9. A ship sails 20km due North. It changes
direction and then sails 15km due East.
How far is it from its starting point?

On solving the question, we can say that - the probability of given will be P(a/c) = 3/6 = 1/2

A branch of mathematics known as probability measures the possibility of an event happening or a proposition being true. The probability of an occurrence is a number between 0 and 1, where roughly 0 denotes the event's improbability and 1 denotes certainty. A probability is a numerical representation of the possibility or probability that a specific event will take place. Probabilities can alternatively be stated as percentages ranging from 0% to 100%, or as percentages from 0 to 1. the proportion between the number of events in a comprehensive collection of equally likely outcomes that lead to a certain occurrence and the entire number of outcomes.

here,

the probability that event the dice will roll is 6

and chances of geting even numbers are = 3

so P(a/c) = 3/6 = 1/2

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

The art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper for proper distribution.

To determine the largest number of identical kits the art teacher can make using all the crayons and drawing paper, we need to find the greatest common divisor (GCD) of the quantities.

The GCD represents the largest number that can divide all the quantities without leaving a remainder.

The GCD of the quantities of crayons can be found by considering the prime factorization:

72 = 2³ × 3²

48 = 2⁴ × 3

48 = 2⁴ × 3

48 = 2⁴ × 3

The GCD of the crayons is 2³ × 3 , which is 24.

Now, we need to find the GCD of the quantity of drawing paper:

120 = 2³ × 3 × 5

The GCD of the drawing paper is also 2³ × 3 , which is 24.

Since the GCD of both the crayons and drawing paper is 24, the art teacher can make a maximum of 24 identical kits using all the crayons and drawing paper.

Each kit would contain an equal distribution of crayons and drawing paper.

Learn more about distribution here:

brainly.com/question/30034780

#SPJ1

Answer:

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

Let each side is x.

The area is 64 in².

Step-by-step explanation:

if the area is 64cm, each side would be 8cm

since Area of square = side by side

\(64 = {s}^{2} \\ \sqrt{64} = \sqrt{s} \\ 8 = s\)

Answer:

B

Step-by-step explanation:

6x -8y = - 16y

6x = -8y

8y = 17x + 4

-8y = -17x - 4

6x = -17x - 4

23x = -4

x = -4/23

Answer: the cost of gas for traveling 1,128.3 miles is $109.73

Step-by-step explanation:

Given:

cost per gallon of gas is $3.89

total miles traveled is 1128.3 miles

the car can travel 40 miles per gallon

gas is required to travel  1128.3 miles= total miles traveled / miles traveled                                            

                                                                per gallon

                                                         =1128.3/40 gallon

                                                         = 28.2075-gallons

we know that the cost per gallon of gas is $3.89

from this, we can find the cost for 28.2075-gallon

the cost for 28.2075 gallons = 28.2075*cost per gallon

                                       = 28.2075*3.89

                                       = $109.727175

                                       ~= $109.73

therefore it takes approximately 109.73 dollars to travel 1,128.3 miles

to know more cost-related problems,

https://brainly.com/question/25109150

Answer:

-7

Step-by-step explanation:

Also for the last two you gave, the answers to your questions were wrong. They gave you the wrong answer. The answer for the other 2 were A ($30) and the slope for the other answer was (1/2)

Answer:

208 cubic units

Step-by-step explanation:

The composite figure in the picture is composed of a triangular prism and a rectangular prism, both which can be calculated by the base * height formula.
First, let’s calculate the volume of the triangular prism:

The base is the area of the triangle base, which is dc/2, or 4*3/2, which is 6. Next, multiply the area of the base by the height “b”: 6 * 8 = 48.

Now, let’s calculate the volume of the rectangular prism:

The base is the rectangular base’s area, which is a*c, or 5*4, which is 20. Next multiply the base by the height “b”: 20 * 8 = 160

Now, add up the volumes of the rectangular and triangular prisms:

160 + 48 = 208 cubic units

Answer:

(a) The function has a minimum value

(b) The minimum value is 2

Step-by-step explanation:

(a)Currently y = x^2 + 4x + 6 is in standard form, whose general equation is

y = ax^2 + bx + c.  

We know that for our function a = 1.

Thus, y = x^2 + 4x + 6 must have a minimum value.

(b) Whenever a problem asks for the minimum value, it's asking for the y-coordinate of the minimum.

Step 1:  First we can find the x-coordinate of the minimum using the equation -b/2a from the quadratic formula.  

Plugging in 4 for b and 1 for a, we get:

x-coordinate of minimum = -4 / 2(1)

x-coordinate of minimum = -4 / 2

x-coordinate of minimum = -2

Step 2:  Now we can plug in -2 for x in the quadratic function.  The result will be our minimum value:

f(-2) = (-2)^2 + 4(-2) + 6

f(-2) = 4 - 8 + 6

f(-2) = -4 + 6

f(-2) = 2

Thus, the minimum value of the quadratic function is 2.

Step-by-step explanation:

0.153 is the largest number

Answer:

I believe 0.153 to be the greatest

Step-by-step explanation:

0.153

15%= 0.15

1/12= 0.0833333

1/7= 0.1428571429

Answer:

The solution for problem a is cross multiplication

5×500=2500 and 15×x=15× so 15×=2500

divide both sides by the coefficient 15. 15x ÷15=×

divide 2500 by 15=500

x=500/3= approximately 166.7

Solution for b:

This one's easy!!

10/20=x/500

cross multiply

10×500=5000

20×X=20x

now we have the equation. 20x=5000

stay with me. I hope this makes sense ^_^

divide both sides by the coefficient 20

20x÷20=x

5000÷20=250

x=250

a is true

i hope this helps ;)

Answer:

Z=20

Y=16

X= 12

Step-by-step explanation:

Hope it helps

We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

Answer:

x = 2

x = -2

Step-by-step explanation:

Divide both sides of the equation by 7.

Moove the constant to the right and change its sign.

Simplify the equation.

Separate the solutions.

Answer:

0.8 minutes

Step-by-step explanation:

From the given information:

The arrival time for the jobs to the computer obeys a Poisson distribution;

Thus, the arrival rate is:

\(\lambda = 0.6 \ jobs \ per \ minute\)

Assuming the average time spent on the jobs in the system is denoted by:

\(W_s= 5 \ minutes\)

The average time a job process in the system can be expressed as follows:

\(W_s = \dfrac{1}{\mu - \lambda}\)

From above formula:

\(\mu =\) service rate

\(\lambda =\) arrival rate

replacing the values;

\(5 = \dfrac{1}{\mu - 0.6}\)

\(5(\mu - 0.6) = 1\)

Open brackets

\(5 \mu - 3 = 1\)

\(5 \mu = 3+ 1 \\ \\ \mu = \dfrac{4}{5}\)

\(\mu =\) 0.8 minutes

The constant of proportionality for the given graph is k = 45.

The ratio that establishes a proportionate link between any two given values is referred to as the constant of proportionality. The constant of proportionality may also be referred to by the labels constant ratio, constant rate, unit rate, constant of variation, or even rate of change.

A proportional connection is simple to graph on a coordinate plane as a straight line. Because it is directly proportional—the slope serves as the proportionality constant—it is a straight line. Because of the constant proportionate change along the x and y axes, the slope or increase is constant.

The constant of proportionality is given as:

y = kx

This equation can be written as follows:

k = y/x

Using the coordinates of point on the graph we have:

k = 225/5 and k = 135/3

k = 45

Hence, the constant of proportionality for the given graph is k = 45.

Learn more about proportionality here:

https://brainly.com/question/29126727

#SPJ1

Answer: The probability of selecting a black marble then a red marble would be 1/20

Step-by-step explanation: 5/20 x 4/20 = 1/4 x 1/5 = 1/20

Answer:

Step-by-step explanation:

If cakes of 4 small and 4 large tiers serve 288 guests, and 3 small and 5 large tiers serve 316 guests, you want to know the number of guests served by a tier of each size.

Let 's' and 'l' represent the numbers of guests served by small and large cake tiers, respectively. The first cake serves ...

  4s +4l = 288

And the second cake serves ...

  3s +5l = 316

Subtracting 3/4 of the first equation from the second gives ...

  (3x +5l) -3/4(4s +4l) = (316) -3/4(288)

  2l = 100

  l = 50

  4s +4(50) = 288 . . . substitute for l in the first equation

  4s = 88 . . . . . . . . . . subtract 200

  s = 22 . . . . . . . divide by 4

A small tier will serve 22 guests; a large tier will serve 50 guests.

Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

Answer:

(9/10) of a pizza per hour.

Step-by-step explanation:

(3/4)*4=3

(5/6)*4= 3hr 20 mins

[3 (1/3)] / [3 (1/3)]=1

3 / [3 (1/3)]= 0.9

Answer:

X

Step-by-step explanation:

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.

Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.

The translation does not change the shape and size of the geometry. But changes the location.

Figure J is rotated 90° clockwise and then translated by 3 units toward the right.

More about the transformation of the shape link is given below.

https://brainly.com/question/27224339

#SPJ1

The sum of expected marks is given as follows:

9375.

Each question has four choices, hence the probability of choosing the correct choice is given as follows:

p = 1/4 = 0.25.

Then the expected number of correct answers is given as follows:

E(X) = 0.25 x 150

E(X) = 37.5.

Then the expected grade for a single student is given as follows:

37.5 - 0.25(150 - 37.5) = 9.375.

The expected sum for the 1000 students is then given as follows:

1000 x 9.375 = 9375.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

M = ((x1+x2)/2, (y1+y2)/2)

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

The six trigonometric ratios are \(\sin{\theta}\\\), \(\cos{\theta}\), \(\tan{\theta}\\\), \(\csc{\theta}\\\), \(\sec{\theta}\\\), \(\cot{\theta}\\\)

\(\sin{\frac{2\pi}{3}} = \sin{\frac{\pi}{3}} = \frac{\sqrt{3}}{2}\\\cos{\frac{2\pi}{3}} = \cos{\frac{\pi}{3}} = \frac{1}{2}\\\tan{\frac{2\pi}{3}} = \tan{\frac{\pi}{3}} = \frac{\sin{\frac{\pi}{3}}}{\cos{\frac{\pi}{3}}} = \frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}} = \frac{2\sqrt{3}}{2} = \sqrt{3}\\\csc{\frac{2\pi}{3}} = \csc{\frac{\pi}{3}} = \frac{1}{\sin{\frac{\pi}{3}}} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}}} = \frac{2\sqrt{3}}{3}\\\)

\(\sec{\frac{2\pi}{3}} = \sec{\frac{\pi}{3}} = \frac{1}{\cos{\frac{\pi}{3}}} = \frac{1}{\frac{1}{2}} = \frac{2}{1} = 2\\\cot{\frac{2\pi}{3}} = \cot{\frac{\pi}{3}} = \frac{1}{\tan{\frac{\pi}{3}}} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}\)

Using the corresponding angle theorem, the value of y is 36 degree.

In the given question, b||c.

We have to find the value of y.

Given: b||c

Find: Value of y

Let x be the value of side angle of (2y+34) degree.

So, using the corresponding angle theorem

x = 74 degree

As we know that the sum of straight line is 180 degree.

So 2y+34+x = 180

Now putting the value of x

2y+34+74=180

After simplifying

2y+108=180

Subtract 108 on both side, we get

2y=72

Divide by 2 on both side, we get

y=36

Hence, the value of y is 36 degree.

To learn more about Corresponding Angle Theorem link is here

brainly.com/question/16017873

#SPJ4

Team A performed 21 shows.

Team B performed 5 shows.

A = 4B + 1

B = A - 16

Substitute 4b + 1 for a in b = a − 16:

b = a − 16

b = 4b + 1 − 16

b= 4b − 15 (Simplify both sides of the equation)

b − 4b = 4b − 15 − 4b (Subtract 4b from both sides)

−3b = −15

−3b/−3 = −15/−3(Divide both sides by -3)

b=5

Substitute 5 for b in a = 4b + 1:

a = 4b + 1

a = (4)(5) + 1

a = 21

An equation is formed of two equal expressions. The number of concerts performed by A and B is 21 and 5, respectively.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of concerts performed by Singer A and Team B be represented by A and B, respectively.

Given that  Singer A performed more than four times as many shows during concert tours as Team B. Therefore, we can write,

A = 4B + 1

Also, the number of Singer A concert tour shows exceeded the number of shows by Team B by 16. Therefore,

A = B + 16

As we got two equations written for A, equate the two equations equal to each other as shown.

A = A

4B + 1 = B + 16

4B - B = 16 - 1

3B = 15

B = 15/3

B = 5

Now, substitute the value of B in any one of the equations of A,

A = B + 16

A = 5 + 16

A = 21

Hence, the number of concerts performed by A and B is 21 and 5, respectively.

Learn more about Equation here:

https://brainly.com/question/14686792

#SPJ2

Answer:

  (3, 7)

Step-by-step explanation:

Given that points (-4,9), (-6,-5), and (1.-7) are three vertices of a parallelogram with segments connecting them in order, you want the point that is the fourth vertex.

The diagonals of a parallelogram bisect each other, which means they have the same midpoint:

  ((-4, 9) +(1, -7))/2 = ((-6, -5) +(x, y))/2

Multiplying by 2 and subtracting the point on the right side, we have ...

  (-4, 9) +(1, -7) -(-6, -5) = (x, y)

  (-4 +1 +6, 9 -7 +5) = (x, y) = (3, 7)

The fourth vertex is (3, 7).

__

Additional comment

In general three points can define three possible parallelograms. Here, the segments connecting the points are presumed to be the sides of the parallelogram, so reducing the number of possibilities to just one.

The fact that the diagonal midpoints are the same is useful for solving a variety of problems involving parallelograms.

Answer:

-4 < x < 4

Step-by-step explanation:

The most general solution to the associated homogeneous differential equation is y=x/2-1/4

C=0

dy/dx+2y=x

Use the formula:

\(\int\ \,xe^(2x)dx=e^(2x)\)((x/2−1/4).

We know that a linear differential equation is written in the standard form:

y' + a(x)y = f(x)

we get that: a(x)=2 and f(x)=x.

We know that the integrating factor is defined by the formula:

u(x)=\(e^{\int\ \, a(x) dx}\)

⇒ u(x)=\(e^{∫ 2 dx}\)= \(e^{2x}\)

The general solution of the differential equation is in the form:

y=\frac{ ∫ u(x) f(x) dx +C}{u(x)}

⇒ y=\frac{\(e^{2x}\)· x dx  + 0}\({e^{2x}}\)

y=\frac{\(e^{2x}\) (x/2-1/4)\(}{e^{2x}\)

y=x/2-1/4

Hence, the most general solution to the associated homogeneous differential equation is y=x/2-1/4.

Learn more about differential equations at:

brainly.com/question/28099315

#SPJ1