The Humber Room advertises two types of entrée, meat and fish. It is known that 70% of all customers order meat, and 30% order fish. All customers are individually asked after their meals if they were satisfied with them. This survey shows that 80% of those who ordered meat and 95% of those who ordered fish were satisfied. Draw a probability tree for this problem to answer the question.

If M represents the event of ordering meat, F is the event of ordering fish, + is the event of being satisfied, and − is the event of not being satisfied, then answer the following questions:
(a) Determine the following probabilities based on the probability tree:

P(M)
P(F)
--------- Determine the conditional probabilities

(iii) P (+ M)
(iv) P (- M)
(v) P (+F)
(vi) P(-F)

(b) Write down the results of calculating the joint probabilities below:
P (M and +)
P (M and -)
P (F and +)
P (F and -)

(c) If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish?

Can someone please explain how to resolve this ?

Answer: X E R

Step-by-step explanation: y=2 x 2x+2

calculate the product

y=4x+2

The domain of a linear function is the set of all real numbers

x E R

a. Perimeter = 72 yd

b. Area = 640 yd².

a. To find the perimeter of the compound figure, we need to add the lengths of all four sides together.

The perimeter is equal to 16 yd + 32 yd + 16 yd + 8 yd = 72 yd.

b. To find the area of the compound figure, we need to separate the figure into two separate shapes and find the area of each.

The figure can be separated into a 16 yd by 32 yd rectangle and a 8 yd by 16 yd rectangle.

The area of the 16 yd by 32 yd rectangle is 16 yd x 32 yd = 512 yd² and the area of the 8 yd by 16 yd rectangle is 8 yd x 16 yd = 128 yd². The total area is 512 yd² + 128 yd² = 640 yd².

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For the given triangles ΔABC ≈ ΔXYZ, the length of the side AB is, 24

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔABC

Another triangle , which is ΔXYZ

Triangle ΔABC and ΔXYZ similar,

So, we can say ΔABC ≈ ΔXYZ

And it is known that

for similar triangles, ratio of lengths of sides are equal for similar triangles

so, AB/BC = XY/ZY

⇒   X/18   =  16/12

⇒   X   =  24

Hence, the value of x is 24

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The ratio of 2 days to 80 hours and 5 days to 80 hours is 1 day : 40 hours and 1 day : 16 hours respectively.

2, 5 days : 80 hours

So,

2 days : 80 hours

= 2/80

= 1/40

= 1 day : 40 hours

Also,

5 days : 80 hours

= 5/80

= 1/16

= 1 day : 16 hours

Hence, the ratio of days to hours is given by 1 day : 40 hours and 1 day : 16 hours respectively.

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Answer:

i hope this help

Step-by-step explanation:

If each question is worth 4 points, then 100 questions would be worth 400 points.

If Chee got 10 questions wrong, she would have answered 100-10 = 90 questions correctly.

Her score would be 90 x 4 = 360 points out of 400 points.

As a percentage, her score would be 360/400 x 100 = 90%.

If Chee got x questions wrong, her score would be (100-x) x 4 points.

Answer:

800

Step-by-step explanation:

I am not so sure because you didn't explain the question well

Answer:

πr2

Step-by-step explanation:

The formula of a circle/finding its area is pi(r)^2

Answer: The formula for the area of a circle is π r squared

The measure of the angle mABF found using the corresponding angles theorem is mABC = 79°

Corresponding angles are angles that formed by a transversal and parallel lines, which are located in the same relative positions, with regards to the transversal and the parallel lines.

The specified information are;

Angle ∠ACD and angle ∠ABF are corresponding angles formed by a common transversal and two parallel lines.

The measure ∠ACD = 79°

According to the corresponding angles theorem, the corresponding angles formed by two parallel lines, and their common transversal are congruent, therefore;

∠ACD ≅ ∠ABF

The definition of congruency indicates that we get;

m∠ACD = m∠ABF

The substitution property of equality indicates that we get;

m∠ACD = 79° = m∠ABF

m∠ABF = 79°

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The number 25 is the value at which the number sentence is true. An enumerated (numbered) list can be presented in sentence form in a variety of ways.

An enumerated (numbered) list can be presented in sentence form in a variety of ways. The number (not the number word) can be placed in parentheses in the following manner: I listed the following three causes: Here is my first justification, this is my second justification, and this is my third justification. A number sentence compares two numerical expressions and states their equivalence (or inequality).

Let the value be x

now 36 + 27 = 88 - x

36 + 27 = 88 - x

63 = 88 - x

x = 88 - 63

x = 25

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The value of y'(2) is 135/16.

The correct option is A.

Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

Given:

y = (x - 1/x)³

Differentiating the function with respect to x,

y' = 3x² +3/x⁴ - 3 - 3/x²

y'(2) = 12 + 3/16 - 3 -3/4

y'(2) = 135/16

Therefore, the value is 135/16.

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Se requiere agregar un volumen adicional de 24 yardas cúbicas para obtener una concentración de grava de 85 %.

Este problema es un caso de aplicación de promedios ponderados, en donde se mezcla un volumen de un porcentaje menor de grava con otro volumen de un porcentaje mayor de grava para obtener una mezcla con un porcentaje deseado. Esta situación queda descrita en la siguiente ecuación:

(6 yd³) · 65 + x · 90 = (6 yd³ + x) · 85

Donde x es el volumen del cargamento de grava al 90 %, en yardas cúbicas. A continuación, procedemos a determinar el volumen requerido:

390 + 90 · x = 510 + 85 · x

5 · x = 120

x = 24 yd³

No aparecen problemas verificados en español sobre promedios ponderados. Se ha agregado un problema en inglés por defecto.

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Peeta worked 9.41 hours on Sunday. The equation 5.5h + 90.2 = 142.2 can be used to determine the number of hours Peeta worked given his earnings.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Let h be the number of hours that Peeta worked on Sunday. We know that he earned $5.50 per hour and $90.20 in tips. So, his total earnings can be represented as:

5.5h + 90.2 = 142.2

Solving for h:

5.5h = 142.2 - 90.2
5.5h = 52

h = 52 / 5.5
h = 9.41 hours

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Applying the angle bisector theorem, the lengths are:

A. KL = 2.4, LW = 3.6

The Angle Bisector Theorem states that in a triangle, the ratio of the length of a side to the length of another side is equal to the ratio of the length of the angle bisector of one of the angles to the angle bisector of the corresponding angle.

In other words, if two angles of a triangle have angle bisectors of lengths x and y, then x/y = a/b where a and b are the lengths of the sides of the triangle corresponding to the bisected angles.

Based on the angle bisector theorem, we have:

(6 - x)/(x) = 4/6

Cross multiply:

4x = 6(6 - x)

4x = 36 - 6x

4x + 6x = 36

10x = 36

x = 36/10

x = 3.6

LW = x = 3.6

KL = 6 - x = 6 - 3.6 = 2.4

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The value of x is 16.2.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Perpendicular = 18

Base = x

Tan Ф = Perpendicular / Base

Tan 48 = 18 / x

1.11 = 18/x

Solve for x.

1.11 = 18/x

x = 18/1.11

x = 16.22

x = 16.2

Thus,

x is 16.2

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The value of 30 dollars in British pounds is 24.3

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We have to convert the 30 us dollars to the British pounds

The value of one dollar in pounds is 0.81

Now let us calculate for 30 dollars

30×0.81

24.3 pounds

Hence, the value of 30 dollars in British pounds is 24.3

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Answer: 500

Step-by-step explanation:

25 x 20 = 500

The person who used more water was Sam and the person who's plant grew the least was Jessica.

The person who used more water in watering their plants is the person who used the most liters of water when they watered their plants. This person is Sam, who used 0. 89 liters of water on his plants every day.

Jessica on the other hand, water less at 0. 87 liters per day. As a result, Sam's plants grew the most was they grew 2. 35 feet, while Jessica's plants grew 2. 32 feet.

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We are given two triangles ABC and DEF... it is given that they are similar and we know that when 2 triangles are similar the ratio of their corresponding sides are equal... Here, the corresponding sides are AB/DE and BC/EF but maryam has taken the wrong ratio.. Maryam has taken AB/EF and BC/DE...

AB/DE = BC/EF

x/18 = 16/12

x/18 = 4/3

3x = 72

x = 24m

Answer:

Step-by-step explanation:

Are you asking to have this sentence put into a mathematical expression?  If so, I think the answer is:

y = (1/4)(x + 8) = 1/4 x + 2

If the customer's water bill was $24.79, 4500 gallons of water were used by the general public as a result.

Quantity and their permutations, theorems and surrounding structures, figures and their locales, and venues where they can found are all parts of the mathematics course of study. The interaction of both a group of values, each of which produce a collective agreements, is referred to as a "function." A utility is a linkage between and outputs where each input produces a single, unique result. Every action has a region but a codomain, often termed as a scope. F is frequently utilised denote formulas (x). An x is the input. In light of the following criteria, there are four primary categories of functions that are available: on functions, yet another functions, so several operations, within functions, and then on functions.

given

(A) given that 7.5 falls between 5 and 8,

As a result, in order to determine C(7.5), we must utilize the definition of C(g) for 5 g 8

Considering that C(g) = 3.75(g - 5) + 19.16, 5 g > 8

calculating g = 7.5

C(7.5) = 3.75(7.5 – 5) + 19.16 = 28.535

Water usage is represented by g, and C(g) provides the cost (before taxes) for that.

In other words, the cost to the citizen before taxes for 7500 gallons of water use will be 28.535.

(B) We must apply the definition of C(g) for g > 8 because 8.2 > 8.

C(g) = 5.33(g – 8) + 30.14, g > 8

So, C(8.2) = 31.206

C(g) = $17.52

C(g) has a value of 19.16 30.14.

If the customer's water bill was $24.79, 4500 gallons of water were used by the general public as a result.

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The lateral surface area of the pyramid is 200 square inches.

A three-dimensional figure is a pyramid. Its base is a flat polygon. The remaining faces are all triangles and are referred to as lateral faces. The number of sides on its base is equal to the number of lateral faces. The line segments that two faces intersect to form its edges. The intersection of three or more edges forms a vertex.

We know the lateral surface area of a pyramid is = (1/2)×P×h, where P is the perimeter of the base.

Given, Each side of the base of a square pyramid measures 10 inches.

So, The perimeter of the pyramid is 4×10 = 40 inches.

Therefore, The lateral surface area of the pyramid is = (1/2)×40×10.

= 200 square inches.

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Answer:

The slope of the line is -5/7

Step-by-step explanation:

[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}=\frac{-1-4}{4-(-3)}=\frac{-5}{4+3}=-\frac{5}{7}[/tex]

the 25 brick masons complete the same job in 120 hours.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

It took 10 brick masons 300 hours to brick a new home.

1 brick mason will take 300*10 =3000 hours

So 25 brick masons will take 3000/25 = 120 hours.

Hence the 25 brick masons complete the same job in 120 hours.

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The production level that achieves a marginal cost of $0.50/L is 1875 litres.

To find the average cost of producing 625 L of maple syrup, we need to find the total cost of producing that amount, and then divide by the number of litres. The total cost can be found using the cost function:

C(x) = 75(√x - 10)

C(625) = 75(√625 - 10) = 75(25 - 10) = 75(15) = 1125

The average cost per litre is the total cost divided by the number of litres:

Average cost = Total cost / Number of litres = 1125 / 625 = 1.8

b. The marginal cost is the derivative of the cost function:

C'(x) = 75(1/(2√x))

C'(1225) = 75(1/(2√1225)) = 75(1/(35)) = 75/35 = 2.14

c. To find the production level at which the marginal cost is $0.50/L, we set the derivative equal to 0.50 and solve for x:

0.50 = 75(1/(2√x))

0.50 * 2√x / 75 = 1

√x = 75 / (2 * 0.50)

x = (75 / (2 * 0.50))^2

x = 1875

So the production level that achieves a marginal cost of $0.50/L is 1875 litres.

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Answer:

d. x = 7

Step-by-step explanation:

[tex]\frac{32}{8} = \frac{28}{x}[/tex]

Cross multiply, the denominator "8" is multiplied by numerator "28", while the numerator "32" is multiplied by denominator "x":

8 * 28 = 224

32 * x = 32x

[tex]32x = 224[/tex]

Divide both sides by 32:

[tex]\frac{32}{32} = \frac{224}{32}[/tex]

[x = 7]

Step-by-step explanation:

At Big Time Pizza, you would need to add 5 toppings in order for the pizza to cost the same as a medium pizza from PizzaPizza, which would cost $9.50. At PizzaPizza, you would need to add 8 toppings in order for the pizza to cost the same as a medium pizza from Big Time Pizza, which would cost $9.50.

If a large equilateral triangle pyramid stands in front of the city's cultural center. The time  it take the painter to paint 75% of the pyramid is 10.8 hours.

The area of the base is:

(1/2) * 40 * 40

= 800 square feet

The area of one lateral face is:

(1/2) * 50 * 40

= 1000 square feet

So, the total area of all four lateral faces is:

4 * 1000

= 4000 square feet

The total surface area of the pyramid is:

800 + 4000 = 4800 square feet

To paint 75% of the pyramid, the painter needs to paint:

0.75 * 4800

= 3600 square feet

Time it will take them is:

3600 / 100 * 18

= 648 minutes or 10.8 hours

Therefore painter will take approximately 648 minutes, or 10 hours and 48 minutes, to paint 75% of the pyramid.

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f(x) and g(x) are closed under subtraction because when subtracted, the result is also a polynomial.

Option B is the correct answer.

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

f(x) = a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex]

g(x) = b(0) + b(1)x + b(2)x² + .......... + b(n)[tex]x^n[/tex]

Now,

f(x) - g(x)

=  a(0) + a(1)x + a(2)x² + ......... + a(n)[tex]x^n[/tex] -  b(0) - b(1)x - b(2)x² - .......... - b(n)[tex]x^n[/tex]

= (a(0) - b(0)) + (a(1) - b(1))x + (a(2) - b(2))x² + ........... + (a(n) - b(n))[tex]x^n[/tex]

This is also a polynomial.

Thus,

f(x) and g(x) are closed under subtraction.

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1) The value of x in the triangle is; x = 25

2) The measure of each interior angle is;

25°, 40° and 115°

Exterior angle = 65°

In a triangle, from the exterior angle property, we know that the exterior angle is always equal to the sum of the interior opposite angles. Thus, we say that any two triangles will be similar provided that their corresponding angles tend to be congruent and the length of their sides will be proportional.

Thus;

x + 15 + 25 = 3x - 10

3x - x = 25 + 15 + 10

2x = 50

x = 50/2

x = 25

The measure of each interior angle is;

25°

25 + 15 = 40°

180 - (25 + 40) = 115°

Exterior angle = 180 - 115 = 65°

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