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marishachu [46]

3 years ago

9

A bag of marbles has 3 red, 4 blue, and 5 white marbles in it. What is the probability of reaching in and selecting a blue marbl

e? (without looking)

1 answer:

goblinko [34]3 years ago

4 0

Answer:

$P(B)=\frac{1}{3}$

Step-by-step explanation:

The number of red marbles in the bag is; $n(R)=3$ .

The number of blue marbles in the bag is; $n(B)=4$ .

The number of white marbles in the bag is; $n(W)=5$ .

The total number of marbles in the bag is: $n(S)=3+4+5=12$ .

The probability of selecting a blue marble is $P(B)=\frac{n(B)}{n(S)}$

We substitute the given information to obtain:

$P(B)=\frac{4}{12}$

We simplify to obtain:

$P(B)=\frac{1}{3}$

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Find b, given that a = 20, angle A = 30°, and angle B = 45° in triangle ABC

Kamila [148]

<span>The side b is opposite to the angle B, applying the law of the sines, we have:

</span> $\frac{a}{sinA} = \frac{b}{sinB}$
$\frac{20}{sin30^0} = \frac{b}{sin45^0}$
$\frac{20}{ \frac{1}{2} } = \frac{b}{ \frac{ \sqrt{2} }{2} }$
$20* \frac{ \sqrt{2} }{2} = b* \frac{1}{2}$
$\frac{20 \sqrt{2} }{2} = \frac{b}{2}$
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$b = \frac{40 \sqrt{2} }{2}$
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3 years ago

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LUCKY_DIMON [66]

Answer: (A)-2, -1

(b) 3,0

(C) 7,2

Step-by-step explanation:

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6 0

3 years ago

I need help with this plz

DochEvi [55]

Answer :

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7 0

3 years ago

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Evaluate exactly without the use of a calculator (remember to rationalize any denominators). a.(cos 60o)(sin 270o) + tan 225o b.

Rom4ik [11]

Given:

The trigonometric expressions are given as,

$\begin{gathered} a)\text{ }(\cos 60\degree)(\sin 270\degree)+\tan 225\degree \\ b)-\tan 240\degree+(cos45\degree)(\sec 135\degree) \end{gathered}$

Explanation:

a)

The given expression can be rewritten as,

$=(\cos 60\degree)(\sin (360\degree-90\degree))+\tan (270\degree-45\degree)\text{ . . . . .(1)}$

Since, from the trigonometric ratios,

$\begin{gathered} \sin (360\degree-90\degree)=-\sin 90\degree \\ \tan (270\degree-45\degree)=\cot 45\degree \end{gathered}$

On plugging the obtained ratios in equation (1),

$=(\cos 60\degree)(-\sin 90\degree)+\cot 45$

Substitute the trigonometric values in the above equation.

$\begin{gathered} =\frac{1}{2}(-1)+1 \\ =-\frac{1}{2}+1 \\ =\frac{1}{2} \end{gathered}$

Hence, the exact value of the expression is 1/2.

b)

The given expression can be rewritten as,

$=-\tan (270\degree-30\degree)+(\cos 45\degree)(\sec (90\degree+45\degree))\text{ . . . ..(2)}$

Since, from the trigonometric ratios,

$\begin{gathered} \tan (270\degree-30\degree)=\cot 30\degree \\ \sec (90\degree+45\degree)=-\csc 45\degree \end{gathered}$

On plugging the obtained ratios in equation (2),

$=-\cot 30\degree+(\cos 45\degree)(-\csc 45)$

Substitute the trigonometric values in the above equation.

$\begin{gathered} =-\sqrt[]{3}+\frac{1}{\sqrt[]{2}}(-\sqrt[]{2}) \\ =-\sqrt[]{3}-1 \end{gathered}$

Hence, the exact value of the expression is -√3-1.

7 0

2 years ago

nikdorinn [45]

Answer:

The answer is below

Step-by-step explanation:

The question is not complete but i would show how to solve.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are dilation, rotation, translation and reflection.

Dilation is the enlargement or reduction in the size of a figure.

a) If an point A(x, y) is dilated by a factor k, the new coordinate is A'(kx, ky). From the above options the ones that represent dilation is (x, y) → (0.5x, 0.5y) and (x, y) → (2x, 2y) . If the object is reduced then the correct option is (x, y) → (0.5x, 0.5y) while if the object is enlarged the correct option is (x, y) → (0.5x, 0.5y)

b)Dilation is the enlargement or reduction in the size of a figure by a factor k. If k < 1, then it is a reduction and if k > 1, it is an enlargement.

Since Triangle XYZ is dilated with the origin as the center of dilation using the rule (x, y)⇒(0.5x, 0.5y) to create Triangle X’Y’Z’, since the factor is less than 1(0.5 < 1), it is a reduction. Hence Triangle X’Y’Z’ is smaller than Triangle XYZ, because the scale factor is less than 1

c) The dilation creates a smaller figure hence the factor of dilation should be less than 1.

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3 years ago