Mike is 3 years old.joe is 6 times as old as mike whict equation shows how to find Joe's age?

2 taps A and B can fill a swimming pool in 3 hours. If turned on alone, it takes tap A 5 hours less than tap B to fill the same

vazorg [7]

Answer:

Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.

Step-by-step explanation:

Let tap B fills the pool alone in the time = x hours

So in one hour part of pool will be filled = $\frac{1}{x}$

Another tap A when turned on, it takes time to fill the pool = x-5 hours

So in one hour part of the same pool filled = $\frac{1}{x-5}$

Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.

Part of the pool filled in one hour by both the taps = $\frac{1}{3}$

Now we form an equation

Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on

$\frac{1}{(x-5)}+\frac{1}{x}=\frac{1}{3}$

$\frac{x-5+1}{x(x-5)}=\frac{1}{3}$

$\frac{x-4}{x(x-5)}=\frac{1}{3}$

3(x - 4) = x(x - 5)

x² -5x = 3x - 12

x² - 8x + 12 = 0

x² - 6x - 2x + 12 = 0

x(x - 6) - 2(x - 6) = 0

(x -2)(x - 6) = 0

x = 2, 6 hours

We will take higher value of x as x = 6 hours for tap B.

Time taken by tap A = 6 - 4 = 2 hours.

Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.

4 0

4 years ago

If the area of a square is 100cm2, then what is its perimeter?

Vinil7 [7]

Answer:

40cm

Step-by-step explanation:

A=s*s

A=10*10

A=100 cm^2

P=4*s

P=4*10

P=40 cm

"s" represents side

6 0

3 years ago

A right circular cylinder has a height of 22 1/4 ft and a diameter 2 2/5 times its height. What is the volume of the cylinder? E

Triss [41]

Answer:

The volume of cylinder is:

49806.06 ft^3

Step-by-step explanation:

We are given a right circular cylinder with:

Height(h)= $22\frac{1}{4}ft=\dfrac{89}{4}ft$

and a diameter is $2\frac{2}{5}$ times it's height.

i.e. $\dfrac{12}{5}$ times it height.

i.e. the diameter is given as:

$\dfrac{12}{5}\times \dfrac{89}{4}=\dfrac{267}{5}ft.$

We know that the radius of cylinder is half the diameter.

Hence, radius(r) of cylinder is:

$\dfrac{1}{2}\times \dfrac{267}{5}\\\\=\dfrac{267}{10}$

The volume(V) of cylinder is given by:

$V=\pi r^2h$

$V=3.14\times (\dfrac{267}{10})^2\times \dfrac{89}{4}\\\\V=\dfrac{19922423.94}{400}\\\\V=49806.06ft^3$

Hence, the volume of cylinder is:

49806.06 ft^3

7 0

4 years ago

g 78% of all Millennials drink Starbucks coffee at least once a week. Suppose a random sample of 50 Millennials will be selected

Tatiana [17]

Answer:

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

$np=50*0.78=39 \geq 10$

$n(1-p)=50*(1-0.78)=11 \geq 10$

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

$p \sim N (p, \sqrt{\frac{p(1-p)}{n}})$

With the following parameters:

$\mu_ p = 0.78$

$\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We know that n = 50 and p =0.78.

We need to check the conditions in order to use the normal approximation.

$np=50*0.78=39 \geq 10$

$n(1-p)=50*(1-0.78)=11 \geq 10$

Since both conditions are satisfied we can use the normal approximation and the distribution for the proportion is given by:

$p \sim N (p, \sqrt{\frac{p(1-p)}{n}})$

With the following parameters:

$\mu_ p = 0.78$

$\sigma_p = \sqrt{\frac{0.78*(1-0.78)}{50}}= 0.0586$

6 0

3 years ago

Determine if the two triangles are congruent. If they are, state how you know.

mr Goodwill [35]

Answer:

B) SAS

Step-by-step explanation:

The angles between the two known equal sides are called a vertical angle and are equal. Thus you know Side-Angle-Side proves congruency.

6 0

3 years ago