there were 100 questions on the social studies test. Arpan answered 97 of the questions Correctly. what fractions and demical presents the fraction of questions Arpan answered correctly?

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[tex](2 {x}^{2} - 3x + 1)( {x}^{2} - 4 - 3) = \\ = 2 {x}^{4} - 8 {x}^{2} - 6 {x}^{2} - 3 {x}^{3} + 12x + 9x + {x }^{2} - 4 - 3 = \\ = 2 {x}^{4} - 3 {x}^{3} - 13 {x}^{2} + 21x - 7[/tex]

For part a, Jackie will have approximately $1217.62 after 10 years with quarterly compounding interest. For part b, Jackie will have approximately $1226.96 after 10 years with continuous compounding interest. For part c, it will take approximately 15.43 years for Jackie's money to double with continuous compounding interest. For part d, it will take approximately 38.51 years for Jackie's money to triple with monthly compounding interest.

For part a, to calculate the amount of money Jackie will have in 10 years with quarterly compounding interest, we can use the compound interest formula: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times compounded per year, and t is the number of years. Plugging in the values, we have A = 800(1 + 0.045/4)^(4*10), which gives us A ≈ $1217.62.

For part b, to calculate the amount of money Jackie will have in 10 years with continuous compounding interest, we can use the formula: A = P * e^(rt), where e is Euler's number and approximately equal to 2.71828. Plugging in the values, we have A = 800 * e^(0.045 * 10), which gives us A ≈ $1226.96.

For part c, to find out how long it will take Jackie's money to double with continuous compounding interest, we can use the formula: t = ln(2) / r, where t is the time in years and r is the interest rate. Plugging in the values, we have t = ln(2) / 0.045, which gives us t ≈ 15.43 years.

For part d, to find out how long it will take Jackie's money to triple with monthly compounding interest, we can use the formula: t = ln(3) / (n * ln(1 + r/n)), where t is the time in years, n is the number of times compounded per year, and r is the interest rate. Plugging in the values, we have t = ln(3) / (12 * ln(1 + 0.045/12)), which gives us t ≈ 38.51 years.

a. If the interest is compounded quarterly, Jackie will have approximately $1,313.63 in 10 years.

b. If the interest is compounded continuously, Jackie will have approximately $1,256.39 in 10 years.

c. If Jackie's money is compounded continuously, it will take approximately 15.4 years for her money to double.

d. If Jackie's money is compounded monthly, it will take approximately 62.47 years for her money to triple.

Step 1

To solve this problem, we can use the compound interest formula:

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

Where:

- A is the amount of money accumulated after t years, including interest.

- P is the principal amount (the initial deposit).

- r is the annual interest rate (as a decimal).

- n is the number of times interest is compounded per year.

- t is the time the money is invested for, in years.

Given:

- [tex]\( P = \$800 \)[/tex]

-[tex]\( r = 0.045 \)[/tex] (4.5% as a decimal)

- n is either 4 for quarterly compounding or tends to infinity for continuous compounding.

Step 2

We'll calculate each part step by step:

a. Quarterly compounding:

- [tex]\( n = 4 \)[/tex]

- [tex]\( t = 10 \)[/tex]

Substituting into the formula:

[tex]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{4 \times 10} \]\[ A = 800 \left(1 + \frac{0.045}{4}\right)^{40} \]\[ A = 800 \left(1 + 0.01125\right)^{40} \]\[ A = 800 \times 1.01125^{40} \]\[ A = 800 \times 1.642032881 \]\[ A = \$1,313.63 \][/tex]

Step 3

b. Continuous compounding:

For continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

Where e is the base of the natural logarithm, approximately equal to 2.71828.

