1) Find the linearization L(x) of the function at a. f(x)= x^4 + 3x^2, a= -1

The statement is true that statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Statistics is a branch of mathematics used to analyze, interpret, and present data. It is used to generalize results and measure the reliability of results obtained from a sample to the population. This is done through the use of probability theory, which helps to develop models for predicting the likelihood of certain outcomes. Statistics also help to identify patterns in data and draw conclusions from them. It also provides information about the relationships between different variables, which can be used to draw conclusions and make decisions. Finally, it helps to test hypotheses and assess the reliability of results.

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The number of different random samples (without replacement) of size 8 that can be selected from the population of 18 items is 20,560.

The number of different random samples (without replacement) of size 8 that can be selected from a population of 18 items can be calculated using the combination formula.

The combination formula is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n is the total number of items in the population and r is the size of the random sample.

In this case, we have a population of 18 items and we want to select a random sample of size 8.

Using the combination formula:

C(18, 8) = 18! / (8! * (18-8)!)

Simplifying the equation:

C(18, 8) = 18! / (8! * 10!)

Now, let's calculate the factorial values:

18! = 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10!

8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

Plugging in the factorial values:

C(18, 8) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10!) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 10!)

Simplifying further:

C(18, 8) = (18 * 17 * 16 * 15 * 14 * 13 * 12 * 11) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)

Calculating the values:

C(18, 8) = 20,560

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The angle is in 4th quadrant and the value of \(sin\theta\) is -(4/5).

One of the most significant areas of mathematics, trigonometry has a wide range of applications. The study of the connection between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry." Therefore, employing trigonometric formulae, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.

There are two other sub-branch classifications for trigonometry. The two varieties of trigonometry are as follows:

Everything is normal in Quadrant I, and Sine, Cosine, and Tangent are all positive.

However, the x direction is negative and the cosine and tangent become negative in Quadrant II.

Sine and cosine have negative values in Quadrant III.

Sine and tangent are negative in Quadrant IV.

since,

\(cos\theta = 3/5 (+ve)\\\ sin\theta\ is\ ( -ve)\).

So the angle is in 4th Quadrant.

we know,

\(sin^{2}\theta + cos^{2}\theta = 1\)

⇒ \(sin^{2}\theta = 1 - (\frac{3}{5}) ^{2}\)

⇒\(sin^{2}\theta = 1 - \frac{9}{25} = \frac{16}{25}\)

⇒ \(sin\theta = -\frac{4}{5}\)     (since The angle is in 4th Quadrant)

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The probability that at least half of the voters contacted supported the current governor is approximately 0.3322 or 33.22%.

The proportion of voters who voted for the current governor in the election can be determined using the formula

\(P=\frac{x}{n}\)

p is the proportion,

x is the number of voters who supported the current governor

n is the number of voters in the sample.

In this case, the sample size is 342, and we don't know the number of voters who supported the current governor.

Therefore, we can estimate the proportion using the sample proportion.

The sample proportion is obtained by dividing the number of voters who supported the current governor by the sample size.

Let us assume that half of the voters contacted supported the current governor.

Since we know that the sample size is 342, the number of voters who supported the current governor is 171, which is half of 342.

Therefore, the sample proportion is  \(p=\frac{171}{342}=0.5\)

In order to calculate the probability that at least half of the voters contacted supported the current governor, we need to use the normal distribution.

The normal distribution is a continuous probability distribution that is widely used to model real-world phenomena.

The normal distribution is characterized by two parameters: the mean and the standard deviation.

In this case, the mean of the normal distribution is given by the sample proportion, which is p = 0.5.

The standard deviation of the normal distribution can be calculated using the formula:

\(σ=sqrt\frac{p(1-p)}{n}\)

σ is the standard deviation,

p is the proportion, and

n is the sample size.

Using the values we have, we can calculate the standard deviation:

\(σ=sqrt\frac{0.5(1-0.5)}{342} =0.0253\)

We want to find the probability that at least half of the voters contacted supported the current governor, which means we want to find the probability that the sample proportion is greater than or equal to 0.5.

Using the normal distribution, we can standardize the sample proportion and find the probability that it is greater than or equal to 0.5.

The standardized score is given by the formula

\(z= \frac{(p-μ)}{σ}\)

z is the standardized score,

p is the proportion,

μ is the mean,

σ is the standard deviation.

Using the values we have, we can standardize the sample proportion:

\(z=\frac{0.5 - 0.5}{0.0253} =0\)

The probability of a standardized score being 0 is 0.5.

