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Answer:

it should be 21 cm the pencil is 21 cm

The commission the sales man was paid is 101

A sales commission is a sum of money paid to an employee upon completion of a task, usually selling a certain amount of goods or services. Employers sometimes use sales commissions as incentives to increase worker productivity. A commission may be paid in addition to a salary or instead of a salary.

For example, if a man is to be given a commission of 10%. And he made a sales of $10000. Therefore his commission is 10/100× 10000 = $1000

The commission of the sales man is 5% of his total sales

His total sales is 2020

Therefore the commission the sales man will be paid is 5/100× 2020

= 10100/100

= 101

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The Formula to calculate the area of the equilateral triangle with side length as "x" units is [tex]\frac{\sqrt{3} }{4} x^{2}[/tex] square units .

What is an Equilateral Triangle ?

An equilateral triangle is defined as a type of triangle in which all the sides and all the angles are equal in measure .

The measure of each angle of equilateral triangle is 60° .

The area of the equilateral triangle can be calculated by the formula :

Area = [tex]\frac{\sqrt{3} }{4} x^{2}[/tex]  , where x is = the side of the equilateral triangle .

For Example : if the side length of equilateral triangle is 2 units ,

then its area will be = [tex]\frac{\sqrt{3} }{4} \times 2^{2}= \frac{\sqrt{3} }{4} \times 4 =\sqrt{3}[/tex] square units .

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Answer:

where x=0 , y=-3

where x=2 ,y =-3

where x= -2 ,y =5

where x= 4 , y = 5

Answer:

(12,-5) and (13,-6) m = (6/-1) = -6

(13,3) and (14,3) m = 0

(3,-20) and (5,8) m = (8- -20)/(5-3) = 28/2 = 14

(1,2) and (3,8) m = (8-2)/(3-1) = 6/2 = 3

(-1,1) and (15,1) m = 0

(1,5) and (6,15) m = (15-5)/(6-1) = 10/5 = 2

(2,-12) and (10,12) m = (12--12)/(10-2) = 24/8 = 3

(1,8) and (3,0) m = (0-8)/(3-1) = -8/2 = -4

(0,0) and (-4,-8) m = (-8-0)/(-4-0) = -8/-4 = 2

(5,3) and (12,10) m = (10-3)/(12-5) = 7/7 = 1

Note that the slope of a line can be found by using the formula m = (y2 - y1)/(x2 - x1)

Step-by-step explanation:

1. (12,-5) and (13,-6) m= -1

2. (13,3) and (14,3) m= 0

3. (3,-20) and (5,8) m= 14

4. (1,2) and (3,8) m= 3

5. (-1,1) and (15,1) m= 0

6. (1,5) and (6,15) m= 2

7. (2,-12) and (10,12) m= 3

8. (1,8) and (3,0) m= -4

9. (0,0) and (-4,-8) m= 2

10 (5,3) and (12,10) m= 1

Answer:

  24

Step-by-step explanation:

You want the largest of three numbers that have the ratios 1 : 2 : 3 and have a sum of 48.

The sum of the ratio units is 1+2+3 = 6. The largest number is 3/6 = 1/2 of the sum:

  (1/2) · 48 = 24

The greatest of the three numbers is 24.

__

Additional comment

The other two numbers are 8 and 16.

Answer:

less than a mile is the answer

The function types of the table of values are

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

The table of values

Function 1

In the table of values of this function, we have

x   2      3     4

y  5.5    7    8.5

In the above table of values, we can see that

As x increases by 1, the value of y constantly increase by 1.5

This means that the function is a linear function

This is so because of the constant increment

Function 2

In the table of values of this function, we have

x   0      3     6

y  1        8    6

In the above table of values, we can see that

As x increases by 1, the value of y is 2 to the exponent of the  corresponding y value

i.e. y = 2^x

This means that the function is an exponential function

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Answer:

i)cl^9. (ii)4^12

Step-by-step explanation:

when multiplying , if the pewers have the same base you add ao 6+3=9

24÷6=4

16-4=12

4^13. 4( to the power of)

Answer:

B. 105

Step-by-step explanation:

right!!

Answer:

  E.  26.25°

Step-by-step explanation:

Given a diagram showing an angle at crossed chords of 2x, you want the value of x/2.

The measure of an inscribed angle is half the measure of the arc it subtends. This means the triangle interior angle at upper left has half the measure of the 40° arc it subtends: 20°.

The sum of angles in the triangle is 180°. The third angle is a vertical angle to the one marked 2x, so has that same measure. Then the relation is ...

  2x +20° +55° = 180°

  2x = 105° . . . . . . . . . . . . . subtract 75°

  x/2 = 26.25° . . . . . . . . . divide by 4

__

Additional comment

You can apply a "reasonableness" test to the answer choices. Any angle where lines cross cannot have a measure more than 180°. If that angle is 2x, then x/2 cannot be more than 180°/4 = 45°. Only one answer choice is less than 45°.

Answer:

3453.5

Step-by-step explanation:

(a(1) + a(2) + a(3) + a(4) + a(5) ) ÷ 5 = 790.6

a(5) = (790.6 × 5) - (80.2+91.6+123+204.7) = 3953 - 499.5 = 3453.5

If a school wants to build a rectangular playground that will have a diagonal length of 75 yards. The wide of the playground be if the length has to be 30 yards is: 68.7.

Using Pythagoreans theorem to find the width of the playground

c² = √a² - b²

Where:

c = Width

a = 75 yards

c = 30 yards

So,

c² = √75² - 30²

c² = √5,625 -900

c² = √4,725

c= 68.7

Therefore we can conclude that the width is 68.7.

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Using Pythagoras theorem, the width is 68.74 yards

The Pythagorean Theorem is a fundamental mathematical principle that states that in a right triangle (a triangle with one angle equal to 90 degrees), the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

It can be expressed mathematically as:

c^2 = a^2 + b^2

Where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

To solve this problem, we have to take the diagonal as the hypothenuse and the length as one of the legs.

75² = 30² + b²

b² = 75² - 30²

b = 68.74yds

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If the straw fits exactly into the box diagonally from the bottom left corner to the top right back corner, the length of the straw is 13.5 inches.

The question is addressing the rectangular box of lengths 10 by  9 by 3

The lengths to be used are the length and the height of the rectangular box

Using the Pythagoras rule that says that in a roght angled triangle, the square on the hypothenuse side is equal to the sum of the squares on the other two sides

This implies that

d² = 10²+9²

d²=100+81

d²=181

d=√181

d=13.5 inches

Therefore, the length of the straw is 13.5 inch

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Distance of a fallen object is 25 feet.

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given:

The formula for the speed of a falling object is v= √64d,

where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.

And also given that v = 200 feet per second.

Substituting the value to the formula,

200 = √64d

d = 200 / √64

d = 200 / 8

d = 25 feet.

Therefore, 25 feet are the distance.

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The minimum of the absolute value function:

y = |x + 3| - 2

is y = -2.

Here we want to find the minimum value of the absolute value function:

y = |x + 3| - 2

Now, this is an absolute value function that opens upwards, then the minimum is at the vertex.

Remember that for an absolute value function:

y = |x - a| + b

The vertex is at (a, b)

So for our function:

y = |x + 3| - 2

The vertex is at (-3, -2)

And the minimum is the y-value of that point, so the minimum of the function is y = -2

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Answer:

y=5x-15

Step-by-step explanation:

Slope intercept form:y=mx+b

m=slope=5

y=0

x=3

b=y intercept

Plug it in

0=5(3)+b

Subtract 15 from both sides

-15=b

y=5x-15

Hope this helps :)

Answer:

10

Step-by-step explanation:

the least number of 2,5,10 is 10 .so we can cut red and blue pieces into 10 pieces each but green pieces stays the same. so we have total of 30 pieces.

The equation that would model this situation is 2a + 3p = 24

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

Also, from the question, we have

These parameters above mean that:

2 * a + 3 * p = 24

Evaluate

2a + 3p = 24

Hence, the equation is 2a + 3p = 24

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The Perimeter of rectangle is 29n + 3 feet.

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Perimeter of the rectangle = 2(length+width)

Given the paramters are;

width of a rectangle is 8n-6.5 feet and the length is 6.5n+8 feet.

W = 8n-6.5

L =  6.5n+8

Perimeter of the rectangle = 2(length+width)

Perimeter = 2(8n-6.5+ 6.5n+8)

= 2(14.5n + 1.5)

= 29n + 3

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A- 37% of 142 is 52.54

B- 137% of 142 is 194.54

To calculate Percent of Number we use,

P% of Number = X

⇒P/100 x Number=X

where P is the percent to be calculated

and X is the required percentage of that number

A-37% of 142=  37/100 x 142

=0.37 x 142

=52.54

B- 137% of 142= 137/100 x 142

=1.37 x 142

194.54

∴ 37% and 137% of 142 are 52.54 and 194.54 respectively.

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The correct answer is (Option B): Observations with values of 200 are included in the class frequency.

When a class interval is expressed as "100 up to 200," it means that the class includes all observations with values greater than or equal to 100 and less than or equal to 200. So observations with a value of 200 would be included in the class frequency.

A. Observations with values of 100 are excluded from the class frequency - This is incorrect, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 100 would be included in the class frequency.

B. Observations with values of 200 are included in the class frequency - This is correct, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 200 would be included in the class frequency.

C. Observations with values of 200 are excluded from the class frequency - This is incorrect, as a class interval typically includes the lower value but not the upper value. For example, if the class interval is 100 up to 200, then observations with values of 200 would be included in the class frequency.

D. The class interval is 99 - This is incorrect, as the class interval is specified as 100 up to 200, not 99. The class interval is the range of values that are grouped together for the purpose of counting the frequency of observations.

