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Ulleksa [173]
3 years ago
10

Find sin theta if theta is an angle in standard position and the point with coordinates (3, -4) lies on the terminal side of an

angle.

Mathematics
1 answer:
alisha [4.7K]3 years ago
4 0

Answer:

\sin \theta=-\frac{4}{5}

Step-by-step explanation:

Given:

Angle is in standard position which means the starting ray is at the origin. The terminal side has coordinates (3, -4).

So, the 'x' value is 3 and 'y' value id -4.

Using Pythagoras Theorem, we find the hypotenuse.

Hypotenuse = \sqrt{3^2+(-4)^2}=\sqrt{9+16}=\sqrt{25}=5

Now, using the sine ratio for the angle, we have

\sin \theta=\frac{Opposite}{Hypotenuse}\\\sin \theta=\frac{-4}{5}\\\sin \theta=-\frac{4}{5}

Therefore, the value of \sin \theta is -\frac{4}{5}.

The value is negative as the point (3, -4) lies in the fourth quadrant and sine ratio is negative in the fourth quadrant,

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Answer:

There is 8% (P=0.08) that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect.

Step-by-step explanation:

We have one-sample z-test with a significance level of 0.08 and a power ot the test of 0.85.

In this test, the null hypothesis will state that the new equipment has the same  productivity of the older equipment. The alternative hypothesis is that there is a significative improvement from the use of new equipment.

The probability that Frances concludes that the new equipment increases the average daily jewelry production when in fact the new equipment has no effect is equal to the probability of making a Type I error (rejecting a true null hypothesis).

The probability of making a Type I error is defined by the level of significance, and in this test this value is α=0.08.

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6 0
3 years ago
One more question...
Alenkinab [10]

Answer:

Step-by-step explanation:

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6 0
3 years ago
Help me answer the question ​
Nastasia [14]

\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Revathi's age is 1/3 of her mother's age. If their difference in age is 24 years, find Revathi's age.

\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}

Given,

  • Mother's age = x
  • Revathi's age = 1/3 x = ?
  • Difference in their age = 24 years ⇨ x - 1/3 x = 24.

Now, let's solve this question using the above equation which we just formed.

\sf \: x -  \frac{1}{3}x  = 24 \\

Combine x and \sf\:-\frac{1}{3}x to get \sf\frac{2}{3}x.

\sf\frac{2}{3}x=24  \\

Multiply both sides by \sf\frac{3}{2}, the reciprocal of \sf\frac{2}{3}.

\sf \: x=24\times \left(\frac{3}{2}\right)

Express \sf24\times \left(\frac{3}{2}\right) as a single fraction.

\sf \: x=\frac{24\times 3}{2}  \\

Multiply 24 and 3 to get 72.

\sf \: x=\frac{72}{2}  \\

Divide 72 by 2 to get 36.

\boxed{ \bf \: x=36 }

We now have the age of Revathi's mother (x) = <u>36 years</u>. Now, let's find Revathi's age ⇨ \sf\:(\frac{1}{3}x)

\rightarrow \sf \:  \frac{1}{3} x  \\  \rightarrow \sf \: \frac{1}{3}  \times 36 \\  \rightarrow \sf \: \frac{1}{ \bcancel  3}  \times  \bcancel{36} \\  \rightarrow \sf \:1 \times 12 \\  =    \boxed{\boxed{\bf \: 12}}

  • So, Revathi is <em><u>1</u></em><em><u>2</u></em><em><u> </u></em><em><u>years </u></em><em><u>old.</u></em>
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3 years ago
3x+y=7<br> 6x+4y=22<br> can somebody help me solve this problem?
swat32
Hey there!

\boxed{x=1;y=4}

3x + y = 7 \\ \\ &#10;    6x + 4y = 22

y = -3x + 7 \\ \\ Plug \ this \ in \ for \ variable \ (y) \ in \ equation \ \\ \\ &#10;&#10;       6x + 4*(-3x+7) = 22 \\ \\ &#10;       -6x = -6 \\ \\ 6x=6 \ x+1 \\ \\ x=1 \ y=-3x+7 \\ \\ \boxed{y=-3(1)+7=4} \\ \\ \boxed{\boxed{x=1;y=4}}

I hope this helps you!
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