One column of numbers consists of 61, 24, and 47. When the digits of the
numbers are added together, the result is 6 + 1 + 2 + 4 + 4 + 7 = 24, and when
the digits of 24 are then added together, the end result is 2 + 4 = 6. If the
same process is performed on the numbers in a second column, what can De
concluded?
• A. If the end result from the second column is not 6, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the second column.
B. If the end result from the second column is also 6, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.
C. If the end result from the second column is not 6, then the sum of
the numbers in the first column is equal to the sum of the
numbers in the second column.
D. If the end result from the second column is also 6, then the sum of
the numbers in the first column is not equal to the sum of the
numbers in the
second column.

The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are two table is shown in figure.

Now,

For first table;

Two points are,

⇒ (x, y) = (3, -6)  (0, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and

(x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for first table;

⇒ m = (- 2 - (-6)) / (0 - 3)

⇒ m = (- 2 + 6) / (-3)

⇒ m = - 4/3

And, For second table;

Two points are,

⇒ (x, y) = (0, -3)  (4, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and (x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for second table;

⇒ m = (- 2 - (-3)) / (4 - 0)

⇒ m = (- 2 + 3) / (4)

⇒ m = 1 / 4

Thus, The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

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Solving the equation 8x − 4 = 2(2x + 4) the required integer to make the equation true is 3

The integer required to be found is solved as follows

The given equation is  8x − 4 = 2(2x + 4)

solving for x

8x − 4 = 2(2x + 4)

8x - 4 = 4x + 8

collecting like terms

8x - 4x = 8 + 4

4x = 12

dividing through by 4

x = 3

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Answer:

120°

Step-by-step explanation:

The 3 angle measures of a triangle will always equal 180.

Since we've already got two angles, all we need to do is a simple equation to get our missing angle:

180-(50+70)=60

Now that we've got the missing angle, we need to calculate the exterior angle, the thing we're here for. We know (hopefully at this point) that an exterior angle and its interior angle are a linear pair, meaning that the two add up to 180. Knowing this, we can do this equation to finish off the question:

180-60=120

And there's your answer, 120°

There's also a shorter way of doing this, let me know if you'd like to see it. But for now, hope I helped!

Answer: your question is not very clear

Step-by-step explanation:

Answer:D is incorrect

Step-by-step explanation:

D is the only one that is incorrect because D is 9x-81

Answer:

  (d)  9(x -9)

Step-by-step explanation:

You want the expression that is not equivalent to the other three.

The simplified versions of the expressions are ...

The expression not equivalent to the other three is 9(x -9).

<95141404393>

Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.

According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.

At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.

Given that,

Elouise and Marcus are 20 km apart (AB)

There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)

Now, according to a Pythagoras theorem,

(AC)² + (AB)² = (BC)²

or, (AC)² = (BC)²- (AB)²

or, (AC)² = (10√3)² - (20)²

or, AC = [tex]\sqrt{500}[/tex]

or, AC = 22.36 km

So, distance bearing of Marcus from Elouise is 22.36 km.

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We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

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.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,

with at least two of the five numbers being consecutive.

I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).

Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.

Hence,  multiplication principle we come to know that there are  13×(123).

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Answer:

6√3 centimeters

Step-by-step explanation:

This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.

Pythagorean theorem: a^2 + b^2 = c^2

a and b are the legs of the triangle. c is the hypotenuse.

Let's replace the variables with the given information we know.

The hypotenuse is 6. One of the legs is 3. the other leg is a/2.

3^2 + b^2 = 6^2

9 + b^2 = 36

b^2 = 27

b = √27 = 3√3

Since this was for half of the base, we will multiply it by 2.

3√3 x 2 = 6√3

That is our answer.

I hope this helps.

An equation to represent the value of the car after 1 year is P(t) = 80,000(1 - 0.25)¹.

An equation to represent the value of the car after t years is P(t) = 80,000(1 - 0.25)^t.

Generally speaking, a physical asset that loses its value at specific period of time represent an exponential decay. Therefore, a mathematical model for any physical asset (car) that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

Note: 1/4 is equal to 0.25.

For a car that loses 1/4 of its value annually, after 1 year its value is given by;

P(t) = 80,000(1 - 1/4)^1

P(t) = 80,000(1 - 0.25)¹

For a car that loses 1/4 of its value annually, after t year its value is given by;

P(t) = 80,000(1 - 0.25)^t

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Answer:

Step-by-step explanation:

The word "Sum" = addition.

"A number" = the unknown, aka 'x'.

"Is equal to" is =.

Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:

4x + (-2) = 5x + (-2)

Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.

