Consider the function represented by the equation 6c = 2p – 10. Write the equation in function notation, where c is the independent variable. F(c) = one-thirdp + five-thirds f(c) = 3c + 5 f(p) = one-thirdp + five-thirds f(p) = 3c + 5

Answer:

144

Step-by-step explanation:

We simply need to input these values into the equation.

S = (ab + ac + bc)

Where: a = 12 b = 6 and c = 4

S = ( 12 × 6 + 12 × 4 + 6 × 4)

S = 72 + 48 + 24 = 144 inch^2

Answer:

the correct answer is c (288 in. squared)

Step-by-step explanation:

i got i correct on the quiz;)

hope this helps you out

(also please let me know if i am wrong)

Answer:

I got 469.8 kilowatt-hours. I got this by taking the total of Frank's bill, which was $85.78, and subtracting the flat monthly fee of $20.00. I did this because I need to find out the number of kilowatt-hours Frank used. Then, I divided $65.78 by $0.14 since that is the price per kilowatt-hour and got about 469.8 kilowatt-hours used by Frank.

The power utilised by frank in the month of march is 470 kilowatts - per hour.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that Franks's electric bill for the month of March was $85.78. The electric company charged a flat monthly fee of $20.00 for service plus $0.14 per kilowatt-hour of electricity used.

The equation will be written as,

B = 20 + 0.14K

85.78 = 20 + 0.14k

k = ( 80.78 - 20 ) / 0.14

K = 65.78 / 0.14

K = 470 Kilowatt-hour

Therefore, the power utilised by frank in the month of march is 470 kilowatts - per hour.

To know more about an expression follow

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Answer:

322.21 feet

Step-by-step explanation:

Flying rate = 6 ft/s

Angle of depression from his balloon to a friend's car= 35 °

One and half minutes later, he observed the angle of depression to be 39°

Time = 1 mins 1/2 seconds

= 3/2 mins

= 3/2 * 60

= 3*30

= 90 secs

Speed = distance /time

Distance = speed * time

= 6*90

= 540 ft

The angle on the ground = 180° - 35° - 39°

= 180° - 74°

= 106°

Let the distance between him and his friend be x

Using sine rule

x/sin 35 = 540/sin 106

x = (540sin 35) / sin 106

x = 322.21ft

Answer: population; independently

Step-by-step explanation:

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same *population* and each element is selected *independently*.

Each element in a random sample is selected independently and comes from the same population, with the principle goal of achieving representation and independence in sample selection.

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same population and each element is selected independently. The crux of random sampling theory is ensuring each member of the population has an equal chance of being selected, maintaining the independence of each selection. For example, if a student wanted to make a study group out of a class of 31 students, she could write each student's name on a separate piece of paper, put all the names in a hat, and pick out three without looking. This is a classic case of simple random sampling, each selection being representative and independent.

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The probability of having 0 typographical errors on an article of 10 pages is approximately 0.8187. The probability of having 2 or more errors is approximately 0.0176.

To find the probability of certain events happening, we can use the Poisson distribution. In this case, the Poisson distribution can be used to model the number of typographical errors on a page. The parameter of the Poisson distribution, lambda (λ), is equal to the expected number of errors on each page, which is 0.2.

(a) To find the probability of 0 errors on an article of 10 pages, we can use the Poisson distribution with λ = 0.2 and x = 0. We can plug these values into the formula:

P(X = x) = (e^-λ * λ^x) / x!

So for (a), the probability is:

P(X = 0) = (e^-0.2 * 0.2^0) / 0! = e^-0.2 ≈ 0.8187

(b) To find the probability of 2 or more errors on an article of 10 pages, we can calculate the complement of the probability of 0 or 1 errors. The complement is 1 minus the sum of the probabilities of 0 and 1 errors:

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1) ≈ 1 - 0.8187 - (e^-0.2 * 0.2^1) / 1! ≈ 1 - 0.8187 - 0.1637 ≈ 0.0176

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Using the Poisson distribution with λ = 0.2, we find the probability of 0 errors on a page and 2 or more errors in a 10-page article, offering insightful predictions.