Substituting the values:

[tex]\[ A = 800 \times e^{0.045 \times 10} \]\[ A = 800 \times e^{0.45} \]\[ A = 800 \times 1.570482165 \]\[ A = \$1,256.39 \][/tex]

Step 4

c. To find out how long it takes for the money to double with continuous compounding, we use the formula:

[tex]\[ A = P e^{rt} \][/tex]

We need to solve for t  when [tex]\( A = 2P \):[/tex]

[tex]\[ 2P = P e^{0.045t} \]\[ 2 = e^{0.045t} \]\[ \ln(2) = 0.045t \]\[ t = \frac{\ln(2)}{0.045} \][/tex]

Substituting the values:

[tex]\[ t = \frac{\ln(2)}{0.045} \]\[ t = \frac{0.693}{0.045} \]\[ t = 15.4 \text{ years} \][/tex]

So, it takes approximately 15.4 years for Jackie's money to double with continuous compounding.

Step 5

d. To find out how long it takes for the money to triple with monthly compounding, we use the compound interest formula again, but this time we set [tex]\( A = 3P \)[/tex]:

[tex]\[ 3P = P \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ 3 = \left(1 + \frac{0.045}{12}\right)^{12t} \]\[ \ln(3) = 12t \ln\left(1 + \frac{0.045}{12}\right) \]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \][/tex]

Substituting the values:

[tex]\[ t = \frac{\ln(3)}{12 \ln\left(1 + \frac{0.045}{12}\right)} \]\[ t = \frac{1.099}{12 \times 0.0037} \]\[ t = 62.47 \text{ years} \][/tex]

So, it takes approximately 62.47 years for Jackie's money to triple with monthly compounding.

Answer:

The letter A represents where the amount of $158.29 should be written.

The letter D  represents where the amount of $250 should be written.

Step-by-step explanation:

Ivan spent $158.29 on groceries so that would be debit -

For letter D he is transferring money

The letter 'a' represents where the amount of $158.29 should be written. And the letter d represents where the amount of $250 should be written.

Debit is an entry in the accounting sheet where there forms an increase in the assets or decrease in the liabilities. Positive values for assets and liabilities are debited and the negative balances are credited on balance sheet.

Given that Ivan spent $158.29 on groceries.

He then transferred $250 to his savings account.

On the check register, there are two letters, letter a and letter d.

a is the amount debited for groceries. So the letter a represents where the amount of $158.29 should be written.

d is the amount debited for a transfer. So the letter d represents where the amount of $250 should be written.

Hence the letter 'a' represents where the amount of $158.29 should be written. And the letter d represents where the amount of $250 should be written.

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The full question is :

Look at ivan’s check register. ivan spent $158.29 on groceries. he then transferred $250 to his savings account. a check register. a is the amount debited for groceries. d is the amount debited for a transfer. the letter represents where the amount of $158.29 should be written. the letter represents where the amount of $250 should be written.

Answer:

92%

Step-by-step explanation:

46/50=?/?

multiply 50 by 2 then 46 by 2

46/50=92/100

92/100= 92%

Answer:

1,4 and 4

Step-by-step explanation:

Answer:

1 4 4

Step-by-step explanation:

Answer:

7,7,12,12,12

Step-by-step explanation:

7+7+12+12+12=50/5=10=Mean

Median=12

The data set could be as follow 7,7,12,12,12 which has a mean of 10 and a median of 12.

The mean is the average value which can be calculated by dividing the sum of observations by the number of observations

Mean = Sum of observations/the number of observations

Median represents the middle value of the given data when arranged in a particular order.

we have given the information of the data set with five numbers that have a mean of 10 and a median of 12.

Mean = 10

Let's assume the given data set 7,7,12,12,12 so, this must satisfy the information

7+7+12+12+12=50/5

Mean =10

Also,

Median=12

Thus, the data set could be as follow 7,7,12,12,12 which has a mean of 10 and a median of 12.

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Answer:

$750

Step-by-step explanation:

Answer:

$750

Step-by-step explanation:

50 times 9 = 450

20 times 15 = 300

450+300=750

Answer:

The probability of the bus getting there BEFORE 8:20 isn't likely

I took an average of all of the numbers and its shows that he bus will be there about 8:20.25

Answer:

choice D . x = 6/11

Step-by-step explanation:

1,331 x ^3 − 216 = 0?

