How many 7/8 cup servings are in 1/2 of a cup of juice? (in simplest fraction form)

Answer:the vertical distance is 1663.2 feet.

The horizontal distance is 7824.8 feet.

Step-by-step explanation:.

The vertical distance between the two aircrafts is represented by x.

To determine x, we would apply trigonometric ratio

Sin θ = opposite side/hypotenuse

Sine 12 = x/8000

x = 8000Sin12 = 8000 × 0.2079

x = 1663.2 feet

The horizontal distance between the two aircrafts is represented by y.

To determine y, we would apply trigonometric ratio

Cos θ = opposite side/hypotenuse

Cos 12 = y/8000

x = 8000Cos12 = 8000 × 0.9781

x = 7824.8 feet

Answer:

89.97% probability that the average of these 100 tires will last greater than 41,000 miles.

Step-by-step explanation:

The solve this problem, it is important to know the Normal Probability distribution and the Central Limit Theorem.

Normal probability distribution

Problems of normally distributed samples can be solved using 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 random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

In this problem, we have that:

[tex]\mu = 42000, \sigma = 7800, n = 100, s = \frac{7800}{\sqrt{100}} = 780[/tex]

What is the probability that the average of these 100 tires will last greater than 41,000 miles?

This is 1 subtracted by the pvalue of Z when X = 41000.

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

By the Central Limit Theorem, we use s instead of [tex]\sigma[/tex].

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

[tex]Z = \frac{41000 - 42000}{780}[/tex]

[tex]Z = -1.28[/tex]

[tex]Z = -1.28[/tex] has a pvalue of 0.1003.

So there is a 1-0.1003 = 0.8997 = 89.97% probability that the average of these 100 tires will last greater than 41,000 miles.

Answer:

The numerical value of the slope is 15, and it is by how much his balance decreases each week.

Step-by-step explanation:

Bryan's balance y after x weeks is given by a first degree function in the following format:

[tex]y = a - bx[/tex]

In which a is his initial balance and b is how much he spends a week. The slope is b., that is, how much is deducted from his balance each week.

In this problem, we have that:

Bryan has a balance of $320 in his checking account. This means that [tex]a = 320[/tex].

He spends $15 each week for next eight weeks. This means that [tex]b = 15[/tex]

So the equation for Bryan's balance is

[tex]y = 320 - 15x[/tex]

The numerical value of the slope is 15, and it is by how much his balance decreases each week.

Answer:

We have 4.25 quarts of gasoline.

4 quarts = 1 gallon

.25 quarts = one sixteenth of a gallon.

1 / 16 = 0.0625  gallons

So, we have 1.0625 gallons of gasoline

We need  2.4 fluid ounces for every gallon of gasoline.

So, we need 1.0625 times 2.4 ounces per gallon which equals

2.55 fluid ounces.

Step-by-step explanation:

Answer:you should add 2.52 fluid ounce of oil

Step-by-step explanation:

You have to mix the oil and gas together in a specific ratio of 2.4 fluid ounce for every gallon of gasoline.

Since you have 4.2 quarts of gas, the first step is to 4.2 quarts of gas to gallons.

1 US liquid quart = 0.25 US liquid gallon.

Therefore, 4.2 quarts of gas would be

0.25 × 4.2 = 1.05 gallon of gasoline.

Therefore,

Since you use 2.4 fluid ounce of oil for every gallon of gasoline, then the amount of oil that you would add to 1.05 gallon of gasoline would be

2.4 × 1.05 = 2.52

By the chain rule,

[tex]\dfrac{\partial z}{\partial u}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial u}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial u}[/tex]

where [tex]u\in\{r,t\}[/tex].