The given situation involves a Poisson distribution, as it deals with the number of events (typographical errors) occurring in a fixed interval of time or space. The expected number of errors per page is λ = 0.2, and the total number of pages is 10.

(a) To find the probability of 0 errors on a page, we use the Poisson probability mass function:

P(X = k) = (e^(-λ) * λ^k) / k!

For k = 0:

P(X = 0) = (e^(-0.2) * 0.2^0) / 0!

Solving this gives the probability of having 0 errors on a single page.

(b) To find the probability of 2 or more errors, we sum the probabilities for k = 2, 3, ..., up to the total number of pages (10):

P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)

This accounts for the complement probability that there are 0 or 1 errors, leaving us with the probability of 2 or more errors on at least one page.

In summary, the Poisson distribution helps model the likelihood of different numbers of typographical errors on a page, providing a useful tool for analyzing such scenarios.

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Answer:

The margin of error is multiplied by [tex]\sqrt{2}[/tex]

Step-by-step explanation:

margin of error (ME) from the mean can be calculated using the formula

ME=[tex]\frac{z*s}{\sqrt{N} }[/tex] where

Since margin of error is proportional with inverse of [tex]\sqrt{N}[/tex],

if we cut the sample size in half, the margin of error is multiplied by [tex]\sqrt{2}[/tex].

Cutting the sample size in half increases the margin of error. The new margin of error will be approximately 1.414 times larger than the original margin of error. Essentially, this effect multiplies the margin of error by 2.

If you cut the sample size in half, the margin of error will increase. The margin of error is inversely proportional to the square root of the sample size. Specifically, the margin of error is multiplied by the square root of the ratio of the original sample size to the new sample size.

Mathematically, if the original sample size is N and the new sample size is N/2, the margin of error (MOE) changes as follows:

Since √(N/2) = √(N) / √(2), the new margin of error will be:

New MOE = Original MOE × √(2) approximately equal to Original MOE × 1.414.

Therefore, cutting the sample size in half multiplies the margin of error by 1.414, roughly 2 times.

Complete Question:

All else being equal, if you cut the sample size in half, how does this affect the margin of error when using the sample to make a statistical inference about the mean of the normally distributed population from which it was drawn? ME= 2·5/√(n) . The margin of error is multiplied by √(0.5)· The margin of error is multiplied by √(2)· The margin of error is multiplied by 0.5. The margin of error is multiplied by 2.

Answer:

x=2

Step-by-step explanation:

9-10x=2x+1-8x

9-10x=1-6x

8=4x

x=2

Combine like terms in the equation 9 − 10x = 2x + 1 − 8x to simplify it to 9 − 10x = −6x + 1. Rearranging the equation to -4x = -8 and dividing by -4, we find that x = 2.

The solution for x in the equation 9 − 10x = 2x + 1 − 8x can be found by first combining like terms on both sides of the equation.

On both the left and right side, the terms involving x are −10x and 2x − 8x respectively. After combining, the equation simplifies to 9 − 10x = −6x + 1.

Then, we can solve for x by shifting terms around. Getting all x-terms on one side and constant terms on the other side, we get -10x + 6x = 1 - 9. This simplifies to -4x = -8.

Finally, dividing the equation by -4 which is the coefficient of x, we obtain the solution x = 2.

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Answer:

Compount interest earns more. Difference between 2 interest is $92 445.39

Step-by-step explanation:

Simple Interest:

[tex]I = \frac{prt}{100} [/tex]

p = $10000

r = 3%

t = 2years

I = (10000×3×2)/100

= $600

Total amount = $10 600

Compound Interest:

[tex]A = p( {1 + \frac{r}{100}) }^{n} [/tex]

p = $100000

r = 3/730 (daily)

t = 730 (2yrs)

A = 100000[1+(3/73000)]^730

= $103 045.39 (2d.p)

Difference = $103045.39 -

$10600

= $92 445.39

(Correct me if i am wrong)

Answer:8.45

Step-by-step explanation:

Answer: 95% confidence interval for the proportion of yellow is (0.125,0.275).

