Given that 2 cos x = √3, where 0° < x < 90°,
find the value of x.

The confidence interval will be narrower and would involve a larger risk of being incorrect.

A 95% confidence interval and a 99% confidence interval must be compared.

The confidence level is lower for a 95% confidence interval compared to a 99% confidence interval.

The margin of error would be smaller if the confidence level were lower.

As a result, the 95% confidence interval is smaller than the 99% confidence interval.

Because a 95% interval is narrower, fewer values that could provide the parameter with the correct estimate are included in the interval.

Therefore, we can say,

A 99% confidence interval will be shorter than a 95% confidence interval and carry a higher risk of being inaccurate.

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Natural Numbers: 13, 17

Whole Numbers: 13, 17

Integers: -15, 13, 17

Rational Numbers: -17/13, 3.63

Irrational Numbers: √7, π/4

First, let us understand what each type of numbers are.

Natural Numbers: All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Whole Numbers: The term "whole numbers" refers to numbers devoid of fractions, which are made up of positive integers and zero. Its symbol is "W," and its range of numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...}. The entire number zero denotes nothing or a null value.

Integers: Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

Rational and Irrational Numbers: An irrational number cannot be stated using fractions, but a rational number may be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating decimals.

Now, in the set provided, we can classify them as follows.

Natural Numbers: 13, 17

Whole Numbers: 13, 17

Integers: -15, 13, 17

Rational Numbers: -17/13, 3.63

Irrational Numbers: √7, π/4

Thus, this is the final classification.

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The congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm.  the length of the base is 7 cm.To calculate the length of the base of an isosceles triangle, we can use the formula of the perimeter.

The perimeter is the sum of all sides of a triangle, so the formula is Perimeter = Side1 + Side2 + Base. In this case, the two congruent sides are each 5 cm long, and the perimeter is 17 cm. So, if we set up an equation, we have 17 = 5 + 5 + Base. We can then solve the equation for Base by subtracting 10 from both sides.

This gives us 17 - 10 = 5 + Base, and then subtracting 5 from both sides gives us 12 = Base. Then, we can divide both sides by 12 to get 1 = Base / 12. Lastly, we can multiply both sides by 12 to get 12 = Base. Therefore, the length of the base is 7 cm.

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The required time taken by the ant to complete whole length of the brick is 5 seconds.

Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar quantity.

Length of brick = 1(1/2) = 3/2

Speed of ant = 0.3 ft/sec

Then,

Speed = distance/time

Time = distance/speed

Time = 1.5/0.3 = 5 seconds

Thus, time taken by ant to cover whole length is 5 seconds

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Standing on the moon, you would be in sunlight for approximately 27.3 days.

Length is a physical measurement of distance, or the dimensions of an object. It can be measured in metres, kilometres, feet, yards, or other units of measurement. Length can also be used to describe the amount of time something takes, or the size of something, such as a book or a piece of clothing. Length is an important concept in mathematics and science, and is used to measure, compare, and quantify objects and events.

This is because the moon has no atmosphere, so it has no day and night cycles. Instead, the sun shines on the moon for an entire month, and then the moon moves into the shadow of the Earth and remains dark for the next month. The length of this daylight cycle is 27.3 days, and this is the amount of time that you would be in sunlight if standing on the moon.

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The expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.

Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.

Then, suppose we want to find the probability of an event E.

Then, its probability is given as:

[tex]P(E) = \frac{Number of Favourable Cases}{Number of Total Cases} = \frac{n(E)}{n(S)}[/tex]

where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as:

[tex]P(X = x) = ^nC_{x} p^{x} (1-p)^{n-x}[/tex]

The expected value and variance of X are:

[tex]E(X) = np\\Var(X) = np(1-p)[/tex]

Each of the 800 spins are independent in terms of their result from each other.

Each spin ends up either in shaded region (call it success), or non-shaded region(failure).

P(success) = P(A spin landing in shaded region) = 4/5 (as there are total 5 partition of spinner possible (assuming no other outcome possible), and that there are 4 shaded regions (favorable elementary events).

If we take X = number of successes in those 800 spins, then:

[tex]X[/tex] ~ [tex]B (n=800, p = 4/5=0.8)[/tex]

The expected value of X is:

[tex]E(X) = np = 800 * 0.8 = 640[/tex]

Thus, the expected number of times out of 800 spins that the spinner will land in the shaded region for this case is 640.

