In this question (https://brainly.com/question/12792658) I derived the Taylor series for [tex]\mathrm{sinc}\,x[/tex] about [tex]x=0[/tex]:
[tex]\mathrm{sinc}\,x=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}[/tex]
Then the Taylor series for
[tex]f(x)=\displaystyle\int_0^x\mathrm{sinc}\,t\,\mathrm dt[/tex]
is obtained by integrating the series above:
[tex]f(x)=\displaystyle\int\sum_{n=0}^\infty\frac{(-1)^nx^{2n}}{(2n+1)!}\,\mathrm dx=C+\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}[/tex]
We have [tex]f(0)=0[/tex], so [tex]C=0[/tex] and so
[tex]f(x)=\displaystyle\sum_{n=0}^\infty\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}[/tex]
which converges by the ratio test if the following limit is less than 1:
[tex]\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(-1)^{n+1}x^{2n+3}}{(2n+3)^2(2n+2)!}}{\frac{(-1)^nx^{2n+1}}{(2n+1)^2(2n)!}}\right|=|x^2|\lim_{n\to\infty}\frac{(2n+1)^2(2n)!}{(2n+3)^2(2n+2)!}[/tex]
Like in the linked problem, the limit is 0 so the series for [tex]f(x)[/tex] converges everywhere.
The Taylor series for the function f(x) = ∫ sinc(t)dt based at 0 is derived from the Taylor series of sinc(x) by integrating it term by term, given in summation notation as ∑ (-1)ⁿ * xⁿ⁺¹ / (n+1)! for n=0 to n=∞. The series converges for all real numbers (-∞, ∞).
Explanation:In order to find the Taylor series for the function f(x) = ∫ sinc(t)dt based at 0, one can use the Taylor series for sinc(x) and integrate term by term. We know the Taylor series for sinc(x) is x - x³/3! + x⁵/5! - ..., so the Taylor series for f(x) can be written as x²/2 - x⁴/4*3! + x⁶/6*5! - ... . In summation notation, this is ∑ (-1)ⁿ * xⁿ⁺¹ / (n+1)! for n=0 to n=∞.
The Taylor series for any function converges to the function itself within a certain interval called the radius of convergence. For the Taylor series of sinc(x), due to the nature of sine being bounded between -1 and 1, the series will converge for all real numbers (-∞, ∞).
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The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 153 cm2, what is the length of the diagonal?
Give your answer to 2 decimal places.
If anyone could explain this I would appreciate it, all the answers I kept getting on similar questions were a few numbers off and I don't know why.
Answer:
diagonal ≈ 18.43 cm
Step-by-step explanation:
Let L represent the length of the rectangle. Then the width is ...
w = 2L -4 . . . . . . 4 less than twice the length
The area is ...
A = wL = (2L -4)L = 2L² -4L
The area is said to be 153 cm², so we have ...
2L² -4L = 153
2L² -4L -153 = 0 . . . . . . subtract 153 to put into standard form
We can find the solution to this using the quadratic formula. It tells us the solution to ax²+bx+c=0 is given by ...
x = (-b±√(b²-4ac))/(2a)
We have a=2, b=-4, c=-153, so our solution for L is ...
L = (-(-4) ±√((-4)²-4(2)(-153)))/(2(2)) = (4±√1240)/4
Only the positive solution is of interest, so L = 1+√77.5.
__
Now we know the rectangle is 1+√77.5 long and -2+2√77.5 wide. The diagonal (d) is the hypotenuse of a right triangle with these leg lengths. Its measure can be found from ...
d² = w² +L² = (-2+2√77.5)² +(1+√77.5)²
It can work well to simply evaluate this using a calculator, or it can be simplified first.
d² = 4 -8√77.5 +4·77.5 + 1 +2√77.5 +77.5 = 392.5 -6√77.5
Taking the square root gives the diagonal length:
d = √(392.5 -6√77.5) ≈ 18.43 . . . . cm
If the nominal interest rate is 6 percent and the rate of inflation is 10 percent, then the real interest rate is A. -16 percent. B. 4 percent. C. -4 percent. D. 16 percent.
Answer: C. -4 percent
Step-by-step explanation:
Nominal interest rate is the interest rate before taking inflation into account.
Real interest rate takes the inflation rate into account.
The equation that links all three values is
nominal rate - inflation rate = real rate
6 - 10 = -4
-4 percent
The real interest rate can be calculated by subtracting the inflation rate from the nominal interest rate. In this case, the real interest rate is -4%, suggesting an investor would lose value due to inflation.
Explanation:The calculation of the real interest rate involves subtracting inflation from the nominal interest rate. This is essential since inflation erodes the purchasing power of money, making it an important factor to consider when dealing with interest rates. In this case, you need to subtract the inflation rate (10 percent) from the nominal interest rate (6 percent).
So, performing this calculation:
6% (Nominal Interest Rate) - 10% (Inflation Rate) = -4%
Thus, in this scenario, the correct option would be C. -4 percent. This implies that an investor would actually lose ground when considering the effect of inflation.
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2x + 1 < 5
Solve the following inequality. Then place the correct number in the box provided.
Answer:
x < 2
Step-by-step explanation:
[tex]2x+1 <5\\ 2x <4\\x <2[/tex]
For this case we have the following inequality:
[tex]2x + 1 <5[/tex]
Subtracting 1 from both sides of the inequality we have:
[tex]2x <5-1\\2x <4[/tex]
Dividing between 2 on both sides of the inequality:
[tex]x <\frac {4} {2}\\x <2[/tex]
Thus, the solution is given by all values of "x" less than 2.
Answer:
[tex]x <2[/tex]
To estimate μ, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 81 full professors. The sample mean is = $77,220 and the sample standard deviation is s = $4500. A 98% confidence interval for μ is _____.
Answer with explanation:
Sample mean of 81 full Professor = $ 77,220
Sample Standard Deviation (S)= $ 4500
Sample mean= $77,220
[tex]Z_{98 \text{Percent}=\frac{98}{100}}\\\\Z_{98 \text{Percent}=0.8365}\\\\Z_{\text Score=\frac{\bar x -\mu}{\sigma}}\\\\0.84=\frac{77220- \mu}{4500}\\\\\mu=77220-3780\\\\ \mu=73440[/tex]
So, When , z=98% , then Mean Salary ( μ)=73,440
2. The Great Pyramid outside Cairo, Egypt, has a square base measuring 756 feet
on a side and a height of 480 feet.
a. [3 pts] What is the volume of the Great Pyramid, in cubic yards?
b. [2 pts] The stones used to build the Great Pyramid were limestone blocks
with an average volume of 1.5 cubic yards. Assuming a solid
pyramid, how many of these blocks were needed to construct the
Great Pyramid?
First convert the dimensions of the pyramid from feet to yards.
1 yard = 3 feet.
756 feet / 3 ft per yard = 252 yards.
480 feet / 3 ft per yard = 160 yards.
The formula for volume of a pyramid is: Area of the base x the height divided by 3.
Volume = 252 yds^2 x 160/3 = 63504 x 160/3 = 3,386,880 cubic yards.
Now to find the number of bricks needed. divide the total volume by the volume of 1 brick:
3,386,880 / 1.5 = 2,257,920 total bricks.
Need help on to algebra questions!!!
14. Fifteen coins consisting of nickels, dimes, and quarters were collected from a newspaper vending machine. The total value of the coins is $1.95, and there are 4 more dimes than quarters. Find the number of each type of coin.
A. 2 nickels; 9 dimes; 5 quarters
B. 5 nickels; 7 dimes; 3 quarters
C. 7 nickels; 6 dimes; 2 quarters
D. 3 nickels; 8 dimes; 4 quarters
17. Which relation is not a function?
A. {(–7,2), (3,11), (0,11), (13,11)}
B. {(7, 11), (11, 13), (–7, 13), (13, 11)}
C. {(7,7), (11, 11), (13, 13), (0,0)}
D. {(7, 11), (0,5), (11, 7), (7,13)}
Answer:
A
Step-by-step explanation:
14 is A because its dividing and operating
Answer:
D, D
Step-by-step explanation:
Nickels are $0.05, Dimes are $0.10 and quarters are $0.25
Simply work out the options and see which one gives you $1.95
A) By observation, we see that this combination has 16 coins, but the question says only 15 coins. Hence we can remove this as an option.
B) 5($0.05) + 7($0.10) + 3($0.25) = $1.70 ≠ $1.95 (wrong)
C) 7($0.05) + 6($0.10) + 2($0.25) = $1.45 ≠ $1.95 (wrong)
D) 3($0.05) + 8($0.10) + 4($0.25) = $1.95 (Correct)
FOr next question, D is not a function because if you observe the values in D, an input of 7 should give 11 i.e (7,11), but there is another option where 7 gives an output of 13 i.e (7,13).
Because for a function to be valid, one input cannot give 2 different outputs, D is not a function.
Please help me! Struggling with Geometry! 45 points (proofs)
Answer:
Step-by-step explanation:
It’s nothing
What is the probability that a randomly drawn hand of four cards contains all black cards or all face cards? The probability is 6 Round to four decimal places as needed.)
Answer: 0.05699
Step-by-step explanation:
The total number of cards in a deck = 52
The total number of black cards = 26
Then ,[tex]\text{P(Black)}=\dfrac{C(26,4)}{C(52,4)}=0.00182842367\approx0.00183[/tex]
The total number of face cards = 12
Then , [tex]\text{P(Face)}=\dfrac{C(12,4)}{C(52,4)}\approx0.05522[/tex]
The number of cards that are black and face cards = 6
Then , [tex]\text{P(Black and Face )}=\dfrac{C(6,4)}{C(52,4)}\approx0.00006[/tex]
Then , the probability that a randomly drawn hand of four cards contains all black cards or all face cards is given by :-
[tex]\text{P(Black or Face)}=\text{P(Black)+P(Face)-P(Black and Face)}\\\\\Rightarrow\ \text{P(Black or Face)}=0.00183+0.05522-0.00006\\\\\Rightarrow\ \text{P(Black or Face)}=0.05699[/tex]
how the graph does the graph behave as x approaches positive or negative infinity. does it keep going at the same rate or does it approach a value but never touch it ?
The graph approaches positive infinity at a constant rate.
The end behavior of this graph is:
As x → -∞, f(x) → +∞
For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)
and
As x → +∞, f(x) → +∞
For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: The graph approaches positive infinity at a constant rate.
Step-by-step explanation:
Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $25 and same-day tickets cost $35. For one performance, there were 45 tickets sold in all, and the total amount paid for them was $1375
. How many tickets of each type were sold?
For this case we propose a system of equations:
x: Variable representing the anticipated tickets
y: Variable representing the same day tickets
So:
[tex]x + y = 45\\25x + 35y = 1375[/tex]
We clear x from the first equation:
[tex]x = 45-y[/tex]
We substitute in the second equation:
[tex]25 (45-y) + 35y = 1375\\1125-25y + 35y = 1375\\10y = 1375-1125\\10y = 250\\y = 25[/tex]
We look for the value of x:
[tex]x = 45-25\\x = 20[/tex]
Thus, 20 of anticipated type and 25 of same day type were sold.
Answer:
20 of anticipated type and 25 of same day type were sold.
Answer: 20 advance tickets and 25 same-day tickets.
Step-by-step explanation:
Set up a system of equations.
Let be "a" the number of advance tickets and "s" the number of same-day tickets.
Then:
[tex]\left \{ {{25a+35s=1375} \atop {a+s=45}} \right.[/tex]
You can use the Elimination method. Multiply the second equation by -25, then add both equations and solve for "s":
[tex]\left \{ {{25a+35s=1,375} \atop {-25a-25s=-1,125}} \right.\\.............................\\10s=250\\\\s=\frac{250}{10}\\\\s=25[/tex]
Substitute [tex]s=25[/tex] into an original equation and solve for "a":
[tex]a+(25)=45\\\\a=45-25\\\\a=20[/tex]
The n candidates for a job have been ranked 1, 2, 3, . . . , n. Let X be the rank of a randomly selected candidate, so the X has the pmf p(x) = 1/n, if x = 1, 2, 3 . . . n, 0, otherwise. This is called the discrete uniform distribution. Compute E(X) and Var(X). (Hint: the sum of the first n positive integers is n(n + 1)/2, whereas the sum of their squares is n(n + 1)(2n + 1)/6.)
By definition of expectation,
[tex]\displaystyle E[X]=\sum_xx\,P(X=x)=\sum_{x=1}^n\frac xn=\frac{n(n+1)}{2n}=\boxed{\frac{n+1}2}[/tex]
and variance,
[tex]V[X]=E[(X-E[X])^2]=E[X^2-2X\,E[X]+E[X]^2]=E[X^2]-E[X]^2[/tex]
Also by definition, we have
[tex]E[f(X)]=\displaystyle\sum_xf(x)\,P(X=x)[/tex]
so that
[tex]E[X^2]=\displaystyle\sum_{x=1}^n\frac{x^2}n=\frac{n(n+1)(2n+1)}{6n}=\frac{(n+1)(2n+1)}6[/tex]
and finally,
[tex]V[X]=\dfrac{(n+1)(2n+1)}6-\dfrac{(n+1)^2}4=\boxed{\dfrac{n^2-1}{12}}[/tex]
Answer:
[tex]\frac{n^{2} - 1 }{12}[/tex]
Step-by-step explanation:
Data:
We collect the variables and simplify the result:
E[X] = [tex]\SIGMA \\[/tex]Σ x · p(x) = [tex]\frac{1}{n}[/tex]= ....
E[X²] =∑ x²· p(x) = ∑x²·[tex]\frac{1}{n}[/tex] = ....
Var [X] = E[X²] - E[X]² = ...
We then use the identities:
∑x = [tex]\frac{n(n+1)}{2}[/tex] and ∑ x² = [tex]\frac{n(n+1)(2n+1)}{6}[/tex]
simplifying the identities above gives:
[tex]\frac{n^{2-1} }{12}[/tex]
what is the y-coordinate of the vertex of the parabola?
f(x)= -x^2 - 2x +6
Answer:
7
Step-by-step explanation:
The function can be written in vertex form as ...
f(x) = -(x +1)^2 +7
The vertex is then identifiable as (-1, 7). The y-coordinate is 7.
_____
Vertex form is ...
f(x) = a(x -h)^2 +k
where "a" is the vertical scale factor, and (h, k) is the vertex point. It is convenient to arrive at this form by factoring "a" from the first two terms, then adding and subtracting the square of the remaining x-coefficient inside and outside parentheses.
f(x) = -(x^2 +2x) +6
f(x) = -(x^2 +2x +1) + 6 -(-1) . . . . completing the square
f(x) = -(x +1)^2 +7 . . . . . . . . . . . . vertex form; a=-1, (h, k) = (-1, 7)
The y-coordinate of the vertex of the parabola defined by the function f(x)= -x² - 2x + 6 is 3. This is found by using the vertex formula and then substituting the x-coordinate back into the original function.
To find the y-coordinate of the vertex of the parabola defined by the quadratic function f(x)= -x² - 2x + 6, we can use the vertex formula for a parabola in standard form, which is y = ax² + bx + c. The x-coordinate of the vertex is given by the formula -b/(2a), and the y-coordinate can then be calculated by applying the x-coordinate to the original function.
First, let's find the x-coordinate of the vertex:
a = -1 (coefficient of x²)b = -2 (coefficient of x)x-coordinate of the vertex, x_v = -(-2)/(2*(-1)) = -(-2)/(-2) = 1
Now, substitute x_v back into the function to find the y-coordinate:
y-coordinate of the vertex, y_v = f(1) = -1² - 2*1 + 6 = -1 - 2 + 6 = 3
Therefore, the y-coordinate of the vertex is 3.
what is the value of X
Answer:
The value of x = 96°
Step-by-step explanation:
Here we consider two angles be <1, <2 and < 3, where <1 is the linear pair of angle measures 130° and <2 be the linear pair of angle measures 134°
To find the value of m<1
m<1 = 180 - 130 = 50°
To find the value of m<2
m<2 = 180 - 134 = 46°
To find the value of m<3
By using angle sum property,
m<1 + m<2 + m< 3 = 180
m<3 =180 - (m<1 + m<2)
= 180 - (50 + 46 = 96
= 84°
To find the value of x
Here x and <3 are linear pair,
x + m<3 = 180
x = 180 - m<3
= 180 - 84 = 96°
Therefore the value of x = 96°
Graph y ≥ -x^2 - 1. Click on the graph until the correct graph appears.
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]y\geq -x^{2}-1[/tex]
The solution of the inequality is the shaded area above the solid line of the equation of the parabola [tex]y= -x^{2}-1[/tex]
The vertex of the parabola is the point (0,-1)
The parabola open downward (vertex is a maximum)
using a graphing tool
see the attached figure
What side lengths should be used to model the rectangle?
A rectangle with an area of x2 - 4x - 12 square units is
represented by the model
(x + 2) and (x-6)
(x+6) and (x - 2)
(x + 2) and (x - 10)
(x + 10) and (x - 2)
-X
-
+X
-
-
- -
- -
-
-
- -
- -
+X
For this case we have that by definition, the area of a rectangle is given by:
[tex]A = ab[/tex]
Where:
a, b: They are the sides of the rectangle
We have as data that the area of the rectangle is given by:
[tex]x ^ 2-4x-12[/tex]
IF we factor the expression, we must find two numbers that when multiplied give as a result "-12" and when summed give as result "-4". These numbers are: -6 and +2:
[tex](x-6) (x + 2)[/tex]
Thus, the sides of the rectangle are given by:
[tex](x-6) (x + 2)[/tex]
Answer:
Option A
Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists. Show your work.
4x - y + 3z = 12
x + 4y + 6z = -32
5x + 3y + 9z = 20
Note that adding the first two equations gives
[tex](4x-y+3z)+(x+4y+6z)=12+(-32)\implies5x+3y+9z=-20[/tex]
But the third equation says [tex]5x+3y+9z=20[/tex], so there is no solution.
Electric power costs 17.8 cents per kWh in Los Angeles in July 2017 (compared to the national average of 14.3 cents per kWh). How much did it cost (in cents) to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017? Assume 3 significant digits in your answer.
The cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017 is:
4.45 cents
Step-by-step explanation:Electric power costs 17.8 cents per kWh in Los Angeles in July 2017.
Now we are asked to find the cost to run a 1500 W hair dryer for 10 minutes in Los Angeles during July 2017.
We know that: 1 w=0.001 kW
This means that:
1500 W= 1.500 kW
Also, it is used for 10 minutes
i.e. 1/6 hours
Hence, the electric power used to run the hair dryer is: 1.500×(1/6)
i.e. Electric power to used by hair dryer is: 0.25 kWh
Cost of 1 kwh is: 17.8 cents
This means that cost of 0.25 kwh is: 17.8×0.25
= 4.45 cents
Hence, the answer is:
4.45 cents
For each of the following statements, state whether it is true (meaning, always true) or false (meaning, not always true): Let X and Y be two binomial random variables. (a) If X and Y are independent, then X+Y is also a binomial random variable.
Answer:
yes
Step-by-step explanation:
it is absolutely true that biononmials always gives biononmials when added
If X and Y are independent, then X+Y is not a binomial random variable and so it is a false statement.
What is the sum of independent binomial random variables?This term is known to be a binomial random variable that occurs when all the parts of the variables is said to have similar success probability.
The best method to check if two random variables are said to be independent is through the calculation of the covariance of the two specific random variables.
Note that if If the variables are said to be independent (X and Y), then their difference is said to be not binomially distributed.
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Find(f/g)(x)for the following functions.
Answer:
[tex]x^{2} \neq -\frac{1}{14}[/tex]
Step-by-step explanation:
The equation will hold true as long as the denominator does not equal zero:
so take the denominator and set it equal to zero and find x. when you find x, that will be your answer:
-14x^2 -1=0
-14x^2=1
-x^2=1/14
x^2=-1/14
I need help with Math Homework
Answer:
Your answer should be -8.
Suppose you invest $150 a month for 5 years into an account earning 7% compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 23 years. How much will you have in the end?
Answer:
About 0.3 billion dollars
Step-by-step explanation:
5 years = 60 months.
The 150 of the first month will be 150*1.07^60 in 5 years.
The 150 of the second month will be 150*1.07^59 in 5 years.
The 150 of the third month will be 150*1.07^58 in 5 years.
And so forth.
So we sum that up:
( sum_(n=1)^(60) 150×1.07^n)
And multiply with
× 1.07^(5×23)
to account for the increase in value in the following 23 years.
A. a relation only
B. both a relation and a function
C. Neither a relation or a function
D.a function only
Answer:
Neither a relation or a function
Answer: B. Both a relation and a function
Step-by-step explanation:
By definition, a relation is a function if and only if each input value has one and only one output value.
For example if an input value [tex]x[/tex] has assigned two or more output values [tex]y_1[/tex] and [tex]y_2[/tex], then the relation is not a function.
You can observe in the image attached that each element in the Domain has assigned one element in the Range. Therefore, you can conclude that it is a relation and a function.
A bottling company uses a filling machine to fill plastic bottles with popular cola. The contents are known to vary according to a normal distribution with mean μ = 300 ml and standard deviation σ = 10 ml. What is the probability that the mean contents of the bottles in a six pack is less than 295 ml?
Answer: 0.3085
Step-by-step explanation:
Given: Mean : [tex]\mu=300\text{ ml}[/tex]
Standard deviation : [tex]\sigma=10\text{ ml}[/tex]
The formula to calculate the value of z-score :-
[tex]z=\dfrac{X-\mu}{\sigma}[/tex]
For X = 295 ml, we have
[tex]z=\dfrac{295-300}{10}=-0.5[/tex]
The p-value of z = [tex]P(Z=z<-0.5)=0.3085[/tex]
Hence, the probability that the mean contents of the bottles in a six pack is less than 295 ml =0.3085
The surface of a pedestrian bridge forms a parabola. Let the surface at one side of the bridge be represented by the origin (0,0) and the surface at the other side be represented by (16,0). The center of the bridge is 2 feet higher than each side and can be represented by a vertex of (8,2). Write a function in vertex form that models the surface of the bridge.
Please help.
Check the picture below. So the bridge more or less looks like so.
since we know the vertex, we'll use that, and we also know a point on the parabola as well, namely (16,0).
[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=8\\ k=2 \end{cases}\implies y=a(x-8)^2+2\qquad (16,0)~~ \begin{cases} x=16\\ y=0 \end{cases}[/tex]
[tex]\bf 0=a(16-8)^2+2\implies -2 = a(8)^2\implies -2=64a \\\\\\ \cfrac{-2}{64}=a\implies \cfrac{-1}{32}=a \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill y=-\cfrac{1}{32}(x-8)^2+2~\hfill[/tex]
Final answer:
The function that models the surface of the pedestrian bridge as a parabola with vertex at (8,2) is y = -(1/32)(x - 8)² + 2.
Explanation:
To find the function that models the surface of the pedestrian bridge, we can use the vertex form of a parabolic equation, which is y = a(x - h)² + k, where (h,k) is the vertex. Since the bridge is 2 feet higher in the center than at the ends, we have the vertex at (8,2). This point gives us h = 8 and k = 2. Additionally, because the bridge starts and ends at ground level, we have two points that the parabola passes through: (0,0) and (16,0).
To find the value of 'a', we substitute one of the points into the equation. Let's use the point (16,0):
0 = a(16 - 8)² + 2 => 0 = a(8)² + 2 => 0 = 64a + 2 => -2 = 64a => a = -2/64 => a = -1/32
Now we have all we need to write the function in vertex form:
y = -(1/32)(x - 8)² + 2
This equation models the surface of the bridge as a parabola, with the vertex at the center of the bridge and the sides touching the ground.
The long jump record, in feet, at a particular school can be modeled by f(x) = 19.6 + 2.5ln(x + 1) where x is the number of years since records began to be kept at the school. What is the record for the long jump 11 years after record started being kept? Round your answer to the nearest tenth.
Answer:
25.8
Step-by-step explanation:
A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.
Answer: 0.0026
Step-by-step explanation:
Given: Mean : [tex]\mu=8.4\text{ hours}[/tex]
Standard Deviation : [tex]\sigma = 1.8\text{ hours}[/tex]
Sample size : [tex]n=40[/tex]
Formula to calculate z-score :-
[tex]z=\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
For X=7.6 hours.
[tex]z=\dfrac{7.6-8.4}{\dfrac{1.8}{\sqrt{40}}}=-2.81091347571\approx-2.8[/tex]
[tex]P(X<7.6)=P(Z<-2.8)=0.0025551\approx0.0026[/tex]
Hence, the probability that their mean rebuild time is less than 7.6 hours = 0.0026
The probability that their mean rebuild time is less than 7.6 hours is 0.0026
Explanation:A study of the amount of time it takes a mechanic to rebuild the transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 7.6 hours.
The Chevrolet Cavalier is the line of small cars produced for the model years 1982 until 2005 by Chevrolet. Mechanics is the physics area concerned with the motions of macroscopic objects. The mean is the number average. To calculate we add up all the numbers then divide by how many numbers there are. In other words it is the sum divided by the count.
[tex]\mu = 8.4 hours[/tex]
[tex]\sigma = 1.8 hours[/tex]
[tex]n=40[/tex]
[tex]z = \frac{Xbar -\mu}{\frac{\sigma}{\sqrt{r} } } = \frac{7.6-8.4}{\frac{1.8}{\sqrt{40} } } = -2.81[/tex]
Therefore the value of Xbar < 7.6 hours. from the standard normal table is 0.0026
Hence, the probability that their mean rebuild time is less than 7.6 hours is 0.0026 = 0.26%.
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3x3 matrix A. r1(3 -2 0) r2(0 1 1) r3(2 -1 0). don't calculate A^-1 or raise any matrix to a power first. calculate det(2A^-2)
Answer with explanation:
For, a 3 × 3, matrix
[tex]r_{1}=(3,-2,0)\\\\r_{2}=(0,1,1)\\\\r_{3}=(2,-1,0)[/tex]
which are entries of First, Second and Third Row Respectively.
So, if written in the form of Matrix (A)
[tex]A=\left[\begin{array}{ccc}3&-2&0\\0&1&1\\2&-1&0\end{array}\right][/tex]
⇒Adjoint A= Transpose of Cofactor of A
[tex]a_{11}=1,a_{12}=2,a_{13}=-2\\\\a_{21}=0,a_{22}=0,a_{23}=-1\\\\a_{31}=-2,a_{32}=- 3,a_{33}=3\\\\Adj.A=\left[\begin{array}{ccc}1&0&-2\\2&0&-3\\-2&-1&3\end{array}\right][/tex]
⇒≡ |Adj.A|=1 ×(0-3) -2×(-2-0)
= -3 +4
=1 --------(1)
⇒For, a Matrix of Order, 3 × 3,
| Adj.A |=| A|²---------(2)
[tex]|2 A^{-2}|=2^3\times |A^{-2}|\\\\=2^3\times |A|^{-2}\\\\=\frac{8}{|A^{2}|}\\\\=\frac{8}{|Adj.A|}\\\\=\frac{8}{1}\\\\=8[/tex]
--------------------------------------------(Using 1 and 2)
[tex]\rightarrow|2 A^{-2}|=8[/tex]
A test for marijuana usage was tried on 170 subjects who did not use marijuana. The test result was wrong 8 times.a. Based on the available results, find the probability of a wrong test result for a person who does not use marijuana.b. Is it "unlikely" for the test to be wrong for those not using marijuana? Consider an event to be unlikely if its probability is less than or equal to 0.05.
Answer:
a. 0.047
b. Unlikely.
Step-by-step explanation:
a. The probability of a test result being wrong for a person not using mrijuana = 8 / 170 = 0.047.
b. As the probability for a wrong result is < 0.05 we can say that the test is unlikely to be wrong.
Find how much should be invested to have $14,000 in 10 months at 9.1% simple interest.
Answer:
[tex]\$13,013.17[/tex]
Step-by-step explanation:
we know that
The simple interest formula is equal to
[tex]A=P(1+rt)[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest
t is Number of Time Periods
in this problem we have
[tex]t=10/12\ years\\ P=?\\ A=\$14,000\\r=0.091[/tex]
substitute in the formula above
[tex]\$14,000=P(1+0.091*(10/12))[/tex]
[tex]P=\$14,000/(1+0.091*(10/12))[/tex]
[tex]P=\$13,013.17[/tex]
The prizes at a carnival tossing game are different stuffed animals. There are 34 tigers, 27 bears, 12 hippopotamuses, 16 giraffes, and 22 monkeys. The carnival manager randomly selects a prize when a player wins the game. Determine the probability that the prize selected is not a hippopotamus. Give your answer as a decimal, precise to three decimal places.
Answer:
Step-by-step explanation:
Your first step is to find the total number of animals, no matter what they are.
34 + 27 + 12 + 16 + 22 = 111 animals.
You could add all the numbers other than the 12 hippopotamuses together. If you did, you would get 99.
The answer is 99/111 = 0.892
Sometimes it is just easier to do the following. Find the the probability of getting a hippo and subtract that from 1.
12/111 = 0.108
And subtract this number from 1. One represents all of the possible animals.
1 - 0.108 = 0.892
Later on, when you get problems that are more complicated, the second way is the way to do it. It gives you lest grief.