Differentiation - The value of g'(x) = [tex]\frac{1}{10}x^{-9}[/tex].
Apart from integration, differentiation is among the two key ideas in calculus. A technique for determining a function's derivative is differentiation. Mathematicians use a process called differentiation to determine a function's instantaneous rate of change predicated on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. Finding an antiderivative is the opposite of differentiation. The rate of change of signal with respect to y has been given by dy/dx if x and y are two variables. The general representation of a function's derivative is given by the equation f'(x) = dy/dx, where y = f(x) is any function.
Given that,
G(x) = [tex]\frac{1}{x^{10} }[/tex]
g’(x)=?
g’(x) is the derivative of g(x).
The derivative of [tex]x^{n} = nx^(n-1)[/tex]
[tex]x^{10} = 10x^(10-1)[/tex]
[tex]x^{10}= 10x^9[/tex]
Then,
[tex]\frac{1}{x^{10} }[/tex] = [tex]\frac{1}{10}x^{-9}[/tex]
Hence, The derivative of g(x) is [tex]\frac{1}{x^{10} }[/tex] = [tex]\frac{1}{10}x^{-9}[/tex].
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find the width of a newer 48-in TV whose screen has an aspect ratio of 16:9what is the width?
The width of the TV is 41.84-in
Explanations:The diagonal size of the TV, d= 48 in
The aspect ratio= 16 : 9
The aspect ratio is usually given in form of width : Height
Let the width = w
Let the height = h
The diagram looks like:
[tex]\begin{gathered} \frac{w}{h}=\text{ }\frac{16}{9} \\ h\text{ = }\frac{9w}{16} \end{gathered}[/tex]Using the Pythagoras theorem:
[tex]\begin{gathered} d^2=h^2+w^2 \\ 48^2\text{ = (}\frac{9w}{16})^2+w^2 \\ 2304\text{ = }\frac{81w^2}{256}+w^2 \\ \text{Multiply through by 256} \\ 589824=81w^2+256w^2 \\ 589824\text{ = }337w^2 \\ w^2\text{ = }\frac{589824}{337} \\ w^2\text{ = 1750.22} \\ w\text{ = }\sqrt[]{1750.22} \\ w\text{ = 41.84 } \end{gathered}[/tex]The width of the TV is 41.84-in
given the function m(a)=27a^2+51a find the appropriate values:
solve m(a)= 56
a=
A function is a relationship between inputs where each input is related to exactly one output.
The value of a when m(a) = 56 is 7/9.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
We have,
m(a) = 27a² + 51a ____(1)
m(a) = 56 ____(2)
From (1) and (2) we get,
56 = 27a² + 51a
27a² + 51a - 56 = 0
This is a quadratic equation so we will factorize using the middle term.
27a² + 51a - 56 = 0
27a² + 71a - 21a - 56 = 0
(9a−7) (3a+8) = 0
9a - 7 = 0
9a = 7
a = 7/9
3a + 8 = 0
3a = -8
a = -8/3
We can not have negative values so,
a = -8/3 is neglected.
Thus,
The value of a when m(a) = 56 is 7/9.
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find the reference angle for -0.8pi
Answer:
What is Meant by the Reference Angle? In mathematics, the reference angle is defined as the acute angle and it is measuring less than 90 degrees. It is always the smallest angle, and it makes the terminal side of an angle with the x-axis.
13. Use the appropriate percent growth todetermine how much money Lyra will have incach ofthe following situations:(a) How much money will Lyra have after 10years if she invests $5,000 at 4% interestcom-poundcl annually?(1) Suppose that Lyra is saving for retirement,and has saved up $20,000. If her retirementaccount earns 3% interest each year, howmuch will she save in 25 years?(o) How much mowy will yra have after 20years if she $5,000 33.5% interestcompoundedannully?(d) How much money will yr hawwur 10 yearsit she is $6,000 AL 15% interestcompounded quarterly?(E) how much money will lyra have after 10years if she invests $5,000 at 0.8% interestcompounded continuously?(F) compare your answer to (a) and (c). Whichone made more money?
Given:
(a) P = $5000
t = 10 years
r = 4%
(b) P = $20,000
t = 25 years
r = 3%
(c) P = $5000
t = 20 years
r = 3.5%
(d) P = $5000
t = 10 years
r = 1.5%
(e) P = $5000
t = 10 years
r = 0.8%
(f) Compare the result of (a) and (c).
Required:
(a) Find the amount when interest is compound annually.
(b) To find the total amount after 25 years.
(c) Find the amount when interest is compound annually.
(d) Find the amount when interest is compound quarterly.
(e) Find the amount when interest is compound continuously.
Explanation:
The compound interest formula is given as:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where p =principal amount
r = rate of interest
n = compound frequency
t = time period in years
(a)
[tex]undefined[/tex]Which property is used in the following calculation?
4 (18) (5)
4 (5) (18)
20 (18)
360
A. Identity Property of Multiplication
B. Distributive Property
C. None of these
D. Associative Property of Multiplication
E. Associative Property of Addition
The property which is used in the following calculation is referred to as Associative Property of Multiplication and is denoted as option D.
What is Associative Property of Multiplication?This is referred to as the process in which the the result of the multiplication of three numbers is always the same regardless of the way and manner in which they are arranged.
We were given: 4 (18) (5)
= 4 (5) (18)
= 20 (18)
= 360
The multiplication of the numbers will give the same result of 360 no matter how the numbers are arranged which is why it was chosen as the correct choice.
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A card is drawn from a standard deck of fifty-two cards. What is the probability of selecting Jack or a red card?
Solution
Step 1:
In a pack or deck of 52 playing cards, they are divided into 4 suits of 13 cards each i.e. spades ♠ hearts ♥, diamonds ♦, clubs ♣. Cards of Spades and clubs are black cards. Cards of hearts and diamonds are red cards. The card in each suit, are ace, king, queen, jack , 10, 9, 8, 7, 6, 5, 4, 3 and 2.
Step 2:
Total possible outcomes = 52
Total number of jacks = 4
Total number of red cards = 26
Step 3:
The probability of selecting Jack or a red card
[tex]\begin{gathered} \text{Probability of any event = }\frac{n\text{umber of required outcomes}}{n\text{umber of possible outcomes}} \\ =\text{ }\frac{4}{52}\text{ + }\frac{26}{52} \\ =\text{ }\frac{30}{52} \\ =\text{ }\frac{15}{26} \end{gathered}[/tex]Final answer
[tex]\frac{15}{26}[/tex]Find the area of the figure below. Type below. 9) 8 in 21 in 28 in B
Explanation
Step 1
to find the total area , we need to divide the figure in a rectangle plus harf circle
so, the area for a rectangle is given by:
[tex]\text{Area}_{rec\tan gle}=length\cdot width[/tex]and the area for a circle is
[tex]\text{Area}_{circle}=\pi\cdot radius^2[/tex]but, we need the area of a half circle ,so
[tex]\text{Area}_{half\text{ circle}}=\frac{Area_{circle}}{2}=\pi\cdot radius^2[/tex]so, the toal area of th figure is
[tex]Area_{figure}=Area_{rec\tan gle}+Area_{half\text{ circle}}\text{ }[/tex][tex]\begin{gathered} Area_{figure}=length\cdot width+\pi\cdot radius^2 \\ \end{gathered}[/tex]Step 2
Let
length= 28 in
width=21 in
radius = 8 in
replace and calculate
[tex]\begin{gathered} Area_{figure}=length\cdot width+\pi\cdot radius^2 \\ Area_{figure}=(28\cdot21)+\pi\cdot8^2 \\ Area_{figure}=588+64\pi \\ Area_{figure}=789.06in^2 \\ \text{rounded} \\ Area_{figure}=789\text{ square inches} \end{gathered}[/tex]I hope this helps you
How much would you need to deposit in an account now in order to have $5000 in the account in 15years? Assume the account earns 8% interest compounded monthly.$
A(t) = amount in t years
P = Principal (original investment)
r = annual interest rate (in decimal form)
n = number of times that interest is compounded each year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Substitute in the given values:
[tex]5000=P(1+\frac{0.08}{12})^{12\times15}[/tex][tex]5000=P(1.0067)^{180^{}}[/tex][tex]5000=P\times3.307[/tex][tex]P=1511.94[/tex]Hence the amount need to deposit is 1511.94 dollar.
5(3a-1) - 2(3a+2)=3(a+2) + vselect two expressions that are equivalent to v.
Let's solve the equation for v to identify the expressions:
[tex]\begin{gathered} 5(3a-1)-2(3a+2)=3(a+2)+v \\ 15a-5-6a-4=3a+6+v \\ 9a-9=3a+6+v \\ v=9a-3a-9-6 \\ v=6a-15 \\ v=3(2a-5) \end{gathered}[/tex]Therefore the equivalent expressions are D and E
A person randomly selects one of four envelopes. Each envelope contains a check that the person gets to keep. However, before the person can select an envelope, he or she must pay $ 15 to play. Determine the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks.
The person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
In the given question,
A person randomly selects one of four envelopes.
Each envelope contains a check that the person gets to keep.
However, before the person can select an envelope, he or she must pay $15 to play.
We have to determine the person's expectation if two of the envelopes contain $5 checks and two of the envelopes contain $35 checks.
As we know that when the person have to select envelope then they have to pay $15.
Total number of envelop = 4
From the 4 envelop 2 have $5 each and 2 have $35 each.
So the probability of getting envelop of $5 = 2/4 = 1/2
Probability of getting envelop of $35 = 2/4 = 1/2
Let x be the amount a person gets after selecting the envelop.
So E(x) = $5×1/2 + $35×1/2
Taking 1/2 common on both side
E(x) = 1/2 ($5+$35)
E(x) = 1/2×$40
E(x) = $20
But he have to pay $15 before selecting the envelop.
So required expectation = $20−$15 = $5
Hence, the person's expectation if two of the envelopes contain $ 5 checks and two of the envelopes contain $ 35 checks is $5.
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A computer part costs $7 to produce and distribute. Express the profit p made by selling 300 of these parts as a function of the price of c dollars. (Do not include $ symbol in your answer)
Given:
Each part costs $7 to produce and distribute.
The total number of parts on selling is 300 to make the profit P.
To write the function expression in terms of sale price C and profit P:
As we know,
[tex]\text{Profit}=\text{Selling price-cost price}[/tex]So, if we produce 1 part and sell that part, then the profit is
[tex]P=C-7[/tex]For 300 parts, the profit is
[tex]\begin{gathered} P=300(C-7) \\ P=300C-2100 \end{gathered}[/tex]Hence, the function is expressed in terms of P and C is,
[tex]P=300C-2100[/tex]Please help with the question below (please try to answer in maximum 5/10 minutes).
Given
Joshira can create 1 item in 3/4 of an hour.
To find:
How many items can she create in 8 hours?
Explanation:
It is given that,
Joshira can create 1 item in 3/4 of an hour.
That implies,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }\frac{3}{4}\text{ }hour=1 \\ Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }1\text{ }hour=1\div(\frac{3}{4}) \\ =1\times\frac{4}{3} \\ =\frac{4}{3} \end{gathered}[/tex]Therefore, number of items created in 8 hours is,
[tex]\begin{gathered} Number\text{ }of\text{ }items\text{ }created\text{ }in\text{ }8\text{ }hours=\frac{4}{3}\times8 \\ =\frac{32}{3} \\ =\frac{30+2}{3} \\ =\frac{30}{3}+\frac{2}{3} \\ =10+\frac{2}{3} \\ =10\frac{2}{3}\text{ }items \end{gathered}[/tex]Hence, she can create 10 2/3 items in 8 hours.
