is 2\-3 a rational number​

A correlation coefficient is consistently a number between 1 and - 1 .

The correlation coefficient is a factual measure that demonstrates the strength and heading of the straight connection between two factors. It goes from - 1 to 1, where - 1 addresses a completely bad correlation (i.e., as one variable expands, different declines), 0 addresses no correlation, and 1 addresses an entirely sure correlation (i.e., as one variable builds, the other likewise increments).

The indication of the correlation coefficient demonstrates the heading of the relationship, while the extent of the coefficient shows the strength of the relationship. A correlation coefficient of 0 shows no straight connection between the factors, while values nearer to - 1 or 1 demonstrate a more grounded direct relationship.

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The rate of increase in the volume of sphere when  diameter is 100 mm is 94285.71 mm³/s.

Let the radius of the sphere be 'r'.

The radius of a sphere is increasing at a rate of 3 mm/s .

Then,

dr / dt = 3 mm/s

Volume of sphere is given as;

v = 4/3 π r³

Then, the change is volume is;

dv / dt = (4/3)  π 3r² .dr/dt

         = 4πr² x 3

         = 12πr²

For radius = 100/2 mm = 50 mm

dv / dt  = 12 x 22/7 x 50²

dv / dt  = 94285.71 mm³/s

Thus, the rate of increase in the volume of the sphere when diameter is 100 mm is 94285.71 mm³/s.

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Answer:

Step-by-step explanation:

a. Length of segment PM=21cm and length of segment PL = 24.6cm.

In geometry, a segment is a part of a line that is bounded by two distinct endpoints and contains all the points between them. It can also be defined as the portion of a line that connects two points.

(a) Using the given information, PQ=42cm and we can see that M is midpoint of PQ. Therefore we can use midpoint formula

PQ=PM+MQ

42=2PM

PM=42/2

PM=21

(b) We used the property that the perpendicular bisector of a chord passes through the center of the circle, which means that LP is the perpendicular bisector of PQ.

(c) We used the Pythagorean theorem again to solve for PL.

\(PL^2 = PM^2 + LM^2\\\\PL^2 = 21^2 + 13^2\\\\PL^2 = 610\\\\PL = \sqrt{(610)\)

PL ≈ 24.6 cm

(d)

\(PM^2=PL^2-LM^2= 610-169=441\\\\PM=21\)

Using the fact that LP is the perpendicular bisector of PQ, we can split PQ in half to get two segments of length 21. Then, using the Pythagorean theorem in right triangle LPL', where L' is the midpoint of PQ, we can solve for PL.

PL ≈ 24.6 cm

Therefore, the length of PL is approximately 24.6 cm.

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Answer:

30%

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The quadrilateral is a parallelogram if and only if it has two pairs of parallel sides option (D) is correct.

In two-dimensional geometry, it is a plane shape having four sides, in which two pairs of sides are parallel to each other and equal in length. The sum of all angles in a parallelogram is 360°.

It is given that:

A parallelogram is a quadrilateral with two pairs of parallel sides.

As we know,

The quadrilateral can be defined as the four-sided polygon in geometry having four edges and four corners.

The quadrilateral, has:

Two pairs of congruent sides.

It has one pair of opposite congruent angles.

The diagonals of a kite are perpendicular.

One diagonal is bisected.

The top and bottom angles are bisected but does not have congruent diagonals.

A quadrilateral is a parallelogram if and only if it has two pairs of parallel sides.

Thus, the quadrilateral is a parallelogram if and only if it has two pairs of parallel sides option (D) is correct.

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Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

For a normal distribution of sat scores with with a mean of 1700 and the fraction of students score between 1350 and 2050 is equals to the 0.983.

We have, a SAT scores are normally distributed, Mean of score

\(\mu\) = 1700

Variance of score \( \sigma²\) = 21500

We have to determine the fraction of students score between 1350 and 2050.

The standard deviations of scores = √variance = √21500 =

Using the Z-Score formula, \(z = \frac{x - \mu}{ \sigma} \)

where, x -> observed value

sigma --> standard deviations

Here, the fraction of students score between 1350 and 2050, P(1350< x < 2050)

= \(P( \frac{1350 - 1700 }{146.63} < \frac{ x - \mu }{ \sigma}< \frac{2050 - 1700}{146.63})\)

= P( \frac{1350 - 1700 }{146.63} < z < \frac{2050 - 1700}{146.63}

= P( -2.387 < z < 2.387 )

= 0.983

So, P(1350< x < 2050) = P( -2.387 < z < 2.387 ) = 0.983. Hence, required fraction value is 0.983.

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The height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

The volume of the cylinder can = 1000 cubic cm

Consider the height of the cylinder as h and the radius of the base is r

Volume of the cylinder = π\(r^2\)h = 1000

h = 1000 / π\(r^2\)

The surface area of the cylinder

A = 2π\(r^2\) + 2πrh

A = 2π\(r^2\) + 2πr(1000 / π\(r^2\) )

A = 2π ( \(r^2\) + 1000 / π\(r^2\))

Differentiate the terms

A' =  2π (2r + 1000 / π\(r^3\))

When the minimum surface area

2π (2r + 1000 / π\(r^3\)) = 0

r = \((1000/2\pi )^\frac{1}{3}\)

r = 5.41 cm

Then,

h =  1000 / π\(r^2\)

= 1000 / (π × 5.41 × 5.41)

= 1000 / 91.94

= 10.87 cm

Hence, the height of the cylinder is 10.81 cm and the radius of the cylinder is 5.41 cm

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Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

The value "x = 3" and "x = -1/2" are part of the solution set.

We can represent any linear inequality using any of the following forms:

Now, if the sign is pointing towards x, it means that x is greater than b., so, the line under the greater sign means that x can also equal b.

The options given are:

Hence, the value "x = 3" and "x = -1/2" are part of the solution set.

Therefore, the Option A and C is correct.

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Answer:

7+10n

Step-by-step explanation:

solve both sides

-1 + -10n +8

solve again

move 8 over to it and add it to -1

7 +10n,

if I'm wrong someone please point it out.

Answer:

5

Step-by-step explanation:

so 12 + 8=20 so they own 5

An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.

Inequality is an algebraic statement that two or more mathematical expressions are unequal.

Inequalities can be represented as:

The total amount received by the island = $32,000

The daily receipt of donations = $4,500

Let the number of days = x

Let the funds raised for aid = y

y ≤ 32,000 + 4,500x

Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.

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Answer:

Case study

Step-by-step explanation:

Case study: Case study method is used to find more information through carefully analyzing existing cases. It is very often used for business research or to gather empirical evidence for investigation purpose.

Answer:

40 mph

Step-by-step explanation:

After the 2 hours Gab travelled 100 miles (50*2), subtract this from 180 to find how many miles Carlos travelled. Divide this number by 2 to figure out the mph

The solution of expression is 8log6.

There are four basic properties of logarithms:

logₐ(xy) = logₐx + logₐy.

logₐ(x/y) = logₐx - logₐy.

logₐ(xⁿ) = n logₐx.

logₐx = logₓa / logₓb.

According to the problem, we will use some of the basic logarithmic properties,

We have been given that expression as

⇒ log6⁸ + 2log6³ + log6¹² - log6²⁴​

[used property : logₐ(xⁿ) = nlogₐx]

⇒ 8log6 + 6×2log6³ + 12log6 - 24log6

⇒ 8log6 + 12log6³ + 12log6 - 24log6

⇒ 8log6

Hence, the solution is 8log6.

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Using the center-of-gravity technique, the best site location for the new distribution center in Charlotte is determined to be at coordinates (X, Y) = (27.92, 19.08).

The center-of-gravity technique is used to find the optimal location for a facility based on the distribution of demand. In this case, we will calculate the weighted average of the coordinates (X, Y) of the three sites, with the weights being the number of weekly packages flowing to each site.

To calculate the X-coordinate of the center of gravity, we use the formula:

Xc = (X1 * W1 + X2 * W2 + X3 * W3) / (W1 + W2 + W3)

Similarly, for the Y-coordinate:

Yc = (Y1 * W1 + Y2 * W2 + Y3 * W3) / (W1 + W2 + W3)

Substituting the given values:

Xc = (16 * 26000 + 35 * 12000 + 40 * 10000) / (26000 + 12000 + 10000) ≈ 27.92

Yc = (28 * 26000 + 10 * 12000 + 18 * 10000) / (26000 + 12000 + 10000) ≈ 19.08

Therefore, the best site location for the new distribution center in Charlotte is approximately at coordinates (X, Y) = (27.92, 19.08) based on the center-of-gravity technique.

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The unit tangent vector T and the principal unit normal vector N can be computed for the given vector-valued function r(t) = (sin(t) + 2, cos(t) + 10, 6t). The unit tangent vector T represents the direction of the curve at each point, while the principal unit normal vector N is perpendicular to the tangent vector and points towards the center of curvature.

To find the unit tangent vector T, we differentiate r(t) with respect to t and divide by its magnitude:

r'(t) = (cos(t), -sin(t), 6)

||r'(t)|| = sqrt((cos(t))^2 + (-sin(t))^2 + 6^2) = sqrt(1 + 1 + 36) = sqrt(38)

Therefore, the unit tangent vector T is given by:

T = r'(t) / ||r'(t)|| = (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38))

To find the principal unit normal vector N, we differentiate T with respect to t and divide by its magnitude:

T'(t) = (-sin(t)/sqrt(38), -cos(t)/sqrt(38), 0)

||T'(t)|| = sqrt((sin(t)/sqrt(38))^2 + (-cos(t)/sqrt(38))^2) = sqrt(1/38 + 1/38) = sqrt(2/38) = sqrt(1/19)

Therefore, the principal unit normal vector N is given by:

N = T'(t) / ||T'(t)|| = (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0)

In summary, the unit tangent vector T for the given vector-valued function is (cos(t)/sqrt(38), -sin(t)/sqrt(38), 6/sqrt(38)), and the principal unit normal vector N is (-sin(t)/sqrt(19), -cos(t)/sqrt(19), 0). These vectors represent the direction and perpendicular direction to the curve defined by r(t).

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Answer:

128 ft^2

Step-by-step explanation:

4ft x 4ft = 16 ft^2

3 x 4 = 12

12 ft x 12 ft = 144 ft^2

144 - 16 = 128 ft^2

The critical value t for the given parameters is approximately 1.753.

To determine the critical value t for a 85% confidence interval with degrees of freedom (df) equal to 15, we can use a t-distribution table or a statistical software.

The critical value t depends on the desired confidence level and the degrees of freedom. In this case, with a confidence level of 85% and 15 degrees of freedom, we need to find the value from the t-distribution table.

Consulting a t-distribution table or using statistical software, the critical value t for a 85% confidence interval with 15 degrees of freedom is approximately 1.753 (rounded to three decimal places).

Therefore, the critical value t for the given parameters is approximately 1.753.

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Determine the critical value t for a 85% confidence interval with df=15.

The critical value t is: _____

(Provide your answer with 3 decimal places)

Answer:

SOH CAH TOA

(Sine,opposite,Hypotenuse) - SOH

(Cosine, adjacent, Hypotenuse) - CAH

(Tangent,opposite,adjacent) - TOA

Step-by-step explanation:

Answer:

SOH CAH TOA

is the answer

The equation is given as

\(y = 12 sin (6t - \pi /2) + 2\)

The Amplitude can be calculated as

\(amplitude = \frac{max + min}{2}\\ amplitude = \frac{10+14}{2} = 12\)

The vertical shift is the average difference between the maximum and minimum.

\(Vertical Shift = \frac{Max - Min}{2} = \frac{14-10}{2} = 2\)

For b value

The Time Period will be twice the distance between max and min.

\(time period = \frac{2\pi }{b} \\time period = 2 * distance between max and min\\b = \frac{2\pi }{2}*\frac{1}{b} = \frac{\pi }{6}\)

The period is calculated as

\(T = \frac{2\pi }{b} \\T = \frac{2\pi }{\frac{\pi }{b} } = 12\)

The equation is given as

\(y = 12 sin (6t - \pi /2) + 2\)

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When researching, here is where each aspect of an index card should be placed: Match the letter that corresponds to one of the items below to the correct location (1,2,3,4,5) on an index card.A.

Title of card (aspect of subject) - (2) This should be the center or topmost part of the index card. It should be clear and concise enough to reflect what is contained in the index card.B.

Source Number - (4) This is the number allocated to each source in your reference list.C. Page Number - (3) This refers to the page number(s) where the information was sourced from. It is usually written on the top right or left corner of the index card.D.

Quotation - (1) This refers to the exact words that were used in the source materials and is written verbatim. This is usually written in quotation marks.E.

Paraphrase - (5) This refers to rewording a particular section of information in your own words without changing its meaning. The paraphrase should be accurate, concise, and written in a sentence format.

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Step-by-step explanation:

explain what 7 c is please and I'll write the answer in the comments:))

The gradient of line A is -2. 67

Gradient = slope = Δy/ Δx

We have,

y2 = 3

y1 = -5

x2 = -3

x1 = 0

Substitute the values

Gradient = \(\frac{3 - (-5)}{-3 -0}\)

Gradient = \(\frac{3 + 5}{-3}\)

Gradient = \(\frac{8}{-3}\)

Gradient = -2. 67

Thus, the gradient of line A is -2. 67

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The graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

What is a misleading graph?

A misleading graph, sometimes referred to as a distorted graph, misrepresents data, amounts to statistical abuse, and may lead to the drawing of an inaccurate conclusion.

What is a data set?

A data set is a grouping of connected, discrete pieces of connected data that can be viewed separately, together, or handled as a single unit. A data structure of some kind is used to arrange a data set.

Here, we have

2 events with a cost of 1,000-1,499;

4 events with a cost of 1,500 to 1,999;

3 events with a cost of 2,000 to 2,499;

1 event with a cost of 3,000 to 3,499

We concluded from the given dataset that the cost of the event is plotted on the x-axis.

In a given dataset, the entry from 2500 to 2599 is missing.

The graph generates a point cluster that isn't actually displayed on the data components because of the missing item.

Hence, the graph is misleading because the x-axis scale shows that the given data is more clustered than it actually is.

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