Answers
Answer:
[tex]log_3(\frac{7}{16}) =-0.753[/tex]
Step-by-step explanation:
Use the laws of log()
[tex]log_x(\frac{a}{b}) =log_x(a)-log_x(b)[/tex]
[tex]log_3(\frac{7}{16}) =log_3(7)-log_3(16)[/tex]
[tex]log_3(\frac{7}{16}) =log_3(7)-log_3(4^2)[/tex] you can move exponent outside of log()
[tex]log_3(\frac{7}{16}) =log_3(7)-2log_3(4)[/tex]
[tex]log_3(\frac{7}{16}) =(1.771)-2(1.262)[/tex]
[tex]log_3(\frac{7}{16}) =-0.753[/tex]
The required value of log₃ (7/16) is 0.753 which is determined by properties of logarithms.
What are the properties of logarithms?There are four basic properties of logarithms:
logₐ(xy) = logₐx + logₐy.
logₐ(x/y) = logₐx - logₐy.
logₐ(xⁿ) = n logₐx.
logₐx = logₓa / logₓb.
The functions of logarithmic are given in the question
log₃ 4 = 1.262 and log₃ 7 = 1.771
We have to determine the value of log₃ (7/16)
⇒ log₃ (7/16) = log₃ 7 - log₃ 16
⇒ log₃ (7/16) = log₃ 7 - log₃ 4²
Using property of logarithm logₐ(xⁿ) = n logₐx.
⇒ log₃ (7/16) = log₃ 7 - 2 log₃ 4
Substitute the values of log₃ 4 = 1.262 and log₃ 7 = 1.771 in the above equation,
⇒ log₃ (7/16) = 1.771 - 2(1.262)
⇒ log₃ (7/16) = 1.771 - 2.524
⇒ log₃ (7/16) = 0.753
Therefore, the required value of log₃ (7/16) is 0.753.
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Related Questions
4. What is the slope of a line that is parallel to the line described by 3x + 2y = 8?
a.
m = 3
b.
m= 3/2
c.
m= -3/2
d.
m= 2
Answers
B. M=3/2
The temperature in Anchorage, Alaska was -3°C in the afternoon. After the sun went down, the temperature dropped 6 degrees. Write an equation to represent the situation. What was the temperature after the sun went down? ( 3 points )
Answers
Answer:
-9
Step-by-step explanation:
-3 - 6
-3 + -6
-9
hope this helps!
In December of 2003, the average price for a gallon of regular gas in the United States was $1.50.
b. Is the relationship between number of gallons and cost proportional? Explain.
Answers
Answer:
yes
Step-by-step explanation:
because the cost stays the same and you would multiply blank gallons of gas by 1.50 every time so it is proportional. For example: it would be $1.50 to 1 gallon, $3 to 2 gallons, $4.50 to 3 gallons and would keep going like that, adding the same amount every time
If a turkey weighs 16 pounds, how many calories does it have? (remember there are
170 calories in 4 ounces of turkey)
Answers
0.608 meter long. The average Chuckwalla is 0.395 meter long. How many times as long is the Gila Monster as the Chuckwalla, to the nearest hundredth?
Answers
Complete question :
The two largest lizards in the United States are the Gila monster and the Chuckuwalla. The average Gila monster is 0.608 meter long. The average Chuckwalla is 0.395 meter long. How many times as long is the Gila Monster as the Chuckwalla, to the nearest hundredth?
Answer:
1.54 times
Step-by-step explanation:
Given that:
Average length of Gila monster = 0.608 meter
Average length of chuckwalla = 0.395 meter
Number of times the Gila monster is than the Chuckuwalla :
Average Length of Gila monster / average Length of chuckwalla
= 0.608 meter / 0.395 meter
= 1.5392405 times
= 1.54 times
Calculate the perimeter for the given figure.
8 ft
8.5 14
.ft
10 11
A. 16.5 feet
B. 25.5 feet
C: 26,5 feet
D. 26.5 feet
Answers
Answer:
the answer is C and D because perimeter is the sum of all sides of a figure
Which set is not closed under addition
A. Natural numbers
B. Even integers
C. Odd numbers
D. Whole numbers
Answers
put x^2+15x+56 and make it into a word problem!
Answers
between 2002 and 2008, more than 26 cubic miles of groundwater disappeared. how much water has disappeared per year
Answers
Explanation:
2008 - 2002 = 6 years have passed
In that time frame, we lost 26 cubic miles of ground water.
This means we lost about 26/6 = 4.333 cubic miles of ground water per year.
Sally and Joan were able to dust the house in 3 hours together. It takes Joan 10 hours to finish the same job alone. Without help, how long would it take Sally to finish the same job ?
Answers
Answer:
4.3 hours
Step-by-step explanation:
Let the number of hours Sally does a job = x
Let the number did hours Joan does a job be equal to y
Sally and Joan were able to dust the house in 3 hours together.
1/x + 1/y = 1/3
It takes Joan 10 hours to finish the same job alone.
Hence,
1/x + 1/10 = 1/3
1/x = 1/3 - 1/10
Least common dey = 30
1/x = 10 - 3/30
1/x = 7/30
Cross Multiply
x × 7 = 30
7x = 30
x = 30/7
x = 4.2857142857 hours
Approximately = 4.3 hours
Without help, it would take Sally 4.3 hours to finish the same job.
[tex] {x}^{ 2} + 4x - 21[/tex]
I'm trying to solve for x but I dont understand and need help
Answers
.A carpenter bought some wood for #900. He used the wood to make a shelf which he sold for #3000. What percentage profit was this?. Single choice.
42.86%
233.33%
2100%
900%
Answers
Answer:
233.33%
Step-by-step explanation:
His profit is 233.33%.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Here, given that,
A carpenter bought some wood for #900.
He used the wood to make a shelf which he sold for #3000
Profit= #(3000-900)
=#2100
So, percentage of profit = 233.33%
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is 2.6666666667 a rational number
Answers
Answer:
No.
Step-by-step explanation:
I believe that the number above is irrational, because it repeats.
The decimal is rational
In fact every repeating decimals are rational because you can turn them into fraction
Can you please mark brainleist
Gabriel cycles 1,200 meters in 6 minutes. What is his speed?
Answers
Jan's flower garden has only daffodils and tulips
in it. There are 15 dallodils and 12 tulips. What
is the ratio of the number of tulins to the total
number of flowers in Jan's garden?
Answers
What is the solution of |x − 1| + 2 = 4? Enter your answers from least to greatest in the boxes
Answers
Answer:
down
Step-by-step explanation:
are there options
The link between the bases on a basketball field is 93 a scale drawing shows the distance between the Bases as 1 1/2 to 1 inch on the drawing equals how many feet
Answers
Answer:
Distance on drawing is 11.7 feet.
Step-by-step explanation:
A scale is a factor that can be used to either increase or decrease the size of an object.
Scale = [tex]\frac{distance on drawing}{original distance}[/tex]
Given that:
scale = [tex]\frac{3}{2}[/tex] to 1 inch, and the original distance = 93 inches
So,
[tex]\frac{3}{2}[/tex] : 1 = [tex]\frac{distance on drawing}{93}[/tex]
[tex]\frac{3}{2}[/tex] ÷ 1 = [tex]\frac{distance on drawing}{93}[/tex]
[tex]\frac{3}{2}[/tex] x [tex]\frac{1}{1}[/tex] = [tex]\frac{distance on drawing}{93}[/tex]
distance on drawing = [tex]\frac{3*93}{2}[/tex]
= [tex]\frac{279}{2}[/tex]
= 139.5
distance on drawing = 139.5 inches
Since 12 inches = 1 foot, then;
Distance on drawing in feet = [tex]\frac{139.5}{12}[/tex]
= 11.625 feet
Distance on drawing is 11.7 feet.
solve of system of equation.
9x + 2y = -38
9x+10y=26.
Answers
Answer:
(-6 , 8 )
Hope this helps!
PLEASE HELP ME!!
BEST ANSWER GETS BRAINLIEST
Which of the following could represent a diver’s position in relation to the surface of the water after diving into a pool? Select all that apply.
3 meters
-2 meters
-3.1 meters
1 and StartFraction 7 over 8 EndFractionmeters
Negative 2 and one-halfmeters
Answers
Answer:
-2, -3.1, -2.5
Step-by-step explanation:
Since the diver dived into the pool, they are below the surface (assuming it is an inground pool). So the correct answers will be the negative answers.
The numbers to represents a diver’s position in relation to the surface of the water after diving into a pool is;
-2 meter
-3.1 meter
Negative 2 and one-half meters
Given that;
A diver’s position is in the surface of the water diving into a pool.
We have to find number to represents a diver’s position in relation to the surface of the water after diving into a pool.
What is Negative number?
A number less than zero is called the negative number.
A diver’s position is in the surface of the water diving into a pool.
Since, Diving into a pool is represents negative number.
Hence, The number to represents a diver's position is in negative sign.
So, The numbers are;
⇒ -2 meter
⇒ -3.1 meter
⇒ Negative 2 and one-half meters.
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Camila started reading a 500 page book. She read of the book in hour. What is the maximum number of pages can she read in hour if she reads at the same rate?
A.
10 pages
B.
15 pages
C.
40 pages
D.
20 pages
Answers
Answer:
Need more information
Step-by-step explanation:
I need to know what percentage/fraction of the book she read in 1 hour or any other information about the rate she is reading
If 3x - 6 = 21, what is the value of x - 2 ?
Answers
Or,3x=27
Or,x=27/3
Or,x=9
So,Now,
X-2=9-2
=7
Hope it helps
The value of x - 2 in the equation 3x - 6 = 21 is 7.
What is an equation ?An equation is comparing two equal quantities in different form.Equations can be of many types like algebraic equation, logarithmic equation,trigonometric equations, exponential equations.We can also graph this equations in 2 dimensional and 3 dimensional plane.
According to the question given an equation 3x - 6 = 21 first we have to solve for x or find the value of x.
∴ 3x - 6 = 21.
3x = 21 + 6.
3x = 27.
x = 27/3.
x = 9.
So, the value of (x-2) will be (9-2) = 7.
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the ratio of the measures of the angles of a triangle is 1:2:3 find the measure of each angle
Answers
Answer: 30, 60, 90
Step-by-step explanation: 30 * (1:2:3)
30+60+90 =180
Sum of all angles of a triangle is 180
The average of your 3 quiz grades is 17 points. Two of your quiz grades are 14 points and 19 points. Write and solve an equation to find the score of your third quiz.
Answers
Answer:
The equation required is [tex]17=\frac{14+19+Grade \ of \ Quiz \ 3}{3}[/tex] and Grade of quiz 3 is 18
Step-by-step explanation:
We are given
Average of 3 quiz grades = 17
Grade of quiz 1 = 14
Grade of quiz 2 = 19
We need to find Grade of quiz 3
The formula used will be: [tex]Average \ of \ 3 \ quiz \ grades = \frac{Grade \ of \ Quiz \ 1+Grade \ of \ Quiz \ 2+Grade \ of \ Quiz \ 3}{3}[/tex]
Using formula and finding the grade of quiz 3
[tex]Average \ of \ 3 \ quiz \ grades = \frac{Grade \ of \ Quiz \ 1+Grade \ of \ Quiz \ 2+Grade \ of \ Quiz \ 3}{3}\\17=\frac{14+19+Grade \ of \ Quiz \ 3}{3} \\17*3=14+19+Grade \ of \ Quiz \ 3\\51=33+Grade \ of \ Quiz \ 3\\Grade \ of \ Quiz \ 3=51-33\\Grade \ of \ Quiz \ 3=18[/tex]
So, The equation required is [tex]17=\frac{14+19+Grade \ of \ Quiz \ 3}{3}[/tex] and Grade of quiz 3 is 18
A snack bar at an outdoor fair is open from 10 A.M. To 5:30 P.M. And has 468 bottles of water for sale. Sales average 1.3 bottles of water per minute.
Answers
Answer:
the question is incomplete, so I looked for similar ones
the number of bottles of water remaining as a function of time:
f(x) = -78x + 468
1.3 bottles are sold per minute x 60 minutes per hour = 78 bottles per hour
x = number of hours
the slope is -78
the y intercept is 468
domain = 0 ≤ x ≤ 7.5 hours (from 10 AM to 5:30 PM)
range = 0 ≤ y ≤ 468 bottles
the snack will run out of bottles of water by 4 PM
78x = 468
x = 468 / 78 = 6 hours
if the snack wants to have enough bottles of water to serve all its customers, it will need:
78 x 7.5 hours = 585 bottles of water
PLease help me find the unit rate for $140 for 18 ft
Answers
Answer:
Step-by-step explanation:
So,
$140 Dollars per 18 feet
Divide by 18 on both sides
140/18=18/18
140/18 is equal to 7 and 2/9
The answer is 7.77777778
Which of the following lists is in order from least to greatest?
V5.4,32,-2.
-2, 5, 4, 32
-2, 4, 3², 5
2, 32, 4, 5
Answers
Answer:
second one
Step-by-step explanation:
Use the inverse variation equation to fill in the table.
Answers
Answer: a= 0.1 b=20.775 c=0.02
Step-by-step explanation:
just got it right on edg
set of integers between -4 and 4
Answers
Answer:
-3, -2, -1, 0, 1, 2, 3
Step-by-step explanation:
-3,-2,-1,0,1,2,3,4
just need 5 and 6 done due in 20 minutes plz help
Answers
Step-by-step explanation:
5. Let the equation of the line be y = mx + c
m = (6-15)/(2-(-1)) = -3
sub (2, 6) and m = -3:
6 = -3(2) + c
c = 12
Equation of the line: y = -3x + 12
6. Let the equation of the line be y = mx + c
y-intercept of 7 means c = 7
y = mx + 7
x-intercept: value of x when y = 0
therefore, sub (4, 0):
0 = m(4) + 7
m = -7/4
Equation of the line: y = -7/4x + 7
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1) (-8,-8), (8,4)
Find the slope of the line through each pair of points
Answers
Answer: 3/4
Step-by-step explanation: