I can enter the problem here so ill add a picture, sorry for the inconvenience
Answers
Given two numbers a and b
Their Arithmetic mean (A), Geometric mean (G) and Harmonic mean (H) are given below,
[tex]\begin{gathered} A=\frac{a+b}{2} \\ G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \end{gathered}[/tex]To find the formula that correctly relates H, a and b,
Relating the last two equations, i.e the geometric and harmonic mean below,
[tex]\begin{gathered} G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \\ \text{relating both equations} \\ \sqrt[]{ab}=\sqrt[]{AH} \\ \text{Square both sides } \\ (\sqrt[]{AH})^2=(\sqrt[]{ab})^2 \\ AH=ab \\ \text{Make H the subject},\text{ by dividing both sides by A} \\ \frac{AH}{A}=\frac{ab}{A} \\ H=\frac{ab}{A} \end{gathered}[/tex]Substituting for A into the above expression,
[tex]\begin{gathered} \text{recall A=}\frac{a+b}{2} \\ H=\frac{ab}{A}=\frac{ab}{\frac{a+b}{2}} \\ H=(2\times\frac{ab}{a+b})=\frac{2ab}{a+b} \\ H=\frac{2ab}{a+b} \end{gathered}[/tex]Hence, A is the correct option.
Related Questions
What is the solution to the equation below? Round your answer to twodecimal places.eX = 7.9
Answers
Solution
For this case we have the following equation:
[tex]e^x=7.9[/tex]For this case we can apply natural log in both sides and we got:
[tex]\ln (x)=\ln (7.9)=2.07[/tex]and then the solution would be:
D. x =2.07
Help the question is attached
Answers
The correct option will be A that is t=(A-P)/Pr by the simplification of equation, "an equation is a mathematical statement that shows that two mathematical expressions are equal ".
What is equation?In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. In mathematics, an equation is a relationship of equality between two expressions written on both sides of the equal to sign. 3y = 16 is an example of an equation. Some examples of important equations are:
Linear equationsQuadratic equationsCubic equationQuadratic equationsDifferential equationsParametric equationsHere,
A=P+Prt
A-P=Prt
t=(A-P)/Pr
The answer is A, which is t=(A-P)/Pr using the equation's simplified form. An equation is a mathematical statement that demonstrates the equality of two mathematical expressions.
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Solve for x in x^3 = 64/27.
Answers
ANSWER
[tex]x\text{ = }\frac{4}{3}[/tex]EXPLANATION
We have that:
[tex]x^3\text{ = }\frac{64}{27}[/tex]64 and 27 are perfect cubes. This is because they are integers that can be gotten when another integer is raised to the third power or multiplies itself three times.
So, to get x, we can find the cube root of both sides:
[tex]\begin{gathered} \sqrt[3]{x^3}\text{ = }\sqrt[3]{\frac{64}{27}} \\ \Rightarrow\text{ x = }\sqrt[3]{\frac{4\cdot4\cdot4}{3\cdot3\cdot3}} \\ x\text{ = }\frac{4}{3} \end{gathered}[/tex]That is the value of x.
Figure T is the result of a transformation on Figure S. Which transformation would accomplish this? 6 -4 -3 2 3 Figure S Figure T -3 -4 -5
Answers
Let:
[tex]\begin{gathered} A=(1,-1) \\ A^{\prime}=(3,-2) \\ A\to(x+a,y+b)\to A^{\prime} \\ so\colon \\ 1+a=3 \\ a=3-1=2 \\ ---- \\ -1+b=-2 \\ b=-2+1=-1 \\ so\colon \\ A\to(x+2,y-1)\to A^{\prime} \end{gathered}[/tex]Therefore, the transformation T is:
A translation 2 units right and 1 unit down
Answer the questions below.(a) The perimeter of a rectangular parking lot is 314 m.If the width of the parking lot is 71 m, what is its length?Length of the parking lot: 0 m(b) The area of a rectangular pool is 8075 m.If the length of the pool is 95 m, what is its width?Width of the pool: m
Answers
We have to use the perimeter formula for rectangles
[tex]P=2(w+l)[/tex]Where P = 314 m and w = 71 m.
[tex]\begin{gathered} 314=2(71+l) \\ \frac{314}{2}=71+l \\ 71+l=157 \\ l=157-71 \\ l=86 \end{gathered}[/tex]Hence, the length is 86 meters.9. Use the figure shown to identify each.
a. Vertical angles
b. Adjacent angles
c. Linear pairs
d. Supplementary angles
e. Complementary angles
Answers
The angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
We are given a figure and we need to identify the angle.
Let us identify the angle:
a. Vertical angles:
Each of the pairs of opposite angles is made by two intersecting lines.
In the given figure,
angle 3 and angle 5 are vertical angles.
b. Adjacent angles:
In the given figure,
angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles:
The sum of the two angles should be 180 degrees.
In the given figure,
angle 4 and angle 5.
e. Complementary angles:
The sum of the two angles should be 90 degrees.
In the given figure,
angle 1 and angle 2.
Thus, the angles in the given figure are:
a. Vertical angles: angle 3 and angle 5.
b. Adjacent angles: angle 1, angle 2, angle 3, angle 4, and angle 5.
c. Linear pairs: angle 3 and angle 4, angle 4 and angle 5.
d. Supplementary angles: angle 4 and angle 5.
e. Complementary angles: angle 1 and angle 2.
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5#Consider the following random sample of diameter measurements (in inches) of 12 softballs.4.72, 4.74, 4.83, 4.75, 4.73, 4.87, 4.69, 4.7, 4.76, 4.7, 4.79, 4.76Send data to calculatorIf we assume that the diameter measurements are normally distributed, find a 90% confidence interval for the mean diameter of a softball. Give the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.)Lower limit:??Upper limit:??
Answers
ANSWER:
Lower limit: 4.73
Upper limit: 4.78
STEP-BY-STEP EXPLANATION:
Given the following data set:
[tex]4.72,4.74,4.83,4.75,4.73,4.87,4.69,4.7,4.76,4.7,4.79,4.76[/tex]We calculate the mean and standard deviation:
[tex]\begin{gathered} \mu=\frac{4.72+4.74+4.83+4.75+4.73+4.87+4.69+4.7+4.76+4.7+4.79+4.76}{12}=\frac{57.04}{12}=4.753 \\ \\ \sigma=\sqrt{\frac{\lparen4.72-4.753^2+\left(4.74-4.753\right)^2+\lparen4.83-4.753)^2+\left(4.75-4.753\right)^2+\left(4.73-4.753\right)^2+\lparen4.87-4.753)^2+\left(4.69-4.753\right)^2+\lparen4.7-4.753)^2+\left(4.76-4.753\right)^2+\left(4.7-4.753\right)^2+\left(4.79-4.753\right)^2+\left(4.76-4.753\right)^2}{12-1}} \\ \\ \sigma=0.054 \end{gathered}[/tex]The critical limit of 90% confidence interval is 1.645
We can determine the limits as follows:
[tex]\begin{gathered} \text{ Lower limit: }\mu-Z\cdot\frac{\sigma}{\sqrt{n}}=4.753-1.645\cdot\frac{0.054}{\sqrt{12}}=4.727\cong4.73 \\ \\ \text{ Upper limit:: }\mu+Z\cdot\frac{\sigma}{\sqrt{n}}=4.753+1.645\cdot\frac{0.054}{\sqrt{12}}=4.778\cong4.78 \end{gathered}[/tex]The probability that an employee will be late to work at a large corporation is 0.21. What is the probability on a given day that in a department of 5 employees at least 3 are late ?
Answers
Given:
Number of employees are 5.
Probability that an employee will be late to work at a large corporation is 0.21.
The given data follows binomial distribution,
[tex]\begin{gathered} X\text{ \textasciitilde{}B(n,p,q)} \\ n=5 \\ p=0.21 \\ q=1-p=1-0.21=0.79 \\ P(X=x)=^nC_xp^xq^{n-x} \end{gathered}[/tex]The probability that at least 3 employees are late is given as,
[tex]\begin{gathered} P(X\ge3)=P(X=3)+P(X=4_{})+P(X=5) \\ P(X\ge3)=^5C_3(0.21)^3(0.79)^{5-3}+^5C_4(0.21)^4(0.79)^{5-4}+^5C_5(0.21)^5(0.79)^{5-5} \\ P(X\ge3)=0.0578+0.0077+0.0004 \\ P(X\ge3)=0.0659 \end{gathered}[/tex]Answer: The probability that in a department of 5 employees at least 3 are late is 0.0659.
x + 6=13 show the steps
Answers
The first two steps to solve the equation 3x2−7=47+7xare shown below:Step 1: 3x2−7x−7−47=0Step 2: 21x2−49x−49−4=0Which property is applied in step 1 to obtain step 2?Adivision property of equalitydivision property of equalityBaddition property of equalityaddition property of equalityCmultiplication property of equalitymultiplication property of equalityDsubtraction property of equality
Answers
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets p left after
t minutes of printing is given by the function p(t) = -8t + 100.