We have component partial derivatives

[tex]\dfrac{\partial z}{\partial x}=\dfrac{2x}{x^2+y}=\dfrac{2re^t}{r^2e^{2t}+te^r}[/tex]

[tex]\dfrac{\partial z}{\partial y}=\dfrac1{x^2+y}=\dfrac1{r^2e^{2t}+te^r}[/tex]

[tex]\dfrac{\partial x}{\partial r}=e^t[/tex]

[tex]\dfrac{\partial x}{\partial t}=re^t[/tex]

[tex]\dfrac{\partial y}{\partial r}=te^r[/tex]

[tex]\dfrac{\partial y}{\partial t}=e^r[/tex]

Putting the appropriate pieces together and setting [tex](r,t)=(1,2)[/tex], we get

[tex]\dfrac{\partial z}{\partial r}(1,2)=\dfrac{2e^3+2}{e^3+2}[/tex]

[tex]\dfrac{\partial z}{\partial t}(1,2)=\dfrac{2e^3+1}{e^3+2}[/tex]

Answer:

[tex] y=(x-29)^2 +60[/tex]

Step-by-step explanation:

For this case we have the original function [tex] y =x^2[/tex]

So let's do the transformations one by one.

The general expression for a parabola like the formula given is:

[tex] y = (x-h)^2 +k[/tex]

If we want to do a shift on the vertical axis we need to modify the value of k, since we want 60 units upward the value of k =60, and then the formula after the first transformation would be:

[tex] y = x^2 + 60[/tex]

For the other part related to the movement on the x axis 29 units to the right we need to modify the value of h in the general expression , since is a translation to the right the value of h = 29 and if we replace we got:

[tex] y=(x-29)^2 +60[/tex]

And that would be our final expression after the transformations on the y and x axis.

On the figure attached we see the original function in red, the blue function represent the shift upward and the green one the two tranformations at the sam time to check that we did the procedure right.

Answer:

The sample standard deviation for given data is 222.69        

Step-by-step explanation:

We are given the following data set:

508, 657, 214, 958, 765, 449, 338, 497

Formula:

[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]  

where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.  

[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]

[tex]Mean =\displaystyle\frac{4386}{8} = 548.25[/tex]

Sum of squares of differences =

1620.0625 + 11826.5625 + 111723.0625 + 167895.0625 + 46980.5625 + 9850.5625 + 44205.0625 + 2626.5625 = 396727.5

[tex]\text{Sample standard Deviation} = \sqrt{\dfrac{396727.5}{7}} =222.69[/tex]

The sample standard deviation for given data is 222.69        

To calculate the sample standard deviation using a calculator, enter the data points in statistical mode, use the function labeled as 'sx' or 'σx' for the sample, not the population, then calculate and round to the nearest tenth. The symbol for sample standard deviation is typically 's' or 'sx' on most calculators.

To find the sample standard deviation of the dataset {508, 657, 214, 958, 765, 449, 338, 497}, you will need to use your calculator's statistical functions. Use the statistical mode in your calculator that corresponds to Equation 4.1.1 for calculating the standard deviation of a sample, not the population. Here are the typical steps for calculating it:

The symbol s or sx represents the sample standard deviation on most calculators, while σ and σx are typically used for a population's standard deviation (which is not needed in this question).

As an example, if your calculated variance is .5125, the standard deviation would be the square root of the variance: S = √.5125 = .715891, and when rounded to two decimal places, s = .72. Always consult your calculator's manual for specific instructions, as they can vary between models.

Answer:

Step-by-step explanation:

Given that the reaction temperature X (in deg C) in a certainchemical process has uniform distribution with A= -5 and B=5

Thus the pdf of X would be

[tex]f(x) = 0.1 , -5\leq x\leq 5[/tex]

the cumulative probability

[tex]F(x) = \frac{x-a}{10} ,-5\leq x\leq 5[/tex]

a) P(X<0) = F(0) = [tex]\frac{0-(-5)}{10} =0.5[/tex]

b) P(x<-2.5) = F(-2.5)

= [tex]\frac{0-(-2,5)}{10} =0.25[/tex]

c) P(X>-2) = 1-F(-2)

=1-0.2 = 0.8

Answer: (18/5) * 11

Step-by-step explanation:

In equations of proportion, to proceed, we need to determine the constant of proportion, let's denote as "k"

Since y ~ x

Means y=kx.

To determine the value of k, we input initial values of y and x.

Initial value of y = 18

Initial value of x = 5

The equation becomes :

18 = 5k

k = 18/5.

Now, If given the value of x as 11,to determine the value of y we go back to the equation.

y= kx

y = 18/5 * 11.

The correct expression to find the value of y when x is 11 is [tex]\( y = \frac{18}{5} \times 11 \)[/tex].

