18+6=__+__=__
/\
2 4

The completed table shows the products of each term. we get

       |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

To use the box method for multiplying the two expressions, let's create a table with the terms of each expression:

         |  2z  |  -4

____________________

22²       |

__________|______|______

3zy       |

__________|______|______

-2y²      |

Now, we will multiply each term from the first expression with each term from the second expression and fill in the table:

         |  2z  |  -4

____________________

22²       | 44z² |

__________|______|______

3zy       | 6zy  | -12z

__________|______|______

-2y²      | -4y² | 8y²

The completed table shows the products of each term.

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Cindy will make a total amount of $1,800 for 10 weeks

Cindy makes $9 an hour working at a local plant nursery

She does this for 10 weeks

She works for about 20 hours each week

Therefore the total amount of money Cindy made in 10 weeks can be calculated as follows

= 9(20) × 10

= 180 × 10

= 1800

Hence Cindy will make a total amount of $1800 in 10 weeks

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Answer:

A

Step-by-step explanation:

-6(4 - x) <= -4(x + 1)

-24 + 6x <= -4x - 4

-24 + 10x <= -4

10x <= 20

x <= 2

Answer:

\(f(x) = \frac{x^{2} -5x-6}{x^{2} -4}\)

Step-by-step explanation:

Let's factorize the 1st option :

⇒ \(f(x) = \frac{x^{2} -5x-6}{x^{2} -4}\)

⇒ \(f(x) = \frac{x^{2}+x-6x-6 }{(x+2)(x-2)}\)

⇒ \(f(x) = \frac{(x+1)(x-6)}{(x+2)(x-2)}\)

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

Finding the zeros :

⇒ Factors of numerator should be equated to 0

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

Solution :

\(f(x) = \frac{x^{2} -5x-6}{x^{2} -4}\)

Answer:

first option

Step-by-step explanation:

the zeros are determined by the numerator of the rational function.

given that the zeros are x = - 1 and x = 6 , then the corresponding factors are

(x + 1) and (x - 6) , that is

(x + 1)(x - 6) ← expand using FOIL

= x² - 5x - 6

the rational function is then

f(x) = \(\frac{x^2-5x-6}{x^2-4}\)

Answer:   255

Step-by-step explanation:

Try thinking backwards first; 51*(0.20)=10.2, or 10.2 is 20% of 52

To find 20% of the unknown number, just divide 51 by 0.20

51/0.20=255

Whatever the answer is, you know it has to be larger than the original number.

Answer:

|J| = - 40

Step-by-step explanation:

(-2)(8) - (6)(4)

-16 - 24

= - 40

Answer:

c=60m+35

Step-by-step explanation:

c is the cost so it should be equal to and 60 a month so 60m and +35

Answer:

130

Step-by-step explanation:

Answer:

130 (C)

Step-by-step explanation:

let convert to decimal

From the smallest ot the largest

Answer:

7x+3y+2z

Step-by-step explanation:

The surface area of a polygon will be 4LW + 2W² square units.

A closed solid with two parallel rectangular bases joined by a rectangle surface is known as a rectangular prism.

Let the prism with a length of L, a width of W, and a height of H. Then the surface area of the prism is given as

SA = 2(LW + WH + HL)

If the two sides of the rectangle become the same that is W = H. Then the surface area of the prism is given as,

SA = 2(LW + W × W + WL)

SA = 2(2LW + W²)

SA = 4LW + 2W²

The surface area of a polygon will be 4LW + 2W² square units.

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We are given a histogram that summarizes the lengths, in feet, of a group of adult female sharks.

Let us analyze each of the given options.

Option A: A total of 9 sharks were measured.

This seems to be incorrect since the number of sharks is way more than that.

Option B: A total of 50 sharks were measured.

Let us count the exact number of sharks from the histogram.

0 to 13 = 0

13 to 13.5 = 1

13.5 to 14 = 1

14 to 14.5 = 4

14.5 to 15 = 10

15 to 15.5 = 10

15.5 to 16 = 9

16 to 16.5 = 10

16.5 to 17 = 4

17 to 17.5 = 1

So, the total number of sharks is

1 + 1 + 4 + 10 + 10 + 9 + 10 + 4 + 1 = 50

Therefore, the statement B is correct.

Option C: The longest shark that was measured was 10 feet long.

As you can see from the histogram, the longest length that was measured is 17 to 17.5 feet.

Therefore, this statement is incorrect.

Option D: Most of the sharks that were measured were over 16 feet long.

As you can see from the histogram, the peaks of the histogram lie in the range of 14.5 to 16.5 feet.

This means that the majority of the sharks that were measured are between 14.5 to 16.5 feet.

Therefore, this statement is incorrect.

Option E: Two of the sharks that mere measured were less than 14 feet long.

As you can see from the histogram, there are two sharks having lengths less than 14 feet long.

13 to 13.5 = 1

13.5 to 14 = 1

Therefore, this statement E is correct.

The correct answer is a. high. In a one-sample chi-square test, the observed frequencies of the variable being studied are compared to the expected frequencies assuming a particular distribution or hypothesis.

The chi-square test statistic measures the difference between the observed and expected frequencies and determines whether this difference is statistically significant.

If the respondents are distributed very unequally across the levels of the variable being studied, the observed frequencies will be very different from the expected frequencies. This will result in a large difference between the observed and expected frequencies, leading to a high value for the chi-square test statistic.

The chi-square value is calculated by summing the squared differences between the observed and expected frequencies, divided by the expected frequencies. If the respondents are distributed very unequally across the levels of the variable being studied, the expected frequencies will be very different from the observed frequencies, resulting in a high value for the chi-square test statistic.

Therefore, in a one-sample chi-square test, if your respondents are distributed very unequally across the levels of your variable, your chi-square value will be high.

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The function below is not provided in the question, therefore, I cannot provide a specific linearization method to fit the data to a linear regression model.

However, in general, the correct linearization method for a function to be fit to a data set using linear regression would depend on the functional form of the equation.

For example, if the function is exponential, taking the logarithm of the data may result in a linear relationship that can be fit using linear regression.

The specific linearization method to fit a function to a linear regression model would depend on the functional form of the equation. For an exponential function, taking the logarithm of the data may result in a linear relationship that can be fit using linear regression. However, since the function in question is not provided, I cannot provide a specific linearization method.

The correct linearization method for a function to be fit to a linear regression model depends on the functional form of the equation and cannot be determined without knowledge of the specific function.

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1 / 3 of peanut butter cookies as the number of boxes of lemon cookies sold

Given: Lila sold 1/3 as many boxes of lemon cookies as peanut butter cookies

What is algebra?

Algebra is a domain in mathematics that is used to describe a problem statement in a short and more precise way, simply by pointing the key points. If consist a sequence or combination of characters containing letters, numbers, symbols and more. It is very helpful in assuming conditions where a single or multiple object or element is under the influence of single or multiple objects or elements. We can easily describe it with the help of algebra. Sometimes the assumed expression itself becomes a solution for a given problem when the unknown variable values are known.

We can also make predictions with our expressions for a future event.

Hence algebra plays an important in our life knowingly or unknowingly and even our names, words etc. all can be thought of as the unknown variables with a name and we are the instances which are acting as values for particular names in unique ways.

Every problem's solution is unique to the problem but it can be extended to make relations with other problems with a similar approach or thoughts.

Now let's solve the given question:

Let the number of boxes of lemon cookies sold be x and the number of boxes of peanut butter cookies sold be y.

According to the question,

boxes of lemon cookies = 1/3 boxes of peanut butter cookies

Hence Lila sold 1 / 3 of peanut butter cookies as the number of boxes of lemon cookies.

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The equation of the line is y = -(3/4)x - 6.

A line is a perfectly straight, one-dimensional shape that extends endlessly in both directions and has no thickness.

Given that, the line passes through the points (-4,-3) and has a slope of -3/4.

The equation of the line in point-slope form is:

y - y₁= m (x -x ₁)

Substitute (x₁,y₁) = (-4,-3) and m = -3/4 into the above equation,

y - (-3) = -3/4 (x - (-4))

y + 3 = -3/4 (x + 4)

y = -(3/4)x -3 -3

y = -(3/4)x - 6

Hence, the equation of the line is y = -(3/4)x - 6.

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Answer:

Step-by-step explanation:

3 -2

The rate of change of the angle of elevation is -2π/3 radians/second.

We can use the tangent ratio to solve this problem. Since the rope is attached to the boat, we can draw a right triangle with the rope as the hypotenuse. The angle of elevation is the angle formed by the rope and the horizon.

The pulley is 5 feet above the water level, so the length of the opposite side (the side adjacent to the angle) is 5 feet. The length of the hypotenuse is 12 feet, since the boat is 12 feet from the dock.

Using the tangent ratio, we can calculate the angle of elevation:

tan(θ) = opp/hyp = 5/12

θ = arctan(5/12) = 0.927 rad

Now, since the rope is being pulled in at 3 ft/sec, the length of the hypotenuse is decreasing at a rate of 3 ft/sec. Therefore, the rate of change of the angle of elevation is:

rate of change of θ = -(3 ft/sec) / (12 ft) = -2π/3 radians/second

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12 total

4+3=7

12-7=5

5km left

Therefore (b). A chi-square statistic is always positive as it is the sum of squared deviations from expected values.

However, it can contain fractions or decimal values as it is based on continuous data. The chi-square distribution is skewed to the right and its shape depends on the degrees of freedom. The possible values for a chi-square statistic depend on the sample size and the number of categories in the data. In general, larger sample sizes and more categories will result in larger chi-square values. It is important to note that a chi-square statistic cannot be negative as it is the sum of squared deviations. Therefore, options (a) and (c) are incorrect. In conclusion, the correct answer is (b) and it is important to understand the properties and interpretation of chi-square statistics in statistical analysis.

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Step-by-step explanation:

When (f + g)(x) = 0,

f(x) + g(x) = x² + 6x + 4 = 0.

Therefore (x + 3)² - 5 = 0, we have

x = sqrt5 - 3 or x = -sqrt5 - 3.

Answer:

$135

Step-by-step explanation:

First, find the unit rate of money earned (36/8=4.5)

Then, multiply the unit rate of money earned by 30 (4.5 x 30 = $135)

I apologize if my wording is incorrect.

The total earnings for the 30 hours is $1350 if John earned $36 for 8 hours of work. Earnings are directly proportional to hours worked.

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

It is given that:

John earned $36 for 8 hours of work. Earnings are directly proportional to hours worked.

Earnings ∝ hours

E ∝ T

E = kT

Here k is the constant

36 = 8k

k = 36/8

E = (36/8)T

Plug T = 30

E = (36/8)(30)

E = $1350

Thus, the total earnings for the 30 hours is $1350 if John earned $36 for 8 hours of work. Earnings are directly proportional to hours worked.

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On solving the provided question we can say that The amount of water lost is: \(V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3\)

A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.

\(V1 = \pi r^2h = \pi (3.5 cm)^2(9 cm) = 346.36 cm^3\\\)

Next, let's calculate the volume of the ball:

The radius of the ball is 5/2 = 2.5 cm. The volume of the ball is:

\(V_ball = (4/3)\pi r^3 = (4/3)\pi (2.5 cm)^3 = 65.45 cm^3\\V_disp = V_ball = 65.45 cm^3\\h_new = 9 + (V_disp/\pi r^2) = 9 + (65.45 cm^3)/(\pi (3.5 cm)^2) = 10.77 cm\\V2 = \pi r^2h_new = \pi (3.5 cm)^2(10.77 cm) = 401.94 cm^3\\\)

The amount of water lost is:

\(V_lost = V1 - V2 = 346.36 cm^3 - 401.94 cm^3 = -55.58 cm^3\)

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The price of the house (y) is directly proportional to the total area of the house (x), you can express the relationship between both variables as follows:

Where "k" is the constant of proportionality.

To determine the price of a house that has 2,000 ft², the first step is to determine the value of the constant of proportionality between both variables. For this, we have to use the known price and size of the house:

-The house has 1,500 ft² → this is the value of x

-The house costs $300,000 → this is the value of y

You can express the relationship as:

To calculate the value of k, you have to divide both sides by 1,500ft²

The constant of proportionality is 200$/ft², this value indicates that the price of the house increases $200 for every additional square foot.

Now that we know the value of the constant of proportionality we can calculate the price of a 2,000ft² house:

For x=2,000ft²

The price of a 2,000ft² is $400,000