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3 years ago

I really need help ;-;

Mathematics

1 answer:

denis23 [38]3 years ago

8 0

Hi there! I can help you!

a. Okay. So we have to make a table for the amount of butterflies to total insects. Let's simplify the ratio. 36:100 simplifies to 9:25. We can use that ratio to make this table. Just multiply 25 by the amount it takes to get to 50 or 100, and multiply by the same amount at the top to find the amount of butterflies. If you do it correctly, your table should be as shown below in the image.

b. On that note, let's solve for the amount of butterflies in the conservatory. There are 450 total of them. Let's divide 450 by 100 to find the amount we will multiply by. 450/100 is 4.5. We will mutliply 36 by that amount to find the total amount of butterflies. 36 * 4.5 is 162. That's it. There are 162 butterflies in the conservatory.

You might be interested in

Please help me, i have been on this problem for 45 minutes.

docker41 [41]

Answer:

Step-by-step explanation:

The absolute difference is 77-(-8)=85. The only option that is equivalent is

|-8|+77

8 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

3 years ago

Prime factorisation of 500

Andrews [41]

$\boxed{\underline{\bf \: ANSWER}}$

2 <u>| 500</u>

2 <u>| 250</u>

5 <u>| 125</u>

5 <u>| 25</u>

5 <u>| 5</u>

1 <u>| 1</u>

Prime factorisation of <u>500 = 2 × 2 × 5 × 5 × 5 × 1</u>

_____

Hope it helps.

ᏒᎯᎨᏁᏰᎾᏯᏕᎯᏝᎿ2222

6 0

2 years ago

Help me please and explain if possible?

creativ13 [48]

Let x = months

so we know that price of software package is $20
Now we need to find x the price of one month

we know that Angie and Kenny spent 115 total

Angie: 20 + 3x ( one software pack + 3(price of one month)
Kenny: 20+ 2x ( one software pack + 2( price of one month)

So Angie + Kenny = $ 115

20 + 3y + 20 + 2y = 115

combine like terms and solve for x. That will give you the cost of one month

40 + 5x = 115
-40 -40

5x= 75
5x/5 = 75/5

x=15

8 0

3 years ago

Solve for x please. :)

solmaris [256]

Answer:

180-130=50

Step-by-step explanation:

done hope you like it

i use the 180 because its a straight line from the x to the 130

6 0

2 years ago