Therefore, the probability that the sample proportion is greater than or equal to 0.5 is 0.5 + (1 - 0.5) x 0.5 = 0.75.

However, this probability is for a normal distribution with a mean of 0.5 and a standard deviation of 0.0253.

We want the probability for a sample of 342 voters, so we need to adjust our answer using the continuity correction factor.

The continuity correction factor is used when we are approximating a discrete distribution with a continuous distribution.

In this case, the sample proportion is a discrete distribution because it can only take on certain values (such as 0.5, 0.51, 0.52, etc.).

However, we are using a continuous distribution (the normal distribution) to approximate the sample proportion.

Therefore, we need to adjust our answer using the continuity correction factor.

The continuity correction factor is given by the formula 0.5 - 0.5/n, where n is the sample size.

Using the continuity correction factor, we can adjust our answer:

\(0.75-\frac{0.5-0.5}{342} =0.3322\)

Therefore, the probability that at least half of the voters contacted supported the current governor in the last election when a telephone survey contacts 342 voters from the last election and asks if they voted for the current governor is approximately 0.3322 or 33.22%.

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Answer: x = 2

Step-by-step explanation:

\(10x - 15x + 5= -45 + 40\)

subtract 5

\(10x - 15x= -45 + 40-5\)

Combine like terms;

\(-5x=-10\)

Divide by -5

\(x=\frac{-10}{-5}\\ x=2\)

Answer:

\(x = 2\)

Step-by-step explanation:

\(10x - 15x + 5 = - 45 + 40 \\ 10x - 15x = - 5 - 45 + 40 \\ - 5x = - 10 \\ \frac{ - 5x}{ - 5} = \frac{ - 10}{ - 5} \\ x = 2\)

The intercept term in a simple linear regression model represents the mean value of y when x equals zero.

In a simple linear regression model, the intercept term represents the value of the dependent variable (y) when the independent variable (x) is equal to zero. It is the point at which the regression line intersects the y-axis.

Mathematically, the simple linear regression model can be expressed as:

y = β₀ + β₁x + ε

where y is the dependent variable, x is the independent variable, β₀ is the intercept term, β₁ is the slope coefficient, and ε is the error term.

The intercept term, β₀, captures the average value of y when x equals zero. It represents the y-intercept of the regression line and determines the starting point of the line on the y-axis.

It is important to note that the interpretation of the intercept term depends on the context and the variables being studied. In some cases, having x equal to zero may not have a meaningful interpretation or may not fall within the observed range of the data. In such situations, caution should be exercised when interpreting the intercept term.

In summary, the intercept term in a simple linear regression model provides the mean value of the dependent variable when the independent variable is zero, indicating the starting point of the regression line on the y-axis.

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Answer:

A quadratic equation is some thing like

(x+2)^2

or

(x+2)(x+5)

In order to solve them, the most basic method is the FOIL method

F-First

O-Outside

I-Inner

L-Last

So for example

(x+2)^2

Which is basically

(x+2)(x+2)

So the first is the 2 Xs

(x+2)(x+2)

x*x=x^2

The outer is the x and the 2,

(x+2)(x+2)

2*x=2x

Now the Inner which is the 2 and the x

(x+2)(x+2)

2*x=2x

And finally the last  which is the 2 and the second 2

(x+2)(x+2)

2*2=4

Now add them all up

X^2+2x+2x+4

Combine like terms

x^2+4x+4

There you have it

Do the same with every other quadratic equation

\( \bf \implies{\angle{JND} = 57 \degree}\)

\( \bf \longrightarrow{\angle{BNL} = 33 \degree}\)

\( \bf \longrightarrow{\angle{JND} = \: ?}\)

\( \bf \longrightarrow \: \: \: \angle{BNL} = \angle{DNS} \: \\ \: \: \: \bf [Verically \: Opposite \: Angle]\)

\( \bf \therefore\angle{DNS } = 33 \degree\)

\( \bf \longrightarrow \angle{JND} + \angle{ DNS} = 90 \degree \\ \bf \: \: \: \: \: \: \: \: \: [form \: a \: right \: angle]\)

\( \bf \longrightarrow \angle{JND} +33 \degree= 90 \degree\)

\( \bf \longrightarrow \angle{JND}= 90 \degree - 33 \degree\)

\( \bf \longrightarrow \angle{JND}= 57 \degree \)

The interest rate will be 7%

A quick and simple way to figure out interest on money is to use the simple interest technique, which adds interest at the same rate for each time cycle and always to the initial principal amount.

