All categories

3 years ago

Find the midpoint of the line segment whose endpoints are given (3/5 , -6/7),(2/5,5/7)

Mathematics

1 answer:

snow_lady [41]3 years ago

3 0

The formula of a midpoint between E and F:

$M_{EF}\left(\dfrac{x_E+x_F}{2};\ \dfrac{y_E+y_F}{2}\right)$

We have the points $\left(\dfrac{3}{5},\ -\dfrac{6}{7}\right)$ and $\left(\dfrac{2}{5},\ \dfrac{5}{7}\right)$ . Substitute:

$\dfrac{\frac{3}{5}+\frac{2}{5}}{2}=\dfrac{\frac{5}{5}}{2}=\dfrac{1}{2}\\\\\dfrac{-\frac{6}{7}+\frac{5}{7}}{2}=\dfrac{-\frac{1}{7}}{2}=-\dfrac{1}{7}\cdot\dfrac{1}{2}=-\dfrac{1}{14}$

Answer: $\boxed{\left(\dfrac{1}{2},\ -\dfrac{1}{14}\right)}$

You might be interested in

3. A clothing manufacturing company makes two types of jogging pants, design A and design B. the design A jogging pants sells to

andriy [413]

Answer:

z(max) = 256000 Php

x₁ = 10

x₂ = 110

Step-by-step explanation:

Jogging pants design Selling Price Cost

weekly production

Design A x₁ 2500 1750

Design B x₂ 2100 1200

1. z ( function is : )

z = 2500*x₁ + 2100*x₂ to maximize

First constraint weekly production

x₁ + x₂ ≤ 120

Second constraint Budget

1750*x₁ + 1200*x₂ ≤ 150000

Then the model is

z = 2500*x₁ + 2100*x₂ to maximize

Subject to

x₁ + x₂ ≤ 120

1750*x₁ + 1200*x₂ ≤ 150000

General constraints x₁ ≥ 0 x₂ ≥ 0 both integers

First table

z x₁ x₂ s₁ s₂ cte

1 -2500 -2100 0 0 0

0 1 1 1 0 = 120

0 1750 1200 0 1 = 150000

Using AtoZmath online solver and after 6 iterations the solution is:

z(max) = 256000 Php

x₁ = 10

x₂ = 110

3 0

3 years ago

A + b − _____ = a<br> help :)

ss7ja [257]

Step-by-step explanation:

Subtract a from both sides

a-a+b-___=a-a

b-__=0

b=___

answer:b

Hope that helps :)

6 0

3 years ago

Read 2 more answers

What is the volume of a sphere with a radius of 4

Ede4ka [16]

Step-by-step explanation: To find the volume of a sphere, start with the formula for the volume of a sphere which is shown below.

$V = \frac{4}{3}\pi r^{3}$

Here, we are given that our sphere has a radius of 4 units.

So plugging into the formula, we have $(\frac{4}{3})(\pi)(4 units)^{3}$ .

Start by simplifying the exponent.

(4 units)³ is equal to (4 units) (4 units) (4 units) or 64 units³.

So we have $(\frac{4}{3})(\pi)(64 units^3})$ .

Next, we multiply (4/3)(64) which can

be thought of as (4/3)(64/1)

So multiplying across the numerators and across the denominators,

we have $\frac{256}{3} \pi units^{3}$ .

5 0

3 years ago

An Epson inkjet printer ad advertises that the black ink cartridge will provide enough ink for an average of 245 pages. Assume t

Neko [114]

Answer:

35.2% probability that the sample mean will be 246 pages or more

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

$\mu = 245 \sigma = 15, n = 33, s = \frac{15}{\sqrt{33}} = 2.61$

What the probability that the sample mean will be 246 pages or more?

This is 1 subtracted by the pvalue of Z when X = 246. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{246 - 245}{2.61}$

$Z = 0.38$

$Z = 0.38$ has a pvalue of 0.6480.

1 - 0.6480 = 0.3520

35.2% probability that the sample mean will be 246 pages or more

4 0

3 years ago

Mi padre compró un radio por cierta suma de dinero, un televisor que costó 10 veces más que el radio y un reproductor cuyo preci

Maru [420]

Answer:

For radio = $40.43

Television = $444.73

Player = $364.73

Step-by-step explanation:

The computation of the each device cost is shown below:

let us assume the following things

radio be x

television x + 10x

player x + 10x - $80

Now the equation is

x + x + 10x + x + 10x - $80 = $850

3x + 20x - $80 = $850

23x = $930

x = $40.43

For radio = $40.43

Television = $40.43 + 10(40.43)

= $40.43 + $404.3

= $444.73

and, the player would be

= $444.73 - $80

= $364.73

7 0

3 years ago