Answer:
x = 10
Step-by-step explanation:
Combining the logarithms, you have ...
ln(20·5) = ln(x²)
100 = x² . . . . . take the antilogs
10 = x . . . . . . . take the positive square root
_____
Alternate solution
ln(2·2·5) +ln(5) = 2·ln(x) . . . . . . . factor 20
2ln(2) +ln(5) +ln(5) = 2·ln(x) . . . . rearrange ln(20)
ln(2) +ln(5) = ln(x) . . . . . . . . . . . . divide by 2
ln(10) = ln(x) . . . . . . . . . . . . . . . . combine logs on the left
10 = x
_____
These solutions make use of the rules of logarithms ...
ln(ab) = ln(a) +ln(b)
ln(a²) = 2·ln(a) . . . . . same as the first rule for a=b
find the slope of the line passing through the points (6,9) and (6, -1)
Answer:
Undefined
Step-by-step explanation:
M=undefined
Slope = y2-y1 /x2- x1
=9 -(-1). / 6-6
= 10/0 = infinity ; undefined
b. David and Andrew are traveling to a Mathematics conference. David travels 110 miles in the same time that Andrew travels 140 miles. Andrew travels 15 miles per hour faster than David. Find the average rate of each person.
Answer:
Its 14 and 19
Step-by-step explanation:
Answer:
b. About 15 miles
Step-by-step explanation:
got it right on edge
Find the value of x.
Answer:
x = 61
Step-by-step explanation:
x and 29 are complementary angles so they add to 90 degrees
x+29 = 90
Subtract 29 from each side
x+29-29 = 90-29
x = 61
Answer:
61 degrees = x
Step-by-step explanation:
Since angle measures x and 29 are complementary angles, subtract 29 from 90 degrees.
90 - 29 = 61 degrees is the value of x
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification: freshmen 83, sophomores 68, juniors 85, and seniors 64. The school superintendent is interested in determine whether there has been a significant change in the classification between last school year and this school year.
Deteremine the correct null hypothesis for this problem
Find the given attachment
in the year 2005 a company made $6.6 million in profit for each consecutive year after that their profit increase by 9% how much would a companies profit be in the year 2009 to the nearest 10th of $1 million
Answer:
$9.3 million
Step-by-step explanation:
Given that the company profit increases by 9% yearly from 2005.
Using the exponential growth formula;
A = P(1+r)^(t) .....1
Where;
A = final amount/value of profit
P = initial amount/value = $6.6 million
r = growth rate yearly = 9% = 0.09
t = time of growth in years = 2009 - 2005 = 4 years
Substituting the values;
A = 6.6(1+0.09)^(4)
A = 6.6(1.09)^(4)
A = 9.3164386 million
A = $9.3 million
The companies profit in the year 2009 to the nearest 10th of $1 million is $9.3 million
A cylindrical tank is half-full of oil. The cylinder has base radius of 100cm.The height of the cylinder is 250cm. 1 litre =1000cm cubed
How many litres of oil are in the tank? Round your answer to the nearest litre.
Answer:
Step-by-step explanation:
area of a cylinder=. V=πx r^2xh
so...
πx100^2x125=3926990.817 (the height is 125 because only half of it has oil)
3926990.817/1000=3927litres
An above-ground swimming pool is 5 feet long, 4 feet wide, and 3 feet deep and is shaped like a rectangular prism. A rectangular prism has a length of 5 feet, height of 3 feet, and width of feet. If you use a net to find the amount of material used to make the pool, what faces are included in the calculation?
Answer:
the faces representing the sides and bottom of the pool are included
Step-by-step explanation:
Obviously, there is no pool material covering the top of the pool. Rather, it is "an open-top box", so the area of the faces of the box does not include the area of the top. The five faces other than the top face are included.
Answer:
First answer is 1
Second is 2
Third is 2
What is the y-value when x equals - 12?
y = -200 - 6(x)
Enter the correct answer
Answer:
y = -6x - 200
Step-by-step explanation:
Batman, who is having a slow year for crime, has resorted to saving cats from very tall buildings. Our fearless 6 foot tall hero is 40 feet from the the Petsmart building the cat was trying to break in to, in order to get his paws on the pumpkin spice cat nip. Batman sights the top of the building at a 30° angle, how high is the building?
Answer:
29.094 feet tall
Step-by-step explanation:
tan(30) = [tex]\frac{x}{40}[/tex]
so tan is opposite over adjacent which means that we should be able to solve for the opposite as we have the angle (30) and the distance from Batman to to building, which is (40 feet), with these numbers you will do, tan(30) = [tex]\frac{x}{40}[/tex] and from that you will solve for x, and from x you add the 6 foot of batmans height
Sherri hikes on the Pacific Coast trail. She plans to hike 3.72 miles. If she hikes at an average speed of 1.2 miles per hour, how long will she hike?
Answer:
3.1 hours
Step-by-step explanation:
Average Speed=Distance Traveled ÷ Time Taken
Sherri plans to hike 3.72 miles at an average speed of 1.2 miles per hour.
Average Speed=1.2 miles per hour.Distance =3.72 milesTherefore:
1.2 miles per hour=3.72 miles ÷ Time
1.2 miles per hour X Time=3.72 miles
Time = 3.72 ÷ 1.2 hours
Time taken by Sherri=3.1 hours
Sherri will hike for 3.1 hours.
If you make $ 18,720 a year what is your monthly wage ?
Answer:
1,560.00 per month
Answer:
1,560
18,720/12 months in a year = 1,560 per month
hope this helps
Step-by-step explanation:
What is the median of the following numbers?
8,10,8,5,4,7,5,10,8
Answer:
the answer is 4
Step-by-step explanation:
Answer:
the median is 7
Step-by-step explanation:
to find the median you need to find the highest number in value and then find the lowest number in value. The median is the middle value.
The amplitude of y= – sin is
b 0
C2
d 1
Answer:
d. 1
Step-by-step explanation:
The amplitude of such a function is the magnitude of the coefficient of the sine function.
|-1| = 1 . . . . the amplitude . . . matches choice D
5lb 7oz -11oz need help quick
Answer:
76 ounces
Step-by-step explanation:
I'm assuming you meant:
5lb+7oz-11oz=
16 ounces in a pound
5lb+7oz-11oz=
80+7-11=
87-11=
76 ounces
The mean temperature for the first 7 days in January was 4 °C.
The temperature on the 8th day was 4 °C.
What is the mean temperature for the first 8 days in January?
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
Answer:
Answer:
4 degrees Celsius
Step-by-step explanation:
Since the mean is (total/amount), we can remake this to get That mean*amount=total. For the first 7 days, 4*7=28 for our total, and add that to the 8th day to get 32 for our total. 32/8=4 for our mean for the first 8 days of january
Please Help With problem 1
Answer:
60
Step-by-step explanation:
To find the volume of a rectangular prism you need to use the formula Base times height or in this case length times-width times height so multiply 5 x 4 x 3 to get your answer
What does X equal?? Please help me out!!
A student used f(x) = 5.00(1.012)* to show how the balance in a savings account will
increase over time. What does the 5.00 represent?
Answer:
the initial balance
Step-by-step explanation:
5.00 is the value of f(0). It is the balance before any time has elapsed, the initial balance.
Add. Enter your answer in scientific notation.
2.25 x
108 +3.50 x 108 +2.25 x 108 =
Answer:
8×10⁸
Step-by-step explanation:
2.25×10⁸ +3.50×10⁸ +2.25×10⁸ = (2.25 +3.50 +2.25)×10⁸ = 8×10⁸
__
Your calculator can do this for you and display the result in scientific notation.
If you were to roll a six-sided number cube 60 times, about how many times would you expect the number cube to land on a 1?
Answer:
10
Step-by-step explanation:
Probability is the likeliness of happening of an event.
Probability of any event A can be be defined by
no. of time event A happens/ total no. all possible event that can occur
___________________________________
In the problem
probability of occurrence of 1 on rolling a cube is needed.
A cube has six sides with one written on one sides and rest has 2,3,4,5,6.
No of times 1 can occur on rolling the dice once will be = 1
Since there six sides and and each has different number (1,2,3,4,5,6)
There is chance that each of the number can come.
Thus, total no possible outcome = 6
Probability of occurrence of 1 = No of times 1 occurs on rolling the dice /total no possible outcome = 1/6
_____________________________________________
If dice is rolled 1 time there is 1/6 chance that 1 will be the outcome.
If dice is rolled 1*60 time then there is 1/6*60= 10 chance that 1 will be the outcome
Thus , If you were to roll a six-sided number cube 60 times, about 10 times it is expected that the number cube to land on a 1.
Answer:
20
Step-by-step explanation:
A fenced enclosure consists of a rectangle (length L and width 2R) attached to a semicircle with a radius R as pictured below. Note: there is fencing between the rectangular and semi-circular portions. The enclosure is to be built to have a total area (the entire shaded region), A, of 2000 ft2. The cost of the fence is $20/ft for curved sections and $30/ft for straight sections. Analytically (show all of your steps using algebra and calculus in the write up), find the minimum cost to build the fence and the dimensions of the enclosure. Show all equations that you derive and use. This part should be done entirely in the write-up: no coding. It is fine to do this by hand and include a high-resolution picture in the writeup rather than using Equation Editor. Hint: you will need to use two equations in order to find the cost as a function of only R or L. Construct a plot to graphically determine the values of R and L (x-axis) that minimize the total cost (y-axis) of the fence. Using the MIN function, determine the R and L that minimize cost and what that cost is Do your answers in A, B and C all agree? Why or why not?
Answer:
A. $ 6053.44
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
Step-by-step explanation:
A. The area A of the enclosure equals, A = 2RL + πR²/2.
The total cost C = 20 × length of curved section + 30 × length of straight section
C = 20πR + 30[2(L + 2R)]
= 20πR + 60L + 120R
Making L subject of the formula from A,
L = A/2R - πR/4
Substituting L into C, we have
C = 20πR + 60(A/2R - πR/4) + 120R
= 20πR + 30A/R - 15πR + 120R
= 5πR + 30A/R + 120R
We now differentiate C with respect to R to find the value of R for minimum cost
dC/dR = 5π - 60A/R² +120
Equating dC/dR to zero, we have
5π - 60A/R² + 120 = 0
So, R = ±√[60A/(5π + 120)]
substituting A = 2000 ft²
R = ±√[60 × 2000/(5π + 120)] = ±29.74 ft
We take the positive answer, R = 29.74 ft since R cannot be negative.
To determine if this is a minimum point, we differentiate dC/dR with respect to R.
So d²C/dR² = 120A/R³
Since d²C/dR² = 120A/R³ > 0 for positive R, it is a minimum point.
Substituting the value of R into C we have
C = 5πR + 30A/R + 120R
= 5π(29.74) + 30 × 2000/29.74 + 120(29.74)
= 467.155 + 2017.485 + 3568.8
= $ 6053.44
and L = A/2R - πR/4
= 2000/2(29.74) - π(29.74)/4
= 33.625 - 23.356
= 10.269
≅ 10.27 ft
B. From the graph, R = 21.027 ft and C = $ 5700.005, L = 31.043 ft
The values in A and B do not all agree. This could be due to error in approximations. Their values are close though.
PLEASE HELP me with the magic square
Fill in each slot in the square with variables a, b, c, d, and e, in order from left-to-right, top-to-bottom. In a magic square, the sums across rows, columns, and diagonals all add up to the same number called the magic sum.
The magic sum is -3.9, since "diagonal 2" (bottom left to top right) has all the information we need:
3 + (-1.3) + (-5.6) = -3.9
Use this to find the remaining elements
row 1:a + b + (-5.6) = -3.9
row 2:c + (-1.3) + d = -3.9
row 3:3 + e + 0.02 = -3.9
column 1:a + c + 3 = -3.9
column 2:b + (-1.3) + e = -3.9
column 3:(-5.6) + d + 0.02 = -3.9
diagonal 1 (top left to bottom right):a + (-1.3) + 0.02 = -3.9
You will find
a = -2.62
b = 4.32
c = -4.28
d = 1.68
e = -6.92
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
x > 5
Step-by-step explanation:
Subtract 7 from both sides, like so:
x + 7 > 12
- 7 - 7
________
x > 5
What is the volume, in cubic cm, of a rectangular prism with a height of 19cm, a
width of 16cm, and a length of 8cm?
Answer: 2432
19 x 16 x 8 = 2432
Answer: 2,432 cm³
Step-by-step explanation: To find the volume of a rectangular prism or a prism whose base is a rectangle, we use the formula below.
Volume = length × width × height
Since the rectangular prism has a length of 8 centimeters, a width of 16 centimeters, and a height of 19 centimeters,
we can plug this information into the formula to get
(8 cm)(16 cm)(19 cm).
This gives us 2,432 cm³.
So the volume is 2,432 cm³.
Jamie spent $12 dollars a day on food for 6 days. What was Jamie’s overall change in her bank account for food over the 6days?
Answer:
-72
Step-by-step explanation:
12 * 6 = 72
Jaime spent 72 dollars for the 12 days
It went down because the money was spent
-72
How to solve #2 if you don’t know any of the side lengths?? (We’re learning about Pythagorean Theorem)
Answer:
Applying Pythagorean theorem in right triangle with c is longest side and a, b are the other sides:
=> c^2 = a^2 + b^2
=> a^2 = c^2 - b^2
=> b^2 = c^2 - a^2
Hope this helps!
:)
Answer:
c² = a² + b²
a² = c² - b²
b² = c² - a²
Which statement is true? Question 10 options: A) |13| = – 13 B) – |13| = 13 C) |–13| = 13 D) – |–13| = 13
Answer:
The answer is C
Step-by-step explanation:
Every negative or positive number in the modulus while be positive at the end
The true statement is C) |–13| = 13, indicating that the absolute value of -13 is 13, representing the distance of -13 from zero on the number line.
How to Solve Absolute Value Equations?The true statement is: C) |–13| = 13, as explained below.
The expression |–13| represents the absolute value of -13, which is the distance of -13 from zero on the number line, always resulting in a non-negative value.
|–13| = 13, because the absolute value of -13 is 13, meaning it is 13 units away from zero on the number line. So, the correct option is C) |–13| = 13.
Learn more about Absolute Value on:
https://brainly.com/question/12928519
#SPJ6
Please help.
Best answer will get brainliest.
Answer:
59.1 for the mean
Step-by-step explanation:
You add all the numbers together and divde it by the amount of numbers there are.
Answer:
Mean= 59.1
Median= 58
Range= 11
Step-by-step explanation:
Mean= Total data/Number of given datas
= 60+58+54+56+63+65+62+59+56+58/10
Mean = 591/10= 59.1
Median= Middle value
= 65, 63, 62, 60, 59, 58, 58, 56, 56, 54
Median= 58
Range= Highest value- Lowest value
= 65-54
Range= 11
a cartographer used a scale of 1 inch :300 meters for the heights of different mountains if the actual height of one of those mountains is 3700 meters high. what is the height on the map?
Answer:
[tex]12\frac{1}{3}[/tex] inches
Step-by-step explanation:
So to go from 300 to 3700 you have to multiply by [tex]12\frac{1}{3}[/tex]
what is the number that has the same value as l6l
Answer:6
Step-by-step explanation: Moving two bars to the edge of 6 will result in 6.