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4 years ago

A class has 4 boys and 10 girls. What is the ratio in simplest form that compares number of boys to total number of students?

1 answer:

4 0

C. The answer is C because the total amount of students is 14, and there are 4 boys, which makes the ratio 4 boys to 14 students in total. 4 and 14 are both divisable by 2, so divide 4 to get 2 and divide 14 to get 7. This leaves you with 2 and 7. The ratio would be 2 boys to 7 total students. Hope this helped

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A steel ball is dropped from a building’s roof and passes a window, taking 0.125 s to fall from the top to the bottom of the win

Anna35 [415]

Answer:

20.425 m

Step-by-step explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s²

$s=ut+\frac{1}{2}at^2\\\Rightarrow u=\frac{s-\frac{1}{2}at^2}{t}\\\Rightarrow u=\frac{1.2-\frac{1}{2}\times 9.81\times 0.125^2}{0.125}\\\Rightarrow u=8.98\ m/s$

Now this will the final velocity when it reaches the top of the window

$v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{8.98^2-0^2}{2\times 9.81}\\\Rightarrow s=4.11\ m$

$v=u+at\\\Rightarrow v=8.98+9.81\times 0.125\\\Rightarrow v=10.21\ m/s$

If the upward flight is an exact reverse of the downward flight then the time taken while going down will be 1 second and going up will be 1 second.

$s=ut+\frac{1}{2}at^2\\\Rightarrow s=10.21\times 1+\frac{1}{2}\times 9.81\times 1^2\\\Rightarrow s=15.115\ m$

Hence total height of the building is 4.11+1.2+15.115 = 20.425 m

4 0

3 years ago

Please sol ve this real quick

Kobotan [32]

Answer:

for question two: 12

for question four: 1/3

for question six: 25.75 (rounded to two decimal places)

8 0

3 years ago

Determine the rule for the number pattern and use it to find the missing values.

Kaylis [27]

9514 1404 393

Answer:

Each term in the pattern will be odd.

Step-by-step explanation:

The first differences are ...

7 -3 = 4

15 -7 = 8

These differ by 4, and the second is double the first.

These relationships between the first differences give rise to two possible sequences: a) an exponential sequence; b) a quadratic sequence. We can use a graphing calculator to find the coefficients of each of the patterns.

Exponential Sequence

a[n] = 2·2^n -1

The sequence is 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047.

The 10th term is 2047.

Quadratic Sequence

a[n] = 2n^2 -2n +3

The sequence is 3, 7, 15, 27, 43, 63, 87, 115, 147, 183.

The 10th term is 183.

Based on the above, the only thing we can say about these sequences is that they are all odd numbers.

Clearly, the 10th term is not 30. 7 is not a multiple of 3, so that observation fails immediately. 15 is not prime, so that observation also fails immediately.

_____

Additional comment

The differences of first differences are called "second differences". The differences of those are "third differences". and so on. If you keep taking differences of a sequence described by a polynomial, the n-th differences being constant means the sequence is described by an n-th degree polynomial.

Here, if we assume the 2nd differences are constant at 4, then the sequence is described by a 2nd-degree polynomial. (Similarly, constant first-differences are described by a 1st-degree polynomial--a linear function.)

If sequential levels of differences are all exponential sequences, then the sequence itself is an exponential sequence. As here, it may have a vertical offset. The base of the exponential will be the common ratio of the differences. (Here, the first differences have a ratio of 8/4 = 2, so the sequence could be exponential with a base of 2.)