complete the equation of the line through (4,-8)and (8,5) use exact numbers

Answer:

X    |   y

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

-2   |   3

-1   |   0

0   |  -3

1   |  -6

Answer:

The angles are adjacent and x=100

c) Mode: 15 (appears 6 times)

Mean: 15.25

Median: 15

d) Probability of being 13 years old: 2/20 = 0.1 or 10%

e) Probability of being 14 or 16 years old: 6/20 = 0.3 or 30%

f) Probability of not having 15 years old: 1 - (6/20) = 14/20 = 0.7 or 70%

a) To create a table and calculate the absolute frequency, relative frequency, and percentual frequency, we organize the given ages in ascending order:

13 13 14 14 15 15 15 15 15 16 16 17 17 17 18 18

Age Absolute Frequency Relative Frequency Percentual Frequency

13 2 2/16 12.5%

14 2 2/16 12.5%

15 5 5/16 31.25%

16 2 2/16 12.5%

17 3 3/16 18.75%

18 2 2/16 12.5%

b) To represent the data graphically with a histogram, we plot the ages on the x-axis and the absolute frequency on the y-axis:

c) To calculate the mode, mean, and median:

Mode: The mode is the most frequently occurring age in the dataset. In this case, the mode is 15, as it appears 5 times.

Mean: The mean is the average of all the ages. To calculate it, we sum up all the ages and divide by the total number of ages:

(13 + 13 + 14 + 14 + 15 + 15 + 15 + 15 + 15 + 16 + 16 + 17 + 17 + 17 + 18 + 18) / 20 = 306 / 20 = 15.3

Median: The median is the middle value in the dataset when arranged in ascending order. In this case, the median is 15 since it falls in the middle.

d) To calculate the probability of having 13 years old, we divide the absolute frequency of 13 (2) by the total number of ages (20):

Probability of 13 years old = 2/20 = 0.1 or 10%

e) To calculate the probability of having 14 or 16 years old, we add the absolute frequencies of 14 and 16 (2 + 2 = 4) and divide by the total number of ages (20):

Probability of 14 or 16 years old = 4/20 = 0.2 or 20%

f) To calculate the probability of not having 15 years old, we subtract the absolute frequency of 15 (5) from the total number of ages (20):

Probability of not having 15 years old = (20 - 5)/20 = 0.75 or 75%

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The statement is asserting that the universal class (V) is defined as the collection of all sets, where every set is included. It signifies that V encompasses all possible sets within the given set theory framework.

The statement "The universal class set, or universe, is the class of all sets: V = {x: x = x}" is referring to the concept of the universal class or the universe in set theory.

In set theory, the universal class set, denoted as V, represents the collection or class that contains all sets. It includes every possible set that can be defined or exists within the context of the set theory being considered.

The notation "{x: x = x}" is used to define the elements of the universal class. Here, "x = x" represents a condition that is always true for any object or element, regardless of its nature. In other words, this condition holds for everything in the universe, as anything is equal to itself.

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Answer:

x=3, = -2

Step-by-step explanation:

Answer:

352,000

Step-by-step explanation:

Subtract 374,000 by 22,000 and you will get 352,000 as your answer

The number 374000 is greater then 22000 by exactly 25200 amount.

What is mathematic expression?

A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Here, to find out by how much times the number 374000 is greater then the number 22000 we simply subtract the number 374000 by 22000 which comes out be 35200.

It should be noted that, To cross verify the answer we can add 35200 with 22000 it must be equal to 374000.

374000 - 22000 = 352000

Therefore, the number 374000 is greater then 22000 by exactly 25200 amount.

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Answer:

It is not a integer, it is a rational number

Answer: No, this isn't. An integer is any whole number, positive or negative. Having extraneous digits to the right of the decimal other than zero, radicals or any fractions are excluded from being considered an integer. Integers, for example, are 2, 85, -923, etc. Hope this helps!

Step-by-step explanation:

The coordinates of the point that divide the segment in a 3:5 ratio is (4, 0).

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

\(\rm m =\dfrac{y_2-y_1}{x_2-x_1}\)

We have:

Line segment AB has coordinates A(1,-6) and B (9,10).

The section formula is:

\(\rm x = \dfrac{mx_2+nx_1}{m+n}\)

\(\rm y = \dfrac{my_2+ny_1}{m+n}\)

\(\rm x = \dfrac{3\times9+5\times1}{3+5}\)

x = 4

Similarly,

y = 0

Thus, the coordinates of the point that divide the segment in a 3:5 ratio is (4, 0).

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The 1st one/Top one.

X value is different each time. Function can have the same y-value (3, 1), (2, 1) but can't have the same x-value (3, 1) (3, 3)

Solving a system of equations we can see that:

We can use the variables:

x = mass of the 60% solution.

y = mass of the 85% solution.

We can write a system of equations.

x + y = 70

x*0.6 + y*0.85 = 70*0.8

We can isolate x on the first equation to get:

x = 70 - y

Replace that in the other one:

(70 - y)*0.6 + y*0.85 = 70*0.8

Now we can solve this for y.

y*0.25 = 70*0.8 - 70*0.6

y = 14/0.25 = 56

Then he needs to use 56 ounces of the 85% solution, and 14 ounces of the 60% solution.

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Answer:

a) \(\frac{dz}{dt} = e^{t}\cdot (2\cdot t+2\cdot t^{2}-1)\)

b) \(\frac{dz}{dt} = [4\cdot \ln t\cdot \sin^{3} 4t - \sin 4t \cdot \sin (2\ln t)]\cdot \left(\frac{2}{t} \right)+[12\cdot (\ln t)^{2}\cdot \sin^{2} 4t + \cos (2\cdot \ln t)]\cdot (4\cdot \cos 4t)\)

Step-by-step explanation:

In this exercise we use implicit differentiation to define \(\frac{dz}{dt}\):

a) \(z = x\cdot e^{x\cdot y}\), \(x = t^{2}\), \(y = t^{-1}\)

\(\frac{dz}{dt} = \frac{dx}{dt}\cdot e^{x\cdot y} +x\cdot e^{x\cdot y}\cdot \left[\frac{dx}{dt}\cdot y+x\cdot \frac{dy}{dt} \right]\)

\(\frac{dz}{dt} = e^{x\cdot y}\cdot \left\{\frac{dx}{dt}+x\cdot \left[\frac{dx}{dt}\cdot y+x\cdot \frac{dy}{dt} \right] \right\}\)

\(\frac{dz}{dt} = e^{x\cdot y}\cdot \left[(1+x\cdot y)\cdot \frac{dx}{dt}+x\cdot \frac{dy}{dt} \right]\)(1)

\(\frac{dx}{dt} = 2\cdot t\), \(\frac{dy}{dt} = -t^{-2}\)

\(\frac{dz}{dt} = e^{t}\cdot \left[(1+t)\cdot 2\cdot t +t^{2}\cdot (-t^{-2})\right]\)

\(\frac{dz}{dt} = e^{t}\cdot (2\cdot t+2\cdot t^{2}-1)\)

b) \(z = x^{2}\cdot y^{3}+y\cdot \cos x\), \(x = \ln t^{2}\), \(y = \sin (4\cdot t)\)

\(\frac{dz}{dt} = 2\cdot x\cdot y^{3}\cdot \frac{dx}{dt} +x^{2}\cdot (3\cdot y^{2})\cdot \frac{dy}{dt}+(\cos x)\cdot \frac{dy}{dt} +y\cdot (-\sin x)\cdot \frac{dx}{dt}\)

\(\frac{dz}{dt} = (2\cdot x\cdot y^{3}-y\cdot \sin x)\cdot \frac{dx}{dt} + (3\cdot x^{2}\cdot y^{2}+\cos x)\cdot \frac{dy}{dt}\)

\(x = \ln t^{2}\)

\(x = 2\cdot \ln t\)

\(\frac{dx}{dt} = \frac{2}{t}\), \(\frac{dy}{dt} = 4\cdot \cos 4t\)

\(\frac{dz}{dt} = [4\cdot \ln t\cdot \sin^{3} 4t - \sin 4t \cdot \sin (2\ln t)]\cdot \left(\frac{2}{t} \right)+[12\cdot (\ln t)^{2}\cdot \sin^{2} 4t + \cos (2\cdot \ln t)]\cdot (4\cdot \cos 4t)\)

Answer: 7x -4

Step-by-step explanation:

Answer:

No Solution

Step-by-step explanation:

5h > -15; h = -5

5(-5) > -15

-25 > -15

-25 is not greater than -15

Hey there!

5h > -15

= 5(-5) > -15

= -25 > -15

Thus, this make this statement FALSE because -25 is NOT bigger than -15

It should be… 5(-5) ≯ -15

(≯ means NOT greater than)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

Answer:

14.875

Step-by-step explanation:

77/8 = 9.625 and 21/4 = 5.25

So, 9.625+5.25 =14.875

Answer: 10  1/8

............................

Answer:

Step-by-step explanation:

Total number of people = 800

To find the number of unemployed people we must first find the total percentage of the pie chart

That's

25 + 10 + 5 + 60 = 100%

5 % out of the 100% are unemployed

To find the number of unemployed people divide 5 % by the total percentage that's 100% and multiply them by the total number of people

That's

\( \frac{5}{100} \times 800\)

5 × 8

We have the final answer as

Hope this helps you

The volume of the solid is 27π cm3.

Using the formula for the volume of a solid of revolution, the solid's volume can be determined.

V = π ∫(y2 - x2)dx

Where y is the height of the cross-sections and x is the radius of the base.

The radius of the base (x) is equal to the height of the cross-sections because the cross-sections are isosceles right triangles with the hypotenuse positioned along the base (y).

Therefore, the equation can be simplified to:

V = π ∫y2 dx

Using the substitution x = y, the equation becomes:

V = π ∫y2 dy

Integrating the equation with respect to y, we get:

V = π [y3/3]

Substituting x = y = 3, we get:

V = π [33/3]

V = 27π cm3

Hence, the volume is 27π cm3.

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Answer:

[-0.2  0.4]

[0.8   -0.6]

The mixed numbers that have 12 as the LCD are 2 11/12 and 6 4/5. All other fractions do not have 12 as the denominator and are not equivalent.

Mixed numbers consist of a whole number and a fractional part. To add or subtract mixed numbers, the fractions must have the same denominator (the bottom number of the fraction).

The LCD (lowest common denominator) is the smallest number that all of the denominators can be divided into evenly. In this case, the LCD is 12.

2 11/12 and 6 4/5 both have 12 as the denominator. The denominator of 11/12 can be divided by 11 and 12, so it is the same as 12/12. The denominator of 4/5 can be divided by 4 and 12, so it is the same as 48/12 (4 x 12 = 48). Therefore, both fractions have the same denominator.

The other fractions do not have 12 as their denominator. 3 1/7 can be divided by 3, 7, and 12, so it is the same as 21/12 (3 x 7 = 21). 5 3/4 can be divided by 4, 5, and 12, so it is the same as 60/12 (4 x 5 = 60). 8 38/47 can be divided by 8, 47, and 12, so it is the same as 376/12 (8 x 47 = 376). Since none of these fractions are equal to 12/12, they are not equivalent to the other two fractions.

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Question :

Which mixed numbers have 12 as the LCD (lowest common denominator)?

2 11/12

3 1/7

5 3/4

6 4/5

8 38/47

The end-points of the line segment will be negative 1.25 and 0.25.

A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.

The length of the line segment is 1.50 units and the midpoint of the line segment is negative 0.50. Then the end-points of the line segment are given as,

⇒ - 0.50 ± (1.50) / 2

Simplify the expression, then we have

⇒ - 0.50 ± (1.50) / 2

⇒ - 0.50 - (1.50) / 2, - 0.50 + (1.50) / 2

⇒ - 0.50 - 0.75, - 0.50 + 0.75

⇒ - 1.25, 0.25

The end-points of the line fragment will be negative 1.25 and 0.25.

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Answer:

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

5+k−5k=−4k+60

5+k+−5k=−4k+60

(k+−5k)+(5)=−4k+60(Combine Like Terms)

−4k+5=−4k+60

−4k+5=−4k+60

Step 2: Add 4k to both sides.

−4k+5+4k=−4k+60+4k

Answer:

x⁴/4

Step-by-step explanation:

(20x‐³/10x‐1)‐²

= > 20/10 = 2

so = (2x-³/x-¹)-²

= (2/x²)-²....................(a/b)-²=(b/a)²

= (x²/2)²

= x⁴/2

Answer:

175.5in

Step-by-step explanation:

12 x 9 + 67.5

If this answer is incorrect (Which it should not be) than try 243

Answer:

9 + 3 + 3 = 15

15 x 12 x 1/2(basically just dividing by 2) = 90

9 x 12 = 108

108 + 90 = 198 in^2 for a

7 x 7 = 49

7 x 7 = 49, 49 divided by 2 ( x 1/2) = 24.5

49 + 24.5 = 73.5 ft^2 for b

Answer:

\(y-2=3(x-4)\)

Step-by-step explanation:

We are given a line contains the point (4, 2).

We also know that the line is parallel to y= 3x - 7.

We want to write the equation of this line.

Parallel lines have the same slopes.

First, let's find the slope of y = 3x - 7.

3 is in the place of where m (the slope) is, so that means it is the slope of that line.

It is also the slope of the line whose equation we want to write.

The equation of the line can be written in three ways:

All of these ways are valid, but for this problem, let's write the equation in point-slope form, as it is the easiest.

Substitute 3 as m in \(y-y_1=m(x-x_1)\).

\(y-y_1=3(x-x_1)\)

Now, substitute 4 as \(x_1\) and 2 as \(y_1\).

\(y-2=3(x-4)\)

Topic: parallel and perpendicular lines

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Answer:

x=18, y=9

Step-by-step explanation:

The lines of y+3 and 12 look equal to each other. So do x-3 and 15. Because of this, we set each equal to each other and solve.

solving for x:

x-3 = 15

+ 3     +3

x=18

solving for y:

y+3=12

- 3    -3

y=9

hope this helps!!!

Answer:

  (x, y) = (18, 9)

Step-by-step explanation:

Assuming the figure is a parallelogram, the diagonals bisect each other. Each half of one diagonal is equal to the other half of that diagonal.

Long diagonal:

  x -3 = 15

  x = 18 . . . . . add 3 to both sides of the equation

Short diagonal:

  y +3 = 12

  y = 9 . . . . . . subtract 3 from both sides of the equation

The variable values are ...

The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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Answer:

3x(7-3)y2=21

Step-by-step explanation:

hope it is write

Complete Question :

An application is using a two-dimensional list defined as follows: 1. Write a statement that creates an empty two-dimensional list named values with 4 rows and 3 columns. 2. Write nested loops that get an integer value from the user for each element in the list, for example: values= [[1, 2, 3], [10, 20, 30], [100, 200, 300],[1000, 2000, 3000]] 3. Write a function named row_values that accepts values as argument and returns the sums of each row and displays the result as a list named row 4. Write a function named column_values that accepts values as arguments and returns the sums of each column and displays the result as a list named column 5. Write a function called sum_values that sums all the elements of the array and displays the result.

Sum of rows : [ 6, 60, 600, 6000 ]

Sum of columns : [ 1111, 2222, 3333]

Sum of all elements : 6666

The nested loops are :

Enter a number at row 0, and column 0 : 1

Enter a number at row 0, and column 1 : 2

Enter a number at row 0, and column 2 : 3

Enter a number at row 1, and column 0 : 10

Enter a number at row 1, and column 1 : 20

Enter a number at row 1, and column 2 : 30

Enter a number at row 2, and column 0 : 100

Enter a number at row 2, and column 1 : 200

Enter a number at row 2, and column 2: 300

Enter a number at row 3, and column 0 : 1000

Enter a number at row 3, and column 1 : 2000

Enter a number at row 3, and column 2 : 3000

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Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

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