The system of equations models the prices per share, y, for two stocks over time, x. Which represents the viable solutions to the system?
−y ≤ 3x + 4
−3x + 3y ≤ −9

A. All real number values of x and y
B. (5, 15)
C. All real number values, with y ≥ 0
D. (15, 5)

In a class of 50 students, there are 365! / 315! ways that no two students will have the same birth date.

The total number of outcomes of two or more independent events equals the product of the number of outcomes of each individual event, according to this concept. A youngster, for example, who chooses six flavors of ice cream and three types of cones will have 6 x 3 = 18 distinct icecream options. According to the fundamental counting principle, if there are p ways to do one thing and q ways to do another, then there are pq ways to accomplish both.

Here,

There are 365 ways to choose the first student's birth date, 364 ways to choose the second student's birth date (since it can't be the same as the first student's), and so on, down to 316 ways to choose the 50th student's birth date (since it can't be the same as any of the first 49 students' birth dates).

So, the number of ways to choose the birth dates of 50 students so that no two are the same is,

= 365 × 364 × ... × 316

= 365! / (365 - 50)!

= 365! / 315!

There are 365! / 315! ways that no two students will have the same birth date in a class of size 50.

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The solution of a system of equations by elimination method is at x = -4 and y = 12.

The points where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all possible values for the variables that satisfy the specified linear equation constitutes the solution set of the system of linear equations.

Given equations,

4x + 3y = 20........(1)

3x + 2y = 12........(2)

using the elimination method,

in elimination, we need to eliminate one of the variables from equations,

eliminating x,

multiply by 3 in equation 1

(4x + 3y)3 = 20 * 3

12x + 9y = 60.........(3)

and multiply by 4 in equation 2

(3x + 2y)4 = 12*4

12x + 8y = 48.........(4)

subtraction equations 3 and 4

12x + 9y - (12x + 8y) = 60 - 48

12x - 12x + 9y - 8y = 12

y = 12

substitute the value of y in the equation

3x + 2y = 12

3x + 12 *2 = 12

3x = 12 - 24

3x = -12

x = -4

Hence the solution is at x = -4 and y = 12.

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Both fractions in the expression 1/3+ 1/3 are examples of proper fractions

A fraction can be defined as the part of a whole variable, element or number.

In mathematics, there are different types of fractions. They include;

Some examples of simple fractions; 1/3, 5/6

Some examples of improper fractions; 6/4, 7/5, 4/3

Some examples of proper fractions; 3/4, 1/2, 2/4

Some examples of mixed fractions; 2 1/2, 3 1/4, 5 2/5

From the information given, we have that;

1/3 + 1/3

Hence, they are proper fractions.

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Answer:

10.4, 6.4

Step-by-step explanation:

The change ratio is -4

Hope this helps

Answer:

B. [tex]11x^2[/tex]

Step-by-step explanation:

Monomials are expressions that only have one term. In A, [tex]\frac{9}{x}[/tex], can actually be rewritten as 9 ÷ [tex]x[/tex], which is also two terms. Therefore, B is the only other option.

Answer:5.39

Step-by-step explanation:

30+21=51+52=103+21=124/23=5.39

The surface area of the pyramid will be 128 square inches.

A three-dimensional object's surface area is the sum of all of its faces. Real-world applications of the concept of surface areas include wrapping, painting, and eventually building things to achieve the best possible design.

Given that each side of the base of a square pyramid measures 8 inches. The height of each lateral face of the pyramid is also 8 inches.

The surface area of the square pyramid will be calculated as:-

SA = 1 / 2 x  Perimeter x Height

SA = 1 / 2 x ( 8 x 4 ) x 8

SA = 16 x 8

SA = 128 square inches

Therefore, the surface area will be 128 square inches.

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The intercept in a regression model is the predicted value of the dependent variable when all predictor variables are equal to zero.

In this context, the intercept can be interpreted as the expected value of the dependent variable when none of the predictor variables are present. Thus, in this context, the intercept does have meaning and can be used to gain insight into the relationship between the predictor and dependent variables.

Regression models are a type of statistical model used to predict a response or dependent variable based on one or more predictor or independent variables. Regression models use a variety of techniques to find the best fit line or curve that describes the relationship between the predictor and dependent variables. Common types of regression models include linear regression, logistic regression, polynomial regression, and stepwise regression.

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The square of the canonical correlation is a measure of the strength of association between two sets of variables. It ranges from 0 to 1, with values closer to 1 indicating a stronger association between the two sets of variables. In this case, with a value of .64, it suggests that there is a moderate to strong association between the two sets of variables being analyzed.

The discriminant function and the square of the canonical correlation are both measures used in statistical analysis to understand the relationship between two sets of variables.

The discriminant function is used in discriminant analysis, a type of statistical analysis that helps to predict which group an individual observation belongs to based on a set of predictor variables. The estimated discriminant function tells us the relationship between the predictor variables and the group membership.

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Answer:

-25/8

Step-by-step explanation:

(-4 3/8) - (-1 1/4)

-35/8 - (-5/4)

-35/8 + 5/4

-35/8 + 10/8

-25/8

Answer: 20

Step-by-step explanation:

To find the original number when you know that 120% of it is equal to 24, you can use the following steps:

So, 120% of the number is 24, the original number is 20.

Answer: 20

Step-by-step explanation:

Let the unknown number be x.

Then, according to the percentage formula,

x * 120/100 = 24.

By carrying over the numbers from LHS to RHS,

x = 24 * 100/120

x = 24 * 10/12

x = 2 * 10

∴ x = 20.

The required points (x ,y ) for the curve x = 6t² + 5 , y = t³ -7  has slope 1/2  are ( 29,1).

Slope of the tangent line to the curve = dy/dx

dy/dx = ( dy / dt ) × ( dt / dx )  __(1)

y = t³ -7

⇒ dy /dt = 3t²

x = 6t² + 5

⇒ dx / dt = 12t

Now substitute the value of dy/dt and dx/dt in (1) we get,

dy / dx = 3t² / 12t

⇒ dy /dx = t /4

Slope (dy /dx ) = 1 /2

⇒ t /4 = 1 /2

⇒ t = 2

Point ( x , y ) = ( 6(2)² + 5 , 2³ -7 )

                    = ( 29, 1 )

Therefore, the points (x ,y ) for the curve with tangent line to the curve has slope 1/2 is equal to ( 29, 1) .

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Given the area code of 07893 followed by 5 more digits, the total phone number would be 07893xxxxx. Tammy requires the last digit to contain only 2 different digits.

To find the total number of different phone numbers possible, we can start by using a mathematical approach.

There are a total of 10 digits that can be used to form the phone numbers, 0 to 9. As Tammy wants the last digit to contain only 2 different digits, we have to choose 2 digits from the 10 available digits. This can be calculated using the formula for combinations, nCr, which gives us the number of ways to choose r elements from a set of n elements. In this case, n = 10 and r = 2, so the number of combinations would be 10C2 = 45.

Therefore, there are 45 different combinations of 2 digits possible from the 10 digits. As each combination can be used as the last digit of the phone number, there are a total of 45 different phone numbers possible for Tammy's office. To summarize, the number of different phone numbers possible for Tammy's office is 45.

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(1) The slope of line X between (-7,6) and (-4,4) is -2/3 .

(2) The slope of line X between (-1,2) and (5,-2) is -2/3 .

(1) The points are (-7,6) and (-4,4).

The formula of the slope of line is

m = [y(2) - y(1)]/[x(2) - x(1)]

From the points; x(1) = -7, y(1) = 6, x(2) = -4 and y(2) = 4.

Now putting the value

m = (4 - 6)/(-4 - (-7))

m = -2/(-4 + 7)

m = -2/3

(2) The points are (-1,2) and (5,-2).

The formula of the slope of line is

m = [y(2) - y(1)]/[x(2) - x(1)]

From the points; x(1) = -1, y(1) = 2, x(2) = 5 and y(2) = -2.

Now putting the value

m = (-2 - 2)/(5 - (-1))

m = -4/(5 + 1)

m = -4/6

m = -2/3

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The complete question is:

(1) What is the slope of line X between (-7,6) and (-4,4) is ________?

(2) What is the slope of line X between (-1,2) and (5,-2) is ________?

The coordinates of the point P along the directed line segment AB are (3, -2).

In this scenario, line ratio would be used to determine the coordinates of the point P on the directed line segment that partitions the segment into a ratio of 5 to 3.

Mathematically, line ratio can be used to determine the coordinates of P and this is modeled by this mathematical expression:

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

Substituting the given parameters into the line ratio formula, we have the following;

P(x, y) = [(mx₂ + nx₁)/(m + n)],  [(my₂ + ny₁)/(m + n)]

P(x, y) = [(5(6) + 3(2))/(5 + 3)],  [(5(1) + 3(7))/(5 + 3)]

P(x, y) = [(30 - 6)/(8)],  [(5 - 21)/8]

P(x, y) = [24/8],  [(-16)/(8)]

P(x, y) = [3, -2]

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The formula for the interior angles is (3-2)180 which equals 180 degrees

It is important to note the properties of a polygon. They include;

A triangle is a two-dimensional shape and has three sides, thus, it is a polygon.

The formula for calculating the sum of the interior angles of any polygon is expressed as;

Sum of interior angles = (n-2)180

where, n is the number of sides

Substitute the number of sides as 3

Sum of interior angles = (3-2)180

expand the bracket

Sum of interior angles = 180 degrees

Hence, a triangle has a measure of 180 degrees

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Answer:29122

Step-by-step explanation:

Update It is 1/4 sorry about that

Answer:

40 feet

Step-by-step explanation:

We need to find the scale factor.  Two corresponding sides are AB and ED.

Let s = scale factor

20x = 12  Divide both sides by 20

x = .6

To find CD take the corresponding side 25 and multiply it by the scale factor of .6

25 x .6 = 15

Side CD is 15

CD + AC = AD

25 + 15 = 40

The shape drawn on a square grid is not an equilateral triangle, the shape is an isosceles triangle.

Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.

Given a square grid and a triangle is drawn between the grid,

let the distance of the grid be 1 unit,

so the base of the triangle is 1 unit.

for the equilateral triangle, the other two sides should be equal to 1 unit

the portion which is not shaded forms a right triangle, and the side of the triangle is hypotenuse if triangle,

using the Pythagorean theorem,

the side of the triangle be x,

height of triangle = 1 unit, base = 0.5 unit

x = √(1² + 0.5²)

x = 1.118 units

only two sides of a triangle are equal so the triangle is an isosceles triangle.

Hence the shape is not an equilateral triangle.

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1. To obtain the graph of g(x) = 2x + 7 from the graph of f(x), we need to perform a translation of the graph of f(x).

Graph is a type of visual representation of data that is used to show the relationship between two or more variables. It is a pictorial representation of data that is used to identify trends, patterns, and correlations. Graphs can be used to compare different sets of data or to show the change in data over a period of time. Graphs can be used to represent data in various forms, including bar graphs, line graphs, scatter plots, histograms, and pie charts. Graphs are a powerful tool for understanding complex data and can be used to make predictions about future trends and behavior.

2. A translation of a graph is a transformation that moves the graph left, right, up, or down without changing its shape.

3. To translate the graph of f(x) up 7 units, we need to add 7 to the y-coordinates of the points on the graph of f(x).

4. This will move the graph of f(x) up 7 units, and the resulting graph will be the graph of g(x) = 2x + 7.

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Answer:

To find the equation of a line that is perpendicular to another line and passes through a given point, we can use the slope-point form of the line equation.

The first step is to find the slope of the given line. To do this, we can rearrange the equation 5x - 3y = 2 into slope-intercept form:

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

So the slope of the given line is 5/3.

Next, we need to find the slope of the line that is perpendicular to this line. The slope of a perpendicular line is the negative reciprocal of the original line's slope.

The negative reciprocal of 5/3 is -3/5.

Now that we have the slope, we can use the point-slope form of a line to find the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5):

y - 3/5 = -3/5 (x + 1/4)

Expanding the right side:

y - 3/5 = -3/5x - 3/20

Adding 3/5 to both sides:

y = -3/5x + 3/4

So the equation of the line that is perpendicular to 5x - 3y = 2 and passes through the point (-1/4, 3/5) is y = -3/5x + 3/4.

Answer:

6

Step-by-step explanation:

Δy =6-0 =6

Δx = 2-1 =1

slope = 6/1 = 6

The solution to the system of inequalities 4x + y > 8 and x - y < 5

is (2.6, - 2.4).

Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.

The symbol a < b indicates that a is smaller than b.

When a > b is used, it indicates that a is bigger than b.

a is less than or equal to b when a notation like a ≤ b.

a is bigger or equal value of an is indicated by the notation a ≥ b.

Given, 4x + y is less than 8, x - y is greater than 5.

Therefore, 4x + y > 8 and x - y < 5.

The solution to the system is (2.6, - 2.4).

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The function inverse of f(x) = 2x2, = -2 is also a function.

In the case of a square matrix, inverse of a matrix is a crucial operation. It only works with square matrices. Finding the determinant and adjoint of the given matrix is necessary to calculate the inverse. The transposition of the cofactor of the specific matrix results in adjoint.

Although every function has an inverse, not all inverses are also functions. The vertical line test might not pass for the inverse. A function will be its inverse if the original function is a one-to-one function. In addition to passing the vertical line, a one-to-one function.

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Answer:

Step-by-step explanation:

To represent the unknowns, let x be the amount of money deposited into the first account paying 0.61% simple annual interest and y be the amount of money deposited into the second account paying 0.70% simple annual interest.

The first situation is that the total deposit into the first account is x and the interest earned on that account is (0.61/100)x. The second situation is that the total deposit into the second account is y and the interest earned on that account is (0.70/100)y.

The equation representing the first situation is: (0.61/100)x = (75/12000)x

The equation representing the second situation is: (0.70/100)y = (75/12000)y

The sum of the deposit in both accounts must be equal to $12,000, so we can write the third equation: x + y = 12,000

The system of equations is:

(0.61/100)x = (75/12000)x

(0.70/100)y = (75/12000)y

x + y = 12,000

You can use systems of equation methods like substitution, elimination or graphing to find the solution.

To find the solution, we can use the substitution method. We can start by isolating x or y in one of the equations, then substitute it into the other equation.

Let's start with the equation x + y = 12,000. We'll solve for x:

x = 12,000 - y

Now we can substitute this value of x into the first equation:

(0.61/100)(12,000 - y) = (75/12000)(12,000 - y)

Solving for y, we get:

y = $7,200

Now we can substitute this value of y back into the equation x + y = 12,000 to find x:

x = 12,000 - y = 12,000 - $7,200 = $4,800

So the solution is:

x = $4,800 and y = $7,200

This means you deposited $4,800 in the first account and $7,200 in the second account.

The probability that a plain pencil was chosen from the first box and a color pencil was chosen from the second box is given as follows:

5/24.

A probability is calculated by the division of the number of desired outcomes by the number of total outcomes.

For each box, the probabilities are given as follows:

The pencils selected from each box are independent, hence the probability of both events is obtained multiplying the probabilities of each event, as follows:

p = 1/2 x 5/12

p = 5/24.

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Therefore , the solution of the given problem of linear equation comes out to be it has infinitely many solutions.

The foundation for a linear regression curve is the equation y=mx+b. B is the slope, and m is the y-intercept. The previous sentence is sometimes referred as a "mathematical equation involving two variables," even though that y or y are separate components. Two variables make up bivariate linear equations. There are no known solutions to application issues involving linear equations. Y=mx+b is the equation for a single set of equations.

Here,

Given :

=> y = -1/2x - 3

=> x + 2y = -6

So,

=> x = -6 -2y

=> y = -1/2(-6-2y) -3

=> y = 3 + y -3

=> y=y= 0

Thus , infinitely many solutions

Therefore , the solution of the given problem of linear equation comes out to be it has infinitely many solutions .

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