5.5 move decimal place over twice 20*.055 =$1.1 in sales tax
<span>Find the focus and directrix of the parabola with the given equation. Then graph the parabola.
y^=-12x
**
y^2=-12x
This is an equation of a parabola with a horizontal axis of symmetry.
Its standard form: (y-k)^2=4p(x-h), with (h,k) being the (x,y) coordinates of the vertex.
For given equation:
Vertex(0,0)
4p=12
p=3
Focus:(-3,0)
Directrix: x=3
see the graph below as a visual check on the answers:
..
y=±(-12x)^.5</span>
X=16
y= -12
X+2( -x+4)=-8
X-2x+8=-8
-1x=-16
X=16
Y=-16+4
Y=-12
To solve the first four problems shown in the picture, you must find out what number was multiplied by the original to get the new number in the second fraction.
In the case of problem 1, 5 was multiplied by 4 to get 20. So, to make the fractions proportional, you multiply the numerator by 4 as well. This would be: 4/5=16/20.
Do this for the next 3 problems.
Now, to solve problem 5, both 3 and 5 can go into 15, so it doesn't really matter what you choose. I will go with 5, as it is the larger number and will be easier to solve with.
3:5=?:15, or 3/5=?/15 is the problem here. You can do the rest of this problem using the same technique I used to help you solve the first three problems.
Problem 6 is the same thing, but instead of enlarging the number, you are decreasing. It is done in the same way, but using division instead of multiplication.
10 cm wide is reduced to 4 cm wide. 30 cm long is reduced to ? cm long. This can be written as: 10/30=4/?
But because 10 isn't divisible by 4 evenly, you can use ratios to answer this. In the original diagram, there is 1cm in length for every 3cm in width. So if there are 4cm in length, multiply that by 3 to get width. 4x3=12. The length of the reduced diagram would be 12cm.
For question 7, you know that in 2 hours, a wood stove burns 4 logs. Assuming that all logs in the problem are same-sized, you can simply multiply 4 by 4, as 2 goes into 8 four times, and 4 logs are used up every 2 hours.
For question 8, you must divide $2.20, or 2.2, by 5. This would be: 2.2/5=0.44
A single stamp is worth $0.44, so multiply that number by 7 to get the price of 7 stamps.
I cannot answer question 9 as it seems to be a multi-part question that includes a diagram that is not shown in the photo.
However, if you need help solving problem 9, feel free to post the rest of the page as another question and if I am not too late, I will try to help. I hope I helped out :-)
Answer:
a) 0.84% of students scored over 32
b) 29.12% of students scored under 17
c) 70.04% of students scored between 17 and 32.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean 
and standard deviation 
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a) About what percent of students scored over 32?
This is 1 subtracted by the pvalue of Z when X = 32. So
has a pvalue of 0.9916
1 - 0.9916 = 0.0084
So 0.84% of students scored over 32
b) About what percent of students scored under 17?
This is the pvalue of Z when X = 17. So
has a pvalue of 0.2912
So 29.12% of students scored under 17
c) About what percent of students scored between 17 and 32?
This is the pvalue of Z when X = 32 subtracted by the pvalue of Z when X = 12. So
X = 32
has a pvalue of 0.9916
X = 17
has a pvalue of 0.2912
0.9916 - 0.2912 = 0.7004
70.04% of students scored between 17 and 32.
