During the candy sale, nick sold 100 bars,Olivia sold 94,Brandon sold 53, and Grace sold 75. (Rank from greatest to least

The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> [tex]8x^2y+12xy-16xz[/tex]

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

As x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.

The behavior of a function refers to how the function changes or behaves as the input values (usually denoted as x) approach certain values, typically positive infinity, negative infinity, or a critical point.

To determine the end behaviour of the function f(x), we need to examine the highest-degree term of the polynomial, which is -4x³.

As x approaches positive infinity (i.e., x → ∞), the term -4x³ dominates the expression and becomes increasingly negative. Therefore, the end behaviour of f(x) as x → ∞ is f(x) → -∞.

Similarly, as x approaches negative infinity (i.e., x → -∞), the term -4x³ dominates the expression and becomes increasingly positive. Therefore, the end behaviour of f(x) as x → -∞ is f(x) → +∞.

In summary, the end behaviour of f(x) is:

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Answer:

The quadratic equation is in the standard form: ax^2 + bx + c = 0. To use the quadratic formula to find the solutions, we need to identify the values of a, b, and c in the equation:

a is the coefficient of the x^2 term, which is -3 in this case.

b is the coefficient of the x term, which is -5 in this case.

c is the constant term, which is 9 in this case.

Therefore, the values of a, b, and c in the quadratic equation -3x^2 - 5x + 9 = 0 are:

a = -3

b = -5

c = 9

Answer:6^21

Step-by-step explanation:

Therefore, it will take about 46.5 minutes for the culture to achieve 10,000 bacteria.

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, x, ÷, etc.) that represents a mathematical quantity or relationship. Expressions can be as simple as a single number or variable, or they can be complex and involve multiple terms and operations. Examples of expressions include 2x + 5, 3y - 7, and (a + b)(c - d).

Here,

We can set up an equation to solve for t:

B(t) = 100 ·[tex]2^{t/20}[/tex]

= 10,000

Dividing both sides by 100, we get:

[tex]2^{t/20}[/tex] = 100

Taking the logarithm of both sides with base 2, we get:

t/20 = log2(100)

t = 20 · log2(100)

Using a calculator, we can simplify this to:

t ≈ 46.5 minutes

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Answer:

Step-by-step explanation:

7xy+3x+3y−3

Answer: 12

Step-by-step explanation:

Use BODMAS, so first solve the inside of the bracket:

2*3= 6

6-4= 2

Now we can multiply that by the number outside the bracket. Why?

Because a number outside a bracket means to multiply that number by everything in the bracket. So:

6 * 2 = 12

Answer: 12

Step-by-step explanation:

2 x 3 = 6

6 - 4 = 2

6 x 2 = 12

Step-by-step explanation:

so, it is

sqrt(y + 3) = sqrt(y) + sqrt(3)

first we square both sides :

y + 3 = y + 3 + 2×sqrt(y)×sqrt(3) =

= y + 3 + 2×sqrt(3y) =

= y + 3 + sqrt(4×3y) = y + 3 + sqrt(12y)

0 = sqrt(12y)

we square again :

0² = 12y

0/12 = 0 = y

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Answer:

40 5/8

Step-by-step explanation:

6 1/2 × 2 1/2

13/2 × 5/2= 65/4

65/4 × 2 1/2

65/4 × 5/2 = 325/8

325/8= 40 5/8

Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

A geometric shape known as an angle is created by two rays or line segments that have a shared termination, or vertex. Angles, which express how much of a turn or rotation there is between two rays or line segments, are measured in degrees or radians. They are frequently employed in physics, engineering, geometry, trigonometry, and other disciplines.

given

The characteristics of parallel lines and transversals allow us to determine that:

Interior angles on the same side of the transversal: 1 + 2 = 180°; 2 + 3 = 180°.

We know that (1) = 147°, thus we can apply the first equation to determine 2:

∠1 + ∠2 = 180°

147° + ∠2 = 180°

∠2 = 33°

We can apply the second equation to determine 3 now that we know 2:

∠2 + ∠3 = 180°

33° + ∠3 = 180°

∠3 = 147°

Hence, the angles' measurements are as follows: ∠1 = 147° , ∠2 = 33° and ∠3 = 147° as Interior angles on the same side of the transversal.

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Answer: X=55 and Y=125

Step-by-step explanation:

y is an external angle

so according to external angle property sum of two angles is equal to external angle. two angles are given- 35 and 90

90+35=y

y=125

now with angle sum property

90+35+x=180

125+x=180

x=55

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Answer:

When you divide 233 by 6 using long division, you get:

38

---

6|233

 216

 ---

  17

Therefore, 233 ÷ 6 = 38 with a remainder of 17

Answer:

38.83 (the 3 goes on and on)

The linear equation that models the number of pages that he reads is:

y = 56*x

So we know that Mark reads 42 pages every 3/4 of an hour, and we want to write an equation that models the number of pages y that mark reads in x hours, to do so we needto get the unit rate.

Take the quotient between the number of pages and the time above to get:

u = (42 pages)/(3/4 hours) = 56 pages per hour.

Then the number of pages that he can read in x hours is modeled by the linear equation:

y = 56*x

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Combining the like terms of the expressions (x² - 4x+9)-(3x² - 6x-9) gives -2x² + 2x + 36

Algebraic expressions are simply described as those mathematical expressions that are known to consist of certain variables, coefficients, terms, factors and constants.

Algebraic expressions are also identified with arithmetic operations. These arithmetic operations are;

From the information given, we have;

(x² - 4x+9)-(3x² - 6x-9)

First, expand the bracket

x² - 4x + 9 - 3x² + 6x + 27

Now, collect the like terms

x²- 3x² - 4x + 6x + 9 + 27

Add or subtract

-2x² + 2x + 36

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The fact that Jeri drew a polygon with precisely three sides serves as the representation of this claim.

A polygon is a closed shape made of line segments rather than curves on a two-dimensional plane.

A minimum of three line segments need to be joined end to end to produce a closed figure. As a result, a triangle and a 3-gon are both terms for a polygon with at least three sides.

The polygons are divided into many categories based on the sides and angles, including:

In this instance, Jeri's drawing of a polygon with precisely three sides serves as the symbolic expression of this argument.

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Answer:

$12.00

Step-by-step explanation:

We know that 1 pound = 16 oz.  Thus, we can create a proportion to find how many ounces (x) is 2.5 pounds:

[tex]\frac{1}{16}=\frac{2.5}{x}\\ x=(2.5*16)\\ x=40[/tex]

Since 2.5 pounds = 40 oz, we can now multiply 40 by 0.30 to find the price of 40 ounces of peacans priced at $0.30/ounce:

40 * 0.30 = $12.00

Step-by-step explanation:

Semi-annual means an interest period is 1/2 year

    1/2 *8% = 4% = .04

       effective annual interest rate is then

                    (1+ .04)^2  - 1  = .0816   or  8.16    (%)

The probability of the maximum number of black hats that could be present in the group is 2.

Since the probability of selecting a student with a green hat is the highest, it is likely that there are more green hats than any other color. Let's assume that there are 7 green hats. If there are 7 green hats, then there are only 5 hats left for the remaining colors. However, we know that there are only 2 red hats and 1 blue hat, leaving a maximum of 2 hats for the black color. Therefore, the greatest possible number of black hats in the group is 2, which would give a total of 2 red hats, 1 blue hat, 7 green hats, and 2 black hats. In conclusion, if the probability of selecting a student with a green hat is the highest, then the greatest possible number of black hats in the group is 2.

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The diameter of the tin is 2/5D and the circumference of the tin is 0.4πD

Given the the scale factor of dilation is

Container = 2/5 smaller than in reality

This means that

Scale factor = 2/5

So, we have

Diameter = 2/5D where D = diameter in reality

Also, we have

Height = 2/5H where H = height in reality

The circumference is then calculated as

C = πD

So, we have

C = π * 2/5D

Evaluate

C = 0.4πD

Hence, the circumference is 0.4πD

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Complete question

The Ricoffy tin container with no dimensions indicated.The container is 2,5 times smaller than what it is in reality

Diameter of the tin on the picture = ? Height of the tin on the picture = ? Actual weight of coffee = 750 g 1.1 Measure the diameter of the tin in mm and write down the real diameter in mm​

A 95% confidence interval that the t population mean number of books  is between 9.89 and 11.11 books.

What is confidence interval ?

A confidence interval is a statistical range that provides an estimate of the likely range of values for a population parameter (such as a mean, proportion, or standard deviation) based on a sample of data. It is calculated using a specific level of confidence, which represents the probability that the true population parameter falls within the calculated range.

Confidence intervals are typically expressed as a range of values with a margin of error or standard error. The margin of error represents the amount of random variation that is expected due to sampling error, while the standard error reflects the variability of the sample data.

According to the question:
C. There is 95% confidence that the population mean number of books read is between a lower bound of approximately 9.89 books and an upper bound of approximately 11.11 books.

To construct the confidence interval, we can use the formula:

[tex]CI =\bar x \± z* (s/\sqrt{n})[/tex]

substitute the values, we get:

CI = 10.5 ± 1.96 * (16.6/√1015)

CI = (9.89, 11.11)

This means that we are 95% confident that the  population mean number of books is between 9.89 and 11.11 books.

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Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

A sequence of numbers known as coordinates is used to describe the location of a point or object in space or on a plane. Coordinates in two-dimensional space typically have two values, which are typically written as (x, y), where x denotes the horizontal position and y denotes the vertical position. Coordinates in three dimensions can have three values, denoted as (x, y, z), where x, y, and z stand for the position along the x, y, and z axes, respectively. In many different fields, such as geometry, physics, and computer graphics, coordinates are used.

given

The coordinates of the new origin must be subtracted from the given point in order to translate the point (-8, -6) to the new origin (h, k) = (5, 4).

x' = -8 - 5 = -13

y' = -6 - 4 = -10

Translation of the point (-8, -6) to the new origin (5, 4) is thus (-13, -10). Hence, the response is (-13, -10).

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the total percentage increase in the investor's stock account is 22%.

In mathematics, a ratio or figure that can be expressed as a fraction of 100 is known as a percentage. If we want to calculate a percentage of a number, we should split it by 100 before multiplying it by the original number. Therefore, the percentage relates to a component per 100. The term percent means "per 100". It is represented by the symbol "%". In mathematics, a percentage is a number or ratio that is represented as a fraction of 100. Although "pct," "pct," and occasionally "pc" are also used as abbreviations, the percent symbol "%" is most commonly used to denote it. A percentage is a number that has neither measurements nor a defined unit of measurement.

In the given question,

Increase in stock A= 24% of $5150 = 1236

Increase in stock = 20% of $5250 = 1050

The  total percentage increase in the investor's stock account= {(1236+1050)/(5150+5250)* 100=

= 21.98%

≈22%

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Answer:

B.  There is no maximum value.

C.  There is no maximum value of z.

Step-by-step explanation:

To solve this linear programming problem using graphical methods, start by graphing the feasible region determined by the given constraints:

We can graph each of these inequalities by first plotting the corresponding boundary line, and then shading in the appropriate region.

Rearrange the first three inequalities to isolate y:

[tex]\boxed{\begin{aligned}2x - 3y & \leq 12\\2x - 12 & \leq 3y \\3y &\geq 2x - 12\\y& \geq \dfrac{2}{3}x-4\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}x + y & \geq 3\\y & \geq -x+3\\ \phantom{w}\\\phantom{\dfrac12}\end{aligned}}[/tex]  [tex]\boxed{\begin{aligned}3x + 4y & \geq 24\\4y & \geq -3x + 24\\y & \geq -\dfrac{3}{4}x + 6\\\phantom{w}\end{aligned}}[/tex]

Graph the inequalities.

The feasible region is the region that is shaded by all of the inequalities.

Please see the attached graph.

A bounded feasible region may be enclosed in a circle and will have both a maximum value and a minimum value for the objective function.

If a feasible region is unbounded, and the coefficients on the objective function are all positive, then an unbounded feasible region will have a minimum but no maximum, since there is no limit on how big it can get.

Therefore, as the feasible region for the given constraints is unbounded, and the coefficients of the objective function z = 3x + 4y are all positive, there is no maximum value.

35/84

It can be simplified to 5/12 by dividing by 7.

Answer:

We can use the formula for compound interest to find the balance in Eliana's savings account after 10 years:

A = P(1 + r/n)^(nt)

where A is the balance, P is the principal (initial deposit), r is the annual interest rate as a decimal, n is the number of times interest is compounded per year, and t is the time in years.

Substituting the given values, we get:

A = $700(1 + 0.04/12)^(12*10)

Simplifying, we get:

A = $700(1.0033333)^120

Using a calculator, we get:

A ≈ $1,038.81

Therefore, the balance in Eliana's savings account after 10 years is approximately $1,038.81.