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The curve has been attached and the answer choices are:
y = 3x² – 2x + 1
y = 3x² – 6x + 3
y = 3x²<span> – 7x + 1
</span>
The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.
Let's start with first equation:
y = 3x² – 2x + 1
using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3
Hence, the vertex would be:
(h,k) = (1/3 , 2/3)
Also, the leading coefficient is positive, so the parabola would be concave up.
Thus the final answer choice will be:
y = 3x² – 2x + 1
y = 3x² – 2x + 1
y = 3x² – 6x + 3
y = 3x²<span> – 7x + 1
</span>
The attached graph has a vertex in the first quadrant. Therefore, the coordinates of the vertex would be both positive.
Let's start with first equation:
y = 3x² – 2x + 1
using the equation of axis:
x = -b/2a
x = 2/6
x = 1/3
SUbstituting the value of x in the main equation to get the y-coordinate of the vertex.
y = 3(1/3)² – 2(1/3) + 1
y = 3/9 – 2/3 + 1
y = 1/3 – 2/3 + 1
y = (1 - 2 + 3)/3
y = 2/3
Hence, the vertex would be:
(h,k) = (1/3 , 2/3)
Also, the leading coefficient is positive, so the parabola would be concave up.
Thus the final answer choice will be:
y = 3x² – 2x + 1
The first part of the question is missing and it says;
Use these parameters: Men's heights are normally distributed with mean 68.6 in. and standard deviation 2.8 in. Women's heights are normally distributed with mean 63.7 in. and standard deviation 2.9 in.
Answer:
A) Percentage of women meeting the height requirement = 72.24%
B) Percentage of men meeting the height requirement = 0.875%
C) Corresponding women's height =67.42 inches while corresponding men's height = 72.19 inches
Step-by-step explanation:
From the question,
For men;
Mean μ = 68.6 in
Standard deviation σ = 2.8 in
For women;
Mean μ = 63.7 in
Standard deviation σ = 2.9 in
Now let's calculate the standardized scores;
The formula is z = (x - μ)/σ
A) For women;
Z = (62 - 63.7)/2.9 = - 0.59
Z = (78 - 63.7)/2.9 = 4.93
The original question cam be framed as;
P(62 < X < 78).
So thus, the probability of only women will take the form of;
P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996
And P(Z > - 0.59) = 0.277595
Thus;
P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.7224
So, percentage of women meeting the height requirement is 72.24%.
B) For men;
Z = (62 - 68.6)/2.8 = -2.36
Z = (78 - 68.6)/2.8 = 3.36
Thus, the probability of only men will take the form of;
P(-2.36 < Z < 3.36) = P(Z<3.36) - P(Z > - 2.36)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<3.36) = 0.99961
And P(Z > -2.36) = 0.99086
Thus;
P(Z<3.36) - P(Z > -2.36) 0.99961 - 0.99086 = 0.00875
So, percentage of women meeting the height requirement is 72.24%.
B)For women;
Z = (62 - 63.7)/2.9 = - 0.59
Z = (78 - 63.7)/2.9 = 4.93
The original question cam be framed as;
P(62 < X < 78).
So thus, the probability of only women will take the form of;
P(-0.59 < Z < 4.93) = P(Z<4.93) - P(Z > - 0.59)
From the normal probability table attached, when we interpolate, we'll arrive at P(Z<4.93) = 0.9999996
And P(Z > - 0.59) = 0.277595
Thus;
P(Z<4.93) - P(Z > - 0.59) =0.9999996 - 0.277595 = 0.00875
So, percentage of women meeting the height requirement is 0.875%
C) Since the height requirements are changed to exclude the tallest 10% of men and the shortest10% of women.
For women;
Let's find the z-value with a right-tail of 10%. From the second table i attached ;
invNorm(0.90) = 1.2816
Thus, the corresponding women's height:: x = (1.2816 x 2.9) + 63.7= 67.42 inches
For men;
We have seen that,
invNorm(0.90) = 1.2816
Thus ;
Thus, the corresponding men's height:: x = (1.2816 x 2.8) + 68.6 = 72.19 inches
Given:
The function is
(-5,n) is an ordered pair of the function rule.
To find:
The value of n.
Solution:
If (-5,n) is an ordered pair of the function rule, then the function must be satisfied by the point (-5,n). It means f(-5)=n.
Substitute x=-5 in the given function.
We know that, . So,
Therefore, the value of n is 10.