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salantis [7]
3 years ago
11

Bethany and her brother ben decided to go through a corn maze. Bethany starts and walks 10 feet north, 30 feet west and then 20

feet north. Ben walks 20 feet North, 25 feet east, and then 15 Feet south. How far apart are Bethany and Ben when they stop walking?

Mathematics
1 answer:
Westkost [7]3 years ago
3 0

Answer:

About 60.77 feet

Step-by-step explanation:

Attached pic.

Blue line is of Bethany

Green line is of Ben

Red line is the distance between them [what we are trying to find]

We can use pythagorean theorem that tells us:

c^2=a^2+b^2

Where c is the hypotenuse of the right triangle [red lines in both respective triangles]

and

a, b are the two other sides of the triangle

Left Triangle (using pythagorean theorem):

Base is 30

Left side is 20 - 10 = 10

So,

c^2=30^2+10^2\\c=\sqrt{30^2+10^2} \\c=31.62

Right Triangle (using pythagorean theorem):

c^2=25^2 + 15^2\\c=\sqrt{25^2 + 15^2} \\c=29.15

Distance between Bethany and Ben = 31.62 + 29.15 = 60.77 feet

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6 2/3 minutes

Step-by-step explanation:

Amare runs 1/10 mile in 2/3 minutes

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3 years ago
Ajay bought a fan and a heater for rs 4000. He sold the fan at a profit of a 25% and the heater at a loss of 5%. If he gained 7%
Alborosie

Answer: Heater -Rs 2400; Fan- Rs 1600

Step-by-step explanation:

Given

Ajay bought a fan and a heater for Rs 4000

Suppose the price of fan is x and that of heater is 4000-x

Profit on the fan is 0.25x

Loss on heater is 0.05\times (4000-x)

Total profit is 7% i.e. 0.07\times 4000

\therefore 0.07\times 4000=0.25x-0.05(4000-x)\\\Rightarrow 280=0.25x-200+0.05x\\\Rightarrow 480=0.3x\\\Rightarrow x=1600

Thus, the price of heater is 4000-1600=Rs.\ 2400

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8 0
2 years ago
The CEO of a clothing company estimates that 52% of customers will make a purchase. Part A: How many customers should a salesper
4vir4ik [10]

Answer:

(a) The expected number of should a salesperson expect until she finds a customer that makes a purchase is 0.9231.

(b) The probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.

Step-by-step explanation:

Let<em> </em>the random variable <em>X</em> be defined as the number of customers the salesperson assists before a customer makes a purchase.

The probability that a customer makes a purchase is, <em>p</em> = 0.52.

The random variable <em>X</em> follows a Geometric distribution since it describes the distribution of the number of trials before the first success.

The probability mass function of <em>X</em> is:

P(X=x)=(1-p)^{x}p

The expected value of a Geometric distribution is:

E(X)=\frac{1-p}{p}

(a)

Compute the expected number of should a salesperson expect until she finds a customer that makes a purchase as follows:

E(X)=\frac{1-p}{p}

         =\frac{1-0.52}{0.52}\\=0.9231

This, the expected number of should a salesperson expect until she finds a customer that makes a purchase is 0.9231.

(b)

Compute the probability that a salesperson helps 3 customers until she finds the first person to make a purchase as follows:

P(X=3)=(1-0.52)^{3}\times0.52\\=0.110592\times 0.52\\=0.05750784\\\approx 0.058

Thus, the probability that a salesperson helps 3 customers until she finds the first person to make a purchase is 0.058.

8 0
3 years ago
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