Prove or disprove each of the following statements.
(i) For all integers a, b and c, if a | b and a | c then for all integers m and n, a | mb + nc.
(ii) For all integers x, if 3 | 2x then 3 | x.
(iii) For all integers x, there exists an integer y so that 3 | x + y and 3 | x − y.

Given :

You order 1.5 pounds of turkey at the deli.

You will accept the turkey if its weight is between 1.54 and 1.46 pounds.

To Find :

What absolute value inequality can be used to describe the tolerance of the weight of the turkey.

Solution :

It is given that the weight cannot be less that 1.46 pounds.

So, mathematical equation is :

x ≥ 1.46 .....1 )

Also, weight cannot be greater than 1.54 pounds.

x ≤ 1.54 ......2)

Combining equation 1 and 2 we get :

1.46 ≤ x ≤ 1.54

Hence, this is the required solution.

Răspuns:

125%

Explicație pas cu pas:

a și B sunt invers proporționale cu numerele 12 și 15

Proporționalitate inversă:

a = k / y

Prin urmare ;

a = k / 12 - - - (1)

b = k / 15 - - - (2)

Procent care reprezintă a de la b

a = 100%

b = x

k / 12 = 1

k / 15 = x

Înmulțirea încrucișată:

x * k / 12 = k / 15

x = k / 12 ÷ k / 15

x = k / 12 * 15 / k

x = 15/12

x = 1,25

1,25 * 100% = 125%

6.08 ounces of Ceylon tea and 1.92 ounces of Formosa tea must be mixed to produce a mixture of 8 oz worth $1.62/oz.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 3 = 7 is an equation.

We have,

Ceylon tea = x

Cost = $1.50

Formosa tea = y

Cost = $2

Now,

To produce a mixture of 8 oz worth $1.62/oz.

We can make two equations:

x + y = 8 _____(1)

1.50x + 2y = 12.96 ______(2)

From (1),

x = 8 - y

Substituting in (2).

1.50x + 2y = 12.96

1.50 (8 - y) + 2y = 12.96

12 - 1.50y + 2y = 12.96

0.50y = 12.96 - 12

y = 0.96/0.50

y = 1.92

And,

x = 8 - 1.92

x = 6.08

Thus,

6.08 ounces of Ceylon tea.

1.92 ounces of Formosa tea.

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Answer:

y = -5/3x + 4

Step-by-step explanation:

slope = -5/3

-1 = -5/3(3) + b

-1 = -5 + b

4 = b

y = -5/3x + 4

Answer:

\(y=-\frac{5}{3}x+4\)

Step-by-step explanation:

To write down a line that is perpendicular to one line, make sure that their slopes give a product of -1:

\(\frac{3}{5}*m_2 =-1\\m_2=-\frac{5}{3}\)

Write down an equation in the point-slope form and replace everything in and simplify:

\(y_2-y_1=m(x_2-x_1)\\y-(-1)=-\frac{5}{3} (x-3)\\y+1=-\frac{5}{3}x+5\\y=-\frac{5}{3}x+4\\\)

Answer:

9:7.

Step-by-step explanation:

14 blue triangles and 18 yellow triangles,

The LCM of them both is 2 so we can divide both of the numbers by 2.

14 divided by 2 = 7

18 divided by 2 = 9

Since they asked for the ratio of yellow triangles to blue triangles,

The answer will be 9:7.

Hope that helps. x

The solution for the agebraic equation 20 = 5(7 -x) is x = 3, which is correct option from the solution set.

Algebra is the branch of mathematics that helps to represent problems or values in the form of mathematical equation or expression

Solving for the solution in the given algebraic equation;

20 = 5(7 -x)

20 = 35 - 5x (expand bracket)

also

5x + 20 = 35 - 5x + 5x {add 5x to both sides}

5x + 20 - 20= 35 - 20 + 20 {subtract 20 from both sides}

5x = 15

x= 15/5 {divide through by 5}

x = 3

Therefore, algebraic equation 20 = 5(7 - x) is true for the value of x = 3.

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Answer:

Increase by 3.

Step-by-step explanation:

4 x 21 = 84

84 x 2 = 168

Begin to try numbers.

5 x 22 = 110

6 x 23 = 138

7 x 24 = 168

7 - 4 = 3

24 - 21 = 3

Increase each side by 3 ft. for a total dimension of 7 ft. x 24 ft.

In the antibiotic experiment described in the textbook, the independent/experimental variable is the antibiotic treatment.

The independent/experimental variable in the antibiotic experiment refers to the factor that the researchers manipulate or control to observe its effect on the outcome of the experiment. In this case, the independent variable is the antibiotic treatment. The experiment likely involves exposing a group of subjects (such as bacteria or animals) to different levels or types of antibiotics.

By varying the antibiotic treatment, researchers can examine how different doses or types of antibiotics affect the outcome of interest, such as the growth or survival rate of bacteria or the health of the animals. This allows them to assess the effectiveness or efficacy of different antibiotics in combating bacterial infections.

The experiment may involve multiple treatment groups, each receiving a different dosage or type of antibiotic, while a control group might receive no antibiotic treatment or a placebo. By comparing the outcomes among the different groups, researchers can determine the impact of the independent variable (antibiotic treatment) on the dependent variable (e.g., bacterial growth, animal health).

Overall, the independent/experimental variable in the antibiotic experiment described in the textbook is the antibiotic treatment, which is manipulated to observe its effects on the relevant outcome variables.

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The relative fitness of red birds is 1, not 0.5.

To determine the relative fitness of each bird type, we need to compare the average number of offspring each type produces in the next generation.

For red birds, the average number of offspring is 10.

For orange birds, the average number of offspring is 8.

For yellow birds, the average number of offspring is 2.

To calculate the relative fitness of each bird type, we divide each average number of offspring by the highest average number of offspring (which is 10):

- Redbirds: 10/10 = 1
- Orange birds: 8/10 = 0.8
- Yellow birds: 2/10 = 0.2

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the point (3/8, -15/8, 0) on the plane z = 4x + 2y + 3 is closest to the origin. To find the point (x, y, z) on the plane z = 4x + 2y + 3 that is closest to the origin, we can use the concept of orthogonal projection.

The closest point will be the point on the plane that is closest to the origin, which is the orthogonal projection of the origin onto the plane.

First, we need to find the normal vector of the plane. The coefficients of x, y, and z in the equation of the plane give us the normal vector. So, the normal vector of the plane is (4, 2, -1).

Next, we need to find the projection of the origin onto the plane. The projection of a vector v onto a plane with normal vector n is given by the formula:

\(proj_n(v) = v - ((v . n) / ||n||^2) * n\)

where "." denotes the dot product, "||n||" denotes the magnitude of the normal vector, and "proj_n(v)" denotes the projection of v onto the plane with normal vector n.

In this case, the vector v is the origin, which is (0, 0, 0), and the normal vector is (4, 2, -1). So, we can calculate the projection of the origin onto the plane as follows:

\(proj_n(v) = (0, 0, 0) - (((0, 0, 0) . (4, 2, -1)) / ||(4, 2, -1)||^2) * (4, 2, -1)\)

= (0, 0, 0) - (0 / 21) * (4, 2, -1)

= (0, 0, 0)

Therefore, the projection of the origin onto the plane is the origin itself.

Finally, we can find the coordinates of the point on the plane that is closest to the origin by setting z = 0 in the equation of the plane:

0 = 4x + 2y + 3

Solving for y, we get:

y = (-2x - 3/2)

So, the coordinates of the point on the plane that is closest to the origin are:

x = 3/8

y = -15/8

z = 0

Therefore, the point (3/8, -15/8, 0) on the plane z = 4x + 2y + 3 is closest to the origin.

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Answer:

3.) rule of thumb

Step-by-step explanation:

Answer:

its 10.

Step-by-step explanation:

if WZ is 12 then YZ has to be 12 too

and for YZ to be 12, x must be 9

2(9)-9=12

so if x=9 then

9+1 = 10

therefore XY= 10 :>

Answer:

$225

Step-by-step explanation:

$100/4hours=$25

$25 hours per one hour

So, $25x9=$225

Answer:

$225

Step-by-step explanation:

The coordinates in the solution to the systems of inequalities graphically is in the shaded region

From the question, we have the following parameters that can be used in our computation:

x + y ≤ 3

x + y > - 2

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

This means that all coordinates in the shaded region are the solutions to the system

One of the coordinates in the solution to the systems of inequalities graphically is (0, 0)

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It is not appropriate to use a statistical test to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools because this would only compare the mean ratios of the two groups.

There are several statistical tests that can be used to determine whether the mean student-to-teacher ratio is the same for the top 10 schools as it is for the bottom 10 schools.

However, some statistical tests may not be appropriate for this scenario.

The main reason for this is that the normal distribution of data may not be assumed in this situation. This is because student-to-teacher ratios may not be normally distributed, with some schools having much higher ratios than others, resulting in skewed data.

In this scenario, a nonparametric statistical test may be more appropriate because it makes fewer assumptions about the distribution of data. The Wilcoxon rank-sum test, for example, may be used to compare the student-to-teacher ratios of the top 10 and bottom 10 schools because it does not assume normality. The Mann-Whitney U test is another nonparametric test that can be used to compare the two groups' ratios.

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A function which could be used to determine the total amount of revenue the company earns from selling moving boxes include the following: B. r(x) = -49x² + 567x.

From the information provided, the amount of revenue with respect to price that's being generated in this scenario can be calculated by using the following function (equation):

R(x) = x × P(x)

Where:

Since it is a revenue function, we would simply substitute the value of the unit price and evaluate as follows:

Revenue, R(x) = x × P(x)

P(0) = 567

By substituting the given parameters into the formula, we have;

Revenue, R(x) = x × (567 - 49x)

Revenue, R(x) = -49x² + 567x

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In this question, we are asked to determine the truth-values of two statements involving sets A and B. For each statement, we need to determine if it is true or false. If it is false, we need to provide specific counterexamples by choosing appropriate sets A and B.

a. (A\B) ⊆ A

The statement (A\B) ⊆ A is true for any sets A and B. This is because the set difference (A\B) contains elements that are in A but not in B. Therefore, by definition, every element in (A\B) is also an element of A. There are no counterexamples to this statement.

b. A^c ⊆ (AUB)

The statement\(A^c\) ⊆ (AUB) is true for any sets A and B. This is because the complement of A, denoted as \(A^c\), contains all elements that are not in A.

On the other hand, the union of A and B, denoted as (AUB), contains all elements that are in A or in B or in both.

Since the complement of A contains all elements not in A, it includes all elements in B that are not in A as well.

Therefore, \(A^c\) ⊆ (AUB) holds true for any sets A and B. There are no counterexamples to this statement.

In conclusion, both statements are true for any sets A and B, and there are no counterexamples.

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Answer:

4,944

Step-by-step explanation:

The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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Answer:

The probability of a person getting their own hat is 1/5 or 20%.

Step-by-step explanation:

If each person has one hat the chances (the probability) of them getting their own hat would be 20%. The chances (the probability) of them getting a hat that belongs to one of the other four students would be 80%. Due to there being 5 hats each person owns 1 hat so there would be a 1 out of 5 chance of them getting their own hat.

First subtract the weight of the suitcase from the total weight they case can weigh when full:

50 - 5.7 = 44.3 pounds

This means she can put 44. 3 pounds of books in the suitcase.

Now find the number of books:

Divide the total Weight of what she can fit in the suitcase by the weight of each book:

44.3 / 2.4 = 18.458

Because the answer has a decimal you round down to the whole number, because if you rounded up it would weigh more than allowed.

The answer is she can carry 18 books

Refer to the image for the graph of the lines.

The common form of the equation of a line is y = mx + c, where m is the slope of the line and c is a constant.

We need to draw any line with a slope m = 2, and

another line with a slope m = -2.

Disclaimer: Let us assume that the constant c = 0.

Then the equation to the line with a slope of "positive" 2 is given by

y = 2x

Then the equation to the line with a slope of "negative" 2 is given by

y = -2x

Refer to the attached image for the graph of the lines with the slope of "positive" 2 and "negative" 2.

f: green line indicates a line with a slope of "positive" 2.

g: blue line indicates a line with a slope of "negative" 2.

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To determine the vertices of the hyperbola using the equation\((x - 3)^2/9 - (y - 2)^2/16 = 1,\) we can identify the values of a and b, where a represents the distance from the center to the vertices along the x-axis, and b represents the distance from the center to the vertices along the y-axis Therefore the correct option is D.

The given equation can be written as (\(x - 3)^2/3^2 - (y - 2)^2/4^2 = 1\), which indicates that \(a^2 = 9\) and\(b^2 = 16\). Taking the square root of a^2 and b^2 yields a = 3 and b = 4. The center of the hyperbola is (3, 2), and since the vertices are symmetrical about the center along the x-axis, the vertices can be found by subtracting and adding a from the x-coordinate of the center.

Consequently, the vertices of the hyperbola are (0, 2) and (6, 2). In summary, the vertices of the given hyperbola are located at (0, 2) and (6, 2).

Therefore the correct option is  D

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Answer:

The answer is explained below

Step-by-step explanation:

Statement                                                        Reason

Triangle ACD is isosceles and                         Given

<1 = <3 (<1 is congruent to <3)                                                            

∠3 = ∠4                                                             Isosceles   triangle base angles.

∠1 = ∠4                                                              Substitution Theorem

∠1 = ∠4                                                             They are produced by two lines .                                                                         AB and CD cut by transversal  

.                                                                         line AD

Segment AB || Segment CD                           Alternate interior angle theorem  

The Alternate interior angle theorem states that if two lines cut by a transversal line form congruent alternate interior angles, then the two lines are parallel to each other.

Answer:

50 years

Step-by-step explanation:

use the simple interest formula :

PRT/100

P is the principle (5000)

R is the rate of interest (4)

T is the time taken (x- unknown)

the amount at the end is double the amount invested  = 5000*2 = 10000

(5000*4 * x )/100 = 10000

20000x/100=10000

20000x = 100*10000

20000x = 1 000 000

x= 1 000 000/ 20 000

x = 50

it will take 50 years

Answer:

50 years

Step-by-step explanation:

Answer:

Step-by-step explanation:

24.5 ft

DF=28

AB=4

BF= square root 35^2-28^2

BF= 21

EF= square root 35^2-25^2

EF= 24.5

ANSWER= 24.5

Using the definition of supplementary angles, we can see that x = 60

Im just answering the first question.

We know that two angles A and B are supplementary if the sum of their measures is equal to 180°.

Then:

A + B = 180°

In this case, we know taht:

m∠A = (3x + 21)° and m∠B = (6x − 21)°

We can replace that in the equation to get:

3x + 21 + 6x - 21 = 180

Now solve that for x:

9x =180

x = 180/9

x = 60

That is the value of x.

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Step-by-step explanation:

they are similar by AA .

plz mark my answer as brainlist plzzzz . hope this will be helpful to you.