Round to the nearest integer 31.4829

The standard form equation of the ellipse with vertices (0, ±4) and co-vertices (±2, 0) is (x²/4) + (y²/16) = 1.

To find the standard form equation of an ellipse, we use the equation (x²/a²) + (y²/b²) = 1, where a and b are the semi-major and semi-minor axes, respectively.

Since the vertices are (0, ±4), the distance between them is 2a = 8, giving us a = 4. Similarly, the co-vertices are (±2, 0), and the distance between them is 2b = 4, resulting in b = 2.

Plugging in the values for a and b, we get (x²/(2²)) + (y²/(4²)) = 1, which simplifies to (x²/4) + (y²/16) = 1.

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The required percentage of regular grade gasoline are;

a) 34%

b) 95.5%

c)4.5%

(a) To determine the percentage of regular grade gasoline sold between $3.25 and $3.65 per gallon, we need to find the proportion of the data that falls within this range. Assuming a bell-shaped distribution, we can use the standard deviation and mean to find the z-scores for these two prices, and then look up the cumulative probability in a standard normal table.

$3.25$ is $1$ standard deviation below the mean and $3.65$ is $0.5$ standard deviation above the mean.

Using a standard normal table, we find that approximately 68% of the data falls within one standard deviation of the mean, and approximately 34% falls between $-0.5$ and $0.5$ standard deviations.

Therefore, approximately 34% of regular grade gasoline is sold between $3.25 and 3.65 per gallon.

(b) To find the percentage of regular grade gasoline sold between $3.25 and $3.85 per gallon, we need to find the cumulative probability for the range $3.25$ to $3.85$.

$3.85$ is $1.5$ standard deviations above the mean.

Using a standard normal table, we find that approximately 95.5% of the data falls within $1.5$ standard deviations of the mean.

Therefore, approximately 95.5% of regular grade gasoline is sold between $3.25 and $3.85 per gallon.

(c) To find the percentage of regular grade gasoline sold for more than $3.85 per gallon, we need to find the cumulative probability for values greater than $3.85$.

Using a standard normal table, we find that approximately 100% - 95.5% = 4.5% of the data falls above $1.5$ standard deviations from the mean.

Therefore, approximately 4.5% of regular grade gasoline is sold for more than $3.85 per gallon.

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Yes, it would be feasible to combine both fixed-length and variable-length formats in a single disk. Variable-length fields can be more difficult to read and write, as the positions of the fields are not fixed.

The reason for this is that both fixed-length and variable-length formats have their own advantages and disadvantages. Fixed-length fields are easier to read and write because the positions of the fields are fixed, and this can also make searching for data faster. However, fixed-length fields can also lead to wasted space if the data in a field is smaller than the allotted space.

In addition to the advantages and disadvantages of fixed-length and variable-length formats, there are also other factors to consider when deciding whether to combine both formats in a single disk. These factors include the nature of the data being stored, the size of the disk, and the performance requirements of the system. For example, if the data being stored consists mainly of records with a large number of fixed-length fields, it may not make sense to use variable-length fields, as the potential space savings may not be significant. On the other hand, if the data being stored consists mainly of records with a small number of fields, variable-length fields may be more appropriate.

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To estimate the standard deviation using the range rule of thumb, we need to find the range of the data set and divide it by 4.

In this case, the range is the difference between the highest and lowest heights, which is cm. Dividing by 4 gives us an estimate of the standard deviation of cm.
Comparing this estimate to the actual standard deviation of cm calculated from the data set, we can see that the estimate is off by quite a bit. This suggests that the range rule of thumb is not a very accurate method for estimating standard deviation.
In fact, the range rule of thumb is only accurate for data sets that are roughly bell-shaped and symmetrical, which may not be the case for body measurements. To get a more accurate estimate of standard deviation, we would need to use a more sophisticated statistical method.
Overall, the result suggests that we need to be cautious when using the range rule of thumb to estimate standard deviation, especially when working with data that is not well-behaved or that has outliers.

To estimate the standard deviation (s) using the range rule of thumb with body measurements, we first need the range of the heights of males provided in the dataset. Unfortunately, the low and high values in centimeters were not included in the question. However, I can explain the process step by step, and you can plug in the correct values to determine the accuracy of the estimate.
Step 1: Calculate the range
Range = High value (in cm) - Low value (in cm)
Step 2: Apply the range rule of thumb
Estimated standard deviation (s) = Range / 4
Step 3: Compare the estimated standard deviation to the given standard deviation (in cm)
Compare the estimated s value from Step 2 to the given standard deviation of cm (again, the value was not provided in the question).
Step 4: Determine the accuracy of the estimate
If the difference between the estimated s and the given standard deviation is within the specified cm (not provided in the question), then the estimate is considered accurate.
By following these steps and inputting the correct values, you can determine whether the range rule of thumb provides an accurate estimate for the standard deviation (s) of male heights in the body measurements dataset.

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The range rule of thumb provides a rough estimate of the standard deviation of data. By comparing the estimated and actual standard deviations, we can determine the accuracy of this rule for the given data set. If the estimated standard deviation is within n cm of the actual one, the estimate is considered accurate.

The range rule of thumb is a rule that provides a rough estimate of the standard deviation of a set of data. We can find it by dividing the range of the data (the difference between the largest and smallest data values) by 4. Thus, if the lowest height is cm and the highest is cm, then the estimated standard deviation ' would be ( − ) / 4.

Comparing this estimated standard deviation ' to the actual standard deviation calculated using the heights can provide a rough idea of how well the range rule of thumb works for this data set. If ' is within cm of , then the estimate can be considered accurate. If not, it suggests that the range rule of thumb may not provide a very accurate estimate for this particular data set.

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Answer:

The answer is DF

Step-by-step explanation:

The opposite side is 4 or EF, so the ADJACENT side would be 3 or DF according to SOH CAH TOA.

The outputs for the given three cases are

\(y1(t) = e−t.u(t), y2(t) = y(t), and y3(t) = 0.\)

Solution:(1) Given input x1(t) and impulse response \(h1(t)x1(t)=e−2(t−2)u(t−2) and h1(t)=e−(t−1)u(t−1)\)

By Shifting property of convolution integral, we havey\(1(t) = x1(t)* h1(t) = ∫∞−∞ x1(τ)h1(t−τ)dτy1(t) = ∫∞−∞ e−2(τ−2)u(τ−2).e−(t−τ−1)u(t−τ−1)dτ\)for \(t ≥ 2\)

Taking \(τ′ = τ − 2\), we getτ =\(y1(t) = ∫∞−∞ e−2τ′u(τ′).e−(t−τ′−3)u(t−τ′−3)dτ′ for t ≥ 2y1(t) = e−t.u(t)\)

Hence, output y1(t) = e−t.u(t)(2)

Given input x2(t) and impulse response\(h1(t)x2(t)=e−2tu(t−2) and h1(t) = h(t)\)

By Time-invariance property of LTI systems, we havey\(2(t) = x2(t)* h1(t) = x2(t)* h(t) = y(t) (as h(t) = impulse response)\)

Hence, output\(y2(t) = y(t)(3)\)

Given input x3(t) and impulse response\(h3(t)x3(t)=x(t) and h3(t)=e−(t−1)u(t)\)

By Shifting property of impulse integral, we havey\(3(t) = x(t)* h3(t) = ∫∞−∞ x(τ)h3(t−τ)dτy3(t) = ∫∞−∞ x(τ)e−(t−τ−1)u(t−τ−1)dτ\)

Using\(x(t) = e−2tu(t)\)and \(u(t − τ − 1) = u(τ + 1 − t)y3(t) = ∫∞−∞ e−2τu(τ).e−(t−τ−1)u(τ+1−t)dτf\)

Hence, output \(y3(t) = 0\)

Therefore, the outputs for the given three cases are \(y1(t) = e−t.u(t), y2(t) = y(t), and y3(t) = 0.\)

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The result in scientific notation is 2 x 10³.

Given,

(5 × 10^-3) (4 × 10^5)

We need to write in scientific notation.

What is scientific notation?

When a large number is written between 1 and 10 with a power of 10.

Multiply (5 × 10^-3) (4 × 10^5).

= (5 x 1/10^3)x (4 x 100000)

= 5 / 1000 x 4 x 100000

=  20 x 100

= 2 x 1000

= 2 x 10³

2 is a number between 1 and 10 and 10^3 is a power of 10.

Thus the result in scientific notation is 2 x 10³.

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Answer:

Idek this

Step-by-step explanation:

Answer:

275 = 25 × 11

The greatest perfect square factor of 275 is 25.

The greatest perfect square that is a factor of 275 is 25.We were able to determine this by breaking down 275 into its prime factors and looking for pairs of factors that were the same.

We can break down 275 into its prime factors to help us determine the greatest perfect square that is a factor of 275.275 = 5 * 5 *11. Since a perfect square is the product of a number multiplied by itself, we need to look for pairs of prime factors that are the same. We can see that 5 is a repeated factor, which means that it is a perfect square. So, we can take out a pair of 5s and get:$$275 = 5 \times 5 \times 11 = 5^2 \times 11$$Therefore, the greatest perfect square that is a factor of 275 is 25.

we have found that the greatest perfect square that is a factor of 275 is 25. Since 5 was a repeated factor, we were able to take out a pair of 5s and get 5 squared, which is 25.

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Answer:

see below

Step-by-step explanation:

you multiply bottom to find their LCM, which is the short form for “Least Common Multiple.” The least common multiple is defined as the smallest multiple that two or more numbers have in common.

then you convert fractions into  improper fractions. An improper fraction is a fraction whose numerator is equal to or greater than its denominator.

now that they have a common denominator, you just add the top up

then simplify

Answer:

f(n) = 32 - 8n

Step-by-step explanation:

24, 16, 8, 0

f(n) = 24 - 8 x (n-1)

f(n) = 32 - 8n

Answer:

2c + 3b= $

Step-by-step explanation:

if they make 2 dollars for every cupcake and 3 dollars for every brownie they just need to plug in however many cupcakes into C and however many brownies to B to find their product

Answer:

the first phot is correct becuase thh way she sets it up shows the right way to set up a number line.

Step-by-step explanation:

The fewest number of swaps needed to reverse the list is  2

This is further explained below.

Generally,  In the field of computer science, a data structure known as an array sometimes referred to simply as an array, is one that is composed of a collection of items, each of which is distinguished by at least one array index or key. An array is saved in such a way that a mathematical formula may use the index tuple of each element to determine the location of that element within the array.

Given an array with values 5, 10, 15, 20, 25

Swaps did reverse the array are

Therefore, the number of swaps necessary to invert the list is two. This is the smallest possible number.

In conclusion,  Two exchanges are the bare minimum required to accomplish the list's reversal.

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Answer:

Width x length

Step-by-step explanation:

Find the width or how wide it is

Then find the length or how long it is

multiply those

Answer:

i think it's congruent .

Step-by-step explanation:

Answer:

complementary i believe

Step-by-step explanation:

smoovin

Answer: 9 inch

Step-by-step explanation:

Given

Distance between city A and city B is 540 miles

Scale on the map is 1 inch: 60 miles i.e. 1 inch on the map is equivalent to 60 miles in the real situation

suppose the distance between city A and B on the map is x

\(\therefore \dfrac{1}{60}=\dfrac{x}{540}\\\\\Rightarrow x=\dfrac{540}{60}=9\ in.\)

Therefore, the distance between city A and B is 9 in.

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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The value of 'x' in x² - 50 = 0 is either - 7.07 or + 7.07.

A quadratic equation is an algebraic expression in the form of variables and constants.

A quadratic equation has two roots as its degree is two.

Given, A quadratic equation x² - 50 = 0, where x belongs to R.

x² = 50.

x = ± √50.

x = ± 7.07.

So, The value of x can be - 7.07 or it can be + 7.07 squaring both numbers will result to approximately 50.

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The requried solution of the given expression is given as x = 7.07, -7.07.

Zeros of an equation are defined as the value of the independent variable where the equation or function gives zero.

Here,
Given expression,
x² - 50 = 0
x² = 50
x = √50
x = ±7.07

Thus, the requried solution of the given expression is given as x = 7.07, -7.07.

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Because angle OPT is a straight angle (PO is perpendicular to QR), angle OTS must be 90° - 15° = 75°.

What is diameter?

Any straight line segment with an endpoint on the circle and that travels through its center is considered a circle's diameter in geometry. The longest chord of a circle is another way to describe it. The diameter of a sphere can be defined using either concept.

The diameter is the length of the line that runs tangent to the circle's two points at either end. Diameter is length if you consider length to be the separation between two points. The distance between a circle's two furthest points is known as its diameter.

We may utilize the properties of angles in a circle and right triangles to solve the problem.

First, we see that angle OPS is a circle-inscribed angle, and because it intersects the diameter QR, it must be a right angle.

Next, we'll look at the right triangle OPS. Because we know that OPS is 75°, the other acute angle is 90° - 75° = 15°. Because angle OPT is a straight angle (PO is perpendicular to QR), angle OTS must be 90° - 15° = 75°.

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well, we know the cash price, that is, if you have cash burning your pockets, is R6900 bucks, however you'd rather do it in installments, or hire purchase with a downpayment of 15% of 6900, hmmm how much is that?

\(\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{15\% of 6900}}{\left( \cfrac{15}{100} \right)6900}\implies 1035\)

now, to that downpayment let's add the 12 installments of R558.50

\(\stackrel{downpayment}{1035}~~ + ~~\stackrel{ installments }{(12)(588.50)}\implies 1035+6702\implies \text{\LARGE 7737}\)

ohhh man!!! you ended up paying 7737 - 6900 = 837 more on hire purchase.

The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.

