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3 years ago

8

four seniors and six juniors are competing for four places on a quiz bowl team. what is the approximate probability that all fou

r seniors will be chosen at random ?

2 answers:

12345 [234]3 years ago

6 0

The answer is 4 out of 10

uranmaximum [27]3 years ago

3 0

Answer:

The probability is:

4/10

Step-by-step explanation:

We are given:

four seniors and six juniors.

Number of seniors=4

Total number of people=10 ( since 6+4=10)

We are asked to fill four places on a quiz bowl team.

We are asked to find the probability that all four seniors will be chosen at random.

The probability is calculated as:

Ratio of the number of seniors to the total number of people.

Hence, the probability is:

4/10

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Option D) h(x), f(x), g(x)

Step-by-step explanation:

we know that

The axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex of the parabola

Part 1) we have

$f(x)=4x^{2} -1$

This is a vertical parabola open upward

The vertex is a minimum The vertex is the point (0,-1)

The x-coordinate of the vertex is 0

so

The axis of symmetry is x=0

Part 2) we have

$g(x)=x^{2}-8x+5$

This is a vertical parabola open upward

The vertex is a minimum

Convert the equation into vertex form

$g(x)-5=x^{2}-8x$

$g(x)-5+16=x^{2}-8x+16$

$g(x)+11=x^{2}-8x+16$

$g(x)+11=(x-4)^{2}$

$g(x)=(x-4)^{2}-11$

The vertex is the point (4,-11)

The x-coordinate of the vertex is 4

so

The axis of symmetry is x=4

Part 3) we have

$h(x)=-3x^{2}-12x+1$

This is a vertical parabola open downward

The vertex is a maximum

Convert the equation into vertex form

$h(x)-1=-3x^{2}-12x$

$h(x)-1=-3(x^{2}+4x)$

$h(x)-1-12=-3(x^{2}+4x+4)$

$h(x)-13=-3(x+2)^{2}$

$h(x)=-3(x+2)^{2}+13$

The vertex is the point (-2,13)

The x-coordinate of the vertex is -2

so

The axis of symmetry is x=-2

Part 4) Rank their axis of symmetry from least to greatest

1) h(x) -----> axis of symmetry -2

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3) g(x) -----> axis of symmetry 4

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4 years ago

"A state legislator wishes to survey residents of her district to see what proportion of the registered voters are aware of her

aliya0001 [1]

Answer:

The correct answer to the following question will be "384".

Step-by-step explanation:

We are having,

$P(-0.05$

On solving, we get

⇒ $P(\frac{-0.05}{\sqrt{\frac{pq}{n}}}$

⇒ $\frac{0.05}{\sqrt{\frac{p(1-p)}{n}}} =1.96$

On applying cross-multiplication, we get

⇒ $0.05^2=1.96^2\times \frac{P(1-p)}{n}$

⇒ $0.05^2n=1.96^2-1.96^2p^2$

⇒ $1.96^2p^2-1.96^2p+0.05^2n=0$ ...(equation 1)

When "p" seems to be the population proportion, (equation 1) approach, which is special

∴ $b^2-4ac=0$

On putting the values in the above expression, we get

⇒ $(1.96)^4-4\times 0.05^2\times 1.96^2n=0$

⇒ $1.98^2-4\times 0.05^2n=0$

⇒ $n=\frac{1.96^2}{4\times 0.05^2}$

⇒ $n=384.16=384$

7 0

3 years ago