11^3 = 1331

6^3 = 216

(11x)^3 - 6^3  = 0

We have   (11x - 6) * ( (11x)^2  + 6*(11x ) + 36) = 0

Solve  11x - 6 = 0

x = 6/11

I will see if i can help you since you had helped me

26. 244611.80  $

27. ?

28. 2568246.87126  $

29. 11850.59

30. 426647.047  $

I do not know about #27

But I do know about the rest

Answer:

2 PM

3 PM

4 PM

8 PM

Step-by-step explanation:

*Note the following:

I used the hours after midnight to calculate the time of day/night.

The lower the graph on the line, the lower (AKA faster) response time.

The paramedics had a faster average response time at the following times:

2 PM

3 PM

4 PM

8 PM

Therefore, we can predict that if this pattern continues, their response time will be faster during those hours.

Answer:

5810 meters

Step-by-step explanation:

800 meters

5km = 5,000 meters

1,000 cm = 10 meters

Add all together to get 5810 meters

Answer:

(B)s greater-than-or-equal-to 4

[tex]s\geq 4[/tex]

Step-by-step explanation:

The function [tex]s(V)=\sqrt[3]{V}[/tex] describes the side length, in units, of a cube with a volume of V cubic units.

If Jason wants to build a cube with a minimum of 64 cubic centimeters,

[tex]V\geq 64 $ cubic meters[/tex]

Therefore:

[tex]s(V)\geq \sqrt[3]{64}\\s\geq 4 $ Units[/tex]

The correct option is B.

Answer:

B. s greater-than-or-equal-to 4

Step-by-step explanation:

Answer:

no

Step-by-step explanation:

assuming these are slopes?? two points cant be parallel theyre just dots, no these are not parallel

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Answer:

The length of the arc is approximately [tex]\( 17.27 \)[/tex] units.

Explanation:

To find the length of the arc, we use the formula:

[tex]\[ \text{Arc Length} = \frac{\text{Central Angle}}{360^\circ} \times 2\pi r \][/tex]

where:

- Central Angle is the measure of the angle formed by the arc and the center of the circle

- [tex]\( r \)[/tex] is the radius of the circle

Given:

- Radius ([tex]\( r \)[/tex]) = 6

- Central Angle = 330º

Plugging the values into the formula:

[tex]\[ \text{Arc Length} = \frac{330^\circ}{360^\circ} \times 2\pi \times 6 \][/tex]

[tex]\[ \text{Arc Length} = \frac{330}{360} \times 2\pi \times 6 \][/tex]

[tex]\[ \text{Arc Length} = \frac{11}{12} \times 2\pi \times 6 \][/tex]

[tex]\[ \text{Arc Length} = \frac{11}{2} \pi \][/tex]

Using [tex]\( \pi \approx 3.14 \)[/tex], we can approximate the value:

[tex]\[ \text{Arc Length} \approx \frac{11}{2} \times 3.14 \][/tex]

[tex]\[ \text{Arc Length} \approx 17.27 \][/tex]

So, the length of the arc is approximately [tex]\( 17.27 \)[/tex] units.

Answer:

V = 36[tex]\pi[/tex] units³

Step-by-step explanation:

Use the formula for the volume of a cylinder, V = [tex]\pi[/tex]r²h, where r is the radius and h is the height:

Plug in the values:

V = [tex]\pi[/tex](2²)9

V = 36[tex]\pi[/tex] units³

The statement is false because parabolas can also open upwards or downwards if the directrix is horizontal. A parabola's open direction depends on the position of the directrix relative to the focus.

The statement that "All parabolas with vertical directrix open to the left or right" is false. A parabola's orientation is determined by the position of its directrix in relation to its focus. If you have a vertical directrix, the parabola will indeed open to the left or the right, depending on the side of the directrix the focus lies. However, if the directrix is horizontal, the parabola will open upwards or downwards. To help understand this, recall that the directrix serves as a line that, in combination with the focus, defines the set of points that make up the parabola—that is, points equidistant from both the focus and the directrix. Furthermore, the equation of a parabola can change based on the orientation and position of the axis, the focus, and the directrix, as shown in various figures and equations related to parabolic motion and geometry.

