Logic, Reasoning and Puzzles Assignment
Solving a Payment Puzzle
A wealthy and generous owner of an Internet company offers two
options of payment to her new vice president.
Option 1: a monthly salary
of $50000 per month paid
at the beginning of each
month
Name: Yaseen
Option 2: a monthly salary
based on 1¢ the first day,
2¢ the second day, 4c the
third day, 8¢ the fourth day,
and so on. The monthly salary
will be the amount calculated
for the last day of the month.
Assume there are 30 days in the month.
A. How can you calculate the vice president's earnings under
Option 2?
B. Compare the monthly earnings for the two options.
1.9
C. Which payment option would you take if you were the vice
president? Why?

Answer:

RS = 6

Step-by-step explanation:

RS² = SU*ST (secant-tangent rule)

Substitute

(x + 6)² = (x + 4 + 5)(x + 4)

(x + 6)(x + 6) = (x + 9)(x + 4)

x(x + 6) +6(x + 6) = x(x + 4) + 9(x + 4)

x² + 6x + 6x + 36 = x² + 4x + 9x + 36

x² + 12x + 36 = x² + 13x + 36

Collect like terms

x² - x² + 12x - 13x = -36 + 36

-x = 0

x = 0

✔️RS = x + 6

Plug in the value of x

RS = 0 + 6

RS = 6

Answer: C

Step-by-step explanation: it says that it's smaller or equal to x and x is smaller than 17

Answer: One way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/2 teaspoon measuring spoon 3 times to measure 3/2 = 1 1/2 teaspoons

and use the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

3 1/2 + 2/3 = 3 1/6

Another way to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2 -teaspoon measuring spoon is to use:

the 1/3 teaspoon measuring spoon 6 times to measure 6 * 1/3 = 2/3 teaspoons

and use the 1/2 teaspoon measuring spoon 6 times to measure 6 * 1/2 = 3 teaspoons

3 + 2/3 = 3 1/6

So, there are two ways to measure 3 1/6 teaspoons of salt using 1/3 -teaspoon and 1/2-teaspoon measuring spoon, one is by using 3 times 1/2 teaspoon measuring spoon and 6 times 1/3 teaspoon measuring spoon and the second one is by using 6 times 1/3 teaspoon measuring spoon and 3 times 1/2 teaspoon measuring spoon.

Step-by-step explanation:

Therefore , the solution of the given problem of volume comes out to be

V =355/113 * (5)² * 7  thus correct option is V equals 355 over 113 times 6 squared times 8.

Volume, which is expressed in cubic units, is a unit of measurement for the 3-dimensional space occupied by matter or encircled by a surface. The SI unit of volume = area * height is the cubic metre (m3), which is a derived unit. A "litre" (L) is the name given to the cubic decimeter (dm3).

Here,

The volume of cylinder = πr²h

Given : Diameter = 12 inches

radius = 12/2 = 6 inches

Height = 8 inches

Thus ,

To find the volume  we put the all the above values in the formula:

=> V = πr²h

=> V = 22/7 * 6² * 8

=> V =355/113 * (6)² * 8

Therefore , the solution of the given problem of volume comes out to be

V =355/113 * (5)² * 7  thus correct option is V equals 355 over 113 times 6 squared times 8.

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Answer:

V equals 355 over 113 times 6 squared times 8.

Step-by-step explanation:

The perimeter of the new octagon be 24 feet.

A closed path that covers, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter.

There are numerous uses in real life for perimeter calculations. The measurement of the fence needed to completely enclose yard or garden is called the perimeter. How far a wheel or circle will roll in one revolution is determined by its circumference, or perimeter.

The length of each side of an octagon is the same. In order to calculate the perimeter of an octagon, multiply 8 by the length of its sides.

Given that the perimeter of an octagon is 27 feet

so the length of its side is 27/8 feet

if the side of the octagon shrink by a scale factor of 8/9

The side of new octagon is (27/8) * (8/9)

The side of new octagon is 3 feet.

So the perimeter of new octagon is 8 * side

⇒ the perimeter of new octagon = 8 * 3 feet

⇒ the perimeter of new octagon = 24 feet

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Answer:

6/7

Step-by-step explanation:

36/42 = 36:6/42:6 = 6/7

Answer shown in bold

The non-bolded values to the left are not to be typed in the answer box. They're present to keep track of the values. In other words, you'll type "40" without quotes into the first box, then "19" without quotes in the second box, and so on.

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

Explanations:

Let me know if you have any questions.

Step-by-step explanation:

this means :

f(x) / (x + 2) = (x² - 5x + 8) + 8/(x + 2)

f(x) = (x + 2)(x² - 5x + 8) + 8 =

= x³ - 5x² + 8x + 2x² - 10x + 16 + 8 =

= x³ - 3x² - 2x + 24

Answer:

EVALUATE THE FUCTION WHEN: f (1/2 % 32)////////21+×_37- 4 = 37.2

EVALUATE THE FUNCTION WHEN f(3+38 x + formula of angle are = _1/2 decimals point 78.32)*/% =3( 92.03

Step-by-step explanation:

HOPE IT HELPS A LOT!!

Answer:

Okay so!

Step-by-step explanation:

33, 34, 38, 42, 47, 47, 48, 49, 51.

The median is 47 because it turns up twice.

Answer:

x= 9

y= 3 root 3

Step-by-step explanation:

to find the shorter leg length you have: hypotenuse/2

[tex] \frac{6 \sqrt{3} }{2} = 3 \sqrt{3} [/tex]

to find the longer leg length you have: shorter leg × root 3

[tex]3 \sqrt{3} \times \sqrt{3} = 3 \sqrt{9 } = 3(3) = 9[/tex]

Step-by-step explanation:

TRY WITH SOME Trigonometric FUNCTION.

IF SOMETHING IS Wrong . I AM STILL A STUDENT

9514 1404 393

Answer:

  342 mm²

Step-by-step explanation:

The triangle shown has a base of 9 mm and a height of 76 mm. Its area is ...

  A = 1/2bh

  A = (1/2)(9 mm)(76 mm) = 342 mm²

The triangle shown has an area of 342 mm².

_____

Additional comment

The other leg of the right triangle with one leg 76 mm and hypotenuse 100 mm will be about 65 mm. The base shown is 9 mm, so any triangle with the dimensions shown will be a fairly skinny obtuse triangle, not the acute triangle in the picture. (This makes us suspect an error: the 9 mm dimension maybe should be 90 mm.)

Given:

D varies as R and S, and inversely as t.

D=12, R=3, S=20, and t=5

To find:

The value of D when R=15, S=4 and t=8.

Solution:

It is given that D varies as R and S, and inversely as t. So,

[tex]D\propto \dfrac{RS}{t}[/tex]

[tex]D=\dfrac{kRS}{t}[/tex]                ...(i)

Where, k is the constant of proportionality.

We have, D=12, R=3, S=20, and t=5. Substituting these values in (i), we get

[tex]12=\dfrac{k(3)(20)}{5}[/tex]

[tex]12=12k[/tex]

[tex]\dfrac{12}{12}=k[/tex]

[tex]1=k[/tex]

Substituting [tex]k=1[/tex] in (i), we get the required equation.

[tex]D=\dfrac{(1)RS}{t}[/tex]

[tex]D=\dfrac{RS}{t}[/tex]

We need to find D when R=15, S=4 and t=8. Substituting R=15, S=4 and t=8 in the above equation, we get

[tex]D=\dfrac{(15)(4)}{8}[/tex]

[tex]D=\dfrac{60}{8}[/tex]

[tex]D=7.5[/tex]

Therefore, the required value of D is 7.5.

Answer:

792ft

Step-by-step explanation:

V=LxWxH, so all you do is do 11 times 8 times 9 to get the answer to that question

Answer:

The answer would be the second and fourth options.

Step-by-step explanation:

This can be solved by using a calculator, the prime factor method, etc. Good luck on your math journey!

Answer:

are there any other information

Answer: 53

Step-by-step explanation:

Answer:

y-4=-7/4(x+4)

Step-by-step explanation:

Point Slope Form: y-y*sub*1=m(x-x*sub*1)

Parallel lines have the same slope as the line to which they are parallel.

y-4=-7/4(x+4)

Hope this helps :)

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph in opposite direction.

Acceleration is the rate of change of velocity of an object. It is a vector quantity that has both magnitude and direction. Mathematically, it is the derivative of velocity with respect to time. In simpler terms, it is the change in speed or direction of an object over time. If an object is speeding up, it is said to have a positive acceleration, while if it is slowing down, it has a negative acceleration.

Velocity is a vector quantity that describes the rate of change of an object's position. It has both magnitude and direction. The magnitude of velocity is the speed of an object, which is the distance covered per unit of time. The direction of velocity is the direction of the motion of an object. The standard unit of velocity is meters per second (m/s) or miles per hour (mph).

Let's call Rahquez's speed "R" and Francesca's speed "F". We know from the problem that:

F = R + 5 (Francesca is traveling 5 mph faster than Rahquez)

We also know that after 3 hours they are 105 miles apart, so we can set up an equation using distance = speed x time:

105 = (R + F) * 3

Now we can substitute the first equation into the second equation:

105 = (R + (R + 5)) * 3

Simplifying and solving for R, we get:

R = 20 mph

So Rahquez is traveling 20 mph, and Francesca is traveling 25 mph (since F = R + 5).

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Answer:

are the values of a or b given?

Step-by-step explanation:

Answer: 120° obtuse.

Step-by-step explanation:

The sum of the angles in a triangle is 180°. Since two of the angles given are 35° and 25°, the third angle will be:

= 180° - (35° + 25°)

= 180° - 60°

= 120°

This is an obtuse angle since it's greater than 90° but less than 180°

Answer:

10

I wish you luck in your assignments.

Answer:

do 180-36-90 and then what you get add a ° and it should be 53°

The  value of the given polynomial equation would be: [tex]6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

In contrast to the vertex form of a quadratic equation, which is y = a (x h) 2 + k, the normal quadratic form is written as an x 2 + b x + c = y. The constant that indicates whether the parabola is facing up (+ a) or down ( a) is called a. It is represented in both forms by the letters y, x, and a.

In the equation we are given the value of y as: 1

[tex]6y2 + 3y - 1 4 \\\\6(1)^2 + 3(1) - 1 = 6 + 3 - 1 = 8.[/tex]

Therefore, we can say that the value of the given polynomial is: 8

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Complete question is: Find 6y2 + 3y - 1 4 for y = 1

The quadratic equation 4(x² − 5) − 1 = 3 has its solutions to be are √6 and -√6

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

4(x 2−5)−1=3

Express properly

This gives

4(x² − 5) − 1 = 3

Subtract -1 from both sides of the equation

So, we have the following representation

4(x² − 5) = 4

Divide both sides by 4

This gives

x² − 5 = 1

Subtract -5 from both sides of the equation

So, we have the following representation

x² = 6

Take the square root of both sides

x = ±√6

Hence, the solution is ±√6

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2 copies of 1/10 can be written as 2/10

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, and 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given here 2 copies of 1/10 thus 2×1/10=2/10

                                                                =1/5

Hence, 2 copies of 1/10 can be written as 2/10

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