 16.

Unless the domain is restricted to a particular interval, the extrema of a polynomial function will be its turning points. The number of possible turning points is 1 less than the degree of the equation.

An even-degree polynomial equation will always have at least one global extreme on the domain of all real numbers.

The given 2nd-degree equation will have exactly one extreme point: its vertex at (-1, 18).

__

Additional comment

The vertex of ax² +bx +c is located at x=-b/(2a). Here, that is x=-(-4)/(2(-2)) = -1. The value of f(-1) is -2 -(-4) +16 = 18, so the extreme point is (-1, 18). A graphing calculator finds it quickly.

Answer:

y- intercept = - 1

Step-by-step explanation:

to find the y- intercept, let x = 0 in f(x) and evaluate

using rule of exponents

[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]

given

f(x) =- 32[tex](2)^{x-3}[/tex] + 3 , then

f(0) = - 32 [tex](2)^{0-3}[/tex] + 3

     = - 32 [tex](2)^{-3}[/tex] + 3

    = - 32 × [tex]\frac{1}{2^3}[/tex] + 3

    = - 32 × [tex]\frac{1}{8}[/tex] + 3

    = - 4 + 3

    = - 1 ← y- intercept

The coordinate pairs that represent possible solutions to the inequality graph are;

(4, 4)

(0, 0)

When it comes to inequality graphs, the shaded portion usually contains all the possible coordinates that represent solutions to the given inequality.

Now, from the inequality graph, we say that the shaded part is below the line and so our possible solutions will be located in that direction.

Thus, the possible solutions from the graph are the coordinates;

(-5, -5), (-4, -4), (-3, -3), (-2, -2), (-1, -1), (0,0), (1, 1), (2, 2), (3, 3), (4, 4)

Lookin at the given options, the only ones that are possible solutions are options B and E.

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No, the Square root of an integer is not always irrational because the square root of perfect squares is not irrational.

Any real number that cannot be written as p/q, where p and q are both integers, the quotient of two integers.

If a number is not a perfect square, the square root of that number is not rational.

For example, the square root is 4 is 2.

The square root of 9 is 3.

But whereas the square root of 5 is 2.23606797755555...... which is irrational

The square root of 8 is 2.8284271247555..... which is irrational.

So, therefore square root of a number is not irrational always it can be rational also.

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Answer:

The answer for the question is 3.7

Using the AND rule of probability and percentage calculations, The answer is 0.0684.

Probability is the likelihood that something will occur. When we don't know how an event will turn out, we might discuss the likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.

Percentages are fractions with a 100 as the denominator. The percent symbol (%) is used next to the number to denote that it is a percentage.

62% goes to college.

% not going to college = 100%-62%

=38%

on that 38%, 18% gets employment,

probability =  0.38 * 0.18

=0.0684

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We determine the mean and standard deviation for a statistical observation by considering the available data set and size of data.

In the statistics, the mean value is the average value of all available data set.

The standard deviation is an estimation that implies how far each data is apart from the mean value.

Suppose we have a list of data. The data list is denoted by X and the total number of data is N. Now we will add all the data set and the result is denoted by ∑X

Mean value formula = the sum of data / number of data = ∑X/N

In the next, we will determine the square value of all data and the list is denoted by X². Finally, we add all the X² and the result is ∑X²

now, standard deviation is calculated by the formula,

  standard deviation = √[∑X²/N - (∑X/N)²]

hence, we can solve for mean and SD

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Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

Mathematicians can add numbers using the counting-on technique. When using this method, a learner begins by adding the larger number, then "counts on" with the other addends to get the sum. The student will recognize 4 as the higher number and add three more numbers, such as integers "4... 5, 6, 7," if the number sentence is 4 + 3.

Here,

Around age 6, kids start to learn how to skip count. Skip counting teaches your youngster to count swiftly and gets them ready to grasp the fundamentals of multiplication.

The simplest way to count is in skip increments of 10, which are essentially identical to regular increments of 10 with the exception of an extra '0': 10, 20, 30,... 80, 90, 100.

Therefore , the 6 year old children can able to  skip count to 1 to 100 counting by making them learn.

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The monthly payment amount is (8000 - 2600) / 12 = $500.

1. The cot of a car is given as 8000. The depoit is given as 2600.

2. The formula for the cot of buying a car is cot = 12 x monthly payment depoit.

3. To find the monthly payment, we can rearrange the formula to monthly payment = (cot - depoit) / 12.

4. Substituting in the values, we get monthly payment amount = (8000 - 2600) / 12 = $500.

The cost of a car can be calculated using a simple formula. The formula is cot = 12 x monthly payment deposit. In this case, the cost of the car is given as 8000 and the deposit is given as 2600. To find the monthly payment, we can rearrange the formula to solve for the monthly payment amount. This gives us the equation monthly payment = (cot-deposit)/12. When we plug in the given values, we get monthly payment = (8000-2600)/12 = $500. This means that the monthly payment amount for this car is $500.

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Units digit - 6

Step-by-step explanation:

A. 12004+ 32004 = 44008

B. 52004+72004 = 124008

Total - 44008+124008+ 92004 = 208016

Units digit - 6

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