Answer:

red im pretty sure

if x is an integer it does not show the median of the 5 numbers to be greater than the average of the 5 numbers

The value that, when a dataset is arranged, falls exactly in the center is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.

Finding the middle number requires sorting all the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers). Example: When the numbers are arranged (1, 4, 7), the number 4 lies in the center, making it the median of 4, 1 and 7.

(1) x must be higher than one or three. It will be the median if it is 8 or fewer.

Consequently, if x = 7, then the list is 1, 3, 7, 8, 12, and median is 7, while the average is 31/5, which equals 6.2, and the answer is YES.

The list is 1, 3, 8, 8, 12, and the median is 8 if x = 8. Average = 32/5 = 6.4; if x = REALLY BIG, the list is 1, 3, 8, 12, and x; and the median is 8; the answer is YES. The answer to the question is NO since the average is REALLY BIG.

insufficient

(2) According to the aforementioned findings, x must be at least 9.

Depending on the amount of x, the list is either 1, 3, 8, x, 12, or 1, 3, 8, x.

The median and mean expressions are the same, regardless of whether order is appropriate:

Mean (average): 8 median = (1 + 3 + 8 + 12 + x)/5 = (24 + x)/5 mean (average):

The mean is at least (24 + 9)/5 = 33/5 = 6.6 since x is at least 9.

This is not convincing because the mean might be either millions or 6.6 (if x = 9) (if x is huge).

insufficient

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A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

The value of x is 47

The value of y is 10.6

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

A quadrilateral is a closed shape with four sides and the four angles add up to 360 degrees.

We have,

A an isoceles trapezium.

Where one pair of sides are equal and parallel.

Two angles are equal.

Now,

94 = 2x

x = 47

Now,

The four angles sum is 360.

94 + 94 + 96 + 3y + 44 = 360

328 + 3y = 360

3y = 360 - 328

3y = 32

y = 32/3

y = 10.7

Now,

3y + 44 = 3 x 10.7 + 44 = 32 + 44 = 76

Thus,

The four angles for the given quadrilateral are,

96, 94, 76, and 94.

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Answer: A = 2(x+3y)+2z=2z+4x+2y

B=2(x+3y)=4x+2y

c=x+3y=2x+y

d=2y=x

Step-by-step explanation:

Answer:

2y=x:D

x+3y=2x+y:C

2(x+3y)=4x+2y:B

2(x+3y)+2z=2z+4x+2y

Step-by-step explanation:

D is the only possibility for 2y=x because it has 3 total. Similarly for C. B only has two different types, so it must be 2(x+3y)=4x+2y.

1. The students that the academy have per teacher is 18.

2. The students per tutor will be 10.

3. The tutors that the academy need if it has 60 students is 6 tutors.

Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.

The students that the academy have per teacher will be:

= Number if students / Teacher

= 72/4

= 18 students per teacher.

The students per tutor will be:

= 30/3

= 10 students per tutor

The number of tutors for 60 students will be:

= 60 / 10

= 6 tutors.

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The total ways in which the student can readd the books are 1512 ways.

What is Combination?

A combination in mathematics is a selection of elements from a set with distinct members, where the order of selection is irrelevant (unlike permutations).

Solution:

Since reading 2 american novels is compulsory

The student therefore needs to read only two more novels

It can be either American Novels or English Novels

Ways to read American Novel = 7C2

Ways to read English Novel = 7C2

Total Ways = 9C2 * (7C2 + 7C2)

Total Ways = 36 * (42)

Total Ways = 1512 ways

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Answer: C

Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.

Answer:

(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4

Step-by-step explanation:

Scales horizontally by 2, Shifts up 4, right 2

Answer:

53

Step-by-step explanation:

PEMDAS

Parenthesis

multiply the numbers

Divide

Add

Subtract

Answer:

Height: 6

Base: 14

Step-by-step explanation:

Area=42 in^2

height=x-1

base=2x

bh/2=42

Substitute in the values:

2x(x-1)/2=42

The 2s cancel out each other.

x(x-1)=42

x^2 - x =42

x^2 - x - 42=0

When we factor that, we get:

(x-7)(x+6)=0

x=7 or x=-6

We will take the positive answer.

height= x-1 = 7-1 = 6

base= 2x = 2(7) = 14

Now let's double check if we are correct.

6(14)/2

=84/2

=42

We are correct!

Answer:

Base: 14 and height: 6 OR Base: -12 and height -7

Step-by-step explanation:

First, set up a proportion. (base x height) divided by 2 on one side and 42 over 1 on the other.

[tex]\frac{2x(x-1)}{2}=\frac{42}{1}[/tex]          Next, cross multiply. This involves taking the numerator of

                            one side (top) and multiplying it by the denominator

                            (bottom) of the other side.

