A statistics professor plans classes so carefully that the lengths of her classes are uniformly distributed between 48.048.0 and 53.053.0 minutes. Find the probability that a given class period runs between 50.550.5 and 51.7551.75 minutes.

Answer:

Her employer should withhold from her check for social security is d) 26.01

Step-by-step explanation:

Given:

Kate Alexander worked 40 hours last week. Her pay rate is $8.50 per hour. Assuming 7.65% social security withholding.

Now, to find the amount her employer should withhold from her check for social security.

Total number of hours = 40.

Pay rate per hour = $8.50.

Now, the total amount of total number of hours she worked in accordance of her pay rate:

[tex]40\times 8.50\\\\=\$340.[/tex]

Social security withholding = 7.65%.

So, to get the amount of social security withholding:

[tex]7.65\%\ of\ \$340[/tex]

[tex]=\frac{7.65}{100} \times 340[/tex]

[tex]=\frac{2601}{100}[/tex]

[tex]=\$26.01.[/tex]

The amount of social security withholding is $26.01.

Therefore, her employer should withhold from her check for social security is d) 26.01

The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously.

The given information can be translated into equations:

1. "The difference of the product of 10 and (x) and the product of 6 and y is -8":

[tex]\[10x - 6y = -8\][/tex]

2. "The sum of the product of -5 and x and the product of 3 and y is -1":

[tex]\[-5x + 3y = -1\][/tex]

Now, we have a system of two equations with two variables:

[tex]\[ \begin{cases} 10x - 6y = -8 \\ -5x + 3y = -1 \end{cases} \][/tex]

Let's solve this system step by step:

Step 1: Eliminate one variable from one of the equations.

Multiply the second equation by 2 to make the coefficients of [tex]\(y\)[/tex] in both equations opposites:

[tex]\[ \begin{cases} 10x - 6y = -8 \\ -10x + 6y = -2 \end{cases} \][/tex]

Now, add the two equations to eliminate [tex]\(y\)[/tex]:

[tex]\[ 0 = -10 \][/tex]

The result is a contradiction, indicating that the system is inconsistent. This means there is no solution that satisfies both equations simultaneously.

Conclusion:

The system of equations is inconsistent, meaning there is no solution for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] that satisfies both equations simultaneously. The given information might contain an error or contradiction. Please double-check the equations and conditions provided.

Answer:

0.0865

Step-by-step explanation:

Binomial Problem with n = 9 and p(triggered) = 0.99

And the photo below is the full answer,

I could not insert the fomula and hope it will find you well.

Answer:

30,000 phone numbers.

Step-by-step explanation:

If the first three numbers are already defined then it means that only the other 4 digits remain to be defined.

The solution would be the number of numbers between 0000 and 9999, because the order here matters, since each number is different.

Therefore between these two numbers there are a total of 10,000 numbers, that is to say that for each of the three initial numbers there are 10,000 numbers, therefore in the town there are a total of 30,000 numbers.

Final answer:

The small town has 30,000 available telephone numbers.

Explanation:

To calculate the number of available telephone numbers in the small town, we need to consider that local phone numbers have seven digits, with the first three being the telephone exchange numbers. The town uses three different telephone exchanges: 313, 359, and 387. Since the last four digits of a phone number can range from 0000 to 9999, that means there are 10,000 possible combinations for the last four digits.

Since there are three possible telephone exchanges, each with 10,000 combinations for the remaining four digits, we calculate the total number of available phone numbers by multiplying the number of exchanges by the number of combinations per exchange:

Number of exchanges x 10,000 (combinations per exchange) = Total number of phone numbers

3 x 10,000 = 30,000

Therefore, the small town has 30,000 available telephone numbers.

Step-by-step explanation:

The total number of members in the crew  = 20

The number of people able to use meat machine  = 17    ⇒n (M)  = 17

The number of people able to use bread machine  = 18  ⇒n (B)  = 18

The number of people able to use both machine  = 15 ⇒n (M∩B)  = 15

Now, a person is chosen at random:

Let us assume the number of people who cannot use either machine = K

Now,as we know:

[tex]n(A\cup B) = n(A) + n(B) - n(A\cap B)[/tex]

So, the number of people who can use either of the machines  

=n (M) + n(B)  -  n(M∩B)  = 17 + 18 - 15  = 20

So, there are 20 people who can use either of the two machines.

Also, as given the total number of people in the crew = 20.

Hence, from the above statement it is clear that there exists no person who can not use either of the machines.

So, such probability = 0

Answer:

A = $822 + $4.49r

Step-by-step explanation:

The question asks to know the equation that describes how much spent in the first six months and also the cost of the home theater.

Firstly, the equation asks to represent the total amount spent by A. She spent $4.49 per rental and made a total of r rentals in the first six months, thus, the total amount of money she spent on rentals is thus 4.49 * r = $4.49r. Now, she also spends $12/month as membership charges. The total membership charges in the first 6 months is thus 6 * 12 = $72

Lastly, she bought the home theater itself $750. Thus, the total amount of money spent A is $750 + $72 + $4.49r

This translates to $822 + $4.49r

In equation form, A = $822 + $4.49r

The statement that is: a. ∠1 and ∠5 are alternate interior angles.

What is the alternate interior angles ?

A pair of angles that are inside the two parallel lines and on opposing sides of the transversal line are known as alternate internal angles. 1 and 5 are situated on opposite sides of the transversal line and inside the parallel lines in the diagram. They are thus different internal angles.

The fact that alternate inner angles have the same measure and are congruent is significant.

Therefore the correct option is A.

Answer:

The correct option is A. 18x - 6y = 20

Step-by-step explanation:

A system of two equations has no solution if the lines having these equations are parallel to each other.

Also, two lines [tex]a_1x+b_1y=c_1[/tex] and [tex]a_2x+b_2y=c_2[/tex] are parallel,

If [tex]\frac{a_1}{a_2}=\frac{b_1}{b_2}\neq \frac{c_1}{c_2}[/tex]

While,

They coincide ( infinitely many solution ) if [tex]\frac{a_1}{a_2}=\frac{ b_1}{b_2}=\frac{c_1}{c_2}[/tex],

They are non parallel ( a unique solution ) if [tex]\frac{a_1}{a_2}\neq \frac{ b_1}{b_2}\neq \frac{c_1}{c_2}[/tex],

Here, the given equation,

-9x + 3y = 12

Since in lines -9x + 3y = 12 and 18x - 6y = 20,

[tex]\frac{-9}{18}=\frac{3}{-6}\neq \frac{12}{20}[/tex]

Hence, system −9x + 3y = 12, 18x - 6y = 20 has no solution.

In lines -9x + 3y = 12 and 3x - y = -4,

[tex]\frac{-9}{3}=\frac{3}{-1}= \frac{12}{-4}[/tex]

Hence, system −9x + 3y = 12, 3x - y = -4 has infinitely many solutions.

In lines -9x + 3y = 12 and  -16x + 9y = 30 ,

[tex]\frac{-9}{-16}\neq \frac{3}{9}\neq \frac{12}{30}[/tex]

Hence, system −9x + 3y = 12,  -16x + 9y = 30  has a solution.

In lines -9x + 3y = 12 and 5x + 8y = -1,

[tex]\frac{-9}{5}\neq \frac{3}{8}\neq \frac{12}{-1}[/tex]

Hence, system −9x + 3y = 12, 5x + 8y = -1 has a solution.

Answer:

There are 48 girls at the banquet

Step-by-step explanation:

Let the number of boys =x

Let the number of girls=y

Ratio Of boys to girls=5:3

Therefore, x:y=5:3......(1)

If 20 boys leave, the ratio becomes 5:4

Sine number of boys=x

If 20 boys leave, new number = x-20

Therefore, x-20:y=5:4......(2)

From (1),

3x=5y

From Equation (2),

4(x-20)=5y

Therefore: 3x=4x-80

x=80

From (1),

3x=5y

5y=3X80

y=240/5=48

Therefore, there are 48 girls at the banquet

Question:

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.

Answer:

The fraction of a chocolate bar will Nick and Tasha will use in total if they each eat one s'more is [tex]\frac{9}{10}[/tex] bar.

Step-by-step explanation:

Here, we are meant to learn how to add fractions and to know about the essence of a common denominator

The portion of the chocolate that Nick makes an s'more with is 1/2

The portion of the chocolate that Tasha makes an s'more with is 2/5

Therefore the fraction of the chocolate bar Nick and Tasha use in total if they each eat one s'more is 1/2 + 2/5

Where [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{5}[/tex]  multiplying the fraction [tex]\frac{1}{2}[/tex] by [tex]\frac{5}{5}[/tex] and  [tex]\frac{2}{5}[/tex]  by  [tex]\frac{2}{2}[/tex] wee have

[tex]\frac{5}{5}[/tex]× [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{2}[/tex]× [tex]\frac{2}{5}[/tex]  =   [tex]\frac{5}{10}[/tex] +  [tex]\frac{4}{10}[/tex] =  [tex]\frac{9}{10}[/tex] bar

Therefore the fraction of the chocolate bar that would be left is

1 bar -  [tex]\frac{9}{10}[/tex] bar = [tex]\frac{1}{10}[/tex] bar.

Here is the complete question

Nick and Tasha are buying supplies for a camping trip. They need to buy chocolate bars to make s’mores, their favorite campfire dessert. Each of them has a different recipe for their perfect s’more. Nick likes to use 1/2 of a chocolate bar to make a s’more. Tasha will only eat a s’more that is made with exactly 2/5 of a chocolate bar.

Answer:

Both Nick and Tacha will use 9/10 of the chocolate bar

Step-by-step explanation:

Nicks share of the chocolate bar is 1/2(fraction of the chocolate bar need to make the s'more

And Tasha requires 2/5 to make her own s'more.

Then if both of them share a single chocolate bar,then it will be:

2/5(Tasha's share) + 1/2(Nick's share)

= 9/10 of a single chocolate bar will be used.

In case they were interested to know the amount remaining, it will be:

1 - 9/10 = 1 1/10

Answer:

The answer to the question is

The kinds of polygons that could be Diedre's quadrilateral are rectangle and square

Step-by-step explanation:

We  note the conditions of the polygon as thus

Number of sides = 4, Which include trapezoid, square, rectangle

Size of angles = 90 ° which eliminates trapezoid

Sizes of opposite sides = Equal opposite sides, includes square and rectangle

With the above we conclude that the possible polygons in Diedre's quadrilateral are rectangle and square

From the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

It is given that:

Death Valley CA is 282 feet below sea level.

Black Mountain, KY is 750 feet above sea level.

Death Valley (282ft) + 282ft = sea level (0).

0 + 750ft = Black Mountain (750ft).

282ft + 750ft = 1032ft.

From Death Valley to Black Mountain, it rises 1032 feet. Death Valley is 1032 ft lower than Black Mountain in elevation.

Thus, from the Death Valley to Black Mountain, it rises 1032 feet because Death Valley is 1032 ft lower than Black Mountain in elevation.

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Answer:

The vectors r and  p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.

Step-by-step explanation:

The dot product of r and p

r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0

The solution is in the attachment

Answer: The test statistic is t= -0.90.

Step-by-step explanation:

Since we have given that

n₁ = 50

n₂ = 25

[tex]\bar{x_1}=3.02\\\\\bar{x_2}=3.04\\\\\sigma_1=0.08\\\\\sigma_2=0.06[/tex]

So, s would be

[tex]s=\sqrt{\dfrac{n_1\sigma_1^2+n_2\sigma_2^2}{n_1+n_2-2}}\\\\s=\sqrt{\dfrac{50\times 0.08^2+25\times 0.06^2}{50+25-2}}\\\\s=0.075[/tex]

So, the value of test statistic would be

[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{s(\dfrac{1}{n_1}+\dfrac{1}{n_2})}\\t=\dfrac{3.02-3.04}{0.074(\dfrac{1}{50}+\dfrac{1}{25})}\\\\t=\dfrac{-0.04}{0.074(0.02+0.04)}\\\\t=\dfrac{-0.04}{0.044}\\\\t=-0.90[/tex]

Hence, the test statistic is t= -0.90.

Answer:

Number of ways to select 3 cars and 4 trucks = 18,480

Step-by-step explanation:

Let x be the number of ways to select 3 cars and 4 truck.

Given:

Total number of cars = 8

Total number of Trucks = 11

We need to find out how many ways can the inspector select 3 cars and 4 truck.

Solution:

Using combination formula.

[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]

Where, n = Total number of object.

m = Number of selected object.

We need to find out how many ways can the inspector select 3 cars and 4 truck from 8 cars and 11 trucks.

So, we write the the combination as given below.

[tex]8C_{3}\times 11C_{4} = Number\ of\ ways\ to\ selection[/tex]

[tex]\frac{8!}{3!(8-3)!} \times \frac{11!}{4!(11-4)!}= x[/tex]

[tex]x = \frac{8\times 7\times 6\times 5!}{3!\times 5!} \times \frac{11\times 10\times 9\times 8\times 7!}{4!\times 7!}[/tex]

Factorial 5 and 7 is cancelled.

[tex]x = \frac{8\times 7\times 6}{6} \times \frac{11\times 10\times 9\times 8}{24}[/tex]                     ([tex]3! = 6\ and\ 4! = 24[/tex])

[tex]x = (8\times 7) \times (11\times 10\times 3)[/tex]                ([tex]\frac{9\times 8}{24}=\frac{72}{24}=3[/tex])

[tex]x=56\times 330[/tex]

x = 18480

Therefore, the Inspector can select 3 cars and 4 trucks in 18,480 ways,

To determine how many ways the state inspector can select 3 cars from 8 and 4 trucks from 11, we need to calculate the combinations separately for each type of vehicle and then multiply them together to find the total number of ways to make both selections simultaneously.
### Selection of Cars:
The number of ways to choose 3 cars from 8 is a combination problem, because the order in which we select the cars does not matter. The formula for combinations, denoted as C(n, k), where n is the total number of items to choose from, and k is the number of items to be chosen, is given by:
C(n, k) = n! / (k! * (n - k)!)
Let's apply this formula to select 3 cars from 8:
C(8, 3) = 8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 × 7 × 6) / (3 × 2 × 1)
Simplify the factorials by canceling out common terms:
C(8, 3) = (8 × 7 × 6) / (3 × 2 × 1) = (8/2) × (7/1) × (6/3) = 4 × 7 × 2 = 56
So, there are 56 ways to choose 3 cars out of 8.
### Selection of Trucks:
Similarly, to choose 4 trucks out of 11 we use the combination formula again:
C(11, 4) = 11! / (4! * (11 - 4)!) = 11! / (4! * 7!) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1)
Simplify the factorials:
C(11, 4) = (11 × 10 × 9 × 8) / (4 × 3 × 2 × 1) = (11/1) × (10/2) × (9/3) × (8/4) = 11 × 5 × 3 × 2 = 330
So, there are 330 ways to choose 4 trucks out of 11.
### Total Ways:
To find the total number of ways to select both the cars and trucks for inspection, we multiply the number of ways to choose the cars by the number of ways to choose the trucks:
Total number of ways = number of ways to choose cars × number of ways to choose trucks
Total number of ways = 56 (from choosing cars) × 330 (from choosing trucks)
Total number of ways = 56 × 330 = 18480
Therefore, the state inspector can select 3 cars out of 8 and 4 trucks out of 11 in 18,480 different ways.

Answer:

c=f(x)−ax^2−bx

Step-by-step explanation:

Answer:

C=1

Step-by-step explanation:

Put the first point in the equation y=ax^2+bx+c where x=0 and y=1 you get

1=a*0+b*0+c

1=c

Final answer:

The result of multiplying −3y by the polynomial (5y³+11y²−y+8) is −15y⁴ − 33y³ + 3y² − 24y when expressed in standard form.

Explanation:

To multiply the expression −3y(5y³+11y²−y+8), we will distribute the −3y across each term inside the parentheses. The process involves the use of the distributive property, often also known as the multiplication of polynomials. Here are the steps:

Multiply −3y by 5y³ to get −15y⁴.

Multiply −3y by 11y² to get −33y³.

Multiply −3y by −y to get 3y².

Multiply −3y by 8 to get −24y.

Combining all these products gives us the expression in standard form:

−15y⁴ − 33y³ + 3y² − 24y

Answer:

12.9

Step-by-step explanation:

AB = [tex]\sqrt{2^{2}+3^{2} }[/tex] = [tex]\sqrt{13}[/tex]

BC = [tex]\sqrt{2^{2}+2^{2} }[/tex] = [tex]2\sqrt{2}[/tex]

CD = [tex]\sqrt{1^{2}+2^{2} }[/tex] = [tex]\sqrt{5}[/tex]

DE = 3

EA = [tex]\sqrt{1^{2} + 2^{2} }[/tex] = [tex]\sqrt{5}[/tex]

The sum of all of these (in decimal form) is (approx.) 12.9

Answer:

13.9 units

Step-by-step explanation:

AB = sqrt(2² + 3²) = sqrt(13)

BC = sqrt(2² + 2² = sqrt(8)

CD = sqrt(1² + 2²) = sqrt(5)

DE = 3

EA = sqrt(1² + 2²) = sqrt(5)

Add all these:

13.9 units

Answer:

The number of ways of selection of 3 items taking 2 at a time in addition to the possible ways in which each girl selects the same style is 9 different ways. Since the list contains 9 different ways in which each of them can select a style, the list is complete.

Step-by-step explanation:

Here we have the number of ways the available styles can be arranged between each girl is given by the number of permutation of 3 items, taking two at a time plus the number of possible selections where both of them select the same style as follows

We note that the formula for permutation is

[tex]_n[/tex]P[tex]_r[/tex] = [tex]\frac{n!}{(n-r)!}[/tex]

Therefore ₃P₂ = [tex]\frac{3!}{(3-2)!}[/tex] = 6 different ways

The number of possible selections where both of them select the same style is given by

(T, T), (s, s), (L, L) = 3 different ways

Total number of ways = 6 + 3 = 9 ways

Number of different ways available in the list = 9 ways

Therefore the list is complete

Answer:

niglgapopfart

Step-by-step explanation:

12(5)6$78$???98

Answer:

8.899s

Solve: -5t^+40t+40

4-2√2 is the time taken by the ball to hit the ground.

Distance is the total movement of an object without any regard to direction

Given that Abraham throws a ball from a point 40 m above the ground. The height of the ball from the ground level after ‘t' seconds is defined by the function h(t) = 40t – 5t². then we need to find the time for ball to hit the ground.

The given function is

h(t)=40t-5t²

Let h(t)=40

We get,

40t-5t²=40

5t²-40t+40=0

t²-8t+8=0

(t-4)²=8

t-4=±√8

t=±√8+4

t=√8+4; t=4-√8

By considering the reality we know t>0

t=4-2√2

Hence  t=4-2√2 is the time taken by the ball to hit the ground.

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Answer:

The answer to your question is C and D are parallel  

                                                    B and C  and B and D are perpendiculars.

Step-by-step explanation:

Data

Line A         (-2, 3)    (2, 2)

Line B         (-3, 0)    (3, -2)

Line C         (2, 4)      (0, -2)

Line D         (0, 6)      (-2, 0)

Process

1.- Calculate the slope of each line

    m = (y2 - y1)/(x2 - x1)

Line A   m = (2 - 3) / (2 + 2)

             m = -1/4

Line B = (-2 - 0) / (3 + 3)

          = -2/6

          = -1/3

Line C = (-2 -4)/(0 - 2)

           = -6/-2

           = 3

Line D = (0 - 6) / (-2 - 0)

           = -6/-2

           = 3

2.- Conclusion

If the slopes are the same, the lines are parallel if are reciprocal, the lines are perpendicular

Line C ║ Line D

Line B ⊥ Line C    and Line B ⊥ Line D

Answer: 14x² - 4x - 17

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

The rectangular back yard measures 5x + 4 by 3x - 2. This means that the area of the rectangular back yard would be

Area = (5x + 4)(3x - 2)

Area = 15x² - 10x + 12x - 8

= 15x² + 2x - 8

The formula for determining the area of a square is expressed as

Area = length²

Length of square patio = x + 3

Area of square patio = (x + 3)(x + 3)

= x² + 3x + 3x + 9

= x² + 6x + 9

The expression for the area of grass that will be left in the back yard after the patio is built is

15x² + 2x - 8 - (x² + 6x + 9)

= 15x² + 2x - 8 - x² - 6x - 9

= 15x² - x² + 2x - 6x - 8 - 9

= 14x² - 4x - 17

Answer:

1/216

Step-by-step explanation:

n{1111,2222,3333,4444,5555,6666}=6

number of every cases =6×6×6×6

6/6^4=1/6^3=1/216

Answer:

 1/216.

Step-by-step explanation:

The probability that all the 4 dice will show a 1 = (1/6)^4.

There  are also 5 other possible outcomes: 4 2's , 4 3's etc.

So the required probability = 6 * (1/6)^4

= 6 * 1/1296

=  1/216.

Answer:

0.2696

Step-by-step explanation:

Number of People who responded Yes=175

Number of People who responded No=474

Total Number of Respondents=175+474=649

We want to determine the Probability that a person chosen at random believes that psychic can help solve murder cases.

Now,

[TeX]Probability=\frac{Number of Possible Outcome}{Total Number of Outcomes}[/TeX]

Number who believe psychic can help solve murder cases=175

Total Number=649

Therefore:

P(a person chosen at random person believes some psychics can help solve murder cases) = [TeX]\frac{175}{649}=0.2696[/TeX]

Final answer:

The probability that a randomly chosen person believes some psychics can help solve murder cases is 175 divided by the total number of respondents (649), resulting in approximately 26.96%.

Explanation:

The question asks for the probability that a chosen person believes some psychics can help solve murder cases, given that out of a group, 175 said 'Yes' and 474 said 'No'. To find this probability, divide the number of people who believe psychics can help (175) by the total number of people asked (175 + 474).

Steps to Calculate the Probability:

Calculate the total number of responses: 175 (Yes) + 474 (No) = 649.

Calculate the number of positive responses (people who believe psychics can help): 175.

Divide the number of positive responses by the total number of responses: Probability = 175 / 649.

Perform the division to get the probability.

Therefore, the probability that a person chosen at random believes some psychics can help solve murder cases is 175/649 or approximately 0.2696, which can be expressed as 26.96%.

Answer:

Step-by-step explanation:

PV =  $2500

r = 6%

Compounded semi annually for ten years => number of periods: 10*2 = 20

a.  the balance of account at end of peroid (FV)

FV = PV [tex](1+r)^{n}[/tex] = 2500[tex](1+0.06)^{20}[/tex] = 8017.8386

b. How much interest is earned; FV - PV = 8017.8386 - 2500 = 5517.8686

c. what is effective rate of interest :

Answer:

The answers to the question are

a) The balance of account at end of period $4515.278

b) The interest earned $2515.278

c) The effective rate of interest is 0.0609 or 6.09 %

Step-by-step explanation:

To solve the question

a) Here we have the compound interest formula given by

[tex]A = P(1+\frac{r}{n})^{nt}[/tex] Where,

P = Initial investment =  $2500

r = Annual interest rate = 6% =0.06

n = Number of compounding periods per year = 2

t = Number of years 10

From which we have

[tex]A = 2500*(1+\frac{0.06}{2})^{2*10}= 2500(1.03)^{20}[/tex] = $4515.278

The balance of account at end of period $4515.278

b) Interest earned = Balance -  initial investment = $4515.278 - $2500 = $2515.278

c)

The effective interest rate is the interest rate that accrues to an investment or loan as a result of the compounding the interest for a given time period of time. It is also known as the effective annual interest rate

The effective rate of interest is given by

Effective rate = [tex](1+\frac{r}{n} )^n -1[/tex]Where

r = Annual interest rate

n = Number of annual compounding periods

this gives [tex](1+\frac{0.06}{2} )^{2} -1[/tex] =  0.0609 = 6.09 %

Answer:

HOPE U UNDERSTOOD

MARK AS BRAINLIEST ONE

Any doubts? please COMMENT

Answer:

1224 cm^3

Step-by-step explanation:

The shape of the box is a rectangular prism.

The volume of a rectangular prism is given by the formula below.

volume = length * width * height

volume = 10.2 cm * 15 cm * 8 cm

volume = 1224 cm^3

Final answer:

The volume of a shoebox with dimensions 10.2 cm x 15 cm x 8 cm is calculated by multiplying these three dimensions together, resulting in a volume of 1224 cm³.

Explanation:

To calculate the volume of a shoebox, you multiply its length by its width by its height. For a shoebox with dimensions of 10.2 cm, 15 cm, and 8 cm, the calculation would look like this:

Volume = Length × Width × Height

Volume = 10.2 cm × 15 cm × 8 cm

Volume = 1224 cm³

Therefore, the volume of the shoebox is 1224 cubic centimeters.

Answer:

x  = 12  hours

Step-by-step explanation:

If one pipe fills store pool in 12 hours   in 1 hour will fill 1/12 of the pool

If one pipe fills a store pool in 6 hours in 1 hour will fill 1/6 of the pool

Let call " x " number of hours needed by the third pipe to fills the pool

then in 1 hour  will fill 1/x

The three pipes working together in 1 hour will fill

1/12  +  1/6  + 1/x

Now we know that the three pipes take 3 hours to fill the pool then in 1 hour three pipes will fill 1/3 of the pool, therefore

1/12  +  1/6  + 1/x  = 1/3

( x + 2*x + 12) /12*x  = 1/3   ⇒ ( 3*x +12 )/ 12*x = 1/3

9*x  + 36  = 12*x

- 3*x  = - 36

x  = 36/3

x  = 12  hours

Final answer:

The third pipe, when operating alone, takes 12 hours to fill the pool. This is found by calculating the combined rate of the first two pipes, then the rate of all three, and deducting to find the third pipe's alone rate.

Explanation:

The question asks how long it takes for a third pipe to fill a pool when utilized alongside two other pipes, where one fills the pool in 12 hours, another in 6 hours, and all three together in 3 hours. This is a rate of work problem, commonly encountered in algebra and practical mathematics. To solve, we first find the rates at which each individual pipe fills the pool and then calculate the third pipe's rate.

Determine the rate at which each pipe fills the pool. The first pipe fills the pool at a rate of 1/12 of the pool per hour, and the second at 1/6 of the pool per hour.

Add these rates to determine the combined rate when the two pipes are working together: (1/12) + (1/6) = 1/12 + 2/12 = 3/12 = 1/4. So, the two pipes fill the pool at a rate of 1/4 of the pool per hour together.

When the third pipe is added, all three fill the pool in 3 hours, which means their combined rate is 1/3 of the pool per hour. The rate of the third pipe alone can be found by subtracting the rate of the first two pipes from this combined rate: (1/3) - (1/4) = 4/12 - 3/12 = 1/12.

Therefore, the third pipe fills the pool at a rate of 1/12 of the pool per hour on its own. To find the time it takes for the third pipe to fill the pool by itself, we take the reciprocal of its rate, resulting in 12 hours.