What is the length of the apothem of the regular pentagon shown below? Round to one decimal place

Total amount of money in the savings account after 11 weeks is $1310.

Total money in the account =

 Initial Money + Money added per week x Number of weeks

Given:

Initial Money = $650

Money added per week = $60

Total money in the account = S

Number of weeks = W

Substituting it in the above equation we get,

S = $650 + $60xW                                          (General Equation)

Total amount of money in the savings account after 11 weeks

S = $650 + $60x11

S = $650 + $660

S = $1310

Thus total amount of money in the savings account after 11 weeks is $1310.

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the range that would be the most appropriate to represent the numerical data on the vertical axis is B. 20 to 100.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

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The range that would be the most approx to represent the numerical data on the vertical axis is B. 20 to 100.

Bar graph :

Bar graphs are the pictorial representation of data (generally grouped), in the form of vertical or horizontal rectangular bars, where the length of bars is proportional to the measure of data

The range that would be the most approximately to represent the numerical data on the vertical axis is B. 20 to 100.

because

it is not possible to have zero number of cars that have a particular color,

in That way, we can eliminate options C and D .

in option A the range is too small which is not possible.

the table is not included but the range of 20 to 100 is most appropriate for the number of cars in town with a particular color.

this is because towns would normally have between hundreds and thousands of cars which means that cars of a particular color would be between 20 and 100 at least.

Using an exponential function, the expected mass of the sample in the year 2001 would be of 16 mg.

The function is:

[tex]A(t) = A(0)e^{-kt}[/tex].

In which:

The information given is as follows:

A(0) = 440, A(8) = 40.

Hence:

[tex]A(t) = A(0)e^{-kt}[/tex].

[tex]40 = 440e^{-8k}[/tex].

[tex]e^{-8k} = 0.09090909[/tex]

[tex]\ln{e^{-8k}} = \ln{0.09090909}[/tex]

[tex]-8k = \ln{0.09090909}[/tex]

[tex]k = -\frac{\ln{0.09090909}{8}[/tex]

k = 0.29973691

Then the function is:

[tex]A(t) = 440e^{-0.29973691t}[/tex]

2001 is 11 years after 1990, hence the amount is:

[tex]A(11) = 440e^{-0.29973691 \times 11} = 16[/tex]

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The equation between the number of days remaining and number of hours is given as y= -5x+50.

Let y be the number of days remaining and x be the no.of hours.

From the graph the slope of the line is given by m.

m=(y2 - y1)/(x2 - x1)

m=(30 - 40)/(4 - 2)

m= -10/2 = -5.

The above slope is in between points 2 and 4. As the line has a constant rate of growth the slope is the same between any points of the line.

Therefore the equation between the no.of days remaining and no.of hours is given by

y=mx +c.

y=-5x+c

Now to find the value of c. This can be determined by substituting the x and y values at a particular instant. For x=0,y=50. Therefore by these values, we get,

50= -5(0)+c

c=50.

Therefore the relation between the number of days remaining and number of hours is given as y= -5x+50.

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Considering the given graph, the meaning of point A is given by:

A can with an 11 cm diameter has an 18 cm height.

The graph gives the height of the can as a function of the diameter. Both measures are in cm. Then, the axis are given as follows:

Point A has coordinates (11,18), that is, x = 11, y = 18, hence the interpretation is:

A can with an 11 cm diameter has an 18 cm height.

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Answer:

A

Step-by-step explanation:

just took the quiz and can confirm the other guy is valid :D

-3x is a term in the expression -3x - 7(x+4)

The expression is given as:

-3x - 7(x+4)

Considering the following expression

Ax + B(x  - b)

The terms in the expressions are Ax and B(x  - b)

This means that -3x is a term in the expression -3x - 7(x+4)

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The province's population is growing at the rate of  58.34 %

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. The calculation for ROC is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

Given:

Initial Population = 4.2 million

Population after 20 years = 6.65 million

Change in population = 6.65 - 4.2 = 2.45 million

Rate at which the province's population growing is

= [tex]\frac{Change in population}{Inital Population}[/tex] x100 %

= [tex]\frac{2.45}{4.2}\\[/tex] x 100%

= 58.34 %

Thus the province's population is growing at the rate of  58.34 %

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Answer:

width = 34 inches

length = 16 inches

Step-by-step explanation:

Given:

1.)The length of a rectangle is two more than double the width

2.)The perimeter is 100 inches

Let's analyze the first part,

The length is 2 more than double the width so if we let x represent the length the width would be 2x + 2

Now the second part,

the perimeter is calculated by the following formula:

2*(w+l)

(w: width, l: length)

2*(x+2x+2) first do inside the parenthesis by adding like terms

x+2x+2 = 3x + 2 now multiply both terms with 2

2*(3x+2) = 6x + 4 this is the perimeter of the rectangle, now write another equation using this

6x + 4 = 100 subtract 4 from both sides

6x = 96 divide both sides by 6

x = 16 this the length and the width would be

2x + 2 = 2*16 + 2 = 34

The monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be better option.

Given that for $200,000 loan Option 1 is a 30-year loan at an APR of 10% Option 2 is a 15-year loan at an APR of 9.5%.

A concept that implies that the future value of money will be lower than its present value due to several factors such as inflation is known as TVM(time of value money).

Monthly Payments

Option 1

Loan Amount = $200,000

Number of payments = 30×12 = 360

Monthly interest rate = 10%/12 = 0.008333333

Monthly payment = Loan amount (1+ monthly interest rate)ⁿ×monthly interest rate/[(1+monthly interest rate)ⁿ- 1]

Monthly payment=200,000×(1+0.008333333)³⁶⁰×(0.008333333)/[(1+0.008333333)³⁶⁰-1]

Monthly payment=33062.328/18.83739

Monthly payment=$1755.144

Option 2

Loan Amount = $200,000

Number of payments = 15 x 12=180

Monthly interest rate = 9.5%/12=0.00792

Monthly payment = 200,000(1+0.00792)¹⁸⁰(0.00792)/[(1+0.00792)¹⁸⁰-1]

Monthly payment=6553.096/3.137

Monthly payment=$2088.97

Total Payments

Option 1

As we've found out the monthly payments, we now need to multiply it by the number of months.

$1755.144×360 = $631851.84

Option 2

$2088.97×180 = $376014.6

Conclusion

Option 2 will always be the better option economically as it saves $255837.24 ($631851.84 - $376014.6) in total payments.

Hence, For $200,000 loan Option 1 a 30-year loan at an APR of 10% Option 2 a 15-year loan at an APR of 9.5% is the monthly payment for option 1 is $1755.144 and option 2 is $2088.97, total amount for option 1 is $631851.84 and option 2 is $376014.6, and on comparing option 2 will be the better option.

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Using the given linear equation, we conclude that you can invite a maximum number of 21 guests.

Here the function is:

C(p) = 325 + 15*p

Where p is the number of guests minus 10, now we know that your budget is $600, then the maximum value of guests allowed is such that:

C(p) = 600 = 325 + 15*p

Now we can solve this equation for p:

600 - 325 = 15*p

275 = 15*p

175/15 = p = 11.67

Then the maximum whole number that p can take is p = 11

This means that the maximum number of guest that you can have is:

Guests = 10 + p = 10 + 11 = 21.

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Answer:

C

Step-by-step explanation:

x²-9x<-8

x²-9x+(-9/2)²<-8+(-9/2)²

(x-9/2)²<-8+81/4

(x-9/2)²<(-32+81)/4

(x-9/2)²<49/4

|x-9/2|<7/2

-7/2<x-9/2<7/2

add 9/2

9/2-7/2<x-9/2+9/2<7/2+9/2

2/2<x<16/2

1<x<8

Answer:

$4800

Step-by-step explanation:

Let's use the simple interest formula, P(1+rt), to find the final amount of the loan

10000(1+.12*4) = 14800, the final amount

14800 - 10000 = 4800 total in interest

The procedure for solving -275+156-(-293)-157 = 17 is to follow bodmas operation

-275+156-(-293)-157 = 17

Using BODMAS

-275+156-(-293)-157 = 17

= -275 + 156 + 293 - 157

= 17

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Step-by-step explanation:

Let take the first derivative

[tex] \frac{d}{dx} ln(x)) = x {}^{ - 1} [/tex]

The second derivative

[tex] - {x}^{ - 2} [/tex]

The third derivative

[tex]2 {x}^{ - 3} [/tex]

The fourth derivative

[tex] - 6 {x}^{ - 4} [/tex]

The fifth derivative

[tex]24 {x}^{ - 5} [/tex]

Let create a pattern,

The values always have x in it so

our nth derivative will have x in it.

The nth derivative matches the negative nth power so the nth derivative so far is

[tex] {x}^{ - n} [/tex]

Next, lok at the constants. They follow a pattern of 1,2,6,24,120). This is a factorial pattern because

1!=1

2!=2

3!=6

4!=24

5!=120 and so on. Notice how the nth derivative has the constant of the factorial of the precessor

so our constant are

[tex](n - 1)[/tex]

So far, our nth derivative is

[tex](n - 1)!x {}^{ - n} [/tex]

Finally, notice for the odd derivatives we are Positve and for the even ones, we are negative, this means we are raised -1^(n-1)

[tex] - 1 {}^{n -1} (n - 1) ! {x}^{-n} [/tex]

That is our nth derivative

Answer:

Step-by-step explanation:

hello :

(4a) × (3b)​ =12ab

Answer: (-4, 0)

Step-by-step explanation: I just took the quiz and got it correct!

The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval.

To determine the interval in which the function is constant, we need to examine the given ordered pairs (x, y) and check if the function's output (y-values) remains the same within that interval.

Let's analyze each interval:

1. (-4, 0): This interval represents all x-values greater than -4 and less than 0. In this interval, the function takes the value 0 for all x-values in the interval. Therefore, the function is constant (equal to 0) within this interval.

2. (4, ∞): This interval represents all x-values greater than 4. In this interval, the function's output is given as "∞" (infinity) for all x-values in the interval. The function is constant (equal to infinity) within this interval.

3. (0, 4): This interval represents all x-values greater than 0 and less than 4. In this interval, the function takes the value 4 for all x-values in the interval. Therefore, the function is constant (equal to 4) within this interval.

4. (-∞, -4): This interval represents all x-values less than -4. In this interval, the function's output is not specified or may not be constant. The information provided does not give us the exact function to determine the output for all x-values in this interval.

The function is constant on the intervals: (-4, 0), (4, ∞), and (0, 4). Within these intervals, the function's output remains the same for all values of x in each interval. However, we don't have enough information to determine if the function is constant on the interval (-∞, -4).

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Using conditional probability, it is found that:

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

Conditional probability is the probability of one event happening, considering a previous event. The formula is:

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which:

For this problem, we are given that:

Then:

[tex]P(A|B^\prime) = \frac{P(A \cap B^\prime)}{P(B^\prime)}[/tex]

[tex]P(A|B^\prime) = \frac{\frac{2}{9}}{\frac{2}{3}}[/tex]

[tex]P(A|B^\prime) = \frac{1}{3}[/tex]

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Answer:

Step-by-step explanation:

Q3 asks for reasons of statements in a theorem proof.

1 Given is correct

2 Definition of right angle is correct

3 should be sum of interior angles in a triangle

4 is substitution

5 subtracting 90degree from left and right hand side

6 is definition of complementary

The triangle ABC is shifted upwards by 3 units and towards the left by 4 units. After translation again it is rotated 90° counterclockwise. All these transformations are shown in the graph below.

The following are the basic transformation rules:

A triangle ABC is given in the graph with vertices as

A(-1, 2), B(1, 4), and C(4, -1)

The transformation to be applied is A"B"C" = Ro 90°(T(-4,3)(ABC))

Where -

T(-4, 3) represents the translation of 3 units upwards and 4 units towards the left

R0 90° represents the rotation of 90° (counterclockwise) of the translated triangle.

Step 1: applying translation (-4, 3):

The new vertices of the triangle ABC translated by (-4, 3) units are represented by A'B'C'. They are:

A' - (-1 - 4, 2 + 3) = (-5, 5)

B' - (1 - 4, 4 + 3) = (-3, 7)

C' - (4 - 4, -1 + 3) = (0, 2)

These are shown in the graph below.

Step 2: applying rotation 90° (counterclockwise): (x', y') → (-y, x)

Now the new triangle formed after the translation is ΔA'B'C'

So, on applying rotation, the vertices are changed to,

A'(-5, 5) → A"(-5, -5)

B'(-3, 7) → B"(-7, -3)

C'(0, 2) → C"(-2, 0)

These are shown in the graph below.

Therefore, Δ ABC → Δ A'B'C' (by T(-4, 3)) → Δ A"B"C" (by Ro 90°) i.e.,

Δ A"B"C" = Ro 90°(T(-4, 3) ABC).

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The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that:

M = (2/3) * log (E/E₀)

Where M is the magnitude, E is the amount of energy and E₀ = 10^4..4

For E = 2.5 * 10¹⁵:

M = (2/3) * log (2.5 * 10¹⁵/10^4.4)

M = 7.33

The magnitude of an earthquake releasing 2.5 * 10¹⁵ Joules of energy is 7.33

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The domain of the function is the set of all real numbers and the range of the function is the set of all values greater than -2

The function is given as:

f(x) = 2(x -4)^2 - 2

A quadratic function can take any real number as its input.

So, the domain of the function is the set of all real numbers

The vertex of the above function is:

Vertex = (4, -2)

And the leading coefficient is:

a = 2

The y value of the vertex is;

y = -2

Because the value of a is positive, then the vertex is a minimum.

This means that the range of the function is the set of all values greater than -2

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The computation shows that the the hospital in-patient admission rate for the employees of the Prendergast Corporation is 104.5 admissions per 1000 employees.

The in-patient admission rate for Ramsey Manufacturing company = 100 admissions per 1000 employees.

It is given that the in-patient rate of Prendergast will be 10% higher than Ramsey's.

So, in-patient rate of Prendergast:

= 100 + 10% of 100

= 110 admissions

Now, it is also given that out of total in-patients, 5% are for tonsillectomies (which are not in-patient).

So, in-patient admission rate for Prendergast:

= 110 - 5% of 110

= 110 - 5.5

= 104.5 admissions per 1000 employees

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Complete question:

The hospital in-patient admission rate for employees of the Ramsey Manufacturing Company is 100 admissions per 1000 employees per year.

The Prendergast Corporation has older employees and is told that its hospital in-patient admission rate will be 10% higher than Ramsey’s. At the same time, however, all tonsillectomies will be done in the hospital’s outpatient department instead of requiring the patient to be admitted as an in-patient. Given that 5% of all in-patient admissions are for tonsillectomies, what is the hospital in-patient admission rate for the employees of the Prendergast Corporation?

A. 110.0 B. 115.0 C. 109.5 D. 100.0 E. 104.5 F. 117.0

you need 628 square feet of sand.

Here we need to find the volume of the sand needed.

The volume filled with sand will be a cylinder of diameter of 20ft, and a height of 2 inches.

First, the radius is half of the diameter, then:

R = 20ft/2 =10ft

Remember that:

1ft= 12in

Then:

R = 10ft = 10*(12 in) = 120 in

And remember that the volume of a cylinder of radius R and height H is:

[tex]V = pi*R^2*H[/tex]

Where pi = 3.14

Then we have:

[tex]V = 3.14*(120 in)^2*2in = 90,432 in^2[/tex]

To get that in feets, we need to divide by 12 squared, then:

[tex]90,432 in^2 = 90,432ft^2/(12^2) = 628 ft^2[/tex]

So you need 628 square feet of sand.

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Answer:

D = 50t

Step-by-step explanation:

we see, with every additional hour the distance increases by 50.

that means in general that the number of hours are multiplied by 50 to get the distance.

in other words, this just calculates for a vehicle going constantly 50 miles per hour the distance it is traveling.

Work Shown:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.2 + 0.8 - 0.07

P(A or B) = 0.93

Answer: A

Step-by-step explanation:

The parabola has an open hole at x=3 and the line has a closed hole at x=3, so there should be [tex]x < 3[/tex] for the parabola and [tex]x \geq 3[/tex] for the line.

This eliminates all the options except for A.

Based on the information provided, the cost function, C(x) is given by 80x + 6000 while the demand function, P(x) is given by -1/20(x) + 920.

Mathematically, the revenue can be calculated by using the following expression:

R(x) = x × P(x)

Revenue, R(x) = x(-1/20(x) + 920)

Revenue, R(x) = x(-x/20 + 920)

Revenue, R(x) = -x²/20 + 920x.

Expressing the profit as a function of x, we have:

Profit = Revenue - Cost

P(x) = R(x) - C(x)

P(x) = -x²/20 + 920x - (80x + 6000)

P(x) = -x²/20 + 840x - 6000.

For the value of x which maximizes profit, we would differentiate the profit function with respect to x:

P(x) = -x²/20 + 840x - 6000

P'(x) = -x/10 + 840

x/10 = 840

x = 840 × 10

x = 8,400.

For the maximum profit, we have:

P(x) = -x²/20 + 840x - 6000

P(8400) = -(8400)²/20 + 840(8400) - 6000

P(8400) = -3,528,000 + 7,056,000 - 6000

P(8400) = $3,522,000.

Lastly, we would calculate the price to be charged in order to maximize profit is given by:

P(x) = -1/20(x) + 920

P(x) = -1/20(8400) + 920

P(x) = -420 + 920

P(x) = $500.

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Answer:

B. quadratic function graph

Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

h(t) = -16t² + 31t + 5

The height is of 19 feet when h(t) = 19, hence:

19 = -16t² + 31t + 5

16t² - 31t + 14 = 0.

Then:

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