NEED HELP DUE TODAY!!!!
2. How do the sizes of the circles compare?





3. Are triangles ABC and DEF similar? Explain your reasoning.

4. How can you use the coordinates of A to find the coordinates of D?

The cost of the notebook is $4.50

Let's call the cost of the necklace "N" and the cost of the scarf "S". We know that Elise spent a total of $184 on the scarf, necklace, and notebook, so we can write:

S + N + NB = 184

We also know that after making her purchases, Elise had $89.50 left, so we can write:

89.5 = 184 - (S + N + NB)

Simplifying this equation, we get:

S + N + NB = 94.5

We're also given that the scarf cost three-fifths the cost of the necklace, so we can write

S = (3/5)N

Finally, we're told that the notebook cost one-sixth as much as the scarf, so we can write:

NB = (1/6)S

Now we can the substitution method here

(3/5)N + N + (1/6)(3/5)N = 184 - 89.5

Simplifying the right-hand side

(3/5)N + N + (1/6)(3/5)N = 94.5

Combining like terms on the left-hand side

(21/10)N = 94.5

Multiplying both sides by 10/21

N = 45

So the necklace cost $45. We can use this to find the cost of the scarf

S = (3/5)N = (3/5)($45) = $27

And we can use the cost of the scarf to find the cost of the notebook

NB = (1/6)S = (1/6)($27) = $4.50

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Assuming a 0.05 significance level, both hypothesis tests would reject the null hypothesis. This means that there is enough evidence to suggest that the shopping cart icon's design affects the users' behavior. Therefore, the design should be changed to improve the user's experience.

Step by step explanation:

The problem is not stated, so we need to make some assumptions. We will assume that the hypothesis tests were done to determine whether a change in the shopping cart icon design would affect the users' behavior.

The null hypothesis (H0) is that the design of the shopping cart icon does not affect the users' behavior, while the alternative hypothesis (Ha) is that the design of the shopping cart icon affects the users' behavior.

The significance level is 0.05, which means that we are willing to accept a 5% chance of making a type I error (rejecting the null hypothesis when it is actually true).

If both hypothesis tests reject the null hypothesis, it means that the p-values were less than 0.05, and there is enough evidence to suggest that the design of the shopping cart icon affects the users' behavior.

Therefore, it is recommended to proceed with changing the design of the shopping cart icon to improve the user's experience.

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The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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Angles AOB and BOC are complimentary angles if AOC is a right angle. Let's use x to represent the angle BOC's size. Next, we have: Angle AOB plus Angle BOC equals 90° (definition of complementary angles).

BOC/AOB angle equals 2/3 (given) Angle AOB may be expressed in terms of angle BOC using the second equation: (3/2) × angle BOC, where angle AOB (multiplying both sides by angle AOB)    Angle BOC plus angle (3/2) equals 90 degrees. When we simplify this equation, we obtain: BOC angle (5/2) times equals 90 degrees. By multiplying both sides by 5, we obtain: BOC angle = (2/5) x 90 degrees BOC angle is 36 degrees. Hence, the angle's size Substituting this expression into the first equation, we get: (3/2) x angle BOC + angle BOC = 90 degrees Simplifying this equation, we get: (5/2) x angle BOC = 90 degrees.

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Answer:

y = 1/7x + 29/7

Step-by-step explanation:

Slope intercept form is y = mx + b

m = the slope

b = y-intercept

m = 1/7

Y-intercept is located at (0, 29/7)

So, the equation is y = 1/7x + 29/7

The steps which can help in minimizing the variance in the four cards are correct selection of the suit with maximum number of cards.

If you have four cards and were to bet based upon suits while flipping them one at a time while trying to minimize variance, you should follow the below steps:

First, you need to check the suits of the four cards you have.

Now, you need to select the suit that has a maximum number of cards. For instance, if the four cards are 5 of hearts, 7 of spades, 2 of diamonds, and 10 of hearts, you need to select hearts as it has two cards.

After selecting the suit with the maximum number of cards, you need to start flipping the cards one at a time.

Keep a count of the number of times you get the chosen suit. For instance, if you chose hearts, you will count the number of times you get hearts after flipping each card.

Once you get the chosen suit, you can place your bet. The amount of your bet can depend on the number of times you have gotten the chosen suit so far.

So, this process doesn't guarantee that you will win every time.

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Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, the population will be 852.78 after another three years.

A logistic model, also known as the Verhulst-Pearl model, is a type of function used to describe population growth that is limited. It’s a form of exponential growth that takes into account the carrying capacity of an environment.

Population growth that is limited and slows down as the population approaches its carrying capacity is modeled using the logistic model. It is given by this equation:

[tex]P(t) = K / (1 + Ae^{-rt})[/tex]

where P(t) is the population at time t, K is the carrying capacity, A is the constant of proportionality, and r is the growth rate.

Suppose a population grows according to a logistic model with initial population 200 and carrying capacity 2,000. If the population grows to 500 after one year, substitute this information into the logistic model: [tex]P(1) = 500[/tex], [tex]K = 2000[/tex], and [tex]P(0) = 200[/tex].

[tex]500 = 2000 / (1 + Ae^{-r(1)})[/tex]

Now, solve for A by dividing both sides by 2000 / (1 + A):

[tex]1 + A = 4A = 3[/tex]

Substitute the value of A back into the logistic model equation:

[tex]P(t) = 2000 / (1 + 3e^{-rt})[/tex]

Solve for r by using the data provided in the problem for the first year (t = 1) and second year (t = 4):

[tex]P(1) = 500 = 2000 / (1 + 3e^{-r(1)})[/tex]

[tex]P(4) = ? = 2000 / (1 + 3e^{-r(4)})[/tex]

Solve the first equation for r:

[tex]500 = 2000 / (1 + 3e^{-r})\\1 + 3e^{-r} = 4e^{-r}\\1 + 3e^r = 4e[/tex]

Solve for e using the quadratic formula to get:

e = 0.4274 and e = 1.1713

Let e = 0.4274:

[tex]1 + 3e^{-r} = 4e^{-r}\\1 + 3(0.4274)^{-r} = 4(0.4274)^{r}\\1 + 0.5746^r = 1.7166^r[/tex]

Take the natural logarithm of both sides:

[tex]ln(1 + 0.5746^r) = ln(1.7166^r) - lnr\\ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex]

Use a graphing calculator to solve for r:

[tex]ln(1 + 0.5746^r) = rln(1.7166) - lnr[/tex];  -0.1568 < r < 0.7534

Solve for r using the second year’s data:

[tex]2000 / (1 + 3e^{-r(4)}) = P(4)\\2000 / (1 + 3(0.4274)^{-r(4)}) = P(4)\\P(4) = 852.78[/tex]

Thus, the population will be 852.78 after another three years.

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Using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.

An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values.

As in 3x + 5 = 15, for example.

There are many different types of equations, including linear, quadratic, cubic, and others.

So, we have:

x + y = 100                        .........A

40 × x + 140 y = 85 × 100

40 x + 140 y = 8500         ........B

Solving (A) and (B) as follows:

(40 x + 140 y) - 40 × ( x + y ) = 8500 - 40 × 100

(40 x - 40 x) + (140 y - 40 y) = 8500 - 4000

0 + 100 y = 4500

y = 4500/100

Hence, the price per unit of grocery is $1.40 = y = 45 pounds.

Now, put the value of y in equation (A) as follows:

x + y = 100

x = 100 - y

x = 100 - 45

x = 55 pounds

The number of groceries at the 40-cent price is x = 55 pounds.

Therefore, using equations we know that 45 pounds are included in the $1.40 worth of groceries and 55 pounds worth of groceries are being purchased for 40 cents.

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Correct question:
A grocer has two kinds of candies, one selling for 40 cents a pound and the other for $1.40 per pound. How many pounds of each kind must he use to make 100 pounds worth 85 cents a pound?

The ratio of the length of the side directly opposite the angle to the length of the hypotenuse is known as the sine of an acute angle in a right triangle.

Hence, the sine of angle T in the right triangle RST with a right angle at S is given by:

opposite side / hypotenuse = sin T

We must know the triangle's side lengths in order to calculate the value of sin T. We can use trigonometric ratios to calculate the lengths of the remaining sides.

if we know the length of the hypotenuse and the measurement of one acute angle.

thus, we cannot define the value of triangle RST.

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Runners and sprinters could be on the track team is 25 distance.

Distance:

Distance is a qualitative measurement of the distance between objects or points. In physics or common usage, distance can refer to a physical length or an estimate based on other criteria (such as "more than two counties"). The term Distance is also often used metaphorically to refer to a measure of the amount of difference between two similar objects.

According too the Question:

Based on the based Information:

15× 5÷3

canceling all the common factor, we get:

5 × 5 = 25

Now, the Product or Quotient is 25.

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In response to the stated question, we may state that As a result, the rectangular pyramid has a surface area of 296 ft2. 296 ft2 is the correct answer.

In Euclidean geometry, a rectangle is a parallelogram with four small angles. It may also be defined as a fundamental rule hexagon or one in which all of the angles are equal. Another alternative for the parallelogram is a straight angle. Four of the vertices of a square are the same length. A quadrilateral with four 90° angle vertices and equal parallel sides has a rectangle-shaped cross section. As a result, it is also known as a "equirectangular rectangle" at times. A rectangle is sometimes referred to as a parallelogram due to the equal and parallel dimensions of its two sides.

To determine the surface area of a rectangular pyramid, first calculate the area of each face and then add them together.

Given the rectangular pyramid's dimensions:

Slant height= 10 ft base length (l) = 12 ft base width (w) = 8 foot

Then, calculate the area of the base. The area of the base is simply l w: because it is a rectangle.

Base area = [tex]12 ft x 8 ft = 96 ft^2[/tex]

A triangle face's area equals 1/2 its base height, where base = w or l and height = sh.

[tex]1/2 *8 ft *10 ft = 40 ft^2[/tex] area of the first triangle face

[tex]1/2 *12 ft *10 ft = 60 ft^2[/tex]area of the second triangular face

Third triangular face area = [tex]1/2 *8 ft *10 ft = 40 ft^2[/tex]

The area of the fourth triangular face is equal to [tex]1/2 *12 ft *10 ft = 60 ft^2.[/tex]

Now put the areas of all the faces together to get the entire surface area:

Total surface area = base area + sum of all triangular face areas

Surface area total =[tex]96 ft^2 + (40 ft^2 + 60 ft^2 + 40 ft^2 + 60 ft^2)[/tex]

296 ft2 total surface area

As a result, the rectangular pyramid has a surface area of 296 ft2.

296 ft2 is the correct answer.

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45.53 ,fencing is needed to build the fence.

A solid object's surface area is a measurement of the total area that the surface of the object takes up.

The definition polyhedra of arc length for one-dimensional curves and the definition of surface area for (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.

A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.

This definition of surface area uses partial derivatives and double much simpler mathematical concepts than the definition of surface area integration and is based on techniques used in infinitesimal calculus.sought a general definition of surface area.



Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.

2*3.14*14.5/2

45.53ft

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Answer: calculate the amount of his refund.

Step-by-step explanation:

The required value of the base of the triangle is   [tex]\frac{7\sqrt{3} }{3}[/tex].

Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.

In the given triangle, we will use tangent function to find the value of x.

tan(∅) = Perpendicular/ base

tan(60°) = 7/x

x = 7/tan(60°)

x = 7/√3                         ∴ (tan(60°) =√3  )

On rationalizing

x = [tex]\frac{7\sqrt{3} }{3}[/tex]

Thus, required value of x is [tex]\frac{7\sqrt{3} }{3}[/tex].

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Jenny works at Sammy's Restaurant and is paid according to the rates in the following

table.

Jenny's weekly wage agreement

Basic wage $600.00

PLUS

$0.90 for each customer served.

In a week when Jenny serves n customers, her weekly wage, W, in dollars, is given by

the formula

W = 600+ 0.90n.

(i) Determine Jenny's weekly wage if she served 230 customers.

(ii) In a good week, Jenny's wage is $1 000.00 or more. What is the LEAST number

of customers that Jenny must serve in order to have a good week?

(iii) At the same restaurant, Shawna is paid a weekly wage of $270.00 plus $1.50 for

each customer she serves.

If W, is Shawna's weekly wage, in dollars, write a formula for calculating Shawna's

weekly wage when she serves m customers.

(iv) In a certain week, Jenny and Shawna received the same wage for serving the same

number of customers.

How many customers did they EACH serve?

3 / 3

(i) If Jenny serves 230 customers, her weekly wage is

W = 600 + 0.90n = 600 + 0.90(230) = $807.00

Therefore, Jenny's weekly wage if she serves 230 customers is $807.00.

(ii) We want to find the least number of customers, n, that Jenny must serve in order to earn $1,000 or more. That is,

600 + 0.90n ≥ 1,000

0.90n ≥ 400

n ≥ 444.44

Since n must be a whole number, Jenny must serve at least 445 customers in order to earn $1,000 or more in a week.

(iii) Shawna's weekly wage, W, in dollars, when she serves m customers is given by the formula:

W = 270 + 1.50m

Therefore, Shawna's weekly wage when she serves m customers is $270.00 plus $1.50 for each customer she serves.

(iv) Let's assume that Jenny and Shawna received the same wage, W, for serving the same number of customers, x. Then we have:

Jenny's wage = 600 + 0.90x

Shawna's wage = 270 + 1.50x

Setting these two expressions equal to each other, we get:

600 + 0.90x = 270 + 1.50x

330 = 0.60x

x = 550

Therefore, Jenny and Shawna each served 550 customers.

To design a cylindrical can (with a lid) to contain 1 liter (= 1000 cm3) of water, using the minimum amount of metal, we need to consider the following parameters:Height and Diameter of the canThickness of the metalMaterial used for making the canLet's assume we use Aluminium as a material. Now, let's start designing the can:Height of the can:

Volume of water = 1000 cm3Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³h = (4000 cm³) / (π d²) h = (4000 cm³) / (3.14 * d²) h = (1273.24) / d²Diameter of the can:

Volume of cylinder = πr²hVolume of cylinder = π (d/2)² hVolume of cylinder = π (d²/4) hVolume of cylinder = 1000 cm³π (d²/4) h = 1000 cm³d²h = 4000 cm³d² = (4000 cm³) / h d² = (4000 cm³) / (1273.24/d²) d² = 3.1425d = 17.8 cmThickness of the metal:We can assume the thickness to be 0.5 mm.Material used for making the can:AluminiumTotal Surface Area of the can:Total Surface Area of cylinder = 2πrhTotal Surface Area of cylinder = 2π(d/2)(1273.24/d²)Total Surface Area of cylinder = 1273.24/d Total Surface Area of lid = πr²Total Surface Area of lid = π (d/2)²Total Surface Area of lid = π (17.8/2)²Total Surface Area of lid = 248.5Total Surface Area of the Can = 1273.24/d + 248.5Now, we can calculate the minimum amount of Aluminium required to make the can by minimizing the Total Surface Area of the can.Total Surface Area of the can = 1273.24/d + 248.5d (in cm)Total Surface Area of the can = 1273.24/7.09 + 248.5(7.09)Total Surface Area of the can = 584.24Therefore, the minimum amount of Aluminium required to make the can is 584.24 cm².

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Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

At x = -2, which is the vertex of the quadratic function, the function f(x) is constant.

To classify the graph of a function as increasing, decreasing, or constant, you need to examine the direction in which the graph is moving.

x = -2 is the vertex of the quadratic function, which is the turning point of the function, where it changes from increasing to decreasing, hence the function is considered to be constant at x = -2, as it has a derivative of zero at x = -2.

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The number of litres (Volume) of oil that is present in the tank of given dimension is calculated to be 806 litres (approximately).

The volume of any cylinder can be calculated using the formula,

V = πr²h

(Here V is the volume, r is the radius of the base, and h is the height of the cylinder)

As, the cylinder is one-fifth full of oil, which means that it is four-fifths empty. Therefore, the volume of oil in the tank is:

Volume of oil = (1/5) x Total Volume

Substituting the given values, we have:

Total Volume =  π(80cm)²(200cm) = 4,031,240 cm³

Volume of oil = (1/5) x 4,031,240 cm³ = 806,248 cm³

Converting cm³ to litres, we have:

1 litre = 1000 cm³

Volume of oil = 806,248 cm³ ÷ 1000 = 806.248 litres

Therefore, after rounding of the final volume (806.248 litres) to the nearest litre, the final answer is found to be 806 litres of oil.

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The price after discount is $33 and option 1 is the correct answer.

A discount is a drop in a product's or service's price. Discounts can be provided for a variety of purposes, such as to entice consumers to make larger purchases, to get rid of excess inventory, or to draw in new clients. Discounts can be represented as a set monetary amount or as a %, as in the example above. For instance, a shop may give customers $10 off any purchase of more than $50.

Given that, one-day discount rate of 45% is applied.

Thus,

Discount = 60.20 * 0.45 = 27.09

Price after discount = 60.20 - 27.09 = 33.11

Hence, the price after discount is $33 and option 1 is the correct answer.

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The standard deviation of a normal distribution of exam scores is 8. A score that is 12 points above the mean would have a z-score of 1.5, and a score that is 20 points below the mean would have a z-score of -2.5.

The z-score can be calculated by dividing the difference between a data value and the mean of the data set by the standard deviation of the data set.

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8.

z = (x−μ)/σ = (x−μ)/σ = (12−0)/8 = 1.5

The z-score of a score that is 12 points above the mean in a normal distribution of exam scores with a standard deviation of 8 is 1.5.

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8.

z = {x-μ}/{σ}  = {-20-0}/{8}  = −2.5

The z-score of a score that is 20 points below the mean in a normal distribution of exam scores with a standard deviation of 8 is -2.5.

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Answer:

Step-by-step explanation:

A graph is proportional if the relationship between the two variables represented on the axes is constant, meaning that if one variable increases, the other variable also increases by the same factor. In other words, the graph forms a straight line that passes through the origin.

To find the unit rate, you need to look for the constant of proportionality, which is the ratio between the two variables represented on the graph. In this case, the variables are the number of books purchased and the cost in dollars.

If the graph is proportional, then the unit rate is the constant of proportionality, which is the cost per book. You can find the unit rate by dividing the total cost by the number of books purchased. For example, if the total cost for 4 books is $16, then the unit rate would be $4 per book.

If the graph is not proportional, then there is no constant of proportionality, and the unit rate cannot be calculated. The relationship between the two variables may be nonlinear, meaning that the rate of change between the variables is not constant.

There are, 6300 different possibilities for the researcher’s study.

Total number of class I railroads = 10Number of class I railroads selected = 3Total number of class II railroads = 6Number of class II railroads selected = 2Total number of class III railroads = 5Number of class III railroads selected = 1Number of different possibilities for selecting 3 class I railroads from 10 class I railroads = 10C3 = (10 x 9 x 8)/(3 x 2 x 1) = 120

Number of different possibilities for selecting 2 class II railroads from 6 class II railroads = 6C2 = (6 x 5)/(2 x 1) = 15Number of different possibilities for selecting 1 class III railroad from 5 class III railroads = 5C1 = 5Total number of different possibilities for selecting 3 class I railroads from 10 class I railroads, 2 class II railroads from 6 class II railroads, and 1 class III railroad from 5 class III railroads = 10C3 x 6C2 x 5C1= 120 x 15 x 5= 6300Therefore, there are 6300 different possibilities for the researcher’s study.

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Answer:

first one

Step-by-step explanation:

The equation that models the future cost of gasoline is y=1.19(1.003)^(x), where "y" represents the future cost of gasoline per gallon and "x" represents the number of months since January 1, 1999.

In this equation, the initial cost of gasoline is $1.19 per gallon, and the cost increases by 0.3% per month, which is represented by the factor of (1.003)^(x).

Using this equation, you can calculate the future cost of gasoline for any number of months after January 1, 1999. For example, if you want to calculate the cost of gasoline 24 months after January 1, 1999, you can plug in x=24 and calculate y as follows:

y = 1.19(1.003)^(24)

y = 1.19(1.08357)

y = 1.288 per gallon

Therefore, the predicted cost of gasoline 24 months after January 1, 1999 is $1.288 per gallon.

The degree measure of the largest angle is 72° in the triangle.

We have, The sum of two angles of a triangle is 6/5 of a right angle.

One of these two angles is 30° larger than the other.

Let A and B be the two angles of the triangle such that A = B + 30°.

We know that the sum of three angles in a triangle is 180°.

⇒ A + B + C = 180°

⇒ B + 30° + B + C = 180°

⇒ 2B + C = 150°

We also know that the sum of two angles of a triangle is 6/5 of a right angle.

⇒ A + B = 6/5 × 90°

⇒ B + 30° + B = 108°

⇒ 2B = 78°

⇒ B = 39°

C = 150° - 2B ⇒ 72°

A = B + 30° ⇒ 39° + 30° ⇒ 69°

Therefore, the degree measure of the largest angle in the triangle is 72°.

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The equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

What is equation?

In mathematics, an equation is a statement that two expressions are equal, usually written with an equal sign (=) between them. Equations can contain variables, which are symbols that represent unknown or unspecified values.

We can simplify and solve the equation 2x + 6 = 30 - x - 3 as follows:

2x + 6 = 30 - x - 3

Adding x and adding 3 to both sides, we get:

3x + 9 = 30

Subtracting 9 from both sides, we get:

3x = 21

Dividing both sides by 3, we get:

x = 7

So the given equation simplifies to x = 7.

We can now substitute this value of x into each of the answer choices to see which one is equivalent to the given equation:

a) 2x + 6 = 30 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 - 3

14 + 6 = 20

20 = 20

b) 2x + 6 = 10 - x - 3

Substituting x = 7, we get:

2(7) + 6 = 10 - 7 - 3

14 + 6 = 0

20 ≠ 0

Therefore, this equation is not equivalent to the given equation.

c) 2x + 6 = 30 - x + 3

Substituting x = 7, we get:

2(7) + 6 = 30 - 7 + 3

14 + 6 = 26

20 ≠ 26

Therefore, this equation is not equivalent to the given equation.

Therefore, the equation that is equivalent to 2x + 6 = 30 - x - 3 is option (a): 2x + 6 = 30 - x - 3.

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The surface area of the triangular prism is 2016 [tex]feet ^2[/tex], we get to the answer by adding area of all faces in this prism.

What is surface area ?

Surface area is the sum of the areas of all the faces or surfaces of a 3D object, measured in square units.

To find the surface area of the triangular prism, we need to calculate the area of each of its faces and then add them up.

First, let's find the area of the triangular base.

Area of triangle = (1/2) x base x height

Area of triangle = (1/2) x 18 x 24

Area of triangle = 216 [tex]feet ^2[/tex]

Next, let's find the area of each rectangular face.

Area of rectangle = length x width

Area of rectangle 1 = 24 x 22 = 528 [tex]feet ^2[/tex]

Area of rectangle 2 = 18 x 22 = 396 [tex]feet ^2[/tex]

Area of rectangle 3 =  22 x 30 = 660 [tex]feet ^2[/tex]

Now, we can add up the areas of all three faces to get the total surface area of the prism:

Surface area = area of rectangle (1+2+3) + 2 x area of triangle

Surface area = 528 + 396 + 660 + 2(216)

Surface area = 2016 [tex]feet ^2[/tex]

Therefore, the surface area of the triangular prism is 2016 [tex]feet ^2[/tex].

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From the graph, the feasible region from the system of linear inequalities is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

a. Let x be the amount of loam soil (in tons) sold, and y be the amount of peat soil (in tons) sold. The system of inequalities representing the constraints of the problem situation is:

x ≥ 0 (non-negative amount of loam soil)

y ≥ 0 (non-negative amount of peat soil)

x + y ≤ 120 (total amount of soil sold is at most 120 tons)

x ≤ 60 (maximum amount of loam soil available is 60 tons)

y ≤ 90 (maximum amount of peat soil available is 90 tons)

To graph these inequalities, we can plot the feasible region (the region that satisfies all the inequalities) in the x-y plane, as shown below;

The feasible region is the triangular region bounded by the x-axis, the y-axis, the line x + y = 120, the line x = 60, and the line y = 90.

b. The profit function P(x, y) for selling x tons of loam soil and y tons of peat soil is:

P(x, y) = 50x + 75y

To maximize profit, we need to find the values of x and y that satisfy the constraints of the problem situation and maximize the profit function P(x, y). One way to do this is to use the method of linear programming, which involves finding the corner points of the feasible region and evaluating the profit function at each corner point.

The corner points of the feasible region are (0, 0), (60, 0), (60, 60), (30, 90), and (0, 90). Evaluating the profit function at each corner point, we get:

P(0, 0) = 0

P(60, 0) = 3000

P(60, 60) = 9000

P(30, 90) = 6750

P(0, 90) = 6750

Therefore, the maximum profit is $9000, which occurs when the company sells 60 tons of loam soil and 60 tons of peat soil.

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Step-by-step explanation:

20% off means you pay 80 % of the original price for two books

80% * ( 2 x 19.95 ) = .8 ( 39.90) = $ 31.92