what is the slope of y = 17x - 39

The first number, 5 x \(10^22,\) can be written as 5 followed by 22 zeros:

5,000,000,000,000,000,000,000

To simplify means to make something easier to understand or do by reducing complexity, removing unnecessary details, or using simpler language or concepts.

The second number , 5 × 10², can be written as 5 followed by 2 zeros: 500

The third number, 3.7 x 10⁵³, can be written as 3.7 followed by 53 zeros:

370,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

or in scientific notation as 3.7 x 10⁵³

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Simplify

2. 5 x 10^22. 5 × 10 2 and 3. 7 x 10^53. 7 × 10 5

Answer:

33 minutes

Step-by-step explanation:

Answer:

33 minutes

Step-by-step explanation:

To go from 13:49 to 14:00, that is 11 minutes

To go from 14:00 to 14:22 is 22 minutes

22 + 11 = 33

Hope this helps!

The exponent of 3 in the prime factorization of 109! is 76.

To find the exponent of 3 in the prime factorization of 109!, we need to first determine how many factors of 3 there are in the prime factorization of each number from 1 to 109. We can do this by dividing each number by 3 and adding up the quotient (ignoring any remainder) until the quotient becomes less than 3. For example, for the number 27, we divide 27 by 3 to get 9, then divide 9 by 3 to get 3, then divide 3 by 3 to get 1. So the exponent of 3 in the prime factorization of 27 is 3.

Doing this for all the numbers from 1 to 109, we get:

- There are 36 numbers that have at least one factor of 3.
- There are 12 numbers that have at least two factors of 3.
- There are 4 numbers that have at least three factors of 3.
- There is 1 number (81) that has at least four factors of 3.

To find the exponent of 3 in the prime factorization of 109!, we need to add up the number of factors of 3 in each of these numbers:

- The 36 numbers with at least one factor of 3 contribute a total of 36 factors of 3.
- The 12 numbers with at least two factors of 3 contribute a total of 24 factors of 3 (since each one has 2 factors of 3).
- The 4 numbers with at least three factors of 3 contribute a total of 12 factors of 3 (since each one has 3 factors of 3).
- The 1 number with at least four factors of 3 contributes 4 factors of 3.

So the total number of factors of 3 in the prime factorization of 109! is 36 + 24 + 12 + 4 = 76. Therefore, the exponent of 3 in the prime factorization of 109! is 76.

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Answer:

Equations:

a + b = 19

a = b + 2

a = Money that spent Laura

b = Money that spent Laureen

then:

(b+2) + b = 19

2b + 2 = 19

2b = 19-2

2b = 17

b = 17/2

b = 8.5

a = b + 2

a = 8.5 + 2

a = 10.5

Check:

10.5 + 8.5 = 19

Answer:

Step-by-step explanation:

\(35 - 21 + 6m\)

Simplify : Subtract

\(35 - 21 = 14 \\ 14 + 6m \\ 6m + 14\)

Answer:

10minutes

Step-by-step explanation:

sorry if I'm wrong

Answer:

Rational number

Step-by-step explanation:

Answer:

Rational number

Step-by-step explanation:

Answer:

Around 3000 BC

Answer:

It is difficult to pinpoint a specific year or time period in which math was "invented," as math is a fundamental aspect of human thought and has likely been present in some form since ancient times.

The study of mathematics has a long and rich history, dating back to ancient civilizations in Mesopotamia, Egypt, Greece, and India. These early societies developed mathematical concepts and techniques to aid in practical tasks such as measuring land, calculating the volume of objects, and tracking the movement of celestial bodies.

As human civilizations developed and advanced, so too did the study of mathematics. Over time, new mathematical concepts and techniques were developed and refined, leading to the development of more advanced branches of mathematics such as algebra, geometry, trigonometry, and calculus.

In summary, math has a long and complex history, and it is difficult to pinpoint a specific year or time period in which it was "invented." It has likely been present in some form since ancient times and has evolved and developed over the course of human history.

Step-by-step explanation:

SELF EXPLANATORY

Answer:

36000

Step-by-step explanation:

Move the decimal to the right four times because of 10^4

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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Answer:

66(2/3) %

Step-by-step explanation:

There are 30 possible outcomes because there are 30 cold drinks.

 The Probability of orange flavored  20/30   = 2/3 = 0.6666....

66.6666....%= 66(2/3) %

Rounding to the nearest tenth, the yield on a 2-year Treasury note is approximately 7.3%. Option b

The yield on a 2-year Treasury note can be calculated by adding up the various components that contribute to the yield. The real risk-free rate is given as 3%, and the inflation rates for this year and next year are 4% and 5% respectively. Additionally, the maturity risk premium is estimated to be 0.20(t-1)%, where t is the number of years to maturity.

To calculate the yield on a 2-year Treasury note, we need to consider the real risk-free rate, inflation expectations, and the maturity risk premium. The yield will be the sum of these components.

In this case, since the maturity is 2 years (t = 2), the maturity risk premium would be 0.20(2-1) = 0.20%.

Therefore, the yield on a 2-year Treasury note would be:

Yield = Real risk-free rate + Inflation rate + Maturity risk premium

= 3% + 4% + 0.20%

= 7.30%

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The statement "I estimate that the probability of my getting married in the next 3 years is 0.7" does make sense.

As individuals, we can make personal estimates or predictions about events that are relevant to our lives, such as the probability of getting married in a certain timeframe. These estimates are based on our own subjective beliefs, experiences, and expectations. While they may not be based on precise mathematical calculations or rigorous statistical analysis, they can still reflect our personal opinions or perceptions.

In this case, the person is providing an estimate that they believe there is a 0.7 (or 70%) probability of getting married within the next 3 years. This estimate is a subjective assessment of their own chances based on various factors such as their current relationship status, personal goals, or cultural norms.

It is important to note that personal estimates like this are not necessarily based on concrete evidence or universally applicable probabilities. They can vary greatly from person to person and are subjective in nature. However, they can still hold personal meaning and influence one's decision-making or expectations regarding future events.

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Answer:

3/8 of an inch

Step-by-step explanation:

3/16 + 2/16 + 1/16 = 6/16 = 3/8 inch

Answer:

3/8 inch

Step-by-step explanation:

So we know there are 6 nickels and we know the height of one nickel: 1/16

So 6*1/16 = 6/16 = 3/8

Answer:

f(x)<7

Step-by-step explanation:

y=−2(|x2−3|)+7

y=−2(|x2−3|)+7

Answer:

1/36

Step-by-step explanation:

since a dice has 6 side and you want to get the probability of one of the dice it would be 1/6. But you have 2 dice and you need them both to have a 4.so you would need to multiply 1/6 by 1/6.

Im pretty sure this is right, its been a while since i did probability, but i hope this helps :)

The probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19.

The probability of picking a green ball on the first pick, given that at least one red is chosen, can be calculated by finding the total number of possible outcomes and then dividing by the number of outcomes that include at least one red ball. In this bag, there are 11 green balls and 5 red balls, for a total of 16 balls. Since two balls are taken out successively without replacement, the total number of outcomes is 16 choose 2, or 120. Of those, there are 10 outcomes that include at least one red ball, so the probability of picking a green ball on the first pick, given that at least one red is chosen, is 11/19. This can be calculated by dividing the number of outcomes that include at least one red ball (10) by the total number of outcomes (120).

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To determine which payment plan the real estate investor would prefer, we need to compare the present value of each payment option. Assuming a discount rate of 0%, meaning no time value of money is considered, we can directly compare the payment amounts.

1. Payment of $2,000 at the first of each month: This results in a total payment of $24,000 over the 12-month lease.

2. Upfront payment of $24,000: This option requires paying the full amount at the beginning of the lease.

3. Payment of $2,000 at the end of each month: Similar to option 1, this results in a total payment of $24,000 over the 12-month lease.

4. Upfront payment of $12,000 and $12,000 half-way through the lease: This option requires paying $12,000 at the beginning of the lease and another $12,000 halfway through the lease.

Since all the payment options have a total cost of $24,000, the real estate investor would likely prefer the payment plan that offers more flexibility or matches their cash flow preferences. Options 1 and 3 provide the investor with the option to pay monthly, while options 2 and 4 require a larger upfront payment. The choice would depend on the investor's financial situation and preferences.

Ashley used 8/25 of the spool for her project.

To determine the fraction of the spool that Ashley used for her project, we need to multiply the fraction of the spool she had (4/5) by the fraction she used (2/5):

(4/5) * (2/5) = 8/25

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Using translation concepts, the graph that shows that function f(x) = x with an input of f(x - 3) is given by:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

The input of the function, of f(x - 3), is missing.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, the function is:

f(x) = x.

The translation is in the input, f(x - 3), meaning that the function is shifted 3 units right and defined by:

f(x - 3) = x - 3.

Hence three points on the graph are:

Hence the correct description is:

A coordinate plane with a line passing through (negative 2, negative 5), (0, negative 3), and (3, 0).

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Answer:

D

Step-by-step explanation:

Answer:

square

Step-by-step explanation:

a square is a quadrilateral which means it has four sides

Answer:

square

Step-by-step explanation:

Answer:

5 hours and 30 minutes

Step-by-step explanation:

Convert all fractions to decimals for easier division

9 and 5/8 = 9.625

1 and 3/4 = 1.75

Then divide 9.625 by 1.75 to get the hours amount

9.625 / 1.75 = 5.5

0.5 of an hour is 30 minutes, so the final answer is 5 hours and 30 minutes

Answer:

5.5 hours

Step-by-step explanation:

9.625/1.75=5.5hr

Answer:-2x=y

4x+10y=16

2x+5y-8=0

x=4

Answer is x=4

Step-by-step explanation:

Answer: \(25 \frac{31}{63}\)

Step-by-step explanation:

The picture in this scenario is simply a rectangle.  The area of a rectangle is length * width.  Thus, simply multiply the two provided values.

3 1/7 = 22 / 7

8 1/9 = 73 / 9

\(\frac{22}{7} *\frac{73}{9} = \frac{1606}{63}\)

1606/63 = 25 31/63

Hope it helps and let me know if you want me to elaborate :)

Answer:

The answer you're looking for is 1470.

Step-by-step explanation:

The method I used was PEMDAS

Since there was no parenthesis, I simplified the exponents.

2.130 x 10³ - 6.6 x 10² = ?
2.130 x 1000 - 6.6 x 100 = ?

After that, I multiplied all terms next to each other.

2.130 x 1000 - 6.6 x 100 = ?
2130 - 660 = ?

The final step I did was to subtract the two final terms and ended up with 1470 as my final answer.

1470 = ?

I hope this was helpful!

The amount of money that Alex originally had would be = £8.4

To calculate the original amount of money that Alex has, the following should be carried out;

Th coins owned by Alex is arranged in piles of coins.

The quantity of coins in piles that is owed by Alex = 2 pence.

Half of the pile of coin = £4.20 = 10 pence.

The original amount she owns = 2 × 4.20 = £8.4

Therefore, the original amount of money that is owned by Alex would be = £8.4

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Gordon Driving School's net capital spending for 2012 was $0.125 million. To calculate the net capital spending, we determine the change in net fixed assets and subtract the depreciation expense.

To calculate the net capital spending for Gordon Driving School in 2012, we need to determine the change in net fixed assets and account for depreciation expense.

Net capital spending represents the net investment in fixed assets during a specific period.

Given that the net fixed assets in 2011 were $1.42 million and in 2012 were $1.69 million, we can calculate the change in net fixed assets:

Change in net fixed assets = Net fixed assets in 2012 - Net fixed assets in 2011

                         = $1.69 million - $1.42 million

                         = $0.27 million

Next, we need to consider the depreciation expense for 2012, which was $145,000.

Depreciation expense represents the allocation of the cost of assets over their useful life.

To calculate the net capital spending, we subtract the depreciation expense from the change in net fixed assets:

Net capital spending = Change in net fixed assets - Depreciation expense

                   = $0.27 million - $145,000

                   = $0.125 million

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Answer:

y=bc-abx

Step-by-step explanation:

Given the equation ax + y/b = c, the first thing you'd want to do is isolate the variable that you are trying to solve for.

To do this, you must first subtract ax from both sides, to leave y/b by itself on one side of the equation, resulting in:

y/b = c - ax

Now all you need to do to isolate y, and you can do so by multiplying both sides by b, cancelling out y being divided by b.

b(y/b) = b(c - ax)

y = b(c - ax)

To simplify and fit one of the answer choices, you simply distribute b via multiplication to both c and -ax:

y = bc - abx

Answer: it is 197 and the second one is 985 feet

Step-by-step explanation:

Answer:

first number is 197 feet and second one is 985 feet.

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