2/3 + 9/12 add fractions with unlike denominators

Answer:

New distance = 2do

Step-by-step explanation:

The distance equation :

Distance = speed * time

If speed is doubled ; time stays the same

If speed is doubled,; new speed becomes

Doubled speed = 2* speed

Time remains the same ;

Hence,

New distance becomes : 2 * speed * time

Original dista, Speed * distance

New distance, dn = 2*do = 2do

The new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees are approximately (4.993, 2.048).

To find the new coordinates of the point (5, 2) after rotating counterclockwise about the origin through an angle of 5 degrees, we can use the rotation formula:

x' = x * cos(theta) - y * sin(theta)

y' = x * sin(theta) + y * cos(theta)

Where (x, y) are the original coordinates, (x', y') are the new coordinates after rotation, and theta is the angle of rotation in radians.

Converting the angle of rotation from degrees to radians:

theta = 5 degrees * (pi/180) ≈ 0.08727 radians

Plugging in the values into the rotation formula:

x' = 5 * cos(0.08727) - 2 * sin(0.08727)

y' = 5 * sin(0.08727) + 2 * cos(0.08727)

Evaluating the trigonometric functions and simplifying:

x' ≈ 4.993

y' ≈ 2.048

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Answer:

x=9

Step-by-step explanation:

13x-32 and 7x+22 are equal to each other (angles) so

13x-32=7x+22

13x-7x=22+32

6x=54

x=54/6

x=9

Using compound interest Arnold will have $412,102.63 in his IRA when he retires at age 67.

To find out how much Arnold will have in his IRA when he retires at age 67, we can use the formula for the future value of an annuity:

FV = PMT × (\((1 + r/n)^{(n*t)}\) - 1) / (r/n)

Where:

Here are the steps to solve the future value of Arnold's IRA:

Convert the annual interest rate to a monthly rate and express it as a decimal:

r = 2.75% / 12 = 0.00229167

Determine the number of compounding periods per year:

n = 12 (since the interest is compounded monthly)

Calculate the number of years until Arnold retires:

t = 67 - 44 = 23

Plug in the values into the formula and solve for FV:

FV = 850 × (\((1 + 0.00229167/12)^{(12 * 23)}\) - 1) / (0.00229167/12)

FV = $412,102.63

Therefore, Arnold will have $412,102.63 in his IRA when he retires at age 67.

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Answer:

b= 8

Step-by-step explanation:

you use Pythagorean theorem to solve this problem

a² + b² = c²

since you already have a and c and you're missing b you rearrange the formula to:

\(c^{2}\)-\(a^{2}\) = b²

17² - 15² = b²

64² = b²

\(\sqrt{64}\) = b

8 = b

Step-by-step explanation:

To find side b use Pythagoras theorem:

Hypotenuse²=Base²+Height ²

17²=B²+15²

289-225=B²

64=B²

√8=B²

So,

8 yards is Side B

Now,

We can use Heron's Formula

√S(S-A) (S-B) (S-C)

Let's find semi perimeter

17+15+8/2

40/2=20

So, S=20

Let A=8,B=15,C=17

√20(20-8) (20-15) (20-17)

√20×12×5×3

√2×2×5×5×2×2×3×3 (Factorising the numbers)

2×5×2×2×3

120 yards Answer

hope it helps...

it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

A cluster sample is a sampling technique where the population is divided into clusters or groups, and a subset of clusters is selected at random to form the overall sample. In this type of sampling, all members of the selected clusters are included in the sample.

In the given example, the airline company selects 555 flights as clusters and surveys every passenger on those flights. Each flight represents a cluster, and by selecting random flights, the company includes every passenger on those selected flights in the survey.

This cluster sampling approach is suitable when each group or cluster is representative of the overall population. It is useful when it is impractical or costly to sample every individual unit within the population, but the selected clusters are expected to reflect the characteristics of the entire population.

Cluster sampling allows for more practical data collection, particularly when dealing with large populations or geographically dispersed units. However, it is important to consider the potential for intra-cluster similarity, as individuals within the same cluster may be more similar to each other than to individuals in other clusters.

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Ingrid needs to deposit approximately $558.95 at the end of each quarter to have enough money to buy the $17,000 car in 6 years.

To calculate the amount Ingrid needs to deposit at the end of each quarter, we can use the future value of an annuity formula. The future value (FV) of an annuity is given by the formula:

FV = P * ((1 + r/n)(n*t) - 1) / (r/n)

Where:

P is the periodic deposit

r is the annual interest rate (as a decimal)

n is the number of compounding periods per year

t is the number of years

In this case, Ingrid wants to accumulate $17,000 in 6 years, with a quarterly compounding rate of 5.5% (0.055) and 4 compounding periods per year. Plugging these values into the formula:

17,000 = P * ((1 + 0.055/4)²⁴ - 1) / (0.055/4)

By solving this equation, we find that Ingrid needs to deposit approximately $558.95 at the end of each quarter to accumulate enough money to pay for her car.

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The value of x is 3√2/2.

Given is a right triangle with acute angles equal to 45-degrees.

We need to find the missing length x,

So, according to theorem of triangles,

Sides opposite to the equal angles are equal.

So, both the sided other than the hypotenuse will be x,

So,

We know that the ratio of the sine of an angle is perpendicular to the hypotenuse,

So,

Sin 45° = x/3

1/√2 = x/3

x = 3√2/2

Alternatively,

Using the Pythagoras theorem we have,

x² + x² = 3²

2x² = 9

x² = 9/2

x = √9/2

x = 3/√2

x = 3√2/2

Hence the value of x is 3√2/2.

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The complete question is attached.

Answer:

A and D could form a triangle

Step-by-step explanation:

if you add up the three inner angles of a triangle it should always be 180°

Answer:

The value of n based on the equation is -410.

Step-by-step explanation:

156 - n - 412 = 154

Subtract 412 from 156.

-n - 256 = 154

Add 256 on both sides of the equation.

-n = 410

Divide both sides of the equation by -1.

n = -410

So, the value of n is -410. We can check this answer by plugging it into the equation.

156 - (-410) - 412 =  566 - 412 = 154

Answer:

Step-by-step explanation:

\(\frac{1.107}{123} \times \frac{1.998}{333} = \)

\( = > 9 \times 6\)

\( = 45\)

Answer:

Step-by-step explanation:

\(\frac{1.107}{123}*\frac{1.998}{333}= 0.009 * 0.006 = 0.000054\)

1107÷ 123 = 9

The dividend has 3 decimal places. So, take 3 decimal places from the right towards left in the result  0.009

1.107 ÷ 123 = 0.0009

0.009 * 0.006

First multiply 9 * 6 = 54

Now, count the number of decimal place in the multiplicands. 0.009 has 3 decimal places and 0.006 has 3 decimal places. So totally, 3+ 3 = 6 decimal places in the result

0.009 * 0.006 = 0.000054

Answer:

119 is the value of x when y = 7

Step-by-step explanation:

Since y varies inversely with x, we can use the following equation to model this:

y = k/x, where

Step 1:  Find k by plugging in values:

Before we can find the value of x when y = k, we'll first need to find k, the constant of proportionality.  We can find k by plugging in 49 for y and 17 for x:

Plugging in the values in the inverse variation equation gives us:

49 = k/17

Solve for k by multiplying both sides by 17:

(49 = k / 17) * 17

833 = k

Thus, the constant of proportionality (k) is 833.

Step 2:  Find x when y = k by plugging in 7 for y and 833 for k in the inverse variation equation:

Plugging in the values in the inverse variation gives us:

7 = 833/x

Multiplying both sides by x gives us:

(7 = 833/x) * x

7x = 833

Dividing both sides by 7 gives us:

(7x = 833) / 7

x = 119

Thus, 119 is the value of x when y = 7.

The conditional probability that the sum of two fair 6-sided dice is greater than 9, given that neither die is a six, is 1/18.

To find the conditional probability that the sum of two fair 6-sided dice is greater than 9, given that neither die is a six, we need to determine the number of favorable outcomes and the total number of possible outcomes.

First, let's consider the possible outcomes for two fair 6-sided dice. Each die can have a value from 1 to 6, so the total number of outcomes is 6 x 6 = 36.

Next, we need to determine the favorable outcomes, which are the outcomes where the sum is greater than 9 and neither die is a six.

To have a sum greater than 9, the possible combinations are (4, 6), (5, 5), (5, 6), and (6, 4), where the first number represents the value on the first die and the second number represents the value on the second die. However, we need to exclude the combinations where either die is a six.

Therefore, the favorable outcomes are (4, 6) and (6, 4), as (5, 5) and (5, 6) contain a six.

The number of favorable outcomes is 2.

Finally, we can calculate the conditional probability using the formula:

Conditional Probability = (Number of Favorable Outcomes) / (Total Number of Outcomes)

Conditional Probability = 2 / 36

Simplifying, we have:

Conditional Probability = 1 / 18

Hence, the conditional probability that the sum of two fair 6-sided dice is greater than 9, given that neither die is a six, is 1/18.

