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(9/-3) - 2

= (-3)(-2)

=  -6

An algebraic equation or polynomial equation is an equation of the frame P=0 where P could be a polynomial with coefficients in a few fields, regularly the field of the rational numbers.

algebraic equation, a statement of the equality of two expressions defined by applying to a set of factors the algebraic operations, namely, expansion, subtraction, increase, division, raising to a control, and extraction of a root.

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At least 5 expected observations in each cell in order to apply the chi-square test of independence, we prefer to have at least 5 expected observations in each cell. The correct answer is c.

The chi-square test of independence is a statistical method used to determine whether two categorical variables are independent or associated with each other.

To apply this test, it is preferred to have at least 5 expected observations in each cell of the contingency table. The expected frequency is calculated based on the assumption of independence between the two variables.

If the expected frequency is less than 5 in any cell, the chi-square test may not be valid and alternative methods, such as Fisher's exact test, should be considered. Having a sufficient sample size can also improve the accuracy and reliability of the test results.

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I understand the instructions and will distribute the points in a way that maximizes the total earned for both participants. Here is how I would allocate the points:

KEEP account: 0 points

GIVE account: 10 points

By allocating all 10 points to the GIVE account, both participants will receive 15 points after the 50% multiplier is applied (10 * 1.5 / 2 = 15). This results in the highest total score compared to any other allocation.

Answer:

\(\frac{5}{14}\)

Step-by-step explanation:

First, find the total number of students:

\(252+140=392\)

Then, divide the number of students at hand by the total number:

\(\frac{140}{392}\)

When possible, reduce the fraction to its simpliest form:

\(\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}\)

Answer: ß

Step-by-step explanation:

Answer:

x=1

Step-by-step explanation:

Add

16

to both sides of the equation.x=−15+16 Add −15 and 16.x=1

Answer:

Step-by-step explanation:

-16 + x = - 15

Add 16 to both sides

-16 + 16 + x  = -15 + 16

              x = 1

Real profits for this company are increasing at a rate of about 3.2%, on average. Therefore, (c)"An increase by 3.2%" is the right response.

To calculate the approximate rate of change in real profits, we need to compare the change in nominal profits with the change in purchasing power due to inflation and exchange rate fluctuations.

First, let's calculate the nominal profits for the base year:

\(\text{Nominal Profits} = \text{Revenue} - \text{Cost of Goods Sold} = 1,000 \text{ euros} - \$800 = 1,000 \text{ euros} - \frac{1,000 \text{ euros}}{\$1.20} = 1,000 \text{ euros} - 833.33 \text{ euros} = 166.67 \text{ euros}.\)

Next, let's calculate the nominal profits for the current year:

Revenue increased at the German inflation rate of 2%:

New Revenue = 1,000 euros + 1,000 euros * 2% = 1,000 euros + 20 euros = 1,020 euros.

Cost of Goods Sold increased at the US inflation rate of 4%:

New Cost of Goods Sold = $800 + $800 * 4% = $800 + $32 = $832.

Converting the new revenue and cost of goods sold to euros using the current exchange rate:

New Revenue in euros = 1,020 euros.

\(\text{New Cost of Goods Sold in euros} = \frac{832 \text{ euros}}{\$1.22} = 681.97 \text{ euros}.\)

Now, let's calculate the new nominal profits:

New Nominal Profits = New Revenue - New Cost of Goods Sold = 1,020 euros - 681.97 euros = 338.03 euros.

The change in nominal profits is:

Change in Nominal Profits = New Nominal Profits - Nominal Profits = 338.03 euros - 166.67 euros = 171.36 euros.

To calculate the approximate rate of change in real profits, we compare the change in nominal profits with the base year nominal profits:

\(\text{Rate of Change in Real Profits} = \left(\frac{{\text{Change in Nominal Profits}}}{{\text{Nominal Profits}}}\right) \times 100\)

\(\text{Rate of Change in Real Profits} = \left(\frac{{171.36 \text{ euros}}}{{166.67 \text{ euros}}}\right) \times 100\)

≈ 102.8%.

Therefore, the approximate rate of change in real profits for this firm is an increase by approximately 3.2%. Therefore, the correct answer is "An increase by 3.2%".

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Answer:

  90° CCW

Step-by-step explanation:

The angle from C to the origin to C' is a right angle when measured counterclockwise (in the usual direction).

ΔA'B'C' is a rotation of ΔABC 90° CCW.

__

This is fully equivalent to a rotation of 270° CW.

The elevator of  John Hancock Center in Chicago travels at a faster rate.

For the equation represented by the height of the elevator of  John Hancock Center in Chicago given as y = 30x, the rate of change is 30 ft/s which is equivalent to 1800 per minute.

Since the express elevator in the Empire State Building in New York City travels nonstop from  the ground floor to the top floor at a rate of 1,400 feet per minute, hence the elevator of  John Hancock Center in Chicago travels at a faster rate.

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Answer:

92 m

Step-by-step explanation:

Use the Pythagorean theorem to find the length of the shorter side.

Let w = length of the shorter side.

\(w^{2} + 30^{2} = 34^{2} \\ w^{2} + 900 = 1156\\w^{2} = 256\\w = \sqrt{256} = 16\)

The perimeter is 2l + 2w = 2(30) + 2(16) = 60 + 32 = 92 m

Answer:

x=13

Step-by-step explanation:

x     4      3     2      1

f      3      5     4      2

Total number of scores in table are ∈ f =  3 + 5 + 4 + 2 = 14

According to the question, given that

x     4      3     2      1

f      3      5     4      2

Total number of scores are ∈ f =  3 + 5 + 4 + 2 = 14

Therefore, after sum of score we get total number of scores is 14

The average or computed center value of a group of values is known as the mean, and it is used to determine the central tendency of the data. The entire collection of data or distribution is identified by a single number using the statistical metric known as central tendency.

We can use the direct technique, the assumed mean method, or the step deviation method to determine the mean of grouped data. The frequency of several observations or variables that are combined together is the subject of the mean of grouped data. Let's examine each of these approaches in turn.

Direct Method

The direct approach is the most straightforward way to determine the mean of the grouped data. The mean of the data is given by, if the values of the observations are x1, x2, x3, and x4 and their associated frequencies are f1, f2, f3, and f4, respectively.

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The least expensive computer after the 20% discount would be $400.

To calculate the price of the least expensive computer after the 20% discount, we need to find 20% of the original price and subtract it from the original price.

Let's assume the original price of the least expensive computer is x. The discount of 20% can be calculated as 0.20 * x. To find the discounted price, we subtract the discount from the original price: x - 0.20 * x = 0.80 * x.

Since we know that the cost of the least expensive computer ranges from $500 to $1000, we can substitute x with $500 and calculate the discounted price: 0.80 * $500 = $400. Therefore, the least expensive computer after the 20% discount would be $400.

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Answer:

My answer

Step-by-step explanation:

First you convert it and it is 0.06 m. This is because

Conversion factor: 1 m = 100 cm

1) m = cm / 100

2) m = 6 / 100

3) m = 0.06

Then you do the error interval. Error interval – the range of values (between the upper and lower bounds) in which the precise value could be. Thn you caculate it by when you do this x2 then do <. For example 5>3. The do that there now you should have the answer. Dont frget put L in frount of 0.06 x2. Thank you. Hoped this helped! :)

The correct option  a) 4 ft. , Service Cable that is attached to a building must be sustained at intervals no greater than 4 ft..

Service cables mounted in close proximity to a building must be supported at no more than four-foot intervals.

Thus,  service cable that is attached to a building must be sustained at intervals no greater than 4 ft.

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Answer: 1/6

Step-by-step explanation:

An easy way for me to find a common denominator is to multiply both denominators: 3 times 2 and then subtract 2-1.

1/6  

Answer:

24°

Step-by-step explanation:

A triangle will always equal 180°. In the triangle, you can see that two angles are already measures.

Angle A = 66°

Angle B = 90° (Right angle)

Angle C = ?

You have all the info you need.

66+90 = 156

If a triangle is equal to 180°, comply subtract 156 from 180. This gives you the answer 24, and that's the measure of angle C.

Hope this helped! I just did this question on my Acellus and got it right. :)

Answer:

0.38

Step-by-step explanation:

Percentage is number/100 = 38/100 = 0.38

Cheers

Consider that the slope of a line passing through two given points, is given by the formula,

So the slope of line passing through the points (5,4) and (0,1) is calculated as,

Thus, the slope of straight lines passing through (5,4) and (0,1) is 3/5 .

Similarly, the slope of line passing through the points (3,7) and (-2,2) is calculated as,

Thus, the slope of line passing through the points (3,7) and (-2,2) is 1 .

In a proportional relationship between two quantities, the constant of proportionality, often denoted by the letter "k," represents the value that relates the two quantities. The equation y = kx is the standard form for expressing a proportional relationship, where "y" and "x" are the variables representing the two quantities.

Here's a breakdown of the components in the equation:

y: Represents the dependent variable, which is the quantity that depends on the other variable. It is usually the output or the variable being measured.

x: Represents the independent variable, which is the quantity that determines or influences the other variable. It is typically the input or the variable being controlled.

k: Represents the constant of proportionality. It indicates the ratio between the values of y and x. For any given value of x, multiplying it by k will give you the corresponding value of y.

The constant of proportionality, k, is specific to the particular proportional relationship being considered. It remains constant as long as the relationship between x and y remains proportional. If the relationship is linear, k also represents the slope of the line.

For example, if we have a proportional relationship between the distance traveled, y, and the time taken, x, with a constant of proportionality, k = 60 (representing 60 miles per hour), the equation would be y = 60x. This equation implies that for each unit increase in x (in hours), y (in miles) will increase by 60 units.

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Answer:

218.57

Step-by-step explanation:

Since it is an isoceles triangle, the sides are 32, 32, and 14.

Using Heron's Formula, which is Area = sqrt(s(s-a)(s-b)(s-c)) when s = a+b+c/2,  we can calculate the area.

(A+B+C)/2  = (32+32+14)/2=39.

A = sqrt(39(39-32)(39-32)(39-14) = sqrt(39(7)(7)(25)) =sqrt(47775)= 218.57.

Hope this helps have a great day :)

Check the picture below.

so let's find the height "h" of the triangle with base of 14.

\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{7}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=\sqrt{ 32^2 - 7^2}\implies h=\sqrt{ 1024 - 49 } \implies h=\sqrt{ 975 }\implies h=5\sqrt{39} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{area of the triangle}}{\cfrac{1}{2}(\underset{b}{14})(\underset{h}{5\sqrt{39}})}\implies 35\sqrt{39} ~~ \approx ~~ \text{\LARGE 218.57}\)

This question is solved using rounding and proportion concepts.

A drinking glass holds 0.3 litres correct to the nearest 0.1 litres

This means that, with 2 decimal places, the drinking glass holds between 0.25 litres and 0.34 litres.

-------------------------------------

Calculate the lower bound for the number of glasses of water which can be filled from the bottle

For the lower bound, we consider that 1 glass holds 0.25 litres, and want to find how many glasses are needed for 25 litres. So

1 glass - 0.25 litres

x glasses  - 25 litres

Applying cross multiplication:

\(0.25x = 25\)

\(x = \frac{25}{0.25} = 100\)

Thus, the lower bound for the number of glasses of water which can be filled from the bottle is 100.

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Answer:

He scored 987 in total.

Step-by-step explanation:

32.9 points on average for 30 games. 32.9 times 30 is 987.

When population grows exponentially with a proportionality constant, k , this population will take 4.620 time to double.

If the population is growing exponentially, the rate of population change is directly proportional to its current size. So assume that the total population at some point in time t is y.

Next, write the differential equation subject to the condition that it increases in proportion to its magnitude. We can get rid of the proportional sign by introducing a constant of proportionality. We then isolate and integrate the variables of the differential equation thus formed and use the initial values to find the value of the constant of proportionality. We have , a population grows exponentially.

The proportionality constant, k = 15% = 0.15

The exponential growth function is y = y₀ eᵏᵗ

where y₀ --> initial population or at t = 0

k --> proportionality constant

t --> time

y --> is value of y at any t

let there be population y₀ at t = 0 . Then, we have to calculate how much time take the population to double.

2 yo = yo e⁰·¹⁵ᵗ

=> 2 = e⁰·¹⁵ᵗ

Introducing natural logarithms on both sides of above equation,

=> ln (2) = ln ( e⁰·¹⁵ᵗ )

=> ln (2) = 0.15t ( since ln e = 1)

=> t = ln(2)/1.5 = 4.620

Hence, required time is 4.620.

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To find the first term of an arithmetic sequence, use the formula: first term = last term - (number of terms - 1) * common difference.

To find the first term of an arithmetic sequence given the number of terms, the last term, and the common difference, you can use the following formula

First term = Last term - (Number of terms - 1) * Common difference

Here's how to use this formula

Identify the number of terms, the last term, and the common difference of the arithmetic sequence.

Plug these values into the formula.

Simplify the formula using order of operations (PEMDAS) to find the first term.

For example, let's say we have an arithmetic sequence with 10 terms, a last term of 50, and a common difference of 5. Using the formula above, we get

First term = 50 - (10 - 1) * 5

First term = 50 - 9 * 5

First term = 50 - 45

First term = 5

Therefore, the first term of the arithmetic sequence is 5.

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Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

n = 2.5

Step-by-step explanation:

We need to isolate n by first moving it to one side.

11n = 13n - 5

11n - 13n = -5

-2n = -5

n = -5/-2

n = 2.5

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Answer:

n = 5/2

Step-by-step explanation:

5 + 11n = 13n

5 = 13n - 11n

5 = 2n

n = 5/2

Check:

5 + 11*5/2 = 13*5/2

10/2 +  55/2 = 65/2

Answer:

I believe it is the last option but I'm not completely sure because the pic is blurry. But if the beginning of the graph is at (-3, -4) then the last option is definitely correct.

Step-by-step explanation:

Remember h controls horizontal movement k controls vertical movements.

always remember to take the opposite of h.

;)

The number of significant digits the product should have = 2

The given numbers are:

\(4.5160 \times 10^{-3}\\ 2.09 \times 10^7\\ 5.8 \times 10^3\)

We first multiply them.

\(4.5160 \times 10^{-3}\times 2.09 \times 10^7\times 5.8 \times 10^3 = 54.743\times10^7\)

In measurement problems, we usually write it as \(5.474\times10^7\)

Significant digits are the numbers which decide the precision and accuracy in measurement problems.

The fewest number of significant digits in each factor of multiplication is considered as the significant digits of the product.

So number of significant digits in \(4.5160\times10^{-3}\) = 5

Number significant digits in \(2.09\times10^7\) = 3

Number of significant digits in \(5.8\times10^3\) = 2

So the product should be rounded into 2 significant digits.

So the product,  \(5.474\times10^7\)= \(5.5\times10^7\) with 2 significant figures.

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Answer:

x = - 15

Step-by-step explanation:

Given

\(\frac{x}{5}\) = 5 + \(\frac{x-9}{3}\)

Multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

3x = 75 + 5(x - 9) ← distribute and simplify right side

3x = 75 + 5x - 45

3x = 5x + 30 ( subtract 5x from both sides )

- 2x = 30 ( divide both sides by - 2 )

x = - 15

As a check

substitute x = - 15 into the equation and if both sides are equal then it is the solution.

left side = \(\frac{-15}{5}\) = - 3

right side = 5 + \(\frac{-15-9}{3}\) = 5 + \(\frac{-24}{3}\) = 5 - 8 = - 3

Thus x = - 15 is the solution