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The correct answer is 5/8. Option b)

In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases.

from given statements that, the product of n x 4/5 is greater than 4/5 because multiplication always increases a number.

n × 4/5 > 4/5  ⇒?

so, what are the "n" values will prove that above statement is incorrect.

so, if we put the all given options values of "n" in n × 4/5, then

⇒ n=2

8/5 > 4/5

⇒ n=5/8

20/40 < 4/5

⇒ n=6/6

1 > 4/5

⇒ n=7/6

28/30 > 4/5

⇒ n=5/4

20/4 > 4/5

Therefore, The correct answer is 5/8. Option b)

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The way to use the Distributive Property to check your work when factoring is;

Once an expression has been factored, use the Distributive Property to expand the expression. The expanded expression should be the original expression.

The Distributive Property is defined as an algebra property that is used to multiply a single term and two or more terms inside a set of parentheses.

For example: 3(2 + 4)

According to the distributive property, the first step is to add these two numbers (2 + 4 = 6) and thereafter, we  multiply the result 6 by 3 to get 18.

Thus, we conclude that the procedure above is basically how we use distributive property of algebra.

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Answer:

x = 90°

y = 43°

Step-by-step explanation:

<B is equal to 47 because their opposite sides are equal.  We are shown the <BAD = <CAD, which means that line segment AD is a bisector of BC.  This makes x = 90

The sum of the interior angles of a triangle add to 180

180 - 47 -47 = 86

The measure of  < BAC is 86  we need to divide this by 2 to find y

86/2 = 43

Answer:

4.6

Step-by-step explanation:

In a 30-60-90 triangle, the length of the side opposite the [tex]30^{\circ}[/tex] angle is [tex]\frac{1}{\sqrt{3}}[/tex] the length of the side opposite the [tex]60^{\circ}[/tex] angle.

[tex]\implies x=\frac{8}{\sqrt{3}} \approx 4.6[/tex]

Mean, because there are no outliers that affect the center

third period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Sorted values : 0, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4

The mean = ΣX / n

n = sample size, n = 15

Mean = 34 / 15 = 2.666

The median = 1/2(n+1)th term.

1/2(16)th term = 8th term.

The 8th term = 2

The best measure of centre is the mean because the values for the second period has no outliers that might have affected the centre of the distribution.

Both interquartile range and standard deviation are measures of spread and not measures of centre.

complete question

A survey was taken of students in math classes to find out how many hours per day students spend

on social media. The survey results for the first., second-, and third-period classes are as follows:

First period: 2,4,3,1,0, 2, 1, 3, 1,4,9,2,4,3,0

Second period: 3,2,3,1,3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2

Third period: 4,5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1,3

Which is the best measure of center for second period and why? (5 points)

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The value of n in the function is 1000

A model function is a way of describing a real-life system or situation using mathematical concepts and language

We have the function N(x) = 20x - (10x + n) models the number of sweaters produced where n is a constant.

Since 500 balls of wool were used to produce 4000 sweaters. To find the value of n, substitute x = 500 and N = 4000 into the function. That is:

N(x) = 20x - (10x + n)

4000 = 20(500) - (10(500) + n)

4000 = 10000 - 5000 - n

4000 = 5000 - n

n = 5000 - 4000

n = 1000

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Perimeter of one triangle is 20.6 inches.

Perimeter is the length of the boundaries of a closed triangle.

if we add the 3 side lengths of a triangle then the perimeter is determined.

Jane wants to have a rectangular stained glasses that has length 7 inches and width 5 inch.

If she fuses together two triangles of colored glass for obtaining a rectangle, then each triangle will have 3 similar side length.

each triangle has first side length = 5 inches

                              second side length = 7 inches

                   other side length = hypotenuse of right-angled triangle

                       =√(5² + 7²) = √74 inches

A rectangle has four right angles and therefore, the triangles that are developed based on the rectangle must be right-angled.

perimeter of triangle = sum of three side length = (5 + 7+√74) = 20.6 inches

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Answer:

16%

Step-by-step explanation:

1) Mean, u = 100 

standard deviation, o = 15

Score specified = x = 115

so, z-score = (x - u)/o

                   = (115 - 100)/15 = 1

From the probability standard normal distribution curve, 84.13% of the test scores falls within 1 SD (z score = 1), so, the percentage of test scores below 115 is 84.13%, so, for the percentage of test scores of 115 or higher = 100% - 84.13% = 16%.

Therefore, the correct answer is 16%.

Answer:

Clyde is correct. The domain is the set of x-values. The range is the set of y-values.

The values of zα for the given significance levels are approximate:

(a) zα ≈ 2.33

(b) zα ≈ 1.34

(c) zα ≈ 0.54

To determine zα (also known as the critical value) for a given significance level α, we need to find the z-score that corresponds to the upper α percentage of the standard normal distribution. In other words, we are looking for the z-value that cuts off an area of α in the right tail of the standard normal curve.

The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

To find zα, we can use a standard normal distribution table or a calculator that provides cumulative probability values for the standard normal distribution.

(a) α = 0.0089

For this case, we are looking for the z-score that corresponds to the upper 0.0089 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 2.33.

(b) α = 0.09

In this case, we need to find the z-score that corresponds to the upper 0.09 percentage of the standard normal distribution. Again, using a calculator or standard normal distribution table, we find that zα ≈ 1.34.

(c) α = 0.707

For α = 0.707, we are interested in the z-score that corresponds to the upper 0.707 percentage of the standard normal distribution. Using a calculator or standard normal distribution table, we find that zα ≈ 0.54.

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The complete question is as follows:
Determine zα for the following. (Round your answers to two decimal places.)

(a) α = 0.0089

(b) α = 0.09

(c) α = 0.707

Please explain where and how you got the answer.

We have explained all the steps to solve an infinite arithmetic sequence.

What is an arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term is the sum of the previous term and a constant called the common difference.

When it comes to solving an infinite arithmetic sequence, you can use the following formulas:

The n-th term of an arithmetic sequence can be represented as a+(n-1)d, where "a" is the first term, "d" is a common difference, and "n" is the position of the term in the sequence.

The sum of the first n terms of an arithmetic sequence is represented as S_n = n/2(2a + (n-1)d), where "a" is the first term, "d" is a common difference, and "n" is the number of terms.

If a sequence is infinite, the sum of all terms can be represented as S_inf = a/(1-r) where "a" is the first term and "r" is the common ratio (r=1+d)

Hence, we have explained all the steps to solve an infinite arithmetic sequence.

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Answer:

Step-by-step explanation:

[tex]3^{y}[/tex] + 1 = 1/9

3^y = -8/9

5^y/125^x = 125

5^y/5^3x = 125

5^(y-3x) = 5^3

y-3x = 3

Your question is incorrect as 3^x can never be negative.

But, now you know y - 3x = 3, so, use this to get the values when you reconsider the correct question.

Thanks

Answer:

y = [tex]\frac{1}{5}[/tex] x + 7

Step-by-step explanation:

y = mx + b  

You need to find m (the slope) and b (y-intercept)

If you start a the far left point and go to the next point that is graphed on the line, you will see that you moved up 1 space and right 5 to land back on the line.  This is your rise / run.  The slope is 1/5.

The y -intercept is where the line crosses the y axis.  It crosses at 7

Answer:

f

(

x

)

=

9

x

−

4

.

Step-by-step explanation:

The inverse of

f

(

x

)

=

9

x

−

4

is a function

g

(

x

)

such that

f

(

g

(

x

)

)

=

(

f

∘

g

)

(

x

)

=

x

but

f

(

g

(

x

)

)

=

9

g

(

x

)

−

4

=

x

Answer:

Step-by-step explanation:

To find the inverse of a function, we need to switch the variables x and y and solve for the new variable.

Given f(x) = x + 2/3, we can write the inverse as f^-1(y) = x.

So we will replace y with 4 in the inverse function f^-1(y) = x and solve for x.

f^-1(4) = x

x + 2/3 = 4

x = 4 - 2/3

x = 8/3

Therefore, f^-1(4) = 8/3

The total number of different passwords that can be made is 1,084,480.

To find this:

There are 26 capital letters in the English alphabet, so there are 26 possible choices for the first character of the password.

There are 10 digits from 0 through 9, inclusive, so there are 10 possible choices for the second character of the password.

There are 8 specified symbols, so there are 8 possible choices for the third character of the password.

For the fourth and fifth characters, there are a total of 62 possible choices (26 capital letters + 26 lowercase letters + 10 digits + 8 specified symbols).

Therefore, using these rules, the total number of different passwords that can be made is:

26 (possible choices for the first character) x 10 (possible choices for the second character) x 8 (possible choices for the third character) x 62 (possible choices for the fourth and fifth characters) = 1,084,480 different passwords.

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If a new information database generates $57,000 in yearly income for your organization over the following seven years. The funds are worth $298,795.93 in current value.

A percentage is a fraction of a whole represented as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent. To calculate a percentage, divide the share of the total by the total and multiply by 100. The term "percent" comes from the Latin per centum, which means "hundred" or "by the hundred". The symbol for "percent" came from the Italian expression per cento, which means "for a hundred".

