3(2 + 4) = (3•2)+(3•4) is an
example of which property?

Answer & Step-by-step explanation:

PEMDAS:

Parentheses

Exponents

Multiplication and Division left to right

Addition and Subtraction left to right

We have two forms of grouping in the expression. Do the inner-most one first, still following PEMDAS within the grouping symbol:

Simplify division:

\(6/4=1.5\\1.5-1=0.5\\\)

Re-insert:

\(40/(19-1+0.5)\)

Simplify subtraction and addition within parentheses:

\(19-1+0.5\\18+0.5\\18.5\)

Re-insert:

\(40/18.5\)

Simplify division:

\(40/18.5=2.162162162162162162.....\)

:Done

The computed value of the test statistic is 2.94.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

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Using mathematical operation we get, to make a total $130 in my bank account I have to mow the garden for 10 hours.

Mathematical operation is the branch of mathematics that includes the study of numbers and the manipulation of numbers that are useful in all other branches of mathematics. It basically includes operations like addition, subtraction, multiplication and division. 

According to the question:

Given, Balance in account = $50

Rate of mowing per hour = $8

So, in order to make the bank account balance $130 we need

$130 - $50 = $80

∴ Number of hours to mow garden = $80/Rate of mowing

                                                           = $80/$8

                                                           = 10 hours

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The equation of the tangent line in Cartesian coordinates for the given parameter t = 1 is: y = -π sin(π)x + cos(π)

To find the equation of the tangent line in Cartesian coordinates for the parametric equations:

x = sin(πt)

y = cos(πt)

We need to find the derivative of both x and y with respect to t, and then evaluate them at the given parameter value.

Differentiating x with respect to t:

dx/dt = π cos(πt)

Differentiating y with respect to t:

dy/dt = -π sin(πt)

Now, we can find the slope of the tangent line at parameter t = 1 by substituting t = 1 into the derivatives:

m = dy/dt (at t = 1) = -π sin(π)

Next, we need to find the coordinates (x, y) on the curve at t = 1 by substituting t = 1 into the parametric equations:

x = sin(π)

y = cos(π)

Now we have the slope of the tangent line (m) and a point (x, y) on the curve. We can use the point-slope form of the equation of a line to write the equation of the tangent line:

y - y1 = m(x - x1)

Substituting the values we obtained:

y - cos(π) = -π sin(π)(x - sin(π))

Simplifying further:

y - cos(π) = -π sin(π)x + π sin(π) sin(π)

y - cos(π) = -π sin(π)x

y = -π sin(π)x + cos(π)

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Answer:

The area of the circle is":

A = 1017.36 in²

The circumference of the circle is:

C = 113.09 in

Step-by-step explanation:

Given

r = 18 in

We need to determine the area and circumference of the circle

Using the formula to determine the area

A = πr²

   = 3.14 × (18)²

   = 3.14 × 324

   = 1017.36 in²  (Rounded to the nearest 0.01 or  the Hundredths Place)

Thus, the area of the circle is":

A = 1017.36 in²

Using the formula to determine the circumference.

C=2πr

  = 2 × 3.14  ×  18

  = 113.09 in

Thus, the circumference of the circle is:

C = 113.09 in

The equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

What is Perpendicular bisector of the segment?

A perpendicular bisector is a line that cuts another line segment through the junction point at a straight angle. As a result, a perpendicular bisector always cuts a line segment through its midway. The term bisect means to divide equally or uniformly.

The midpoint of the segment GH is the point (3,-3).

The slope of the line perpendicular to GH is the negative reciprocal of the slope of GH, which is -6/8 = -3/4

The slope-intercept form of the equation of the line is y = mx + b, where m is the slope and b is the y-intercept.

The point-slope form of the equation of the line is y - y1 = m(x - x1)

So we have

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

y + 3 = (-3/4)x + (9/2)

We can find the equation of the perpendicular bisector of the segment G(x1, y1) and H(x2, y2) by using the midpoint of the segment, (x1 + x2)/2, and (y1 + y2)/2, and the slope of the segment, (y2 - y1)/(x2 - x1)

so our final equation is y = -(3/4)x + (9/2)

Therefore, equation of the perpendicular bisector of the segment with endpoints G (-2,0) and H(8,-6) would be, y = -(3/4)x + (9/2)

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Answer:

5/24.

Step-by-step explanation:

2/6 of 5/8 were beginners and girls

= 1/3 * 5/8

= 5/24.

Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Consequently, there exist four numbers z:

√3/2 ± I 1/2

-√3/2 ± I 1/2

The three unique vertices of an equilateral triangle are 0, z, and z3: (z^3=0)= e ^iπ/3(z -0 ) ⇔ z^3=e^(±iπ/3)z

=(z^2-e^±iπ/3)z=0⟺z=0

or z^2=e^±iπ/3

Since we have z\(\neq\)0, z=e^±iπ/6= ±(√3/2 ± I 1/2  )

There are thus four numbers in z:

√3/2 ± I 1/2

-√3/2 ± I 1/2

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Answer:

distance between -5 to 0 = 5 units

Answer:

C=89.2

Step-by-step explanation:

The formula of the circumference of a circle is C=2piR (or C=piD). Now, when calculating, plug in the numbers, giving you C=2pi14.2. Multiply everything, you get a super long irrational number; just round. You will get 89.2.

The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:I think it’s c

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Here in this question, we want to select which of the options particularly represents what was given in the question.

Mathematically 10^4 means that we are raising 10 into a continued exponential raising up to 4 times.

So 10^4 is pronounced as the first option in the question.

10 raised to power 10 , raised to power 10 etc

Compute the Gaussian density for the following cases. (a) x=0, m=0, s-1. Give the name of question5a (b) x-2, m=0, s-1. The value of the account on January 1, 2021, would be $2,331.57.

To calculate the value of the account on January 1, 2021, we need to consider the compounding interest for each year.

First, we calculate the value of the initial deposit after three years (12 quarters) using the formula for compound interest:

Principal = $1,000

Rate of interest per period = 8% / 4 = 2% per quarter

Number of periods = 12 quarters

Value after three years = Principal * (1 + Rate of interest per period)^(Number of periods)

                           = $1,000 * (1 + 0.02)^12

                           ≈ $1,166.41

Next, we calculate the value of the additional $1,000 deposit made on January 1, 2019, after two years (8 quarters):

Principal = $1,000

Rate of interest per period = 2% per quarter

Number of periods = 8 quarters

Value after two years = Principal * (1 + Rate of interest per period)^(Number of periods)

                         = $1,000 * (1 + 0.02)^8

                         ≈ $1,165.16

Finally, we add the two values to find the total value of the account on January 1, 2021:

Total value = Value after three years + Value after two years

                ≈ $1,166.41 + $1,165.16

                ≈ $2,331.57

Therefore, the value of the account on January 1, 2021, is approximately $2,331.57.

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The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

In order to determine the probability of exactly two flaws in a 50-yard piece of material, we will use the Poisson distribution formula.

The Poisson distribution is used to calculate the probability of a given number of events occurring in a fixed interval of time or space when these events happen independently of each other and at an average rate.

To find the probability of exactly two flaws in a 50-yard piece of material, we will use the following formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where: P(X = k) is the probability of k flaws occurring in a 50-yard piece of material

λ = the average rate of flaws per unit of material (in this case, 50 yards)

k = the number of flaws we want to calculate is the mathematical constant ≈ 2.71828...

k! is the factorial of k, which is the product of all positive integers up to k

Let's plug in the values we have for this problem:

P(X = 2) = (e^(-λ) * λ^2) / 2!

λ = 2 flaws per 50 yards of material produced = 2/50 = 0.04 flaws per yard.

Therefore, the average number of flaws in a 50-yard piece of material is:

λ = 0.04 * 50 = 2e is a mathematical constant that equals ≈ 2.71828...

Then, let's plug in these values into the formula:

P(X = 2) = (e^(-2) * 2^2) / 2!P(X = 2) = (0.1353 * 4) / 2P(X = 2) = 0.2706

The probability of exactly two flaws occurring in a 50-yard piece of material is 0.2706 or approximately 27.06%.

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

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a. The base calculation of the ticket price can be determined by considering various costs and factors associated with operating the bus. The calculation should include costs such as the initial price of the bus, fuel expenses, driver wages, insurance, maintenance, and other operational costs. By dividing the total costs by the number of passengers expected to be carried during the bus's lifespan, the base ticket price can be determined.

b. When suggesting the actual accumulated charges to be imposed in the future, it is important to consider factors such as inflation, changes in operating costs, market demand, and competitive pricing. The government should conduct market research and analysis to understand the dynamics of the transportation industry, evaluate the impact of potential charges on consumers and businesses, and strike a balance between affordability for passengers and profitability for bus operators. The suggested charges should aim to ensure sustainability and a fair return on investment for the operators, while also considering the economic well-being of the population.

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Answer:

5<x<19

Step-by-step explanation:

Answer

Answer:

Step-by-step explanation:

aa+1=4a                         ∴ (Simplify both sides of the equation)

a2+1−4a=4a−4a            ∴ (Subtract 4a from both sides)

a2−4a+1=0

For this equation:  a=1,  b=-4,  c=1

1a2+−4a+1=0

a = −b ±  √b2 − 4ac2a divided by 2a    ⇒(Use quadratic formula with a=1, b=-4, c=1)

−(−4) ± √(−4) 2−4 (1) (1) /2 (1)

a=4±√12/2

a=2+√3 or a=2−√3

a=2+√3 or a=2−√3

Answer:

-1.6

Step-by-step explanation:

\(-4.4y = 7.04\)

\(+4.4\)      

___________

\(y = 11.44\),  is the answer.

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Using the concept of Unit Cost, $5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

The unit price is  measurement used to represent the price of a particular good or service to be exchanged with the customers or consumers for money. The unit price refers to the price/unit of measures, such as price per pound, quart, ounce, or other units of weight or volume of the food package.

The unit price is important for both of customers and organizations. An organization cannot sustain without unit price itself for a long period by selling products at a lower price. Similarly, customers would not be able to buy the product if the value of the product is less than the price. The researcher suggests that the unit price information helps shoppers to save around 17-18% in supermarkets when they are educated on how to actually use it.

We are given Carrot cost of per pound is $0.99.

Therefore Carrot cost for 3.5 pounds=3.5×0.99= $3.465

Similarly, Broccoli cost of per pound is $1.50.

Therefore, broccoli cost for 1.25 pounds =1.25×1.50=1.875

Total bill = Broccoli cost+ Carrot cost

Total bill =3.465+1.875=$5.34

Hence,$5.34 is Jacks` total bill for buying 3.5 pounds of carrot and 1.25 pound of broccoli.

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The series 6.6 + 15.4 + 24.2 + ... for 5 terms can be represented by the summation notation Σ^4_n=0 (8.8 + 6.6n), where n ranges from 0 to 4.



The correct answer is option b: Σ^4_n=0 (8.8 + 6.6n).In summation notation, the given series can be written as:Σ^4_n=0 (8.8 + 6.6n)

Let's break it down:

- The subscript "n=0" indicates that the summation starts from the value of n = 0.- The superscript "4" indicates that the summation continues for 4 terms.- Inside the parentheses, "8.8 + 6.6n" represents the pattern for each term in the series.

To find the value of each term in the series, substitute the values of n = 0, 1, 2, 3, 4 into the expression "8.8 + 6.6n":

When n = 0: 8.8 + 6.6(0) = 8.8

When n = 1: 8.8 + 6.6(1) = 15.4

When n = 2: 8.8 + 6.6(2) = 22.0

When n = 3: 8.8 + 6.6(3) = 28.6

When n = 4: 8.8 + 6.6(4) = 35.2

Thus, the series 6.6 + 15.4 + 24.2 + ... for 5 terms can be expressed as Σ^4_n=0 (8.8 + 6.6n).

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Answer:

7x, or seven times in multiplication

Step-by-step explanation:

Hope it helps

Using dimensional analysis, In order to pack 288 eggs, the student would require 24 cartons.

How to find?

To find out how many cartons the student would need to pack 288 eggs, we can use dimensional analysis.

We want to find:
- The number of cartons needed to pack 288 eggs.

To solve this, we can set up a proportion:

12 eggs / 1 carton = 288 eggs / x cartons

Cross-multiplying, we have:

12x = 288

Now, divide both sides of the equation by 12:

x = 288 / 12

Simplifying, we get:

x = 24

Therefore, the student would need 24 cartons in order to pack 288 eggs.

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Using dimensional analysis, we can determine that the student would need 24 cartons to pack 288 eggs.

To determine the number of cartons needed to pack 288 eggs, we can use dimensional analysis.
Step 1: Identify the given information and the conversion factor.
Given:
- 288 eggs
Conversion factor:
- 1 dozen = 12 eggs
Step 2: Set up the dimensional analysis equation.
We can set up the equation as follows:
288 eggs x (1 dozen/12 eggs) = ?
Step 3: Perform the calculation.
To solve the equation, we can cancel out the "eggs" unit and calculate the number of dozens:
288 eggs x (1 dozen/12 eggs) = 24 dozens
Step 4: Interpret the result.
Therefore, the student would need 24 cartons to pack 288 eggs.

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a) The utility depends on both health (H) and consumption of other goods (X).

b) The coefficient is negative, indicating a negative relationship between two variables.

c) Health (H) is greater than zero, suggesting a positive value for health.

d) Health (H) is a function of a variable denoted as 'm'.

e) The variable 'm' is greater than zero and the coefficient is negative.

f) The product of two variables, 'm' and 'm', is negative.

a) The expression in (a) is reasonable as it acknowledges that utility is influenced by both health and consumption of other goods. It recognizes that happiness or satisfaction is derived not only from health but also from other aspects of life.

b) The expression in (b) suggests a negative coefficient and a negative relationship between the variables. This could imply that an increase in one variable leads to a decrease in the other. The reasonableness of this relationship would depend on the specific variables involved and the context of the theoretical framework.

c) The expression in (c) states that health (H) is greater than zero, which is reasonable as health is generally considered a positive attribute that contributes to well-being.

d) The expression in (d) indicates that health (H) is a function of a variable denoted as 'm'. The specific nature of the function or the relationship between 'm' and health is not provided, making it difficult to assess its reasonableness without further information.

e) The expression in (e) states that the variable 'm' is greater than zero and the coefficient is negative. This implies that an increase in 'm' leads to a decrease in some other variable. The reasonableness of this relationship depends on the specific variables involved and the theoretical context.

f) The expression in (f) suggests that the product of two variables, 'm' and 'm', is negative. This implies that either 'm' or 'm' (or both) are negative. The reasonableness of this expression would depend on the meaning and interpretation of the variables involved in the theoretical framework.

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Answer:

bsdqư

Step-by-step explanation:

Answer:

33.3%

Step-by-step explanation:

10/ 30= 0.3(3 would be a reoccurring decimal)

0.3*100=33.3

10% of students take the bus

To make a division between two integer, for example -6÷5. The first thing we need to do is:

• Define the sign of the result.

For that we use the law of signs:

• when you divide a negative number by a positive number, the answer will be negative.

• When you divide a positive number by a negative number, the answer will be also negative

• When you divide a negative number by a negative number, the answer will be a positive number.

In this example, we have the first case, so the answer will be negative.

Now we move to making th division between 6 and 5, for that we arrange the numbers as follows:

And we start by finding how many times does the number 5 fits into the number 6. The answer to that is that 5 can fit into 6 one time.