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3 years ago

Which Exponential equation is equivalent to the logarithmic equation below? C= in 3

Mathematics

1 answer:

Bess [88]3 years ago

7 0

Answer

e^c = 3

Step by step explanation

The general exponential equation is y = a^x, where "a" is the base and "x" is the exponent.

We are given c = ln 3

Here the base is "e"

e^c = e^ln 3

e^c = 3 [base "e" and "ln" get cancelled because they are inverse]

Therefore, the answer is e^c = 3

Hope you will understand the concept.

Thank you.

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The altitude (i.e., height) of a triangle is increasing at a rate of 2 cm/minute while the area of the triangle is increasing at

aksik [14]

The formula for the area of a triangle is
$A=\frac{1}{2}bh$
$\rightarrow\frac{dA}{dt}=\frac{1}{2}(b\frac{dh}{dt}+h\frac{db}{dt})$

We are given:
$\frac{dh}{dt}=2$
$\frac{dA}{dt}=4.5$
$h=9.5$
$A=92$

Plug in:
$4.5=\frac{1}{2}(b*2+9.5\frac{db}{dt})$
We can find $b$ with:
$A=\frac{1}{2}bh\rightarrowb=\frac{2A}{h}=\frac{2*92}{9.5}=\frac{184}{9.5}$
So $4.5=\frac{1}{2}(2*\frac{184}{9.5}+9.5\frac{db}{dt})$
$\rightarrow9=\frac{368}{9.5}+9.5\frac{db}{dt}$
$\rightarrow9-\frac{368}{9.5}=9.5\frac{db}{dt}$
$\rightarrow\frac{db}{dt}=\frac{9-\frac{368}{9.5}}{9.5}\approx-3.130$

So the base is decreasing at a rate of 3.130 cm/minute.

6 0

2 years ago

Carmen used a random number generator to simulate a survey of how many children live in the households in her town. There are 1,

kiruha [24]

About 296 households have more than three children. Then the correct option is C.

<h3>How to find that a given condition can be modeled by binomial distribution?</h3>

Suppose we have random variable X pertaining to a binomial distribution with parameters n and p, then it is written as

The expected value will be

E(X) = np

Carmen used a random number generator to simulate a survey of how many children live in the households in her town.

There are 1,346 unique addresses in her town with numbers ranging from zero to five children.

The results of 50 randomly generated households are shown below.

Children in 50 Households

Number of Children Number of Households

0 5

1 11

2 13

3 10

4 9

5 2

Then the value of p and n will be

p = 11/50

n = 1346

Then the expected value will be

E(x) = (11/50) x 1346

E(x) = 296.12 ≈ 296

Then the correct option is C.

Learn more about binomial distribution here:

brainly.com/question/13609688

#SPJ1

4 0

2 years ago

Please answer this correctly

Rom4ik [11]

Hey!

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Solution:

This company has a budget of $9,009

They want to send employees to a conference which is $21/person.

9,009 / 21 = $429

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

Answer:

They can send <u>$429 employees</u> to the conference.

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

Hope This Helps :)

5 0

3 years ago

I need help please fast

Lemur [1.5K]

6 x 10^3
This would be a good enough answer.

3 0

3 years ago

Read 2 more answers

14. What is the length of a diagonal of rectangle EFGH? Show your work

Serhud [2]

Answer:

The length of the diagonal of the rectangle is of $\sqrt{58}$ units.

Step-by-step explanation:

Pythagorean theorem:

The square of the hypothenuse h is equal to the sum of the squares of sides a and b, that is:

$h^2 = a^2 + b^2$

Diagonal of a rectangle:

The diagonal is the hypothenuse, while the sides are a and b.

In this question:

The height has coordinates are y = 9 and y = 12, so the height is $a = 12 - 9 = 3$

The length has coordinates at $x = -6, x = -13$ , so the length is $b = -6 - (-13) = 7$

Diagonal:

$d^2 = a^2 + b^2$

$d^2 = 3^2 + 7^2$

$d^2 = 9 + 49$

$d^2 = 58$

$d = \sqrt{58}$

The length of the diagonal of the rectangle is of $\sqrt{58}$ units.

6 0

2 years ago