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3 years ago

13

The ratio of red candies to blue candies is 5:4 in the bag. If there are 20 blue candies in the bag, how many red candies are th

ere?

1 answer:

maxonik [38]3 years ago

5 0

25 candy_*_>/>_*%*%`=`:`:*/`:&

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The point (1/3,1/4) lies on the terminal said of an angle. Find the exact value of the six trig functions and explain which func

katrin2010 [14]

Answer:

sine and cosec are inverse of each other.

cosine and sec are inverse of each other.

tan and cot are inverse of each other.

Step-by-step explanation:

Given point on terminal side of an angle ( $\frac{1}{3},\frac{1}4$ ).

Kindly refer to the attached image for the diagram of the given point.

Let it be point A( $\frac{1}{3},\frac{1}4$ )

Let O be the origin i.e. (0,0)

Point B will be ( $\frac{1}{3},0$ )

Now, let us consider the right angled triangle $\triangle OBA$ :

Sides:

$Base, OB = \frac{1}{3}\\Perpendicular, AB = \frac{1}{4}$

Using Pythagorean theorem:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow OA^{2} = OB^{2} + AB^{2}\\\Rightarrow OA^{2} = \frac{1}{3}^{2} + \frac{1}{4}^{2}\\\Rightarrow OA = \sqrt{\frac{1}{3}^{2} + \frac{1}{4}^{2}}\\\Rightarrow OA = \sqrt{\frac{4^2+3^2}{3^{2}.4^2 }}\\\Rightarrow OA = \frac{5}{12}$

$sin \angle AOB = \dfrac{Perpendicular}{Hypotenuse}$

$\Rightarrow sin \angle AOB = \dfrac{\frac{1}{4}}{\frac{5}{12}}\\\Rightarrow sin \angle AOB = \dfrac{3}{5}$

$cos\angle AOB = \dfrac{Base}{Hypotenuse}$

$\Rightarrow cos \angle AOB = \dfrac{\frac{1}{3}}{\frac{5}{12}}\\\Rightarrow cos\angle AOB = \dfrac{4}{5}$

$tan\angle AOB = \dfrac{Perpendicular}{Base}$

$\Rightarrow tan\angle AOB = \dfrac{3}{4}$

$cosec \angle AOB = \dfrac{Hypotenuse}{Perpendicular}$

$\Rightarrow cosec\angle AOB = \dfrac{5}{3}$

$sec\angle AOB = \dfrac{Hypotenuse}{Base}$

$\Rightarrow sec\angle AOB = \dfrac{5}{4}$

$cot\angle AOB = \dfrac{Base}{Perpendicular}$

$\Rightarrow cot\angle AOB = \dfrac{4}{3}$

3 0

3 years ago

In the figure, the horizontal lines are parallel and AB = BC = CD. If LM = 3 Find JM? A. 12 B. 6 C. 3 D. 9

ziro4ka [17]

A.12 because i had same question

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5 0

3 years ago

Find the Total surface area

Veseljchak [2.6K]

Answer:

You may not recognize this...but the base forms a "Pythagorean" right triangle with legs of 6 and 8 cm

The area of a right triangle is (1/2) ( product of leg lengths)

So...the area of the base = (1/2) (6 * 8 ) = (1/2) 48 = 24 cm^2

And the volume of the prism is just the base area x height = 24 x 7 = 192 cm^2

Step-by-step explanation:

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=-2%5Csqrt%7B18%7D%20%2B2%5Csqrt%7B2%7D" id="TexFormula1" title="-2\sqrt{18} +2\sqrt{2}" alt="-

UkoKoshka [18]

Answer:

- 4 $\sqrt{2}$

Step-by-step explanation:

Using the rule of radicals

$\sqrt{a}$ × $\sqrt{b}$ ⇔ $\sqrt{ab}$

Simplify $\sqrt{18}$ using this rule

$\sqrt{18}$

= $\sqrt{9(2)}$

= $\sqrt{9}$ × $\sqrt{2}$ = 3 $\sqrt{2}$

Then

- 2 $\sqrt{18}$ + 2 $\sqrt{2}$

= - 2(3 $\sqrt{2}$ ) + 2 $\sqrt{2}$

= - 6 $\sqrt{2}$ + 2 $\sqrt{2}$

= - 4 $\sqrt{2}$

5 0

3 years ago

Statisticians use ______ scores to divide the ______ under a curve the way people use a knife to cut pizza. Just as the pizza is

solong [7]

Answer:

Statisticians use z-scores to divide the area under a curve the way people use a knife to cut pizza.

Step-by-step explanation:

Statisticians use z-scores to divide the area under a curve the way people use a knife to cut pizza.

z-score:

A z-score is a numerical measurement which is measured in terms of standard deviations from the mean.
Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

If a z-score is 0, it tells that the data point is same as the mean.
Area under the normal curve is 1.

6 0

3 years ago