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3 years ago

Use Natural Logarithms to solve the equation

Mathematics

1 answer:

Rus_ich [418]3 years ago

7 0

Answer:

A) 0.106

Step-by-step explanation:

8e^3x + 4 = 15

Subtract 4 from each side

8e^3x + 4-4 = 15-4

8e^3x = 11

Divide each side by 8

8/8e^3x = 11/8

e^(3x) = 11/8

Take the natural log of each side

ln(e^(3x)) = ln(11/8)

3x = ln(11/8)

Divide by 3

3x/3 = 1/3 ln(11/8)

x = 1/3 ln(11/8)

x =.106151244

To the nearest thousandth

x = .106

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Jan is 2/3 of Karyn's age. Jan's age 8 years ago is 2/5 of Katyn's age 4 yeats from now. Jan is how many younger than Karyn?

Elden [556K]

Answer:

12 years younger.

Step-by-step explanation:

Let Jan's age be J and Karyn's age be K.

$J= \frac{2}{3} K$

Jan's age 8 years ago is 2/5 of Karyn's age 4 yeaRs from now.

$J-8 = \frac{2}{5} (K+4)$

=> $(\frac{2}{3} - \frac{2}{5} ) K = \frac{8}{5} + 8$

=> 4K = 48 X 3

=> K= 36.

=> J= 24.

So Jan is 12 years younger.

8 0

3 years ago

Where is the hundred thousand place

ozzi

The 6th to the left

4 0

3 years ago

A hat contains four balls. The balls are numbered 2, 4, 4, and 7. One ball is randomly selected and

vfiekz [6]

Answer:

If the sum is 6, a small cone will be ordered.
If the sum is 8 or 9, a medium cone will be ordered.
If the sum is 11, a large cone will be ordered.

Step-by-step explanation:

The table below shows the possible outcomes from drawing two balls. We see the relative frequencies to be ...

6: 4

8: 2

9: 2

11: 4

To make a fair decision, we want the relative frequencies of the decision possibilities to be the same. If we combine sums 8 and 9 to one category (medium cone, for example), then 6, (8 or 9), and 11 will all have the same relative frequency: 4.

The appropriate "fair decision" choice is ...

6: small cone

8 or 9: medium cone

11: large cone

6 0

4 years ago

The sum of the measures of the interior angles of a polygon is 2880°. How many sides does the polygon have?

harina [27]

Let

S------> The sum of the measures of the interior angles of a polygon

n-------> number of sides of a polygon

we know that

The formula to find the sum of the measures of the interior angles of a polygon is equal to

$S=(n-2)*180$ °

in this problem

$S=2880$ °

Solve for n

$S=(n-2)*180\\ \\ n=\frac{S}{180}+2\\ \\ n=\frac{2880}{180}+2\\ \\ n=16+2\\ \\ n=18\ sides$

therefore

the answer is

$18\ sides$

5 0

3 years ago

Read 2 more answers

I ONLY HAVE 10 POINTS SRY. PLS ANSWER RESPECTFULLY AND CORRECTLY FOR BRANLIEST. THX THX THX THX

Solnce55 [7]

Answer:

06.07 Equivalent Expressions

by Dominique

The ending of Sarah 's story

By the end of the day Sarah had found 4 shark teeth . John had found 2 shark teeth , together they had 6 shark teeth. When Sarah and John showed her neighbor the teeth he or she paid Sarah $30 dollars. Sarah and John had split the money so John would have $15 dollars and Sarah would have $15 dollars.

i already did this exact answer with someone else so i just copied my answer from that and placed it on this on

Step-by-step explanation:

Substitution: Two

Use substitution to prove that your two expressions are equivalent.

7(9j+ 6j + 2)

63j + 14 + 42j

63 x 1 + 42 x 1 + 14

63 x 1= 63

42 x 1=42

42 + 63 + 14

42 + 63 = 105

105 + 14 = 119

Part 2: Writing Expressions

Substitution : One

2. Translate the algebraic expression you created in Question 1 to a verbal expression

The product of seven and the sum of the product of nine and some number, two, and the product of six and some number.

Use substitution to prove that your two expressions are equivalent.

7(9j+ 6j + 2)

7( 9 x 1 + 6 x 1+ 2 )

9 x 1= 9

6 x 1= 6

7 ( 9 + 6 + 2 )

9 + 6 = 15

15 + 2 += 17

7 x 17 = 119

Part 1: Writing Expressions

1. Write an expression that looks like Sarah’s expression: 5(2j + 3 + j). Replace the coefficients so that your expression is not equivalent. You may use any number that you choose to replace the coefficients. Be sure to leave the variables the same. For example, 8(3j + 7 + 3j) looks like Sarah’s expression but is not equivalent.

My expression is 7(9j+ 2 + 6j) .

Writing Equivalent Expressions

Sarah’s neighbor offers to pay her $5 for every shark tooth she finds on the beach. After collecting only three shark’s teeth, Sarah decides to share the opportunity with her friend John. Sarah can find shark teeth twice as fast as John, but she can earn even more money with his help.

Sarah can use the expression 5(2j + 3 + j) to represent the amount of money she can earn.

You will now use mathematical properties to create two expressions that are equivalent to the expression you created in Question 1. Make sure you show all steps in your work.

7(9j+ 2 + 6j) = 7(9j+ 6j + 2) = The Commutative Property of Addition.

7(9j+ 2 + 6j) = 63j + 14 + 42j = The Distributive Property

The beginning of Sarah 's story

3 0

3 years ago

Read 2 more answers