A carpenter wants to cut a board that is 5/6 ft long into pieces that are 5/16 ft long. The carpenter will use the expression shown to calculate the number of pieces that can be cut from the board.5/6 divided by 5/16How many pieces can be cut from the board?
The expression which is used to calculate the number of pieces that can be cut from the board is:
[tex]\frac{5}{6}\div\frac{5}{16}[/tex]We solve this by changing the division sign to multiplication and taking the reciprocal of the second fraction.
Therefore:
[tex]\begin{gathered} \frac{5}{6}\div\frac{5}{16}=\frac{5}{6}\times\frac{16}{5} \\ =\frac{16}{6} \\ =2\text{ }\frac{4}{6} \\ =2\frac{2}{3}\text{ pieces} \end{gathered}[/tex]The carpenter can cut 2 2/3 pieces from the board.
I need help on number 14!!! Please help and justify your answer!! PLEASE
as the rate of company B is greater, the company B will reach the top first
Explanationto solve this we can find the rate of each company and then compare
let
[tex]rate=\frac{finished\text{ length of construction}}{time\text{ taken}}[/tex]so
Step 1
convert the mixed number into fractions
remember how
[tex]a\frac{b}{c}=\frac{(a*c)+b}{c}[/tex]so
[tex]\begin{gathered} 5\text{ }\frac{1}{2}=\frac{(5*2)+1}{2}=\frac{11}{2} \\ 3\text{ }\frac{1}{2}=\frac{(3*2)+1}{2}=\frac{7}{2} \end{gathered}[/tex]Step 2
Find the rate of each company
A) Company A
replace
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_A=\frac{550}{\frac{11}{2}}=\frac{1100}{11}=100\text{ ft per month} \end{gathered}[/tex]B) Company B
[tex]\begin{gathered} rate=\frac{finished\text{ length of construction}}{time\text{ taken}} \\ rate_B=\frac{385}{\frac{7}{2}}=\frac{770}{7}=110\text{ ft per month} \end{gathered}[/tex]Step 3
finally, compare
[tex]\begin{gathered} 110\text{ ft per month }>100\text{ ft per month} \\ hence \\ rate_B>rate_A \end{gathered}[/tex]as the rate of company B is greater, the company B will reach the top first
Find the surface area to the nearest tenth.19 m4536.5 m22268.2 m2O 238.8 m2477.5 m2
Answer:
Explanation:
The given solid is a sphere of radius 19m.
The surface area of a sphere is calculated using the formula:
[tex]A=4\pi r^2[/tex]Substitute 19 for r:
[tex]\begin{gathered} A=4\times\pi\times19^2 \\ =4536.46m^2 \\ \approx4536.5\; m^2 \end{gathered}[/tex]The surface area of the sphere to the nearest tenth is 4536.5 square mete.
A motorboat takes 3 hours to travel 108 miles going upstream. The return trip takes 2 hours going downstream. What is the rate in still water and what is the rate of the current?Rate of the boat in still water: mi/hRate of the current: mi/hmi/h= miles per hour
Given:
It takes the boat 3 hours to travel 108 miles going upstream
Return trip = 2hours going downstream
Distance, d = 108 miles
Time going upstream = 3 hours
Time going downstream = 2 hours
Let's find the rate in still water and the current rate.
Let s represent the still rate
Let c represent the current rate.
Apply the distance formula:
Distance = Rate x Time
We have the set of equations:
(s - c) x 3 = 108.................................Equation 1
(s + c) x 2 = 108.................................Equation 2
Apply distributive property:
3s - 3c = 108
2s + 2c = 108
Let's solve both equations simultaneously using substitution method.
Rewrite the first equation for s:
3s - 3c = 108
Add 3c to both sides:
3s - 3c + 3c = 108 + 3c
3s = 108 + 3c
Divide all terms by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{108}{3}+\frac{3c}{3} \\ \\ s=36+c \end{gathered}[/tex]Substitute s for (36 + c) in equation 2:
2s + 2c = 108
2(36 + c) + 2c = 108
72 + 2c + 2c = 108
72 + 4c = 108
Subtract 72 from both sides:
72 - 72 + 4c = 108 - 72
4c = 36
Divide both sides by 4:
[tex]\begin{gathered} \frac{4c}{4}=\frac{36}{4} \\ \\ c=9 \end{gathered}[/tex]Substitute c for 9 in either of thee equation.
Take the first equation:
3s - 3c = 108
3s - 3(9) = 108
3s - 27 = 108
Add 27 to both sides:
3s - 27 + 27 = 108 + 27
3s = 135
Divide both sides by 3:
[tex]\begin{gathered} \frac{3s}{3}=\frac{135}{3} \\ \\ s=45 \end{gathered}[/tex]Thus, we have the solutions:
c = 9
s = 45
The rate of boat in still water is 45 miles per hour
The rate of the current is 9 miles per hour
Therefore, we have:
Rate of boat in still water: 45 mi/h
Rate of current: 9 mi/h
Take the firs
ANSWER:
Rate of boat in still water: 45 mi/h
Rae of the current: 9 mi/h
Subtract 9 1/4 - 4 3/4 . Simplify the answer and write as a mixed number.
Upon subtracting 9 1/4 from 4 3/4 we get 18/4.
Given
9 1/4 - 4 3/4
solution:
[tex]9\frac{1}{4}[/tex] can be written as 37/4 ( 9 * 4 + 1 thus 37/4) and
[tex]4\frac{3}{4}[/tex] can be written as 19/4 ( 4 * 4 + 3 thus 19/4)
37/4 - 19/4 as 4 is the common denominator for both the fractions so take 4 as the denominator
[tex]= \frac{37-19}{4}[/tex] = 18/4 if we further simplify 18/4 = 4.5
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7^2 × 7^8. 7^a------------ = -------- = 7^b7^4 7^4
We have to find the values of a and b:
[tex]\frac{7^2\cdot7^8}{7^4}=\frac{7^a}{7^4}=7^b[/tex]We can use the laws of exponents to write:
[tex]\begin{gathered} 7^2\cdot7^8=7^a \\ 7^{2+8}=7^a \\ 7^{10}=7^a \\ 10=a \end{gathered}[/tex]Then, we can solve for b as:
[tex]\begin{gathered} \frac{7^a}{7^4}=7^b \\ 7^{a-4}=7^b \\ a-4=b \\ 10-4=b \\ 6=b \end{gathered}[/tex]Answer: a=10 and b=6
To produce g, function f was reflected over the x-axis andFunction g can be defined as
The graph of the functions f and g are given.
It is required to complete the statement concerning how to produce g.
The graph of the parent function f is shown:
Reflect the graph of f across the x-axis:
Translate the function 5 units vertically upwards:
The given parent function is y=f(x).
Reflect the graph across in the x-axis to get the equation y=-f(x).
Translate the graph 5 units up to get y=-f(x)+5
Answers:
To produce g, the function f was reflected over the x-axis and shifted up 5 units.
Function g is defined as g(x)=-f(x)+5.
Determine the equation of the graphed circleReminder that the equation should look like the example I provided
The equation of a circle of radius r and center at (h, k) is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]The image provided shows a circle and we must find the radius and center by simple inspection.
The center is located at (-5, 3).
From that point, until I find a point of the circumference I can count 4 units. It is confirmed when I see the segment from (-9, 3) to (-1, 3) as a diameter of length 8. The radius is half the diameter, thus r = 4.
Substituting, we have the required equation:
[tex]\begin{gathered} (x+5)^2+(y-3)^2=4^2 \\ \boxed{\mleft(x+5\mright)^2+\mleft(y-3\mright)^2=16} \end{gathered}[/tex]A growing number of thieves are using keylogging programs to steal passwords and other personal information from Internet users. The number of keyloggingprograms reported grew approximately exponentially from 0.3 thousand programs in 2001 to 11.0 thousand programs in 2008. Predict the number of keyloggingprograms that will be reported in 2013
Exponential growth (EG):
2001 = 0.3
2008 = 11
2013 = ?
