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3 years ago

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a carpenter has a wooden stick that is 84 centimeters long. She cuts off 25% from the end of the stick. then she cuts the remain

ing stick into 6 equal pieces. What is the length of each piece?

1 answer:

Karo-lina-s [1.5K]3 years ago

3 0

She cuts off 21 cm. this leaves 63cm. cut into 6 equal pieces gives 10.5 cm pcs

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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2-cm and a standard dev

Varvara68 [4.7K]

Answer:

The probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is 0.65173.

Step-by-step explanation:

We are given that a company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 259.2 cm and a standard deviation of 2.1 cm. For shipment, 17 steel rods are bundled together.

Let $\bar X$ = <u><em>the average length of rods in a randomly selected bundle of steel rods</em></u>

The z-score probability distribution for the sample mean is given by;

Z = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\mu$ = population mean length of rods = 259.2 cm

$\sigma$ = standard deviaton = 2.1 cm

n = sample of steel rods = 17

Now, the probability that the average length of rods in a randomly selected bundle of steel rods is greater than 259 cm is given by = P( $\bar X$ > 259 cm)

P( $\bar X$ > 259 cm) = P( $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ > $\frac{259-259.2}{\frac{2.1}{\sqrt{17} } }$ ) = P(Z > -0.39) = P(Z < 0.39)

= <u>0.65173</u>

The above probability is calculated by looking at the value of x = 0.39 in the z table which has an area of 0.65173.

8 0

3 years ago

Y varies inversely as x. If y=5 and x=12, find y if x=4

yan [13]

Answer:

x igual 5 ,12,4

Step-by-step explanation:

xjxxixix

holghb

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3 years ago

1 4 cm 4 cm 5 cm 3 cm Perimeter: Area:

ohaa [14]

Answer:

Step-by-step explanation:

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3 years ago

Find the maximum and minimum values attained by f(x, y, z) = 5xyz on the unit ball x2 + y2 + z2 ≤ 1.

Allushta [10]

Check for critical points within the unit ball by solving for when the first-order partial derivatives vanish:
$f_x=5yz=0\implies y=0\text{ or }z=0$
$f_y=5xz=0\implies x=0\text{ or }z=0$
$f_z=5xy=0\implies x=0\text{ or }y=0$

Taken together, we find that (0, 0, 0) appears to be the only critical point on $f$ within the ball. At this point, we have $f(0,0,0)=0$ .

Now let's use the method of Lagrange multipliers to look for critical points on the boundary. We have the Lagrangian

$L(x,y,z,\lambda)=5xyz+\lambda(x^2+y^2+z^2-1)$

with partial derivatives (set to 0)

$L_x=5yz+2\lambda x=0$
$L_y=5xz+2\lambda y=0$
$L_z=5xy+2\lambda z=0$
$L_\lambda=x^2+y^2+z^2-1=0$

We then observe that

$xL_x+yL_y+zL_z=0\implies15xyz+2\lambda=0\implies\lambda=-\dfrac{15xyz}2$

So, ignoring the critical point we've already found at (0, 0, 0),

$5yz+2\left(-\dfrac{15xyz}2\right)x=0\implies5yz(1-3x^2)=0\implies x=\pm\dfrac1{\sqrt3}$
$5xz+2\left(-\dfrac{15xyz}2\right)y=0\implies5xz(1-3y^2)=0\implies y=\pm\dfrac1{\sqrt3}$
$5xy+2\left(-\dfrac{15xyz}2\right)z=0\implies5xy(1-3z^2)=0\implies z=\pm\dfrac1{\sqrt3}$

So ultimately, we have 9 critical points - 1 at the origin (0, 0, 0), and 8 at the various combinations of $\left(\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3},\pm\dfrac1{\sqrt3}\right)$ , at which points we get a value of either of $\pm\dfrac5{\sqrt3}$ , with the maximum being the positive value and the minimum being the negative one.

5 0

3 years ago

What is 3a+2b-5a+b simplified?

marishachu [46]

Answer:

-a + b

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers