how do you write x is less than 4 in symbols​

Answer:

C.

Step-by-step explanation:

Slope = m = (y2 - y1)/(x2 - x1) = (5-(-1))/(4 - 2) = 6/2 = 3

Slope - point form:

y - y1 = m(x -x1)

y - 5 = 3(x - 4)

y - 5 = 3x - 12

- 3x + y = - 12 + 5

- 3x + y = - 7

Answer:

Option C is the correct option.

Step-by-step explanation:

A line passes through ( 2 , -1 ) and ( 4 , 5 )

The equation of line:

\( \frac{y - y1}{x - x1} = \frac{y2 - y1}{x2 - x1} \)

Plug the values

\( \frac{ y - ( - 1)}{x - 2} = \frac{5 - ( - 1)}{4 - 2} \)

When there is a ( - ) in front of an expression in parentheses, change the sign of each term in the expression

\( \frac{y + 1}{x - 2} = \frac{5 + 1}{4 - 2} \)

Add the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{4 - 2} \)

Subtract the numbers

\( \frac{y + 1}{x - 2} = \frac{6}{2} \)

Reduce the numbers with 2

\( \frac{y + 1}{x - 2} = 3\)

Apply cross product property

\(3x - 6 = y + 1\)

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

\(3x - y = 1 + 6\)

Add the numbers

\(3x - y = 7\)

\( - 3x + y = - 7\)

Hope this helps...

Best regards!

Y in represents the following in this linear regression Y = α₀+α₁X+α₂X₂+ε: C. dependent variable.

In Mathematics and Geometry, a regression line is a statistical line that best describes the behavior of a data set. This ultimately implies that, a regression line simply refers to a line which best fits a set of data.

In Mathematics and Geometry, the general functional form of a linear regression can be modeled by this mathematical equation;

Y = α₀+α₁X+α₂X₂+ε

Where:

In conclusion, Y represent the dependent variable or response variable in a linear regression.

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Answer:

Slope=10 Y=15

Step-by-step explanation:

Goes up by 10

Starts at 0,15

The slope of an equation is 10 and the y-intercept is 15. Therefore, option B is the correct answer.

The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

Given that, the equation y= 10x + 15 represents a gym that charges.

By comparing y=10x+15 with y=mx+c, we get

Slope (m)=10 and y-intercept (c)=15

Therefore, option B is the correct answer.

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The problem involves two functions that represent the amount and rate of pollution discharged by a factory into a lake. The functions are evaluated for the first 7 years of operation and the answers are rounded to two decimal places.

1. To calculate the amount of pollution discharged by the factory into the lake over the first 7 years of operation, we evaluate the integral of x(n) from 0 to 7. Plug in the values of n into the function x(n) = 2/(n^2 + 1) and integrate with respect to n. Round the result to two decimal places.

2. To calculate the rate at which pollution is being discharged into the lake at each year within the first 7 years, we evaluate the function r(t) = t/(t^2 + 1) for each year within the interval [0, 7]. Substitute the values of t from 0 to 7 into the function and calculate the rate. Round the results to two decimal places.

Note that the units for both x(n) and r(t) are given as tons.

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The asked transformation is dilation.

A transformation is a process that manipulates a polygon or other two-dimensional object on a plane or coordinate system.

Given that, f(x)= -x+5; g(x) = 2f(x)

The original function was = f(x) = -x+5

After transformation = g(x) = 2f(x)

We see, that,

The function is resulted in 2 times the main function.

It is showing an enlargement with a scale factor of 2.

Hence, the transformation is dilation.

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Answer:

The coordinates of its image are (2, -4)

Step-by-step explanation:

Let us revise the rules of reflection across the axes

∵ The point (2, 4) is reflected across the x-axis

→ By using the first rule above rx-axis (x, y) → (x, -y)

∴ Change the sign of its y-coordinate

∴ Its image is (2, -4)

∴ The coordinates of its image are (2, -4)

Answer:

\(\huge\boxed{\sf 44\ units}\)

Step-by-step explanation:

Solution:

So,

= 3 + 8 + 3 + 6 + 5 + 6 (again) + 4 + 5 + 4

\(\rule[225]{225}{2}\)

Answer:

8-4=4

therefore 6+4=10

then perimeter =2(5)+10+6+2(3)+8+4=44units

The values in b are compared with the true volume. And we conclude that b is precise and accurate.

Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.

First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.

From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.

From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.

From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.

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The number of zeros are in the product of the number 50 and 6000 is 50 x 6000 = 300,000 are five.

Integers, natural numbers, fractions, real numbers, complex numbers, and quaternions are examples of typical special instances where it is possible to define the product of two numbers or the multiplication of two numbers.

A product is the outcome of multiplication in mathematics, or an expression that specifies the elements (numbers or variables) to be multiplied.

The commutative law of multiplication states that the result is independent of the order in which real or complex numbers are multiplied. The result of a multiplication of matrices or the elements of other associative algebras typically depends on the order of the components. For instance, matrix multiplication and multiplication in general in other algebras are non-commutative operations.

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An algorithmic state machine (ASM) is a type of finite-state machine that is designed specifically for describing the behavior of an algorithm.

ASM offers several advantages over Moore and Mealy machines, including:

Ease of design: ASM allows for a more intuitive and structured approach to designing algorithms, as it provides a clear separation between the control and data paths.

Modularity: ASM allows for the design of complex algorithms by breaking them down into smaller, more manageable modules, which can be independently designed and tested.

Scalability: ASM allows for the easy addition of new functionality to an algorithm by simply adding new modules or modifying existing ones.

Reusability: ASM provides a high degree of code reuse, as modules can be easily combined to form new algorithms.

Flexibility: ASM can handle a wider range of input and output conditions than either Moore or Mealy machines, making it more versatile in many applications.

Overall, an ASM offers a more powerful and flexible approach to algorithm design than either a Moore or a Mealy machine.

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Answer:

74

Step-by-step explanation:

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The value of the given expression (14-30)/2(-4) when simplified is 2.

PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.

The given expression can be simplified as shown below.

(14 - 30)/ 2 (- 4)

Using the rule of PEMDAS, solving parenthesis first,

= (14-30) / (-8)

= (-16)/ (-8)

Solving the division,

= 2

Hence, The value of the given expression (14-30)/2(-4) when simplified is 2.

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We can get the joint pmf of X and Y using the below probabilities in the formula given below. The joint pmf is given as `P(X = i, Y = j) = {3! / i! (j-1)! (3-i-j)!} * (1/3)j * (2/3)3-i-j`

Suppose 3 balls are distributed completely at random into 3 cells.

Let X be the number of cells that remain empty, and let Y be the number of balls in cell number 1.

The joint pmf of X and Y is given as follows: `P(X = i, Y = j) = {3! / i! (j-1)! (3-i-j)!} * (1/3)j * (2/3)3-i-j`Where, i = 0, 1, 2, 3 and j = 0, 1, 2, 3 with i + j ≤ 3.

Explanation: Since the balls are distributed completely at random into 3 cells, each ball has three choices to select one of the three cells.

Therefore, there are a total of `3^3 = 27` possible outcomes.

Let us consider each possible outcome. Total Outcomes: 27 Outcomes where 0 cells are empty: (1, 1, 1) only 1 Outcomes where 1 cell is empty:  1st cell 2nd cell 3rd cell (0, 1, 2) (0, 2, 1) (1, 0, 2) (1, 2, 0) (2, 0, 1) (2, 1, 0) 6 Outcomes where 2 cells are empty:  1st cell 2nd cell 3rd cell (0, 0, 3) (0, 3, 0) (3, 0, 0) 3

Therefore, we have i = 0, 1, 2, 3, and j = 0, 1, 2, 3 with i + j ≤ 3. For i = 0, j = 0, there is only one outcome, and the probability is 1/27. For i = 1, j = 0, there are three outcomes, and the probability is 3/27. For i = 2, j = 0, there are three outcomes, and the probability is 3/27. For i = 3, j = 0, there is only one outcome, and the probability is 1/27. For i = 0, j = 1,

there are three outcomes, and the probability is 3/27. For i = 1, j = 1, there are three outcomes, and the probability is 3/27. For i = 2, j = 1, there are six outcomes, and the probability is 6/27. For i = 0, j = 2, there are three outcomes, and the probability is 3/27. For i = 1, j = 2, there are six outcomes, and the probability is 6/27. For i = 0, j = 3, there is only one outcome, and the probability is 1/27.

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Answer:

Step-by-step explanation:

5x - 2 = 55

5x = 57

x = 57/5

Answer:

Step-by-step explanation:

6000FT, is the shortest length of fence that the rancher can use.

Area is the total amount of space that an object's shape or a flat (2-D) surface occupy.

Create a square on paper by using a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Imagine that your square is made up of smaller unit squares.

The area of a figure is equal to the number of unit squares required to completely cover the surface area of a particular 2-D shape. Square cms, square feet, square inches, square meters, etc. are a few common units for measuring area.

To get the area of the square figures presented below, draw unit squares with 1-centimeter sides. Therefore, the shape will be measured.

According to our question-

Let the rectangular field's length be x.

rectangle field width = y

square feet of a rectangular field's area

Because length is always positive, it is always positive.

Once more, discriminate with respect to x

replace x=1500

Therefore, at x=1 500, fencing is minimal.

Change x to 1 500.

the rectangular field is 1500 feet long.

rectangle field's width is 1000 feet.

Replace the values

shortest used fence length =6000ft

Hence, 6000FT, is the shortest length of fence that the rancher can use.

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Answer: Tyler has 22 cards

Step-by-step explanation:

To begin, we know that Morgan has 12 less than 5x Tyler's cards, so...

12+98=110

Now that we had 110, we then read that it is the PRODUCT of 5 and the number that Tyler has, so we will show that algebraically.

110=5x

Now, divide 110 by 5 to find X.

110/5=22

Tyler has 22 cards.

The critical value of z separates the rejection region from the nonrejection region while observed value of z is the value calculated for a sample statistic such as x.

A critical value of z is used when the sampling distribution is normal, or close to normal. The critical value of z refers to the point that cuts off area under graph for the standard normal distribution separating the rejection and nonrejection region of the data. The Critical value of z can indicate what probability any particular variable will have. These values are typically obtained from a table such as the standard normal distribution table. The observed value of z is a value determined for a sample statistic x. It is a test statistic for Z-tests that measures the difference between an observed statistic and its hypothesized population parameter in units of the standard deviation.

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To find the coordinates of points A and B, go to Desmos and graph the given equation.

The word gradient means slope.

The slope is the coefficient of x in the equation. See it?

The gradient is 2.

Answer:

Here is an actual answer.

(2x + z)(x + 2.5).

Step-by-step explanation:

In general, a quadratic equation in standard form is: ax2 + bx + c and other stuff I forget.Therefore, from 2x2 - bx -20, we obtain: (2x + z)(x + 2.5).

Answer:

9.5m

Step-by-step explanation:

Answer:

9.5 is the height

Step-by-step explanation:

I just looked it up with the term "find height of triangle with base and area"

Answer: 1619.15

Step-by-step explanation:

cp = 1378

sp = cp + profit % of cp

= 1378 + 17.5/ 100 * 1378

= 1378 + 241.15

= 1619.15

The A⁻¹ of the given matrix is \(\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The inverse of the matrix is calculated by the ratio of the adjoint of the given matrix A to the determinant of the matrix A.

The inverse of a matrix is a matrix that, when multiplied by the original matrix, results in the identity matrix.

The formula to calculate the inverse of a matrix is,

\(A_{Adj}=\left[\begin{array}{cc}8&-4\\-2&-3\\\end{array}\right]\).

The determinant of the matrix is,

D = [ad - bc ]

D = [ (-3 x 8 ) - ( 4 x -2 ) ]

D = -12

The inverse of the matrix will be,

\(A^{-1}=\dfrac{1}{ab-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\A^{-1}=\dfrac{1}{(-3\times 8)-(4\times -2)}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\A^{-1}=\dfrac{1}{-12}\left[\begin{array}{cc}8&-4\\2&-3\\\end{array}\right]\\\\\)

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Answer:

-129

Step-by-step explanation:

f(x) = 4x +7

Answer:

Gary would weigh 176 ounces.

Step-by-step explanation:

One pound is sixteen ounces so just multiply sixteen and 11. ( 16 * 11 = 176 )

I hope this helped you! Have an amazing day :)

Answer: 176 ounces

Step-by-step explanation:

To convert pounds to ounces, multiply the initial value by 16. Since we have  the weight of Gary's cat as 11 pounds, their weight in ounces should be 11 * 16 = 176 ounces.

a)The probability that a randomly selected person from this sample used the Internet Explorer or the Chrome browser is0.42

b) The probability that a randomly selected person from this sample used the Internet Explorer and the Firefox browser is :0.03

c)The probability that a randomly selected person from this sample used the Safari browser or used a laptop computer is :0.86

d) The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is :0.32

e)the probability that the computer was a laptop is: 0.76.

a) The probability that a randomly selected person from this sample used the Internet Explorer or the Chrome browser is :

P(Internet Explorer or Chrome) = P(Internet Explorer) + P(Chrome)= (18+24)/(18+56+7+37+24+77+3+18+3+7)= 0.42

b) The probability that a randomly selected person from this sample used the Internet Explorer and the Firefox browser is :

P(Internet Explorer and Firefox) = 7/(18+56+7+37+24+77+3+18+3+7)= 0.03

c) The probability that a randomly selected person from this sample used the Safari browser or used a laptop computer is :P(Safari or Laptop) = P(Safari) + P(Laptop) - P(Safari and Laptop)= (3+56+37+77+18)/(18+56+7+37+24+77+3+18+3+7) = 0.86

d) The probability that a randomly selected person from this sample used the Chrome browser and used a laptop computer is :P(Chrome and Laptop) = 77/(18+56+7+37+24+77+3+18+3+7) = 0.32

e) Given that the randomly selected computer used the Chrome browser, the probability that the computer was a laptop is:P(Laptop|Chrome) = P(Laptop and Chrome) / P(Chrome)= 77 / (24+77) = 0.76

Hence, the required probabilities are: a) 0.42, b) 0.03, c) 0.86, d) 0.32 and e) 0.76.

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The solution is Option A.

The translation of the center of circle is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

Given data ,

Let the equation for the circle A be represented as

( x - 7 )² + ( y - 1 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( 7 , 1 )

Let the equation for the circle A be represented as

( x + 8 )² + ( y - 2 )² = 16

Now , the equation is of the form ( x - h )² + ( y - k )² = r²

So , the radius of the circle is 4 and the center of the circle is ( -8 , 2 )

So , the translation of circle A to B is given by

( 7 , 1 ) to ( -8 , 2 )

So , the x coordinate is translated by 15 units to left and the y coordinate is translated by 1 unit up

Hence , the translation is given by ( x , y ) ⟶ ( x - 15 , y + 1 )

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