Answers
n = - 3
How is the given equation [tex]5^{n} =\frac{1}{125}[/tex] solved to find n ?
Converting the fraction to negative exponential form,
[tex]5^{n} ={125}^{-1} \\\\5^{n} ={(5^{3})}^{-1} \\\\\text{We know } (a^{n} )^{m} =a^{nm} \\\\\text{Applying this exponent power rule in the above expression},\\\\5^{n} = 5^{-3} \\\\\text{As the corresponding exponents are equal}\\\\n= -3[/tex]
What are laws of exponents?
Exponent rules, commonly referred to as the laws of exponents or properties of exponents.They make it simpler to simplify statements involving exponents. Expressions with decimals, fractions, irrational numbers, and negative integers as their exponents can be made simpler by using these rules.Additionally, by applying these laws, it is possible to simplify numbers with complex powers that involve fractions, decimals, and roots.To learn more about laws of exponents, refer:
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Related Questions
At a book fair, a tote bag costs $5 and books cost $3.50 each. you spend a total of $19.00 before taxes. how many books did you buy in addition to the tote bag?
Answers
Answer:
4 books
Step-by-step explanation:
Let b equal the number of books.
[tex]5 + 3.50b = 19[/tex]
[tex]3.50b = 14[/tex]
[tex]b = 4[/tex]
GCF(a, b)• LCM (a, b) = 77
What are the possible values of a and b?
Answers
The variables a and b have a possible value of 7 and 11
How to determine the possible values of a and b?The given parameters are
GCF(a, b)• LCM (a, b) = 77
As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers
This implies that
a * b = GCF(a, b)• LCM (a, b)
So, we have
a * b = 77
Express 77 as 7 * 11
a * b = 7 * 11
By comparison, we have
a = 7 and b = 11
Hence, the possible values are a = 7 and b = 11
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Find the equation of the line.
Use exact numbers.
Answers
Answer:
y = 4x + - 9
Step-by-step explanation:
(3, 3), (4, 7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 7 - 3 4
m = ------------ = ------------ = ------- = 4
x₂ - x₁ 4 - 3 1
y - y₁ = m(x - x₁)
y - 3 = 4(x - 3)
y - 3 = 4x - 12
+3 +3
----------------------
y = 4x - 9
I hope this helps!
The lateral surface area of a cylinder is given by the formula S = 2pirh . Solve the equation for r.
Answers
S = 2*pi*r*h
hen solving for the radius gives
r = S/(2*pi*h)
ndustry standards suggest that 10% of new vehicles require warranty service within the first year. jones nissan in sumter, south carolina, sold 12 nissans yesterday. (round your mean answer to 1 decimal place and the other answers to 4 decimal places.)
Answers
The probability that none of these vehicles requires warranty service is 0.2824
The probability exactly one of these vehicles requires warranty service is
0.3766
The probability that exactly two of these vehicles require warranty service is 0.2301
The mean of this probability distribution is 1.2
Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:
[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]
The probability that none of these vehicles requires warranty service
[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]
=0.2824
The probability exactly one of these vehicles requires warranty service
[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]
=0.3766
The probability that exactly two of these vehicles require warranty service.
[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]
=0.2301
Compute the mean of this probability distribution
Mean = n*P, where n = 12, P=0.1
=12*0.1
=1.2
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What do you add to
[tex]3 \frac{3}{8} [/tex]
to make 7?
Answers
Answer:
[tex]\frac{29}{8}[/tex]
Step-by-step explanation:
3[tex]\frac{3}{8}[/tex] equals to [tex]\frac{27}{8}[/tex], then we can write out the equation:
[tex]\frac{27}{8} + x = 7[/tex]
then subtract [tex]\frac{27}{8}[/tex]on both sides of the equal sign,
[tex]x = 7 - \frac{27}{8}[/tex]
and then we calculate x
[tex]x=\frac{56-27}{8}[/tex]
[tex]x=\frac{29}{8}[/tex]
Thus the answer is [tex]\frac{29}{8}[/tex]
Writing to Explain Timothy is solving the problem 50+ 108x ÷ 4.
What order of operations should he follow?
Answers
PEMDAS
Answer:
27x+50
Step-by-step explanation:
How to solve your problem
50 + 108x/4
Simplify
Cancel terms that are in both the numerator and denominator
50+ 108x/4
50+ 27x
Rearrange terms
50 + 27x
27x +50
=27x+50
The point ( 3, -7 )is on a line with the slope . 2/3 Find another point on the line.
Answers
Answer: (6, -5)
Step-by-step explanation:
The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.
➜ Slope is written as y over x
➜ Coordinate points are written as (x, y)
(3, -7)
(3 + 3, -7 + 2)
(6, -5)
We can also find a point on the line by graphing. See attached.
CAN SOMEONE PLEASE HELP ME
Answers
Answer:
^2¤{{●○|<♤7◇○◇○◇7~♡6°<♤~{¡\ ~announced unbeknownst.fi
it took 2/3 minute to fill a barrel 1/4 full of water. find the unit fate in barrels per minute
Answers
Answer:
3/8 barrels / minute.
Step-by-step explanation:
Rate = fraction of barrel filled / time
= 1/4 / 2/3
= 1/4 * 3/2
= 3/8.
A rental car company charges $40 per day to rent a car and $0.08 for every mile driven. Justin wants to rent a car, knowing that:
He plans to drive 125 miles.
He has at most $170 to spend.
Write and solve an inequality which can be used to determine xx, the number of days Justin can afford to rent while staying within his budget.
Answers
Answer:
He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.
Step-by-step explanation:
Brett earns a base salary of £78 per week plus a commission of 20% of sales. How much did Brett make last week if he managed to sell £85 worth of merchandise?
Answers
By taking the 20 percent of £85 and adding that to the base salary, we can see that last week Brett earned £95
How much did Brett make last week?Here we need to work with percentages. We know that Brett wins a commission of 20% of sales.
So, if he sells a total amount of A (A is in dollars). Then what he gets is:
0.2*A
Where 0.2 is the decimal form of 20%.
Here we know that Brett wins £78 as a base, and last week he sell a total of £85, then the amount he gets by the commission is:
0.2* £85 = £17
Adding that to the base he already earns each week, we get:
£78 + £17 = £95
In this way, we conclude that last week Brett earned £95
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Solve the x and y
1.5x-4.5y=9
Answers
Answer:
1.5x=9+4.5y
x= [tex]\frac{9+4.5y}{1.5}[/tex]
x = 6 + 3y
3y= x - 6
y = x/3-2
2) Mr. Jonas took out a loan of $12,400. The interest rate is 3% per year, and the
interest is not compounded. How much amount will Mr. Jonas have to repay
after 4 years?
Answers
The amount which Mr. Jonas will have to repay after 4 years is $13,888 when the interest rate is 3% per year on a loan of $12,400.
According to the question,
We have the following details:
The amount of the loan or the principal amount = $12,400
Interest rate = 3% per year
Time = 4 years
Now, it is given that the interest is not a compound interest. So, the total interest can be found using the formula of simple interest.
Simple Interest (S.I.) = (Principal*rate*time)/100
S.I. = (12400*3*4)/100
S.I. = (12400*12)/100
S.I. = 148800/100
S.I. = $1,488
Now, the total amount Mr. Jonas have to repay will be the sum of the loan he has taken out and the simple interest after 4 years.
Total amount = Principal + S.I.
Total amount = 12400+1488
Total amount = $13,888
Hence, the total amount of loan Mr. Jonas has to repay is $13,888.
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If g(x) and f(x) are inverse functions, which graph represents g(x)?
--6-5 1-3-2-1 1 2 3 4 5 6
Mark this and return
7 7 7 7 4
Save and Exit
Next
Submit
Answers
Answer:
A) 2nd graph
Explanation:
The 1st graph shows a radical expression, where:
to find the inverse, replace f(x) with y, switch the x and the y, then solve for y. The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)
Select three names for the angle.
Answers
∠K , ∠1 and ∠JKL are the three names of the angle 1 indicated by red color in the figure given in the question.
We need to select three names of the angle 1 indicated by red color in the figure given in the question . We are provided with the following options ∠JLK , ∠K , ∠LJK , ∠1 , ∠JKL and ∠J .
∠JLK is not similar to ∠1 . ∠K and ∠1 are same angle. ∠LJK is not similar to ∠1 . ∠JKL and ∠1 are same angle. ∠J and ∠1 are different angles. So, we can finally conclude that the three names of the angle 1 indicated by red color in the figure given in the question are ∠K , ∠1 and ∠JKL .
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Which function is odd? Check all that apply.
A. y = sin x
B. y = csc x
C. y = tan x
D. y = cos x
Answers
The odd function is
y = sin x
y = cos x
A function f is deemed weird if f(-x) Equals -f for any value of x. (x). A function is said to be an even function if f(-x) = f for any value of x. (x).
What do odd functions entail?
The meaning of odd function
T function where the absolute value does not change if the independent variable's sign is reversed but the sign of the function itself does.
If f(-x) = -f for any number x, a function f is considered strange (x). When f(-x) = f for any number x, a function is referred to as an even function (x). Even while most functions are neither odd nor even, some of the most significant functions are.
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Answer:
A. y = sin x
B. y = csc x
C. y = tan x
Step-by-step explanation:
Pls help
Step by step
Answers
When you multiply powers that have the same base (in this case, the base is 6), you can simply add the exponents.
-1 + 3 + -2 = 0 : anything raised to the power of 0 is equal to 1. Therefore, 6^0 = 1.
Find y' if arctan (xy) = 4 + xy².
Answers
Answer:
y=2x
Step-by-step explanation:
hope this helps
:) :3
The hypotenuse of a right triangle is 29.0 centimeters. the length of one of its legs is 20.0 centimeters. what is the length of the other leg? a. 49.0 centimeters b. 24.5 centimeters c. 21.0 centimeters d. 4.5 centimeters e. 9.0 centimeters
Answers
We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.
In this question we have to make an equation by using the right triangle's value which is given in the question,
by putting these values in the Pythagoras’ theorem.
As given, the hypotenuse of a right triangle = 29.0 centimeters.
The length of one of its leg = 20.0 centimeters
Now, by using Pythagoras’ theorem we will find the length of the other leg:
hypotenuse^2 = base^2 + perpendicular^2,
We put the value according as given in question:
29^2 = 20^2 + y^2
After finding the square of number of both side:
841 = 400 + y^2
Now we will rearrange this equation:
y^2 = 841 - 400
y = 21 centimeters is the length of the other leg.
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Which equation shows a line perpendicular to y = 3x + 2
a) y-1=1/3 (x-2)
b) y-1=3(x-2)
c) y-1=-1/3(x-2)
d) y-1=-3(x-2)
Answers
The straight line y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .
The common form for two-variable linear equations is Ax + By = C which is also the general form of a straight line.
For instance, the linear equation 6x+5y=11 uses standard form. Finding an equation's two intercepts (x and y) is fairly straightforward with this procedure.
The cartesian equation for a straight line is Y = mx + c, where m stands for the gradient or slope of the line and c for the point at which it intersects the y-axis.
If two geometrical objects cross at a right angle, they are perpendicular.
We know that when two line are perpendicular the product of their respective slopes equal to -1.
Now in the given options let us find the slope of each line.
a) y-1=1/3 (x-2)
slope = 1/3
b) y-1=3(x-2)
slope = 3
c) y-1=-1/3(x-2)
slope = -1/3
d) y-1=-3(x-2)
slope = -3
Therefore the slope of the third equation is the negative reciprocal of the slope of the given line.
Hence y-1=-1/3(x-2) is perpendicular to y = 3x + 2 .
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K
An investor has $75,000 to invest in a CD and a mutual fund. The CD yields 7% and the mutual fund yields 6%
The mutual fund requires a minimum investment of $9,000, and the investor requires that at least twice as much
should be invested in CDs as in the mutual fund. How much should be invested in CDs and how much in the
mutual fund to maximize the return? What is the maximum return?
DO
To maximize income, the investor should place $ in CDs and $
dollar as needed.)
The maximum return is $ (Round to the nearest dollar as needed.)
H
min
CH
point(s) possible
MA
√i Vi
P
in the mutual fund. (Round to the nearest
X
(,)
More
Next
x
Answers
25000 in mutual funds
50000 in CD
Pool of money managed by a professional Fund Manager is termed mutual fund. It is a trust that collects money from other investors who have a common investment objective and invests the same in equities and bonds.
Let X be the amount in Mutual Funds
Y be the amount in CDs
the constraints:
Y = 2x
x>9000
Y = 75000 - x
There has to be at least 2x + x = 75000
3x = 75000
x = 25000
Objective function for the return of investment is R(x,y) = 0.06X + 0.07Y
After graphing linear equations and inequalities, the vertices of the critical region are as:
(9000,18000) --> 1710
(25000,50000) ---> 4750
(75000,0) --> 3750
25000 in mutual funds
50000 in CD
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The speed of a car from point A to D is m/s however the velocity is 10 m/s due West. Calculate the speed of vehicle in m/s if it covers a distance of 1.5 km in 5 minutes.
Answers
Speed of car is 5 m/sec
What is speed?
In ordinary language and kinematics, an object's speed is defined as the magnitude of its position change over time or the magnitude of its position change per unit of time; it is therefore a scalar number. The distance traveled by an item in a time interval is divided by the duration of the period; the instantaneous speed is the limitation of the average speed as the length of time period tends to zero. Velocity is not the same as speed. Distance divided by time is the dimension of speed. The metre per second (m/s) is the SI unit of speed, while the kilometre per hour (km/h) is the usual unit.
The speed of the car = 1.5/5 km/min = 0.3 km/min
Speed in m/sec = 0.3x1000/60 = 5m/sec
Hence, speed of car = 5 m/sec
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Find the value of (-10)⁰
Answers
Answer:
1
Step-by-step explanation:
Anything to the power of 0 is 1 except for 0. If the base is o, the answer is undefined. It is will dividing by 0. That is also undefined.
Answer:
-10degree
Step-by-step explanation:
because the 0 is the degree
solve the system of equations
Answers
hope this helps
4,-1,6
x=4
y=-1
z=6
At a garage sale, Liyah priced
her scooter for $15.50. She
ended up selling it for $10.75.
Find the percent of decrease
in the price of the scooter.
Round to the nearest tenth if
necessary
Answers
If she priced scooter for $15.50 and ended up selling it for $10.75, then the percentage of decrease in the price of the scooter is 30.64%
The initial price of the scooter = $15.50
The selling price of the scooter = $10.75
The amount decrease in the price of the scooter = Initial price of the scooter - The selling price of the scooter
= 15.50-10.75
= $4.75
The percent of decrease in the price of the scooter = (The amount decrease in the price of the scooter ÷ The initial price of the scooter)×100
= (4.75/15.50)×100
= 30.64%
Hence, if she priced scooter for $15.50 and ended up selling it for $10.75. then the percentage of decrease in the price of the scooter is 30.64%
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30 POINTS!
Select ALL the correct answers
Which figures show that ST || QR?
Answers
The figure that shows that ST || QR is the first figure
How to find the figure that show that ST is parallel to QR
For lines ST and QR to be parallel they have equal distance form the base of the triangle.
Taking the ratio of the distances from the apex we have
PS / SQ = PT /TR
The figure that has it's ratio equal is the figure that the lines ST and QR are parallel
Checking the first figure gives
= PS / SQ
= 7.5 / 17.5
= 0.428571
Also
= PT /TR
= 8.7 / 20.3
= 0.428571
since the ratio is equal the two lines are parallel in the
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Answer:I’m not sure what the second one is
Step-by-step explanation:
If you know the names of the remaining students in the spelling bee, what is the probability of randomly selecting an order and getting the order that is used in the spelling bee?.
Answers
The probability of randomly selecting an order and getting the order that is used in the spelling bee is 0.001388888
Given we have the following:
Number of students in the spelling bee = 6
Number of ways selecting a student in the spelling bee = 6!
The probability of randomly selecting an order and getting the order that is used in the spelling bee :
P(selecting the correct spelling bee order) = 1/6!
= 1/6*5*4*3*2*1
= 1/720
= 0.001388888
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71.1g of sugar is needed to make 9 cakes. How much sugar is needed for 4 cakes?
Answers
Base on the given ratio of quantity of sugar to number of cakes, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar
How much sugar is needed for cakes?Ratio refers to a number representing a comparison between two named things or quantities. The ratio of sugar and cake is the comparison between the quantity of sugar used to make cake.
If 71.1g of sugar is needed to make 9 cakesQuantity of sugar needed to make 4 cakes = xFind the ratio of quantity of sugar to number of cakes
Quantity of sugar : Number of cakes
71.1 g : 9 cakes = x : 4 cakes
71.1 / 9 = x / 4
cross product71.1 × 4 = 9 × x
284.4 = 9x
divide both sides by 9x = 284.4 / 9
x = 31.6g of sugar
In conclusion, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar
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How can you write the expression using rational exponents?
5 square root n4
Answers
By using exponent properties, we can see that the equivalent expressions are:
[tex]5*\sqrt{n^4} = 5*n^2[/tex]
How to rewrite the expression?Here we need to use some rules for exponents and roots. Remember that:
[tex]\sqrt[n]{x} = x^{1/n}[/tex]
We also will use that:
[tex](a^n)^m = a^{n*m}[/tex]
Now we have the following expression:
[tex]5*\sqrt{n^4}[/tex]
Particularly, the square root is equivalent to an exponent of 1/2, then we can write:
[tex]5*\sqrt{n^4} = 5*(n^4)^{1/2}[/tex]
Using the second property we can rewrite:
[tex]5*(n^4)^{1/2} = 5*n^{4*1/2} = 5*n^2[/tex]
So the equivalent expressions are:
[tex]5*\sqrt{n^4} = 5*n^2[/tex]
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