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umka21 [38]
3 years ago
10

Diagram shows a framework consisting of 16 wooden rods. The length of each rod is 8 cm.

Mathematics
1 answer:
Umnica [9.8K]3 years ago
8 0

Answer:

1024 cm²

Step-by-step explanation:

There are 16 rods.  A square has 4 equal sides, so each side must consist of 4 rods.  The length of each rod is 8 cm, so the length of each of the square's sides is 32 cm.  Therefore, the area of the square is:

A = s²

A = (32 cm)²

A = 1024 cm²

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WILL MARK BRAINLIEST!!!
Naddika [18.5K]
I've never seen the terminology 'slope-intercept' form before, but it seems fairly self-explanatory that it means 'of the form y = m + c'.

Hence it is a simply rearrangement of the equation to start with, in order to make  the subject:






This is the graph in 'slope-intercept' form. From here it is easy to see that gradient  = and that y-intercept = 490.

The easiest way to draw a straight-line graph, such as this one, is to plot the y-intercept, in this case (0, 490), then plot another point either side of it at a fair distance (for example substitute  = -5 and  = 5 to procure two more sets of co-ordinates). These can be joined up with a straight line to form a section of the graph, which would otherwise extend infinitely either side - use the specified range in the question for x-values, and do not exceed it (clearly here the limit of -values is 0 ≤ x ≤ 735, since neither x nor y can be negative within the context of the question - the upper limit was found by substituting  = 0).

In function notation, the graph is:



The graph of this function represents how the value of the function varies as the value of x varies. Looking back at the question context, this graph specifically represents how many wraps could have been sold at each number of sandwich sales, in order to maintain the same profit of $1470.

When the profit is higher, the gradient is not changed (this is defined by the relationship between the $2 and $3 prices, not the overall profit) - instead the -intercept is higher:






Therefore we have gleaned that the new y-intercept is 531.

Clearly I cannot see the third straight line. However the method for finding the equation of a straight line graph is fairly simple:

1. Select two points on the line and write down their coordinates
2. The gradient of the line = 
3. Find the change in  (Δ
4. Find the change in  (Δ
5. Divide the result of stage 3 by the result of stage 4
6. This is your gradient
7. Take one of your sets of coordinates, and arrange them in the form , where your  is the gradient you just calculated
8. There is only one variable left, which is  (the y-intercept). Simply solve for this
9. Now generalise the equation, in the form , by inputting your gradient and y-intercept whilst leaving the coordinates as  and 

For example if the two points were (1, 9) and (4, 6):

Δ = 6 - 9 = -3
Δ = 4 - 1 = 3
 =  = -1
I choose the point (4, 6)
6 = (-1 * 4) + c
6 = c - 4
c = 10
Therefore, generally, 

Within the context of the question, I imagine the prices of the two lunch specials will be the same in the third month and hence the gradient will still be  - this means steps 1-6 can be omitted. Furthermore if the axes are clearly labelled, you may even be able to just read off the y-intercept and hence dispose with steps 1-8!

I hope this helps you
5 0
2 years ago
Which of the following statements is true?<br><br> a.<br> b.<br> c. <br> d.
ludmilkaskok [199]

Answer:

confused on what you are asking

Step-by-step explanation:

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2 years ago
A sample of 300 FM residents was taken and 135 said their favorite season was summer. Calculate a 99% confidence interval for th
erma4kov [3.2K]

Answer:

The 99% confidence interval for the proportion of FM residents whose favorite season is summer is between (0.376, 0.524).

The lower bound of this interval is 0.376.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

For this problem, we have that:

n = 300, \pi = \frac{135}{300} = 0.45

99% confidence level

So \alpha = 0.01, z is the value of Z that has a pvalue of 1 - \frac{0.01}{2} = 0.995, so Z = 2.575.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 - 2.575\sqrt{\frac{0.45*0.55}{300}} = 0.376

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.45 + 2.575\sqrt{\frac{0.45*0.55}{300}} = 0.524

The 99% confidence interval for the proportion of FM residents whose favorite season is summer is between (0.376, 0.524).

The lower bound of this interval is 0.376.

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Answer:

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Step-by-step explanation:

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What is the slope of the line shown?<br> у<br> (-6, 7)<br> (-2, 6)<br> (2,5)<br> (6,4)<br> X
nasty-shy [4]

Answer:

The slope of the line shown is -1/4.

Step-by-step explanation:

Change in y/Change in x = - 1/4

8 0
2 years ago
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