Answer:
Mathematics shaping the modern world.
f(x)=x 3 −9xf, Over which interval does f have a positive average rate of change?
The interval in which the function has positive average rate of change is x > √3
How to determine the interval which the function has positive average rate of change?The function is given as
f(x) = x^3 - 9x
Differentiate the above function to determine the average rate of change
So, we have
f'(x) = 3x^2 - 9
Set the function to greater than 0
So, we have
3x^2 - 9 > 0
Add 9 to both sides
3x^2 > 9
Divide by 3
x^2 > 3
Take the square root of both sides
x > √3
Hence, the interval in which the function has positive average rate of change is x > √3
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A diver is located at -157 feet relative to the surface of the water. If there is a shark swimming 38 feet above him,what is the position of the shark relative to the surface of the water
Answer: -119 feet relative to the surface of the water.
Step-by-step explanation:
Shark Depth ( x ) + Distance from Shark and Diver ( 38 ) = Divers position (-157)
x = -119
The diver is at -157 feet relative to the surface. The shark is swimming 38 feet above the diver, making its position -119 feet relative to the surface.
Given that,
Diver's depth: -157 feet (relative to the surface of the water)
Shark's position: 38 feet above the diver
The question asks for the position of the shark relative to the surface of the water.
The position of the shark can be determined by adding the distance above the diver to the depth of the diver.
So, the position of the shark would be:
-157 feet (diver's depth) + 38 feet (distance above the diver) = -119 feet relative to the surface of the water.
Hence,
The shark is located at -119 feet relative to the surface of the water.
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36-9 divided by 9 = 3 insert parentheses to make the statement true
Answer:(36-9)÷9
Step-by-step explanation: If 36-9=27 then 27÷9=3 since 9×3=27hope this helped :)
Q8. How many triangles are there in the figure?
Answer:
I don't know there's no figure
Step-by-step explanation:
I don't have any clue is the answer because their is no figure so stop being umb and show me the pic lo ser
Please help!!! 10 point.
Answer:
x+20
Step-by-step explanation:
because ist correct
6 What types of decimal numbers are rational? What types are irrational?
7 Write down two more examples (decimal, fraction, etc.) of each type of number: rational and irrational. Explain your choices.
On December 31, 2019, Akron, Inc., purchased 5 percent of Zip Company's common shares on the open market in exchange for $16,050. On December 31, 2020, Akron, Inc., acquires an additional 25 percent of Zip Company's outstanding common stock for $94,000.
During the next two years, the following information is available for Zip Company:
Income Dividends Declared Common Stock
Fair Value (12/31)
2019 $321,000
2020 $79,000 $6,200 376,000
2021 89,000 15,800 478,000
At December 31, 2020, Zip reports a net book value of $280,000. Akron attributed any excess of its 30 percent share of Zip's fair over book value to its share of Zip's franchise agreements. The franchise agreements had a remaining life of 10 years at December 31, 2020.
On Akron’s December 31, 2021, balance sheet, what amount is reported for the Investment in Zip account?
The amount reported for the investment in Zip Company by Akron's December 31, 2021, balance sheet is $143,400, which is the fair value of the Common Stock of Zip Company.
What is the fair value of an investment?The fair value of an investment is the current value and not the historical cost when the investment was made.
Fair value refers to the intrinsic worth of an asset or security.
Data and Calculations:Income Dividends Common Stock Akron's Investment
Declared Fair Value (12/31) in Zip Company
2019 $321,000 $16,050 ($321,000 x 5%)
2020 $79,000 $6,200 376,000 $94,000 ($376,000 x 25%)
2021 89,000 15,800 478,000 $143,400 ($478,000 x 30%)
Excess attributed to share of Zip's franchises = $33,350 ($143,400 - $110,050).
Thus, the amount reported for the investment in Zip Company by Akron's December 31, 2021, balance sheet is $143,400.
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Admission to a baseball game is $4.00 for general admission and $6.50 for reserved seats. The receipts were $4589.50 for 988 paid admissions. How many of each ticket were sold?
There were 733 general tickets sold and 255 reserved tickets.
