Raj eats 1/11 of a pound of grapes in 1/25 of a minute. How many minutes will it take him to eat a full pound of grapes?

Collagen is a major structural protein in connective tissue, made of fibrous materials predominantly secreted by fibroblasts. It provides strength and flexibility to tissues like tendons, ligaments, and skin. This protein is crucial for maintaining the body's structural integrity.

The complete list of possible pairs of rodents from the choices woodchuck, prairie dog, beaver, and chipmunk includes six combinations, showcasing an application of combinatorics in mathematics to determine all possible selections.

The question involves determining the complete list of possible pairs of rodents that radio listeners could choose from four options: woodchuck, prairie dog, beaver, and chipmunk. This is a matter of combinatorics, a branch of mathematics focused on counting, arrangement, and combination of sets of elements. Since each listener picks two favorites and the order in which they pick them does not matter (choosing a beaver and a woodchuck is the same as choosing a woodchuck and a beaver), we use combinations to find the total number of possible pairs.

Mathematically, the number of ways to choose 2 favorites out of 4 is given by the combination formula C(n, r) = n! / r!(n-r)!, where n is the total number of options and r is the number being chosen. Here, n=4 and r=2, resulting in C(4, 2) = 4! / 2!(4-2)! = 6, which matches our list of 6 possible pairs.

Priscilla and Herb can address 10,000 envelopes together in approximately 44.44 hours, when we combine their individual work rates of 100 and 125 envelopes per hour respectively.

Priscilla and Herb are addressing envelopes for a firm, and we need to determine how long it would take them to address 10,000 envelopes if they work together. Priscilla can address 10,000 envelopes in 100 hours, and Herb can do the same in 80 hours.

To solve this, we can calculate each person's work rate and then combine these work rates to get the rate at which they complete the task together.

First, we calculate their work rates:

Working together, their combined rate would be:

Combined rate = Priscilla's rate + Herb's rate

Combined rate = 100 envelopes/hour + 125 envelopes/hour

Combined rate = 225 envelopes per hour

To address 10,000 envelopes at this combined rate, we can divide the total number of envelopes by their combined rate:

Time to address 10,000 envelopes together = 10,000 envelopes / 225 envelopes/hour

Time to address 10,000 envelopes together = approximately 44.44 hours

Answer:

Pay more than the required premiums

Step-by-step explanation:

The loan contract is of for 60 months. If Steve wants to repay the loan before 60 months , he need to pay more than the promised premiums.

In this way , the Steve will have more payment and as there is no prepayment charges, he will not be paying any penalties also. So the extra payment will help him to reduce the borrowed principle and thus thereby reducing the interest charged.

Hence out answer is option one , which says make more than the minimum payments

The smaller number of the two numbers that have a difference of 30 and a ratio of 7:2 is 12.

The difference between the two numbers is 30.

The ratio of the bigger number to the smaller number is 7:2.

The smaller number can be calculated as follows;

let

x = bigger number

y = smaller number

Hence, the difference in the numbers is as follows:

x - y = 30

Also, the ratio of the bigger number to the smaller number is 7:2.

The bigger number can be found using the ratio. Recall x + y is the total sum of the numbers.  

x = 7 / 9(x + y)

x = 7 / 9x + 7 / 9y

x - 7 / 9x = 7 / 9 y

2 / 9 x  = 7 / 9 y

multiply both sides by 9

2x  = 7y

The bigger number is 7 / 2 of the smaller number.

x = 7 / 2 y

Therefore, let's substitute the value of x in equation(i).

Recall x - y = 30

7 / 2 y - y = 30

5 / 2 y = 30

cross multiply

5y = 60

y = 60 / 5

y = 12

Hence,

x = 30 + 12

x = 42

Therefore,

smaller number = 12

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y/9 +5 =0

 subtract 5 from each side

y/9 = -5

 multiply both sides by 9

y = -5 * 9

y = -45

Final answer:

The probability of rolling a 12 with two six-sided dice is 1/36, since there is only one combination (6+6) that yields a sum of 12 out of 36 possible outcomes.

Explanation:

The question requires calculating the probability of getting a specific sum when rolling a pair of six-sided dice, which is a common problem in probability theory. To find the probability of getting a sum of 12, we first need to understand that each die has 6 faces, and therefore, there are a total of 6 x 6 = 36 possible outcomes when rolling two dice.

Now, only one combination yields a sum of 12: when both dice show a six (6 + 6). Therefore, there is only one favorable outcome that gives the sum of 12. The probability of this outcome is then 1 (favorable outcome) divided by 36 (total possible outcomes), which gives us a probability of 1/36.

To put it mathematically, we apply the fundamental principle of probability which states that the probability of an event is equal to the number of ways the event can happen divided by the total number of possible outcomes. Hence:

Probability of rolling a sum of 12 = Number of ways to get a sum of 12 / Total number of possible outcomes = 1/36.

Answer:

True I hoped this helped!

Step-by-step explanation

Got it right on my quiz

It will take Rafael 10 months to save the down payment.

Method:

To solve this question, round out one of the factors to estimate the product

We have:

340 ≈ 300 (we rounded 340 to the nearest hundred)

Let x represent the number of months, then we have:

300 x X = 3000

3 x 100 x X = 3 x 100 times 10 (for better understanding)

X = [tex]\frac{3000}{300}[/tex]

X = 10

so, it will take him about 10 months to save the down payment.

Notably, we rounded 340 to 300 so that it can be easier to use when calculating.

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If the function d(x) = 1375 − 110x represents the distance (in miles) a high-speed  train is from its destination after x hours:

a) The train is 495 miles from its destination after 8 hours

b) It will take the train 12.5 hours to travel before reaching its destination

The given function is:

d(x)  =  1375  -  110x

Where d(x) is the distance (in miles) a high-speed  train is from its destination after x hours.

a) How far is the train from its destination after 8 hours?

To find how far the train is from its destination after 8 hours, substitute x = 8 into d(x)  =  1375  -  110x

d(8)  =  1375  -  110(8)

d(8)  =  1375  -  880

d(8)  =  495

The train is 495 miles from its destination after 8 hours

b) How long does the train travel before reaching its destination?

Note that:

d(x)  =  1375  -  110x

From the equation above, the speed at which the train is traveling is 110 miles/hr

The distance of the destination = 1375

The time it will take to reach the destination will be calculated as:

Time = Distance / speed

Time = 1375 / 110

Time = 12.5

It will take the train 12.5 hours to travel before reaching its destination

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It's important to understand and apply various mathematical concepts taught in high school, including basic algebra, arithmetic, and vector representation. Success also often comes from group work and discussions, which can provide new perspectives.

In mathematics, figuring for yourself and collaborative group activities are essential aspects of learning. When we talk about basic algebra and arithmetic, it means we are dealing with mathematical operations such as addition, subtraction, multiplication, division, and solving equations. The principles given in a chapter can be applied to various questions. For instance, if you understand the concept of 'solving for x', you can apply it in different scenarios and questions.

Similarly, when vectors are represented with an arrow above them, this is one of the common notations in mathematics, specifically in vector algebra. It is also important to note that working in groups and participating in discussions can bring another perspective and help understand the subject better.

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The value of 4.5+ π is Irrational because it is a non-terminating and non repeating.

An irrational number is a real number that cannot be expressed as a ratio of integers. Again, the decimal expansion of an irrational number is neither terminating nor recurring.

Given: 4.5+ π

As, the value of π is 3.1415926535 8979323846 2643383279 50288....

We can see that the value of π is non terminating and non recurring.

Hence, 4.5+ π= 7.6415926535 8979323846 2643383279 50288..

which is also a non terminating and non recurring.

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