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Zigmanuir [339]

2 years ago

11

The domain is x≥ 2 and the range is y≥ 5. The domain is x≥ 2 and the range is y≥ 6. The domain and range are all positive real n

umbers. The domain is x≥ 2 and the range is all positive real numbers.

1 answer:

Dmitry [639]2 years ago

4 0

Answer:

A

Step-by-step explanation:

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Rockwell hardness of pins of a certain type is known to have a mean value of 50 and a standard deviation of 1.2.a. If the distri

zalisa [80]

Answer:

a

$P(\= X \ge 51 ) =0.0062$

b

$P(\= X \ge 51 ) = 0$

Step-by-step explanation:

From the question we are told that

The mean value is $\mu = 50$

The standard deviation is $\sigma = 1.2$

Considering question a

The sample size is n = 9

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{9} }$

=> $\sigma_x = 0.4$

Generally the probability that the sample mean hardness for a random sample of 9 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_{x}} \ge \frac{51 - 50 }{0.4 } )$

$\frac{\= X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ \= X )$

$P(\= X \ge 51 ) = P( Z \ge 2.5 )$

=> $P(\= X \ge 51 ) =1- P( Z < 2.5 )$

From the z table the area under the normal curve to the left corresponding to 2.5 is

$P( Z < 2.5 ) = 0.99379$

=> $P(\= X \ge 51 ) =1-0.99379$

=> $P(\= X \ge 51 ) =0.0062$

Considering question b

The sample size is n = 40

Generally the standard error of the mean is mathematically represented as

$\sigma_x = \frac{\sigma }{\sqrt{n} }$

=> $\sigma_x = \frac{ 1.2 }{\sqrt{40} }$

=> $\sigma_x = 0.1897$

Generally the (approximate) probability that the sample mean hardness for a random sample of 40 pins is at least 51 is mathematically represented as

$P(\= X \ge 51 ) = P( \frac{\= X - \mu }{\sigma_x} \ge \frac{51 - 50 }{0.1897 } )$

=> $P(\= X \ge 51 ) = P(Z \ge 5.2715 )$

=> $P(\= X \ge 51 ) = 1- P(Z < 5.2715 )$

From the z table the area under the normal curve to the left corresponding to 5.2715 and

=> $P(Z < 5.2715 ) = 1$

So

$P(\= X \ge 51 ) = 1- 1$

=> $P(\= X \ge 51 ) = 0$

5 0

2 years ago

5/8 - 3/4(7 - 1/3) + 1

erastovalidia [21]

-3.375 :))))))))))))))

8 0

3 years ago

A garden flower grows a total of 10 cm in July and August. Assuming that the flower grows at a consistent rate for a full year,

d1i1m1o1n [39]

9514 1404 393

Answer:

60 cm

Step-by-step explanation:

July and August are 2 of the 12 months in the year. The growth for the year can be expected to be 6 times the growth in a 2-month period, so 60 cm.

_____

You could get down to particulars as to the number of days in those two months versus the total number of days in a year. You would have to specify whether it is a leap year. In a non-leap year, the growth might be ...

365/(31+31) × 10 cm ≈ 58.9 cm

In a leap year, it would be 59.0 cm.

6 0

2 years ago

Bob the builder is making 480 kg of concrete mix concrete is made by mixing cement sand and gravel in the ratio 1:3:4 how much d

Vera_Pavlovna [14]

Answer:

see the explanation

Step-by-step explanation:

Let

x ---> kilograms of cement needed

y ----> kilograms of sand needed

z ----> kilograms of gravel needed

we know that

$x:y:z=1:3:4$ ----> $x+y+z=1+3+4=8$

$x+y+z=480\ kg$

Divide 480 by 8

$480/8=60$ ----> scale factor

Multiply the scale factor by the ratio $1:3:4$

<em>Find out the kilograms of cement needed</em>

$60(1)=60\ kg$

<em>Find out the kilograms of sand needed</em>

$60(3)=180\ kg$

<em>Find out the kilograms of gravel needed</em>

$60(4)=240\ kg$

4 0

3 years ago

What is the simplest form of the number 5/5

Likurg_2 [28]

1
It's whole number
So I think it's the answer

6 0

3 years ago

Read 2 more answers