Rewrite the following problems using exponent rules. Then, solve using logarithms.
1. 3(0.99)4t = 15
2. 4(1.01)3 + t = 8

Rewrite The Following Problems Using Exponent Rules. Then, Solve Using Logarithms.1. 3(0.99)4t = 152.

Answers

Answer 1

9514 1404 393

Answer:

  1. 3(0.96059601^t) = 15; t = -40.03

  2. 4.121204(1.01^t) = 8; t = 66.66

Step-by-step explanation:

The applicable rules of exponents are ...

  (a^b)^c = a^(bc)

  (a^b)(a^c) = a^(b+c)

The solution for an exponential problem using logarithms is ...

  a·b^x = c   ⇒   log(c/a)/log(b) = x

_____

1. Rewrite: (3)(0.99^4)^t = 15  ⇒  3(0.96059601^t) = 15

Solution: t = log(15/3)/log(0.96059601) ≈ -40.03

__

2. Rewrite: 4(1.01^3)(1.01^t) = 8  ⇒  4.121204(1.01^t) = 8

Solution: t = log(8/4.121204)/log(1.01) ≈ 66.66


Related Questions

Can someone help me with this it’s timed !!!

Answers

Answer:

c

Step-by-step explanation:

Answer:

1. A

2. Missouri Compromise

3. Abolition

Step-by-step explanation:

There are 10 marbles in a bag : 5 red and 5 blue she draws a marble from the bag at random. The marble is red. She put the marble back into the bag. What is the probability that next marble she draws at random is red ?

Answers

Answer:

1/ 2

Step-by-step explanation:

Given that:

Number of marbles, = 10

Number of Red marbles = 5

Number of Blue marbles = 5

Probability, p = required outcome / Total possible

Probability of picking a red marble :

Required outcome = number of red marbles = 5

Total possible outcomes = total number of marbles = 10

Hence,

Probability of picking a red marble, P(picking a red marble) = 5 / 10 = 1/2

Which inequality represents "six times a number is less than negative thirty-nine and three-quarters"?

Answers

Answer:

6*n < - (39 + 3/4)

Step-by-step explanation:

Let's do it in steps:

"Six times a number" can be written as:

6*n

Where n is the "number"

"... is less than negative thirty-nine and three-quarters "

then we have:

6*n < - (39 + 3/4)

This is the inequality we wanted, now we can also solve this for n as:

n < -(39 + 3/4)/6

which pic you choose

Answers

.............that apple do be looking good doe........ : /

Examine the following sequence 1, 4, 9, 16, 25…. Why is 36 the next number in the sequence? Because the pattern is:
a.
Add the next even number
c.
Cube the number of the term, n
b.
Square the number of the term, n
d.
Add 2 + the number of the term, n



Please select the best answer from the choices provided


A
B
C
D

Answers

Answer:36

Step-by-step explanation:it just is

If I played at 2am and for my friend his time 8am so now if it 6pm for me now , what time is it for him? Hint For him will be Am

Answers

Answer:

12am

Step-by-step explanation:

Add 6 hrs to 6pm, you will get 12am

Answer: 12

Step-by-step explanation:

help it is due tomorrow morning​

Answers

1) complementary; angles add up to 90°
2) supplementary; angles add up to 180°
3) neither; angles add up to only 89°
1. is complementary
2. supplementary
3.neither

song I made wonder what yall think of it

Answers

Niceeeee that really good
Good job

Answer: Oop if you put that on spotify i would listen to that on repeattttttt

Find the value of x, 110°, 4x+2, and if you can help with steps that would be great :,)

Answers

Answer:

x = 17

Step-by-step explanation:

The two angles with measures form a linear pair and are supplementary.

The measures of supplementary angles has a sum of 180°.

If you add the two given measures, the sum must equal 180°.

4x + 2 + 110 = 180

4x + 112 = 180

4x = 68

x = 68/4

x = 17

In the figure, all lines intersect at point W.
What is the value of n?

Please help quick

Answers

Answer:

n = 15

Step-by-step explanation:

A straight line equals 180 degrees

Angle SWT is congruent to angle XWV meaning:

SWT (55 degrees) = XWV (55 degrees)

Set up an equation:

3n + 80 + 55 = 180

Combine like terms

3n + 135 = 180

Subtract both sides by 135 to isolate variable n

3n = 45

Divide both sides by 3 to isolate variable n

n = 15

The five-number summary suggests that about 75% of salons in Janesville have fewer than how many stylists employed?

Answers

The 5 - number summary :

Min____ Q1 ___ median ____ Q3 ____ max

7 ______ 9 _____ 12 _______ 15 _____ 18

Answer:

Hence, from the 5 number summary, about 75% of sons have fewer than 15 stylist.

Step-by-step explanation:

Explaining the table :

Minimum number of stylist salons have = 7

Maximum number of stylist = 18

Q1 = first quartile, (25 /100) ;About 25% of salons have fewer Than 9 stylist

Q2 = second quartile or median ; About 50% of salons have fewer Than 12 stylist

Q3 gives the 75th percentile value.

Q3 = third quartile (75/100) ; About 75% of salons have fewer Than 15 stylist

Answer: 15 salons would be your answer

Step-by-step explanation:

khan academy said it was right

Anne solved 5(2x−3)=20x+15 for x by first multiplying 5 and 2x on the left side of the equation. She got the answer x = −95. When she substituted −9/5 into the original equation her answer was incorrect. Explain Anne’s error, and find the correct answer.

Answers

Answer:   x=-3

Step-by-step explanation:

Anne's error is that she only multiplies 5 and 2x on the left side, she needs to multiply 5 and 2x, and also that she needs to multiply 5 and -3.

5(2x−3)=20x+15

5(2x) + 5(-3) = 20x + 15

10x - 15 = 20x + 15

-10x - 15 = 15

-10x = 30

x = -3

simplify and write in exponential form (5⁶÷5⁸)³×5^-3​

Answers

Answer:

Exact form:

1/1953125

Decimal form:

5.12x10^-7

Step-by-step explanation:

Help will mark Brainlest

Answers

I think it’s B have a good day

10 POINTS! I NEED THIS QUESTION PLS! FIND THE AREA!!! THERE IS A SQUARE LEFT SIDE OF THE SQUARE IS 12 INCHES, WHATS THE AREA?

Answers

Answer:

144

Step-by-step explanation:

12x12=144

answer: 144 in

explanation: A= a^2 = 12^2 = 144
or
explanation: 12^2


The point g (2,2) is translated 3units to the right and 4units up what are the coordinates of this resulting point, g?

Answers

Answer:

(5,6)

Step-by-step explanation:

Generally, is the coordinate (x,y) is translated right by a units and up by b units, the resulting coordinate wil be;

g(X, Y)  = (x+a, y+b)

To the right is along the positive x axis while up is along the positive y axis

Given a = 3 and b = 4

g(X,Y) = (2 + 3, 2 + 4)

g(X, Y) = (5, 6)

Hence the resulting coordinate of g is (5,6)

Your task is to determine how much tile is needed to lay tile in the kitchen and each bathroom. Each tile is a square measuring 1 ft by 1 ft: Some tiles may need to be cut in half. Kitchen: 15 ft 8 ft 1st Bathroom 6ft 6 ft 2nd Bathroom 8 ft 8 ft

Answers

Answer:

Kitchen = 120 tiles

Bathroom 1 = 36 tiles

Bathroom 2 = 64 tiles

Step-by-step explanation:

Dimension of kitchen = 15 ft 8 ft

Area of Kitchen = 15 * 8 = 120 ft²

Number of kitchen tiles needed = 120ft² / 1ft² = 120 tiles.

Area of tile = 1 ft by 1 ft = 1* 1 = 1ft²

Dimension of bathroom 1 = 6 ft 6 ft

Area of bathroom 1= 6 * 6 = 36 ft²

Number of bathroom 1 tiles needed = 36ft² / 1ft² = 36 tiles.

Dimension of bathroom 2 = 8 ft 8 ft

Area of bathroom 2 = 8 * 8 = 64 ft²

Number of bathroom 2 tiles needed = 64ft² / 1ft² = 64 tiles.

there are 28 students in a classroom. the ratio girls to boys 4 to 3. write and solve a proportion to find how many boys are there in the classroom? include labels!!!!​

Answers

Total = 28

Girls. Boys.
4. 3

28/4= 7
7 x 3 = 21

ANSWER = 21

Ahmed doubled his savings, then deposited another hundred dollars. Let s represent the amount he originally had in savings. Which shows an expression to represent his current amount and the current value of his account if s = 80? StartFraction s Over 2 EndFraction + 100; when s = 80 the latest balance of Ahmed's savings is $140 2 s + 100; when s = 80 the latest balance of Ahmed's savings is $260 s squared + 80; when s = 80 the latest balance of Ahmed's savings is $6,480 s squared + 100; when s = 80 the latest balance of Ahmed's savings is $6,500

Answers

Answer:

2s + 100; when s = 80 the latest balance of Ahmed's savings is $260

Step-by-step explanation:

s = amount he originally had in savings

doubled his savings, then deposited another hundred dollars

2s + 100

If s = 80

2s + 100

= 2(80) + 100

= 160 + 100

= 260

2s + 100; when s = 80 the latest balance of Ahmed's savings is $260

A clothing store charges a 10% tax on each purchase. If a shopper’s total before tax is $63, how much is the tax? Explain how you got your answer

Answers

Answer:

To calculate the sales tax that is included in a company's receipts, divide the total amount received (for the items that are subject to sales tax) by "1 + the sales tax rate". In other words, if the sales tax rate is 6%, divide the sales taxable receipts by 1.06.

18x+y written using the commutative property of addition

Answers

Answer:

18x+y = y+18x

Step-by-step explanation:

PLEASE HELP!!! :(
Consider the following figure
What is BD? ​

Answers

Answer:

BD = 16

Step-by-step explanation:

32/BD = BD/8

BD² = 256

BD = 16

For each Situation Find the Sample Space


Tossing a coin and spinning a spinner to the right spineer goes up to 5

Answers

Here's link to the answer:

tinyurl.com/wpazsebu

Find the slope using points ( 7,-3) and (11,-4)

Answers

Answer:

1/4

Step-by-step explanation:

Answer:

m = [tex]-\frac{1}{4}[/tex]

Step-by-step explanation:

Use the following equation:

slope (m) = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1 , y_1) = (11 , -4)\\(x_2 , y_2) = (7 , -3)\\[/tex]

Plug in the corresponding numbers into the corresponding variables:

slope (m) = [tex]\frac{-3 - (-4)}{7 - 11} = \frac{-3 + 4}{7 - 11} = \frac{1}{-4} = -\frac{1}{4}[/tex]

[tex]-\frac{1}{4}[/tex] is your answer.

~

Indique la propuesta correcta con respecto a los instrumentos de medida: a) El Voltímetro A.C. Mide valor medio b) El Voltímetro D.C. Mide valor máximo c) El Amperímetro A.C. Mide valor medio d) El Amperímetro A.C. Mide valor eficaz c) El Amperímetro D.C. Se conecta en paralelo

Answers

Answer:

Las propuestas correctas son;

a) Voltímetro de CA Mide el valor medio

La magnitud del voltaje de corriente alterna varía periódicamente con el tiempo, dentro de un rango dado

El voltímetro de CA proporciona la lectura y, por lo tanto, mide el valor medio del voltaje, el voltaje pico o el R.M.S. valor de la tensión

b) El voltímetro de CC mide el valor máximo

Los valores de voltaje de un circuito de corriente de CC se fijan con el tiempo y, por lo tanto, el voltímetro de CC mide los voltajes máximos en el circuito.

c) El amperímetro de CA mide el valor medio

Similar a la medición de voltaje de CA, el amperímetro de CA mide el valor de corriente medio

d) El A.C. mide el valor efectivo

La raíz cuadrada media o R.M.S. valor es el valor medido por un R.M.S. Medidor de A.C.

e) El D.C. se conecta en paralelo

Todos los voltímetros se colocan en paralelo con el circuito desde el que se va a medir el voltaje.

Sin embargo, un amperímetro de CC está conectado en serie

Step-by-step explanation:

It says find the volume of the prism.

Answers

Answer:

the answer is 3 1/8 cubic cm

Step-by-step explanation:

brainliest if correct hope this helps have a blessed day! :)


Order the ANGLES in each triangle from LARGEST to smallest.

Answers

Answer:

the answer to your question is

Step-by-step explanation:

x,z and y

What are the values of x and y? y /35​

Answers

Answer:

the X is 35

Step-by-step explanation:

A clock has a diameter of 16 inches. Which measurement is closest to the area of the clock in square inches? 804.25 in2 50.27 in2 25.13 in2 200.96 in2

Answers

Answer:

200.96 in2

Step-by-step explanation:

Area of a circle = nr²

n = 3.14

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

diameter = 2r

radius = 16 inches / 2 = 8 in

Area = 3.14 x 8² =  200.96 in²

HELP PLEASE! What’s the domain and range?

Answers

Answer:

Domain → (-∞, -1)∪(-1, ∞)

Range (-∞, ∞)

Step-by-step explanation:

Given function is,

[tex]\frac{f(x)}{g(x)}=\frac{x^2+2x-5}{2x+2}[/tex]

This function is not defined when the denominator is zero.

2x + 2 = 0

2x = -2

x = -1

Therefore, x = -1 is not in the domain of this function.

And the domain will be,

(-∞, -1)∪(-1, ∞)

For all values of x (except x = -1) we get some output values (value of [tex]\frac{f(x)}{g(x)}[/tex]).

Therefore, range of the function will be (-∞, ∞).

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