What is commutative associative and distributive property?

The minimum value of the sum of two positive numbers whose product is 784 is 56. The numbers that satisfy this condition are 28 and 28.

To find the minimum sum, we need to determine the two positive numbers whose product is 784 and find their smallest possible sum. In this case, the prime factorization of 784 is 2^4 * 7^2. To obtain the smallest sum, we need to distribute the factors as equally as possible between the two numbers.

By dividing the factors evenly, we can assign two factors of 2 and one factor of 7 to each number. Therefore, the two numbers are 2^2 * 7 = 28 and 2^2 * 7 = 28.

The sum of these two numbers is 28 + 28 = 56, which is the minimum value of their sum. Any other combination of factors would result in a larger sum. Therefore, the minimum sum of two positive numbers whose product is 784 is 56.

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Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

Given Information :A study conducted several years ago reported that 21% of public accountants changed companies within 3 years.

The American Institute of CPAs would like to update the study.

They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.

Required:a. To update this study, how many public accountants should be contacted? Solution: Given that: the percentage of public accountants changed companies within 3 years is 21%.The level of confidence is 95%.

The margin of error is 3%.We have to find out the sample size.To find the sample size we use the formula :n = [Z² x p x q ] / E²

Where, Z = Standard normal deviation corresponding to a 95% confidence level is 1.96.p = proportion = 21/100 = 0.21q = 1-p = 1-0.21 = 0.79E = margin of error = 3/100 = 0.03

Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

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1- Ferald follows school rules
2- Lex and Jaye are gems
3- Jay loves adbobo and beef stew
4- Jake's best friend is his dog
5- Kim has self-discipline

Answer:

I found that the answer is (5,1)

Step-by-step explanation:

4 times x(5) is 20

3 times y(1) is 3

20 + 3 = 23

bottom equation:

x(5) -- 5y(1) = 0

Answer:

she can by 5 pounds of raspberries

Step-by-step explanation:

4 - 19 = 15

15 ÷ 3 = 5

The radius of the spherical part is 3 inches and the length of the tube is 21 cm.

The capacity of a cylinder, which determines how much material it can hold, is determined by the cylinder's volume. There is a formula for the volume of a cylinder that is used in geometry to determine how much of any quantity, whether liquid or solid, can be immersed in it uniformly.

Given that the volume when the water is fully dipped is 4554 / 7 cm³. The volume when the length is 9 cm empty is 396 cm³.

The two equations can be formed as below:-

4554 / 7 = πr²l + (2/3)πr³

396 = πr²( l - 9 ) + (2/3)πr³

Subtract the second equation from the first,

( 4554 / 7 ) - 396 = 9πr²

9πr² = 254.5

r² = 9

r = 3 cm

The length will be calculated as:-

4554 / 7 = πr²l + (2/3)πr³

4554 / 7 = π( 3 )²l + (2/3)π(3)³

l = 21 cm

Therefore, the tube's length is 21 cm, and the spherical part's radius is 3 inches.

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Answer:

d. 20%

Step-by-step explanation:

6*100=600

600 divided 30= 20

20%

Answer:

I want to say 20%

Step-by-step explanation:

the amount of days rained divided by the amount of days in April. and the make the decimal a percent (x100)

Answer:

A. 2x²-13x+15 / (x-3)(x+3)(x-4)

Step-by-step explanation:

Step-by-step explanation:

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

                multiply L term by   (x-4)/ (x-4)    and the R term by (x-3)/(x-3)

                      to get a common denominator

[ 2x (x-4)       -    5(x-3)  ] / ((x-3)(x+3)(x-4)        then simplify a bit to get

(2x^2 -13x +15 )  ((x-3)(x+3)(x-4)        Done.

The equation of this circle in standard form is: D. (x - 4)² + (y - 1)² = 25.

In Geometry, the standard form of the equation of a circle is modeled by this mathematical equation;

(x - h)² + (y - k)² = r²

Where:

From the information provided above, we have the following equation of a circle:

x² - 8x + y² - 2y - 8 = 0

x² - 8x + y² - 2y = 8

x² - 8x + (-8/2)² + y² - 2y + (-2/2)² = 8 + (-8/2)² + (-2/2)²

x² - 8x + 16 + y² - 2y + 1 = 8 + 16 + 1

(x - 4)² + (y - 1)² = 25

(x - 4)² + (y - 1)² = 25

Therefore, the center (h, k) is (4, 1) and the radius is equal to 5 units.

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As per the unitary method, Gordon is correct because the Gordon would charge more than Ironing Palace

In math the term unitary method is defined as the value of a single unit and then find the value of more or fewer units by multiplying their quantity with the value of a single unit.

Here we have given that the total weight of these shirts is 9. 5 kg.

And here we have also given that each shirt weighs 190 g.

And Gordon charges £38 to iron these shirts.

And the charges in the Ironing Palace is 90p for each.

Here we have to use the unitary method to calculate the values for each of them,

The Total cost for Gordon is calculated as,

=> 38 x (9.5 / 0.19)

=> 1900

And the total cost for Ironing Palace is calculated as,

=> 90 x 9.5

=> 855

Therefore, while we looking into the values we have identified that Gordon is correct.

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\(\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}\)

Actually Welcome to the Concept of the Modulus functions.

Since here, the value of h and k are zero,hence

the value of the function f(x) = 3|x| is 3

====> answer is 3

Answer:

X equals 6°.

Step-by-step explanation:

There is a geometry rule that states the outer angle of a triangle's interior angle is equivalent to the sum of the remaining two interior angles of the triangle. Following this rule, you can get that (6x + 8) + (5x + 8) = 82° ⇒ 11x + 16 = 82° ⇒ 11x = 66° ⇒ x = 6°.

Answer:

6.53 X 10^5

Step-by-step explanation:

Answer:6.53 x 10*5

Step-by-step explanation:i don’t know how to show 5 as a small number but it’s an exponent

Answer:

your answer would be D

Step-by-step explanation:

Substitute the x= 3y-1 in place of the x in the second equation

Subtract Like terms

Add 3 to both sides

Divide by 3(the coeffcient of y)

Answer is 5

The answer is 5. This is the y intercept

From the AAS property of congruency the side ab≅ac in the isosceles triangle.

Congruency generally shows the similarities between two triangles or any other shape for the similarity of the two shapes they should have any three properties same like their three sides, Three angles or one angle two sides and so on.

Now for an Isosceles triangle abc given in the figure

\(\angle bad=\angle cad\)

\(\angle abd=\angle acd\)

\(ad=ad\)   (common side)

So from the AAS property, the triangle \(\Delta bad=\Delta acd\) are congruence

The side ab will also be equal to the side ac.

So from the AAS property of congruency is the side ab≅ac in the isosceles triangle.

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Answer:

The answer would be "A". Converse of the isosceles triangle theorem.

Step-by-step explanation:

You're Welcome :)

The system of equations is consistent and has a unique solution at (-4, 1).

To solve the system of equations by graphing, we can plot the lines represented by each equation on a coordinate plane and find their point of intersection.

The given system of equations is:

1) 3x + y = -3

2) 6x - 6y = -30

Let's graph these equations:

For equation 1, 3x + y = -3, we can rewrite it as y = -3x - 3.

For equation 2, 6x - 6y = -30, we can simplify it to x - y = -5, and then y = x + 5.

Now, let's plot these lines on a graph:

The line for equation 1, y = -3x - 3, has a slope of -3 and y-intercept of -3. It will have a negative slope, and we can plot two points on the line: (0, -3) and (-1, 0).

The line for equation 2, y = x + 5, has a slope of 1 and y-intercept of 5. We can plot two points on this line as well: (0, 5) and (-5, 0).

Plotting these lines on a graph, we can see that they intersect at the point (-4, 1).

Now, let's analyze the system:

Since the lines intersect at a single point, the system is consistent. The solution to the system is the coordinates of the point of intersection, which is (-4, 1).

In summary, the system of equations is consistent and has a unique solution of x = -4 and y = 1.

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Answer:

\(10(n - 2p + 2) \\ = 10n - 20p + 20\)

I hope I helped you^_^

The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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Answer:

D

Step-by-step explanation:

absolute value of -25 is 25

and 25>24

Answer:

D

Step-by-step explanation:

A is wrong because the values are equal.

B is wrong because 5 is greater than 2

C is wrong because 1 is less than 2.

The ball hits the surface at 43.5° and bounces back at 43.5°.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Given that When a ball is bounced on a smooth surface, the angles formed by the path of the ball are congruent.

If the path of a ball forms a 53 angle with the floor, find  the angle with the floor, x

Let the angle with the floor, x

Using, to find x, setup the equation:

x+ 53 +x=180

2x+ 53 =180

2x = 127

x= 43.5°

Therefore, the ball hits the surface at 43.5° and bounces back at 43.5°.

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Answer:

Equivalent fractions to 11/8

11/8, 22/16, 33/24, 44/32, 55/40, 66/48, 77/56, 88/64, 99/72, 110/80

Answer:

B can make tons more

Step-by-step explanation:

1/9   123456789    (+9)

multiples of 11 11 22 33 44 55 66  77 88 99    (+9)

9+9=18

A=18

B=

213

438

SO MANY MORE

B=more

The area of the shaded region is 5π  

The sector of a circle refers to the region enclosed by two radii of a circle and the arc between them. It is a part of the whole circle, and its area can be calculated using the following formula:

where θ is the central angle (in degrees) of the sector, r is the radius.  

Here we have

The length of arc FG = 5/3 π  and measure of ∠FEG = 50°

As we know Arc Length = θ × (π/180) × r  

=> Length of arc FG = 50 × (π/180) × r

From the given data,

=> 50 × (π/180) × r = 5π/3

=> 5 × (1/18) × r = 5/3

=>  (1/6) × r = 1

=> r = 6 units  

Hence, the radius of the circle is 6 units

By using the formula,

Area of a Sector of Circle = (θ/360°) × πr²

Area of shaded region = (50/360) × π(6)²  

= (5/36) × π(36)

= (5/36) × π(36)

= 5π  

The area of the shaded region is 5π  

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Answer:

289 yards

Step-by-step explanation:

All you have to do is 1156 yards divided by 4 to get a grand total of 289 yards per side  

Answer:

the answer is c.

Step-by-step explanation:

there's no explanation

(Apologies since this super late; I hope future students will find this helpful)

Answer:

In a scalene triangle, none of the angles are congruent.

Step-by-step explanation:

As shown, the angles in each scalene triangle all have different measurements. Hence, you can conclude that none of the angles in a scalene triangle are congruent.

You can also see the image below if you'd like to confirm this :)

Answer:

B

Step-by-step explanation:

50+55+48+50+52=255

255/5=51

Anwser 51