please help with #6, thank
you!
6. Find the derivative of the following. *SIMPLIFY your answers (4 Marks Each] a) y = (3x/V5x2-x2)3 b) f(x) = (5x – 3)5(3x - 1)3

We can expect to find 185 defective fuses each day.

The correct answer is c) 185.

At first we have to find the expected number of defective fuses each day, we can use the formula for the expected value of a binomial distribution:

Expected Value (μ) = n * p

where:

n = number of trials (in this case, the number of fuses produced each day) = 500

p = probability of success (in this case, the probability that a fuse is defective) = 37/100 = 0.37

Expected Value (μ) = 500 * 0.37 = 185

So, we can expect to find 185 defective fuses each day.

The correct answer is c) 185.

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The value of x in terms of the length of the chord BC is x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees

Draw a diagram of the circle and label the given points and segments.

Identify the relevant circle properties: Recall the properties of circles such as the radius, diameter, circumference, and central angle. Identify any angles or lengths that can be determined from the given information.

Use the tangent-chord theorem: Since AD is tangent to the circle, we can use the tangent-chord theorem to find that angle ADB is equal to angle ABD.

This implies that triangle ABD is an isosceles triangle.

Use the properties of isosceles triangles: Since triangle ABD is isosceles, we know that angle BAD is equal to angle ADB.

We also know that the sum of the angles in a triangle is 180 degrees.

Therefore, angle ABD is equal to (180 - 2x) degrees.

Use the angle sum property: Since A, B, C, and D are points on the circle, angle BAC is equal to half of the central angle BOC.

Therefore, angle BOC is equal to 2 * angle BAC.

Use the angle subtraction property: Since angle ABD is an exterior angle of triangle BCD, we know that angle ABD is equal to the sum of angles BCD and BDC.

Therefore, (180 - 2x) degrees is equal to (2 * angle BAC) + angle BDC.

Use the angle sum property again: Since B, C, and D are points on the circle, angle BDC is equal to half of the central angle BOC.

Therefore, angle BDC is equal to angle BAC.

Substituting this value into the equation from step 6, we get (180 - 2x) degrees

= (2 * angle BDC) + angle BAC

= 2 * angle BAC + angle BAC

= 3 * angle BAC.

Therefore, angle BAC is equal to (180 - 2x) / 3 degrees.

2 * angle BAC = 2 * (180 - 2x) / 3 degrees.

Use the chord length formula: Using the chord length formula, we can find that BC

= 2 * r * sin(angle BOC / 2), where r is the radius of the circle.

Substituting the value of angle BOC from step 9, we get BC = 2 * r * sin[(2 * (180 - 2x) / 3) / 2]

= 2 * r * sin[(180 - 2x) / 3] .

Solve for x:

We need to express x in terms of BC, so we can use the formula from step 10 to get 2 * r * sin[(180 - 2x) / 3] = BC.

Solving for x gives x = (1/2) * arcsin(BC / (2 * r)) - 30 degrees.

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Answer:

13

Step-by-step explanation:

1/4 of 52 is actually telling us to multiply 1/4 by 52 over 1.

1/4×52/1

=13

Answer:

The answer is 7.

Step-by-step explanation:

Cant you math bro?

Yes, when graphing two variables and observing an upward slope as you move from left to right, it indicates a positive relationship between the variables.

As one variable increases, the other variable also tends to increase. This positive correlation can be visually represented by a line that slopes upward in a graph. It implies that there is a direct and proportional relationship between the variables being studied.

But downward-sloping line indicate a negative relationship, where as one variable increases, the other variable tends to decrease. The slope of the line provides insights into the magnitude and direction of the relationship between the variables.

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The centroid is a point of concurrency of the medians of a triangle. The medians are the line segments that connect each vertex of the triangle to the midpoint of the opposite side. The centroid is located at the intersection of the three medians, and it is often denoted by the letter G.

Every triangle has a centroid, and it is one of the most important points in a triangle. The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice as long as the segment connecting the midpoint to the centroid. Therefore, the centroid is located two-thirds of the distance from each vertex to the midpoint of the opposite side.

To illustrate a triangle with a centroid, we can take any triangle and draw its three medians. The centroid is the point at which these three medians intersect. Any type of triangle, whether it is acute, obtuse, or right, will have a centroid. Therefore, any triangle can illustrate a centroid, and it is a fundamental concept in geometry that is used to solve many problems and prove theorems related to triangles.

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Answer: The answer is 4

Step-by-step explanation: First multiply 1/6 by its opposite or 6. Next multiply 6 by 4/6 and you would get 4. then check your answer by filling in the blank. The answer is then complete.

Hope this helps :)

Answer:

Yes it is

Step-by-step explanation:

Each x value is represented by exactly one y value.

The length of the other leg is 8.48 cm

What is Pyhtagorean Theorem?

The Pythagorean theorem states that the sum of the squares on the legs of a right triangle equals the square on the hypotenuse (the side opposite the right angle)

Solution:

Given that:

Length of One Leg = 17 cm

Length of Hypotenuse = 19 cm

To Find:

Length of the other leg

= We know that by pythagorean theorem

\(base^{2} + length^{2} = hypotenuse^{2}\)

17*17 + x^2 = 19*19

289 + x^2 = 361

x^2 = 72

x = 8.48 cm

The length of the other leg is 8.48 cm

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The integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

To determine the values of p for which the integral ∫10x^p * ln(x) dx converges, we need to consider the convergence of the integrand for different values of p. The integral will converge if the integrand is well-behaved and does not exhibit any divergence.

Let's analyze the integrand in two separate cases:

Case 1: p ≠ -1

When p ≠ -1, the integrand is well-defined for all x > 0. We can proceed with evaluating the integral.

∫10x^p * ln(x) dx = [x^(p+1) * ln(x)] / (p+1) + C

To calculate the value of the integral for a specific value of p, we can substitute the limits of integration into the antiderivative expression and evaluate the resulting expression.

Case 2: p = -1

When p = -1, the integrand becomes 10x^(-1) * ln(x), which poses a potential issue at x = 0. To determine if the integral converges for this case, we need to examine the behavior of the integrand near x = 0.

As x approaches 0, the expression ln(x) approaches negative infinity, which would cause the integrand to diverge. Therefore, for p = -1, the integral does not converge.

In summary, the integral ∫10x^p * ln(x) dx converges for all values of p except p = -1.

Please note that when evaluating the definite integral for specific limits of integration, you should substitute the limits into the antiderivative expression and then calculate the difference of the resulting expressions evaluated at the upper and lower limits.

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Answer:

a

Step-by-step explanation:

72,64,145

Answer:its 5

Step-by-step explanation: cuz

Adding the values of area  of 105, 56.52, and 244.53, we get: 105 + 56.52 + 244.53 = 406.05sq unit

The area of different shapes in the given figure are :-

Area of rectangle having length of 15 And width of 7

To find the area of a rectangle, we simply multiply the length by the width. So, for a rectangle with a length of 15 and a width of 7, the area would be:

Area = length x width

Area = 15 x 7

Area = 105

Therefore, the area of the rectangle would be 105 square units.

Area of semi circle having radius of 6

The formula for the area of a semicircle is:

Area = (π x r2) / 2

Where "r" is the radius of the semicircle and π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the value of radius (r) as 6 in the above formula, we get:

Area = (π x 6²) / 2

Area = (3.14 x 36) / 2

Area = 56.52 square units (approx)

Therefore, the area of the semicircle with a radius of 6 would be approximately 56.52 square units.

Area of cone having height of 9 And slant height of 7 and diameter 12

If the diameter of the cone is 12, then the radius (r) is equal to half of the diameter, i.e., r = 12/2 = 6 units.

Using the Pythagorean theorem, we can find the height (h) of the cone, which is given by:

h = √(ℓ² - r²)

Substituting the values of slant height (ℓ) as 7 and radius (r) as 6, we get:

h = √(7² - 6²)

h = √(49 - 36)

h = √13

Therefore, the height of the cone is √13 units.

Now, we can use the formula for the surface area of a cone:

Surface Area = πr²+ πrℓ

Substituting the values of radius (r) as 6 and slant height (ℓ) as 7, we get:

Surface Area = π(6)² + π(6)(7)

Surface Area = 36π + 42π

Surface Area = 78π

Therefore, the surface area of the cone with a height of 9, slant height of 7, and diameter of 12 would be 78π square units (approximately 244.53 square units if we use the approximation π = 3.14).

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Answer:

Step-by-step explanation:

If p = t + v and t is 5/2 and p is 0, then

0 = 5/2 + v and

v = -5/2

Answer:

6 cubes

Step-by-step explanation:

Considering the given cuboid, it can be deduced that;

length of the cuboid = 7 cm

width of the cuboid = 3 cm

height of the cuboid = 5 cm

Thus,

volume of the cuboid = length x width x height

                                    = 7 x 3 x 5

                                    = 105 cubic centimetres

The cubes has sides of length 2.5 cm.

volume of each cube = length x width x height

                                    = 2.5 x 2.5 x 2.5

                                    = 15.625 cubic centimetres

The greatest number of cubes that can be made = \(\frac{105}{15.625}\)

                                              = 6.72

The greatest number of cubes that can be made from the cuboid is 6.

The first 4 terms are 4 ,16,36 and 64 of the sequence (bn)n>=1 of partial sums of the sequence.

To find the first 4 terms of the sequence (bn)n≥1, we will calculate the partial sums as follows:

1. b1 = 4 (the first term)
2. b2 = b1 + 12 = 4 + 12 = 16 (sum of the first two terms)
3. b3 = b2 + 20 = 16 + 20 = 36 (sum of the first three terms)
4. b4 = b3 + 28 = 36 + 28 = 64 (sum of the first four terms)

So, the first 4 terms of the sequence (bn)n≥1 are 4, 16, 36, 64.

Now let's determine a recursive definition for bn. Notice that the difference between each term in the original sequence is 8 (12 - 4, 20 - 12, and 28 - 20). So, we can write the recursive definition as:

bn = bn-1 + 8n, for n > 1, and b1 = 4 (the first term).

This recursive definition can be used to find any term in the sequence (bn)n≥1 of partial sums.

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Answer:

Number  = 15.

Step-by-step explanation:

Given : If you multiply a number by 3 and then subtract 5, you will get 40.

To find : what is the number.

Solution : We have given if you multiply a number by 3 and then subtract 5, you will get 40.

According to question :

Let the number =  x

Multiply is with 3 = 3x

Subtract 5 from it we get 40 .

3x -5 = 40

On adding both sides by 5

3x = 45 .

On dividing both sides by 3

x =  15.

Therefore, Number  = 15.

Answer:

15

Step-by-step explanation:

3×y-5=40

3y-5=40

3y=40+5

3y=45

y=45÷3

y=15

The following statements are TRUE about hypothesis testing ;

hypothesis testing is known as statistical inference type that uses data from a sample to develop inferences about a population parameter or population probability distribution. An educated guess is first made on the parameter or distribution.

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The sample means are distributed along the x-axis for a sampling distribution of a sample mean.

A sample mean is an average of a set of data, that can be used to calculate the central tendency, standard deviation and the variance of a data set.

Now,

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Answer:

11

Step-by-step explanation:

Answer:

The factor pairs of the number 48 are: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8. When you multiply each of these factor pairs together, you get 48.

Step-by-step explanation:

1 x 48 = 48

2 x 24 = 48

3 x 16 = 48

4 x 12 = 48

6 x 8 = 48

HOPE IT'S HELP:)

Step-by-step explanation:

First, we need to find the actual dimensions of the rectangle in centimeters by converting meters to centimeters and multiplying:

Length = 12m = 1200cm

Width = 16m = 1600cm

Next, we need to find the dimensions of the rectangle on the blueprint. Since the scale is 1:80, we can divide the actual dimensions by 80 to get the blueprint dimensions:

Length on blueprint = 1200cm ÷ 80 = 15cm

Width on blueprint = 1600cm ÷ 80 = 20cm

Finally, we can calculate the area of the rectangle on the blueprint by multiplying the length and width:

Area on blueprint = 15cm x 20cm = 300cm²

Therefore, the answer is A. 300cm².

The second triangle will have the same side lengths and angles as the initial triangle.

The correct option is D.

The reflection of an equilateral triangle relative to the line passing through its side results in a new equilateral triangle that is the same size as the initial triangle. Therefore, the correct answer is D: The second triangle is the same size as the initial triangle.

When a figure is reflected across a line, every point on the figure is flipped to the opposite side of the line, maintaining the same distances and angles. In the case of an equilateral triangle, each side is reflected to the opposite side of the line, resulting in a new equilateral triangle with the same side lengths and angles.

The property of an equilateral triangle is that all three sides are equal in length, and all three angles are equal to 60 degrees. The reflection does not alter these properties. Therefore, the second triangle will have the same side lengths and angles as the initial triangle.

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A 95% confidence interval for the estimated proportion of Canadians who refused the H1N1 vaccination can be calculated as follows:

Let p be the true proportion of Canadians who refused the vaccination.

The sample proportion is estimated by:

p_hat = 700 / 1000 = 0.7

The standard error of the sample proportion is:

SE = sqrt(p_hat * (1 - p_hat) / 1000) = sqrt(0.7 * 0.3 / 1000) = 0.0247

Using a normal approximation and a z-score of 1.96 (corresponding to a 95% confidence level), the confidence interval can be calculated as:

p_hat +/- z * SE = 0.7 +/- 1.96 * 0.0247 = [0.6511, 0.7489]

So, with 95% confidence, we can estimate that the true proportion of Canadians who refused the H1N1 vaccination lies between 0.6511 and 0.7489.

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The order in which the kids sit is an illustration of arrangement.

We understand that: Bella is two seats away from Ella.

This arrangement is represented as: (E)_ (B)

Freddy sits between Bella and Ella.

This arrangement is represented as: (E) (F) (B)

Danielle does not sit next to Ella, and Charlie is at the end of the table.

This arrangement is represented as: (D) _ (E) (F) (B) (C)

So, Adam will occupy the seat between Danielle and Ella

This arrangement is represented as: (D) (A) (E) (F) (B) (C)

Hence, the order in which the 6 kids sit is: Danielle, Adam, Ella, Freddy, Bella and Charlie

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Answer:

The answerrrrrrrrrrr is x=-6

Answer: =-2x - 8

Step-by-step explanation:

Answer

X=10 and y=20

Step-by-step explanation:

since y=2x, you need to substitute that into the equation to get:

3x-(2x)=10

And evaluate:

x=10

Then substitute 10 into the equation: 2x=y:

2(10)=y

evaluate:

20=y

Now go back to the original equation to check your answer and substitute the values in:

3(10)-(20)=10

30-20=10

10=10

Answer:

---------------

Given equation:

Rearrange and factorize it:

According to factors we got, there are two real and two imaginary zeros:

x² = - 16 ⇒ x = ± 4i

The zeros of the equation 12\(x^2\) - 64 = -\(x^4\) are x = 2 and x = -2.

To find all the zeros of the equation 12\(x^2\) - 64 = -\(x^4\) , we can rearrange the equation to set it equal to zero and then solve for x.

First, let's rewrite the equation as \(x^4\) + 12\(x^2\) - 64 = 0.

Now, we can factor the equation.

Factoring a quadratic equation can be quite complex, so let's use a substitution to simplify it.

Let's substitute y = \(x^2\)

Substituting y = \(x^2\), we get \(y^2\) + 12y - 64 = 0.

Now we have a quadratic equation, which is easier to factor.

Factoring the quadratic equation, we have (y - 4)(y + 16) = 0.

Setting each factor equal to zero, we have two possible solutions: y - 4 = 0 and y + 16 = 0.

Solving for y in each equation, we find y = 4 and y = -16.

Now, we substitute back the value of y into our substitution equation y = \(x^2\).

For y = 4, we have \(x^2\) = 4, which gives us two solutions: x = 2 and x = -2.

For y = -16, we have \(x^2\) = -16. Since the square of any real number is always nonnegative, there are no real solutions for this case.

Therefore, the zeros of the equation 12\(x^2\) - 64 = -\(x^4\)  are x = 2 and x = -2.

In summary, the equation has two real zeros: x = 2 and x = -2. The equation does not have any other real zeros.

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Answer:

Step-by-step explanation:

To find the area of the base of the box, we need to determine the length, breadth, and height of the box. We can set up a system of equations to represent the given information:

breadth = 2/3 * length

height = 1/3 * length

volume = length * breadth * height

Substituting the second equation into the third equation, we get:

volume = length * breadth * (1/3 * length)

      = length^2 * (2/3) * (1/3)

      = (2/9) * length^2

      = 48

      = 2^4 * 3

Solving for length, we find that length = 6. Plugging this value back into the first equation, we find that breadth = 4.

Therefore, the area of the base of the box is length * breadth = 6 * 4 = 24 square meters.