Any bank where we deposit our funds will pay us interest on our investment. One of the different types of interest charged by banks is simple interest. Now, before exploring the idea of basic curiosity in further detail,

The formula for simple interest is:

S = p*t*r/100

the simple interest on ​$7000 for 7 years is ​$3430

r = S*100/(p*t)

r = (3430*100)/(7000*7)

r = 7%

Hence the interest rate will be 7%

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Answer:

let cp of 17 water bottle is x

cp of 1 water bottle = x/17

from the question

sp of 16 water bottles = x

sp of 1 water bottle = x/16

profit = sp -cp

        = x/16 - x/17

      =  x/272

profit % = profit /cp * 100%

            = (x/272)/ (x/17) * 100%

= 6.25%

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number can only be divided evenly by 1 and itself.

To find the multiples of a prime number, you can use the following steps:

For example, if the prime number is 5, the multiples of 5 are 5, 10, 15, 20, 25, and so on.

It's important to note that a prime number only has two divisors: 1 and itself. This means that a multiple of a prime number will never be a prime number.

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Answer:

66 percent

Step-by-step explanation:

⅔ are shaded which is 0.6 recurring which as a percentage is 66 percent. may have to say 66.6

The missing coordinate of point P on the unit circle in the given quadrant is (5, -12). Point P has a positive x-coordinate and lies below the x-axis.

To find the missing coordinate of point P on the unit circle, we need to consider the given information. In the first case, the x-coordinate of P is positive, and the y-coordinate of P is -5. Since the point lies on the unit circle, we can use the Pythagorean theorem to find the missing coordinate. The Pythagorean theorem states that for any point (x, y) on the unit circle, x^2 + y^2 = 1. Plugging in the given values, we have x^2 + (-5)^2 = 1. Solving this equation, we get x^2 + 25 = 1, which leads to x^2 = -24. Since the x-coordinate must be positive, we discard the negative solution, giving us x = sqrt(24) = 2√6. Therefore, the missing coordinate of P is (2√6, -5).

In the second case, the x-coordinate of P is missing, but we know that P lies above the x-axis. Since the point lies on the unit circle, the y-coordinate can be found using the Pythagorean theorem. Since the x-coordinate is missing, we can represent it as x = sqrt(1 - y^2). Plugging in the given y-coordinate of -12, we have x = sqrt(1 - (-12)^2) = sqrt(1 - 144) = sqrt(-143). However, since the x-coordinate cannot be imaginary, we conclude that there is no point P with a positive x-coordinate lying above the x-axis for this case.

Therefore, based on the given information, the missing coordinate of point P on the unit circle is (5, -12), satisfying the conditions of a positive x-coordinate and lying below the x-axis.

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Answer:

Decimal

Step-by-step explanation:

Im going to assume you double pasted, happens sometimes. so the answer would be decimal.

Answer:

\( \frac{ {y}^{2} }{4 {x}^{5} } \)

The length of each side of Georgia's garden is about 8.37 feet

From the question, we have the following parameters that can be used in our computation:

Area = 70 square feet

The length of each side is calculated as

Length = √Area

So, we have

Length = √70

Evaluate

Length = 8.37

Hence, the length is 8.37 feet

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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Answer:

∅=30°

Step-by-step explanation:

\(sin\)∅\(=\frac{1}{\sqrt{3} }sin60^{0}\)

sin∅=\(\frac{\frac{\sqrt{3} }{2} }{\sqrt{3} } =\frac{\sqrt{3} }{2\sqrt{3} }=\frac{1}{2}\)

∅=\(sin^{-1}(\frac{1}{2})= 30^{0}\)

I hope this help you

Answer:

AB and A'B' are both parallel to the y-axis ( A ).

AB and A'B' have the same lengths ( B ).

Step-by-step explanation:

Answer:

D) 2•10^9

Hopes this helps wish you well

Answer:

d.) 150 billion dollars

Step-by-step explanation:

As per the given bar graph, we can draw the following conclusions:

Net exports for United States = ~ -110 Billion Dollars (It means import of 110 Billion Dollars)

Net exports for Denmark = ~ -30 Billion Dollars (It means import of 30 Billion Dollars)

Net exports for China = ~ 115 Billion Dollars

Net exports for Germany = ~ 35 Billion Dollars

We have to find the sum of net exports of Germany and China:

\(\Rightarrow\) 35 + 115 = 150 Billion Dollars.

Hence, correct answer is d. 150 Billion Dollars.

Answer: d

Step-by-step explanation:

150 billion dollars

Answer:

I think it's 6 or 0.6

The correct answer is d) To avoid a large number of classes with very small frequencies.

