15. [-/3 Points] DETAILS 0/2 Submissions Used Use differentials to estimate the amount of paint needed (in m3) to apply a coat of paint 0.06 cm thick to a hemispherical dome with diameter 60 m. (Round your answer to two decimal places.) ms

Answer:

above sea level

Step-by-step explanation:

The solution x(t) of the equation x = rx + x', where r > 0 is fixed, approaches infinity in finite time starting from any initial condition x = 0.

We can solve the differential equation x' = rx + x using separation of variables. Rearranging the equation, we get:

x' - rx = x

This is a linear first-order differential equation with integrating factor e^(-rt). Multiplying both sides by e^(-rt), we obtain:

e^(-rt)x' - re^(-rt)x = e^(-rt)x

Using the product rule for derivatives, the left-hand side becomes:

(d/dt)[e^(-rt)x] = e^(-rt)x'

Substituting this into the equation, we get:

(d/dt)[e^(-rt)x] = e^(-rt)x

This equation can be integrated to obtain:

e^(-rt)x = C

where C is a constant of integration. Solving for x, we get:

x = Ce^(rt)

Since r > 0, the exponential function e^(rt) grows without bound as t approaches infinity. Therefore, the solution x(t) of the differential equation also grows without bound in finite time starting from any initial condition x = 0. This means that x(t) approaches infinity as t approaches a certain finite value, which depends on the value of r.


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On solving the equation of factorial we got the value of the expression \(\frac{10! }{ 7!3! }\)  is  120.

To evaluate the expression \(\frac{10! }{ 7!3! }\), we can simplify the factorials in the numerator and denominator separately.

First, let's simplify the numerator:

10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Now, let's simplify the denominator:

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

3! = 3 × 2 × 1

We can cancel out the common terms in the numerator and denominator:

\(\frac{10! }{ 7!3! } = \frac{(10 * 9 * 8)}{ (3 * 2 * 1)}\)

Now, we can calculate the expression:

\(\frac{(10 * 9 * 8)}{ (3 * 2 * 1)}= \frac{720}{6} = 120\)

Therefore, the value of the expression \(\frac{10! }{ 7!3! }\) is 120.

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Answer: 3.33

Step-by-step explanation:

Multiplication and division should be solved left to right.

\(37/100*9\\\\Divide(100)\\\\0.37*9\\\\Multiply(9)\\\\3.33\)

Hope it helps <3

Answer:

=37/100×9=.

=divide 37 by 100

=0.37 ×9

=3.33

The shaded sections of the trapezoid are triangles.

We know how to find the area of triangles

A = 1/2 bh

Lets start with the left triangle

The bases is 1.1 inches and the height is 3.8 inches

A left triangle is

A = 1/2 ( 1.1) * 3.8 = 2.09

The right triangle has the same dimensions

A right triangle is

A = 1/2 ( 1.1) * 3.8 = 2.09

Add the two triangles together

2.09+2.09 = 4.18 in^2

The area of the shaded region is 4.18 in^2

Answer:

230cm²

Step-by-step explanation:

The shape can be split into two shapes horizontally: a triangle and a rectangle.

Area of the rectangle

The area of a rectangle = length × width

In this case, the length is 20cm and the width is 7cm. 20 × 7 = 140cm²

Area of the triangle

The area of a triangle = 1/2 × base × height

In this case, the base is 20cm and the height is 9cm (16cm - 7cm). 1/2 × 20 × 9 = 90cm²

Area of the shape

To find the area of the total shape, we can add 140cm² and 90cm² to get 230cm².

Hope this helps!

The z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

The z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

How to find the Z score

P(Z ≤ z) = 0.60

We can use a standard normal distribution table or a calculator to find that the z-score corresponding to a cumulative probability of 0.60 is approximately 0.25.

Therefore, the z-score for P(? ≤ z ≤ ?) = 0.60 is approximately 0.25.

For the second question:

We want to find the z-score such that the area under the standard normal distribution curve to the right of z is 0.30. In other words:

P(Z ≥ z) = 0.30

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.30 is approximately -0.52 (since we want the area to the right of z, we take the negative of the z-score).

Therefore, the z-score for P(z ≥ ?) = 0.30 is approximately -0.52.

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Given data:

The standard expression for the proportionality is,

It means the graph must pass through the origin.

