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3 years ago

Zachary travels on a journey of 50 miles. He spends half

Mathematics

1 answer:

ExtremeBDS [4]3 years ago

7 0

Answer: 8 hours.

Step-by-step explanation:

We have the relation:

Time = distance/velocity

Distance = 50 miles

Velocity in horse = 9mph

Velocity walking = 3 1/2 mph = 3.5 mph

Then, if T is the total time, X is the distance that he travels in horse and Y is the distance that he travels by foot, we have:

X + Y = 50 miles:

T/2 = X/9mph

T/2 = Y/3.5mph

Then we have:

X/9mph = Y/3.5mph

X = Y*(9/3.5)

And by the first relation:

X = 50 mi - Y

then we have:

50mi - Y = Y*(9/3.5)

50mi = Y + Y*(9/3.5) = Y*(1 + 9/3.5) = Y*3.57

Y = 50mi/3.57 = 14mi

Then we have:

T/2 = 14mi/3.5mph

T = 2*(14/3.5) hours = 8 hours

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4 years ago

The amount of calories consumed by customers at the Chinese buffet is normally distributed with mean 2885 and standard deviation

aliina [53]

Answer:

a. X~N(2,885, 651)

b. 0.086291

c. 0.00058

d. 3213.10 calories

Step-by-step explanation:

a. -A normal distribution is expressed in the form X~N(mean, standard deviation).

-Let X a random variable denoting the number of calories consumed.

-X is a is a normally distributed random variable with mean 2885 and standard deviation 651.

-This distribution is expressed as X~N(2,885, 651)

b. The probability that less than 2000 calories are consumed is calculated using the formula:

$P(X$

#substitute the given values in the formula to solve for P:

$P(X$

Hence, the probability of consuming less than 2000 calories is 0.08691

c. The proportion of customers consuming more than 5000 calories is calculated as:

$P(X>x)=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(Z>\frac{5000-2885}{651})\\\\=P(z>3.2488)\\\\=1-0.99942\\\\=0.00058$

Hence, the proportion of customers consuming over 5000 calories is 0.00058

d. The least amount of calories to get the award is calculated as:

1% is equivalent to a z value of 0.50399.

-We equate this to the formula to solve for the mean consumption:

$0.01=P(z>\frac{\bar X-\mu}{\sigma})\\\\=P(z>\frac{\bar X-2885}{651})\\\\\1\%=0.50399 \\\\\frac{\bar X-2885}{651}=0.50399 \\\\\bar X=0.50399\times 651+2885\\\\=3213.09$

Hence, the least amount of calories consumed to qualify for the award is 3213.10 calories.

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4 years ago

A straight line that is parallel to one of the sides of a given triangle intersects its other two sides (or their extensions) an

timurjin [86]

Answer:

We know that this triangle is similar because it will have all of the same angles as the first triangle. This is because two parallel lines cut by a transversal will create the same angles. In addition, they share the final angle because we are not changing that angle. Therefore, all 3 are the same, which makes them similar triangles.

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3 years ago

Read 2 more answers

Find the interval in which f(x)=sinx−cosx is increasing or decreasing?

alisha [4.7K]

Answer:

There is no short answer.

Step-by-step explanation:

To find to intervals which f(x) increases or decreases, we first need to find it's derivative.

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