Write the correct inequality sign (< or >) that belongs between the two

Mathematics

1 answer:

daser333 [38]2 years ago

4 0

Answer:

15 divided by 3 = 5

Square root of 30 = somewhere around 5

5 = 5

Step-by-step explanation:

It's equal too.

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At a local ice cream parlor, there are 6 different flavors of ice cream from which to select (strawberry, chocolate, vanilla, ro

Neko [114]

Answer:

1/30

Step-by-step explanation:

let, vanilla be the first ice cream.

hence, the probability of choosing vanila= 1/6

let, chocolate be the second ice cream.

hence, the probability of choosing chocolate=1/5

hence, the probability that the next customer's sundae will have vanilla and chocolate (in either order)= (1/6)×(1/5)

=1/30

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2 years ago

If the length and the breadth of a rectangle are each increased by 1 meter, the area of the rectangle is increased by 22 square

bazaltina [42]

Answer:

42 m

Step-by-step explanation:

l+1 * (b+1) = lb+22

lb+b+l+1 = lb+22

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2 years ago

A tank contains 30 lb of salt dissolved in 300 gallons of water. a brine solution is pumped into the tank at a rate of 3 gal/min

sesenic [268]

$A'(t)=(\text{flow rate in})(\text{inflow concentration})-(\text{flow rate out})(\text{outflow concentration})$
$\implies A'(t)=\dfrac{3\text{ gal}}{1\text{ min}}\cdot\left(2+\sin\dfrac t4\right)\dfrac{\text{lb}}{\text{gal}}-\dfrac{3\text{ gal}}{1\text{ min}}\cdot\dfrac{A(t)\text{ lb}}{300+(3-3)t\text{ gal}}$
$A'(t)+\dfrac1{100}A(t)=6+3\sin\dfrac t4$

We're given that $A(0)=30$ . Multiply both sides by the integrating factor $e^{t/100}$ , then

$e^{t/100}A'(t)+\dfrac1{100}e^{t/100}A(t)=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$\left(e^{t/100}A(t)\right)'=6e^{t/100}+3e^{t/100}\sin\dfrac t4$
$e^{t/100}A(t)=600e^{t/100}-\dfrac{150}{313}e^{t/100}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+C$
$A(t)=600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)+Ce^{-t/100}$

Given that $A(0)=30$ , we have

$30=600-\dfrac{150}{313}\cdot25+C\implies C=-\dfrac{174660}{313}\approx-558.02$

so the amount of salt in the tank at time $t$ is

$A(t)\approx600-\dfrac{150}{313}\left(25\cos\dfrac t4-\sin\dfrac t4\right)-558.02e^{-t/100}$