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3 years ago

The ratio of dogs to cats at the pet store is 4 to 5. If there are 18 dogs and cats in the store, how many of each are there?

Mathematics

1 answer:

Karolina [17]3 years ago

4 0

Answer:

23 cats

Step-by-step explanation:

So the ratio is basically saying that for every 4 dogs at the store there is one more cat, or 5 cats. 16 dogs there would be 20 cats. 18 dogs there would be approximately 23 cats if you would round up.

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URGENT: If θ is a second-quadrant angle and cosθ = -2/3, then tanθ = _____.

dangina [55]

In the second quadrant, both cos and tan are negative while only sin is positive.

To find tan, we will use the following property below:

$\large \boxed{ {tan}^{2} \theta = {sec}^{2} \theta - 1}$

Sec is the reciprocal of cos. If cos is a/b then sec is b/a. Since cos is 2/3 then sec is 3/2

$\large{ {tan}^{2} \theta = {( - \frac{3}{2}) }^{2} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - 1} \\ \large{ {tan}^{2} \theta = \frac{9}{4} - \frac{4}{4} \longrightarrow \frac{5}{4} } \\ \large{tan \theta = \frac{ \sqrt{5} }{ \sqrt{4} } } \\ \large \boxed{tan \theta = \frac{ \sqrt{5} }{2} }$

Since tan is negative in the second quadrant. Hence,

$\large{ \cancel{ tan \theta = \frac{ \sqrt{5} }{2} } \longrightarrow \boxed{tan \theta = - \frac{ \sqrt{5} }{2} }}$

Answer

tan = -√5/2

3 0

2 years ago

Find the approximate solution of this system of equations. y = |x^2 − 3x + 1|

Aneli [31]

*Hint: When you have two y's, they could equal each other in order to solve for the x value.

|x^2 -3x + 1| = - (x - 1)
x^2 -3x + 1 = -x + 1
x^2 - 2x + 1 = 1
x^2 - 2x = 0
x (x - 2)
x = 2 and x = 0

Once both of them are plugged in, only x = 2 works so that's the value for x. Now we just plug it in order to solve for y.

y = x - 1
y = 2 - 1
y = 1

(2, 1)
The answer would be C.

5 0

3 years ago

Hip traveled 150 nautical miles in 6 hours at a constant speed. How far did the cargo ship travel in one hour?.

alukav5142 [94]

Answer:

25 nautical miles

Step-by-step explanation:

150/6=25

5 0

2 years ago

A bag contain 3 black balls and 2 white balls.

Troyanec [42]

Answer:

Step-by-step explanation:

Total number of balls = 3 + 2 = 5

$Probability \ of \ taking \ 2 \ black \ ball \ with \ replacement\\\\ = \frac{3C_1}{5C_1} \times \frac{3C_1}{5C_1} =\frac{3}{5} \times \frac{3}{5} = \frac{9}{25}\\\\$

$Probability \ of \ one \ black \ and \ one\ white \ with \ replacement \\\\= \frac{3C_1}{5C_1} \times \frac{2C_1}{5C_1} = \frac{3}{5} \times \frac{2}{5} = \frac{6}{25}$

Probability of at least one black( means BB or BW or WB)

$=\frac{3}{5} \times \frac{3}{5} + \frac{3}{5} \times \frac{2}{5} + \frac{2}{5} \times \frac{3}{5} \\\\= \frac{9}{25} + \frac{6}{25} + \frac{6}{25}\\\\= \frac{21}{25}$

Probability of at most one black ( means WW or WB or BW)

$=\frac{2}{5} \times \frac{2}{5} + \frac{3}{5} \times \frac{2}{5} \times \frac{2}{5} + \frac{3}{5}\\\\= \frac{4}{25} + \frac{6}{25} + \frac{6}{25}\\\\=\frac{16}{25}$

a) Probability both black without replacement

$=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}$

b) Probability of one black and one white

$=\frac{3}{5} \times \frac{2}{4}\\\\=\frac{6}{20}\\\\=\frac{3}{10}$

c) Probability of at least one black ( BB or BW or WB)

$=\frac{3}{5} \times \frac{2}{4} + \frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{6}{20} + \frac{6}{20} \\\\=\frac{18}{20} \\\\=\frac{9}{10}$

d) Probability of at most one black ( BW or WW or WB)

$=\frac{3}{5} \times \frac{2}{4} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{3}{4}\\\\=\frac{6}{20} + \frac{2}{20} + \frac{6}{20} \\\\=\frac{14}{20}\\\\=\frac{7}{10}$

6 0

3 years ago

Based on the area of the squares determine whether the triangle shown is a right triangle.

VMariaS [17]

Answer:

No, it is not a right triangle.

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers