Rewrite 32 1/2 as a radical form

The variance of the actuary's wait time is 36 / 121.

From the information, at the airport, there are three counters for checking the luggage. the employees at each counter work independently with the time for each customer modeled as an exponential distribution. the average time is one minute for one counter, two for the next, and three minutes for the third. an actuary, who is next in line, will take the next available counter,

From the complete question, the variance of the actuary's wait time will be:

= 1 / (11/6)²

= (6/11)²

= 36 / 121

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The solution to the equation 30 + q = 43 is q = 13.

Given the equation in the question:

30 + q = 43

To determine the value of q in the equation 30 + q = 43, isolate q on one side of the equation by performing the same operation on both sides of the equation.

30 + q = 43

q + 30 = 43

Next, we can isolate q by subtracting 30 from both sides of the equation:

q + 30 - 30 = 43 - 30

q = 43 - 30

Subtract 30 from 43

q = 13

Therefore, the value of q is 13.

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The two types of transformations that are produced by the matrix include:

We can see that a 90° counter-clockwise rotation followed by a dilation produces a transformation that stretches and rotates the figure.

On the other hand, a 90° counter-clockwise rotation followed by a reflection in the vertical axis produces a transformation that reflects and rotates the figure.

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To show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line but does not have a denominator of 6.

One way to do this is to find the least common multiple (LCM) of 5 and 7, which is 35, and then find a fraction with a denominator of 35 that falls between 1/5 and 1/7.

To do this, we can find the equivalent fractions of 1/5 and 1/7 with a denominator of 35:

1/5 = 7/35

1/7 = 5/35

Now we need to find a fraction between 7/35 and 5/35. One such fraction is:

6/35

This fraction is located between 7/35 and 5/35 on the number line, but its denominator is 35, not 6. Therefore, Maria's claim is incorrect.

Another way to show that Maria's claim is incorrect is to find a counterexample by simply listing all the fractions between 1/5 and 1/7 and showing that not all of them have a denominator of 6. For example:

1/6, 1/7, 1/8, 1/9, 1/10, ..., 1/34, 1/35

As we can see, not all of these fractions have a denominator of 6, so Maria's claim is incorrect.

Answer:

13/70

Step-by-step explanation:

In order to  show that Maria's claim is incorrect, we need to find a fraction that is located between 1/5 and 1/7 on a number line,  but does not have a denominator of 6.

Let's  find the  common multiple (CM) of 5 and 7, which is 70, or 35. But this case try 70  and then find a fraction with a denominator of 70 that falls between 1/5 and 1/7.

equivalent fractions of 1/5 and 1/7 with a denominator of 70
1/7 < x < 1/5 , will be equivalent to 1/7 ( 10/10 ) < x < 1/5 ( (14/14)
10/70 < x < 14/70..
x is the fraction   between 10/70  and 14 /70.  Unknown  fraction is:

13/70

This fraction is located between 10/70  and 14/70  on the number line, but its denominator is 70 , not 6. Therefore, Maria's claim is incorrect.

It is not possible for the graph of a height function of a car on a roller coaster to be a step function. Hence Amy is wrong.

A sort of function called a step function is one that only varies at discrete, isolated places in its domain and is constant everywhere else. A step function is one that "steps" down to the next integer at each integer input while remaining constant in between. An example of this is the floor function, which rounds down any input to the nearest integer.

On the other hand, it is doubtful that the height of a roller coaster car as a function of time is a step function because it is anticipated to fluctuate continually as opposed to hopping from one value to another at certain moments. Instead of abrupt increases in height that would be consistent with a step function, roller coasters often entail smooth, continuous curves and elevation changes.

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Here is the probability distribution table:

|Outcome|Probability|
|-------|-----------|
|$0     |1/10       |
|S100   |4/10       |
|$200   |3/10       |
|$500   |2/10       |

To create the table, you simply list each possible outcome (in this case, the different amounts that could be won on the spinner), and then calculate the probability of each outcome occurring. In this case, there are 10 sectors in total, so the probability of landing on each sector is 1/10. There is 1 sector that says "$0," so the probability of getting that outcome is 1/10.

