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3 years ago

The function C(t) = 400 + 30t models the number of classrooms, C. in the town of Sirap, t years from

Mathematics

2 answers:

maks197457 [2]3 years ago

7 0

Answer:

1) S(t) = C(t) × D(t)

2) S(t) = (400 + 30t)(25 + t)

Step-by-step explanation:

The function C(t) = 400 + 30t ........... (1), models the number of classrooms, C. in the town of Sirap, t years from now.

The function D(t) = 25 + t ......... (2) models the number of students per classroom, D, t years from now.

Then if S(t) represents the number of students in Sirap's school system t years from now, then, we can write the relation

1) S(t) = C(t) × D(t) (Answer)

2) Hence, the formula of S(t) in terms if t is given by

S(t) = (400 + 30t)(25 + t) (Answer)

katen-ka-za [31]3 years ago

7 0

Answer:

S(t)=C(t)×D(t)

S(t)= $30t^{2}+1150t+10000$

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-12 increased by half of a number is 28. What is the number

Nadya [2.5K]

Answer:

Step-by-step explanation:

28-28=0

0-12= -12

28+12 = 40

28-40 = -12

40 is the increase

40 is half of 80

So, the answer is 80

To check: -12 + 40 (half of a number; 80) = 28

Hope this makes sense. If you require further information, do not hesitate to ask!

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2 years ago

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Fill in the blank (correctly). 20 points each.

lyudmila [28]

Distributing same key numbers

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3 years ago

What is the slope of a line parallel to the line whose equation is 3x – 3y = -45.

Karolina [17]

Answer:

One

Step-by-step explanation:

A parallel line has the same slope of the original graph. Because of this, all we need to do is put the equation you gave into slop-intercept form, or:

y = mx + b

Don't forget that m is the slope, and b is the y-intercept!

3x - 3y = 45

-3y = -3x + 45

y = x + 15

Compare this to the equation of the slope-intercept form and look for m:

y = mx + b

There's nothing in front of the variable! No worries, that's the same thing as saying 1x.

But mathematicians are a little lazy (lol) and they don't want to mistake the number 1 for the lowercase letter L or a capital i. Because of that, they made 1x equal x.

Long story short, the slope for the equation (3x – 3y = -45) is one. And because parallel lines have the same slope as their original counterparts, the slope is one as well!

I recommend trying a few other problems like these. You'll end up using them a lot in the future!

Good luck and keep studying!

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3 years ago

The amount a spring will stretch varies directly with the amount of weight attached to the spring. If a spring stretches 2.1 inc

aleksklad [387]

Answer:

$1.05\ in$

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form $y/x=k$ or $y=kx$

Let

x -----> the amount of weight

y ----- the amount a spring will stretch

we know that

For x=80 lb, y=2.1 in

Find the value of k (constant of proportionality)

$k=y/x$

substitute the values

$k=2.1/80$

The linear equation is

$y=(2.1/80)x$

How far will it stretch when 40 pounds is attached?

For x=40 lb

substitute the value of x in the linear equation and solve for y

$y=(2.1/80)(40)=1.05\ in$

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3 years ago

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3. Using the sample size of 800 and the proportion 0.47, calculate the margin of error associated with the estimate of the propo

salantis [7]

Answer:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

We assume for this case a confidence level of 95%. In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And if we replace the values obtained we got this:

$ME=1.96\sqrt{\frac{0.47 (1-0.47)}{800}}=0.0346$

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