Two buses leave Boston at the same time traveling in opposite directions. One bus travels at 53mph and the other at 64mph. How soon will they be 936 miles apart?

With a manufacturing cost of $80 per phone, the selling price of $292.5 would result in the largest annual profit.

Profit is the amount of gain realized from a transaction. The profit formula is useful for figuring out the profit from selling a specific product, typically in a business, or for figuring out the gain in any financial transaction. If the selling price is more than the cost price, a profit can be determined.

Given,

q = -6p+3030

p = 505 - q/6

R(q) = 505q - q²/6

C(q) = 80q

Now, the profit function,

P(q) = R(q) - C(q)

      = (505q - (q²/6)) - 80q

P(q) = 425q - q²/6

P(q) = 425 - q/3

q = 1275 units

Now, put it in the demand function,

p = 505 - q/6

  = 505 - 212.5

  = 292.5

Therefore, the selling price is $292.5.

To know more about profit, visit:

https://brainly.com/question/19426350

#SPJ1

Answer:

B. Positive linear

Step-by-step explanation:

First, this graph is a linear graph because a linear graph is a straight line. The graph in the diagram is also a straight line, so it is linear.
Also, notice how as x increases, y increases. This means that the graph is positive

Answer:

-1/5

Step-by-step explanation:

y2-y1/x2-x1

1-2=-1

-4-1=-5

-1/5

Answer:

C) 1/5

Step-by-step explanation:

Find the Slope (1, 2) and (−4, 1)

Slope is equal to the change in y over the change in x, or rise over run.

              change in y

    m =     __________

               change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates (also called rise).

               y2 − y1

    m =     _________

                x2 − x1

Substitute in the values of x and y into the equation to find the s lope.

               1 − (2)

    m =    _________

               −4 − (1)

Simplify the numerator.

                 −1

    m =     _________

                −4 − (1)

Simplify the denominator.

                −1

     m =    ________

                −5

Dividing two negative values results in a positive value.

                 1

     m =    ________

                 5

The total number of workers that were studied can be found to be 139,340,000.

The percent of workers unemployed would be 5. 4 %.

Percentage of unemployed men is 5. 6 % and unemployed women is 5. 1%.

Number of employed workers :

= 74,624,000 + 64, 716, 000

= 139,340,000

Percentage unemployed :

= ( 4, 209,000 + 3,314,000 ) / 139,340,000

= 5. 4 %

Percentage of unemployed men :

= 4,209,000 / 74,624,000

= 5.6 %

Percentage of unemployed women:

= 3,314,000 / 64, 716, 000

= 5. 1 %

Find out more on unemployment at https://brainly.com/question/13280244

#SPJ1

The full question is:

a. How many workers were studied?

b. What percent of the workers were unemployed?

c. Compare the percent unemployed for the men and the women.

Answer:

the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

Step-by-step explanation:

Let assume that n should represent the number of the students

SO, \(\bar x\) can now be the sample mean of number of students  in GPA's

To obtain n such that \(P( \bar x \leq 2.3 ) \leq .04\)

⇒ \(P( \bar x \geq 2.3 ) \geq .96\)

However ;

\(E(x) = \int\limits^4_2 Dx (2+e^{-x} ) 4x = D \\ \\ = D(e^{-x} (e^xx^2 - x-1 ) ) ^D_2 = 12.314 D\)

\(E(x^2) = D\int\limits^4_2 (2+e^{-x})dx \\ \\ = \dfrac{D}{3}[e^{-4} (2e^x x^3 -3x^2 -6x -6)]^4__2}}= 38.21 \ D\)

Similarly;

\(D\int\limits^4_2(2+ e^{-x}) dx = 1\)

⇒ \(D*(2x-e^{-x} ) |^4_2 = 1\)

⇒ \(D*4.117 = 1\)

⇒ \(D= \dfrac{1}{4.117}\)

\(\mu = E(x) = 2.991013 ; \\ \\ E(x^2) = 9.28103\)

∴  \(Var (x) = E(x^2) - E^2(x) \\ \\ = .3348711\)

Now; \(P(\bar \geq 2.3) = P( \bar x - 2.991013 \geq 2.3 - 2.991013) \\ \\ = P( \omega \geq .691013) \ \ \ \ \ \ \ \ \ \ (x = E(\bar x ) - \mu)\)

Using Chebysher one sided inequality ; we have:

\(P(\omega \geq -.691013) \geq \dfrac{(.691013)^2}{Var ( \omega) +(.691013)^2}\)

So; \((\omega = \bar x - \mu)\)

⇒ \(E(\omega ) = 0 \\ \\ Var (\omega ) = \dfrac{Var (x_i)}{n}\)

∴ \(P(\omega \geq .691013) \geq \dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2}\)

To determine n; such that ;

\(\dfrac{(.691013)^2}{\frac{.3348711}{n}+(691013)^2} \geq 0.96 \\ \\ \\ (.691013)^2(1-.96) \geq \dfrac{-3348711*.96}{n}\)

⇒ \(n \geq \dfrac{.3348711*.96}{.04*(.691013)^2}\)

\(n \geq 16.83125\)

Thus; we can conclude that; the minimum records to be retrieved by using Chebysher - one sided inequality is 17.

You will be able to withdraw $3,548.50 per month for 20 years if you have $400,000 saved for retirement and earn 10% interest.

To calculate the monthly withdrawals for a given time period, we can use the present value annuity formula. This formula allows us to calculate the fixed monthly withdrawal amount needed to deplete a given initial amount (in this case, $400,000) over a specified time period (20 years) at a given interest rate (10%).

The formula for present value annuity is:

PMT = PV * r / (1 - (1 + r)⁻ⁿ)

Where:

PMT = the fixed monthly withdrawal amount

PV = the present value of the initial investment ($400,000)

r = the interest rate per month (10%/12 = 0.00833)

n = the total number of monthly withdrawals (20 years * 12 months per year = 240)

Plugging in the values, we get:

PMT = 400,000 * 0.00833 / (1 - (1 + 0.00833)⁻²⁴⁰) = $3,548.50 (rounded to the nearest cent)

To learn more about withdrawals click on,

https://brainly.com/question/28098166

#SPJ1

Answer:

The answer would be 20 because 2x2=4 right so 10x2=20

Step-by-step explanation:

The minimum number οf peοple οver age 32 is 23.

Standard deviatiοn is a measure οf the amt. οf variatiοn  in a set οf data values. It is a way tο quantify hοw much the individual data pοints differ frοm the mean οf the dataset.

Tο determine the minimum sample size required tο estimate the pοpulatiοn mean cοnsumptiοn οf meat per week, we can use the fοllοwing fοrmula:

\(n = (Z^{2} * \sigma ^{2}) / E^{2}\)

where:

n is the sample size

Z is the Z-scοre assοciated with the desired level οf cοnfidence (80% = 1.28)

σ is the standard deviatiοn

E is the maximum errοr

Plugging in the given values, we get:

\(n = (1.28^{2} * 1^{2}) / 0.09^{2}\)

n = 22.91

Rοunding up tο the next integer, we get a minimum sample size οf 23 peοple οver age 32.

To learn more about standard deviation visit the link:

https://brainly.com/question/475676

#SPJ1

The preparation of the segmented income statement for Alard Company is as follows:

Alard Company

For the past year.

                                           Blenders    Coffee Makers     Total

Sales revenue                $1,560,000       $2,175,000     $3,735,000

Cost of sales                      1,170,000        2,025,000       3,195,000

Contribution margin        $390,000          $150,000       $540,000

Avoidable fixed costs      $184,000          $142,500        $326,500

Unavoidable fixed costs                                                         13,500

Net income                     $206,000              $7,500       $200,000

Segmented income statement is a financial statement showing the financial performances of different business segments or product lines.

The purposes of preparing a segmented income statement are to show the individual contributions to the net income of the company from the various segments and to enable management decide on the profitability and discontinuance of the segments.

                                         Blenders   Coffee Makers   Total

Production and sales units 65,000        75,000

Fixed costs                       $184,000      $142,500    

Unavoidable fixed costs = $13,500 ($340,000 - $326,500)

Selling price per unit             $24                $29

Variable expense per unit     $18                $27

Contribution per unit               $6                 $2 ($29 - $27)

Learn more about segmented income statements at https://brainly.com/question/30568093.

#SPJ1

                                         Blenders   Coffee Makers

Selling price per unit             $24                $29

Variable expense per unit    $18                 $27

Prepare segmented income statements.

Answer:

There is no variable so -3 therefore cannot be a solution to this.

Answer:

The answer is: NOt applicable

Step-by-step explanation:

The equation comes down to -2=6 which is impossible

The quantity of popcorn each friend of the students receive is 5/36 gallons.

Quantity of popcorn each friend receive = Number of gallons of popcorn the student has / Number of the student's friends

= 5/9 ÷ 4

= 5/9 × 1/4

= (5 × 1) / (9 × 4)

= 5/36

Therefore, the quantity of popcorn each friend of the students receive is 5/36 gallons

Learn more about division of fraction:

https://brainly.com/question/1622425

#SPJ1

The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

Learn more about quadratic equations by reading:

https://brainly.com/question/1214333

#SPJ1

Each friend had originally 13 action figures before buying 11 more.

Given that there are 5 friends and each of them has x action figures in his or her collection. When they buy 11 more action figures, the total number of action figures they will have is 120.

a) We need to find an equation that models the problem. Let x be the original number of action figures that each friend had.

Therefore, the total number of action figures that each friend will have after purchasing 11 more is x + 11.

The total number of action figures will be 5(x + 11) = 5x + 55.

Now, according to the problem,5x + 55 = 120

This is our equation that models the problem.

b) We have to solve the equation 5x + 55 = 120 to find the original number of action figures, x, that each friend had before buying 11 more action figures.

5x + 55 = 120

5x = 120 - 55 (subtract 55 from both sides)

5x = 65x = 13

Therefore, each friend had originally 13 action figures before buying 11 more.

For more such questions on figures, click on:

https://brainly.com/question/24491627

#SPJ8

ANSWER

EXPLANATION

We want to solve for x in the figure given.

The given triangle is an isosceles triangle, and so the perpendicular line drawn divides the line into equal halves.

This implies that we now have a right triangle as follows:

Now, we can solve for x using Pythagoras theorem:

Simplify and solve for x:

That is the value of x.

Isolate the variable by dividing each side by factors that don't contain the variable.

h = −8

Answer:

question is not complete

Answer: The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Step-by-step explanation: irst, we calculate the amount of discount that is applied to the original price:

30% of $1199 = 0.3 x 1199 = $359.70

So, the discounted price is:

$1199 - $359.70 = $839.30

Next, we apply the additional 10% off coupon to this discounted price:

10% of $839.30 = 0.1 x $839.30 = $83.93

The final price after the coupon is applied is:

$839.30 - $83.93 = $755.37

Finally, we calculate the sales tax on this final price:

7% of $755.37 = 0.07 x $755.37 = $52.88

The amount you would pay (including tax) for the item is:

$755.37 + $52.88 = $808.25

Answer:

-5/6

Step-by-step explanation:

(9, 5) and (21, -5)

slope = m = (difference in y)/(difference in x)

m = (-5 - 5)/(21 - 9)

m = -10/12

m = -5/6

Answer: -5/6

The slope of the line that passes through points (9,5) and (21,-5) is -5/6.

We can use the two-point formula to find the slope for the given line. The formula is as follows:

(y2 - y1) = m*(x2 - x1)

Where (x1, y1, x2, and y2) represent the points on the line, and m is the slope of the line.

In the given case:

x1=9, x2=21

y1=5, y2=-5

Using these values in the two-point formula, we get:

(-5-5)=m*(21-9)

-10=m*12

m=-10/12

m=-5/6

Hence the slope of the line is -5/6.

To find out more about the two-point formula:

brainly.com/question/30241830

The initial investment of the function is 20 dollars.

The rate growth in percentage is 4%.

The investment after 10 years is 29.6 dollars.

The function \(y=20(1.04)^{t}\) represents the value y of a saving account after t years.

Therefore, the initial investment of the function is 20 dollars.

The rate growth in percentage can be calculated as follows;

rate growth in percent = 0.04 × 100

rate growth in percent = 4 %

Let's find the value of the investment after 10 years.

Therefore,

\(y=20(1.04)^{t}\)

t = 10

\(y=20(1.04)^{10}\)

\(y=20(1.48024428492)\)

y = 29.6048856984

Therefore, the investment after 10 years is as follows:

y = 29.6 dollars

learn more on function here: https://brainly.com/question/12431044

#SPJ1

Answer:

a for the fist c  for 2 d for 3 and idontknow

4

Step-by-step explanation:

===================================================

Explanations:

Problem 1

v = 9i - 4j means we move 9 units to the right and 4 units down.

Another way to write this is v = <9, -4>

----------------------

Problem 2

R = (-19, 6)

S = (-35, 13)

Subtract x coordinates:  xS - xR = -35 - (-19) = -16

Subtract y coordinates: yS - yR = 13 - 6 = 7

Those results form the vector v = -16i + 7j

This vector indicates we move 16 units left and 7 units up when going from point R(-19,6) to point S(-35,13).

----------------------

Problem 3

t = -5i + 12j

||t|| = sqrt( (-5)^2 + (12)^2 )

||t|| = 13

theta = arctan(12/(-5))

theta = -67.38

Add on 180 to get to the proper quadrant Q2

-67.38 + 180 = 112.62

Therefore,

\(t = 13\bigg\langle \cos(112.62^{\circ}), \ \sin(112.62^{\circ})\bigg\rangle\)

----------------------

Problem 4

The x, y components are the coefficients of the linear form.

This allows us to go immediately from <-39,16> to -39i + 16j

----------------------

Problem 5

P = (-5,11)

Q = (-16,4)

Subtract x coords: xQ - xP = -16 - (-5) = -11

Subtract y coords: yQ - yP = 4 - 11 = -7

The component form of vector t is <-11, -7> and this vector is in Q3.

r = sqrt(a^2 + b^2)

r = sqrt( (-11)^2 + (-7)^2 )

r = 13.038 is the approximate length of the vector.

theta = arctan(b/a)

theta = arctan(-7/(-11))

theta = 32.471

Add on 180 so we get to Q3

32.471+180 = 212.471

Therefore, we have

\(x = r\cos(\theta) = 13.038\cos(212.471^{\circ})\\\\y = r\sin(\theta) = 13.038\sin(212.471^{\circ})\\\\t = xi + yj\\\\t = 13.038\cos(212.471^{\circ})*i + 13.038\sin(212.471^{\circ})*j\\\\\)

in which you could write into this slightly more compact form

\(t = 13.038\bigg\langle\cos(212.471^{\circ}),\sin(212.471^{\circ})\bigg\rangle\\\\\)

For more info, check out polar to cartesian conversion formulas.

Step-by-step explanation:

since the x differences are constantly 1, we can focus only on the pure y differences point by point :

28 - 18 = 10

35 - 28 = 7

39 - 35 = 4

40 - 39 = 1

38 - 40 = -2

and now the second differences = the difference differences :

7 - 10 = -3

4 - 7 = -3

1 - 4 = -3

-2 - 1 = -3

because the second differences are constant, we have a quadratic relation.

The angle 7 is the alternative interior angle to angle 2.

Given that,In the diagram a || bWe need to find the alternate interior angle to <2 .Alternate interior angles are the angles that are formed when a transversal crosses two parallel lines.

