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3 years ago

What is the value of x in the equation below?

Mathematics

1 answer:

sveta [45]3 years ago

7 0

Answer: C

Step-by-step explanation:

1+2e^x+1=9

2e^x+1=9-1

e^x+1= 8/2

e^x+1 = 4

Here we can applicate the Ln:

ln e^x+1 = ln 4

Applicating the log property for exponent:

(x+1).ln e = ln 4

Ln e = 1, so:

x+1 = ln 4

x = ln 4-1

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a bag contains 4 red, 3 orange and 5 purple marbles. what is the probability of drawing 2 purple marbles in a row without replac

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Read 2 more answers

On section AB, whose length is 192 cm, take the point C so that AC: CB = 1: 3. The point D is taken on the AC section so that CD

jasenka [17]

Answer:

112 cm

Step-by-step explanation:

Given:

AB = 192 cm
AC : CB = 1 : 3
CD = BC/12
The distance between midpoints of AD and CB = x

Find the length of AC and CB:

AC + CB = AB
AC + 3AC = 192
4AC = 192
AC = 192/4
AC = 48 cm

Find CB:

CB = 3AC = 3*48 = 144 cm

Find the length of CD:

CD = BC/12 = 144/12 = 12 cm

Find the length of AD:

AD = AC - CD = 48 - 12 = 36 cm

Find the midpoint of AD:

m(AD) = 36/2 = 18 cm

Find the midpoint of CB:

m(CB) = AC + 1/2CB = 48 + 144/2 = 48 + 82 = 130 cm

Find the distance between the midpoints:

x = 130 - 18 = 112 cm

4 0

3 years ago

Factor the polynomial by grouping : x^3+5x^2-6x-30

andrew-mc [135]

The idea is to pair up the terms, factor each sub-group, and then pull out the overall GCF to fully factor.

x^3+5x^2-6x-30

(x^3+5x^2)+(-6x-30)

x^2(x+5)+(-6x-30)

x^2(x+5)-6(x+5)

(x^2-6)(x+5)

-------------

Answer: (x^2-6)(x+5)

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3 years ago

As part of a study done for a large corporation, psychologists asked randomly selected employees to solve a collection of simple

zhenek [66]

Answer:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

Step-by-step explanation:

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: $P(A)+P(A') =1$

On this case we have that n= 56 represent the employees selected to solve the puzzles.

We know that 23 out of the 56 selected solved the puzzles in less than 7 minutes.

Let's define the events A and A' like this:

A: Employees solved puzzles in less than 7 minutes

By the complement rule then:

A' : Employees solved puzzles in more than 7 minutes

Based on this we are interested to find the probability for A'

We can begin finding P(A), from the definition of probability we know:

$P(A)=\frac{Possible outcomes}{Total outcomes}$

For this case if we replace we got:

$P(A) =\frac{23}{56}=0.411$

And using the complemnt rule we got:

$0.411 +P(A')=1$

And solving for P(A') we got:

$P(A')=1-0.411=0.589$

And that represent the probability that they take longer than 7 minutes to solve the puzzles.

4 0

3 years ago