Part A
How long would it take the printer to use all 100 sheets of paper? Explain how you found your answer.
Answers
It will take 12.5 minutes by the printer to use all 100 sheets of paper as the function is p(t) = -8t + 100 where p is the number of sheets left after t minutes of printing.
What is function?A mathematical expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). The property that every input is related to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets. Four broad categories can be used to classify different types of functions. dependent upon element Function is a one-to-one relationship, a many-to-one relationship, onto function, one-to-one and into function.
Here,
p(t)=-8t+100
Tanya is printing a report. There are 100 sheets of paper in the printer, and the number of sheets of paper p left after t minutes of printing is given by the function .When all the 100 sheets printed , then the number of sheets will left to print =0.
Substitute p(t)=0 in the given function, to find the value of t,
0=-8t+100
8t=100
t=12.5 minutes
The function is p(t) = -8t + 100, where p is the number of sheets left after t minutes of printing, and it will take the printer 12.5 minutes to use all 100 sheets of paper.
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Please assist me, oh great smart people of the internet!
Answers
The value of x in (5 + 2x)/3 < (2x + 2)/4 is x < - 7.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, Inequality is (5 + 2x)/3 < (2x + 2)/4.
Now, (5 + 2x)/3 - (2x + 2)/4 < 0.
{4(5 + 2x) - 3(2x + 2)}/12 < 0.
{20 + 8x - 6x - 6}/12 < 0.
(2x + 14)/12 < 0.
2x + 14 < 0.
x + 7 < 0.
x < - 7.
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A skating rink manager finds that revenue R based on an hourly fee F
for skating is represented by the function R = -480F² + 3120F.
What hourly fee will produce maximum revenues?
Answers
The hourly fees of $3.25 will produce the maximum value of revenue in the Skating rink.
Given function of the form:
R = -480F² + 3120F
Here R is the revenue and F is the hourly fees.
Now we will differentiate with respect to F
Hence.
[tex]\frac{dR}{dF} = -960F + 3120[/tex]
Now to find the maximum value we have to find the value of F for which [tex]\frac{dR}{dF}[/tex] is zero.
hence :
-960F+3120 = 0
or, F=3.25
Hence the value of F is 3.25 for which the revenue will be maximum.
Maxima and minima, the corresponding plurals of lower and upper bound of a function, are used in mathematical analysis to refer to the highest and lowest value of such a function, whether it be within or a defined range, the local the relative extrema, or throughout the entire domain.
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help meeeeeeeeeeeeeee pleaseeeeeee
Answers
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Solve the quadratic equation by using the quadratic formula. 3x^2-5x+1=4 Enter your solutions below from smallest to largest. If a solution is repeated type that answer for both values of x. If your answer is not an integer then type it as a decimal rounded to the nearest hundredth.
Answers
Answer:
x = -0.47, x = 2.14
Step-by-step explanation:
Quadratic formula is my favorite!!
Let's first take that four over to the other side
Subtract 4 from both sides
3x^2-5x-3
a = 3
b = -5
c = -3
Remember quadratic formula: [tex]x=\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex]
IGNORE THE A BEFORE THE ±
Plug in our a, b, and c values: [tex]x=\frac{-(-5)±\sqrt{5^2-4(3)(-3)} }{2(3)}[/tex]
Simplify: [tex]x=\frac{5±\sqrt{25+36} }{6}[/tex]
Simplify some more: [tex]x=\frac{5±\sqrt{61} }{6}[/tex]
Solve:
x ≈ -0.47
x ≈ 2.14
Solve for x:
2.50+1.50x=3.25+1.25x
Answers
Answer:
x = 3
Step-by-step explanation:
Multiply both sides by 100
2.5 · 100 + 1.5x · 100 = 3.25 · 100 + 1.25x · 100
Refine:
250 + 150x - 250 = 325 + 125x - 250
Simplify:
150x = 125x + 75
Subtract 125x from both sides:
150x - 125x = 125x + 75 - 125x
simplify:
25x = 75
Now all you have to do is Divide both sides by 25:
[tex]\frac{25x}{25}[/tex] = [tex]\frac{75}{25}[/tex]
Now Finally the last part Now just Simplify so therefore the answer is
x = 3
Find (f + g)(x), if f(x) = - 5x2 + 6 and g(x) = x2 - 6.4x2- 6x2 + 12- 4x2- 6x2 - 12
Answers
Given the functions:
[tex]\begin{gathered} f(x)=-5x^2+6 \\ g(x)=x^2-6 \end{gathered}[/tex][tex]\begin{gathered} (f+g)(x)=f(x)+g(x) \\ (f+g)(x)=(-5x^2+6)+(x^2-6)=-5x^2+x^2+6-6 \\ (f+g)(x)=-4x^2+0=-4x^2 \end{gathered}[/tex]The answer is: C. -4x^2.
-6.75 Natural, whole, integer, rational, irracional, real,
Answers
-6.75 is a rational number.
Let us understand about natural, whole, integer, rational, and irrational numbers one by one.
Natural number:
Natural numbers are numbers that start from 1 and end at infinity. These are non-negative numbers.
Whole number:
Whole numbers are numbers that start from 0 and end at infinity.
We can also natural numbers including 0 is known as whole numbers.
These are non-negative numbers.
Integer:
An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Rational number:
A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the rational number is terminating and recurring.
Irrational number:
An irrational number is a number that can not be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.
Also, the decimal representation of the irrational number is non-terminating and non-recurring.
The given number is -6.75.
The decimal form is terminating.
So, it is a rational number.
Thus, -6.75 is a rational number.
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Beginning with the equation 27x=54, write the new equation produced by dividing both sides by 9
Answers
Answer:
3x=6
Step-by-step explanation:
27/9=3, 54/9=6 so answer is 3x = 6
how long will it take for the population to reach 5656 fish, according to this model?
Answers
Question:
Solution:
The population growth is given by the following equation:
[tex]P(t)=(707)2^{\frac{t}{3}}[/tex]where P represents the number of individuals and t represents the number of years from the time of introduction. Now, if we have a population of 5656 fish, then the above equation becomes:
[tex]5656=(707)2^{\frac{t}{3}}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }\frac{5656}{707}[/tex]this is equivalent to:
[tex]2^{\frac{t}{3}}\text{ = }8[/tex]this is equivalent to:
[tex](2^t)^{\frac{1}{3}}\text{ = }8[/tex]now, the inverse function of the root function is the exponential function. So that, we can apply the exponential function to the previous equation:
[tex]((2^t)^{\frac{1}{3}})^3\text{ = }8^3[/tex]this is equivalent to:
[tex](2^t)^{\frac{3}{3}}^{}\text{ = }512[/tex]this is equivalent to:
[tex]2^t\text{ = }512[/tex]now, we can apply the properties of the logarithms to the previous equation:
[tex]\log _2(2^t)\text{ = }log_2(512)[/tex]this is equivalent to:
[tex]t=log_2(512)\text{ = 9}[/tex]we can conclude that the correct answer is:
9 years
A restaurant uses 8 ¼ pounds of flour to make 6 cakes. Beatriz wants to use the same recipe. How many pounds of flour does she need for one cake?
Answers
If A restaurant uses [tex]8\frac{1}{4}[/tex] pounds of flour to make 6 cakes. Beatriz wants to use the same recipe, then [tex]1\frac{3}{8}[/tex] pounds of flour is used for one cake
What is Division?A division is a process of splitting a specific amount into equal parts.
Given,
A restaurant uses [tex]8\frac{1}{4}[/tex] pounds of flour to make 6 cakes
We need to find how many pounds of flour does she need for one cake
To find this we just need to divide [tex]8\frac{1}{4}[/tex] pounds by 6.
[tex]8\frac{1}{4}[/tex] is 33/4
33/4/6
33/24
11/8
[tex]1\frac{3}{8}[/tex] pounds
Hence [tex]1\frac{3}{8}[/tex] pounds of flour is used for one cake
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What is the length of the segment shown on the graph? (Label your answer "units".)
Answers
Using the above graph, we can calculate that the segment has a length of 8 units.
What is the definition of a line segment?A line segment in geometry has two different points on it that define its boundaries. A line segment is sometimes referred to as a section of a line that links two places. The difference between a line and a line segment is that a line has no endpoints and can go on forever in any direction.Describe a line segment example.In real life, a line segment may be a stick, a pencil, or a ruler. The sun's beams are an illustration of a segmentThe graph shows the segment and dimensions given at the end of the segment are -4 and 4.
Thus we can say that, the first half of the segment is having the length 4 units and the other half also has the same length of 4 units.
By, adding both these lengths we get,
4 + 4 = 8 units
Therefore, the length of the segment is 8 units which is computed using the given graph.
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cost: $41.80
rate of tip: 20%
Answers
Answer:
50.16 if you add 20 %
if you need the original price and this is with the 20% included then 33.44
Step-by-step explanation:
points (-2,1) and (3,y) have a slope of -3. find the y coordinate of the point
Answers
y coordinate of the point is -14
Explanation:Slope = change in y/change in x
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ m\text{ = -3} \end{gathered}[/tex]Since m is negative, it means the slope is negative.
