67. A new operation,
is defined this way:= p¤q - q. What is the value of 4¤(5¤6)

using trignometric ratio of sine thee measure of the angle x to the nearest degree is 28 degrees

Trigonometric ratios are ratios of the sides of a right triangle, such as sine, cosine, and tangent, that are used to find missing side lengths or angles.

An angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. It is typically measured in degrees or radians.

According the given information:

We can use the trigonometric ratio of sine to find the measure of the angle x.

sin(x) = opposite/hypotenuse

In this case, the opposite side is the height of the triangle, which is 13, and the hypotenuse is the length of the diagonal line connecting the base and the top of the triangle. We can use the Pythagorean theorem to find the length of the hypotenuse.

hypotenuse² = base² + height²

hypotenuse² = 22² + 13²

hypotenuse² = 769

hypotenuse ≈ 27.73

Now we can substitute the values into the sine ratio:

sin(x) = 13/27.73

x ≈ 28 degrees

Therefore, the measure of the angle x to the nearest degree is 28 degrees.

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On average, the number of cars on the busy road increases by 25 cars per hour from midnight to 12:00pm

The average rate of change of a function from x=a to x=b is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

Using this formula, we can calculate the average rate of change of the function f(x) from x=0 to x=12 as follows:

average rate of change = (f(12) - f(0)) / (12 - 0)

Where

f(0) = 0 and f(12) = 300 -- from the graph

So, we have

Rate = (300 - 0) / 12

Rate = 25

Therefore, the approximate average rate of change of the function from x=0 to x=12 is 25 cars per hour.

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The surface area of the rectangular pyramid is 75 m².

Surface area is the sum of all the surfaces on each side of a three-dimensional shape.

To calculate the surface area of the rectangular pyramid, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equaation 1

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in this case since it's a cylinder always have to do is multiply the two given measurements dancing that she gets all you need to do is run it off to the nearest two decimal places when you say to the nearest two decimal places while trying to say they are two numbers after the coma

The answer of the given question based on the rectangle is , The MNOP congruence is shown by  Side-Angle-Side (SAS) and the steps are given below.

In geometry, a diagonal is a straight line that connects two non-adjacent vertices of a polygon or a polyhedron. In other words, a diagonal is a line segment that joins two corners or vertices of a shape that are not next to each other. For example, in a rectangle, the diagonals are the line segments that connect opposite corners of the rectangle.

To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following steps:

Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent.

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The volume of the figure is approximately 50101mm^3 and the surface area is approximately 8253mm^2.

The figure consists of a sphere and a cylinder. We can find the volume and surface area of the figure by calculating the volume and surface area of each component separately and adding them together.

The height of the cylinder is given as 76mm, which means the remaining height of the figure must be occupied by the sphere. Thus, the radius of the sphere can be calculated as half the difference between the total height of the figure and the height of the cylinder:

Radius of sphere = (102mm - 76mm)/2 = 13mm

Now we can calculate the volume and surface area of each component:

Volume of cylinder = πr^2h = π(13mm)^2(76mm) ≈ 40899mm^3

Surface area of cylinder = 2πrh + 2πr^2 = 2π(13mm)(76mm) + 2π(13mm)^2 ≈ 6128mm^2

Volume of sphere = (4/3)πr^3 = (4/3)π(13mm)^3 ≈ 9202mm^3

Surface area of sphere = 4πr^2 = 4π(13mm)^2 ≈ 2125mm^2

Finally, we can find the total volume and surface area of the figure by adding the values for the cylinder and sphere:

Total volume = Volume of cylinder + Volume of sphere ≈ 50101mm^3

Total surface area = Surface area of cylinder + Surface area of sphere ≈ 8253mm^2

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Answer:

1. is (18,4)

2. is (8,10)

3. (-9,-8)

4. (9,-8)

Step-by-step explanation:

i promise its right please give brainliest

The missing lengths of a geometric system are listed below: AC = 114, BC = 96, BE = 3

In this problem we find a geometric system formed by two similar triangles. Two triangles are similar if every pair of corresponding sides have the same proportion. Then, the system is described by this proportion formula:

AB / AC = AE / AD = BE / CD

18 / AC = 15 / 95 = BE / 19

Then,

18 / AC = 15 / 95

AC = 18 × (95 / 15)

AC = 114

15 / 95 = BE / 19

BE = 19 × (15 / 95)

BE = 3

Now, we determine the length of side BC:

BC = AC - AB

BC = 114 - 18

BC = 96

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The total surface area of the prism is  177.2 m².