84=2x(x-1)            42*2=84 and anything multiplied by 1 equals itself. Next,

                            distribute (multiply) the 2x by each term in the

                            parentheses.

84=2[tex]x^2[/tex]-2x            2x*x=2[tex]x^2[/tex]. 2x*-1=-2x. Next, subtract 84 from both sides.

0=2[tex]x^2[/tex]-2x-84        Now, you can simplify this by dividing by 2 on both sides.

0=[tex]x^2[/tex]-x-42             This is a quadratic equation, which means you have to

                             factor or use the quadratic formula. In this case, you can

                             factor by using product and sum. You have to find what

                             multiplies to -42 and adds to -1. Those numbers would be

                              -7 and 6. -7*6=-42 and -7+6=-1 Therefore, you will have

                              x-7 and x+6

0=(x-7)(x+6)           Next, solve each equation with each binomial set equal

                              to 0. For x-7=0, x=7 because you add 7 to both sides. For

                              x+6=0, x=-6 because you subtract 6 from both sides.

x=7   x=-6

You can check if these values work by plugging them into the formula.

[tex]\frac{2x(x-1)}{2}- > \frac{2*7(7-1)}{2}- > \frac{14(6)}{2}- > \frac{84}{2}- > 42[/tex]. x can be 7.

[tex]\frac{2x(x-1)}{2}- > \frac{2*-6(-6-1)}{2}- > \frac{-12(-7)}{2}- > \frac{84}{2}- > 42[/tex]   x can be -6

The base and height are the numbers in the numerator of the equation after the 3rd arrow for both processes.

Answer:

y={7,10,19,22}

Step-by-step explanation:

3(2)+1 = 6+1 = 7

3(3)+1 = 9+1 = 10

3(6) + 1 = 18+1 = 19

3(7) + 1 = 21+1 = 22

Answer:

15%

Step-by-step explanation:

Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:

60 = 100%

68 = x

x = 69x100/60

x = 115

That means 69 is 115% of 60, which means that the error is of:

115 - 100 = 15%

Hope this helps, have a great day! :D

By using the formula for sample size, it can be calculated that the sample size is 62

What is sample?

At first it is important to know about population.

Population is the group of items from where samples are taken for study and research and for statistical purpose

A subset of population is called sample.

Here, margin of error E = 2

Value of z for 95 % confidence interval = 1.96

Standard deviation = 8

Sample size  = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62

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Answer:

Step-by-step explanation:

kakaka

Answer: 2 degrees.

Step-by-step explanation: If it is -4 degrees in Iceland at 7 am and the temperature increases by 6 degrees, the new temperature would be -4 + 6 = 2 degrees.

Answer:

y=4x+4

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

B is y intercept

To find slope we use y2-y1/x2-x1

16-(-4)/3-(-2)

20/5

4 is the slope

We can fill this in

y=4x+b

To find b we fill in any coordinates

-4=4(-2)+b

-4=-8+b

+8. +8

4=b

Now we can fill it in

y=4x+4

Hopes this helps please mark brainliest

Answer:

Irrational, rational, rational, rational, rational.

Step-by-step explanation:

√23 is an irrational number since the value of square root 23 cannot be expressed in the form of p/q.

104.42 this is a rational number! An irrational number has repeating values or just random numbers after the decimal point.

Here's an example...

Tell, does this number look rational?

4.2359712309458730495870192354870394587234098657293085412364781236409584790853467923456790324785098234570923845702398547 (and it goes on forever...and ever...and ever......)

√64 is a rational number. As we know that √64 = 8, a rational number.

49.396 with the 6 repeating is rational because we can express 49.39 as:

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

10.97846727460 is rational because the decimal places stop, it is rational. Remember, an Irrational number is non-repeating and non-terminating. Since the number terminates, it is rational

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The year 2029 written as a roman numeral is MMXXIX.

Roman numerals are mathematical representations of numbers in the Roman alphabet. Roman numerals are a numeral system that originated in ancient Rome and remained the standard way of writing numbers in Europe until the late Middle Ages.

Roman numerals are the symbols used in a system of numerical notation based on the ancient Roman system. The symbols are I, V, X, L, C, D, and M, which stand for 1, 5, 10, 50, 100, 500, and 1,000, respectively.

In this case, it should be noted that 2029 is MMXXIX.

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An inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

[tex]r = \sqrt{x^2+y^2}[/tex]

​

Therefore,

[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and cos⁡θ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]

Similarly using,

[tex]r = \sqrt{x^2+y^2}[/tex]

we get,

 [tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]

Therefore we showed that holds

[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]

Hence the answer is an inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

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Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

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Step-by-step explanation: