Find the particular solution of the differential equation.
dydx=−8x7e−x8​;
y(0)=8
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Part 1
y=enter your response here

a) Contribution (objective value) = $132.14

b) The firm earns $132.14 at the optimal solution.

c) An additional hour of time available for the third machine is worth $0.14 to the firm.

d) An additional 5 hours of time available for the second machine will increase the objective value by $3.69.

The best result obtained from using computer software to solve the LP problem is: X1 = 11.43, X2 = 12.86, X3 = 5.71

b) The number of unused hours at the ideal solution is:

Machine 1 still has 8.57 hours of time left.

There are no hours left on Machine 2 at the moment.

There are still 94.29 hours left on Machine 3.

c) The shadow price of the third limitation is worth an extra hour of time available for the third machine. With the exception of increasing the right-hand side of the third constraint by one unit, we can solve the LP problem using the same constraints to determine the shadow price. Using LP to solve this issue, we discover that the shadow price for the third constraint is

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Answer:

The total number of burritos consumed is 68 and an equation to determine the total number of burritos consumed is \(\frac{1}{2}x+16=\frac{3}{4}x-1\)

Step-by-step explanation:

Let x be the total number of burritos consumed

We are given that On Tuesday, Delainey ate 16 more than 1/2 the total number of burritos consumed

So, Number of burritos ate by Delainey on Tuesday=\(\frac{1}{2}x+16\)

We are also given that  Louie ate 1 less than 3/4 of the total number of burritos consumed.

So, Number of burritos ate by Louie on Wednesday =\(\frac{3}{4}x-1\)

We are given that The number of burritos Delainy ate on Tuesday is the same as the number of burritos Louie ate on Wednesday.

So, \(\frac{1}{2}x+16=\frac{3}{4}x-1\\1+16=\frac{3}{4}x-\frac{1}{2}x\\17=\frac{x}{4}\\68=x\)

Hence  the total number of burritos consumed is 68 and an equation to determine the total number of burritos consumed is \(\frac{1}{2}x+16=\frac{3}{4}x-1\)

Answer: 25:68

Step-by-step explanation:

If 68 is the total number of students, and 25 is the number of students who have vanilla, the ratio of the number of students who have vanilla to the total number of students is 25:68.

The ratio of the number of students who have chocolate to the total number of students is \(\frac{43}{68}\)

In the above question it is given that,

There are students some of them have gotten the vanilla ice-cream and some have chocolate ice-cream

The total number of students are = 68

The number of students who had vanilla ice-cream are = 25

The number of students who had chocolate ice-cream are = 68 - 25 = 43

We need to find the ratio of the number of students who have chocolate to the total number of students

Therefore, the ratio of the number of students who have chocolate to the total number of students = \(\frac{43}{68}\)

Hence, the ratio of the number of students who have chocolate to the total number of students is \(\frac{43}{68}\)

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Answer:

9z^8

Step-by-step explanation:

2z^8 + 7z^8

Answer:

what is P(A), the probability that the first student is a boy? 3/5

what is P(B), the probability that the second student is a girl? 3/4

what is P(A and B), the probability that the first student is a boy and the second student is a girl? 1/2

No, évents A and B are not independent events

Step-by-step explanation:

The probability that the first student is a girl P(A)= 3/4.

The probability that the second student is a girl P(B)= 3/4.

The probability that the first student is a girl and the second student is a girl P(A and B)=9/16.

Given that there are three girls (Sandra, Marta, Jane) and one boy (Franklin), and the sample space of possible outcomes is:

{SA, SM, SJ, SF, MA, MS, MJ, MF, JA, JS, JM, JF, FA, FS, FM, FJ}

P(A): Probability that the first student is a girl (Sandra, Marta, or Jane).

Number of favorable outcomes where the first student is a girl: 3 (Sandra, Marta, Jane)

Total outcomes: 4 (total number of students)

P(A) = Number of favorable outcomes / Total outcomes = 3 / 4

P(B):

Probability that the second student is a girl (Sandra, Marta, or Jane).

Number of favorable outcomes where the second student is a girl: 3 (Sandra, Marta, Jane)

Total outcomes: 4 (total number of students)

P(B) = Number of favorable outcomes / Total outcomes = 3 / 4

P(A and B):

Probability that the first student is a girl and the second student is a girl.

