Solve for u. - 4(w + 1) = -24
2 answers:
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Answer:
Step-by-step explanation:
The mean SAT score is , we are going to call it \mu since it's the "true" mean
The standard deviation (we are going to call it ) is
Next they draw a random sample of n=70 students, and they got a mean score (denoted by ) of
The test then boils down to the question if the score of 613 obtained by the students in the sample is statistically bigger that the "true" mean of 600.
- So the Null Hypothesis
- The alternative would be then the opposite
The test statistic for this type of test takes the form
and this test statistic follows a normal distribution. This last part is quite important because it will tell us where to look for the critical value. The problem ask for a 0.05 significance level. Looking at the normal distribution table, the critical value that leaves .05% in the upper tail is 1.645.
With this we can then replace the values in the test statistic and compare it to the critical value of 1.645.
Answer:
1) Area of frame: ; Area of picture:
; Total Area:
.
2) Area 1 = ; Area 2 =
; total area =
[first answer line :
]
Step-by-step explanation:
1. So to answer this question, you have to find the inner photo area first (which you will then subtract from the overall rectangle area to get the photo frame area).
To find area, you multiply length x width. For this question, there are not enough measurements given to initially multiply length and width. So, assuming that the photo is centered on the frame and the frame width is consistent along all sides, you find the difference between the overall length (12) and the picture length (5).
12 - 5 = 7
The leftover area (outside of the picture) is 7 cm (half of seven on both sides), so one side can be assumed to be : 3.5 cm
this means that 15 cm - 3.5 cm of both sides lengths (difference between the two lengths given) is the height of the photo, 15 - 3.5(2) = 8
So, the dimensions/measurements of the photo are 5 cm by 8 cm.
This means that the inner photo area is 40 (5 x 8) cm
The area of the frame will be the area of the total rectangle [12 x 15] - the inner photo area [40]. [ (12)(15) - 40 ]
[180 - 40] = 140 cm
(area is measured in squared units, so the area of the frame should be written as ; and the area of the photo should be written as
)
The total area is the entire area of the rectangle: (12)(15) = 180. (This should be written as )
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2) Finding the area of a shape that isn't a simple rectangle is easier if you separate the shape into smaller rectangles. I will separate the two rectangles into 4 x 12 and 2 x 6 [6 cm would be the remaining side length if you remove the length of 4].
{you can separate the shape in multiple ways, so my answer is only one answer to this problem out of other splits.}
as mentioned, the area is length x width.
4 x 12 = 48.
2 x 6 = 12. Once again, you should write area in squared units.
(the area 1 should be written as ; the area 2 should be written as
)
you can combine the separated areas (add them) to find the total area. 48 + 12 = 60.
(the total area should be written in squared units also, so the total area should be written as: )
The area of the figure is