Reflect point M across the axis

The ships and the port form a right triangle and hence, their distance is 72.1 nautical miles

Knot is a velocity unit equals to nautical miles per hour.

The situation can be depicted in the attached picture.

The distance travelled by the 1st ship after 2.5 hours is:

s1 = 16 knots x 2.5 hours = 40 nautical miles.

The distance travelled by the 2nd ship id:

s2 = 24 knots x 2.5 hours = 60 nautical miles.

Since the angle difference between those 2 ships is 90⁰, the distance between the ships can be obtained using the Pythagorean Theorem.

Referring to the attached picture,

d² = 40² + 60²

d² = 1600 + 3600

d² = 40² + 60²

d² = 5200

d = 72.1 nautical miles

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The numerical value of side RS of the rectangle with a perimeter of 144 units is 30 units.

A rectangle is simply a 2-dimensional shape with parallel opposite sides equal to each other and four angles are right angles.

The perimeter of a rectangle is expressed as;

P = 2( l + w )

Given the data in the question;

First we determine the value of the variable z, plug the given values into the perimeter formula and solve for z.

P = 2( l + w )

144 = 2( (4z + 2 ) + (3z) )

144 = 2( 4z + 2+ 3z )

144 = 2( 7z + 2 )

144 = 14z + 4

14z = 144 - 4

14z = 140

z = 140/14

z = 10

Now, find the numerical value of side RS.

Width RS = 3z

RS = 3( 10 )

RS = 30

Therefore, the length of side RS of the rectangle is 30 units.

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Answer:

the answer is A

Step-by-step explanation: the reason i said A is because the answer is litteraly in the question if you think about it

Answer:

A)

If you are driving many miles a day, Alpha Car Rental is cheaper. If you are driving fewer miles a day, then Amazing Car Rental is cheaper.

B)

You can find this out by graphing the 2.

Alpha: y = 0x + 72.

Amazing: y = 0.30x +22.9

Where y is cost, and x is miles.

When you graph the 2, Alpha is a straight line because it has no mileage charge. The 2 linear functions meet at point (163.6, 72). Meaning if you drive more than 163 miles, it is cheaper to use Alpha Car Rental over Amazing Car rental.

Hope that helps

The number of bottled drinks bought by Marisol is 10 in the student council party.

For the given linear equation;

The total budget of the party is $50.

The linear function function which represents the number of pizzas x and the number of bottled drinks y is;

15x + 2y = 50

Now, the number of pizza bought = 2.

To find the value of bottled drinks, put x = 2 in the linear function.

15×2 + 2y = 50

Simplify the equation;

30 + 2y = 50

2y = 50 - 30

2y = 20

y = 10

Thus, the total number of bottled drink bought by the Marisol is 10.

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The probability that the three tax returns submitted were self-prepared is 0.0325.

So, the formula for the binomial probability distribution of x successes in n tries:

Where the probability of success is p, and n is the number of trials.

If three electronically filed tax returns are randomly chosen, the likelihood that all three were prepared by the taxpayer is given by:

Therefore, the probability that the three tax returns submitted were self-prepared is 0.0325.

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The correct question is given below:

Suppose that a poll finds that 31.9​% of taxpayers who filed their tax returns electronically​ self-prepared their taxes. If three tax returns submitted electronically are randomly​ selected, what is the probability that all three were​ self-prepared?

The two events are mutually exclusive if they cannot occur at the same time. A triangle is equiangular if it is equilateral. The two events are mutually exclusive if they cannot occur at the same time.

What pairs of occurrences can never coexist?

Two events are mutually exclusive in statistics and probability theory if they cannot happen simultaneously.

A coin toss is the most basic illustration of two events that cannot coexist. The result of tossing a coin can be either heads or tails, but neither outcome can happen at the same time.

What are some examples of mutually exclusive events?

Several instances of occurrences that can never occur simultaneously include:

The outcomes of receiving head or tail while flipping a coin are mutually exclusive.

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Answer:

[tex]{ \rm{ - \frac{2}{3}( - \frac{1}{5} ) }} \\ \\ = { \rm{( - 1 \times - 1)( \frac{2}{3} \times \frac{1}{5} )}} \\ \\ = { \rm{( \frac{2 \times 1}{3 \times 5} )}} \\ \\ = { \rm{ \frac{2}{15} }}[/tex]

Answer: [tex]\frac{2}{15}[/tex]

Step-by-step explanation:

1. Simplify the expression

[tex]-2/3(-1/5)[/tex]

2. Multiply the fractions

[tex]\frac{\left(-2\cdot -1\right)}{\left(3\cdot 5\right)}\\[/tex]

3. Simplify the arithmetic

[tex]\frac{2}{\left(3\cdot 5\right)}[/tex]

4. Simplify the arithmetic

[tex]\frac{2}{15}[/tex]

The current temperature based on the information given about Sussane is 74°.

It should be noted that temperature is used to illustrate the hotness and the coldness that's in a a particular body.

Let the current temperature be represented as x.

Since Susanne checks the temp. at 11:00am and she notices that if the temp. rises by 8 more degrees it will break the record high temp. for the day witch is 82 degrees, the current temperature will be:

x + 8 = 82

x = 82 - 8

x = 74°

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Answer:

x = 7 units

Step-by-step explanation:

Left area = (3x-1)(4)

Right area = 8*12  - (4 (  x -3))     and the areas are =

(3x-1)4 = 8*12 - ( 4(x-3))    expand both sides

12x - 4  = 96 - 4x + 12       solve for x = 7 units

Answer:

Area of big rectangle: 8 x 12 =96

Area of white part : 4(x-3)

96-(4(x-3))

96-(4x-12)

96-4x+12

Area of rectangular grey part: 108-4x

Area of other grey figure:

4(3x-1)

= 12x- 4

Finding x:

12x-4 = 108 -4x

-4-108 = -4x - 12x

112 = 16x

x= 7

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Answer:

See below

Step-by-step explanation:

Comment

This is a good question. It makes you think about when you should round and maybe when you shouldn't.

You have a building side that is 38 square yards. You want to know how much paint to buy to cover the given side.

Let us say that each can of paint could cover 5 square yards. You cannot buy any can that might be smaller to take care of the 3 remaining square yards.

You have no choice. You have to round the answer from 7 R 3 to 8.

Total 20 students should go to the trip to not to lose money.

Cost of bus = 100 dollars

For students the charge is 7 dollars per student.

Amount professor donated to defray the cost is 40 dollars.

School is charging 10 dollars per student for the trip.

Therefore, reduced cost = 100 - 40 = 60 dollars

Profit earned from each student is 10 - 7 = 3  dollars.

Hence, minimum students should go to the trip will be 60 ÷ 3 = 20.

Since, 20 × 3 = 60, the cost is covered and no money is lost.

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Answer:

8p+32

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

The greatest divisor of 8 that is less than 18 is 16, and 16 divided by 8 is 2.

The next digit of quotient is 16.

Here given that,

4184 is divisible by 8

since we know that,

Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.

4184 is divisible by 8 we get,

⇒ 4148/8

⇒ 516

So, the quotient is 516

Hence,

The next digit is 16.

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John is putting 10 books in a row on his bookshelf. he would arrange it in

40,320 ways.

Generally, A permutation is a rearrangement of a set of elements. In other words, it is a way to arrange a set of items in a specific order. For example, the permutations of the set {1, 2, 3} are {1, 2, 3}, {1, 3, 2}, {2, 1, 3}, {2, 3, 1}, {3, 1, 2}, and {3, 2, 1}. The number of possible permutations of a set of n elements is n!.

John is placing 8 books on the shelf in between Pride and Prejudice and Little Women.

The number of ways to arrange these 8 books is 8! (8 factorial).

since the order of the books in the first and last spots is predetermined,

The final answer is 8! = 40320ways

= 40,320 ways.

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Answer:

y = 3

Step-by-step explanation:

given y is inversely proportional to x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of proportion

to find k use the condition x = 3, y = 8

8 = [tex]\frac{k}{3}[/tex] ( multiply both sides by 3 )

24 = k

y = [tex]\frac{24}{x}[/tex] ← equation of proportion

when x = 8 , then

y = [tex]\frac{24}{8}[/tex] = 3

Answer

3

Step-by-step explanation:

when one is increasing the other one should decrease.since 3 has increased by 5 ,then y should decrease by 5.

The answer to the following verbal expressions of inequality are:

A: x ≤ 69;

B: The option that shows the graph of the inequality d<2 is Option C.

C: The option that shows the graph of the inequality of x ≤ 5 is option B.

D: represents the graph of the inequality given in option C that is x > -8

E: The inequality that describes the situation is ≥ 49 (Option B)

In mathematics, inequality is defined as a declaration of an order connection between two integers or algebraic expressions (greater than, greater than or equal to, less than, or less than or equal to).

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You can see the following steps to know the solvation

x² = 36

x = √36

x = 6.

Answer: C.

Step-by-step explanation:

X would represent the number of golf balls he brought back and .10 is the amount of money he makes for each of them.

Answer:

0.10x

Step-by-step explanation:

x stands for the amount of golf balls he brings back to the shop and 0.10 stands for the 10 cents he gets paid for each ball.

In the given parallelogram,

∠W = 85°

∠WXV = 59°

Since, VW is parallel to XY,

So,

∠YVX = ∠WXV ............... (Alternate interior angles)

⇒ ∠YVX = 59°

Now,

∠W = ∠Y .................. (Opposite angles of a parallelogram are equal)

⇒ ∠Y = 85°

As we know that opposite sides of a parallelogram are equal,

Therefore,

VW = YX

⇒ 2x = 6

⇒ x = 6/2 = 3 units

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Answer:

most have 455 T-shirts

Step-by-step explanation:

if u do $7,280÷$16= 455

Answer:most have 455 T-shirts

Step-by-step explanation:if u do $7,280÷$16=

566567889988766433678

Answer:

$3.25

Step-by-step explanation:

This question tests on the concept of conversion.

Given from the question,

8.5 pounds = $27.63

(8.5 ÷ 8.5) pounds = $27.63 ÷ 8.5

1 pound = $3.25 (Rounded off to 2 decimal places)

Yes the acceptable move that proves the two equation are equivalent.

What is equivalent equation?

equivalent equation are algebraic equations that have identical solutions or roots. Adding or substracting the same number or expression to both side of an equation produce an equivalent equation. Systems of equations that have the same solutions are said to be equivalent equations. Finding and resolving equivalent equations is an important skill for everyday life as well as for algebra classes. Consider some illustrations of equivalent equations, how to solve them for one or more variables, and practical applications of this knowledge.

Sol-

By observing both equations

In equation A : -3(x+9)=18

Divide the equation A by -3

=> (x+9)=-6

And this result equals to equation B

Hence both equations are equivalent

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The cost of a rugby ball is $6.57

The cost of a golf ball is $1.75

Let x represent the cost of a rugby ball and y represent the cost of a golf ball

2x + 3y= 18.39.........equation 1

5x + 7y= 45.10.........equation 2

multiply equation 1 by 5 and equation 2 by 2

10x + 15y= 91.95

-

10x + 14y= 90.2

y= 1.75

Substitute 1.75 for y in equation 2

5x + 7(1.75)= 45.10

5x + 12.25= 45.10

5x= 45.10-12.25

5x= 32.85

x= 32.85/5

x= 6.57

Hence the cost of a rugby ball is $6.57 and the cost of a golf ball is $1.75

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Answer:

Step-by-step explanation:

rhombus formed by 4 right triangles, 51ft hypotenuse and 45ft cathetus (90: 2 = 45). we use pythagoras to find the missing side so that we can find the area of ​​a triangle and multiply it by 4

c = √(51²-45²)

c = √(2601 - 2025)

c = √576

c = 24ft

Area triangle= (½)×b×h

(½)45 * 24 =

(½)1080=

540ft²

multiply by 4

540 * 4 =

2160ft² (Area of the rhombus)

or

Rhombus Area Using Diagonals:

A = ½ × d1 × d2

A = ½ * 90 * 48

A = 2160ft² (Area of the rhombus)

Answer: x=17

Step-by-step explanation:

1.Identify relationship

Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary

2. set up equation

because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180

3. solve the equation

3x+6+123=180

3x+129=180 | combine like terms

3x=51 | subtract 123 from both sides

x=17 | divide by 3 on both sides

By using the method of subtraction, the profit earned by charles is £4.8

To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The action of subtracting a matrix, vector, or other quantity from another according to predetermined rules in order to find the difference.

Given that,

There are 15 pens in each pack.

Each pack costs £4.20.

Charles sells each pen for 60p but he only manages to sell of the pens.

60p x 15 = 9

So, the profit earned by charles is 9- 4.20 = 4.8

Therefore, the profit earned by charles is £4.8

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