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3 years ago

Write three ordered pairs for direct variation relationship where y= 12 when x= 16

Mathematics

1 answer:

Kruka [31]3 years ago

3 0

Ordered pairs that work for this direct variation are (4, 3), (8, 6) and (12, 9).

In order to find these, we must first find the value of the direct variation coefficient. We can do that using the base equation y = kx and then by plugging in to find k.

y = kx

12 = k(16)

3/4 = k

Now that we have k, we can model the equation as y = 3/4x. We can also find any number of ordered pairs by using the x value and finding the y value. All of the above answers work.

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Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are inches long, inches wide, and 8 inche

allochka39001 [22]

Answer:

- The number of small boxes that will fill the large box 1 = 64

- The number of small boxes that will fill the large box 2 = 56

Step-by-step explanation:

Complete Question

Items for a fundraiser are packaged in small boxes shaped like rectangular prisms that are 4.5 inches long, 4.5 inches wide, and 8 inches tall. To transport the items to an event, you want to know how many of the small boxes will fit in larger boxes. The larger boxes are available in two sizes. Large Box 1 is 24.25 inches long, 18 inches wide, and 24 inches tall. Large Box 2 is 20.5 inches long, 18.5 inches wide, and 24 inches tall. Both the small and large boxes must remain upright.

Solution

To know how many of the small boxes will fit in larger boxes, we need to obtain the volumes of the small box, large box 1 and large box 2.

Volume of a cuboid = L × W × H

For the small box,

Length = L = 4.5 inches

Width = W = 4.5 inches

Height = H = 8 inches

Volume of the small box = 4.5 × 4.5 × 8 = 162 in³

For large box 1,

Length = L = 24.25 inches

Width = W = 18 inches

Height = H = 24 inches

Volume of the large box 1 = 24.25 × 18 × 24 = 10,476 in³

For large box 2

Length = L = 20.5 inches

Width = W = 18.5 inches

Height = H = 24 inches

Volume of the large box 2 = 20.5 × 18.5 × 24 = 9,102 in³

The number of small boxes that'll fill the large box 1 = (10,476/162) = 64.667 = 64 small boxes (rounded down because the fraction cannot be forced into the large box 1.

The number of small boxes that will fill the large box 2 = (9,102/162) = 56.185 = 56 small boxes.

Hope this Helps!!!

7 0

3 years ago

Look at image for question

kotegsom [21]

Answer:

r=0.5 or 1/2

Step-by-step explanation:

if you multiply 0.5 to each Xs you can find out why r is 0.5

8 0

3 years ago

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its average number of unoc

Bingel [31]

Answer:

We need a sample size of at least 719

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.96$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

How large a sample size is required to vary population mean within 0.30 seat of the sample mean with 95% confidence interval?

This is at least n, in which n is found when $M = 0.3, \sigma = 4.103$ . So

$M = z*\frac{\sigma}{\sqrt{n}}$

$0.3 = 1.96*\frac{4.103}{\sqrt{n}}$

$0.3\sqrt{n} = 1.96*4.103$

$\sqrt{n} = \frac{1.96*4.103}{0.3}$

$(\sqrt{n})^{2} = (\frac{1.96*4.103}{0.3})^{2}$

$n = 718.57$

Rouding up

We need a sample size of at least 719

6 0

3 years ago

How do you expand (x+2)^5

just olya [345]

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2
by
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5
.
x
5
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x
4
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10
x
3
⋅
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2
3
+
5
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⋅
2
4
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2
5
x
5
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10
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+
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3
⋅
2
2
+
10
x
2
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5
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+
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5
Raise
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2
to the power of
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2
.
x
5
+
10
x
4
+
10
x
3
⋅
4
+
10
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2
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5
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5
+
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+
10
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5
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4
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5
Multiply
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10
.
x
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10
x
4
+
40
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3
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5
Raise
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3
.
x
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16
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5
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5
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10
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5
Multiply
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by
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5
.
x
5
+
10
x
4
+
40
x
3
+
80
x
2
+
80
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+
2
5
x
5
+
10
x
4
+
40
x
3
+
80
x
2
+
80
x
+
2
5
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2
2
to the power of
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5
.
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5
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x
4
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40
x
3
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3 years ago

And electronic store sells a large flat screen television for $1699 last month the store sold eight of those television sets abo

Lerok [7]

Answer:

$13,592

Step-by-step explanation:

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