Step-by-step explanation:
25 as binary number is
11001
1×2⁴ + 1×2³ + 0×2² + 0×2¹ + 1×2⁰ = 16 + 8 + 1 = 25
25×2 = 50 = 11001 × 2 = 110010
multiplying a binary number by 2 is the save effect as multiplying a normal decimal number by 10 : all digits move one position to the left, and a 0 is put into the empty right position.
and so, we see
110P = 110010
P = 010
FYI : you normally don't mix binary and decimal numbers. if one of the numbers is binary, then all the others have to be binary too.
so, the problem should have looked like
110P/10 = 11001
110P = 11001×10 = 110010
P = 010
Answer:
01
Step-by-step explanation:
From decimal to binary;
25/2==> 1 (remainder)
12/2===>0
6/2==>0
3/2===>1
1
=11001
Checking the answer;
11001
=1*2^4+1*2^3+0*2*2+0*1+1*2^0
=1*16+1*8+0+0+1*1
=16+8+0+0+2
=25
Quick algebra 1 question for 10 points!
Only answer if you know the answer, quick shout-out to tariqareesha2 and MrBrainly, tysm for the help!
Answer:
C (Third option)
Step-by-step explanation:
The prime factorization of 675 is 5*5*3*3*3 or 5^2*3^3. With the square root, we take out all square integers, leaving (5*3)(sqrt3). The answer is 15(sqrt3) or C.
Break
√225×3√225√3√15²√315√3Option C
can someone help me with these kind of fractions
[tex]\frac{1}{2} of \frac{2}{3}[/tex]
Answer:
[tex]\frac{2}{6}[/tex] or [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
To find a fraction of a fraction simply multiply the numerators and denominators into another fraction:
[tex]\frac{1}{2}*\frac{2}{3} = \frac{2}{6} = \frac{1}{3}[/tex]
Answer:
1/3.
Step-by-step explanation:
'of' means multiply. so
1/2 of 2/3
= 1/2 * 2/3
= 1*2 / 2*3
= 2/6
= 1/3.
I NEED THIS ANSWER QUICK (5 1/6 - x) ∙ 2.7 - 5 3/4 = -1.25 what is x
Answer:
x = 3 1/2
Step-by-step explanation:
You could simplify the given equation first, then solve the resulting 2-step linear equation. It might work better to undo the operations done to the variable.
Solution(5 1/6 -x)(2.7) -5 3/4 = -1 1/4 . . . . . given
(5 1/6) -x)(2.7) = 4 1/2 . . . . . . . add 5 3/4 to both sides
(5 1/6 -x) = 4.5/2.7 = 5/3 . . . divide by 2.7
31/6 -10/6 = x . . . . . . . . . . add x-5/3, use common denominators
21/6 = x = 7/2
x = 3 1/2
ind the present value that will grow to $4000 if the annual interest rate is 8.5% compounded quarterly for 9 yr.
Answer:
$1876.31
Step-by-step explanation:
The present value can be found using the compound interest formula.
Present valueThe formula for the future value of an investment of P earning annual interest rate r compounded n times per year for t years is ...
FV = P(1 +r/n)^(nt)
Filling in the known values gives ...
4000 = P(1 +0.085/4)^(4·9) = P(1.02125^36)
Then the amount to be invested is ...
P = 4000/1.02125^36 ≈ 1876.31
The present value is $1876.31.
Complete the following sentences.
To emphasize the decrease in the number of gas-fueled cars sold, it would be best for Roger to use
for his presentation.
Roger should use this graph for his presentation because the number of gas-fueled cars sold
on this graph.
A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a Cartesian coordinate, which are the x-axis and y-axis.
By critically observing the graphs (see attachment) of the number of gas-fueled cars that were sold by Roger's car company for the first 8-months since the introduction of electric cars, we can logically deduce that it's much easier to determine the slope of graph A than that of graph B.
This ultimately implies that, it would be best for Roger to use graph A in emphasizing a decrease in the number of gas-fueled cars that were sold.
In conclusion, we can infer and logically deduce that Roger should use graph A for his presentation because the number of gas-fueled cars that were sold appears to decrease on this graph.
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Complete Question:
A car company wants to reduce the use of gas-fueled cars by introducing and promoting the use of electric cars. The graphs below show the number of gas-fueled cars sold, y, for the first eight months since the introduction of electric cars. Both graphs show the same information.
Complete the following sentences.
1. To emphasize the decrease in the number of gas-fueled cars sold, it would be best for Roger to use ______ for his presentation.
2. Roger should use this graph for his presentation because the number of gas-fueled cars sold ______ on this graph.
The graph of function f is shown. The graph of an exponential function passes through (minus 10, minus 1), (2, 8) also intercepts the x-axis at minus 2 units and y-axis at 2 units Function g is represented by the table. x -2 -1 0 1 2 g(x) 0 2 8 26 Which statement correctly compares the two functions? A. They have the same x-intercept and the same end behavior as x approaches ∞. B. They have the same x- and y-intercepts. C. They have the same y-intercept and the same end behavior as x approaches ∞. D. They have different x- and y-intercepts but the same end behavior as x approaches ∞.
The correct description that cab made of these graphs is that They have the same x- and y-intercepts.
What is the end behavior of a function?This is the term that is used to describe the behaviors of these functions as they approach infinity.
the y-intercept of a function
This is what is used to tell us the y value when we put x to be = 0
The y-intercept of f(x) is y = -2
The y-intercept of g(x) is y = -2
the x-intercept of a function
It is the value of x when y = 0.
The x-intercept = 2
The x-intercept = 2
Hence statement B is correct. They have the same x- and y-intercepts.
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Factor the GCF:-12x4y - 9x³y² + 3x²y³ (5 points)
O-3x²y(4x2 + 3xy - y²)
O 3x²y(-4x² + 3xy - y²)
O-3(4x²y + 3x³y² - x²y³)
O-3x²y(-4x2-3xy + y²)
Answer:
A. 3x^2y(4x2 + 3xy - y^2)
Step-by-step explanation:
-12(x^4)y - 9x³y² + 3x²y³
-3x²y(4x² + 3xy - y²)
A bank loans a family $90,000 at 4.5% annual interest rate to purchase a house. The family agrees to pay the loan off by making monthly payments over a 15 year period. How much should the monthly payment be in order to pay off the debt in 15 years? Show all your calculations
Using it's formula, it is found that the monthly payment should be of $688.49 in order to pay off the debt in 15 years.
What is the monthly payment formula?It is given by:
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
In which:
P is the initial amount.r is the interest rate.n is the number of payments.For this problem, the parameters are given as follows:
A = 90000, r = 0.045, n = 15 x 12 = 180.
Hence:
r/12 = 0.045/12 = 0.00375.
Then we solve for A to find the monthly payment, as follows.
[tex]A = P\frac{\frac{r}{12}\left(1 + \frac{r}{12}\right)^n}{\left(1 + \frac{r}{12}\right)^n - 1}[/tex]
[tex]A = 90000(0.00375)\frac{(1.00375)^{180}}{(1.00375)^{180} - 1}[/tex]
A = $688.49
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pleasee mwa mwa mwa help me
Answer: About (-2.414, 0) and (0.414, 0)
Step-by-step explanation:
Let us graph the equation given and see what the x-intercepts are. These are points where the line intercepts the x-axis. See attached.
This means our x-intercepts are at about (-2.414, 0) and (0.414, 0).
These are also equal to [tex]-1-\sqrt{2}[/tex] and [tex]-1+\sqrt{2}[/tex]
Answer:
[tex]x = \bold{0.414} \textrm{ and } x= \bold{-2.414}[/tex]
Step-by-step explanation:
See attached graph for a visual
The x-intercepts of a graph are where the graph crosses the x-axis ie where the value of y = 0 The equation of the graph is y=-x^{2}-2x+1
Setting y = 0 and solving for the resultant equation will provide the x-intercepts
[tex]0=-x^{2}-2x+1or-x^{2}-2x+1=0[/tex]
Reversing the signs gives us
[tex]x^{2}+2x-1=0[/tex]
This is a quadratic equation of the form [tex]ax^{2}+bx+c=0[/tex] with a = 1, b = 2 and c=-1
For an equation of this form the roots of the equation ie the values of x which satisfy the equation are given by
[tex]\frac{-b\pm\sqrt{{b^{2}-4ac}}}{2a}[/tex]
Substituting we get the two roots as
[tex]x=\frac{-2\pm\sqrt{{2^{2}-4(1)(-1}}}{2}=\frac{-2\pm\sqrt{{4-(-4)}}}{2}x=\frac{-2\pm\sqrt{8}}{2}8 = 4(2)\sqrt{8}=\sqrt{4}\sqrt{2} = 2\sqrt{2}[/tex]
So the two roots are
[tex]x=\frac{-2\pm2\sqrt{2}}{2}[/tex]
Dividing by 2 we get the two roots(x-intercepts) as
[tex]x=-1\pm\sqrt{2}\\\\x_{1}=-1+\sqrt{2} =-1+1.414=\bold{0.414}[/tex]
[tex]x_{2}=-1-\sqrt{2}=-1-1.414=\boldsymbol{-2.414}[/tex]
Find the area of a circle that has a radius of 9 mm. Use 3.14 for π.
254.34 mm²
56.52 mm²
63.59 mm²
28.26 mm²
Answer: 254,34 mm².
Step-by-step explanation:
[tex]S{circle}=\pi R^2\\S{circle}=3,14*9^2\\S{circle}=3,14*81\\S{circle}=254,34\ mm^2.[/tex]
Hi :)
Let's first find the area of this circle
—————————For finding the area of a circle we use
[tex]\longrightarrow\sf{A_{\circ}=\pi r^2}[/tex], where only r (radius) is squared
[tex]\textit{We know that :}\begin{cases} \sf{Radius = 9 mm} \\ \sf{\pi =3.14} \end{cases}}[/tex]
Thus
[tex]\longrightarrow\sf{A_{\circ}=3.14\cdot9^2}[/tex]
[tex]\longrightarrow\sf{A_{\circ}=3.14\times81}[/tex]
[tex]\longrightarrow\sf{\underline{A_{\circ}=254.34\: mm}}[/tex]
[tex]\tt{Learn\:More;Work\;Harder}[/tex]
:)
S is a subset within a universal set, U
If S = {x, y, 4, 9, ?}, which could
describe U?
U = {keys on a keyboard}
U = {letters}
U = {numbers}
U = {punctuation marks}
The solution is, U={ keys on a keyboard}, could describe U .
What is set?A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.
Here, we have,
S is a subset of U,
so all of the elements of S must be also elements of U
If U was {letters}, 4, 9, ? would not belong there
If U was {numbers }, x, y, ? would not belong to U
If U was {punctuation marks }, 4, 9, x, y would not be in U
all the elements of S are in U={ keys on a keyboard}
Answer: U={ keys on a keyboard}, could describe U.
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Pls help with middle school math (2 questions in photo)
Question 8
Part (a)
The gradient is the coefficient of x after isolating y.
[tex]3x+y=15 \\ \\ y=\boxed{-3}x+15 [/tex]
Part (b)
The line crosses the y-axis when x=0. So, the line crosses tne y-axis at (0,15).
By similar logic, the answers to Question 9 are:
(a) -3
(b) (0, -4.5)
Which system of measurement uses the minim as the basic unit of liquid measure?
The apothecary system uses the minim as the basic unit of liquid measure and the grain as the basic unit of solid measure.
What is apothecary measurement?
The apothecary system was once a system of weights and measurements used for drug prescription and dispensing. A pound was divided into 12 ounces in the English version, which also divided an ounce into eight drams or drachms and a dram into three scruples, or 60 grains.What are the units of the apothecary system?
The grain, scruple (20 grains), dram (3 scruples), ounce (8 drams), and pound—a ancient scale of weight used in the British Isles for measuring and distributing pharmacological goods (12 ounces).
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Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? explain why this is true.
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
The money received from routine business activities is referred to as revenue, sales, or the top line.Revenue (from the sale of goods or services) less operational expenses equals operating income.Non-operating income is irregular or irregular money that comes from other sources (e.g., lawsuit proceeds).Governments, nonprofit organizations, and private persons are examples of non-business entities that also declare revenue, albeit their methods and resources vary.Let us assume,
charge = b
customer= c
revenue= r
We know that,
r= bc
⇒ [tex]r=16\times 10[/tex]
⇒ [tex]r=\ 160[/tex]
Also,
[tex]b+1[/tex] ⇒ [tex]c-2[/tex]
with a target of [tex]r \geq 130[/tex]
Therefore,
[tex]b=10+x[/tex] ⇒ [tex]c=16-2x[/tex]
[tex](10+x)(16-2x)\geq 130\\160-20x+16x-2x^2 \geq 130\\-2x^2 -4x+30\geq 0\\x^2+2x-15\leq 0\\(x+1)^2 \leq 4^2\\x+1 \leq 4[/tex]
as negative value is not considered.
[tex]x\leq 3[/tex]
We get the result that [tex]\[/tex]3 is the maximum increase amount.
Therefore, revenue will be:
[tex](10+3)(16-3\times2)=13\times 10\\[/tex]
revenue = [tex]\[/tex]130
Full Question: Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour. Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions. Assuming that any increase occurs in whole dollar amounts, what is the maximum possible increase that maintains the desired minimum revenue? Explain why this is true.
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Answer:
The desired minimum revenue is $130.
What is revenue?
Revenue, which is determined by multiplying the average sales price by the quantity of units sold, is the money made from regular business operations. The top line (or gross income) figure is what is used to calculate net income by deducting costs. Sales are another name for revenue in the income statement.
Step-by-step explanation:
Worked out for me :)
How long does it take for millions of dollars worth of emerald transactions to occur in bogota? a year three months a day a week
Answer: It will be A Day
Step-by-step explanation:
A number, h, rounded to 1 d.p. is 47.2
Another number, k, rounded to 1 d.p. is 4.8
What are the lower and upper bounds of
h - k?
The lower and upper bounds of h - k are 42.31 and 42.49 respectively.
Upper and lower bounds are the maximum and minimum values that a number could have been before it was rounded. They can also be called limits of accuracy.
The upper and lower bounds can be written using error intervals
The lowest value of h is 47.15
The greatest value of h is 47.24
The greatest value of k is 4.84
The lowest value of k is 4.75
Thus upper bound of h -k = 47.24 - 4.75 = 42.49
Thus lower bound of h -k = 47.15 - 4.84 = 42.31
Thus the lower and upper bounds of h - k are 42.31 and 42.49 respectively.
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It’s the start of a new football season and my favorite team, the WACO Hawks, is looking good! They won their first
game by beating Dublin Irish 28-27 on a last second play.
In the course of the game they piled up a lot of running yards, divided among four players:
• The bruising fullback, Vernon Variable, accounted for a chuck of those yards.
• The star halfback, Reggie Root, ran for 15 less than three times as many yards as Vernon did.
• The speedy wide-out, Larry Linear, only ran once but he picked up 11 more yards than Vernon’s total on that
play, a fancy reverse that went for a touchdown.
• The crafty quarterback, Quentin Quadratic, ran for a total of 18 yards on a variety of scrambles.
If the WACO Hawks ran for 229 yards, how many yards did each of the four players gain? Remember to define a
variable, write an equation, and explain your work (focusing on the why you did what you did)
Vernon Variable ran 43 yards, Reggie Root ran 114 yards, Larry Linear ran 54 yards, and Quentin ran 18 yards.
How to solve Linear Equations Word Problems?We are told that the total number of yards the WACO Hawks ran is 229. Thus, we can say that: W = 229
Now, we know that Vernon Variable gained many yards. Thus, the amount of yards will be indicated by "V"
Now, Reggie Root ran for 15 less than three times as many yards as Vernon did. Thus, distance Reggie root ran is represented by;
R = 3V-15
Larry Linear picked up 11 more yards than Vernon’s total. Thus, total yards by Larry Linear is: L = V + 11
Quentin Quadratic ran a total of 18 yards. Thus; Q=18.
Now, all of the player's totals add up make what the total team ran. Thus, the expression is;
V + 3V - 15 + V + 11 + 18 = 229
Simplifying this gives;
5V + 14 = 229
5V + 14 = 229
Subtract 14 from both sides to get;
5V = 215
Divide both sides by 5 to get;
V = 43
Thus, Vernon ran a total of 43 yards.
Total run by Reggie is:
R = 3(43) -15
R = 129 - 15
R = 114 yards.
Total run by Larry:
L = V + 11
L = 43 + 11
L = 54 yards.
Thus, we conclude that Vernon Variable ran 43 yards, Reggie Root ran 114 yards, Larry Linear ran 54 yards, and Quentin ran 18 yards.
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The function p(x) = 2x +1 determines how many pizzas need to be purchased for an after school meeting, where x is the number of students at the meeting. The club leader uses r(p(x)) to find the amount of money to bring for the pizza purchase. The function r(x) = 4x − 3. Solve for how much money to bring when there are 9 students in the meeting. (6 points)
Answer:
The club leader needs $73 for pizzas for 9 students.
Step-by-step explanation:
p(x) = 2x +1
r(x) = 4x − 3
r(p(x)) = 4(2x +1) − 3
r(p(x)) = 8x +4 − 3
r(p(x)) = 8x +1
r(p(9)) = 8(9) +4 − 3
r(p(9)) = 72 +1
r(p(9)) = $73
A coffee shop sells coffee, tea and pastries. The owner analysed her profits from the shop this week and found that
two-fifths of the profit was from the sale of collee and one third of the profit was from the sale of pastries. The rest of
the profit was from the sale of tea.
What fraction of the colfee shop's profit was from the sale of tea?
HELP ASAP
Consider functions H and K
What is the value of (h o k)(2)?
and look at this graph and please tell me what the answers are
Answer:
-3
Step-by-step explanation:
(h o k)(2) means
h( k(2)).
Remember when you have a function like f(x) or g(x) or h(x) or k(x), whatever number (or expression) is inside of the parenthesis, they're telling you to use that in place of x.
What h( k(2) ) means is we're going to put k(2) into h.
Well, what's k(2)? We need to find that first. k(x) is given as the oval and arrows thing going on there. If we're looking for k(2) then 2 is being the x. Find 2 in the first oval, follow the arrow to the output which is k(2).
If x = 2, the k(2)= -2
So back to
(h o k)(2):
(h o k)(2)
= h( k(2) )
= h(-2)
Since h(x)= 3/x+1
and x is -2, we'll put -2 in place of x.
h(-2) = 3/-2+1
= 3/-1
= -3
2/5x + 7/8y - 4/15x - 1/4y=?
Answer:
Simplified: 2x/15 + 5y/8
Step-by-step explanation:
Simplify the expression.
Answer:
Answer: 2x/15 + 5y/8
Step-by-step explanation:
Just Simplify the expression dude.
On June 10, Bertha Wooten deposited $8,241.78 in a savings account that pays 5.5% interest compounded
daily. How much interest will the money earn in 31 days?
The amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59, which is the difference between the future value and the present value.
What is the future value?The future value represents the amount that will be in the account after the present value investment is compounded at an interest rate periodically.
The future value of an investment can be calculated using the future value formula, A = P (1 + i)^n.
Where:
A = future value
P = Present value of investment
i = interest rate
n = number of periods.
The future value of the investment can also be determined using an online finance calculator, as follows.
Then the interest is the difference between the future value and the present value.
Data and Calculations:Initial deposit = $8,241.78
Interest rate = 5.5% compounded daily
Investment period = 31 days
N (# of periods) = 31 days
I/Y (Interest per year) = 5.5%
PV (Present Value) = $8,241.78
PMT (Periodic Payment) = $0
Results:
FV = $8,280.37
Total Interest $38.59 ($8,280.37 - $8,241.78)
Thus, the amount of interest that Bertha Wooten's deposit will earn in 31 days is $38.59.
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To pass a particular score a student has to achieve a mean of at least 50% in the ten pieces of work that form the assessment items. In the first nine of these pieces of work the student achieved a mean of 46%. What percentage mark must the student achieve in the tenth item if he is to pass the course?
Step-by-step explanation:
the mean value is the sum of all data points divided by the number of data points.
so, in our case we have after 9 pieces of work
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) / 9 = 46
that means
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) = 46×9 =
= 414
now we need to add a p10, so that
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10) =
= 50 × 10 = 500
only then do we get
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9 + p10)/10 =
= 50
so,
(p1 + p2 + p3 + p4 + p5 + p6 + p7 + p8 + p9) + p10 = 500
414 + p10 = 500
p10 = 500 - 414 = 86%
the student must at least achieve 86% for the 10th piece of work.
Which equation represents the relationship shown in the
graph?
What is the slope of a line that is perpendicular to the line whose equation is 3x 2y=6?
2/3 is the slope of a line that is perpendicular to the line whose equation is 3x 2y=6.
What is slope?
Slope, Numerical measure of a line's inclination relative to the horizontal. In analytic geometry, the slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).we can find the slope from the equation that is given buy solving the equation for y
3x+2y = 6
2y = 6-3x
y = 3-3/2x
y = -3/2x+3
now that the equation is in slope-intercept form, we can easily see that the slope of the given line is -3/2
perpendicular lines have slopes that are negative reciprocals, so we can just take the negative reciprocal of the slope we have
-3/2 → 3/2 → 2/3
Therefore, the slope of the perpendicular line is 2/3.
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In each of the following, the type of variation is given along with 1 data point. Find the variation constant. a. direct variation; y = Kx where x = 3 and y = 6 b. inverse square variation; y = K/x2 where x = –2 and y = 1 c. inverse variation; y = K/x where x = 8 and y = 10 d. inverse variation; y = K/x where x = 3 and y = 3 e. direct square variation; y = Kx 2 where x = 5 and y = 15 f. direct variation; y = Kx where x = –7.5 and y = 6.3
For direct variation, variation constant = 2.
