Which equations represent inverse variation? Check all that apply.
y = 2x
pv = 13
z = (2/x)
4 = (y/x)
h = (9g/5)

Final answer:

Kate ran approximately 9.66 kilometers after converting her distance run in miles to kilometers using the conversion factor of 1 mile equaling 1.60934 kilometers.

Explanation:

Kate ran 6 miles and we need to convert that distance into kilometers. To do this, we use the conversion factor that 1 mile is approximately equivalent to 1.60934 kilometers. By multiplying 6 miles by this conversion factor, we get:

6 miles × 1.60934 km/mile = 9.65604 kilometers

So, from the above calculation Kate ran roughly 9.66 kilometers, considering we usually round the result to two decimal places when dealing with distances unless high precision is required.

To find the differential operator that annihilates the given function e^(-x) + 8xe^x - x^2e^x, we individually find differential operators for each term. The operators d^2, d^3, and d^4 annihilate e^(-x), 8xe^x, and x^2e^x respectively. The least common multiple of these operators is d^4, which is the common operator that annihilates the entire function.

To find a linear differential operator that annihilates the function e−x + 8xex − x2ex, we must apply an operator that, when used on these functions, yields zero. For simplicity, we can use d to represent the differential operator d/dx. We annihilate each term independently and find a differential operator common to all terms.

Starting with the first term e−x, we note that d(e−x) = −e−x. Applying d again gives us d(d(e−x)) which is e−x. Thus, applying d2 annihilates e−x.

Next, consider the second term 8xex. Applying the operator d3 to 8(xex) would be: d3(8xex) = d3(8(ex + xex))= d3(8ex) + d3(8xex) which results in zero.

For the third term x2ex, applying d4 annihilates the term, following the pattern: d4(x2ex) = d(d(d(d(x2ex)))) = 0.

The common differential operator that annihilates all three terms is the least common multiple of the individual operators for each term, in this case, d4.

Answer: i think it is 22

Step-by-step explanation:

Answer:

 -divide both sides by -2

                                -2x-y=-9

                                 2x+3y=15

                           -sum the equations vertically to

                             eliminate at least one variable

                              2y=6 divide both sides of the equation

                                        by 2

                              y=3

            -substitute the given value of y into the simplest equation

                              2x+3*3=15

                                   -solve for x

                                        x=3

                 -the solution of the system is the ordered pair (x,y)

                                  (x,y)= (3,3)

                                        Check √

-check if the given ordered pair is a solution of the system of equations

{4*3+2*3=18

{2*3+3*3=15

simplify the inequalities  

{18=18

{15=15

-since all of the equalities are true the ordered pair is the solution of the system

Step-by-step explanation:

Sir, please show your work

Answer:

30.2 mph

Step-by-step explanation:

Hello, I think I can help you with this

the speed average is the  is the quotient of the distance traveled and the time used to do it,  mathematical speaking

[tex]Average\ speed =\frac{distance}{time}\\[/tex]

Step 1

Put the values into the equation

Let

Distance:302 miles

Time:10  hours

[tex]Average\ speed =\frac{distance}{time}\\\\Average\ speed =\frac{302\ miles}{10\ hours}\\Average\ speed =30.2 \frac{miles}{hour} \\[/tex]

Average speed=30.2 mph

Have a great day.

so the syrup is just water and sugar, we know that the sugar percent is just 12%, and that happens to be 5grams.

now 100% - 12% is 88%, so the 88% leftover will just be water.

if 12% is 5g, how much is 88%?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 5&12\\ x&88 \end{array}\implies \cfrac{5}{x}=\cfrac{12}{88}\implies \cfrac{5}{x}=\cfrac{3}{22}\implies 110=3x \\\\\\ \cfrac{110}{3}=x\implies 36\frac{2}{3}=x[/tex]

Answer:

[tex]36\dfrac{2}{3}[/tex] g of water.

Step-by-step explanation:

You know that 5 g of sugar form 12%. Let x g be the amount of water needed. The total amount of syrup will be x+5 g. Then

5 g - 12%,

x+5 g - 100%.

Mathematically, you can write a proportion:

[tex]\dfrac{5}{x+5}=\dfrac{12}{100}\Rightarrow 500=12(x+5),\ 500=12x+60,\ 12x=440, \\ \\x=\dfrac{440}{12}=\dfrac{110}{3}=36\dfrac{2}{3}.[/tex]

Just got this question in a practice test on Edge. The answer is definitely Alex, or D.

Answer:

The expressions equivalent to 'the product of a number minus 17 and 5' are (n - 17) x 5 and 5(n - 17), where n is the unknown number. These cannot be simplified further without additional information.

Step-by-step explanation:

The statement 'the product of a number minus 17 and 5' can be translated into an algebraic expression. This expression would look like (n - 17) × 5 or 5(n - 17), where n represents the unknown number. Both expressions are equivalent and represent the same mathematical operation.

When simplifying algebraic expressions, it is important to eliminate terms wherever possible to get a more straightforward expression. However, in this case, since we don't have a specific value for n, we cannot simplify the expression further without additional information.

Always remember to check your answer to ensure that the expression makes sense and is reasonable within the context of the problem.

To calculate the probability of winning the Powerball, you need to identify all possible combinations for drawing 5 unique numbers from a set of 59, then multiply that with the separate 35 options for the 'powerball'. Your chance of winning equals one (the exact match to your ticket) divided by the total possible combinations.

The probability of winning the Powerball jackpot can be determined using the concept of combination in probability theory. Probabilities are calculated by taking the total number of successful outcomes or combinations and dividing it by the total number of possible outcomes or combinations.

In the case of Powerball, there are 5 unique numbers to be drawn from a pool of 59 (ignoring order), and 1 'powerball' from a pool of 35. For the 5 unique numbers, there are C(59,5) combinations where C(n,r) = n! / [r!(n-r)!], n being the total number of options available and r being the number of options chosen at a time.

For the 'powerball', since it is a separate pool of 35 numbers and only 1 is chosen, the number of combinations is simply 35. As such, you multiply the two outcomes for total possible combinations: C(59,5)*35.

For the probability of winning, you want to know combinations that match exactly your selection, of which there is only one. Therefore the probability is 1 / [C(59,5)*35], resulting in extremely low chances of winning.

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