Given that y varies directly as x, we can express this relationship using the formula [tex]\( y = kx \)[/tex], where k is the constant of proportionality. To find the value of k, we use the given values of y and x when [tex]\( y = 18 \)[/tex] and [tex]\( x = 5 \)[/tex]. Thus, we have:

[tex]\[ k = \frac{y}{x} = \frac{18}{5} \][/tex]

Now, we want to find the value of y when [tex]\( x = 11 \)[/tex]. Using the direct variation formula with our calculated k:

[tex]\[ y = kx = \frac{18}{5} \times 11 \][/tex]

This expression will give us the value of y when x is 11. The other options provided are incorrect because they either divide by 11 or use the inverse relationship, which does not apply in the case of direct variation.

Answer:

The values of x that makes these vectors orthogonal are x = 2 and x = 4.

Step-by-step explanation:

Orthogonal vectors

Suppose we have two vectors:

[tex]v_{1} = (a,b,c)[/tex]

[tex]v_{2} = (d,e,f)[/tex]

Their dot product is:

[tex](a,b,c).(d,e,f) = ad + be + cf[/tex]

They are ortogonal is their dot product is 0.

Solving quadratic equations:

To solve this problem, we are going to need tosolve a quadratic equation.

Given a second order polynomial expressed by the following equation:

[tex]ax^{2} + bx + c, a\neq0[/tex].

This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:

[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]

[tex]\bigtriangleup = b^{2} - 4a[/tex]

Find all values of x such that (4, x, −6) and (2, x, x) are orthogonal.

[tex](4,x,-6)(2,x,x) = 8 + x^{2} - 6x[/tex]

These vectors are going to be orthogonal if:

[tex]x^{2} -6x + 8 = 0[/tex]

This is a quadratic equation, in which [tex]a = 1, b = -6, c = 8[/tex]. So

[tex]\bigtriangleup = 6^{2} - 4*1*8 = 4[/tex]

[tex]x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4[/tex]

[tex]x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2[/tex]

The values of x that makes these vectors orthogonal are x = 2 and x = 4.

The values of x that make the vectors (4, x, −6) and (2, x, x) orthogonal are x = 2 and x = 4, determined by setting their dot product to zero and factoring the resulting quadratic equation.

To find all values of x such that the vectors (4, x, −6) and (2, x, x) are orthogonal, we need to perform the dot product of the vectors and set it equal to zero. Two vectors are orthogonal if their dot product is zero.

The dot product is calculated as follows:

Next, we factor the quadratic equation:

Hence, the two values of x that make the vectors orthogonal are x = 2 and x = 4.

Final answer:

The domain of f(x) = 8/(1 + eˣ) is all real numbers, or (-∞, ∞). For f(x) = 5/(1 - eˣ), the domain is all real numbers except x = 0, which in interval notation is (-∞, 0) ∪ (0, ∞).

Explanation:

Finding the Domain of Functions

To find the domain of a function, we look for all possible values of x for which the function is defined. The exponential function eˣ is defined for all real numbers, so we mainly need to be concerned with the denominators in these functions not being equal to zero.

Answer:

Yes a

Step-by-step explanation:

I took the test

The answer is:

You​ shouldn't expect to get exactly 5000​ heads, because you cannot predict precisely how many heads will occur.

The outcome in tossing a fair coin is based on chance.

However, according to the law of large numbers, the frequencies of events with the same likelihood of occurrence even out, given enough trials or instances.

For example, in the case of  a fair coin, where both head and tail have equal probability of occurrence, as the number of tosses becomes sufficiently large (say 1 million tosses), the ratio heads to tails in the outcome will be extremely close to 1:1.

So according to the law, we should expect to approach a point where half of the outcomes are heads and the other half are tails, as the number of tosses become very large.

The answer is (a). You should not expect to get exactly 5000 heads, because you cannot predict precisely how many heads will occur.

The law of large numbers states that as the number of independent trials of a random experiment increases, the observed frequency of each outcome approaches the expected frequency. In other words, the more times you toss a fair coin, the closer the proportion of heads will get to 50%.

However, the law of large numbers does not guarantee that you will get exactly 5000 heads even if you toss a fair coin 10,000 times. It is still possible to get more or fewer than 5000 heads, even though it is unlikely.