Step-by-step explanation:

Since we have given that

n = 22+22+22+12+15+15=108

x = yellow = 22

So, [tex]\hat{p}=\dfrac{22}{108}=0.20[/tex]

We need to find the 95% confidence interval.

So, z = 1.96

So, Interval would be

[tex]\hat{p}\pm z\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\\\\=0.20\pm 1.96\times \sqrt{\dfrac{0.2\times 0.8}{108}}\\\\=0.20\pm 0.075\\\\=(0.20-0.075, 0.20+0.075)\\\\=(0.125, 0.275)[/tex]

Hence, 95% confidence interval for the proportion of yellow is (0.125,0.275).

Answer:

Step-by-step explanation:

12) A(x, 5) and B(-4,3)

slope = -1

We want to determine the value of x so that the line AB is parallel to another line whose slope is given as -1

Slope, m is expressed as change in y divided by change in x. This means

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= 3

y1 = 5

x2 = -4

x1 = x

Slope = (3-5) / (-4-x) = -2/-4-x

Recall, if two lines are parallel, it means that their slopes are equal. Since the slope of the parallel line is -1, therefore

-2/-4-x = -1

-2 = -1(-4-x)

-2 = 4 + x

x = -2 - 4 = - 6

x = -6

13) R(3, -5) and S(1, x)

slope = -2

We want to determine the value of x so that the line RS is parallel to another line whose slope is given as -2

Slope = (y2 - y1)/(x2 - x1)

From the information given

y2= x

y1 = -5

x2 = 1

x1 = 3

Slope = (x - -5) / (1 - 3) = (x+5)/-2

Since the slope of the parallel line is -2, therefore

(x+5)/-2 = -2

x + 5 = -2×-2

x + 5 = 4

x = 4 - 5 = - 1

Answer:

In a one-way ANOVA, the [tex]SS_{within}[/tex] is calculated by taking the squared difference between each person and their specific groups mean, while the [tex]SS_{between}[/tex] is calculated by taking the squared difference between each group and the grand mean.

Step-by-step explanation:

The one-way analysis of variance (ANOVA) is used "to determine whether there are any statistically significant differences between the means of two or more independent groups".

The sum of squares is the sum of the square of variation, where variation is defined as the spread between each individual value and the mean.

If we assume that we have p groups and each gtoup have a size [tex]n_j[/tex] then we have different sources of variation, the formulas related to the sum of squares are:

[tex]SS_{total}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 [/tex]

A measure of total variation.

[tex]SS_{between}=\sum_{j=1}^{p} n_j (\bar x_{j}-\bar x)^2 [/tex]

A measure of variation between each group and the grand mean.

[tex]SS_{within}=\sum_{j=1}^{p} \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 [/tex]

A measure of variation between each person and their specific groups mean.

Chain rule when it's one function inside another.

d/dx f(g(x)) = f’(g(x))*g’(x)

Product rule when two functions are multiplied side by side.

d/dx f(x)g(x) = f’(x)g(x) + f(x)g’(x)

Final answer:

The chain rule is used when you have a composite function, while the product rule is used when you have a product of two functions.

Explanation:

The chain rule and product rule are both rules used in calculus to differentiate functions.

The chain rule is used when you have a composite function, where one function is inside another function. To differentiate a composite function, you multiply the derivative of the outer function by the derivative of the inner function.

For example, if you have y = f(g(x)), where f(x) and g(x) are functions, the chain rule states that dy/dx = f'(g(x)) * g'(x).

The product rule is used when you have a product of two functions. To differentiate a product, you take the derivative of the first function times the second function, plus the first function times the derivative of the second function.

For example, if you have y = f(x) * g(x), the product rule states that dy/dx = f'(x) * g(x) + f(x) * g'(x).

Answer:

[tex]\frac{7}{120}[/tex]  of seed planted in each flower pot.

Step-by-step explanation:

Given:

Total number of marigold seeds packages Trixie have=  ¾

Number of  seeds Trixie planted in the garden=  1/6

Number of fraction into which Trixie dived the remaining seed =10

To Find:

Fraction of seed planted in each flower pot=?

Solution:

Seed left after planting  1/6 of seeds in the garden = [tex]\frac{3}{4}-\frac{1}{6}[/tex]

=>[tex]\frac{18-4}{24}[/tex]

=>[tex]\frac{14}{24}[/tex]

=>[tex]\frac{7}{12}[/tex]

Now Trixie divides these remaining seeds into 10 parts

=>[tex]\frac{\frac{7}{12} }{10}[/tex]

=>[tex]\frac{7}{12}\times\frac{1}{10}[/tex]

=>[tex]\frac{7}{120}[/tex]

Answer:

Your answer id D.

Step-by-step explanation:

PLEASE MARK BRAINLIEST!!!

Answer:

[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]

Step-by-step explanation:

Given that a presidential candidate claims that the proportion of college students who are registered to vote in the upcoming election is at least 62% .

Let p be the proportion of college students who are registered to vote in the upcoming election

we have to check the claim whether p is actually greater than or equal to 62%

For this a hypothesis to be done by drawing random samples of large size from the population.

The hypotheses would be the proportion is 0.62 against the alternate that the proportion is greater than or equal to 0.62

[tex]H_0: p =0.62\\H_a: p\geq 0.62[/tex]

(right tailed test at 5% level)

Answer:

416025

Step-by-step explanation:

For confidence interval of 99%, the range is (0.005, 0.995). Using a z-table, the z-score for 0.995 is 2.58.

Margin of error = 0.2% = 0.002.

Proportion is unknown. So, worse case proportion is 50%. p = 50% = 0.5.

\\ [tex]n = \left(\frac{\texttt{z-score}}{\texttt{margin of error}} \right )^2\cdot p\cdot (1-p) \\ = \left(\frac{2.58}{0.002} \right )^2\cdot 0.5\cdot (1-0.5)=416025[/tex]

So, sample size required is 416025.

Answer:

Step-by-step explanation:

y = (-1/4)x - 4 has a y-intercept of (0, -4).  Place a dark dot at (0, -4).  

Now we use the info from the slope, -1/4:

Starting with your pencil point on the dot (0, -4), move the pencil point 4 units to the right and then 1 unit down.  You will now be at (4, -5).  Place a dark dot there.  

Then draw a straight, solid line through (0, -4) and (4, -5).

Answer:

  There is no error

Step-by-step explanation:

While it is not necessary to guess an answer, because the answer can be calculated using the properties of equality, guessing is a legitimate solution method actually taught in (some) schools these days.*

The equation is properly written, data properly filled in, and the solution properly verified. There is no error.

_____

* What doesn't seem to be taught in US schools are methods of refining an incorrect guess. These are actually well-developed, and are legitimate ways to get to a good answer.

Final answer:

The correct formula to find the current is I = P ÷ V, which gives 0.5 amps for a 60W lightbulb at 120V. The error in the calculation is in Step 1 where the formula was not rearranged to solve for current.

Explanation:

The calculation for determining the current drawn by a 60-watt (W) lightbulb with a voltage supply of 120 volts (V) requires use of the power formula, which relates power (P), voltage (V), and current (I): P = V × I, where P stands for power in watts, V for voltage in volts, and I for current in amperes (amps).

In this scenario, the correct step to find the amperage of the bulb would be to rearrange the power formula to solve for current (I): I = P ÷ V. By inserting the known values, we get I = 60 W ÷ 120 V, which simplifies to I = 0.5 amps.

The error in the intern's calculation is in Step 1, as the formula written should be amps = watts ÷ volts, not volts × amps = watts as it needs to be rearranged to solve for the unknown current.

Final answer:

The value of a car worth $18,500 that loses 10.3% annually decreases by approximately $158.8 per month.

Explanation:

To find the approximate monthly decrease in value of a car worth $18,500 that loses 10.3% of its value every year, we first calculate the annual decrease and then divide by 12 to get the monthly decrease.

The annual decrease is calculated as 10.3% of $18,500, which is:

0.103 imes $18,500 = $1,905.50 per year.

To find the monthly decrease, we divide the annual decrease by 12:

$1,905.50 \/ 12 \\approx $158.79 per month.

Therefore, the car's value decreases approximately $158.8 per month.

Answer:

(a)€2048

(b)€4095

Step-by-step explanation:

So the amount of money we would save at nth month is

[tex]2^{n-1}[/tex] where n = 1, 2, 3, 4, ...

At the 12th month, meaning n = 12, we would save

[tex]2^{12-1}[/tex] = €2048 for that month

The total amount we would save in a year is

1 + 2 + 4 + 8 + 16 + ... + 2048

[tex]2^{n} - 1 = 2^{12} - 1 [/tex] = €4095

Answer:

[tex]y = (-2)(x + 2)^2 - 4[/tex].

Step-by-step explanation:

The vertex form of a quadratic function is in the form

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

where

In this question, the vertex of this quadratic function is at the point [tex](-2, -4)[/tex]. In other words, [tex]h = (-2)[/tex] and [tex]k = (-4)[/tex]. Substitute these value into the general equation:

[tex]y = a (x - (-2))^2 +(- 4)[/tex].

Simplify to obtain:

[tex]y = a (x + 2)^2 - 4[/tex].

The only missing piece here is the coefficient [tex]a[/tex]. That's likely why the problem gave [tex](-1, -6)[/tex], yet another point on this quadratic function. If this function indeed contains the point [tex](-1, -6)[/tex], [tex]y[/tex] should be equal to [tex](-6)[/tex] when [tex]x = (-1)[/tex]. That is:

[tex]-6 = a(-1 + 2)^2 -4[/tex].

Solve this equation for [tex]a[/tex]:

[tex]a = -6 - (-4) = -2[/tex].

Hence the equation of the quadratic function in its vertex form:

[tex]y = (-2)(x + 2)^2 - 4[/tex].

The quadratic function in vertex form that the student is looking for is f(x) = -2(x+2)² - 4. We obtained this by substituting the given vertex (-2, -4) and the point (-1, -6) into the general form of a vertex form quadratic function.

The question is asking us to find the equation of a quadratic function, also known as a second-order polynomial, in vertex form. The vertex form of a quadratic function can be written as f(x) = a(x-h)² + k, where (h, k) is the vertex and 'a' is a non-zero number.

The vertex is given as (-2, -4). Therefore, h = -2 and k = -4. The equation becomes f(x) = a(x+2)² - 4. We also know that the graph passes through the point (-1, -6), which we can substitute into the equation to get: -6 = a(-1 + 2)² - 4. We solve this equation for 'a', and find that a = -2. Therefore, the quadratic function in vertex form is f(x) = -2(x+2)² - 4.

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Answer:

B) The diagonals of the parallelogram are congruent.

Step-by-step explanation:

Since, If the diagonals of a parallelogram are equal in length, then is the parallelogram a rectangle.

For proving this statement.

Suppose PQRS is a parallelogram such that AC = BD,

In triangles ABC and BCD,

AB = CD,   ( opposite sides of parallelogram )

AD = CB,   ( opposite sides of parallelogram )

AC = BD ( given ),

By SSS congruence postulate,

[tex]\triangle ABC\cong \triangle BCD[/tex]

By CPCTC,

[tex]m\angle ABC = m\angle BCD[/tex]

Now, Adjacent angles of a parallelogram are supplementary,

[tex]\implies m\angle ABC + m\angle BCD = 180^{\circ}[/tex]

[tex]\implies m\angle ABC + m\angle ABC = 180^{\circ}[/tex]

[tex]\implies 2 m\angle ABC = 180^{\circ}[/tex]

[tex]\implies m\angle ABC = 90^{\circ}[/tex]

Since, opposite angles of a parallelogram are congruent,

[tex]\implies m\angle ADC = 90^{\circ}[/tex]

Similarly,

We can prove,

[tex]m\angle DAB = m\angle BCD = 90^{\circ}[/tex]

Hence, ABCD is a rectangle.

That is, OPTION B is correct.

Answer:

B

Step-by-step explanation:

I just took it

Answer:

  x⁵ +x⁴ +x³ +x² +x +1

Step-by-step explanation:

Your expression matches the pattern with n=6, so fill in that value of n in the quotient the pattern shows:

  [tex]\dfrac{x^6-1}{x-1}=x^5+x^4+x^3+x^2+x+1[/tex]

Answer: Our required probability is 0.11.

Step-by-step explanation:

Since we have given that

Number of workers in first shift = 21

Number of workers in second shift = 15

Number of workers in third shift = 13

We need to find the probability of choosing exactly two second shift workers and two third shift workers.

So, it becomes,

[tex]\dfrac{^{15}C_2\times ^{13}C_2\times ^{21}C_4}{^{49}C_8}\\\\=0.11[/tex]

Hence, our required probability is 0.11.

The probability question asks to determine the chance of choosing two second shift and two third shift workers from a warehouse workforce. Combinations are used to calculate the number of ways to select the workers, and the probability is found by dividing the desired combination by the total number of ways to choose eight workers.

The question involves calculating the probability of choosing a specific combination of warehouse workers from different shifts for interviews. There are a total of 49 workers (21 first shift, 15 second shift, and 13 third shift). To find the probability of choosing exactly two second shift workers and two third shift workers, we need to consider the total number of ways to choose eight workers and the number of ways to choose two workers from each of the specified shifts.

The probability of selecting exactly two second shift workers is calculated as the combination of 2 from 15, and the probability of selecting exactly two third shift workers is the combination of 2 from 13. Since we're choosing 8 workers in total, we also have to choose the remaining 4 workers from the first shift, which can be done in combinations of 4 from 21. The probability is then calculated by dividing these combinations by the total number of ways 8 workers can be chosen from all 49 workers.

To calculate the combinations, we use the combination formula C(n, k) = n! / (k!(n-k)!). Then the overall probability is a fraction where the numerator is the product of the combinations for each selection and the denominator is the combination of 8 from 49.

Answer:

65.56°

Step-by-step explanation:

We know that if we take dot product of two vectors then it is equal to the product of magnitudes of the vectors and cosine of the angle between them

That is let p and q be any two vectors and A be the angle between them

So, p·q=|p|*|q|*cosA

⇒[tex]cosA=\frac{u.v}{|u||v|}[/tex]

Given u=-8i-3j and v=-8i+8j

[tex]|u|=\sqrt{(-8)^{2}+ (-3)^{2}} =8.544[/tex]

[tex]|v|=\sqrt{(-8)^{2}+ (8)^{2}} =11.3137[/tex]

let A be angle before u and v

therefore, [tex]cosA=\frac{u.v}{|u||v|}=\frac{(-8)*(-8)+(-3)*(8)}{8.544*11.3137} =\frac{40}{96.664}[/tex]

⇒[tex]A=arccos(\frac{40}{96.664} )=arccos(0.4138 )=65.56[/tex]

Therefore angle between u and v is 65.56°

Answer:

420 ft

Step-by-step explanation:

The given equation of a parabola is

[tex]y=630[1-\left(\frac{x}{290}\right)^{2}][/tex]

An arch is 630 ft high and has 580=ft base.

Find zeroes of the given function.

[tex]y=0[/tex]

[tex]630[1-\left(\frac{x}{290}\right)^{2}]=0[/tex]

[tex]1-\left(\frac{x}{290}\right)^{2}=0[/tex]

[tex]\left(\frac{x}{290}\right)^{2}=1[/tex]

[tex]\frac{x}{290}=\pm 1[/tex]

[tex]x=\pm 290[/tex]

It means function is above the ground from -290 to 290.

Formula for the average height:

[tex]\text{Average height}=\dfrac{1}{b-a}\int\limits^b_a f(x) dx[/tex]

where, a is lower limit and b is upper limit.

For the given problem a=-290 and b=290.

The average height of the arch is

[tex]\text{Average height}=\dfrac{1}{290-(-290)}\int\limits^{290}_{-290} 630[1-\left(\frac{x}{290}\right)^{2}]dx[/tex]

[tex]\text{Average height}=\dfrac{630}{580}[\int\limits^{290}_{-290} 1dx -\int\limits^{290}_{-290} \left(\frac{x}{290}\right)^{2}dx][/tex]

[tex]\text{Average height}=\dfrac{63}{58}[[x]^{290}_{-290}-\frac{1}{84100}\left[\frac{x^3}{3}\right]^{290}_{-290}][/tex]

Substitute the limits.

[tex]\text{Average height}=\dfrac{63}{58}\left(580-\frac{580}{3}\right)[/tex]

[tex]\text{Average height}=\dfrac{63}{58}(\dfrac{1160}{3})[/tex]

[tex]\text{Average height}=420[/tex]

Therefore, the average height of the arch is 420 ft above the ground.

The average height of the arch above the ground is approximately  420 feet.

To find the average height of the arch, we need to find the average value of this function over the interval x=0 to x=580 (the base of the arch).

[tex]\[ \text{Average height} = \frac{1}{580 - 0} \int_{0}^{580} 630 \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \int_{0}^{580} \left(1 - \left(\frac{x}{290}\right)^2\right) \, dx \]\[ = \frac{630}{580} \left(x - \frac{1}{3} \cdot \frac{x^3}{290^2}\right) \Bigg|_{0}^{580} \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2} - 0\right) \][/tex]

[tex]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ = \frac{630}{580} \left(580 - \frac{1}{3} \cdot \frac{580^3}{290^2}\right) \]\[ \approx \frac{630}{580} \times 420 \]\[ \approx 420 \text{ ft} \][/tex]

Calculate the mean and standard deviation for the binomial distribution, adjust for continuity correction, find the z-score, and use the standard normal distribution to estimate the probability of scoring at least 10 correct out of 47 purely guessed multiple-choice questions.

To estimate the probability of a student guessing and scoring at least 10 correct answers out of 47 multiple-choice questions using normal approximation to binomial distribution, we start by finding the mean ( extmu) and standard deviation ( extsigma) of the binomial distribution. Since each question has five options, the probability of guessing a question correctly (p) is 1/5, and the probability of guessing incorrectly (q) is 4/5.

The expected number of correct answers (mean) is  extmu = np = 47(1/5) = 9.4, and the variance ( extsigma^2) is npq = 47(1/5)(4/5) = 7.52. So, the standard deviation is  extsigma =  extsqrt{7.52}.

To apply the continuity correction, we adjust the score of 10 down by 0.5, giving us a z-score. The z-score is calculated by (X -  extmu)/ extsigma, where X is the adjusted score. Finally, we use the standard normal distribution to find the probability associated with this z-score, which will yield the likelihood of the student scoring at least 10 correct answers.

Answer: y = x + 4

Step-by-step explanation:

Let "y" be the total number of gallons in the tank, and let "x" be the total number of unfilled gasoline.

Since we already have an initial "4 gallons" in the tank, the total capacity of the tank will be "x + 4".

Answer:

A y=4+x

Step-by-step explanation:

For this case we have that by definition, the equation of a line in the point-slope form is given by:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

m: It is the slope of the line

[tex](x_ {0}, y_ {0})[/tex]: It is a point that belongs to the line

According to the statement we have the following point:

[tex](x_ {0}, y_ {0}): (- 10,8)[/tex]

Substituting we have:

[tex]y-8 = m (x - (- 10))\\y-8 = m (x + 10)[/tex]

Thus, the most appropriate option is option C. Where the slope is[tex]m = -0.2[/tex]

Answer:

Option C