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Suzanne ran 3 3/4 miles in the morning and 4 1/2 ​ miles in the afternoon. How many kilometers did she run altogether? Assume 1 mile = 1.6 kilometers.

The value of f is 0.02.

Expression is a formation of numbers and variables with mathematical operations.

According to the given question we have to solve for f or we can say we have to find the value of f for the given expression which is

2+1.25f=10−2.75f                (lets multiply each term by 100 to remove

                                                                                              decimals )  

∴ 200 + 125f = 1000 - 275f

125f + 275f = 1000 - 200

400f = 800

      f = 800/400

      f = 2.

As we have multiplied by 100 we have to divide by 100 we obtain the exact result.

So, 2/100 is = 0.02

f = 0.02.

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Age of son = 19 years

Age of father = 57 years

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Given,

A father is three times as old as his son

Sum of their age is 76 years

Let age of son is x, age of father = 3x

x + 3x = 76

4x = 76

x = 76/4

x = 19

Age of son = 19 years

Age of father = 3×19 = 57 years

Hence, 19 years is the age of son and

57 years is the age of father.

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The product of two irrational numbers can be either rational or irrational.

The product of two irrational numbers is not always irrational. To understand this, let's consider an example and a counterexample.

Example of an Irrational Product

Take the square root of 2 (\/(2)) and the square root of 3 (\/(3)). Both of these numbers are irrational. Their product is:

\/2 × \/3 = \/6

Since \/6 cannot be expressed as a fraction of two integers (making it irrational), this is an example where the product of two irrational numbers is irrational.

Counterexample of a Rational Product

Now, consider another example with \/(2) and \/(2). Since both are irrational, their product is:

\/2 × \/2 = 2

Here, 2 is a rational number because it can be written as a fraction (2/1). Therefore, this is a counterexample where the product of two irrational numbers is rational.

In summary, the product of two irrational numbers can be either rational or irrational depending on the specific numbers involved.

The vector field f(x, y) = (yex + sin y) i + (ex + x cos y) j is conservative because its curl vanishes everywhere. The function F such that ∇F = f is yex + cos y + C.

To determine if the given function f(x, y) = (yex + sin y) i + (ex + x cos y) j is a conservative vector field, we need to see if the curl of the vector field vanishes everywhere. The curl of a vector field in two dimensions is the partial derivative of the j component with respect to x minus the partial derivative of the i component with respect to y.

For f(x, y), the partial derivative of the j component (ex + x cos y) with respect to x is ex + cos y, and the partial derivative of the i component (yex + sin y) with respect to y is ex + cos y. Both derivatives are equal, implying the curl is zero. Hence, f(x, y) is a conservative vector field.

Next, to find a function F such that ∇F = f, we need to integrate. The potential function, F, can be obtained by integrating the i component of f with respect to x (since it does not involve y), and the j component of f with respect to y (since it does not involve x): ∫yex dx + ∫sin y dy = yex + cos y + C. This is the function F such that ∇F = f.

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The conditional probability that event a will occur given that event b has occurred, denoted as p(a | b), is approximately 0.3 or 30%.

The question is asking for the conditional probability of the event a given that event b has occurred, written as p(a | b). In probability theory, the formula for conditional probability is p(a | b) = p(a ∩ b) / p(b). Here, we already know that p(a ∩ b) = 0.14 and p(b) = 0.46. Substituting these values into the formula gives us:

p(a | b) = 0.14 / 0.46 = 0.304347826.

So, the probability of event a occurring given that event b has occurred is approximately 0.3 or 30%.

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Answer:

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

As a professional what you put on social media matters a lot. Social Media postings show all what you are thinking or doing to hundreds, thousands, or even millions of people. If you are an artist you depend on those people (fans) to continue supporting you and your art so a single wrong post can turn a lot of people against you.

If you work for a company you are not only representing yourself through your posts but the company as well. This is because a company hires you for the person that you are therefore it is seen through the public eye that they share your way of thinking.

The best way for your postings to reflect you professionally, is to post only things relating to your own career and journey. While leaving out any opinions, personal information, and controversial topics.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

B. Decreasing

Step-by-step explanation:

We have been given formula of a function [tex]F(x)=9\cdot (\frac{1}{7})^x[/tex]. We are supposed to determine the type of our given function.

We know that an exponential function is in form [tex]y=a\cdot b^x[/tex], where,

a = Initial value,

b = If [tex]b>1[/tex], then the function is growth function. If [tex]b<1[/tex], then the function is decay function.

Upon looking at our given function we can see it is in form of exponential function.

Upon comparing our given function with standard exponential function, we can see that the value of a is 9 and value of b is [tex]\frac{1}{7}[/tex].

Since [tex]\frac{1}{7}<1[/tex], therefore, our function is decreasing and option B is the correct choice.

The probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.

To find the probability that a random variable ( x) is between $34 and $38, we need to use the probability density function (PDF) if ( x) follows a continuous distribution. Let's assume ( x ) follows a normal distribution with a mean [tex](\( \mu \))[/tex] of $36 and a standard deviation [tex](\( \sigma \))[/tex] of $2.

Calculate the z-scores for $34 and $38:

[tex]\[ z_1 = \frac{34 - 36}{2} = -1 \][/tex]

[tex]\[ z_2 = \frac{38 - 36}{2} = 1 \][/tex]

Look up the z-scores in the standard normal distribution table:

[tex]\[ P(z_1 < Z < z_2) = P(-1 < Z < 1) \][/tex]

Find the probabilities corresponding to these z-scores:

[tex]\[ P(Z < 1) = 0.8413 \][/tex]

[tex]\[ P(Z < -1) = 0.1587 \][/tex]

Subtract the two probabilities:

[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]

So, the probability that ( x) is between $34 and $38 is 0.6826 or 68.26%.

The limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] means that the term  [tex]a_n[/tex] becomes large as n becomes large

The limit of a function describes the behavior of such function as the independent variable approaches a certain value

Infinity [tex]\infty[/tex] represents a very large number

In the limit, both n and [tex]a_n[/tex] tend to infinity

The given limit is:

[tex]\lim_{n \to \infty} a_n = \infty[/tex]

The limit above describes the behavior of [tex]a_n[/tex] as n approaches infinity

As n approaches infinity [tex]a_n[/tex]  also approaches infinity

Therefore, the description of the limit [tex]\lim_{n \to \infty} a_n = \infty[/tex] is that the term  [tex]a_n[/tex] becomes large as n becomes large

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The statement 'lim n → ∞ an = ∞' means that the terms an become large as n becomes large.

The statement lim n → ∞ an = ∞ means that the terms an become large as n becomes large.

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The length and width of the rectangle will be 19 meters.

The sum of all the sides of the rectangle will be known as the perimeter of the rectangle. Let L be the length and W be the width of the rectangle.

Then the perimeter of the rectangle will be

Perimeter of the rectangle = 2(L + W) units

The perimeter of a college athletic field is 104 meters and the length is 16 meters more than the width.

L = 14 + W

Then the length and width of the rectangle will be

P = 2(L + W)

104 = 2(14 + W + W)

52 = 14 + 2W

2W = 38

W = 19 meters

The length and width of the rectangle will be 19 meters.

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