How can proportional reasoning help solve a problem?

Assume the total cost of a college education will be $235,000 when your child enters college in 18 years. You presently have $53

Andrei [34K]

Answer:

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1+r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = $235,000

P = $53,000

n = 1 because it was compounded once in a year.

t = 18 years

Therefore,.

235000 = 53000(1 + r/1)^1 × 18

235000/53000 = (1 + r)^18

4.43 = (1 + r)^18

Raising both sides to the power of 1/18, it becomes

4.43^(1/18) = (1 + r)^18 × 1/18

1.086 = 1 + r

r = 1.086 - 1

r = 0.086

r = 0.086 × 100 = 8.6%

6 0

3 years ago

The temperature of a certain solution is estimated by taking a large number of independent measurements and averaging them. The

Mademuasel [1]

Answer:

(a) The 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b) The confidence level is 68%.

(c) The necessary assumption is that the population is normally distributed.

(d) The 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

Step-by-step explanation:

Let X = temperature of a certain solution.

The estimated mean temperature is, $\bar x=37^{o}C$ .

The estimated standard deviation is, $s=0.1^{o}C$ .

(a)

The general form of a (1 - α)% confidence interval is:

$CI=SS\pm CV\times SD$

Here,

SS = sample statistic

CV = critical value

SD = standard deviation

It is provided that a large number of independent measurements are taken to estimate the mean and standard deviation.

Since the sample size is large use a z-confidence interval.

The critical value of z for 95% confidence interval is:

$z_{0.025}=1.96$

Compute the confidence interval as follows:

$CI=SS\pm CV\times SD\\=37\pm 1.96\times 0.1\\=37\pm0.196\\=(36.804, 37.196)\\\approx (36.80^{o}C, 37.20^{o}C)$

Thus, the 95% confidence interval for the temperature is (36.80°C, 37.20°C).

(b)

The confidence interval is, 37 ± 0.1°C.

Comparing the confidence interval with the general form:

$37\pm 0.1=SS\pm CV\times SD$

The critical value is,

CV = 1

Compute the value of P (-1 < Z < 1) as follows:

$P(-1$

The percentage of z-distribution between -1 and 1 is, 68%.

Thus, the confidence level is 68%.

(c)

The confidence interval for population mean can be constructed using either the z-interval or t-interval.

If the sample selected is small and the standard deviation is estimated from the sample, then a t-interval will be used to construct the confidence interval.

But this will be possible only if we assume that the population from which the sample is selected is Normally distributed.

Thus, the necessary assumption is that the population is normally distributed.

(d)

For n = 10 compute a 95% confidence interval for the temperature as follows:

The (1 - α)% t-confidence interval is:

$CI=\bar x\pm t_{\alpha/2, (n-1)}\times \frac{s}{\sqrt{n}}$

The critical value of t is:

$t_{\alpha/2, (n-1)}=t_{0.025, 9}=2.262$

*Use a t-table for the critical value.

The 95% confidence interval is:

$CI=37\pm 2.262\times \frac{0.1}{\sqrt{10}}\\=37\pm 0.072\\=(36.928, 37.072)\\\approx (36.93^{o}C, 37.07^{o}C)$

Thus, the 95% confidence interval for the temperature if 10 measurements were made is (36.93°C, 37.07°C).

3 0

3 years ago

60 teachers voted on a rule to allow students to have prom open to 7th and 8th graders the ratio was 7:5 how many teacher voted

Firdavs [7]

The answer is 60

Hope this helped

7 0

3 years ago

A patient needs 0.024g of a sulfa drug. There are 8 mg tablets in stock. How many tablets should be given?

Varvara68 [4.7K]

3 tablets. there are 1000 mg in a g so youd need 24 mg and 8x3=24

5 0

3 years ago

Read 2 more answers

May someone explain to me how to do this?

lara31 [8.8K]

Answer:

All you gotta do is go to "desmos" and type in all of the 4 solutions. A, B, C, and D. and see which answer matches the graph

Step-by-step explanation:

4 0

3 years ago