They are the angles that are on opposite sides of the transversal and inside the two parallel lines.

Thus, in the given diagram, the angle that is opposite to angle <2 and is inside the two parallel lines a and b is the alternate interior angle to angle <2.

We can see that the alternate interior angle to angle <2 is <7. Therefore, the alternate interior angle to angle <2 is <7.

To learn more about : angle

https://brainly.com/question/25770607

#SPJ8

Usando la distribución binomial, se encuentra que hay una probabilidad de 0.0012 = 0.12% que realmente haya sido fruto de la coincidencia. El argumento para conseguir que te devuelvan el dinero seria de que 6 ítems defectuosos es un resultado inusualmente alto.

Para cada ítem, solo hay dos resultados posibles. O está defectuoso o no lo es. La probabilidad de que un ítem sea defectuoso es independiente de cualquier otro ítem, lo que significa que se utiliza la distribución binomial para resolver esta cuestión.

Distribuición binomial:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

Los parámetros son:

La media de la distribución binomial es:

\(E(X) = np\)

La desviación estándar de la distribución binomial es:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Una medida se considera inusualmente alta si está más de 2.5 desviaciones estándar por encima de la media.

En este problema:

La probabilidad de que realmente haya sido fruto de la coincidencia es P(X = 6), o sea:

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 6) = C_{10,6}.(0.15)^{6}.(0.85)^{4} = 0.0012\)

Probabilidad de 0.0012 = 0.12% que realmente haya sido fruto de la coincidencia.

Para el argumento:

\(E(X) = np = 10(0.15) = 1.5\)

\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{10(0.15)(0.85)} = 1.13\)

\(6 > 1.5 + 2(1.13)\), o sea, el argumento para conseguir que te devuelvan el dinero seria de que 6 ítems defectuosos es un resultado inusualmente alto.

Un problema similar es dado en https://brainly.com/question/22304471

The image coordinates of K′ if the preimage is reflected across y = −7 is (-4, -8)

Based on the given question, we have certain variables that can be utilized for our calculations.

K = (-4, -6)

First, find the equation of the reflection line

The reflection line is y = -7.

This can be expressed as

y = a = -7

The image of the reflection is then calculated as

K' = (x, -(y + 2|a|))

Replace the given or established values in the equation mentioned earlier, resulting in the following expression

K' = (-4, -(-6 + 2 * 7))

Evaluate

K' = (-4, -8)

Hence, the image coordinates of K′ are (-4, -8).

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1

A Reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

The function f(x) = -|x| − 3 can be graphed by following these steps:

Therefore, the correct graph is an option (D). The graph of the option (D) shows a reflection over the y-axis and a shift downwards by three units, which is consistent with the function f(x) = -|x| − 3.

For more questions on Reflection.

https://brainly.com/question/29788009

#SPJ8

Answer:

92170

I hope it's helps you

Answer:

After calculating values from test statics we come to know that value of if null hypothesis is true then it will rejected

As critical values of z is ±1.96 after apply the test statics formula , we get the value of z that is - 4.50 As we consider the equation that

H₀ > z

Apply test statistic we fine the true value . So there is sufficient evidence to reject the claim.

Step-by-step explanation:

critical values z₀ = ±1.96; standardized test statistic z ≅ -4.50;

reject H₀

There is sufficient evidence to reject the claim.

The amount of fabric used to make the number cube is given as follows:

C. 294 cm².

The amount of fabric used to make the number cube is represented by the surface area of the number cube.

The surface area of a cube of side length a is given by the equation presented as follows:

S = 6a².

The side length for this problem is given as follows:

a = 7 cm.

Hence the surface area of the cube is calculated as follows:

S = 6 x 7²

S = 294 cm².

More can be learned about the surface area of a cube at https://brainly.com/question/26403859

#SPJ1

Answer:

-4 1/2

Step-by-step explanation:

1/3(-15+3/2)

1/3(-13 1/2)

1/3(-27/2)

-27/6

-4 3/6

-4 1/2