The graph of an exponential function shows a geometric increase or decrease using a curve
Exponential graphsExponential functions are inverse of logarithmic functions. The standard exponential function is expressed as:
y = ab^x
where
a is the base
x is the exponent
The graph of an exponential function shows a geometric increase or decrease using a curve. According to the function given there will a decrease rate due to the value of the rate value given which is less than 1. The graph of the function given is attached below;
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Based on the family the graph below belongs to, which equation could represent the graph?
Considering the asymptotes of the function, the equation that represents the graph is:
[tex]y = \frac{1}{x + 2} + 3[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.This function, from the graph, has a vertical asymptote at x = -2, hence the denominator is given by:[tex]y = \frac{1}{x + 2} + 3[/tex]
x + 2, as x + 2 = 0 -> x = -2.
The horizontal asymptote is of y = 3, hence:
[tex]\lim_{x \rightarrow \infty} f(x) = 3[/tex]
Which means that the function is described by the following rule:
[tex]y = \frac{1}{x + 2} + 3[/tex]
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There are three novels on Sam's reading table: Light, Zami, and Money.
. On his next trip, he can choose to take some, none, or all of these novels. In the braces below, list all the possible sets of novels that Sam can take.
Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol Ø.
The subsets of the set of novels is given as follows:
{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.
How to find the subsets of a set?Suppose we have a set with cardinality n, that is, with n elements. This set will have 2^n subsets, which are all the possible combinations with the elements of the set, including the empty set.
In this problem, the novels are given as follows:
Light, Zami, and Money.
Hence the possible subsets are given as follows:
{Ø, {Light}, {Zami}, {Money}, {Light, Zami}, {Light, Money}, {Zami, Money}, {Light, Zami, Money}}.
With is the list that is asked for this problem, which are the subsets of the set of novels.
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Underwood Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of manufacturing overhead that should be assigned to each of the two product lines from the information given below. Wall Mirrors Specialty Windows Total units produced 30 30 Total number of material moves 7 18 Direct labor hours per unit 145 145 Budgeted material-handling costs are $30,000. The material-handling cost per wall mirror under activity-based costing is:
The material-handling cost per wall mirror under activity-based costing is $280
What is activity-based costing?
Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.
There 25 materials move in both divisions (i.e. 7+18=25)
Material-handling cost per material move=Budgeted material-handling costs /total material moves
Budgeted material-handling costs =$30,000
Material-handling cost per material move=$30,000/25
Material-handling cost per material move=$1,200
Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move
Total material-handing costs for wall mirror=7*$120
Total material-handing costs for wall mirror=$8,400
material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors
material-handling cost per wall mirror=$8,400/30
material-handling cost per wall mirror=$280
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How many pairs of parallel faces does this shape have?
Answer: one
Step-by-step explanation:
parallel faces are the ones that are opposite to each other.
Answer:
one
Step-by-step explanation:
there is only one pair of parallel faces.
27. Identify the domain of the set (6,2), (-1,-5), (4,4), (9, 2) and tell if the relation is a function.
O {-1, 4, 6, 9); not a function
O {-5, 2, 4}; a function
O {-1,4,6,9}; a function
O {-5, 2, 4); not a function
Answer:
the third one
Step-by-step explanation:
it is function that contain four domain
Hey guys I need some help with #11 so if anyone could help that would be great THANK YOU!!
Suppose follows the standard normal distribution. Use the calculator provided, or this table, to determine the value of so that the following is true.
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Answer:
c = 2.25
Step-by-step explanation:
The normal distribution function is symmetrical, so the area not in the central zone is split evenly between the lower and upper tails.
SolutionWe can find -c from ...
P(x < -c) = (1 - 0.9756)/2 . . . . . the area in the lower tail
The calculator tells us -c = -2.25.
c = 2.25
Given the following function, find f(-5), f(0), and f(3).
f(x) = x^2+5
Answer:
f(-5) = 30
f(0) = 5
f(3) = 14
Step-by-step explanation:
=> f(x) = x²+5
for , f(-5) = (-5)² +5
=> 25 +5
=> 30
for , f(0) = (0)² +5
=> 5
for , f(3) = (3)² + 5
=> 9 + 5
=> 14
A rectangular box is designed to have a square base and an open top. The volume is to be 500in.3 What is the minimum surface area that such a box can have?
The minimum surface area that such a box can have is 380 square
How to determine the minimum surface area such a box can have?Represent the base length with x and the bwith h.
So, the volume is
V = x^2h
This gives
x^2h = 500
Make h the subject
h = 500/x^2
The surface area is
S = 2(x^2 + 2xh)
Expand
S = 2x^2 + 4xh
Substitute h = 500/x^2
S = 2x^2 + 4x * 500/x^2
Evaluate
S = 2x^2 + 2000/x
Differentiate
S' = 4x - 2000/x^2
Set the equation to 0
4x - 2000/x^2 = 0
Multiply through by x^2
4x^3 - 2000 = 0
This gives
4x^3= 2000
Divide by 4
x^3 = 500
Take the cube root
x = 7.94
Substitute x = 7.94 in S = 2x^2 + 2000/x
S = 2 * 7.94^2 + 2000/7.94
Evaluate
S = 380
Hence, the minimum surface area that such a box can have is 380 square
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Difference of Squares gives which complex factors for the expression +3?
A. (x+3i)(x-3i)
B. (x-i-√3)(x-i√3)
C. (x+3i)^2(x-3i)²
D. (x+i√3)(x-i√3)
The difference of squares is:
(x+i√3)(x-i√3)
So the correct option is the last one, D.
Which expression gives x^2 + 3?For a complex number:
[tex]Z = a + b*i[/tex]
We define the complex conjugate of Z as:
[tex]Z' = a - b*i[/tex]
Such that the product between the complex number and its complex conjugate gives:
[tex]Z*Z' = a^2 + b^2[/tex]
Now, of you look at option D, you can see we have the product of a number and its conjugate, then we can write the product and use the above rule to get:
[tex](x + i\sqrt{3} )*(x - i\sqrt{3} ) = x^2 + (\sqrt{3} )^2 = x^2 + 3[/tex]
Which is what we wanted to get, so that is the correct option.
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The controller of MingWare Ceramics Inc. wishes to prepare a cost of goods sold budget for September. The controller assembled the following information for constructing the cost of goods sold budget: Direct materials: Enamel Paint Porcelain Total Total direct materials purchases budgeted for September $35,870 $7,530 $139,890 $183,290 Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 2,980 2,710 7,150 12,840 Direct labor cost: Kiln Department Decorating Department Total Total direct labor cost budgeted for September $51,550 $149,500 $201,050 Finished goods inventories: Dish Bowl Figurine Total Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850 Desired inventory, September 30 3,720 4,590 4,360 12,670 Work in process inventories: Estimated inventory, September 1 $3,540 Desired inventory, September 30 1,980 Budgeted factory overhead costs for September: Indirect factory wages $80,400 Depreciation of plant and equipment 10,550 Power and light 5,110 Indirect materials 3,390 Total 99,450 Use the preceding information to prepare a cost of goods sold budget for September. For those boxes in which you must enter subtracted or negative numbers use a minus sign. MingWare Ceramics Inc. Cost of Goods Sold Budget For the Month Ending September 30 Finished goods inventory, September 1 $Finished goods inventory, September 1 Direct labor $Direct labor Direct materials: $- Select - - Select - $- Select - - Select - $- Select - Direct labor fill in the blank 15 - Select - - Select - $- Select - Work in process inventory, September 30 fill in the blank 22 - Select - $- Select - - Select - $- Select - 4,100
The preparation of the Cost of Goods Sold Budget for MingWare Ceramics Inc. in September is as follows:
Cost of Goods Sold Budget:Beginning inventory of finished goods $11,850
Cost of goods manufactured 485,310
Ending inventory of finished goods (12,670)
Cost of Goods Sold $484,490
What is the cost of goods sold budget?The cost of goods sold budget sums the costs of the beginning inventory of finished goods with the cost of goods manufactured and subtracts the ending inventory of finished goods.
