which statement is true and represent the correct form of scientific notation
A. 5.3 x \(10^{-2}\) = -0.053
B. 2 x \(10^{4}\) < 20,000
C.-74.308 < -0.74 x \(10^{3}\)
D. 12,000,000 = 1.2 x \(10^{7}\)

Using compound interest, it is found that:

a) Pietro will have $1,719.49 in his account after 5 years.

b) The interest rate is of 8.19%.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

Item a:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(A(5) = 1500\left(1 + \frac{0.0275}{2}\right)^{2(5)}\)

\(A(5) = 1719.49\)

Pietro will have $1,719.49 in his account after 5 years.

Item b:

Then:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

\(1.5(1500) = 1500\left(1 + \frac{r}{4}\right)^{20}\)

\(1.5 = (1 + \frac{r}{4}\right)^{20}\)

\(\sqrt[20]^{(1 + \frac{r}{4}\right)^{20}} = \sqrt[20]{1.5}\)

\(1 + 0.25r = 1.02048015365\)

\(0.25r = 0.02048015365\)

\(r = \frac{0.02048015365}{0.25}\)

\(r = 0.0819\)

The interest rate is of 8.19%.

To learn more about compound interest, you can take a look at https://brainly.com/question/25781328

Answer:

2187

Step-by-step explanation:

1. 3

2. 9

3. 27

4. 81

5. 243

6. 729

7. 2187

Answer:

fddjjfhfufifjffjjfrzurhdudifudjdddjddh

Answer:

7. 70

11. 40

12. 11

13.300

14.90

16. 60

17. 32

18. 100

19. 50

20. 270

21. 50

22. 200

23. 100

24. 40

Step-by-step explanation:

Answer:

EF = 10;   AD = 3 ;     BC = 17        

Step-by-step explanation:

The median (EF) of a trapezoid equal half the sum of the length of the two bases of the trapezoid (AD and BC)

EF = 1/2 (AD + BC)

x = 1/2( x - 7 + 2x - 3)

x = 1/2 (3x - 10)      

2x = 3x - 10                  Multiply all terms by 2     or   x = 3/2x - 5

-x = -10                                                                         x - 3/2x  = -5

x = 10                                                                             -1/2x = -5

                                                                                      x = 10

So EF = 10

     AD = x - 7               BC = 2x - 3

     AD = 10 - 7             BC = 2(10) - 3

     AD = 3                   BC = 20 - 3    

                                    BC = 17                                                    

Answer:33 units

Step-by-step explanation:

Answer:

33 answer in the question

Answer:

So you can divide by 2 for the picture. 4/2 = 2

So you can get 2 x 2 picture. The ratio would be 1

if you have a variable it would always be

x by x.

If you want to cover whole wall multiply by 4/3 on the 4 x 4 picture

The original needs to be scaled up by a factor of 75.

Given that, reproducing a 4 cm × 4 cm picture on a 3 m × 3 m wall.

We need to find what ratio we should use.

Ratio, in math, is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another.

We know that 1 m=100cm, then 3 m=300 cm.

The picture on the wall is (300 cm)/(4 cm) = 75 times as large in each dimension as the original.

Therefore, the original needs to be scaled up by a factor of 75.

To learn more about the ratio visit:

https://brainly.com/question/13419413.

#SPJ2

Answer:

Step-by-step explanation:

−4x^2+72x=0

(−4)⋅x^2+(72)⋅x=0

x⋅[(−4)⋅x+(72)]=0

x=0

OR

(−4)⋅x^2+(72)=0

x=−(72)−4

x=−(4)⋅(18)/(4)⋅(−1)=18

The demand function for the baseball game is p(x) = -0.00036x + 11.72, where x is the number of spectators. To maximize revenue, the ticket price should be set at $11.72.

To find the demand function, we can use the information given about the average attendance and ticket prices. We assume that the demand function is linear.

Let x be the number of spectators and p(x) be the ticket price. We have two data points: (22000, 11) and (29000, 8). Using the point-slope formula, we can find the slope of the demand function:

slope = (8 - 11) / (29000 - 22000) = -0.00036

Next, we can use the point-slope form of a linear equation to find the equation of the demand function:

p(x) - 11 = -0.00036(x - 22000)

p(x) = -0.00036x + 11.72

This is the demand function for the baseball game.

To maximize revenue, we need to determine the ticket price that will yield the highest revenue. Since revenue is given by the equation R = p(x) * x, we can find the maximum by finding the vertex of the quadratic function.

The vertex occurs at x = -b/2a, where a and b are the coefficients of the quadratic function. In this case, since the demand function is linear, the coefficient of \(x^2\) is 0, so the vertex occurs at the midpoint of the two data points: x = (22000 + 29000) / 2 = 25500.

Therefore, to maximize revenue, the ticket price should be set at p(25500) = -0.00036(25500) + 11.72 = $11.72.

Hence, the ticket prices should be set at $11.72 to maximize revenue.

Learn more about coefficients here:

https://brainly.com/question/1594145

#SPJ11

The present value of the annuity that Ian deposits $2,400 each quarter for 3 years and earning 10% interest compounded quarterly is A. $24,618.62.

The present value represents the future annuity deposits or payments compounded at a periodic interest rate to the current period.

The present value can be computed using an online finance calculator as follows:

N (# of periods) = 12 quarters )(3 years x 4)

I/Y (Interest per year) = 10%

PMT (Periodic Payment) = $2,400

FV (Future Value) = $0

Results:

Present Value (PV) = $24,618.62

Sum of all periodic payments = $28,800.00

Total Interest = $4,181.38

Learn more about the present value at https://brainly.com/question/20813161.

#SPJ1

Answer:

18 and 6

Step-by-step explanation:

i know this because all you have to do is multiply the tow numbers by 2

The correct answer is (a) standard deviation. The measure of central tendency that is NOT included among the given options is the standard deviation (a).

Measures of central tendency are statistical measures that represent the central or average value of a dataset. They provide insight into the typical or central value around which the data tends to cluster. The three commonly used measures of central tendency are the mean, median, and mode.

a. Standard deviation is not a measure of central tendency. It is a measure of dispersion or variability in a dataset. It quantifies how spread out the data points are from the mean. Standard deviation provides information about the spread or scatter of the data rather than representing a central value.

b. Median is a measure of central tendency that represents the middle value in a dataset when the data points are arranged in ascending or descending order. It divides the data into two equal halves.

c. Mean is a measure of central tendency that represents the arithmetic average of a dataset. It is calculated by summing all the data points and dividing by the total number of observations.

d. Mode is a measure of central tendency that represents the most frequently occurring value or values in a dataset. It identifies the value(s) that appear(s) with the highest frequency.

Therefore, the standard deviation (a) is the measure of central tendency that is NOT included among the given options.

Learn more about measure of central tendency here:

https://brainly.com/question/29751853

#SPJ11

The variance of the sample means that is found in the sample distribution that we have here is 0.3333

This is the measure of dispersion that is used to show the spread of the data that is contained in a data set

The formula that we are to use here is given as

b² - a² / b - a

we have to put the values in this question

(14 - 2)² / 14 - 2

= 144 / 12

= 12

From here we would have to solve for the variance.

The variance = 12 / 35

= 0.3333

Hence the variance that we have in the question is equal to 0.3333

Read more on variance here: https://brainly.com/question/25639778

#SPJ1

The Taylor polynomials P1, P2, P3, and P4 centered at a0 for f(x) are given as:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

We will apply the Taylor's theorem formula, which is supplied as follows, to determine the Taylor polynomials P1, P2, P3, and P4 centred at a0 for f(x) in the given question:f'(a)(x-a)/1 = f(x) = f(a) + f'(a)! + f''(a)(x-a)²/2! + ... + fⁿ(a)(x-a)ⁿ/n!We have f(0) = 1f'(0) = 0f''(0) = -1f'''(0) = 0f4(0) = 1 for f(x) = cos(x) at x = 0.We can get the following polynomial expressions by using these values in the Taylor's theorem formula:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!Consequently, the Taylor polynomials P1, P2, P3, and P4 for f(x) are provided as follows:P1(x) = 1P2(x) = 1 - x²/2!P3(x) = 1 - x²/2! + x⁴/4!P4(x) = 1 - x²/2! + x⁴/4! - x⁶/6!

To know more about Taylor polynomials Visit:

https://brainly.com/question/30481013

#SPJ11

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

For more such question on probability. visit :

https://brainly.com/question/251701

#SPJ8

Answer:

37.50 per hour for 2 hours. 37.50 x 2 =7575 + 75 =150 it will cost $150. I hope this helps and is correct!!!

The smallest possible value of (a+b) is 2, and this value is attained when a = 1 and b = 1.

Let r and s be the roots of the equation x^2 + ax + 2b = 0, and let p and q be the roots of the equation x^2 + 2bx + a = 0. Since both equations have real roots, their discriminants are nonnegative:

a^2 - 8b ≥ 0

4b^2 - 4a ≥ 0

Simplifying the second inequality, we get:

b^2 - a ≥ 0

b^2 ≥ a

We want to minimize (a+b). Adding the two given equations, we get:

(x^2 + ax + 2b) + (x^2 + 2bx + a) = 0

2x^2 + (a+2b+2b)x + (a+2b) = 0

This equation has real roots if and only if its discriminant is nonnegative:

(a+2b+2b)^2 - 8(2x^2)(a+2b) ≥ 0

(a+4b)^2 - 16b(a+2b) ≥ 0

a^2 + 8ab + 12b^2 ≥ 0

This inequality is always true for positive a and b, so we can safely assume that a and b are positive. Therefore, we can divide both sides by 4b^2 to get:

(a/b)^2 + 8(a/b) + 12 ≥ 0

Letting t = a/b, we can rewrite this as a quadratic inequality:

t^2 + 8t + 12 ≥ 0

This inequality is true for all values of t, so there are no restrictions on the ratio a/b. Therefore, we can minimize (a+b) by choosing a and b to be as small as possible subject to the constraint that b^2 ≥ a. Since a and b are both positive, we can take a = 1 and b = 1 to achieve this minimum. This gives:

(a+b) = 1+1 = 2

Therefore, the smallest possible value of (a+b) is 2, and this value is attained when a = 1 and b = 1.

Learn more about :

real roots : brainly.com/question/30288169

#SPJ11

Answer:

6^9 over 6^9 is 1

If you know about the power rule,

d/dw (2w² + 1) = 2 d/dw (w²) = 2 • 2w = 4w

If you have to use the limit definition of the derivative, let f(w) = 2w² + 1. Then

\(f'(w)=\displaystyle\lim_{h\to0}\frac{f(w+h)-f(w)}h\)

\(f'(w)=\displaystyle\lim_{h\to0}\frac{(2(w+h)^2+1)-(2w^2+1)}h\)

\(f'(w)=\displaystyle\lim_{h\to0}\frac{2(w^2+2wh+h^2)-2w^2}h\)

\(f'(w)=\displaystyle\lim_{h\to0}\frac{4wh+2h^2}h\)

\(f'(w)=\displaystyle\lim_{h\to0}(4w+2h)=\boxed{4w}\)

The volume of the shred is 777.6 cubic feet

The volume of a shape is the amount of space inside the shape.

For most regular shapes, the formula of the volume is the product of the base area and the height

The given parameters are

Length = 20.25 ft

Width = 12 ft

Height = 3 1/5 feet

The volume of the shred is calculated using the following volume formula i.e. the volume of a cuboid or rectangular prism

Volume = Length x Width x Height

Substitute the known values in the above equation

So, we have

Volume = 20.25 x 12 x 3 1/5

Evaluate the product in the above equation

So, we have

Volume = 777.6 cubic feet

So, the required volume of the shred is 777.6 cubic feet

Hence, the volume of the shred is 777.6 cubic feet

Read more about volume at

https://brainly.com/question/463363

#SPJ1

The exact value of the slope of the secant line connecting (-1, f(-1)) and (1, f(1)) is m = 5.

To find the exact value of the slope of the secant line connecting (-1, f(-1)) and (1, f(1)) for the function f(x) = -x^2 + 5x - 3 on the closed interval [-1, 1), follow these steps:

1. Calculate the function values at the endpoints of the closed interval, f(-1) and f(1):
  f(-1) = -(-1)^2 + 5(-1) - 3 = -1 - 5 - 3 = -9
  f(1) = -(1)^2 + 5(1) - 3 = -1 + 5 - 3 = 1

2. Write down the coordinates of the two points: (-1, -9) and (1, 1)

3. Calculate the slope of the secant line (m) using the formula m = (y2 - y1) / (x2 - x1):
  m = (1 - (-9)) / (1 - (-1)) = (1 + 9) / (1 + 1) = 10 / 2 = 5

The exact value of the slope of the secant line connecting (-1, f(-1)) and (1, f(1)) for the function f(x) = -x^2 + 5x - 3 on the closed interval [-1, 1) is m = 5.

