Ask question

Ask question

All categories

2 years ago

8

An oil tank is being filled at a constant rate the depth of the oil is a function of the number of minutes has been filling, as

shown in the table find the depth of the oil 1/2 hour after filling begins
Time:0,10,15
Depth:3,5,6
(0,3) (10,5) (15,6)

1 answer:

satela [25.4K]2 years ago

5 0

We are given time in minutes.

According to given table, we are given times 0 minute, 10 minutes and 15 minutes.

And depths are given 3, 5 and 6.

Times represents x coordinates and depths represents y-coordinates.

First we need to find the depth of the tank in per unit time( in a minute).

In order to find the depth of the tank in per unit time, we need to find th slope between two coordinates.

Let us take first two coordinate made using table (0,3) (10,5)

We know, slope formula

$m=\frac{y_2-y_1}{x_2-x_1}$

Plugging values in slope formula, we get

m= $\frac{5-3}{10-0}=\frac{2}{10}=\frac{1}{5}$

We got slope m= 1/5=0.2.

We can say that depth of the tank is increasing by rate 0.2 per minute.

From the given table, we can see that for x=0, y value is 3.

Therefore, y-intercept is 3.

Let us write an equation of the line for given table in slope-intercept form y=mx+b.

Plugging values of m and b in slope-intercept form, we get

y= 0.2x+3.

We need to find the depth after 1/2 hours.

1 hour = 60 minutes,

Therefore, 1/2 hours = 60/2 = 30 minutes.

Plugging value of x=30 in above slope-intercept form of the equation, we get

y= 0.2(30)+3.

y= 3+6 = 9.

y=9

Therefore, the depth of the oil 1/2 hour after filling begins is 9 units.

You might be interested in

Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random sample of

nikitadnepr [17]

Answer:

a) Reject H₀

b) [0.31; 3.35]

Step-by-step explanation:

Hello!

a) The objective of this example is to compare if the population means of the production rate of the assembly lines A, B and C. To do so the data of the production of each line were recorded and an ANOVA was run using it.

The study variable is:

Y: Production rate of an assembly line.

Assuming that the study variable has a normal distribution for each population, the observations are independent and the population variances are equal, you can apply a parametric ANOVA with the hypothesis:

H₀ μ₁= μ₂= μ₃

H₁: At least one of the population means is different from the others

Where:

Population 1: line A

Population 2: line B

Population 3: line C

α: 0.01

This test is always one-tailed to the right. The statistic is the Snedecor's F, constructed as the MSTr divided by the MSEr if the value of the statistic is big, this means that there is a greater variance due to the treatments than to the error, this means that the population means are different. If the value of F is small, it means that the differences between populations are not significant ( may differ due to error and not treatment).

The critical region is:

$F_{k-1;n-k; 1-\alpha } = F_{2;15; 0.99} = 6.36$

If F ≥ 3.36, the decision is to reject the null hypothesis.

Looking at the given data:

$F= \frac{MSTr}{MSEr}$ = 11.32653

With this value the decision is to reject the null hypothesis.

Using the p-value method:

p-value: 0.001005

α: 0.01

The p-value is less than the significance level, the decision is to reject the null hypothesis.

At a level of 5%, there is significant evidence to say that at least one of the population means of the production ratio of the assembly lines A, B and C is different than the others.

b) In this item, you have to stop paying attention to the production ratio of the assembly line A to compare the population means of the production ratio of lines B and C.

(I'll use the same subscripts to be congruent with part a.)

The parameter to estimate is μ₂ - μ₃

The populations are the same as before, so you can still assume that the study variables have a normal distribution and their population variances are unknown but equal. The statistic to use under these conditions, since the sample sizes are 6 for both assembly lines, is a pooled-t for two independent variables with unknown but equal population variances.

t= (X[bar]₂ - X[bar]₃) - ( μ₂ - μ₃) ~t $_{n_2+n_3-2}$

Sa√(1/n₂+1/n₃)

The formula for the interval is:

(X[bar]₂ - X[bar]₃) ± $t_{n_2+n_3-2; 1 - \alpha /2}$ * $Sa\sqrt{*\frac{1}{n_2} + \frac{1}{n_3} }$

$Sa^{2} = \frac{(n_2-1)*S_2^2+ (n_3-1)*S_3^2}{n_2+n_3-2}$

$Sa^{2} = \frac{(5*0.67)+ (5*0.7)}{6+6-2}$

$Sa^{2} = 0.685$

Sa= 0.827 ≅ 0.83

$t_{n_2+n_3-2;1-\alpha /2}= t_{10;0.995} = 3.169$

X[bar]₂ = 43.33

X[bar]₃ = 41.5

(43.33-41.5) ± 3.169 * $*0.83\sqrt{*\frac{1}{6} + \frac{1}{6} }$

1.83 ± 3.169 * 0.479

[0.31; 3.35]

With a confidence level of 99% you'd expect that the difference of the population means of the production rate of the assemly lines B and C.

I hope it helps!

8 0

2 years ago

For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations

Nookie1986 [14]

Option C

The expression 20(22 - x) represents the value of the $20 traveler's checks she has.

<u>Solution:</u>

Given, For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations travelers checks in all,

We have to find how many of each denomination does she have?

Let x represent the number of $10 traveler's checks she has,

Then, $10(x) + $20(number of $20 checks) = 300

10x + 20($20 checks) = 300

x + 2(number of $20 checks) = 30 ⇒ (1)

Now let us see the given options, for value of $20 checks,

It should be in format, that, $20 x number of $20 checks

⇒ 20(total checks - $10 checks) ⇒ 20(total checks – x), as we can see only C is in that format, it is correct and total number of checks = 22.

Then, (1) ⇒ x + 2(22 – x) = 30

⇒ x + 44 – 2x = 30

⇒2x – x = 44 – 30

⇒ x = 14

So, $10 checks count = 14, then, $20 checks count = 22 – 14 = 8.

Hence, there are 14 $10 checks and 8 $20 checks, and option c is correct.

7 0

2 years ago

Assume that the national average score on a standardized test is 1010, and the standard deviation is 200, where scores are norma

kotykmax [81]

Answer:

0.00

Step-by-step explanation:

If the national average score on a standardized test is 1010, and the standard deviation is 200, where scores are normally distributed, to calculate the probability that a test taker scores at least 1600 on the test, we should first to calculate the z-score related to 1600. This z-score is $z=\frac{1600-1010}{200}=2.95$ , then, we are seeking P(Z > 2.95), where Z is normally distributed with mean 0 and standard deviation 1. Therefore, P(Z > 2.95) = 0.00

4 0

2 years ago

Read 2 more answers

To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices

White raven [17]

Answer:

Step-by-step explanation:

The prices he was quoted are listed below: $663, $273, $410, $622, $174, $374

We would first determine the mean.

Mean = sum of terms in the data/ number of terms in the data.

Sum of terms =

663 + 273 + 410 + 622 + 174 + 374

= 2516

Number of terms = 6

Mean = 2516/6 = 419.33

Standard deviation = √summation(x - m)^2/n

summation(x - m)^2/n = (663 - 429.33)^2 + (273 - 419.33)^2 + (410 - 419.33)^2 + (622 - 419.33)^2 + (174 - 419.33)^2 + (374 - 419.33)^2

= 179417.9334/6 = 29902.9889

Standard deviation = √29902.9889

= 172.9

6 0

2 years ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

2 years ago

Read 2 more answers