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3 years ago

14

In a seventh grade class, 14 out of 30 students are boys. In simplest terms, what is the ratio of the number of boys to the numb

er of girls in this grade?
A. 7:15
B. 15:7
C. 7:8
D. 8:15

1 answer:

Triss [41]3 years ago

8 0

${Hello,\;There!}$

They already give you the number of boys {14}, so all you need to do is subtract 30 - 14 which will give you the ratio of girls.

It does this because 14 takes up $\frac{14}{30}$ of the seventh grade class.

$\text{30 - 14 = 16}$

So your answer is going to be 14:16 un-simplified.

However, since they ask you to put it in the simplest terms, we are going to simplify $\frac{14}{16}.$

You can do this by dividing both numbers by 2.

= $\frac{14 \div 2}{16 \div 2}=\frac{7}{8}$

$\bold{So\;your\;answer\;is\;going\;to\;be}$

$= \frac{7}{8}$ or $\text{7:8}$

$\rule{300}{1.0}$

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Ymorist [56]

Answer:

b = 1

Step-by-step explanation:

Given the equation is:

- 5b + 2b - (-b) + 7 = 5

We separate the terms of b and the constants. To do that we subtract 7 from both the sides. We get:

- 5b + 2b - (-b) + 7 - 7 = 5 - 7

⇒ - 5b + 2b - (-b) = - 2

Now, simplifying the terms with 'b'.

⇒ -5b + 2b + b = - 2

⇒ (-5 + 2 + 1)b = - 2

⇒ -2b = -2

Dividing both the sides by -2, we get:

b = 1 which is the required answer.

7 0

3 years ago

How do I solve this equation to get the solution?<br><br> y= -2x - 1<br><br> -3x + 6y = 24

swat32

There are a few ways to solve this. The method I will use is the substitution method. Since they give us a "y = " statement, we can replace the y in the second equation with what it gives us to the right of the equal sign.

- 3x + 6(- 2x - 1) = 24

Simplify by using the distributive property.

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- 3x - 12x - 6 = 24.

Combine like terms

- 15x - 6 = 24

Add 6 to each side.

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Divide both sides by - 15 to isolate variable X

x = 30 / - 15
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6 0

3 years ago

Find the surface area of the triangular prism shown below.

Slav-nsk [51]

Answer:

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6 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:

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

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

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

=> $n = 5^2$

=> $n = 25$

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3 years ago

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DiKsa [7]

Answer:

Step-by-step explanation:

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Hope this helps

(Also, do you want how the answers came up? If so please comment below this and tell me that. I would be more than happy to write the equations if you want.)

3 0

3 years ago