5)

Thus, the amount of money raised by Phil's is proportionally related.

6)

The unit rate change is the slope of the line which is,

Thus, the unit rate change is $7.5/mile.

Answer:

The area is 12.56 units^2 (same as circumference?)

Step-by-step explanation:

Assuming pi is 3.14, the equation for the circumference is C = 2 pi r

Fill it out for the radius (r)

12.56 = 2 3.14 r

12.56 = 6.28 r

r = 2

With the radius, the equation for the area is A = pi r^2

Fill it out for the area

A = 3.14 2^2

A = 3.14 4

A = 12.56

To determine which interval has the most confidence in capturing the population mean, we need to look at the confidence level associated with each interval. A confidence interval is a range of values that we believe contains the true population parameter.

If we have three intervals with different confidence levels, the interval with the highest confidence level would be the one with the most confidence in capturing the population mean. For example, if Interval A has a confidence level of 90%, Interval B has a confidence level of 95%, and Interval C has a confidence level of 99%, then Interval C would have the most confidence in capturing the population mean.

It's important to note that the level of confidence we choose affects the width of the interval. The higher the confidence level, the wider the interval will be. Therefore, we need to balance the desire for a high level of confidence with the need for a narrow interval.

In summary, the interval with the highest confidence level is the one with the most confidence in capturing the population mean. Confidence intervals are a powerful tool in statistics that allows us to estimate population parameters from a sample with a known degree of uncertainty.

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Answer:

=-8x^3

Step-by-step explanation:

=2x^-1×4x^2

=-2x×4x^2

=-8x^3

(2x)⁻¹ × (4x)² = 8x

2x to the power of negative 1 is represented as follows

The value((2x)⁻¹) multiplied by 4x squared is represented as follows

Therefore,

(2x)⁻¹ × (4x)²  = (2x)⁻¹ × 16x²

(2x)⁻¹ × 16x²  = \(\frac{1}{2x}\) × 16x²

\(\frac{1}{2x}\) × 16x²  = 8x

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A) To find \(\( f'(t) \) for \( f(t) = \left(\frac{{6t - 6}}{{t}}\right)^2/9 \)\), we can use the chain rule. First, let's simplify the expression:

\(\[ f(t) = \left(\frac{{(6t - 6)^2}}{{t^2}}\right)/9 \]\)

Applying the chain rule, we differentiate the numerator and denominator separately:

\(\[ f'(t) = \frac{{2(6t - 6)(6) \cdot t^2 - (6t - 6)^2(2t)}}{{9t^4}} \]\)

Simplifying further:

\(\[ f'(t) = \frac{{72t^3 - 72t^2 - 12t(6t - 6)^2}}{{9t^4}} \]\)

B) To find \(\( f'(x) \) for \( f(x) = e^{\sqrt{5x + 2}} \)\), we can use the chain rule.

The derivative of the exponential function \(\( e^u \) with respect to \( u \) is \( e^u \cdot u' \).\)

In this case, \(\( u = \sqrt{5x + 2} \), so \( u' = \frac{d}{dx}(\sqrt{5x + 2}) \).\)

Applying the chain rule:

\(\[ u' = \frac{1}{2\sqrt{5x + 2}} \cdot \frac{d}{dx}(5x + 2) = \frac{1}{2\sqrt{5x + 2}} \cdot 5 = \frac{5}{2\sqrt{5x + 2}} \]\)

Now, we can apply the chain rule to find \(\( f'(x) \):\)

\(\[ f'(x) = e^{\sqrt{5x + 2}} \cdot \frac{5}{2\sqrt{5x + 2}} \]\)

C) To find the derivative of \(\( f(x) = x^3 \cos(x) \)\), we can apply the product rule. The derivative of the product of two functions \(\( u \) and \( v \)\) is given by \(\( (uv)' = u'v + uv' \).\) In this case, \(\( u = x^3 \) and \( v = \cos(x) \).\) Differentiating \(\( u \) and \( v \):\)

\(\[ u' = 3x^2 \quad \text{and} \quad v' = -\sin(x) \]\)

Applying the product rule:

\(\[ f'(x) = (x^3 \cdot \cos(x))' = 3x^2 \cdot \cos(x) + x^3 \cdot (-\sin(x)) \]\)

Simplifying further:

\(\[ f'(x) = 3x^2 \cos(x) - x^3 \sin(x) \]\)

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The absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.

