On a coordinate plane, the x-axis is labeled Number of Days and the y-axis is labeled Number of Computers. A line goes through points (3, 36), (4, 48), (5, 60). The graph shows a proportional relationship between the number of computers produced at a factory per day. In three days, 36 computers are produced; 48 computers are produced in 4 days; and 60 computers are produced in 5 days. Find the unit rate of computers per day using the graph. Unit rate: computers per da

Answer:

We can solve this integral using the u-substitution method.

Let u = 3x, then du/dx = 3 and dx = du/3.

Substituting these values, we get:

∫2x * 2/3x dx = ∫4/3 du

Integrating, we get:

= (4/3)u + C

Substituting back u = 3x, we get:

= (4/3)(3x) + C

= 4x + C

Therefore, the solution to the integral ∫2x * 2/3x dx is 4x + C.

Yes, 5x=7y is a linear equatiοn.

First οrder equatiοns include linear equatiοns. In the cοοrdinate system, the linear equatiοns are defined fοr lines. A linear equatiοn in οne variable is οne in which there is a hοmοgeneοus variable οf degree 1 (i.e., οnly οne variable). Multiple variables may be present in a linear equatiοn. Linear equatiοns in twο variables, fοr example, are used when a linear equatiοn cοntains twο variables.

Linear equatiοn is an algebraic equatiοn in οne οr mοre variables where the pοwer οf each variable is less than οr equal tο 1.

Fοr example,

y = mx + c , an equatiοn in this fοrm can be called as linear equatiοn.

Sο in equatiοn 5x = 7y

We can write this equatiοn as 7y = 5x + 0.

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A point that represents the ordered pair (0, -3) is: D. Point G.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.

Based on the ordered pair (0, -3), we can logically deduce that the coordinates would be located in quadrant IV as shown in the image attached below.

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Disjunctive Syllogism is the logical form of the given argument. Therefore, the correct option is option A.

An argument seems to be a statement or set of claims, known as premises, that seeks to assess the plausibility or acceptance of a conclusion. The logical, dialectical, and rhetorical perspectives are the three basic areas of study for arguments.

An argument in logic can be defined as a collection of propositions whereby a single one is tried to claim to follow the rest through deductively obtain reasonable that maintain truth from either the premises towards the conclusion. Disjunctive Syllogism is the logical form of the given argument.

Therefore, the correct option is option A.

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Step-by-step explanation:

Since u and w are orthogonal, their dot product is 0. Thus,

u · w = 0

Using the Pythagorean Theorem,

||u - w||^2 = ||u||^2 + ||w||^2 - 2(u · w)

Since u and w are unital (i.e., their lengths are 1), we have

||u||^2 = ||w||^2 = 1

Substituting these values and u · w = 0, we get

||u - w||^2 = 1 + 1 - 0 = 2

Taking the square root of both sides, we get

||u - w|| = √2

Therefore, we have shown that if u and w are unital orthogonal vectors, then ||u - w|| = √2.

By analytic geometry, the equation of the line y = - (1 / 12) · x + 11 is perpendicular to the line y = 12 · x + 3.

In accordance with analytic geometry, lines are described by algebraic equations of the form:

y = m · x + b

Where:

The relationship between the slopes of two perpendicular lines:

m · m' = - 1

First, write the original line:

y = 12 · x + 3

Second, write the slope and the intercept of the original line:

m = 12, b = 3

Third, the slope and the intercept of the perpendicular line:

m = - 1 / 12, b = 11

Fourth, write the equation of the perpendicular line:

y = - (1 / 12) · x + 11

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The evaluation of the inequalities are presented as follows;

2. x ≤ -5

3. x  ≤ -14

4. x ≤ 4

5. x < -10

An  inequality is an expression or comparison of two expressions that posses different values using an inequality sign.

2. -14·x + 1 ≥ 71

-14·x + 1 - 1 ≥ 71 - 1

-14·x  ≥ 70

x ≤ 70/(-14) = -5

x ≤ -5

3. -3·x - 1 ≥ 41

-3·x - 1  + 1 ≥ 41 + 1 = 42

-3·x - 1  + 1 ≥ 42

-3·x  ≥ 42

x ≤ 42/(-3) = -14

x ≤ -14

4. (x/2) + 11 ≤ 13

(x/2) + 11  - 11 ≤ 13 - 11  = 2

x/2  ≤ 2

x ≤ 2 × 2

x ≤ 4

5. x/(10) - 6  < -7

x/(10)  - 6 < -7

x/(10) -6 + 6 < -7 + 6 = -1

x/(10) < -1

x  < -10

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According to the ratio , the three girls shares are R2000,R3000 and R7000.

