y=e[tex]e=^{x-4}[/tex]

The value of the triple integral xy dV over the solid tetrahedron with vertices (0,0,0), (9,0,0), (0,8,0), and (0,0,6) is approximately 490.5. The limits of integration for x, y, and z are 0 to 9, 0 to 8 - (8/9)x, and 0 to 6 - (1/3)x - (1/4)y, respectively.

To evaluate the triple integral, we need to set up the limits of integration for the three variables x, y, and z. Since the solid is a tetrahedron with vertices at (0,0,0), (9,0,0), (0,8,0), and (0,0,6), we can write the limits of integration as follows:

0 ≤ x ≤ 9

0 ≤ y ≤ 8 - (8/9)x

0 ≤ z ≤ 6 - (1/3)x - (1/4)y

The limits of integration for x are straightforward, as x ranges from 0 to 9. For y, we need to consider that the solid is bounded by the x-axis (y=0), the y-axis (x=0), and two planes that intersect along the line x=9, y=8. The equation of the plane containing the points (0,8,0), (9,0,0), and (0,0,6) is given by 8x/9 + 6z/9 = 8, which simplifies to y = 8 - (8/9)x - (2/3)z. Solving for z, we get z = (3/2)(4 - (3/4)x - (3/4)y), so the limits of integration for z depend on both x and y.

With these limits of integration, we can set up the triple integral as follows:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) ∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz dy dx

Evaluating the innermost integral with respect to z, we get:

∫0(⁶-(¹/³)ˣ-(¹/⁴)ʸ) xy dz = xyz |z=0 to z=(6-(1/3)x-(1/4)y) = x y (6 - (1/3)x - (1/4)y)

Substituting this expression back into the triple integral and evaluating the remaining integrals, we get:

∭E xy dV = ∫0⁹ ∫0(⁸-(⁸/⁹)ˣ) x y (6 - (1/3)x - (1/4)y) dy dx

= ∫0⁹ x [(3/4)y²(8/9 - (1/3)x) - (1/12)y³(8/9 - (1/3)x)] |y=0 to y=(8-(8/9)x) dx

= ∫0⁹ x [(3/4)(8/9 - (1/3)x)³ - (1/12)(8/9 - (1/3)x)⁴] dx

≈ 490.5

Therefore, the value of the triple integral is approximately 490.5

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(i) 61/2000

(ii) 9/2

(iii) 261/400

Total no. of drivers = 2000

(i) exactly 3 accidents (18-29 years of age)

[ P(E)= no. of favourable outcomes/total no.of Outcomes]

P(E) = 61/2000

(ii) one or more accidents in a year (30-50 years of age )

= 125 +60 + 22 + 18

= 225

P( E) = 225/ 2000

= 9/2

(iii) having no accidents in one year

= 440 +505 +360

= 1305

P(E) = 1305/2000

=261/400

hope it helps

- Creativexcolours

Answer:

1/2

Step-by-step explanation:

The numbers are: 1, 2, 4, 5, 7, 8, 9, 10

We see that only 7, 8, 9, and 10 are greater than 5

So, 4 possible numbers are greater than 5 in the total of 8 numbers.

So, the probability is 4/8 = 1/2

So, the answer is 1/2.

85 degrees Celsius is equal to 185 degrees Fahrenheit.

To convert Celsius (C) to Fahrenheit (F), you can use the formula:

F = (C × 9/5) + 32

where C is the temperature in Celsius and

F is the temperature in Fahrenheit.

Using this formula,

we can convert 85 degrees Celsius to Fahrenheit as follows:

F = (85 × 9/5) + 32

F = 153 + 32

F = 185

The average body temperature is widely regarded to be between 36.5 °C (97.7 °F) and 37.5 °C (99.5 °F).

Fever is defined as an increase in body temperature of one degree Celsius or more over the average of 37.0 degrees Celsius (98.6 degrees Fahrenheit).

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Answer:

24 : 8

Step-by-step explanation:

24/4 is equal to 6

8/4 is equal to 2

Answer:

24:8

Step-by-step explanation:

The easiest way to do these kinds of problems is by doing some simple division.  Usually you only need to look at the first number, which in this case is 6, and see if any numbers can be divided by this number.  The first ratio is 24:8, and since the other first number can't be divisible by 6, we know the answer is 24:8

Answer: B. 7

The ratio of the two triangles indicates that BOY is 1/2 the size of GRL. Therefore, the ratio of the sides of the triangles is also 1:2. Since the length of BO is given as x + 3, this means that the length of GR must be 2(x + 3) - 1 = 2x + 5. Therefore, the length of GR is 7.

The area covered by 19, 602 square feet in acres is around 0.45, according to the relation between the two.

As per the known relation between acre and square foot, the two quantities are related through the formula -

1 acre is equal to 43, 560 square feet

Therefore, formula to convert square feet to acre will be -

Amount of area in acres = area covered in square feet/unit equivalent area in square feet

So, rewriting the above mentioned relation.

43, 560 square feet is equal to 1 acre

Thus, 19, 602 square feet will be equal to acres = 19, 602/43, 560

Performing division on Right Hand Side of the equation

The amount of area in acres = 0.45 acres

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Answer:

5, 10 20, etc.

Step-by-step explanation:

You can skip count like you do in multiplying.

De acuerdo con la información previa, el sudoku se completaría con los números como se muestra en la imagen anexada.

Un sudoku es un juego numérico en el que tenemos 9 cuadrículas de 3 x 3 cuadros en los que tenemos que ubicar los números de 1 al 9 sin que se repitan en columnas, filas o en el mismo cuadro de 9 cuadrículas. Este juego se asocia con un buen nivel de análisis matemático. Adicionalmente, para solucionar un juego de Sudoku debemos analizar los números que ya están puestos en él como pistas para ubicar el resto de números.

De acuerdo con lo anterior, el Sudoku de la imagen muestra cómo se completó correctamente. En él ningún número se repite en filas, columnas o cuadrículas.

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In observational studies, the variable of interest is not controlled.

The correct answer is D.

Observational studies are a type of research design used to investigate the relationship between variables. In an observational study, the researcher observes and records data without manipulating any variables. The variable of interest is the one that the researcher wants to investigate and understand its relationship with other variables.

Numerical variables are those that can be measured and expressed as numbers. Examples of numerical variables include age, weight, height, temperature, and income. These variables are important in observational studies because they can be analyzed quantitatively and compared to other variables of interest.

In contrast, categorical variables are not numerical, and they cannot be measured or expressed as numbers. Examples of categorical variables include gender, race, occupation, and marital status. These variables are not appropriate as the variable of interest in observational studies because they cannot be analyzed quantitatively.

In observational studies, the variable of interest is not controlled, meaning the researcher does not manipulate or control it. Instead, the researcher observes and records data on the variable and its relationship with other variables. This is in contrast to experimental studies, where the researcher manipulates one or more variables to observe their effect on another variable. Therefore the answer is D) is not controlled.

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The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

The difference between the highest and lowest values for a given data collection is the range in statistics.

In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. It indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.

The range is the difference between the largest and smallest values in a data set.

For the given data, the largest value is 8 and the smallest value is 3.5.

Thus,

range = 8 - 3.5 = 4.5.

Hence, the range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

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Answer:

Step-by-step explanation:The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.

The given expression is (2⋅3)2−52. Therefore, the simplified expression is 11.

To simplify this expression, we first need to apply the exponent rule, which states that (a⋅b)c = ac⋅bc. In this case, we have:

(2⋅3)2 = 22⋅32

Next, we need to simplify the exponents. We have:

22⋅32 = 4⋅9 = 36

Finally, we need to subtract 52 from 36. We have:

36−52 = 36−25 = 11

Therefore, the simplified expression is 11.

Answer: 11.

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Answer:

Step-by-step explanation:

(1)To write this in standard form, we want the x and y terms on the same side of the equation and the constant on the other side. To do this, we can subtract 3x from both sides:

-3x + y = 1

So the standard form of the equation is:

-3x + y = 1

(2)y = -9/5x + 3

To write this in standard form, we want to eliminate the fraction by multiplying both sides by the denominator (5):

5y = -9x + 15

Next, we can move the x term to the left side by adding 9x to both sides:

9x + 5y = 15

So the standard form of the equation is:

9x + 5y = 15

There are 142,506 different committees of 5 students that can be selected from a group of 30 students.

The number of different committees that can be formed by selecting 5 students from a group of 30 students can be calculated using the formula for combinations, which is:

n C r = n! / r!(n - r)!

where n is the total number of items (in this case, the number of students) and r is the number of items to be selected (in this case, 5).

Substituting the values, we get:

30 C 5 = 30! / (5! * (30 - 5)!)

= (30 * 29 * 28 * 27 * 26) / (5 * 4 * 3 * 2 * 1)

= 142,506

Therefore, there are 142,506 different committees of 5 students that can be selected from a group of 30 students.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. It is a measure of the chance or likelihood of an event happening, expressed as a number between 0 and 1. A probability of 0 means the event will not occur, and a probability of 1 means the event will definitely occur.

The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This is known as the classical probability, and it assumes that all outcomes are equally likely.

There are also other types of probability, including empirical probability (based on observations and data), subjective probability (based on personal judgment and beliefs), and conditional probability (the probability of an event given that another event has occurred).

Probability has applications in many fields, including statistics, science, finance, and engineering. It is used to model and predict the occurrence of events, to make decisions under uncertainty, and to design systems and processes that can minimize risk and maximize the chances of success.

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A number from 1 to 20 is any integer between 1 and 20, inclusive of both endpoints. A number from 1 to 20 can be any integer between 1 and 20, inclusive.

The set of numbers from 1 to 20 includes 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. This set of numbers is commonly used in a variety of contexts, such as in statistics, probability, and mathematics. For example, when rolling a fair six-sided die, the probability of rolling a number from 1 to 20 is 1, since there are no numbers on a six-sided die that are greater than 6.

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Answer:

Step-by-step explanation:

Answer:

32/7 = 4 + 5/7

Step-by-step explanation:

The measure of angle of a, b, and c are a = 90, b = 9- and c = 60 degrees

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

The figure

The angle at the circumference in a semicircle is 90°

This means that

a = b = 90 degrees

Also, we have

Angle c and angle with a measure of 60 degrees are equal

This means that

Angle c = 60 degrees

Hence, the measure of the angles are a = 90, b = 9- and c = 60 degrees

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A statistic is a number that describes a sample, whereas a parameter is a number that describes the complete population.

To characterise the whole population under consideration, a parameter is utilised. For instance, we could be curious about a butterfly's typical length. Given that it contains data on the whole butterfly population, this qualifies as a parameter.

The most often used sample is a simple random sample. Every practicable sample of the selected size must be given an equal probability of being used. An element is a population characteristic. The statistic is a property of the sample.

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(f • g)(x) = f(g(x))

         = f(x-1)

         = 2(x-1)^2

Therefore, (f • g)(3) = 2(2)^2 = 8

Answer:

(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.

Step-by-step explanation:

We have, to substitute g(x) into f(x) wherever we see x in f(x),to find (f • g)(x).

Which will give,

(f • g)(x) = f(g(x))

             = f(x-1)

             = 2(x-1)^2

We have to put x = 3 to evaluate this expression,

(f • g)(3) = 2(3-1)^2

             = 2(2)^2

             = 8

Therefore,

(f • g)(x) = 2(x-1)^2 and (f • g)(3) = 8.

The hole for the function f(x) = √(x-2) is x < 2.

A function has an input and an output.

A function can be one-to-one or onto one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

A hole in a graph refers to a point where a function is undefined or missing.

Now,

f(x) = √(x-2)

Now,

To determine where this function is undefined, we need to consider the domain of the function, which is the set of all possible values of x that can be input into the function.

Since the square root function is defined only for non-negative numbers, The expression inside √(x-2) must be greater than or equal to zero:

i.e

x - 2 ≥ 0

Solving for x.

x ≥ 2

Therefore,

The function f(x) = √(x-2) is undefined for any value of x that is less than 2.

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The complete question.

what is the hole for this equation f(x) = √(x-2)?

The parametric vector form of the matrix is AX = < t 0 3/5t> where t is any real number.

Matrices are an important mathematical tool that can be used to represent and solve a wide array of problems.

In this problem, we are given a matrix A, which is row equivalent to the given matrix [1 -3 -8 5 0 12 -4] and asked to describe all solutions of Ax = 0 in parametric vector form.

To answer this question, we first need to use row operations to transform the given matrix into row-echelon form. After applying row operations, the matrix becomes [1 0 -5/3 0 2/3 0 1].

We can now use this matrix and the equation Ax = 0 to identify the solutions in parametric vector form.

The first column of the matrix has a coefficient of 1, indicating that x₁ is free and can take on any real value.

The second column has a coefficient of 0, indicating that x₂ = 0.

The third column has a coefficient of -5/3, indicating that x₃ = 3/5t, where t is a real number.

Then the resulting vector form is written as,

=> AX = < t 0 3/5t> where t is any real number.

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Therefore , the solution of the given problem of probability comes out to be P(not same color) = 236/361.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

There are three cases to consider:

Case 1: both marbles are red

Case 2: both marbles are yellow

Case 3: both marbles are blue

The probability of drawing two red marbles can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a red marble on the second draw (5/19):

P(red and red) = (5/19) * (5/19) = 25/361

Similarly, the probability of drawing two yellow marbles is:

P(yellow and yellow) = (6/19) * (6/19) = 36/361

And the probability of drawing two blue marbles is:

P(blue and blue) = (8/19) * (8/19) = 64/361

So, the probability of drawing two marbles that are the same color is:

P(same color) = P(red and red) + P(yellow and yellow) + P(blue and blue)

P(same color) = (25/361) + (36/361) + (64/361)

P(same color) = 125/361

d. If two marbles are drawn, what's the chance they are NOT the same color?

