Solve by using substitution. Express your answer as an ordered pair.
{4x+y=1
y=x−4

The probability that one of the following numbers is rolled is 0.135.

We are provided a 37 sided dice. Hence, each of the number between 1 to 37 can be rolled. Now, to find the probability of rolling any of these five numbers, we will simply perform the multiplication.

The formula to be used for calculation of probability to roll any one number on the dice -

Probability = number of favourable outcomes ÷ total number of outcomes

Keep the values in formula

Probability = 1/37

Now, for the mentioned five numbers among which any can be rolled, the probability is -

Probability = 5 × (1/37)

Performing multiplication

Probability = 5/37

Performing division

Probability = 0.135

Hence, the probability is 0.135.

Learn more about probability -

https://brainly.com/question/13604758

#SPJ4

Answer:

Step-by-step explanation:

2 and 2 equal 5

The number of infected students after 5 days = 694

The number of infected students  with respiratory virus is modeled by an exponential function f(t) = 25000 /1+332e^(-0.45t) where time t, is measured in days.

We need to find the number of students infected with the virus after 5 days.

For t = 5,

f(5) = 25000 /1+332e^(-0.45 * 5)

f(5) = 25000 /(1+332*0.1054)

f(5) =  25000 /35.9928

f(5) = 694.58

f(5) ≈  694

Therefore, the number of students infected with the virus after 5 days = 694

Learn more about exponential function here:

https://brainly.com/question/14355665

#SPJ4

The complete question is:

75 students are currently infected with respiratory virus- that is spreading through a population of college students_ The number of infected students is modeled by f(t) = 25000 /1+332e^(-0.45t) where time; t, is measured in days. How many students are predicted to be infected with the virus after 5 days? Round your answer to the nearest whole number.

If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80 then s2 = 18 and C. M = 85

The standard deviation (s2) is a measure of the variability of the sample data, while the mean (M) is a measure of the central tendency. The higher the mean and the higher the standard deviation, the more likely it is that the null hypothesis will be rejected. Therefore, the set of sample characteristics that is most likely to lead to a rejection of the null hypothesis is M = 85 and s2 = 18.

Learn more about null hypothesis here

https://brainly.com/question/28920252

#SPJ4

From the compound inequality explained below in concept, it has been proven that compound inequality has a solution of all real numbers except 3.5.

We are given the inequalities as;

5x – 3 > 14.5 or (2x + 5)/3 < 4

For the first inequality;

Add 3 to both sides to get;

5x > 17.5

Divide both sides by 5 to get;

x > 3.5

For the second inequality, we have;

(2x + 5)/3 < 4

Multiply both sides by 3 to get;

2x + 5 < 12

Subtract 5 from both sides to get;

2x < 7

Divide both sides by 2 to get;

x < 3.5

The first inequality gives the solution as x > 3.5.

The second inequality gives the solution as x < 3.5.

The solution of an “or” compound in equality is everything in both solution sets, so the solution set is all of the numbers less than 3.5 and greater than 3.5. Since neither of the inequalities includes 3.5, the compound inequality has a solution of all real numbers except 3.5.

Read more about Inequality problems at; https://brainly.com/question/25275758

#SPJ1

The answer is A & C

To determine if a set of ordered pairs represents a function, you can check if each input (x value) is associated with only one output (y value).

In set A, input 4 is paired with output 1 and input 8 is paired with output 2. These two inputs are paired with only one output, so the set A can represent a function.

In set B, input -2 is paired with two different outputs.

-1 and 5. This means that -2 has multiple exits, so set B does not represent a function. In set C, input 7 is paired with output 4 and input 8 is paired with output 3. The set C can represent a function because these two inputs are paired with only one output.

Read more about functions on brainly.com/question/10741291

#SPJ4

Answer:

The error is when 6y = 12 it will be -6y = 12 and the intercept would be -2.

Step-by-step explanation:

Since the initial displacement is made by s0 and body moves with initial velocity and acceleration after that, the final displacement after time t is

[tex]s= \frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]

The displacement is only the difference between the locations of the two marks and is unrelated to the route used to get there.

The formula is:

[tex]a= \frac {Velocity}{Time}[/tex] (Acceleration)

[tex]v= \frac {Displacement}{Time}[/tex](Velocity)

Initial Displacement = s0

Displacement from position s0 after time t  = [tex]\frac {1}{2} at ^{2} + v_{0}t[/tex]

Total Final Displacement (s) = [tex]\frac {1}{2} at ^{2} + v_{0}t+s_{0}[/tex]

To learn more about Displacement visit:

https://brainly.com/question/11934397

#SPJ4

a) Combining like terms (7a + 10b) − (4a − 6b) = 3a + 16b
b) The Simplify expression −5x + 8y + 2x − 3y the answer is -3x + 5y
c) The inequality x - 4 ≤ -1 Graph is given below.

What do you mean by algebraic expression?

When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.

Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).

An algebraic expression is composed of various parts.

a) Given expression:

(7a + 10b) - (4a - 6b)

= 7a + 10b - 4a + 6b

On combining like terms we get,

(7a - 4a) + (10b + 6b)

= 3a + 16b

Therefore, (7a + 10b) − (4a − 6b) = 3a + 16b

b) Given expression :

−5x + 8y + 2x − 3y

On combining like terms we get,

-5x + 2x + 8y - 3y

= (-5x + 2x) + (8y - 3y)

= -3x + 5y

therefore, −5x + 8y + 2x − 3y  = -3x + 5y

c) Given expression:

x - 4 ≤ -1

⇒ x ≤ -1 + 4

⇒ x ≤ 3

Graph of the function is given below:

To learn more about the algebraic expression from the given link.

https://brainly.com/question/28036476

#SPJ1

Answer:

I am not exactly sure what they want you to put in the boxes, but hopefully the explanation below will shed some light on what is going on with this problem.

Step-by-step explanation:

The equation would be

y = 3x  

It looks like your question wants you to write the equation in the form

r(x) = 3x

y would be the student's score on the test.

x would be the number of questions that the student got right.

The x is the independent variable.  It tells us how many questions the student got right.

The y is the dependent variable.  It is the student's score.  The student's score depends on how many questions the student got right.

R(25) is saying what would be the score if the student got 25 answer correct?

3(25) = 75.  The student would get a score of 75

The new value of  correlation will be 0.20.

What is correlation?

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

Given that the size of the sample is n = 15.

The correlation is r = 0.20.

The degree of the association between two measurement variables is quantified and determined via correlation analysis. Regression aims to describe the relationship as an equation at the same time. For patients who visit an emergency room (ED), for instance, we could use correlation and regression.

The correlation coefficient is unaffected by the change of origin.

Thus r = 0.20.

To learn more correlation coefficient, click on below link:

https://brainly.com/question/15402346

#SPJ1

First convert 50 mm into cm : 5

base :9

height :5

formula of traingle= ½*(b*h)

.'. ½* (9*5)

½*45

.'. area : 22.5 cm²

The given statement is true.

How it is true ?

Because if the matrix of coefficients of a homogenous system of n linear equations is non-singular then there will be the inverse for that matrix.

We know ,

If matrix is non-singular then it has unique solution

and if it singular then it has either no-solution or infinite solution.

So, the above statement is always true.

Learn more about homogeneous system using link :

https://brainly.com/question/14934034

#SPJ4

The unknown angle measures are 51.5° and 51.5° respectively.

What is an isosceles triangle?

An isosceles triangle in geometry is a triangle with two equal-length sides.

Given, side DE = side EF

Then, ∠D = ∠F

So, the sum of all angles of the triangle = 180°

or, ∠D + ∠E + ∠F = 180°

or, ∠F + 77° + ∠F = 180°

or, 2∠F = 180° - 77°

or, ∠F = 103/2 = 51.5°

And, ∠D = 51.5°

Hence, the unknown angle measures are 51.5° and 51.5° respectively.

To learn more about an isosceles triangle

https://brainly.com/question/29618252

#SPJ1

Katie runs fastest among all .

What is the units of conversion ?

Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.

Given:

Speed of Adam = 13 feet per second

Speed of Stephanie = 199 feet in 17 seconds

Speed of Noah = 1 mile in 592 seconds

Speed of Katie = 878 feet in 1 minute

Now on converting all the units to one single unit,we get  

1 mile = 5280 feet

1 minute = 60 seconds

Speed of Adam = 13 feet per second

Speed of Stephanie = 199 feet in 17 seconds

                                 = [tex]\frac{199}{17}[/tex] feet per second

                                 = 11.705 feet per second

Speed of Noah = 1 mile in 592 seconds

                         = 5280 feet in 592 seconds

                         = [tex]\frac{5280}{592}[/tex] feet per second

                        = 8.919 feet per second

Speed of Katie = 878 feet in 1 minute

                         = 878 feet in 60 seconds

                         = [tex]\frac{878}{60}[/tex] feet per second

                         = 14.6333 feet per second

Hence ,Katie runs fastest among all sice its speed is the highest .

Learn more about the units conversion by:

https://brainly.com/question/19420601

#SPJ1

In an isosceles triangle, the angle opposite the base is referred to as the vertex angle.

A triangle refers to a two-dimensional shape which comprises of three sides and three angles. The isosceles triangle is a type of triangle in which two sides are congruent i.e., they are the same length. The third side of an isosceles triangle is of different length and is referred to as the base. The three angles of any triangle add up to a sum of 180°. In isosceles triangles, the two angles located along the base are referred to as the base angles which are always congruent, or equal. The angle opposite the base is referred to as the vertex angle and is different value from the two base angles. The value for the vertex angle can always be calculated by subtracting the base angles from 180° using the general formula: 180° - 2B = A, where B refers to the base angle and A is the vertex angle.

Note: The question is incomplete. The complete question probably is: Which is the vertex angle of an isosceles triangle.

Learn more about Isosceles triangle:

https://brainly.com/question/1475130

#SPJ4

Answer:

Step-by-step explanation:

You want to fill a table using the given rules, then describe the relationship between the table values.

Starting with 100, you want to subtract 20 to get next terms:

  100

  100 -20 = 80

  80 -20 = 60

  60 -20 = 40

The next terms are 80, 60, 40.

Starting with 20, you want to subtract 4 to get next terms:

  20

  20 -4 = 16

  16 -4 = 12

  12 -4 = 8

The next terms are 16, 12, 8.

Looking at second terms, we can determine which description is true:

  80 -80 = 0 ≠ 16 . . . . . the description "subtract 80" fails

  80/5 = 16 . . . . . . . . . . the description "divide by 5" works

Each term in pattern B can be found by dividing the corresponding term in pattern A by 5.

A₂ₓ₃ matrix and B₃ₓ₄ matrix, The dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.

Matrices represent data in the form of rows and columns in an array form.

Suppose we have two matrices and their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.

Let A₂ₓ₃ matrix and B₃ₓ₄ matrix, Then the dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.

learn more about matrices here :

https://brainly.com/question/11367104

#SPJ1

.

The percentage of 35 percent of 80 is 28

In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.

For example, 45% (read as "forty-five per cent") is equal to the fraction

45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.

The percentage of 35 percent of 80 is

= [tex]\frac{35}{100}[/tex]× 80

=28

The percentage of 35 percent of 80 is 28

To learn more about  percentage:

https://brainly.com/question/29306119

#SPJ4

There are No Real Roots possible for the Quadratic Equation

What is Quadratic Equation?

Quadratics are polynomial equations of the second degree, which means that they contain at least one squared term. Quadratic equations are another name for it. The quadratic equation has the following general form: ax² + bx + c = 0. where x is an unknown variable and the numerical coefficients a, b, and c.

Solution:

x² - 12x + 52 = 0

Formula to Solve the equation is -b +- (D) / 2a

D is the discriminant

D = √b² - 4ac

D = √12*12 - 4*52

D = √144 - 208

D = √-64

Since the value of Discriminant is negative

Therefore there are no real roots possible for the equation

To learn more about Quadratic Equation from the given link

https://brainly.com/question/1214333

#SPJ1

Answer: They always have one pair of parallel lines.

Step-by-step explanation:

Answer:

Q1. The sum of your hat size and shoe size is 54.

Q2. The correct answer is 101.

