The tape diagram represents the ratio of the numbers of planets in two different solar systems. There are 8 planets in Solar System B. How many planets are in Solar System A?

The correct answer is 6 planets

Explanation:

The image presented shows the ratio of planets in solar system A vs those in solar system B. In this way, the general ratio is 3 : 4 or 3 to 4; this means for each 4 four planets in solar system B there are 3 planets in solar system A and vice versa. Now, to find the total of planets in system A if there are 8 planets in system B, follow this process:

8 planets / 4 = 2 planets - This means each of the sections in the diagram represents 2 planets

2 section x 3 = 6 planets as in the solar system A there are 3 sections and each of this represents 2 planets, the total of planets in this system are 6

This result can also be found by converting the ratio to a fraction and multiplying this by the 8 planets

8 planets x

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: