By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].
How to simplify logarithmic functions
In this problem we are supposed to eliminate all exponents of a logarithmic function by applying any of the following properties:
㏒ x · y = ㏒ x + ㏒ y㏒ x/y = ㏒ x - ㏒ y㏒ yˣ = x · ㏒ yNow, we proceed to simplify the function:
[tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex]
[tex]\log_{c} x + \log_{c} y^{6} + \log_{c} z^{-4}[/tex]
[tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex]
By eliminating exponents, the logarithmic expression [tex]\log_{c} x\cdot y^{6}\cdot z^{-4}[/tex] is equivalent to the logarithmic expression [tex]\log_{c} x + 6\cdot \log_{c} y - 4\cdot \log_{c} z[/tex].
To learn more on logarithms: https://brainly.com/question/24211708
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[tex] \frac{ \sqrt{40} }{ \sqrt{3} } [/tex]
Answer:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
Step-by-step explanation:
Given
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Required
Simplify
[tex]\frac{ \sqrt{40} }{ \sqrt{3} }[/tex]
Rationalize:
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40} }{ \sqrt{3} }*\frac{ \sqrt{3} }{ \sqrt{3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{40*3} }{ \sqrt{3*3} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ \sqrt{9} }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{120} }{ 3 }[/tex]
Expand the numerator
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4*30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ \sqrt{4}*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{ 2*\sqrt{30} }{ 3 }[/tex]
[tex]\frac{ \sqrt{40} }{ \sqrt{3} } =\frac{2\sqrt{30} }{ 3 }[/tex]
WHAT IS THE PRUDTUCT OF 7\9 AND 6 A. 1 4/9 B. 3 7\9 C. 4 2\3 D. 7 5\7
Answer:
C.
Step-by-step explanation:
Sam has saved 1400 cents from selling lemonade how many dollars does Sam have
Answer: $14.
Step-by-step explanation: 100 cents is equal to 1 dollar. 1400 cents divided by 100 cents = 14. Therefore, you have 14 dollars.
vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed. Determine the following: a. The percentage of time the machine is busy b. The average number of customers waiting in line c. The average time customers spend in the system d. The average number in the system
Answer:
0.667 ;
0.667 customers ;
0.0166708 hour ;
1.334 customers
Step-by-step explanation:
Given that:
Service time (μ) = 30 seconds ; 2 customers per minute ; 2 * 60 = 120 customers per hour
Arrival time, λ = 80 customers per hour
a.) percentage of time machine is busy (p) ; Utilization factor :
P = λ/ μ = 80 / 120 = 0.667
b.) average number of customers waiting in line Li = p² / 2(1-p)
= 0.667² / 2(1-0.667) = 0.667 customers
c) Average time customer spend in the system = Li/λ + 1/μ
= (0.667 / 80) + (1 / 120)
0.0083375 + 0.0083333
= 0.0166708 hour
= 0.0166708 * 60 = 1.00025 minutes
D) average number in the system ;
Li + p
= 0.667 + 0.667 = 1.334 customers
The store bought a table for $150, and sold it for $240. What percentage was the markup?
Answer:50%
Step-by-step explanation:
Answer:
the bought 65% porcentege
Solving
This figure is made up of two rectangular prisms.
12 in.
What is the volume of the figure?
in.
Enter your answer in the box.
2 in.
7 in.
in
21 in.
1
2.
3
4
Answer:
The question is invalid. Please provide a diagram.
Melanie and Mark borrowed $2500 at a simple interest rate of 7% for a period of 3 years. What was the interest?
Answer:
525 $
Step-by-step explanation:
Amount borrowed = $2500
Rate = 7%
Time = 3 years
therefor interest = $2500 X 7/100 X 3
Hope it help You
Enter the correct value in the space provided
Mariah is shopping at the mall for a sweatshirt. She finds a sweatshirt that is marked down 55% off the original price. The original price of the sweatshirt is $78.25. what is the sale price of the sweatshirt
Answer:
$35.21
Step-by-step explanation:
100%:$78.25
45% :$?
100?=78.25×45
?= 78.25×45/100
=$35.21
Answer: $35.21
Step-by-step explanation: 100%:$78.25
45% :$?
100?=78.25×45
?= 78.25×45/100
=$35.21
please help me solve this geometry problem:)
Given:
The endpoints of a line segment are (-5,12) and (-5,0).
To find:
The coordinates of a points which divides the line segment in 2:1.
Solution:
Section formula: If a point divides a line segment in m:n.
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
Let point P divides the given line segment in 2:1. They, by using section formula, we get
[tex]P=\left(\dfrac{2(-5)+1(-5)}{2+1},\dfrac{2(0)+1(12)}{2+1}\right)[/tex]
[tex]P=\left(\dfrac{-10-5}{3},\dfrac{0+12}{3}\right)[/tex]
[tex]P=\left(\dfrac{-15}{3},\dfrac{12}{3}\right)[/tex]
[tex]P=\left(-5,4\right)[/tex]
Therefore, the coordinate of the point that partitions the given segment in the ratio 2:1 are (-5,4).
Your friend says that the solutions to the inequality 7x-20x<52 are x<-4 Solve the inequality correctly. What error did your friend make?
What are the solutions of the inequality?
Answer:
instead of x < -4 it should be x > -4
Step-by-step explanation:
7x - 20x < 52
subtract 20x from 7x which is -13x
now the equation is -13x < 52
divide both sides by -13 but when you divide by a negative you switch the sign so it would x > -4 not x < -4
hope this helps :)
A scientist wanted to measure the constant rate of the current in a particular section of the river. She released a tracker into the river. The tracker sent her back the following information:
After 3.5 seconds since the tracker was released into the river the tracker had traveled 5.5 meters.
After 10.9 seconds since the tracker was released into the river the tracker had traveled 16.5 meters.
What is the constant rate of the current?
Answer:
1.486m/s
Step-by-step explanation:
The rate of change is defined as the change in distance divided by the change in time
Rate = ∆distance/∆time
Distance = 16.5 and 5.5
Time = 10.9 and 3.5
When we put this into the formula above, we have:
Rate of change = 16.5 - 5.5 / 10.9 - 3.5
= 11/7.4
= 1.486m/s
The constant rate of change has been calculated to be equal to 1.486m/s
You can use the fact that the rate of the change of a value when some other independent value changes is the ratio of change in the dependent variable to the change in the independent variable.
The constant rate of the current is given by 1.4865 meters per second.
How to measure the rate of change of something as some other value changes?Suppose that we have to measure the rate of change of y as x changes, then we have:
[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where we have
[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]
Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.
(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)
How to measure the constant rate of the current for the given situation?The distance traveled by the tracker depends on the time passed.
Let the variable "t" tracks the amount of time passed and let the variable "d" tracks the distance traveled by the tracker, then we have:
[tex]\rm At \: t = t_1 = 3.5, d=d_1 = 5.5 \: m\\At \: t = t_2 = 10.9, d = d_2 = 16.5 \: m[/tex]
Thus, the constant rate of current is obtained by
[tex]Rate = \dfrac{d_2 - d_1}{t_2 - t_1} = \dfrac{16.5 - 5.5}{10.9 - 3.5} = \dfrac{11}{7.4} \\\\Rate \approx 1.4865 \: \text{meters per second}[/tex]
Thus,
The constant rate of the current is given by 1.4865 meters per second.
Learn more about rate of change here:
https://brainly.com/question/2460159
Find the midpoint between each pair of points.
13. (7,-2) (-4,2)
BONUS POINTS IF RIGHT
Out of 4/10, 3/4, 2/5, and 1/3 which fraction is the biggest?
Answer:
3/4
Step-by-step explanation:
3/4 = .75
4/10 = .40
2/5 = .40
1/3 = .33
Answer:
3/4 is greater then 4/10 and 2/5 is greater then 1/3 and that's all I know
Step-by-step explanation:
7/16+3/8
Simplify or answer in regular fractions or improper fractions
Answer:
hope it helps you
https://youtu.be/RTFkRTT0EUY
pls subscribe my channel
Answer:
13/16
Step-by-step explanation:
Turn [tex]\frac{7}{16} +\frac{3}{8}[/tex] into [tex]\frac{7}{16} +\frac{6}{16}[/tex]
If both denominators are the same the number it makes it easier to add.
Since 8*2 is 16 you have to do 3*2 in order for 3/8 and 6/16 to be equivalent.
then add the top numbers, not the bottom bc the bottom stays the same.
7+6=13 so the answer is 13/16
hope that helps:)
-1 subtracted by 2.5
Answer:
-3.5
Step-by-step explanation:
NEED HELP ASAPPP please
Answer:
it might be d I am not shore but I think that one sounds the best branley is making me do this to sigh. up sorry donjot use this
Write the ratio as a fraction in lowest terms. Be sure to make necessary conversions:
12 feet to 15 inches
------/---------
Answer:12533
Step-by-step explanation:
To complete her holiday wrapping, Bella needs identical
strips of ribbon measuring 3.5 feet each. She has 85 feet of
ribbon in total. About how many pieces of ribbon can she
cut from this long strip?
Answer:
24
Step-by-step explanation:
Answer:
The answer would be At least 20 box.
Step-by-step explanation:
i anwerd it in the lesson and got it right. Hope this helps. :)
An automobile manufacturer claims that its car has a 57.7 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the MPG for this car since it is believed that the car has an incorrect manufacturer's MPG rating. After testing 210 cars, they found a mean MPG of 57.4. Assume the standard deviation is known to be 1.9. A level of significance of 0.1 will be used. Find the value of the test statistic. Round your answer to 2 decimal places.
Answer:
The value of test statistic
|Z| = |-2.2883| = 2.2883
Step-by-step explanation:
Step(i):-
Given that the mean of the Population = 57.7miles/gallon
The standard deviation of the Population = 1.9
The mean of sample x⁻ = 57.4
Given that the sample size 'n' =210
level of significance = 0.1
Step(ii):-
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{57.4-57.7}{\frac{1.9}{\sqrt{210} } }[/tex]
Z = -2.2883
|Z| = |-2.2883| = 2.2883
Final answer:-
The value of test statistic
|Z| = 2.2883
The population of a city decreases by 4.6% per year. If this year's population is
329,000, what will next year's population be, to the nearest individual?
Answer:
Your answer
313866
Mark it as Brainlist answer. Follow me to get more answer
Step-by-step explanation:
Daniel has a total collection of 200 marbles. 10% of them are red. How many are red marbles in his collection? What is missing in the problem?
Answer:
40(i think)
Step-by-step explanation:
Are there any vertical, complimentary, or any supplementary angles here ? And label for ex. 1 supplementary
Supplementary: 1 and 2 & 3 and 4
Supplementary angles: A pair of angles whose sum is equal to 180°.
Vertical: 1 and 3 & 2 and 4
Vertical angles: A pair of opposite angles that are made by two intersecting lines.
Complimentary: None
Complimentary angles: A pair of angles whose sum is equal to 90°.
Hope this helps! :D
Which of the following points have a distance of five units between them? Select all that apply 
A.)(-2,5) and (3,7)
B.)(10,5) and (7,9)
C.)(1,10) and (6,5)
D.)(-4,-8) and (-4,-5)
E.)(2,-5) and (6,-8)
Answer:
C. (1, 10) and (6, 5)
Step-by-step explanation:
To find the point with a distance of 5 units.
Let the points be x and y.
x = x1 and x2
y = y1 and y2
x2 - x1 = 5 units
y2 - y1 = 5 units.
A quick look at the options, we can tell that the correct option is C.
From points (1, 10) and (6, 5)
x1 = 1, x2 = 6, y1 = 10 and y2 = 5
Substituting into the equation above, we have;
x2 - x1 = 6 - 1 = 5 units
y2 - y1 = 5 - 10 = -5 units.
Therefore, option C with points (1,10) and (6,5) have a distance of five units between them.
Find the value of x.
a) 21
b) 27
c) 31
d) 34
Answer:
21 is the answer
a question arises how?? right
so, 3x+1
3×21+1
63+1
64
Answer:
a) 21
Step-by-step explanation:
Since, in the figure
64° = (3x+1)° [Vertically Opposite Angles]
=> (3x+1)° = 64°
=> 3x = 64° - 1° = 63°
[tex] => x = \frac{63}{3} [/tex]
=> x = 21 (Ans)
When 2 times a number is increased by 9, the answer is the same as
when 30 is decreased by the number. Find the number. HELP ME
Answer:
its 7
Step-by-step explanation:
why did u delete my answer if its right?
At a recent soccer game at Red Bulls stadium, 7500 fans were rooting for the New England Revolution while 17,500 fans were rooting for the New York Red Bulls. What percent of the soccer fans were rooting for the New England Revolution?
Answer:
30%
Step-by-step explanation:
add the number of fans together: 7500+17500 = 25000
write as fraction, fans of New England Revolution over total number: 7500/25000
simplify or use calculator: 3/10 or 0.3
convert fraction or decimal to percentage: 30%
I WILL GIVE BRAINLIEST!!!! ~PLEASE HELP (all the answers for all the questions please for the second and first picture)
Answer:
Question 6: I know that (8 + 9) + 3 is equal to 8 + (9 + 3) because of the associative property states that you can change the grouping of addends in any order you want. The benefit to using this property is that you can first add numbers that you can combine more easily. For example, (743 + 51) + 49 can be written as 743 + (51 + 49) or 743 + 100. It is more straightforward to add the numbers that equal 100 first and then add the final number.
Question 3: -3(4x + 3) + 5x [Given]; -12x - 9 + 5x [Distributive Property]; -12x + 5x - 9 [Commutative Property]; -7x - 9 [Combine like-terms]. [tex]\frac{1}{2}[/tex] (6k + 10) + 5k [Given]; 3k + 5 + 5k [Distributive Property]; 3k + 5k + 5 [Commutative Property]; 8k + 5 [ Combine like-terms].
Question 4: 4(2 - 5) - 8 = 4 * (-3) - 8 = -12 - 8 = -20; 4 * 2 - 28 = 8 - 28 = -20.
Question 5: 15 * 3 - 2(2 * 3 + 6) = 45 - 2(6 + 6) = 45 - 2(12) = 45 - 24 = 21; 11 * 3 - 12 = 33 - 12 = 21.
BRAILIEST for correct answer!! Pls help
What's the slope of a line that passes through (−12,15) and (0,4)?
Answer:
-11/12
Step-by-step explanation:
slope for points (x1,y1) and (x2,y2)
slope=(y2-y1)/(x2-x1)
(x,y)
(-12,15)
(0,4)
x1=-12
y1=15
x2=0
y2=4
slope=(4-15)/(0-(-12))=-11/(0+12)=-11/12
Answer:
Slope: -11/12x
Step-by-step explanation:
Slope-intercept equation:
y = mx + b
(m = slope)
The formula for slope is below.
m = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
With your two points, you can accurately determine your slope.
(-12, 15) (0,4)
x1 = -12
y1 = 15
x2 = 0
y2 = 4
Apply this information in the slope formula to get:
[tex]\frac{4 - 15}{0 - -12}[/tex]
Change the 0 - -12 to 0 + 12
[tex]\frac{4 - 15}{0 + 12}[/tex]
4 - 15 = -11
0 + 12 = 12
Place -11 and 12 into a fraction.
[tex]\frac{-11}{12}[/tex] OR -11/12
Add "x" to the end from "mx" within the slope-intercept equation
-11/12x
Given that a linear function goes through the points (3,2) and (5, 6) determine the slope
of the line.
Answer:
2
Step-by-step explanation:
The formula of slope from 2 points is change in y divided by change in x, so you can apply that to this problem.
First, find the change in y between the two points. To do this, do y2 - y1.
y2 = 6 and y1 = 2, so you have 6 - 2 = 4.
Next, find the change in x between the two points. To do this, do x2 - x1.
x2 = 5 and x1 = 3, so you have 5 - 3 = 2.
All you're really doing here is finding the distance between the x values and the y values of the points, if that makes sense.
The last step is to do change in y divided by change in x, so 4 / 2 = 2.
This means that the slope of the line is 2.
what is the meaning of XII in roman numeral
Answer:
its 12 in mathematics....