According to Natural logarithm Rules, ln(400) is same as [tex]2( ln 4 + ln 5)[/tex].
What does natural log mean?A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Typically, the natural logarithm of x is denoted by the symbols ln x, loge x, or, if the base e is implicit, just log x.Euler's Number, e, came before logarithms.One of the most significant mathematical constants, e, is an irrational number that is intimately connected to growth and pace of changeNatural logarithm Rules :
ln (mn) = ln m + ln nln (m/n) = ln m - ln nln [tex]m^{n}[/tex]= n ln mln a = (log a) / (log e)ln e = 1ln 1 = 0so we can rewrite the expression :
ln(400) = ln([tex]4^{2} . 5^{2}[/tex])= ln [tex]4^{2} + ln 5^2[/tex]= [tex]2( ln 4 + ln 5)[/tex]
To learn more about Natural logarithm refer,
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Working alone it takes mark 7 hours to mop the whole house it takes sue 9 determine to the nearest hundredth of the hour how long it will take then to mop the house together
Answer:
3.9375 hours
Step-by-step explanation:
Working alone it takes mark 7 hours to mop the whole house it takes sue 9 determine to the nearest hundredth of the hour how long it will take then to mop the house together
This is calculated as
1/Time it would take them to work together = 1/ Number of hours Mark mopped + 1/ Number of hours Sue mopped
= 1/T = 1/7 + 1/9
Lowest common denominator = 63
1/T = 9 + 7/63
1/T = 16/63
T = 63/16
T = 3.9375 hours
Santosh spent $200, before tax, on a DVD player and DVDs. The player cost $120, new DVDs cost $15 and used DVDs cost $5. Santosh purchased the same number of new and uses DVDs. Write and solve an equation to find the number of each type of DVD Santosh purchased.
Answer:
Santosh purchased 4 new and 4 used DVDs.
Step-by-step explanation:
From the information given, as you know that Santosh spent $200 and that the DVD player cost $120, you can say that the new and used DVDs cost $80, which can be expressed as:
15x+5y=80, where:
x refers to the number of new DVDs
y refers to the number of used DVDs
Now, as the statement indicates that Santosh purchased the same number of new and used DVDs, this means that x is equal to y and you can replace y with x and solve for x:
15x+5x=80
20x=80
x=80/20
x=4
According to this, the answer is that Santosh purchased 4 new and 4 used DVDs.
Lily wants to ride her bicycle 43 miles this week. She has already ridden 16 miles. If she rides for 6 more days, what is the average number of miles she would have to ride each day to meet her goal?
Answer:
43-16=miles left to go. divide that by the 6 days left.
43-16= 27 miles.
27÷6= 4.5 miles per day
Answer:
4 1/2 miles
Step-by-step explanation:
43 - 16 = 27 miles remaining
27/6 = 4 3/6 or 4 1/2
Which set of angle measures CANNOT be the angle measures of a triangle?
A. 59,60,61
B. 60,60,61
C. 1,1,178
D. 13.9,16.1,150
Answer:
Mmm either B or D one of those two
How did 15/24 become an equivalent fraction of 5/8?
Answer:
You divide 15 by 3, and divide 24 by 3
Step-by-step explanation:
15/3 = 5
24/3=8
5/8
Mrs. Tirado picked 5/6 pounds of lettuce from her garden. Mrs. Rampulla picked 2/3 less pounds than Mrs. Tirado. How much lettuce did they pick altogether?
Step-by-step explanation:
Total amount of lettuce = x pounds
Mrs. Tirado picked 5/6 pounds of lettuce from her garden.
5 / 6 * Total amount = 5/6 x
Mrs. Rampulla picked 2/3 less pounds than Mrs. Tirado.
Mrs. Rampulla = 2/3 (Mrs. Tirado) = 2/3 (5/6 x)
Mrs. Rampulla = 5/9 x
How much lettuce did they pick altogether?
Mrs. Rampulla + Mrs. Tirado
5/9 x + 5/6 x
(25/18) x pounds
A)The function has two x-intercepts
B)The y-Intercept is at (0,7)
C)The maximum value is 1
D)The minimum value is 1
E) The range includes all real numbers
In August, James begins school shopping for his triplet daughters. One day, he bought 10 pairs of socks for $2.50 each and 3 pairs of shoes for d dollars each. He spent a total of $135.97. Write and solve an equation to find the cost of one pair of shoes.
