Reasoning with linear equations

The amount of vanilla in one container of pudding is given as follows:

One teaspoon.

The amount of vanilla in one container of pudding is found applying the proportions in the context of the problem, via a rule of three.

The rule of three is defined as follows:

1/6 teaspoon - 2/12 containers.

x teaspoon - 1 container.

The first line can be simplified as follows:

1/6 teaspoon - 1/6 containers.

(as 2/12 = 1/6).

Hence there is one teaspoon of vanilla in one container of pudding.

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Answer:

f(11) = 87

Step-by-step explanation:

substitute n = 11 into f(n) , that is

f(11) = 7 + 8(11 - 1) = 7 + 8(10) = 7 + 80 = 87

The midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)

The midpoint between two points in a Cartesian plane is the point that is equidistant from both points and is located exactly in the middle of the line segment connecting the two points. To find the midpoint, we need to average the x-coordinates and the y-coordinates of the two given points.

Given the points (-7,-9) and (-0.5,-3), the midpoint can be found by:

averaging the x-coordinates (-7 + -0.5) / 2 = -3.75

averaging the y-coordinates (-9 + -3) / 2 = -6

So, the midpoint between (-7,-9) and (-0.5,-3) is (-3.75,-6)

Alternatively, the midpoint formula is:

(x1+x2)/2 , (y1+y2)/2

So for the given points,

(x1,y1)= (-7,-9) and (x2,y2)= (-0.5,-3)

Midpoint (x,y) = (-7+(-0.5))/2 ,(-9+(-3))/2

= (-3.75,-6)

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The distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

The length of the line segment bridging two points on a plane is known as the distance between the points. d=((x2 - x1)2 + (y2 - y1)2) is a common formula to calculate the distance between two points.

This equation can be used to calculate the separation between any two locations on an x-y plane or coordinate plane.

So, we have the points:

(-2, 3) and (5, -3)

Distance formula: d=((x2 - x1)² + (y2 - y1)²)

Insert values and calculate as follows:

d=((5 - (-2))² + (-3 - 3)²)

d=((7)²+(-6)²)

d=√85
d=9.21

Therefore, the distance between the given 2 points (-2, 3) and (5, -3) is 9.21 units.

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Someone has no enough wire fencing to enclose the rectangular garden.

Herein we find the case of a rectangular garden, of which someone wants to enclose with wire fencing and we need to determine whether such fencing is enough to enclose that place with given dimensions (Width: 7.5 feet, area: 78.75 square feet).

The area of the rectangular garden is described by following formula:

A = w · l

Where:

First, determine the length of the rectangular garden:

l = A / w

l = 78.75 / 7.5

l = 10.5 ft

Second, calculate the perimeter of the rectangular garden:

p = 2 · (w + l)

p = 2 · (7.5 ft + 10.5 ft)

p = 36 ft

Thrid, determine if the fencing wire is enough to enclose the garden: (1 yard - 3 feet)

l = 36 ft × 1 yd / 3 ft

l = 12 ft

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Answer:

Hint: everything in that big [] is to the power of zero. anything to the power of zero is one. so

1+(6-8)=?

The binomial probability that exactly 4 out of 8 customers will use the Self-Checkout is 0.008.

Binomial probability is the probability based on the binomial distribution.

The binomial distribution is used in statistics to summarize the likelihood that a value will take one of two independent values (for example, success or failure) under a given set of parameters or assumptions.

The binomial distribution formula is:

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

P = binomial probability

x = number of times for a specific outcome within n trials

{ⁿ \ ₓ} = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trials

Random sample, n = 8

Specific outcome within n trials = 4

pˣ = 0.5⁴

= 0.0625

qⁿ = (1 - 0.5)⁸ ⁻ ⁴

= 0.5⁴

= 0.0625

Pₓ = {ⁿ \ ₓ} pˣ qⁿ ⁻ ˣ

= 8/4 x 0.0625 x 0.0625

= 2 x 0.0625 x 0.0625

= 0.0078125

= 0.008

Thus, the probability of precisely 4 customers using the Self-Checkout is 0.008.

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The two factors of the first number 36 which their sum is equal to 13 are 4 and 9.

Factor is a number that divides another number without a remainder. That is if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product.

The first number 36 have the following factors:

1, 2, 3, 4, 6, 9, 12, 18, and 36.

the factors 4 and 9 will be the factors in question because;

4 × 9 = 36

4 + 9 = 13

Therefore, 4 and 9 are the two factors of 36 that their product is the first number 36 and their sum is the second number 13.

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Answer:

6.8125

Step-by-step explanation:

Answer:

60

Step-by-step explanation:

360 degrees divided by 6 sides equal 60 degrees

Answer:

23

Step-by-step explanation:

1/2-2.5=9

1/2x=9+2.5

x=11.5/0.5

x=23

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases}[/tex]

[tex]A = 2000\left(1+\frac{0.03}{12}\right)^{12\cdot 20}\implies A=2000(1.0025)^{240} \implies \boxed{A \approx 3641.51} \\\\\\ 3641.51~~ - ~~2000~~ \approx~~ \stackrel{earned~interest}{\boxed{1641.51}}[/tex]

The answer is 1.4

In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

Given here:

2.6-1.2=1.4

Hence, The answer is 1.4

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If the equation be 3/2X+6 =2/5x+9 then the length of side AB is -15/11.

The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Two expressions joined by an equal sign form a mathematical statement known as an equation.

A condition on a variable (or variables) is a pair of expressions in the variable (or variables) that have the same value. The solution, also known as the root of the equation, is the quantity for which the equation holds true. Even if the LHS and RHS are switched, an equation still holds true.

Let the equation be 3/2X + 6 = 2/5x + 9

simplifying the equation, we get

15x + 27 = 4x + 12

15x = 4x - 15

11x = -15

Divide both sides by 11, we get

[tex]$\frac{11 x}{11}=\frac{-15}{11}$$[/tex]

[tex]$x=-\frac{15}{11}$$[/tex]

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Answer: Here is the calculation:

The cost of the wings is $0.25 per wing

The cost of the pitcher of beverage is $5

The cost of the ranch dip is $1.50

Sales tax is 8.5%, so you need to add 8.5/100 * (5+1.5) = 0.0825 to the cost of the beverage and dip.

The cost of the beverage and dip after tax is 5+1.5+0.0825 = 6.5825

The total cost of the wings, beverage, and dip before tip is 6.5825 + 20 = 26.5825

You need to leave a 20% tip, so you need to add 0.2*26.5825 =5.31650 to the total cost

The total cost of the wings, beverage, dip and tip is 26.5825+5.31650 = 31.899

So you have $20 and you want to spend $31.899 including tax and tip, you can purchase 20/0.25 = 80 chicken wings.

Step-by-step explanation:

Poopy man is my husband uwu

anyways ur answer is 3^x

The values of the variables in the similar triangles are y = 2.25 units, x = 5 units and r = 3.75 units

Similar triangles are triangles that have the same shape, but possibly different size. Two triangles are similar if and only if their corresponding angles are congruent, that is, they have the same measure. When two triangles are similar, their corresponding side lengths are in proportion.

Since the triangles are similar. We write:

h/y = y/3

Since h = 3, we have:

3/4 = y/3

y = 9/4 = 2.25 units

x = √(4² + h²)        (Pythagoras theorem)

x = √(4² + 3²) = 5 units

r = √(y² + 3²)

r = √(2.25² +  3²)  = 3.75 units

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f(1) = -1

Quadratic equations form the shape of a parabola, which looks like a U-shape.

Graph

To find f(1) we need to find the y-value when x = 1. To do this, we can just look at the graph. Find where on the graph x = 1, then look for where the graph intersects this value. This graph has an x value of 1 when y = -1. We can see this at the coordinate point (1,-1). Thus, f(1) = -1.

Equation

We can also solve this using the equation of the function. This function is represented by f(x) = x² - 2. Now, to find f(1), plug 1 in for x.

This also shows that f(1) = -1.

A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

given

y = 5000x - 250

y = 5000 * 0.29 - 250

y = 1200

A speculator estimates that the price of the 0.29 carat diamond ring will be y = 1200 by y = 5000x - 250.

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Answer:

[tex] {w}^{2} - 7w + 10 = (w - 2) ( w- 5) \\ ( {w}^{2} - 7w + 10) \div (w - 5) = (w - 2)[/tex]

Answer: 250

Step-by-step explanation:

249 is closer to 250 than 240

Answer:

Step-by-step explanation:

249 is rounded to closest to 250

distance between two points is given by √ (5x² +14x +61)

Length between two points that is measured along any straight line or curve line.

Assume two points p (x, y) and Q (a, b). The distance between P and Q is determined by a formula.

distance PQ = √ [(a -x) ²+ (b - y²]

We are given two points (5, -1) and (x, 2x+5)

the distance between two points = √[(x- 5)² + {(2x+5) - (-1)}²]

                                                         √[(x-5) ²+ (2x+5+1) ²]

                                                       = √[(x- 5)² + (2x+6)²]

hence, distance between two points = √ (5x² + 14x+61)

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60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

An expression is combination of variables, numbers and operators.

The given expression is (9.42×10⁴)(6.45×10²)

We have to find the value of the expression.

9.42×6.45×10²×10⁴

60.759×10²×10⁴

Bases are same then the powers will be added.

60.759×10⁶

Hence, 60.759×10⁶ is the value of the expression (9.42×10⁴)(6.45×10²).

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1.20C + 3 >= 13.50

Where C is the number of chores Janie does.

On the left side of the inequality, 1.20C represents the amount of money Janie earns from doing chores, and 3 represents the amount of money she already has. The inequality states that the sum of the money she earns from doing chores and the money she already has must be greater than or equal to the cost of the CD (13.50).

This inequality can be simplified:

1.20C >= 10.50

C >= 8.75

Thus, Janie could do at least 8.75 chores to have enough money to buy the CD, since she can do fractions of chores.

Answer:

3 + 1.2 c > 13.50

Step-by-step explanation:

First of all, let's write an equation that gives us the income Janie gets for doing chores. As she earns 1.20 (I will omit the $ symbol for simplicity) for each chore c she makes we can write income depending on the amount of chores as:

income(c) = 1.2 c

If she  does 1 chore she gets 1.2, if she does 4 chores she gets 4.8 and so on for any c (obviously c is positive as she can do negative chores).

So, her total money will be the sum of what she earns for chores and the money she already has: 3.

money (c) = 3 + 1.2 c

If she does 2 chores she has 3+2.4=5.4 and so on for any c.

Now we need her money to be greater or equal to 13.50 in order to buy the CD. The inequality is:

money (c) > 13.50

3 + 1.2 c > 13.50

We can go further and solve it. First lets subtract 3 in both sides:

12 c > 10.50

Now, divide both sides by 1.2:

c > 10.50 / 1.2

c > 8.75

So, she needs at least 8.75 chores to earn enough money to buy the CD. As she can do fractions of chores the answer is 8.75 chores. Is she couldn't do fractions she would need at least 9 chores.

Janie is a student in a science fair. Her project tracks how far a rumor can get spread throughout a school.

f(x) = 8, x ≈ 8.

Generally, To isolate x, we need to take the natural logarithm (ln) of both sides of the equation:

ln(f(x)) = ln(4) + 1.5xln(1 + 0.3)

then we can divide both sides by 1.5ln(1 + 0.3)

x = (ln(f(x)) - ln(4)) / (1.5ln(1 + 0.3))

To find x when f(x) = 8, we can substitute 8 for f(x) and solve for x:

x = (ln(8) - ln(4)) / (1.5ln(1 + 0.3))

x ≈ 8

Therefore, when f(x) = 8, x ≈ 8.

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Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x

A whole can be represented by any number of equal parts, or fractions. The number of units of a particular size is expressed as a fraction in standard English. 8, 3/4. Fractions are included in wholes. Numbers are expressed in mathematics as the ratio of the numerator to the denominator. In simple fractions, each of these is an integer. A complicated fraction contains a fraction in either the numerator or denominator. There is a difference between the numerators and denominators of true fractions. A sum that is a fraction of a whole is referred to as a fraction. You can evaluate it by dissecting the whole into smaller pieces. For example, 12 is used to represent one-half of a full number or item.

given

she is correct as  Barbara picked 36 apples

in one time she put 12 apples in the basket

Barbara would choose the apples three times, so a visual model using Whole Numbers by Fractions would be created to determine the outcome. 2x

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The table of w = t + 11.2 is:

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

w = t + 11.2

The table can be calculated as,

When t = 1, w = 1 + 11.2 = 12.2

When t = 2, w = 2 + 11.2 = 13.2

When t = 3, w = 3 + 11.2 = 14.2

When t = 4, w = 15.2

So on..

Thus,

t     w

0    11.2

1     12.2

2    13.2

3    14.2

4    15.2

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