A bank features a savings account that has an annual percentage rate of r=4.5r=4.5% with interest compounded semi-annually. Monique deposits $2,000 into the account.

The account balance can be modeled by the exponential formula S(t)=P(1+rn)ntS(t)=P(1+rn)nt, where SS is the future value, PP is the present value, rr is the annual percentage rate, nn is the number of times each year that the interest is compounded, and tt is the time in years.

(A) What values should be used for PP, r, and nn?

P=, r=, n=

(B) How much money will Monique have in the account in 9 years?

Answer = $ .

Round answer to the nearest penny.
(C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year).

APY= %.

Round answer to 3 decimal places.

According to the given figure, minor arc RS, diameter RT, chord PS, central angle QTR, major arc QRS, semicircle QRP, and radius RT

What is a major and minor arc?

An arc is a portion of the circumference of a circle. It is a curve that connects two points on the circumference.  A major arc is an arc that measures more than 180 degrees, which is greater than a semi-circle. It covers more than half of the circumference of the circle. A minor arc is an arc that measures less than 180 degrees, which is less than a semi-circle. It covers less than half of the circumference of the circle.

If the angle formed by the two points and the center is less than 180 degrees, then it is a minor arc. Conversely, if the angle formed is greater than 180 degrees, then it is a major arc.

In summary, a major arc covers more than half of the circumference of the circle and measures more than 180 degrees. A minor arc covers less than half of the circumference of the circle and measures less than 180 degrees.

1. Minor arc RS

2. Diameter RT

3. Chord PS

4. Central angle QTR

5. Major arc QRS

6. Semicircle QRP

7. Radius RT

To know more about major & minor arcs visit:

brainly.com/question/9785690

#SPJ1

Given:

The inequality is

\(q+12-2(q-22)>0\)

To find:

The solution of the given inequality.

Solution:

We have,

\(q+12-2(q-22)>0\)

It can be written as:

\(q+12-2q+44>0\)

\((q-2q)+(12+44)>0\)

\(-q+56>0\)

Subtract 56 from both side.

\(-q>-56\)

Multiply both sides by -1 and change the inequality sign.

\(q<56\)

Therefore, the correct option is D.

Answer:

Step-by-step explanation:

Answer:

first evening = 21 phone calls

second evening = 11 phone calls

third evening = 84 phone calls

Step-by-step explanation:

Total phone calls = 116

Let

Number of calls in the first evening = x

The second evening = x - 10

The third evening = 4x

Total phone calls = first evening + second evening + third evening

116 = x + (x - 10) + 4x

116 = x + x - 10 + 4x

116 + 10 = 6x

126 = 6x

x = 126 / 6

x = 21 phone calls

Number of calls in the first evening = x

= 21 phone calls

The second evening = x - 10

= 21 - 10

= 11 phone calls

The third evening = 4x

= 4(21)

= 84 phone calls

Answer:

160 degrees

Step-by-step explanation:

To change from radians to degrees, multiply by 180 / pi

8 pi/9 * 180/pi

160 degrees

Using Poisson distribution formula;

a. The probability of receiving exactly ten request with a 2 hour period is 9.9%.

b. The probability the operator does not miss any call for assistance is 13/5%

c. We expect 2 calls during the break.

d. The probability that 10 of them arrived within that period is 10.4%

(a) To compute the probability of receiving exactly ten requests during a particular 2-hour period, we can use the Poisson probability formula. For a Poisson process with rate λ, the probability of observing exactly k events in a given time interval is given by:

\(P(X = k) = (e^(^-^\lambda^) * \lambda^k) / k!\)

In this case, the rate λ is 4 requests per hour, and the time interval is 2 hours. Therefore, the average number of requests in a 2-hour period would be λ = 4 * 2 = 8.

Using k = 10 and λ = 8 in the formula, we have:

P(X = 10) = (e⁻⁸ * 8¹⁰) / 10!

Calculating this expression, we find the probability of exactly ten requests during the 2-hour period.

P(X = 10) = 0.099

P(X = 10) = 9.9%

(b) If the operators take a 30-minute lunch break, the probability that they do not miss any calls for assistance can be calculated by considering the probability that no calls occur during that 30-minute period.

The average number of requests in a 30-minute interval would be λ = 4 * 0.5 = 2. Therefore, using the Poisson probability formula, we can find the probability of no requests during this interval:

P(X = 0) = (e⁻² * 2⁰) / 0!

P(X = 0) = 0.135 = 13.5%

This probability represents the likelihood that no calls occur during the 30-minute lunch break.

(c) To determine the expected number of calls during the operators' 30-minute lunch break, we can use the average rate of requests per hour and adjust it for the 30-minute duration. The average rate is 4 requests per hour, which corresponds to 4/2 = 2 requests per 30 minutes. Therefore, we can expect approximately 2 calls during their break.

(d) If 30 requests were received between 10 a.m. and 5 p.m., and we want to determine the likelihood that 10 of them arrived between 2 p.m. and 5 p.m., we can use the Poisson distribution again.

First, we need to calculate the average number of requests during the 3-hour period from 2 p.m. to 5 p.m. The average rate is 4 requests per hour, so the average number of requests during this period would be λ = 4 * 3 = 12.

Using k = 10 and λ = 12 in the Poisson probability formula, we can find the probability of exactly 10 requests during the 3-hour period.

P(X = 10) = (e⁻¹² * 12¹⁰) / 10!

P(X = 10) = 0.105 = 10.5%

This probability represents the likelihood that 10 requests arrived between 2 p.m. and 5 p.m.

Learn more on Poisson distribution here;

https://brainly.com/question/30388228

#SPJ4

Answer:

I think that the front one would be D) 20

Step-by-step explanation:

It is 4 times bigger than the smaller one so it is 20

Answer:

2 x 6 x 3.14 = 37.68

Arrays are used to represent data sets in rows and columns

The librarian could use 3 and 18 as a factor pair

The number of books is given as:

n = 54

Express 54 as a product of two numbers

54 = (1, 54), (2, 27),(3, 18) and (6, 9).

From the options, we have the following factor pair

3 and 18

Hence, the librarian could use 3 and 18 as a factor pair

Read more about factor pairs at:

https://brainly.com/question/3074301

The range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

To measure the amount of money college students spend on rent per month, the most appropriate measure of spread would be the range. The range is the simplest measure of spread and is calculated by subtracting the lowest value from the highest value in a data set. In this case, the range would be $1,300 - $300 = $1,000.

The median would not be the best choice in this scenario because it only represents the middle value in a data set. It does not take into account extreme values like the $1,300 rent expense.

Standard deviation would not be the most appropriate measure of spread in this case because it calculates the average deviation of each data point from the mean. However, it may not accurately represent the spread when extreme values like the $1,300 rent expense are present.

The interquartile range (IQR) would not be the best choice either because it measures the spread of the middle 50% of the data set. It does not consider extreme values and would not accurately represent the range of rent expenses in this scenario.

In summary, the range would be the most appropriate measure of spread in this case because it takes into account the extreme values of $300 and $1,300 and provides a clear measure of the difference between them.

Know more about Standard deviation here,

https://brainly.com/question/29115611

#SPJ11

Answer and Step-by-step explanation:

2(5x - 5) = 6x + 50

Distribute the 2 to the 5x and -5.

10x - 10 = 6x + 50

Add 10 to both sides, and subtract 6x from both sides.

4x = 60

Divide both sides by 4.

x = 15

5y + 5 = 7y - 9

Subtract 5 from both sides, and 7y from both sides.

-2y = -14

Divide both sides by -2.

y = 7

#teamtrees #PAW (Plant And Water)

Answer:

-8.4 is the answer.(cross multiply )

Answer:

p= -8.4

Step-by-step explanation:

cross multiply

p=-7* 1.2

p=-8.4000001

Answer:

9 cm

Step-by-step explanation:

Since PQ and RS are opposite each other, then in a parallelogram, the lengths will be congruent.

Therefore 2x+5=4x+1

2x=4

x=2

If you plug x=2 into the the original equation, you get 9 cm.

The measure of PQ is 9 centimeters.

Important information:

The oppositie sides of a parallelogram are equal.

\(PQ=RS\)

\(2x+5=4x+1\)

\(5-1=4x-2x\)

\(4=2x\)

Divide both sides by 2.

\(2=x\)

Now, find the measure of PQ.

\(PQ=2x+5\)

\(PQ=2(2)+5\)

\(PQ=4+5\)

\(PQ=9\)

Therefore, the measure of PQ is 9 centimeters.

Find out more about 'Parallelogram' here:

https://brainly.com/question/7099686

The matrix equation [4 5 40 - 9 - 5 27 1 - 7 32] can be written as a vector equation Ax = <40 27 32>

A matrix is a rectangular array of numbers, often denoted as Ax, where A is the matrix itself and x is the vector of numbers that make up the columns of the matrix.

In this problem, we are given the matrix equation 4 5 40 - 9 - 5 27 1 - 7 32 and asked to use the definition of Ax to write it as a vector equation.

To do this, we need to identify which numbers are in the matrix A and which numbers are in the vector x.

The numbers 4, 5, -9, -5, 1, and -7 represent the matrix A, while the numbers 40, 27, and 32 represent the vector x.

Therefore, the matrix equation can be written as Ax = 40 27 32.

To know more about matrix here.

https://brainly.com/question/28180105

#SPJ4

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.

Learn more about probability here:

https://brainly.com/question/31828911

#SPJ11

Answer:

4 km per hour

Step-by-step explanation:

Use the point (15,1)  Since the line is proportional, the slope is y/x or 1/15

1/15 this is in minutes

1/15 x 60/1  To convert  to hours

4 km per hour

Answer:

4 Km per hour

Step-by-step explanation:

average speed (S) is calculated as

S = \(\frac{D}{T}\) ( D is distance and T is time, in hours )

the distance ( vertical axis )  from her home to the newspaper shop is 1 Km

time ( horizontal axis )

from 09 00 to 09 30 has 6 divisions

then 1 division = 30 minutes ÷ 6 = 5 minutes

time to walk to the shop is 3 divisions = 3 × 5 = 15 minutes

15 minutes = \(\frac{15}{60}\) of an hour = \(\frac{1}{4}\) hour

then average speed from home to newspaper shop is

S = \(\frac{1}{\frac{1}{4} }\) = 4 Km per hour

Answer:

The average is 85

Step-by-step explanation:

In order to find the average, you add all the number and divide with the number of numbers:

76+85+97+82= 340

340/4= 85

Answer:

31.3 feet

Step-by-step explanation:

-23.6+13.4 = -10.2

-10.2 - 21.1 = -31.3

Answer:

31.3 feet

Step-by-step explanation:

0 -23.6 + 13.4 - 21.1 = -31.3

So to get back to sea level she must ascend 31.3 feet.

Answer:

27 people

Step-by-step explanation:

If 6 chairs are empty, that means 1/4 of the chairs is 6.

6*4 = 24, the total amount of chairs.

24 - 6 = 18, the number of chairs occupied.

If 18 people is 2/3 of the amount of people, if we divide 18 by 2, getting 9, that is 1/3 of the amount of people.

9 * 3 = 27, the total amount of people.

Answer:

Select all of the coefficients in the expression. 12xy^3+ 2x^5y +4x^5y^2 +7x^5y.

If we take an equation like 2xyz = 0 then,

The coefficient of x in 2xyz is term that is multiplied by x. so here the coefficient of x will be 2yz.

So here in the equation 12xy^3 +2x^5y +4x^5y^2 +7x^5y = 0 the coefficients will be:

First we take the common factor form the equation:

So we get form the equation is as ;

= xy * (12y^2 + 2x^4 + 4x^4y + 7x^4) so this basically represents multiplicative distribution law

if we simplify using exponent rule with same base

a^n . a^m = a^n+am

That is 12xy^(2+1) + 2x(4+1)y + 4x(4+1)y(1+1) + 7x(4+1)y

so,

12xy^3 +2x^5y +4x^5y^2 +7x^5y = 0

xy * (12y^2 + 2x^4 + 4x^4y + 7x^4) =0

So the coefficients are : xy and (12y^2 + 2x^4 + 4x^4y + 7x^4)

Know more about “coefficients in the expression” here: https://brainly.com/question/28316633

#SPJ4

Disclaimer: The question was given incomplete on the portal. Here is the complete question.

Question: Select all of the coefficients in the expression. 12xy^3+ 2x^5y +4x^5y^2 +7x^5y.

The coefficient in the expressions 12xy³, 2x⁵y, 4x⁵y²  and 7x⁵y. will be 12, 2, 4 and 7 respectively.

We are given the expressions:

12xy³

2x⁵y

4x⁵y²

7x⁵y.

We need to identify the coefficients for the expression.

For the expression 12xy³, the coefficient will be 12 as it is the numerical value written with the variable.

Similarly, for the expression 2x⁵y , the coefficient will be 2 for the variable x⁵y.

For the expression 4x⁵y², the coefficient will be 4 for the variable x⁵y².

For the expression 7x⁵y, the coefficient will be 7 for the variable x⁵y.

Therefore, we get that, the coefficient in the expressions 12xy³, 2x⁵y, 4x⁵y²  and 7x⁵y. will be 12, 2, 4 and 7 respectively.

Learn more about coefficients here:

https://brainly.com/question/4219149

#SPJ4

The number of horizontal asymptotes that a function can have depends on its behavior as x approaches positive or negative infinity.

a) If the function approaches a specific value or constant as x approaches positive or negative infinity, it can have 0 horizontal asymptotes.

b) If the function approaches the same value or constant as x approaches positive or negative infinity, it can have 1 horizontal asymptote.

c) If the function approaches different values or constants as x approaches positive or negative infinity, it can have 2 horizontal asymptotes.

d) It is not possible for a function to have exactly 3 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 4.

e) It is not possible for a function to have exactly 4 horizontal asymptotes. Asymptotes come in pairs, so the number of horizontal asymptotes can be 0, 1, 2, or 3.

the correct options are:

a) 0

b) 1

c) 2

d) 3

e) 4

To learn more about number visit:

brainly.com/question/3589540

#SPJ11

Answer:

Step-by-step explanation:

ol

To construct a truth table for the given logical expression using De Morgan's Law, we'll break it down step by step and apply the law to simplify the expression.

Let's start with the given expression:

Xyz + X(Y Z)' + X'(Y + Z) + (Xyz)' (X + Y')(X' + Z')(Y' + Z')

Step 1: Apply De Morgan's Law to the term (Xyz)'

(Xyz)' becomes X' + y' + z'

After applying De Morgan's Law, the expression becomes:

Xyz + X(Y Z)' + X'(Y + Z) + (X' + y' + z')(X + Y')(X' + Z')(Y' + Z')

Step 2: Expand the expression by distributing terms:

Xyz + XY'Z' + XYZ' + X'Y + X'Z + X'Y' + X'Z' + y'z' + x'y'z' + x'z'y' + x'z'z' + xy'z' + xyz' + xyz'

Now we have the expanded expression. To construct the truth table, we'll create columns for the variables X, Y, Z, and the corresponding output column based on the expression.

The truth table will have 2^3 = 8 rows to account for all possible combinations of X, Y, and Z.

Here's the complete truth table:

```

| X | Y | Z | Output |

|---|---|---|--------|

| 0 | 0 | 0 |   0    |

| 0 | 0 | 1 |   0    |

| 0 | 1 | 0 |   0    |

| 0 | 1 | 1 |   1    |

| 1 | 0 | 0 |   0    |

| 1 | 0 | 1 |   0    |

| 1 | 1 | 0 |   1    |

| 1 | 1 | 1 |   1    |

```

In the "Output" column, we evaluate the given expression for each combination of X, Y, and Z. For example, when X = 0, Y = 0, and Z = 0, the output is 0. We repeat this process for all possible combinations to fill out the truth table.

Note: The logical operators used in the expression are:

- '+' represents the logical OR operation.

- ' ' represents the logical AND operation.

- ' ' represents the logical NOT operation.

to know more about expression visit:

brainly.com/question/30091641

#SPJ11

Answer:

\(\left \{ {{p=3} \atop {q=1}} \right.\)

Step-by-step explanation:

First, we'll expand \((x-p)^2+q\). It's equal to \(x^2-2px+p^2+q\).

Then, we'll compare this to \(x^2-6x+10\).

