Allison traveled a distance of 130 miles in 2
1
hours. What was Allison's average driving
speed, in miles per hour?

Answer:

5840

Step-by-step explanation:

16 x 365 is 5840

Answer:

5,840

Step-by-step explanation:

16x365=?

16x365=5,840

Answer:

Step-by-step explanation:

From the given information:

[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]

Given that the solution is pumped at a slower rate of 4gal/min

Then:

[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]

[tex]R_{out}= \dfrac{2A}{50+t}[/tex]

The differential equation can be expressed as:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]

Integrating the linear differential equation; we have::

[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]

[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]

multiplying above integrating factor fields; we have:

[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]

[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]

[tex](50 + t)^2 A = (50 + t)^3+c[/tex]

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c =  -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]

A(35) =69.6193 pounds

A(35) [tex]\simeq[/tex] 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.

Answer:

See Attachment.

General Formulas and Concepts:

Algebra I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define variables

Slope m = -1

y-intercept b = 3

Step 2: Write linear equation

Substitute into general form.

Slope-Intercept Form:   y = -x + 3

Step 3: Graph

Answer:

[tex]\frac{dy}{dx}[/tex] = 3 cos² y ⇒ B

Step-by-step explanation:

∵ 3x - tan(y) = 4

∵ The differentiation of tan(y) with respect to x is sec² y · dy/dx

∵ The differentiation of 3x with respect to x is 3

∵ the differentiation to 4 with respect to x is 0

∴ d/dx [3x - tan(y) = 4] is 3 - sec² y · dy/dx = 0

∵ 3 - sec²(y) · dy/dx = 0

→ Subtract 3 from both sides

∴ - sec² y · dy/dx = -3

→ Divide both sides by -1

∴ sec² y · dy/dx = 3

→ Divide both sides by sec²(x)

∴ [tex]\frac{dy}{dx}=\frac{3}{sec^{2}y}[/tex]

→ Remember [tex]\frac{1}{secy}[/tex] = cos y

∵ [tex]\frac{1}{sec^{2}y}[/tex] = cos² y

∴  [tex]\frac{3}{sec^{2}y}[/tex] = 3 cos² y

∴ [tex]\frac{dy}{dx}[/tex] = 3 cos² y

dy/dx of 3x – tan y = 4 in terms of y is;

dy/dx = 3cos²y

We are given;

3x - tan y = 4

Let's differentiate in terms of y to get;

3 - sec²y(dy/dx) = 0

This is because the derivative of tan y in terms of y is sec²y(dy/dx).

Thus, using addition property of equality, we have;

3 = sec²y(dy/dx)

Now, in trigonometric ratios;

sec y = 1/cos y

Thus;

sec²y = 1/cos²y

Therefore;

3 = (1/cos²y) (dy/dx)

Thus;

dy/dx = 3cos²y

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Answer:

a

 The upper bound of the 99% prediction level is [tex] 98.2  [/tex]  

b

 The  95% confidence interval is [tex]9.7383 <  \mu < 10.2617 [/tex]

Step-by-step explanation:

Considering first question

From the question we are told that

   The sample size is  n  =  30  

   The sample mean is  [tex]\= x = 96.2\%[/tex]

   The standard deviation is [tex]s = 0.8\%[/tex]

Generally the degree of freedom is mathematically represented as

        [tex]df = n - 1[/tex]

=>      [tex]df = 30 - 1[/tex]

=>      [tex]df = 29[/tex]

From the question we are told the confidence level is  99% , hence the level of significance is    

      [tex]\alpha = (100 - 99 ) \%[/tex]

=>   [tex]\alpha = 0.01[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of is  

   [tex]t_{\alpha , 29} = 2.462[/tex]

Generally the  99%  prediction level is mathematically represented as

      [tex]\= x \pm [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]

Generally the upper bound of the 99%  prediction level is mathematically represented as

      [tex]\= x + [(t_{\alpha  , df }) * s * (\sqrt{1 + \frac{1}{ n} } )}] [/tex]  

=>    [tex] 96.2 + (2.462 ) * 0.8 * (\sqrt{1 + \frac{1}{ 30} } )}] [/tex]  

=>    [tex] 98.2  [/tex]  

Considering second question

 Generally the sample is mathematically represented as

             [tex]\= x = \frac{\sum x_i}{n}[/tex]

=>           [tex]\= x = \frac{ 9.8 + 10.2 + \cdots +9.6 }{7}[/tex]  

=>           [tex]\= x = 10[/tex]    

Generally the standard deviation  is mathematically represented as

           [tex]\sigma = \sqrt{ \frac{ \sum ( x_ i - \= x)}{n-1} }[/tex]

=>        [tex]\sigma = \sqrt{ \frac{ ( 9.8 -10)^2 + ( 10.2 -10)^2 + \cdots + ( 9.6 -10)^2 }{7-1} }[/tex]

