MATHEMATICS HIGH SCHOOL

State the next term of each sequence
a) 1, 16, 81, 256....
b) 1, 1, 2, 4, 7, 13, 24....

Answers

Answer 1
Answer: a) 1, 16, 81, and 256 are all perfect squares. Find their squares:
1, 4, 9, 14.
In this sequence, you first at 3, then 5, then 7. So, logically, you would add 9 next. 14 + 9 is 23, and 23 squared is 529.
b) I'm not sure the data points for this sequence are correct. I'd have to guess 42 based on this difference chart:
1    1    2     4     7     13     24   42
  +0  +1  +2    +3   +6   +11  +18
      +1  +1  +1    +3   +5   +9
         +0  +0   +2   +2   +4
            +0   +2  +0   +2
Answer 2
Answer: a)
1,16,81,256,\underline{625}\n\text{The general formula is } n^4 \text{ where } n\in \mathbb{N}

b)
1,1,2,4,7,13,24,\underline{44}\n\text{Each number is the sum of three preceding numbers.}

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The distance from Joe's house to his school is 3/4 of a mile. If Joe goes to school and comes back home, what is the total distance he travels?A. 6/4 milesB. 3/6 of a mileC. 3/2 milesD. 6/8 of a mile
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Which is a valid velocity reading for an object?A. 45 m/s

B. 45 m/s north

C. 0m/s south

D. 0m/S

Answers

the answer is B. 45m/s north

An airplane took off and flew at an angle of elevation 12° with the ground. What was the approximate altitude of the airplane, (high how is the plane directly from the ground), after it had flown 8,000 meters (hypotenuse)?

Answers

Answer:

1663 m approx.

Step-by-step explanation:

We have a right triangle in which we know the hypotenuse and need to find the opposite side, so we use the sine function:

sin 12 = h / 8000

h = 8000 sin 12

= 1663 m approx.

What is 2/5 x 15 and what is 7 x 3/7

Answers

The first one 2/6 x 15 is =6
The Second one 7 x 3/7 =3

The volume of a cube can be written as a function of its edge length, V(x) = x^3. Which is a correct interpretation of V(2x)?(A) The volume of a cube doubles when its edge length doubles.
B) The volume of a cube increases by a factor of 4 when its edge length doubles.
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The volume of a cube increases by a factor of 6 when its edge length doubles.
D The volume of a cube increases by a factor of 8 when its edge length doubles.

Answers

Answer:

D The volume of a cube increases by a factor of 8 when its edge length doubles

Step-by-step explanation:

Volume of a cube is represented by the function

V(x)=x^3

where x represents the edge length of the cube

Now when x=2x i.e., when the edge length is doubled we have

V(2x)=(2x)^3\n\Rightarrow V(2x)=8x^3\n\Rightarrow V(2x)=8(V(x))

It can be seen that the volume of the cube increased by 8 times when edge length doubles.

Answer:

the answer is d

Step-by-step explanation:

What is the domain of the discrete finite function F(x)?G(x) = {(–2, 1), (–1, 3), (1, 4), (7, 3), (2, 5)}
A. {–2, –1, 1, 2, 7}
B. {–2, 1, 3, 4, 5, 7}
C. {1, 2, 7}
D. {1, 3, 4, 5}

Answers

A. {–2, –1, 1, 2, 7}

a jar of cookies contains 18 different types of cookies. Each type is equally likely to be chosen. Based on your simulation, how many times must a cookie be chosen in order to get each type?

Answers

Answer:

Number of Cookies in the jar =18={A,B,C.......,...P,Q,R}

It is given that, each type is equally likely to be chosen.

Probability of an event

                 =\frac{\text{Total favorable outcome}}{\text{Total possible outcome}}

Probability of Getting any of the cookies out of 18 cookies

                           =(1)/(18)

When number of outcomes increases , probability of getting each type of cookie will be Higher.

So, there are 18 cookies , when number of each type of cookie will be

=18 × 18

=324 cookies ,means each distinct single cookie is available in 18  containers, means that is there is total of 324 containers.

So, out of 324 containers each cookie must be chosen 18 times.
1/18th of a chance each time you draw. But it really depends on how many are in the jar. I'd say 18.
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