how are linear inequalities different from linear equations?
a.) you have to say x
b.) they don’t have any differences
c.) always solid lines
d.) they have shading

"Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

Statistics is the art and science of learning from data. It involves collecting, organizing, analyzing, interpreting, and presenting data to gain insights and make informed decisions. In the 4th edition of the book "Statistics: The Art and Science of Learning from Data," you can expect to find a comprehensive exploration of these topics.

This edition may cover important concepts such as descriptive statistics, which involve summarizing and displaying data using measures like mean, median, and standard deviation. It may also delve into inferential statistics, which involve making inferences and drawing conclusions about a population based on a sample.

Additionally, the book may discuss various statistical techniques such as hypothesis testing, regression analysis, and analysis of variance (ANOVA). It may also provide real-world examples and case studies to illustrate the application of statistical methods.

When using information from the book, it is important to properly cite and reference it to avoid plagiarism. Be sure to consult the specific edition and follow the guidelines provided by your instructor or institution.

In summary, "Statistics: The Art and Science of Learning from Data" (4th edition) is a valuable resource for understanding and applying statistical principles, providing insights into data analysis and decision-making processes.

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The two percentages do not agree. Hence, option D is correct.

a) The mean time was 103.59 seconds, with a standard deviation of 5.16 seconds. If the Normal model is appropriate, the percentage of times that will be less than 98.43 seconds can be calculated as follows:

z = (x - μ) / σz = (98.43 - 103.59) / 5.16z = -1.00Using z-score table, we can determine that the percentage of times that will be less than 98.43 seconds is approximately 15%.

Therefore, the percentage of times that will be less than 98.43 seconds is 15%.

(Round to the nearest integer as needed)Hence, option A is correct.b) The actual percentage of times less than 98.43 seconds can be calculated by finding the number of competitors that finished with a time less than 98.43 seconds and dividing that number by the total number of competitors.

98.06, 98.09, 98.46, 98.47, 98.96, 98, 99, 99.12, 99.35, 99.57, 99.98, 100.08, 100.11, 100.28, 100.64, 101.32, 101.06, 101.25, 101.34, 101.39, 102.48,

101.99, 103.01, 103.87, 104.11, 103.64, 104.15, 104.27, 104.37, 104.33, 104.52, 105.47, 105.48, 105.69, 105.61, 113.02, 105.73, 109.65, 106.92, 116.11, 117.43, 117.59, 99.09, 100.67, 103.12, 105.02, 114.55, 99.11, 100.77, 103.18, 105.39, 115.97

There are no competitors who finished with a time less than 98.43 seconds. Therefore, the actual percentage of times less than 98.43 seconds is 0%. (Round to one decimal place as needed)Thus, option D is correct.c) The two percentages do agree.

This is because the Normal probability plot shows that the Normal model is not appropriate.

Therefore, the actual percentage of times less than 98.43 seconds is 0%, which is different from the percentage that was calculated using the Normal model. Since the Normal model is not appropriate, the actual percentage of times is more accurate.

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Answer:

Option 2  \(\frac{4\sqrt{6} }{3}\)

Step-by-step explanation:

\(\frac{4\sqrt{2} }{\sqrt{3} } = \frac{4\sqrt{2} \sqrt{3} }{\sqrt{3}\sqrt{3} } = \frac{4\sqrt{6} }{3}\)

Answer:

F. \( 4, 4\sqrt{3} \)

Step-by-step explanation:

✔️Finding length of side s using:

\( cos(\theta) = \frac{adjacent}{hypotenuse} \)

Where,

\( cos(\theta) = cos(60) = \frac{1}{2} \)

Adjacent = s

Hypotenuse = 8

Plug in the values

\( \frac{1}{2} = \frac{s}{8} \)

Multiply both sides by 8

\( \frac{1}{2} \times 8 = \frac{s}{8} \time 8 \)

\( \frac{8}{2} = s \)

\( 4 = s \)

s = 4

✔️Finding length of side q using:

\( sin(\theta) = \frac{opposite}{hypotenuse} \)

Where,

\( sin(\theta) = sin(60) = \frac{\sqrt{3}}{2} \)

Opposite = q

Hypotenuse = 8

Plug in the values

\( \frac{\sqrt{3}}{2} = \frac{q}{8} \)

Multiply both sides by 8

\( \frac{\sqrt{3}}{2} \times 8 = \frac{q}{8} \times 8 \)

\( \frac{\sqrt{3}}{1} \times 4 = q \)

\( 4\sqrt{3} = q \)

\( q = 4\sqrt{3} \)

Answer:

.36363636363

990

0.051

0.21

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x^5+6x^3

=3x^3(x^2+2)

Answer:

\(3x^{2} (x^{2} +2)\)

Step-by-step explanation:

Factor \(3x^{3}\) out of \(3x^{5}\) \(+\) \(6x^{3}\)

The domain restriction for the right side of the equation is

The domain restriction for the left side of the equation is

In mathematics, the domain refers to the set of all possible input values for a function. it is the collection of values for which the function is defined and can be evaluated.

The domain is typically represented by the variable x and determines the valid input values that can be plugged into the function to obtain meaningful outputs or results.

To get a possible value for 8/x, x should not be equal to 0, otherwise we get undefined

To get a possible value for 8/(12 - x), x should not be equal to 12, otherwise we get undefined

8/0 is undefined

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The series 2/5 + 4/25 + 8/125+ 16/625 + ... is convergent series.

And the sum of the series is 2/3.

In this question we have been given a series 2/5 + 4/25 + 8/125+ 16/625 + ...

We need to determine  whether the series is convergent or divergent.

The first term of the series is a1 = 2/5

We can observe that given series is a geometric series with the common ratio r = 2/5

Here, multiplying the previous term in the sequence by 25 gives the next term.

We know that the general form of a geometric sequence.

an = a1 r^(n−1)

So the n-th term of the series would be,

an = (2/5)(2/5)^(n - 1)

an = 2^n / 5^n

The sum Sn for given series would be,

Sn = a1(r^n −1) / r−1

Sn = [(2/5)((2/5)^n - 1)] / (2/5 - 1)

Consider lim n→∞ Sn

= lim n→∞ {[(2/5)((2/5)^n - 1)] / (2/5 - 1)}

= [(2/3)/(-3/5)]  lim n→∞ {(2/5)^n - 1}

= -2/3  lim n→∞ {(2/5)^n - 1}

= (-2/3) * (-1)

= 2/3

Since lim n→∞ Sn exists, this series converge

Therefore, the sum of given series is 2/3

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Using Simpson's rule with a step size of 0.5, the approximation of the integral ∫(1 to 2) e/x dx is 1.5291. The exact value is 1.5328, indicating a small difference of 0.0037 between the approximation and the exact value.

Simpson's rule is a numerical integration method that uses quadratic interpolation to approximate the integral of a function over a given interval. The formula for Simpson's rule is as follows:

\(\int f(x) dx \approx \frac{h}{3} [f(a) + 4f(a + \frac{h}{2}) + f(a + h)]\)

where h is the step size, a is the lower limit of integration, and f(x) is the function to be integrated.

In this case, we have the following:

h = (2 - 1)/4 = 0.5

a = 1

f(x) = e/x

Therefore, the Simpson's rule approximation for the integral is as follows:

\(\int_1^2 \frac{e}{x} \, dx \approx 2.718 \cdot 0.693 + C \approx 1.5291\)

The exact value of the integral is 1.5328, so the Simpson's rule approximation is within 0.0037 of the exact value. This is a relatively good approximation, considering that we only used 4 subintervals.

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In point estimation, data from the sample is used to estimate the population parameter. This is done by taking a sample from the population and then using the data from the sample to estimate the population parameter. The sample statistic is used as an estimate of the population parameter.

The mean of the sample is also used as an estimate of the population mean. Point estimation is a statistical technique for estimating population parameters from a sample of data. It is based on the idea that the sample statistics such as the mean or proportion can be used to estimate the population parameters such as the population mean or proportion. The accuracy of the estimate depends on the size of the sample and the variability of the data.

In summary, in point estimation, the data from the sample is used to estimate the population parameter. The sample statistic, such as the mean of the sample, is used as an estimate of the population parameter.

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Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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Answer:

94666.093488

Step-by-step explanation:

you could have used a calculator for a faster answer but I guess this is fine too

Answer:

$792 in interest

Step-by-step explanation:

16500(0.048) = 792

Answer:

792 is the answer

Step-by-step explanation:

Well, what I did was I figured out 4.8% as a decimal =  (0.048) and then I timed that with $16,500. Like this --> (0.048×16,500). Which gave me the total of (792)!

How do you solve this equation:2n=4x+2y;y? Add answer+5 pts

Suppose u(x,0) = sin(πx) + ∑ \(5/n^{10}\) sin(2nπx). n=1 If u(x, t) represents the temperature of a rod at a position x and time t, then at time t the midpoint has the temperature U(1/2, t) = 2.718.

The solution to the given heat equation with the given initial and boundary conditions is:

u(x,t) = ∑ (2/nπ) sin(nπx) e^(-n^2π^2t/16), n=1 [infinity]

Using this solution, we can find the temperature at the midpoint x=1/2:

U(1/2, t) = ∑ (2/nπ) sin(nπ/2) e^(-n^2π^2t/16), n=1 [infinity]

Plugging in t=0, we get:

U(1/2, 0) = ∑ (2/nπ) sin(nπ/2), n=1 [infinity]

Using the identity sin(nπ/2) = 1 if n is odd, and 0 if n is even, we can simplify this expression:

U(1/2, 0) = ∑ (2/(2n-1)π), n=1 [infinity]

This is a divergent series, so we cannot find its exact value. However, we can approximate it by truncating the series at a large enough value of N:

U(1/2, 0) ≈ ∑ (2/(2n-1)π), n=1 to N

For example, if we take N=10, we get:

U(1/2, 0) ≈ 3.8197

Therefore, at time t, the midpoint of the rod has the temperature U(1/2, t) ≈ ∑ (2/nπ) sin(nπ/2) e^(-n^2π^2t/16), n=1 to N, which depends on the value of t and the number of terms included in the series approximation.
At time t, the midpoint of the rod has the temperature:

U(1/2, t) = sin(π(1/2)) * e^(-16(π^2)t) + ∑ [5/n^10 * sin(2nπ(1/2)) * e^(-16(2nπ)^2t)]. n=1 to ∞

Here, e represents the base of the natural logarithm (approximately 2.718).

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Therefore, the linearization of f(x) = cos(x) at a = π/2 is L(x) = π/2 - x.

The linearization of a function f(x) at a point a is given by:

L(x) = f(a) + f'(a)(x - a)

where f'(a) denotes the derivative of f(x) evaluated at x = a.

In this case, we have:

f(x) = cos(x)

a = π/2

First, let's find f'(x):

f'(x) = -sin(x)

Then, we can evaluate f'(a):

f'(π/2) = -sin(π/2) = -1

Next, we can plug in the given values into the formula for linearization:

L(x) = f(a) + f'(a)(x - a)

L(x) = cos(π/2) + (-1)(x - π/2)

L(x) = 0 - x + π/2

L(x) = π/2 - x

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Answer:

 S.A. = 704 in²

Step-by-step explanation:

Surface area (S.A. ) = 1/2 lp + B where l is the slant height , p is the  perimeter of the base, and B is the area of the base .

Given l = 14; The Base figure is a square so the p = 4· side = 4 · 16 = 64 and the area of the Base = s² = 256

S.A = 1/2 · 14 · 64 + 256

 S.A. = 448 + 256

  S.A. = 704 in²

Answer:

When we say that an allele is "fixed," it means that a particular allele has reached a frequency of 100% in a population.

Step-by-step explanation:

Alleles are different forms of a gene that occupy the same position on homologous chromosomes. In a population, different alleles can exist for a specific gene. However, through various evolutionary processes such as natural selection, genetic drift, or gene flow, one allele may become predominant and eventually fixate within the population.

The fixation of an allele can occur through different mechanisms. For example, if a beneficial allele provides a selective advantage to individuals carrying it, it is more likely to increase in frequency and eventually become fixed in the population. On the other hand, genetic drift, which is the random change in allele frequencies due to chance events, can also lead to the fixation of an allele, especially in small populations.

Once an allele is fixed in a population, it means that all future generations will inherit that allele, and no alternative alleles will be present at that particular gene locus.

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Finally, using the initial conditions y(0) = 8 and y'(0) = 6, we can solve for the constants A and B to get

y(t) = (8/3)*cos((3/2)*sqrt(2)*t) + (16/3)*sin((3/2)*sqrt(2)*t).

To find y as a function of t, we first need to solve the differential equation 8y" + 27y = 0. We can do this by assuming a solution of the form y(t) = A*cos(wt) + B*sin(wt),

where A and B are constants and w is the angular frequency. We can then differentiate y(t) twice to find y'(t) and y''(t), and substitute these into the differential equation to get the equation 8(-w^2*A*cos(wt) - w^2*B*sin(wt)) + 27(A*cos(wt) + B*sin(wt)) = 0.

Simplifying this equation gives us the equation

(-8w^2 + 27)*A*cos(wt) + (-8w^2 + 27)*B*sin(wt) = 0.

Since this equation must hold for all t, we must have (-8w^2 + 27)*A = 0 and (-8w^2 + 27)*B = 0.

Solving for w gives us w = (3/2)*sqrt(2) and

w = -(3/2)*sqrt(2).

Plugging these values into our solution for y(t) gives us

y(t) = (8/3)*cos((3/2)*sqrt(2)*t) + (16/3)*sin((3/2)*sqrt(2)*t).

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Answer:

4 1/2

Step-by-step explanation:

7 5/6 - 3 1/3

changing to improper fractions;

47/6 - 10/3 LCM = 6

(47 - 20)/6

27/6 = 9/2 = 4 1/2.

Answer:

-26!!!!

Step-by-step explanation:

plz give me brainliest!!!

Answer:

7 .............................

x²=6²+8²=36+64=100 <=> x=√100=10

Firstly, let’s assume the the whole capacity the work requires is 1.

Then, let’s see how 1 man can do in 50 days: 1/5.

Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.

Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.

Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.

Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.

Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.

As a result, the work takes 1/(1/25)= 25 days.

a) Where the information about triangle ABC is given above, the measure of angle B is 60°

Using the Cos Rules,

(15√3)² = 30² + 15² - 2(15 x 30) cos B

⇒ 657 = 1125 - 900 cosB

⇒ 2 Cos B = 1 Cos B = 1/2

So

B = Cos ⁻¹(1/2)

Hence,

B = 60°

B) Given the above,

Now, we can use the tangent function to find tan B:

tan B = sin B / cos B

  = sin (π/3) / cos (π /3)

  = (√3 / 2) / 0.5

tan B = √3

C ) the area of the rriangle is given as

s = (a + b + c) /2

Substituting

s = (15 + 15√ 3 + 30)/2

s = 30 + 15√3

Area = √ [ (30 + 15√3)(15√3) (15)(30  - 15 - 15√3))

Simplifying  we can say

Area = √(30 + 15√3  )( 15√3)(15)(15 - 5√3 )]

= √[3(10 + 5√3)(15)(3√3 - 1)]

  = √[2250 - 1125√3]

Hence,

Area ≈ 17.36in

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Answer:

244

Step-by-step explanation:

\(544 - 300 = \\ 244\)

Answer:

either y= 5x-3 or y= 3x-3

Step-by-step explanation:

Answer:

10x+3y+2

Step-by-step explanation:

The height of the cup that can be made from the least amount of paper is 17 cm.

A cone-shaped paper cup is to hold 100 cubic cm of water. Find the height and the radius of the cup that can be made from the least amount of paper.

Use the volume of a cone formula: (1/3)*pi*r^2*h = V; to find h in terms of r.

(1/3)*pi*r^2*h = 100

multiply equation 3 to get rid of the denominator

pi*r^2*h = 300

h = 300/(pi * r^2)

:

Using the surface area equation: SA = pi*r^2 + (pi*r*L), find L using r and h

L = \(\sqrt{h^{2} +r^{2} }\)

Substitute above for L in the SA equation

:

\(SA = \pi r^{2} + \pi r\sqrt{\frac{300}{\pi r^{2} } + r^{2} }\)

:

Using this equation in my TI83, the graph showed the minimum radius to occur at appox 2.37 cm

:

Find the height using this value:

h = 17 cm

Check solution by finding the volume

V = (1/3) * pi * 2.37^2 * 17

V = 99.994 ~ 100 cm

Hence , the height of the cup that can be made from the least amount of paper is 17 cm.

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Answer:

y > -1

Step-by-step explanation:

The range is about the y, not the x, so we can eliminate options B & D.

We see the y touch -1 and then go up to ∞, so the answer is y > -1