The cost of goods sold budget is based on the cost of goods manufactured budget.
Data and Calculations:Direct materials: Enamel Paint Porcelain Total
Total direct materials purchases
budgeted for September $35,870 $7,530 $139,890 $183,290
Estimated inventory, September 1 1,730 4,150 6,920 12,800 Desired inventory, September 30 (2,980) (2,710) (7,150) (12,840)
Materials used in production $183,250
Direct labor cost: Kiln Department Decorating Department Total
Total direct labor cost
budgeted for September $51,550 $149,500 $201,050
Finished goods inventories: Dish Bowl Figurine Total
Estimated inventory, September 1 $5,810 $3,310 $2,730 $11,850
Desired inventory, September 30 3,720 4,590 4,360 12,670
Cost of goods manufactured budget:Work in process inventories:
Estimated inventory, September 1 $3,540
Direct materials used in production $183,250
Direct labor costs $201,050
Total factory overhead costs $99,450
Desired inventory, September 30 (1,980)
Cost of goods manufactured $485,310
Budgeted factory overhead costs for September:Indirect factory wages $80,400
Depreciation of plant and equipment 10,550
Power and light 5,110
Indirect materials 3,390
Total 99,450
Thus, to prepare the cost of goods sold, as above, MingWare Ceramics, requires to determine the cost of goods manufactured for September.
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find derivative of y= sin x sin 3x
The derivative of y= sin x sin 3x is [tex]$=3 \cos x-3 \cos 3 x$[/tex]
What is a derivative?Futures contracts, options contracts, and credit default swaps are typical types of derivatives. Beyond this, a sizable number of derivative contracts satisfy the requirements of a wide range of counterparties.To find the derivative of y= sin x sin 3x:
[tex]$y=3 \sin (x)-\sin (3 x)$[/tex]
[tex]$y^{\prime}=3 \cos x-[\cos (3 x) \cdot 3]$[/tex]
[tex]$y^{\prime}=3(\cos x-\cos 3 x)$[/tex]
[tex]\frac{dx}{dy} =3 cosx - 3 cos x[/tex]
Differentiate [tex]sin 3x[/tex] using the chain rule
Given [tex]y=f^{'} (g(x))*g^{'}[/tex]←chain rule
y=[tex]y=3 sin x-sin 3x[/tex]
[tex]\frac{dx}{dy} =3 cos x - cos 3x*\frac{d}{dx} (3x)[/tex]
[tex]=3cosx-3cos3x[/tex]
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Manufacturers of tires report that car tires should be able to last an average of 50,000 miles. A new tire company produces a different type of tread and tests 100 randomly selected tires. This sample of 100 tires lasted an average of 51,500 miles. Assuming the new type of tread does not improve the mileage of the tire, 200 sample means were simulated and displayed on the dotplot.
Using the dotplot and the sample mean mileage, is there convincing evidence that the new type of tread improves the mileage of the tire?
Yes, because a mean mileage of 51,500 or more occurred only 14 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
Yes, because a mean mileage of 51,500 or less occurred 186 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 51,500 or less occurred 186 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
No, because a mean mileage of 51,500 or more occurred 14 out of 200 times, the mean mileage is not statistically significant. There is not convincing evidence the new type of tire tread improves mileage of the tire.
There is convincing evidence the new type of tire tread improves mileage of the tire.
How to interpret the mean mileage?The given parameter is:
Average = 50000 miles
New average = 51500 miles
The dot plot is added as an attachment
From the dot plot, we can see that the mean value of 51500 or more occurred 14 times out of the 200 samples
So, the conclusion is that: (a) Yes, because a mean mileage of 51,500 or more occurred only 14 out of 200 times, the mean mileage is statistically significant. There is convincing evidence the new type of tire tread improves mileage of the tire.
