which property of addition is used in the following (5+12)+6=5+(12+6)

Answer:

1, 2 +, 3 | 1, +, + | 1 +, 2 +, +

1, 2, 3, 4 | 2, 3, 5, 6 | 1, 3, 4, 5, 6

Step-by-step explanation:

The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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The probability of at least one defective rivet in a seam requiring 27 rivets, assuming they are independently defective with the same probability, is approximately 68.3%.

To solve this problem, we can use the concept of probability and the binomial distribution.

The probability of a rivet being defective is denoted by "p". Since each rivet is defective independently of the others, the probability of a rivet not being defective (i.e., being good) is 1 - p.

The seam will need to be reworked if any of the 27 rivets is defective. Therefore, we want to calculate the probability that at least one rivet is defective.

The probability of at least one defective rivet can be found using the complement rule: subtracting the probability of no defective rivets from 1.

The probability of no defective rivets is given by (1 - p) raised to the power of 27 (since each rivet is independent).

So, the probability of at least one defective rivet is:

P(at least one defective rivet) = 1 - P(no defective rivets)

P(at least one defective rivet) = 1 - (1 - p)^27

Now, we can substitute any desired value for the probability of a defective rivet, "p," to calculate the probability of at least one defective rivet.

For example, if we assume a defective rivet probability of p = 0.05 (5%), the calculation would be as follows:

P(at least one defective rivet) = 1 - (1 - 0.05)^27

P(at least one defective rivet) ≈ 0.683

Therefore, with a 5% probability of a rivet being defective, the probability of at least one defective rivet in the seam is approximately 0.683 or 68.3%.

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Answer:

There are infinite solutions for this plug in any number for t, and you will always get 0

Step-by-step explanation:

Hope this helps:)

Answer: The correct answer is Yes, the relationship between x and y is a non-linear function.

I hope this helps.

Step-by-step explanation:

Given the table

Edge Length, x            Surface Area, y

1                                             6

2                                            24

3                                            54

4                                             96

The table values clearly represent a function, because each input value has one and only one output value. i.e. there is no repetition of x values.

Also from the table values and the graph, it is clear that the function is not a linear function, because the graph is not a straight line. Also, In a cubic function, the highest power over the x variable(s) is 3. So, it is not a linear function.

Hence, we conclude that Yes, the relationship between x and y is a non-linear function.

Therefore, the 'last option' is correct.

Answer:

False

Step-by-step explanation:

Even though I said that, an object that moves with a velocity has momentum but on the other way around as far the object is at rest the object will have a momentum of zero a.k.a no momentum.

Answer: 0.00462962962...

Step-by-step explanation:

The probability that the sum of the die rolls is odd is 1, which is equivalent to 100% (option a.)

To find the probability that the sum of the die rolls is odd, we need to consider the possible outcomes of the coin tosses and die rolls.

There are four possible outcomes for the coin tosses: HH, HT, TH, and TT.

For each head (H) that results, one fair die is rolled. The sum of the die rolls will be odd if there is an odd number of dice rolled.

Let's analyze each outcome:

1. HH: In this case, both coins show heads, so two dice will be rolled. The sum of the dice can only be even (2, 4, or 6). Probability = 0.

2. HT: One coin shows heads and the other shows tails. One die will be rolled. The sum of the die can be odd (1, 3, or 5) or even (2, 4, or 6). Probability of odd sum = 1/2.

3. TH: Similar to the previous case, one die will be rolled, and the sum can be odd or even. Probability of odd sum = 1/2.

4. TT: Both coins show tails, so no dice are rolled, and the sum is 0. Probability of odd sum = 0.

Now, let's calculate the overall probability of an odd sum:

Probability of HT = 1/2

Probability of TH = 1/2

Total probability of an odd sum = Probability of HT + Probability of TH = 1/2 + 1/2 = 1.

Therefore, the probability that the sum of the die rolls is odd is 1, which is equivalent to 100%.

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Complete Question:

Two fair coins are to be tossed once. for each head that results, one fair die is to be rolled. what is the probability that the sum of the die rolls is odd? (note that if no die is rolled, the sum is 0.)

\((a) $1 \\\\(b) $\frac{1}{2}$ \\\\(c) $\frac{43}{72}$ \\\\(d) $\frac{5}{8}$ \\\\(e) $\frac{2}{3}$\)

Answer: -3, -2, -1, 0, 1 and 2

Answer:

0, 1, and 2

Step-by-step explanation:

A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers. Whereas the values of -3, 100.01, 365 ¼, and 2006.3 are not.

9514 1404 393

Answer:

  a = 7

Step-by-step explanation:

The Pythagorean theorem tells you the value of 'a' is ...

  a^2 = b^2 - c^2

  a^2 = 25^2 -24^2 = 625 -576 = 49

  a = √49 = 7

The length of side 'a' is 7 units.

Answer:

The answer is K(2.5,-2)

Step-by-step explanation:

The coordinates of point K will be K( 2.5, -2 ).

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Let A (x₁, y₁) and B (x₂, y₂) be a line segment. Then the point P (x, y) divides the line segment in the ratio of m:n. Then we have

The ratio of JK and KL will be 1 : 3

x = (mx₂ + nx₁) / (m + n)

y = (my₂ + ny₁) / (m + n)

x = [ 1 x ( -2 )  + 3 x 4]  / ( 1 +  3)

x = [ 1 x ( -2 )  + 3 x 4]  / ( 1 +  3 )

x = [ -2  + 12 ]  / ( 4 ) ] = 2.5

y = (1 x 13 ) + 3 x ( -7 ) / ( 1 + 3 )

y = [ 13 - 21 ] / 4 = -2

Therefore, the coordinates of point K will be K(2.5, -2 )

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A) Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE

B)The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.

To find the speed and direction of the wind, we can use the fact that the ground speed vector (GS) is the sum of the air speed vector (AS) and the wind speed vector (WS).

Given that:

AS = 480 miles per hour at a bearing of N82°E

GS = 518 miles per hour at a bearing of 79°E

We can use the law of cosines to find the wind speed (WS) and the angle between AS and WS.

WS = √(GS² - AS² + 2AS * GS * cos(GS - AS))

WS = √(518² - 480² + 2(480)(518)cos(79 - 82)) = √(268816 - 230400 + 466560cos(-3)) = √(28672) = 168 miles per hour

Then we can use the angle between AS and WS to find the direction of the wind:

Direction of the wind = (bearing of AS + bearing of WS) / 2 = (82 + 79) / 2 = 80.5 ° NE

To find the resulting ground speed and direction of the plane if the pilot increased the air speed to 500 miles per hour, we can use the same method as before.

Given that:

AS' = 500 miles per hour at a bearing of N82°E

GS' = √(AS'² + WS² - 2AS'WS * cos(direction of WS - direction of AS'))

GS' = √(500² + 168² - 2(500)(168)cos(80.5 - 82)) = √(250000 + 28672 + 118400cos(1.5)) = √(284872) = 535.5 miles per hour

The resulting ground speed and direction of the plane would be 535.5 miles per hour at a bearing of 80.7°E.

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Answer:

Step-by-step explanation:

7a + 33° = 10a - 12° ( being vertically opposite angle )

33° - 12° = 10a - 7a

21° = 3a

a = 21/3

a = 7°

Now,

6b - 42 = 3b ( vertically opposite angle )

6b - 3b = 42°

3b = 42°

b = 42/3

b = 14

hence , the value of a is 7°and b is 14°...

☘☘☘....

So, on solving the provided question, we can that the derivative of ln(x) is = \(\frac{d(lm(x))}{dx} =\) 1/x.

The derivative of a function with real variables in mathematics gauges how sensitively the function's value will change in response to changes in its arguments. Calculus's fundamental tools are derivatives. Differentiation (in mathematics, the rate of change of a function with respect to a variable) (in mathematics, the rate of change of a function with respect to a variable). Calculus and differential equation problem-solving depend heavily on derivatives. Finding the "slope" of a specific function is the definition of "derivative" or "taking a derivative" in calculus. Because it is often the slope of a straight line, the slope should be enclose in quotations. While applying to practically every function, derivatives are measures of rate of change.

The derivative of ln(x) is

= \(\frac{d(lm(x))}{dx} =\) 1/x.

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The two solutions are m = 4 and m = -5.

We are given that;

Equation m^2+m=20

Now,

A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

To solve the equation m^2 + m = 20 by the quadratic formula, we first need to write it in the standard form ax^2 + bx + c = 0. In this case, we have a = 1, b = 1, and c = -20. Then we can plug these values into the quadratic formula:

m = (-b ± √(b^2 - 4ac))/(2a)

m = (-(1) ± √((1)^2 - 4(1)(-20)))/(2(1))

m = (-1 ± √(81))/2

m = (-1 ± 9)/2

m = (-1 + 9)/2 or m = (-1 - 9)/2

m = 4 or m = -5

Therefore, by the equation the answer will be m = 4 and m = -5.

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Answer:

(x+2)(x-3)(x+3) this is ans

Answer:

a. (x + 2)

Step-by-step explanation:

x^2(x + 2) - 9(x + 2)

(x + 2)(x^2 - 9)

(x + 2)(x - 3)(x + 3)

Therefore the answer is (x + 2)

You might need to utilise algebra to answer for the variable x in a word problem if there isn't a particular number provided for it.

Create an equation involving x using the information provided.

For instance, if the question is, "What is the value of x if x is 5 more than twice y and y is 3?" you may write up an equation like this:

x = 5 + 2y

x = 5 + 2(3) (3) (Replace y = 3)

x = 11

By changing the supplied value of y, you can answer for x in this situation by first solving the ensuing equation.

You might need to utilise many equations and algebraic techniques like substitution, elimination, or graphing to solve for x if the issue is more complicated. It could be beneficial to divide the problem into smaller steps and work through each step methodically if you are unclear of how to proceed.

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Answer:

7

Step-by-step explanation:

The new expression would be: 2(10) / 5 + 3. Using PEMDAS, first multiply 2(10) to get 20. Now you get: 20 / 5 + 3. Using PEMDAS, now divide 20 / 5 to get 4. The new expression is 4 + 3. Now, add to get 7 as your answer.

Hope it helps!

Michael’s child is going to college in 13 years. If he saves $ 7,000 a year at 9% compounded annually. Therefore,  the amount available for Peter's child education will be $147,330.55.

Given that Michael is saving $7,000 per year for his child's education which will occur in 13 years. If the interest rate is 9% compounded annually,

The problem of finding the amount of money Michael will have saved in 13 years is a compound interest problem.

In this case, the formula for calculating the future value of the annuity is: $FV = A[(1 + r)n - 1] / r

where: FV is the future value of the annuity, A is the annual payment,r is the annual interest rate, and n is the number of payments.

Using the above formula; the future value of Michael's savings is:

FV = 7000[(1 + 0.09)^13 - 1] / 0.09= 7000(1.09^13 - 1) / 0.09= 147,330.55

Therefore, the amount available for Peter's child education will be $147,330.55.

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Answer:

A. 2.43 kg x 1000 g/1 kg

Step-by-step explanation:

i dont really know how to explain it

but yea its A

Answer:

Same as the other person, cant explain much, im a horrible explainer, even if i did explain it would be false

Step-by-step explanation:

Its A

Answer:

(a) a = 22 or 2

(b) The equations of AD are

y = x/2 + 7

or

y = x/2 + 17

(c) The equation of CD is y = -2·x - 3

(d) The coordinate of the point D is either (-8, 13) or (-4, 5)

(e) the possible areas are;

250 square units or 270 square units

Step-by-step explanation:

With only the details of the trapezium, without the drawing, we have as follows;

(a) The given points are;

A(a, 18), B(12, -2), and C(2, -7)

The length of BC is given from the formula for finding the length, l, of a line with the coordinates of the end points as follows;

\(l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}\)

\(l_{BC} = \sqrt{\left ((-7)-(-2) \right )^{2}+\left ((2)-(12) \right )^{2}} = \sqrt{\left ((-5) \right )^{2}+\left (-(10) \right )^{2}} = 5\cdot \sqrt{5}\)

∴ From \(l_{AB} = l_{BC}\), we have;

\(l_{AB}\) = 2 × 5·√5 = 10·√5

Which gives;

\(l_{AB} = \sqrt{\left ((18)-(-2) \right )^{2}+\left (a-12 \right )^{2}} = \sqrt{\left 20 \right ^{2}+\left (a-12 \right )^{2}}= 10 \cdot \sqrt{5}\)

20² + (a - 12)² = 500

(a - 12)² = 500 - 20² = 500 - 400 = 100

(a - 12)² = 100

a - 12 = ±√100 = ±10

a = 10 + 12 or -10 + 12

a = 22 or 2

(b) The equation of BC is given as follows;

The slope, m, of BC = (-7 -(-2)/(2 - 12) = -5/-10 = 1/2

The equation of BC is therefore;

y - (-7) = 1/2×(x - 2)

y + 7 = x/2 - 1

y = x/2 - 1 - 7 = x/2 - 8

y = x/2 - 8

Therefore, the slope of AD = m = 1/2

The equation of AD can be

y - 18 = 1/2×(x - 22)

y = x/2 -11 + 18 = x/2 + 7

y = x/2 + 7

or

y - 18 = 1/2×(x - 2)

y = x/2 -1+ 18 = x/2 + 17

y = x/2 + 17

(c) The equation of CD is given as follows;

CD is perpendicular to BC, therefore, the slope of CD = -1/m = -2

The equation of CD is therefore;

y - (-7) = -2×(x - 2)

y = -2·x + 4 - 7 = -2·x - 3

y = -2·x - 3

(d) The coordinate of the point D is found as follows;

At point D,

At

x/2 + 17=-2·x - 3

2.5·x = -20

x = -8

y = -8/2 + 17 = 13

or

x/2 + 7 =-2·x - 3

2.5·x = -10

x = -4

y = -4/2 + 7 = 5

The possible coordinates of the point D are (-8, 13) or (-4, 5)

(e) The area of the trapezium is found as follows;

The vertices points are;

(2, 18) or (22, 18), (12, -2), (2, -7) and (-8, 13) or (-4, 5)

The formula for the area of a trapezium = (a + b)/2×h

Length of a = \(l_{BC}\) =  5·√5

h = \(l_{CD} = \sqrt{\left ((13)-(-7) \right )^{2}+\left ((-8)-2 \right )^{2}} = \sqrt{\left 20 \right ^{2}+10^{2}}= 10 \cdot \sqrt{5}\)

or

\(l_{CD} = \sqrt{\left ((5)-(-7) \right )^{2}+\left ((-4)-2 \right )^{2}} = \sqrt{\left 12 \right ^{2}+6^{2}}= 6 \cdot \sqrt{5}\)

b = \(l_{AD} = \sqrt{\left (13-18 \right )^{2}+\left ((-8)-2 \right )^{2}} = \sqrt{\left (-5 \right )^{2}+(-10)^{2}}= 5 \cdot \sqrt{5}\)

\(l_{AD} = \sqrt{\left (5-18 \right )^{2}+\left ((-4)-22 \right )^{2}} = \sqrt{\left (-13 \right )^{2}+(-26)^{2}}= 13 \cdot \sqrt{5}\)

Therefore, the possible areas are;

(5×√5 + 5×√5)/2 × 10×√5 = 250 square units

(5×√5 + 13×√5)/2 × 6×√5 = 270 square units

The value of 'a' is 22 or 2, the equation of AD is (y = 0.5x + 17) or (y = 0.5x + 7) and the point D is (-8,13) or (-4,5) and this can be determine by using the point slope form.

Given :

a) To determine the value of 'a' use the relation (AB = 2 BC).

\(\sqrt{(12-a)^2+(-2-18)^2}=2\times \sqrt{(2-12)^2+ (-7+2)^2}\)

\(\sqrt{(12-a)^2+400}=2\times \sqrt{125}\)

Squaring both sides in the above expression.

\((12-a)^2+400=4\times 125\)

\(144+a^2-24a=100\)

\(a^2-24a+44=0\)

\(a^2-22a-2a+44=0\)

\(a(a-22)-2(a-22) = 0\)

a = 2 or 22

b) The equation of BC is given by:

\(\dfrac{y+2}{x-12}=\dfrac{-7+2}{2-12}\)

\(2(y+2)=(x-12)\)

2y + 4 = x - 12

2y - x + 16 = 0

y = 0.5x - 8

Given that AD is parallel to BC so, the slope of 0.5.

First, take a = 2. The equation of line AD is given by:

\(y-18 =0.5(x-2)\)

Now, take a = 22. The equation of line AD is given by:

\(y-18 =0.5(x-22)\)

c) The line CD is perpendicular to line BC. So, the slope of line CD is -2. The equation of the line CD is given by:

y - (-7) = -2(x - 2)

y + 7 = -2x + 4

y + 2x + 3 = 0

d) The point D is given by:

0.5x + 17 = -2x - 3

2.5x = -20

x = -8

y = -4 + 17 = 13

or

0.5x + 7 = -2x - 3

x = -4

Now, y = - 2 + 7 = 5

e) Area of the trapezium is given by:

\(\rm A = L_{CD} \times L_{AD}\)

So, the possible area of the trapezium is:

\(\dfrac{(5\times \sqrt{5} +5\times \sqrt{5} )}{2}\times 10 \times \sqrt{5} = 250\)

\(\dfrac{(5\times \sqrt{5} +13\times \sqrt{5} )}{2}\times 6 \times \sqrt{5} = 270\)

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Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

To write the decimal places for all the parts: 1) 50.628, 2) 0.8088, 3) 10.2406, 4) 5.0439, 5) 0.6824.

A decimal point separates a number's fractional component from its whole value in a number type called a decimal. The decimal point is a . that appears between the elements of a whole number and a fraction. There are two parts to a decimal number: the whole and the fraction.

To represent whole and partially whole quantities between integers numerically, decimal numbers are used. Geographic coordinates are expressed as decimal fractions of a degree and are denoted by the notation decimal degrees (DD). OpenStreetMap, many geographic information systems (GIS), and GPS devices frequently include DD.

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Note that the full question is:

Write the decimal numbers inside the box. Assumethat all other place values not mentioned are zeroes.

1) 5 in the tens place

6 in the tenths place

2 in the hundredths place

8 in the ten thousandths place

2) 8 in the ten thousandths place

8 in the thousandths place

8 in the tenths place

3) 4 in the hundredths place

1 in the tens place

2 in the tenths place

6 in the ten thousandths ou poses only

ndths place

4) 3 in the thousandths place

4 in the hundredths place

5 in the ones place

9 in the ten thousandths place

5) 8 in the hundredths place

6 in the tenths place

4 in the ten thousandths place

2 in the thousandths place

Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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Answer:

7 Hours

Step-by-step explanation:

Because it takes Ryan 10hrs to finish the job, and with both Ryan and Molly it takes 3hrs to finish the job, so subtract 10 minus 3 and you get 7, therefore it takes Molly 7hrs to finish the job

Hope it's right

The equation of the tangent line to the curve y = sin(sin x) at the point (4π, 0) is y = -1.

To find the equation of the tangent line, we need to determine the slope of the tangent at the given point. We can start by finding the derivative of the function y = sin(sin x) using the chain rule. The derivative of sin(sin x) with respect to x is cos(sin x) × cos x.

Evaluating the derivative at x = 4π, we have cos(sin(4π)) * cos(4π). Since cos(4π) is equal to 1 and cos(sin(4π)) is also equal to 1, the derivative evaluates to 1 × 1 = 1.

Thus, the slope of the tangent line at x = 4π is 1. Using the point-slope form of a line, we can write the equation of the tangent line as y - y1 = m(x - x1), where m represents the slope and (x1, y1) represents the given point (4π, 0). Plugging in the values, we get y - 0 = 1(x - 4π), which simplifies to y = x - 4π.

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Answer:

To solve this problem, we need to find the least common multiple between 12 and 18.

This is written as:

LCM(12, 18)

And to find this, you can calculate:

LCM(12, 18) = 12*18/GCF(12,18)

Where GCF is the greatest common factor.

To find the greatest common factor let's factorize 12 and 18 in prime numbers:

12 = 2*2*3

18 = 2*3*3

now we can write them as:

12 = 2*(2*3) = 2*6

18 = (2*3)*3 = 6*3

Then the greatest common factor between 12 and 18 is 6.

Now the LCM will be:

12*18/6 = 2*18 = 36.

Then he must make 36 muffins of each type.

This means that he needs to do:

36/12 = 3 batches of blueberry muffins

36/18 = 2 batches of bran muffins.