A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 minutes after the woman starts walking

The cost per gallon of regular gasoline will be $2.69 per gallon.

The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.

MOBIL Service station sells various types of fuel: standard, besides, and premium. Mr.Adams burned through $36.25 on 12.5 gallons of standard fuel at the MOBIL Service station.

The cost per gallon for regular gasoline will be given as,

Rate = $36.25 / 12.5

Rate = $2.69 per gallon

The cost per gallon of regular gasoline will be $2.69 per gallon.

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Answer and explanation:

Given : Suppose you and a friend each choose at random an integer between 1 and 8, inclusive.

The sample space is

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)  (1,7) (1,8)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)   (2,7) (2,8)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)   (3,7) (3,8)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)   (4,7) (4,8)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)   (5,7) (5,8)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)   (6,7) (6,8)

(7,1) (7,2) (7,3) (7,4) (7,5) (7,6)   (7,7) (7,8)

(8,1) (8,2) (8,3) (8,4) (8,5) (8,6)   (8,7) (8,8)

Total number of outcome = 64

To find : The following probabilities ?

Solution :

The probability is given by,

[tex]\text{Probability}=\frac{\text{Favorable outcome }}{\text{Total outcome}}[/tex]

a) p(you pick 5 and your friend picks 8)

The favorable outcome is (5,8)= 1

[tex]\text{Probability}=\frac{1}{64}[/tex]

b) p(sum of the two numbers picked is < 4)

The favorable outcome is (1,1), (1,2), (2,1)= 3

[tex]\text{Probability}=\frac{3}{64}[/tex]

c) p(both numbers match)

The favorable outcome is (1,1), (2,2), (3,3), (4,4), (5,5), (6,6), (7,7), (8,8) = 8

[tex]\text{Probability}=\frac{8}{64}[/tex]

[tex]\text{Probability}=\frac{1}{8}[/tex]

The probabilities for choosing specific integers or pairs with a particular sum between 1 and 8 are computed based on the total number of possible combinations, which is 64 (8x8).

The probability of choosing a specific pair of integers when you and a friend each pick an integer at random between 1 and 8 can be found using the principles of probability. With 8 choices for each person, there are 64 (8 × 8) possible combinations.

To compute the probability that the sum of the two numbers picked is < 4, notice that there are very few combinations: (1,1), (1,2), (2,1). So, P(sum < 4) is 3/64.

Answer:

40

Step-by-step explanation:

Since your only buying stickers you divide 10 by 0.25 to see how many you can purchase.

Answer:

It means a sticker costs $0.25 and a charm costs $0.5

Therefore without buying any charm

You can use $10 to buy 10/0.25

40 stickers

Step-by-step explanation:

Answer:

  A.  0

Step-by-step explanation:

The value of the discriminant is ...

  b² -4ac = (-3)² -4(1)(4) = 9 - 16 = -7

The negative discriminant means the roots will be complex.

There are 0 real solutions.

Answer:

Gina's pay rate next month will be =$9.9 per hour

Step-by-step explanation:

Gina was initial earnings was = $10 per hour

She received an increase by = 10%

Increase in amount received = [tex]10\%\ of\ \$10= 0.1\times\$10 =\$1 [/tex]

New earnings = [tex]\$10+\$1=\$11[/tex] per hour

Next month her pay rate will decrease by = 10%

Decrease in pay rate next month will be = [tex]10\%\ of\ \$11= 0.1\times\$11 =\$1.1 [/tex]

Thus, Gina's pay rate next month will be = [tex]\$11-\$1.1=\$9.9[/tex] per hour

Answer: the distance it can travel on full tank is 675 miles

Step-by-step explanation:

Gas Mileage is how many miles you travel on one gallon of gasoline.

A new Honda Accord Hybrid ( part electric, part gasoline ) tests for its gas mileage by traveling 432 miles on 8 gallons of gasoline.

This means that its gas mileage is

Number of miles travelled / number of gallons of gasoline used.

Gas mileage = 432/8 = 54 miles per gallon

If a full tank containing 12 1/2 = 25/2 gallons is used, the distance that it can travel will be

Gas mileage × volume of the full tank. it becomes

54 × 25/2 = 675miles

Answer:

  H = 30

Step-by-step explanation:

The value of a fraction is zero when its numerator is zero. The value of h that makes the numerator zero is 20.

  h = 20

Answer:

The answer to your question is r = 2x

Step-by-step explanation:

Volume of a cylinder = V = π r² h

r = radius

h = height = x

Volume = 4x³

Then

                  r² = [tex]\frac{volume}{\pi h}[/tex]

                  r² = [tex]\frac{4x^{3} }{\pi x}[/tex]

                  r² = 4x²

                  r = 2x

Answer: There were 40 adult tickets and 28 children's tickets

Step-by-step explanation:

Let x represent the number of adult tickets sold.

Let y represent the number of children's tickets sold.

An event sold $608 worth of tickets adult tickets cost $11 while children's tickets cost $6. It means that

11x + 6y = 608 - - - - - - 1

If 68 tickets were sold, it means that

x + y = 68

Substituting x = 68 - y into equation 1, it becomes

11(68 - y) + 6y = 608

748 - 11y + 6y = 608

- 11y + 6y = 608 - 748

- 5y = 140

y = 140/5 = 28

x = 68 - y = 68 - 28

x = 40

Answer:

each paid $2.45

Step-by-step explanation:

9.80/4 = 2.45

Check the picture below.

Answer:

72/4=18 so she could make their lunch for 18 days

Step-by-step explanation:

so it would be 6x12 for the bagels which would be 72

for the apples it would be 8x9 which is 72

the cookies would be 12x6 to get 72

and the juice boxes would be 9x8 to get 72

divide that by 4 to get 18

Answer:

x = 12

Step-by-step explanation:

Given expression is \[7x-9-11=3x+4+2x\]

Simplifying: \[7x -(9+11) = (3x+2x)+4\]

Or, \[7x - 20 = 5x + 4\]

Bringing all terms containing x to the left side of the equation and all the numeric terms to the right side:

\[7x-5x = 20 + 4\]

=> \[(7-5)x = 24\]

=> \[2x = 24 \]

=> x = \[\frac{24}{2}\]

=> x= 12

Hence the value of x which satisfies the given equation \[7x-9-11=3x+4+2x\] is 12

Answer:

8.5 seconds to hit the ground

Step-by-step explanation:

A soccer ball is thrown upward from the top of a 204 foot high building at a speed of 112 feet per second.

[tex]h(t)=-16t^2+V_0t+h_0[/tex]

Vo is the speed 112 feet per second

h0 is the initial height = 204 foot

So the equation becomes

[tex]h(t)=-16t^2+112t+204[/tex]

When the soccer ball hit the ground then the height becomes 0

[tex]0=-16t^2+112t+204[/tex]

Apply quadratic formula

[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]t=\frac{-112+\sqrt{112^2-4 (-16) \cdot 204}}{2(-16)}[/tex]

[tex]t=\frac{-112+\sqrt{25600}}{-32}=-1.5[/tex]

[tex]\frac{-112-\sqrt{25600}}{-32}=8.5[/tex]

time cannot be negative

so it takes 8.5 seconds to hit the ground

The statements that must be true are:

a. m∠CEA = 90°

b. m∠CEF = m∠CEA + m∠BEF

e. ∠AEF is a right angle.

Here's why:

a. m∠CEA = 90°

b. m∠CEF = m∠CEA + m∠BEF

c. m∠ CEB = 2(m∠ CEA)

d. ∠ CEF is a straight angle.

e. ∠ AEF is a right angle.

Answer:

Easy, it is C) $136,800

Step-by-step explanation:

All you need to do is multiply $3,800 by 12 to get the yearly rent. To get $45,600 per year. You now multiply $45,600 by 3 to get the total price of the 3 year lease. You now have a total cost of $136,800 over the 3 year time period of the lease.

Answer: Andre picked 252 pounds of apples

Step-by-step explanation:

Let x = number of pounds of apple picked by Jane.

Let y = number of pounds of apple picked by Andre

Let z = number of pounds of apple picked by Maria

Andre picks three times as many pounds as maria. It means that

y = 3z

Jane picks two times as many pounds as Andre. It means that

x = 2y

The total weight of the apples is 840 pounds. It means that

x + y + z = 840 - - - - - - - - - 1

We will substitute z = y/3 and x = 2y into equation 1

2y + y + y/3 = 840

Cross multiplying with 3

6y + 3y + y = 2520

10y = 2520

y = 2520/10 = 252

x = 2y = 252× 2 = 504

z = y/3 = 252/3 = 84

Answer:

option B)[tex]\frac{1}{12}[/tex]

Step-by-step explanation:

According to the given conditions, the total number of outcomes are 24.

The probability that of drawing hearts card is

P=[tex]\frac{(total number of hearts cases)}{(total number of cases)}[/tex]

total number of hearts cases= 6

thus P= [tex]\frac{6}{24} = \frac{1}{4}[/tex]

now the probability of 4 or 6 is,

P=[tex]\frac{(total number of 4 or 6 cases)}{(total number of cases)}[/tex]

thus P= [tex]\frac{8}{24} = \frac{1}{3}[/tex]

thus, by multiplication law,

final probality is P= [tex](\frac{1}{4})(\frac{1}{3})[/tex]

P= [tex]\frac{1}{12}[/tex]

Answer:  The required probability is [tex]\dfrac{14}{15}.[/tex]

Step-by-step explanation:  Given that the probabilities that A, B and C can solve a particular problem are [tex]\dfrac{3}{5},~ \dfrac{2}{3},~\dfrac{1}{2}[/tex] respectively.

We are to determine the probability that at least one of the group solves the problem , if they all try.

Let E, F and G represents the probabilities that the problem is solved by A, B and C respectively.

Then, according to the given information, we have

[tex]P(E)=\dfrac{3}{5},~~~P(F)=\dfrac{2}{3},~~P(G)=\dfrac{1}{2}.[/tex]

So, the probabilities that the problem is not solved by A, not solved by B and not solved by C are given by

[tex]P\bar{(A)}=1-P(A)=1-\dfrac{3}{5}=\dfrac{2}{5},\\\\\\P\bar{(B)}=1-P(B)=1-\dfrac{2}{3}=\dfrac{1}{3},\\\\\\P\bar{(C)}=1-P(C)=1-\dfrac{1}{2}=\dfrac{1}{2}.[/tex]

Since A, B and C try to solve the problem independently, so the probability that the problem is not solved by all of them is

[tex]P(\bar{A}\cap \bar{B}\cap \bar{C})=P(\bar{A})\times P(\bar{B})\times P(\bar{C})=\dfrac{2}{5}\times\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{15}.[/tex]

Therefore, the probability that at least one of the group solves the problem is

[tex]P(A\cup B\cup C)\\\\=1-P(\bar{A\cup B\cup C})\\\\=1-P(\bar{A}\cap \bar{B}\cap \bar{C})\\\\=1-\dfrac{1}{15}\\\\=\dfrac{14}{15}.[/tex]

Thus, the required probability is [tex]\dfrac{14}{15}.[/tex]

Final answer:

To find the probability that at least one of A, B, or C solves the problem, calculate 1 minus the probability that none solve it. The individual non-solving probabilities are multiplied together and subtracted from 1, resulting in a final answer of 14/15.

Explanation:

To determine the probability that at least one person out of A, B, and C solves a problem, we must first understand that the probability of at least one event occurring equals 1 minus the probability that none of the events occur (in this case, that none of the people solve the problem).

We have the individual probabilities as follows:

Probability A solves the problem: 3/5

Probability B solves the problem: 2/3

Probability C solves the problem: 1/2

The probabilities that A, B, or C do not solve the problem are then 1 - (3/5), 1 - (2/3), and 1 - (1/2), respectively. To find the probability that none of them solve the problem, we multiply these probabilities:

P(none solve) = (1 - 3/5) × (1 - 2/3) × (1 - 1/2)

Calculating this gives us P(none solve) = (2/5) × (1/3) × (1/2) = 2/30 = 1/15. Thus, the probability that at least one person solves the problem is:

P(at least one solves) = 1 - P(none solve) = 1 - 1/15 = 14/15.

Answer:

The result is [tex]-\frac{371}{6}[/tex]

Step-by-step explanation:

The given expression is:

[tex]\frac{7}{-2.5+8.5}+\frac{0.6(8+13)}{-0.2}[/tex]

First, we solve the denominator of the left-hand fraction

[tex]\frac{7}{6}+\frac{0.6(8+13)}{-0.2}[/tex]

Then we find the sum in the numerator of the right-hand fraction

[tex]\frac{7}{6}+\frac{0.6(21)}{-0.2}[/tex]

Now we solve the second fraction

[tex]\frac{7}{6}-63[/tex]

The final result is the subtraction of both expressions

[tex]-\frac{371}{6}[/tex]

Answer: -1.17522136 hertz

there you go :) just to let you know I’m in 7th

Answer:

16+h=c

Step-by-step explanation:

Answer:

There are 6 teams will play for each team.

Step-by-step explanation:

Given;

Total amount of money = $ 2040

Cost for blue team = $ 160

Cost for red team = $ 180

Solution,

Let number of blue teams be x and the  number of red teams be y.

Total cost =[tex]160x + 180y = 2040[/tex]

Since it is a league match and so both divisions must have equal teams.

∴ x=y

∴ [tex]160x + 180x = 2040[/tex]

[tex]340x = 2040\\x = 6[/tex]

Hence the number of teams in each division is 6.

Answer: the price of an adult ticket is $11

the price of a child ticket is $11

Step-by-step explanation:

Let x represent the price of an adult ticket.

Let y represent the price of a student ticket.

On the first day of ticket sales the school sold 7 adult tickets and 6 student tickets for a total of $143. This means that

7x + 6y = 143 - - - - - - - - - -1

The school took in $187 on the second day by selling 4 adult tickets and 13 student tickets. This means that

4x + 13y = 187 - - - - - - - - - -2

Multiplying equation 1 by 4 and equation 2 by 7, it becomes

28x + 24y = 572

28x + 91y = 1309

Subtracting

-67y = -737

y = -737/-67 = 11

Substituting y = 11 into equation 1, it becomes

7x + 6×11 = 143

7x + 66 = 143

7x = 143 - 66 = 77

x = 77/7 = 11

The intensity at a distance of 2.7 meters is 77.17 milliroentgens per hour.

Given:

I= 62.5 milliroentgens per hour

Distance = 3 meters

If the intensity of radiation varies inversely as the square of the distance from the machine, use the inverse square law formula:

[tex]I = k/d^2[/tex]

Where:

I represents the intensity of radiation,

k is a constant,

d represents the distance from the machine.

Substituting the value back to formula as

62.5 = k/(3²)

62.5 = k/9

k = 62.5 x 9

k = 562.5

So, the intensity at a distance of 2.7 meters:

I = 562.5/(2.7²)

I = 562.5/7.29

I = 77.17 milliroentgens per hour

Therefore, the intensity is 77.17 milliroentgens per hour.

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The intensity of radiation from a machine at a distance of 2.7 meters is 77.16 milliroentgens per hour, according to the inverse square law in Physics.

The question is related to inverse square law in Physics. The intensity (ℤ) of radiation varies inversely as the square of the distance (d) from the machine. Mathematically, this relationship is represented as ℤ = k/d^2 where k is a constant. Given that at a distance of 3 meters, the intensity is 62.5 milliroentgens per hour, we can find the constant k = ℤ * d^2, i.e., k = 3^2 * 62.5 = 562.5.

Now, you want to know the intensity at a distance of 2.7 meters, which we can find by substituting this value and the constant k in our equation: ℤ = k/d^2, which results in ℤ = 562.5/(2.7^2) = 77.16 milliroentgens per hour. Therefore, the intensity at a distance of 2.7 meters from the radiation machine is 77.16 milliroentgens per hour.

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Answer:

We conclude that cheddar popcorn weighed less than 5.5 ounces.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ =5.5 ounces

Sample mean, [tex]\bar{x}[/tex] = 5.23 ounces

Sample size, n = 64

Alpha, α = 0.05

Sample standard deviation, σ = 0.24 ounce.

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 5.5\text{ ounces}\\H_A: \mu < 5.5\text{ ounces}[/tex]

We use One-tailed z test to perform this hypothesis.

Formula:

[tex]z_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }[/tex]

Putting all the values, we have

[tex]z_{stat} = \displaystyle\frac{5.23 - 5.5}{\frac{0.24}{\sqrt{64}} } = -9[/tex]

Now, [tex]z_{critical} \text{ at 0.05 level of significance } =-1.645[/tex]

Since,  

[tex]z_{stat} < z_{critical}[/tex]

We reject the null hypothesis and accept the alternate hypothesis. Thus, we conclude that cheddar popcorn weighed less than 5.5 ounces.

The z test is mathematically given as z=-1.86, and a>p value.

therefore we failed to accept null hypothesis.

Question Parameters:

A random sample of 64 bags

weighed, on average, 5.23 ounces

the standard deviation of 0.24 ounce.

µ = 5.5 ounces

Generally, hypothesis  is mathematically given as

H_0:\mu = 5.8 null

H_a:\mu < 5.8 alter

Using z test

[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}\\\\z=\frac{5.74-5.8}{\frac{0.26}{\sqrt{65}}}[/tex]

z=-1.86

In conclusion,

p value = 0.0314

α = 0.10

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There are 3 individual instances of each of the 'x' and 'y' members, while there's only one instance of static member 'z'. The value of 'x' and 'y' members in each object is 0.

The subject of this question pertains to class declarations in the field of programming, with a focus on how variables are instantiated among objects of a class. Specifically, the interest is on the number of instances and values of private and static member variables in the class Thing which includes private int x, private int y and static int z.

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Final answer:

There are three separate instances each of the non-static members x and y, one instance of the static member z, and since the constructor initializes x and y to z's value, they will both have the value 0.

Explanation:

The question involves understanding the concept of members and static members in the C++ programming language, specifically within the context of class instances. When considering the provided class declaration and the creation of three instances of the Thing class, we are dealing with object-oriented programming principles.

A) Each instance of a class has its own separate set of non-static members. Since x is a non-static member and we have three instances, there are three separate instances of the x member.

B) Similarly, y is a non-static member. Thus, there are also three separate instances of the y member.

C) The z member is declared as static, meaning that it is shared across all instances of the class. Therefore, there is only one instance of the z member that exists across all instances of the class.

D) Because the constructor initializes x and y with the value of z, and z is initially set to 0, the value stored in the x and y members of each object will be 0.

Answer:

The number of games sold by Chris  = [tex](\frac{g}{8}  - 17)[/tex]

Step-by-step explanation:

The total number of employees in the team = 8

The total number of games sold by the whole team = g

The number of games sold by Chris = Average Games sold by each member - 17

Now, [tex]\textrm{Average number of games sold by each}  = \frac{\textrm{Total number of games sold by team}}{\textrm{Total number of people in team}}\\[/tex]

=[tex]\frac{g}{8}[/tex]

⇒The average number of games sold by each of the team member = g/8

Hence, the number of games sold by Chris  = [tex](\frac{g}{8}  - 17)[/tex]

Answer:

The smallest poster has dimension 25.6 cm by 32.05 cm.

Step-by-step explanation:

Let "x" and "y" be the length and the width of the poster.

The margin of a poster are 4 cm and the side margins are 5 cm.

The length of the print = x - 2(4) = x - 8

The width of the print = y - 2(5) = y - 10

The area of the print = (x- 8)(y -10)

The area of the print is given as 388 square inches.

(x-8)(y -10) = 388

From this let's find y.

y -10 = [tex]\frac{388}{(x - 8)}[/tex]

y = [tex]\frac{388}{x - 8} + 10[/tex] -------------------(1)

The area of the poster = xy

Now replace y by [tex]\frac{388}{x - 8} + 10[/tex], we get

The area of the poster = x ([tex]\frac{388}{x - 8} + 10[/tex])

= [tex]10x + \frac{388x}{x - 8}[/tex]

To minimizing the area of the poster, take the derivative.

A'(x) =  [tex]10 + 388(\frac{-8}{(x-8)^{2} } )[/tex]

A'(x) = [tex]10 - \frac{3104}{(x-8)^2}[/tex]

Now set the derivative equal to zero and find the critical point.

A'(x) = 0

[tex]10 - \frac{3104}{(x-8)^2}[/tex] = 0

[tex]10 = \frac{3104}{(x-8)^2}[/tex]

[tex](x - 8)^2 = \frac{3104}{10}[/tex]

[tex](x - 8)^2 = 310.4[/tex]

Taking square root on both sides, we get

x - 8 = 17.6

x = 17.6 + 8

x = 25.6

So, x = 25.6 cm takes the minimum.

Now let's find y.

Plug in x = 25.6 cm in equation (1)

y =  [tex]\frac{388}{25.6 - 8} + 10[/tex]

y = 22.05 + 10

y = 32.05

Therefore, the smallest poster has dimension 25.6 cm by 32.05 cm.

The minimum area of the poster given that the printed area is 388 sq.cm and the margins are 4cm top/bottom and 5cm on the sides, is found by using calculus and the area constraints. The problem can be solved by expressing width and height in terms of one another and then optimizing the area equation.

To solve the problem, we use calculus and the area constraint to find the dimensions with a minimum area. Let's denote that width of the poster is w and height is h. The entire area of the poster would then be expressed as:

(w+2*5cm)*(h+2*4cm) = poster area

On the other hand, we have a fixed constraint that states the printed area is 388cm², so we have:

w*h = 388 cm²

We can express h as 388/w and substitute this in the poster's area equation, and then use calculus to find the minimum area given these constraints.

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