The total surface area of the prism is calculated by applying the formula for total surface area of prism.

S.A = bh + (s₁ + s₂ + s₃)L

where;

The surface area of the prism is calculated as;

S.A = 4 m (3 m) + (3.8 m + 4 m + 4 m) x 14 m

S.A = 177.2 m²

Thus, the surface area of the prism is calculated using the formula for surface of right prism.

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Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years.

To determine the rate Hannah needs to earn to reach $1,000,000 in 25 years, we can use the future value formula for an annuity:

[tex]FV = Pmt * [(1 + r)^n - 1] / r[/tex]

where:

FV = future value (in this case, $1,000,000)

Pmt = periodic payment (in this case, Hannah's annual contribution)

r = annual interest rate

n = number of periods (in this case, 25 years)

Hannah will deposit $3,000 this year and increase her deposits by $750 each following year. So her annual contributions will be:

Year 1: $3,000

Year 2: $3,750

Year 3: $4,500

...

Year 25: $21,750

To simplify the calculation, we can use the average annual contribution over the 25-year period, which is:

[tex][(3,000 + 21,750) / 2] = $12,375[/tex]

Now we can plug in the values into the formula and solve for r:

[tex]1,000,000 = 12,375 * [(1 + r)^25 - 1] / r[/tex]

Multiplying both sides by r and dividing both sides by 12,375, we get:

[tex]r x (1 + r)^25 = 120.75[/tex]

We can solve for r using trial and error, or using a financial calculator or spreadsheet. Using trial and error, we can try different interest rates until we find the one that makes the equation true. One possible method is to start with a reasonable guess, such as 6%, and adjust up or down until we get close to 120.75. After a few iterations, we find that:

r = 5.88%

Therefore, Hannah needs to earn an annual interest rate of approximately 5.88% to reach $1,000,000 in 25 years, assuming she deposits $3,000 this year and increases those deposits by $750 each following year.

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The radius of the pool is changing at a rate of 3 / (20π) cm/min when the radius is 10 cm.

To solve this problem, we'll use the given information and the area formula for a circle.
Write the formula for the area of a circle:

[tex]A = \pi r^2[/tex],

where A is the area and r is the radius.
Differentiate both sides of the equation with respect to time (t): [tex]dA/dt = d(\pi r^2)/dt.[/tex]
Apply the chain rule on the right side: [tex]dA/dt = 2\pi r(dr/dt),[/tex]

where dr/dt is the rate of change of the radius.
Plug in the given values:

dA/dt = 3 cm²/min (given) and r = 10 cm (given at the moment of interest).
Solve for dr/dt:
3 = 2π(10)(dr/dt).

Isolate dr/dt:
dr/dt = 3 / (20π)
Simplify:
dr/dt = 1 / (20π/3) = 3 / (20π).

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Answer: Work done= F.d

= 15000 J

Step-by-step explanation:

Work done= Force*distance

where

Force= mass*acceleration

mass=30kg,  acceleration= 10 m/s^2, distance

=30*10

=300 N

then by formula of work done

Work done= F.d

= 300*50

=15000J

The total number of cards drawn is 16 and As a result, we have the following:

6 face cards, Aces 1, 9 numbered cards

Because there are 12 face cards, half of them are 6 face cards.

There are 4 aces, so we draw 1.

There are 36 numbered cards in total, therefore one-fourth of them are 9 numbered cards.

We draw a total of 6 + 1 + 9 = 16 cards.

We may use the information provided in the problem to determine how many of each card type we have. We chose:

6 face cards make up half of the deck.

1 ace: 1 ace

9 numbered cards are one-fourth of the numbered cards.

As a result, we have:

6 face cards

Aces: 1

9 numbered cards

We can also ensure that the total number of cards drawn (16) corresponds to the number of cards in a regular deck by subtracting the cards we drew from the total number of cards: a deck of playing cards (52)

There are 52 - 16 = 36 cards left.