Let ___ =
Equation:
Solution:
Answer:
2.50*10 350+d
Step-by-step explanation:
thats the answer up belowDescribe the translation that maps ABCD onto A’B’C’D’
Of a total of 422 indigenous and immigrant languages spoken in the united states, 10 more spoken languages are indigenous than are immigrant. How many indigenous languages and how many immigrant languages are spoken in the united states?
Answer: 63
Step-by-step explanation: On Edge!!!!!!!!!
help asap im giving 27 points, dont guess and please help I tried getting help and everyones dissing me
Answer:
Q= 1,3
P= -3,0
R= 0,-1
Step-by-step explanation:
I have done this before
Answer:
P'= (-3,0) Q'= (1,3) R'= (0,-1)
Step-by-step explanation:
I moved each dot 4 units left and 2 units down. If I'm right brainliest pls, if not then flag the answer.
Combine like terms for the following expression:
-3x +14 - 11+ 11x
what is the lcm of 6 and 8
Answer:
The LCM, or least common multiple, of 6 and 8 is 24.
Answer: 2
Step-by-step explanation:
First you find the multiples of 6 and 8 then you do this.
2x3
2x2x2x2x2x4
Then you circle the 2’s and so the lcm on 6 of six and 8 is 2.
The area of a rectangle is 10 square inches. If the length of the rectangle is 3 more
than the width, find the length and width.
Answer:
its 2 and 5 ma brotha
Step-by-step explanation:
see 2 + 3 is 5
2 * 5 = 10
if you need anymore help.....
I GOTCHU
I NEED THE ANSWER please
Answer:
[tex]1 \frac{2}{5} [/tex]
Step-by-step explanation:
[tex]4 - 2 \frac{3}{5} [/tex]
[tex] = 4 - \frac{13}{5} [/tex]
[tex] = \frac{20 - 13}{5} [/tex]
[tex] = \frac{7}{5} [/tex]
[tex] = 1 \frac{2}{5} [/tex]
it takes mike 18 minute to read 4 pages of a book how long does it take for him to finish read a 30 pages?
Answer:
135 minutes / "2 hr. and 15 minutes
Step-by-step explanation:
PLEASE SHOW YOUR WORK FAM, I NEED HELP
What is x + 25 = 76?
Is it...
A. 51
B. 101
C. 41
Or D. 52
Answer:
76-25= 51
Step-by-step explanation:
Answer:
A. 51
Step-by-step explanation:
Subtract 25 from each side to isolate the variable
it would look like this:
x + 25 = 76
-25 -25
x = 51
hopefully that helps!
-3( 3y - 5 ) + 7( 11 + 6y )
Answer:
= 33y+92
Step-by-step explanation:
i hope this helps :)
Answer: 33y+92 Hope this help :)
solve for x
similar triangles advanced
Answer:
x = 2.57
Step-by-step explanation:
6/x = 7/3
7x = 18
x = 2.57
check:
if x = 2.57
then:
2.57/6 = 3/7
0.4283 = 0.4283
that checks as correct
Find the value of x that makes Triangle DEF~ triangle XYZ.
Answer:
x = 4
Step-by-step explanation:
DE / XY = EF / YZ
5 / 10 = 2x-1 / 14
cross-multiply:
10(2x-1) = 14(5)
20x - 10 = 70
20x = 80
x = 4
The ratio of their corresponding side will remain constant. Then the value of x is 4.
What is the triangle?Triangle is a polygon that has three sides and three angles. The sum of the angle of the triangle is 180 degrees.
The two triangles are ΔDEF and ΔXYZ.
It is given that the ΔDEF and ΔXYZ are similar.
Then the ratio of their corresponding side will remain constant. That is
[tex]\rm \dfrac{5}{10} = \dfrac{2x -1 }{14} =\dfrac{11}{5x +2 }[/tex]
From the first two, we have
[tex]\rm \dfrac{5}{10} = \dfrac{2x -1 }{14}\\[/tex]
On simplifying, we have the value of x
x = 4
More about the triangle link is given below.
https://brainly.com/question/25813512
Frank made cookies for his class. He gave away half of them in his first period class, but then his mom dropped off 12 more cookies. If he now has 32 cookies, how many did he start with?
