Arithmetic mean and geometric mean of a and b are equal when a = b
Arithmetic mean
Arithmetic mean of two numbers is their sum divided by 2. Generally, arithmetic mean is the sum of the values divided by the total value. It gives the average of two or numbers. It is accurate when the data values are not much skewed.
For two numbers a and b, arithmetic mean = a + b /2
Geometric mean
Geometric mean of two numbers is the square root of its product. It is also used for the calculation of averages. For more than two numbers, the geometric mean is the 1/n th power of the product of the numbers. The skewness of the data values does not affect the accuracy in calculating the geometric mean.
For two numbers a and b, geometric mean = [tex]\sqrt{ab}[/tex]
Always arithmetic mean is larger than the geometric mean.
Arithmetic mean = Geometric mean
⇒ (a+b)/2 = [tex]\sqrt{ab}[/tex]
⇒ a+b = 2 [tex]\sqrt{ab}[/tex]
On squaring,
⇒ [tex]a^2 +2ab+b^2[/tex] = 4ab
⇒ [tex]a^2 -2ab+b^2[/tex] = 0
⇒ [tex](a-b)^2[/tex] = 0
⇒ a -b = 0
⇒ a = b
Arithmetic mean is equal to the geometric mean if the two numbers are equal.
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Use the properties of logarithms to evaluate each expression. log₁₅ 25+log₁₅9
Expression is [tex]log_{15}25[/tex] + [tex]log_{15} 9[/tex] = 2
The properties of logarithms are
log ab = log a + log b
log a/b = log a - log b
Evaluating it:
[tex]log_{15} 25[/tex] + [tex]log_{15} 9[/tex]
= [tex]log_{15} 25*9[/tex]
= [tex]log_{15} 225[/tex]
= [tex]log_{15}15^{2}[/tex]
= 2[tex]log_{15} 15[/tex]
= 2 × 1
= 2
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2,2y÷3-5y^2÷3+5y^3÷2,-4÷3+2y^2-y÷2,5y^2÷3+3y^3+3y+6÷5
Answer:
27#(2828282(2(282)2828282828282827
Mr. Delgado gets paid $40 per breaking
gig. If he has $120 saved, how many
breaking gigs will it take him to have
$400 if he doesn't spend any money?
Write AND Solve the Equation.
Answer:
7
Step-by-step explanation:
→ Write the equation
40x + 120 = 400
→ Minus 120 from both sides
40x = 280
→ Divide by 40 on both sides
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Mr. Delgado gets paid $40 per breaking gig. If he has $120 saved. If he doesn't spend any money.
Then the number of breaking gigs that it takes him to have is $400 will be
40x + 120 = 400
Simplify the equation then we have
40x = 280
x = 280/40
x = 7
The number of breaking gigs that it takes him to have is $400 will be 7 breaking gigs.
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Choose the equation that represents the graph.
PLS NEED FAST IF CORRECT ILL AWARD U
y = −2x − 4
y = 2x + 4
y = −2x + 4
y = 2x − 4
Answer:
y=-2x - 4
Step-by-step explanation:
The slope is 2 and the y-intercpt is -4
what property is 0x = 0
Answer:
Additive Identity Property of 0
Step-by-step explanation:
It means that additive identity is "0," as adding 0 to any number gives the sum as the number itself.
Find the percent of the given number. 79 % of 623
A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.
The percent of the given number 79 % of 623 is 492.17.
What is meant by percentage?A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.
Let the equation be 79 % of 623
Percentage = (value/total value) × 100 %.
Since, finding the fraction of a number is same as multiplying the fraction with the number, we have
79 % of 623 = 79/100 of 82
79/100 × 623 = 492.17
Therefore, the percent of the given number 79 % of 623 is 492.17.
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer: The decimal moves 9 places left- 1.322 x 10^-9
Step-by-step explanation:
Answer: The decimal moves 9 places left 1.322 x 10^9 so option 5
Step-by-step explanation:
Write a two-column proof for each case of Theorem 10.6 Case 3
Given: P lies outside
Prove: m< ABC = 1/2m AC
The measure of an inscribed angle is one-half the measure of the central angle.
What is the inscribed angle and the circumscribed angle?An inscribed angle in geometry is the angle formed in the interior of a circle when two chords intersect on the circle. It can also be defined as the angle formed by two given points on a circle at a given point on the circle.
The measure of an inscribed angle is one-half the measure of the central angle. The measure of a circumscribed angle is 180 degrees minus the measure of the central angle.
Given: P lies outside
m ∠ABC = m ∠DBC – m ∠DBA ( Addition Postulate, Subtraction Property of Equality)
m ∠DBC = m 1/2(arc DC)
m ∠DBA = m 1/2(arc DA) (The measure of an inscribed ∠ whose side diameter is half the measure of the intercepted arc (Case 1)).
m ∠ABC = m 1/2 (arc DC) – m 1/2(arc DA) (Substitution)
m ∠ABC = 1/2 [m(arc DC) – m(arc DA)] (Factor)
m(arc DA) + m(arc AC) = m(arc DC) (Arc Addition Postulate)
m(arc AC) = m(arc DC) – m(arc DA) (Subtraction Property of Equality)
m ∠ABC = m 1/2 (arc AC) (Substitution)
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Which is an equivalent expression for 4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity? 88 over d raised to the twelfth power 2 over quantity 11 times d raised to the twelfth power end quantity negative 2 over quantity 11 times d raised to the sixth power end quantity 0.2d12
The expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or 4d^(-3)/(22d^9) is equivalent to "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
An algebraic expression is a number, variable, or the combination of both and operational symbols.
To determine the equivalent of the expression "4 times d raised to the negative third power all over quantity 22 times d raised to the ninth power end quantity" or simply 4d^(-3)/(22d^9), combine all like terms and perform the necessary operations.
Using the following rules of exponents:
Quotient Rule for Exponents : a^m/a^n = a^(m - n)
Negative Exponent Rule : a^-m = 1/a^m
Simplify the expression.
4d^(-3)/(22d^9)
⇒ (4/22) [d^(-3)/d^9]
⇒ (2/11) [d^(-3 - 9)]
⇒ (2/11) d^-12
⇒ 2/(11d^12)
Hence, the equivalent expression is "2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
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Answer:
2 over quantity 11 times d raised to the twelfth power end quantity" or 2/(11d^12).
Step-by-step explanation:
Take has a square-shaped garage with 32 square meters of floor space. she plans to build an addition that will increase the floor space by 50%. what will be the length of one side of the new garage?
The length of one side of the new square-shaped garage is 4√3 meters.
A square is a two dimensional figure that has 4 equal sides. The area of a square can be solved by multiplying the length of its side by itself.
A = s^2
where s = side length
If the initial square-shaped garage has an area of 32 square meters and will be increased by 50%, then the new area should be 50% more than the initial area.
new floor area = 50% initial area + initial area
new floor area = 50%(32) + 32
new floor area = 16 + 32
new floor area = 48 square meters
If the new garage has a floor area of 48 square meters, using the formula for the area of a square, solve for the length of its side.
A = s^2
48 = s^2
s = 4√3 meters
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K
A woman traveled 2436.5 miles in 18 hours 15 minutes. Find the average speed of her flight in miles per hour. (Change
18 hours 15 minutes into hours and use the formula d=rt.)
The average speed of the woman's flight was mph.
(Do not round until the final answer. Then round to the nearest tenth of a mile per hour as needed?
Answer:
133.5
This is because transfer it to hours nd then divide and this is what you get
A soccer team brings a 4.5 -gallon cooler of water to their games. How many 4 -ounce cups can the team drink per game?
The number of 4 -ounce cups that the team can the team drink per game is 144.
It is given in the question that the soccer team brings a 4.5 gallon cooler of water to their games.
We have to find the number of 4 -ounce cups that the team can drink per game.
We know that,
1 gallon = 128 ounces
Hence, we can write,
4.5 gallon = 128*4.5 = 576 ounces
Hence, by using unitary method, we can write,
Number of 4 ounce cups the team can fill per game = ounces in 4.5 gallons/ounces in a cup = 576/4 = 144 cups.
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60 POINTS AND BRAINLIE$T
Is this table linear? I need help!
Given from the table below, Is the table linear or nonlinear?
Answer:
The table is linear because as x increases by 1, y changes by an average rate of |2|. You can also notice the tables both end in |+1|, which shows that the table has a constant rate of change between the two points at the end. Thus, the table is linear. If the table was nonlinear, there would be no constant rate of change between the 2 sets of data.
Solve each formula for the indicated variable. v = s² + 1/2 s h , for h
The solution of the formula v = s² + 1/2sh for the indicated variable h is 2(v - s²)/s.
According to the given question.
We have a formula v = s² + 1/2sh.
Since, we have to solve the above formula v = s² + 1/2sh for the indicated variable h.
Therefore, the solution of the above formula v = s² + 1/2sh for the indicated variable h is given by
v = s² + 1/2sh
⇒ v - s² = 1/2sh (subtracting s² from both the sides)
⇒ 2(v - s²) = sh (multiplying both the sides by 2)
⇒ 2(v - s²)/s = h (dividing both the sides by s)
⇒ h = 2(v - s²)/s
Hence, the solution of the formula v = s² + 1/2sh for the indicated variable h is 2(v - s²)/s.
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How many ways can five of the nine U.S supreme court justices agree? (With solution)
Mathematics: Combinations and Permutations
The number of ways can five of the nine us supreme court justices agree is 3024 ways.
How to compute the value?The number of ways that five of the nine us supreme court justices agree will be calculated thus:
= 9! / 5!
= (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2) / (5 × 4 × 3 × 2)
= 3024
There'll be 3024 ways.
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What is each number in scientific notation?
Drag the answer into the box to match each number.
Answer: the 1st one is 8.55 X 10^-5 the second one is 8.55 X 10^5
Step-by-step explanation:
when the decimal goes to the left, the exponents it's negative; when it's to the right, the exponent is positive. so one the 1st problem the decimal moved 5 spaces to the left giving it the value of 8.55 X 10^-5
The average weight of an apple is normally distributed with a mean of 0.33 of a pound with a standard deviation of 0.07. Michael went to the store and found an apple that weighted 0.50. What percent of the apples weigh less than the one Michael found?
Step-by-step explanation:
MEAN:0.33
STANDARD DEVIATION:0.07
WEIGHTED:0.50
0.33×0.07=0.0231÷0.50=0.0462
I am 3 units less than -3
Hi!
your answer is 0
hope this helps!
For each function, find the y -intercept
y=-3(x+2)²-4 .
Answer:
-16
Step-by-step explanation:
The y-intercept is when x=0.
[tex]y=-3(0+2)^2-4 \\ \\ =-3(4)-4 \\ \\ =-16[/tex]
Adelaide is the employee of the month at her job. Her reward is to select at random from 4 gift cards, 6 coffee mugs, 7 DVDs, 10 CDs, and 3 gift baskets. What is the probability that an employee receives a gift card, coffee mug, or CD?
According to the question, Adelaide is the employee and she has to select a reward from four gifts. And those are 6 coffee mugs, 7 DVDs, 10 CDs and 3 gift baskets.
Now, calculate the probability that the gift is either a coffee mug or CD.
Let us assume, ‘G’ represents the gift card, ‘C’ represents the coffee mug and ‘D’ represents the CD.
The total number of items are [tex]4+6+7+10+3 = 30[/tex] items
P(G or C or D) = P(G) + P(C) + P(D)
[tex]= \frac{4}{30} + \frac{6}{30} + \frac{10}{30} = \frac{20}{30} = \frac{2}{3} = 67%[/tex]
Therefore , the probability to receive either a gift card or coffee mug or CD is [tex]67[/tex] percent.
What is Probability?
The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.
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Find the 10 th term of each geometric sequence. a₉ =-5, r=-1/2
The 10th term of the geometric sequence as described in the task content is; 5/2.
