if the shaded cross sections of the solids have the same area, which of the following corresponds to the value of a: the side length of the base of the square prism?

The equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3) which can be written in the form y = mx + b is:

y = 3√3x - π√3/2 + 3, where m = 3√3 and b = -π√3/2 + 3.

To obtain the equation of the tangent line to the curve y = 6sin(x) at the point (π/6, 3), we need to determine the slope (m) of the tangent line and the y-intercept (b).

The slope of the tangent line is equal to the derivative of the function y = 6sin(x) evaluated at x = π/6.

Let's calculate it:

dy/dx = d/dx(6sin(x))

      = 6 * d/dx(sin(x))

      = 6 * cos(x)

Substituting x = π/6 into the derivative, we get:

m = 6 * cos(π/6)

 = 6 * cos(π/6)

 = 6 * (√3/2)

 = 3√3

Now that we have the slope (m), we can determine the y-intercept (b) using the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

Plugging in the point (π/6, 3), we get:

y - 3 = 3√3(x - π/6)

Next, we can simplify and rewrite the equation in the form y = mx + b:

y = 3√3(x - π/6) + 3

 = 3√3x - π√3/2 + 3

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Answer:

9/19  or  47.4% (nearest tenth)

Step-by-step explanation:

A roulette wheel is numbered 1 to 36 with 0 and 00.

Therefore, there is a total of 38 evenly-spaced pockets.

The number of odd numbers from 1 to 36 is 18

(1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35)

\(\sf Probability\:of\:an\:event\:occurring = \dfrac{Number\:of\:ways\:it\:can\:occur}{Total\:number\:of\:possible\:outcomes}\)

\(\implies \textsf{Probability of odd number}= \sf \dfrac{18}{38}=\dfrac{9}{19}=47.4\%\)

Roulette wheel contains 1 to 36 numbers excluding 0 and 00

Total odd nos

{1,3,5,7,9,11,13,15,17,19,21,23,25,29,31,33,35}

Probability

Answer:

Rs 2,or 2%profit

Step-by-step explanation:

the price he marked:

\(100 \times \frac{120}{100} = 120\)

(20 percent more than cost price)

The discount he put: 15 percent

\(120 \times \frac{85}{100} \)

Rs102

102 is 2 more than 100

and is 2%profit.

Brainliest please

We need the angle AOD to find the x value

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

Missed data: ABCD is a QUADRILATERAL

'O'  is a point in the middle joining OA,OB,OC and OD , find the angle AOD  which is x here

Adding 3 angles we get 11x+22,

Equation is :

11x+22 + AOD = 360

=> AOD = 360 - 22- 11x

     AOD= 338- 11x  

We need the angle AOD to find the x value

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Answer:

Yes

Step-by-step explanation:

If you plug the numbers into the equation and solve it

18 = -2(-9)

18 = 18

The value of variables are,

⇒ k = 60

⇒ m = 120

We have to given that;

A quadrilateral DEFG is inscribed in a circle.

And, The measure of angle EDG is 60 degrees and the measure of angle DGF is 60 degrees. The measure of angle DEF is labeled m degrees and the measure of angle EFG is labeled 2k degrees.

Now, We can formulate;

⇒ ∠GDE + ∠EFG = 180°

⇒ 60° + 2k = 180

⇒ 2k = 180 - 60

⇒ 2k = 120

⇒ k = 60

And, We have;

∠DEF + ∠DGF = 180°

m + 60 = 180

m = 180 - 60

m = 120°

Hence, The value of variables are,

⇒ k = 60

⇒ m = 120

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Answer: 1729 trout.

Step-by-step explanation:

We can use the logistic growth model to estimate the number of trout after 2 years:

N(t) = K / (1 + (K/N0 - 1) * e^(-rt))

where:

N(t) is the number of trout at time t

K is the carrying capacity of the lake (2700 trout)

N0 is the initial population (275 trout)

r is the growth rate (75% or 0.75, per year)

e is the base of the natural logarithm, approximately equal to 2.71828

To estimate the number of trout after 2 years, we can plug in t = 2 and solve for N(t):

N(2) = 2700 / (1 + (2700/275 - 1) * e^(-0.75*2))

N(2) = 2700 / (1 + 8.8 * e^(-1.5))

N(2) ≈ 1728.7

Therefore, we can estimate that the number of trout after 2 years will be approximately 1729 trout.

Answer:

To find the measure of angle A, we substitute the given expression into the formula for the measure of an angle:

A = 12x + 12 degrees

To find the measure of angle C, we substitute the given expression into the formula for the measure of an angle:

C = 3x + 18 degrees

The measure of angle B is already given as 15 degrees.

Therefore, the measures of the three angles are:

Angle A = 12x + 12 degrees

Angle B = 15 degrees

Angle C = 3x + 18 degrees

1. y-12 =9

y = 12 + 9

y = 21

2. 42=7x

x = 42/7

x = 6

3. 5p-7=28

5p = 28 + 7

5p = 35

p = 7

4. 1.5x+1.3x=-8.4

2.8x = - 8.4

x = - 8.4 : 2.8

x = - 3

5. 4/3w -12=2/3w

w = 18

6. 4 (3q-2)=16q

12q - 8 = 16q

4q = -8

q = - 2

7. -h+4=-h+9

4 = 9

∅

8. t+3t-7=4t-7

4t - 7 = 4t - 7

4t = 4t

0 = 0

9. 1/4(n-6)=1/4-3/2

n = 1

10. 2d+1/6=6(1/3d+1)

2d + 1/6 = 2d + 6

1/6 = 6

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

Answer:

0.4375

Step-by-step explanation:

u divided 10,500 and 24,000 and u will get 0.4375

Answer:

(x+1)^2 = x^2 + 2x +1

so b =2

Step-by-step explanation:

Given:

Where the Mean (μ ) and Standard Deviation (σ) for a Normal Distribution, you need to find:

Where "X" is the number of hours worked per worker.

In order to calculate that probability, you should approximate to a Standard Normal Distribution. Therefore, you need to find z-statistic:

The value of "X" you must use is:

Then, substituting values and evaluating, you get:

Therefore, now you need to find:

Now you need to use the Standard Normal Distribution Table in order to find the value of the probability. Then, you get:

Hence, the answer is:

Answer:

14

Step-by-step explanation:

4 - 5 * -2 =

4 - -10 =

14

Hope this helped :]

Answer:

14

Step-by-step explanation:

b = 4

y = -2

Therefore;

(4) - 5(-2)

=> 4 - (-10)

=> 4 + 10

=> 14

Hope this helps!

Answer:

1) you use any parallel lines or rectangles we can double the triangle to get the area and then divide by 2 as we know the length is 92.5yards and we know the width is 53.5 yards.

We would x these by each other and then divide by 2.

We have the width 53 1/2 yards wide and convert this to decimal if we want.

= 53.5 yards.

We then can count the yards for the length =  90 hash marks = 90 yards+ 2.5

= 92.5yards.

We square then add to find the hypotenuse diagonal line but it is an estimate as the lines inscribed subtends into the corner and it becomes a little larger as bottom line is used. Diagonal is found after by doing a reverse equation on the area.

53.5 x 92.5 then divide by 2 = 4948.75/2 = 2474.375

then 2474.375/ 26.75 = 92.5

This proves the line is isosceles and also find the height of the triangle.

But only as an estimate as the actual line distends

Last answer is B and W are equal measures this is because we do not see a right angle and if we bisected the triangle from the goal line to the left side we would prove the midpoint goal line is actually equal and makes lines of play isosceles where two sides are the same at point B and W.

So the answer is 1 yard as B runs the length of the goal back to a position of diagonal run.

The diagonal length is 92.5 yards

Step-by-step explanation:

The linear function that models the population of bloater fish is y2= -92.57x + 1, 052

The linear equation that determines when the two populations were equal is

-19.76x + 227 = -92.57x + 1052

The solution is x= 11.33 years

(A) Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

(A) Average speed = Distance / Time

Average speed = 200 meters / 19.30 seconds

Average speed = 10.36 meters per second

Therefore, Usain Bolt's average speed in meters per second was approximately 10.36 m/s.

(B) 1 mile = 2580 feet

Converting the distance from meters to miles:

Distance in miles = Distance in meters / (1 meter / 3.28 feet) / (1 mile / 5280 feet)

Distance in miles = 200 meters / 3.28 / 5280 miles

Time in hours = Time in seconds / (60 seconds / 1 minute) / (60 minutes / 1 hour)

Time in hours = 19.30 seconds / 60 / 60 hours

Average speed = Distance in miles / Time in hours

Average speed = (200 meters / 3.28 / 5280 miles) / (19.30 seconds / 60 / 60 hours)

Average speed = 23.35 miles per hour

Therefore, Usain Bolt's average speed in miles per hour was approximately 23.35 mph.

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The formula to calculate the expected loss is given by the following formula: Expected Loss = Σ (Loss Amount * Probability of Loss)To calculate the expected loss, we need to first multiply the loss amount with the probability of loss, and then add the products.

a. $0 .30Loss amount, X = $0Probability of loss, P(X) = 0.30Expected loss = 0 * 0.3 = $0b. $120 .50Loss amount, X = $120Probability of loss, P(X) = 0.50Expected loss = 120 * 0.5 = $60c. $200 .20Loss amount, X = $200Probability of loss, P(X) = 0.20Expected loss = 200 * 0.2 = $40, the expected loss for the given probabilities of various losses is $0 for a), $60 for b) and $40 for c). The total expected loss would be the sum of all expected losses i.e. $100.

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Answer:

1.09 seconds

Step-by-step explanation:

I need the image that I am going to attach to solve the exercise.

We have the following information:

Confetti height from the ground is 25 feet

Person's height is 6 feet

So, the distance that the confetti would fall would be the subtraction of these heights, that is:

25-6 = 19 feet

d = 19 feet

We use the 5th equation of the attached image:

t = d ^ (1/2) / 4

replacing:

t = 19 ^ (1/2) / 4

t = 1.09 seconds

In summary d²y/dx² in terms of x and y is given by: d²y/dx² = 3/2 x + 1/4 y

Why is it?

To find d²y/dx², we need to differentiate the given differential equation with respect to x:

dy/dx = x² - 1/2 y

Differentiating both sides with respect to x:

d²y/dx² = d/dx(x² - 1/2 y)

d²y/dx² = d/dx(x²) - d/dx(1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

Now, we need to express d/dx(y) in terms of x and y. To do this, we differentiate the original differential equation with respect to x:

dy/dx = x² - 1/2 y

d/dx(dy/dx) = d/dx(x² - 1/2 y)

d²y/dx² = 2x - 1/2 d/dx(y)

d²y/dx² = 2x - 1/2 (d²y/dx²)

Substituting this expression for d²y/dx² back into our previous equation, we get:

d²y/dx² = 2x - 1/2 (2x - 1/2 y)

d²y/dx² = 2x - x/2 + 1/4 y

d²y/dx² = 3/2 x + 1/4 y

Therefore, d²y/dx² in terms of x and y is given by:

d²y/dx² = 3/2 x + 1/4 y

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Cost of Goods Manufactured is an accounting term used to describe the total cost of producing and manufacturing goods. It includes all direct and indirect costs of production, including labor, materials, overhead, and other expenses. Below are the five components of the cost of goods manufactured.

Direct Materials: It includes the cost of raw materials used in manufacturing a product.

Direct Labor: It includes the wages paid to workers who directly worked on the production line or in manufacturing a product.

Factory Overhead: It includes all indirect costs of manufacturing a product such as depreciation on equipment, rent, insurance, utilities, etc. Work-in-Process

Inventory: It includes the cost of materials, labor, and overhead that has been incurred but has not yet been completed. Finished Goods Inventory: It includes the cost of goods that have been fully manufactured but have not yet been sold.

To calculate the cost of goods manufactured, the sum of all these five components is calculated. It helps manufacturers to determine the total cost of goods manufactured and the cost per unit of production. Cost of goods manufactured is essential in determining the pricing strategy for a product as it helps to ensure that the product is profitable.

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Answer:

y = -5/3x -7

Step-by-step explanation:

See screenshot.

The minimum yield value of the key material should be determined based on the yield stress of the shaft, which is 36 kg/m², the dimensions of the key, and the safety factor of 2.

To ensure that the key smoothly transmits the torque of the shaft, it is essential to choose a key material with a minimum yield value that can withstand the applied forces without exceeding the yield stress of the shaft.

The dimensions of the key given are 20x20x120 mm. To calculate the torque transmitted by the key, we need to consider the dimensions and the applied forces. However, the specific values for the applied forces are not provided in the question.

The safety factor of 2 indicates that the material should have a yield strength at least twice the expected yield stress on the key. This ensures a sufficient margin of safety to account for potential variations in the applied forces and other factors.

To determine the minimum yield value of the key material, we would need additional information such as the expected torque or the applied forces. With that information, we could calculate the maximum stress on the key and compare it to the yield stress of the shaft, considering the safety factor.

Please note that without the specific values for the applied forces or torque, we cannot provide a precise answer regarding the minimum yield value of the key material.

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Answer:

7.67 liters

Step-by-step explanation:

Answer:

The point which is the midpoint is equally spaced from both ends of the line. We know the coordinates of A and we know the coordinates of M, the midpoint.

Step-by-step explanation:

Answer: 10 km

Step-by-step explanation:

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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