What is ratio?

When two numbers are compared, the ratio between them shows how often the first number contains the second. As an illustration, the ratio of oranges to lemons in a dish of fruit is 8:6 if there are 8 oranges and 6 lemons present.

Here the given total share amount is R12000.

Now the ratio for three girls is 2:3:7.

Total = 2+3+7=12

Now the share amounts are,

=> [tex]\frac{2}{12}\times 12000[/tex] = [tex]2\times1000=R2000.\\[/tex]

=> [tex]\frac{3}{12}\times=3\times1000=R3000[/tex]

=> [tex]\frac{7}{12}\times12000=7\times1000=R7000[/tex]

Hence the three girls shares are R2000,R3000 and R7000.

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Answer:

A. After 3 years, the amount in the account will be $6730.40.

B. The interest earned will be $230.40.

Step-by-step explanation:

The solution to the system of equations is (1/2, 5).

The elimination method involves manipulating these equations to eliminate one of the variables. This is done by multiplying one or both of the equations by a constant so that the coefficients of one of the variables are equal in both equations, but with opposite signs. The equations are then added or subtracted, depending on the signs, to eliminate one of the variables.

To solve the system of equations by elimination, we can follow these steps:

Multiply the first equation by 2 to get rid of the y-term:

16x + 14y = 78

Add the second equation to the new equation to eliminate the y-terms:

16x + 14y + 4x - 14y = 78 - 68

20x = 10

Solve for x:

x = 1/2

Substitute x = 1/2 into the first equation to solve for y:

8(1/2) + 7y = 39

4 + 7y = 39

7y = 35

y = 5

Check the solution by substituting both x = 1/2 and y = 5 into both original equations:

8(1/2) + 7(5) = 39 (true)

4(1/2) - 14(5) = -68 (true)

Therefore, the solution to the system of equations is (1/2, 5).

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Answer:

we can estimate that about 7632 people in the city have visited the city's community garden.

Step-by-step explanation:

You can use a proportion to estimate the number of people in the city who have visited the city's community garden. The proportion is:

(Number of people in the city who have visited the community garden) / (Total number of people in the city) = (Number of people in the sample who have visited the community garden) / (Total number of people in the sample)

We can plug in the values given in the problem to get:

(x) / (14200) = (43) / (80)

To solve for x, we can cross-multiply and simplify:

80x = 14200 * 43

x = (14200 * 43) / 80

x ≈ 7632

Therefore, we can estimate that about 7632 people in the city have visited the city's community garden.

Answer:

It is impossible, because u can say x is 5 and y is 1 or x is 9 and y is 3

Answer:I’ll give more points!! A

Step-by-step explanation:I’ll give more points!! A

C

Find the mAB

A parallelogram has two pairs of equal angle.

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. Also, the interior angles on the same side of the transversal are supplementary. The Sum of all the interior angles equals 360 degrees.

The properties of a parallelogram are as follows: The opposite sides are parallel and equal. The opposite angles are equal.

A parallelogram has two pairs of equal sides.

It has two pairs of equal angles.

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The probability that at least 5 of the callers received a busy signal is given as follows:

0.3712 = 37.12%.

The mass probability formula, giving the probability of x successes on n trials, is given by the equation presented as follows:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are listed as follows:

The parameter values for this problem are given as follows:

n = 1000, p = 0.004.

The probability of less than 5 busy signals is:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

P(X < 5) = 0.6288.

Hence the probability of at least 5 busy signals is of:

P(X >= 5) = 1 - P(X < 5)

P(X >= 5) = 1 - 0.6288

P(X >= 5) = 0.3712.

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The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Let three consecutive numbers are, (x - 1) , x , (x + 1).

Hence, By given condition we get;

⇒ (x - 1)² + 2 (x + x + 1) = 38

⇒ x² - 2x + 1 + 4x + 2 = 38

⇒ x² + 2x - 35 = 0

⇒ x² + 7x - 5x - 35 = 0

⇒ x (x + 7) - 5 (x + 7) = 0

⇒ (x - 5) (x + 7) = 0

⇒ x = 5 or x = - 7

When, x = 5

All the integers are,

x - 1 = 5 - 1 = 4

x = 5

x + 1 = 5 + 1 = 6

When x = - 7

All the integers are,

x - 1 = - 7 - 1 = - 8

x = - 7

x + 1 = - 7 + 1 = - 6

Thus, The value of all the integers are,

4, 5, 6

or, - 8, - 7, - 6

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The role of GCF, its placement and verification has been explained below. The solution has been obtained by using the concept of Greatest Common Factor.

The greatest common factor, or largest number, is the product of two or more numbers (GCF). The greatest number (factor) that separates them yields a natural number.

1. The GCF is a factor that all terms in a polynomial share.

For instance, if the polynomial has the form R * S + R * T, the GCF is R because both terms share the factor R.

2. The GCF is positioned in front of the remaining polynomials, outside of the parenthesis, once we have factored out the GCF.

R * S + R * T, given the prior example, is R (S + T).

3. By allocating the GCF to the polynomial enclosed in parenthesis, we can verify that our factoring is accurate.

Hence, the above stated is the role of GCF in factoring a polynomial.

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The value of the variables are as follows:

The value of the variables is given as follows:

sin 45° = 39/z

z = 39/sin 45°

sin 45° = 1/√2

z = 39 / 1/√2

z = 39√2

Let the height of the triangle be h;

cos 45 = h/39√2

cos 45 = 1/√2

h = 39√2 * 1/√2

h = 39

tan 60° = 39/y

tan 60° = √3

y = 39/√3

y = 13√3

sin 60° = 39/x

x = 39 / sin 60°

sin 60° = √3/2

x = 39 /√3/2

x = 26√3

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In response to the given question, we have that The baseball takes 3 function seconds to reach its highest point as a result.

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The formula for the height of the baseball is [tex]h(t) = -4.9t2 + 29.4t + 1.[/tex]

A = -4.9 and B = 29.4 in this instance. The vertex's x-coordinate is as follows:

[tex]x = -b/2a = -29.4/(2*(-4.9)) = 3[/tex]

We need to assess h(3) in order to determine the maximum height:

[tex]h(3) = -4.9(3)^2 + 29.4(3) + 1 = 44.1[/tex]

Hence, the baseball may reach a height of up to 44.1 metres.

The x-coordinate of the vertex, which we discovered to be 3, may be used to determine how long it takes the baseball to reach its maximum height. The baseball takes 3 seconds to reach its highest point as a result.

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The smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.

Natural numbers are a set of positive integers that are used for counting and ordering. In other words, natural numbers are the set of numbers that are used to represent the quantity of objects, such as 1, 2, 3, 4, 5, 6, and so on. Some definitions include zero as a natural number, while others define natural numbers to start from 1. In mathematics, natural numbers are denoted by the symbol "N" or "N+", and are sometimes referred to as counting numbers.

Whole numbers are a set of non-negative integers that include all natural numbers (positive integers) and zero. Whole numbers are used to represent quantities that cannot be divided into smaller parts, such as the number of people in a room, the number of apples in a basket, or the number of books on a shelf.

In the given question,

We know that 105 is a multiple of 3, 5, and 7. Therefore, if 3^x+5^y+7^z is divisible by 105, it must also be divisible by 3, 5, and 7.

If 3^x+5^y+7^z is divisible by 3, then 3^x ≡ 0 (mod 3), which means x ≥ 1.

If 3^x+5^y+7^z is divisible by 5, then 5^y ≡ 0 (mod 5), which means y ≥ 1.

If 3^x+5^y+7^z is divisible by 7, then 7^z ≡ 0 (mod 7), which means z ≥ 1.

Therefore, we have x+y+z ≥ 3.

We also know that 105 is the smallest multiple of 3, 5, and 7. Therefore, we want to find the smallest values of x, y, and z that will make 3^x+5^y+7^z divisible by 105.

If we want 3^x+5^y+7^z to be divisible by 105, we need x, y, and z to be multiples of 4, 4, and 3, respectively.

The smallest such values are x=4, y=4, and z=3. Therefore, the smallest possible value of x+y+z is 4+4+3=11.

So, the smallest possible value of x+y+z such that 3^x+5^y+7^z is divisible by 105 is 11.

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The recursive formula model to represent this situation is L(n) = L(n-1) + 5 where you can swim 15 laps every day.

A recursive formula is a formula that defines a sequence in terms of one or more of its preceding terms. In other words, it is a way to generate the terms of a sequence using the previous terms of the same sequence.

        L(n) = L(n-1) + 5

        where

        L(n-1) represents the number of laps swum in the previous week.

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Answer:

(-3,-2,2,3}

that is the answer

Answer:

1.2 mi/hr

Step-by-step explanation:

y=12/x
y=12/10
y=1.2 mi/hr

Answer:

[tex]\huge\boxed{\sf y = 1.2 \ mph}[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{12}{x}[/tex]

Given that, x = 10

So,

[tex]\displaystyle y=\frac{12}{10} \\\\y = 1.2 \ mph\\\\\rule[225]{225}{2}[/tex]

It would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

A square meter is a unit of measurement that denotes the surface area of a two-dimensional object or surface that is one metre long and one meter broad. It is frequently used to determine the dimensions of rooms, structures, and other areas as well as the surface area of land or other objects. The imperial method of measurement converts one square metre into 10.764 square feet. Science, engineering, and other fields frequently utilise the square metre, a core unit of the International System of Units (SI).

The area of the room is:

Area = 5m x 5m = 25 square meters

Then, we multiply the area by the cost per square meter:

Cost = 25 square meters x N5.00 per square meter = N125.00

Hence, it would cost N125.00 to furnish a square room of 5m at N5.00 per square meter.

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Answer:

b

Step-by-step explanation:

The probability that the next person will purchase no costume is 80%.

What is the difference between a probability and an odds?

The possibility of an event occurring can be expressed using odds and probability, but they are computed and understood in different ways.

Probability, which is stated as a number between 0 and 1 (or between 0% and 100%), is the possibility that an event will occur. By dividing the number of positive possibilities by the total number of potential outcomes, the probability of an event happening is determined.

The possibility of an event happening is expressed differently by odds, which are expressed as a ratio of the number of favourable events to the number of negative outcomes. It is possible to state odds as "odds for" or "odds against."

Now,

The total number of visitors who purchased costumes is:

71 (exactly one) + 12 (more than one) = 83

The total number of visitors who did not purchase a costume is: 349

The probability that the next person will purchase no costume is:

349 / (349 + 83) = 349 / 432 ≈ 0.8079

Hence, the probability that the next person will purchase no costume is 80%.

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Answer:

1a. Decay

1b. r = 0.43

1c. a = 35

1d. y = 6.481755

2a. Growth

2b. r = 2.23

2c. a = 225

2d. y = 340.4025

Step-to-Step Explanation:

1.

  (a)Decay

  (b) [tex]y=a(1-r)^{x}[/tex]

       r = rate of decay, a is the initial value

       1-r=0.57 = r=1-0.57 = r = 0.43

  (c) a = 35

  (d) [tex]y=35(0.57)^{3}\\\\y=35(0.185193)\\y=6.481755[/tex]

2.

   (a) Growth

   (b)[tex]y=a(1+r)^{x} \\[/tex]

        r = rate of growth, a is the initial value

         1+r=1.23 = r=1+1.23 = r = 2.23

   (c) a = 225

   (d) [tex]y=225(1.23)^{2} \\y=225(1.5129)\\y=340.4025[/tex]

Problem 1

Set the base of the exponent equal to 1+r and solve for r.

1+r = 0.57

r = 0.57-1

r = -0.43

The result is negative, which tells us we have exponential decay. Notice that b = 0.57 fits the interval 0 < b < 1.

The rate of decay is 43%

The initial value is a = 35 since this is the first value mentioned in the equation. Plugging x = 0 into the equation will lead to y = 35.

Let's now plug in x = 3

y = 35*(0.57)^x

y = 35*(0.57)^3

y = 35*0.185193

y = 6.481755

-----------------------------

======================================================

Problem 2

We'll follow similar steps as problem 1.

1+r = 1.23

r = 1.23-1

r = 0.23

The r value is positive, so we have growth this time. Notice that b = 1.23 fits the interval b > 1.

The growth rate is 23% since r = 0.23 converts to this.

The initial value is a = 225. Compare y = a(1+r)^x to y = 225(1.23)^x to see how the terms match up. If you want you can think of it like y = 225(1+0.23)^x. Plugging x = 0 into the equation will lead to y = 225.

Let's plug in x = 2.

y = 225*(1.23)^x

y = 225*(1.23)^2

y = 225*1.5129

y = 340.4025

-----------------------------

Answer:

-7 and -1

Step-by-step explanation:

Remember, a negative times a negative equals a positive