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1 year ago

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If the standard deviation of an exam is 5, the z-score us 1.95 and the mean is 80; what is the actual test score? (Round the ans

wer to the nearest hundredth)

1 answer:

skad [1K]1 year ago

6 0

If the standard deviation of an exam is 5, the z-score us 1.95 and the mean is 80, the actual test score is; 89.75

<h3>How to solve z-score problems?</h3>

We are given;

Standard deviation; s = 5

z-score = 1.95

Mean = 80

Formula for z-score is;

z = (x' - μ)/σ

Thus;

1.95 = (x' - 80)/5

1.95 * 5 = (x' - 80)

9.75 = x' - 80

x' = 80 + 9.75

x' = 89.75

Read more about Z-score Problems at; brainly.com/question/25638875

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3 years ago

A toy rocket is launched from a platform that is 48 ft high. The rocket height above the ground is modeled by h=-16t^2+32t+48. a

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a) 64 feet

b) 3 seconds

Step-by-step explanation:

a)

The maximum height of $h=h(t)$ can be bound by finding the y-coordinate of the vertex of $y=-16x^2+32x+48$ .

Compare this equation to $y=ax^2+bx+c$ to find the values of $a,b,\text{ and } c$ .

$a=-16$

$b=32$

$c=48$ .

The x-coordinate of the vertex can be found by evaluating:

$\frac{-b}{2a}=\frac{-32}{2(-16)$

$\frac{-b}{2a}=\frac{-32}{-32}$

$\frac{-b}{2a}=1$

So the x-coordinate of the vertex is 1.

The y-coordinate can be found be evaluating $y=-16x^2+32x+48$ at $x=1$ :

$y=-16(1)^2+32(1)+48$

$y=-16+32+48$

$y=16+48$

$y=64$

So the maximum height of the rocket is 64 ft high.

b)

When the rocket hit's the ground the height that the rocket will be from the ground is 0 ft.

So we are trying to find the second t such that:

$0=-16t^2+32t+48$

I'm going to divide both sides by -16:

$0=t^2-2t-3$

Now we need to find two numbers that multiply to be -3 and add to be -2.

Those numbers are -3 and 1 since (-3)(1)=-3 and (-3)+(1)=-2.

$0=(t-3)(t+1)$

This implies we have either $t-3=0$ or $t+1=0$

The first equation can be solved by adding 3 on both sides: $t=3$ .

The second equation can be solved by subtracting 1 on both sides: $t=-1$ .

So when $t=3$ seconds, is when the rocket has hit the ground.

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