[tex]n\text{ = }a\times b^t[/tex]a = initial amount = 0.3
b= growth factor = ?
t = period = 7
n = 11
[tex]\begin{gathered} 11=0.3\times b^7 \\ b^7=\frac{11}{0.3} \\ b\text{ = }\sqrt[7]{\frac{11}{0.3}} \\ b=1.67 \end{gathered}[/tex]b = 1.67
Solving the number of keylogging programs that will be reported in 2013:
[tex]\begin{gathered} n\text{ = }0.3\times1.67^{12} \\ n=144.12 \end{gathered}[/tex]The inequality 3x +2> x+8 is equivalent to
A. x>-12
C. x > 3
B. x > 2/2/1
D. x <3
Answer: C
Step-by-step explanation:
3x + 2 > x +8
= 3x + 2 -2 > x + 8 -2
= 3x > x + 6
= 3x - x > x - x + 6
= 2x/2 > 6/2
= x > 3
Answer:
C
Step-by-step explanation:
It is the only one that makes sense.
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How do I solve this problem? 1 - 9/5x = 8/6
The given equation is
[tex]1-\frac{9}{5x}=\frac{8}{6}[/tex]Adding -1 on both sides, we get
[tex]1-\frac{9}{5x}-1=\frac{8}{6}-1[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-1[/tex][tex]\text{Use 1=}\frac{6}{6}\text{ as follows.}[/tex][tex]-\frac{9}{5x}=\frac{8}{6}-\frac{6}{6}[/tex][tex]-\frac{9}{5x}=\frac{8-6}{6}[/tex][tex]-\frac{9}{5x}=\frac{2}{6}[/tex][tex]-\frac{9}{5x}=\frac{1}{3}[/tex]Using the cross-product method, we get
[tex]-9\times3=5x[/tex][tex]-27=5x[/tex]Dividing by 5 into both sides, we get
[tex]-\frac{27}{5}=\frac{5x}{5}[/tex][tex]x=-\frac{27}{5}=-5.4[/tex]Hence the required answer is x=-5.4.
on one side of the balance scale, Henry placed gram weight. on the other side of the scale, he placed a ballet slipper. how many milligrams does the slipper weigh?
Solution
Step 1
Convert gram to milligram
1 gram = 1000 milligram
Step 2
Find the answer
Assuming it is 1 gram weight on one side of the balance scale then, the ballet slippers will weigh 1 gram for the scale to be balanced.
I gram = 1000 milligram
Hence the ballet slippers will weigh 1000 milligrams
find the Medina number of campsites.9,11,12,15,17,18
To find the median of the composite numbers, we will first have to sort the numbers
We will arrange from least to greatest.
By doing so, we will obtain
[tex]9,11,12,15,17,\text{ and 18}[/tex]Next, we will find the middle number of the set.
The median will be the average of the two numbers
[tex]\frac{12+15}{2}=\frac{27}{2}=13.5[/tex]The median of the numbers is 13.5
Leila wrote an equation to represent the revenue of a parking lot for one day. She let x represent the number of cars that paid to park and y represent the number of trucks that paid to park. If a car costs $8 per day, a truck costs $10 per day, and the total revenue for the day was $830, which equation could Leila use to represent the number of cars and trucks that paid to park that day?
8 x + 10 y = 1,660
10 x + 8 y = 1,660
8 x + 10 y = 830
The equation that Leila can use to represent the number of cars and trucks that paid to park that day is C. 8 x + 10 y = 830
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario
Let x represent the number of cars that paid to park.
Let y represent the number of trucks that paid to park.
Therefore, the equation will be:
= (8 × x) + (10 × y) = 830
8x + 10y = 830
In conclusion, the correct option is C.
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Write an exponential function in the form y = ab that goes through points (0,18) and (3,6174).
