The base of an open rectangular box is of length (2x + 5) cm and width x cm.
The area of this base is 58 cm².
The height of the open box is (x - 2) cm.

I have attached a pic
(I already did part (a) and (bi) and you may use the answers to help you do the (bii) question)

+ the answer for (bi) if you can’t see it, it is 4.28 and -6.78

This is the question:
b) (ii) Hence calculate the volume of the box, stating the units of your answer.

Answer: y = 2/5x + 4

Step-by-step explanation:

       We will write a point-slope form equation for this line, then simplify it into a slope-intercept form equation.

Given point-slope form:

➜ m is the slope

➜ (x1, y1) is the point given

       y - y1  = m(x - x1)

Substitute values in:

       y - (4)  = (2/5)(x - (0))

Distribute 2/5:

       y - 4  = 2/5x - 0

Add 4 to both sides of the equation:

       y = 2/5x + 4

Step-by-step explanation:

since we have the slope and a point, we can start with the point-slope form

y - y1 = a(x - x1)

a is the slope, (x1, y1) is the given point.

y - 4 = (2/5)(x - 0) = 2x/5

y = 2x/5 + 4

or

y = (2/5)x + 4

The difference between their ages is obtained as 35/12.

Let us recall that the term fraction has to do with a part of a whole. In this case, we have been told that Marcelle and Megan realized that they could express their ages more specifically if they used fractions.

Age of Marcelle  = 15 1/2 or 31/2 years

Age of Megan  = 12 7/12 or 151/12 years

The difference between their ages is;

31/2 - 151/12

=186 - 151/12

=35/12

There ages would have a difference of 35/12.

In the computation that has gone on above, we can clearly see that the difference in the ages is 35/12.

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Missing parts;

Marcelle and Megan realized that they could express their ages more specifically if they used fractions. Doing this will allow them to calculate their difference in their ages. Marcelle is 15 1/2 years old, and Megan is 7 7/12. What is the difference in their ages? Express your answer as a simplified mixed number.

The value of a=0 in a given expression.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of phrases. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the equation x/2 + 6.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

If the value of 2x² - a*5 when x = 0 is 0, then we can substitute x = 0 into the equation and solve for a.

So,

[tex]2(0)² - a5 = 0[/tex]

[tex]-a5 = 0[/tex]

[tex]a = 0[/tex]

Therefore, the value of a should be 0.

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Answer:

rate of change = 5

Step-by-step explanation:

the slope m gives the measure of the rate of change of the function

calculate the slope m using the slope formula

m = [tex]\frac{y_{2-y_{1} } }{x_{2-x_{1} } }[/tex]

with (x₁, y₁ ) = (3, 38) and (x₂, y₂ ) = (1, 18) ← 2 ordered pairs from the table

m = [tex]\frac{18-38}{1-3}[/tex] = [tex]\frac{-20}{-2}[/tex] = 5

then rate of change = 5

The perimeter expression of a rectangle has a perimeter represented by the expression 4x−8 is 2(2x - 4)

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

Perimeter = 4x - 8

Factor out 2 from the expression

So, we have the following representation

Perimeter = 2 * 2x - 2 * 4

So, we have

Perimeter = 2(2x - 4)

Hence, the perimeter is 2(2x - 4)

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%, a relative figure signifying hundredths of any amount. Before the raise, I was making $45,000.

A percentage that represents a tenth of a quantity. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).

Calculating a percentage involves dividing an item by its sum and multiplying the result by 100.

Considering the query

It was $52,200 after a 16% raise in my pay.

In light of the conditions stated, come up with

[tex]$=\frac{52200}{1+16 \%}$$=\frac{52200}{1+0.16}$$=\frac{52200}{1.16}$$=\frac{5220000}{116}$[/tex]

= $45000

Before the raise, I was making $45,000.

Therefore, the answer is $45,000.

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The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line.

The 5th interval is called perfect

Interval notation is a method to represent an interval on a number line. In other words, it is a way of writing subsets of the real number line. An interval comprises the numbers lying between two specific given numbers. For example, the set of numbers x satisfying 0 ≤ x ≤ 5 is an interval that contains 0, 5, and all numbers between 0 and 5.

Interval Notation is a way of expressing a subset of real numbers by the numbers that bound them. We can use this notation to represent inequalities. We know an interval expressed as 1 < x < 5 denotes a set of numbers lying between 1 and 5.

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Based on the description above, the individuals in this setting is option A: homes.

The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.

In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.

Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.

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Answer: the answer is the option

Employee B: gross pay $32,900, total job benefits $34,000

hope this helped you

The correct answer will be:

Quantitative data, both sample sizes are greater than 30 or Both population distributions could be Normally Distributed, Random Samples or Random application of treatments

There should be just one group for each subject. The observations in each category are unrelated to one another. There were no notable outliers in any category.

The following are the presumptions for a percentage significance test: Data come from a random sample [Sample is large enough, which is presumed to be true when. It should be noted that both quantitative and categorical data can be subjected to a significance test for a proportion.

Most parametric tests begin with the underlying presumption of population distribution. The ratio scale or interval scale measurements, easy random extraction, normal distribution of the data, a sufficient sample size, and homogeneity of variance are all prerequisites for performing the t-test.

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Answer:

Step-by-step explanation:

divide them both by 2

which is 3/ 9

divide them both by 3

whic is 2/6

and finally divide them both by 6

which is 1/3

you can multiply them both by an number as well

take care

Answer:

Below

Step-by-step explanation:

3% loss means 97% (.97 in decimal ) remains

after 2 years :

 27 900 ( .97)^2 = £  26251 .11

The expressions for the number of sweets that Tony and Sue now have are:

Given:
Sue has 18 sweets

Sue = 18

Tony also has 18 sweets, that is:

Toney = 18

Sue gives Tony × sweets; that is

Sue = 18 - x; and

Tony = 18 + x

Sue then eats 5 of her sweets, Tony then eats half of his ⇒ Sweets:

that is ⇒

Sue = 18 - x - 5

Tony = (18 + x) / 2

Thus, simplifying the above, we have:

Sue = 13 - x

Tony = (18 + x) / 2

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I feel that dividing based off actual zoning laws and regulations would provide the best source of data. I feel as such because if you simply devise your own areas, that may make your data incorrect depending on what area a person actually associates with. If you're creating your own area, information could get misconstrued leading to inaccurate conclusions.

Sampling

Sampling means selecting the group that you will actually collect data from in your research.

zoning

Zoning is a method of urban planning in which a municipality or other tier of government divides land into areas called zones, each of which has a set of regulations for new development that differs from other zones.

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Answer:

14 Quarts

Step-by-step explanation:

1 Gallon = 4 Quarts.

3x4 = 12 + 2 = 14 Quarts.

function f(x) = 75 - 4.5 w.

where w = number of weeks.

this question is related to function and solution is as follows,

The owner of a mall Restaurant bought rice = 75 kg

Each week, the restaurant use rice = 4. 5 kg

so we have to make an equation of function by which we can find out the remaining rice after w number of weeks,

f(x) = 75 - 4.5 w

where ,w = number of weeks

example, find out rice after 6 weeks

number of weeks (w) = 6

put it in the function,

f(x) = 75 - 4.5(6)

f(x) = 75 - 27

f(x) = 48.

so the function is ,f(x) = 75 - 4.5 w.

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The 98% confidence interval for the true difference between testing averages for students using Method 1 and students using Method 2 as calculated from the given data is 5.20 and 7.60.

The confidence interval for the difference of the population mean is calculated as,

CI = ( x1 - x2 ) +- z x √SD1²/n1 + SD2²/n2

= ( 82.9 - 76.5) +- 1.96 x √7.97²/293+ 6.66²/n2.82

=6.4 ± 1.199

=(v5.201 , 7.599)

therefore , approximately 5.20 , 7.60 .

Therefore , the confidence interval between them is found to be as , ( 5.20 , 7.60 ) answer.

The confidence interval is a calculation based on the statistics of the observed data that estimates the amount of uncertainty associated with a sample.

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Answer:

y = 9.75x

Step-by-step explanation:

y = the money earned

x = number of lawns.

The inequality when apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift is 3a + 2o ≤ 24.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

In this case, Aleris is sending a fancy organic fruit basket to her grandma for her birthday. apples cost $3 and oranges cost $2 and Aleris can spend no more than $24 on the gift.

Let apple = a

Let orange = o

Therefore, the inequality will be:

3a + 2o ≤ 24.

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Answer:

1,536

Step-by-step explanation:

1 pound equals 2 cups, so 8 pounds will be 16 cups.

[tex]\frac{16}{\frac{1}{4} }[/tex] = 16 x 4 = 64

She can make 64 2 dozen fasnachts.  There are 24 fasnachts in 2 dozen.

64 x 24 = 1536 individual fasnachts doughnuts.

Correct options are: A. Zeros: -2 and 1

E. x-Intercepts: (-2, 0) and (1, 0)

What are zeros & x-intercepts of quadratic function?

The zero of the function is where the y-value is zero.

The x-intercept is where the graph crosses the x-axis.

The zeros of a quadratic function are the values of x for which the function equals zero. In other words, they are the solutions to the equation f(x) = 0. For the given quadratic function, the zeros

are -2 and 1.

The x-intercepts of a function are the points at which the function crosses the x-axis. In other words, they are the solutions to the equation f(x) = 0 when y = 0. For the given function, the x-intercepts are (-2, 0) and (1, 0) which are the points on the x-axis where the function crosses it.

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The correct option is B.Because when i use deduction and start from a given set of rules and condition is what must be true.If you analyze it to be true then it must be definitely true.

Deduction is a conclusion from something known or assumed. This is the type of reasoning we use in almost every step in a mathematical argument. For example to solve 2x = 6 for x we divide both sides by 2 to get 2x/2 = 6/2 or x = 3.

In mathematical logic a deduction theorem is that justifies doing conditional proofs—to prove an implication A → B, assume A as an hypothesis and then proceed to derive B—in systems that do not have an explicit inference rule for this.

Now we able to know

Deduction is a term used to known as validated principle.This is when you analyze points through logic from a given set of rules and condition.

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3 and -3 are additive inverses because 3 + (-3) = 0.

Therefore, -3 is the additive inverse of 3.

Additive Inverse:

The additive reciprocal/ Inverse of a number is its inverse. When a number is added to the additive reciprocal, both numbers sum to zero. A simple rule is to change positive numbers to negative numbers and vice versa. We know that 3+ (-3) =0. So -3 is the additive reciprocal of 3, and 3 is the additive reciprocal of -3.

If the sum of two real numbers is 0, each real number is said to be the additive reciprocal of the other real number. Therefore, R + (-R) = 0. where R is a real number. R and -R are the additive reciprocals of each other. Example: 3/4 + (-3/4) = 0. where 3/4 is the additive reciprocal of -3/4 and vice versa. This is an example of the additive reciprocal of a fraction.

We have room temperature water in a bucket. Adding 1 liter of hot water raises the temperature of the entire bucket by a certain amount. Then add another liter of cold water. Opposite temperature water in the bucket will cancel out, resulting in a bucket of room temperature water. The same rules apply when taking the additive reciprocal of a number. The additive inverse property applies to both real and complex numbers.

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The reflection that maps ST onto itself is a reflection in the line y = -7.

What is the line of symmetry?

Reflection symmetry, line symmetry, mirror symmetry, or mirror-image symmetry is symmetry with respect to a reflection. That is, a figure which does not change upon undergoing a reflection has reflectional symmetry. In 2D there is a line/axis of symmetry, in 3D a plane of symmetry.

A reflection maps a geometric figure onto itself by "flipping" it across a line of symmetry. In this case, the reflection maps ST onto itself, so the line of symmetry must be a line that ST is reflected across.

To find this line, we can look at the two given vertices of ST, S(-7, 1) and T(-7, 5).

We can see that these points have the same x-coordinate (-7), which means that the line of symmetry must be a vertical line passing through the x-coordinate of -7.

Therefore, the reflection that maps ST onto itself is a reflection in the line y = -7.

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The solution to the system of linear equations (x, y) lies along 4 and 7 and the graph is attached below.

A graph of a system of linear equations is a set of points in a coordinate plane that represent all the solutions to the system of equations. The graph can be visualized as a collection of lines that intersect at the points that are solutions to the system.

In the given problem, we have two linear equations which are

y = 3x - 6 ...eq(i)

y = 2/5x + 5 ...eq(ii)

Plotting the two equations on a graph using a graphing tool, the point of intersection is the solution to the system of linear equation.

The coordinates to the nearest integer are (x, y) 4 and 7

The value of x is 4 and y is 7

Kindly find attached graph below.

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The required point-slope form of the equation of the line is y - 20= -5(x + 1).

Given that, To determine an equation in point-slope form for the line that passes through the point with the given slope. point: (-2,-20) and m=-5.

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To add a function in FG, open the functions. php file in your theme folder, add the code for the function at the bottom of the file, save the file, and add the code for the function in the template files where you want it to appear.

To add a function in FG, you first need to open the functions. php file in your theme folder. This is where all the functions for your theme will be stored. Once you have the file open, you can add the code for the function that you want to create. This code should go at the bottom of the file. After you have added the code, save the file. Now, you need to add the code for the function in the template files where you want it to appear. To do this, add the following code: <?php your_function_name(); ?>. This code will call the function that you created in the functions.php file. Once you have added this code, save the file and the function should now appear in your theme.

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On solving the provided question, we can say that - here in this inequality 17[tex]\leq[/tex]2x - 3[tex]\leq[/tex]25

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

17[tex]\leq[/tex]2x - 3[tex]\leq[/tex]25

[tex]20\leq 2x\leq 28\\10\leq x\leq 14[/tex]

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