To know more about secant line, visit:

https://brainly.com/question/31124520#

#SPJ11

Answer:

(1/2,4)

Step-by-step explanation:

First, determine y in first equation: 2x+y=5 or  y=5-2x

replace value of y determined in first equation (5-2x) into 2nd equation    

4x-3(5-2x)=-10

4x-15+6x=10

10x=5

x=1/2

put value of x into either equation to solve for y so

2(1/2)+y=5

1+y=5

y=4

answer: x=1/2, y=4

check answer by substituting x and y into either equation:

4x-3y=-10

4(1/2)-3(4)=-10

2-12=-10

-10=-10

or

2x+y=5

2(1/2)+4=5

1+4=5

5=5

Answer:

C

Step-by-step explanation:

3x - 9y = 9 → (1)

- 2x +2y = 8 ( subtract 2y from both sides )

- 2x = - 2y + 8 ( divide through by - 2 )

x = y - 4

substitute x = y - 4 into (1)

3(y - 4) - 9y = 9

3y - 12 - 9y = 9

- 6y - 12 = 9 ( add 12 to both sides )

- 6y = 21 ( divide both sides by - 6 )

y = \(\frac{21}{-6}\) = - \(\frac{7}{2}\)

The parameter often associated with enzyme affinity for substrates is Km.

Km, also known as the Michaelis constant, is a parameter commonly used to quantify the affinity of an enzyme for its substrate. It is an important parameter in enzyme kinetics and plays a crucial role in determining the efficiency of an enzyme-substrate interaction.

Km represents the substrate concentration at which the rate of the enzymatic reaction is half of its maximum velocity (Vmax). In other words, enzymes with lower Km values have higher affinity for their substrates, as they can achieve half of their maximum velocity at lower substrate concentrations. Therefore, Km serves as an indicator of the enzyme's ability to bind and convert substrates into products efficiently.

Learn more about substrates here : brainly.com/question/6107295

#SPJ11

Answer:

Your correct answer is 169.65 square units.

Step-by-step explanation:

Since the radius of the cylinder is 3, and the height of it is 6, you get a total of 169.65 square units.

Here is proof that I am correct:

Answer:

54 pi

Step-by-step explanation:

khan

Tony's rounding process does not introduce any errors. Therefore, he does not get any questions wrong.

Tony completes a series of rounding operations, starting from the hundred thousandth place and gradually rounding to the nearest whole number. The question asks how many questions Tony gets wrong based on this rounding process.
Let's analyze Tony's rounding process step by step:
1. Rounding to the nearest hundred thousandth: Since Tony rounds to the nearest hundred thousandth and uses that as his answer, it means that his answer is already rounded to the nearest whole number.
2. Rounding to the nearest ten thousandth: In this step, Tony rounds his already rounded answer to the nearest ten thousandth. Since his original answer is already rounded to the nearest whole number, rounding to the nearest ten thousandth will not change the value.
3. Rounding to the nearest thousandth: Again, this step involves rounding his already rounded answer to the nearest thousandth. Rounding to the nearest thousandth will not change the value of a whole number.
4. Rounding to the nearest hundredth: Tony's already rounded answer, which is a whole number, will not be affected by rounding to the nearest hundredth.
5. Rounding to the nearest tenth: Similarly, since Tony's answer is a whole number, rounding to the nearest tenth will not alter the value.
6. Rounding to the nearest whole number: Finally, Tony rounds his already rounded answer to the nearest whole number. Since his answer is already a whole number, this step will not change the value.
Based on this analysis, Tony's rounding process does not introduce any errors. Therefore, he does not get any questions wrong.

Learn more about whole number here:

https://brainly.com/question/29766862

#SPJ11

Answer:

Step-by-step explanation:

total number of students=21

students play neither sport=6

students who play at least one sport=21-6=15

Let play basketball=X

and play baseball=Y

n(XUY)=n(X)+n(Y)-n(X∩Y)

15=11+6-n(X∩Y)

n(X∩Y)=17-15=2

reqd. probability=2/21