For example, if you toss a fair coin 100 times, you might get 55 heads and 45 tails. This is within the normal range of variation, even though it is not exactly 50 heads and 50 tails.

As the number of tosses increases, the probability of getting exactly 50/50 heads and tails decreases. However, the probability of getting close to 50/50 heads and tails increases.

In conclusion, you should not expect to get exactly 5000 heads even if you toss a fair coin 10,000 times. However, you can expect the proportion of heads to be close to 50%.

For such more question on heads

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Answer:

A. The value is a parameter because the men who had walked on the moon are a population.

Correct option the value reported represent the mean for all the individuals in the population of interest and for this reason represent a parameter.

Step-by-step explanation:

For this case we know that the average age of men who had walked on the moon was 39 years, 11 months, 15 days.

So then we need to assume that this value was calculated from the average of all the mean who walked on the moon, so then we have a population represented by a parameter.

And let's analyze one by one the possible options given:

A. The value is a parameter because the men who had walked on the moon are a population.

Correct option the value reported represent the mean for all the individuals in the population of interest and for this reason represent a parameter.

B. The value is a parameter because the men who had walked on the moon are a sample.

The value represent a parameter but the reason is not because represent a sample, is a parameter because represent the population of interest.

C. The value is a statistic because the men who had walked on the moon are a sample.

False the men who had walked on the moon are a population since they know the information about the men who walked on the moon and not represent a sample for this case.

D. The value is a statistic because the men who had walked on the moon are a population.

False the men who had walked on the moon are a population since they know the information about the men who walked on the moon, and if is a population then can't be a statistic.

The average age of men who had walked on the moon represents a parameter because it describes a characteristic of a specific population: all men who have walked on the moon.

In the context of statistical study, a parameter refers to a characteristic of a population, while a statistic is a measure that describes a sample. In this case, the group referred to is 'all men who had walked on the moon,' which is a population, not a sample, because it includes every individual of interest that fits a specific criteria. Therefore, the average age of men who walked on the moon is a parameter, not a statistic. So, the correct response is:
A. The value is a parameter because the men who had walked on the moon are a population.

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Answer:

The answer is already in the question. The coordinates of the entrance to the Mount Rushmore parking area are given by latitude 43.8753972 and longitude -103.4523083.

Step-by-step explanation:

I believe the person asking the question wants some other detail that s/he did not state explicitly.

Final answer:

The coordinates for the entrance to the Mount Rushmore parking area are Latitude: 43.8753972 and Longitude: -103.4523083, used for precise geographical positioning on Earth.

Explanation:

The latitude and longitude coordinates of the entrance to the Mount Rushmore parking area are as follows: Latitude: 43.8753972, Longitude: -103.4523083. These coordinates provide precise location details required to pin-point specific places on Earth using geographic positioning systems.

Latitude and longitude are measured in degrees, minutes, and seconds, with latitude representing the distance north or south of the equator and longitude representing the distance east or west of the Prime Meridian. When you search for landmarks such as the Washington Monument or use GPS coordinates to find a specific location, such as the Grand Canyon, you are utilizing these two fundamental geographic references to navigate and observe various parts of the world.

Answer:

Assume that for the communication to be available means that at least one of the [tex]n[/tex] circuits is operational. It would take at least 3 circuits to achieve a [tex]0.99999[/tex] overall availability.

Step-by-step explanation:

The probability that one circuit is not working is [tex]1 - 0.99 = 0.01[/tex].

Since the circuits here are all independent of each other, the probability that none of them is working would be [tex]\displaystyle \underbrace{0.01 \times 0.01 \times \cdots \times 0.01}_{\text{$n$ times}}[/tex]. That's the same as [tex]0.01^n[/tex].

The event that at least one of the [tex]n[/tex] circuits is working is the complement of the event that none of them is working. To find the probability that at least one of the [tex]n[/tex] circuits is working, simply subtract the probability that none of the circuit is working from one. That is:

[tex]\begin{aligned}&P(\text{At least one working}) \cr &= 1 - P(\text{None is working}) \cr &= 1- 0.01^n\end{aligned}[/tex].

The question requests that

[tex]P(\text{At least one working}) \ge 0.99999[/tex].

In other words,

[tex]1- 0.01^n \ge 0.99999[/tex].

[tex]0.01^n \le 1 - 0.99999 = 0.000001 = 10^{-6}[/tex].

Note that [tex]0.01 = 10^{-2}[/tex]. Hence, the inequality becomes

[tex]\left(10^{-2}\right)^n \le 10^{-6}[/tex].

[tex]10^{-2\,n} \le 10^{-6}[/tex]

Take the natural log of both sides of the equation:

[tex]\ln\left(10^{-2\, n}\right) \le \ln \left(10^{-6}\right)[/tex].

[tex](-2\, n)\ln\left(10\right) \le (-6) \ln\left(10\right)[/tex].

[tex]10 > 1[/tex], hence [tex]\ln(10) > 0[/tex]. Divide both sides by [tex]\ln(10)[/tex]:

[tex]-2\,n \le -6[/tex].

[tex]n \ge 3[/tex].

In other words, at least three parallel circuits must be set up to achieve that availability.

Answer:

Every 10th product in the line is selected

Step-by-step explanation:

Convenience sampling also available sampling, or nearest in reach sampling.

it is a type of non-probability sampling that involves the sample being drawn from a population that is in reach or that is easily at hand.

example. A questionnaire being distributed to people met in a mall.

for the manufacturing company in question, the first 10 product in line were the first set of product the machine will produce (at hand).

it is normally use to test run the operation of the machine.

Convenience sampling in manufacturing is best described as selecting every 10th product in the line for testing. It is a simple, quick, and cost-effective way to identify potential issues.

In the context of manufacturing, convenience sampling represents a type of sampling where samples are chosen because they are readily available or easy to obtain. In the provided choice list, the best description of convenience sampling is 'Every 10th product in the line is selected'. This method is chosen for its simplicity and speed. While it may not provide a comprehensive result since it won't cover all the various different scenarios, it is a cost-effective and time-efficient way of identifying potential issues in machine operations.

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Answer:

4) "Everyone in Spain speaks at most 9 languages."

Step-by-step explanation:

A negation is a statement that contradicts the original statement. Since the original statement regards people in Spain, options 2, 5, 6 and 7 can be ruled out as they refer to speakers outside of Spain.

Evaluating the remaining statements.

1) "Everyone in Spain speaks at least 10 languages."

If that is true, then someone in Spain speaks at least 10 languages, it doesn't negate the original statement.

3) "There is someone in Spain who speaks at most 9 languages."

It only refers to one specific individual, it doesn't negate the original statement.

4) "Everyone in Spain speaks at most 9 languages."

This means that nobody in Spain speaks more than 9 languages, contradicting the original statement.

The answer is statement 4.

Answer:the missing values are 7, 28 and 31.5

Step-by-step explanation:

What makes the relationship between two variables to be proportional is the constant of proportionality. With the constant of proportionality determined, if there is a change in the value of one variable, the corresponding change in value of the other variable is easily determined.

The variables given are servings and ounces.

Let the missing values be represented by a,b and c.

Therefore,

21/12 = a/4

a = 1.75 × 4

a = 7

21/12 = b/16

b = 1.75 × 16

b = 28

21/12 = c/18

c = 1.75 × 18

c = 31.5

Answer: B. Jonesville is growing linearly and Smithville is growing exponentially.

Step-by-step explanation:

Linear growth :

Exponential growth :

Given : Jonesville​'s population grows by 170 people per year.

i.e .Population grow by a constant amount per year.

⇒ Jonesville is growing linearly.

The population of smithville grows by 7​% per year.

i.e. Population grow by a constant ratio.

⇒Smithville is growing exponentially.

Hence, the true statement is "B. Jonesville is growing linearly and Smithville is growing exponentially."

Final answer:

Jonesville is experiencing linear growth with a constant increase of 170 people per year, while Smithville is experiencing exponential growth, with its population growing by 7% yearly. The correct answer is B, signifying two different types of growth for the towns.