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The cost of each company would be the same for 6 hours of landscaping.

Finding the intersection of the two lines, which reflects the number of hours where the costs of the two companies are equal, requires setting the two equations equal to one another. This is because the y-values of the two equations—i.e., the costs—are identical at that moment.

Given that, Company A charges $50 per hour and a $150 equipment fee.

The equation is:

A = 50t + 150

For company B:

B = 25t + 300

To graph the function find different values of A and B by substituting different values of t.

The two equations would make the same cost at the intersection of the two equations on the graph.

Or, through the equation we can calculate the same cost as:

50t + 150 = 25t + 300

25t = 150

t = 6

The two lines intersect at point t = 6.

Hence, the cost of each company would be the same for 6 hours of landscaping.

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The mean absolute percent error (MAPE) is 25%.

The mean absolute percent error (MAPE) is a measure of forecasting accuracy that quantifies the average deviation between predicted and actual values as a percentage of the actual values. In this case, the mean absolute deviation (MAD) is given as 25 units for the past 10 periods, and the total demand is 1,000 units.

To calculate the MAPE, we need to divide the MAD by the total demand and multiply by 100 to express it as a percentage. In this scenario, the MAPE is calculated as follows:

MAPE = (MAD / Total Demand) * 100

     = (25 / 1,000) * 100

     = 2.5%

Therefore, the MAPE is 2.5%, which means that, on average, the forecasts have a 2.5% deviation from the actual demand.

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When designing a security system, it is essential to consider the needs and roles of administrators, end-users, and auditors. Each user type plays a unique role in maintaining the security and functionality of the system.

By understanding their requirements and incorporating them into the design, a robust and effective security system can be achieved.

Three types of users that are considered in the design of a security system are:

1. Administrators: Administrators have the highest level of privileges and are responsible for managing and configuring the security system.

They have access to all system functions and controls, allowing them to set up user accounts, define access rights, and monitor system activities. Administrators play a critical role in ensuring the overall security of the system.

2. End-users: End-users are the individuals who interact with the security system on a daily basis. They include employees, customers, or any other individuals who require access to the system.

End-users typically have limited privileges and can perform specific actions based on their assigned roles and permissions.

It is important to design the security system with user-friendly interfaces and intuitive controls to enhance usability and productivity.

3. Auditors: Auditors are responsible for assessing the effectiveness and compliance of the security system.

They review system logs, conduct security audits, and analyze security controls to ensure that the system is functioning as intended and meeting regulatory requirements.

Auditors provide valuable feedback and recommendations for improving the security system's design and implementation.

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The solution to the system of equations is (x, y, z) = (13, -23, 0).

To solve the system of equations:

-2x + 6y + 4z = -32,

-2x - 3y + 2z = 17,

3x + 2y + z = -21,

we can use the method of elimination or substitution. Let's use the method of elimination:

Multiply the second equation by 3 and the third equation by 2 to create cancellation of the x term when added to the first equation:

-2x + 6y + 4z = -32,

-6x - 9y + 6z = 51,

6x + 4y + 2z = -42.

Add the modified second and third equations to the first equation to eliminate the x term:

(-2x + 6y + 4z) + (-6x - 9y + 6z) + (6x + 4y + 2z) = -32 + 51 - 42.

This simplifies to:

y + 12z = -23.

Substitute this result back into the second equation to solve for x:-2x - 3y + 2z = 17,

-2x - 3(-23 - 12z) + 2z = 17,

-2x + 69 + 36z + 2z = 17,

-2x + 38z = -52.

Multiply the third equation by 2 and subtract it from the fourth equation to eliminate the x term:

(-2x + 38z) - (6x + 4y + 2z) = -52 - (-42).

This simplifies to:

-8x + 36z - 4y = -10.

Substitute the value of y from the first equation into the equation obtained in Step 4:

-8x + 36z - 4(-23 - 12z) = -10,

-8x + 36z + 92 + 48z = -10,

-8x + 84z = -102.

Divide both sides of the equation by -4 to solve for x:

2x - 21z = 26.

Multiply the equation obtained in Step 6 by 4 and add it to the equation from Step 3:

4(2x - 21z) + (-2x + 38z) = 4(26) + (-52),

-6z = 0,

z = 0.

Substitute the value of z into the equation from Step 6 to solve for x:

2x - 21(0) = 26,

2x = 26,

x = 13.

