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Vera_Pavlovna [14]

3 years ago

6

President of Salas Products, is reviewing the warranty policy for her company's new model of automobile batteries. Life tests pe

rformed on a sample of 100 batteries indicated:
(1) an average life of 75 months,
(2) a standard deviation of 5 months,
(3) a bell shaped battery life distribution. What percentage of the batteries will fail within the first 65 months of use?

1 answer:

never [62]3 years ago

3 0

Answer:

2.28 %

Step-by-step explanation:

It is stated that battery life distribution is normal. First we need to find out where 65 hour battery life in this distribution falls by finding its z-score. We can use the following formula

z(x)= $\frac{X-M}{s}$ where

X the point we are looking to find its z-score, which is 65
M is the mean of the sample, which is 75
s is the standard deviation of the sample, which is 5

Replacing these numbers in the formula, z-score of the 65 hour battery life :

z(x)= $\frac{65-75}{5}$ =-2

All the batteries fail within the first 65 months if their z-score is smaller than -2. Or we can state this also as: P(z≤-2) which is 0.0228

Thus 2.28 % of the batteries will fail within the first 65 months of use.

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Here is rectangle QRST.

ValentinkaMS [17]

Answer:

QR = 5 units

RS = 10 units

Perimeter of QRST = 30 units

Step-by-step explanation:

The perimeter of a rectangle is given by the formula:

$p=2(l+w)$

where

$p$ is the perimeter of the rectangle

$l$ is the length of the rectangle

$w$ is the width of the rectangle

Now, to find the width, QR, and the length, RS, of the rectangle, we are using the distance formula:

$d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

where

$d$ is the distance

$(x_1,y_1)$ are the coordinates of the first point

$(x_2,y_2)$ are the coordinates of the second point

- For QR:

The first point of QR is Q(-3, 0) and the second is R(0, 4), so $x_1=-3$ , $y_1=0$ , $x_2=0$ , and $y_2=4$ .

Replacing values

$d=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$d=\sqrt{(0-(-3))^{2}+(4-0)^{2}}$

$d=\sqrt{(0+3)^{2}+(4)^{2}}$

$d=\sqrt{3^{2} +4^{2}}$

$d=\sqrt{9+16}$

$d=\sqrt{25}$

$d=5$

- For RS

The first point of RS is R(0, 4) and the second is S(8, -2), so $x_1=0$ , $y_1=4$ , $x_2=8$ , and $y_2=-2$ .

Replacing values

$d=\sqrt{(8-0)^{2}+(-2-4)^{2}}$

$d=\sqrt{(8)^{2}+(-6)^{2}}$

$d=\sqrt{64+36}$

$d=\sqrt{100}$

$d=10$

Now that we know that the width QR is 5 units and the length RS is 10 units, we can find the perimeter of our rectangle:

$p=2(l+w)$

$p=2(RS+QR)$

$p=2(10+5)$

$p=2(15)$

$p=30$

We can conclude that QR = 5 units, RS = 10 units, and the perimeter of rectangle QRST is 30 units.

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Use the distributive property to express 30 + 75

OleMash [197]

Click on the box for more details on how to <span>distributive property to express 30 + 75.</span>

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Alex777 [14]

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Step-by-step explanation:

125=(1/25)^(y-1)

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Collect like terms

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