What is number 61 and a step by step explaination please?
1/3 ln(x) + ln(2) - ln(3) = 3
Recall that [tex]m\log_b(n)=\log_b(n^m)[/tex], so
ln(x ¹ʹ³) + ln(2) - ln(3) = 3
Condense the left side by using sum and difference properties of logarithms:
[tex]\log_b(m)+\log_b(n)=\log_b(mn)[/tex]
[tex]\log_b(m)-\log_b(n)=\log_b\left(\dfrac mn\right)[/tex]
Then
ln(2/3 x ¹ʹ³) = 3
Take the exponential of both sides; that is, write both sides as powers of the constant e. (I'm using exp(x) = e ˣ so I can write it all in one line.)
exp(ln(2/3 x ¹ʹ³)) = exp(3)
Now exp(ln(x)) = x for all x, so this simplifies to
2/3 x ¹ʹ³ = exp(3)
Now solve for x. Multiply both sides by 3/2 :
3/2 × 2/3 x ¹ʹ³ = 3/2 exp(3)
x ¹ʹ³ = 3/2 exp(3)
Raise both sides to the power of 3:
(x ¹ʹ³)³ = (3/2 exp(3))³
x = 3³/2³ exp(3×3)
x = 27/8 exp(9)
which is the same as
x = 27/8 e ⁹
The table below shows the amount of rainfall in Maryville during each week of April. What was the total amount of rainfall in the month of April?
Week 1: 2 2/3
Week 2: 1/8
Week 3: 1 3/4
Week 4: 1/2
Answer:
Step-by-step explanation:
Just add the fractions after finding the common denominator 3 times 8 = 24
Please check my math and typing for accuracy.
Week 1: 2 2/3 = 8/3 x 8/8 = 64/24
Week 2: 1/8 = 1/8 x 3/3 = 3/24
Week 3: 1 3/4 = 7/4 x 6/6 = 42/24
Week 4: 1/2 = 1/2 x 12/12 = 12/24
= (64+3+42+12)/24
= 121/24 24 times 5 = 120
= 5 1/24
If a car's cost, when new, is
$15,000, the rate of
depreciation is 30%, how
much will the car be worth in
6 years?
Answer:
$27 000
Step-by-step explanation:
15 000*30*6÷100
=$27 000
What is the equation of the line shown in the graph at the right?
A farmer is trying to decide how many acres of land he has planted by
finding the area, A, of his plot. x represents a measuring chain he is
using. If the plot has length (5x – 3) and width (2x + 7), which of the
following is the area in terms of x?
F 10x2 + 41x-21
H 10x2 + 29x - 21
G. 7X2 + 7x + 4
J. x2 - 6x +4
Answer:
H
Step-by-step explanation:
(5x-3) x (2x+7)
10x^2 + 35x - 6x - 21
10x^2 + 29x - 21
1.Charlie buys two circular pizzas.
The first pizza has a 12- The second pizza has a
inch diameter
14-inch diameter.
How much greater, in square inches, is the area of the second pizza than the first pizza?
Round your answer to the nearest tenth
Answer:
Step-by-step explanation:
What is the volume of the square pyramid, in cubic inches?
Which of the following choices shows the proper use of the distributive property?
оооо
-2(6x - y) = -12x + 2y
-2(6x - y) = 12x + 2y
-2(6x - y) = 12x - 2y
-2(6x - y) = -12x - 2y
What’s the answer
Answer:
[tex]-2(6x - y) = -12x +2y[/tex]
Step-by-step explanation:
Required
Which shows distributive property
Distributive property states that:
[tex]a(b + c) = a * b + a * c[/tex]
So, the solution to -2(6x - y) is:
[tex]-2(6x - y)[/tex]
Open bracket
[tex]-2(6x - y) = -2 * 6x -2 *-y[/tex]
[tex]-2(6x - y) = -12x +2y[/tex]
(a) is true
geometry homework!!
A cylinder is shown below.
Answer: 244. 92 cm
Step-by-step explanation:
The surface area formula for a cylinder is written as SA = 2πrh + 2πr^2
The dimensions of the cylinder has a length of 6 cm diameter and a height of 10 cm. Radius is basically half of the diameter, so 3 cm. We use these numbers to substitute into the formula.
SA = 2π(3)(10) + 2π3^2
SA = 2π(30) + 2π(9)
SA = 60π + 18π
SA = 78π
SA = 245.044 cm
244.92 is close enough to 245.004, so 244.92 is the answer.
madyson has 2 vases of flowers. Each vase has 6 flowers. Madyson must divide the flowers equally into three vases. how many flowers will be in each vase?
You toss a coin in the air and it lands on the table. What is the probability that it lands on heads? *
Answer:
Hi! The answer to your question is D. 0.5
Step-by-step explanation:
☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆☆*: .｡..｡.:*☆
☆Brainliest is greatly appreciated!☆
Hope this helps!!!
Stay Safe!!!
- Brooklynn Deka
Which figures can have all of the properties shown below
Answer:
quatrolatiral, square, rectangle
Which expression is equivalent to 5c + 3c?
the correct Number is 8c
38% of what number is 171?
Answer:
450
Step-by-step explanation:
We know that 171 is 38%, since they are trying to find the number which is 100%.
38% = 171
1% = 171 ÷ 38 = 4.5
100% = 4.5 x 100 = 450
A burrito was cut into 6 equal pieces. If Carmen ate 2/6of the burrito, and Chris ate 1/6of the burrito,
how many whole pieces of the burrito are left?
Answer:
3/6 peices are left
Step-by-step explanation:
A graph shows the survey results for a group of students who
were asked how many honors classes they have taken and
how many elective classes:
Class Choices
Number of Elective Classes
0
lo 1 2 3
4
5 6 7 8
9 10 11
Number of Honors Classes
How many elective classes would students likely have taken if
they have taken 12 honors classes? (4 points)
Solve for x given the picture
I need an explanation
Will mark brainliest
Answer:
C. 10
Step-by-step explanation:
all the other answers are negative so the triangle would be impossible to make
Brainiest as promised pls
4) You are making a batch of cookies. Each batch uses 3 cups of flour and will give 7 servings. You
are going to multiply your recipe to offer more servings, so you use 11 cups of flour. How many
servings will you actually be able to offer?
a. 22
b. 25
31
d. 38
C.
rolexing and upsetting. For at that time I had already
Answer:
B is correct
Step-by-step explanation:
CO Use the following coordinate plane to write the ordered pair for each point
Answer:
A. (0,4)
B. ( 0,-3)
C (-1,1)
Step-by-step explanation:
QUESTION 5 of 10: Throughput is the number of units a machine or process can produce in a given time. Cycle time is the time to produce
one unit. If the cycle time of your machine is 35 seconds and it runs 24/7, what is the throughput for a year period?
O a) 901,029
Ob) 969,623
c) 1,180,336
d) 1,173,322
9514 1404 393
Answer:
a) 901,029
Step-by-step explanation:
The production volume for 1 year is ...
1 unit/(35 s) × (3600 s)/(1 h) × (24 h)/(1 day) × (365 day)/(1 year)
= 3600×24×365/35 unit/year = 901,029 unit/year
What is the volume of the cylinder shown? (Use 3.14 for it.)
6.838.92 in.^3
1.413.56 in^3
1.243.44 in^3
11.190.8 in.^3
Step-by-step explanation:
11^2= 121
multiply by pi
121×3.14=379.94
then multiply the height
379.94×18=6,838.92
A circular patio has a radius of 4 yards. The patio is expanded so that the
radius increases by 2 yards. By how many square yards does the area of the
patio increase?
Answer:
20pi or 62.83
Step-by-step explanation:
when r=4
pi r^2
16pi
when r=6
pi r^2
36pi
36pi-16pi=20pi or 62.83
Which linear equation is written in slope-intercept form?
Answer:
Where is the question. and answer choices
Help for 20 points please
Answer:
The Answer is 12 - 15= 129
Step-by-step explanation:
x2−15=129
Step 1: Add 15 to both sides.
x2−15+15=129+15
x2=144
Step 2: Take square root.
x=±√144
x=12
After sitting out of a refrigerator for a while, a turkey at room temperature (69°F) is
placed into an oven. The oven temperature is 300°F. Newton's Law of Heating
explains that the temperature of the turkey will increase proportionally to the
difference between the temperature of the turkey and the temperature of the oven, as
given by the formula below:
T = Ta + (T. – T.)e-kt
Tg = the temperature surrounding the object
To = the initial temperature of the object
t= the time in hours
T = the temperature of the object after t hours
k = decay constant
The turkey reaches the temperature of 127°F after 3 hours. Using this information,
find the value of k, to the nearest thousandth. Use the resulting equation to
determine the Fahrenheit temperature of the turkey, to the nearest degree, after 5
hours.
Enter only the final temperature into the input box.
Answer:157
Step-by-step explanation:
What is 1.827 rounded to the nearest tenth
Answer:
1.8
Step-by-step explanation:
Answer:
1.8
Step-by-step explanation:
decimals go tenth hundredth thousandth ten thousandth hundred thousandth millionth ten millionth and so on
Hurry The mass of a standard hockey puck
must be at least 156 grams. What is
this weight in kilograms
Answer:
.156 kg
Step-by-step explanation:
The conversion from grams to kilograms is kg = g/1000
156/1000 = .156
Help me!!
I’ll return the favour
Answer:
Sin A = 15/17 = 0.8823529411....
Cos A = 8/17 = 0.4705882352...
Tan A = 15/8 = 1.875
Step-by-step explanation:
SOH CAH TOA!!!!
im almost done with this hw. plz help!!! give explanation if you actually know the answer so ik u dont just want points
Answer:
B
Step-by-step explanation:
Elizabeth planted a garden in a 16 foot by 8 foot area. To calculate the square foot area of the garden, she multiplied 16 by 8 and got a product of 128 square feet Which equation could Elizabeth use to check her answer? A) 16 x 8 = 128 B) 128 - 8 = 16 © 128 + 8 = 136 D. 128 - 8 = 120 please help
B 128 divide 8 = 16
took test
Answer:
128 / 8 = 16
Step-by-step explanation:
