The mathematics faculty at a college consists of 4 ​professors, 5 associate​ professors,  6 assistant​ professors, and 8 instructors. If one faculty member is randomly​ selected, find the probability of choosing a professor or an instructor.

a) When the interest rate is increased by 1%, the simple interest increases from $180 to $240, a difference of $60.

b) When the time (period) is increased by 1 year, the simple interest increases from $180 to $216, a difference of $36.

Simple interest is the interest system that does not compute interest on the accumulated interest.

Unlike the compound interest system, simple interest calculates interest on the principal for each period.

Interest rate = 3%

Principal deposit = $1,200

Investment period = 5 years

Simple interest at 3% = Principal x Rate x Time

= $180 ($1,200 x 3% x 5)

Simple interest at 4% = Principal x Rate x Time

= $240 ($1,200 x 4% x 5)

Simple interest at 3% = Principal x Rate x Time

= $216 ($1,200 x 3% x 6)

Simple interest at 4% = Principal x Rate x Time

= $288 ($1,200 x 4% x 6)

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Increasing the interest rate from 3% to 4% on a $1200 deposit for 5 years raises the simple interest from $180 to $240, while extending the time from 5 to 6 years at the initial rate results in a raise from $180 to $216 in simple interest.

Understanding Simple Interest with Changes in Rate and Time

Simple interest is calculated by multiplying the principal amount, the interest rate, and the time the money is borrowed or invested. Using the provided example, if you deposit $1200 at a simple interest rate of 3% for 5 years, the interest is calculated as follows:

$1200 times 0.03 times 5 = $180

If the interest rate increases by 1%, the new interest rate becomes 4%. Thus, the simple interest for the increased rate is:

$1200 times 0.04 times 5 = $240

Therefore, an increase of 1% in the interest rate raises the simple interest earned from $180 to $240, an increase of $60.

If the time is increased by 1 year while keeping the original interest rate of 3%, the new time period is 6 years. The simple interest for the increased time is:

$1200 times 0.03 times 6 = $216

Extending the time by 1 year increases the total simple interest from $180 to $216, which is an extra $36 earned.

Answer:

75% of the planets have moons

Step-by-step explanation:

In order to calculate this you just have to do a simple rule of three, in which you will use 888 as the 100 percent and you want to discover what percentage of that does 666 represents:

[tex]\frac{888}{100} \frac{666}{x} \\x=\frac{666*100}{888}\\ x=75\\[/tex]

So you have that 666 is the 75% of 888, that means that 75% of the planets have moons.

Using the Empirical Rule, it is determined that 95% of students are likely to get a GRE score between 350 and 650, and 50% of students will get a score above 500.

According to the Empirical Rule (also known as the 68-95-99.7 Rule), about 95% of the values in a data set with a normal distribution will fall within two standard deviations of the mean. In this case, the mean GRE score is 500 and the standard deviation is 75. Using this rule, we can determine that 95% of the students would likely score between 500 - (2 imes 75) and 500 + (2 imes 75), equating to scores between 350 and 650.

Regarding the percentage of students that will get a score above 500, the distribution is symmetric around the mean in a normal distribution. Since the mean is 500, 50% of the values will lie above the mean and 50% will lie below. Therefore, 50% of students are expected to score above 500.

The eighteenths of 2/3 is 12/18.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

let,

2/3 = n/18

What is the GCF of 3 and 18

3: 1,3

18: 1,2,3,6,9,18

GCF-3

Therefore, 2/3 = 12/18

because 3 × 6= 18

what you do to the denominator you have to do the numerator

so 2 × 6= 12.

hence, eighteenths of 2/3 is 12/18.

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Answer:

the answer is a

Step-by-step explanation:

The exponential equation that models the number of bacteria in hours is N = 8000 * (1 + 0.125)^t. The doubling time of the bacteria is 5.55 hours.

To find an exponential equation that models the number of bacteria in hours, we can use the formula: N = N0 * (1 + r)^t.

Where:

Plugging in the values, we have:

9000 = 8000 * (1 + r)^1

Dividing both sides by 8000, we get:

1.125 = 1 + r

Subtracting 1 from both sides, we find:

0.125 = r

Therefore, the exponential equation that models the number of bacteria in hours is: N = 8000 * (1 + 0.125)^t.

To find the doubling time of the bacteria, we can use the formula: t = log(2)/log(1 + r).

Plugging in the value of r (0.125), we have:

t = log(2)/log(1 + 0.125)

Using a calculator, we find that t is approximately 5.5452 hours. Rounded to the nearest 0.01 hours, the doubling time of the bacteria is 5.55 hours.

Answer:

f(x)=45x

Step-by-step explanation:

if the home is 495 miles away, 11 hours would take to drive home.

f(11)=45X11=495

56.69 - 0.145(56.69)

= 56.69 - 8.22

= 48.47

the formula for discount price

Subtract the final price from the original price. Divide this number by the original price. Finally, multiply the result by 100. You've obtained a discount in percentages.

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Answer:

45

Step-by-step explanation:

We know that,

If we have the numbers of the form xyz.

This gives that, x is placed at the hundredth place, y is placed at the tens place and z is located at ones place.

Since, we need a number between 20 and 50 having both tens and ones place.

We can take any number from 20 to 50.

For e.g. Let us take 45.

In 45, 4 is placed at the tens place and 5 is placed at the ones place.

Hence, 45 is the number between 20 to 50 having both tens and ones place.

The logistic function is [tex]S[/tex] shaped curve which use to determine the statistical distribution over the energy states of a system.

The time will take for 2,700 student to hear the rumor is 2.495 days.

Given:

The given logistic function is,

[tex]R(t)=\frac{3000}{1+Be^{kt}}[/tex]

As per the question, at initial stage 5 students heard the rumor. At initial stage [tex]t=0[/tex].

Calculate the constant [tex]B[/tex] at initial stage.

[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(0)=\frac{3000}{1+Be^{k\times 0}}\\R(0)=\frac{3000}{1+B}[/tex]

Substitute [tex]R(0)=5[/tex].

[tex]\begin{aligned}5=\frac{3000}{1+B}\\1+B= \frac{3000}{5}\\B=599\\\end[/tex]

As per the question, after 1 day 149 students heard the rumor. After 1 day stage [tex]t=1[/tex].

[tex]R(t)=\frac{3000}{1+Be^{kt}}\\R(1)=\frac{3000}{1+Be^{k\times 1}}\\R(1)=\frac{3000}{1+B^k}[/tex]

Substitute [tex]R(1)=149[/tex] and [tex]B=599[/tex].

[tex]\begin{aligned}149=\frac{3000}{1+599e^k}\\e^k=\frac{(3000-1149)}{(599)(149)} \\\end{aligned}[/tex]

Calculate the time take to hear rumor by 2,7000 students.

[tex]\begin {aligned}2700=\frac{3000}{1+599(\frac{3000-149}{599\times 149})^t }\\\frac{3000}{2700}-1 =599(\frac{3000-149}{599\times 149})^t }\\t=\frac{ln(\frac{1}{(599)(9)})}{ln(\frac{3000-149}{599\times 149}) }\\t=2.495\:\rm days\\\end{aligned}[/tex]

Thus, the time will take for 2,700 student to hear the rumor is 2.495 days.

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The lengths of the three wire pieces are 20 cm for the first piece, 60 cm for the second piece, and 120 cm for the third piece.

A wire that is 200 cm long is cut into three pieces.

We are told that the second piece is 3 times as long as the first piece and the third piece is 2 times as long as the second piece.

Let's denote the first piece's length as x centimeters.

According to the problem, the second piece will then be 3x centimeters long, and the third piece will be 2 * 3x = 6x centimeters long.

