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harina [27]
3 years ago
13

The rules of a contest say there is 8% chance of winning a prize. Seven hundred people enter the contest. Predict how many peopl

e win a prize
Mathematics
1 answer:
vesna_86 [32]3 years ago
4 0

8%=0.08

0.08 times 700=56

56 people win a prize.

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Answer:oh okay

Step-by-step explanation:

4 0
2 years ago
Find , , and if and terminates in quadrant .
ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

We can now proceed to find the values of ainx and cosx.

Using the trigonometric ratio;

\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})=\frac{12}{13}

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

\tan 2x=\frac{2\tan x}{1-\tan ^2x}=\frac{2(\frac{2}{3})}{1-(\frac{2}{3})^2}=\frac{\frac{4}{3}}{1-\frac{4}{9}}=\frac{\frac{4}{3}}{\frac{9-4}{9}}=\frac{\frac{4}{3}}{\frac{5}{9}}=\frac{4}{3}\times\frac{9}{5}=\frac{4}{1}\times\frac{3}{5}=\frac{12}{5}

OR

\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

3 0
1 year ago
Using 6 as a denominator, what fraction completes the following
mixas84 [53]

Answer:

B

Step-by-step explanation:

We can start by converting 1 into 6/6 and 1/3 into 2/6. This makes subtraction much easier, and by subtracting the numerators, (6/6 - 2/6) you should get 4/6.

5 0
2 years ago
What is the area in square inches of this quadrilateral
Lerok [7]

Answer:

160 in²

Step-by-step explanation:

20 * 16 / 2

if we wouldn't devide with 2, we would calculate the rectangle around the quadrilateral

7 0
2 years ago
Read 2 more answers
Which theorem or postulate could be used to prove the congruence of the triangle?
Darina [25.2K]

Answer:

SAS

By using. Side angle side

4 0
3 years ago
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