Q3. The correct answer is 6561.

Step-by-step explanation:

Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:

H = 2S

H = S + 18

Substituting the first equation into the second equation, we get:

2S = S + 18

S = 18

Then, substituting this value back into the first equation, we get:

H = 2S

H = 2 * 18

H = 36

The sum of your hat size and shoe size is S + H = 18 + 36 = 54.

Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.

Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.

Using Poisson distribution to calculate the probability distribution of the event, the probability is 0.2084

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty.

A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a particular value or set of values. It is used to describe the behavior of random variables, either discrete (e.g. coin flips) or continuous (e.g. temperatures), and is often used in the field of statistics to predict the behavior of a system or process.

Using Poisson distribution;

P(X ≥ 5) = 1 - P(X ≤ 4)

P= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))

P= 1 - (e^(-4.615) + (4.615*e^(-4.615))/1! + (4.615^2*e^(-4.615))/2! + (4.615^3*e^(-4.615))/3! + (4.615^4*e^(-4.615))/4!)

P = 0.2084

Learn more on probability distribution here;

https://brainly.com/question/14802212

#SPJ1

Answer:

7/9

Step-by-step explanation:

Using vieta's formulas, we know that a + b = 4 and ab = -6.

1/a^2 + 1/b^2 can be written as (a^2 + b^2)/a^2b^2.

(a^2 + b^2)/a^2b^2 can be written as (a+b)^2 - 2ab/(a^2)(b^2)

{4^2 - 2(-6)}/(-6)^2 = 28/36 = 7/9

The positive integers that meet the requirement that the product of their digits be 120 are: 1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5461, 5416, 5614, and 5641.

To find the integer numbers that meet the aforementioned requirement that the product of its digits be 120, we must take a positive 4-digit integer number and multiply its digits until obtaining the result of 120.

In this case, the four digits would be 1456. So, we must find all the four-digit numbers that are made up of these numbers, the numbers are shown below:

1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5 4161, and 5 614, and 4

Finally, we can check it with any of the numbers and the result will be 120 because the order of the factors does not change the result.

Learn more about integers in: https://brainly.com/question/1768255

#SPJ1

Answer: 227

Step-by-step explanation: (5 + 4 ) = 9                                                      

= 3 x 9^2 - 4^2

9^2 = 81

= 3 x 81 - 4^2

4^2 = 16

= 3 x 81 - 16

3 x 81 = 243

= 243 - 16

243 - 16 = 227

= 227.

Answer: 108

Step-by-step explanation:
8.78x12.356=108.48568 so the estimate would be 108

The complete type of bipartite graphs ,[tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] will have the maximum possible of all number incliding edges among all the present triangle-free nodes i.e., graphs with all same number of vertices.

Approach: The wide variety of edges can be most whilst each vertex of a given set has an aspect to each different vertex of the opposite set i.e. edges = m * n in which m and n are the wide variety of edges in each the sets. that allows you to maximize the wide variety of edges, m need to be same to or as near n as possible.

The two main sets are X = {A, C}, Y = {B, D}.

The vertices for the given set X join, with the vertices Y and vice-versa.

Similar proposition will always holds for bipartite planar type of  graphs: any n-vertex bipartite  graph (n ≥ 3) includes at most 2n − four edges, moreover, each n-vertex bipartite planar graph may be prolonged to an n-vertex bipartite planar graph with 2n − four edges.

To learn more about bipartite graphs, refer: brainly.com/question/28062985

#SPJ4

Correct Question:

Among what g will have a complete bipartite graphs  [tex]K_{n.n}[/tex] and [tex]K_{n.n+1}[/tex] have the maximum possible number of edges among it.

The side lengths of the new phone are proportional to the old phone, then the width of the new phone is 5.125 inches.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given information in the question,

The dimensions of the older phones are,

Length, L(1) = 1.4 inches

Width, W(1) = 4.1 inches

The dimensions of the new phone are,

Length, L(2) = 1.75 inches

Width, W(2) = ?

Then the width of the new phone is,

1.4 × W(2) = 4.1 × 1.75

W(2) = (4.1 × 1.75)/1.4

W(2) = 5.125 inches.

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ1