A person can burn about 9 calories per minute bicycling. Let x represent the number of minutes bicycled, and let y represent the number of calories burned. Create a mapping diagram to show the number of calories burned by bicycling for 50, 100, 150, or 200 minutes. Determine the domain and range of the relation in context and explain whether or not this represents a function.

The luminosity of Jupiter compared to the Sun is [tex]\( 9.57 \times 10^{27} \)[/tex] Watts.

To find the luminosity of Jupiter compared to the Sun, we can use the inverse square law of brightness. The luminosity of a celestial body depends on its distance from the observer. Given that Jupiter's orbital radius r = 5 AU (Astronomical Units) and the Sun's luminosity is [tex]\( L_{\odot} = 3.828 \times 10^{26} \)[/tex] Watts, we can calculate the luminosity of Jupiter [tex](\( L_J \)).[/tex]

Find the distance ratio [tex](\( \frac{r_{\text{Jupiter}}}{r_{\text{Sun}}} \))[/tex]:

[tex]\[ \text{Jupiter's distance ratio} = \frac{5 \, \text{AU}}{1 \, \text{AU}} = 5 \][/tex]

Apply the inverse square law:

[tex]\[ \frac{L_{\text{Jupiter}}}{L_{\odot}} = \left( \frac{r_{\text{Sun}}}{r_{\text{Jupiter}}} \right)^2 \][/tex]

[tex]\[ L_{\text{Jupiter}} = L_{\odot} \times \left( \frac{r_{\text{Jupiter}}}{r_{\text{Sun}}} \right)^2 \][/tex]

[tex]\[ L_{\text{Jupiter}} = 3.828 \times 10^{26} \times (5)^2 \][/tex]

[tex]\[ L_{\text{Jupiter}} = 3.828 \times 10^{26} \times 25 \][/tex]

[tex]\[ L_{\text{Jupiter}} = 9.57 \times 10^{27} \, \text{Watts} \][/tex]

So, the luminosity of Jupiter compared to the Sun is [tex]\( 9.57 \times 10^{27} \)[/tex] Watts.

Michael makes a total of $400 from his land investment after calculating the total losses and gains from the lands sold.

In order to find out the total money that Michael has made from his land investment, you need to calculate the losses and the gains individually. Michael sells two of his lands at a loss of $1,200 each, hence his total loss is 2 * $1,200 = $2,400. On the other hand, he sells the other two lands at a profit of $1,400 each, hence his total profit is 2 * $1,400 = $2,800.

To get the total money that he made on his investment, you subtract the total loss from the total profit. That is $2,800 (total profit) - $2,400 (total loss) = $400. Hence, Michael makes $400 on his investment.

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The probability that the product of the numbers selected by Neil and Jean is even is approximately 0.8889.

To answer your question, let's first classify the numbers from the given set 1,2,3,4,5,6,7,9,10 into two categories: even numbers (2, 4, 6, 10) and odd numbers (1, 3, 5, 7, 9). Each of the people, Neil and Jean, can pick any number independently. Hence we have two scenarios which result in the product being even - either both pick even numbers or at least one of them picks even.

The probability of both picking an even number is (4/9)*(4/9) = 16/81. Also, there is no constraint on the second scenario, so, total probabilities = 1. Hence, the probability of at least one picking an even is 1 - probability(both picking odd) = 1 - (5/9)*(5/9) = 1 - 25/81 = 56/81.

Therefore, the total probability that the product of the numbers selected by Neil and Jean is even is the sum of the above two probabilities i.e., 16/81 + 56/81 = 72/81 = 0.8889 (approx).

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Answer:

45 :)

Step-by-step explanation:

Answer:

the next term would be 5

The simplified value of the number √3/10 will be 3/√30.

What is mean by Fraction?

A fraction is a part of whole number, and a way to split up a number into equal parts.

Or, A number which is expressed as a quotient is called fraction.

It can be written as the form of p : q, which is equivalent to p / q.

Given that;

The number is,

⇒ √3/10

Now,

Simplify the number as;

⇒ √3/10 = √3/10 x √3/3

             = 3 / √30

Thus, The simplified value of the number √3/10 will be 3/√30.

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Answer:

The missing value in last step is 3

Step-by-step explanation:

Given the function f(x)

[tex]f(x)=18x+3x^2[/tex]

Here some steps are given to write the above function in vertex form.

Step 1: Factor a out of the first two terms

[tex]f(x)=3(x^2+6x)[/tex]

Step 2: Form a perfect square trinomial.

[tex]f(x) = 3(x^2 + 6x + 9) - 3(9)[/tex]

Write the trinomial as a binomial squared.

By the identity of binomial square

[tex]a^2+2ab+b^2=(a+b)^2[/tex]

[tex]x^2 + 6x + 9=x^2+2(x)(3)+3^2[/tex]

[tex]\text{Put a=x and b=3 in the identity, we get}[/tex]

[tex]x^2+2(x)(3)+3^2=(x+3)^2[/tex]

[tex]x^2 + 6x + 9=(x+3)^2[/tex]

Hence, the f(x) can be written as

[tex]f(x) = 3(x+3)^2 - 3(9)[/tex]

Therefore, the missing value in last step is 3

38 is most likley the answer am i right?!

Final answer:

To simplify the expression 23 · 16 + 24 ÷ 4, we first perform the multiplication and division according to PEMDAS, resulting in 368 + 6, and then add those results to get the final answer, 374.

Explanation:

To simplify the expression 23 · 16 + 24 ÷ 4, we need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).

First calculate the multiplication: 23 × 16 = 368.

Then, the division: 24 ÷ 4 = 6.

Finally, add the two results together: 368 + 6 = 374.

Therefore, the simplified expression equals 374.

The receiver is situated 10.125 inches from the vertex, is the correct response.

What is Parabola?

According to our question-

Make the origin of the parabola the vertex. Then, it has the equation y = bx^2.

The parabola crosses via (18,8), therefore 8 = b(182^) b = 0.02469 because

Its equation is y = 0.02469x2.

For best reception, the receiver should be positioned at the paraboloid's focus point.

The focus has a y-coordinate of

a = 1/(4b) = 1/0.098765

= 10.125 in

The receiver is situated 10.125 inches from the vertex, is the correct response.

Hence we can say that, the receiver is situated 10.125 inches from the vertex.

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Final answer:

Using the formula [tex]f = \(\frac{d^2}{16h}\)[/tex] for a parabolic dish, where the dish is 36 inches wide (diameter) and 8 inches deep, the optimal location of the receiver is calculated to be approximately 10.125 inches from the vertex for best reception.

Explanation:

The question asks where the receiver should be placed on a satellite dish that has the shape of a paraboloid for optimal reception. The given dimensions are that the dish is 36 inches wide and 8 inches deep. A parabolic dish reflects signals to a focal point where the receiver is typically placed for optimal signal reception. We can use the properties of a parabolic shape to find the location of the focal point, also known as the focus of the parabola.

To find the focal length (distance from the vertex to the focus) of a paraboloid, we use the formula [tex]f = \(\frac{d^2}{16h}\)[/tex], where d is the diameter and h is the depth. Substituting our values in (d = 36 inches, h = 8 inches) we get the focal length [tex]f = \(\frac{36^2}{16 \times 8}\) = \(\frac{1296}{128}\) \approx 10.125[/tex] inches. Therefore, the receiver should be located approximately 10.125 inches from the vertex of the satellite dish for optimal reception.

The receiver's optimal location, rounded to the nearest thousandth, is therefore 10.125 inches from the vertex.

1 package of plates = 10 plates  and 2 package of cups = 10 cups

 so 3 packages is least amount

Final answer:

The student's question involves finding the derivative dy/dx for the equation [tex]x^3 + y^3 = 18xy[/tex]. This is done through implicit differentiation, resulting in dy/dx = [tex](18y - 3x^2) / (3y^2 - 18x).[/tex]

Explanation:

The student has presented an equation involving x and y and has asked for the derivative of y with respect to x (dy/dx). To find dy/dx, we use implicit differentiation because y is not isolated on one side of the equation. The given equation is [tex]x^3 + y^3 = 18xy.[/tex]

Start by differentiating both sides with respect to x:

The derivative of [tex]x^3[/tex] with respect to x is [tex]3x^2.[/tex]

The derivative of [tex]y^3[/tex] with respect to x is [tex]3y^2[/tex] times dy/dx (chain rule).

The derivative of 18xy with respect to x is 18y + 18x times dy/dx (product rule).

Bringing all terms involving dy/dx to one side gives:

[tex]3x^2 + 3y^2(dy/dx) = 18y + 18x(dy/dx)[/tex]

Solve for dy/dx:

[tex]3y^2(dy/dx) - 18x(dy/dx) = 18y - 3x^2[/tex]

Factor out dy/dx:

[tex]dy/dx (3y^2 - 18x) = 18y - 3x^2[/tex]

Finally, solve for dy/dx:

[tex]dy/dx = (18y - 3x^2) / (3y^2 - 18x)[/tex]

This expression represents the slope of the tangent to the curve at any point (x, y).

The number of possible sets with 0 heads when flipping a coin five times is 1, represented by five consecutive tails (TTTTT).

When flipping a coin five times, the number of possible sets that have 0 heads (meaning all tails) is just one. This single microstate is TTTTT.

The reason for this is that each coin flip is an independent event with two possible outcomes: heads (H) or tails (T). When we are only concerned with the total head and tail count and not the order in which they appear, the only set with 0 heads is the set where every coin lands on tails.

the answer is 5

1: a^3

2: 3a^2b

3: 4ab

4: 11b

5: 7

anything seporated by a + or - is a term

Answer:

[tex]9b+10u > 1,000[/tex]