Answers
Answer:
i) Using log law: [tex]\log_aa=1[/tex]
[tex]\implies \log_55+1=1+1=2[/tex]
ii) [tex]\log \left(\dfrac{15}{8}\right)+4 \log 2-\log 3[/tex]
Using log law [tex]a \log b=\log b^a[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 2^4-\log 3[/tex]
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log 16-\log 3[/tex]
Using log law [tex]\log a-\log b=\log (\frac{a}{b})[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\right)+\log\left(\dfrac{16}{3}\right)[/tex]
Using log law [tex]\log a+\log b=\log(ab)[/tex]:
[tex]\implies \log \left(\dfrac{15}{8}\cdot \dfrac{16}{3}\right)[/tex]
[tex]\implies \log 10[/tex]
Using log law: [tex]\log_aa=1[/tex]
[tex]\implies \log_{10} 10=1[/tex]
iii) Take log of base 10:
[tex]\log_{10}(\sqrt{8.357}\times0.895^2)[/tex]
[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]
Log tables
The characteristic of the logarithm of a number is the exponent of 10 in its scientific notation.
The mantissa is found using the log tables and is always prefixed by a decimal point.
The row is the first two non-zero digits of the number, and the column is the 3rd digit of the number
Use the log tables to find [tex]\log_{10}(8.357)[/tex]:
8.357 = 8.357 × 10⁰
⇒ characteristic = 0
log table: row 83, column 5 ⇒ mantissa 9217
(as there is a 4th digit) Mean difference 7 = 4
mantissa + mean difference = 9217 + 4 = 9221 ⇒ 0.9221
characteristic + mantissa = 0 + 0.9221 = 0.9221
Therefore, [tex]\log_{10}(8.357)=0.9221[/tex]
Use the log tables to find [tex]\log_{10}(0.895)[/tex]:
[tex]0.895 = 8.95\times 10^{-1}[/tex]
⇒ characteristic = -1
log table: row 89, column 5 ⇒ mantissa 9518⇒ 0.9518
characteristic + mantissa = -1 + 0.9518= -0.0482
Therefore, [tex]\log_{10}(0.895)=-0.0482[/tex]
Therefore,
[tex]\implies \dfrac12\log_{10}(8.357)+2\log_{10}(0.895)[/tex]
[tex]\implies \dfrac12 \cdot 0.9221+2\cdot-0.0482[/tex]
[tex]\implies 0.36465[/tex]
Therefore,
[tex]\log_{10}(\sqrt{8.357}\times0.895^2)=0.36465[/tex]
Using [tex]\log_ab=c \implies a^c=b[/tex]
[tex]\implies \sqrt{8.357}\times0.895^2=10^{0.36465}[/tex]
[tex]\implies \sqrt{8.357}\times0.895^2=2.3155[/tex]
Related Questions
What fractions are less than 5/6
Answers
Answer:
4/6 and lower.
Step-by-step explanation:
Step-by-step explanation: The fraction with numerator as 16/3 and denominator 8 becomes 2/3 which is less than 5/6.
Please help with math
domain and range of a linear function that models a real world situation
Answers
The domain of the function is the amount of fuel in the airplane's tank,
The set of values of the domain is all set of real numbers from 0 to 200The range of the function is the weight of the airplane, and the set of values is all set of real numbers from 3000 to 4400How to determine the domain and the rangeThe weight of the plane as a function of the amount of fuel is given as:
W=7F + 3000
The plane can take up to 200 gallons of fuel.
This means that, the domain of the function is the amount of fuel in the airplane's tank, and the set of values is all set of real numbers from 0 to 200
When F = 0, we have:
W = 7*0 + 3000
W = 3000
When F = 200, we have:
W = 7*200 + 3000
W = 4400
This means that, the range of the function is the weight of the airplane, and the set of values is all set of real numbers from 3000 to 4400
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What is the value of 2 in 304.72 in decimal form?