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a population of bobcats increase by 5% per year if the population is currently 40 in how many years will the population reach 80 round your answer to the nearest tenth. The population will reach 80 in about _____years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & 80\\ P=\textit{initial amount}\dotfill &40\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years \end{cases} \\\\\\ 80=40(1 + 0.05)^{t}\implies \cfrac{80}{40}=1.05^t\implies 2=1.05^t\implies \log(2)=\log(1.05^t) \\\\\\ \log(2)=t\log(1.05)\implies \cfrac{\log(2)}{\log(1.05)}=t\implies 14.2\approx t[/tex]
On a map, 3 inches represents 50 miles. Which proportion can be used to find the actual distance represented by 5 inches on the map?
StartFraction 3 over 50 EndFraction = StartFraction x over 5 EndFraction
StartFraction 3 over 50 EndFraction = StartFraction 5 over x EndFraction
StartFraction 3 over x EndFraction = StartFraction 50 over 5 EndFraction
StartFraction x over 3 EndFraction = StartFraction 50 over 5 EndFraction
The correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Given that 3 inches on a map represents 50 miles.
We are told to find the proportion which can be used to represent 5 inches.
Multiplication is basically finding the product of two numbers but it can be used to convert the units also.
If 3 inches represents 50 miles then,
1 mile=50/3
Multiply both sides by 5.
5 miles=5*50/3
If we see the options then we will get that the most appropriate and correct option which represents 5 inches is that start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
Hence the correct proportion that can be used to find the actual distance represented by 5 inches on the map is start fraction over 50 end fraction=start fraction 50 over 5 end fraction which is 3/50=5/x.
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Answer:
B
Step-by-step explanation:
3/50 = 5/x
(Subtracting rational coefficients-Mixed numbers)
Simplify by combining like terms:
1/3k - 8 3/4k
[?] ?
_k
?
Answer:
-8 5/12
Step-by-step explanation:
Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below. General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. Find G n M and G u S .
The computation shows that:
G n M = Anael and Max
G u S = Acel, Action, Anael, Max, Carl, Dario, Catlin, Kai, and Barek.
How to illustrate the information?From the information, ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table.
The subjects include general Knowledge Math Science.
Therefore, G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. The intersection is illustrated above.
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A line with slope
-1/3
passes through the point (-4, 4).
Find the coordinates of another point on the line.
Answer:
(0, 8/3) = y-intercept
Step-by-step explanation:
I chose to find the y-intercept since it is easy to find with the given information.
The equation for a line is y = mx + b
To find the y-intercept, we must plug in the info we have and solve for b:
4 = -1/3 (-4) + b
4 = -4/3 + b
8/3 = b
To find a point on the line, you also could have added -1 to 4 and 3 to -4 since slope means rise/run or change in y/change in x:
(y - 1) / (x + 3) = (4 - 1) / (-4 + 3) = (3, -1) (flip since it's the y and x coordinate) = (-1, 3)
Find f. f ″(x) = x^−2, x > 0, f(1) = 0, f(6) = 0
If you do in fact mean [tex]f(1)=f(6)=0[/tex] (as opposed to one of these being the derivative of [tex]f[/tex] at some point), then integrating twice gives
[tex]f''(x) = -\dfrac1{x^2}[/tex]
[tex]f'(x) = \displaystyle -\int \frac{dx}{x^2} = \frac1x + C_1[/tex]
[tex]f(x) = \displaystyle \int \left(\frac1x + C_1\right) \, dx = \ln|x| + C_1x + C_2[/tex]
From the initial conditions, we find
[tex]f(1) = \ln|1| + C_1 + C_2 = 0 \implies C_1 + C_2 = 0[/tex]
[tex]f(6) = \ln|6| + 6C_1 + C_2 = 0 \implies 6C_1 + C_2 = -\ln(6)[/tex]
Eliminating [tex]C_2[/tex], we get
[tex](C_1 + C_2) - (6C_1 + C_2) = 0 - (-\ln(6))[/tex]
[tex]-5C_1 = \ln(6)[/tex]
[tex]C_1 = -\dfrac{\ln(6)}5 = -\ln\left(\sqrt[5]{6}\right) \implies C_2 = \ln\left(\sqrt[5]{6}\right)[/tex]
Then
[tex]\boxed{f(x) = \ln|x| - \ln\left(\sqrt[5]{6}\right)\,x + \ln\left(\sqrt[5]{6}\right)}[/tex]
2(−6c+3)+4c2, left parenthesis, minus, 6, c, plus, 3, right parenthesis, plus, 4, c
Answer:
[tex]-8c+6[/tex]
Step-by-step explanation:
[tex]2(-6c+3)+4c=-12c+6+4c=\boxed{-8c+6}[/tex]
Answer:
-8c + 6 and 3(-4c+2) + 4c
Step-by-step explanation:
khan
Find a formula for the nth term in this arithmetic sequence first term -2 common difference an=
Find the measures of angles x and y
i need help with these 2
Answer:
Step-by-step explanation: Hey for the second one I got y = -3/4x -0.5 I'm not sure if its correct though sorry if not
ill try my best to explain my solution though
1. From the parallel equation (3x + 4y = 12) all we need to do is find the slope
So the easiest way to do so is to put the said equation in y-intercept form
y=mx +b
m= slope
b= y intercept
so 1. 3x + 4y = 12
=
4y = 12-3x
divide that by 4 to get only y
y=3-3/4x
-3/4 is our slope
y=-3/4x+b
than we have a point -2, -2
if we put -2 for y
-2=-3/4x+b
and then we put our -2 for x
-2 = -3/4 * -2 + b
=
-2 = -1.5 +b
b=-0.5
Answer : y=-3/4x-0.5
Two trains leave towns 664 miles apart at the same time and travel toward each other. One train travels 16 mih faster than the other. If they meet in 4 hours, what is the rate of each train?
Answer:
I think that I am right. One train is traveling at 75 mph and the other train is traveling at 91 mph
Step-by-step explanation:
Choose the number (X) that should come next in this series (1, 2, 6, 15, X, 56, 92)
Answer:
31
Step-by-step explanation:
The numbers in the sequence increase by (n+1)^2. So the sequence is (1, 1+1^2 (which is 2), 2+2^2 , 6+3^2, 15+4^2, 31+5^2, 56+6^2) and the fifth term of that sequence is 15+4^2, which is 31
The unknown number(x) in the series is 31.
The given series 1, 2, 6, 15, x, 56, 92.
We need to find the value of x.
What is a series?In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, and mathematical analysis.
The numbers in the series increase by (n+1)².
So the sequence is 1, 1+1² (which is 2), 2+2², 6+3², 15+4², 31+5², 56+6² and the fifth term of that sequence is x=15+4²=31.
Therefore, the unknown number(x) in the series is 31.
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Donna has a $300 loan through the bank she is charged a simple rate The total interest she paid on the loan was $63 As a percentage what was the annual interest rate on her loan
Answer:
21%
Step-by-step explanation:
($63*100%) / $300 = 21%
ASAP help me with this question
Answer:
SAS and SSA
Kindly award branliest
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Congruency refers to the criteria of making two identical shapes that can hide each other properly when overlapped.
The criterias that guarantee congruence are :
SSSSASASAAAS[tex] \qquad \large \sf {Conclusion} : [/tex]
Correct options are : b, c, d, eA circle has a circumference of 50.24 units.
What is the radius of the circle?
Use 3.14 for π and enter your answer as a decimal.
units
Answer: 8 units
Step-by-step explanation:
Write an inequality for the following statement, 1 is greater than x
The inequality suitable if 1 is greater than x is x<1.
Given that 1 is greater than x.
We are required to form an inequality which shows that 1 is greater than x.
Inequality is like an equation showing relationship between two or more variables.It is mostly not found in equal to form.
It shows the range of quantities.
When 1 is greater than x means the greater than sign will be used for 1 not x and the inequality will be as under:
x<1
We have not used equal to sign because 1 is greater than x not equal to x.
Hence the inequality suitable if 1 is greater than x is x<1.
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DIRE NEED OF HELP, pleaseee help
(not a lot of points sorry)
Answer:
C. Subtract 4 from both sides.
Step-by-step explanation:
You need the equation in the form x² + ax + b = 0 to then either try factoring or use the quadratic formula.
In order to achieve that, you need to first:
Subtract 4 from both sides.