how can you fluently add, subtract, mulitply, and divide decimals? how can you multiply and divide fractions?​

Answer:

B

Step-by-step explanation:

The probability that the sum is 4 or higher is 11/12.

Probability in mathematics is the possibility of an event in time. In simple words, how many times does that incident is happening in any given time interval.

Given:

You rolled two fair 6 sided dice.

The total number of outcomes = 6 x 6 = 36.

The sample space that does not satisfy the condition,

S = {1 + 1, 1 + 2, 2 + 1}

The possible outcomes = 36 - 3 = 33

The probability that the sum is 4 or higher,

= 33/36

= 11/12

Therefore, 11/12 is the probability.

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To bring the 2,000 kg wagon to rest, the buffer stop needs enough springs to absorb its kinetic energy. The number of springs and their stiffness can be calculated using given parameters and formulas.



To calculate the number of springs required in the buffer stop, we need to find the energy of motion that needs to be absorbed. The kinetic energy (KE) of the wagon is given by KE = (1/2)mv^2, where m is the mass (2,000 kg) and v is the velocity (0.69 m/s). The KE is 477.9 J.Next, we calculate the potential energy stored in the compressed springs. The compression distance is 15 cm, which is 0.15 m. The potential energy (PE) stored in each spring is given by PE = (1/2)kx^2, where k is the stiffness of the spring and x is the compression distance.

The total energy absorbed by all the springs is equal to the kinetic energy of the wagon. Therefore, the number of springs required is given by N = KE / PE, where N is the number of springs.To determine the stiffness of the spring, we use the formula k = (Gd^4) / (8nD^3), where G is the shear modulus (0.8 x 10^5 N/mm^2), d is the wire diameter (2 cm), n is the number of coils (15), and D is the mean diameter of the coils (20 cm).

By substituting the values into the equations, we can find the number of springs and the stiffness of each spring.

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The total surface area of the triangular pyramid is: 381 yd²

To find the surface area of the pyramid, we have to find all the surface area of the surfaces and add them together.

Area of base = 11 * 9

Area = 99 yd²

Area of 2 big triangles is:

A = 2(¹/₂ * 11 * 15)

A = 165 yd²

Area of two small triangles is:

A = 2(¹/₂ * 9 * 13)

A = 117 yd²

Thus:

Total surface area = 99 + 165 + 117

Total surface area = 381 yd²

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Answer:

25 rows of seats

Step-by-step explanation:

20 + 4 + 4=28 (the middle and both wings)

700/28=25 (divide the whole row by the total number of seats)

Therefore, the value of the investment after 3.5 years is $2325.28.

Percent is a unit of measurement that represents a fraction of 100. It is often used to express a proportion or rate in relation to a total of 100. For example, if a sales tax is 7%, that means that for every $100 spent, $7 goes towards the tax. The symbol used to represent percent is %.

Here,

The formula for the value of the investment after t years is:

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

where:

A is the amount of money after t years

P is the principal investment (initial amount invested)

r is the annual interest rate (as a decimal)

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

t is the time in years

Using this formula, we can plug in the values given in the problem:

P = 2000

r = 0.04

n = 12 (monthly compounding)

t = 3.5

A = \(2000(1 + 0.04/12)^{12*3.5}\)

A = \(2000*(1.003333)^{42}\)

A = 2000(1.162641)

A = $2325.28

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Answer:

D

Step-by-step explanation:

The answer is point D(-2,1).

1. If the point D was moved down 2 units, then its coordinates became (-2,-1).

2. If point (-2,-1) was reflected over the x-axis, then its coordinates became (-2,1).

3. If the point (-2,1) was moved 4 units to the right, then its coordinates became (2,1).

4. If point (2,1) was reflected over y-axis, its coordinates became (-2,1).

Answer:

Step-by-step explanation:

\(\dfrac45-\dfrac13\cdot\dfrac45=\dfrac{4\cdot3}{5\cdot3}-\dfrac4{15}=\dfrac{12}{15}-\dfrac4{15}=\dfrac8{15}\)

The monthly repayment for the first loan is $1,370.55 and the total interest paid over the life of the loan is approximately $290

The monthly repayment for the second loan is $6,523.96 and the total interest paid over the life of the loan is approximately $1,160,310.00.

Loan 1:

Loan amount = $210,000

Interest rate = 6.57% per year (compounded monthly)

Duration = 25 years

Payment frequency = Monthly

Using the formula for monthly loan payments, we can calculate the repayment amount:

Repayment = [P * r * \((1 + r)^n\)] / [\((1 + r)^n\) - 1]

where P is the loan amount, r is the monthly interest rate, and n is the number of payments.

First, we need to convert the annual interest rate to a monthly rate:

r = 6.57% / 12 = 0.5475% per month

n = 25 years * 12 months per year = 300 months

Substituting the values into the formula, we get:

Repayment = [210,000 * 0.005475 * (1 + 0.005475)^300] / [(1 + 0.005475)^300 - 1]

Repayment ≈ $1,370.55

Total interest paid over the life of the loan = Repayment * number of payments - P

Total interest = $1,370.55 * 300 - $210,000

Total interest ≈ $290,165.00

Therefore, the monthly repayment for the first loan is $1,370.55 and the total interest paid over the life of the loan is approximately $290,165.00.

Loan 2:

Loan amount = $731,500

Interest rate = 8.75% per year (compounded monthly)

Duration = 20 years

Payment frequency = Monthly

Using the same formula as above, we can calculate the repayment amount:

r = 8.75% / 12 = 0.7292% per month

n = 20 years * 12 months per year = 240 months

Repayment = [731,500 * 0.007292 * (1 + 0.007292)^240] / [(1 + 0.007292)^240 - 1]

Repayment ≈ $6,523.96

Total interest paid over the life of the loan = Repayment * number of payments - P

Total interest = $6,523.96 * 240 - $731,500

Total interest ≈ $1,160,310.00

Therefore, the monthly repayment for the second loan is $6,523.96 and the total interest paid over the life of the loan is approximately $1,160,310.00.

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Answer + Step-by-step explanation:

an= 4(2)ⁿ⁻¹

First term (n = 1) :

a1= 4(2)¹⁻¹ = 4(2)⁰ = 4×(1) = 4

Second term (n = 2) :

a2= 4(2)²⁻¹ = 4(2)¹ = 4×(2) = 8

Third term (n = 3) :

a3= 4(2)³⁻¹ = 4(2)² = 4×(4) = 16

Fourth term (n = 4) :

a4= 4(2)⁴⁻¹ = 4(2)³ = 4×(8) = 32

Answer:

So this is scientific notation what you do is

2.9x10^5 so you put however many zeros the is powered to 10. See there is a 5 It has to be behind or in front of the decimal you might be saying how do you know if its behind or in front well negative is in front and positive is behind .

290,000 there was a number already behind the decimal so there you go 5 number behind the decimal.  

Same for the second one

290,000  870,000 is your answers so now you add hem together

1,160,000 is your final answer

Step-by-step explanation:

To find the coefficient of the term with t^6 in the expansion of (x - 2)^12 without expanding the entire binomial, we can use the binomial theorem.

The binomial theorem states that the term at index k in the expansion of (a + b)^n can be calculated using the formula: C(n, k) * a^(n-k) * b^k. where C(n, k) represents the binomial coefficient, given by: C(n, k) = n! / (k! * (n - k)!). In this case, a = x and b = -2. We are interested in finding the term with t^6, so we need to find the k value that satisfies n - k = 6.

In the expansion of (x - 2)^12, the term with t^6 will have the following form: C(12, k) * x^(12-k) * (-2)^k. To find the k value that corresponds to t^6, we solve the equation n - k = 6: 12 - k = 6. Simplifying, we find: k = 12 - 6 = 6. Therefore, the term with t^6 in the expansion of (x - 2)^12 is given by: C(12, 6 ) * x^(12-6) * (-2)^6. C(12, 6) represents the binomial coefficient, which is calculated as: C(12, 6) = 12! / (6! * (12 - 6)!). Plugging in the values, we have: C(12, 6) = 924. Therefore, the term with t^6 in the expansion of (x - 2)^12 is: 924 * x^6 * (-2)^6. Simplifying further, we get: 924 * x^6 * 64. Finally, the simplified expression is: 59040 * x^6

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The height of the 5th player would be 69 inches

To find the Height, first, we have to calculate the mean value.