Answer:
Work backwards to solve this problem.
If he ends with 32 cookies, then subtract 12. That gives 20 cookies. 20*2 is 40, so now he has 40 cookies.
Solve for x
-3/4(x+2)=6
X=?
Answer:
-10
Step-by-step explanation:
Can someone help me
the first one
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May someone please show the full steps please! I will mark brainlist. I’m having a hard time understanding this.
Answer:
x=12 y=6 m(ABC)=102 m(BCD)=78 m(DAB)=78
Step-by-step explanation:
alright mate so lets start with the properties of parallelogram:
Opposite angles are equal Sum of any two adjacent angles is 180degree(there are more but we will use those here)
so lets start with 1st property for help:m(BCD) is opposite angle for m(DAB) so those equations should be equal each other and this will give us a hint
[tex]6x+y=4x+5y\\2x=4y\\x=2y[/tex] i just changed the places of x to be in one place and s same for y then divided both sides by 2
Now lets use the 2nd property (sum of two adjacent angles is 180)m(ABC) is adjacent to m(BCD) so
[tex](7x+3y)+(4x+5y)=180[/tex] add x to x and y to y it will be
[tex]11x+8y=180\\[/tex]
Now we going to use the first one x=2y in this equation so we can deal with one variablereplace x with 2y so 11x will be 22y
[tex]22y+8y=180\\30y=180\\y=6[/tex] added the y to y and then divided both sides by 30
[tex]x=2y \\x=2*6=12[/tex]
now we got x and y
then lets start to substitute every x and y in the equations
[tex]7x+3y\\7*12+3*6=102\\[/tex] [tex]4x+5y\\4*12+5*6=78[/tex]3.[tex]6x+y\\6*12+6=78[/tex]
now we got everthing hope i helped you sorry also for being late it toook alot to type it so you can understand
Race organizers want to survey the participating runners on the difficulty of the running course. Which of the following most effectively uses cluster sampling?
Separate the runners into men and women, then randomly select 20 men and 20 women.
Organize the runners into groups (elite runners, fast runners, moderate runners, and walkers). Randomly select a group, and survey all the runners in that group.
Put the same number of marbles as runners into a bag, with 20 of the marbles being red. Have each runner select a marble from a bag at the finish line. If they choose a red marble, they take the survey.
Place the runners into groups based on the seconds part of their finishing time (0:00–0:05, 0:06–0:10, etc.). Randomly select 2 of these groups, and survey every runner within the chosen groups.
Answer: Place the runners into groups based on the seconds part of their finishing time (0:00–0:05, 0:06–0:10, etc.). Randomly select 2 of these groups, and survey every runner within the chosen groups.
Step-by-step explanation: Just got it right on Edge
Two angles in a triangle measure 102° and 670. What is the measure of the third angle?
0 110
0789
1139
O 169°
Step-by-step explanation:
step 1. wow! 670° I think you mean 67°
step 2. the 3 internal angles of a triangle add up to 180°. let x be the third angle
step 3. x + 102 + 67 = 180
step 4. x + 169 = 180
step 5. x = 11°.
Please someone help ASAP
What value of x satisfies the equation below?
[tex]\frac{-2x - 6}{5} = 4[/tex]
Answer: -13
Step-by-step explanation:
1. Isolate x: move 5 to the otherside
=> -2x-6=4*5 => -2x-6=20
2. Move 6 to the otherside: -2x=20+6 => -2x=26
3. Divide both sides by -2
=> x=26/-2 => x=-13
Have a nice day! :D
.........Help pls!!!!!!
Answer:
median is 75. range is 50 to 95.
Step-by-step explanation:
help me with this please
Answer:
Step-by-step explanation:
if 45+47=t and t=45+47 t would equal 92 in both
45+47<t than t<45+47
so basically its saying 92<t (92is less than t) and t<92 (t is greater than 92)
he is not right. When you have an equation like that the answer is 92. Its not going to be greater or less than 92. It is 92. It should be t=92
hope that masks some kind of sense. It after 1am here so I apologize if it doesn't sound right...