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3 years ago

A shelf can hold 32 pounds of fruit. Each basket weighs 32 ounces. How many baskets can the shelf hold?

Mathematics

1 answer:

wariber [46]3 years ago

7 0

Answer:

Step-by-step explanation:

you have to see how many pounds is in 32 oz then divide it 32÷2=16.

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What is 2x times x squared?

tresset_1 [31]

We want to multiply the monomial $2x$ by the monomial $2x^2$ .

Remember that to multiply monomials we need to use the laws of exponents; in this case, the law for multiplying powers with the same base. The rule says that, when you multiply powers of the same base, you just need to add the exponents: $(a^m)(a^n)=a^{m+n}$ , $(x^2)(x^4)=x^{2+4}=x^6$ . Also, is worth pointing out that the exponent of a variable with no exponent is 1: $x=x^1$ .

Remember that we also need to multiply their coefficients , which are the numbers that multiply the variables; again, variables with no numbers have a coefficient of 1, so $x=1x$ . Multiply coefficients is easy, you just need to multiply them as you usually do with everyday numbers.

Let's apply all of that to our multiplication:

$(2x)(x^2)=(2x^1)(1x^2)=2*1x^{1+2}=2x^3$

We can conclude that 2x times x squared is 2x cubed.

3 0

3 years ago

Read 2 more answers

12 of the 28 dogs at the shelter are purebred what percent of the dogs are pure breed?HELP!

harina [27]

Answer:

57.142%

Step-by-step explanation:

28-12=16

16/28*100=57.142%

3 0

3 years ago

What’s the domain and range of this graph look at the arrow.

viva [34]

Answer:

This is a acute angle in the digits 1,4,6 should help the answer is acute

4 0

3 years ago

3 times a number m use a equation plz

lawyer [7]

Answer: 3m

Step-by-step explanation:

You're multiply 3 by m. Since this isn't possible unless you have m's value, you must write the expression as 3m.

7 0

3 years ago

A 500-gallon tank initially contains 220 gallons of pure distilled water. Brine containing 5 pounds of salt per gallon flows int

Wittaler [7]

Answer: The amount of salt in the tank after 8 minutes is 36.52 pounds.

Step-by-step explanation:

Salt in the tank is modelled by the Principle of Mass Conservation, which states:

(Salt mass rate per unit time to the tank) - (Salt mass per unit time from the tank) = (Salt accumulation rate of the tank)

Flow is measured as the product of salt concentration and flow. A well stirred mixture means that salt concentrations within tank and in the output mass flow are the same. Inflow salt concentration remains constant. Hence:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = \frac{d(V_{tank}(t) \cdot c(t))}{dt}$

By expanding the previous equation:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt} + \frac{dV_{tank}(t)}{dt} \cdot c(t)$

The tank capacity and capacity rate of change given in gallons and gallons per minute are, respectivelly:

$V_{tank} = 220\\\frac{dV_{tank}(t)}{dt} = 0$

Since there is no accumulation within the tank, expression is simplified to this:

$c_{0} \cdot f_{in} - c(t) \cdot f_{out} = V_{tank}(t) \cdot \frac{dc(t)}{dt}$

By rearranging the expression, it is noticed the presence of a First-Order Non-Homogeneous Linear Ordinary Differential Equation:

$V_{tank} \cdot \frac{dc(t)}{dt} + f_{out} \cdot c(t) = c_0 \cdot f_{in}$ , where $c(0) = 0 \frac{pounds}{gallon}$ .

$\frac{dc(t)}{dt} + \frac{f_{out}}{V_{tank}} \cdot c(t) = \frac{c_0}{V_{tank}} \cdot f_{in}$

The solution of this equation is:

$c(t) = \frac{c_{0}}{f_{out}} \cdot ({1-e^{-\frac{f_{out}}{V_{tank}}\cdot t }})$

The salt concentration after 8 minutes is:

$c(8) = 0.166 \frac{pounds}{gallon}$

The instantaneous amount of salt in the tank is:

$m_{salt} = (0.166 \frac{pounds}{gallon}) \cdot (220 gallons)\\m_{salt} = 36.52 pounds$

3 0

3 years ago