Answers
Answer: 0.02
Step-by-step explanation: hundreds is 0.0 and its 2 so it would be 0.02
Using place value chart value of [tex]2[/tex] in the [tex]304.72[/tex] is quals to [tex]0.02[/tex] (decimal form).
What is place value?
" Place value is defined as the value represented by each digit of a number on the basis of its position on a number."
According to the question,
Given number ,
[tex]304.72[/tex]
Place value of all digits in [tex]304.72[/tex]
Place value of [tex]4 = ones[/tex]
Place value of [tex]0 = tens[/tex]
Place value of [tex]3= hundreds[/tex]
Place value of [tex]7= tenth[/tex]
Place value of [tex]2 = hundredth[/tex]
[tex]= \frac{2}{100}[/tex]
[tex]=0.02[/tex] (decimal form)
Hence, value of [tex]2[/tex] in the [tex]304.72[/tex] is quals to [tex]0.02[/tex] (decimal form).
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CAN ANYBODY PLEASE HELP ME FOR BRAINLIEST, I'VE BEEN ASKING FOR DAYS AND POSTING DAILY THE SAME QUESTION :(
There was a sample of 650 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 9.3% each year.
Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams.
Write an exponential function showing the relationship between y and t.
Answers
Answer: [tex]y = 650(0.907)^t[/tex]
This is the same as writing y = 650(0.907)^t
=====================================================
Explanation:
Exponential equations can be of the form y = a*b^t
a = initial amountb = growth or decay factorIn this case, we have
a = 650 mg to start withb = 1 - 0.093 = 0.907 as the decay factorIf we had exponential growth, then we'd compute 1 + 0.093 instead.
Based on those values, we go from y = a*b^t to y = 650(0.907)^t which is the same as writing [tex]y = 650(0.907)^t[/tex]
Other exponential forms are possible, but I think this form is the most intuitive. The 0.907 means that 90.7% of the sample remains after each year.
What is the measure of Zr?
Angles are not necessarily drawn to scale.
B
156°
4
C
0
Answers
Answer:
24°
Step-by-step explanation:
Two angles that form a linear pair are supplementary. That is, their total is 180°.
x° +156° = 180°
x° = 180° -156° = 24°
The probability that Sue will go to Mexico in the winter and France in the summer is 4/10. The probability that
she will go to Mexio in the winter is 6/10. Find the probability that she will go to France this summer, given that
she just returned from her winter vacation in Mexico.
Answers
Answer:
40%
Step-by-step explanation:
4 / 10 = 40%
A stamp cost 25 kobo, how many Stamp can a man buy with 2.85 Naira
Answers
Answer:
11 stamps approximately
Step-by-step explanation:
convert 25 Kobo to naira
which is 25/100 = 0.25 naira
therefore, a stamp will cost 0.25 naira.
number of stamps the man can buy with 2.85 naira will be 2.85/0.25 =11.4 stamp
which is 11 stamps (approximately)
MATH QUESTION ASAP!!!!! SCREEN SHOT DOWN BELOW
Answers
Answer:
Option 1 looks most suitable
Step-by-step explanation:
Check image below:
Brainliest please
Over a 14-day period, Jamal went to the store 4 times. Based on this
information, which statement best describes how many times Jamal will go
to the store in a 5-week period?
Answers
Answer:
He will go to the store 10 times in a 5-week period.
Step-by-step explanation:
We can assume that in one week, Jamal went to the store 2 times, considering he went to the store 4 times in 2 weeks. Next, we can assume that he will go to the store 10 times in 5 weeks, since 2×5=10.
I need help with a math problem
Answers
find the sum of 6a - 5b + c, -2a +4b -2c
Answers
Answer:
4a-b-c
Step-by-step explanation:
we first look at the letters of each number. if there is only a letter, there is an imaginary 1 in front of it. we need to make sure that we add the numbers that have the exact same letters because they are known as like terms. we cannot add 6a and 4b because the letters are different and they are known as unlike terms. When we add numbers with the same letter ONLY the number changes
Determine if true:
3x4 divided by 3*8=34
Answers
Answer:
False
Step-by-step explanation:
3x4=12
12 divided by 3=4
4x8=32
32=34
Hence, this equation is false.
Using an old post still need help
Answers
Answer:
12x+20
Step-by-step explanation:
2(5x+2)+2(x+8)
or (simplified)
10x+4+2x+16=12x+20
Answer:
12x+20
Step-by-step explanation:
5x+2+x+8+5x+2+x+8
12x+20
An elevator at a construction site has a maximum capacity of 2760 pounds. If the elevator operator weighs pounds and each cement bag weighs240 pounds, how many bags of cement can be safely lifted on the elevator in one trip?
Answers
Answer:
11.5
Step-by-step explanation:
divide 2760 by 240
2760/240=11.5
How many faces does the solid made from the net below have?
Answers
Explanation: Every flat shape on the 3D surfaced shape is called a face so this gives us a total of 8.
5 books cost 21. what is cost of 7 of the same books? show working
Answers
Answer:
$29.40Explanation:
5 books cost $21. That means you have to divide 21 by 5 to find the price of one book, which is $4.20. Then you multiply 4.2 by 7 to find the price of 7 books. 7 x $4.20= $29.40
Hank is making chili. He uses 2/3 cup of black beans, 1/4 cup of kidney beans, and 2/3 cup of pinto beans. How many cups of beans does hank use. (use equivalent row using 1/12
Answers
Answer:
Hank uses 19/12 cans of beans.
Step-by-step explanation:
1. 2/3 X 4/4 = 8/12
2. 2/3 X 4/4 = 8/12
3. 1/4 X 3/3 = 3/12
4. 8/12 + 8/12 + 3/12=19/12
what is the product of -4 and 8.1?
a.-32.4
b.-12.1
c.12.1
d.32.4
Answers
Answer:
a - 32.4
Step-by-step explanation:
-4 * 8.1 = -32.4
First, multiply .1 by -4 and you get -.4
Then multiply 8 by -4 and get -32
Combining these,
-32 -.4 = -32.4
Answer:
a. -32.4
Step-by-step explanation:
2. Factorisation of the algebraic expression 169x2 - 52xy + 4y2
Answers
Answer:
(13-2y)(13-2y)
Step-by-step explanation:
Algebraic identity of x^2-2ab+b^2
Bryce went to the zoo at 10:15 am, and got home at 4:40 pm. How long was he gone?
Answers
Answer: 6 hours and 25 min
Step-by-step explanation:
What is the perimeter of a square if it has an area of 10 sq. cm.
Answers
Answer: [tex]4\sqrt{10}[/tex] cm
Step-by-step explanation:
The area of the square is equal to the side length^2.
We can let s be the length of the side.
Therefore, s^2 = 10 cm^2
Square root both sides:
s = [tex]\sqrt{10}[/tex] cm
The perimeter of a square is 4 multiplied by the side length.
Therefore, the perimeter of the square is 4s = [tex]4\sqrt{10}[/tex] cm
There was a carton of 27 bottles of water at the beginning of a sports meet. The carton, with 27 bottles of water in it, weighed 11.53 kg. After the sports meet had ended, there were 24 bottles of water left in the carton. The carton then weighed 10.33 kg. What would be the mass of the carton in grams if it were to be empty?
Answers
Answer:
is the ans 0.73
Step-by-step explanation:
is the ans 0.73 gram and time xa ra
The mass of the carton in grams if it were to be empty is 530 g
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Let us find the weight of one bottle of water.
We have to subtract the weight of the carton with 27 bottles from the weight of the carton with 24 bottles
11.53 kg - 10.33 kg = 1.20 kg
So, the weight of 3 bottles of water is 1.20 kg.
Divide 1.2 by 3 to find the weight of one bottle of water
1.20 kg / 3 = 0.4 kg
Now the weight of the empty carton
Subtract the weight of 27 bottles from the weight of the carton with 27 bottles:
11.53 kg - 27(0.4 kg) = 0.53 kg
Convert the weight of the empty carton from kilograms to grams:
0.53 kg × 1000 g/kg = 530 g
Therefore, the mass of the carton in grams if it were to be empty is 530 g
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What should be the index of x so that the value of x so that it's value will be equal to 1?
Don't spam okie
Answers
Answer:
In our ordinary division, we are clear about the division of a number by the same number. The quotient is always 1 in such case.
For example:-
Divide 4 by 4.
Here,
[tex] \frac{4}{4} = 1[/tex]
Now let solve the above examples by using the laws of indices.
[tex] \frac{4}{4} = {4}^{1 - 1} = {4}^{0} = 1[/tex]
Similarly,
[tex] \frac{ {x}^{m} }{ {x}^{m} } = {x}^{m - m} = {x}^{0} = 1[/tex]
Thus,any base with zero index is equal to 1.
We need to tell the index of x for which x will be 1 , First of all , always remember that index of a number means power of the number or to which power it's raised to, like in 2³ , 2 is raised to 3 so 3 is the index. Also we knows an identity i.e
[tex]{\boxed{\bf{\dfrac{a^m}{a^n}=a^{m-n}}}}[/tex]Let's put , m = n
[tex]{:\implies \quad \sf \dfrac{a^m}{a^m}=a^{m-m}}[/tex]
[tex]{:\implies \quad \boxed{\bf{a^{0}=1}}}[/tex]
Also , you should note that for a = 0 , the given expression becomes 0⁰ ,which is not defined , so the above expression is true only for [tex]{\bf{a\in (-\infty,0)\cup (0,\infty)}}[/tex]
Now , as we can replace variables , so , if we replace a by x , we get x⁰ = 1 .
Hence , the required index is 0
What are the solutions to 9x^2-63x=0
Answers
Answer: x = 0 and x = 7
Step-by-step explanation:
9x^2 - 63x = 0.
We can factor out 9x from both terms on the left side:
9x(x - 7) = 0.
To be equal to 0, one of the terms has to be 0.
Therefore, either 9x = 0 or x - 7 = 0.
First, we solve the case where 9x = 0.
Then, x = 0.
Second, we solve the case where x - 7 = 0.
We add 7 to both sides:
So, x = 7
Will give crown to the answer!
Answers
Answer:Calculate the amount of total value in each case substituting x or d by 7 and compare the amounts:f(7) = 100*7 + 1000 = $1700g(7) = 1000*(1.1)^7 = $1948.72 (rounded)As we see the option 2 is better choice and the difference is:$1948.72 - $1700 = $248.72:For partb
Step-by-step explanation:
What percent of 300 is 120?
O A) 25%
O B) 250%
OC) 4%
OD) 40%
Answers
Answer:
D) 40%
Step-by-step explanation:
I just looked it up on a calculator.
It took a car 4 days to travel 3827 miles. What was this car's average speed, in miles per hour?
Answers
Answer:
39.864
Step-by-step explanation:
24*4=96
1827/96
=39.864
Determine if true:
3x8-63=-39
Answers
Answer:
True
Step-by-step explanation:
3x8=24
24-63=-39
39=39
Hence, the equation is true.
Answer:
The answer is true.
Step-by-step explanation:
3 x 8 = 24
24 - 63 = -39
Hope this helps. :)
Solve each expression by factoring. Match the solutions to the correct expressions.
20x^2 + 48x + 16 = 0
2x^2 - 5x -1 = -4
Answers
Answer:
Step-by-step explanation:
how many ways can i choose 5 goldfish from 28
Answers
Answer:
5 3/5 or 5
Step-by-step explanation:
Because it is