Here,

PVA= Present value = ?

r = Interest rate = 7.8%

t = Time = 7 years

Let plug in the formula

PVA = $57,000{[1 − (1/(1+.078)^7)]/.078}

PVA = $57,000{[1 − (1/1.078^7)]/.078}

PVA = $57,000{[1 − (1/1.6917)]/.078}

PVA = $298,795.93

If your organization will make $57,000 in annum income from a new information database over the next seven years. The current value of the savings is $298,795.93.

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Answer:

[tex]\boxed{\mathrm{108 \pi \;cubic\; inches}}[/tex]

3rd Choice

Step-by-step explanation:

Volume of a cylinder V is given by the equation:
[tex]V = \pi r^2h\\\\\textrm{where r = radius of the cylinder}\\\\\textrm{and, h = height of the cylinder}\\\\[/tex]

[tex]\textrm{From the diagram we see the diameter of the cylinder = 6 in }\\\\\mathrm{radius = \dfrac{diameter}{2} }\\\\\mathrm {So\; radius = \dfrac{6}{2} = 3\;in}\\\\[/tex]

[tex]\mathrm{h = 12\;in}\\\\\\\\\mathrm{V= \pi \cdot 3^2 \cdot 12}\\\\\mathrm{V = \pi \cdot 9 \cdot 12}\\\\\mathrm{V = 108 \pi}[/tex]

Answer

Volume of cylinder =  [tex]\boxed{\mathrm{108 \pi \;cubic\; inches}}[/tex]

The largest possible sample you can take from a population of 5000 football fans and still be able to calculate the standard deviation of the sampling distribution is the entire population, or 5000 people.

The standard deviation of a population is denoted as σ and can be calculated using the formula:

σ = √(Σ(x - μ)^2 / N)

where

x is each individual value in the population

μ is the mean of the population

N is the size of the population. In this case 5000 people.

When it comes to statistics and sampling, the larger the sample size, the more accurate and reliable the results will be. However, in some cases, such as when studying a small population, obtaining a large sample may not be possible.

In the case of a small town with only 5000 football fans, it would be impossible to take a sample larger than the entire population. Therefore, the largest possible sample size would be 5000 and this would allow us to calculate the standard deviation of the sampling distribution, which is a measure of the spread of the data.

This can give us an idea of how much variation there is within the population and how much confidence we can have in the results, but without more information such as the individual values and mean of the population, it is rather impossible to calculate the standard deviation.

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The oldest type of currency still in use today, according to the claim, is metal.

Money is a good that is frequently used as a basis of economic exchange. It is used to communicate values and prices and is the primary determinant of value. By effortlessly traveling from one person to another and from one country to another, money fosters commerce.

Money is derived from the Latin term moneta, which means "coin," through the French term monnaie. It is thought that the Latin phrase came from a temple dedicated to Juno on Capitoline, being one Poland's seven hills. Juno was frequently linked to riches in ancient times.

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To determine the number of smartphones sold in 2012 with the exponential function.

What is exponential function ?

An exponential function is a mathematical function in which the variable, or the input, is in the exponent (power) of the function. It takes the form of f(x) = ab^x, where a and b are constants and x is the variable. The variable x is often time and the constant b is often greater than 1, which causes the function to grow at an increasing rate. It is often used to model growth and decay phenomena, such as population growth, radioactive decay, and others.

To estimate the number of smartphones sold in 2012, we would need to find the exponential function that models the worldwide sales of the smartphone brand from 2008 to 2011. Once we have this function, we can plug in the year 2012 as the input to estimate the number of smartphones sold in that year. However, without more information it is impossible to know the exact exponential function and the exact number of smartphones sold in 2012.

To determine the number of smartphones sold in 2012 with the exponential function.

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In given word problem Deana takes 4 weeks to complete the 462 miles.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement.

Here to find Rate per week we need to divide the miles by weeks then,

Pavel weekly rate = [tex]\frac{672}{21}[/tex] = 32 miles per week.

Alberto weekly rate = [tex]\frac{420}{12}[/tex] = 35

Here Deana weekly mileage rate was greater than Pavel's rate but less than Alberto's rate . Then it must be 33 or 34.

Now divide Deana miles by 33 then

=> [tex]\frac{462}{33}[/tex] = 14 weeks

Now divide Deana miles by 34 then

=> [tex]\frac{462}{34}[/tex] = 15.58

Here weeks can't be in decimal.

Hence it takes 14 weeks to complete her run.

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Answer: Devra biked - 15 miles

or

Devra biked - 15

You may also decide to replce Devra biked with y,x,or d for example x - 15

This expression shows that the number of miles Devra biked is 15 miles less than the actual distance.

Step-by-step explanation: