consider a binomial experiment with n=2 and p=0.6

To find the equation of the sphere tangent to the plane 2x + 3y - 6z = 5 with center C(-2, 3, 7), we need to find the radius of the sphere. The equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

The distance from the center of the sphere to the plane is equal to the radius. We can use the formula for the distance between a point (x, y, z) and a plane Ax + By + Cz + D = 0:

Distance = |Ax + By + Cz + D| / sqrt(A^2 + B^2 + C^2)

In this case, the plane equation is 2x + 3y - 6z - 5 = 0. Plugging in the coordinates of the center C(-2, 3, 7) into the formula, we have:

Distance = |2(-2) + 3(3) - 6(7) - 5| / sqrt(2^2 + 3^2 + (-6)^2)

= |-4 + 9 - 42 - 5| / sqrt(4 + 9 + 36)

= |-42| / sqrt(49)

= 42 / 7

= 6

So, the radius of the sphere is 6.

The equation of a sphere with center C(-2, 3, 7) and radius 6 is:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 6^2

Simplifying further, we have:

(x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36

Therefore, the equation of the sphere is (x + 2)^2 + (y - 3)^2 + (z - 7)^2 = 36.

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30 is the probability that the critical path for this project will be completed within 200 days.

EXPECTED TIME = (OPTIMISTIC TIME + (4 * MOST LIKELY TIME) + PESSIMISTIC TIME) / 6

Y = (26 + (4 * 29) + 38) / 6 = 30.

The probability of an event can be calculated by simply dividing the number of favorable outcomes by the total number of possible outcomes using the probability formula.

Probability = number of paths to success. A total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

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The solution to the initial value problem is \(y = 4e^{(5x^{10})\). The domain of the function is all real numbers.

Ordinary differential equations of the first order only take into account the dependent variable y's first derivative with regard to the independent variable x. They could be written as follows:

f(x,y) = dy/dx

where the supplied function of both x and y is f(x,y). There are numerous methods for solving first-order ordinary differential equations, which are crucial in many branches of science and engineering. One such method is variable separation. Other methods include Bernoulli equations, integrating components, and precise equations.

The given differential function is:

\(dy/dx = 10x{^9}y\)

Separating the variables we have:

dy/y = 10x^9 dx

Now, integrating on both sides:

\(]int dy/y = \int 10x^9 dx\\ln (y) = 5x^{10} + C\)

Solving for y:

\(y = ke^{(5x^{10})\)

Now, for the initial values y = 4 and x = 0 we have:

\(4 = ke^{(0)}\)

k = 4

Hence, the solution to the initial value problem is \(y = 4e^{(5x^{10})}\).

The domain of the function is all real numbers.

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The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).

The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.

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The required sum of the positive integers x and y with the given condition of product of x and y as  square and cube is equal to 85.

Two positive integers are x and y.

Product of 360 and x is a square.

Product of 360 and y is a cube.

Prime factors of 360 equals to ,

360 = 2³ × 3² × 5

To make a product of 360 and x as square ,

Multiply by 2 and 5 and 3 is already a perfect square.

x = 2 × 5

 = 10

360 × 10 = 3600

Now , to make product of 360 and y as cube.

Multiply by 3  and 5² and 2 is already a perfect cube.

y = 3 × 5²

   = 75

360 × 75 = 27000

Sum of the values of x and y is equal to,

x + y

= 10 + 75

= 85

Therefore, the sum of the positive integers x and y are 85.

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Answer: 56.548

Step-by-step explanation:  Circumfrance = (radius x pi) x2

Answer:

The answer is 56.57miles

Step-by-step explanation:

(s - t)(-1) evaluates to 0.

To find the expressions for (s + t)(x) and (s * t)(x), we can simply add and multiply the given functions s(x) and t(x) accordingly.

(s + t)(x) = s(x) + t(x)

           = (2x - 4) + (6x)

           = 2x - 4 + 6x

           = 8x - 4

(s * t)(x) = s(x) * t(x)

           = (2x - 4) * (6x)

           = 12x^2 - 24x

To evaluate (s - t)(-1), we substitute x = -1 into the expression (s - t)(x) and simplify:

(s - t)(x) = s(x) - t(x)

           = (2x - 4) - (6x)

           = 2x - 4 - 6x

           = -4x - 4

Now, substitute x = -1:

(s - t)(-1) = -4(-1) - 4

           = 4 - 4

           = 0

Therefore, (s - t)(-1) evaluates to 0.

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Suppose that the functions s and t are defined for all real numbers x as follows. s(x) = 2x - 4 t(x) = 6x Write the expressions for (s + t)(x) and (s t)(x)and evaluate(s - t)(-1)

Answer:

\(AB = \frac{11}{2}\)

Step-by-step explanation:

Given

The above diagram

\(AB = 3y + 4\)

\(AC = 11y\)

Required

Determine length AB

Tangents drawn from the same point of a circle are equal;

This implies that

\(AB = AC\)

Substitute values for AB and AC

\(3y + 4 =11y\)

Subtract 3y from both sides

\(3y - 3y + 4 = 11y - 3y\)

\(4 = 8y\)

Divide both sides by 8

\(\frac{4}{8} = \frac{8y}{8}\)

\(\frac{4}{8} = y\)

\(\frac{1}{2} = y\)

Substitute \(\frac{1}{2}\) for y in \(AB = 3y + 4\)

\(AB = 3 * \frac{1}{2} + 4\)

\(AB = \frac{3}{2} + 4\)

\(AB = \frac{3 + 8}{2}\)

\(AB = \frac{11}{2}\)

Answer:

The answer is (3/4)100=75

Hope this helps!

Mark me brainliest if I'm right :)

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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you just need to put the values of a and b where they have to be

.

hope I helped!

Answer:

The value of x is 10.

3x+15=5x-5

3x=5x-5-15

3x=5x-20

3x-5x=(-20)

(-2x)=(-20)

x=10

We operate as follows:

**First problem:

*We divide the total number of messes by the value of the sum of the ratio.

391 / (14 + 9) = 17

After that, we multiply this value times the ration for the Gooey messes and we will obtain the number of Gooey messes present in the 391 messes:

17 * 14 = 238

So, we can expect 238 Gooey messes.

**Second problem:

*We have 174 purple yogi berries; we will have to calculate the number of berries that represent the 76% if we want to know how many are not purple. We also have the following ration 24:76 here there are 24 purple yogi berries to 76, not purple yogi berries, now we calculate:

So, we would expect 551, not purple yogi berries.

Answer:

Area= 2(x-3)

Area= (x-3)2

Step-by-step explanation:

not sure if that's right but I think it is

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Re-draw the given circe to show the radius

STEP 2: Explain the radius

A radius is a line drawn from the centre of a given circle to any part on the circumference. This line divides a circle into equal quarters as seen on the image. The radius divides the circle equally both vertically and horizontally.

STEP 3: Show the centre

Since the line of the radius goes from the centre, therefore the part identified below will be the centre

STEP 4: Get the coordinate of the centre

The coordinate of the centre will be the point on the x-axis as agianst the point on the y-axis.

Hence, the center of the given circle is:

Answer:

To find the total length of the two sides, we simply add them together:

Total length = Side 1 + Side 2

Total length = (8x^2 - 5x - 2) + (7x - x^2 + 3)

Total length = -x^2 + 8x^2 - 5x + 7x - 2 + 3

Total length = 7x^2 + 2x + 1

Therefore, the total length of the two sides of the triangle is 7x^2 + 2x + 1.

Step-by-step explanation:

To find the length of the third side of the triangle, we need to use the formula for the perimeter of a triangle:

Perimeter = Side 1 + Side 2 + Side 3

We are given the perimeter of the triangle as 4x^3 - 3x^2 + 2x - 6 and we know the lengths of Side 1 and Side 2. Therefore, we can rewrite the formula as:

4x^3 - 3x^2 + 2x - 6 = (8x^2 - 5x - 2) + (7x - x^2 + 3) + Side 3

Simplifying the right-hand side:

4x^3 - 3x^2 + 2x - 6 = 7x^2 + 2x + 1 + Side 3

Side 3 = 4x^3 - 3x^2 + 2x - 6 - 7x^2 - 2x - 1

Simplifying further:

Side 3 = 4x^3 - 7x^2 - x - 7

Therefore, the length of the third side of the triangle is 4x^3 - 7x^2 - x - 7.

Yes, the answers for Part A and Part B show that the polynomials are closed under addition and subtraction.

Closure under addition means that when two polynomials are added, the result is also a polynomial. In Part A, we added the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 to get the total length of the two sides of the triangle, which is 7x^2 + 2x + 1. Since the total length is also a polynomial, this shows that the polynomials are closed under addition.

Closure under subtraction means that when one polynomial is subtracted from another polynomial, the result is also a polynomial. In Part B, we subtracted the two polynomials 8x^2 - 5x - 2 and 7x - x^2 + 3 from the given perimeter of the triangle, 4x^3 - 3x^2 + 2x - 6, to get the length of the third side of the triangle, which is 4x^3 - 7x^2 - x - 7. Since the length of the third side is also a polynomial, this shows that the polynomials are closed under subtraction.

Therefore, the answers for Part A and Part B demonstrate that the polynomials are closed under addition and subtraction.

The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

According to statement

In location A the chance that two people have four repeats is  1 in 100.

In location B the chance that two people have eight repeats is  1 in 50.

In location C the chance that two people have three repeats is  1 in 200.

So, to find the probability that two people would have matching DNA fingerprints for these three locations

Multiply the all chances in these locations:

1/100 x 1/50 x 1/200 = 1/1,000,000    

So, The chances that two people would have matching DNA fingerprints for these three locations is 1/1,000,000  

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Answer:

The numerator (a*c) is the product of two integers ( a and c) and the denominator (b*d) is also ( b and d). This is why multiplying rational numbers is like multiplying integers.

Step-by-step explanation:

Step-by-step explanation:

the total surface area is the sum of the individual areas.

we have the ground area : a 6×6 square. = 36 cm²

and we have 4 equal triangles.

the area of a triangle is baseline × height / 2.

which is for each of these triangles

6 × 12 / 2 = 3 × 12 = 36 cm²

so, the total surface area of the pyramid is

36 + 4×36 = 5×36 = 180 cm²

Solution:

We know that:

This means that:

First, let's find the area of the triangle and square. Then, substitute them in the surface area equation to find the surface area of the pyramid.

Finding the area of a triangle:

Finding the area of a square:

Finding the surface area of the pyramid:

When dealing with the simultaneous occurrence of two events A and B, the probability can be determined by using the probability of one event and the conditional probability of the other event given that the first event has occurred. Both P(A) * P(B|A) and P(B) * P(A|B) are valid ways to calculate this probability.

The concept of probability is fundamental in various fields such as mathematics, statistics, and even in everyday life. The probability of the simultaneous occurrence of two events A and B is a critical concept in probability theory. According to the definition, the probability of A and B occurring at the same time is equal to the probability of A multiplied by the conditional probability of B given that A has occurred. This equation is also valid in the reverse case, where the probability of B and A occurring simultaneously is equal to the probability of B multiplied by the conditional probability of A given that B has occurred.

Understanding the relationship between the probability of two events and their conditional probabilities is essential in predicting the likelihood of these events happening together. In real-life situations, this concept can be used to determine the probability of two events such as the success of a product launch and the corresponding increase in sales. The probability of these two events occurring simultaneously can be predicted by analyzing the probability of the product launch's success and the conditional probability of sales increasing given that the product launch is successful.

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The coordinates for the local extrema are (0, 0) and (2/3, 4e^(-2)).

To find the coordinates for any local extrema of the function h(x) = 3x^2e^(-3x), we need to find the critical points by taking the derivative of h(x) and setting it equal to zero.

Step 1: Find the derivative of h(x)

h'(x) = d/dx (3x^2e^(-3x))

To differentiate the function, we can use the product rule and the chain rule:

h'(x) = 6xe^(-3x) + 3x^2(-3e^(-3x))

= 6xe^(-3x) - 9x^2e^(-3x)

= e^(-3x)(6x - 9x^2)

Step 2: Set h'(x) = 0 and solve for x

e^(-3x)(6x - 9x^2) = 0

We have two factors: e^(-3x) = 0 and 6x - 9x^2 = 0.

For e^(-3x) = 0, there are no real solutions since the exponential function is always positive.

For 6x - 9x^2 = 0, we can factor out x:

x(6 - 9x) = 0

Setting each factor equal to zero:

x = 0 and 6 - 9x = 0

Solving the second equation:

6 - 9x = 0

9x = 6

x = 6/9

x = 2/3

So the critical points are x = 0 and x = 2/3.

Step 3: Find the corresponding y-values

To find the corresponding y-values, we substitute the critical points into the original function h(x).

For x = 0:

h(0) = 3(0)^2e^(-3(0))

= 0

For x = 2/3:

h(2/3) = 3(2/3)^2e^(-3(2/3))

= 4e^(-2)

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If the scale factor is 3 and the point is (-3, 3). Then the point after the dilation will be (-9, 9).

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

The point is given below.

(-3, 3)

And the scale factor is 3.

Then the point after the dilation will be

Let (x, y) be the dilated point.

Then we have

(x, y) = (-3 × 3, 3 × 3)

(x, y) = (-9, 9)

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For a polynomial, Leading coefficient is the coefficient of the term with the degree of polynomial. For \(a^{2}+bx+c\) , The leading coefficient is 'a'.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

Example of leading coefficient are:

\(2x^{2}+x+1\), leading coefficient=2

\(8x^{3}+5x^{2}+3x+1\), leading coefficient =8

\(3x^{5}+8x^{3}+7x+6\), leading coefficient = 3

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Answer:

5.83units

Step-by-step explanation:

from Pythagoras theorem;

a^2=b^2+c^2

where a is the hypotenuse,b is the opposite and c is the adjacent

b=3 and c=5

a^2=3^2+5^2

a^2=9+25

a^2=34

find the square root of both sides,

√a^2=√34

a=5.83units

Answer:5.83

Step-by-step explanation:

Step-by-step explanation:

Expanding the expression (C+8)(8C+2), we get:

(C+8)(8C+2) = 8C^2 + 2C + 64C + 16

= 8C^2 + 66C + 16

Therefore, (C+8)(8C+2) simplifies to 8C^2 + 66C + 16.

Answer:

Hope this helped!~

Step-by-step explanation:

Expanding the expression using the distributive property, we get:

(c + 8)(8c + 2) = 8c^2 + 2c + 64c + 16

Simplifying, we can combine like terms:

(c + 8)(8c + 2) = 8c^2 + 66c + 16

Therefore, the polynomial in standard form is 8c^2 + 66c + 16.

Your answer would be 39.85 ♡

Answer:

14 - n.

Step-by-step explanation:

If he donated 'n' shirts, we can simply subtract 'n' from his initial amount of shirts, which is stated as '14'. Therefore:

'14 - n' is an expression that can represent how many shirts are remaining after he donated them.

(a) lim(x→1) (x-1)/(1-2x):
We can directly substitute x=1:
lim(x→1) (1-1)/(1-2) = 0/(-1) = 0
(b) lim(x→0) (1+2e^3)/(1-32):
Again, we can substitute x=0:
lim(x→0) (1+2e^3)/(1-32) = (1+2e^3)/(-31)

(a) lim(x→∞) (√(x+2) - √x)/(2-x):
To simplify, we can rationalize the numerator:
lim(x→∞) ((√(x+2) - √x)/(2-x)) * ((√(x+2) + √x)/(√(x+2) + √x))
= lim(x→∞) (x+2 - x)/((2-x)(√(x+2) + √x))
= lim(x→∞) 2/(√(x+2) + √x) = 2/2 = 1
(b) lim(x→0) (18/(x+2)^2)/(2-x)^2:
We can simplify the expression:
lim(x→0) (18/(x+2)^2)/(2-x)^2 = 18/(2^2) = 18/4 = 9/2
(c) lim(r→∞) (x^4 + x^2 + 1)/(e^2r):
As r approaches infinity, e^2r also approaches infinity. Thus, we have:
lim(r→∞) (x^4 + x^2 + 1)/(e^2r) = 0/∞ = 0

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When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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