There are 75 balloons in each package. How many are in 20 packages

Amy reached into a bag, recorded the color of the tile she picked, returned the tile and drew again. These are the tiles she has

Vedmedyk [2.9K]

Answer:

(a) P(next ball with blue) = $\frac{3}{10}$ (b) P(Not to be red) = $1-\frac{2}{5} =\frac{3}{5}$

(c) P(drawing 70 times yellow ball) = $\frac{1}{10} \times 70 = 7$ .

Step-by-step explanation:

Given that,

The total outcomes of the color of tile are :-

Red , Red, Blue, Yellow, Blue, Red, Green, Red, Blue, Green.

From the Question,

Total number of outcomes = 10

(a) What is the probability that her next draw will be blue ?

Red = 4,

Blue = 3,

Green = 2,

Yellow = 1.

P(next ball with blue) = $\frac{3}{10}$ .

(b) What is the probability that her next draw will NOT be red?

P(Red ball) = $\frac{4}{10} = \frac{2}{5}$

But we have to find

P(Not to be red) = $1-\frac{2}{5} =\frac{3}{5}$

(c) If Amy draws 70 more times with the same tiles from the question above, what probability would you expect a yellow?

P(Yellow ball) = $\frac{1}{10}$

drawing it 70 times we get the probability

P(drawing 70 times yellow ball) = $\frac{1}{10} \times 70 = 7$ .

5 0

3 years ago

Find the angle between u =the square root of 5i-8j and v =the square root of 5i+j.

fenix001 [56]

Answer:

The angle between vector $\vec{u} = 5\, \vec{i} - 8\, \vec{j}$ and $\vec{v} = 5\, \vec{i} + \, \vec{j}$ is approximately $1.21$ radians, which is equivalent to approximately $69.3^\circ$ .

Step-by-step explanation:

The angle between two vectors can be found from the ratio between:

their dot products, and
the product of their lengths.

To be precise, if $\theta$ denotes the angle between $\vec{u}$ and $\vec{v}$ (assume that $0^\circ \le \theta < 180^\circ$ or equivalently $0 \le \theta < \pi$ ,) then:

$\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ .

<h3>Dot product of the two vectors</h3>

The first component of $\vec{u}$ is $5$ and the first component of $\vec{v}$ is also

The second component of $\vec{u}$ is $(-8)$ while the second component of $\vec{v}$ is $1$ . The product of these two second components is $(-8) \times 1= (-8)$ .

The dot product of $\vec{u}$ and $\vec{v}$ will thus be:

$\begin{aligned} \vec{u} \cdot \vec{v} = 5 \times 5 + (-8) \times1 = 17 \end{aligned}$ .

<h3>Lengths of the two vectors</h3>

Apply the Pythagorean Theorem to both $\vec{u}$ and $\vec{v}$ :

$\| u \| = \sqrt{5^2 + (-8)^2} = \sqrt{89}$ .
$\| v \| = \sqrt{5^2 + 1^2} = \sqrt{26}$ .

<h3>Angle between the two vectors</h3>

Let $\theta$ represent the angle between $\vec{u}$ and $\vec{v}$ . Apply the formula $\displaystyle \cos(\theta) = \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|}$ to find the cosine of this angle:

$\begin{aligned} \cos(\theta)&= \frac{\vec{u} \cdot \vec{v}}{\| u \| \cdot \| v \|} = \frac{17}{\sqrt{89}\cdot \sqrt{26}}\end{aligned}$ .

Since $\theta$ is the angle between two vectors, its value should be between $0\; \rm radians$ and $\pi \; \rm radians$ ( $0^\circ$ and $180^\circ$ .) That is: $0 \le \theta < \pi$ and $0^\circ \le \theta < 180^\circ$ . Apply the arccosine function (the inverse of the cosine function) to find the value of $\theta$ :

$\displaystyle \cos^{-1}\left(\frac{17}{\sqrt{89}\cdot \sqrt{26}}\right) \approx 1.21 \;\rm radians \approx 69.3^\circ$ .

3 0

2 years ago

43.9<br> 44.3<br> 45.7<br> 46.2<br> Are possible answers.

Aneli [31]

Answer:

44.3 would be the correct answer if I looked at it correctly

5 0

3 years ago

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines

Brrunno [24]

Hope this helps make sure you rate me 55555 stars and bam your happy

3 0

3 years ago

Please answer these Math questions

natulia [17]

#1 Pi was originally as the ratio of a circle's circumference to it's diameter.
#3 Pi cannot be completely represented as a fraction, but 355/113 is pretty close.
#6 A irrational number is a number that can't be represented as a ratio/fraction
#8<span> Is because March is the third month, and 14 is the first to decimals. Month/Day: 3/14, Pi: 3.14.
</span>
Sorry, that's all I know.

8 0

3 years ago