Using the first point given in the statement you can find a, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 0 and y = 18} \\ 18=ab^0 \\ 18=a\cdot1 \\ 18=a \end{gathered}[/tex]Now, since you already have the value of a, you can find the value of b using the second point, like this
[tex]\begin{gathered} y=ab^x \\ \text{ Replace x = 3 and y = 6174} \\ 6174=18\cdot b^3 \\ \text{ Divide by 18 into both sides of the equation} \\ \frac{6174}{18}=\frac{18\cdot b^3}{18} \\ 343=b^3 \\ \text{ Apply cube root to both sides of the equation} \\ \sqrt[3]{343}=\sqrt[3]{b^3} \\ 7=b \end{gathered}[/tex]Therefore, the exponential function that passes through the points (0,18) and (3,6174) is
[tex]y=18\cdot7^x[/tex]Writing the equation of a circle centered at the origin given it’s radius or appoint on the circle
The equation of the circle has the following form:
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where
(h,k) are the coordinates of the center of the circle
r is the radius of the circle
If the center of the circle is at the origin, (0,0) and it passes through the point (0,-9), since both x-coordinates are equal, the length of the radius is equal to the difference between the y-coordinates of the center and the given point:
[tex]r=y_{\text{center}}-y_{point=}0-(-9)=0+9=9[/tex]The radius is 9 units long.
Replace the coordinates of the center and the length of the radius in the formula:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=9^2 \\ x^2+y^2=81 \end{gathered}[/tex]So, the equation of the circle that has a center in the origin and passes through the point (0.-9) is:
[tex]x^2+y^2=81[/tex]Cheng-Yu ordered a book that cost $24 from an online store. Hertotal with the shipping charge was $27. What was the percent ofmarkup charged for shipping?
Given:
Cost of book = $24
Total cost of book (shipping charge inclusive) = $27
The shipping charge is:
Total cost - cost of book = $27 - $24 = $3
The shipping charge is $3
To find the percentage markup charged for shipping, use the formula:
[tex]\frac{ship\text{ charge}}{Total\text{ cost}}\ast100[/tex][tex]\frac{3}{27}\ast100\text{ = }0.111\text{ }\ast\text{ 100 = }11.1percent^{}[/tex]Therefore, the percent of markup charged for shipping is 11.1%
ANSWER:
11.1%
Maria made 97% of her penalty kicks in soccer. Her teammates' percentages were uniformly distributed between 65% and 80%.Select all the statements that must be true?O A The mean would decrease by omitting Maria's score.B. The median would decrease by omitting Maria's score.O c The range would decrease by omitting Maria's score.D. The interquartile range would decrease by omitting Maria's score.E The standard deviation would decrease by omitting Maria's score,
Let's evaluate each statement to check wheter they are true or not.
A. "The mean would decrease by omitting Maria's score".
The mean is the sum of all the scores divided by the number of attempts. Since Maria had a higher score, if we omitted it then the sum would decrease and by extension the mean would decrease as well.
This option is true.
B. The median would decrease by omitting Maria's score.
The median is the value on the middle of the series, if we omit Maria's score, which was one of the highest then the middle of the series should move to the left, decreasing it.
This option is true.
C. The range would decrease by omitting Maria's score.
The range of a function are the values that said function can have as an output. If we omit Maria's score then the output of the function would be only the values scored by their team mates, which would go from 65 to 80, instead of 65 to 97. Therefore the range would decrease.
This option is true.
D. The interquartile range would decrease by omitting Maria's score.
The interquartile range are the values between the 25% values of the series and the 75% values of the series. Since Maria is the highest score between her teammates, she is not considered into the IQR and the value wouldn't change by removing her score.
This option is false.
E. The standard deviation would decrease by omitting Maria's score.
The standard deviation is the mean amount of variation in a series, since all her teammates are in the range of 65% to 80% and Maria is way above on the 97% score, by taking her score out we decrease the standard deviation, because there will be less variation in the serie.
This option is true.