Answer:

the symmetry for each function is -8 and -4

hoped that helped:P

The axis of symmetry for the function f(x) = -4(x - 8)^2 + 3 is x = 0.

The axis of symmetry of a quadratic function can be found using the formula:

x = -b / (2a)

For the function f(x) = -4(x - 8)^2 + 3, the coefficient of the x^2 term is -4 (which is a) and the coefficient of the x term is 0 (which is b).

Therefore, the axis of symmetry can be found as:

x = -b / (2a) = -0 / (2*(-4)) = 0

So, the axis of symmetry for the function f(x) = -4(x - 8)^2 + 3 is x = 0.

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Answer: The correct is answer is: The subset consists of all the sandwiches with either white bread and ham or rye bread and turkey.

Step-by-step explanation: I got this question correct.

The statement of the subset is given below. Then the correct options are A, C, and D.

Sets are groups of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

You are at a sandwich shop.

You can choose from white or rye bread, turkey or ham, and Swiss or American cheese to make your sandwich.

Then the number of the sample will be

Total sample = 2 x 2 x 2 = 8

The set will be {(WTS), (WTA), (WHS), (WHA), (RTS), (RTA), (RHS), (RHA)}.

All eight possible sandwich combinations are listed below.

If we take sandwiches 3, 4, 5, and 6 as a subset of the sample space.

Then the statements below describe this subset will be {(WHS), (WHA), (RTS)(RTA)}

The subset consists of all the sandwiches with either white bread and Swiss cheese or rye bread and American cheese.

The subset consists of all the sandwiches with white bread and ham.

The subset consists of all the sandwiches with rye bread and turkey.

Then the correct options are A, C, and D.

The complete question is attached below.

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Answer:

The Graph has a x- intercept at (3,0)

Step-by-step explanation:

-3 +3 =0

so x=-3

Answer:

84%

Step-by-step explanation:

1,050÷1250

= 0.84

=84%

Answer:

8

Step-by-step explanation:

4 x 6

-------

3

to... 24

---- = 8

3

Answer:

8

Step-by-step explanation:

[tex]\frac{\sqrt{16}*\sqrt{36} }{\sqrt{9} } =\frac{4 * 6}{3}=\frac{24}{3} =8[/tex]

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Answer:

100mm

Step-by-step explanation:

Multiply the length times the width

Answer: 100 mm or 20 mm

Step-by-step explanation:  You ethier times it together or add it together

Hope this helps :)

Answer:

0

Step-by-step explanation:

It is 0 because that is not negative and it is the closest to positive as positive is usually warmer than negative temperatures

-48r^2−10r+3

Step-by-step explanation:

(6r-1)(-8r-3)

Apply the distributive property by multiplying each term of 6r−1 by each term of -8r−3

-48r^2−18r+8r+3

Combine -18r and 8r to get -10r.

-48r^2−10r+3

Therefore the product of this equation is -48r^2−10r+3

Hope this helps! If you have any more questions or you need further clarification on anything please comment down below. Good luck!

The value of the product of the expression is,

⇒ - 48r² - 10r + 3

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition

Given that;

The expression is,

⇒ (6r - 1) (- 8r - 3)

Now, We can multiply as;

⇒ (6r - 1) (- 8r - 3)

⇒ - 48r² - 18r + 8r + 3

⇒ - 48r² - 10r + 3

Thus, The value of the product of the expression is,

⇒ - 48r² - 10r + 3

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Answer:

  A.  93°

Step-by-step explanation:

The inscribed angle has half the measure of the arc it subtends.

  ∠Y = 186°/2 = 93°

The measure of angle XYZ is 93°.

Answer:

32 cubic meter

Step-by-step explanation:

Volume  for any pyramid  is given by  following expression

volume of pyramid = 1/3( area of base of pyramid * height of pyramid)

________________________________

In the problem

base area of pyramid = 24 sq. m

height = 4 m

Therefore substituting the above given value in formula for volume of pyramid we have

volume of pyramid = 1/3( 24 sq. m * 4 m) = 8 sq. m * 4 m   (since 24/3 = 8)

volume of pyramid =  32 cubic meter.