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BlackZzzverrR [31]

3 years ago

12

A shelf holds 10 cans of beans, 6 cans of corn, 3 cans of tomatoes, and 1 can of carrots. Without looking you grab one can of ve

getables. What's the probability that it's a can of beans or tomatoes?

1 answer:

dlinn [17]3 years ago

4 0

Answer:

13/20

Step-by-step explanation:

Add up the total number of cans.

Add up the total number of beans and tomatoes.

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Solve the quadratic in form equation x^4-14x^2+45=0

Anastaziya [24]

X⁴-14x²+45=0
(x²) ²-14x²+45=0
let y=x²
y²-14y+45=0
(y-9) (y-5) =0
y=9 or y=5
x²=9 or x²=5
x=±3 or x=±√5

7 1

3 years ago

an inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a

viktelen [127]

Answer:

the rate of change of the water depth when the water depth is 10 ft is; $\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

Step-by-step explanation:

Given that:

the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.

We are meant to find the rate of change of the water depth when the water depth is 10 ft.

The diagrammatic expression below clearly interprets the question.

From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t

Then the similar triangles ΔOCD and ΔOAB is as follows:

$\dfrac{h}{r}= \dfrac{20}{8}$ ( similar triangle property)

$\dfrac{h}{r}= \dfrac{5}{2}$

$\dfrac{h}{r}= 2.5$

h = 2.5r

$r = \dfrac{h}{2.5}$

The volume of the water in the tank is represented by the equation:

$V = \dfrac{1}{3} \pi r^2 h$

$V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h$

$V = \dfrac{1}{18.75} \pi \ h^3$

The rate of change of the water depth is :

$\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec

Then,

$\dfrac{dv}{dt}= - 4 \ ft^3/sec$

Therefore,

$-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}$

the rate of change of the water at depth h = 10 ft is:

$-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}$

$100 \pi \dfrac{dh}{dt} = -4 \times 6.25$

$100 \pi \dfrac{dh}{dt} = -25$

$\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}$

Thus, the rate of change of the water depth when the water depth is 10 ft is; $\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}$

4 0

4 years ago

Fill in the blanks.<br> (3b^3)^2 = _b^_

Radda [10]

We can seperate (3b³) into two different parts, the constant and the variable.

The constant (3) and the variable (b) can both be squared and multiplied to get the correct answer, so:

3² = 9

(b³)² = $b^{6}$

So, $(3b^{3})^{2} = 9b^{6}$

6 0

3 years ago

Suzy earns $7.50 per hour she worked 32.5 hours last week what was the amount of her check

expeople1 [14]

$7.50 per hour times <span>32.5 hours equals $243.75
$ 7.50 per hour
x 32.5 worked hours
----------
$243.75 is her check</span>

6 0

3 years ago

A jar contains 150 coins. If it is very likely that you will randomly choose a penny out of the jar, how many pennies could be i

arsen [322]

149 pennies.

Very likely: extremely likely, highly reasonable, almost certainly.

Considering the above definitions of "very likely", a jar of 150 coins, 149 of them being pennies, would satisfy each definition given for "very likely".

Almost certainly indicates that there is a possibility that you'd choose a coin that's not a penny, so a jar of 150 coins which are all pennies doesn't satisfy this definition.

7 0

3 years ago