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3 years ago

Divide 70 in the ratio of 4:10

1 answer:

8 0

Easy! just compare then cross multiply 70:1 × 10:4 because you need to use the negative reciprocal of either one to create division with ratios/fractions
$\frac{70}{1} = \frac{10}{4}$

You might be interested in

Make t the subject of this formula. r = 7 (t + 3)

kari74 [83]

Answer:

t= r-21

Step-by-step explanation:

r = 7(t+3)

expanding the bracket

r = 7t + 21

bringing t to the left hand side

7t = r - 21

divide both sides by seven

t= r-21

3 0

3 years ago

What's the product of 72100 multiplied by 1.02

butalik [34]

72100 multiplied by 1.02 is 73542

5 0

3 years ago

Read 2 more answers

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:

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

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

$\= x = 41. 795$

$n = 25$

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

$P( Z< - 2.4 ) = 0.0081975$

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

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

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

Explain why the equation 5z + 2 = 5z has no solution.

suter [353]

$5z + 2 = 5z \\ 5z - 5z = - 2 \\ 0 = - 2$

Answer : This is because when 5z minus 5z, it is nullified, with no way to determine the value of z. 5z - 5z = 0
That is why there is no solution for this equation.

Hope this helps. - M

5 0

3 years ago

Human civilization, at least since the time of ancient Egypt, is on the order of 5000 years old. The age of the Earth is on the

olchik [2.2K]

Write and solve an equation of ratios:

5 *10^9 years 100 m
------------------- = --------------
5 * 10^3 yrs x

Reducing the first fraction,

100 m
10^6 = ----------
x
100 m
Solving for x, x = ------------- = 10^(-4) m, or [10^(-1)] * [10^(-3))]
10^6
this comes out to one tenth of 1 millimeter.

5 0

3 years ago