Lauren was given a gift card for a coffee shop. Each morning, Lauren uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 each cup of coffee costs $2. Make a table of values and then write an equation in terms of x, representing the amount money remaining on the card after buying x cups of coffee.

slope(m) of the perpendicular line is 1/3.

Slope of a line in mathematics is defined as its steepness. It is calculated as rise(difference of y- coordinates) over run(differences of x- coordinates) .

Two lines which intercept each other at an angle of 90 degree are known as perpendicular lines.

According to the given data and using the formula of perpendicular slope(m1*m2=-1);

Slope(m1) of original line =-3

Let the slope of perpendicular line be m2

m1*m2=-1

-3*m2=-1

m2=1/3

hence slope (m2) =1/3

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The two equations that could be used to find the number of

treats each dog gets is B) 18 / 6 = 3 and 6 X 3 = 18 So, the option B is the correct answer

What is an equation?

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero. Since we can balance this by deducting the right-side expression from both sides' expressions, this won't limit the generality.

A condition on a variable is what an equation in algebra is. It can only be satisfied if the variable has a specific value. That indicates that only the value of x = 9 may satisfy the equation 2x - 5 = 13.

There are several sorts of equations as well, including:

Linear equations

Quadratic equations

cube-based equations

Differential equations

Parametric equations

As Tolen has 18 dog treats and he has 6 dogs to feed so each dog will get 3 treats i.e. (18 / 6 = 3) or we can there are 6 dogs and Tolen has 18 dog  treats to finish so he will give 3 dog treats to each dog  i.e.

(6 X 3 = 18)

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The value of ∠ DEG = 20° in the given triangle. The value of b in the given triangle is 22.6.

a) ∠ DEG = ? if ∠DFE = 70°

Here, ∠F = ∠D = 70°

∠G = 90°

Sum of triangle = 180°

∠D + ∠E + ∠G = 180°

70° + 90° + x = 180°

160° + x = 180°

x = 180° - 160°

x = 20°

b) if a = 8 , c =24 then b = ?

∠DGE is right angle. It follows Pythagoras theorem:

What is pythagoras theorem?

DG² + GE² = DF²

8² + X² = 24²

X² = 576 - 64

X² = 512

X = 22.6

Hence, the value of b in the given triangle is 22.6.

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The correct match for each linear system with one of the phase plane direction fields will be:

1:B

2:C

3:D

4:A

What is plane?

In geometry, a plane is a surface made up of all the straight lines connecting any two locations on it. It is, in other words, a level or flat surface. A plane is uniquely defined in a Euclidean space of any number of dimensions by one of the following: three non-collinear points are used. Other names for it include a two-dimensional surface. A plane has an unlimited width, an endless length, zero thickness, and no curvature. The flat surfaces of a cube or cuboid, as well as the flat surface of paper, are all true instances of geometric planes, despite the fact that it is difficult to envision a plane in real life.

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Answer:

  z ∈ (-∞, -3]

Step-by-step explanation:

You want the solution to −2(2z−3)≥2z+24.

Simplify the inequality:

  -4z +6 ≥ 2z +24

  -18 ≥ 6z . . . . . . . . . add 4z -24

  -3 ≥ z . . . . . . . . divide by 6

The solution is z ∈ (-∞, -3].

Answer:

30

Step-by-step explanation:

40% of what number is 12?

.4n = 12  Divide both sides by .4

n = 30

Answer:

30

Based on the given conditions, formulate: 12/40%

Multiply both the numerator and denominator with the same integer: 120/40

Cross out the common factor:30

Answer: 30

Answer:

9-|12x-1|=9

Step-by-step explanation:

Solve for x over the real numbers:

9 - abs(12 x - 1) = 9

Subtract 9 from both sides:

-abs(12 x - 1) = 0

Multiply both sides by -1:

abs(12 x - 1) = 0

Eliminate the absolute value:

12 x - 1 = 0

Add 1 to both sides:

12 x = 1

Divide both sides by 12:

Answer: x = 1/12

Answer:

Answer is B

Step-by-step explanation:

For  102 batches of chilli, 85 number of teaspoons of seasoning needed.

What do you mean by fraction?

Fraction represents a part of a whole, or more generally, any number of equal parts. In everyday English, fractions represent how many parts of a particular size are there.

For positive common divisors, the numerator and denominator are natural numbers. The numerator represents the number of equal parts and the denominator shows the number of parts that make up the unit or whole. A zero part can never make up a whole, so the denominator is never zero.

It is given that a recipe calls for 5 teaspoons of seasoning for every 6 batches of chilli.

For  6 batches of chilli, number of teaspoons of seasoning needed = 5

For 1 batch of chilli, number of teaspoons of seasoning needed = 5/6

For  102 batches of chilli, number of teaspoons of seasoning needed = [tex]\frac{5}{6}\times 102[/tex] = 85

Therefore, For  102 batches of chilli, 85 number of teaspoons of seasoning needed.

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The total volume is given as 195.36 m³.

Volume can be defined as the capacity of any object. It can be calculated by multiplying the base area to the height.

The composite figure consists of three cuboids and two right circular cylinders.

The volume of a cuboid is the product of its length, breadth and height.

And, the volume of cylinder is given as πr²h

As per the figure given in the question the total volume is given as,

3(1 × 5 × 8) + 2 (π × 2² × 3)

= 40 × 3 + 12π × 2

= 120 + 24 × 3.14

= 195.36

Hence, the volume of composite figure is given as 195.36 m³.

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Answer:

66

Step-by-step explanation:

y = 58 e^(0.027 * 5)

y = 58 e^(0.135)

y = 58 * 1.144537

y = 66.383133

y = 66

The function that relates the distance traveled to the time is given as follows:

d = vt.

In which v is the average velocity during the time traveled.

The average velocity is calculated as the division of the total distance by the total time, hence the following equation is built to model the proportional relationship between these variables:

v = d/t.

In this problem, we want to relate the distance traveled to the time, hence we have to solve the expression for d, as follows:

d = v x t

d = vt.

(applying cross multiplication to isolate the variable d).

Then it is a proportional relationship in which the average velocity acts as the constant of proportionality.

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The solution to the given integration problem is;

[tex]\frac{[(x^{2} + 1)x^{\frac{3}{2} } *(3x^2 - 2)]}{15} + C[/tex]

We want to integrate the function x³[√(x² + 1)dx]

This is expressed as;

∫x³[√(x² + 1)dx]

Preparing for substitution we have;

∫2x[x²√(x² + 1)/2dx]

Make u = x²

du/dx = 2x

dx = (1/2x) du

Thus, we now have;

¹/₂∫u√(u + 1)du

¹/₂∫(u^(3/2) - √u) du

Applying power rule and solving this gives us;

[tex]\frac{(x^2 + 1)x^{\frac{5}{2} } }{5} - \frac{(x^2 + 1)x^{\frac{3}{2} } }{3}[/tex]

= [(x² + 1)^(3/2) (3x² - 2)]/15 + C

Thus, that is the solution of solving the integration problem.

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The value of x is 3 units.

What is the mid-point segment of the triangle?

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

We have,

In ΔBCD

QR = x - 2 units

BD = x + 7 units

A line segment that connects two midpoints of the sides of a triangle is called a midsegment.

Mid-point segment of the triangle:

QR = 1/2(BD)         .............(1)

x - 2 = 1/2(x + 7)

2(x - 2) = x + 7

2x - 4 = x + 7

2x - x = 7 - 4

x = 3

Hence,  the value of x is 3 units.

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The simplified expression of 2√x²y is 2x√y

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

2\sqrt[]{x^2y}

Rewrite properly

So, we have the following representation

2√x²y

Take the square root of x²

So, we have

2x√y

Hence, the solution is 2x√y

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Answer:

the equation 10 = x - y

Step-by-step explanation:

Let x represent the initial value of the investment, and let y represent the amount of money that each person receives after the investment is withdrawn.

We know that the cost of withdrawing the investment is $10, so we can write the equation 10 = x - y. We also know that each person receives $40, so we can write the equation y = 40.

We can now solve for x by substituting the value of y into the first equation. Since y = 40, we can substitute 40 for y in the equation 10 = x - y to get 10 = x - 40. Solving this equation for x, we find that x = 50.

Therefore, the initial value of the investment was $50.

The graph of the inequality is attached.

What is closed circle in inequality?

Open circles are used for numbers that are less than or greater than (< or >). Closed circles are used for numbers that are less than or equal to and greater than or equal to (≤ or ≥).

Given inequality is x > 3.2.

The inequality sign of the given inequality is grater than.

The graph of the inequality will starts with open circle.

Since x is greater than 3.2. Therefore the given inequality will represent all real numbers that are greater than 3.2.

Thus the inequality will represent all number that lie on right of 3.2 on the number line.

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The range  of this absolute value function is  -∞ < y ≤ 7

What are the domain and range of a function?

The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

Consider the vertical extent of the graph along y axis.

It starts from +7 extends till    -∞

So, the range is  -∞ < y ≤ 7

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With the Application of Algebraic expression first minute call charge is $1.126 and next every minute will be charge at $0.14

what is Algebraic expression?

Using the operations +, -,, or, a group of numbers or variables can be combined to form an expression. Expressions in algebra that include variables, numbers, and mathematical operators differ from expressions in arithmetic that simply contain numbers and mathematical operators.

solution:

Let first min charge =x

And charge for each additional minute = y

Now we have two equations

x+11y=2.35……(1)

x+17y=3.65……..(2)

Sub. (1) from (2)

6y = 1.3

y= 0.316

Put value in equation (1)

x+11×0.316=2.35

x=2.35- 3.476

X= 1.126

Therefore, first minute call charge is $1.126 and next every minute will be charge at $0.14

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Andrea could use 28÷7 = 4 this division problem to check her work.

Check one-by-one:

A. 0÷4=7

The answer to 7 divided by 0 is 0. This is due to the fact that dividing a non-zero number by zero is mathematically impossible. See complete response below.

B. 7÷4 = 28

7 * 4 = 28 is the correct value where this value is 1.7

C. 14÷4 = 7

The value of the above is not equated because 3.5 ≠ 7

D. 21÷7 = 4

Where 21÷7  is 3. Hence this is also not a correct answer.

E. 28÷7=4

7 * 4 = 28, which is correct equation.

Hence, Andrea could use 28÷7 = 4 this division problem to check her work.

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On average, men drive faster then women

The statement is true.

What is p-value?

The p-value, used in null-hypothesis significance testing, represents the likelihood that the test findings will be at least as extreme as the result actually observed, assuming that the null hypothesis is true.

We are given a statement that,

A hypothesis test was used to test the hypothesis that men drive faster on average than women.

The p-value in that case was 0.16 and the level of significance used was 0.1

As the p value is greater than level of significance we can say that the null hypothesis is correct

Hence we can say that on average men drive faster than women

The statement is correct

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The correct answer to the task above about the statements which identifies and describes the student model that is most consistent with the data in the table is:

What is describes?

To describe something is to put into words its appearance, nature, attributes, etc. The word is frequently used to describe a scene or an event with vividness of personal perception. To narrate is to describe what happened in detail, usually by describing an event or series of events in the chronological sequence in which they occurred.

Student Model 1 shows that sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups.

The correct answer choice is option b.

What is meant by the classification of living organisms?

The classification of living organisms simply refers to the grouping of living things together on the basis of their similarities and differences.

However, based on the information given on the table in the image above, the sharks and ray-finned fishes share some structural similarities and are the most closely related among the four groups which is most consistent therein.

In conclusion, it can therefore be deduced from the explanation given above that the students model 1 gave a very good description of features which are consistent in the organisms.

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Answer:

the total number of random sample n 10

probability of is 0.267

A system of hardware, software, information, people, and used to further an organization's goal is known as a business information system (BIS).

Given that,

Students can prepare for a range of positions in business, industry, government, and the military with a Bachelor of Business Administration with a major in Business Information Systems (BIS). Business information systems, often utilising computer systems and technology, provide information that firms utilise to govern themselves successfully and efficiently. Hardware, software, data, procedures (design, development, and documentation), and people make up the bulk of business information systems. Students majoring in BIS will learn how to use technology and information systems to enhance corporate processes and decision-making.

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We can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.

Compounding is the method through which interest is added to both the principal balance already in place and the interest that has already been paid.

Thus, compounding can be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

So, the time that will be taken to make the investment triple is:

Amount invested: $2500

Interest rate: 3.4%

Compounding: Semiannually

Now, consider a period of 2 years:

3.4 * 6/12 = 1.7%

The interest rate that is effective will be 1.7%.

Currently, the future value of the compounded rate at 1.7% for a period of 65 factors equals 2.9913.

Consequently, the value will be $2,500 2.9913 = 7,478.25.

65 months divided by six years equals 10.833 years in total.

0.833 * 12 makes up  10 months a year.

Therefore, we can conclude that it will take Bob 10 years and 10 months to triple his investment when the compounding is happening semi-annually.

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(a) The probability that more than three aircraft arrive within an hour is 0.2970.

(b) The probability that no interval contains more than three arrivals is 2.56.

(c) The length of an interval of time is 0.891 hours.

The time between arrivals of small aircraft at a country airport is exponentially distributed with a mean of one hour.

(a) We will find the probability that more than three aircraft arrive within an hour,

P(X > 3) = 1 - P(X ≤ 3)

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

             = 1 - [ ( [tex]e^{-4/3}[/tex] 1° / 0!) + ( [tex]e^{-4/3}[/tex] 1¹ / 1!) + ( [tex]e^{-4/3}[/tex] 1² / 2!) + [tex]e^{-4/3}[/tex] 1³/ 3!]

             = 1 - (0.7029)

P(X > 3) = 0.2970

(b) Now we calculate probability that no interval contains more than three arrivals if 30 separate one-hour intervals are chosen,

(1 - P(X > 3)³°) = (1 - 0.2970)³°

                      = 2.56

(c) Let the length of an interval of time is t, the calculation for t is given as;

P(X = 0) = 0.41

[tex]e^{-t}[/tex](t)° / 0! = 0.41

          [tex]e^{-t}[/tex] = 0.41

          - t = ln(0.41)

          - t = -0.891

            t = 0.891 hours

Therefore the length of an interval of time such that the probability that no arrivals occur during the interval is 0.41 is 0.891 hours.

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Answer:

Step-by-step explanation:

area = pi * r^2

area = pi * 2^2

area = 4pi

area = pi * 4^2

area = 16pi

The probability of 'It will definitely turn dark tonight' would be 1.

So option (B) is correct.

What is a probabilty?

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.

If by "likelihood" probability, the word definitely implies the probability would be 1, certainty.

Because definitely after daylight, the light will turn dark at the night.

So the probability would be 100% or 1.

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