Therefore, The correct answer is (Option B): Observations with values of 200 are included in the class frequency.

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Answer:

6.5

Step-by-step explanation:

y = 6.5x

Answer:

23,2.3,0.23,0.023

Step-by-step explanation:

*23÷10^0=23/1=23

*23÷10^1=23/10=2.3

*23÷10^2=23/100=0.23

*23÷10^3=23/1000=0.023

I hope it helps you..

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Answer:

23

23.23

0.23

0.023

The man threw the basketball from 30 inches above the ground. It traveled 45 inches to the floor, then 40 inches to the boy, who caught it. The angles formed by the path were congruent. The distance from the floor to the boy catching the ball was 85 inches.

Distance from man to floor: 30 in. + 45 in. = 75 in.

Distance from floor to boy: 40 in.

Total distance: 75 in. + 40 in. = 115 in.

Distance from floor to boy catching the ball: 115 in. - 30 in. = 85 in.

The man threw the basketball from 30 inches above the ground. This is the distance from the man to the floor. The basketball then traveled 45 inches from the man to the floor, making the total distance 75 inches. It then traveled 40 inches from the floor to the boy who caught it. This makes the total distance 115 inches. To find the distance from the floor to the boy catching the ball, we subtract the distance from the man to the floor (30 inches) from the total distance (115 inches). This gives us a result of 85 inches, which is the distance from the floor to the boy catching the ball.

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Answer:

12 (c)

Step-by-step explanation:

13.5 / 1.125

The number of comparisons required for an array of length 512 is

1+log2(512)=1+9=10.

Binary search:

Searching is an operation done to find the required element (or key) among a group of elements (an array).

Binary search or logarithmic search is a type of searching algorithm that can be used on a sorted array.

In this algorithm, we always check the middle number and compare the key with it. If the key equals the middle number, we're done. If the key is greater than the middle number, we know the key (if it's in the array at all) must be in the right half of the array. Conversely, if the key is less than the middle number, we know the key (if it's in the array at all) must be in the left half of the array. In other words, at every step of the search, we cut the array we're searching through in half. Of course, this only works because the array we started with is sorted.

In a binary search, at every step we compare the key with the middlemost value. If the key is greater than the middlemost value, we discard the left half of the data. If the key is less than the middlemost value, we discard the right half of the data. This process is repeated until we find the element we are looking for.

If we start with an array of length 2=21

, the worst-case scenario is we have to compare the key with both elements: 2 comparisons.

If we start with an array of length

4=22, the worst-case scenario is the key is not the middlemost element, we reduce our search to a 2-element array, and then we're in the worst-case scenario of the previous case: 1+2=3 comparisons.

If we start with an array of length

8=23

, the worst-case scenario is the key is not the middlemost element, we reduce our search to a 4-element array, and then we're in the worst-case scenario of the previous case: 1+3=4 comparisons.

Do you see a pattern? If we start with an array of length

2k, the worst-case scenario is we make 1+k

comparisons. Since 512=2log2(512)=29

The number of comparisons required for an array of length 512 is

1+log2(512)=1+9=10.

In general, the number of comparisons required for an array of length

n is 1+log2(n)

. We usually just round this to

log2(n). Remember that

log2(n)

is basically the number of times n can be cut in half until we get down to 1 or less, so this makes sense.

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Answer:

range of r is between -1 and 1.

Step-by-step explanation:

(-1)^2 = 1, 0^2 = 0 and 1^2 = 1

An equation for the boiling point of this liquid is y = -0.001845x + 214.37. Also, the boiling point of this liquid at 2600 ft is equal to 209.573°F.

In order to write an equation for the boiling point of this liquid, we would have to first calculate its slope because the relationship between altitude and the boiling point of this liquid is linear.

Mathematically, the slope of any linear equation can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided about the altitudes and boiling points of this liquid, we have the following parameters:

Point (x, y) = (8300, 199.06)

Point (x, y) = (4300, 206.44)

Substituting the given points into the formula, we have;

Slope, m = (206.44 - 199.06)/(4300 - 8300)

Slope, m = 7.38/-4000

Slope, m = -0.001845

At point (8300, 199.06), the equation of this line is given by:

y - y₁ = m(x - x₁)

Where:

y - 199.06 = -0.001845(x - 8300)

y - 199.06 = -0.001845x + 15.31

y = -0.001845x + 15.31 + 199.06

y = -0.001845x + 214.37

Now, we can calculate the boiling point of this liquid at 2600 ft:

y = -0.001845(2600) + 214.37

y = -4.797 + 214.37

y = 209.573°F.

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Complete Question:

The relationship between altitude and the boiling point of a liquid is linear. At an altitude of 8300 ft, the liquid boils at 199.06°F. At an altitude of 4200 ft, the liquid boils at 206.44°F. Write an equation giving the boiling point b of the liquid, in degrees Fahrenheit, in terms of altitude a, in feet. What is the boiling point of the liquid at 2600 ft?

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