Explanation:

The correct answer to the question is B: Jonesville is growing linearly and Smithville is growing exponentially. This can be determined by looking at the type of growth each town is experiencing. Jonesville's population increases by a fixed amount each year (170 people), which is characteristic of linear growth. Conversely, Smithville's population increases by a percentage (7%) of the population each year, which is a key feature of exponential growth as the rate of growth increases with an increasing population base.

Linear growth occurs when a quantity increases by the same fixed amount over equal increments of time. In the case of Jonesville, it grows by 170 people every year, resulting in a straight line if graphed over time. On the other hand, exponential growth refers to an increase that is proportional to the quantity's current value, leading to faster and faster growth as time goes on. For Smithville, a 7% growth rate implies that each year the town will grow by 7% of its population at the end of the previous year, meaning the actual number of people added each year will continue to increase as the population grows.

Answer:

There are 64 possible birth orders in a family with six children.

Step-by-step explanation:

Let's start from 1 children.

You can have M or F. So two possible birth orders.

With two children, you can have M-M, M-F, F-M, F-F. So 2^2 = 4 possible birth orders.

For three children.

M-M-M, M-M-F, M-F-M, M-F-F, F-M-M, F-M-F, F-F-M, F-F-F. So 2^3 = 8 possible birth orders.

Generalizing:

For n children, you can have [tex]2^{n}[/tex] birth orders.

In this problem, we have that:

The family has 6 chilren.

So there are [tex]2^{6} = 64[/tex] possible birth orders.

Answer:

Used wire in circle  x = 2.64 m

Used in square   L - x = 3.36 m

Total wire used 6 m

Step-by-step explanation:

We have a wire of 6 meters long.

We will cut it a distance x from one end, to get two pieces

x    and   6 - x

We are going to use the piece x  to get the circle then

So Perimetr of a circle is 2π*r    (r is the radius of the circle) then:

x = 2*π*r    ⇒    r = x/2*π

And area would be  A(c) = π* (x/2*π)²   ⇒ A(c) = x²/4π

From 6 - x we will get a square, and as the perimeter is 4 times the side

we have

( 6 - x )/ 4  is the side of the square

And the area is  A(s) = [( 6 - x ) /4]²

Total area as function of x is

A(t)  = A(c) + A(s)

A(x)  =  x²/4π  + [ ( 6  -  x  ) / 4 ]²

A(x)  =   x²/4π  + (36 + x² - 12x) /16

A(x)  = 1 / 16π [ 4x² + 36π + πx² -  12π x ]

Taking drivatives on both sides of the equation we get:

A´(x) = 1/ 16π [8x +2πx - 12π]

A´(x) = 0    ⇒      1/ 16π [8x +2πx - 12π]  = 0

[8x +2πx - 12π]  = 0

8x + 6.28x -  37.68  = 0

14.28x - 37.68 =  0      ⇒  x  = 37.68 /14.28

x = 2.64 m   length of wire used in the circle

Then the length L  for the side of the square is  

(6 - x )/4    ⇒ ( 6 - 2.64 )/ 4   ⇒ 3.36 / 4    

L = 0.84 m   total length of wire used in the square is

3.36 m

And total length of wire used is 6 m

The function is a quadratic  function and "a" coefficient is positive then is open upward parabola there is not a maximun

Answer:

Wire used in circle , x = 2.64 m

Wire used in square, L - x = 3.36 m

Total used wire is 6 m

Step-by-step explanation:

We have a wire of 6 metres long.

We will cut it a distance x metre from one end, to get two pieces x metre and 6 - x metres.

We are going to use the piece of x metre to get the circle

So, Perimeter of the circle is [tex]2\pi r[/tex] (r is the radius of the circle) then

[tex]x = 2\pi r[/tex] ⇒ [tex]r = \frac{x}{2} \pi[/tex]

And area would be [tex]A(c) =\pi (\frac{x}{2} \pi )^{2}[/tex]⇒[tex]A(c) = \frac{x^{2} }{4\pi }[/tex]

From [tex]6 - x[/tex] we will get the square, and as the perimeter is 4 times the side

we have

[tex]\frac{6 - x}{4}[/tex] is the side of the square

and the area is [tex]A(s) = (\frac{6 - x}{4}) ^{2}[/tex]

Total area of the function of x is

[tex]A(t) = A(c) + A(s)[/tex]

[tex]A(x) = \frac{x^{2} }{4\pi } +(\frac{6 - x}{4} )^{2}\\A(x) = \frac{x^{2} }{4\pi } + \frac{36+x^{2} -12x}{16} \\A(x) = \frac{1}{16\pi } (4x^{2} +36\pi +\pi x^{2} -12\pi x)[/tex]

Taking derivative on the both side of the equation we get :

[tex]A^{'} = \frac{1}{16\pi } (8x+2\pi x-12\pi )\\[/tex]

[tex]A^{'} = 0[/tex]

[tex]\frac{1}{16\pi } (8x+2\pi x-12\pi ) = 0\\(8x+2\pi x-12\pi ) = 0\\8x + 6.28x-37.68=0\\14.28x-37.68=0\\x=2.64 m[/tex]

length of wire used in the circle is x = 2.64 m

Then the length L of the wire used in the square is

[tex]\frac{6 - x}{4}[/tex] ⇒[tex]\frac{6 - 2.64}{4}[/tex] ⇒ [tex]\frac{3.36}{4}[/tex]

L = 0.84 m

Total length of the wire used in the square is 4L = 3.36 m

And total length of the wire used is 6 m

The function is a quadratic function and "a" coefficient is positive then is open upward parabola there is not a maximum.

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The Question is understood as asking for [the Level of] Education of the respondents in a survey classified as [with values] Institutional, Autodidactic, or Other.

Answer:

The level of measurement is the Nominal Scale.

Step-by-step explanation:

The variable studied here is Education (of the respondents), and it is measured using three categories: Institutional, Autodidactic or Other.

As can be seen, the variable Education is measured using those categories that act as labels. These labels are simply names and they have neither relation in order to the other categories ---that is, no value is higher or lower than other--- and nor numerical meaning at all, as it is with other levels of measurement like Ordinal, Interval or Ratio.

For instance, having an Institutional value is not saying that it represents a higher value than having Autodidactic value or Other value. Moreover, if we substituted Institutional, Audidactic and Other by 0, 1, or 2, these values have no numerical value but are a way to classify the different possible values for the Education variable.

In other words, they represent only a way to classify values for the Education variable. No more than this.

As a result, the level of measurement for the variable Education is the Nominal Scale.

By using the distance formula, we calculate the distances between the house, library, and post office, finding the total minimum distance to be approximately 14.8 kilometers.

This question requires the use of the distance formula in mathematics, which is derived from the Pythagorean theorem. The formula is √[(x₂ - x₁)² + (y₂ - y₁)²]. To find the total minimum distance you ride your bike, you calculate the distance from your house to the library, then the library to the post office, and finally, the post office back to your house.

First, calculate the distance from your house at (-3, 2) to the library at (-2, -2): √[(-2 - (-3))² + (-2 - 2)²] = √[1² + -4²] = √[1 + 16] = √17 ≈ 4.1 kilometers.

Second, calculate the distance from the library at (-2, -2) to the post office at (2, 2): √[(2 - (-2))² + (2 - (-2))²] = √[4² + 4²] = √[16 + 16] = √32 ≈ 5.7 kilometers.

Finally, calculate the distance from the post office at (2, 2) back to your house at (-3, 2): √[(-3 - 2)² + (2 - 2)²] = √[-5² + 0²] = √[25 + 0] = √25 = 5 kilometers.

Adding these distances together, 4.1 km + 5.7 km + 5 km = 14.8 kilometers.

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Answer:

It is shown in the pic.

Step-by-step explanation:

We can call this unit vector u, that points down the plane (parallel to the plane) and v is an unit vector that points in a direction that is normal to the plane.

The cumulative frequency distribution of a data set is found by adding the frequency of each category to the sum of the frequencies of all previous categories. Using this method, the cumulative frequency distribution for the given data set is as follows: 35-39: 11, 40-44: 33, 45-49: 77, 50-54: 90, 55-59: 156, 60-64: 244, 65-69: 255.

To construct the cumulative frequency distribution for the given data, we need to take into account the sum of all frequencies to the current one in addition to its own frequency. Let's look at how this works using the provided data:

Therefore, the cumulative frequency distribution for the given data set is:

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A cumulative frequency distribution adds each frequency to the cumulative total of the previous ones. The sequence of cumulative frequencies for the given temperature data is 11, 33, 77, 90, 156, 244, and 255 respectively.

