Answer:
the equation D ) would cause a consistent-independent system.
Step-by-step explanation:
A ) 5 x + y = 7 /*( -2 )
10 x + 2 y = 14
--------------------
- 10 x - 2 y = - 14
10 x + 2 y = 14
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0 x = 0 ( Dependent system )
B ) 5 x + y = 7 / * 3
- 15 x - 3 y = - 6
--------------------------
15 x + 3 y = 21
- 15 x - 3 y = - 6
-------------------------
0 x = 15 ( Inconsistent system )
C ) 5 x + y = 7
5 x + y = - 7 / * ( - 1 )
---------------------------
5 x + y = 7
- 5 x - y = 7
------------------
0 x = 14 ( Inconsistent system )
D ) 5 x + y = 7 / * ( - 2 )
6 x + 2 y = 7
------------------
- 10 x - 2 y = - 14
6 x + 2 y = 7
-----------------------
- 4 x = - 7; x = 7/4; y = - 7/4
Answer:
Third option is correct. Scale factor 3 ; enlargement.
Step-by-step explanation:
It is given that the figure A'B'C'D' is a dilation of figure ABCD.
We know that after dilation the corresponding sides of image and preimage are in the same proportion.
The image of AD is A'D'.
From the figure it is noticed that the A(-1,2), D(-1,-1), A'(-3,6) and D'(-3,-3).
Distance formula is
Scale factor is constant which represents the relation between image and preimage.
Therefore the scale factor is 3.
If k>0 it means enlargement and if k<0 it means reduction. Therefore third option is correct.
Answer:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Step-by-step explanation:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where 
and 
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
The answer is 32
Solution for 40 is what percent of 125:
40:125*100 =
( 40*100):125 =
4000:125 = 32
Now we have: 40 is what percent of 125 = 32
Question: 40 is what percent of 125?
Percentage solution with steps:
Step 1: We make the assumption that 125 is 100% since it is our output value.
Step 2: We next represent the value we seek with $x$x.
Step 3: From step 1, it follows that $100\%=125$100%=125.
Step 4: In the same vein, $x\%=40$x%=40.
Step 5: This gives us a pair of simple equations:
$100\%=125(1)$100%=125(1).
$x\%=40(2)$x%=40(2).
Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have
$\frac{100\%}{x\%}=\frac{125}{40}$
100%
x%=
125
40
Step 7: Taking the inverse (or reciprocal) of both sides yields
$\frac{x\%}{100\%}=\frac{40}{125}$
x%
100%=
40
125
$\Rightarrow x=32\%$⇒x=32%
Therefore, $40$40 is $32\%$32% of $125$125.
Given that
the weight of football players is distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
And we need to find What is the minimum weight of the middle 95% of the players?
Explanation -
Using the Empirical Rule, 95% of the distribution will fall within 2 times of the standard deviation from the mean.
Two standard deviations = 2 x 25 pounds = 50 pounds
So the minimum weight = 200 pounds - 50 pounds = 150 pounds
Hence the final answer is 150 pounds.