This means that there are 36 - 6 - 1 - 9 = 20 undrawn cards in the deck.

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Ann drinks 125 milliliters of water each hour to stay on track and finish her 1-liter water bottle by the end of the school day.

To solve this problem, we first need to convert the given volume of water from liters to milliliters since milliliters are a more appropriate unit of measurement for the amount of water that Ann drinks each hour.

1 liter = 1000 milliliters

Therefore, Ann drinks 1000 milliliters of water in total for the day.

To find out how many milliliters of water Ann drinks each hour, we can divide the total amount of water by the number of hours she drinks it for.

1000 milliliters / 8 hours = 125 milliliters per hour

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Answer:

B

Step-by-step explanation:

the equation y=3/2x-3 has a slope of 3/2 and a y intercept of -3

So, first find the graph(s) that have the y intercept of -3.  The only options would be B and C.

Next, from the y-intercept of -3, go UP 3, and to the RIGHT 2 to find your next point.  This eliminates option C for the slope.  The slope of option C is 2/3, not 3/2.

So, option B is correct.  Hope this helps ;)

Answer:

B

Step-by-step explanation:

y = mx + b

y = mx (slope) + b (y-intercept)

The y-intercept of y = 3/2x - 3 is -3, so the graph needs to have a point at (0, -3). The slope is 3/2, if you go up 3 times and to the right twice from the point (0, -3), it will point (2, 0).

The measure of angle ABP from the given circle is 90°.

From the given figure,

11) Measure of angle ABP is 90°.

12) Measure of angle BAK is 180°-(90°+25°)

= 180°-115°

= 65°

13) Measure of angle AQP is 90°.

14) Measure of angle QAK is 180°-(90°+25°) (Because ∠BPA=∠QPA=25°)

15) Measure of Arc BK = Measure of angle BAK = 65°

16) Measure of Arc BQ = Measure of angle BAQ = 65°×2

= 130°

17) m∠CAD=m∠BAK=65°

Therefore, the measure of angle ABP from the given circle is 90°.

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The slope and derivative of a vertical tangent are both undefined due to the vertical nature of the tangent line.

The slope/derivative of a vertical tangent.
A vertical tangent occurs when a curve has a point where its tangent line is vertical.

In terms of the slope and derivative, the following is true about the vertical tangent:
Slope:

The slope of a vertical tangent is undefined because the vertical line has no run (change in x). Slope is calculated as the rise (change in y) divided by the run (change in x), and division by zero is not possible.
Derivative:

The derivative of a function at a point represents the slope of the tangent line to the curve at that point.

When the tangent is vertical, the derivative is also undefined because the slope is undefined.

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55% of the claims are within one standard deviation of the mean claim size.

To find the percentage of claims that are within one standard deviation of the mean claim size, we first need to calculate the mean and standard deviation of the distribution.

The mean claim size is:

u = (20 × 0.10) + (30 × 0.10) + (40 × 0.10) + (50 × 0.20) + (60 × 0.15) + (70 × 0.10) + (80 × 0.25) = 54

The variance can be calculated as follows:

s^2 = [[tex](20-54)^{2}[/tex] × 0.10] + [[tex](30-54)^{2}[/tex] × 0.10] + [[tex](40-54)^{2}[/tex] × 0.10] + [[tex](50-54)^{2}[/tex] × 0.20] + [[tex](60-54)^{2}[/tex] × 0.15] + [[tex](70-54)^{2}[/tex] × 0.10] + [[tex](80-54)^{2}[/tex] × 0.25] = 340

The standard deviation is the square root of the variance:

s = √340 ≈ 18.44

To find the percentage of claims that are within one standard deviation of the mean claim size, we need to find the range of claim sizes that fall within the interval (u - s, u + s).

(u - s) = 54 - 18.44 = 35.56

(u + s) = 54 + 18.44 = 72.44

We can see from the table that the claim sizes 40, 50, 60, and 70 fall within this range, and their probabilities add up to:

0.10 + 0.20 + 0.15 + 0.10 = 0.55

Therefore, 55 percentage of the claims are within one standard deviation of the mean claim size.

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The two fractions with denominators of 2 and 6 that add up to 19/3 are 3/6 and 29/3, respectively.

First, let's break down what that mixed number means in terms of fractions. 6 1/3 is the same as 19/3.

Now, we need to find two fractions with different denominators that add up to 19/3. One way to do this is to use a common denominator. To find a common denominator, we need to find the least common multiple (LCM) of the two denominators.

Let's say we want to find two fractions that add up to 19/3, with denominators of 2 and 6. The LCM of 2 and 6 is 6. So, we can rewrite the fractions with a denominator of 6:

1/2 = 3/6

x/6

Now we need to find the value of x that makes the sum of the fractions equal to 19/3:

3/6 + x/6 = 19/3

To solve for x, we can multiply both sides by 6:

3 + x = 38/3

Then, we can subtract 3 from both sides:

x = 29/3

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The answers are:

1) The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. For the given triangles:

Triangle 1: A = (1/2)(2ft)(4ft) = 4 sq ft (for one tablecloth), so for two tablecloths, the total area is 8 sq ft.

Triangle 2: A = (1/2)(6ft)(10ft) = 30 sq ft, so for two tablecloths, the total area is 60 sq ft.

Triangle 3: A = (1/2)(12m)(15m) = 90 sq m, so for two tablecloths, the total area is 180 sq m.

2) The area of a parallelogram is given by the formula A = Bh, where B is the base and h is the height. Rearranging this formula, we get h = A/B. For the given parallelogram:

A = 78 mm2 and B = 13 mm, so h = 78/13 = 6 mm.

3) The area of a rectangle is given by the formula A = LW, where L is the length and W is the width. For Charles' den:

The total wall space to be painted is (2 x 9 x 15) + (2 x 8 x 10) = 342 sq ft. One gallon of paint covers 440 sq ft, so Charles needs (342/440) = 0.7778 gallons of paint. Therefore, he does not have enough paint.

4) To calculate the total area of the walls to be painted, we can calculate the area of each wall and add them together.

The area of the two walls that are 9 ft high and 15 ft long is (9 x 15) = 135 sq ft each, for a total of 270 sq ft. The area of the other two walls that are 8 ft high and 10 ft long is (8 x 10) = 80 sq ft each, for a total of 160 sq ft. Adding them together, we get a total of 430 sq ft.

Since one gallon of paint covers 440 sq ft of wall space, Charles has enough paint to cover the den walls.

5) The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Rearranging this formula, we get h = 2A/(b1 + b2). For the given trapezoids:

A = (1/2)(6ft + 7ft)(10ft) = 65 sq ft and h = 2(65)/(6ft + 7ft) = 5 ft.

A = (1/2)(5yds + 8yds)(4yds) = 26 sq yds and h = 2(26)/(5yds + 8yds) = 2 sq yds.

A = (1/2)(9in + 11in)(13in) = 143.5 sq in and h = 2(143.5)/(9in + 11in) = 13.05 in.

For the application in part (d), we are given A = 32 km2 and (b1 + b2) = 16 km.

Rearranging the formula for A, we get h = 2A/(b1 + b2). Substituting the given values, we get h = 4

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The median nerve and Klumpke's palsy are both related to nerve injuries in the arm, but they involve different nerve pathways and result in different symptoms.

The median nerve runs from the brachial plexus in the neck through the arm to the hand, and controls movement and sensation in the thumb, index, middle, and part of the ring fingers. Damage to the median nerve can result in symptoms such as weakness, numbness, and tingling in these fingers, as well as muscle wasting in the thumb.

Klumpke's palsy, on the other hand, involves damage to the lower brachial plexus nerves, specifically the C7, C8, and T1 nerve roots. This can result in weakness or paralysis in the hand and wrist, with symptoms such as a claw-like deformity, decreased grip strength, and loss of sensation in the affected areas.

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The hypothesis statement h: μ < 60 is an example of an alternative hypothesis in a one-tail test is true

A hypothesis is a proposed explanation or prediction for an observation or phenomenon that is based on limited evidence or data. It is a tentative statement or idea that can be tested through further observation, experimentation, or data analysis. Hypotheses are often used in scientific research as a starting point to investigate a research question or problem.

The hypothesis statement "μ < 60" is an example of an alternative hypothesis in a one-tailed test.

In a one-tailed test, the alternative hypothesis is directional and states that the population parameter is either greater than or less than the null hypothesis value.

In this case, the alternative hypothesis states that the population mean is less than 60.

The null hypothesis, in contrast, is typically a statement of "no effect" or "no difference" and is often denoted by H0.

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The picture below shows the graph of the inequality of x² ≤ 4

Option B is correct.

In mathematics, an inequality is described as a relation which makes a non-equal comparison between two numbers or other mathematical expressions which is used most often to compare two numbers on the number line by their size.

A graph of inequality denotes that the variables is the set of points that represents all solutions to the inequality.

A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality.

Therefore, the correct option is B. x² ≤ 4

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The like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division. It does not have an equal sign and can be simplified or evaluated by applying the appropriate rules of arithmetic.

According to the given information:

The like radicals have the same radicand (expression under the radical sign) and the same index (the number outside the radical sign). Checking each expression:

Therefore, the like radicals are 3x√x²y and x√yx², and the answer is:

3x√x²y, -2x√xy³², x√yx²,  2√xy

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Nathan needs 24 cups of water to make his lemonade recipe.

Let's call the amount of lemon juice Nathan uses "x".

We know that Nathan uses 3 cups of lemon juice, so we can substitute x = 3 into the problem.

According to the recipe, the amount of sugar Nathan needs is twice the amount of lemon juice, so he needs 2x cups of sugar.

Substituting x = 3, we get that Nathan needs 2(3) = 6 cups of sugar.

The amount of water Nathan needs is four times the amount of sugar he needs, so he needs 4 times 6 cups of water, which is equal to 24 cups of water.

Therefore, Nathan needs 24 cups of water to make his lemonade recipe.

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The expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

Let s be the number of slices each friend received.

Then the total number of slices on the pizza is n and we have: 44s = n because pizza was evenly divided among the 44 friends). Harris ate 11 fewer slices than he received, so he ate s - 11 slices.

The no of slices he  received is s and we have:

s = (s - 11) + Harris's slices eaten

Substituting 44s = n, we will solve for s:

44s = n

s = n/44

So, the expression for the number of slices Harris ate is [tex](n/44) - 11.[/tex]

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We have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.

Let A and B be two sets in a generalized rectangle R, i.e., R = A x B. The boundary of R, denoted by bd(R), is defined as the closure of the set of points that are not in the interior of R. In other words, bd(R) = cl(R) \ int(R), where cl(R) is the closure of R and int(R) is the interior of R.

To show that bd(R) is the union of finitely many closed generalized rectangles with volume zero, we first note that the closure of R can be expressed as the union of R and its boundary, i.e., cl(R) = R ∪ bd(R). Therefore, it suffices to show that R can be expressed as the union of finitely many closed generalized rectangles with volume zero and that bd(R) can also be expressed as the union of finitely many closed generalized rectangles with volume zero.

Let (a,b) be a point in R. Then there exists an open ball B((a,b), r) around (a,b) that is contained in R, where r > 0. Without loss of generality, we can assume that r is small enough so that B((a,b), r) is a generalized rectangle. Since B((a,b), r) is open, it follows that int(R) is the union of all such generalized rectangles. Therefore, R can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such generalized rectangles.

Next, we show that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero. Let (a,b) be a point in bd(R). Then every open ball B((a,b), r) around (a,b) contains points both in R and in the complement of R. By definition of bd(R), the closure of B((a,b), r) intersects both R and the complement of R. Therefore, B((a,b), r) can be expressed as the union of two closed generalized rectangles, one contained in R and one contained in the complement of R. It follows that bd(R) can be expressed as the union of finitely many closed generalized rectangles with volume zero, namely the closures of all such balls B((a,b), r) and their decompositions into closed generalized rectangles.

Therefore, we have shown that the boundary of a generalized rectangle is the union of finitely many closed generalized rectangles with volume zero.

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Answer:

5.25 or 5 1/4

Step-by-step explanation:

-8(0.5x-3)=3

first, just multiply -8 by 0.5x and -8 by -3 and you'll get:

-4x+24=3

next, subtract 24 on both sides, meaning subtract 24 by 24 on the left side and subtract 24 by 3 on the ride side:

-4x=-21

the final thing you have to do is divide -4 on both sides to get the x by itself:

x=5.25 or 5 1/4