=>        [tex]\sigma = 0.283[/tex]

Generally the degree of freedom is mathematically represented as

      [tex] df =  n- 1 [/tex]

=>    [tex] df =  7- 1 [/tex]

=>    [tex] df =  6 [/tex]

From the question we are told the confidence level is  95% , hence the level of significance is    

      [tex]\alpha = (100 - 95 ) \%[/tex]

=>   [tex]\alpha = 0.05[/tex]

Generally from the t distribution table the critical value  of   at a degree of freedom of  is  

   [tex]t_{\frac{\alpha }{2} , 6 } =  2.447[/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 6 } *  \frac{\sigma }{\sqrt{n} }[/tex]

=>    [tex]E =2.447*    \frac{0.283 }{\sqrt{7} }[/tex]

=>    [tex]E =0.2617[/tex]

Generally 95% confidence interval is mathematically represented as  

      [tex]\= x -E <  \mu <  \=x  +E[/tex]

=>   [tex]10 -0.2617 <  \mu < 10 + 0.2617[/tex]

=>   [tex]9.7383 <  \mu < 10.2617 [/tex]

Answer:

Step-by-step explanation: 1,872

Answer: 1,872

Step-by-step explanation:

Answer:

Value of x=4 and y=-13/3

Step-by-step explanation:

We need to solve the systems of equations

[tex]5x+3y=7 \ and \ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}[/tex]

Solving using substitution method:

Let:

[tex]5x+3y=7---eq(1) \\ \frac{3}{2}x-\frac{3}{4}y =9\frac{1}{4}---eq(2)[/tex]

Find value of x from eq(1) and put in eq(2)

[tex]5x+3y=7\\5x=7-3y\\x=\frac{7-3y}{5}[/tex]

Put value of x in eq(2)

[tex]\frac{3}{2}(\frac{7-3y}{5}) -\frac{3}{4}y =\frac{37}{4}\\\frac{21-9y}{10} -\frac{3}{4}y =\frac{37}{4}\\Taking \ LCM\\\frac{21*2-9y*2-3y*5}{20} =\frac{37}{4}\\\frac{42-18y-15y}{20} =\frac{37}{4}\\42-33y=\frac{37}{4}*20\\42-33y=185\\-33y=185-42\\-33y=143\\y=\frac{143}{-33}\\y=-\frac{13}{3}[/tex]

Now, finding value of x by putting value of y in eq(1)

[tex]x=\frac{7-3y}{5}\\x= \frac{7-3(-\frac{13}{3}) }{5}\\x=\frac{7+13}{5}\\x=\frac{20}{5}\\x=4[/tex]

So, Value of x=4 and y=-13/3

Answer:

0.7143

- You know the minimum possible grade of the student

- You want to find out the probability that that grade which is greater than 72 is also greater than 84

- Expect the answer to be 0.7143

- The explanation/steps is given below

- The answer seems (and is) reasonable. You only created a new lower limit.

Step-by-step explanation:

Distribution Type: Normal

Mean: 78

Standard deviation: 36

Range of marks: [78 - 36], [78 + 36]  = [42 to 114]

If you know that a student's grade is greater than 72, what is the probability that it's greater than 84?

In this case, the full probability level is between 72 and the upper limit of 114 (instead of between 42 and 114). First, find the fraction of this probability.

[114 - 72] ÷ [114 - 42]  = 42/72  = 0.5833

So, the probability of a student's mark falling between 72 and 114 is 0.5833.

Now making this a whole interval, 114 - 72 = 42

What fraction of this interval of 42 will bear marks between 84 and 114?

[114 - 84]  = 30

30/42  = 0.7143

Because of the first part of the question "If you know (are sure) that a student's grade is greater than 72...", your answer stops at 0.7143, since 72 was used as the lower limit.

Answer:

d=-124

Step-by-step explanation:

To find the discriminant use the equation b^2-4ac

So, 20^2-4(-131)(-1)

400-524= -124

d=-124

Answer:

The answer should be x = -7/8 but it doesn't say that for any of the choices

Step-by-step explanation:

Answer:

y=-2

Step-by-step explanation:

its like in the paper sorry it if crops out

Answer:

lol

Step-by-step explanation:

The electrician will have 56 inches of wire left on the spool after he makes the repair.

First, we need to convert the length of the wire that the electrician needs to cut into inches. 11 feet is equal to 11 * 12 = 132 inches, and 4 inches is equal to 4, so the total length of the wire that the electrician needs to cut is 132 + 4 = 136 inches.

The electrician started with a spool of wire that was 16 feet long, or 16 * 12 = 192 inches long. If he needs to cut 136 inches of wire, he will have 192 - 136 = 56 inches of wire left on the spool.

Therefore, the electrician will have 56 inches of wire left on the spool after he makes the repair.

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Answer:

A is the correct answer

Step-by-step explanation:

The not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.

