The enrollment in summer stuff camp went from 10 people to 28 in 5 days. What was the percent of the increase in enrollment

A scientist used 2 gallons of liquid for every 3 hours he works. He uses __ of a gallon each hour he works.

tiny-mole [99]

He uses 2/3 of a gallon each hour he works.

8 0

2 years ago

A cleaning company charges a fixed amount for a house call and a second amount for each room it cleans. The total cost to clean

yanalaym [24]

Answer:

$110

Step-by-step explanation:

Let the fixed amount charged be f and the amount charged to clean a room be r.

To clean six rooms , the company would charge the following, the fixed amount for the call plus the amount charged per room multiplied by 6 which of course is 6r.

Writing this in equation form,

f + 6r = 250

In likewise manner, same applies for 8 rooms.

this gives f + 8r = 320

We now have 2 equations that we will need to solve simultaneously

f + 6r = 250........(i)

f + 8r = 320........(ii)

We subtract equation ii from I to yield

2r = 70, hence r = 70/2 = 35.

We now substitute this in equation 1

f + 6(35) = 250

f + 210 = 250

f = 250 - 210 = 40

Hence, we now know that the amount charged per call is $40 while the amount charged to clean a room is $35.

We now calculate the amount charged by the company to clean 2 rooms.

This is mathematically = f + 2r

40 + 2(35) = $110.

6 0

2 years ago

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min, and its coarseness is such that it forms a pile in the shap

11Alexandr11 [23.1K]

Answer:

0.25 feet per minute

Step-by-step explanation:

Gravel is being dumped from a conveyor belt at a rate of 20 ft3/min. Since we are told that the shape formed is a cone, the rate of change of the volume of the cone.

$\dfrac{dV}{dt}=20$ ft^3/min$

$\text{Volume of a cone}=\dfrac{1}{3}\pi r^2 h$

Since base diameter = Height of the Cone

Radius of the Cone = h/2

Therefore,

$\text{Volume of the cone}=\dfrac{\pi h}{3} (\dfrac{h}{2}) ^2 \\V=\dfrac{\pi h^3}{12}$

$\text{Rate of Change of the Volume}, \dfrac{dV}{dt}=\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}$

Therefore: $\dfrac{3\pi h^2}{12}\dfrac{dh}{dt}=20$

We want to determine how fast is the height of the pile is increasing when the pile is 10 feet high.

$h=10$ feet$\\\\\dfrac{3\pi *10^2}{12}\dfrac{dh}{dt}=20\\25\pi \dfrac{dh}{dt}=20\\ \dfrac{dh}{dt}= \dfrac{20}{25\pi}\\ \dfrac{dh}{dt}=0.25$ feet per minute (to two decimal places.)$

When the pile is 10 feet high, the height of the pile is increasing at a rate of 0.25 feet per minute

5 0

3 years ago

Ben tiene 3 veces la edad de Daniel y es 4 años mayor que él.<br>¿Cuántos años tiene Ben?

brilliants [131]

Answer:

Ben es 6, Daniel es 2

Step-by-step explanation:

No hablo mucho español, ¡pero intentaré dar una respuesta!

8 0

3 years ago

A study of bone density on 5 random women at a hospital produced the following results.

IRINA_888 [86]

Answer:

- 0.9503 ; r is not statistically significant ; 0.9031

Step-by-step explanation:

Given the following :

Age (X) :

37

41

57

65

73

Bone density (Y)

355

345

340

315

310

Using the pearson R value calculator :

The r value of the data % - 0.9503.

This value depicts a very strong negative correlation between age and density of bone.

Using the pearson R calculator to obtain the P- value, the P value obtained is .01332 and hence the r is not significant at P < 0.01.

The Coefficient of determination R^2 can be obtained by getting the square value of R

R^2 = - 0.9503^2

R^2 = 0.90307009

R^2 = 0.9031

8 0

3 years ago