what is the name of the property given below? if a • b = 0, then a = 0, b = 0, or both a = 0 and b = 0.

Answer:

Jada should have multiplied both sides of the equation by 108.

Step-by-step explanation:

The question is incomplete. Find the complete question in the comment section.

Given the equation -4/9 = x/108, in order to determine Jada's error, we need to solve in our own way as shown:

Step 1: Multiply both sides of the equation by -9/4 as shown:

-4/9 × -9/4 = x/108 × -9/4

-36/-36 = -9x/432

1 = -9x/432

1 = -x/48

Cross multiplying

48 = -x

x = -48

It can also be solved like this:

Given -4/9 = x/108

Multiply both sides by 108 to have:

-4/9 * 108 = x/108 * 108

-4/9 * 108 = 108x/108

-432/9 = x

x = -48

Jada should have simply follow the second calculation by multiplying both sides of the equation by 108 as shown.

Answer: A

Step-by-step explanation: Took the test

By strong mathematical induction, we have proven that for all integers n > 2, either n is prime or n is a product of prime numbers.

To prove that for all integers n > 2, either n is prime or n is a product of prime numbers using strong mathematical induction, we will first establish the base case.

Base case: When n = 3, 3 is a prime number.

Inductive hypothesis: Assume that for all integers k such that 2 < k ≤ n, either k is prime or k is a product of prime numbers.

Inductive step: We need to show that n + 1 is either prime or a product of prime numbers. We can do this by considering two cases:

Case 1: n + 1 is prime. In this case, we are done.

Case 2: n + 1 is composite. This means that n + 1 can be expressed as products of two integers a and b, where 2 ≤ a ≤ b < n + 1. By the inductive hypothesis, we know that a and b are either prime or a product of prime numbers.

If a and b are both prime, then n + 1 is a product of prime numbers.

If a and b are not both prime, then we can apply the inductive hypothesis again to a and b. This means that a and b can each be expressed as a product of prime numbers. Therefore, n + 1 can also be expressed as a product of prime numbers.

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happy with solution rate this

Step-by-step explanation:

A) distribute: 12x +16 = 0; 12x/12 = -16/12

x = -4/3

B) distribute: 420x +180 = 0; 420x/420 = -180/420

x = -3/7

Hope this helps! :)

The equation of the  circle , with diameter  DEis (x - 5)² + (y - 7)² = 80

An equation is an expression that appears as the relationship between two or more variables and numbers. since the  standard equation  for a circle  is (x - h)² + (y - k)² = r², where    (h, k)  is the center of the circle and r is the radius. It is given that the diameter of the circle is at D(-3, 3) and E(13, 11). So the coordinate of the center is:

h = (13 + (-3))/2 = 5

k = (3 + 11)/2 = 7

(h, k) = (5, 7) and the  Radius is diameter / 2 = 8√5 ÷ 2 = 4√5.

the equation will be : (x - 5)² + (y - 7)² = (4√5)² => (x - 5)² + (y - 7)² = 80

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Answer:

(x - 5)² + (y - 7)² = 80

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf x = 16}\)

Step-by-step explanation:

Using Pythagoras Theorem since it is a right angled triangle.

Where,

Base = 12

Perpendicular = x

Hypotenuse = 20

\((Hypotenuse)^2=(Base)^2+(Perpendicular)^2\)

\((20)^2=(12)^2+x^2\\\\400 = 144 + x^2\\\\Subtract \ 144 \ to \ both \ sides\\\\400-144=x^2\\\\256 =x^2\\\\Take\ Sq. \ root\ on \ both \ sides\\\\\sqrt{256} =x^2\\\\16 = x\\\\x = 16\\\\\rule[225]{225}{2}\)

Based on percentage composition, the mass of recycled paper in Ophelia’s paper napkins is 203 g.

A percentage gives an amount of a given quantity out of a whole value expressed in 100 units.

The total mass of the napkins = 580 g

b recycled paper in napkin = 35% of 580 g

Then;

The mass of recycled paper = 35/100 * 580 g

mass of recycled paper = 203 g

Therefore, the mass of recycled paper in Ophelia’s paper napkins is 203 g.

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The optimal solution is x1 = 2, and the maximum value of the objective function is 3.

To apply the simplex method to the given maximization problem, we first need to convert the problem into standard form by introducing slack variables.

