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 function is used frequently in electrical engineering and signal processing.) Use this list of Basic Taylor Series to find the Taylor Series for f(x) = sinc(x) based at 0. Give your answer using summation notation and give the largest open interval on which the series converges. (If you need to enter [infinity] , use the [infinity] button in CalcPad or type "infinity" in all lower-case.)

Answer:

B. (f - g)(x) = -3x² - x - 4

Step-by-step explanation:

→Set it up like so:

(-4x² - 6x - 1) - (-x² - 5x + 3)

→Distribute the -1 to (-x² - 5x + 3):

-4x² - 6x - 1 + x² + 5x - 3

→Add like terms (-4x² and x², -6x and 5x, -1 and -3):

-3x² - x - 4

Answer:

DID IT oN EDGEN UITY

Step-by-step explanation:

The first graph correctly represents our piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.

A function that is piecewise-defined by numerous subfunctions, each of which has a separate domain interval for which it is applicable.

Piecewise definition is more of an expression of the function than it is a property of the function.

Given a piecewise function f(x) = - 1.5x + 3.5 for x < 2 and 4 + x for x ≥ 2.

Now, strictly less or greater than will be shown as an open circle in the graph and less than or greater than equal to will be shown by a closed circle on the graph.

If we observe the first graph when x = 0, y = 3.5, and the end is represented as an open circle which is < 2 and when x ≥ 2 it is 6 and represented with a closed circle.

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Answer:

The area of the rectangle increasing at the rate of 140 cm²/s

Step-by-step explanation:

Rectangle area:

A rectangle has two dimensions, length l and width w.

It's area is:

A = l*w.

When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing?

We apply implicit differentiation to solve this question:

[tex]A = l*w[/tex]

So

[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]

Length is 20, so [tex]l = 20[/tex].

Width is 10, so [tex]w = 10[/tex]

The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s.

This means that [tex]\frac{dl}{dt} = 8, \frac{dw}{dt} = 3[/tex]

So

[tex]\frac{dA}{dt} = l\frac{dw}{dt} + w\frac{dl}{dt}[/tex]

[tex]\frac{dA}{dt} = 20*3 + 10*8 = 140[/tex]

Area in cm².

So

The area of the rectangle increasing at the rate of 140 cm²/s

Answer:

C:second coordinates

Step-by-step explanation:

A range is the set of output coordinates

The domain is the input coordinates

Domain is the x, range is the y

Answer: its definitly c

Step-by-step explanation:

Answer:

CI = (70.861 , 94.418)

Step-by-step explanation:

In order to determine the 90% confidence interval you use the following formula (for a population approximately normal):

[tex]CI=(\overline{x}-Z_{\alpha/2}\frac{\sigma}{\sqrt{n}},\overline{x}+Z_{\alpha/2}\frac{\sigma}{\sqrt{n}})[/tex]    (1)

[tex]\overline{x}[/tex]: mean = 82.64

σ: standard deviation = 14.32

n: sample = 4

α: tail area = 1 - 0.9 = 0.1

Z_α/2 = Z_0.05: Z factor =  1.645

You replace these values and you obtain:

[tex]Z_{0.05}(\frac{14.32}{\sqrt{4}})=(1.645)(\frac{14.32}{\sqrt{4}})=11.778[/tex]

The confidence interval will be:

[tex]CI=(82.64-11.778,82.64+11.778)=(70.861,94.418)[/tex]

The 90% confidence interval is (70.861 , 94.418)

Answer:

A.

