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3 years ago

15

Kelly has 4 times as many songs on her music player as Lou. Tiffany has 6 times as many songs on her music player as Lou. Altoge

ther, they have 682 songs on their music players. How many songs does Kelly have?

1 answer:

OlgaM077 [116]3 years ago

8 0

The answer is 248. Working out is in the picture.

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Annabelle the ant and Archibald the ant are on a large coordinate grid. Annabelle is at (3,4) and Archibald is at (33,44). If bo

kvasek [131]

<u>Part a)</u> If both ants skate directly towards each other, starting at the same time and skating the same speed, what will be the coordinates of their meeting place?

Let

A(3,4) B(33.44)

we know that

If both ants skate directly towards each other, starting at the same time and skating the same speed

then

the coordinates of their meeting place is the midpoint AB

<u>Find the midpoint AB</u>

in the x-coordinate

(3+33)/2=18

in the y-coordinate

(4+44)/2=24

the midpoint AB is (18,24)

therefore

<u>the answer Part a) is </u>

the coordinates of their meeting place is (18,24)

<u>Part b)</u> How far will each ant skate?

<u>Find the distance AB</u>

$d=\sqrt{(x2-x1)^{2}+(y2-y1)^{2}}$

substitute the values

$dAB=\sqrt{(33-3)^{2}+(44-4)^{2}}$

$dAB=\sqrt{2,500}$ units

$dAB=50$ units

<u>Find the half distance AB</u>

50/2=25 units

therefore

<u>the answer part b) is</u>

Each ant will skate 25 units

7 0

2 years ago

Find the point P that is 2/5 of the way from A to B on the directed line segment AB

Kruka [31]

The point P(–4, 4) that is $\frac{2}{5}$ of the way from A to B on the directed line segment AB.

Solution:

The points of the line segment are A(–8, –2) and B(6, 19).

P is the point that bisect the line segment in $\frac{2}{5}$ .

So, m = 2 and n = 5.

$x_1=-8, y_1=-2, x_2=6, y_2=19$

By section formula:

$$P(x, y)=\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)$

$$P(x, y)=\left(\frac{2\times 6+5\times (-8)}{2+5}, \frac{2\times 19+5\times (-2)}{2+5}\right)$

$$P(x, y)=\left(\frac{12-40}{7}, \frac{38-10}{7}\right)$

$$P(x, y)=\left(\frac{-28}{7}, \frac{28}{7}\right)$

P(x, y) = (–4, 4)

Hence the point P(–4, 4) that is $\frac{2}{5}$ of the way from A to B on the directed line segment AB.

4 0

3 years ago

A long novel is opened to a random page; the probability that the page is numbered something between 21 and 31.

Harrizon [31]

Using the uniform distribution, considering that the novel has 435 pages, the probability that the page is numbered something between 21 and 31 is:

$p = \frac{10}{435}$

<h3>What is the uniform probability distribution?</h3>

It is a distribution with two bounds, a and b, in which each outcome is equally as likely.

The probability of finding a value between c and d is:

$P(c \leq X \leq d) = \frac{d - c}{b - a}$

Researching the problem on the internet, it is found that the novel has 435 pages, hence a = 0, b = 435, and the probability that the page is numbered something between 21 and 31 is given by:

$P(21 \leq X \leq 31) = \frac{31 - 21}{435 - 0} = \frac{10}{435}$

More can be learned about the uniform distribution at brainly.com/question/13889040

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5 0

1 year ago

Suppose that y varies directly with x and at the same time varies inversely with z and y=12 when x=6 and z=-2. Write the equatio

ki77a [65]

Answer:

Answer:

y =18

Explanation

Step-by-step explanation:

3 0

2 years ago

Write the algebraic expression for the difference between the squares of two numbers.

V125BC [204]

The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is

a² - b² = (a + b)(a - b).

An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).

The terms are combinations of numerals and variables.

Variables are represented alphanumerically, which can hold any value as per the expression they are used in.

In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.

We assume the two numbers to be a and b respectively.

Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².

We know that a² - b² is an identity, which can be shown as (a + b)(a - b).

Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).

Learn more about algebraic expressions at

brainly.com/question/2241589

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6 0

1 year ago