[tex]\begin{gathered} It\text{ also means the 2nd y value will be smaller than the 1st y value to get negative slope} \\ x_1=-2,y_1=1,x_2=3,y_2\text{ = y} \\ m\text{ = }\frac{y-1}{3-(-2)} \end{gathered}[/tex][tex]\begin{gathered} -3\text{ = }\frac{y-1}{3+2} \\ -3\text{ = }\frac{y-1}{5} \\ -3(5)\text{ = y - 1} \\ -15\text{ = y - 1} \\ \end{gathered}[/tex][tex]\begin{gathered} -15\text{ + 1 = y} \\ y\text{ = -14} \\ y\text{ coordinate of the point is -14} \end{gathered}[/tex]you are planning a survey of starting salaries for recent business majors. in the 2018 survey by the national association of colleges and employers, the average starting salary was reported to be $56,720. if you assume that the standard deviation is $11,500, what sample size do you need to have a margin of error equal to $1,000 with 95% confidence?
Answers
The sample size you need to have a margin of error equal to $1,000 with 95% confidence is; 508
How to find the sample size?Formula for margin of error is given by the formula;
E = z(σ/√n)
where;
z is z-score at significance level
σ is standard deviation
n is sample size
We are given;
σ = $11500
z at significance level of 0.05 is 1.96
margin of error; E = $1000
Thus;
1000 = 1.96(11500/√n)
√n = (1.96 * 11500/1000)
√n = 22.54
n = 22.54²
n ≈ 508
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Create and solve a story problem that would use this equation: y=5x+3 Be sure to define x, y, the constant, and the variable.
Answers
Answer:
A group of 3 teenagers wants to go out to a movie each ticket is 5 dollars, they all decide to share popcorn wich costs 3 dollars
Step-by-step explanation:
X=3 of the teenagers Y=18 the total cost
The constant is 5 because all the tickets cost and stay 5 dollars
And the variable is x because the amount of teenagers can change
Answer:
A Group Of 3 Family members wants to go out But the Table for 3 People cost 5 Dollars, So they just all decide to just Eat Icecream
Step-by-step explanation:
Which is $3. X=3 of the Family Members Y=18 The Total Cost The Constant is 5 because all of the tickets cost & stay $5 dollars & The variable is X because of the amount of money The Family Members have.
How do I figure out what graph(s) is linear or exponential? can someone explain how to do this for me?
Answers
Answer:
Linear functions are graphed as straight lines while exponential functions are curved. Linear functions are typically in the form y = mx + b, which is used to discover the slope, or simply the change in y divided by the change in x, while exponential functions are typically in the form y = (1 + r) x.
Step-by-step explanation:
What is the solution to the equation 7x−4=3x−8 , given the replacement set {−3, −1, 1} ?
A. -3
B. -1
C. 1
D. I don't know
Please answer fast!
I will give 85 points to whoever answers this question first, and I will also give whoever answers first brainliest.
Answers
Answer: B
Step-by-step explanation:
7x-4=3x-8
Combine like terms
7x-3x=4-8
Simplify
4x=-4
Divide
x=-1
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If x machines are made in the unit cost is given by the function C(x)=x^2-520x+79,797. What is the minimum unit cost? Do not round your answer.
Answers
Answer:
The minimum unit cost is $12,197.
Explanation:
The cost function is given below:
[tex]C\mleft(x\mright)=x^2-520x+79,797[/tex]To find the minimum unit cost, first, find the derivative of C(x).
[tex]C^{\prime}(x)=2x-520[/tex]Next, set the derivative equal to 0 and solve for x.
[tex]\begin{gathered} 2x-520=0 \\ 2x=520 \\ x=520\div2 \\ x=260 \end{gathered}[/tex]Finally, substitute x=260 into C(x) to find the minimum cost.
[tex]\begin{gathered} C\mleft(x\mright)=x^2-520x+79,797 \\ \implies C(260)=(260)^2-520(260)+79,797 \\ =67600-135,200+79,797 \\ =12,197 \end{gathered}[/tex]The minimum unit cost is $12,197.
Which of these pieces of data about a package delivered by the post office is considered categorical data?A. Surface areaB. WeightC. Volume D. Dropoff location
Answers
Answer
D. Dropoff location
Step-by-step explanation
Quantitative variables are any variables where the data represent amounts (e.g. surface area, weight, or volume of a package). Categorical variables are any variables where the data represent groups (for example classifications like cities or brands).