what must be included in a algebriac expression?

The meaning of the equation x=1 is that the numerical value of variable X is; 1.

It follows from the task content that the mathematical meaning of the equation x=1 be explained.

By virtue of the equality sign, it follows that the numerical value of variable x is 1 and hence, 1 can be substituted for variable x in any mathematical expression within the context of discuss.

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The width of the delivery box is 9 inches.

Given that  volume of delivery box is 756 cubic inches,length is 6 inches less than twice the width, height is 2 inches less than width.

let width be x

Length = 2x- 6

Height = x - 2

Width = x

We can find the value of x by putting values one by one and then we will be able to get the value of  x which is width.

Because the delivery box is cuboid in shape so the volume is equal to product of length,breadth and height.

When x=7: Volume=7 x (7 - 2) x (2x7 - 6) = 7 x 5 x 8 = 280

When x=9,Volume will be 9 x (9 - 2) x (2x9 - 6) = 9 x 7 x 12 = 756

Therefore, the width of the delivery box is 9 inches.

Hence the width of the delivery box is 9 inches.

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Answer:

d. 15√5

Step-by-step explanation:

Perimeter = 3√5 × 5 sides

= 15√5

Answer: B - 15√5

Step-by-step explanation:

As said in the question, the perimeter is the total length of all sides of a figure. The question also says that all sides are the same length, and the length of one side is 3√5 yards.

In that case, all 5 sides have length 3√5 yards, so the perimeter would be this value added 5 times, or this value multiplied by 5:

[tex]P=3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}+3\sqrt{5}=5*3\sqrt{5}[/tex]

[tex]P=15\sqrt{5}[/tex]

Hence, the perimeter of the chicken coop is 15√5 yards.

Answer:

option A. is the midpoint of the graph

The the next step in the proof is D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

It should be noted that vertical angles are the angles that are opposite each other when the two line cross.

In this case, 7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem.

In conclusion, the correct option is D.

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A = 6 cm; B = 3 cm; C = 8 cm; D = 10 cm

The Surface area of the prism = 120 cm².

Surface area = Area of A + B + C + D

The side lengths are:

A = 6 cm

B = 3 cm

C = 8 cm

D = 10 cm

Surface area of the prism = 2(area of triangular face) + area of rectangle 1 + area of rectangle 2 + area of rectangle 3

Area of triangular face = 1/2(b)(h) = 1/2(8)(6) = 24 cm

Area of rectangle 1 = (length)(width) = (10)(3) = 30 cm²

Area of rectangle 2 = (length)(width) = (6)(3) = 18 cm²

Area of rectangle 3 = (length)(width) = (8)(3) = 24 cm²

Surface area of the prism = 2(24) + 30 + 18 + 24 = 120 cm².

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Using the t-distribution, the upper bound of the 95 percent confidence interval for the gift baskets average shipping weight is of 69.06 ounces.

The confidence interval is:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]\voerline{x} = 66, t = 2.0154, s = 10.2, n = 45[/tex]

Hence the upper bound of the interval is:

[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 66 + 2.0154\frac{10.2}{\sqrt{45}} = 69.06[/tex]

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Answer:

Area of parallelogram = 9600 m²

Step-by-step explanation:

• We can find the measure of angle x using the cos rule:

[tex]160^2 = 100^2 +100^2 -2(100)(100) \cdot cos (x)[/tex]

Make x the subject of the equation:

⇒  [tex]20000 \cdot cos(x) = 100^2 +100^2 - 160^2[/tex]

⇒  [tex]cos(x) = -0.28[/tex]

⇒  [tex]x = cos^{-1} (-0.28)[/tex]

⇒  [tex]x = 106.26 \textdegree[/tex]

• Now we can find the area of one the triangles formed using the formula:

[tex]Area =\frac{1}{2} ab \cdot sin \theta[/tex]

where a and b are two sides of a triangle, and θ is the angle between them (angle x).

Substituting the values:

Area of one triangle = [tex]\frac{1}{2}[/tex]  × (100)(100) × sin(106.26°)

                             = 4800 m²

• Since the parallelogram is formed by two such triangles, we have to double the area of the triangle to find the parallelogram's area:

Area of parallelogram = 2 × 4800

                                     = 9600 m²

Answer:

[tex]x = \bf -7[/tex]

Step-by-step explanation:

[tex]\frac{3}{4} (x + 21) = 10\frac{1}{2}[/tex]

• Divide both sides by [tex]\frac{3}{4}[/tex] :

⇒ [tex]x + 21 = 10\frac{1}{2} \space\ \div \frac{3}{4}[/tex]

⇒  [tex]x + 21 = 10\frac{1}{2} \space\ \times \frac{4}{3}[/tex]

⇒ [tex]x + 21 = 14[/tex]

• Subtract 21 from both sides:

⇒ [tex]x = 14 -21[/tex]

⇒  [tex]\boxed {x = \bf -7}[/tex]

The statements that are true for the box plots are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

The median of a data set is the center value, which is indicated on a box plot by a vertical line that divides the box.

Given the two box plots, we can conclude that:

Median for the data of Nadia is 92, which is the same for Ben.

The extreme whisker to the right for Nadia is at 100, which is the highest value for Nadia while that of Ben is 99.

The true statements are:

C. The median of Nadia’s data = median of Ben’s data.

D. Nadia had the highest score on a test

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Answer:

"C" and "D"

Step-by-step explanation:

took test on edge 2023

The correct values for a and b which models this relationship through an exponential function are 8 and 2 respectively.

An exponential function can be defined as a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function is represented by this formula:

f(x) = eˣ

Based on the information provided, we can logically deduce that the other copy machine can reduce image dimensions by a different percentage and this is defined by the following exponential function:

f(x) = abˣ

From the graph (see attachment), we have;

When x = 0, y = f(x) = 8. Thus, f(0) = 8

f(x) = abˣ

8 = ab⁰

8 = a × 1

a = 8.

Also, from the graph (see attachment), we have;

When x = 1, y = f(x) = 4

f(x) = abˣ

4 = 8b¹

4 = 8 × b

4 = 8b.

b = 8/4

b = 2.

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[tex]{\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}[/tex]

[tex]\diamond\:{\boxed{\tt{\purple{{ part \:(i) :}}}}}[/tex]

❍ Prime factorisation :-

‣ Prime factors of 12 -

[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]

‣ Prime factors of 18 -

[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&18 \\\hline 3&9\\\hline 3&3 \\ \hline &1\end{array}} \end{gathered}\end{gathered} [/tex]

Therefore,

[tex]\star \: 12 = {2}^{2} \times {3}^{1}[/tex]

[tex]\star \: 18= {2}^{1} \times {3}^{2}[/tex]

✧ LCM of 12 and 18 = [tex]\sf {2}^{2} \times {3}^{2}[/tex]

[tex]\implies 36[/tex]

✧ HCF of 12 and 18 = [tex]\sf {2}^{1} \times {3}^{1}[/tex]

[tex] \implies 6[/tex]

[tex] \diamond\:{\boxed{\tt{\red{{ part \:(ii) :}}}}}[/tex]

❍ Prime factorisation :-

‣ Prime factors of 12 -

[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}2&12 \\\hline 2&6 \\ \hline 3&3\\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]

‣ Prime factors of 15 -

[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&15 \\\hline 5&5 \\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]

‣ Prime factors of 21 -

[tex]\begin{gathered}\begin{gathered}{\begin{array}{ c|c}3&21 \\\hline 7&7 \\ \hline &1\end{array}} \end{gathered}\end{gathered}[/tex]

Therefore,

[tex]\star \: 12 = {2}^{2} \times {3}^{1}[/tex]

[tex] \star \: 15 = {3}^{1} \times {5}^{1}[/tex]

[tex]\star \: 21 = {3}^{1} \times {7}^{1}[/tex]

✧ LCM of 12, 15 and 21 = [tex]\sf {2}^{2} \times {3}^{1} \times {5}^{1} \times {7}^{1}[/tex]

[tex] \implies 420[/tex]

✧ HCF of 12, 15 and 21 = [tex]\sf {3}^{1} [/tex]

[tex] \implies 3[/tex]

[tex] {\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}[/tex]

Using,

LCM × HCF = Product of two given numbers

Putting the values,

[tex]\longrightarrow \sf 48 \times 12 = 16 \times y[/tex]

[tex]\longrightarrow \sf \dfrac{ \cancel{48} _{3} \times 12}{ \cancel{16}{ _1} } = y[/tex]

[tex]\longrightarrow \sf y = 3 \times 12[/tex]

[tex] \longrightarrow {\sf{{{\boxed{\green{\bold {\sf y = 36 }}}}}}}[/tex]

Therefore,

The value of y = 36

[tex]{\large{\textsf{\textbf{\underline{\underline{Important \: points :}}}}}}[/tex]

• A natural number "P" > 1 having only two factor one and "P" itself is called prime number.

• A prime number is never negative.

• H.C.F is the product of smallest power of each common prime factor.

• L.C.M is the product of greatest power of each prime factor.

• HCF is always a factor of LCM.

[tex]\underline{\rule{300pts}{3pt}}[/tex]

Answer: 23/26

Step-by-step explanation:

Let’s say we have 3 spots, one for each of the three exchange students. It doesn’t matter who goes with who, we’re just going to choose people.

If LaQuinta is NOT one of the people chosen, then there are 25 possible people left to become tour guides. We will need to choose 3 of them, so there are (25 choose 3) = 2,300 ways.

With no restrictions, there are 26 people to choose from and 3 spots to fill. Therefore there are (26 choose 3) = 2,600 ways to fill these 3 spots with no restrictions.

The total probability is 2,300/2,600, which simplifies to 23/26.

Using a system of equations, the parts are of 14 and 20.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are x and y. The total is of 34, hence:

x + y = 34 -> y = 34 - x.

The ratios are given as follows:

[tex]\frac{4}{7}x = \frac{2}{5}y[/tex]

Then:

[tex]\frac{4}{7}x = \frac{2}{5}(34 - x)[/tex]

20x = 14(34 - x)

34x = 34 x 14

x = 14, y = 34 - 14 = 20.

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Answer:

5:9

Step-by-step explanation:

So since 18 chose to do oral report, that means (28-18) or 10 students decided to do a written report.

To find the written to oral report ration, we need to find for each student that did a written report, how many did an oral report? We can express this as a fraction and simplify to get the simplified ratio. So the the written will be the numerator and the oral will be the denominator: 10/18, to simplify this simply divide both sides by 2, to get 5/9 which gives us the simplified ratio of 5:9 meaning that for every 5 students who decided to do a written report 9 students decided to do an oral report.

In light of the provided confidence interval, the following is the best answer on the outcome of the hypothesis test:

Yes, because 0 is not in the confidence interval.

[tex]$H_{0}: \mu=0$[/tex]

[tex]$H_{1}: \mu \neq 0$[/tex]

yes, because 0 is not in the confidence interval

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Answer:

36

Step-by-step explanation:

Chad's original garden is 3 ft x 8 ft.

original area = 3 x 8 = 24 square feet

Chad's super Chadly new garden is 3 feet wider, and 2 feet longer.

new width = 3 + 3 = 6

new length = 8 + 2 = 10

new Area = 6 x 10 = 60 square feet

To find how much larger the new area is, subtract the original area.

60 – 24 = 36 square feet

Answer:

[tex] \frac{6}{20} = \frac{3}{10?} [/tex]

Step-by-step explanation:

total amount of acts = 4+10+6 = 20

amount of dancers = 6

probability of picking a dancer = number of dancers / total number of talents = 6/20 = 3/10

The probability that a dancer performs first is 3/10.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

The acts in a talent competition consist of 4 instrumentalists, 10 singers, and 6 dancers.

Total participants = 4+ 10 +6 = 20

So, the probability that a dancer performs first

= 6 /20

= 3/10

Hence, the probability that a dancer performs first is 3/10.

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Answer:

standard deviation sign is σ

mean sign is x , and sometimes it have a hyphen directly above x.

Step-by-step explanation:

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean of the set, while a high standard deviation indicates that the values are spread out over a wider range.

It is the sum (total) of all the values in a set of data, such as numbers or measurements, divided by the number of values on the list. To find the mean, add up all the values in the set. Then divide the sum by how many values there are.

The symbol ∑ indicates summation and is used as a shorthand notation for the sum of terms that follow a pattern.

Answer:

Question 6) Neither (Not an inverse variation)

Question 7) Inverse variation

Question 8) Inverse variation

Step-by-step explanation:

These are the two formulas we need to know prior to solving the question.

Direct variation: c times x

Inverse variation: c times 1/x --> c/x

- Here, c is the constant

6. y = x + 7

This is neither. It is not in the form of a direct, or inverse variation, so it does not belong in any category.

7. 14 = xy

This equation is an inverse variation.

xy = 14

y = 14/x

14 is the constant, and the format is the same as for an inverse variation.

8. x = -8/y

This equation is an inverse variation.

yx = -8

y = -8/x

-8 is the constant, and the format is the same as for an inverse variation.

So we can conclude that questions 7 and 8 is an inverse variations, while question 6 isn't.

General forms

Direct

Inverse

so

#6

Not inverse and direct also as 7 is present

#7

Yes

#8

Yes

Answer:

H. 10 h

Step-by-step explanation:

40.50-5.5 = 35

35/3.5 = 10 hours

The ratio between the circle and triangle is described as 3:4.

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The equation that could be used to find how many gallons Erin would need to drive 92 miles is 92 = 23g (option c)

The first step is to determine the gallons needed to drive 1 mile. To do this, divide the  6 gallons by 138 miles. Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷.

Gallons needed for 1 mile = 6/138

In order to determine the gallons needed for 92 miles, multiply the ratio gotten in the previous step by 92

(6/138) x 92 = 4 gallons

The option that gives 4 gallons is : 92 = 23g

g = 92 / 32 = 4

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The interface validation that would help to confirm that you meet the minimum age is the range check.

This is the term that is used to refer to the check that is done in such a way that it shows the data that are in a particular range.

This would help to ensure that there is a specified upper and lower boundary for the values to fall into.

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which of the following interface validation checks is useful in verifying that the birth data you entered on your job application indicates that you meet the minimum age requirement to serve alcohol?

Consistency check

Format check

Completeness check

Range check

Answer:

The volume of the cylinder is 2,400pi cubic units

Step-by-step explanation:

I hope this helps and have a good day!

Answer:

Hi, I'm not for sure but I think for sure for the answer is, I haven't done this math in a while btw I like math lol, but I will try my best for this answer:

The quotient:   x + 4

The remainder: - 2

Step-by-step explanation:

I hope this helps you and have a lovely day of learning!

Total distance travelled = (x.a + 2x -10) miles .

How to solve such time related questions?

The key concept for solving such questions is the relationship between speed, distance and time.

The relationship between them is Distance = Speed X Time

The whole trip can be divided into two parts

Part 1 :- Speed = x mph  and time =  a hours

        ∴ Distance = x .a miles

Part 2 :- Speed = x -5mph  and time =  2 hours

        ∴ Distance =(x-5).2 = (2x -10)miles

Total distance = (x.a + 2x -10) miles

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