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3 years ago

Del ray can run 20 1/2 miles in 2 1/4 hours. How many miles per hour can he run?

1 answer:

5 0

$20 \frac{1}{2} :2 \frac{1}{4} = \frac{41}{2}: \frac{9}{4}= \frac{41}{2}* \frac{4}{9} =\frac{82}{9} = 9 \frac{1}{9} \ \ \text{miles per hour}$

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The sum of two numbers is 110.The larger number is 2 less than 7 times the smaller.Find the Large number

natima [27]

Answer:

The larger number is 96.

Step-by-step explanation:

$let \: the \: two \: numbers \: be \: a \: and \: b \\ a + b = 110 \\ let \: a \: be \: the \: larger \: number \\ a = 7b - 2 \\ we \: can \: get \: the \: value \: of \: b \: by \: substituting \: the \: value \: above \: for \: a \: in \: eq \: 1 \\ 7b - 2 + b = 110 \\ 8b - 2 = 110 \\ 8b = 110 + 2 \\ 8b = 112 \\ b = \frac{112}{8} \\b = 14\\ calculate \:the \: value \: of \: a \: using \: the \: equation \: above \\ a + b = 110 \\ a = 110 - 14 \\ a = 96 \\ hence \: the \: large \: number \: is \: 96$

8 0

2 years ago

The distance between (9,10 and (9,3)

spayn [35]

Using the distance formula
d= square root of (x2-x1)^2+(y2-y1)^2

(9-9)^2+(10-3)^2
0^2+7^2
0+49
Square root of 49 is 7
d=7

4 0

4 years ago

3. You are a senior consultant at a highly prestigious agency. You did a great job in 2020,

Anastasy [175]

Answer:

(a)The highest expected payout option 1

(b)1 and 3

(c)Option 1

Step-by-step explanation:

In this you just multiply the amount you are paid by chance if all are favorable to you, so in option 1 you would get $2,000 for each head you get on a flipped coin, so that would be 10*$2,000=$20,000 that's the highest paid, in the dice you get a maximum of 6 dots each, that would make $6,000*3=$18,000.

Rolling the dice can get you 5 scenarios where you don't get $6,000 when all three are lower than $6,000 which would be getting three 1's, two 1's and a 2, ot two 2's and a 1. That's why only option 3 and 1 are available for an almost certainity of getting $6,000

To know this you have to remember last problem, the getting $9,000 will never give you $16,000, and the dice would give you only 3 scenarios where you could end up winning $16,000 whihc would be getting all 6's, two 6's and a 5, or twop 5's and a 6, so your best option would be flipping the coin.

5 0

3 years ago

Solve the inequality for w.

ahrayia [7]

Answer

Example 1 Solve for x and check: x + 5 = 3

Solution

Using the same procedures learned in chapter 2, we subtract 5 from each side of the equation obtaining

Example 2 Solve for x and check: - 3x = 12

Solution

Dividing each side by -3, we obtain

Step-by-step explanation: here is your anserw the let me know if it right

8 0

3 years ago

A plane flying horizontally at an altitude of 3 miles and a speed of 500 mi/h passes directly over a radar station. Find the rat

konstantin123 [22]

Answer:

The rate at which the distance from the plane to the station is increasing is 331 miles per hour.

Step-by-step explanation:

We can find the rate at which the distance from the plane to the station is increasing by imaging the formation of a right triangle with the following dimensions:

a: is one side of the triangle = altitude of the plane = 3 miles

b: is the other side of the triangle = the distance traveled by the plane when it is 4 miles away from the station and an altitude of 3 miles

h: is the hypotenuse of the triangle = distance between the plane and the station = 4 miles

First, we need to find b:

$a^{2} + b^{2} = h^{2}$ (1)

$b = \sqrt{h^{2} - a^{2}} = \sqrt{(4 mi)^{2} - (3 mi)^{2}} = \sqrt{7} miles$

Now, to find the rate we need to find the derivative of equation (1) with respect to time:

$\frac{d}{dt}(a^{2}) + \frac{d}{dt}(b^{2}) = \frac{d}{dt}(h^{2})$

$2a\frac{da}{dt} + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

Since "da/dt" is constant (the altitude of the plane does not change with time), we have:

$0 + 2b\frac{db}{dt} = 2h\frac{dh}{dt}$

And knowing that the plane is moving at a speed of 500 mi/h (db/dt):

$\sqrt{7} mi*500 mi/h = 4 mi*\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{\sqrt{7} mi*500 mi/h}{4 mi} = 331 mi/h$

Therefore, the rate at which the distance from the plane to the station is increasing is 331 miles per hour.

I hope it helps you!

4 0

3 years ago