There are 90 yellow flowers, 54 red flowers, and 36 white flowers for centerpieces. If the flowers need to be divided equally into separate centerpieces with the same number of each color of flower in each centerpiece, how many different centerpieces will there be?

Answers

Answer 1

Answer:

Answer:

You can create the fewest centerpieces for the smallest number of any color, which is 2 centerpieces using the white flowers. Therefore, you will have 2 centerpieces with an equal number of each color of flower in each centerpiece.

Step-by-step explanation:

First, find the GCD of 90, 54, and 36:

Find the GCD of 90 and 54:

GCD(90, 54) = 18

Find the GCD of the result (18) and 36:

GCD(18, 36) = 18

So, the GCD of 90, 54, and 36 is 18.

Now, you can create centerpieces with 18 flowers of each color (yellow, red, and white) in each centerpiece. To find out how many centerpieces you can create, divide the total number of each color by 18:

Number of yellow flowers / 18 = 90 / 18 = 5 centerpieces

Number of red flowers / 18 = 54 / 18 = 3 centerpieces

Number of white flowers / 18 = 36 / 18 = 2 centerpieces

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The population of the country of Oz was 600,000 in the year 2010. The population is expected to grow by a factorof 5% annually. The annual food supply of Oz is currently sufficient for a population of 700,000 people and is
increasing at a rate that will supply food for an additional 10,000 people per year.
c. At what point does the population exceed the food supply? Justify your response.

Answers

Answer:

After 5 years (2015)

Step-by-step explanation:

The population is increasing 5% per year, so the first year it will be 1.05 of the initial, the next year 1.05x1.05 of the initial, and then successively, so, for n years:

P(n) = 600,000*(1.05)ⁿ

The food suply increase 10,000 people per year, so the first year will be 10,000 + the initial, the next year 10,000 + 10,000 + the initial, and then successively, so, for n years:

F(n) = 70,000 + 10,000*n

P(n) > F(n)

600,000*(1.05)ⁿ > 70,000 + 10,000*n

(1.05)ⁿ > 1.167 + 0.0167n

Solving in a computer:

n > 4.42

So, after 5 years the population exceed the food supply.

Can someone please help me with this trig question.For a given right triangle, side a = 76.4 feet and side b = 39.3 feet What is the length of side c to the nearest tenth of a foot?

Answers

Let 76.4 be the longestest side. ( hyportinues)
Let 39.3 be the base of right triangle.

so we have to find the adjacent side of right side.
By Pythagoras Theorem.
76.4² = c² + 39.3²
c² = 76.4² - 39.3²
c² = 4261.95
c = √4261.95
c = 65.3 feet

86 is 45% of what number

Answers

To get the answer we can use proportion
86 --------------45%
x ---------------- 100%
Now cross multiply
x*45%=86*100
45x=8600 /:45 (divide both sides by 45)
x=191.11 - its the answer

The best thing to do is to find 1%, and you can do this by diving 86 by 45. 86/45= 1.9111, and you've then got to multiply this by 100, and this gives you 191.11Hope this helps :)

Use the Pythagorean identity sin^2 Θ + cos^2 Θ = 1 to derive the other Pythagorean identities, 1 + tan^2 Θ = sec^2 Θ and 1 + cot^2 Θ = csc^2 Θ. Discuss how to remember these identities and other fundamental identities.

Answers

1 ) 1 + tan² t = sec² t
1 + sin² t / cos² t = 1 / cos² t
( This is because we know that tan x = sin x / cos x and csc x = 1 / cos x )
Then we will multiply both sides of an equation by cos² t
1 * cos² t + sin² t * cos² t / cos² t = 1
cos² t + sin² t = 1 ( and we know that it is the identity - true )
2 ) 1 + cot ² t = csc² t
1 + cos² t / sin² t = 1 / sin² t / · sin² t ( multiply both sides by sin² t )
sin² t + cos² t = 1 ( true )

If y=2 when x=3. What is the value of y when x=9?

Answers

because x was *3 you had to y*3 which is
y=6

y = 2
x = 3

If x = 9, = x * 3

Thus, y * 3 = 6.

Thus, y = 6.

what fraction of a clockwise revolution does the hour of a clock turn through when it goes from a) 4 to 7 b) 8 to 2 c) 1 to 10

Answers

Answer:

a)3/12 = 1/4

b)6/12 = 1/2

c)9/12 = 3/4

Step-by-step explanation:

To find the distance traveled by the hour hand, subtract the beginning position from the ending position. For example, in a, the distance traveled between 4:00 and 7:00 is three hours. Since there are 12 total hours on a clock, the fraction would be 3/12 (traveled/whole revolution). Simplify further to get 1/4.

The other two problems are very similar to the explanation above. Treat the second problem's ending time as 14:00, since it is two hours after 12:00.

Hope this helps!

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