How to calculate the values?Let the general admission = g
Let the reserved seats = r
Therefore, the appropriate equation will be:
g + r = 988
4g + 6.5r = 4589.50
From equation i r = 988 - g
4g + 6.5r = 4589.50
4g + 6.5(988 - g) = 4589.50
4g + 6422 - 6.5g = 4589.50
6.5g - 4g = 6422 - 4589.50
2.5g = 1832.50
g = 1832.50/2.5
g = 733
Since g + r = 988
r = 988 - 733
r = 255
Therefore, there were 733 general tickets sold and 255 reserved tickets.
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If the mean of a +1, a +4, a +7, a +8 and a + 10 is 12, find a
To find the mean of a set of numbers, we find their sum and divide it by the number of terms there are.
Solving the Question
We're given:
The mean of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) is 12Find aThe sum of (a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10) divided by 5 (because there are 5 numbers) is 12. Write this as an equation:
[tex]12=\dfrac{(a + 1) + (a + 4) + (a + 7) + (a + 8) + (a + 10)}{5}[/tex]
Simplify:
[tex]12=\dfrac{a + 1 + a + 4 + a + 7 + a + 8 + a + 10}{5}\\\\12=\dfrac{5a + 30}{5}\\\\12=a +6\\a=6[/tex]
Answera = 6
To collect data on the signal strengths in a neighborhood, Tracy must drive from house to house and take readings. She has a graduate student, Dave, to assist her. Tracy figures it would take her 8 hours to complete the task working alone, and that it would take Dave 12 hours if he completed the task by himself.
How long will it take Tracy and Dave to complete the task together?
Tracy and Dave together complete the task in [tex]\frac{24}{5}[/tex] hours
Given Tracy alone take 8 hours to complete work and dave alone take 12 hours to complete the work.
Let's say together they worked in x hours
⇒in 1 hour they worked [tex]\frac{1}{x}[/tex]th part of the work
Tracy herself worked 8 hours to complete the whole task
⇒ in 1 hour Tracy completes [tex]\frac{1}{8}[/tex]th part of the task
Dave himself worked 8 hours to complete the whole task
⇒ in 1 hour Dave completes [tex]\frac{1}{12}[/tex]th part of the task
By proportions
⇒[tex]\frac{1}{8}[/tex]+[tex]\frac{1}{12}[/tex]=[tex]\frac{1}{x}[/tex] { using operation addition}
⇒ x= [tex]\frac{24}{5}[/tex]
Therefore,Tracy and Dave together complete the task in [tex]\frac{24}{5}[/tex] hours
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PLEASE HELP !! 20 POINTS
A piecewise function f (x) is defined by f of x is equal to the piecewise function of 3 to the power of the quantity x plus 1 end quantity minus 2 for x is less than or equal to 1 and the quantity negative x squared plus x plus 2 end quantity over the quantity x squared minus 3 times x plus 2 end quantity for x is greater than 1
Part A: Graph the piecewise function f (x) and determine the range. (5 points)
Part B: Determine the asymptotes of f (x). Show all necessary calculations. (5 points)
Part C: Describe the end behavior of f (x). (5 points)
From the graph of the piecewise function, we have that:
a) The range of the function is (-∞,7).
b) The vertical asymptote is of x = 2, and the horizontal asymptotes are y = -1 and y = -2.
c) The end behavior of the function is described as follows: As x -> -∞, y -> -2 and as x -> ∞, y -> -1.
What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
For this problem, the definitions of the function are given as follows:
[tex]f(x) = 3^{x+1} - 2, x \leq 1[/tex].[tex]f(x) = \frac{-x^2 + x + 2}{x^2 - 3x + 2}, x > 1[/tex]The graph of the function is given at the end of the answer.
What is the range of the function?The range of the function is the set that contains all the output values of the function, and in a graph, this is the values of y.
Hence:
The range of the function is (-∞,7).
What are the asymptotes of the function?The asymptotes of the functions are the values of x for which the function is not defined. In this problem, the function is not defined for x = 2, hence the vertical asymptote is of x = 2.
The horizontal asymptotes are the values of the function when it goes to infinity, hence they are y = -2 and y = -1.
What is the end behavior of the function?The end behavior is given by the limits of the function as it goes to infinity, being closely related to the horizontal asympotes.
Hence:
As x -> -∞, y -> -2 and as x -> ∞, y -> -1.
Please ignore the (60,1) point plotted on the graph, it should be (60,-1).
