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3 years ago

There are 3/4 as many girls as there are boys.There are 63 students in the fifth grade. How many students are girls?

Mathematics

1 answer:

klemol [59]3 years ago

7 0

Answer:

27 students are girls.

Step-by-step explanation:

Given:

There are 3/4 as many girls as there are boys.

In the fifth grade total there are 63 students.

Now, to find the number of students that are girls.

Let the number of students that are boys be $x.$

So, the number of students that are girls = $\frac{3}{4} \ of\ x=\frac{3x}{4} .$

Total number of students = 63.

Now, to get the number of students that are girls we solve an equation:

$x+\frac{3x}{4} =63\\\\\frac{4x+3x}{4} =63\\\\\frac{7x}{4} =63\\\\Multiplying\ both\ sides\ by\ 4\ we\ get:\\\\7x=252\\\\Dividing\ both\ sides\ by\ 7\ we\ get:\\\\x=36.$

Now, substituting the value of $x$ :

$\frac{3x}{4} \\\\=\frac{3\times 36}{4} \\\\=\frac{108}{4} \\\\=27.$

Therefore, 27 students are girls.

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Suppose that the amount of time T a customer spends in a bank is exponentially distributed with an average of 10 minutes. What i

Bad White [126]

Answer:

The probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

Step-by-step explanation:

The random variable T is defined as the amount of time a customer spends in a bank.

The random variable T is exponentially distributed.

The probability density function of a an exponential random variable is:

$f(x)=\lambda e^{-\lambda x};\ x>0$

The average time a customer spends in a bank is β = 10 minutes.

Then the parameter of the distribution is:

$\lambda=\frac{1}{\beta}=\frac{1}{10}=0.10$

An exponential distribution has a memory-less property, i.e the future probabilities are not affected by any past data.

That is, P (X > s + x | X > s) = P (X > x)

So the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is:

P (X > 15 | X > 10) = P (X > 5)

$\int\limits^{\infty}_{5} {f(x)} \, dx =\int\limits^{\infty}_{5} {\lambda e^{-\lambda x}} \, dx\\=\int\limits^{\infty}_{5} {0.10 e^{-0.10 x}} \, dx\\=0.10\int\limits^{\infty}_{5} {e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10}|^{\infty}_{5}\\=[-e^{-0.10 \times \infty}+e^{-0.10 \times 5}]\\=0.6065$

Thus, the probability that a customer will spend more than 15 minutes total in the bank, given that the customer has already waited over 10 minutes is 0.6065.

8 0

3 years ago

Find the slope of the line through the points (1,-2) and (-7,4)

horrorfan [7]

Answer:

-3/4

Step-by-step explanation:

To find the slope, plug the coordinates into the slope formula.

y2 - y1 / x2 - x1

4 - (-2) / -7 - 1

6 / - 8

-3/4