Flying to miami whit a tailwind a plane averaged 376 mph. On the return trip the plane only averaged 312 mph while flying back into the same wind. Find the speed of the wind and speed of the plane in still air.


please show me the work

Answer:

280.51

Step-by-step explanation:

Answer:  [tex]x+3y=-15[/tex]

Step-by-step explanation:

The equation of a line passes through (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Then, the equation of a line that passes through (-6,-3) (6,-7) will be :-

[tex](y-(-3))=\dfrac{-7-(-3)}{6-(-6)}(x-(-6))\\\\\Rightarrow y+3=\dfrac{-7+3}{6+6}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-4}{12}(x+6)\\\\\Rightarrow\ y+3=\dfrac{-1}{3}(x+6)\\\\\Rightarrow\ 3(y+3)=-x-6\\\\\Rightarrow\ 3y+9=-x-6\\\\\Rightarrow\ x+3y=-15.[/tex]

Hence, the required equation is [tex]x+3y=-15[/tex].

The correct answer is D

Nick ran 9.2 miles less than Perry last week. If Nick ran 12.8 miles, how many miles did Perry run?

x - 9.2 = 12.8

x = 12.8 + 9.2

x = 22

Perry ran 22 miles for the week, 9.2 miles more than Nick.

Answer:

correct answer is D

Step-by-step explanation:

Answer:

The formula for the volume of the cube is v=a3 where a is the length of the edge the volume of the cube is 1/8 cube inches v= 1/8 cube inches a3=(1/2)3 cubic inches

Step-by-step explanation:

Answer:

Point A is labeled at x=-5 and point B is labeled at x=5.

Step-by-step explanation:

It is given that two numbers have a distance of 5 units from 0 on a number line.

Let the unknown number be x.

Case 1: x is 5 units less than 0.

[tex]x=0-5[/tex]

[tex]x=-5[/tex]

The point A is labeled at x=-5.

Case 2: x is 5 units more than 0.

[tex]x=0+5[/tex]

[tex]x=5[/tex]

The point B is labeled at x=5.

Answer:

43 and 44

Step-by-step explanation:

Using the division operation, the fraction of the total area mowed by each person is [tex] \frac{4}{9}[/tex]

Total fraction mowed = [tex] \frac{8}{9}[/tex]

Number of persons who mowed the area = 2

Since, the same amount of area ws mowed by each person, then the area mowed per person can be calculated thus :

[tex] \frac{48}{9} \div 2 = \frac{4}{9}[/tex]

Hence, each person mowed [tex] \frac{4}{9}[/tex]

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The points that were labelled by the manager on the graph are (0, 10) and (24, 0). These points are found by dividing the total amount of soil by the amount of soil required by each type of pot.

In this Mathematics problem, we need to determine which points were labelled on the graph created by the nursery manager representing combinations of small and large pots. We can find these points, the intercepts, by understanding that these occur when one variable is zero. The x-intercepts happen when all soil is used for large pots (i.e., the y-axis, or number of small pots, is zero), and the y-intercepts occur when all the soil is used for small pots (i.e., the x-axis, or number of large pots, is zero). For the x-intercept, if each large pot requires 12lb of soil, then the manager could fill 120/12 = 10 large pots if no soil is used for small pots. Therefore, the x-intercept is (0, 10). Similarly, the y-intercept would be obtained by dividing the total amount of soil with the amount used for a small pot. That gives us 120/5 = 24. Hence, the y-intercept is (24, 0). So, the points labelled by the manager are option 2: (0, 10) and (24, 0).

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the slope is -5/6 and y intercept is -4

 so the first dot  goes on (0,-4)

 the next dot would go

-5/6 x 4 = -29/6

(1,-29/6)

The number of different recital programs that are possible is 230230 programs

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula:

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time

The information will be illustrated as:

= 26! / (26 - 6)! 6!

= 26! / 20!6!

= 230230

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Answer:

120$

Step-by-step explanation:

We must calculate the prices with the application of discounts successively

The last discount he got was 10%, so $ 91.80 equals 90% of the price

We calculate the price before this discount by applying with a simple rule of three

[tex]90 \% \longrightarrow 91.80\\100\% \longrightarrow x\\x=\frac{(100)(91.80)}{90}\\ x= 102\$[/tex]

She pays $ 102 with a 15% discount, so this value equals 85% of the original price

We calculate the price before this discount by applying with a simple rule of three

[tex]85\% \longrightarrow 102\\100\% \longrightarrow x\\x=\frac{(100)(102)}{85}\\ x= 120\$[/tex]

$1803.34 will be the balance after 3 years if the account pays 2.4% annual interest compounded quarterly

Compound interest is the interest on a loan or deposit that accrues on both the initial principal and the accumulated interest from previous periods.

let's call the amount of money A, the initial amount P, the yearly rate r, the number of compounds per year n.

[tex]A = P(1 + \dfrac{r}{n})^{(nt)[/tex]

[tex]A = 1600(1 + \dfrac{.024}{4})^{((4)(5)[/tex]

[tex]A = 1600(1.006)^{(20)[/tex]

[tex]A = \$1803.34[/tex]

Hence $1803.34 will be the balance after 3 years if the account pays 2.4% annual interest compounded quarterly

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The graph of the equation of line y = -3x + 4 is plotted

Given data ,

Let the equation of line be represented as A

Now , the value of A is

y = -3x + 4

where the equation is in the form of slope intercept

where the y-intercept is given by b = 4

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = -3

So , the slope of -3 indicates that for every 1 unit increase in x, the value of y decreases by 3 units. The negative slope means that the line is decreasing as x increases, sloping downward from left to right.

Hence , the equation of line is plotted on the graph

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Answer:

Sophie's ratio is greater.

Step-by-step explanation:

Sophie and Eleanor are making bouquets using daisies and tulips. Each bouquet will have the same total number of flowers.

Eleanor uses fewer daisies in her bouquet than Sophie.

Lets say the total flowers used in each bouquet is 15.

Eleanor uses 5 daisies. So, her ratio for daisies to total flowers become = [tex]\frac{5}{15}=\frac{1}{3}[/tex]

Suppose Sophie uses 10 daisies so her ratio becomes = [tex]\frac{10}{15}=\frac{2}{3}[/tex]

Now comparing both ratios, we can see that Sophie's ratio is greater.

The cost of the two DVDs before the sales tax was added is  $21.60.

To find the cost of the two DVDs before sales tax, let's first calculate the total cost including tax and then backtrack to find the cost before tax.

Calculate Total Cost with Tax:

The total cost including tax is given by: Total Cost = Price + Tax

Calculate Tax Amount:

Tax = Price * Tax Rate

Given that the sales tax rate is 8 percent (0.08 in decimal form), the tax amount is: Tax = 0.08 * $21.60 = $1.728

Calculate Total Cost:

Total Cost = Price + Tax

Total Cost = $21.60 + $1.728 = $23.328

Find Cost of DVDs Before Tax:

Let the cost of the two DVDs before tax be represented by x.

Total Cost = Price of DVDs + Price of DVDs * Tax Rate

$23.328 = x + 0.08x

$23.328 = 1.08x

Solve for x:

Divide both sides by 1.08:

x = $23.328 / 1.08 = $21.60

So, the cost of the two DVDs before the sales tax was added is  $21.60.

Complete Question:

Anthony decided to buy two DVDs that we're not included in the deal. His price was $21.60. The sales tax is 8 percent. What was the cost of the two DVDs before the sales tax was added?