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#2 i
ZAINE COOPER
USING RATIOS An entrepreneur wants to rent a billboard at least 30 feet tall to display an advertisement for her business. She
is 5 feet 6 inches tall and casts a shadow 7 feet long. At the same time, a billboard casts a shadow 35 feet long. Is the billboard
tall enough? how do you solve this?
The billboard is not tall enough as the height is 27.5ft which is less than 30ft.
The comparison of two quantities having the same units is called as Ratio.
ratio between quantity a and b is represented by a:b .
In the given question
The bill board should have at least 30ft height.
Height of lady = 5 ft 6 inches
=5.5 ft ...( as 6inch=0.5ft )
If the height of the lady is 5.5ft shadow length = 7 feet
Since the units of height of lady and length of shadow is same .
hence ratio can be used ,
also given that length of billboard = 35 ft.
Let the height of the bill board = x ft
The above situation can be represented using ratio as
(height of lady) / (length of shadow of lady)=(height of billboard)/( length of billboard shadow)
Substituting the values we get
5.5/7=x/35
On solving further we get
(5.5/7)*35=x
5.5*5=x
x=27.5
The height of the billboard is 27.5 ft .
Since , it is given that the height of the bill board should be at least 30ft tall , and the height of the billboard is 27.5ft.
Therefore , the billboard is not tall enough as the height is less than 30ft.
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How do we know the following relation is NOT a function
A relation that does not have the function property of each and every input having exactly one output.
A function is defined as a relation between a group of inputs having one output each. In simple words, a function may be a relationship between inputs where each input is related to exactly one output. Every function features a domain and range. A function is usually denoted by f(x) where x is the input.
The types of functions can be broadly classified into four types. supported Element: One to one Function, many to at least one function, onto function, one to at least one and onto function, into function.
A function may be a relation between a set of inputs (called the domain) and a permissible set of outputs (called the codomain), such each input is related to exactly one output.
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If 1 shoe equals 6.5 socks, how many socks are equivalent to 2.3 shoes?
The equivalent number of socks to 2.3 shoes is 14.95 socks
Ratio and proportionsFractions are expression written as a ratio of two integers. For instance If 1 shoe equals 6.5 socks, this can be written as:
1 shoe = 6.5 socks
In order to determine the number of socks for 2.3 shoes, we will have:
2.3 shoes = x socks
Determine the ratio
1/2.3 = 6.5/x
Cross multiply
1 * x = 2.3 * 6.5
x = 2.3 * 6.5
x = 14.95
Hence the equivalent number of socks to 2.3 shoes is 14.95 socks
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what is 3x + 7 = 5x + 15?
Answer:
Step-by-step explanation:
if solved for x the answer is x=−4
step wise step
3x+7= 5x+15
3x-5x=15-7
-2x=8
x=8÷2
×=4
Reflexive Property of Angle Measure: mZB = ?- - -
Answer:
example of compound interest with solution
4. To make a specific hair dye, a hair stylist uses a ratio of 1 } oz of red tone, À oz of gray
tone, and oo | ur
Oz of brown tone.
a.
If the stylist needs to
b.
make 20 oz of dye, how much of each dye color is needed?
If the stylist needs to make 100 oz of dye, how much of each dye color is needed?
The answers to both the questions are as follows:
We need 3 ounces of red tone, 6 ounces of gray tone, and 5 ounces of a brown tone to make 20 ounces of dye.We need 15 ounces of red tone, 30 ounces of gray tone, and 25 ounces of a brown tone to make 100 ounces of dye.The quantity of specific hair dye produced by given ingredients are:
= 1(1/8) + 3/4 + 5/8= 9/8 + 3/4 + 5/8= (9+6+5)/8 = 20/8 = 5/2ozAs a result, the amount of specific hair dye produced by given ingredients = 5/2qz
To calculate the amount of each ingredient needed to make 1 oz of specific hair dye, multiply the reciprocal of 5/2 by each ingredient.The amount of red tone required to make 1 oz of a specific dye:
= 3/8 × 2/5 = 3/20 oz
Gray tone = 3/1 × 2/5 = 3/10 Oz Brown tone = 5/8 × 2/5 = 1/4 Oz=Now, multiply each by 20.
The amount of red tone required to make 20 oz of a specific dye:
3/20 × 20 = 3 oz
Gray tone = 3/10 × 20 = 6oz Brown tone = 1/4 × 20 = 5ozTo find each dye needed to make 100 ounces of dye, multiply the above amounts by 5.
