Answer:
0.01296
Step-by-step explanation:
I looked it up on this website: https://www.symbolab.com/solver/simplify-calculator/simplify%206%5E%7B-1%7D.6%5E%7B5%7D?or=input
That's the link to the solution, it shows you the steps, and you can look up other simplify questions there. It used to help me a lot.
To multiply powers with the same base, add their exponents. Add −1 and 5 to get 4.
6⁴
To calculate a power, multiply the base as indicated by its exponent. So:
The number 6 is the base.4 is the exponent.Therefore the number 6 will be multiplied 4 times,
6 × 6 × 6 × 6 = 12961296 ===> Answer
if the total debt in 2012 was 2978 billion, about how much was total credit card debt
Answer:
120Million
Step-by-step explanation:
thatev whwu g U (EDIT: IM SO SORRY THATS NOT THE ANSWER MY SISTER DID THAT)
It rained all day on Father's Day and the temperature dropped ten and seven tenth degrees. The next day the rain
stopped and the temperature rose twelve and six tenths degrees. If the temperature at the beginning of Father's Day
was sixty five and eight tenths degrees, what was the temperature at the end of the day after Father's Day?
Write numerical answer only (no sentences, no units)
BEER
Activate
Go to Settings
p. 10 of 19
Answer:
67.7
Step-by-step explanation:
Temperature at beginning of Father's Day = 65.8 degrees
Drop in temperature because of rain = 10.7 degrees
Rise in temperature after the rain the next day = 12.6 degrees
Therefore, temperature at the end of the day after the Father's Day
= Temperature at beginning of Father's Day minus Drop in temperature because of rain plus Rise in temperature after the rain the next day
= 65.8 - 10.7 + 12.6
= 67.7 degrees
NB: The answer was written as only 67.7 as requested by the questioner.
Simplify (c4)−5.
1 over c
c
1 over c raised to the twentieth power
−c20
The expression is simplified to 1 over c raised to the twentieth power. Option C
What are index forms?The index form of a number can be defined as the number written as an exponential expression.
It is expressed as a single number raised to another number.
Another name for index form is standard form or scientific notation.
Index notation is also a way of representing variables or constants multiplied by themselves a number of times.
Example of index forms are:
a²
b³
c²
From the information given, we have to simplify
(c^4)^−5
Using the rule of indices, we have to multiply the powers
c^-20
Thus, the expression is simplified to 1 over c raised to the twentieth power. Option C
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Answer:
1 over c raised to the twentieth power
Step-by-step explanation:
lesson 7.2 NEED HELP!
Find the missing length indicated. Leave your answer in simplest radical form.
The missing length of the given triangle with measurements using triangle proportion are;
For first diagram; x = 48
Foe second diagram; x = 60
For third diagram; x = 100
For fourth diagram; x = 25
What is triangle proportion?
According to the Triangle proportion rule, When a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
In first diagram;
The side with x is a reflexive side of both triangles and as such from triangle proportionality theorem we can say that;
⇒ x/64 = 36/x
After cross multiply we get;
x² = 64 * 36
x = √2304
x = 48
Thus, we conclude that the missing length indicated is x = 48.
In second diagram;
Let y is the smaller side of the base out of which 64 has been taken.
Thus; y = 100 - 64
y = 36
Let the perpendicular height of triangle is 'z';
z/36 = 64/z
z² = 64 * 36
z = √2304
z = 48
Now, For finding the value of x we can apply the Pythagoras theorem;
x² = 48² + 36²
x² = 2304 + 1296
x² = 3600
x = √3600
x = 60
So, The missing length indicated is x = 60.
In third diagram;
Let the perpendicular height of triangle is 'y'.
Then apply Pythagoras theorem as;
60² = 36² + y²
y² = 3600 - 1296
y = √2304
y = 48
Now, Apply the triangle proportionality theorem we get;
48/36 = (x - 36)/ 48
48 * 48 = 36 (x - 36)
64 = x - 36
x = 64 + 36
x = 100
Hence, The missing length indicated is x = 100.
In fourth diagram;
Let the perpendicular height of triangle is 'y';
Apply Pythagoras theorem as;
15² = 9² + y²
y² = 225 - 81
y = √144
y = 12
Now, Apply the triangle proportionality theorem we get;
12/9 = (x-9) /12
144 = 9 (x-9)
16 = x - 9
x = 25
So, The missing length indicated is x = 25.
Therefore, The missing length of the given triangle with measurements using triangle proportion are;
For first diagram; x = 48
Foe second diagram; x = 60
For third diagram; x = 100
For fourth diagram; x = 25
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TIMED PLEASE HELP When f = 2 and g = 8, n = 4. If n varies jointly with f and g, what is the constant of variation?
1/4
1/2
4
64
The Answer is 1/4
Step-by-step explanation:
The required constant of variation for given data is k = 1/4
The correct option is (a)
What is constant of variation?In a direct variation, the product of two variables; in an inverse variation, the ratio of two variables, is called constant of variation
Formula:
k = \(\frac{n}{fg}\)
How calculate constant of variation?Here we have given that n = 4, f = 2 and g = 8
Substitute the given values into above formula
k = \(\frac{4}{2(8)} =\frac{1}{4}\)
The required constant of variation is 1/4
Therefore the correct option is (a)
This is the conclusion to the answer.
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In 2-3, graph the system of equations to find the solution to the system. Then, use the check step to prove that the solution works in both equations. Show all work
The system of equations has an infinite number of solutions.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 = 8 is an equation.
We have,
3x + 2y = 6 ____(1)
6x + 4y = 12 _____(2)
Applying the substitution method.
3x + 2y = 6
x = (6 - 2y)/3 in (2)
6 (6 - 2y)/3 + 4y = 12
2 (6 - 2y) + 4y = 12
12 - 4y + 4y = 12
12 = 12
This means,
It has an infinite number of solutions.
Thus,
An infinite number of solutions.
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The complete question is:
Graph the system of equations
3x + 2y = 6
6x + 4y = 12
and find the solution to the system.
21x =7?
A. x=3
B. None of these
C. x=147
D. x=28
Answer: B
Step-by-step explanation:
To isolate x, you divide both sides by 21
21x=7
\(\frac{21x}{21}=\frac{7}{21}\)
x = 7/21
Simplify by dividing both the numerator and denominator by 7
x = 1/3
Since, 1/3 is not an option, B is the correct answer
Help help please I really need it
Find the area of the triangle.
b ft
h yd
Question content area bottom
Part 1
The area of the triangle is
enter your response here or
enter your response here .
The area of the triangle is 52.32 square units
Finding the area of the trianglefrom the question, we have the following parameters that can be used in our computation:
The triangle (see attachment)
The base of the triangle is calculated as
base = 12 * tan(36)
The area of the triangle is then calculated as
Area = 1/2 * base * height
Where
height = 12
So, we have
Area = 1/2 * base * height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 12 * tan(36) * 12
Evaluate
Area = 52.32
Hence, the area of the triangle is 52.32 square units
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Find the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity.
Step-by-step explanation:
To calculate the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity, we can use the formula for the present value of an annuity due:
PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)
where:
- PV is the present value of the annuity due ($32,000)
- PMT is the monthly payment we want to find
- r is the annual interest rate (7.9%)
- n is the number of times interest is compounded per year (12 for monthly compounding)
- t is the number of years (10)
PMT = PV / ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n) = **$292.07**
Therefore, the required monthly payment to accumulate $32,000 in 10 years at an APR of 7.9% compounded monthly for an annuity is **$292.07**.
1.8x7+3 (1 point)
o 67
o 80
o 59
o 18
From a group of 10 people, you randomly select 3 of them.
What is the probability that they are the 3 oldest people in the group?
Give your answer as a fraction
The probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.
What is fraction?
A fraction is a method of representing a part of a whole or a ratio of two numbers. It is a number that is written in the form of one integer (the numerator) over another integer (the denominator), separated by a line or slash.
The probability of selecting the 3 oldest people in a group of 10 people depends on the assumption that all 10 people are distinct individuals and that the selection process is truly random.
The total number of ways to select 3 people from a group of 10 people is given by the combination formula:
C(10, 3) = 10! / (3! * 7!) = 120
This means that there are 120 possible ways to select a group of 3 people from a group of 10 people.
Since we are interested in selecting the 3 oldest people, we assume that the 3 oldest people are identified and we only need to select them from the group of 10 people. There is only 1 way to select the 3 oldest people out of the group of 10 people.
Therefore, the probability of selecting the 3 oldest people in a group of 10 people is:
P = Number of ways to select the 3 oldest people / Total number of ways to select 3 people from a group of 10 people
P = 1 / 120
P = 0.0083
So, the probability of selecting the 3 oldest people in a group of 10 people is approximately 0.0083 or 0.83%.
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Nina is buying 8 avocados. each avocados weighs 8 oz. how much will they cost her if avocados cos $2.99 per pound
If avocados costs $2.99per pound, Nina will be paying $1.495
How to solve for the amount Nina would payThe information given in the problem shows that
avocado's have their price in pounds hence we convert the quantity given to pounds
1 pound = 16 ounces
? = 8 ounces
cross multiplying
8 * 1 = ? * 16
? = 8 / 16
? = 1/2
hence 8 ounces is 0.5 pounds
Then the cost of 0.5 pounds of avocados will be solved for
1 pounds = $2.99
0.5 pounds = ?
cross multiplying
? = 0.5 * 2.99
? = $1.495
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please help! What is the distance, rounded to the nearest tenth, between the points (0,5) and (8,0)? ___ units
Please explain how to do this problem. it confused me
21n over 9n in lowest terms
Answer:
21n/9n
= 7n/3n
21n/9n in the lowest terms is 7n/3n
Elena’s bowling league tracks the number of strikes that each player on her team gets. It also tracks the number of games bowled. The table shows the results. Name Games Strikes Elena 10 7 Jenna 7 8 Freya 3 6 Ginny 6 12 Carol 13 15 Katie 9 18 The graph shows the relationship between each player’s games and strikes. Determine which team members have the same ratio of games to strikes, and select their corresponding points on the graph.
Answer:
Step-by-step explanation:
It's asking for those who have the same amount of strikes to the amount of games. For example Jenna gas played 7 games, and Elena has gotten 7 strikes. Their asking how many members have gotten the same amount of strikes to the amount of games they've played.
This should be a big help.
When the dilation has a scale factor greater than 1, it is considered an _____
A. enlargement
B. reduction
Answer:
A. enlargement.
Step-by-step explanation:
when you multiply a number by anything greater than one the number will go up. and if it is 1 or less than one the number will go down
Five years older than Mukhari. Find the value of the expression if Mukhari is 43 years old.
The volume of this prism is 2 1/2 cubic centimeters.
Its height is 1/3 of a centimeter.
What are possible values for its length and width?
One of the Possible values of length and width of the prism are 15 cm and 0.5 cm
What is the volume of the prism?In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases.
Given here: The volume of the prism is 2¹/₂=2.5 cm³
And the height is 1/3 cm
let the length and breadth of the prism is x and y respectively.
We know the volume of the prism as
1/3 × x×y=2.5
x×y=7.5
Thus possible values of length and breadth are the factors of 7.5
out of which one of the pair whose length is 15 cm and width 0.5 cm
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Evaluate the expression when x = 8 and y = 1.
x2y
Answer:
1/8
Step-by-step explanation:
I took the test this is it
HELP? IF CAN DOESNT MATTER WHEN I JUST NEED A HELP
Answer:
5
Step-by-step explanation:
Mark spins a penny 100 times and it lands head-side up 41 times. Explain why Mark's experimental probability may be different from the theoretical probability of spinning a coin. (10 points)
Answer:
Mark's experimental probability may be different from the theoretical probability of spinning a coin due to several factors. First, the penny may not be perfectly balanced, which can affect how it lands. Secondly, Mark may have spun the penny with a particular technique or force, which can also affect the way the penny lands. Thirdly, the surface on which the penny is spun may not be perfectly level, which can introduce factors that affect the way it lands.
Overall, these factors can cause Mark's experimental probability to deviate from the theoretical probability, which assumes that the coin is perfectly balanced and spun randomly on a level surface. However, over a large number of spins, the experimental probability should become closer to the theoretical probability, as the effects of these factors average out.
Demonstrate the deference types of equipment that can be used to introduce numeracy to young children
Introducing numeracy to young children can be done through various types of equipment and resources that engage their senses and make learning math concepts more interactive and enjoyable.
Here are some different types of equipment commonly used to introduce numeracy to young children:
Counting blocks: Colorful blocks that children can use to physically count and group numbers.Number rods: Wooden rods or bars of different lengths that help children understand number values and comparisons.Counting bears: Small bear-shaped counters that children can use for counting, sorting, and basic addition and subtraction.Number puzzles: Jigsaw puzzles or manipulative puzzles with numbers, helping children recognize and order numerals.Math storybooks: Books that incorporate mathematical concepts into stories, making math more relatable and enjoyable for children.Picture books with numeracy themes: Books that use illustrations and visuals to introduce and reinforce numeracy concepts.Thus, by incorporating a variety of equipment and resources, educators and parents can create a rich learning environment that supports children's numeracy development and fosters a positive attitude towards math.
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En un triatlón, Jenny nadó durante 1 hora, anduvo en bicicleta durante 1,75 horas y corrió durante 1 hora. Su velocidad promedio en bicicleta fue 2 veces su velocidad promedio para correr, y su velocidad promedio para correr fue 8 veces su velocidad promedio para nadar. La distancia total del triatlón fue de 55,5 kilómetros. Escribe una ecuación y resuélvela para encontrar la velocidad de nado promedio de Jenny en kilómetros por hora. Explique su ruta de solución y el razonamiento detrás de su trabajo.
Jenny's Average swimming speed is 1.5 km/h.
Jenny's average swimming speed as S (in km/h). We can then use the given information to set up equations and solve for S.
We know that Jenny swam for 1 hour, so the distance she swam is given by the formula: Distance = Speed * Time.
Thus, the distance she swam is S * 1 = S km.
Next, we know that her average running speed is 8 times her average swimming speed. Therefore, her average running speed is 8S km/h.
Since she ran for 1 hour, the distance she ran is 8S * 1 = 8S km.
Furthermore, we are given that her average bicycling speed is 2 times her average running speed. Therefore, her average bicycling speed is 2 * 8S = 16S km/h.
She biked for 1.75 hours, so the distance she biked is 16S * 1.75 = 28S km.
The total distance of the triathlon is the sum of the distances for each segment: Distance(swimming) + Distance(running) + Distance(biking) = 55.5 km.
Therefore, we can write the equation:
S + 8S + 28S = 55.5.
Simplifying the equation, we get:
37S = 55.5.
To solve for S, we divide both sides of the equation by 37:
S = 55.5 / 37 = 1.5.
Thus, Jenny's average swimming speed is 1.5 km/h.
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Rewrite the function by completing the square. h ( x ) = x 2 + 3 x − 18 h(x)=x 2 +3x−18
The quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
We are given a quadratic function:
h (x) = x^2 + 3x − 18
We need to rewrite the function by completing the square.
We can see the coefficient of x is 3.
So, we will add and subtract the square of half that.
So, find the square of half of 3, we will get;
(3 / 2)^2 = 9 / 4 = 2.25
add and subtract the square of half of 3 from the given function, we will get;
h(x) = x^2 +3x + -18 2.25 -2.25
arrange the expression, we will get;
h(x) = (x^2 +3x +2.25) -18 -2.25
write the expression in parentheses as a square, and simplify the constant, we will get;
h(x) = (x + 1.5)^2 - 20.25
So, the square function is written as h(x) = (x + 1.5)^2 - 20.25.
Thus, the quadratic function h (x) = x^2 + 3x − 18 by completing the square is witten as h(x) = (x + 1.5)^2 - 20.25.
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If you are dealt 4 cards from a shuffled deck of 52 cards, find the probability of getting two queens and two kings.
If you are dealt 4 cards from a shuffled deck of 52 cards, the probability of getting two queens and two kings is: 0.000133.
ProbabilityNumber of ways to get two of the four queens = 4C2 = 6 ways
Number of ways to get two of the four kings = 4C2 = 6 ways
Number of ways to get none of the deck = 48C0 = 1 way
Hence,
Number of ways to get four cards = 6 x 6 x 1
Number of ways to get four cards = 36 ways
Number of ways 4 cards can be chosen from 52 cards = 52C4 = 270725 ways
So,
Probability = 36 ways / 270725 ways
Probability = 0.0001329
Probability = 0.000133 (Approximately)
Therefore the probability is 0.000133.
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List all the subsets of the given set.
{e, n, t}
The subsets of the set {e, n, t} are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
How to obtain the number of subsets in a set?Considering a set with n elements, the number of subsets in the set is the nth power of 2, that is:
\(2^n\)
The set for this problem is given as follows:
{e, n, t}
The cardinality is given as follows:
n = 3.
Hence the number of subsets is given as follows:
2³ = 8.
The subsets are given as follows:
{{}, {e}, {n}, {t}, {e,n}, {e,t}, {n,t}, {e,n,t}}.
In which {} is the empty set.
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Determine whether the equation below has a one solutions, no solutions, or an
infinite number of solutions. Afterwards, determine two values of x that support your
conclusion.
X
6
-
X
The equation has Select an option
0
attempt 1 out of 2
The equation has one solution.
A value of x that makes the equation true is 6 which when substituted into the equation and simplified makes the equation turn into x = 0.
A value of x that makes the equation false is 8 which when substituted into the equation and simplified makes the equation turn into x = 2.
How to evaluate the equation?From the information provided, we have the following equation:
x - 6 = 6 - x
Rearranging the equation by collecting like terms, we have the following solution:
x + x = 6 + 6
2x = 12
x = 12/2
x = 6
Substituting the value "6" into the equation, we have the following solution;
x - 6 = 6 - 6
x - 6 = 0
Assuming x = 8, we have the following solution;
x - 6 = 8 - 6
x - 6 = 2
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Complete Question:
Determine whether the equation below has a one solutions, no solutions, or an infinite number of solutions. Afterwards, determine two values of x that support your conclusion.
x - 6 = 6 - x
The equation has _____.
A value of x that makes the equation true is ___ which when substituted into the equation and simplified makes the equation turn into ____.
A value of x that makes the equation false is ___ which when substituted into the equation and simplified makes the equation turn into ___.
a rectangular area of 24000 square feet is to be fenced on all four sides. fencing east and west sides cost $10 per foot fencing for the other two sides cost $20 per foot. what s the cost of least expensive
Answer:
C(min) = 8763.4 $
Step-by-step explanation:
Area = 24000 ft²
In a rectangle, A = x * y x is the base side and y the height side
Cost of low and upper side (x) is 20 $ per foot
Cost of east and west sides ( y) is 10 $per ft
total cost is:
C(r) = 2 * 20* x + 2* 10* y
from A = x * y y = A / x y = 24000 / x
And by substitution in C(r) we get:
C(x) = 2 * 20* x + 2* 10* 24000 / x
C(x) = 40 * x + 480000 / x
Tacking derivatives on both sides of the equation:
C´(x) = 40 - 480000 / x²
C´(x) = 0 40 - 480000/x² = 0
40* x² - 480000 = 0
x² = 480000 / 40
x² = 12000
x = √ 12000 = 109,54 ft
and y = 24000 / 109,54
y = 219,09 ft
Chequing for second derivative
C´´(x) = 480000 / x⁴ is always positive so we have a minimum of C at the value x = 109,54
Minimum cost C (min) = 40* 109,54 + 20 * 219,09
C(min) = 4381.6 + 4381.8
C(min) = 8763.4 $
According to Masterfoods, the company that manufactures M&M’s, 12% of peanut M&M’s are brown, 15% are yellow, 12% are red, 23% are blue, 23% are orange and 15% are green. [Round your answers to three decimal places, for example: 0.123]
Compute the probability that a randomly selected peanut M&M is not yellow.
Compute the probability that a randomly selected peanut M&M is brown or red.
Compute the probability that three randomly selected peanut M&M’s are all brown.
If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
P(brown) = 12% = 0.12
P(Yellow) = 15% = 0.15
P(Red) = 12% = 0.12
P(blue) = 23% = 0.23
P(orange) = 23% = 0.23
P(green) = 15% = 0.15
A.) Compute the probability that a randomly selected peanut M&M is not yellow.
P(not yellow) = P(Yellow)' = 1 - P(Yellow) = 1 - 0.15 = 0.85
B.) Compute the probability that a randomly selected peanut M&M is brown or red.
P(Brown) or P(Red) :
0.12 + 0.12 = 0.24
C.) Compute the probability that three randomly selected peanut M&M’s are all brown.
P(brown) * P(brown) * P(brown)
0.12 * 0.12 * 0.12 =0.001728
D.) If you randomly select three peanut M&M’s, compute that probability that none of them are blue.
P(3 blue)' = 1 - P(3 blue)
P(3 blue) = 0.23 * 0.23 * 0.23 = 0.012167
1 - P(3 blue) = 1 - 0.012167 = 0.987833
If you randomly select three peanut M&M’s, compute that probability that at least one of them is blue.
P(1 blue) + p(2 blue) + p(3 blue)
(0.23) + (0.23*0.23) + (0.23*0.23*0.23)
0.23 + 0.0529 + 0.012167
= 0.295067