What is the 10tg term of the geometric sequence as given in the task content?It follows from the task content that the 10th term of the sequence is to be determined.
On this note, since the 10th term differs from the 9th term by a factor of r, common ratio.
Hence; a(10) = a(9) × r
= -5 × (-1/2)
a(10) = 5/2.
Ultimately, the 10th term is; 5/2.
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A used car has a value of $15,250 when it is purchased in 2012. The value of the car decreases at a rate of 7.5% per year.
Write an exponential function that models the value
of the car over
years.
To the nearest cent, what will be the value of the car after eight years?
Answer:
after 8 years the value of the car would be $8,173.42
Step-by-step explanation:
the given P=15250
r=7.5/100=0.075
t=x
y = 15250*(1 - 0.075)^x
after 8 years we would have
x = 8
y = 15250*(1 - 0.075)^8
y = $8,173.42
after 8 years the value of the car would be $8,173.42
Answer:
8173.42
Step-by-step explanation:
I just know it's correct
Determine whether ΔA B C ≅ ΔX Y Z . Explain. A(5,2), B(1,5), C(0,0), X(-3,3), Y(-7,6), Z(-8,1)
The given triangles are congruent its that ΔA B C ≅ ΔX Y Z.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
There are many types of triangles such that right-angle triangles, equilateral triangles, and much more.
If ΔA B C ≅ ΔX Y Z then the corresponding sides will be the same.
Its that AB = XY , BC = YZ
The distance associated with two points (x₁, y₁) and (x₂, y₂) is given by
[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]
So,
(AB) = [tex]\sqrt {\left( {5 - 1 } \right)^2 + \left( {2 - 5 } \right)^2 }[/tex]
AB = 5
(XY) = [tex]\sqrt {\left( {-3 + 7 } \right)^2 + \left( {3 - 6 } \right)^2 }[/tex]
XY = 5
Similarly BC = YZ and CA = ZX.
Hence "The given triangles are congruent its that ΔA B C ≅ ΔX Y Z".
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URGENT!!!!! ILL GIVE BRAINLIEST! AND 100 POINTS
Put the numbers in order from smallest to largest.
Answer:
(from smallest to largest)
1. 3.24 × 10^-5
2. 5.48 × 10 ^-2
3. 1.2 × 10¹
4. 4.68 × 10⁶
5. 8.34 × 10⁶
Step-by-step explanation:
We can put these in order through the exponents.
Hope this helps!
Katherine is very interested in cryogenics (the science of very low temperatures).
With the help of her science teacher she is doing an experiment on the affect of low
temperatures on bacteria. She cools one sample of bacteria to temperature of -51°C
and another to -76°C. What was the temperature difference in the two experiments?
Temperature difference of experiments is -25°C.
Step-by-step explanation:
Given that
Katherine is very interested in cryogenics (the science of very low temperatures).With the help of her science teacher she is doing an experiment on the affect of low temperatures on bacteria.She cools one sample of bacteria to temperature of -51°C and another to -76°C.To find
Temperature difference in the two experimentsSo, according to the question
we have,
Temperature of 1st experiment = -51°C, andTemperature of 2nd experiment = -76°CWe have to find Temperature difference of experiments
So, we can say that
Temperature difference of experiments
= Temperature of 2nd experiment - Temperature of 1st experiment
Now, putting the all given values,
We, will get
Temperature difference of experiments = -76 - (-51)
= -76+51
= -25°C,
Answer:
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Determine whether y varies directly with x. if so, find the constant of variation k. 6y = 2x
Given the equation 6y = 2x, y varies directly with x and the constant of variation k has a value of 1/3.
There are two kinds of variations: direct and inverse.
Direct variation is a linear function defined by an equation of the form y = kx where variable y varies directly as x. On the other hand, inverse variation is a nonlinear function defined by an equation in the form y = k/x where variable y varies inversely as x.
Transforming 6y = 2x into a function of y,
y = 2/6 x
y = 1/3 x
where k = 1/3
Notice that it resembles the form y = kx which describes a direct variation between x and y.
Hence, the equation 6y = 2x shows that y varies directly with x and k = 1/3.
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b. What is another equation in point-slope form of the line through the points (-5,0) and (0,7) ? Explain.
0 - 7 = 7/5(-5 - 0) is the another equation in point-slope form of the line through the points (-5,0) and (0,7)
What is a slope of line?A line's steepness and direction are determined by the slope of the line. Without actually using a compass, determining a line's slope in a coordinate plane allows one to anticipate whether a line is parallel, perpendicular, or not.
The change in a line's y coordinate relative to its change in x coordinate is referred to as the line's slope. Δy is the net change in the y coordinate, while Δx is the net change in the x coordinate.
Therefore,
m = y₂-y₁/x₂-x₁ (where m denotes the slope) can be used to express how the y coordinate changes in relation to the x coordinate.
Be aware that tan ∅ = y/x
We also refer to this tan as the line's slope
If we reverse the point (-5,0) and (0,7) as (0,7) and (-5,0) line we will get another equation for (-5,0) and (0,7)
We know that point-slope form = y₂ - y₁ = m(x₂ - x₁)
But first we will find slope(m)
We know that slope = m = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]
For the pairs of points (0,7) and (-5,0)
⇒ m = [tex]\frac{0- 7}{-5 - 0}[/tex]
⇒ m = [tex]\frac{7}{5}[/tex]
⇒ m = 7/5
After we substitute the given information we get
0 - 7 = 7/5(-5 - 0)
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What is summation notation for the series?
a. -5+2+9+16+ . . . . . . . +261+268
The arithmetic series -5+2+9+16+ . . . . . . . +261+268 can be written using the summation notation as
[tex]7\sum\limits^{40}_{n=1} {n} -480[/tex]
Let
a(1) + a(2) + a(3) + ... + a(n)
be an arithmetic series.
Then, the nth term will follow the formula:
a(n) = a(1) + (n-1) . d
where d = the common difference.
The value of d is:
d = a(2) - a(1) = a(n) - a(n-1).
The series given is:
-5+2+9+16+ . . . . . . . +261+268
This is an arithmetic series with a(1) = -5 and
d = 2 - (-5) = 7
Substitute these parameters into the formula of the nth term:
a(n) = a(1) + (n-1) . d
a(n) = -5 + (n-1) . 7
a(n) = 7n - 12
Let a(n) = 268, then:
268 = 7n - 12
7n = 280
n = 40
The series can, then, be expressed as:
-5+2+9+16+ . . . . . . . +261+268
[tex]=\sum\limits^{40}_{n=1} {a(n)}[/tex]
[tex]=\sum\limits^{40}_{n=1} {(7n-12)}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -\sum\limits^{40}_{n=1} {12}[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -40\times12[/tex]
[tex]=7\sum\limits^{40}_{n=1} {n} -480[/tex]
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Simplify by combining like terms.
5+10 s-8 s
By combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
Given,
The algebraic expression = 5+10s-8s
Combine the like terms
5+10s-8s = 5+2s
Simplified form is 2s+5
Hence, by combining the like terms, the simplified form of the expression 5+10s-8s is 2s+5
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Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake. How many meters to the nearest tenth did Alexi's sister save by swimming?
Alexi’s sister saved about 18.4 meters by swimming across the river.
In this question,
Alexi walks 27 meters south and 38 meters east to get around a lake. Her sister swims directly across the lake.
The south and east directions are perpendicular.
The distance across the south, east and across the river form a right triangle, with the distance across the river as hypotenuse of right triangle.
Let x be the distance across the river.
Using Pythagoras theorem,
27² + 38² = x²
729 + 1444 = x²
2173 = x²
x = 46.6
The distance saved would be the difference between the sum of the two legs of the triangle and the hypotenuse (distance across the river).
distance saved = (27+38) - 46.6
= 18.4
Therefore, Alexi’s sister saved about 18.4 meters by swimming across the river.
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