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3 years ago

A factory worker can make 14 products in 45 minutes.what is the workers unit rate

Mathematics

2 answers:

jok3333 [9.3K]3 years ago

3 0

3.2 products a minute.

Whitepunk [10]3 years ago

3 0

Answer: The unit rate is 0.311 products per minute.

Step-by-step explanation: Given that a factory worker can make 14 products in 45 minutes.

We are to find the unit rate.

We will be using the unitary method to solve the given problem.

In 45 minutes, the number of products made by the worker = 14.

Therefore, in 1 minute, the number of products made by the worker is given by

$\dfrac{14}{45}=0.311.$

Thus, the required unit rate is 0.311 products per minute.

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Giving 40 Points...need help as soon as possible

PIT_PIT [208]

The correct answers are:

The first system matches with (-4, 5);
The second system matches with (2, 2);
The third system matches with (-1, -3);
The fourth system matches with (3, 4);
The fifth system matches with (2, -1); and
The sixth system matches with (-5, 6).

Explanation:

The sixth system is the easiest one to find. We are given the value of x and the value of y in the equations: x=-5 and y=6.

For all other systems, we must solve the system. For the first system:
$\left \{ {{2x-y=-13} \atop {y=x+9}} \right.$

Since we have the y-variable isolated in the second equation, we will use substitution. We substitute this value in place of y in the first equation:
2x-y=-13
2x-(x+9)=-13

Distributing the subtraction sign,
2x-x-9=-13

Combining like terms:
x-9=-13

Add 9 to each side:
x-9+9=-13+9
x=-4

Substitute this into the second equation:
y=x+9
y=-4+9
y=5

The coordinates (-4, 5) represent the solution point.

For the second system:
$\left \{ {{3x+2y=10} \atop {6x-y=10}} \right.$

We can make the coefficients of x the same and use elimination. To do this, we will multiply the first equation by 2:
 $\left \{ {{2(3x+2y=10)} \atop {6x-y=10}} \right. \\ \\ \left \{ {{6x+4y=20} \atop {6x-y=10}} \right.$

Since the coefficients of x are now the same, we can cancel it. They are both positive, so we subtract:
$\left \{ {{6x+4y=20} \atop {-(6x-y=10)}} \right. \\ \\5y=10$

Divide both sides by 5:
5y/5=10/5
y=2

Substitute this into the second equation
6x-y=10
6x-2=10

Add 2 to each side:
6x-2+2=10+2
6x=12

Divide both sides by 6:
6x/6 = 12/6
x=2

The coordinates (2, 2) represent the solution to this system.

For the third system:
$\left \{ {{4x-3y=5} \atop {3x+2y=-9}} \right.$

We can make the coefficients of x the same by multiplying the first equation by 3 and the second by 4:
$\left \{ {{3(4x-3y=5)} \atop {4(3x+2y=-9)}} \right. \\ \\ \left \{ {{12x-9y=15} \atop {12x+8y=-36}} \right.$

Since the coefficients of x are the same, we can cancel them. Since they are both positive, we will subtract:
$\left \{ {{12x-9y=15} \atop {-(12x+8y=-36)}} \right. \\ \\-17y=51$

Divide both sides by -17:
-17y/-17 = 51/-17
y=-3

Substitute this into the first equation:
4x-3y=5
4x-3(-3)=5
4x--9=5
4x+9=5

Subtract 9 from each side:
4x+9-9=5-9
4x=-4

Divide each side by 4:
4x/4 = -4/4
x=-1

The coordinates (-1, -3) represent the solution of the third system..

For the fourth system:
$\left \{ {{x+y=7} \atop {x-y=-1}} \right.$

Since the coordinates of x are the same and both are positive, we can cancel x by subtracting:
$\left \{ {{x+y=7} \atop {-(x-y=-1)}} \right. \\ \\2y=8$

Divide both sides by 2:
2y/2 = 8/2
y=4

Substitute this into the first equation
x+y=7
x+4=7

Subtract 4 from each side:
x+4-4=7-4
x=3

The coordinates (3, 4) represent the solution to the fourth system.

For the fifth system:
$\left \{ {{y=3x-7} \atop {y=2x-5}} \right.$

Since y is isolated in each equation, we can set them equation to each other:
3x-7=2x-5

Subtract 2x from each side:
3x-7-2x=2x-5-2x
x-7=-5

Add 7 to each side:
x-7+7=-5+7
x=2

Substitute this into the first equation:
y=3x-7
y=3(2)-7
y=6-7
y=-1

The coordinates (2, -1) represent the solution to the fifth system.

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3 years ago

Tameron took two hikes this week. The first hike was 4.7 miles

Afina-wow [57]

Answer:

1.4

Step-by-step explanation:

we have to subtract the length of the first hike from the second to see how much longer the second hike was.

6.1 - 4.7 = 1.4

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3 years ago

Read 2 more answers

graph the relation in the table. then use the vertical-line test. is the relation a function? x y -3 -4 0 5 1 -5 3 1

Katen [24]

To solve this using the vertical line test, graph the points then see if any of them fall on the same vertical line (vertical lines run up and down), or in other words, see if any point is right above another. If there are any like this, then the graph is not a function. To graph the points from a t-chart, use one x-value, and the y-value right next to (or above it) as one point. For example, the first x-value is -3 and the first y-value is -4. Put these together as the first point: (-3, -4).

4 0

3 years ago

How much water does it take to completey fill a pool that is 50 m long, 25 m wide, and 2 m deep?

elixir [45]

Answer:

2500

Step-by-step explanation:

So it seems like we have to find the volume in this problem

The equation of volume it

lwh

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So all we do now is simply multiply.

50x25x2= 2500.

(Hope you find this helpful)

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3 years ago

Jerry is trying to earn two hundred nine dollars for some new video games. if he charges forty-seven dollars to mow a lawn, how

qwelly [4]

We could represent this as an equation:

47x = $209, where x is the number of lawns mowed.

What we could do is divide 209 by 47 to find out how many lawns Jerry would need to mow. This would give us about 4.4 (when rounded). Since Jerry has to mow entire lawns, we would have to round that up to 5 lawns. Jerry would earn $235 for those, which is more than enough for those new video games.

4 0

3 years ago