Answer: Kara should have written the proportion in step 1 as;
Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)
Step-by-step explanation: The two similar triangles are given with the following dimensions;
Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.
For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures 1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.
Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;
VX = ZX
VW = ZY
XW = XY
What Kara did was as follows;
VX/ZY = VW/ZX
Which translates to 14/72 = 12/x
This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.
The correct step should therefore have been;
VW/ZY = VX/ZX
12/72 = 14/x (Step 1)
12x = (72) (14) {Step 2}
x = 1008/12 (Step 3)
x = 84 (Step 4)
Answer:the weight after 225 days is
22885 kilograms
Step-by-step explanation:
The initial weight of the blue whale calf at birth is 2725 kilograms. blue whale calf gains 90 kilograms of weight each day for the first 240 days after its birth. The weight increases in arithmetic progression. This means that the first term of the sequence, a is 2725, the common difference, d is 90.
The formula for the nth term of an arithmetic sequence is expressed as
Tn = a + (n - 1)d
Where
n is the number of terms of the sequence.
a is the first term
d is the common difference
We want to determine its weight, T225 after 225 days after it’s birth. It means that n = 225
Therefore
T225 = 2725 + (225 - 1)90
T225 = 2725 + 224×90 = 2725 + 20160
T225 = 22885
Answer:
The decision made by the researcher based on this information is to reject the null hypothesis.
Step-by-step explanation:
Two-tailed hypothesis test:
Critical value: 
Test statistic: z
If 
, we do not reject the null hypothesis.
If 
, we reject the null hypothesis.
In this question:
Since , we reject the null hypothesis.
The decision made by the researcher based on this information is to reject the null hypothesis.
Remember that the period of a sinusoidal function <span>is the vertical distance between the t-axis and one of the extreme points.</span> From the graph we can infer that the period of the function is 4.5.
Also, the amplitude is<span> the distance between two consecutive maximum or two consecutive minimum points. From the graph we can infer that the amplitude of the function is 0.05 seconds.
We can conclude that the correct answer is: 0.05 seconds; 4.5
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