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klemol [59]
3 years ago
10

Two mountain bikers take off from the same place at the same time One travels north at 4 mph and the other travels east at 3 mph

. How far apart are they after 5 hr?
Mathematics
1 answer:
Sonbull [250]3 years ago
6 0

Answer:

Step-by-step explanation:60mph

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Anthony works at a company where he gets a set 5% raise every year. If his current salary is
algol13
117,150


5% of 71,000 is 3,550, 3,550 c 13(years) = 46,150(what the company will add to his salary) 71,000 + 46,150 = 117,150
3 0
3 years ago
The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th
vitfil [10]

Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by P(t)=1.394(1.006)^t

To find the derivative you need to:

\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t

To find the population growing at the start of 2014 we say t = 0

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year

To find the population growing at the start of 2015 we say t = 1

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year

To convert billion to million you multiple by 1000

P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year

6 0
3 years ago
Jennifer is shopping with her mother. They pay $2 per pound of tomatoes.
elena-14-01-66 [18.8K]

Answer:

The constant of proportionality is 2

The equation is y=2x

Step-by-step explanation:

The unit price or unit rate is $2

Let y represent the price of tomatoes, then the price of x tomatoes is

y=2x dollars.

This represents a direct variation.

This equation is of the form y=kx, where k=2 is the constant of proportionality.

4 0
3 years ago
A mechanic is using a machine that makes metal parts. She measures each part to confirm it is the correct size. Negative numbers
Hunter-Best [27]

Answer:

A

Step-by-step explanation:

In the figure attached, the complete question is shown.

We have to transform all the fractions to new fractions with the same denominator, as follows:

1/8 *4/4 = 4/32

-3/16 *2/2 = -6/32

-1/4 *8/8 = -8/32

1/32

5/32

-1/16 *2/2 = -2/32

Now we can order the list simply comparing numerators:

-8/32, -6/32, -2/32, 1/32, 4/32, 5/32

or

-1/4, -3/16, -1/16, 1/32, 1/8, 5/32

3 0
3 years ago
A piece of fabric is 2 yards long Marcus puts one patch at each end of the fabric and at each quarter foot mark how many patches
klio [65]
Conversion.
1 yard = 3 feet

So the fabric has 2 yards. Then the size of the patch is 1/4 foot. 
So the number of patches that Marcus used is..
= 3 * 2
= 6 / (1/4)
= 24 patches.

So a total of 24 patches Marcus used.
5 0
4 years ago
Read 2 more answers
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