Suppose that the functions r and s are defined for all real numbers x as follows.
r(x)=x+5
s(x) = 4x+2
Write the expressions for (r*s) (x) and (r-s) (x) and evaluate (r+s)(1).

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.

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Answer:

4 is the smallest number

Step-by-step explanation:

4 times 8 is 32. 4 + 8 is 12. 4 is smaller than 8 so it would be the smaller number

Answer:

18

Step-by-step explanation:

72/12=6

6×3=18

.....

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 value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is : -

1.5(x + 4) - 3 = 4.5(x - 2)

Using the distributive property, multiply the terms in the equation.

1.5x + 1.5 × 4 - 3 = 4.5x - 4.5 × 2

1.5x + 6 - 3= 4.5x - 9

Isolate the variable x using transposing method

4.5x - 1.5x = 6 - 3 + 9

3x=15-3

3x = 12

Therefore,  x = 12/3 = 4

The value of x satisfying the equation 1.5(x + 4) - 3 = 4.5(x - 2) is 4.

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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

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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.

Using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

A conversion factor is a quantity or formula required to change a measurement from one system of units to another system of the same measurement.

The amount is often expressed as a fraction or ratio with a multiplication factor.

A conversion ratio (or unit factor), if the numerator and denominator have the same value represented in various units, always equals one (1).

So, we know that:

1 kg = 100 g

Weight of the adult penguin: 5 1/2 kg that is,

5 1/2 = 10+1/2 = 11/2 = 5.5

5.5kg = 5500 g

Weight of the newborn penguin: 150 g

Weight gain from chick to adult:

5500 - 150

5,350 g

Therefore, using the conversion factor we know that the penguin gained 5,350 grams of weight from a chick to an adult.

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[tex]\begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\log(x)=2\hspace{5em}\log(y)=3\hspace{4em}\log(2)\approx 0.3\hspace{4em}\log(3)\approx 0.48 \\\\[-0.35em] ~\dotfill\\\\ \log\left(\sqrt[3]{x^4\cdot y^2} \right)\implies \log\left(\left( x^4\cdot y^2 \right)^{\frac{1}{3}} \right)\implies \cfrac{1}{3}\log(x^4 y^2) \\\\\\ \cfrac{1}{3}[\log(x^4)~~ + ~~\log(y^2)]\implies \cfrac{1}{3}[4\log(x)~~ + ~~2\log(y)]\implies \cfrac{1}{3}[4(2)~~ + ~~2(3)] \\\\\\ \cfrac{1}{3}[8~~ + ~~6]\implies {\Large \begin{array}{llll} \cfrac{14}{3} \end{array}}[/tex]

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.

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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 measure of the angle ∠BDC is 68°.

What is the straight line angle?

A straight angle in geometry is one that is 180 degrees in length. It looks like a straight line, which is why it is known as a straight angle. In other words, it is an angle whose sides are in the same straight line but opposite to the vertex.

We have,

∠BDA is a straight angle

so ∠BDA = 180°

We need to find the ∠BDC

∠CDA = -8x + 48°

∠BDC = -7x + 12°

∠BDA = ∠BDC + ∠CDA = 180°

(-8x + 48°) + (-7x + 12°) = 180°

-15x + 60° = 180°

-15x = 120°

x = -8°

∠BDC = -7x + 12°

= -7(-8°) + 12°

= 56° + 12°

= 68°

Hence, the measure of the angle ∠BDC is 68°.

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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]

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The number with the given features in this problem is given as follows:

36.

First we consider that the number is a square number, meaning that it has a perfect square root.

The number is between 10 and 99, hence the possible square numbers between 10 and 99 are given as follows:

The numbers with a sum of the digits of 9 are given as follows:

The factors of each number are given as follows:

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Answer:

f(6) = 21

Step-by-step explanation:

f(6) = 3x + 3

f6) = 3(6) + 3

f(6) = 18 + 3

f(6) = 21

Although part of your question is missing, you might be referring to this full question: If P is the incenter of ΔJKL, find each measure (triangle as attached).

Based on the property of incenter, the measurements of the sides and the angles will be:

JK = 21.2 units

KL = 26.63 units

JL = 28.33 units

m∠K = 36°

By using the property of incenter:

PM = PN = PO = 7 units

∠MJP = ∠OJP = 32°

∠NLP = ∠OLP = 22°

By using the triangle sum theorem,

m∠JKL + m∠KLJ + m∠LJK = 180°

2(m∠NKP) + 2(m∠NLP) + 2(m∠MJP) = 180°

2(m∠NKP) + 2(22°) + 2(32°) = 180°

2(m∠NKP) = 180° - 108°

m∠NKP = 36°

Then, from ΔJMP,

tan(32°) = MP/MJ

tan(32°) =  7/MJ

MJ =  7/tan(32)°

MJ = 11.20

And from ΔPOL,

tan(22°) = OP/OL

tan(22°) = 7/OL

OL = 17.33

And from ΔKNP,

tan(36°) = NP/KN

tan(36°) = 7/KN

KN = 9.63

Hence, JK = MJ + MK = 21.2 units

KL = LN + KN = 26.63 units

JL = JO + OL = 28.33 units

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It is false that if the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular

The augmented matrix is an extension of a matrix in which we add a column ( non homogeneous part of the system)

Say , Ax = b

Here , b is column part

So , Augmented matrix will be [ A : b ]

The Rank of augmented matrix can be found by performing elementary row operations on a augmented matrix and counting the number of the rows without zero comparing the rank of an augmented matrix

The rank of coefficient matrix can determined if there is a  solution to the system of solution

In the question this statement,

If the rank of the augmented matrix of a system of n linear equations in n unknowns is greater than the rank of the matrix of coefficients, then the matrix of coefficients is nonsingular is false

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a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).

