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3 years ago

The quotient of a number and 4 is at most 15

Mathematics

1 answer:

ivolga24 [154]3 years ago

5 0

Answer:

x÷4≤15

Step-by-step explanation:

the quotient of a number (x) and 4: x÷4

the phrase "at most" means ≤, less than or equal to

so if we put the parts together, we get x÷4≤15

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A car traveling at a rate of 54 miles per hour. What is the car's rate in feet per secondHow many fect will the car travel in 2

Lena [83]

The car's speed in feets per second is 79.2, Hence, it will cover a distance of 158.4 feets in 2 seconds.

Car's speed in miles per hour = 54 miles per hour

Recall :

1 mile = 5280 feets
1 hour = 3600 seconds

Car's rate in feet per second

54 miles per hour = (54 × 5280 × 1/3600) feet per second = 79.2 feets per second.

Distance in 2 seconds :
Distance = speed × time
Distance = 79.2 × 2 = 158.4 feets

Therefore, the car will cover a distance of 158.4 feets in 2 seconds.

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3 years ago

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zubka84 [21]

Answer:

Step-by-step explanation:

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3 years ago

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tekilochka [14]

Easy

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3 years ago

What are the intercepts of the line 2x + 4y = 12?

Darina [25.2K]

<span>if you're finding the x intercept, y is ALWAYS 0, so in this, you can just get rid of the -4y because you know that it's 0, so you're left with 2x=12 divide by 2 on both sides so you find x intercept is (6,0) on the graph
the y works the same way, if you're looking for the y, you know that the x is zero, so you're left with -4y=12, divide by -4y on both sides and you end up with the y intercept being (0,-3)

x int.= (6,0)
y int.= (0,-3)

by the way, when it's written like that, it's called standard form, so to find the intercepts on 2x=12+4y, you'd have to convert it into standard form (Ax=By=C) so you subtract 4y on both sides to make it 2x-4y=12, and then once you have it like that you can do the math to find the y and x intercepts.
</span>

6 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:

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

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