Manuel had 4 times as many crayons as markers. After he bought 250 crayons and 100 markers he had 3 times as many crayons at markers. How many crayons did he have in the beginning?

Answers

Answer 1

Let's start by assigning variables to represent the unknowns in the problem.

Let's use "c" to represent the number of crayons Manuel had in the beginning and "m" to represent the number of markers he had in the beginning.

From the problem, we know that:

Manuel had 4 times as many crayons as markers in the beginning, so:

c = 4m

After he bought 250 crayons and 100 markers, he had 3 times as many crayons as markers, so:

c + 250 = 3(m + 100)

Now we can use algebra to solve for c:

c + 250 = 3m + 300 // distribute the 3

c = 3m + 300 - 250 // simplify by combining like terms

c = 3m + 50

Substitute c = 4m from the first equation into the second equation:

4m = 3m + 50 // subtract 3m from both sides

m = 50

So Manuel had 4 times as many crayons as markers in the beginning, which means he had:

c = 4m = 4(50) = 200 crayons in the beginning.


Related Questions

100 POINTS PLEASEE HELPPP BRAINLIEST

Answers

Answer:

C

.........................

Answer: the answer is A

Step-by-step explanation: The process of nuclear fusion is the union of two light atomic nuclei into one heavier one while releasing enormous quantities of energy.

9. The price of a Delta Air Lines ticket from New York to Orlando increased to $450. This is an 8% increase. What was the old fare to nearest cent?

Answers

Answer:

$416.66

Step-by-step explanation:

We take

450 divided by 108, then time 100 = $416.66

So, the old fare is $416.66

The ratio of the birth weight to the adult weight of a male black bear is 3:1000. The average birth weight is 12 ounces. Find the average adult weight. Your answer is probably in ounces. If there are 16 ounces in 1 pound, how many pounds does the adult bear weigh?

Answers

In response to the stated question, we may state that As a result, an expressions adult black bear weighs 250 pounds.

what is expression ?

An expression in mathematics is a collection of numbers, variables, and mathematical (such as addition, reduction, multiplication, division, exponentiation, etc.) that express a quantity or value. Expressions might be as basic as "3 + 4" or as complicated as "(3x2 - 2) / (x + 1)". They may also contain functions like "sin(x)" or "log(y)". Expressions can also be evaluated by substituting values for the variables and performing the mathematical operations in the order specified. If x = 2, for example, the formula "3x + 5" equals 3(2) + 5 = 11. Expressions are commonly used in mathematics to describe real-world situations, construct equations, and simplify complicated mathematical topics.

Let B represent the birth weight of a male black bear and A represent the mature weight. The ratio of B to A is supplied to us as 3:1000. As a result, we may write:

B/A = 3/1000

The average birth weight (B) is also reported as 12 ounces. We may use these data to get the average adult weight (A):

[tex]B/A = 3/1000\\12/A = 3/1000\\A = 12/(3/1000)\\A = 4000[/tex]

A male black bear's typical mature weight is 4000 ounces.

To convert ounces to pounds, divide by 16 (since one pound contains 16 ounces):

[tex]4000/16 = 250[/tex]

As a result, an adult black bear weighs 250 pounds.

To know more about expressions visit :-

https://brainly.com/question/14083225

Allison cut 4 pieces of ribbon to make bookmarks. Each piece of ribbon was 50 cm long. How many meters of ribbon did Allison use to make the bookmarks?

Answers

Answer:

2 meters

Step-by-step explanation:

If she cut 4 pieces and each was 50 cm, we know that she used 200 cm of ribbon.

Cm to M conversion is that 100 cm = 1 meter, so 200 cm would be 2 meters

Follow the steps below to find the value of x that makes A||B. offende 8x + 30 B 10x A Set the alternate exterior angles equal to each other. [ ? ]x = X + Enter​

Answers

The value of x that makes A parallel to B is 15.

Describe Alternate Exterior Angles?

Alternate exterior angles are a pair of angles that lie outside of two parallel lines and are on opposite sides of the transversal. In other words, they are a pair of non-adjacent angles that are formed when a transversal intersects two parallel lines. The angles are congruent, meaning that they have the same measure.

The term "alternate" refers to the fact that they are on opposite sides of the transversal and "exterior" indicates that they are outside of the parallel lines. Alternate exterior angles are important in geometry because they can be used to prove that two lines are parallel. If the alternate exterior angles are congruent, then the lines are parallel.

Since the alternate exterior angles are equal, we can set them equal to each other:

8x + 30 = 10x

Subtracting 8x from both sides, we get:

30 = 2x

Dividing both sides by 2, we get:

15 = x

So the value of x that makes A||B is 15.

To know more about angles visit:

https://brainly.com/question/23134598

#SPJ1

Bro leave me alone pls

Answers

Answer:

Step-by-step explanation:

(PLEASE HELP MY GRADES WRE DUE TMRO)Scientists are preparing two satellites to be launched. The graph below represents the
number of miles, y, that the satellite, Space Explorer A, flies in a hours.
Miles

Answers

The rate of change is equal to 6,800 miles per hour.

What is the rate of change?

In Mathematics and Geometry, the rate of change can be determined by using the following mathematical equation (formula);

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

Next, we would determine the rate of change of the value of y with respect to the value of x for Space Explorer A;

Rate of change, m = (68,000 - 34,000)/(10 - 5)

Rate of change, m = 34,000/5

Rate of change, m = 6,800 miles per hour.

Read more on rate of change here: brainly.com/question/25184007

#SPJ1

Complete Question:

Scientists are preparing two satellites to be launched. The graph below represents the number of miles, y, that the satellite, Space Explorer A, flies in a hours. Find the rate of change.

The proof shows that ABCD is a rhombus. Which of the following is the
missing reason?
A. Reflective property
B. Symmetric property
C. Transitive property
D. Addition property

Answers

The correct answer is B. Symmetric property.

The symmetric property states that if a = b, then b = a. In the context of geometry, this property can be used to show that if one side of a figure is congruent to another side, then the second side is also congruent to the first. In the case of the given proof, it is possible that the symmetry of the figure is used to show that opposite sides of the rhombus are congruent.

The reflective property (A) is not typically used to prove that a figure is a rhombus, as it relates to the reflection of a figure across a line. The transitive property (C) and the addition property (D) are also unlikely to be used in this context, as they relate to the properties of equality and addition, respectively, rather than geometric properties of figures.

To know more about problems related to geometry, click here:

https://brainly.com/question/25766008

#SPJ1

Reflections; rotations and translations are transformations that change the what of a figure

Answers

Answer:

eflections, rotations, and translations are all transformations that change the position of a figure in the plane. These transformations change the orientation, location, or both of a figure without altering its size or shape. In other words, they change the position or location of the figure in the plane while maintaining the same size and shape.

I need help on question 30 and 32.

Answers

Refer to the attached images.

Simplify 1/cos x + 1/cos x -1

Answers

Answer:

-2cotxcscx

Step-by-step explanation:

Step 1: Find a common denominator

Step 2: Simplify

Mrs. Brown has constructed a pool that has a capacity of 800cm3 and a depth of 8cm what is the area of the upper surface?

Answers

Answer:

Step-by-step explanation:

To find the area of the upper surface of the pool, we need to know the dimensions of the pool. If we assume the pool has a rectangular shape, we can use the formula:

Area = length x width

We can find the length and width by using the given volume and depth. Since the volume of the pool is 800 cubic cm and the depth is 8cm, we can find the length and width using the formula:

Volume = length x width x depth

800 = length x width x 8

length x width = 800/8

length x width = 100

Now, we do not have enough information to determine the exact dimensions of the pool. However, we do know that the area of the upper surface of the pool is equal to the length times the width. Therefore, the area of the upper surface is 100 square cm.

A business analyst wants to determine if the prices of goods at a supermarket have changed significantly since the new owner of the company took over. She looks at the prices of ten items before the new owner took over compared to after the new owner started.
(Chart in photo below)
Based on the data in the table and using a significance level of 0.05, what is the correct P-value and conclusion?

A. With a t statistic of 1.4789 and a P-value of 0.173292, reject the no hypothesis that prices have not changed

B. With a T statistic of 1.4789 and a P value of 0.173292, fail to reject the null hypothesis. The prices have not changed.

C. With a T statistic of 0.7394 and a P value of 0.478505, reject the no hypothesis that prices have not changed.

D. With a T statistic of 0.7394 anda P value of 0.478505, fail to reject the no hypothesis that prices have not changed.

Please answer quickly, 100 points thank you !

Answers

Answer: Option A

Step-by-step explanation:

The t-statistic and P-value can be calculated using statistical software or a t-test calculator. Using a two-tailed t-test with a significance level of 0.05 and 8 degrees of freedom (n1 + n2 - 2), we obtain:

t = -1.4789

P-value = 0.173292

Therefore, the correct answer is A. With a t statistic of -1.4789 and a P-value of 0.173292, we fail to reject the null hypothesis that the prices have not changed significantly since the new owner took over. We cannot conclude that the prices have changed significantly.

With a T statistic of 0.7394 and a P value of 0.478505, fail to reject the no hypothesis that prices have not changed. The correct option is D.

What is null hypothesis?

A null hypothesis is a type of statistical hypothesis that asserts that there is no statistical significance in a given set of observations.

Using sample data, hypothesis testing is used to assess the credibility of a hypothesis.

To determine if the prices of goods at a supermarket have significantly changed since the new owner took over, we can perform a two-sample t-test with the null hypothesis being that the mean difference in prices before and after the new owner took over is zero.

Using a significance level of 0.05, the critical t-value for a two-tailed test with 9 degrees of freedom is approximately 2.306.

To calculate the t-statistic, we first need to calculate the mean and standard deviation of the differences in prices:

Mean difference = (0.30 - 0.07) / 10 = 0.023

Standard deviation = 2.967

t-statistic = (0.023 - 0) / (2.967 / sqrt(10)) = 0.7394

The calculated t-value of 0.7394 is less than the critical t-value of 2.306, and the corresponding p-value is 0.4785. This means we fail to reject the null hypothesis that the mean difference in prices is zero.

Therefore, based on the given data and using a significance level of 0.05, the correct P-value and conclusion are:

Thus, the correct option is D.

For more details regarding null hypothesis, visit:

https://brainly.com/question/28920252

#SPJ2

Find the missing length indicated. * A) 12 C) 8 A OB D 16 24 36 B) 18 D) 15​

Answers

Answer:

Is D

Step-by-step explanation:

Taylor wants to take out a mortgage of $380,000 with interest that compounds monthly. Use the formula A = P(1 +)*t to find which of these loans will have the lowest total cost. A) 20 years at 10% interest B) 25 years at 6.5% interest C) 30 years at 5% interest D) 35 years at 4% interest​

Answers

Using the compound interest formula it is obtained that the loans which will have the lowest total cost is option C) - 30 years at 5% interest.

What is Compound Interest?

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

We can use the formula of compound interest [tex]A = P\big(1 + \frac{r}{n} \big)^{(nt)}[/tex] to calculate the total cost (A) of each loan, where P is the principal (the initial amount borrowed), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the total number of years.

For all loans, the principal P is $380,000.

For Loan A, the annual interest rate is 10%, and the interest is compounded 12 times per year (monthly), so r = 0.1/12 and n = 12.

The total time is 20 years, so t = 20.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.1/12)^{(12 \times20)} = $1,245,956.70[/tex]

For Loan B, the annual interest rate is 6.5%, and the interest is compounded 12 times per year (monthly), so r = 0.065/12 and n = 12.

The total time is 25 years, so t = 25.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.065/12)^{(12 \times25)} = $844,275.92[/tex]

For Loan C, the annual interest rate is 5%, and the interest is compounded 12 times per year (monthly), so r = 0.05/12 and n = 12.

The total time is 30 years, so t = 30.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.05/12)^{(12 \times30)} = $766,726.73[/tex]

For Loan D, the annual interest rate is 4%, and the interest is compounded 12 times per year (monthly), so r = 0.04/12 and n = 12.

The total time is 35 years, so t = 35.

Plugging in the values, we get -

[tex]A = $380,000(1 +0.04/12)^{(12 \times35)} = $810,780.25[/tex]

Therefore, Loan C with 30 years at 5% interest has the lowest total cost, with a total cost of $766,726.73.

To learn more about compound interest from the given link

https://brainly.com/question/28020457

#SPJ1

Matt increased his typing speed from 32 to 38 words per minute. What is the percent of increase

Answers

Answer:

Matt's typing speed increased by 18.75%.

Step-by-step explanation:

To find the percent increase, we can use the following formula:

percent increase = (new value - old value) / old value x 100%

Using this formula, we can calculate the percent increase in Matt's typing speed as follows:

percent increase = (38 - 32) / 32 x 100%

percent increase = 6 / 32 x 100%

percent increase = 0.1875 x 100%

percent increase = 18.75%

Write an equation to determine each unknown length. Then, solve the equation. Round your answer to the nearest tenth, if necessary.
X=___ Round to the nearest tenth (One number after the decimal)

Answers

Answer: 40

Step-by-step explanation:

a(2) + b(2) = c(2)

a(2) + 9(2) = 11(2)

121 - 81 = 40

Write the ratio of corresponding sides for the similar triangles and reduce the ratio to lowest terms. 2 similar right triangles. Triangle 1 has side length 12, hypotenuse 15, and blank side. Triangle 2 has side length 4, hypotenuse 5, and blank side. a. StartFraction 4 Over 15 EndFraction = StartFraction 5 Over 12 EndFraction = StartFraction 4 Over 15 EndFraction b. StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction c. StartFraction 4 Over 12 EndFraction = StartFraction 5 Over 15 EndFraction = StartFraction 1 Over 3 EndFraction d. StartFraction 5 Over 4 EndFraction = StartFraction 15 Over 12 EndFraction = StartFraction 5 Over 4 EndFraction

Answers

Answer:

Step-by-step explanation: To find the ratio of corresponding sides for the two similar triangles, we need to match up the corresponding sides of the triangles and write the ratios of their lengths.

For Triangle 1, we have:

Side length = 12

Hypotenuse = 15

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 15^2 - 12^2

(Blank side)^2 = 225 - 144

(Blank side)^2 = 81

Blank side = 9

So, for Triangle 1, we have the following ratios:

Side length : Hypotenuse = 12 : 15

Side length : Blank side = 12 : 9

Hypotenuse : Blank side = 15 : 9

For Triangle 2, we have:

Side length = 4

Hypotenuse = 5

We can use the Pythagorean theorem to find the length of the blank side:

(Blank side)^2 = (Hypotenuse)^2 - (Side length)^2

(Blank side)^2 = 5^2 - 4^2

(Blank side)^2 = 25 - 16

(Blank side)^2 = 9

Blank side = 3

So, for Triangle 2, we have the following ratios:

Side length : Hypotenuse = 4 : 5

Side length : Blank side = 4 : 3

Hypotenuse : Blank side = 5 : 3

Therefore, the ratio of corresponding sides for the two similar triangles is:

Side length : Side length = 12 : 4 = 3 : 1

Hypotenuse : Hypotenuse = 15 : 5 = 3 : 1

Blank side : Blank side = 9 : 3 = 3 : 1

Reducing each ratio to lowest terms, we get:

Side length : Side length = 3 : 1

Hypotenuse : Hypotenuse = 3 : 1

Blank side : Blank side = 3 : 1

So the correct answer is (b) StartFraction 4 Over 5 EndFraction = StartFraction 12 Over 15 EndFraction = StartFraction 4 Over 5 EndFraction.

Tauri is 3 years older than Treasure. In 5 years the sum of their ages will be 63. How old is Tauri now?

Answers

Answer:

Tauri is currently 28 years old

Step-by-step explanation:

The diagram shows two circles with center O.
The radius of the outer circle is 3 units and the radius of the inner circle is 2 units.
What is the area of the shaded ring (annulus)?

Look at the picture below please answer quick because of my appointment?

Answers

Answer:

5

Step-by-step explanation:

S1=R1²=*3²=9 (the outer circle)

S2=R2²=*2²=4 (the inner circle)

S=S1-S2=9-4=5 (the shaded ring)

Answer: 5 BECASUE of how the raids is in the inner circle

how do i solve this problem?

Answers

Option A correctly describes the area of the graph of the function.

How is an area of the graph calculated?

The area of a graph is the area under the function curve enclosed within the X-axis of the graph. Thus, it is the area of the figure formed by enclosing the function graph with the X-axis.

It is the integration of the function polynomial of the possible values of x that the function curve lies in.

Here the function equation is : [tex]f(x) = ( 25 - x^{2} )[/tex]

From the figure, we can see that the value of x varies from -5 to 5.

Initial x-value of integration = minimum value of x

                                          = -5

Final x-value of integration = maximum value of x

                                          = 5

Thus, the area of the graph can be correctly calculated as. :

               [tex]Area = \int\limits^{maxX}_ {minX} \, f(x)dx[/tex]

               [tex]Area = \int\limits^5_ {-5} \, (25-x^{2} )dx[/tex]

Hence, Option A correctly calculates the area of the graph given.

To learn more about Graphs, visit

https://brainly.com/question/29548482

#SPJ1

Solid metal support poles in the form of right cylinders are made out of metal with a
density of 6.6 g/cm³. This metal can be purchased for $0.38 per kilogram. Calculate
the cost of a utility pole with a diameter of 17.6 cm and a height of 790 cm. Round
your answer to the nearest cent.

Answers

The cost of the utility pole is $127.36.

What is the answer to this?

Answers

Answer:

B

Step-by-step explanation:

x + 3y = 2 → (1)

4x - 3y = 23 → (2)

adding (1) and (2) term by term will eliminate y

(x + 4x) + (3y - 3y) = 2 +  23

5x + 0 = 25

5x = 25 ( divide both sides by 5 )

x = 5

How will the product change if one number is decreased by a factor of 2 and the other is decreased by a factor of 8 ?

Answers

The product is decreased by a factor of 16.

What is a factor?

In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.

Let's say we have two numbers, A and B, and we want to find the product of A and B.

The product of A and B is AB.

If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.

So the new product of A/2 and B/8 is:

(A/2)(B/8) = AB/16

Therefore, the product is decreased by a factor of 16.

To learn more about factors, visit the link:

https://brainly.com/question/25829061

#SPJ1

Find the simplified form of the expression. Give your answer in scientific notation.
(8 × 10^4)(9 × 10^–8)

Answers

Answer:

7.2×10^-3

Step-by-step explanation:

8 × 10^4×9 × 10^–8

=8×9×10^(4-8)

=72×10^-4

=7.2×10^-3

which of the following is not an identity?

Answers

The trigonometry expression which is not an identity is 1+cos² x/sin²x + 1. The Option A is correct.

What is a trigonometric identities?

Trigonometric Identities refers to equalities that involve trigonometry functions and hold true for all variables in the equation. There are numerous trigonometric identities involving the side length and angle of a triangle.

The primary trigonometry functions are sine, cosine, and tangent, while the other three functions are cotangent, secant, and cosecant. All six trig functions are used to derive the trigonometric identities.

Read more about trigonometric identities

brainly.com/question/7331447

#SPJ1

Find x
Given: x=AC, m

Answers

Answer:

x = 15.733

Step-by-step explanation:

Which of the following are true of
all linear functions?
A. The rate of change is
non-zero.
B. The domain is all real
numbers.
C. The range is all real
numbers.
D. There is one x-intercept.
E. There is one y-intercept.

Answers

The domain is all real numbers, The range is all real numbers and There is one y-intercept is true from the given option in context of all linear functions. option B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept is right choice.

All linear functions have a domain that includes all real numbers, a range that includes all real numbers, and exactly

one y-intercept.

The rate of change of a linear function is non-zero only if the function is not constant (i.e. its slope is not zero).

However, there are linear functions that have a slope of zero, such as the function f(x) = 2, which is a horizontal line.

This means that statement A is not true of all linear functions.

Furthermore, there are linear functions that have no x-intercept (if the line is parallel to the x-axis) or that have more

than one x-intercept (if the line intersects the x-axis more than once).

Therefore, statement D is also not true of all linear functions.

The correct answers to this question are B. The domain is all real numbers, C. The range is all real numbers , and E. There is one y-intercept.

for such more question on linear functions

https://brainly.com/question/9753782

#SPJ11

How many solutions does this equation have? –8 + 3s + 17s = 20s + 8

Answers

Answer: There are no solutions

Step-by-step explanation:

Step 1: simplify both sides of the equation

-8 + 3s + 17s = 20s + 8

(3s+17s) + (-8) = 20s + 8 (combine like terms)

20s + -8 = 20s + 8

20s - 8 = 20s + 8

Step 2: Subtract 20s from both sides

20s - 8 - 20s = 20s + 8 - 20s

-8 = 8

Step 3: Add 8 to both sides

-8 + 8 = 8 + 8

0 = 16

Thus, there are no solutions

Write 2/8 in lowest terms.

Answers

Answer: 1/4

Step-by-step explanation:

2 divided by 2 is 1 and 8 divided by 2 is 4 so 1/4

Answer: 1/4

Step-by-step explanation: We can simplify by divideing both the numerator and the denominator by 2. That will leave us with the answer of 1/4.

Other Questions
Pick a piece of art, music, or architecture and explain how it reflects our era. What will historians in the future learn about us by studying the elements of our culture? janet receives $100 with the stipulation that she must split it any way she wants with her friend evelyn. what is the smallest amount of money evelyn must receive such that she will judge the transaction to be fair and not reject the offer? The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 48 miles apart. When the satellite is on one side of the two stations, the angle of elevation at A Is 87 and the angle of elevation at B Is 84.How far is the satellite from station A?How High is the satellite above the ground? Round all answers to 3 decimal places. would marx agree that higher wages (such as those brought about by a minimum wage) would solve the issues he is discussing? give evidence. Find the equation of the line.Use exact numbers. which of the following most favors elimination rather substitution in a reaction with 2-bromopropane? question 6 options: sodium methoxide sodium ethoxide sodium isoproxide sodium tert-butoxide the health care provider has ordered epinephrine for a client admitted emergently with bronchospasms. the nurse will prepare to administer this drug via which route? for a normal distribution, with a mean of 37 and a standard deviation of 3.7, what is the probability of randomly drawing a participant with a score of 34 or less? what is the last thing mcwhorter says he would want to know if he had the ability to go into the future? the lease term includes a bargain purchase option that is reasonably expected to be exercised, when does the lease term end for accounting purposes? Which expression represents the distance between point J and point K? J=6, -2 K= 6, -9 an emf source with a resistor with and a capacitor with are connected in series. as the capacitor charges, when the current in the resistor is 0.900 a, what is the magnitude of the charge on each plate of the capacitor? makani is participating in an on-the-job training program at work. he is learning how to configure computers in a network. he is told to use private ip addresses because all organizations could use them without conflict since they are not routable. if the addresses are not routable, he wonders, how will the computers have internet access? The character disintegration of Macbeth and Lady Macbeth could be blamed on tragic flaws, like excessive ambition or hubris. It could also be blamed on external forces, like peer pressure, relationships, or the convincing words of others. From the perspective of either Macbeth or Lady Macbeth, write an 8-10 sentence paragraph in which you explain whether the cause of your character disintegration or downfall was due to internal or external forces. Cite textual evidence from the play to support your character's perspective and response. Your response will be written from a first-person point of view. I couldn't imagine what ____ to her. how can the chemical potential energy in an endothermic reaction best be described?(1 point) responses THIS IS FOR ECONOMICS (please help)What is the United States' current status in this business cycle if you were what tools or policies would you implement to bring the economy back into a growth cycle? Im so confused please help me if sandler files a proper election to waive the family attribution rules, what is the amount of his gain? who does the board ultimately hold responsible for establishing an erm framework and for managing risks faced by the organizatio