N is an integer -1 < n < 4 list the possible values of n

A farmer is tilling a rectangular field that is 65 meters long and 72 meters wide. What is the distance between opposite corners

ss7ja [257]

Answer:

97m

Step-by-step explanation:

From the image below we solve using pythagoras's theorem

x^2 = 72^2 + 65^2

x^2 = 5184 + 4225

x^2 = 9408

x = 97 m.

Further explanation is shown 8n the image.

3 0

3 years ago

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and

Firdavs [7]

Answer:

1a

$P(39 < X < 48 ) = 0.8767$

1b

95% of all sample means will fall between $40.1 < \mu < 49.9$

1c

$\= x = 41. 795$

2

$n = 25$

Step-by-step explanation:

From the question we are told that

The mean is $n = 45$

The population standard deviation is $\sigma = 10$

The sample size is n = 16

Generally the standard error of the mean is mathematically represented as

$\sigma_{x} = \frac{ \sigma}{\sqrt{n} }$

=> $\sigma_{x} = \frac{ 10 }{\sqrt{16 } }$

=> $\sigma_{x} = 2.5$

Generally the probability that the sample mean will be between 39 and 48 minutes is

$P(39 < X < 48 ) = P( \frac{ 39 - 45}{ 2.5} < \frac{X - \mu }{\sigma } < \frac{ 48 - 45}{ 2.5} )$

=> $P(39 < X < 48 ) = P(-2.4 < Z< 1.2 )$

=> $P(39 < X < 48 ) = P( Z< 1.2 ) - P(Z < -2.4)$

From the z table the area under the normal curve to the left corresponding to 1.2 and -2.4 is

=> $P( Z< 1.2 ) = 0.88493$

and

$P( Z< - 2.4 ) = 0.0081975$

So

$P(39 < X < 48 ) = 0.88493 -0.0081975$

=> $P(39 < X < 48 ) = 0.8767$

From the question we are told the confidence level is 95% , hence the level of significance is

$\alpha = (100 - 95 ) \%$

=> $\alpha = 0.05$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }$

=> $E = 1.96 * 2.5$

=> $E =4.9$

Generally the 95% of all sample means will fall between

$\mu -E < and \mu +E$

=> $45 -4.9\ and \ 45 + 4.9$

Generally the value which 90% of sample means is greater than is mathematically represented

$P( \= X > \= x ) = 0.90$

=> $P( \= X > \= x ) = P( \frac{\= X - \mu }{ \sigma_x} > \frac{\= x -45 }{ 2.5} ) = 0.90$

=> $P( \= X > \= x ) = P( Z > z ) = 0.90$

Generally from the z-table the critical value of 0.90 is

$z = -1.282$

$\frac{\= x -45 }{ 2.5} = -1.282$

=> $\= x = 41. 795$

Considering question 2

Generally we are told that the standard deviation of the mean to be one fifth of the population standard deviation, this is mathematically represented as

$s = \frac{1}{5} \sigma$

Generally the standard deviation of the sample mean is mathematically represented as

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

=> $\frac{1}{5} \sigma = \frac{\sigma }{ \sqrt{n} }$

=> $n = 5^2$

=> $n = 25$

5 0

3 years ago

Insert parentheses to make each statement true20-25

Rashid [163]

20: 30-4 x (2+5)=2
21. 17-(8-5)= 14
22. You put (10/2)-3+1, but it isn't necessary

Explanation: to solve these equations, use PEMDAS (parentheses, exponents, multiplication, division.) these equations don't involve exponents, though, so ignore that part. If 30 is left alone, you would multiply 4x2 before doing anything else. This would mean you would have 30-8+5' which gets you to 27, an incorrect answer. However, if you put parentheses around (2+5), you add those first, meaning you would then have 30-4(2+5) = 30-4(7) = 30-28= 2.
Try to do the rest; if you're still having trouble add a comment

7 0

3 years ago

I need serious help with this equation.

garri49 [273]

Answer:

First, it’s already telling you that you need to find d, which is the opposite of degree 59. This means you have to do the exact thing for degree 37. Since it’s already telling you to use sine, you need to look at the opposite side of 37 which is 98.4.

So ? is 98.4

Now, you need to find sin 59 / d.

First, plug in sin 98.4 sin (37) in your calculator (make sure it’s in degree setting)

The result is 59.2.

Now, 59.2 = sin 59 / d.

Switch sides like this: d = 59.2 sin (37)

And the answer is approximatley d = 35.6

? = 98.4

d = 35.6

8 0

3 years ago

Complete the equivalent fractions: 3/ = 15/20= /100

Genrish500 [490]

Your answer would be 3/4 = 15/20 = 75/100
Now their are two ways to figure out this problem.
You can look at the relationship with 3 and 15. 3 x 5 is 15 so you can determine that something x 5 equals 20. Well 20 x 5 = 4 so your answer is 3/4.
You would then do the same thing with 15/20.
20 x 5= 100, so do 15 x 5 which is 75. Answer is 75/100
Now here is the 2nd way you could have done it.
well we know that 3/4 equals .75 and that equals 75/100 as a fraction. Then divide top and bottom by 5 to get 15/20.

5 0

3 years ago