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2 years ago

5

1. Determine if the following situation is biased or unbiased: 500 students at a local high school are randomly chosen and asked

what their favorite local restaurant is

1 answer:

faltersainse [42]2 years ago

8 0

The correct answer is unbiased.

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A jumping spider's movement is modeled by a parabola. The spider makes a single jump from the origin and reaches a maximum heigh

Stella [2.4K]

A parabola is a mirror-symmetrical U-shape.

The equation of the parabola is $\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$
The focus is $\mathbf{Focus = (80, -1760)}$
The directrix is $\mathbf{y = \frac{1}{640}}$
The axis of the symmetry of parabola is: $\mathbf{x = 80}$

From the question, we have:

$\mathbf{Vertex: (h,k) = (80,10)}$

$\mathbf{Origin: (x,y) = (0,0)}$

The equation of a parabola is:

$\mathbf{y = a(x - h)^2 + k}$

Substitute the values of origin and vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{0 = a(0 - 80)^2 + 10}$

$\mathbf{0 = a(- 80)^2 + 10}$

$\mathbf{0 = 6400a + 10}$

Collect like terms

$\mathbf{6400a =- 10}$

Solve for a

$\mathbf{a =- \frac{1}{640}}$

Substitute the values of a and the vertex in $\mathbf{y = a(x - h)^2 + k}$

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

The focus of a parabola is:

$\mathbf{Focus = (h, \frac{k+1}{4a})}$

Substitute the values of a and the vertex in $\mathbf{Focus = (h, \frac{k+1}{4a})}$

$\mathbf{Focus = (80, \frac{10+1}{4 \times -\frac{1}{640}})}$

$\mathbf{Focus = (80, -\frac{11}{\frac{1}{160}})}$

$\mathbf{Focus = (80, -11\times 160)}$

$\mathbf{Focus = (80, -1760)}$

The equation of the directrix is:

$\mathbf{y = -a}$

So, we have:

$\mathbf{y = \frac{1}{640}}$ ----- the directrix

The axis of symmetry is:

$\mathbf{x = -\frac{b}{2a}}$

We have:

$\mathbf{y = -\frac{1}{640}(x - 80)^2 + 10}$

Expand

$\mathbf{y = -\frac{1}{640}(x^2 -160x + 6400) +10}$

Expand

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x - 10 +10}$

$\mathbf{y = -\frac{1}{640}x^2 +\frac{1}{4}x }$

A quadratic function is represented as:

$\mathbf{y = ax^2 + bx + c}$

So, we have:

$\mathbf{a = -\frac{1}{640}}$

$\mathbf{b = \frac{1}{4}}$

Recall that:

$\mathbf{x = -\frac{b}{2a}}$

So, we have:

$\mathbf{x = -\frac{1/4}{2 \times -1/640}}$

$\mathbf{x = \frac{1/4}{1/320}}$

This gives

$\mathbf{x = \frac{320}{4}}$

$\mathbf{x = 80}$

Hence, the axis of the symmetry of parabola is: $\mathbf{x = 80}$

Read more about parabola at:

brainly.com/question/21685473

6 0

2 years ago

What is the value of the expression 4x−y/2y x when x = 3 and y = 3? −3 1 9 18

ziro4ka [17]

(4x - y)/(2y + x) when x = 3 and y = 3 is
(4(3) - 3)/(2(3) + 3) = (12 - 3)/(6 + 3) = 9/9 = 1

5 0

3 years ago

Bob bought a new book and paid $2.10 tax on the book. If the tax rate was 7 ½%, what was the cost of the book?

scoray [572]

$15.75
2 x 7.5 = 15
0.10 x 7.5 = 0.75
15 + 0.75 = $15.75
Hope this helped

8 0

2 years ago

Read 2 more answers

Can anyone solve it plzzzz

Vedmedyk [2.9K]

Answer:

1.A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns.

2.

Solution given:

We have

Sin² $\theta$ -Cos ² $\theta$ =1

Sin² $\theta$ =1+Cos² $\theta$

Sin $\theta$ = $\sqrt{1-Cos²\theta}$

3.

4Tan² $\theta$ +4Cot² $\theta$ -3Tan² $\theta$ -3Cot² $\theta$

4Tan² $\theta$ -3Tan² $\theta$ +4Cot² $\theta$ -3Cot² $\theta$

Tan² $\theta$ -Cot² $\theta$

7 0

2 years ago

Every repair bill at Chuckie’s Service Spot includes a fixed charge for an estimate of the repairs plus an hourly fee for labor.

lakkis [162]

Answer:

overpriced is all I can say.....

8 0

3 years ago