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2 years ago

Pablo spit 3/4 pounds of candy amping 4 people what is the unit rate in pounds per person

Mathematics

1 answer:

Sunny_sXe [5.5K]2 years ago

8 0

The unit rate is $\frac{3}{16}$ pounds per person.

Step-by-step explanation:

Given,

Quantity of candy Pablo have = $\frac{3}{4}$ pounds

Number of people = 4

We will divide the Quantity of candy by number of people.

Quantity of candy per person = $\frac{3}{4}*\frac{1}{4}$

Quantity of candy per person = $\frac{3}{16}$ pounds of candy

The unit rate is $\frac{3}{16}$ pounds per person.

Keywords: fraction, unit rate

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Consider the system of equations.

Harman [31]

The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:

x = -3, y = 2

The given system of equations:

x + 2y = 1............(1)

-3x - 2y = 5..........(2)

This can be written in matrix form as shown:

$\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Find the determinant of $\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right]$

$\triangle = 1(-2) - 2(-3)\\\triangle = -2+6\\\triangle = 4$

$\triangle_x = \left[\begin{array}{ccc}1&2\\5&-2\end{array}\right]\\\triangle_x = 1(-2)-2(5)\\\triangle_x = -2-10\\\triangle_x =-12$

$\triangle_y = \left[\begin{array}{ccc}1&1\\-3&5\end{array}\right]\\\triangle_y = 1(5)-1(-3)\\\triangle_y = 5 + 3\\\triangle_y =8$

$x = \frac{\triangle_x}{\triangle} \\x = \frac{-12}{4} \\x = -3$

$y = \frac{\triangle_y}{\triangle} \\y = \frac{8}{4} \\y = 2$

The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:

x = -3, y = 2

Learn more here: brainly.com/question/4428059

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1 year ago

What is the answer too 2 7/10 - 4/5 ?

aivan3 [116]

19/10 or 1.9 or 1 9/10

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2 years ago

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Find the area of quadrilateral ABCD in each case.<br> HElp PLEase ASAP

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<h2><u>PLEASE MARK BRAINLIEST!</u></h2>

Answer:

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Step-by-step explanation:

*Note: we can't find the exact area of the shaded figure right off the bat, we have to find the area of a bigger figure and divide it by 2.

<h3>The coordinates of the bigger figure:</h3>

A = (0,0)

B' = (0,4)

C = (5,4)

D' = (5,0)

Note: the little [ ' ] next to the B and D indicate that it is not the same coordinate as B and D, just that those points would be the same as point B and D.

<h3>That being said, what is the area of the bigger figure?</h3>

A = l * w

A = 4 * 5

A = 20 units²

<h3>Now, divide the Area by 2:</h3>

A = 20 ÷ 2

<em>A = 10 units²</em>

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Name the figure below in two different ways. B. N<br><br>

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Answer:

Step-by-step explanation:

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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

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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

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