Select the correct answer.

Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This func

gayaneshka [121]

Answer:

Step-by-step explanation:

To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that

$\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}$

which is the taylor series expansion based at 0. Then for $x\neq 0$ , by dividing both sidex by x, we have that

$\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}$

which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.

3 0

2 years ago

Charlie bought a pair of shorts at the store when they were having a 45% off sale. If the regular price of the pair of shorts wa

spayn [35]

Answer:

$13.20

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

The average annual amount American households spend for daily transportation is $6312 (Money, August 2001). Assume that the amou

lions [1.4K]

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = <u><em>the amount spent on daily transportation</em></u>

The z-score probability distribution for the normal distribution is given by;

Z = $\frac{X-\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = average annual amount American households spend on daily transportation = $6,312

$\sigma$ = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

P(X < $1,000) = 0.05

P( $\frac{X-\mu}{\sigma}$ < $\frac{\$1000-\$6312}{\sigma}$ ) = 0.05

P(Z < $\frac{\$1000-\$6312}{\sigma}$ ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

$\frac{\$1000-\$6312}{\sigma}=-1.645$

$\sigma=\frac{-\$5312}{-1.645}$ = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

P($4000 < X < $6000) = P(X < $6000) - P(X $\leq$ $4000)

P(X < $6000) = P( $\frac{X-\mu}{\sigma}$ < $\frac{\$6000-\$6312}{\$3229.18}$ ) = P(Z < -0.09) = 1 - P(Z $\leq$ 0.09)

= 1 - 0.5359 = 0.4641

P(X $\leq$ $4000) = P( $\frac{X-\mu}{\sigma}$ $\leq$ $\frac{\$4000-\$6312}{\$3229.18}$ ) = P(Z $\leq$ -0.72) = 1 - P(Z < 0.72)

= 1 - 0.7642 = 0.2358

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

P(X > x) = 0.03 {where x is the required range}

P( $\frac{X-\mu}{\sigma}$ > $\frac{x-\$6312}{3229.18}$ ) = 0.03

P(Z > $\frac{x-\$6312}{3229.18}$ ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

$\frac{x-\$6312}{3229.18}=1.88$

${x-\$6312}=1.88\times 3229.18$

x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

8 0

2 years ago

Anu bought an air cooler as shown below. Its water tank is in the shape of a cuboid and can take 40 litres of water. Its dimensi

Ksivusya [100]

Answer:

40 cm

Step-by-step explanation:

Using the conversion

1 litre = 1000 cm³, then

40 litres = 40 × 1000 = 40000 cm³

The volume ( V) of a cuboid is

V = lbh ( divide both sides by bh )

l = $\frac{V}{bh}$ = $\frac{40000}{50(20)}$ = $\frac{40000}{1000}$ = 40 cm

8 0

1 year ago

At a bake shop, the cost of flour is $2.50 per pound and increases at a rate of $0.07 per month. The cost of cocoa is $6.00 per

Vesna [10]

Answer:

Step-by-step explanation:

We will find two equations for this system, one representing flour and the other representing cocoa. For the flour, we start with $2.50, and the cost goes up .07 per month, x. The equation for that is

y = .07x + 2.50

For the cocoa, the equation is written in the exact same way, but the cost goes down. Down is a negative thing while up is a positive thing. The cost starts at $6.00 and goes down .03 per month, x. The equation for that is

y = -.03x + 6.00

Comparing the first equation to the second, the .07 is positive because the cost goes UP that amount per month and the .03 is negative because the cost goes DOWN that amount per month. Get it?

If y is cost and we are tryong to find out where the cost is the same, we are looking for when y is the same. If the first y is equal to .07x + 2.50 and the second y is equal to -.03x + 6.00, and y is equal to y, then

.07x + 2.50 = -.03x + 6.00 (this is setting the first y equal to the second y). This is the system that describes how to find the number of months x when the cost y is the same. We'll solve it just for practice.

Combining like terms we get

.10x = 3.5 so

x = 35

Now back sub in what x equals to solve for y. If x = 35, then in the first equation,

.07(35) + 2.50 = y and

y = 4.95 (you could have used the second equation and subbed in 35 for x and you will get the exact same y value. Promise!)

What this answer tells us is that 35 months after the start of this pricing, the cost of flour will be the same as the cost of cocoa. But immediately after 35 months, the costs will not be the same anymore. It is only AT 35 months. At 36 months, the costs will be different.

7 0

1 year ago