For inverse square variation, variation constant = 4.
For inverse variation, variation constant =80.
For inverse variation, variation constant = 9.
For direct square variation, variation constant = 0.6
For direct variation, variation constant = -0.84
(a) Direct variation: y = Kx where x = 3 and y = 6
Variation constant(k) = y/x = 6/3 =2
(b) Inverse square variation: y = K/[tex]x^{2}[/tex] where x = -2 and y = 1
Variation constant(k) = y[tex]x^{2}[/tex] = 1(-2)(-2) =4
(c) Inverse variation: y = K/x where x = 8 and y = 10
Variation constant(k) = y*x = 8*10 =80
(d) Inverse variation: y = K/x where x = 3 and y = 3
Variation constant(k) = y*x = 3*3 =9
(e) Direct square variation: y = K[tex]x^{2}[/tex] where x = 5 and y = 15
Variation constant(k) = y/[tex]x^{2}[/tex] = 15/25 =0.6
(f) Direct variation: y = Kx where x = -7.5 and y = 6.3
Variation constant(k) = y/x = -6.3/7.5 = -0.84
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Find the taylor series for f(x) centered at the given value of a. [assume that f has a power series expansion. do not show that rn(x) → 0. ] f(x) = 8/x, a = −4
The taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
Given a function f(x)=9/x,a=-4.
We are required to find the taylor series for the function f(x)=8/x centered at the given value of a and a=-4.
The taylor series of a function f(x)=[tex]f(a)+f^{1}(a)(x-a)/1!+ f^{11}(a)(x-a)^{2} /2! +f^{111}(a)(x-a)a^{3}/3!+..........[/tex]
Where the terms in f prime [tex]f^{1}[/tex](a) represent the derivatives of x valued at a.
For the given function.f(x)=8/x and a=-4.
So,f(a)=f(-4)=8/(-4)=-2.
[tex]f^{1}[/tex](a)=[tex]f^{1}[/tex](-4)=-8/([tex]-4)^{2}[/tex]
=-8/16
=-1/2
The series of f(x) is as under:
f(x)=f(-4)+[tex]f^{1}(-4)(x+4)/1!+ f^{11}(-4)(x+4)^{2}/2!.............[/tex]
[tex]=8/(-4)-8/(-4)^{2} (-4)(x+4)/1!+ 24/(-4)^{3} (-4)(x+4)^{2}/2!.............[/tex]
=-2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
Hence the taylor series for the f(x)=8/x centered at the given value of a=-4 is -2+2(x+4)/1!-24/16 [tex](x+4)^{2}[/tex]/2!+...........
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Consider the first four terms of the sequence below. -3, -12, -48, -192, . . . what is the 8th term of this sequence?
Answer: -49152
Step-by-step explanation: the pattern here is that each term is subtracting 3 times its absolute value. Going from -3 to -12 there is a difference of 9 which is 3 times to absolute value of -3. So, the sequence will continue like this : -192, - 768, -3072, - 12288, -49152.
A pizza has a radius of 10 inches. A slice is removed. The length of the crust of the missing slice is 3 inches. What is the area of the missing slice?
The area of the missing slice is 15 inches ²
How to determine the area
From the information given, we can see that the pizza takes the form of a circle;
Area of the missing slice takes the shape of a triangle
Area of a triangle = 1/ 2 base × height
base = 10 inches
height = 3 inches
Area of missing slice = 1/ 2 × 10 × 3
Area = 1/ 2 × 30
Area = 15 inches ²
Thus, the area of the missing slice is 15 inches ²
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please help I'm so tired and I need to turn this in tomorrow
Considering the given box plots, it is found that:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles.
d) Athlete B had a greater median distance.
What is a box plot?It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.
The smallest value.The first quartile.The median.The third quartile.The highest value.Hence, for Athlete A, we have that:
The smallest value is 12.The first quartile is 27.The median is of 29.The third quartile is 34.The highest value is of 45.IQR: 34 - 27 = 7.For Athlete B, we have that:
The smallest value is 18.The first quartile is 32.The median is of 37.The third quartile is 39.The highest value is of 41.IQR: 39 - 32 = 7.Hence:
a) They had the same IQR.
b) Athlete A went on the shortest training ride.
c) Athlete B went on more rides longer than 35 miles(as it is less than his median).
d) Athlete B had a greater median distance.
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