Aliens have injected Ana with mathematical nanobots. These nanobots force Ana to think about math more and more. Initially, there were only five nanobots. The population of the nanobots doubles every hour. The population of the nanobots follows the equations p(t) = 5·2^t. After there are 106nanobots, Ana will cease thinking of anything other than math. How many hours will it take for math to take over Ana's brain?

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

____________________________

*100% CORRECT ANSWERS

Question 1

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?

$1082.84    

Question 2

A family is purchasing a house and needs to finance a 195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the total amount the family will pay back to the bank (to the nearest dollar)?

$389,822    

Question 3

Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?  

$450.71

Answer:

C) ¼ ∫ u⁵ du, where u = sin(4x)

Step-by-step explanation:

∫ cos(4x) sin⁵(4x) dx

Using u substitution:

u = sin(4x)

du = 4 cos(4x) dx

¼ du = cos(4x) dx

¼ ∫ u⁵ du

Answer:

1998

y=6x+1944

Step-by-step explanation:

The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss

it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph

y=the year

x=the percentage of men who prefer a female boss

s=y2-y1/(x2-x1)

s=1998-1974/(9-5)

s=24/4

s=6

therefore we have

y=mx+c

y=6x+c........1

when y=1998,x=9

1998=6(9)+c

c=1944

from equation 1

y=6x+1944

Answer:

Step-by-step explanation:

1) The formula for simple interest is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T = 2 years

P = $500

R = 5%

Therefore

I = (500 × 5 × 2)/100

I = $50

2) Principal, P = $500

It was compounded monthly. This means that it was compounded 12 times in a year. So

n = 12

The rate at which the principal was compounded is 3%. So

r = 3/100 = 0.03

It was compounded for just 2 years. So

t = 2

The formula for compound interest is

A = P(1+r/n)^nt

A = total amount in the account at the end of t years. Therefore

A = 500 (1+0.03/12)^12 × 2

A = 500 (1.0025)^24

A = $530.88

The interest is

530.88 - 500 = $30.88

Answer:question 1)$6.66.67

Question2) Rent and expenses =$760

Rent and expenses are too high for the budget

Step-by-step explanation:

1)$2000×(1/3)= $666.67

2)Rent and expenses =$(650+60+10+20+20)= $760

$2100×(1/3)= $700

Rent and expenses should not exceed one third of $2100, which is $700 but it exceeded by$60. Therefore budget is too high.

Final answer:

These Mathematics questions involve calculating budgets to manage income and expenses. For budgeting housing costs, the recommendation is not to exceed one-third of income. A budget table is used to track all monthly expenses against income to determine savings potential and necessary adjustments.

Explanation:

The subject of these questions is Mathematics, specifically focusing on budgeting and personal finance. In these scenarios, students are learning to apply mathematical operations to real-life situations involving income, expenses, and budget planning.

For question 1, you would calculate the maximum amount you should spend on housing from a $2,000 monthly budget by dividing $2,000 by 3, which gives you $666.67. This is because it's recommended to spend no more than one-third of your income on housing.

For question 2, adding together the rent and housing expenses ($650 + $60 + $10 + $20 + $20), you get a total of $760. If you have an income of $2,100, you should not spend more than $700 on housing (which is one-third of your income), so $760 is indeed too high for the budget.

Creating a budget table is an essential skill for financial literacy. When constructing one, you list your monthly income and subtract all your expenses, including housing, utilities, groceries, and any other costs, to see what is left for savings and discretionary spending. For example, with an after-tax monthly income of $2,589.10, if you spend $790 on rent, $75 on a cell phone, and have other listed expenses, you'd subtract all these from your income to see if you can save the desired 10%.

well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.

[tex]\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}[/tex]

[tex]\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}[/tex]

Answer:

A. 15, 20, and 25

Step-by-step explanation:

Note that 3-4-5 is a pythagorean triple via following:

[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]

Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.

The correct answer would be B.

The lower e is used for continuous compounding and it is raised by the interest rate times the amount of time

Formula  that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].

" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."

Formula used

[tex]A(t) = P e^{rt}[/tex]

[tex]A(t) =[/tex] Final amount

[tex]P =[/tex] Principal amount

[tex]t =[/tex]  time period interest is applied

[tex]r=[/tex] rate of interest

According to the question,

Given,

Principal amount [tex]= \$300[/tex]

Rate of interest [tex]= 6\%[/tex]

As per the given condition interest compounded continuously,

Substitute the value in the formula of interest compounded continuously  we get,

[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]

Hence, Option (B) is the correct answer.

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Answer: the wire should be cut into 12 cm and 28 cm

Step-by-step explanation:

All sides of a square is equal.

The perimeter of a square is the distance around the square.

Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.

The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4

The perimeter of the other square would be 4(L + 4) = 4L + 16

Since the piece of wire is 40 cm long, then

4L + 4L + 16 = 40

8L = 40 - 16 = 24

L = 24/8 = 3

The perimeter of the first square is

4L = 4 × 3 = 12

The perimeter of the second square is

4L + 16 = 4 × 3 + 16= 28

Final answer:

To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.

Explanation:

The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.

Combining the total length of both squares, we have:

4x + 4(x + 4) = 40

This simplifies to:

8x + 16 = 40

Subtracting 16 from both sides, we get:

8x = 24

Dividing both sides by 8, we find:

x = 3

Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:

Smaller square wire length: 4(3) = 12 cm

Larger square wire length: 4(7) = 28 cm

So the wire should be cut into one 12 cm piece and one 28 cm piece.

Answer: the cost of Parker's tuition is $17955

Step-by-step explanation:

Let x represent the cost of Parker's tuition.

Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be

44/100 × x = 0.44 × x = 0.44x

The amount that is remaining for him to pay would be

x - 0.44x = 0.56x

If he paid the remaining $10,054.52 with a student loan, it means that

0.56x = 10054.52

x = 10054.52/0.56

x = 17954.5

Rounding up to the nearest whole number, it becomes

x = $17955

Answer:

  2 1/2

Step-by-step explanation:

Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...

  -3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2

a9 is 2 1/2.

I'm pretty sure the answer to

a1=−32

an=an−1+12

is 5/2

Answer:

4%

Step-by-step explanation:

Let the stock be $10

A 20% decline = 80/100 * 10

= 8

A 30% increase = 30/100 * 8

= 2.4 + 8 = 10.4.

Overall increase = 10.4 - 10 = 0.4

Percentage overall increase = 0.4/10 * 100

= 4%

Answer:

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle

DF represents the hypotenuse of the right angle triangle.

With m∠D as the reference angle,

DE represents the adjacent side of the right angle triangle.

EF represents the opposite side of the right angle triangle.

To determine EF, we would apply the Sine trigonometric ratio

Sin θ = opposite side/hypotenuse. Therefore,

Sin 26 = EF/4.5

0.44 = EF/4.5

EF = 4.5 × 0.44 = 1.98 yo 2 decimal places

Answer:

g6h12

Step-by-step explanation:

Answer:  mmmmm.

Step-by-step explanation:

The function f(x) has a removable discontinuity at x=0. To make f(x) continuous at x=0, we must redefine f(0) as -1/3.

To determine if f(x) has a removable discontinuity at x=0, we need to check if f(x) is either not defined or not continuous at x=0.

Looking at the definition of f(x), we see that f(0) is defined as 3. Therefore, f(x) is defined at x=0.

Next, let's examine the continuity of f(x) at x=0. We need to evaluate the limit of f(x) as x approaches 0.

Using the given definition of f(x), we have:

lim(x->0) (6/x) + (-5x + 18)/(x(x-3))

To evaluate this limit, we can simplify the expression by finding a common denominator. The common denominator is x(x-3):

lim(x->0) [6(x-3) + (-5x + 18)] / [x(x-3)]

Simplifying the numerator:

lim(x->0) (6x - 18 - 5x + 18) / [x(x-3)]

= lim(x->0) (x) / [x(x-3)]

Now, we can cancel out the x term:

lim(x->0) 1 / (x-3)

As x approaches 0, the denominator (x-3) approaches -3. Therefore, the limit is:

lim(x->0) 1 / (x-3) = 1 / (-3) = -1/3

Since the limit of f(x) as x approaches 0 exists and is equal to -1/3, we can redefine f(0) to be -1/3 to make f(x) continuous at x=0.

Thus, f(x) has a removable discontinuity at x=0, and we must redefine f(0)=-1/3 to make f(x) continuous at x=0.

Answer:

3 employees

Step-by-step explanation:

The complete question is

The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.

Let

x ---> is the number of employees working registers

y ---> is the total amount of time waited in seconds

we have

[tex]y=-70x+300[/tex]

This is the equation of a line in slope intercept form

where

The slope is equal to

[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function

The y-intercept is equal to

[tex]b=300\ sec[/tex]

For y=90 seconds

substitute in the linear equation and solve for x

[tex]90=-70x+300[/tex]

[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]

To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.

To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.

Assuming we have a trend line equation of the form y = mx + b,

you can substitute 90 for x and solve for y.

For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:

y = -0.1(90) + 10

y = -9 + 10

y = 1

Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.

Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.

Step-by-step explanation:

Let w represent the number of small marbles Amy has.

Let x represent the number of medium marbles Amy has.

Let y represent the number of large marbles Amy has.

a) She has five times as many small marbles as medium marbles. This means that

w = 5x

b) The number of large marbles is two more than three times the number of medium marbles. This means that

y = 3x + 2

c) If Amy has a total of 560 marbles, it means that

5x + x + 3x + 2 = 560

9x = 560 - 2

9x = 558

x = 558/9 = 62

w = 5x = 62 × 5

w = 310

y = 3x + 2 = 3 × 62 + 2

y = 188

Answer:

A. s = 5x

B. y = 3x + 2

C y=166

Step-by-step explanation:

Answer:

B, An  n-by-m array.

Step-by-step explanation:

when working with  2D arrays, rows come first and then columns. so all options here are correct except option B

Answer:

Step-by-step explanation:

Let h represent the number of hours that Jamarcus can rent the truck.

To rent a truck, the charge is $16 per hour and also a fueling fee of $25

The total cost of renting the truck for x hours would be

16h + 25

Since Jamarcus wants to rent the truck and can spend no more than $125, the inequality representing the situation would be

16h + 25 ≤ 125

16h ≤ 125 - 25

16h ≤ 100

h ≤ 6.25

2) 3x - 5 ≥ - 11

3x ≥ - 11 + 5

3x ≥ - 6

x ≥ - 6/3

x ≥ - 2

The correct graph is option A

Answer:

a

Step-by-step explanation:

Answer: $4.50 per candle

Step-by-step explanation:

$32.55 - $17.50 - $1.55 = $13.50 for all the candles

To find the price of a single candle we divide our answer by 3

13.50/3 = $4.50

Answer: The  length of the shorter side of a golden rectangle is about 24.7 inches.

Step-by-step explanation:

Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.

Since 1.62 > 1 , so

[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]

If the length of the longer side is 40 inches , then we have

[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]

Hence, the  length of the shorter side of a golden rectangle is about 24.7 inches.

To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.

To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.

Using this method:

Let's do the calculation:

Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)

Step-by-step explanation:

(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:

g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)

g = 8 − 2.5t

(b) If d is the distance traveled:

d = 60 mi/hr × t hr

d = 60t

(c) When George runs out of gas, g = 0.

0 = 8 − 2.5t

t = 3.2

The distance he travels is:

d = 60(3.2)

d = 192

George travels 192 miles.

3.2 hours after 8AM, the time is 11:12AM.

Answer:

Step-by-step explanation:

Part 1:

An equation of sine wave can be written as y = 5 Sin(2x + 3).

The amplitude of the above equation is 5.

The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].

The frequency of the function is [tex]\frac{1}{\pi }[/tex].

Part 2:

[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]

The above given equations numbered 1, 2 and 3 represents three different sound waves.

For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].

For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].

For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].

Frequency of sounds refers the speed of vibration.

The taken three siounds has different frequencies.

Answer:

10 years

40 years

Step-by-step explanation:

let present ag e of son=x

5 years ago age of son=x-5

5 years ago age of man=7(x-5)=7x-35

present age of man=7x-35+5=7x-30

after 5 years

age of son=x+5

age of man=7x-30+5=7x-25

also 7x-25=3(x+5)

7x-25=3x+15

7x-3x=15+25

4x=40

x=10

age of son=10 years

age of man=7*10-30=70-30=40 years

Final answer:

By creating equations from the given information and solving them, it was found that the man is currently 40 years old, and his son is 10 years old.

Explanation:

Let's solve the problem using algebra. Suppose the current age of the man is M years and the current age of his son is S years.

According to the problem, 5 years ago, the age of the man was 7 times the age of his son. Therefore, M - 5 = 7(S - 5).

After 5 years, the age of the man will be 3 times the age of his son from now. Therefore, M + 5 = 3(S + 5).

Solving these equations:

M - 5 = 7S - 35

M + 5 = 3S + 15

Simplifying both:

M = 7S - 30

M = 3S + 10

Equating both equations we get:

7S - 30 = 3S + 10

4S = 40

S = 10

Substituting the value of S in the first equation:

M = 7*10 - 30 = 40

Therefore, the man is currently 40 years old, and his son is 10 years old.

Step-by-step explanation:

The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)

To find, the area of the shape (quadrilateral) = ?

We know that,

The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]

= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]

= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]

= [tex]\dfrac{1}{2} [4+0-28+0][/tex]

= [tex]\dfrac{1}{2} [32][/tex]

= 16 square units.

Thus, the area of the shape (quadrilateral) is 16 square units.

Answer: 233,168

Step-by-step explanation:

Formula: 1 + 2 + 3 + ... + n = n(n+1)/2

Sum of all the numbers below 1000 that is divisible by 3:

3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833

Sum of all the numbers below 1000 that is divisible by 5:

5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500

As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:

Sum of all numbers below 1000 that is divisible by 15:

15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165

Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168

To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.

To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).

Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:

3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833

Similarly, the sum of the multiples of 5 below 1000 is:

5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500

Finally, the sum of the multiples of 15 below 1000 is:

15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330

Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:

166,833 + 99,500 - 33,330 = 233,003

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Answer: $116.99

Step-by-step explanation:

By using compound interest formula which said:

A = P ( 1 + r/n )^(n×t)

P=Principal= 1000

r=rate=4/100

n=1

t= 4

Apply the above formula

A = P ( 1 + r/n )^(n×t)

A = 1000(1 + 0.04/1)^(1 × 4)

A= 100(1.04)^4

A= 100 × 1.17

A = 116.99

Answer:

Step-by-step explanation:

p = 120 ± 4

Answer:

$ 270

Step-by-step explanation:

Do 250 X 1.08 to get the answer

Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.

To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).

Step-by-step calculation:

Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.