To find the length of each piece, we need to set up the following equation based on the total length of the wire:

x + 3x + 6x = 200

Combining terms, we have:

10x = 200

Dividing both sides by 10, we find:

x = 20

Therefore, the first piece is 20 cm long, the second piece is 3 * 20 cm = 60 cm long, and the third piece is 6 * 20 cm = 120 cm long.

Jamal use 1/2 yards of ribbon

Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. How many yards of ribbon did Jamal use?

Jamal used 1/3 yard of ribbon to tie a package and 1/6 yard of ribbon to tie a bow. Therefore the total of ribbon Jamal used is:

[tex]\frac{1}{3} + \frac{1}{6} = \frac{2}{6} +\frac{1}{6}= \frac{3}{6} or \frac{1}{2}[/tex] yards of ribbon

How many yards of ribbon did Jamal use? Jamal use 1/2 yards of ribbon

The yard (yd) is English unit of length comprises 3 feet or 36 inches. It is by international agreement standardized as exactly 0.9144 meters. Yard is defined as a measurement of length that equals 3 feet or 36 inches. An example of a yard is the length measurement that is used to sell fabric.

A ribbois a thin band of material, typically cloth but also plastic or sometimes metal, used as decorative binding and tying.

We also can draw 1/3 yard of ribbon as 33.333% of all yards, and 1/6 as 16.6666% of all yards as shown in the picture below.

Grade:  5

Subject:  math

Chapter:  yards

Keywords:   ribbon, yard, package, bow, tie

Final answer:

At an interest rate of 2%, below the equilibrium rate of 5%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers and reach the equilibrium.

Explanation:

If the equilibrium interest rate in the money market is 5%, then at an interest rate of 2%, sellers of interest-bearing financial assets would need to raise interest rates to find willing buyers. This situation outlines how the market responds when the interest rate is below the equilibrium level. If the interest rate is below equilibrium, there is an excess demand for financial capital; too many borrowers and not enough lenders at this low rate. To attract more lenders (sellers of financial assets), the interest rate would need to be increased. Conversely, when the interest rate is above the equilibrium, there is an excess supply, meaning there are more suppliers of loans than there are borrowers. Sellers in this scenario lower interest rates to attract more borrowers, bringing the market back to equilibrium.

This concept is parallel to the example where, at an interest rate of 21%, the supplied funds increase greatly while the demand falls sharply, leading to excess supply. Suppliers of financial capital, such as credit card companies, will then reduce their rates to encourage more borrowing, pushing the interest rate back toward the equilibrium. In the case of a government borrowing increase, if it leads to a higher demand for financial capital, this would cause the demand curve to shift to the right and result in a higher interest rate, potentially crowding out private investment.

there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.

To determine the number of ways the three men and four women can stand in line at the checkout counter if we only consider their gender, we can use the concept of permutations.

There are 3 men and 4 women, so there are a total of (3 + 4 = 7) people in line.

We need to arrange these 7 people in a line. Since the order matters, we use permutations.

The number of ways to arrange (n) objects is given by (n) (n factorial).

So, the number of ways the 7 people can stand in line is [tex]\(7\).[/tex]

[tex]\[ 7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040 \][/tex]

Therefore, there are 5040 ways for the three men and four women to stand in line at the checkout counter if we only consider their gender.

Answer with explanation:

Number of Envelopes possessed by the person = 6

Probability of selecting an Envelope is equal to [tex]/frac{1}{6}[/tex].

It is given that,three envelopes contains $ 533 check and another 3 Envelope contain $ 1039 check.We can consider that any of three checks contain $ 533 and another three $ 1089.

Expectation

[tex]E(x)=x_{1}p_{1}+x_{2}p_{2}+x_{3}p_{3}+x_{4}p_{4}+x_{5}p_{5}+x_{6}p_{6}\\\\\frac{1}{6} \times [533+533+533+1039+1039+1039]\\\\=\frac{1}{6} \times [4716]\\\\=786[\tex]

E(x)=786