The given problem is:

Maximize: 3x1

Subject to:

-2x1 + x2 + x3 + s1 = 1

2x1 - 3x2 + x4 = 4

x1, x2, x3, x4, s1 ≥ 0

We introduce slack variables s2 and s3 to convert the inequalities into equations:

Maximize: 3x1

Subject to:

-2x1 + x2 + x3 + s1 = 1

2x1 - 3x2 + x4 + s2 = 4

x1, x2, x3, x4, s1, s2 ≥ 0

We create the initial tableau based on the augmented matrix of the system:

   | -2  1  1  0  1  0 |

   |  2 -3  0  1  0  4 |

T = |  3  0  0  0  0  0 |

   |________________|

Next, we need to find the pivot column. We select the column with the most negative coefficient in the objective row, which is column 2.

Dividing the right-hand column by the pivot column, we find that the minimum ratio occurs in row 2 (s2).

We perform the pivot operation by selecting the element in row 2, column 2 as the pivot (which is -3).

The new tableau after the pivot operation is:

   |  0.67  0.33  1  0 -0.33  1.33 |

   |  0.67 -1.00  0  0  0.33  1.33 |

T = |  3.00  0.00  0  0  0.00  0.00 |

   |_____________________________|

The pivot column for the next iteration is column 1 since it has the most negative coefficient in the objective row.

Dividing the right-hand column by the pivot column, we find that the minimum ratio occurs in row 1 (x1).

We perform the pivot operation by selecting the element in row 1, column 1 as the pivot (which is 0.67).

The new tableau after the pivot operation is:

   |  1  0.5   1.5  0 -0.5   2 |

   |  0 -1.5 -0.5  0  0.5   1 |

T = |  0  1.5  -1.5  0  1.5  -3 |

   |________________________|

Since all coefficients in the objective row are non-negative, the current solution is optimal. The maximum value of the objective function is 3, and the optimal values for the variables are:

x1 = 2

x2 = 0

x3 = 0

x4 = 0

s1 = 0

s2 = 1

Therefore, the optimal solution is x1 = 2, and the maximum value of the objective function is 3.

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Answer: 1. You have to multiply 9.75x1.2= 11.7

2.You have to multiply 24.5x0.8= 20.4

3. Add the to products 11.7+20.4= 32.1

4. Answer is- 31.3 minutes

Step-by-step explanation: Hopefully this helped a lot ;D

The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This theorem is important as it provides a way to prove the existence of solutions to polynomial equations and provides an analytical tool to find the exact location of the solutions.

This theorem is also known as the algebraic version of the Intermediate Value Theorem as it states that if a polynomial is continuous on a closed interval, then it must take on all values between its maximum and minimum.

The theorem can be easily proven by considering a single-variable polynomial of degree n and transforming it into a polynomial of degree n−1 with the same roots. By repeating this process, the polynomial can be reduced to a constant and hence, it must have at least one root.

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The family ate a total of 85/22 units of pizza, or approximately 3.864 units of pizza.

To create a line plot to represent the amount of pizza each family member wants to eat, we can use a number line to mark off the fractional amounts of pizza, with each family member represented by a dot at their respective position on the number line. Here is the line plot:

  |    

8/8|       O

  |

7/8|             O

  |  

6/8|       O

  |  

5/8|                       O

  |  

4/8|     O         O

  |  

3/8|    

  |  

2/8|       O

  |  

1/8|  O  

  |  

 0|_____________________________

To find out how much pizza the family ate in all, we can add up the fractional amounts for each family member:

Kamirah: 4/8

Mother: 5/8

Father: 4/11

Older brother: 7/8

Older sister: 4/8

Younger brother: 1/8

Uncle: 7/8

Total: 4/8 + 5/8 + 4/11 + 7/8 + 4/8 + 1/8 + 7/8

To add these fractions, we need to find a common denominator. The smallest common multiple of 8 and 11 is 88, so we can rewrite the fractions with a denominator of 88:

Total: 44/88 + 55/88 + 32/88 + 77/88 + 44/88 + 11/88 + 77/88

     = (44 + 55 + 32 + 77 + 44 + 11 + 77)/88

     = 340/88

We can simplify this fraction by dividing both numerator and denominator by their greatest common factor, which is 4:

Total: 85/22

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The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

What is Confidence interval?

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

As given,

n = 150 = drivers

x = 100 = wear seat belts.

We have to find 95% confidence interval for proportion P that do not wear seat belt.

From 150 we have 100 wear seat belts

Not wear seat belt = 150 - 100

Not wear seat belt = 50

P = 50/150

P = 0.33

95% confidence interval for P is

CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))

For 95% CI, zα/2 = 1.96

Substitute values,

CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))

CI = (0.33 - 0.075, 0.33 + 0.075)

CI = (0.255, 0.405)

Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

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The surface area of the rectangular prism is 174 in²

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism.

Given is a net for a rectangular prism, we need to find the surface area of the rectangular prism,

We know that,

The surface area of the rectangular prism = 2(lxb+bxh+hxl)

Length = l, height = h and b = breadth

Therefore, here we have, l = 9 in, b = 3 in and h = 5 in

Surface area = 2(9x3+3x5+5x9)

= 2(27+15+45)

= 2x87

= 174 in²

Hence, the surface area of the rectangular prism is 174 in²

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Answer:

135

Step-by-step explanation:

Because 54 is greater than 40, we automatically know that the resulting percentage has to be more than 100, which helps us proofread our math and eliminate wrong answers. To calculate percentages, I like to use the "out of" phrase. In this case, 54 out of 40. All you do is replace the out of with the divide sign, and the resulting answer is going to be 1.35. 1.35 is going to be 1, and 35/100ths as a fraction. With percentages, 100/100 is a whole, as in all the percentages add up to 1, which is 100/100. 1.35 is just adding 35/100ths to that 1, so you get 135%, but you cant use the percentage sign for your answer, thus you are left with 135. Hope this helps and brainliest is always appreciated!

Answer:

The value of ? is 1004.

Step-by-step explanation:

I'll use x instead of ?:

\(9^x+9^x+9^x=3^{2009}\\3\cdot9^x=3^{2009}\\3\cdot(3^2)^x=3^{2009}\\3\cdot3^{2x}=3^{2009}\\3^{2x+1}=3^{2009}\\2x+1=2009\\2x=2008\\x=1004\)

Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Volume of the sphere is  1437.3 cube cm.

In the given picture of Sphere, we have

Radius of the Sphere is 7 cm

To find the Volume of the Sphere

Now, According to the question;

We know that

Volume (V) of the Sphere is  = \(\frac{4}{3}\)π\(r^3\)

Plug the value of radius in above formula

V = \(\frac{4}{3}\) × \(\frac{22}{7}\) × 7 × 7 × 7

V = 4/3 × 22 × 7 × 7

V = 4,312 / 3

V =  1437.3 cube cm.

Hence, Volume of the sphere is  1437.3 cube cm.

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Answer:

123 PER PERSON

Step-by-step explanation:

All you have to do is divide 2,460 by 20 to get 123

J in 55min

J in 45min ( bigger hose)

Alternative method

The trick is to convert the numbers you are given to numbers that you can add together.

You have minutes per pool. You can’t work with that. But if you take the reciprocal of each you get pools per minute.

So if the first hose fills 1/55 = 0.01818 pools per minute and the second one fills 1/45 = 0.0222 pools per minute, then both of them will fill 0.1818 + 0.0222 = 0.04040 pools per minute. If we take the reciprocal of that we end up with 1/0.04040 = 24.75 minutes per pool.

The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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Answer:

x = 30°

Step-by-step explanation:

Use the sine rule:

Answer:

3x + 88

Step-by-step explanation:

Add the numbers

3 + 28 + 60

3 + 88

Solution:

3x + 88

have a good day

We can infer that the set of vectors represented by (-1, 2), (8, 4) is orthogonal in Rⁿ since their dot product is equal to zero.

We must determine whether the dot product of any two vectors in the set is equal to zero in order to demonstrate the orthogonality of the set of vectors in Rⁿ.

Let's determine the dot product of the vectors provided:

(-1, 2) ⋅ (8, 4) = (-1)(8) + (2)(4)

(-1, 2) ⋅ (8, 4) = -8 + 8

(-1, 2) ⋅ (8, 4) = 0

We can infer that the set of vectors (-1, 2), (8, 4) is orthogonal in Rⁿ because the dot product of (-1, 2) and (8, 4) equals zero.

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Answer:

2.8

Step-by-step explanation:

You can simplify √7894/1000 to √19735/50

The current exchange rate for 1 Iraqi Dinar to USD dollar can be found on financial websites or by contacting a bank.

It's important to note that the exchange rate fluctuates constantly and can be affected by various economic and political factors.

To get the most accurate and up-to-date exchange rate, it is best to check multiple sources. Additionally, you can also contact your bank or a currency exchange service provider for the current exchange rate.

It's worth mentioning that the Iraqi Dinar is considered a highly volatile currency, it's value has been fluctuating over the years due to the instability of the country and the political and economic conditions.

It's also important to consider any additional fees or charges that may be applied when converting currency, such as bank charges or commission fees.

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Answer:

x = 20

Step-by-step explanation:

The sum of the angles in a triangle is 180. A right triangle has one angle of 90. Thus, the sum of the other two angles will be 90. So, 90+31 = 121 and 180-121 = 59. (3x-1) = 59. Solve for x. This would mean that x would be 20. 3*20 = 60 and 60-1 = 59. All the angles add together would get 180: 59+90+31.

1. For the function f(x) = 5x - 6x² + 4x - 2, we found the derivative f'(x) to be -12x + 9 and after evaluating we found f'(2) = -15.

2. For the function f(x) = x^0e, we found the derivative f'(x) to be e * ln(x)   and after evaluating we found f'(1) = 0.

3. Limit of the expression (x^3 + x^2 + 8x + 15) / (x^2 + 8x + 15) is 1.

1. To find f'(x) for the function f(x) = 5x - 6x² + 4x - 2, we can differentiate each term using the power rule and the constant rule.

Using the power rule, the derivative of x^n (where n is a constant) is nx^(n-1). The derivative of a constant is 0.

f'(x) = (5)(1)x^(1-1) + (6)(-2)x^(2-1) + (4)(1)x^(1-1) + 0

      = 5x^0 - 12x^1 + 4x^0

      = 5 - 12x + 4

      = -12x + 9

To find f'(2), we substitute x = 2 into the derivative expression:

f'(2) = -12(2) + 9

     = -24 + 9

     = -15

Therefore, f'(x) = -12x + 9, and f'(2) = -15.

2. To find f'(x) for the function f(x) = x^0e, we can apply the constant rule and the derivative of the exponential function e^x.

Using the constant rule, the derivative of a constant times a function is equal to the constant times the derivative of the function. The derivative of the exponential function e^x is e^x.

f'(x) = 0(e^x)

     = 0

To find f'(1), we substitute x = 1 into the derivative expression:

f'(1) = 0

Therefore, f'(x) = 0, and f'(1) = 0.

3. To find the limit of (x^2 - x - 12)/(x^3 + 8x + 15) as x approaches infinity without using L'Hopital's Rule, we can simplify the expression and analyze the behavior as x becomes large.

(x^2 - x - 12)/(x^3 + 8x + 15)

By factoring the numerator and denominator, we have:

((x - 4)(x + 3))/((x + 3)(x^2 - 3x + 5))

Canceling out the common factor (x + 3), we are left with:

(x - 4)/(x^2 - 3x + 5)

As x approaches infinity, the highest degree term dominates the expression. In this case, the term x^2 dominates the numerator and denominator.

The limit of x^2 as x approaches infinity is infinity:

lim (x^2 - x - 12)/(x^3 + 8x + 15) = infinity

Therefore, the limit of the given expression as x approaches infinity is infinity.

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Answer:i dunno

Step-by-step explanation:e

Answer:

Step-by-step explanation:

Where are the answer choices?

Still, it's possible to help you without your having shared those choices.

The "difference quotient" is defined as:

 f(x + h) - f(x)

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

           h

where h represents an incremental (small) change in x.

Here f(x) = 3 - log x, and so f(x + h) = 3 - log (x + h).

Therefore the difference quotient is:

{3 - log (x + h)} - {3 - log x}

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

                    h

This can be simplified.  In the numerator we have 3 - 3, so the numerator simplifies to -log (x + h) + log x

and the difference quotient is

-log ( x + h) + log x

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

              h

This can be rewritten as

log x - log (x + h)                                x                                  x

--------------------------- , or (1/h)*log ------------ , or  (1/h) log { ----------- }

              h                                       (x + h)                            x + h          

Answer:

B

Step-by-step explanation:

I guessed and got it right.