19. The mass of a radioactive element is 35
milligrams. The mass of the element decreases by
12.9% every year.
a. Write a function that represents this situation.
b. Predict the mass of the element in 4 years. Round
your answer to the nearest tenth.
c. Will the mass of the radioactive element ever be 0
milligrams? Explain.

The value of 10p - 3p/4- 2 +5 for p=10 is 95.5.

An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.

Given:

We have 10p - 3p/4- 2 +5.

Now put the value of p =10 we get

= 10p - 3p/4- 2 +5

= 10(10) - 3(10)/4- 2 +5

= 100 - 30/4 -2 + 5

= 100 -7.5 -2 +5

= 95.5

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The correct answers are given below:

(a) 1 to 55

(b) 40%

Since Mansour scores 55% of his kicks, we'd want exactly 55% of the simulated numbers to denote Mansour scoring a penalty, thus, 1 to 5 is a possible range.

To find the percentage of trials where Mansour scored exactly one penalty, we have to count the trials where one of the simulated numbers is in the range of 1 to 5 (denoting Mansour scoring the penalty) and the other is in the range of 56 to 100 (denoting Mansour missing the penalty)

Trails 1, 3, and 4, 6 are such trials. Thus, Mansour scored exactly one penalty kick in 40% of the trials.

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Answer:

Step-by-step explanation:

A) In a geometric sequence, t_(1)=625 and the common ratio is r=(1)/(5). For what value of n is t_(n)=(1)/(25)?

Step 1: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 2: Substitute the given values into the formula

t_n = 625 * (1/5)^(n-1)

Step 3: Solve for n when t_n = (1/25)

(1/25) = 625 * (1/5)^(n-1)

(1/25) / 625 = (1/5)^(n-1)

(1/5)^(n-1) = (1/25) / 625

(n-1) = log base (1/5) of ((1/25) / 625)

Step 4: Solve for n

n = 1 + log base (1/5) of ((1/25) / 625)

The value of n is the number of terms that have passed when t_n = (1/25).

B) (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Step 1: Determine the type of sequence

A sequence is an arithmetic sequence if the difference between any two consecutive terms is constant. Since this sequence does not have a constant difference, it is not an arithmetic sequence.

A sequence is a geometric sequence if the ratio between any two consecutive terms is constant. We can see that the ratio between any two consecutive terms is constant, so this sequence is a geometric sequence.

Step 2: Find the common ratio

To find the common ratio, we can divide any two consecutive terms. For example, the common ratio is (3/6) / (2/5) = (3/2) / (6/5) = 5/6.

Step 3: Write the formula for the nth term

The formula for the nth term of a geometric sequence is t_n = t_1 * r^(n-1), where t_1 is the first term and r is the common ratio.

Step 4: Substitute the given values into the formula

To use this formula, we need to know the value of t_1. We are given t_1 = (2/5), so:

t_n = (2/5) * (5/6)^(n-1)

This is the formula for the nth term of the sequence (2)/(5),(3)/(6),(4)/(7),(5)/(8),...

Answer:

10 minutes

Step-by-step explanation:

1/4 in 2 minutes

1 1/4 = 1/4 x 5

2 x 5 = 10

(That's REALLY good honestly)

Answer:

The island is 728 feet off the coast.

Step-by-step explanation:

Answer:

The difference in height is 8cm

Step-by-step explanation:

Volume of a cylinder=hπr²

When the bottle is full 5652:

5652=hπr²

5652=h*3.14*7.5²

5652=h*176.625

5652/176.625=h

Height=32cm

When the bottle is full by 4239:

4239=hπr²

4239=h*3.14*7.5²

4239=h*176.625

4239/176.625=h

Height=24cm

Difference in height:

32-24=8

The difference in height is 8cm

The height of the object at a time of 2 seconds is given as follows:

1106 feet.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The function for this problem is defined as follows:

h(t) = -16t² + 1170.

At a time of 2 seconds, the height is found replacing the lone instance of t by two, hence:

h(2) = -16(2)² + 1170

h(2) = 1106 feet.

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The slope is 2.5

The y-intercept is 5.8.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

y = 5.8 + 2.5x

This is in the form of y = mx + c

So,

m = 2.5

And,

The y-intercept is when x = 0.

So,

y = 5.8 + 2.5x

Substitute x = 0,

y = 5.8

Thus,

Slope is 2.5

The y-intercept is 5.8.

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Answer:

It will turn on again, just charge it. All phones come with a charger.

Answer: 9/4

Step-by-step explanation:

A scale factor is the number by which all components of an object are multiplied in order to create a proportional enlargement or reduction.

The option that was not an impact of the crusades is B. End of the Roman Empire.

The Crusades were a series of religious wars fought between Christians and Muslims in the Middle East during the medieval period. The Crusades had a significant impact on European society and culture, including:

Monarchs grew more powerful: The Crusades helped to strengthen the power of monarchs in Europe, as they became more involved in financing and organizing the Crusades.

However, the Crusades did not bring about the end of the Roman Empire. The Roman Empire had already collapsed centuries earlier, in the 5th century AD, and the Crusades took place in the 11th-13th centuries AD, during the medieval period.

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Answer:

The percentage of students in Kiri's brother's class who think aliens exist is 11/25 = 44%.

Since the number of students in Kiri's class is not given, it's not possible to compare the percentage of students in Kiri's class who think aliens exist to the percentage in her brother's class. We need to know the number of students in Kiri's class and the number of students who believe in aliens in order to compare the percentages.

Mortgage B requires $27,336.60 more interest than mortgage A. The solution has been obtained by using arithmetic operations.

What are arithmetic operations?

There are four fundamental mathematical operations that can be used to express any real number; these are referred to as "arithmetic operations." The four operations are multiplication, division, addition, and subtraction.

We are given the principal amount as $80,000.

So, interest on Mortgage A = Total amount payable - principal amount

Interest = $110,158.20 - $80,000

Interest = $30,158.20

Similarly, interest on Mortgage B = Total amount payable - principal amount

So,

Interest = $137,494.80 - $80,000

Interest = $57,494.80

So, difference in interest = $57,494.80 - $30,158.20 = $27,336.60

Hence, mortgage B requires $27,336.60 more interest than mortgage A.

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The interest for the first quarter would be $ 15

The value of the CD when it matures is $ 2, 030. 11

The interest is said to compound quarterly which means that the periodic interest rate per quarter is:

= 3 % / 4

= 0. 75 % per quarter

The interest in the first quarter :

= 0. 75 % x 2, 000

= $ 15

The value of the CD at maturity is:

= 2, 000 x ( 1 + 0. 75% ) ²

= $ 2, 030. 11

Note : 2 periods because 6 months is 2 quarters.

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Answer:

Answer is in the attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note the perimeter of the rectangle is:

2 x Length + 2 x Width.

Answer:

2 x Length + 2 x Width.

Step-by-step explanation:

The average velocity, to the nearest hundredth, of a ceiling tile that fell 43 feet is 344 feet per second

Velocity is the pace and direction of an item's movement, whereas speed is the time rate at which an object is travelling along a route.

Given that the formula for the speed of a falling object is v= √64d,

where v is the speed of the object in feet per second and d is the distance the object has fallen, in feet.

And also given that d = 43 feet.

Substituting the value to the formula,

v = √64 (43)

v = 8 x 43

v = 344

Therefore, 344 feet per second is the velocity.

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Answer:

y = ( x - 4 )² - 4

Step-by-step explanation:

a² ± 2ab + b² = ( a ± b )²

~~~~~~~~~~~~

y = x² - 8x + 12

y = ( x² - 2(4)(x) + 4² ) - 4² + 12 = ( x - 4 )² - 4

y = ( x - 4 )² - 4

The solution to the equation 4x² = 16 is x = 2.

Given the equation in the question;

4x² = 16

x = ?

To solve for x, first divide both terms by 4.

4x² = 16

4x²/4  = 16/4

x² = 4

Take the square roots of both sides

√x² = ±√4

x = ±2

x = -2 or 2.

Therefore, the value of x is 2.

Option D)2 is the correct answer.

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Answer:

D.2

Step-by-step explanation:

[tex]4 {x}^{2} = 16 \\ \frac{4 {x}^{2} }{4} = \frac{16}{4} \\ {x}^{2} = 4 \\ \sqrt{ {x}^{2} } = \sqrt{4} \\ x = \sqrt{4} \\ x = 2[/tex]

Answer:

3,291 pints used

Step-by-step explanation:

There are 8 pints in a gallon

Started with 412 gallons, multiply that by 8 to get 3,296 pints

At the end of day, he only had 5

So we can subtract 5 from the 3,296 that he started the day with, and we get the answer of 3,291 used throughout the day.

By subtraction we get that, Isabel has to pour 35.25 grams of salt into the container.

The operation or process of finding the difference between two numbers or quantities is known as subtraction. To subtract a number from another number is also referred to as 'taking away one number from another'.

According to the information in question:

Total salt = 90.45 grams

Amount of salt poured = 55.2 grams

Thus, the total amount of salt left with her which has to be poured will be calculated by subtraction:

Amount of salt left = 90.45 - 55.2

                               = 35.25 grams

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The discount on each orange is 81.3%

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

A sales discount is a reduced price offered by a business on a product or service.

The total price for the oranges is;

0.75 × 7 = $5.25

She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95

Therefore the percentage discount on all the oranges = 0.95/5.25 × 100

= 18.1%

by discount each orange = 4.30/7 =$ 0.61

Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %

Therefore the discount on each orange is 81.3%

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The probability distribution does not add up to 1.0, in other words.

The complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

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Answer:

It is not accurate

Step-by-step explanation:

If the complete question is:

A researcher records the number of mistakes made during a memory skills task. He finds that the probability that participants in this study made 0 mistakes is p = .22; made 1 mistake is p = .30; made 2 mistakes is p = .16; made 3 mistakes is p = .12; and made 4 or more mistakes is p = .25. Is this probability distribution accurate?

THEN:

To determine whether the probability distribution is accurate, we need to check two conditions:

The sum of the probabilities should be equal to 1.

All probabilities should be between 0 and 1.

Let's check these conditions:

Sum of probabilities:

p(0) + p(1) + p(2) + p(3) + p(4 or more) = 0.22 + 0.30 + 0.16 + 0.12 + 0.25 = 1.05

The sum of the probabilities is greater than 1, which violates the first condition. Therefore, this is not a valid probability distribution.

All probabilities should be between 0 and 1:

The probability of making 0, 1, 2, or 3 mistakes are all between 0 and 1, so they satisfy this condition.

However, the probability of making 4 or more mistakes is 0.25, which is a valid probability, but it implies that the probability of making 0, 1, 2, or 3 mistakes is negative, which is impossible. Therefore, this distribution does not satisfy this condition.

Since this probability distribution violates both conditions for a valid probability distribution, it is not accurate, and the researcher should revise their data.

Answer:     [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300} } } )[/tex]

Step-by-step explanation:

[tex]P=\frac{22}{100} =0.22, n=300[/tex]     [tex]q=1-p=0.78[/tex]

[tex]p' = \frac{27}{100}=0.27[/tex]

[tex]p(z > \frac{p'-p}{\sqrt{\frac{p*q}{n} } } )[/tex]

 [tex]p(z > \frac{0.27-0.22}{\sqrt{\frac{(0.22)(0.78)}{300}} }[/tex]

The solution of the logarithm expression  logₐ 60 is 2.1. Therefore, the answer is D.

The logarithm expression can be solved as follows; Using the logarithm rule,

Law of multiplication of logarithm,

logₐ x + logₐ y = logₐ xy

Therefore,

logₐ 2 = 4

logₐ 3 = 5

logₐ 5 = 8

Hence, let's find logₐ 60.

logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60

Hence,

0.8 + 0.5 + 0.4 + 0.4 = 2.1

Therefore,

logₐ 60 = 2.1

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The value of log a 60 is 21. The correct option is D.

Logarithms are another way of writing exponents.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

log a 60 = log a (12 x 5)

log a 60 = log a 12 x log a 5

log a 60 = log a (4 x 3) x log a 5

log a 60 = log a 4 x log a 3 x log a 5

log a 60 = 2 log a 2 x log a 3 x log a 5

Substituting the values for the logs

log a 60 = 2 (4) + 5 + 8

log a 60 = 21

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Answer:

x = 50 tablets

Step-by-step explanation:

Ket's call the number of tablets taken in a week "x".

A typical dose for a 100-pound person is 22 mg every six hours, so in 24 hours, they would take 22 mg * 24 hours / 6 hours = 88 mg.

In one week, they would take 88 mg * 7 days = 616 mg.

And since each tablet is 12.3 mg, they would take 616 mg / 12.3 mg/tablet = 50 tablets in a week.

So the answer is x = 50 tablets.

If the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] then the value is 1.22222

The term "numerical evidence" describes information that is expressed in a numerical manner, such as numbers, quantities, or statistical data. It is thought to be objective and quantifiable, and it is used to support a claim or argument.

The quantity of sales made during a specific business quarter is an example of numerical data. Simply put, if the response includes a number, the data is quantitative (numerical).

Let the equation be [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex]

Simplifying the above equation, we get

[tex]$\frac{x^2-x-30}{x^2-3 x-18}= \frac{x+5}{x+3}$[/tex]

[tex]$=\lim _{x \rightarrow 6}\left(\frac{x+5}{x+3}\right)$$[/tex]

Plug in the value x = 6

= (6 + 5)/(6 + 3)

= 11/9 = 1.22222

Therefore, the equation of [tex]$\lim _{x \rightarrow 6}\left(\frac{x^2-x-30}{x^2-3 x-18}\right)$$[/tex] be 1.22222.

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Answer:

the scale factor that Samir used in his drawing is 5/1.

Step-by-step explanation:

Here's a step by step explanation of how to find the scale factor of a drawing:

Identify the scale used in the drawing. In this case, the scale used in Samir's drawing is 5 inches = 1 yard.

Express the scale as a ratio between the two sizes. In this case, the ratio is 5 inches : 1 yard.

Simplify the ratio, if possible. In this case, the ratio 5 inches : 1 yard can be simplified to 5/1.

The simplified ratio, 5/1, is the scale factor of the drawing. This means that for every 5 inches on the drawing, the actual length in the real world is 1 yard.

So, the scale factor that Samir used in his drawing is 5/1.

Answer:

14v-2

Step-by-step explanation:

1. distribute

2. combine like terms

see photo for more information

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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Answer:

50 + 5x^2 + 4x.

Step-by-step explanation:

To find the sum of the expressions, we need to simplify each expression first and then add them up.

10 + 3x represents the first expression.

25 - 4x + 2x^2 represents the second expression. By simplifying this expression, we get 25 + 2x^2 - 4x.

3x^2 - 5x represents the third expression.

-x^2 + 2x + 15 represents the fourth expression.

Adding all four expressions gives us:

10 + 3x + 25 + 2x^2 - 4x + 3x^2 - 5x - x^2 + 2x + 15

By combining like terms, we get:

10 + 5x^2 + 4x + 25 + 15

The final simplified sum is:

50 + 5x^2 + 4x.