(Since, 100 = 20 × 5)The amount of red tone required to make 20 oz of specific dye: 15oz
Gray tone is similar: 30 ozBrown tone is: 25 ozTherefore, the answers to both the questions are as follows:
We need 3 ounces of red tone, 6 ounces of gray tone, and 5 ounces of a brown tone to make 20 ounces of dye.We need 15 ounces of red tone, 30 ounces of gray tone, and 25 ounces of a brown tone to make 100 ounces of dye.Know more about ratios here:
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The correct question is given below:
To make a specific hair dye, a hair stylist uses a ratio of 1 1/8 ounces of red tone, 3/4 ounces of a gray tone, and 5/8 ounces of brown tone. If the stylist needs to make 20 ounces of dye, how much of each dye color is needed? If the stylist needs to make 100 ounces of dye, how much of each dye color is needed?
find the product 5/8 - 3/10
Answer: (FINDING THE PRODUCT)
Exact form:
-3/16
Decimal form:
-0.1875
Step-by-step explanation:
<3
Answer:
13/40
Please mark my answer as the brainliest, that would mean a lot to me
Step-by-step explanation:
5/8 - 3/10
50/80 - 24/80
26/80
13/40
If √128 = 2k , find the value of k.
Answer: k=[tex]{4\sqrt{2}[/tex]
Step-by-step explanation:
√128 = 2k
k=[tex]\frac{\sqrt{128}}{2}[/tex]
k=[tex]\frac{\sqrt{64*2}}{2}[/tex]
k=[tex]\frac{8\sqrt{2}}{2}[/tex]
k=[tex]{4\sqrt{2}[/tex]
Someone please help me I’m lost i don’t understand
1. 'x' = -18/4
2. 'x' = -4/3
The equations are Not Equivalent.
1. Linear Equation :An equation between two variables that gives a straight line when plotted on a graph. Or we can say,
A linear equation is defined as an equation that is written in the form of Ax+By=C. It is the combination of two variables and a constant value present in them.
We have given
(x/3) - 2 = (5x/3) + 3
(5x/3) - (x/3) = -2 - 3
4x/3 = -6
4x = -6 × 3
x = -18/4
In first equation we got the value of x is -18/4.
2. Equivalent to Linear Equation :Two systems of linear equations are equivalent if and only if they have the same set of solutions.
To determine the equivalent of linear equation,
First, we need to find the value of "x" for each equation. If "x" is the same for both equations, then they are equivalent. If "x" is different then the equations are not equivalent.
We have equation
x(x + 1) = (x + 2)²
x² + x = x² + 4 + 4x
(We have solved (x + 2)² by using algebraic identity (a + b)² = a² + b² + 2ab.)
4x - x = x²- x² - 4
3x = -4
x = -4/3
In the second equation we got the value of x is -4/3.
Hence, as we can see it clearly that the value of x is not same in both equations so this is Not Equivalent.
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Solve for rate in the following application problem. A company reports that office income last month was $315,400, while advertising expenses were $21,447.20. What percent of last month's income was spent on advertising?
Answer:
6.8%
Step-by-step explanation:
[tex]\frac{21447.20}{315400}[/tex] When you divide this, you get 0.068. This is in decimal form. To change to a percent move the decimal to places to the right 6.8%
7.Ms. Levine went to the store to
buy candy for Star Time. She
purchases Skittles for $9.75 box
per
and she bought 8 boxes. How much
did she spend in all?
Answer:
78 dollars
Step-by-step explanation:
9.75 multiplied by 8 is 78.
Paulette is paid 2 1/2 % commission on all sales, and an extra 1 1/2 % on all sales over $6,500. Her sales last week totaled $17,400. What were her total earnings for the week?
The total earnings in the form of commission for Paulette is $ 598.5.
Commission till sales of $ 6,500 = 2 1/2 %
So amount of commission will be
A = 5 / 200 × 17400
A = 5 / 2 × 174
A = $ 435
Extra commission:
E = 3 / 200 × ( 17400-6500)
E = 3 / 200 × 10900
E = 3 / 2 × 109
E = $ 163.5
Total commission = $ 435 + $ 163.5
T = $ 598.5
Therefore, the total earnings in the form of commission for Paulette is $ 598.5.