The stress tensor σ given in the problem is:

σ = 201504−400−1500−1010

The normal stress is given by

σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ

where

θ = 30°

θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)

σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)

σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)

σn = 12−15√3+4√3

σn = 16−15√3

The normal stress is σn = 16−15√3

The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11

σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ

where

θ = 30°

θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)

τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)

τ = 4(1/2)+0.5(35)(√3/2)

τ = 2+15√3/4

The shear stress is τ = 2+15√3/4

Maximum shear stress
The maximum shear stress is given by

τmax = 0.5(σ1−σ2)

whereσ1σ1 andσ2σ2 are the first and second principal stresses.

The eigenvalues of the stress tensor σ are found by solving the characteristic equation:

det(σ−λI)=0

Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]

σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]

σ−λI = 0λ³+35λ²−605λ−1875

σ−λI = 0

λ = −25,5,3

The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.

The maximum shear stress is found to be

τmax = 0.5(σ1−σ2)

τmax = 0.5(20−(−15))

τmax = 17.5.

Therefore, the maximum shear stress is τmax = 17.5.

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In order to divide these numbers, first let's start with a 0 in the unit place, since 9.2 is smaller than 52.063.

Then, we multiply 9.2 by 10, this way we will calculate the tenths place.

Now, dividing 92 by 52.063, we have 1 as the result.

The remainder will be 92 - 52.063 = 39.937.

Again, let's multiply the remainder by 10, so now we will calculate the hundredths of the result.

Dividing 399.37 by 52.063 we have 7.

The remainder is 399.37 - 7*52.063 = 34.929.

Multiplying by 10, we have 349.29, and now we calculate the thousandths.

Dividing 349.29 by 52.063 we have 6.

Until now, the result of the division is 0.176.

Rounding to the nearest hundredth, we have 0.18 as the result of the division.

The function is an exponential growth since it is increasing with time and k is positive

Given that at t =6, P = 167075

Then;

167075 =110.8e^6k

167075/110.8 = e^6k

1507.9 = e^6k

ln(1507.9) = 6k

k = ln(1507.9)/6

k = 1.2

Thus in the year 2020;

P = 110.8e^20(1.2)

P = 2.9 * 10^12

In the year 2025;

P = 110.8e^25(1.2)

P = 1.18 * 10^15

To reach 290,000

290,000 = 110.8e^1.2t

290000/110.8 = e^1.2t

2617.3 = e^1.2t

t = ln(2617.3 )/1.2

t = 7 years

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Hey there! The answer you're looking for is 3000 centimeters^3. If we take the first number, 30 cm, and multiply it by the second number, 25 cm, we're left with 750 cm^2. We use the last digit to multiply the 750 cm^2 into 3000 cm^3. Hope this helped!

Deciles are 61.3 and 67.7

What are deciles?

Deciles are measures of position calculated on a set of data. The deciles are the values that separate a distribution into ten equal parts, where each part contains the same number of observations). The decile is a member of the wider family of quantiles.

Given:

Normal distribution =64.5 inches

Standard deviation=σ =2.5 inches

​

So, here the z- score for left decile= -1.28

and for right decile= +1.28

we know,

z= x-\(\mu\)/σ

x= zσ + \(\mu\)

x=-1.28*2.5 + 64.5

x= 61.3  and,

x= 1.28*2.5 + 64.5

x=67.7

hence, the deciles are 61.3 and 67.7

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The 98% confidence interval estimate of the mean age of all race car drivers, based on the provided data, is (27.67, 39.33) years.

To calculate the 98% confidence interval estimate of the mean age of all race car drivers, we can use the formula:

CI = x ± (t * (s/√n))

where x is the sample mean, s is the sample standard deviation, n is the sample size, and t is the t-score corresponding to the desired confidence level. Using the given data, we find that the sample mean (x) is 32.53 and the sample standard deviation (s) is 7.93.

The sample size (n) is 15. With a desired confidence level of 98%, we find the t-score for a two-tailed test to be approximately 2.947. Plugging these values into the formula, we calculate the confidence interval to be (27.67, 39.33) years. This means that we can be 98% confident that the true mean age of all race car drivers falls within this interval.

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9514 1404 393

Answer:

  59.8 cm

Step-by-step explanation:

The length of arc ABC is ...

  s = rθ

  s = (9 cm)(220/180π) = 11π cm ≈ 34.558 cm

The length of segment CD is 9 cm less than the length of segment OD. OD can be found using the law of sines.

  OD/sin(A) = AD/sin(O)

  OD = AD·sin(A)/sin(O) = (21 cm)sin(24°)/sin(140°) ≈ 13.288 cm

Then the length of CD is ...

  CD = OD -9 cm = (13.288 cm) -(9 cm) = 4.288 cm

The perimeter is the sum of the segment and arc lengths:

  P = ABC + CD +AD

  P = 34.558 cm + 4.288 cm + 21 cm = 59.846 cm

The perimeter of the shape is about 59.8 cm.