There are three cases to consider:

Case 1: one marble is red and one marble is yellow

Case 2: one marble is red and one marble is blue

Case 3: one marble is yellow and one marble is blue

The probability of drawing one red marble and one yellow marble can be found by multiplying the probability of drawing a red marble on the first draw (5/19) by the probability of drawing a yellow marble on the second draw (6/19), and then multiplying by 2 (since the order of the marbles doesn't matter):

P(red and yellow) = 2 * (5/19) * (6/19) = 60/361

Similarly, the probability of drawing one red marble and one blue marble is:

P(red and blue) = 2 * (5/19) * (8/19) = 80/361

And the probability of drawing one yellow marble and one blue marble is:

P(yellow and blue) = 2 * (6/19) * (8/19) = 96/361

So, the probability of drawing two marbles that are not the same color is:

P(not same color) = P(red and yellow) + P(red and blue) + P(yellow and blue)

P(not same color) = (60/361) + (80/361) + (96/361)

P(not same color) = 236/361

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All the angle measures are;

m∠A = 160°

m∠B  = 142°

m∠C = 120°

m∠D  = 156°

m∠E = 31°

m∠F = 111°

A hexagon is a six-sided polygon. And a convex hexagon means the hexagon's vertices are pointed outwards.

And no interior angle has an angle measuring of more than 180°.

Given:

The number of sides in the polygon = 6.

The total sum of the irregular angle = (4 - 2) x 180° = 720°.

7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720°.

28x = 720 - 48

x = 24

Substituting all the values of x = 24 to all the interior angle measures,

Now, all the measures are:

m∠A = 7x - 8 = 160°

m∠B = 4x + 46 = 142°

m∠C = 5x = 120°

m∠D = 6x + 12 = 156°

m∠E = x + 7 = 31°

m∠F = 5x - 9 = 111°

Therefore, all the measures are given above.

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The complete question is given in the image below.

Answer:

7.64

Step-by-step explanation:

1 week: (100% + 11%) × 6.2

111% × 6.2 = 6.882 cm

OR

11% × 6.2 = 0.682 cm

6.2 + 0.682 = 6.882 cm

Because the plant grows 11% additional to its original height.

1 week = 6.882 cm

2 weeks = 111% × 6.882 cm

OR

11% × 6.882cm = 0.75702 cm

0.75702 cm + 6.882 = 7.63902 cm

Because an additional 11% is added to what was grown in week 1.

=7.63902 cm

= 7.64 cm (rounded to 2 decimal places)

hope this helps!

Step-by-step explanation:

x = number of sold sodas

y = number of sold hot dogs

x + y = 124

x = 3y

so,

3y + y = 124

4y = 124

y = 31

x = 3y = 3×31 = 93

there were 93 sodas and 31 hot dogs sold.

Answer:

X=7

Y=6

Step-by-step explanation:

Divide the 1st equation by 2.

2x+3y=32

2x-y=8

When you subtract those 2 numbers, you get that 4y=24.

Y=6

32-6*3=14=2x

X=7

John's purchasing power increased by 0.97%.

What is the inflation?

The definition of inflation in the field of economics is "mean increased money supply, but the general public often refer to a sustained increase in the general price level of goods and services in an economy over a period".

If the inflation rate was 3% and John's salary grew 4%, his salary increased more than the rate of inflation. However, his real increase in purchasing power depends on the difference between his salary growth rate and the inflation rate.

To calculate the change in John's purchasing power, we can use the following formula:

Change in purchasing power = (1 + Salary growth rate) / (1 + Inflation rate) - 1

Plugging in the values, we get:

Change in purchasing power = (1 + 0.04) / (1 + 0.03) - 1

Change in purchasing power = 1.01 / 1.03 - 1

Change in purchasing power = 0.0097 or 0.97%

Hence, John's purchasing power increased by 0.97%.

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The function that is positive for the entire interval [-3, -2] is:

The function has a minimum value of (0, -3) and crosses the x-axis at (-3, 0) and (3, 0). This means that the function is positive for the entire interval [-3, -2] because it is above the x-axis for this interval.

To further explain, a function is positive when its value is above the x-axis on a coordinate plane. In this case, the first function has a minimum value of (0, -3) which means that it is below the x-axis at this point. However, it crosses the x-axis at (-3, 0) and (3, 0), meaning that it is above the x-axis for the entire interval between these two points, including the interval [-3, -2].

The other functions are not positive for the entire interval [-3, -2] because they either have minimum values that are below the x-axis within this interval, or they cross the x-axis within this interval, meaning that they are not positive for the entire interval.

In conclusion, the function that is positive for the entire interval [-3, -2] is the first one because it is above the x-axis for this entire interval.

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Answer:

56.8 AND 33.2

Step-by-step explanation:

Complementary angles add up to 90 degrees, so we can set up the equation:

x + (x - 23.6) = 90

Simplifying the equation, we get:

2x - 23.6 = 90

Adding 23.6 to both sides, we get:

2x = 113.6

Dividing by 2, we get:

x = 56.8

So one angle measures 56.8 degrees, and its complementary angle measures:

90 - 56.8 = 33.2 degrees.