A residual plot shows the difference between the observed response and the fitted response values.

Given that, Which statement about residual plots is not true

In the given options,

If there is an obvious pattern, the model is probably reasonable, this option is not correct because, The pattern in the residual plot suggests that predictions based on the linear regression line will result in greater error as we move from left to right through the range of the explanatory variable.

So, it is not needed if there is an obvious pattern, then the model is probably reasonable,

Hence, the not correct statement about residual plot is If there is an obvious pattern, the model is probably reasonable.

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Answer:

The Point estimate p = 0.342

Step-by-step explanation:

For the sample, 95% confidence interval (0.202,0.482) . The Confidence interval width = (0.482 - 0.202) = 0.28

The margin of error = 0.28/2

The margin of error = 0.14

So, Point estimate p = Lower bound + Margin of error

Point estimate p = 0.202 + 0.14

Point estimate p = 0.342

Therefore, the Point estimate p = 0.342

Answer:

The backpack weighs more

Step-by-step explanation:

9.5kg = 20.94391 lbs

Answer:

a backpack that weighs 9.5kg

Step-by-step explanation:

kilogram (kg) is stated to be 2.2 times heavier than a pound

Answer: 4

Step-by-step explanation:

6/9 = m/6  We can multiply both sides of the equation by 6 to solve for m

so we get 36/9 = m. m = 4

Answer:

The sample size 'n' = 26

Step-by-step explanation:

Explanation:-

Given a researcher wishes to estimate within $5 the average repair cost of for a refrigerator

Given estimate "E" = $5

The  estimate within  the average is determined by

                [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

 Level of significance    ∝ = 90 % or 10%

                                            = 0.90 or o.10

Z₀.₁₀ = 1.645

                                 [tex]E = \frac{Z_{0.10}S.D }{\sqrt{n} }[/tex]

                             [tex]5 = \frac{1.645 X15.50 }{\sqrt{n} }[/tex]

                        √n =  [tex]\frac{25.49}{5} = 5.099[/tex]

Squaring on both sides , we get

                        n = 26

Conclusion:-

The sample size 'n' = 26

Answer:

is this question complete? there is nothing after the word “that”

Step-by-step explanation:

Answer:

(8,1)

Step-by-step explanation:

(8,1) you have to add do to the same to B

Pont B is located at coordinates at the line AB (8, 1)

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

Given, The midpoint of AB is M(6,-3). If the coordinates of A are (4, - 7)

From the general formula of midpoints of a line

coordinates of midpoint = ((x₂ + x₁)/2, (y₂ + y₁)/2)

where,

(x₁, y₁) are the coordinates of A

(x₂, y₂) are the coordinates of B

And in our case Coordinates of the midpoint are (6, -3)

Thus,

6 = (4 + x₂)/2

x₂ = 8

-3 = (-7 + y₂)/2

y₂ = 1

therefore, the coordinates of Pont B at line AB are (8, 1)

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Answer: Approximately 51 years.

Step-by-step explanation: A population grows by changing exponentially over time, which can be mathematically demonstrated as:

[tex]P=P_{0}e^{rt}[/tex]

where

P is the population after time

P₀ is initial population, when time = 0

r is a percentage rate of growth

t is time passed

In this case, we have to calculate the amount of time it has passed for a population to double, so [tex]P=2P_{0}[/tex]:

[tex]2P_{0}=P_{0}e^{0.0135t}[/tex]

[tex]e^{0.0135t}=2[/tex]

[tex]ln(e^{0.0135t})=ln2[/tex]

Using Logarithm Rule [tex]ln(e^{k})=k[/tex]:

[tex]0.0135t=0.693[/tex]

t = 51.34

For a population with rate of 1.35%, it will take approximately 51 years to double.

Answer:48 sq. Inches

Step-by-step explanation:

Answer:

65.5

Step-by-step explanation:

Answer:

65.5

Step-by-step explanation:

Answer: A.) 10x + 15

Step-by-step explanation:

You would distribute (multiply) the 5 to the 2x which would then make it 10x and you would distribute (multiply) the 5 to the 3 which would then make it 15. Because the 5 is a positive number the sign stays the same.

Therefore, 10x + 15 is your answer.

Answer:

27200

Step-by-step explanation:

Answer:C

Step-by-step explanation: slope of 0 will always be horizontal

Answer:

375/1,000

Step-by-step explanation:

3/8=0.375

375/1,000 =0.375

Answer:

1)  10

2) (not enough info) I got 6/7

3) 12

4) 10

Step-by-step explanation:

Find a GCF and find the numerator.

Answer:

18

Step-by-step explanation:

If we know she will have a 25% discount, we know she will only pay 75%. So you divide by 4 and get 6. So now, If we subtract 25% (6), our 75% will be 18.

Answer:

It's 18

Step-by-step explanation:

25 percent of 24 is 6 dollars, subtract 6 from 24, you get 18, your welcome :D