There are 4 sectors that say "S100," so the probability of getting that outcome is 4/10, or 2/5. Similarly, there are 3 sectors that say "$200," so the probability of getting that outcome is 3/10, or 3/10.

And finally, there are 2 sectors that say "$500," so the probability of getting that outcome is 2/10, or 1/5.

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The number of bows Lulu can make  from the remaining ribbon is 13 bows.

To find the remaining ribbon, first, convert 1 1/3 to an improper fraction (1*3 + 1 = 4, so 1 1/3 = 4/3). Now, subtract 4/3 from 10 feet.

10 - (4/3) = (30/3) - (4/3) = 26/3 feet of ribbon remaining.

She uses 8 inches of ribbon for each bow. Since there are 12 inches in a foot, convert the remaining ribbon to inches:

(26/3) * 12 = 104 inches of ribbon remaining.

Now, divide 104 inches by the 8 inches required for each bow to find the number of bows she can make:

104 / 8 = 13 bows.

Lulu can make 13 bows with the remaining ribbon.

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The correct words are number of defective items from the sample of 109 items chosen at random and correct symbol is X ~ B(109, 0.8).

Percent of defective rate in manufacturing machine = 80%

Random number of items chosen = 109

The correct wording for the random variable in this situation is,

The number of defective items in a sample of 109 items chosen at random from the manufacturing machine.

Number of defective items is successes.

A common symbol for the number of successes in a binomial distribution is X.

Use X to represent the random variable in this situation.

The notation for the binomial distribution is usually written as,

X ~ B(n, p)

where X is the random variable,

n is the sample size,

and p is the probability of success on each trial.

X ~ B(109, 0.8).

Therefore, the correcting wording is number of defective items in a sample of 109 items chosen at random and the correct symbol is equal to  X ~ B(109, 0.8).

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Answer:

V = 1,728 mi³

SA = 864 mi²

Step-by-step explanation:

We can find the volume of the triangular prism by multiplying the area of one of the triangle faces by the prism's depth.

First, we can solve for the area of one of the triangle sides:

A(triangle) = (1/2) · b · h

A(triangle) = (1/2) · 24 · 18

A(triangle) = 12 · 18

A(triangle) = 216 mi²

Next, we can get the volume of the prism by multiplying the area of the triangle face by the prism's depth.

V = A(triangle) · depth

V = 216 · 8

V = 1,728 mi³

__

We can find the surface area by finding the area of each side, then adding all of those areas together.

We already know that the area of each of the triangle sides is 216 mi².

Now, we can solve for the area of the base.

A(base) = length · width

A(base) = 24 · 8

A(base) = 192 cm²

Then, we can find the area of the top side.

A(top) = length · width

A(top) = 30 · 8

A(top) = 240 mi²

Finally, we can solve for the surface area of the prism by adding the areas of each of its sides.

SA = (2 · A(triangle)) + A(base) + A(top)

SA = 2(216) + 192 + 240

SA = 432 + 192 + 240

SA = 624 + 240

SA = 864 mi²

The component form of u + v can be found using the given lengths and angles and it  is (6, √3).

To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.

Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.

To find u + v, we add the corresponding components of u and v. This gives us:

u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)

Therefore, the component form of u + v is (6, √3).

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The equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

To find the equation of a circle with center (2, 3) that passes through the point (5, 3), we'll need to use the standard equation of a circle and the given information.

The standard equation of a circle is[tex](x - h)^2 + (y - k)^2 = r^2[/tex], where (h, k) is the center and r is the radius.

Step 1: Substitute the center coordinates (h, k) = (2, 3) into the equation:
[tex](x - 2)^2 + (y - 3)^2 = r^2[/tex]

Step 2: Use the point (5, 3) to find the radius. Plug the coordinates of the point into the equation and solve for  [tex]r^2[/tex]:
[tex](5 - 2)^2 + (3 - 3)^2 = r^2\\3^2 + 0^2 = r^2\\9 = r^2[/tex]

Step 3: Plug[tex]r^2[/tex] back into the equation:
[tex](x - 2)^2 + (y - 3)^2 = 9[/tex]

So, the equation of the circle with center (2, 3) that passes through the point (5, 3) is [tex](x - 2)^2 + (y - 3)^2 = 9.[/tex]

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Answer:

60 square inches

Step-by-step explanation:

Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up

10mL of the baraclude oral solution to the patient.

To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:

Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)

In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:

Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL

Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.

To find the required mL, divide the prescribed dose by the solution's strength:

0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL

You will administer 10 mL of Baraclude (entecavir) oral solution daily.

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U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

To determine whether U(1,1), Q(4,4), and A(6,2) form a right triangle, we will follow the given guide:

Find the slopes of sides UQ, QA, and UA:

Determine which segments are perpendicular and how we know they are perpendicular:

To determine if two lines are perpendicular, we need to check if their slopes are negative reciprocals of each other.

Find the lengths of each side:

Use the Pythagorean Theorem to show that it is a right triangle:

Since we have determined that UQ and QA are perpendicular, we can use the Pythagorean Theorem to show that it is a right triangle.

Since (Length of UA)² + (Length of QA)² = (Length of UQ)², we know that the triangle is a right triangle.

U(1,1), Q(4,4), and A(6,2) form a right triangle with UQ and QA being the legs and UA being the hypotenuse.

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The linearization of the function f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) is L(x, y) = -10x - 8y + 1. The correct option is C.

To find the linearization of the given function at the point (0, 0), we need to compute the partial derivatives with respect to x and y and then evaluate them at the given point.

The function is f(x, y) = [tex]e^{(-10x-8y)[/tex] - 8y.

First, find the partial derivative with respect to x:
∂f/∂x = [tex]-10e^{(-10x-8y).[/tex]

Now, evaluate ∂f/∂x at (0, 0):
∂f/∂x(0, 0) = [tex]-10e^{(0)[/tex] = -10.

Next, find the partial derivative with respect to y:
∂f/∂y = [tex]-8e^{(-10x-8y)[/tex] - 8.

Now, evaluate ∂f/∂y at (0, 0):
∂f/∂y(0, 0) = [tex]-8e^{(0)[/tex] - 8 = -8 - 8 = -16.

Now, we can form the linearization:
L(x, y) = f(0, 0) + ∂f/∂x(0, 0)(x - 0) + ∂f/∂y(0, 0)(y - 0).

Evaluate f(0, 0):
f(0, 0) = [tex]e^{(-10(0)-8(0))} - 8(0) = e^{(0)} - 0 = 1.[/tex]

Finally, substitute the values into the linearization formula:
L(x, y) = 1 - 10x - 16y.

Comparing to the given options, the answer is:
C) L(x, y) = -10x - 8y + 1

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The volume of the pyramid is approximately 41.67 cubic meters.

To find the volume of the pyramid, we can use the formula:

V = (1/3) x base area x height

Since the base of the pyramid is a square with side length 5 meters, its area is:

base area = side² = 5² = 25 square meters

The height of the pyramid is also given as 5 meters.

Now, we need to find the area of one of the square cross-sections. Since the pyramid has congruent triangular sides, we know that each of these triangles is similar to the original base square.

Therefore, the side length of each square cross-section is proportional to the height of the pyramid, and we can use the ratio of corresponding side lengths to find the area of one of the squares:

5 / 5 = x / 5

where x is the side length of the square cross-section.

Solving for x, we get:

x = 5

Therefore, each of the square cross-sections has an area of 5 x 5 = 25 square meters.

