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Norma-Jean [14]
2 years ago
13

Today, John ran 15 miles in 2 hours and 30 minutes. He wants to represent the relationship between the distance he ran, in miles

, and the time, in hours, as proportional in order to examine his times at various distances. Write an equation that John can use to represent a proportional relationship between distance, d, in miles, and time, t, in hours.
Mathematics
1 answer:
jeyben [28]2 years ago
3 0

Answer:

d = 6t

Step-by-step explanation:

Firstly, lets change the 2 hours and 30 minutes to 2.5 hours, you could devide the time in minutes by 60 to get that number 2[hours]+(\frac{30}{60})[minutes to hours] = 2.5Hours.

Anyway, John ran 15 miles in 2.5 hours which means he ran (15÷2.5) in one hour which is equal to 6miles per hour. That means if you multiply the hours he ran by 6 you will get the miles he ran.

So the answer would be:

d = 6t

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Eli, Freda and Geoff were given £800 to share in the ratio of their ages.
algol13
First, we are going to find the sum of their age. To do that we are going to add the age of Eli, the age Freda, and the age of <span>Geoff:
</span>9+13+18=40
The combined age of Eli, Freda, and Geoff is 40, so the denominator of each ratio will be 40.

Next, we are going to multiply the ratio between the age of the person and their combined age by <span>£800:
For Eli: </span>\frac{9}{40} *800=180
For Freda: \frac{13}{40} *800=260
For Geoff: \frac{18}{40} *800=360
<span>
We can conclude that Eli will get </span>£180, Freda will get £260, and Geoff will get <span>£360.</span>
4 0
2 years ago
Hank invested a total of $20,000, part at 7% and part at 10%. How much did he invest at each rate if the total interest earned i
jolli1 [7]

Answer:

The amount invested at 7% is $12,000 while the amount invested at 10% is $8,000

Step-by-step explanation:

The given parameters are;

The total amount Hank invested = $20,000

The interest earned in one year = $1640

Hank invested part of the $20,000 at 7% interest and part of the $20,000 at 10%

Let the part invested at 7% = X and the part invested at 10% = Y, we have;

7% of X + 10% of Y = $1640 which gives;

0.07×X + 0.1×Y = $1640.....................(1)

X + Y = $20,000.................................(2)

Multiply equation (1) by 10 and subtract equation (1) from equation (2) to get;

X + Y - 10×(0.07×X + 0.1×Y) = $20,000 - 10×$1640

X - 0.7·X - Y - Y = $20,000 - $16,400 = $3,600

0.3·X = $3,600

X = $3,600/0.3 = $12,000

X = $12,000

Y = $20,000 - X = $20,000 - $12,000 = $8,000

Y = $8,000

Therefore, the amount invested at 7% = $12,000 and the amount invested at 10% = $8,000.

7 0
2 years ago
Read 2 more answers
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Stels [109]

Answer: A  y=4x -5 and y=4x+5

Step-by-step explanation:

They have no solutions because they have the same slopes but different y intercepts. That works with any equation.

8 0
2 years ago
G find the area of the surface over the given region. use a computer algebra system to verify your results. the sphere r(u,v) =
Svetach [21]
Presumably you should be doing this using calculus methods, namely computing the surface integral along \mathbf r(u,v).

But since \mathbf r(u,v) describes a sphere, we can simply recall that the surface area of a sphere of radius a is 4\pi a^2.

In calculus terms, we would first find an expression for the surface element, which is given by

\displaystyle\iint_S\mathrm dS=\iint_S\left\|\frac{\partial\mathbf r}{\partial u}\times\frac{\partial\mathbf r}{\partial v}\right\|\,\mathrm du\,\mathrm dv

\dfrac{\partial\mathbf r}{\partial u}=a\cos u\cos v\,\mathbf i+a\cos u\sin v\,\mathbf j-a\sin u\,\mathbf k
\dfrac{\partial\mathbf r}{\partial v}=-a\sin u\sin v\,\mathbf i+a\sin u\cos v\,\mathbf j
\implies\dfrac{\partial\mathbf r}{\partial u}\times\dfrac{\partial\mathbf r}{\partial v}=a^2\sin^2u\cos v\,\mathbf i+a^2\sin^2u\sin v\,\mathbf j+a^2\sin u\cos u\,\mathbf k
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So the area of the surface is

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=-2\pi a^2(\cos\pi-\cos 0)
=-2\pi a^2(-1-1)
=4\pi a^2

as expected.
6 0
2 years ago
3. A balloon with a small leak loses 0.5% of its volume each day. If it originally contained 40 liters of gas, what is the volum
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V=40L
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7 0
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