Unequal class intervals are sometimes used in a frequency distribution to avoid a large number of classes with very small frequencies. This can occur when the data range is very large or when there is a lot of variability in the data.

For example, if we have a dataset with values ranging from 0 to 1000, using equal class intervals of size 100 would result in 10 classes. However, if the data is skewed and most of the values fall in the lower range, many of the classes may have very small frequencies. Using unequal class intervals can help group the data in a way that results in more meaningful class frequencies.

Additionally, unequal class intervals can be used to better represent the distribution of the data. For example, if there is a cluster of values around a certain range, using a smaller class interval around that range can provide more detail and information about the data distribution.

Therefore, the correct answer is d) To avoid a large number of classes with very small frequencies.

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The surface area of the two solids are listed below:

Case 1 - 232 square centimeters

Case 2 - 240 square centimeters

The surface area of a solid is the sum of the areas of all its faces. There are two cases of solids whose surface areas must be determined. The area formulas for triangle and rectangle are, respectively:

Triangle

A = 0.5 · b · h

Rectangle

A = b · h

Case 1

A = (6 cm) · (8 cm) + 2 · 0.5 · (6 cm) · (12 cm) + 2 · 0.5 · (8 cm) · (14 cm)

A = 232 cm²

Case 2

A = 2 · 0.5 · (8 cm) · (3 cm) + (8 cm) · (12 cm) + 2 · (5 cm) · (12 cm)

A = 24 cm² + 96 cm² + 120 cm²

A = 240 cm²

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Answer:

420 + 15 = 435

360 + 45 = 405

435 - 405 = 30.

30 minutes less sunlight

Step-by-step explanation:

Answer:

The east side gets 30 minutes less sunlight.

Step-by-step explanation:

To find the answer we have to subtract 6 hours 45 minutes from 7 hours 15 minutes. As we see that 15 is less than 45, we turn 7 hours 15 minutes to 6 hours 75 minutes, and now we can subtract. 6 hours 75 minutes - 6 hours 45 minutes = 30 minutes. Now, we see that the answer is 30 minutes less sunlight.

The expression  \(a_n = a_1 + (n-1)d\)  can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.

The given sequence is 0, 1, 2, 3, .......

We will use n to represent the position of a term such that n = 1 for the first term, n = 2 for the second term, n= 3 for the third term, and n = 3 for the third term in the given sequence.

What is an arithmetic sequence?

It is a sequence of numbers where the difference between the consecutive terms is same.

The nth term in an arithmetic sequence is given by:

\(a_n = a_1 + (n-1)d\\where~a_1=first~term~and ~d=common~difference\).

The given sequence 0, 1, 2, 3, ...... is an arithmetic sequence.

d = 1 - 0 = 1

d = 2 - 1 = 1

d = 3 - 2 = 1

The difference between the consecutive terms is the same.

In the sequence 0, 1, 2, 3, ......

\(a_1 = 0, a_2=1, a_2=2, a_3=3, and~so~on.\)

If we use the arithmetic sequence nth term formula

we get,

\(a_1=0+(1-1)1=0\\a_2=0+(2-1)1=1\\a_3=0+(3-1)1=2\\a_4=0+(4-1)1=3\\...\\...\\...\)

Thus the expression  \(a_n = a_1 + (n-1)d\) can be used to describe the sequence 0,1,2,3,... where n will represent the position of a term in the sequence where n = 1 is for the first term.

Or we can simply say  \(a_n=n-1\)  since  \(a_1=0 ~and~ d=1\).

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Answer: 81

Step-by-step explanation:

Answer:

3^4

Step-by-step explanation:

You can use the rule:

\( {n}^{a} \times {n}^{b} = {n}^{a + b} \)

2+2 = 4 so that's your answer

and 3^ 4 is 81 when you put it in a calculator

Answer:

B

Step-by-step explanation:

The Kruskal-Wallis test is a non-parametric test used to compare three or more independent groups to determine if there is a significant difference between the medians of the groups. The test statistic used in this test is denoted by the letter "H," which is calculated based on the ranks of the data.

True. The test statistic calculated in the Kruskal-Wallis test is denoted by the symbol H, not to be confused with the Shapiro-Wilk test statistic denoted by W. The Kruskal-Wallis test is a non-parametric test used to compare the median ranks of three or more independent groups. The test statistic H is calculated by comparing the between-group sum of squares to the total sum of squares. H follows a chi-squared distribution with degrees of freedom equal to the number of groups minus one. The p-value obtained from the chi-squared distribution is used to determine whether to reject or fail to reject the null hypothesis that there is no significant difference between the groups.

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