(05.06 MC)
Choose the function to match the graph.
-6
5
3
3
2.
1
-2
0
2.
3
4
5
6
-1
-21

Solution :

Given data :

[tex]c_{in}[/tex] = 1 g/L

[tex]r_{in}[/tex] = 5 L/min

[tex]r_{out}[/tex] = 5 L/min

[tex]$v_0$[/tex] = 250 L

[tex]A_0[/tex] = 20 g

∴ [tex]r_{net} = r_{in}- r_{out}[/tex]

         = 5 - 5

          = 0

[tex]c_{out} = \frac{A}{250} \ g/L[/tex]

Now, [tex]\frac{dA}{dt}=(r_{in} \times c_{in}) - (r_{out} \times c_{out})[/tex]

[tex]$\frac{dA}{dt} = 5-5\left(\frac{A}{250}\right)$[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5[/tex]

[tex]\frac{dA}{dt}+5 \left(\frac{A}{250}\right) = 5 \text{ with} \ A_0 = 20[/tex]

Integrating factor = exp(5 t/250)

Therefore,

[tex]A \times \exp (5t \ /250) = \text{integral of}\ 5 \times \exp (5t / 250) + C[/tex]

Put [tex]A_0=250+C[/tex]

C = -230

[tex]A \times \exp(5t/250) = 250 \exp(5t/250) + (-230)[/tex]

[tex]A(t) = 250-230 \exp(-5t/250)[/tex]

[tex]A(t) = 250-230e^{\left(\frac{-t}{50}\right)} \ g[/tex]

Answer:

I don't know for sure, but I'm pretty sure its 1,640.

Step-by-step explanation:

80% of 8,200 is 6560, and then do 8,200- 6,560, you get 1,640.

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According to question, The price at which it was sold is equal to :

The car was sold at $ 6560

Now, loss is equal to :

Answer:

4.56% of the deliveries are likely to be outside the specification limits.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The average weight was 95.0 grams. The standard deviation was 0.25 grams.

This means that [tex]\mu = 95, \sigma = 0.25[/tex]

What percentage of the deliveries is likely to be outside the specification limits (outside the interval of [94.5, 95.5])?

Less than 94.5, or more than 95.5. Since the normal distribution is symmetric, these probabilities are the same, so we can find one of them and multiply by two.

The probability that it is less than 94.5 is the p-value of Z when X = 94.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{94.5 - 95}{0.25}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

2*0.0228 = 0.0456

0.0456*100% = 4.56%

4.56% of the deliveries are likely to be outside the specification limits.

Answer:

Option B. A = (5/6)^-⅛

Step-by-step explanation:

From the question given above, we obtained:

(5/6)ˣ = A¯⁸ˣ

We can obtain the value of A as follow:

(5/6)ˣ = A¯⁸ˣ

Cancel x from both side

5/6 = A¯⁸

Recall:

M¯ⁿ = 1/Mⁿ

A¯⁸ = 1/A⁸

Thus,

5/6 = 1/A⁸

Cross multiply

5 × A⁸ = 6

Divide both side by 5

A⁸ = 6/5

Take the 8th root of both sides

A = ⁸√(6/5)

Recall

ⁿ√M = M^1/n

Thus,

⁸√(6/5) = (6/5)^⅛

Therefore,

A = (6/5)^⅛

Recall:

(A/B)ⁿ = (B/A)¯ⁿ

(6/5)^⅛ = (5/6)^-⅛

Therefore,

A = (5/6)^-⅛

Answer:

the speed in 18mph

Step-by-step explanation:

Answer:

(-2, 3).

Step-by-step explanation:

2x + y = -1

3x- 5y = -21

Multiply the first equation by 5:

10x + 5y = -5     Adding this to the second equation:

13x = -26

x = -2.

Substituting this into equation 1:

2(-2) + y = -1

y = -1 + 4 = 3.

Checking this result in the second equation:

3(-2) - 5(3)

= -5 - 15 = -21

- Checks OK.

Answer:

At this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

Given that a certain country has 586.08 million acres of forest, and every year, the country loses 7.92 million acres of forest mainly due to deforestation for farming purposes, to determine, if this situation continues at this pace, how many years later will the country have only 237.6 million acres of forest left, the following calculation must be performed:

Current amount - (amount lost per year x number of years) = 237.6

586.08 - (7.92 x X) = 237.6

586.08 - 7.92X = 237.6

-7.92X = 237.6 - 586.08

-7.92X = -348.48

X = -348.48 / -7.92

X = 44

Therefore, at this pace the country will have only 237.6 million acres of forest left in 44 years.

Step-by-step explanation:

51 and 51

maybe

The answer is B

the method use to solved this is called foil

Answer:

78 miles

Step-by-step explanation:

Given that:

Original length, L = 47 miles

Additional length (miles) added per day, = 1 mile

Representing as an equation :

L(D) = original length + additional length per day * number of days

Let, D = number of days

L(D) = 47 + D

Length after 31 days :

L(31) = 47 + 31

= 78 miles

Answer:

(8x + 1)° + ( 4x+11)° = 180° (linear pair )

8x +1 + 4x +11 = 180

8x + 4x + 1 + 11 = 180

12x + 12 = 180

12x = 180 - 12

12x = 168

x= 168/12

x = 14

Answer:

1

Step-by-step explanation:

The y intercept is when x =0

We need to use the second equation

-x+1  since -2 < 0 <3

0+1

The y intercept is 1

Answer:

y = -3/8x -41/8

Step-by-step explanation:

Perpendicular lines intersect at 90° and their slopes are opposite reciprocals.

Therefore the slope changes from 8/3 to -3/8.

Now we must solve for the new y-intercept (b) by plugging in the given coordinate (-3,-4).

The result is b = -41/8 so our new equation is:

y = -3/8x -41/8

9514 1404 393

Answer:

  90° CCW

Step-by-step explanation:

The transformation from B to B' is ...

  B(-4, 1) ⇒ B'(-1, -4)

  (x, y) ⇒ (-y, x) . . . . . matches the transformation for 90° CCW

Answer:

90 degrees

Step-by-step explanation:

OPTION C is the correct answer.

Hope it helps you.

Answer:  

7.79771≤x≤8.20229  

Step-by-step explanation:  

Given the following  

sample size n = 8  

standard deviation s = 0.238  

Sample mean = 2.275  

z-score at 980% = 1.282

Confidence Interval = x ± z×s/√n  

Confidence Interval = 8 ± 1.282×0.238/1.5083)  

Confidence Interval = 8 ± (1.282×0.15779)

Confidence Interval = 8 ±0.20229    

CI = {8-0.20229, 8+0.20229}  

CI = {7.79771, 8.20229}

Hence the required confidence interval is 7.79771≤x≤8.20229

Answer:

There was a 45% increase in furniture sales.

Furniture sales rose by 9 percentage points.

Step-by-step explanation:

absolute difference = new - old

29-20= 9 percentage points

absolute difference / initial value = 9/20 = .45 * 100 = 45%

Two statements which are true about furniture sales are  [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and  [tex](f)[/tex]  Furniture sales rose by [tex]9[/tex] percentage points.

Percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%".

Percentage [tex]=\frac{Obtained\ number}{Total\ number}\ * 100[/tex]

We have,

Sales of furniture in [tex]2015=20\%[/tex]

Sales of furniture in [tex]2016=29\%[/tex],

So,

Change in Percentage [tex]=29-20=9\%[/tex]

i.e.

Sales rise by [tex]9\%[/tex] points,

And,

Increase in Percentage [tex]=\frac{9}{20}\ *100=45\%[/tex]

Hence, we can say that Two statements which are true about furniture sales are [tex](a)[/tex] There was a [tex]45\%[/tex] increase in furniture sales and [tex](f)[/tex] Furniture sales rose by [tex]9[/tex] percentage points.

To know more about Percentage click here

https://brainly.com/question/24159063

#SPJ3

Answer:

the answer is 3.5

Step-by-step explanation:

Answer:

Volume = 111.33 in.³

Step-by-step explanation:

The volume of the shape = volume of the rectangular prism part + volume of the triangular prism part

✔️volume of the rectangular prism part:

V = L*W*H

Where,

L = 5.1 in.

W = 3.4 in.

H = 5.9 in.

V = 5.1*3.4*5.9

V = 102.306 in.³

✔️volume of the triangular prism part:

V = ½*b*h*l

b = 6 - 5.1 = 0.9 in.

h = 5.9 in.

l = 3.4 in.

V = ½*0.9*5.9*3.4

V = 9.027 in.³

✅Volume of the shape = 102.306 + 9.027

= 111.333 in.³

≈ 111.33 in.³ (approximated to 2 decimal places)

Answer:

angle M = 60

angle Q = 70

Step-by-step explanation:

M 180/3 = 60

Q 180-40 = 140/2 = 70

Answer:

(-1.5, 0.5)

Step-by-step explanation:

x = -1.5

y = 0.5

(-1.5, 0.5)

Answer:

Auto Credit Express, Carvana, Capital one auto loan

Answer:

good for them i think

Step-by-step explanation:

this doesnt make any sense

Answer:

65

Step-by-step explanation:

See image below:)

Answer:

x=0

Step-by-step explanation:

0/3 = 0

0+5=5

Answer:

q.12

angle ACB=180-123

therefore ACB=57

again 5x-15+7x+6+57=180

or,12x+48=180

or,x=132/12

or x=11

Answer:

5

Step-by-step explanation:

The median is the middle when the numbers are lined up from smallest to largest

3,4,4,6,7,15

There are 6 number so the middle is the  between the 3rd and 4th number

3,4,4,    6,7,15

Take the 3rd and 4th numbers and average

(4+6)/2 = 10/2 = 5

Answer:

median = 5

Step-by-step explanation:

Arrange the data in ascending order :

3 , 4 , 4 , 6 , 7 , 15

Choose the middle number.

Here there are even number of data. Take the average of the middle

numbers .

4 and 6 are the middle number. average of 4 and 6 = ( 4 + 6 ) /2 = 5

Therefore , median = 5

Answer:

<V = 40

Step-by-step explanation:

The exterior angle is equal to the sum of the opposite interior angles

20x = 60+7x+5

Combine like terms

20x = 7x+65

Subtract 7x from each side

20x -7x = 7x+65-7x

13x = 65

Divide each side by 13

13x/13 = 65/13

x = 5

<v = 7x+5 = 7*5+5 = 35+5 = 40

answer:

it's U = 60°

V = 50°

T = 70°

Answer:

use photo math. it will help