The light in a lighthouse flashes every 20 seconds.

How many times will it flash in one hour?

========================================================

Work Shown:

A = set of multiples of 3 between 1 and 16

A = {3, 6, 9, 12, 15}

B = set of even natural numbers up to and including 20

B = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

A u B = {3, 6, 9, 12, 15,       2, 4, 6, 8, 10, 12, 14, 16, 18, 20}

A u B = {2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20}

---------------

Explanation:

The U stands for "set union". It's where we combine two or more sets together to form a larger set. The duplicates are tossed out. This is what your teacher meant when writing "Make sure each element is only listed once". Writing A u B indicates "the set of values in either set A, set B, or both".

In this case, the duplicates are "6" and "12" since they are found in set A and B simultaneously. They are in the overlapped area of both sets. It might help to draw out a Venn Diagram.

Common convention is to sort the items in the set. Though technically a set like {1,2,3} is the same as {3,1,2}.

Don't forget about the curly braces to indicate to the reader that this is a set of values.

Answer:

49 leaves

Step-by-step explanation:

7 days x 7 leaves per day = 49 leaves in total

After 15 years, Zephan will have a balance of $13181.07 in his savings account.

Given,

In the question:
Compound Interest is given by the formula.

A = P(1 + r)^t

Zephan invested $5500 in a savings .

Rate of interest is 6%

Time = 15 years

Now, According to the question:

We know that :

P = 5500

r = 6%

n = 1

t = 15

Compound Interest is given by the formula.

A = P(1 + r)^t

Substitute the values in above formula.

A = 5500. [tex](1+\frac{6}{100}/1 )^1^5[/tex]

Evaluate the equation/expression:
A = 13181.070062

Round 13181.070062 to the required place

= 13181.07

Hence, After 15 years, Zephan will have a balance of $13181.07 in his savings account.

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The solution of the differentiated equation is dy/dx = 40x³+ 3

From the question, we have the following equation that can be used in our computation:

Y=10 x^4+3 x+50

Rewrite properly

So, we have

y = 10x⁴ + 3x + 50

The rule of first principle of differentiation is represented as

If y = axⁿ, then dy/dx = naxⁿ⁻¹

Using the above as a guide, we have

dy/dx = 4 * 10x⁴⁻¹ + 1 * 3x¹⁻¹ + 0 * 50

Evaluate

dy/dx = 40x³+ 3

Hence, the equation result is dy/dx = 40x³+ 3

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The probability that they two people are chosen and travel by different transport is 47/144

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen.

Probability is given as sample space / total outcome

Probability to travel by car p(C)= 5/12

Probability to travel by bus P(B)= 4/12=1/3

Probability to travel by train P(T)= 3/12= 1/4

for two people chosen at random

P(C ×B)= 5/12×1/3= 5/36

P(B×T)= 1/3×1/4= 1/12

P(C×T)= 1/4×5/12= 5/48

Therefore the probability that the two chosen travel by different car is

P(C ×B)+P(B×T)+P(C×T)= 5/36+1/12+5/48

= 141/432

divide through by 3

= 47/144

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Answer:

slope is 3/2

Step-by-step explanation:

m = y2 - y1 / x2 - x1

m = -1 - 2 / 2 - 4

m = -3/-2 ( can be simplified )

simplified ver. = 3/2

Answer:

Slope is 3/2

Step-by-step explanation:

To find slope, subtract the y's, put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction.

(4,2) and (2,-1)

Subtract y's:

2 - -1

=3

Put it on top of a fraction:

3/something

Subtract the x's:

4 - 2

= 2, put that on the bottom of the fraction.

3/2

Slope is 3/2.

f(5)=17

Step-by-step explanation:

f(5)=3(5)+3

=15+2=17....

The Least Common Denominator (LCD) of 9/8 and 11/12 is 24.

The two given fractions are -

9/8 and 11/12

We have to find out the Least Common Denominator (LCD) of 9/8 and 11/12.

Firstly, we have to check if we can simplify the two given fractions. In this case, we have 9/8 and 11/12 which cannot be simplified further.

Now, we have to multiply the denominators with natural numbers until they there is a first common number in the denominators of the two given fractions.

Multiplying 8 with 2 gives 16. However, there 16 is not a multiple of 12,

Multiplying 8 with 3 gives 24. 12 when multiplied with 2 also gives 24.

So, the Least Common Denominator (LCD) of 9/8 and 11/12 is 24.

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Answer:

4.1c

Step-by-step explanation:

8.4-4.3 is 4.1, and because you can combine like terms its 4.1c.

The equation y=2(1/5)ˣ is satisfy the graph with points (-1,10) and (0,2).

Given that,

In the picture we have a graph with two points (-1,10) and (0,2).

We have to find the equation of the graph from the given equation.

Basic Functions Graphing. if possible, identifying the shape. A line would be the graph of a linear function of the type f(x) = ax + b, for instance; a parabola would be the graph of a quadratic function.

We check by substituting the points in the equation of the option a,b,c and d.

The option c.

y=2(1/5)ˣ

The point (-1,10)

10=2(1/5)⁻¹

10=2(5)

10=10

The point (0,2)

2=2(1/5)⁰

2=2(1)

2=2

Therefore, The equation y=2(1/5)ˣ is satisfy the graph with points (-1,10) and (0,2).

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Answer:

4x+3y=15

Step-by-step explanation:

y=-4/3x+5

4/3x+y=5

4x+3y=15

:]

The value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

It is given that the expression is,

x + 20 ≤ -10

Rearrange the expression as

x≤ -10-20

x≤ -30

Thus, the value of x for the given expression, x + 20 ≤ -10 will be -30. The value of x is obtained by applying the arithmetic operation.

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The required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.

Given that,
$1000 become in a saving account at 3% per year for 3 years when the interest is not compounded.

Simple interest is defined as the percentage of earning on the lending for a period of time

Here,
Simple interest earned = P × r × t /100
                                      = 1000 × 3 × 3 /100 = 90
Amount = P + SI = 1000 + 90 = $90
Now, when interest is compounded annually,
Amount =  1000(1.03)³
Amount = $1092.72

Thus, the required amount after 3 years is $1090, but when compounded annually the amount becomes $1092.72.

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The value of a = 16

The process of making something less complicated and hence easier to accomplish or understand, or the thing that arises from this process: The organization offers advice on how to simplify trade procedures. Simplification is classified into two types: You must be conversant with both sorts of simplification questions, the first of which is 'Finding the missing number.' The second type of simplification difficulty is 'the relationship between the numbers and simplifying the numbers using simplification principles.'

Given that b= 6 and c= 13

Given equation is a = 35-b-c

Now substitute b and c values in the given equation

A = 35 - 6 -13

A = 35 – 19

A = 16

Therefore the value of a = 16

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The follow up questions about the statistics that you might ask in order to obtain the data needed to make a decision about the validity of that statement include:

Statistics is the science that studies and develops methods for collecting, analyzing, interpreting, and presenting empirical data.

Statistics is the study and manipulation of data, which includes methods for gathering, reviewing, analyzing, and drawing conclusions from data. Statistics is divided into two categories: descriptive statistics and inferential statistics. Such questions can be asked to gain a better understanding of the statement's validity.

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Area of circle of diameter with 13cm is 132.74

What is area of circle?

Given :

Diameter of circle, d = 13cm

Radius of a circle, r = d/2

=13/2

=6.5

Area of circle = πr²

= 3.142 * 6.5 * 6.5

= 132.74

Hence, the Area of circle of diameter with 13cm is 132.74.

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Answer:

$34,417

Step-by-step explanation:

Hello,

As we can see liquid assets are things that can be easily converted to cash.

So, noting my previous statement we can see that investments are a liquid asset since it can be quickly or easily converted to cash.

Se me da mal algebra pero la b tiene buena pinta porque no se

Answer:

48

Step-by-step explanation:

I=prt

8/100= 0.08

I=100(6)(0.08)

48

Answer:30

Step-by-step explanation:

Step-by-step explanation:

Original prices of the office equipments

Computer = £650

Calculator = £27.75

Telephone = £69.50

45. The computer has a discount of 15%

[(100 - 15)/100]% × £650

85/100 % × £650

=£552.5

46. The calculator has a discount of 20%

[(100 - 20)/100]% × £27.75

80/100 % × £27.75

=£22.2

47. The telephone has a discount of 10%

[(100 - 10)/100] % × £69.50

90/100 % × £69.50

=£62.55

48. The saving for the computer is

= £(650 - 552.5)

= £97.5

49. The saving for the calculator is

= £(27.75 - 22.2)

= £5.55

50. The saving for the telephone is

= £(69.50 - 62.55)

=£6.95

The number of ways in which 6 pictures can be hung from 8 picture nails on the wall is b) 20160.

Given:

The number of ways in which 6 pictures can be hung from 8 picture.

Number of ways = [tex]8_C_{6}[/tex]*6!

[tex]8_C_{6}[/tex] = 8!/(8-6)!6!

= 8!/2!*6!

= 8*7*6! / 2*1*6!

= 56/2

= 28

6! = 6*5*4*3*2*1

= 30*4*3*2*1

= 120*3*2*1

= 360*2*1

= 720*1

= 720

[tex]8_C_{6}[/tex]*6! = 28*720

= 20160

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Answer:

answer is 20160 ..........

The explorer stood 2.63m away from the flag pole.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

If the pole is 3m high, and his eye is 1.6 meters from the ground.

Then distance from the top of the pole and his eyes  would be 3 - 1.6 = 1.4m

The angle of elevation between the line of sight and the horizontal = 28°

so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.

Let the distance of the explorer from foot of pole be x,

so that,

tan 28 = 1.4/x

by cross multiplying,

x tan28 = 1.4

x = 1.4/tan28

x = 1.4/0.5317

x = 2.63m

In conclusion, the distance of the explorer to the base of the flagpole is 2.63m

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Answer:

B

Step-by-step explanation:

point T is on the y-axis with x- coordinate 0 and y- coordinate 5, then

the ordered pair for point T is (0, 5 )

The graph of f(x) is transformed 6 units horizontally to get the graph g(x). g(x) is a transformation form of the graph of f(x).

What is the reciprocal function?

The typical instance of reciprocal functions that we might run into is y = a/x, where a is a real number. Accordingly, reciprocal functions are those that have an algebraic expression in the denominator and a constant on the numerator.

Given functions are:

f(x) = -1/(2x-5)

g(x) = f(x-3)

The points on the graph f(x) = -1/(2x-5) are:

When x = 0, f(x) = 1/5

When x = 1, f(x) = 1/3

When x = -1, f(x) = 1/7

The graph of f(x) is added.

Putting x = x-3 in f(x) = -1/(2x-5) to find the function g(x):

g(x) = -1/(2x-6-5)

g(x) = -1/(2x-11)

The points on the graph g(x) = -1/(2x-11) are:

When x = 0, g(x) = 1/11

When x = 1, g(x) = 1/9

When x = -1, g(x) = 1/13

The graph of g(x) is added.

The graph g(x) is translated  6 units  horizontally.

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The value of a³ + b³ is 64.184

Here,

a + b = 5 .........(1)

and ab = 6

a = b/6

Substitute above value of 'a' in equation(1)

b/6 + b = 5

7b/6 = 5

7b = 30

b = 30/7

b = 4.28

So, a = 5 - 4.28

a = 0.72

We know that the formula of a³ + b³

a³ + b³

= (a + b)(a² + b² - ab)

= 5 * (0.72² + 4.28² - 6)

= 5 * 12.8368

= 64.184

Therefore, the value of a³ + b³ is 64.184

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6 Boxes of colored pencils

15 Pencils in each box

Total Number of colored pencils : 15 x 6 = 90 Pencils