Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible

The expected value for the construction company if they bid on the contract is $7,500, calculated by weighing the potential profit and loss with their respective probabilities.

The question is asking us to calculate the expected value of the construction company's bid on a building contract. To find the expected value, we need to multiply each outcome by its probability and sum these amounts.

There are two possible outcomes:

The expected value (EV) is calculated as follows:
EV = (Probability of acceptance × Net profit when accepted) + (Probability of not being accepted × Loss when not accepted)
EV = (1/10 × $92,100) + (9/10 × -$1,900)
EV = $9,210 - $1,710
EV = $7,500

The expected value for the construction company if they bid on the contract is $7,500.

Answer:

[tex]12[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]

In this problem we have

For [tex]x=3[/tex] -----> [tex]f(x)=8[/tex]

so

Find the value of k

[tex]f(x)*x=k[/tex]

substitute the value of x and f(x)

[tex]8*3=k[/tex]

[tex]k=24[/tex]

therefore

the equation is equal to

[tex]f(x)=24/x[/tex]

For [tex]x=2[/tex] -------> substitute in the equation and find the value of f(x)

[tex]f(x)=24/2=12[/tex]

Answer:

it is right

Step-by-step explanation:

To find the total distance David travels during the three days, we add up the distances he travels on each day: m + (m + 35) + 2m = 4m + 35 miles.

To find the total distance David travels during the three days, we need to add up the distances he travels on each day.

On Monday, David travels m miles.

On Tuesday, he travels 35 more than he did on Monday, so he travels m + 35 miles.

On Wednesday, he travels twice the distance he traveled on Monday, so he travels 2m miles.

To find the total distance, we add up the distances on all three days:

Total distance = m + (m + 35) + 2m = 4m + 35 miles.

Answer:

  76

Step-by-step explanation:

The last two digits of powers of 36 repeat in a pattern of length 5:

  36^1 mod 100 = 36

  36^2 mod 100 = 96

  36^3 mod 100 = 56

  36^4 mod 100 = 16

  36^5 mod 100 = 76

  36^6 mod 100 = 36

The last two digits of the power 2015 are the same as those of the 5th power: 76.

Final answer:

To convert 1.375 to a fraction, express it as 1,375/1,000 and simplify by dividing by the greatest common divisor, which is 125, to get 11/8.

Explanation:

To convert the decimal 1.375 to a fraction, we will follow a few steps. First, count the number of decimal places, which in this case is three. This tells us that the denominator of the fraction should be a power of 10; specifically, 1,000. So we write 1.375 as 1,375/1,000. Next, we simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 1,375 and 1,000 is 125. When we divide both the top and the bottom by 125, we get 11/8, which is the simplest form of the fraction.

Converting decimals to fractions involves aligning the decimal with the appropriate power of 10 in the denominator and simplifying by finding the greatest common divisor. This systematic approach ensures the representation of the decimal as a simplified fraction, such as 11/8 in the case of 1.375.

"The answer is: 50 + 7 x 5 = 85 is correct due to the order of operations.

To understand why 50 + 7 x 5 equals 85, we must follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). According to this rule, multiplication and division are performed before addition and subtraction.

 Let's break down the expression step by step:

1. Identify the multiplication part of the expression: 7 x 5.

2. Perform the multiplication first: 7 x 5 = 35.

3. Now, we have 50 + 35, since we have already computed 7 x 5.

4. Finally, perform the addition: 50 + 35 = 85.

So, following the order of operations, we correctly get that 50 + 7 x 5 equals 85."

The mass of 10,000 peanuts is 4,500 g or 4.5 kg.

The question asks for a reasonable guess for the mass of 10,000 peanuts, given that each peanut has a mass of about 0.45 g. To calculate this, we simply multiply the number of peanuts by the mass of each peanut:

Mass of one peanut = 0.45 g
Number of peanuts = 10,000
Total mass = 0.45 g/peanut x 10,000 peanuts

Now we will carry out the multiplication:

Total mass = 4,500 g

Since we are dealing with a large quantity of peanuts, it is more convenient to express this mass in kilograms:

4,500 g is equivalent to 4.5 kg (since 1 kg = 1,000 g).

Answer:

Step-by-step explanation:

b=6

The decimal labeled with the letter A on the scale is 0.75.

A number line can be defined as a straight line with numbers placed at equal intervals or segments along its length.

Here, the number starts with zero.

There are 8 division between 0 and 1.

So, first one represent 1/8=  0.125

second one =0.25

third one= 0.375

fourth one= 0.50

fifth one= 0.625

sixth one= 0.75

Hence, the decimal labeled with the letter A on the scale is 0.75.

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To carry out the student's request, you would first raise 'g' to the 7th power to obtain g^7, then subtract 'h' from this result to get the final expression 'g^7 - h'.

To solve the expression mentioned by the student, you need to carry out two mathematical operations in sequence. The first operation is raising 'g' to the 7th power, which can be expressed as g^7. The second operation is subtracting 'h' from the result of the first operation. This can be represented mathematically as g^7 - h.

For example, if g equals 2 and h equals 3, then you would first calculate 2^7 which equals 128. Then you would subtract 3 from 128, yielding an answer of 125.

Answer:10

Step-by-step explanation:

7.02 is approximately 10.4 percent of 67.5.

To find what percent 7.02 is of 67.5,

Since we know that,

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means. The letter "%" stands for it.

We can use a proportion.

Let's call the unknown percent "x."

The proportion would be:

7.02/67.5 = x/100

We can cross-multiply to solve for x:

(7.02 * 100) / 67.5 = x

Simplifying this expression, we get:

x = 10.4

Therefore, 7.02 is approximately 10.4% of 67.5.

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Final answer:

Using a system of equations, we found that 454 student tickets were sold at the event.

Explanation:

To determine how many student tickets were sold for the event, we need to set up a system of equations based on the information given. Let's define x as the number of student tickets sold at $4 each, and y as the number of non-student tickets sold at $6 each.

The total number of tickets sold (student plus non-student) is given as 845 tickets:

x + y = 845

The total amount of money made from selling these tickets is $4162:

4x + 6y = 4162

Now we have a system of two equations:

x + y = 845

4x + 6y = 4162

We can solve this system by multiplying the first equation by 4:

(4)(x + y) = (4)(845)

4x + 4y = 3380

Now, we subtract this new equation from the second equation given by the total amount made to eliminate y:

4x + 6y - (4x + 4y) = 4162 - 3380

2y = 782

Dividing both sides of this equation by 2 gives us:

y = 391

Now, substitute y back into the first equation to find x:

x + 391 = 845

x = 845 - 391

x = 454

So, 454 student tickets were sold.