Substitute the values of x and z into the equation y + 12z = -23 to solve for y:

y + 12(0) = -23,

y = -23.

Therefore, the solution to the system of equations is (x, y, z) = (13, -23, 0).

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Answer:

Each calculator cost $30 because $180 divided by 6 is 30

Step-by-step explanation:

Answer:

105 = (5x-70)

Step-by-step explanation:

You are trying to find x so you would have to place that in to finally get to the end where x = 5

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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The standard form of the equations are 9x + 7y = -49, x + 2y = 2,

3x - y = 7 and x + 5y = -20 respectively.

What is the standard form?

Ax + By + C = 0, A, B ≠ 0, is the standard form of an equation for a first-degree line in two variables. A, B, and C are constants that belong to the category of real numbers.

When we represent the equation geometrically, we consistently obtain a straight line.

a) y = -9/7x - 7

⇒y = (-9x - 49)/7

⇒7y = (-9x - 49)

⇒9x + 7y = -49

b) y = -1/2x + 1

⇒y = (-1x + 2)/2

⇒2y = -x + 2

⇒x + 2y = 2

c) y = 3x - 7

⇒ 3x - y = 7

d) y = - 1/5x - 4

⇒y = (-1x - 20)/5

⇒5y = -x - 20

⇒x + 5y = -20

Hence, the standard form of all the equations have been obtained.

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When two biased dice are rolled, the probability of obtaining a sum of 6 is 5/18 or approximately 0.2778. There are five possible ways to roll a sum of 6.

When two dice are thrown and each of them is biased, a four is obtained four times as often as any of the other numbers. In this problem, we have to find out the probability of getting a sum of 6 when the dice are rolled. The probability of rolling a sum of 6 is obtained by summing the probabilities of all the ways of rolling a sum of 6.

There are five ways to roll a sum of 6, and we have to compute the probability of each one. The first way is to roll a 2 on one die and a 4 on the other die. The probability of rolling a 2 on one die is 1/6, and the probability of rolling a 4 on the other die is 4/6.

So the probability of getting a sum of 6 is 1/6 × 4/6 = 4/36 = 1/9. The second way is to roll a 4 on one die and a 2 on the other die. The probability of rolling a 4 on one die is 4/6, and the probability of rolling a 2 on the other die is 1/6.

So the probability of getting a sum of 6 is 4/6 × 1/6 = 4/36 = 1/9. The third way is to roll a 3 on one die and a 3 on the other die. The probability of rolling a 3 on one die is 1/6, and the probability of rolling a 3 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fourth way is to roll a 5 on one die and a 1 on the other die. The probability of rolling a 5 on one die is 1/6, and the probability of rolling a 1 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. The fifth way is to roll a 1 on-one die and a 5 on the other die. The probability of rolling a 1 on one die is 1/6, and the probability of rolling a 5 on the other die is 1/6.

So the probability of getting a sum of 6 is 1/6 × 1/6 = 1/36. Therefore, the total probability of rolling a sum of 6 is 1/9 + 1/9 + 1/36 + 1/36 + 1/36 = 5/18, which is approximately 0.2778.

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Answer:

299

Step-by-step explanation:

The solution to the expression is A = 299

Given data ,

Let the expression be represented as A

Now , the value of A is

Let the first number be represented as p

The value of p = 23

Let the second number be represented as q

The value of q = 13

So, A = pq

On simplifying the equation , we get

A = p multiplied by the value of q

And , A = 23 x 13

A = 299

Therefore , the value of A is 299

Hence , the expression is A = 299

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Answer:

1) 21.16

2) 6.97

3) 62.08

4) 61.43

5) 2.8

6) 14.86

7) 63.16

8) 73.47

9) 83.10

10) 88

Answer:

1, 2, 3, 6

Step-by-step explanation:

I don't really know how to explain this but if the only change between the two triangles is that it was reflected, then there was no change of any of the angles or side lengths, you just have to make sure you match up the rights angles and the right sides.

Answer:

Hi how are you doing today Jasmine

Answer:

276 unit^2.

Step-by-step explanation:

This area  is the sum of the area of 2 rectangles

= 12 * 13 + 8 * 15

= 156 + 120

= 276.

Answer:

Step-by-step explanation:

the answer is (10,2) in point form, in equation form it is x=10, y= -2.

Answer:

sue = 13 - x

tony = (18 + x) / 2

Step-by-step explanation:

sue = 13 - x

tony = (18 + x) / 2

Answer:

sue is 13-x, then Tony is (18-x)/2