Fifty percent of the customers who go to ABC Tires for tires buy four tires and 32% buy two tires. Moreover, 13% buy fewer than two tires, with 6% buying none. a. What is the probability that a customer buys three tires? (Round your answer to 2 decimal places.) b. Construct a cumulative probability distribution for the number of tires bought. (Round your answers to 2 decimal places.) x P(X ≤ x) 0 1 2 3 4

Shaded region in venn diagram is the common area of set A and set B. It represent A∩B.

How to present a set can also be expressed with a picture or diagram called a Venn Diagram. The Venn diagram was introduced by a British mathematician named John Venn (1834 – 1923).

Instructions for creating a Venn diagram include:

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If knowing the probability of an event occurring is known then it can be turned into one's favour as well as it can be obstructed if not in favour.

A way to determine the likelihood of something occurring is through probability. Many things are hard to predict with 100 percent certainty. We can only predict the likelihood of an event occurring or how likely it is using it. A probability can be between 0 and 1, with 0 signifying an impossibility and 1 signifying a certainty.

If the likelihood of an event occurring is known, one can attempt to influence the outcome in accordance with the likelihood.

The possibility of altering the likelihood that the event will go in one's favour is another useful tool.

Therefore, being aware of the probability can be beneficial.

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The point (-5,-3) reflected over the y-axis is (5, -3).

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

(-5, -3)

Along y-axis:

(x, y) → (-x, y)

So,

(-5, -3) → (-(-5), -3) = (5, -3)

Thus,

(5, -3) is the reflected point.

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Answer:8k

Step-by-step explanation:i did the test and got it write

Answer:

i- 72000 * π radians per hour,  ii- 65,940 miles per hour.

Step-by-step explanation:

(i) To find the car's angular speed in radians per hour, we need to find the number of radians the wheel rotates in one revolution, then multiply that by the number of revolutions per second. The number of radians in one revolution is equal to the circumference of the wheel divided by the wheel's radius. The wheel's circumference is given by 2 * π * r, where r is the wheel's radius (18 inches / 2 = 9 inches). Then, the number of radians per revolution is:

2 * π * r / r = 2 * π

So, the number of radians per second is:

2 * π * 10 revolutions per second = 20 * π radians per second

Finally, to convert radians per second to radians per hour, we multiply by 3600 (the number of seconds in an hour):

20 * π * 3600 seconds/hour = 72000 * π radians per hour

(ii) To find the car's linear speed in miles per hour, we need to multiply the wheel's circumference by the number of revolutions per hour. The wheel's circumference is given by 2 * π * r, so the linear speed is:

2 * π * r * 10 revolutions per second * 3600 seconds/hour = 18 * π * 10 * 3600 miles per hour

The answer is approximately equal to 65,940 miles per hour.

Is your 2050 prediction realistic?

No, the 2050 prediction is not realistic because the literacy rate cannot exceed 100%

Given data is

x0=1976, y0=63.2

x1=2001, y1=86.7

x2=2012, y2=94.5

Then the Lagrange interpolation formula is

[tex]y - y_1 = \frac{y_2 - y_1}{x_2 -x_1} (x - x_1)[/tex]

Here we have to interpolate to predict the literacy rate in 1992.

i.e. x=1992.

It lies between 1976 and 2001.

Then

x1=1976, y1=63.2

x2=2001, y2=86.7

Then interpolation function become

[tex]63.2 + \frac{23.5}{25}(16)[/tex]

= 63.2 + 15.04 = 78.24

i.e. The predicted literacy rate in 1992 is 78.24%.

Now, to find the literacy rate in 2050, we have to use extrapolation.

Since, 2050 is not in between any of the given data, we will have to take last two datas.

i.e.

x1=2001, y1=86.7

x2=2012, y2=94.5

And x=2050.

Then our extrapolation formula become

[tex]86.7 + \frac{7.8}{11} (49)[/tex]

= 86.7 + 34.75

=121.45

i.e. The literacy rate in 2050 is 121.45%.

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Answer: A = 6

Step-by-step explanation: Here to help! So, if "a" wants to know the numerator of the fraction, all you have to do is to multiply 0.6 by 10, and that would get you 6/10. 6/10 is equivalent to 60% or 0.6. :))))

The total amount of acid in the final equation solution is 700% + 420% = 1120%, which is 40% of the total volume:

In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.

Here,

Let x be the number of liters of pure acid solution needed, and y be the number of liters of 20% acid solution needed to make 28 liters of a 40% acid solution.

x + y = 28 (total volume of the solution)

100x + 20y = 40(28) (total amount of acid in the solution)

Simplifying the second equation, we get:

100x + 20y = 1120

Dividing both sides by 20, we get:

5x + y = 56

Now we can solve the system of equations by substitution or elimination. Here we will use the substitution method.

Solving the first equation for y, we get:

y = 28 - x

Substituting this expression for y into the second equation, we get:

5x + (28 - x) = 56

Simplifying and solving for x, we get:

4x = 28

x = 7

So the technician needs 7 liters of pure acid solution and 21 liters of 20% acid solution to make 28 liters of a 40% acid solution.

To check this answer, we can calculate the amount of acid in each solution and verify that the total amount of acid in the final solution is indeed 40%.

7 liters of pure acid solution contain 7 × 100% = 700% acid.

21 liters of 20% acid solution contain 21 × 20% = 420% acid.

The total amount of acid in the final solution is 700% + 420% = 1120%, which is 40% of the total volume:

1120% ÷ 28 liters = 40%

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The new function of Jennifers's investment is f(t) = 50000 * (1.15)^t

From the question, we have the following parameters that can be used in our computation:

Initial investment, a = 50000

Rate of growth, r = 15%

Using the above as a guide, we have the following:

f(t) = a * (1 + r)^t

Substitute the known values in the above equation, so, we have the following representation

f(t) = 50000 * (1 + 15%)^t

So, we have

f(t) = 50000 * (1.15)^t

Hence, the function is f(t) = 50000 * (1.15)^t

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Complete question

ennifer starts a new investment account that grows exponentially. Her financial advisor tells her the initial investment of $50,000 grows at a rate of about 15% annually.

Write a new function, N(t), that represents the amount of money in Jennifer’s new account after t years. Be sure to use correct notation

The phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

A ratio in mathematics shows how many times one quantity is present in another.

For instance, if a dish of fruit's fully oranges and six lemons, the ratio of oranges and lemons is eight to six.

This ratio of oranges to the overall amount of fruit is 8:14, and the ratio of lemons and oranges is 6:8.

Two quantities are compared to form a ratio.

An equality of two ratios is a percentage.

So, the following are some of the car models that Alex has collected:

There are 8 airplanes.

There are 4 trains in all.

There are 12 vehicles.

Consequently, the car-to-train ratio is 12:4.

This is further simplified to its most basic form:

= 12:4

= 3:1

Therefore, the phrase "3 over 1" would be used to describe the proportion of vehicles to trains. The (C) option is that.

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Complete question:

Alex has a collection of vehicle models. He built 8 model airplanes, 4 model trains, and 12 model cars. Write a ratio to represent the ratio of cars to trains.

A. 12:24 FAST HELP

B. 1:3

C. 3 over 1

D> 4 to 12

The perimeter of the square is 12√2 units

A square is a quadrilateral that has all it's sides equal and all it's angles equal. The sum of interior angles of a square is 360°. This means that each angle of a square is 90°.

The perimeter of a square is obtained by adding all the sides.

Therefore the perimeter of a square = 4l

A (-1,4) and B ( 2,7)

line AB = √2-(-1))² + (7-4)²

AB = √ 3²+3²

AB = √9+9

AB = √18 units

therefore since the sides of a square are equal, the perimeter = 4× √18

= 4×3√2

= 12√2 units

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Answer:

Option A. 12√2 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

The wooden frame is a cuboid

and the volume of a cuboid = Length x Width x Depth

Therefore,

The volume of this wooden frame = (8 feet) x (5 feet) x (4 feet)

                                                         = 160 cubic feet

The purchasing rate for the sand is $20 per cubic meter (which is NOT the same as cubic feet)

Unit conversion has to be applied then:

1 foot = 0.3048 meters

1 cubic feet = (0.3048 meters) x (0.3048 meters) x (0.3048 meters)

                                           1 cubic feet = [tex]0.3048^{3}[/tex] cubic meters

Therefore:                     160 cubic feet = (160)([tex]0.3048^{3}[/tex]) cubic meters

                                                                 Cost of sand:
                                                          1 cubic meter = $20

     Therefore:             (160)([tex]0.3048^{3}[/tex]) cubic meters = $(20)(160)([tex]0.3048^{3}[/tex])

                                                                                = $90.61

                                                           = $91 (Rounded to the nearest dollar)

It will cost Andrea $91 to purchase sand for the sandbox

Answer:

3/8 feet²

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

Area of the rectangle is the product of its two dimensions:

Substitute the dimensions and find the area:

The volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis is 8π/3 cubic units.

The volume of the solid generated by revolving this region about the x-axis can be found using the method of cylindrical shells. The volume is given by:

V = ∫[0, 2] 2πx(2 - 2√x) dx

Evaluating the definite integral:

V = π ∫[0, 2] (4x - 4x^(3/2)) dx

= π [2x^2 - 4/3 x^(3/2) ] |_0^2

= π [4 - (4/3)(2^(3/2))]

= 8π/3.

Therefore, the volume of the solid generated by revolving the region bounded by the lines y = 2 and y = 2√x and the x-axis about the x-axis is 8π/3 cubic units.

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--The question is incomplete, answering to the question below--

"Find the volumes of the solids generated by revolving the regions bounded by the lines and curves about the x-axis

y=2√x, y=2, x=0"

Angle of triangle AFC is 37°

An angle is the formed when two lines meet at the same vertex. It is measured is degrees. There are three types of angles based on their measurements.

From the given figure consider ABCF as trapezium,

Given that angle of triangle BCF is 37°

Two pairs of adjacent angles of a trapezium formed between the parallel sides and one of the non-parallel side, add up to 180°

Therefore, ∠BCF + ∠CBF = 180°

                                  ⇒∠B = 180° - 37°⇒143°

Similarly ∠A = ∠B = 143°

⇒∠A+∠F=180°

⇒∠F=180°-143° ⇒ 37°

Hence, m∠AFC = 37°.

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Answer:

A vertical line that passes through the coordinate (25, 0).

Equation of the vertical line is x = 25

Step-by-step explanation:

2x = 50

x = 25

The original cost of the sweater is $60.

Percentage is simply defined as the parts of a number per fraction of 100.

Percentage is usually denoted by the symbol '%'.

Percentage of a number in a whole can be calculated by dividing the number by the whole and then multiply with 100.

Given that,

A sweater is on sale for a 20% discount. The amount of the discount is $12.

Percentage of discount = 20%

Amount of the discount = $12

Let x be the original cost of the sweater.

20% of x = 12

0.2x = 12

x = 60

Hence the original price of the sweater was $60.

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To better understand the relationship between education level and organic produce sales, we need to have data on these variables.

The data would typically be in the form of a table or a graph, with education level on one axis and organic produce sales on the other. Once we have the data, we can look at the pattern of the points to determine the relationship between education level and organic produce sales. If there is a positive relationship between the two variables, then as the education level increases, we would expect to see an increase in organic produce sales. This positive relationship could be represented by a line that slopes upward from left to right on a graph.

The slope of the line represents the rate of change of organic produce sales with respect to education level. A steep slope would indicate that even small changes in education level lead to significant changes in organic produce sales, while a shallow slope would suggest that changes in education level have little effect on organic produce sales.

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H is a subgroup of G since it is closed under the group operation, contains the identity element and inverses of its elements.

A subset H of a group G is a subgroup of G if it satisfies the following three properties:

1. Closure: H is closed under the group operation, that is, if α, β∈H then αβ∈H.

2. Identity element: H contains the identity element e of G.

3. Inverses: For each element α∈H, its inverse (or reciprocal) α−1 is also an element of H.

In this case, the subset of G consisting of elements of finite order (H) satisfies all of these three properties. Since H is closed under the group operation, if α, β∈H then αβ∈H. The identity element of G, e, is also an element of H since the order of the identity element is always 1, which is finite. Finally, for each element α∈H, its inverse α−1 is also an element of H since the inverse of a finite order element is also of finite order. Therefore, by satisfying all of the three properties of a subgroup, H is indeed a subgroup of G.

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[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 5 &\implies x -5=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +2 )( x -5 ) = \stackrel{0}{y}}\hspace{5em}\stackrel{\textit{since the leading coefficient is 2, let's a = 2}}{2(x+2)(x-5)=y} \\\\\\ 2\stackrel{\textit{F O I L}}{(x^2-3x-10)=y}\implies \boxed{2x^2-6x-20=y}[/tex]

Answer:

1.55 x [tex]10^{15}[/tex]

or 1,550,000,000,000,000

Step-by-step explanation:

2.5 x 1.034 x [tex]10^{3}[/tex] x 6 x [tex]10^{11}[/tex]

15.51 x [tex]10^{14}[/tex]

1.551 x [tex]10^{15}[/tex]

Answer:

Below

Step-by-step explanation:

This is an exercise in 'completing the square'

x^2 - 6x -3      

   take 1/2 of the x coefficient  (6) square it and add it and subtract it

x^2 - 6x + 9    - 9   - 3        Now you can reduce the underlined portion

(x-3)^2      - 12          a = 3   b= -12          Done

The Height is 10 inch and radius is 10 inch.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as litres, gallons, pounds, etc., volume is measured in cubic units.

Given:

Volume = 10,000π in³

Volume of b= π r² h

So, 10,000π= π r² h

10,000 =  r² h

r² h = 10 x 10 x 10

r² h = 10² x 10

Now, comparing the values

r= 10 inch and h= 10 inch

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Answer:

Step-by-step explanation:

The formula for the area of a triangle is:

1/2×base×height

If you know the area of the triangle and height you can apply the area formula:

A=1/2×base×height

in reverse to calculate the length of the base:

b=2A/h

given, h=60dam

A=18

so, b=2×18/60

b=36/60

b=0.6

The answer is 0.6

Natural numbers: 0.1 Whole numbers: 0, Integers: -7, -3, 0, 1, Rational numbers: -7.2, -3.0, 0.1, 3.5,Irrational numbers: √5, √64, Real numbers: -7.2, -3.0, 0.1, √5, 3.5, √64.

Natural numbers are the positive integers, 1, 2, 3, 4, 5, and so on. They are also known as the counting numbers or the positive integers. They are the numbers used for counting and measuring. Natural numbers are the building blocks of mathematics, and are used in the formation of other number systems, such as integers, rational numbers, real numbers, and complex numbers.

Natural numbers are also used in the formation of equations and formulas, as well as in the counting of objects, in the measurement of distances, and in many other areas of mathematics. Natural numbers are an important part of everyday life, and are used in everything from telling time to counting money.

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The percentage of increase is given by the equation A = 85 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage change be represented as P

Now , the equation will be

The initial value be represented as A = 40

The final or increased value be B = 74

So , the percentage change P = [ ( | A - B | ) / A ] x 100

Substituting the values in the equation , we get

The percentage change P = [ ( 34 ) / 40 ] x 100

The percentage change P = 0.85 x 100

The percentage change P = 85 %

Hence , the percentage change is 85 %

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The perimeter of this parallelogram is equal to 236/10 or 23 6/10 meters.

In Mathematics, a parallelogram simply refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Mathematically, the perimeter of a parallelogram can be calculated by using this mathematical expression;

Perimeter = A + B + C + D

Where:

A, B, C, and D represents the length of sides of a parallelogram.

Substituting the given parameters into the perimeter of a parallelogram  formula, we have the following;

Perimeter = 3 3/10 + 8 5/10 + 3 3/10 + 8 5/10

Perimeter = 33/10 + 85/10 + 33/10 + 85/10

Perimeter = 66/10 + 170/10

Perimeter = 236/10 or 23 6/10 meters.

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The angular speed of the wheel is 0.314 rad/sec and the linear speed of the car is 8.164 feet/second .

Angular speed is defined as the rate of change of angular displacement, and it is expressed as follows: ω = θ/ t

one revolution = 360°

180° = π

360° = 2π

3 revolution = 3× 2π = 6π

1 minute = 60 ×1 = 60s

angular speed = 6× 3.14/60

= 0.314 rad/s

The linear velocity =

V = wr

r = d/2

r = 52/2 = 26 feet

V = wr

V = 0.314× 26

V = 8.164 feet/second

Question: A Ferris wheel at a carnival has a diameter of 52 feet. Suppose it turns at a rate of 3 revolutions per minute. i. What is the angular speed of the wheel.

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