Answer:

p = 3, q = 1

Step-by-step explanation:

Using the method of completing the square

add/ subtract ( half the coefficient of the x- term )² to x² - 6x

x² + 2(- 3)x + 9 - 9 + 10

= (x - 3)² + 1 ← in the form (x - p)² + q

with p = 3 and q = 1

Answer:4

Step-by-step explanation:ts is = ed

\({\large{\textsf{\textbf{\underline{\underline{Question \: 1 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\purple{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

2, 3, 4, 7, 9, 11

❍ Number of terms in data [n] = 6 which is even.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: even)} = {\underline{\boxed{\sf{\purple{ \dfrac{ { \bigg (\dfrac{n}{2} \bigg)}^{th}term +{ \bigg( \dfrac{n}{2} + 1 \bigg)}^{th} term } {2} }}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ { \bigg (\dfrac{6}{2} \bigg)}^{th}term +{ \bigg( \dfrac{6}{2} + 1 \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \dfrac{6 + 2}{2} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ \bigg( \cancel{ \dfrac{8}{2}} \bigg)}^{th} term } {2} }\)

\(\\\)

\( \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ {3}^{rd} term +{ 4}^{th} term } {2} }\)

• Putting,

3rd term as 4 and the 4th term as 7.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 4 + 7 } {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} ={ \dfrac{ 11} {2} }\)

\(\longrightarrow \: \sf Median_{(when \: n \: is \: even)} = \purple{5.5}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 2 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\red{Solution:}}}}}\)

❍ Arrange the given data in order either in ascending order or descending order.

1, 2, 3, 4, 5, 6, 7

❍ Number of terms in data [n] = 7 which is odd.

As we know,

\(\star \: \sf Median_{(when \: n \: is \: odd)} = {\underline{\boxed{\sf{\red{ { \bigg( \frac{n + 1}{2} \bigg)}^{th} term}}}}}\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = {{ \bigg(\dfrac{ 7 + 1 } {2} \bigg) }}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} = { \bigg(\cancel{\dfrac{8}{2}} \bigg)}^{th} term\)

\(\\\)

\( \sf Median_{(when \: n \: is \: odd)} ={ 4}^{th} term\)

• Putting,

4th term as 4.

\(\longrightarrow \: \sf Median_{(when \: n \: is \: odd)} = \red{ 4}\)

\(\\\)

\({\large{\textsf{\textbf{\underline{\underline{Question \: 3 :}}}}}}\)

\(\star\:{\underline{\underline{\sf{\green{Solution:}}}}}\)

The frequency distribution table for calculations of mean :

\(\begin{gathered}\begin{array}{|c|c|c|c|c|c|c|} \hline \rm x_{i} &\rm 3&\rm 1&\rm 7&\rm 4&\rm 6&\rm 2 \rm \\ \hline\rm f_{i} &\rm 4&\rm 6&\rm 2&\rm 2 & \rm 1&\rm 1 \\ \hline \rm f_{i}x_{i} &\rm 12&\rm 6&\rm 14&\rm 8&\rm 6&\rm \rm 2 \\ \hline \end{array} \\ \end{gathered} \)

☆ Calculating the \(\sum f_{i}\)

\( \implies 4 + 6 + 2 + 2 + 1 + 1\)

\( \implies 16\)

☆ Calculating the \(\sum f_{i}x_{i}\)

\( \implies 12 + 6 + 14 + 8 + 6 + 2\)

\(\implies 48\)

As we know,

Mean by direct method :

\( \: \: \boxed{\green{{ { \overline{x} \: = \sf \dfrac{ \sum \: f_{i}x_{i}}{ \sum \: f_{i}}}}}}\)

here,

• \(\sum f_{i}\) = 16

• \(\sum f_{i}x_{i}\) = 48

By putting the values we get,

\(\sf \longrightarrow \overline{x} \: = \: \dfrac{48}{16}\)

\(\sf \longrightarrow \overline{x} \: = \green{3}\)

\({\large{\textsf{\textbf{\underline{\underline{Note\: :}}}}}}\)

• Swipe to see the full answer.

\(\begin{gathered} {\underline{\rule{290pt}{3pt}}} \end{gathered}\)

Answer: 1/2

Step-by-step explanation: Never fear the great answerer is here!

Answer:

I think it's 8 or 1/2. not completely sure.

Answer:

9

Step-by-step explanation:

Mode: the value that occurs most frequently in a given set of data

9 has the most dots stacked up for the number of hours slept--

(in that particular data set)

Hope this made sense!