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2 years ago

An animal shelter has a ratio of cats to dogs that is 9:7.

Mathematics

2 answers:

melamori03 [73]2 years ago

5 0

Answer:

A) C. 7:16

B) second shelter

Step-by-step explanation:

A) Given that the shelter has a ratio of cats to dogs that is 9:7 and only houses dogs and cats, then there are 7 dogs for every 7+9 = 16 total number of animals, that is, the ratio of dogs to total animals is 7:16.

B) A ratio of 6:5 means that there are 6 cats for every 5 dogs. If the second shelter has 18 (=6*3) cats, then it has 3*5 = 15 dogs. That is, 6:5 is equivalent to 18:15

The first shelter has 9 cats for every 7 dogs. If it has 18 (=9*2) cats, then it has 7*2 = 14 dogs. That is, 9:7 is equivalent to 18:14

Luda [366]2 years ago

3 0

Answer:

C 7/16

Shelter B has more dogs

Step-by-step explanation:

Part A

Cats : dogs : total

9 7 9+7=16

dogs/ total

7/16

Part B

Cats : dogs : total

6 5 6+5=11

If they both have 18 cats

Shelter A

Cats : dogs : total

9 7 16

Multiply by 2

18 14 32

Shelter B

Cats : dogs : total

6 5 11

Multiply by 3

18 15 33

Shelter A has 14 dogs, Shelter B has 15 dogs

Shelter B has more dogs

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sp2606 [1]

<h3>The first time when the ball will reach a height of 20 feet is 0.42 seconds</h3>

Solution:

Given that,

The height of a ball thrown into the air after t seconds have elapsed is:

$h = -16t^2 + 40t + 6$

What is the first time, t, when the ball will reach a height of 20 feet?

Substitute h = 20

$20 = -16t^2 + 40t + 6\\\\-16t^2 + 40t + 6 -20 = 0\\\\-16t^2 + 40t -14 = 0\\\\16t^2 -40t + 14 = 0\\\\8t^2 -20t + 7=0$

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$\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}$

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$\mathrm{For\:}\quad a=8,\:b=-20,\:c=7$

$t = \frac{-\left(-20\right)\pm \sqrt{\left(-20\right)^2-4\cdot \:8\cdot \:7}}{2\cdot \:8}\\\\t = \frac{20 \pm \sqrt{176}}{16}\\\\t = \frac{20 \pm 4\sqrt{11}}{16}\\\\t = \frac{ 5 \pm \sqrt{11}}{4}\\\\We\ have\ two\ solutions\\\\ t=2.07915, \:t=0.42084$

Rounding off we get,

t = 2.08 , t = 0.42

Thus the first time when the ball will reach a height of 20 feet is 0.42 seconds

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