How do you get from 5^0 to 5^-3
Answers
First, we know that 5^0 = 1, since any number raised to the power of 0 is equal to 1.
To get to 5^-3, we use the concept of negative exponents, which tells us that a number raised to a negative exponent is equal to 1 divided by the number raised to the corresponding positive exponent. In other words:
a^(-n) = 1 / a^n
Using this formula, we can rewrite 5^-3 as 1/5^3. Substituting 5^0 with 1, we get:
5^0 = 1
1 / 5^3 = 1 / (5 x 5 x 5) = 1/125
Therefore, 5^0 = 1 and 5^-3 = 1/125.
Related Questions
Maria sold 91 tickets and Sarah sold 70 tickets. What is the ratio of the number of tickets Maria sold to the total number of tickets sold?
Answers
Answer:000000 mdmdjdjc
Step-by-step explanation:ok
Questions attached. Please help
Answers
Line PQ is parallel to EF in the triangle DEF. So, ABC, DPQ, etc. Thus, we can state that A = D, B = P, and C = Q, indicating that the triangle ABC is comparable to the triangle DEF.
Are △ ABC and △ def similar?All sides are equal. The same triangles Two triangles ABC and DEF are comparable if the three related angles are all equal (written ABC DEF). Similar Lines Two lines are parallel if their paths do not cross.If the included sides are congruent and two of each triangle's angles match up with two of its other angles, the triangles are said to be congruent. the use of labels If angles A, B, and AB in triangle ABC equal angles D, E, and DE, then triangles ABC and DEF are congruent.DE is the same as 9, EF as 12, and DF as 7 centimetres. DO is the angle's bisector The idea being used: BAC follows if AD is the triangle's angle bisector.To learn more about triangle refer to:
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2(y+7)=46 Solve for y. Simplify equation as much as possible
Answers
Answer:
y=16
Step-by-step explanation:
2(y+7)=46
2y+14=46
-14 -14
2y=32
2y/2 = 32/2
y = 16
Answer:
y=16
Step-by-step explanation:
2(y+7) = 46
2y + 14 = 46
-14 -14
2y=32
divide by 2
y=16
Determine that the value x=9 of the following expiration given x2+3x-5
Answers
Step-by-step explanation:
To determine the value of x that satisfies the expression x^2 + 3x - 5 when x = 9, we simply substitute 9 for x and evaluate the expression:
9^2 + 3(9) - 5 = 81 + 27 - 5 = 103
Therefore, when x = 9, the expression x^2 + 3x - 5 evaluates to 103.
rate my answer, please.
The population of a city of 826,000 people decreases 3% per year.
Determine what the population of that city would be after 10 years.
Answers
Answer:
588200
Step-by-step explanation:
3% of 826,000 is 24780, 24780 x 10 years is 247800
826,000-247800= 588200
Find k so that the line x+y=k is a tangent to the circle x²+y²=9
Answers
Answer:
The values of k so that the line x + y = k is a tangent to the circle x² + y² = 9 are:
k = 3√2k = -3√2Step-by-step explanation:
A tangent line to a circle intersects the circle at exactly one point.
Rearrange the equation of the tangent line to isolate y:
\(\implies y=-x+k\)
Substituting this into the equation of the circle gives a quadratic equation in the x-coordinates of the points of intersection:
\(\implies x^2+(-x+k)^2=9\)
\(\implies x^2+x^2-2kx+k^2=9\)
\(\implies 2x^2-2kx+k^2-9=0\)
As we want this equation to have exactly one real solution, we can use the discriminant to find the value of k.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real solutions.\\when $b^2-4ac=0 \implies$ one real solution.\\when $b^2-4ac < 0 \implies$ no real solutions.\\\end{minipage}}\)
Substitute a = 2, b = -2k and c = (k² - 9) into the discriminant formula and set it equal to zero:
\(\implies (-2k)^2-4(2)(k^2-9)=0\)
Solve for k:
\(\implies 4k^2-8(k^2-9)=0\)
\(\implies 4k^2-8k^2+72=0\)
\(\implies -4k^2+72=0\)
\(\implies -4(k^2-18)=0\)
\(\implies k^2-18=0\)
\(\implies k^2=18\)
\(\implies k=\pm \sqrt{18}\)
\(\implies k=\pm \sqrt{9 \cdot 2}\)
\(\implies k=\pm \sqrt{9}\sqrt{2}\)
\(\implies k=\pm 3\sqrt{2}\)
Therefore, the values of k so that the line x + y = k is a tangent to the circle x² + y² = 9 are:
k = 3√2k = -3√2
Find the 37th term of the arithmetic sequence: -38,-8,22,52
Answers
Answer:
1042
Step-by-step explanation:
-38,-8,22,52
The common difference is 52 - 22 = 30
a_1 = -38
a_2 = -38 + 30
a_3 = -38 + 2 * 30
a_4 = -38 + 3 * 30 (notice that the common difference is multiplied by 1 less than the term number)
a_n = -38 + (n - 1)30 (since the term number is n, we multiply the common difference by n - 1)
a_n = -38 + 30(n - 1)
a_37 = -38 + 30(37 - 1)
a_37 = 1042
A truck with 30-in.-diameter wheels is traveling at 50 mi/h.
Find the angular speed of the wheels in rad/min, "hint convert miles to inches & hours to minutes:
_________rad/min
How many revolutions per minute do the wheels make?
___________rpm
Answers
Answer:
A. the angular speed is 3771.4 rad/min
b. 5921 rpms
Step-by-step explanation: I just got this same question right on a test.
If the statement shown is rewritten as a conditional statement in if-then form, which best describes the conclusion? When a number is divisible by 9, the number is divisible by 3. Then the number is divisible by 3 Then the number is divisible by 9 If a number is divisible by 3 If a number is divisible by 9
Answers
Correct conclusion for statement : When a number is divisible by 9, the number is divisible by 3 is "the number is divisible by 3".
What is statement and conclusion ?
The statement and conclusion section is basically a logical reasoning section, in which a statement is given followed by a few conclusions from which you are supposed to choose the one that makes the most sense logically after the statement.
The statement provided is:
When a number is divisible by 9, the number is divisible by 3.
The general form of a conditional statement in if-then form is :
p → q
This implies that if p, then q.
The part after the "if" is known as the hypothesis and the part after the "then" is known as the conclusion.
The if-then form of the provided statement is:
If a number is divisible by 9, then the number is divisible by 3.
So, the conclusion is:
"the number is divisible by 3"
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Answer: A (then the number is divisible by 3)
Step-by-step explanation: did it on edge
1. Plot the supply and demand schedule for the blu-ray movie "Frozen."
What is the equilibrium price?
What is the equilibrium quantity?
2. Best Buy decides to charge a price of $30.00 for the movie "Frozen."
What is the quantity demanded?
What is the quantity supplied?
Is this an example of a shortage or surplus?
What would Best Buy do to the price to get it back to equilibrium? _
3. Target decides to charge a price of $10.00 for the movie "Frozen."
What is the quantity demanded?
What is the quantity supplied?
Is this an example of a shortage or surplus?
What would Target do to the price to get it back to equilibrium?
Answers
1) the supply and demand schedule for Blue-ray movie "Frozen is attached accordingly.
Equilibrium price and quantity are $20 and 40 units respectively.
2) At a price of $30, quantity demand and supplied are 20 and 60 units respectively
This is an example of supply surplus.
To get the price back to equilibrium, they have to setthe price at $20 /unit
3) at $10 the quantity demand and supplied are 60 units and 20 units respectively.
This is an example of supply shortage.
increasing the price to $20 per unit will help achieve equilibrium.
What is market equilibrium?Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.
Equilibrium is important to create both balanced and efficient markets. If the market is in price-quantity equilibrium, then there is no reason for it to deviate from this point because it balances the quantity supplied and quantity demanded.
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3 1/8 divided by (x - 4 7/28) = 17/18 + 1 5/6
(Key on how to write the mixed numbers: Three is a whole number and then the fraction is 1/8, 4 is the whole number and 7/28 is the fraction, 1 is the whole number and 5/6 is the fraction)
Please provide the work and the answer! :)
Answers
x = 301/56
Algebraic expressionsAlgebra is the branch of mathematics that deals with numbers and values which are represented with letters and symbols.
Sometimes, we do not want to mention a particular number, we can represent the number by a letter or a suitable symbol. This approach is algebraic.
For example, d + d = 2d
This is an example of an algebraic expression
Given the algebraic expression,
\(3\frac{1}{8} \div (x - 4 \frac{7}{28} ) = \frac{17}{18} + 1 \frac{5}{6} \)
Step 1:
Simplify the expression by converting the mixed numbers into improper fractions:
25/8 ÷ ( x - 119/28) = 17/18 + 11/6
Step 2: Simplify the right side of the equation
25/8 ÷( x - 119/28) = 17/18 + 33/18
25/8 ÷( x - 119/28) = 50/18
Step 3: Multiply both sides of the equation by (x - 119/28)
25/8 = 50/18 × (x - 119/28)
Step 4: Multiply both sides of the equation by (18/50)
25/8 × (18/50) = (x - 119/28)
Step 5: Simplify the left side of the equation
9/8 = (x - 119/28)
Step 6: Add 119/28 to both sides of the equation
9/8 + 119/28 = x
Step 7: Calculate the value of x:
x = 9/8 + 119/28
= 63/56 + 238/56
= 301/56
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A bag contains five batteries, all of which are the same size and are equally likely to be selected. Each battery is a different brand. If you select four batteries at random, use the counting principle to determine how many points will be in the sample space if the batteries are selected
a) with replacement.
b) without replacement.
Answers
a) 625
b) 120
=============================================
Explanation:
If we select with replacement, then the first battery chosen is put back or we put a cloned copy in the bag. The contents of the bag have not changed. This means the second selection has the exact same identical situation as the first selection. By extension, any future selection has the same idea.
We have 5 batteries for any given selection, and we select 4 batteries. That gives 5*5*5*5 = 5^4 = 625 different outcomes in the sample space.
---------------
Now consider a situation where we don't apply replacement. Whatever is selected is not put back, and we don't put in a cloned copy. We go from 5 choices in the first selection, then 5-1 = 4 choices for the second, 5-2 = 3 choices for the third, and 5-3 = 2 choices for the fourth.
Overall there are 5*4*3*2 = 120 different outcomes in the sample space this time.
Another way to calculate this value is to plug n = 5 and r = 4 into the nPr permutation formula below
\(nPr = \frac{n!}{(n-r)!}\)
The exclamation marks represent factorials.
Does anyone know the answer?
Answers
Answer:
1 is the answer
(i) Write the zeroes of the polynomial by using above graph.
(ii)Form a quadratic polynomial for above graph.
(iii)If a,1/a are the zeroes of polynomial 2x² -x +8k, then find the value of k.
please answer
no spam only for darkparadox #darkparadox
Answers
There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
(i) Zeroes of the polynomial:
In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:
From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.
We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:
We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.
The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a
Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,
we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0
Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))
Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.
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2/21 into a decimal for pasted do work
Answers
Answer:
0.0952381
Step-by-step explanation:
you divide 21 from 2 (2/21)
A car shop has 12 mechanics, of whom 8 can work on transmissions and 7 can work on brakes. a) What is the minimum number who can do both? b) What is the maximum number who can do both? c) What is the minimum number who can do neither? d) What is the maximum number who can do neither?
Answers
Answer:both a and b are correct
Step-by-step explanation:
A later leans against the site of a house. The angle of deration of the latter is when the bottom of the latter is 14 from the side of the tone Find thelength of the latter. Round your answer to the nearest ten
Answers
Determine the length of ladder by using trigonometry in the triangle.
\(\begin{gathered} \cos 63=\frac{14}{l} \\ l=\frac{14}{\text{cos}63} \\ =30.83 \\ \approx30.8 \end{gathered}\)So length of ladder is 30.8 ft.
time series data of a typical the gap store should show which of the following data patterns? multiple choice a. trend b. cyclical c. seasonal d. all of the options are correct. e. random
Answers
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
What is time series data:
Time series data refers to a collection of data points that are measured over time at regular intervals. The time series data could refer to various metrics such as sales, revenue, foot traffic, website traffic, inventory levels, and other relevant business metrics that change over time.
By analyzing time series data, businesses can gain insights into trends, patterns, and other factors that can affect their operations.
Time series can be used for forecasting. By analyzing past trends and patterns, businesses can make predictions about future performance and take proactive measures to achieve their goals.
Since the time series will follow the trend, have multiple choices, and will be cyclical and it will analyze the patterns over time periods seasonally.
Therefore,
The time series data should show a. trend b. cyclical c. seasonal, so the correct answer is d. all of the options are correct.
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RATS is a parallelogram. M
Answers
Answer:
Answer:
x = 12
Step-by-step explanation:
m∠S + m∠T = 180
8x + 7x = 180
15x = 180
x = 12
does this help?
SOLVE FOR T
t+3/2 = -2
T =
Answers
Answer:\(t= -\frac{7}{2}\)
Step-by-step explanation:
\(=t+\frac{3}{2}=-2\\=t=-2-\frac{3}{2} \\=t=-\frac{7}{2}\)
I need help!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Its not A!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Its not!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Add quotation marks to the
sentence.
Take out your pencil, said
the teacher.
Answers
Step-by-step explanation:
Wylie is renting a bicycle from a local shop that charges $5 to rent a helmet, plus an hourly rate of $8.50 for the bike. For how long can Wylie rent a bicycle if he pays a total of $47.50? Enter your answer in the box.
hours
Answers
Answer:
Wylie can rent a bike for 5 hours.
Step-by-step explanation:
Since Wylie is renting a bicycle from a local shop that charges $ 5 to rent a helmet, plus an hourly rate of $ 8.50 for the bike, to determine for how long can Wylie rent a bicycle if he pays a total of $ 47.50 the following calculation has to be done:
(47.50 - 5) / 8.50 = X
42.50 / 8.50 = X
5 = X
Therefore, Wylie can rent a bike for 5 hours.
Cristina uses a ruler to measure the length of her math textbook. She says that the book is 4/10 meter long. Is her measurement in simplest form? If not, what is the length of the book in simplest form?
Answers
Answer:
2/5 meters
Step-by-step explanation:
what is the value of 4/15 ÷ 2/3
Answers
When you divide fractions you multiply by the reciprocal.
So you do 4/15 divided by 2/3 get the reciprocal of 2/3 and you have 3/2. 3 would become the nominator and 2 would become the denominator.
So then you would multiply right across 4/15 x 3/2, it would look like 4x3 and 15x2. (4x3=12) (15x2=30)
Then you’d get 12/30 which can be simplified it by 2 it’d be 6/15 but if you simplify it again by 3 you get your final answer 2/5
You know your done simplifying when both the nominator and denominators are prime numbers meaning they can only be divisive ale by 1 and itself
The value of 4/15 ÷ 2/3 is 2/5
In order to solve this, the first thing is to change the division sign to multiplication sign and this will be:
= 4/15 ÷ 2/3
= 4/15 × 3/2
= 12/30
Reduce to lowest term
12/30 = 2/5
In conclusion, the value of 4/15 ÷ 2/3 is 2/5.
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WILL GIVE BRAINILY 5 STARS AND THANKS FOR CORRECT ANSWERLenora wants to buy granola bars for her hiking trip. Eight bars cost $2.40. She wants to buy 12 bars. How much will 12 bars cost?
Answers
Answer:
$3.60
Step-by-step explanation:
2.40/8=.30
$.30 per bar
.3 x 12= $3.60
Answer:
$3.60
Step-by-step explanation:
Proportions
8 bars ⇔ $2.4
12 bars ⇔ $W
W = 12*2.4/8
W = $3.6
im getting confused on this part, i wasnt there the day for class to do this stuff
Answers
From the graph, it can be seen that it took 4 days to mow 30 lawns. 12 lawns can be mowed in 1 days.
A graph is what?Analyzing numerical data can be done using graphical representation. It uses a diagram to show the relationship between the data, ideas, information, and concepts. One of the most crucial learning strategies, it is also simple to understand. The kind of information in a particular domain is always a factor.
What are some examples of graphs?Examples include pictures, sketches, line art, graphs from mathematics, charts, diagrams, typography, numbers, symbols, geometric patterns, engineering drawings, or other images. Often, text, illustration, and color are combined in graphics.
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a. Lori packed 72 apples in 4 boxes and 184 apples in 8 boxes. B. Austin put 23rd in marbles and three bags and 126 marbles and 14 bags. C. Liza sold eight candy bars for $24 and 26 candy bars for $78
Answers
What is the five number summery for this set of numbers 34,35,37,38,42,45,49
Answers
The five number summary of the set of numbers is :
Minimum: 34First Quartile (Q1): 37Median: 38Third Quartile (Q3): 42Maximum: 49What is the five number summary ?A five number summary is a way to summarize a set of numerical data by providing five key values: the minimum, the first quartile (Q1), the median, the third quartile (Q3), and the maximum.
For the set of numbers 34, 35, 37, 38, 42, 45, and 49, the five number summary would be:
The minimum value is 34, the lowest value in the set.
The first quartile, also known as Q1, is the value that separates the lowest 25% of the data from the rest of the data, which is 37.
The median is the middle value, which is 38.
The third quartile, also known as Q3, is the value that separates the highest 25% of the data from the rest of the data, which is 42.
The maximum value is 49, the highest value in the set.
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Please help will mark Brainly
Answers
The number of tickets day and evening combined should be more then 8 since it says at least 8 tickets. However the cost of the tickets which is 15x+30y (multiply the amount of tickets bought by the cost) should be less then 300 bucks since they have a budget. Hope this helps!