Let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = 2ab + 5
show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:










show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution:












a. let ⋆ be the binary operation on z (set of integers) defined by
a ⋆ b = a + b + ab
1. show that ⋆ is commutative. hint: show that a ⋆ b = b ⋆ a
solution:

2.show that ⋆ is associative. hint: show that (a ⋆ b) ⋆ c = a ⋆ (b ⋆ c)
solution: ​

Answer:

50.27 cm

Step-by-step explanation:

We Know

The area of the circle = r² · π

Area of circle = 64π cm²

r² · π = 64π

r² = 64

r = 8 cm

Circumference of circle = 2 · r · π

We Take

2 · 8 · (3.1415926) ≈ 50.27 cm

So, the circumference of the circle is 50.27 cm.

Answer: C=16π cm or 50.24 cm

Step-by-step explanation:

The formula for area and circumference are similar with slight differences.

\(C=2\pi r\)

\(A=\pi r^2\)

Notice that circumference and area both have \(\pi\) and radius.

\(64\pi=\pi r^2\)        [divide both sides by \(\pi\)]

\(64=r^2\)             [square root both sides]

\(r=8\)

Now that we have radius, we can plug that into the circumference formula to find the circumference.

\(C=2\pi r\)          [plug in radius]

\(C=2\pi 8\)          [combine like terms]

\(C=16\pi\)

The circumference Is C=16π cm. We can round π to 3.14.

The other way to write the answer is 50.24 cm.

Volume= 4/3πr^3

r = 18m

Volume = 4/3*3.14*18^3

Volume = 4/3*3.14*5832

Volume= 24416.639999 m^3

Answer:

-1.3333333333333

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The amount she withdrew is 45*4 =180

405 - 4*45=

405 -180 =225

There is 225 in the account

Answer: a) $225

Step-by-step explanation:

405 - 45 (4) = x

405 - 180 = x

225 = x

Answer:

b = 5/4  ( or  = 1.25)

Step-by-step explanation:

2b + (1/2) =3    (subtract 1/2 from each side

2b = 3 - (1/2)

2b = 2 1/2   (express 2 1/2 as an improper fraction = 5/2)

2b = 5/2     (divide both sdes by 2)

b = (5/2) / 2

b = 5/4

Answer:

look at the screenshot

Step-by-step explanation:

Answer:

c=2 k=11 n=14

Step-by-step explanation:

9514 1404 393

Answer:

  -19.2

Step-by-step explanation:

Fill in the given values and do the arithmetic.

  \(\displaystyle x\ \blacksquare\ y=\frac{x}{y}-xy\\\\4\ \blacksquare\ 5=\frac{4}{5}-4\cdot5=0.8-20\\\\\boxed{4\ \blacksquare\ 5=-19.2}\)

Answer:

1/2

Step-by-step explanation:

The red markings is not clear but I think the larger one is triangle DEF, if not, then the answer is 2

Answer:

1/2

Step-by-step explanation:

The dude above said if the big triangle is not DEF then it's two, but the big triangle is DEF therefore it is: 1/2.

Managers, goods, services, and technology are all needed in developing countries, and therefore, they provide new markets for companies that can supply these essentials.

Developing countries often have growing economies and increasing consumer demands. As these countries strive for development and improvement, they require effective management to drive their businesses and organizations. Managers play a crucial role in overseeing operations, implementing strategies, and maximizing efficiency.

Additionally, developing countries require goods and services to meet the needs of their populations. This includes basic necessities such as food, clothing, and shelter, as well as other essential products and services like healthcare, education, infrastructure development, and transportation. Companies that can provide these goods and services have an opportunity to enter new markets and cater to the demands of the growing population.

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Answer:

SAS Postulate (third option)

Step-by-step explanation:

A trick that I use is that s stands for side and a for angle

the picture shows that two sides are the same which means the SS

and one angle is the same, hence the one A

Hope this helps!

Microliters (µL) and liters (L) are both units of volume measurement. A microliter is a very small unit of volume, equivalent to one millionth of a liter. To convert microliters to liters, we can use a simple conversion factor.

The conversion factor is based on the fact that one liter is equivalent to one million microliters. Therefore, to convert microliters to liters, we divide the number of microliters by one million. This can be expressed as:

L = µL / 1,000,000

For example, if we have a volume of 500 µL that we want to convert to liters, we can use the formula above as follows:

L = 500 µL / 1,000,000

L = 0.0005 L

Therefore, 500 µL is equivalent to 0.0005 liters.

It is important to keep track of the units when making conversions and to use appropriate significant figures. Additionally, it is worth noting that microliters are often used in situations where very small volumes are involved, such as in medical or laboratory settings, whereas liters are used for larger volumes such as in the context of cooking or liquid measurements.

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Gina must divide a fraction by a whole number.

The amount of nuts in each bag will be less than 7/8 because 7/8 is divided by 4.

Gina will be able to put 7/32 pounds of nuts in each bag.

Unit cost = total price / total amount.

A) 2.99 / 200 = $0.01495 per ml

B) 3.80 / 450 = $0.00844 per g

Round the answers as needed.

Mrs. Adams will have earned $3,900 in interest at the end of 8 years with an annual simple interest rate of 3.25% on her $12,000 deposit.

To calculate the interest earned by Mrs. Adams, we need to use the formula for simple interest: Interest = Principal × Rate × Time.

In this case, the principal (amount deposited) is $12,000, the rate is 3.25% (or 0.0325 as a decimal), and the time is 8 years.

Plugging these values into the formula, we get: Interest = $12,000 × 0.0325 × 8 = $3,900.

Therefore, Mrs. Adams will have earned $3,900 in interest at the end of 8 years. Simple interest is calculated based on the initial principal amount and does not take into account any compounding or additional deposits or withdrawals. It is a straightforward calculation where the interest earned remains the same each year.

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Answer:

7

Step-by-step explanation:

Given expression:

The constant is a term that has no variables. Let's verify the terms in the expression to determine which term is the constant.

Determining if 6x³y is a constant:

Determining if 8x² is a constant:

Determining if 5x is a constant:

Determining if 7 is a constant:

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Answer:

7

Step-by-step explanation:

The constant term in an expression is the term without a variable.

The variables in this expression are x and y, so the constant term is 7 as this term does not have a variable.

The range of the possible values of x is:

x  >  4

For the given triangle:

AB = 4x + 25

BC = 3x - 2

AC = 9x - 5

The sum of two of the sides of the triangle should be greater than the length of the third side

That is:

AC  +  BC   >  AB

9x - 5  +  3x  -  2  >  4x + 25

12x - 7  >  4x  +  25

Collect like terms

12x  -  4x  >  25  +  7

8x  >  32

x   >  32/8

x  >  4

Therefore, the range of the possible values of x is:

x  >  4

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The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

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Multiplying the width by a factor of k will result in a new width of 16k inches and a new length of 20 inches. This will affect the perimeter and the area of the figure as follows:

Perimeter:
The original perimeter of the figure is P = 2(16 + 20) = 72 inches. When we multiply the width by k, the new perimeter becomes P' = 2(16k + 20) = 32k + 40 inches. Therefore, the perimeter decreases by 72 - (32k + 40) = 32(2.25 - k) inches. This means that if k is greater than 2.25, the new perimeter will be smaller than the original perimeter.

Area:
The original area of the figure is A = 16 x 20 = 320 square inches. When we multiply the width by k, the new area becomes A' = (16k)(20) = 320k square inches. Therefore, the area decreases by a factor of 320k/320 = k. This means that if k is less than 1, the new area will be smaller than the original area.

In summary, multiplying the width by a factor of k will decrease the perimeter by 32(2.25 - k) inches and the area by a factor of k.

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Answer:

The answer is option 2 6y(4y+1)

Step-by-step explanation:

if you use the FOIL system you would multiply 6y by 4y to get 24y^2

then multiply 6y and 1 to get 6y

then put your two answers together to get 24y^2+6y

The relation R  is reflexive and transitive, but not symmetric.

a. Define a relation R on Z as xRy of and only If Xy >.

IS R reflexive?

Let us start by considering if R is reflexive.

A relation R on a set A is said to be reflexive if and only if every element in A is related to itself.

In other words, every element in A is an R-related to itself.

Let us assume an element x from Z such that xRy. Since xRy implies that x*y > x, then it implies that x*x>x.

This means that xRy is true.

Thus, R is reflexive.

IS R symmetric?

Next, let's consider if R is symmetric.

A relation R on a set A is said to be symmetric if and only if for every element a and b in A, if aRb then bRa.

If x and y are in Z and xRy, then xy > x.

Dividing by x, we have y > 1.

This means that if xRy, then yRx is false.

Thus, R is not symmetric.

IS R transitive?

Let's now consider if R is transitive.

A relation R on a set A is said to be transitive if and only if for every a, b, c in A, if aRb and bRc then aRc.

Let us assume that x, y, and z are elements in Z such that xRy and yRz.

We then have x*y > x and y*z > y.

Multiplying these inequalities, we get x*y*z > x*y. Since y > 0,

we can divide both sides by y to get x*z > x.

Thus, xRz is true.

Hence R is transitive.

R is reflexive and symmetric, but not transitive.

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Answer:10X^2 +7

Step-by-step explanation:

It's 38*23 =874 dollars

Answer: 1 7/16

Step-by-step explanation: If you look at a ruler 1 7/8 is just a little behind 1 7/16 while 1 3/4 is far behind. Also 2 1/8 is past where the green line stops.

Answer:

option 1) 1 7/8"

Step-by-step explanation:

its clearly visible that the green line covers 1 unit completely.

but it stops before it can reach 2 units.

check the attachment

it will be at a distance of 1/ 2 units from the "unit 1".

( since 1 and 2 are 1 unit apart their mid point will lie exactly at rhe center that is 1/ 2 = 0.5)

since the "mid point" is at a distance of 0.5 units from "unit 2", second mid point will be at a distance of (1/ 2)/ 2 = 1/ 4 units from "mid point".

since they're 1/ 4 units apart the third mid point will be (1/ 4)/2 units away from "second mid point"

and this is where the green line stops!

we got these points now well just add them up, to get the distance of required point from unit 1.

1/ 2 + 1/ 4 + 1/ 8

= 7/ 8

and this is in centimeters so add a " after it

1 7/ 8"

that is option 1.

To determine the assignment of employees to jobs that minimizes the total time required to perform the four jobs, we need to consider the time taken by each person to complete each job. Using the given Table 50, we can analyze the data and identify the optimal assignment.

By examining Table 50, we can identify the minimum time taken by each person for each job. Starting with Job 1, we see that Person 4 takes the least time of 16 hours. Moving to Job 2, Person 2 takes the least time of 18 hours. For Job 3, Person 1 takes the least time of 25 hours. Lastly, for Job 4, Person 4 takes the least time of 14 hours.

Therefore, the optimal assignment would be:

- Person 4 for Job 1 (16 hours)

- Person 2 for Job 2 (18 hours)

- Person 1 for Job 3 (25 hours)

- Person 4 for Job 4 (14 hours)

This assignment ensures that the minimum total time is required to perform the four jobs, resulting in a total time of 16 + 18 + 25 + 14 = 73 hours.

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Answer:125.666

Step-by-step explanation:

Answer:

a:

$m×5

b:

$2m×2

Explanation:

a:

If one muffin=$m

then 5 muffins=$m×(number of muffins)

b:

If three cupcakes=$2m

then 6 cupcakes=$2m×(number of cupcakes)

since 3=3×2

We can write the algebraic expression in [m] as -

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Given is that the cost of one muffins is $[m]. The cost of three cupcakes is $2[m].

Therefore, we can write the algebraic expression in [m] as -

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Answer:

x = \(\frac{3wyz}{4wz+wy-2yz}\)

Step-by-step explanation:

Given

\(\frac{2}{w}\) + \(\frac{3}{x}\) - \(\frac{4}{y}\) = \(\frac{1}{z}\)

Multiply through by wxyz to clear the fractions

2xyz + 3wyz - 4wxz = wxy ( subtract wxy from both sides )

2xyz + 3wyz - 4wxz - wxy = 0 ( subtract 3wyz from both sides )

2xyz - 4wxz - wxy = - 3wyz ( factor out x from each term on the left side )

x(2yz - 4wz - wy) = - 3wyz ( divide both sides by (2yz - 4wz - wy )

x = \(\frac{-3wyz}{2yz-4wz-wy}\) ( multiply numerator/ denominator by - 1 )

x = \(\frac{3wyz}{4wz+wy-2yz}\)