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1. Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?
The meeting point of the diagonal is the interior of the quadrilateral which is Point O.
Here is the quadrilateral PQRS you can find it is given below.
In this image you can see that a quadrilateral has four sides which is PQRS and two diagonals which is PR and QS,
then both diagonals intersects interior of quadrilateral each other at Point O.
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Jennifer has a total of 25
marbles. She gives 5 marbles
to her friend, Elizabeth.
What fraction of marbles did
Elizabeth receive?
Answer:1/5
Step-by-step explanation:
Answer:
1/5
Step-by-step explanation:
Ex) You pick a marble from a bag containing 2 blue marbles, 5 red marbles, and 3 purple marbles. You replace the marble and select a second marble.
What is the decimal form for the given fraction 640/1000
Answer:
0.64
Step-by-step explanation:
1.) 1000 = 10×10×10
2.) 640÷10=64
3.) 64÷10=6.4
4.) 6.4÷10=0.64
find the lcm of the following set of number using decomposition method.
8,16 and 24 =lcm=
Answer:
48
Step-by-step explanation:
[tex]\mathrm{The\:LCM\:of\:}a,\:b\mathrm{\:is\:the\:smallest\:positive\:number\:that\:is\:divisible\:by\:both\:}a\mathrm{\:and\:}b[/tex]
LCM of 8, 16 and 24
Decompose to prime factors
8/2 = 4; 4/2 = 2. So 8 = 2 x 2 x 2
16 = 8 x 2 = (2 x 2 x 2) x 2
24 = 8 x 3 = (2 x 2 x 2) x 3
2 x 2 x 2 is common, 2 appears once more as a factor in 16 and 3 appears in 24 so the LCM = (2 x 2 x 2) x 2 x 3 = 48
Write a system of equations modeling the given conditions. Then solve the system by the
substitution method and find the two numbers.
The sum of two numbers is 94. One number is 36 more than the other. Find the
numbers.
System of equations modeling the given conditions:
x + y = 94
x - y = 36
Solving:
In order to use substitution, you have to isolate one of the variables in either of the equations
Using the second equation and isolating the variable x:
x - y = 36
x = 36 + y
then you can substitute x back into the first equation
36 + y + y = 94
36 + 2y = 94
2y = 58
y = 29
and then substitute 29 for y into either one of the equations
x + 29 = 94
x = 65
Pre algebra pick a yes or no
Answer:
see explanation
Step-by-step explanation:
to determine if the values of y are a solution to the equation, substitute the values of y into the left side and if equal to the right side then they are a solution.
y = 70
[tex]\frac{70}{7}[/tex] - 1 = 10 - 1 = 9 ≠ - 2 → NO
y = 56
[tex]\frac{56}{7}[/tex] - 1 = 8 - 1 = 7 ≠ - 2 → NO
y = - 7
[tex]\frac{-7}{7}[/tex] - 1 = - 1 - 1 = - 2 → YES
y = 0
[tex]\frac{0}{7}[/tex] - 1 = 0 - 1 = - 1 ≠ - 2 → NO
Answer:
Yes. I think that is a pre algebre question.
o qualify for security officers’ training recruits are tested for stress tolerance. The scores are normally distributed, with a mean of 62 and a standard deviation of 8.
If only the top 15% of recruits are selected, find the cutoff score.
The cutoff score is mathematically given as
x_n=70.32 (cutoff)
This is further explained below.
What is the cutoff score.?Generally, the equation for is mathematically given as
[tex]&P\left(X > x_0\right)=0.15 \Rightarrow P\left(X < x_0\right)=0.85 \\[/tex]
[tex]&\Rightarrow P\left(\frac{X-\mu}{\sigma} < \frac{x_0-\mu}{\sigma}\right)=0.85 \\[/tex]
[tex]&\Rightarrow P\left(Z < \frac{x_0-\mu}{\sigma}\right)=0.85 \\\\&\Rightarrow \frac{x_0-\mu}{\sigma}=\text { invNorm }(0.85) \\\\&\Rightarrow x_0=\mu+\sigma \times \text { invNorm }(0.85)[/tex]
Use z-table to get inv Norm() = 1.04
x_0=62+8 *(1.04)=70.32
In conclusion, Top 15% are above x_n=70.32 (cutoff)
Clearly this is 85th percentile
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