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Elena L [17]
2 years ago
14

The student council wanted to know students’ opinions about the music at school dances. They asked all the girls in a dance clas

s to fill out a survey. Was the survey collected in a biased manner? Explain how you decided.
Mathematics
1 answer:
Pavlova-9 [17]2 years ago
7 0

Answer:

Yes

Step-by-step explanation:

The student council only asked a specific group of people for their opinion on the music. They will only have the dance class' opinions and not an accurate representation of the whole student population.

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That type of graph is called a line plot
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Given the quadratic function f(x) = 4x^2 - 4x + 3, determine all possible solutions for f(x) = 0
solong [7]

Answer:

The solutions to the quadratic function are:

x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}

Step-by-step explanation:

Given the function

f\left(x\right)\:=\:4x^2\:-\:4x\:+\:3

Let us determine all possible solutions for f(x) = 0

0=4x^2-4x+3

switch both sides

4x^2-4x+3=0

subtract 3 from both sides

4x^2-4x+3-3=0-3

simplify

4x^2-4x=-3

Divide both sides by 4

\frac{4x^2-4x}{4}=\frac{-3}{4}

x^2-x=-\frac{3}{4}

Add (-1/2)² to both sides

x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{3}{4}+\left(-\frac{1}{2}\right)^2

x^2-x+\left(-\frac{1}{2}\right)^2=-\frac{1}{2}

\left(x-\frac{1}{2}\right)^2=-\frac{1}{2}

\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}

solving

x-\frac{1}{2}=\sqrt{-\frac{1}{2}}

x-\frac{1}{2}=\sqrt{-1}\sqrt{\frac{1}{2}}                 ∵ \sqrt{-\frac{1}{2}}=\sqrt{-1}\sqrt{\frac{1}{2}}

as

\sqrt{-1}=i

so

x-\frac{1}{2}=i\sqrt{\frac{1}{2}}

Add 1/2 to both sides

x-\frac{1}{2}+\frac{1}{2}=i\sqrt{\frac{1}{2}}+\frac{1}{2}

x=i\sqrt{\frac{1}{2}}+\frac{1}{2}

also solving

x-\frac{1}{2}=-\sqrt{-\frac{1}{2}}

x-\frac{1}{2}=-i\sqrt{\frac{1}{2}}

Add 1/2 to both sides

x-\frac{1}{2}+\frac{1}{2}=-i\sqrt{\frac{1}{2}}+\frac{1}{2}

x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}

Therefore, the solutions to the quadratic function are:

x=i\sqrt{\frac{1}{2}}+\frac{1}{2},\:x=-i\sqrt{\frac{1}{2}}+\frac{1}{2}

4 0
2 years ago
What is the length of the mural
salantis [7]

Answer:

23? mabey

Step-by-step explanation:

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4 0
3 years ago
H is the interior of <JAK. <JAH=3x-8 degrees and <KAH= x+2 degrees. What is the measure of all angles?
mart [117]
In this problem, we could use the Angle Addition Postulate property. This property states that all interior angles within should sum of to the total angle. It is specifically stated that point H is interior of angle ∠JAK. Looking at the diagram attached in the picture, line segment AH is drawn in the middle. Therefore, the Angle Addition Postulate tells us that the sum of interior angles JAH and angle HAK, is equal to the total angle JAK. 

∠JAK = ∠JAH + ∠HAK
∠JAK = (3x - 8) + (x+2)

But there is a missing information. Without knowing the total angle JAK, we can't solve for x. Consequently, we can't solve for the interior angles. So, let's just assume that ∠JAK = 45°. This is just for sample purposes. 

45° = (3x - 8) + (x+2)
45 = 4x - 6
4x = 45+6
4x = 51
x = 12.75°

Therefore, the interior angles are equal to
∠JAH = 3(12.75) - 8 = 30.25°
∠HAK = 12.75 + 2 = 14.75°

6 0
3 years ago
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