10. use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true. (a) q

After completing the task, we can state that Therefore, it will take amount approximately 11.90 years for the account to contain $2,000.

aggregate attempting to determine the time required, total number or amount. The quantity at hand or under consideration is extremely active. the overall effect, relevance, or import. Principle, interest, and a third accounting are all included. Word forms include amounts, amounting, and amounted. pliable noun A quantity is how much there is, how much you have, how much you need, or how much you get. He needs that amount of money to get by.

\(A = P(1 + r/n)^(nt)\\A = 1000(1 + 0.06/1)^(1*3)\\A = 1000(1.191)\\A = $1,191\\\)

Therefore, after 3 years, the amount in the account will be $1,191.

\(A = 1000(1 + 0.06/1)^(1*16)\\A = 1000(1.06)^16\\A = $2,011.17\\\)

Therefore, after 16 years, the amount in the account will be $2,011.17.

\(A = 1000(1 + 0.06/1)^(1*t) = 1500\\(1 + 0.06)^t = 1.5\\t = log(1.5)/log(1 + 0.06)\\t = 11.55\\\)

Therefore, it will take approximately 11.55 years for the account to contain $1,500.

\(A = 1000(1 + 0.06/1)^(1*t) = 2000\\(1 + 0.06)^t = 2\\t = log(2)/log(1 + 0.06)\\t = 11.90\\\)

Therefore, it will take approximately 11.90 years for the account to contain $2,000.

To know more about amount visit :-

brainly.com/question/8082054

#SPJ1

The evaluated the integral of the product of tangent and secant functions  is -(1/6) ln| sin(6x)| + C, where C is the constant of integration.

Integration is an important topic in calculus that deals with finding the antiderivative or indefinite integral of a given function. In this problem, we are required to evaluate the integral of the product of tangent and secant functions.

To evaluate the given integral, we need to use the substitution method. Let u = 6x, then du/dx = 6, and dx = du/6. Substituting these values, we get:

∫tan(6x) sec(6x) dx = ∫tan(u) sec(u) (du/6)

Now, we need to simplify the integrand by using trigonometric identities. Recall that secant is the reciprocal of cosine, so we can write sec(u) = 1/cos(u). Similarly, we know that tangent is the quotient of sine and cosine, so we can write tan(u) = sin(u)/cos(u). Substituting these values, we get:

∫tan(u) sec(u) (du/6) = ∫(sin(u)/cos(u)) (1/cos(u)) (du/6)

Simplifying the expression further, we get:

∫tan(6x) sec(6x) dx = (1/6) ∫sin(u)/cos^2(u) du

We can now integrate this expression by using another substitution. Let v = cos(u), then dv/dx = -sin(u) du/dx = -sin(u) * 6. Rearranging this equation, we get du = dv/(-6sin(u)) = -dv/(6v * √(1 - v^2)). Substituting these values, we get:

∫sin(u)/cos^2(u) du = -∫(1/v^2) (-dv/(6v * √(1 - v^2)))

Simplifying the expression further, we get:

∫tan(6x) sec(6x) dx = (1/6) ∫(1/v^2) (dv/√(1 - v^2)))

This expression can be integrated by using the substitution v = sin(x), then dv/dx = cos(x), and dx = dv/cos(x). Substituting these values, we get:

∫(1/v^2) (dv/√(1 - v^2))) = -∫(1/(1 - v^2)) (-dv/v)

Integrating this expression, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln|v| + C

Substituting back the value of v, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln| sin(u)| + C

Finally, substituting back the value of u, we get:

∫tan(6x) sec(6x) dx = -(1/6) ln |sin(6x)| + C

To know more about integration here.

https://brainly.com/question/18125359

#SPJ4

Complete Question:

Evaluate ∫tan(6x) sec(6x) dx.

Answer:

5/12

Step-by-step explanation:

2/10 can be simplified to 1/5

3/6 can be simplified to 1/2

4/8 can be simplified to 1/2

5/12 is already simplified

Answer:

4 2/3

Step-by-step explanation:

\( \sf{\blue{«} \: \pink{ \large{ \underline{A\orange{N} \red{S} \green{W} \purple{E} \pink{{R}}}}}}\)

Expression: \(\displaystyle\sf (6-2x) +(15-3x)\)

Substituting \(\displaystyle\sf x=0.2\):

\(\displaystyle\sf (6-2(0.2)) +(15-3(0.2))\)

Simplifying the expression inside the parentheses:

\(\displaystyle\sf (6-0.4) +(15-0.6)\)

\(\displaystyle\sf 5.6 +14.4\)

Calculating the sum:

\(\displaystyle\sf 20\)

Therefore, \(\displaystyle\sf (6-2x) +(15-3x)\) evaluated at \(\displaystyle\sf x=0.2\) is equal to \(\displaystyle\sf 20\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:4(5x+1)

Step-by-step explanation: you want to subtract the numbers 4+5x(6-2)/4+5x(4) so you'll need to  multiply 5 and 4 so 4+5x*4 but i'm goin to make it smaller so it would be 4+20x  but you have to rearrange it instead of it being 4+20x it would be 20x+4 .And the common factor would be 4(5x+1).

I hope this helps and makes sense.

The true statement is; II. Option D

From the information given, we have that;

I. The set of all second-degree polynomials with the standard operations is a vector space

II. The set of all first-degree polynomial functions 'mx' with the standard operations is a vector space

III. The set of second quadrant vectors with the standard operations is a vector space

Note that;

Learn more about polynomials at: https://brainly.com/question/4142886

#SPJ1

Answer:

2 Blocks

Step-by-step explanation:

Answer:2/3

Step-by-step explanation: 2 blocks apart so just 1/3 times 2=2/3

The fraction of the class that is sophomores is \(35/43\).

The fraction of the class that is sophomores, divide the number of sophomores by the total number of students in the class.

Number of sophomores = 35

Total number of students = 43

Fraction of sophomores = (Number of sophomores)/(Total number of students Fraction of sophomores)

Fraction of sophomores  \(= 35 / 43\)

Therefore, the fraction of the class that are sophomores is = \(35/43\).

To learn more about Fraction here,

https://brainly.com/question/10354322

Answer:

C. x is y less than z

Step-by-step explanation:

x+y=z

by using transposition

x = z-y

whatever x is, it is equal to the value of y taken from z

Answer:

The answer is C.

I did the practice.

The biker needs to travel 45 km more to complete his journey.

Given that, a biker traveled 2/5 of the road on the first day, then traveled 5 kilometers less on the next day, which is equal to 3/8 of the road, we need to find how much he need to cover more,

Let the total distance of the road be x,
So,

2x/5 - 5 = 3x/8

2x/5 - 3x/8 = 5

Solving for x,

Multiply by 40 to both sides,

16x-15x = 200

x = 200

Therefore, the total distance of the road is 200 km.

Since, he travelled =

200 (2/5) = 80 km + 200 (3/8) = 75 km = 155 km

Therefore, he needs to travel 200-155 = 45 km more.

Hence, the biker needs to travel 45 km more to complete his journey.

Learn more about equations, click;

https://brainly.com/question/29657983

#SPJ1

The expression 2 - 5(x - 1) is a linear expression

From the question, we have the following parameters that can be used in our computation:

2 - 5(x - 1)

The general rule is that

Using the above as a guide, we have the following:

2 - 5(x - 1) is a linear expression

Read more about functions at

brainly.com/question/15602982

#SPJ1

We would expect John to weigh approximately 199.8 pounds at the end of week 8 if he continues to burn 6100 calories per week and maintains a proper diet.

Finding the best linear relationship between the independent and dependent variables is the aim of linear regression. To put it another way, it seeks out the line (or plane, or hyperplane in higher dimensions) that best fits the data. The dependent variable's future values for new values of the independent variable can then be predicted using this line.

We may build a linear regression model using the provided data, with activity (in calories) serving as the independent variable and weight (in pounds) serving as the dependent variable. Using this model, we can then forecast John's weight at the conclusion of week eight depending on the number of calories he burned in that week.

Using a spreadsheet or statistical software, we can calculate the regression equation:

Weight = -0.0049 x Exercise + 229.85

We can plug in the exercise value for week 8 (6100 calories) and solve for weight:

Weight = -0.0049 x 6100 + 229.85

Weight ≈ 199.8 pounds

Therefore, we would expect John to weigh approximately 199.8 pounds at the end of week 8 if he continues to burn 6100 calories per week and maintains a proper diet.

To know more about weight visit:

https://brainly.com/question/28571689

#SPJ1

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

For more questions on bags

https://brainly.com/question/31835238

#SPJ8

Answer:

76

Step-by-step explanation:

Hope this helps

Answer:

A

Step-by-step explanation:

If each of X, Y, and N are positive integers, then the value of X+Y+N is 212.1

A collection of inequalities for which we consider common solution for all inequalities is called a system of inequalities.

WE are given that A red purse contains $7, and a black purse contains $10. Each package contains X red purses and Y black purses.

X = 7

Y = 10

If there are N packages (N ≥ 2) and the total value of them is $2021

X + Y = One packages

N packages = N(X + Y ) = 10 N

if each of X, Y, and N are positive integers, then;

10 N = 2021

N = 2021/10

N = 202.1

Therefore, X+Y+N = 10 + 202.1 = 212.1

Learn more about solutions to the system of inequalities here:

https://brainly.com/question/16339562

#SPJ1

The price of the cost per quart of laundry detergent is A = $ 3.47

Given data ,

Let the unit cost rate be A

Now , There are 4 quarts in a gallon, so a 2-gallon container contains 8 quarts.

To find the price per quart, we can divide the total cost by the number of quarts:

Price per quart = Total cost / Number of quarts

Price per quart = $27.76 / 8 = $3.47

Hence , the price per quart of laundry detergent is $ 3.47

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ1

Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

To learn more about : time

https://brainly.com/question/26862717

#SPJ8

The simplified mixed number upon evaluation is \(3\frac{11}{27}\).

Given:

a = −3/5 and b = −6.75

We have to determine the value of (2a−1/3) ÷ b/15.

Substituting the values of a and b in the expression, we get

(2(−3/5)−1/3) ÷ (−6.75)/15

⇒ (-6/5 - 1/3) ÷ (-0.45)

⇒ (-23/15) ÷ (-0.45)

⇒ 23/15 × 100/45

⇒ 92/27

⇒ \(3\frac{11}{27}\)

To know more about mixed numbers visit:

https://brainly.com/question/2639375

#SPJ13

Answer:

x=3y

Step-by-step explanation:

divide both sides by 20

20x = 60y

------   -------

20        20

x=3y

Answer:

x = 3y

Step-by-step explanation:

20x = 60y

Divide 20 into both sides.

20x/20 = 60y/20

1x = 6/2y

x = 3y

Answer:

Domain= {4,p,3,7}

Range= {p,0,3,m}

Step-by-step explanation:

⇒Domain: is the set of the first number in every pair.

⇒Range: is the set of the second number in every pair

TO FIND THE DOMAIN: S= {(4,p),(p,0),(3,3),(7,m)}

so Domain= {4,p,3,7}

TO FIND THE RANGE: S= {(4,p),(p,0),(3,3),(7,m)}

so Range= {p,0,3,m}

Hope this helps :)

yes yes yes yes yes yes yes yes yes yes yes yes

The number in decimal form is written as;

⇒ 0.959

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The number ''Zero and nine hundred fifty nine thousandths'' written as a decimal.

Now, We can write as;

⇒ Zero and nine hundred fifty nine thousandths

⇒ 0.959

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

EXPLANATION

Since we have the given graph, the points that we can use are the following:

The points (-5,5) is above the line and is not a solution to the inequality.

The point (0,10) is on the line and is not a solution to the inequality.

The point (0,0) is below the line and is a solution to the inequality.

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

For such more questions on Credit Card Payoff

https://brainly.com/question/26867415

#SPJ8

Answer:

1.5 cars/hour

Step-by-step explanation:

if you look at the graph and go up by hour it calculates to 1.5 cars/hour

hope it helps

Brainliest if right :)

Answer:

The average would be 5.25

Step-by-step explanation:

If you add up all of the points

1.5+3+4.5+6+7.5+9=31.5

Divide that by the number of points there are, which is 6

31.5/6

and you should get your answer of 5.25 cars Quick-E-Clean can detail in an hour.

Answer:

hey my friend please come over to spend the Christmas holidays with me and my family this year. If you are afraid of your dad it's ok I'll ask my mom to call him and ask him

============================================================

Explanation:

Let's go through the answer choices one by one

We've eliminated choices B, C and D from the list. Only choice A remains. Luckily the answer "none of these" is a perfect fit since we've eliminated everything else.

Answer:

Using the process of elimination you can tell the answer is A.

B and D dont make sense, it may be C but I dont think so, so it is A.

Answer:

no

yes

no

no

Step-by-step explanation:

this should be true

a+b>c

a+c>b

b+c>a