Properties of log:
[tex]log\ ab=log\ a + log\ b[/tex][tex]log\ a/b =log\ a-log\ b[/tex][tex]log\ a^b=b\ log\ a[/tex]Evaluate given using the properties above:
Q1
[tex]ln((xy)^5) = 5ln(xy) = 5(ln x + ln y) = 5\ ln\ x + 5\ ln\ y[/tex]Q2
[tex]ln(\sqrt[7]{t} ) = ln(t^{1/7})=1/7\ ln\ t[/tex]Q3
[tex]ln(\sqrt{x^2}/y^5)=ln(x/y^5)= ln\ x - ln\ y^5 = ln\ x - 5\ ln\ y[/tex]Answer:
[tex]\textsf{1.} \quad 5 \ln x + 5 \ln y[/tex]
[tex]\textsf{2.} \quad \dfrac{1}{7} \ln t[/tex]
[tex]\textsf{3.} \quad \ln x - \dfrac{5}{2}\ln y \;\; \;\;\textsf{or} \;\;\;\; \ln x - 5\ln y[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6 cm}\underline{Natural log laws}\\\\Product law: \;$\ln xy=\ln x + \ln y$\\\\Quotient law: $\ln \left(\dfrac{x}{y}\right) = \ln x - \ln y$\\\\Power law: \;\;\;\;$\ln x^n=n \ln x$\\\end{minipage}}[/tex]
Question 1Apply the power law followed by the product law:
[tex]\begin{aligned}\ln (xy)^5 & = 5 \ln (xy)\\ & = 5\left( \ln x + \ln y \right) \\ & = 5 \ln x + 5 \ln y\end{aligned}[/tex]
Question 2[tex]\textsf{Apply the exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}[/tex]
then apply the power law:
[tex]\begin{aligned}\ln \sqrt[7]{t} & = \ln t^{\frac{1}{7}} \\ & = \dfrac{1}{7} \ln t\end{aligned}[/tex]
Question 3It is not completely clear where the square root sign begins and ends, so I have provided answers for both permutations:
[tex]\begin{aligned}\ln \left(\sqrt{\dfrac{x^2}{y^5}}\right) & = \ln \left(\dfrac{\sqrt{x^2}}{\sqrt{y^5}}\right) \\\\& = \ln \left(\dfrac{x}{y^{\frac{5}{2}}}\right) \\\\&=\ln x - \ln y^{\frac{5}{2}}\\\\&=\ln x - \dfrac{5}{2}\ln y\end{aligned}[/tex]
[tex]\begin{aligned}\ln \left(\dfrac{\sqrt{x^2}}{y^5}\right)& = \ln \left(\dfrac{x}{y^5}\right) \\\\&=\ln x - \ln y^5\\\\&=\ln x - 5\ln y\end{aligned}[/tex]
claire is writing a report about kangaroos. the report must be two full pages. if she can fit 20 lines on each page with about 20 words per line, approximately how many words in all will claires report be?
Answer:
800
Step-by-step explanation:
20 lines per page with 20 words per line means 400 words per page
2 pages means 400 x 2 which is 800 words
9. The sum of 10 and 7 times a number is 59. What is the
number? (Use n as the variable.)
Answer:
7Step-by-step explanation:
Let,
The number be = n
According to the question,
First 7 times of n = 7n
Sum of 10 and the number = 7n + 10
Said that,
The sum of 10 and 7 times of the number is 59.
Therefore,
By the problem ,
=> 7n + 10 = 59
=> 7n = 59 - 10
=> 7n = 49
[tex] = > n = \frac{49}{7} [/tex]
=> n = 7
Hence,
The required number is 7 (Ans)
The midpoint of AB is M(1,-2). If the coordinates of A are (-3, -8), what are the coordinates of B?
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Answer:
B(5, 4)
Step-by-step explanation:
The midpoint formula is ...
M = (A +B)/2
Solving for B gives ...
B = 2M -A
B = 2(1, -2) -(-3, -8) = (2+3, -4+8) = (5, 4)
The coordinates of B are (5, 4).
If you invested $2000 in an account that paid 8% annual interest compounded quarterly, how much would the account be worth in 10 years?
Answer:
4,317.85
Step-by-step explanation:
Answer:
$1600
Step-by-step explanation:
8 = 0.08% Turn the percent to a decimal
2000 / 0.08 = 160 Divide it by 2000
160 * 10 = 1600 Mutiply by 10
Have a good day
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results SampleService Life (hours) 1495500505500 2525515505515 3470480460470 If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control
Answer:
Sample number 3
Step-by-step explanation:
From the given information:
Sample Service life(hours) Total Mean(X)
1 2 3 4
1 495 500 505 500 2000 500
2 525 515 505 515 2060 515
3 470 480 460 470 1880 470
Total = [tex]\text{addition \ of \ numbers \ of \ observations}[/tex]
Mean = [tex]\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}[/tex]
Thus;
[tex]UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480[/tex]
To plot on an X_Bar chart, we have:
Sample Mean (X) UCL LCL
1 500 520 480
5 515 520 480
6 470 520 480
The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.
Determine whether the point (7,4) is on the circle, or inside or outside the circle x^2+y^2=62
Answer:
Outside.
Step-by-step explanation:
7^2 + 4^2 = 62
65 does not equal 62 so outside of the circle.
What is this number in standard form? (5×1,000)+(9×1)+(2×1/10)+(6×1/1,000)
Answer:
5009.206
Step-by-step explanation:
The answer is 5009.206. We see that the first portion of this question asks, "(5×1,000)+(9×1)". 5x1000 is 5000. 9x1 is 9. 5000+9= 5009. The second portion of this question asks for the numbers that go after the decimal. 2x1/10 is 2/10. 6x1/1000 is 6/1000. The decimal place stands for one. So we do .206. If the decimal stands for ones that means in this case the 2 is in the tenths place (like it should be since the question asks for 2/10) and the 6 is in the 1000 place (like it should be since the question asks for 6/1000). We add this up together and our answer is 5009.206. Hope this explanation helps! Happy learning!
-7x-13 >(or equal) 8
Answer:
x ≤-3
Step-by-step explanation:
Which of the following is an equation?
Answer:
B) y/9 = 3
Step-by-step explanation:
What makes an equation is that two things are equal. It consists of two expressions, one on each side of an 'equals' sign.
Only choice B does that
Write the equation of the line in SLOPE- INTERCEPT form:
1. (4, 2); slope 3
2. (3, -1); slope 4
3. (-4,-2), (4,0)
Answer:
Step-by-step explanation:
1) slope = m = 3
(4 , 2) ; x₁ = 4 ; y₁ = 2
y - y₁ = m(x - x₁)
y - 2 = 3(x - 4)
y - 2 = 3x - 4*3
y - 2 = 3x - 12
y = 3x - 12 + 2
y = 3x - 10 {Slope -intercept form: y = mx + b}
3) (-4 , -2) , (4 , 0)
We have to find the slope
[tex]Slope =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\= \frac{0-[-2]}{4-[-4]}\\\\=\frac{0+2}{4+4}\\\\=\frac{2}{8}\\\\=\frac{1}{4}\\[/tex]
m = 1/4 ; (4 , 0)
y - y₁ = m(x - x₁)
[tex]y - 0 = \frac{1}{2}(x - 4)\\\\y =\frac{1}{2}x - 4 *\frac{1}{2}\\\\y =\frac{1}{2}x - 2[/tex]
A rectangular playing field at a scale of 1:1000, 100m
Answer:
0.1
Step-by-step explanation:
1cm:1000cm
100m=10000cm
so if 1cm=1000cm what about 10000cm
=0.1
A triangular prism has faces.
Answer:
5
Step-by-step explanation:
Answer:
The answer above is correct, a triangular prism has 5 faces.
Step-by-step explanation:
Count the faces that it has.
1. What number will make this expression a perfect square trinomial? Show your work. x2 - 6x +
Answer:
.......
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Take half of b (6/2=3)
Square it (3^2=9)
A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at
random. How many possible outcomes are there?
0 3
O 5
0 6
O 14
Answer:
14
Step-by-step explanation:
hope it helps!
The radius of a cylindrical construction pipe is 1.5 ft. If the pipe is 17 ft long, what is the volume?
Use the value 3.14 for π and round your answer to the nearest whole number.
Answer:
120.105 square feet.
Step-by-step explanation:
Given that the radius of a cylindrical construction pipe is 1.5 ft, to determine its volume, given that the pipe is 17 ft long, the following calculation must be performed, knowing that the volume of a cylinder arises from multiplying the number pi by the radius at square of the cylinder, and that result by the height of it:
(3.14 x (1.5^2)) x 17 = X
(3.14 x 2.25) x 17 = X
7.065 x 17 = X
120.105 = X
Thus, the volume of the cylinder is 120.105 square feet.
What is the complementary angle
of 65 degrees
The angle of 25° is the complement of the angle of 65° and the angle of 65° is the complement of the angle of 25°.
Answer:
25°
Step-by-step explanation:
Two angles are complementary if the sum of the angle measures add up to (90) degrees. To find the complementary angle of a given angle, subtract the given angle from (90) degrees, the result will be the complementary angle.
(90) - (65) = (25)
You are surveying students to find out their opinion of the quality of food served in the school cafeteria. Which of the following samples would be random?
Answer:
aint random
Step-by-step explanation:
The sample is not random. For being a random sample opinion of all the students must be taken whether they are eating hot lunch or not.
What is a Random Sample?A random sample is a subset of a statistical population where "each subset member has the same probability of being picked". A random sample is meant to accurately reflect a group of people.
Random sampling is used in science to conduct blinded studies or randomized control testing.
This sample cannot be called a random sample. This is because a "random sample is an unbiased representation of the group and here we have not taken the opinions of the students who don’t eat hot lunch". So this sample can’t be a random one.
Learn more about random sample here:
https://brainly.ph/question/13096146
#SPJ2
What is the absolute value of 2 1/2
Write your answer as a mixed number.
Answer:
it is 2 1/2
Step-by-step explanation:
I hope this helps
Please help! What is the volume? Answer and explanation please! <3 (No links please..)
V = ____ pi inches cubed
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Answer:
562.5π in³
Step-by-step explanation:
The volume of a sphere is given by the formula ...
V = 4/3πr³
where r is the radius, half the diameter.
V = (4/3)π(7.5 in)³ = 562.5π in³
for each of the figures write an absolute value equation to satisfy the given solution set
5 and 17
Answer:
|x-11|=6
hope this helps
Step-by-step explanation:
answer this please thanks
Answer:
4. c
6. e, a
Step-by-step explanation:
Hopefully, it correct
A city has the population of 210,000 people. Suppose that each year the population grows by 7.5%. What will the population be after 13 years?
Answer:
6 5
Step-by-step explanation:
4 5 6 7
A shipment of sugar fills 8 containers. If each container holds 2 1/6 tons of sugar, what is the amount of sugar in the entire shipment?
Answer:
17 1/3 tons of suger
Step-by-step explanation:
2 1/6 * 8 = 17 2/6 or 17 1/3
What is the volume, in cubic centimeters, of a cube with an edge length of 15 centimeters?
Answer:
3375cm
Step-by-step explanation:
because it is asking for volume it is cubed
wich 15 x 15 x 15 3 times equals volume of cube hope that makes sense
Solve the quadratic equation 2x2 = 5x + 9. <33 please besties
Answer:x=-1
Step-by-step explanation:
Find the surface area of the regular pyramid.
help TvT
HELP PLEASE 40 Points both questions please
6. It's B. x2+y2=25
9. (x + 3)² + (y – 2)² = 25
Hope this helps since this is solved by a 10-year old girl, me.
An item originally costs $49.95 and is on sale for 33% off the original price. The sales tax is 5.75%. Find the cost of the item.
Answer:
$35.39
Step-by-step explanation:
PLEASE HELP
A town has a population of 40,000 persons.
There are 6000 school-age children in the
town. What is the ratio of the school children
to the total population?
And please add the formula or how you did it
Answer:
3:20
Step-by-step explanation:
6000:40,000
find HCF (2000)
divide both sides by 2000
3:20
#3 please Question Is in the photo above please help me extra points will be given
Answer:
the answer to the problem is d