No. of players=5

The height of 4 players is 60 inches, 67 inches, and 64 inches, 65 inches.

Mean =Sum of observations/No of observations

Mean of the  5th players=65

To find, Height of 5th player

As we know,

Assuming the height of the 5th player is x

Mean =Sum of observations/No of observations

65=(60+67+64+65+x)/5

65*5=60+67+64+65+x

325=256+x

x=69

Thus, the height of the 5th player is 69 inches.

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Answer:

your answer is D.        hope this helped

Answer:

its 0

Step-by-step explanation:

Answer:

have a nice day loves <3

Step-by-step explanation:

picture below

Answer:

Step-by-step explanation:

Answer:

g(x) = (x - 2)²

Step-by-step explanation:

If we want to shift a function to the right, we subtract the number we are asked to move to the right inside the function's argument:

⇒ To shift f(x) b units to right → f(x - b)

Similarly, in function notation, if we want to shift a function to the left, we add the number we are asked to move to the left inside the function's argument:

⇒ To shift f(x) b units to left → f(x + b)

Given function f(x) = x²

Shift 2 units to the right:  f(x - 2) = (x - 2)²

Therefore, g(x) = (x - 2)²

----------------------------------------------------------------------

Additional info:

g(x) = (x - 2)²

      = (x - 2)(x - 2)

      = x² - 4x + 4

Answer:

Step-by-step explanation: First things first, you have to have the variables on one side. To do that, subtract 4x from each side.

4x + 6 = 8x - 10

-4x         -4x

Now you have your equation that is ready to graph.

6 = 4x - 10

Use a graphing calculator and put in the equation. You can also go to desmos.com

When you are done you will see your graph as well as the answer.

Answer:

y = -2 and x = 4

Step-by-step explanation:

8x + 14y = 4

-6x - 7y = -10

First, find the lowest common multiple of 8 and 6 (which is 24). Multiply the first equation by 3:

8x + 14y = 4

3(8x + 14y) = 3(4)

24x + 42y = 12

Multiply the second equation by 4:

-6x - 7y = -10

4(-6x - 7y) = 4(-10)

-24x - 28y = -40

Now, add the two equations together:

24x + 42y = 12

-24x - 28y = -40

24x + -24x = 0

42y + -28y = 14y

12 + -40 = -28

14y = -28

Divide both sides by 14:

14y ÷ 14 = -28 ÷ 14

y = -2

Plug this known variable back into the first equation:

8x + 14(-2) = 4

8x + (-28) = 4

8x - 28 = 4

Add 28 to both sides:

8x - 28 + 28 = 4 + 28

8x = 32

Divide both sides by 8:

8x ÷ 8 = 32 ÷ 8

x = 4

So y = -2 and x = 4.

Hope this helps!

Answer:

y=-3x

Step-by-step explanation:

The value of ? and X are 24 and 32 respectively

A triangles is 2D shape with three sides and angles.

From the given diagram, the ratio of similar sides is equal to a constant as shown;

15/20 = 9+15/20+x

Cross multiply

15/9+15 = 20/20+x

15/24 = 20/20+x

Comparing with the given ratio

? = 24

X = 20+x

Find x

15(20+x) = 480

300 + 15x = 480

15x = 180

x =12

X = 20 +x

X= 32

Hence the value of ? and X are 24 and 32 respectively

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Answer:

2

Step-by-step explanation:

3-5/-2-(-1)

-2/-1 =

2

Answer:

2

Step-by-step explanation:

The slope is rise over run,

the equation for finding it is,

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

given the points

-2, 3

-1, 5

\(x_{1}\) = -2

\(x_{2}\) = -1

\(y_{1}\) = 3

\(y_{2}\) = 5

substitute in

\(\frac{y_{2} - y_{1} }{x_{2} - x_{1} }\)

=\(\frac{(5) - (3)}{ (-1) - (-2)}\)

simplify,

\(\frac{2}{1}\)

= 2

Answer:

117 megabytes

Step-by-step explanation:

Por regla de tres:

72 mb son a 8 mins

D mb son a 13 minutos

D = 13*72/8

D = 117 mb

Answer:

1 / 5^11

Step-by-step explanation:

5^ -6  * 5 ^ -5

We know that a^ b * a^ c = a^( b+c)

5^ ( -5+-5)

5^ -11

We also know that

a^-b = 1/ a^b

1 / 5^11

Answer:

1/5^11

Step-by-step explanation:

5^-6 * 5^-5

5^-6+(-5)

5^-6-5

5^-11

1/5^11

Note : In multiplication if the bases are same then u can add their exponent and when the base have ngative exponent just do it's reciprocal.Then u the base will have positive exponent.

Answer:

10

Step-by-step explanation:

An average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

To determine the number of people who are stepping onto the roller coaster per minute at peak time, you need to divide the number of people on the roller coaster by the duration of the ride. Hence, the correct option is B) 6.

To be more specific, this means that at peak time, an average of 3 people is getting on the ride per minute. This is how you calculate it:

Number of people per minute = Number of people on the roller coaster / Duration of the ride

Number of people on the roller coaster = 24

Duration of the ride = 8 minutes

Number of people per minute = 24 / 8 = 3

Therefore, an average of 3 people are stepping onto the roller coaster per minute at peak time. The answer is option B) 6.

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Main Answer:

The solution region to the system described is bounded.

Explanation:

The system of inequalities, 4x - 2y ≤ 28 and x ≤ 20, y ≤ 20, represents a set of linear equations that define a region in the xy-plane. By examining the inequalities, we can determine whether the solution region is bounded or unbounded.

The first inequality, 4x - 2y ≤ 28, represents a line in the xy-plane. If we plot this line, we can see that it has a finite length and is bounded. The second and third inequalities, x ≤ 20 and y ≤ 20, define the boundaries of the region by restricting the values of x and y to be less than or equal to 20.

Since all three inequalities restrict the values of x and y within specific ranges, the solution region is confined to a bounded area in the xy-plane. It is important to note that the specific shape of the solution region is not mentioned in the question, so we cannot definitively conclude that it is a circle based on the given information.

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The relation r defined on a is an equivalence relation, as it is reflexive, symmetric, and transitive.

Given x = {−1, 0, 1} and a = (x), where a is the set of all subsets of x. We define a relation r on a as follows:

For all sets s and t in a, s r t ⇔ the sum of the elements in s equals the sum of the elements in t.

To understand this relation, let's consider an example. Suppose s = {−1, 1} and t = {0, 1}. The sum of the elements in s is −1 + 1 = 0, and the sum of the elements in t is 0 + 1 = 1. Since the sum of the elements in s is not equal to the sum of the elements in t, s is not related to t under r.

Now, let's consider another example. Suppose s = {−1, 0, 1} and t = {−1, 1}. The sum of the elements in s is −1 + 0 + 1 = 0, and the sum of the elements in t is −1 + 1 = 0. Since the sum of the elements in s is equal to the sum of the elements in t, s is related to t under r.

We can also observe that the relation r is reflexive, symmetric, and transitive.

Reflexive: For any set s in a, the sum of the elements in s equals the sum of the elements in s. Therefore, s r s for all s in a.

Symmetric: If s r t for some sets s and t in a, then the sum of the elements in s equals the sum of the elements in t. But since addition is commutative, the sum of the elements in t also equals the sum of the elements in s. Therefore, t r s as well.

Transitive: If s r t and t r u for some sets s, t, and u in a, then the sum of the elements in s equals the sum of the elements in t, and the sum of the elements in t equals the sum of the elements in u. Therefore, the sum of the elements in s equals the sum of the elements in u, and hence, s r u.

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Answer:

b ≤ 24

Step-by-step explanation:

Treat it like a two-step equation:

1/3b - 4 ≤ 4​

Add 4 on both sides: 1/3b - 4 (+4) ≤ 4​ (+4)

1/3b ≤ 8

Multiply 3 on both sides (3)1/3b ≤ 8(3)

b ≤ 24