To find the absolute maximum and minimum values of the function F(x) = x^2 - 4x - 9, we need to calculate the function's critical points and calculate the function at these points.

The critical points can be found by setting the first derivative of the function equal to zero and solving for x:
F'(x) = 2x - 4 = 0
2x = 4
x = 2

We now need to calculate the function at x=-1, x=2, and x=3 to find the absolute maximum and minimum values:
F(-1) = (-1)^2 - 4(-1) - 9 = -16
F(2) = 2^2 - 4(2) - 9 = -3
F(3) = 3^2 - 4(3) - 9 = 8

Therefore, the absolute maximum value is 8 at x=3, and the absolute minimum value is -16 at x=-1.

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The value of a and b is 1.

The probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is ab, where a and b are integers.

To find the value of a and b, we need to determine the total number of ways Nate can place the disk (the denominator of the probability fraction) and the number of ways he can place the disk so that it touches an equal number of shaded and unshaded squares (the numerator of the probability fraction).

Since the center of the circle must be at the meeting point of four squares, the only possible places for the center are the points where four squares meet. Since the grid is made of 2 cm x 2 cm squares, there are 4 shaded squares and 4 unshaded squares. So, there are 4 centers that could be placed on a shaded square and 4 centers that could be placed on an unshaded square.

So the denominator of the probability fraction is 8.

Now, to calculate the numerator, we need to determine the number of ways Nate can place the disk so that it touches an equal number of shaded and unshaded squares.

As the center of the circle is at the meeting point of four squares, the center of the circle is placed at the intersection of 2 shaded and 2 unshaded squares.

So, the numerator of the probability fraction is 8.

Therefore, the probability that Nate places the disk so that it is touching an equal number of shaded and unshaded squares is 8 ÷ 8 =1.

So the value of a and b is 1.

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Answer: 36/104

There are 104 students that play sports and only 36 out of 104 students has the favorite color blue, green, or purple.

Step-by-step explanation:

The value of P(B|S) is mathematically given as

36/104

Question Parameter(s):

samples 222 high school students

event S =104

event B = 36

In conclusion, the value of P(B|S) is

36/104

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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The experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is approximately 0.263

The experimental probability is found by dividing the number of times the desired outcome occurred by the total number of trials. In this case, the desired outcome is selling a slice of pepperoni pizza as the first slice tomorrow.

Since we only know the number of slices sold today, we don't have any specific information about the number of slices that will be sold tomorrow. However, we can assume that the same types of pizzas will be sold tomorrow, and the probability of selling a slice of pepperoni pizza tomorrow will be the same as the proportion of pepperoni slices sold today.

So, the experimental probability that the first slice sold during lunch tomorrow will be a slice of pepperoni pizza is

Experimental probability = Number of pepperoni slices sold today / Total number of slices sold today

Experimental probability = 20 / 76

Experimental probability = 0.263

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(a) The probability that both John and Jane watch the show is 0.15 or 15% (rounded to 2 decimal places).
(b)The probability that Jane watches the show, given that John does, is 0.3 or 3.

(c) Since these probabilities are equal, John and Jane watch the show independently of each other.

The answer is Yes.

John and Jane watch the show independently of each other if

(a) To find the probability that both John and Jane watch the show, we can use the conditional probability formula:

P(A and B) = P(A|B) * P(B),

where A represents John watching the show and B represents Jane watching the show.
Given, P(A|B) = 0.5 and P(B) = 0.3.
P(A and B) = 0.5 * 0.3 = 0.15.
Therefore, the probability that both John and Jane watch the show is 0.15 or 15% (rounded to 2 decimal places).
(b) To find the probability that Jane watches the show, given that John does, we can use the conditional probability formula: P(B|A) = P(A and B) / P(A).
Given, P(A and B) = 0.15 and P(A) = 0.5.
P(B|A) = 0.15 / 0.5 = 0.3.
Therefore, the probability that Jane watches the show, given that John does, is 0.3 or 30% (rounded to 3 decimal places).
(c) John and Jane watch the show independently of each other if P(A and B) = P(A) * P(B).

In this case, P(A and B) = 0.15 and P(A) * P(B) = 0.5 * 0.3 = 0.15.

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Answer:

The equation is 3g= c

Step-by-step explanation:

this is how much 11 gallons will cost 3 x 11= $33

1 gallon costs 3$

2 gallons cost 6$

3 gallons cost 9$

4 gallons cost 12$

5 gallons cost 15$

6 gallons cost 18$

7 gallons cost 21$

8 gallons cost 24$

Answer:

On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Which is the graph of the given function?

Here we have the exponential decay:

f(x) = 100*(0.7)^x

So, as x increases, y will tend to zero (because this is a decay, the number with the exponent x is between zero and 1).

Now, if we evaluate in x = 0 we get:

f(0) =  100*(0.7)^0 = 100

Then it goes through the point (0, 100).

If we evaluate in x = 2, we get:

f(2) = 100*(0.7)^2 = 49

Then it also goes through the point (2, 49).

With all that in mind, the correct option is:

"On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100)."

The probability that exactly 18 of the 25 smartphones selected are purchased with warranty is:  The probability that exactly 8 of the 25 smartphones selected are not purchased with warranty is: The probability that all 25 smartphones selected are purchased with warranty is:  

The probability that at most 15 of the 25 smartphones selected are purchased with warranty is: The probability that at least 14 of the 25 smartphones selected are purchased with warranty is: f) The probability that more than half (i.e. > 12) of the 25 smartphones selected are purchased with warranty is: 9) The probability that at least 14 but no more than 23 of the 25 smartphones selected are purchased with warranty is:

h) The probability that less than 12 or more than 19 of the 25 smartphones selected are purchased with warranty is: Part 2Mean = Standard Deviation =  Part 3To find the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty, we use the following formula: N = [(Z * σ) / E]^2 where Z is the z-score corresponding to the desired level of confidence, σ is the standard deviation, and E is the maximum error of estimation. Using a 95% level of confidence, Z = 1.96.Using the calculated standard deviation of 2.91 and expecting to find exactly 72 smartphones, the maximum error of estimation is 0.5.N = [(1.96 * 2.91) / 0.5]^2N

= 337.11

Therefore, the minimum sample size required to expect to find exactly 72 smartphones that are purchased with warranty is 338.

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Answer:

hondred thosend

Step-by-step explanation:

Answer:

The place value is the hundred thousands place.

Step-by-step explanation:

<3

The correct answer is x = 2

(x + 1 < 4) ∩ (x-8>-7)

Make x the subject in each case:

(x<4-1)(x>-7+8)

        (x<3)∩(x>1)

If x<3, then x could be 2, 1, -1, etc.

If x>1, then x could be 2, 3, 4, etc.

Thus (x<3)∩(x>1) = 2

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Answer:

x = 2

Step-by-step explanation:

Hello!

We are looking at the intersection of two sets, or common values found between two sets of data.

We can solve for x on each side and find any common values between.

As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.

Therefore, the intersection of these sets is 2.

F is the numerator of the fraction. To solve move g over to the opposite side by multiplying both sides by g:

F = h * g

The signof function is defined as follows:

def signof(num):
   if num > 0:
       return 1
   elif num == 0:
       return 0
   else:
       return -1

In the above code snippet, we have defined a function named signof which receives an integer argument named num. The if condition checks if the num is greater than 0, if yes, the function will return 1 as it is positive. Else if the num is equal to 0, then it will return 0, as per the requirement. Otherwise, it will return -1 as the number is negative. This code snippet will give the required output as per the requirement of the problem statement.

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The total number of ways or permutations in which that  can be done are: d. 5040 different ways

To solve this problem the formula and the permutation procedure we must use is:

nPr = n! / (n-r)!

Where:

Information about the problem:

Applying the permutation formula we have:

nPr = n! / (n-r)!

7P7 = 7! / (7-7)!

7P7 = 7! / 0!

7P7 = 7! / 1

7P7 = 7 * 6 * 5 * 4 * 3 * 2 * 1 / 1

7P7 = 5040

It is the ordered arrangement of members belonging to a set with no repeats.

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Step-by-step explanation:

Hey there!

The given points are; (-2,4) and (3,-6).

Slope formula;

\(slope(m) = \frac{y2 - y1}{x2 - x1} \)

Put all values.

\(m = \frac{ - 6 - 4}{3 + 2} \)

\(m = \frac{ - 10}{5} \)

Therefore the slope is -2.

Hope it helps...