Step-by-step explanation:

Volume of cone = 1/3πr²h

= (1/3)(3.14)(1.5)²(5)

= (1/3)(3.14)(2.25)(5)

= (1/3)(35.3)

= 11.78

≈ 11.8 cubic inches

Answer:

x =44

Step-by-step explanation:

0.2x + (-0.9) + 1.7 = 9.6

Combine like terms

.2x +.8 = 9.6

Subtract .8 from each side

.2x +.8 -.8 = 9.6 -.8

.2x = 8.8

Divide each side by .2

.2x/.2 = 8.8/.2

x =44

Answer: 5 (estimate)

Step-by-step explanation:

x - 17 4/5 = -13 1/5

Estimate:  x - 18 = -13

x - 18 + 18 = -13 + 18

x = 5

actual answer without estimating using exact numbers is 4 3/5 (so estimate is reasonable)

Answer:

12.08

Step-by-step explanation:

For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Seventy-six percent of sunflower seeds will germinate into a flower

This means that [tex]p = 0.76[/tex]

Samples of 800:

This means that [tex]n = 800[/tex]

The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]

Answer:

a) 3 standard deviations above 16

b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.

c) Less than 2 standard deviations, so not far away.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If Z < -2 or Z > 2, X is considered to be far away from the mean.

In this question, we have that:

[tex]\mu = 16[/tex]

​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 ​inches?

This is Z when [tex]X = 22, \sigma = 2[/tex].

So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{2}[/tex]

[tex]Z = 3[/tex]

So 22 inches is 3 standard deviations fro 16 inches.

​(b) Is 22 inches far away from a mean of 16 ​inches?

3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.

(c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 ​inches?

Now [tex]\sigma = 4[/tex]

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{22 - 16}{4}[/tex]

[tex]Z = 1.5[/tex]

1.5 standard deviations from the mean, so 22 inches is not far away from the mean.

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

The given equation is x²+24x=33.

We need to factorise the equation using completing the square method.

Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.

Now, x²+24x-33=0

Add and subtract (b/2)²=144 to the equation.

x²+24x-33+144-144=0

⇒x²+24x+144-33-144=0

⇒(x+12)²-177=0

⇒(x+12)²=177

The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.

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Answer: choice B

Step-by-step explanation:

The graph of y=-3x^n is the reflection of the graph of y=3x^n about the x-axis.

Answer: B

Step-by-step explanation:

A) $400

B) $800

C) 400*X

D) revenue=400x

Answer:

True.

Step-by-step explanation:

A tree diagram is a diagram used in general mathematics, statistics, and probability to show a sequence of events. This tool is used to calculate the number of possibilities of an event to occur. Commonly, the tool of a tree diagram is used to find the possibility of outcome while flipping a coin. It is a diagram in which connections between the events is shown using the strucure of branching connecting lines.

So, the given statement is true, that is a simple way of showing events in a sequence.

Answer:

0.7125

Step-by-step explanation:

The binomial distribution with parameters n and p is the discrete probability distribution of the number of successes (with probability p) in a sequence of n independent events.

The probability of getting exactly x successes in n independent Bernoulli trials =  [tex]n_{C_{x}}(p)^x(1-p)^{n-x}[/tex]

Total number of watches in the shipment = 50

Number of defective watches = 6

Number of selected watches = 10

Let X denotes the number of defective digital watches such that the random variable X follows a binomial distribution with parameters n and p.

So,

Probability of defective watches = [tex]\frac{X}{n}=\frac{6}{50}=0.12[/tex]

Take n = 10 and p = 0.12

Probability that the shipment will be rejected = [tex]P(X\geq 1)=1-P(X=0)[/tex]

[tex]=1-n_{C_{x}}(p)^x(1-p)^{n-x}\\=1-10_{C_{0}}(0.12)^0(1-0.12)^{10-0}[/tex]

Use [tex]n_{C_{x}}=\frac{n!}{x!(n-x)!}[/tex]

So,

Probability that the shipment will be rejected = [tex]=1-\left ( \frac{10!}{0!(10-0)!} \right )(0.88)^{10}[/tex]

[tex]=1-(0.88)^{10}\\=1-0.2785\\=0.7125[/tex]

Answer:

y = -1/2x - 2

Step-by-step explanation:

If it's parallel, that means that the slope is the opposite of the one in the given equation, meaning that 2 would be flipped and turned negative into -1/2.

Then, fill in the x and y values to get the y-intercept.

1 = -1/2(-6) + b

1 = 3 + b

-2 = b

So your answer is y = -1/2x - 2

Answer:

1. Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean

2. 15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

1. In which of the preceding two cases, part a or part b, do we have a higher probability of obtaining a smaple estimate within $10,000 of the population mean? why?

The lower the standard deviation, the less dispersed the values are, meaning it is more likely to find values within a certain threshold of the mean.

So

Due to the lower standard deviation, it is more likely to obtain a sample of females within $10,000 of the population mean.

2. What is the probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean?

We have that:

[tex]\mu = 168000, \sigma = 40000, n = 100, s = \frac{40000}{\sqrt{100}} = 4000[/tex]

This probability is the pvalue of Z when X = 168000 - 4000 = 164000. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{164000 - 168000}{4000}[/tex]

[tex]Z = -1[/tex]

[tex]Z = -1[/tex] has a pvalue of 0.1587

15.87% probability that a simple random sample of 100 male graduates will provide a sample mean more than $4,000 below the population mean

Answer:

All college freshman is called Population and Right handed students are excluded is called sample from Population

Step-by-step explanation:

Explanation:-

Population:-  The total of the observations which we are concerned

given data all college freshman is called Population

Sample :-

A sample is a subset of a Population

Given data  all college freshman is called Population and Right handed students are excluded is called sample from Population

Answer:

Use the quadratic formula:

a =  1  b= -5   c= 2

x = - -5 +-sqr root (25 - 4 * 1 * 2) / 2 * 1

x =  5  +-sqr root (25 - 8) / 2

x =  5  +- sqr root (17) / 2

x1 = 5 +4.1231056256  / 2

x1 = 4.5615528128

x2 = 5 -4.1231056256  / 2

x2 = 4.5615528128

Step-by-step explanation:

Answer:

y = [tex]\frac{1}{2}[/tex]x - 5

Step-by-step explanation:

Use rise over run to find the slope, which will get you 1/2 as the slope

The y-intercept is at (0, -5) so put -5 in the equation

Answer: y= 1/2x + -5

Step-by-step explanation: slope is 1/2 because the line is going up one and over 2 (rise over run),  the y intercept is -5 because that is where the line hits on the y axis

Answer: B

Step-by-step explanation:

For this problem, to solve for x, you want to move all like terms to one side.

[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]

Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.

[tex]-\frac{1}{4} x=1[/tex]

x=-4

Answer:

[tex]x = - 4[/tex]

Second answer is correct

Step-by-step explanation:

[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]

hope this helps you

Answer:

  the sum is 01011000₂ = 88

Step-by-step explanation:

For numbers of magnitude less than 128, it is convenient to use an 8-bit representation. I find it works will to convert back and forth through the octal (base-8) representation, as each base-8 digit converts nicely to three (3) base-2 bits.

  61 = 8·7 +5 = 075₈ = 00 111 101₂

  27 = 8·3 +3 = 033₈ = 00 011 011₂

Then ...

  [tex]\begin{array}{cc|ccc}&61&&00111101\\+&27&+&00011011\\ &\overline{88}&&\overline{01011000}\end{array}[/tex]

__

Starting from the right, we can convert the binary back to octal, then to decimal by considering 3 bits at a time:

  01 011 000₂ = 130₈ = 1·8² +3·8 +0 = 64 +24 = 88

The binary sum is the same as the decimal sum.

Answer:

E(X ¯)=210,000.

Step-by-step explanation:

A sampling distribution for samples of size n=49 from a population with means μ=210,000 and standard deviation σ=35,000, has the following means anda standard deviation:

[tex]\mu_s=\mu=210,000\\\\\sigma_s=\sigma/\sqrt{n}=35,000/\sqrt{49}=35,000/7=5,000[/tex]

If X ¯ is the mean sales price of the sample, it will have a mean value of E(X ¯)=210,000.

Answer:

Since the blue graph is the red graph translated 3 units to the left the answer is D.

Answer:

[tex]=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]

Step-by-step explanation:

[tex]x^{\frac{1}{3}}\left(x^{\frac{1}{2}}+2x^2\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=x^{\frac{1}{3}},\:b=x^{\frac{1}{2}},\:c=2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+x^{\frac{1}{3}}\cdot \:2x^2\\=x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\\mathrm{Simplify}\:x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}:\quad x^{\frac{5}{6}}+2x^{\frac{7}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}+2x^2x^{\frac{1}{3}}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=x^{\frac{5}{6}}[/tex]

[tex]x^{\frac{1}{3}}x^{\frac{1}{2}}\\\mathrm{Apply\:exponent\:rule}:\quad \:a^b\cdot \:a^c=a^{b+c}\\x^{\frac{1}{3}}x^{\frac{1}{2}}=\:x^{\frac{1}{3}+\frac{1}{2}}\\=x^{\frac{1}{3}+\frac{1}{2}}\\\mathrm{Join}\:\frac{1}{3}+\frac{1}{2}:\quad \frac{5}{6}\\\frac{1}{3}+\frac{1}{2}\\\mathrm{Least\:Common\:Multiplier\:of\:}3,\:2:\quad 6\\Adjust\:Fractions\:based\:on\:the\:LCM\\=\frac{2}{6}+\frac{3}{6}[/tex]

[tex]\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\=\frac{2+3}{6}\\\mathrm{Add\:the\:numbers:}\:2+3=5\\=\frac{5}{6}\\=x^{\frac{5}{6}}\\2x^2x^{\frac{1}{3}}=2x^{\frac{7}{3}}\\=x^{\frac{5}{6}}+2x^{\frac{7}{3}}[/tex]

Answer:

B

Step-by-step explanation:

3/5 is a fraction, meaning it isn't irrational, natural, whole or an integer, therefore the answer is rational (B).

Answer:

B.rational

Step-by-step explanation:

3/5 is written as a fraction so it is a rational number

It is not a whole number since it is a reduced fraction that is less than 1

Answer:

x ≤ -4

Step-by-step explanation:

2(3 - x) ≥ 14

Divide by 2

2/2(3 - x) ≥ 14/2

(3 - x) ≥ 7

Subtract 3 from each side

3-x-3  ≥ 7-3

- x ≥ 4

Divide each side by -1, remembering to flip the inequality

x ≤ -4

Answer:

-4

Step-by-step explanation:

6-2x≥14 (/expand )

-2x≥14-6=-2x≥8

x≤8/-2=-4

Answer:

  1) h = -1/2t^2 +10t

  2) h = -1/2(t -10)^2 +72

  3) domain: [0, 20]; range: [0, 50]

Step-by-step explanation:

1.) I find it easiest to start with the vertex form when the vertex is given. The equation of the presumed parabolic path for Firework 1 is ...

  h = a(t -10)^2 +50

To find the value of "a", we must use another point on the graph. (0, 0) works nicely:

  0 = a(0 -10)^2 +50

  -100a = 50 . . . . . . subtract 100a

  a = -1/2 . . . . . . . . . divide by -100

Then the standard-form equation is ...

  h = (-1/2)(t^2 -20t +100) +50

  h = -1/2t^2 +10t

__

2.) The path of Firework 2 is translated upward by 22 units from that of Firework 1.

  h = -1/2(t -10)^2 +72

__

3.) The horizontal extent of the graph for Firework 1 is ...

  domain: 0 ≤ t ≤ 20

The vertical extent of the graph for Firework 1 is ...

  range: 0 ≤ h ≤ 50

Answer:

A.

Step-by-step explanation:

Add 4:

-5x ≤ 10

Divide by -5:

x ≥ -2