To construct a cumulative frequency distribution, we add up the frequencies as we go down the list of daily low temperatures. We will begin with the first frequency and add each subsequent frequency to the cumulative total of the previous frequencies. Here is how it would look for the data provided:

35-39: 11 (11)

40-44: 22 (11 + 22 = 33)

45-49: 44 (33 + 44 = 77)

50-54: 13 (77 + 13 = 90)

55-59: 66 (90 + 66 = 156)

60-64: 88 (156 + 88 = 244)

65-69: 11 (244 + 11 = 255)

The numbers in brackets represent the cumulative frequencies. Remember, to calculate Heating Degree Days (HDD) and Cooling Degree Days (CDD), you sum the number of days when the average temperature is below or above 65°F, respectively, multiplied by the difference from 65°F.

Answer:

Collectively, the total sample took 9000 course credits.

Step-by-step explanation:

The mean number of course credits taken is the total number of credits which the sample took collectively divided by the size of sample. Mathematically

[tex]M = \frac{T}{N}[/tex]

In which

M is the mean number of course credits taken

T is the total number of course credits taken

N is the size of the sample.

In this problem, we have that:

[tex]M = 18, N = 500[/tex]

We have to find T. So

[tex]M = \frac{T}{N}[/tex]

[tex]18 = \frac{T}{500}[/tex]

[tex]T = 500*18[/tex]

[tex]T = 9000[/tex]

Collectively, the total sample took 9000 course credits.

Answer:

Option B) [tex]H_0: \text{Mean} = 2.5[/tex]

Step-by-step explanation:

We are given the following in the question:

A researcher is interested in studying the perceived life satisfaction among younger adults.

The hypothesis is conducted to check  that life satisfaction among younger adults is different than the general public.

Life satisfaction for general public = 2.5

Data:

4, 3, 3, 4, 5, 2, 2, 2, 2

We have to design the null hypothesis.

The researcher claims that life satisfaction is different for younger adult and general public.

But the null hypothesis always state equality between the population and the sample.

Thus, the null hypothesis will be

Option B) [tex]H_0: \text{Mean} = 2.5[/tex]

Answer:

720 different choices of officers are possible if there are no restrictions.

The number of ways in which Worf and Troi will not serve together is 672.

Step-by-step explanation:

Consider the provided information.

We have 3 post admiral, captain, and commander, and 10 Starfleet officers.

Part (A) there are no restrictions?  

We need to select 3 people out of 10. And these 3 people can again rearranged into different rank.

Thus, the number of ways are: [tex](^{10}C_3)3!=\left(\dfrac{10!}{3!7!}\right)3!=720[/tex]

Hence, 720 different choices of officers are possible if there are no restrictions.

Part (B) Worf and Troi will not serve together?

Subtract those cases in which both of them are selected from total number of ways.  

If both of them selected then we need to select only 1 person out of 8. And further they can rearranged into 3 different rank.

Thus, the number of ways are: [tex]720-(^{8}C_1)3!=720-8\times3!=672[/tex]

Hence, the number of ways in which Worf and Troi will not serve together is 672.

Answer:

a) The slope of the graph of c is 8.34.

b) The dosage for a newborn is 8.34mg.

Step-by-step explanation:

A first order function in the following format

[tex]c(a) = ba + d[/tex]

Has slope b.

The appropriate dosage c is a function of the age a.

In this problem, we have that:

[tex]c(a) = 0.0417D(a + 1)[/tex]

Suppose the dosage for an adult is 200 mg. This means that [tex]D = 200[/tex]

So

[tex]c(a) = 0.0417*200(a + 1)[/tex]

[tex]c(a) = 8.34a + 8.34[/tex]

(a) Find the slope of the graph of c.

The slope of the graph of c is 8.34.

(b) What is the dosage for a newborn? (Round your answer to two decimal places.)

A newborn has age a = 0. So this is c(0).

[tex]c(a) = 8.34a + 8.34[/tex]

[tex]c(0) = 8.34*0 + 8.34 = 8.34[/tex]

The dosage for a newborn is 8.34mg.