(b)The P-value is 0.0068.

To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.

A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.

C.I=x-t(alpha/2)xs/sqrt{n}

=3150+_2.01*250/sqrt{50}

=(3078.9358,3221.0642)

b) P value =P(t<-2.83)+P(t>2.83)

use calculator

                 =0.0034+0.0034

                  =0.0068

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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 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.

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Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

To find an unknown quantity in a problem we use the algebraic expression. These are combinations of variables and constant terms. Here variables are used to represent the Unknown Numbers.

Here we have

Martina, Ahmad, and Ryan served a total of 87 orders

Since we don't how many orders served each one

Let's assume that each of them with different variables

Martina served 'm' orders

Ahmad served 'a' orders

Ryan served 'r'

Given that

Ahmad served 9 fewer orders than Martina  

=> a = m - 9 ---- (1)

Ryan served 2 times as many orders as Martina.

=> r = 2m --- (1)    

Given that total served orders = 87

=> m + a + r = 87

=> m + m - 9  + 2m = 87        [ from (1) and (2) ]

=> 4m = 87 + 9

=> 4m = 96

=> m = 24

Number of orders served by Ahmad, a = 24 - 9 = 15  

Number of orders served by Ryan, r = 2(24) = 48

Therefore,

Martin served 24 orders, Ahmad served 15, and Ryan served 48 orders.

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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.

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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.

1) The probabilities are given as follows:

a) More than 75: 0.0301 = 3.01%.

b) Between 60 and 73: 0.4484 = 44.84%.

c) Less than 50: 0.1057 = 10.57%.

2) The proportion of students who fail the module is of: 0.0062 = 0.62%.

3) The measures are given as follows:

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation in this problem are given as follows:

[tex]\mu = 60, \sigma = 8[/tex]

The probability that an score is more then 75 is one subtracted by the p-value of Z when X = 75, hence:

Z = (75 - 60)/8

Z = 1.88

Z = 1.88 has a p-value of 0.9699.

1 - 0.9699 = 0.0301 = 3.01%.

The probability of an score between 60 and 73 is the p-valeu of Z when X = 73 subtracted by the p-value of Z when X = 60, hence:

Z = (73 - 60)/8

Z = 1.63

Z = 1.63 has a p-value of 0.9484.

Z = (60 - 60)/8

Z = 0

Z = 0 has a p-value of 0.5.

Then:

0.9484 - 0.5 = 0.4484 = 44.84%.

The probability of an score less than 50 is the p-value of Z when X = 50, hence:

Z = (50 - 60)/8

Z = -1.25

Z = -1.25 has a p-value of 0.1057.

The proportion who might fail the test is the p-value of Z when X = 40, hence:

Z = (40 - 60)/8

Z = -2.5

Z = -2.5 has a p-value of 0.0062.

Then the statistical measures are obtained as follows:

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Answer:

Step-by-step explanation:

Therefore , Scatter plot1 0.342 ,Scatter plot2 -0.994, Scatter plot 3 0.743 ,Scatter plot4 -0.743 and  Scatter plot5 0.994.

An example of a plot or mathematical diagram is a scatter plot, which uses Cartesian coordinates to show the values of typically two variables given a collection of data. One more variable can be presented if the points are programmed.

Here,

The observed data are highly erratic, according to scatter plot 1. The relationship between the two variables is thus weak. There is a 0.342 correlation coefficient.

Observations in the scatter plot 2 are aligned with the straight line. A reduction in y values follows a rise in x values. Therefore, there is a significant negative connection between the two variables. This means that the correlation coefficient is -0.994.

The scatter plot's third scatter plot shows that the observations are slightly yet positively divergent. Consequently, there is a weakly positive connection between the two variables. The correlation coefficient is therefore 0.743.

Scatter plot 4: The observations show a considerably negative deviation from the mean. Consequently, there is a light negative correlation between the two variables. Consequently, the correlational coefficient is -0.743.

Scatter plot 5: The observations are aligned with the straight line in the scatter plot. The matching y values rise as the corresponding x values do. Therefore, there is a significant positive connection between the two variables. So, 0.994 is the correlation coefficient. As follows is the matching table:

Spread layout 1 0.342 Spread plot 2 -0.994 3.743% Scatter plot Dispersion plot4 -0.743 Spread plot5 0.994

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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

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Answer:

Step-by-step explanation:

2 and 2 equal 5

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.

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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.

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.  A well-formed formula consisting of two expressions linked by an equals sign is considered to be an equation in English, but the word's cognates in other languages may have slightly different definitions. For instance, an équation is defined as having one or more variables in French. 

There are 3 solutions  to the system of equations

1)single solution

2)infinite solutions

3)no solutions

Therefore , most of the time, a system of linear equations has a single solution, but it is occasionally possible for it to have infinite or no solutions (parallel lines).

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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.

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