Number of favorable outcomes where both students are girls: 3 (Sandra, Marta, Jane)

Total outcomes: 4 (total number of students)

P(A and B) = P(A).P(B)

= 3/4 × 3/4

=9/16

Hence, P(A)=3/4

P(B)=3/4

P(A and B)=9/16

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Answer:

10:23

Step-by-step explanation:

Total number of players on the team = 20 + 26 = 46 players

Number of girls = 20

Ratio of the number of girls to the number of players on the team = 20/46 = 10/23 = 10:23

Ratio is 10:23

Given:-

To find the value when f(x) is 44.

So now we substitute the value and simplify to find the value of x. so we get,

So the value of x is 10.

The Spinners landing on green is 10%, blue is 40%,  yellow is 15% and red is 35%.

Given,

Green–6: The spinner lands on green with a relative frequency of 6/60.

Blue – 24: Spinners landing on blue have a relative frequency of 24/60.

Yellow – 9: The spinner's relative landing frequency on yellow is 9/60.

Red – 21:  The spinner lands on red with a relative frequency of 21/60.

Then the simplified fraction, decimal, and percentage are as follows:

When the spinner lands on green, it does so relatively often, especially 6/60

Simple Fraction: 1/10

0.1 in decimal

percent equals 10%

The spinner's landing on blue occurs with a relative frequency of 24/60

Simple Fraction: 2/5

Decimal: 0.4.

percent equals 40%

The spinner's relative frequency of landing on yellow is 9/60

Simple Fraction: 3/20

Decimal: 0.15

Percentage equals 15%

The spinner typically lands on red with a relative frequency of 21/60

Simple Fraction: 7/20

Decimal: 0.35

Percentage: 35%

Hence, the spinners landing on green is 10%, blue is 40%,  yellow is 15% and red is 35%.

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Roxanne could save only $1 per Month by switching to Jasmine Bank.

The given table shows the checking account features and fees for Jasmine Bank and East Medina Bank. Here are the features and fees for both banks:

Jasmine Bank East Medina Bank Checking account services $10 per month $6 per month transactions (bank ATM) No ATM fees $1 per transaction ATM transactions (nonbank ATM) No ATM fees $3 per transaction online banking $4 per month Free online banking with a linked savings account

Otherwise, $5 per month Roxanne has a checking account at East Medina Bank. She uses online banking to pay bills and send birthday money to her nieces and nephews.

Roxanne uses a bank ATM once a month and a nonbank ATM near her apartment 2 times each month .

Roxanne's monthly fees at East Medina Bank :

East Medina Bank checking account service: $6 per month Nonbank ATM transaction fees:

$3 x 2 = $6 per month Online banking fee: Free Bank ATM transaction fee: $1 x 1 = $1 per month total monthly fees: $13 per month Roxanne's monthly fees at Jasmine Bank:

Jasmine Bank checking account service:

$10 per month on bank ATM transaction fees:

$0Online banking fee: $4 per monthBank ATM transaction fee:

$0Total monthly fees: $14 per monthRoxanne would save $1 per month by switching to East Medina Bank.

This is because she would be paying $14 per month at Jasmine Bank and $13 per month at East Medina Bank. Therefore, Roxanne could save only $1 per month by switching to Jasmine Bank.

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Answer:

24 sandwich shops are in Nevada

Step-by-step explanation:

Answer:

0.02275

Step-by-step explanation:

We use the z score formula to solve for this

z-score is given as: z = (x-μ)/σ

where x is the raw score,

μ is the population mean

σ is the population standard deviation

In the above question:

mean of μ=500

a standard deviation of SD=100

raw score x = 700

Hence, z score = (700 - 500)/ 100

= 200/100

= 2

z score = 2

Using the z score table of normal distribution to find the Probability of z = 2

P( x = z)

= P(x = 700)

= P( z = 2)

= 0.97725

P(x>700) = 1 - P(x = 700)

= 1 - 0.97725

= 0.02275

Therefore, the probability of randomly selecting an individual from this population who has an SAT score greater than 700 is 0.02275

Answer:

Step-by-step explanation:

Alright so we are going to be simplifying here

-6 + x = 4x Flip sides

x-6=4x

After that,

x-6=4x  Subtract 4x from both sides

-3x-6=0

Step 3

-3x-6=0  Add 6 to the sides

-3x=6

Step 4

-3x=6  Divide the sides by 3

-2

So therefore,

Your answer would be x=-2

The inequality used to determine v, the minimum number of visits Taylor needs to earn her first free movie ticket is 75 + 6.5v ≥ 100.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Given,

Points for signing up = 75 points

Points for each visit to the movie theater = 6.5 points

Let v be the minimum number of visits Taylor needs to earn her first free movie ticket.

Points earned for v visits = 6.5v

She needs at least 100 points for a free movie ticket.

75 + 6.5v will be the points she earn for a free movie ticket.

This expression must be greater than 100, which is the required points for a free movie.

75 + 6.5v ≥ 100

Hence the inequality representing the situation is 75 + 6.5v ≥ 100.

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To determine if a set of ordered pairs represents a function, we need to check if each input (x-value) is associated with exactly one output (y-value).

Let's analyze each set of ordered pairs:

{(-6,-5), (-4, -3), (-2, 0), (-2, 2), (0, 4)}

In this set, the input value -2 is associated with two different output values (0 and 2). Therefore, this set does not represent a function.

{(-5,-5), (-5,-4), (-5, -3), (-5, -2), (-5, 0)}

In this set, the input value -5 is associated with different output values (-5, -4, -3, -2, and 0). Therefore, this set does not represent a function.

{(-4, -5), (-3, 0), (-2, -4), (0, -3), (2, -2)}

In this set, each input value is associated with a unique output value. Therefore, this set represents a function.

{(-6, -3), (-6, -2), (-5, -3), (-3, -3), (0, 0)}

In this set, the input value -6 is associated with two different output values (-3 and -2). Therefore, this set does not represent a function.

Based on the analysis, the set {(-4, -5), (-3, 0), (-2, -4), (0, -3), (2, -2)} represents a function since each input value is associated with a unique output value.

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Answer:

Below in bold.

Step-by-step explanation:

4y + 2 > 2.8

4y > 2.8 - 2

4y > 0.8

y > 0.8/4

y > 0.2.

Answer:

c = 4

Step-by-step explanation:

Given system of linear equations:

\(\begin{cases}y=-x-4\\3y=cx-19\end{cases}\)

A system of linear equations will have infinite solutions if the two equations are equivalent.

A system of linear equations will have no solutions if the two equations have the same slope (i.e. parallel lines).

A system of linear equations will have one solution if the equations are different, yet the substitution of the same x-value yields the same y-value in both equations.

Rewrite the second equation to isolate y:

\(\implies y=\dfrac{c}{3}x-\dfrac{19}{3}\)

Therefore, the y-intercept of the first equation is -4 and the y-intercept of the second equation is -19/3.

No value of "c" can make the second equation equivalent to the first equation since the y-intercepts are different.

To find the value of "c" where there are no solutions, equate the slopes of both equations and solve for c:

\(\implies \dfrac{c}{3}=-1\)

\(\implies c=-3\)

Therefore, if c = -3, the slopes of the two lines will be the same and there will be no solutions.  So "c" cannot equal -3.

Therefore, for there to be exactly one solution for the given system of linear equations, "c" can be any value except -3.

Let's choose c = 4 as an example.

Therefore:

\(\begin{cases}y=-x-4\\3y=4x-19\end{cases}\)

Substitute the first equation into the second equation and solve for x:

\(\implies 3(-x-4)=4x-19\)

\(\implies -3x-12=4x-19\)

\(\implies -7x=-7\)

\(\implies x=1\)

Substitute x = 1 into the first equation and solve for y:

\(\implies y=-1-4\)

\(\implies y=-5\)

Therefore, the solution to the given system of equations when c = 4 is:

Check by inputting x = 1 into both equations and comparing the resulting y-values:

\(\textsf{Equation 1}: \quad y=-1-4=-5\)

\(\textsf{Equation 2}: \quad 3y=4(1)-19=-15 \implies y=-5\)

As both equations yield y = -5 when c = 1, this confirms that when c = 5, there is one solution to the given system of equations.

The correct option  d.) lower limit: 0.172 upper limit: 0.228, are the lower and upper limit of the interval.

An estimate's level of uncertainty is described by a confidence interval, which is a range of numbers.

The formula for Confidence Interval:

p ± z × √[p(1 - p)/n]

n = Total number of red candies

n = 550 red candles

p = proportion

p = Number of counted red candies / Total number of red candies

Thus,

p = 110/550

p = 1/5

p = 0.2

z score is found as;

For confidence interval of 90%. The z score = 1.6449

Confidence Interval = p ± z × √[p(1 - p)/n]

Confidence Interval = 0.2 ± 1.6449 × √[0.2(1 - 0.2)/550]

CI  = 0.2 ± 1.6449 √0.2 × 0.8/550

CI = 0.2 ± 1.6449 × 0.0170560573

CI = 0.2 ± 0.0280555087

So,

lower limit : 0.2 - 0.0280555087 = 0.1719444913

lower limit =  0.172

upper limit: 0.2 + 0.0280555087 = 0.2280555087

upper limit = 0.228

Thus, the Confidence Interval = (0.172, 0.228)

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Score of 62.816 is the lowest score that can be earned in the California Police Officer Standards and Training test to be eligible to be hired by the agency.

We have a normal distribution of scores for the california peace officer standards and training Let X be the random variable representing scores for the California Police Officer Standards and Training test, X ~ Normal(50, 10²).

Mean = 50

Standard deviations = 10

Let x be the lowest score that can be earned to be eligible to be hired by the agency that is x is the lowest score than can be earned to get in top 10%. Therefore, P(X > x) = 0.10

P((X- 50)/10 > (x- 50)/10) = 0.10 (converting Normal variate to Standard Normal variate)

P(Z > (x - 50)/10) = 0.10 --(1)

From the Standard Normal Distribution table, P(Z > 1.2816) = 0.10 -- (2)

From comparing the equation (1) and (2),

=> (x- 50)/10 = 1.2816

=> x-50 = 12.816

=> x = 62.816

Thus, the required lowest score is 62.816.

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Answer:

h = 6 units

Step-by-step explanation:

area of a parallelogram = bh

where:

area = 54 sq. units

b = 9 units

h = ? units

plugin values into the formula:

54 = 9 (h)

h = 54 / 9

h = 6 units

Answer:

1.35 is the cost of the regular ice cream

Step-by-step explanation:

Answer:

( x + 4 ) ²-16

Step-by-step explanation:

Answer:

 point slope form: y - y1 = m(x - x1)

m = slope, (x1, y1) is a point on the line

y - (-9) = 2(x - 1)

y + 9 = 2(x-1)

Step-by-step explanation:

Step-by-step explanation:

These two angles are same side corresponding interior angles so they are equal to each other

\(5x + 20 = 120\)

\(5x = 100\)

\(x = 20\)

Answer:

6.28571428571

Step-by-step explanation:

In order to find constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9, the following steps should be used. Let f(x) = axe^(bx)F'(x) = a(e^bx) + baxe^(bx)

We have to find the constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9. So, let's begin by first finding the derivative of the function, which is f'(x) = a(e^bx) + baxe^(bx). Next, we need to plug in x = 1/9 in the function f(x) and solve it. That is, f(1/9) = 1.

We can obtain the value of a from here.1 = a(e^-1)Therefore, a = e.Now, let's find the value of b. We know that the function has a local maximum at x = 1/9. Therefore, the derivative of the function must be equal to zero at x = 1/9. So, f'(1/9) = 0.

We can solve this equation for b.0 = a(e^b/9) + bae^(b/9)/9 Dividing the above equation by a(e^-1), we get:1 = e^(b/9) - 9b/9e^(b/9)Simplifying the above equation, we get:b = -9 Thus, the values of constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9 are a = e and b = -9.

The constants a and b in the function f(x) = axe^(bx) such that f(1/9) = 1 and the function has a local maximum at x = 1/9 are a = e and b = -9. The solution is done.

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Answer:

\(\sf A) \quad \begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}\)

B)  see below

C)  points C, E and F

Step-by-step explanation:

Given points:

A system of inequalities is a set of two or more inequalities in one or more variables.

To create a system of inequalities that only contains C and F in the overlapping shaded region, create a linear equation where points C, F and E are to the right of the line and a linear equation where points C, F, A, B and D are to the left of the line.

The easiest way to do this is to find the slope of the line that passes through points C and F, then add values to move the lines either side of the points.

\(\sf slope\:(m)=\dfrac{change\:in\:y}{change\:in\:x}=\dfrac{y_F-y_C}{x_F-x_C}=\dfrac{-4-1}{3-2}=-5\)

Therefore:

\(\sf y = -5x + 5\)  →  points C, F and E are to the right of the line.

\(\sf y=-5x+12\)  →  points C, F, A, B and D are the left of the line.

Therefore, the system of inequalities that only contains points C and F in the overlapping shaded regions is:

\(\begin{cases}\sf y > -5x+5\\\sf y < -5x+12\end{cases}\)

To graph the system of inequalities:

To verify that the points C and F are solutions to the system of inequalities created in Part A, substitute the x-values of both points into the system of inequalities.  If the y-values satisfy both inequalities, then the points are solutions to the system.

Point C (2, 1)

\(\implies \sf x=2 \implies 1 > -5(2)+5 \implies 1 > -5\quad verified\)

\(\implies \sf x=2 \implies 1 < -5(2)+12\implies 1 < 2 \quad verified\)

Point F (3, -4)

\(\implies \sf x=3 \implies -4 > -5(3)+5 \implies -4 > -10\quad verified\)

\(\implies \sf x=3 \implies -4 < -5(3)+12\implies -4 < -3 \quad verified\)

Method 1

Graph the line y = 7x - 4 (making the line dashed since it is y < 7x - 4).

Shade below the dashed line.

Points that are contained in the shaded region are the houses in which Erica is interested in living:  points C, E and F.

Method 2

Substitute the x-value of each point into the given inequality y < 7x - 4.

Any point where the y-value satisfies the inequality is a house that Erica is interested in living.

\(\sf Point\: A: \quad x=-5 \implies 5 < 7(-5)-4 \implies -5 < -39 \implies no\)

\(\sf Point\: B: \quad x=-4 \implies -2 < 7(-4)-4 \implies -2 < -32 \implies no\)

\(\sf Point\: C: \quad x=2 \implies 1 < 7(2)-4 \implies 1 < 10 \implies yes\)

\(\sf Point\: D: \quad x=-2 \implies 4 < 7(-2)-4 \implies 4 < -18 \implies no\)

\(\sf Point\: E: \quad x=2 \implies 4 < 7(2)-4 \implies 4 < 10 \implies yes\)

\(\sf Point\: F: \quad x=3 \implies -4 < 7(3)-4 \implies -4 < 17 \implies yes\)

Answer:

What forces act on the ball in the horizontal direction as it rolls? None. So that means there is no horizontal acceleration and therefore the horizontal component of the ball's speed is constant.

And since the ball was only travelling horizontally at the instant it rolled off the table, initially the vertical component of its speed is 0. That means the time taken to hit the ground after rolling off the table is the same as if it was just dropped 0.950 m. We can find this time using one of the kinematic equations of motion in the vertical direction, taking downwards as positive. Then we have the following information:

u = initial velocity = 0 m/s

d = distance fallen = 0.950 m

a = acceleration (due to gravity) = 9.8 m/s²

t = time = ?

d = ut + 1/2 at². Since u = 0 this reduces to d = 1/2 at² and rearranges to t = √(2d/a) = √(2*0.95/9.8) = 0.4403 s.

In the same amount of time, the ball travels a horizontal distance of 0.352 m. We already know the horizontal velcoity is constant, so horizontal velocity is just horizontal distance divided by time = (0.352 m)/(0.4403 s) = 0.799 m/s.

No as their no difference in Mr. Goodman's evaluation and the History department

What is Statistics ?

The study of statistics is the field that deals with the gathering, structuring, analyzing, interpreting, and presenting of data. In order to apply statistics to an issue in science, business, or society, it is customary to start with a statistical population or a statistical model that will be investigated.

descriptive statistics types in mathematics The data in this type of statistics is summarized using the provided observations. Statistics that are inferential. To interpret the meaning of descriptive statistics, this kind of statistics is employed. Example of Statistics.

Seeing the data we can conclude that their no difference in Mr. Goodman's evaluation and the History department

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