Now, we can substitute the values we have found into the formula for the volume:

V = (1/3) x base area x height

= (1/3) x 25 x 5

= 41.67 cubic meters

Therefore, the volume of the pyramid is approximately 41.67 cubic meters.

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The mZDPC is approximately 15 degrees.

We know that the length of an arc of a circle is given by the formula:

length of arc = (central angle / 360°) × 2πr

where r is the radius of the circle.

In this case, the length of arc DC is 9.77 inches and the radius of the circle is 8 inches. Let's use the above formula to find the central angle mZDPC:

9.77 = (mZDPC / 360°) × 2π(8)

Simplifying this equation, we get:

mZDPC = (9.77 / (2π(8) / 360°))

mZDPC = (9.77 / 0.670206) degrees

mZDPC ≈ 14.58 degrees

Rounding to the nearest degree, we get:

mZDPC ≈ 15 degrees

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Answer:

Let's start by drawing a diagram of the cornfield with the plowed strip around it:

markdown

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_____________________________

|                             |

|                             |

|                             |

|                             |

|        _____________________|__

|       |                       |

|       |                       |

|       |                       |

|       |                       |

|_______|_______________________|

The plowed strip has a uniform width, which we'll call w. We want to find w such that half of the cornfield is plowed.

The total area of the cornfield is:

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12 km x 9 km = 108 km^2

If we plow a strip of width w around the cornfield, the new dimensions of the cornfield will be:

scss

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(12 + 2w) km x (9 + 2w) km

The area of the plowed strip is the difference between the area of the new cornfield and the area of the original cornfield:

scss

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(12 + 2w)(9 + 2w) - 12(9) = 108 + 42w + 4w^2

We want half of the cornfield to be plowed, so we set the area of the plowed strip equal to half the area of the original cornfield:

scss

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108 + 42w + 4w^2 = (1/2)(108)

Simplifying, we get:

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4w^2 + 42w - 54 = 0

We can solve this quadratic equation using the quadratic formula:

css

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w = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 4, b = 42, and c = -54. Substituting these values, we get:

scss

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w = (-42 ± sqrt(42^2 - 4(4)(-54))) / 8

arduino

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w = (-42 ± sqrt(1936)) / 8

makefile

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w = (-42 ± 44) / 8

So we have two possible solutions:

makefile

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w = 1/2 km (discarded since it does not satisfy the given condition)

or

makefile

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w = 11/2 km

Therefore, the width of the plowed strip is 11/2 km = 5.5 km if half of the cornfield is plowed.

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Answer:

89

Step-by-step explanation:

construct the formula to obtain the total of marks in first 9 tests:

79 = x/9

79 * 9 = 711

x = 711

so to get 80% in the next test we construct this formula:

80 = 711 + y / 9 + 1

the value we get for y is 89

to confirm the answer, 711+89/10 gives us 80, which is the correct value we want

Using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

To calculate the interest and new balance using the Adjusted Balance Method, we need to first find the adjusted balance.

This method takes the previous balance, adds the purchases made before the payment, and then subtracts the payment.

Here's the calculation:

Calculate the adjusted balance:

Previous balance: $500

Purchases before May 20: $25 (May 12)

Subtotal: $525

Payment: $110

Adjusted balance: $525 - $110 = $415

Calculate the interest:

Interest rate: 1% per month

Interest: $415 * 1% = $4.15

Calculate the new balance:

Adjusted balance: $415

Purchases after May 20: $100 (May 22) + $50 (May 30) = $150

Interest: $4.15

New balance: $415 + $150 + $4.15 = $569.15

So, using the Adjusted Balance Method:

Interest: $4.15

New Balance: $569.15

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The missing lengths of BE and IJ using the concept of similar quadrilaterals are:

BE = 32

IJ = 18

Similar quadrilaterals are defined as quadrilaterals that have the same shape, but their sizes may vary. Thus, if two quadrilaterals are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

From the image, we are told that Quadrilateral GHIJ is similar to Quadrilateral BCDE.

Thus:

GJ/BE = IJ/DE = HI/CD

Thus:

12/BE = 6/16

BE = (16 * 12)/6

BE = 32

Similarly:

IJ/48 = 6/16

IJ = (48 * 6)/16

IJ = 18

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When the subject or predicate is missing from a sentence, the sentence error is a sentence fragment.

Sentence Errors are errors related to grammar and mechanics within sentences in Standard Written English.

An example of a sentence error will be "The children re us"

The phrase "re" is the error word in this sentence.

The three types of sentence errors we have are run-on sentences, sentence fragments and overloaded sentence.

In this problem, the type of sentence error that occurs when a sentence is missing a subject of predicate is a sentence fragment

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The constant of proportionality between the number of yards Jackson can mow and the number of hours is 3/4.

To find the area of the part with cement, we need to find the area of the entire rectangle and then subtract the area of the part with grass.

The area of the rectangle is: length x width = 5 m x 4 m = 20 m²

The area of the part with grass is: length x width = 3 m x 2 m = 6 m²

So the area of the part with cement is:

20 m² - 6 m² = 14 m²

Therefore, the area of the part with cement is 14 square meters.

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The focus so far has been on similar triangles, but there are also theorems that deal with similar polygon

Theorems of similar triangles are important properties that hold true for any pair of similar triangles. Some of the most commonly used theorems are:

AA Similarity Theorem: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

SSS Similarity Theorem: If the three sides of one triangle are proportional to the three corresponding sides of another triangle, then the triangles are similar.

SAS Similarity Theorem: If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

These theorems are also applicable to similar polygons

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The focus so far has been on similar triangles, but there are also theorems that deal with similar polygons.

Answer:

The answer is 5.8cm to 1 d.p

Step-by-step explanation:

volume of cube=L³

200=L³

cube root both sides

³√200=³√L³

L=5.8cm to 1 d.p

The inflation rate for Ken's gas expenses between the two years is approximately 42.26%.

To calculate the inflation rate for Ken's gas expenses, we can use the following formula: (Current Year Expense - Previous Year Expense) / Previous Year Expense × 100%.

In this case, the previous year's gas expense was $1,098 and the current year's expense is $1,562.

To find the difference in expenses, subtract the previous year's expense from the current year's expense: $1,562 - $1,098 = $464.

Now, divide this difference by the previous year's expense: $464 / $1,098 ≈ 0.4226.

Finally, multiply the result by 100% to get the inflation rate: 0.4226 × 100% ≈ 42.26%.

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The statements that  gives the best reasons that ben’s rent payment is an essential (fixed) expense is he agreed to pay the same amount every month. The correct answer is D.

In personal finance, an essential expense is a regular expenditure that is necessary for maintaining a basic standard of living. These expenses are typically fixed, meaning that they do not fluctuate from month to month, and are difficult or impossible to eliminate without sacrificing basic needs like food, housing, or healthcare.

Since, this is his rent, the amount of money that he is legally bound to pay every month in order to keep on living in that location.

He has an agreement with his landlord to pay $215 each month and thus he has to do it.

Essential expenses are often considered a top priority in budgeting because they are critical to maintaining health, safety, and overall well-being. In the given scenario, Ben's rent payment is an essential expense because it is a fixed expense that is necessary for maintaining his housing, which is a basic need. The correct answer is D.

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Answer:

it would be at point (6,3)

Step-by-step explanation:

If you were to reflect it over the x-axis you would get (-6,3)

Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.

In Kendall correlation,

Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.

A concordant pair is when the rank order of the two variables is the same both increase or decrease together.

A discordant pair is when the rank order is different one variable increases while the other decreases.

If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.

Which suggests a positive correlation relationship between them.

Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.

Which suggests a negative  relationship between them.

Example ,

two variables, X and Y, that are positively correlated.

If we plot the observations of X and Y on a scatter plot.

Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.

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