a/(2x - 3) + b/(3x + 4) = (x + 7)/(6x ^ 2 - x - 12)​

Answer:

?

Step-by-step explanation:

?

Answer:

Volume : 300

Surface Area : 280

Step-by-step explanation:

Volume : 6*5*10

Surface Area : 50+50+30+30+60+60

The vertex for the graph of the equation [tex]v - 3 = - (x+2)^2 is (-2, 3).[/tex]

To find the vertex of the graph of the equation [tex]v - 3 = - (x+2)^2,[/tex] we can rewrite it in the standard vertex form: [tex]v = a(x - h)^2 + k,[/tex]

where (h, k) represents the vertex coordinates.

First, let's rearrange the given equation:

[tex]v - 3 = - (x+2)^2[/tex]

[tex]v = - (x+2)^2 + 3[/tex]

Comparing this with the standard vertex form, we can see that h = -2 and k = 3.

Therefore, the vertex of the graph is (-2, 3).

For similar question on vertex.

https://brainly.com/question/25651698  

#SPJ8

Han will have 2 liters (or 2000 milliliters) of sparkling juice after combining 1.5 liters of juice and 500 milliliters of sparkling water.

To make sparkling juice, Han mixes 1.5 liters of juice and 500 milliliters of sparkling water.

To add the quantities together, we need to convert the units to the same measurement. We can convert the liters to milliliters since 1 liter is equal to 1000 milliliters.

1.5 liters is equal to 1.5 x 1000 = 1500 milliliters.

Now we have 1500 milliliters of juice and 500 milliliters of sparkling water.

To find the total quantity of the sparkling juice, we add the volumes of juice and sparkling water together:

1500 milliliters + 500 milliliters = 2000 milliliters

Therefore, Han will have a total of 2000 milliliters (or 2 liters) of sparkling juice by mixing 1.5 liters of juice and 500 milliliters of sparkling water.

For more such questions on combining visit:

https://brainly.com/question/28065038

#SPJ8

The correct answer is: O How to produce? How much to produce?

The statement "A manufacturing firm employs workers to monitor and maintain specialized machines making small metal parts" answers the economic questions of "How to produce?" and "How much to produce?"

How to produce: The statement indicates that the manufacturing firm has chosen to employ workers to monitor and maintain specialized machines. This suggests that they have made a decision regarding the production process and how they will go about manufacturing the small metal parts.

How much to produce: The fact that the manufacturing firm has employed workers to monitor and maintain the machines implies that they have determined a level of production that is deemed appropriate or necessary. The number of workers and the capacity of the machines can influence the quantity of small metal parts produced.

Therefore, the correct answer is: O How to produce? How much to produce?

for such more question on produce

https://brainly.com/question/4344214

#SPJ8

Answer:

Multiply to remove the fraction, then set it equal to 0 and solve.

Exact Form: x = −124/5

Decimal Form: x = −24.8

Mixed Number Form: x = −24 4/5

Please give the brainliest, really appreciated. Thank you

Based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.

To determine whether Millman's golfing group is ready to turn pro, we can compare their performance to that of professional golfers. Based on the provided data, Millman's group consists of 9 amateurs with an average score of 82 and a standard deviation of 2.6.

On the other hand, the professional golfers consist of 500 individuals with an average score of 71 and a standard deviation of 3.1.

To make a meaningful comparison, we can look at the average scores of the two groups. The average score is an indicator of the overall performance, with lower scores being better in golf.

In this case, the professional golfers have an average score of 71, while Millman's group has an average score of 82. This suggests that the professional golfers perform better, on average, than Millman's group.

However, it is also essential to consider the standard deviation, which measures the variability of scores within each group. A smaller standard deviation indicates less variation and greater consistency in performance.

The professional golfers have a standard deviation of 3.1, while Millman's group has a standard deviation of 2.6. This suggests that Millman's group has slightly less variation in scores compared to the professional golfers.

Overall, based on the average scores and standard deviations, it appears that Millman's group still has room for improvement before they can reach the level of professional golfers.

The professional golfers demonstrate better performance, on average, and a slightly higher variability in scores compared to Millman's group. Therefore, it would be advisable for Millman's group to continue refining their skills and striving to improve their scores before considering turning pro.

For more such question on standard deviations visit:

https://brainly.com/question/475676

#SPJ8

Based on the pattern we identified, the next term in the sequence would be 55.

The sequence should be 7, 10, 19, 34, 55

To identify the pattern and determine what comes next in the given sequence (7, 10, 19, 34), we need to examine the relationship between the terms and look for a consistent pattern.

If we calculate the differences between consecutive terms, we get:

10 - 7 = 3

19 - 10 = 9

34 - 19 = 15

By examining the differences, we notice that they are increasing by 6 each time.

This suggests that the sequence might be formed by adding an increasing number to each term.

Let's calculate the next difference:

15 + 6 = 21

Now, let's add this difference to the last term of the sequence:

34 + 21 = 55

Therefore, based on the pattern we identified, the next term in the sequence would be 55.

To summarize:

7, 10, 19, 34, 55

It's important to note that without further context or information, this pattern is just one of the possibilities and may not be the only correct answer.

Additional terms or a different pattern may emerge if more information is provided.

For similar question on sequence.

https://brainly.com/question/6561461

#SPJ8

Naomi will take approximately 93 quarters (around 23 years and 3 months) to save $100,000 by making quarterly payments of $1,500 with a 4.4% interest rate.

Doubling her payment amount would save her time, but the exact time saved would require recalculating with the new payment amount.

To calculate the time it will take for Naomi to reach her goal of $100,000, we can use the future value formula for a series of periodic payments:

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

Where:

FV = Future value (goal amount) = $100,000

P = Payment amount per period = $1,500

r = Interest rate per period = 4.4% per year / 4 (quarterly compounding) = 1.1% per quarter

n = Number of periods (quarters) to reach the goal (what we need to find)

Plugging in the values, we have:

$100,000 = $1,500 * [(1 + 0.011)^n - 1] / 0.011

Simplifying the equation, we have:

[(1 + 0.011)^n - 1] = $100,000 * 0.011 / $1,500

[(1.011)^n - 1] = 0.073333...

Now, we can solve this equation for n using logarithms:

n = log(0.073333...) / log(1.011)

Using a financial calculator or an online calculator, we find that n ≈ 92.33 quarters.

Since Naomi is making quarterly payments, we round up to the next whole number, giving us a total of 93 quarters.

Therefore, it will take Naomi approximately 93 quarters (or around 23 years and 3 months) to reach her goal of $100,000.

Doubling her payment amount to $3,000 per quarter would indeed save her time in reaching her goal. The higher payment amount means she would accumulate the desired amount faster. However, to determine the exact time saved, we would need to recalculate using the same formula as above with P = $3,000. The time saved will depend on the specific calculation result.

For more question on payments visit:

https://brainly.com/question/27926261

#SPJ8

The estimates are not correct because we are to find the proportion and sample error of the given values. The proportion expresses the number of opposing votes to the total number of voters. Also, the sampling error follows the formula of [tex]SE = Z\sqrt{P(1 - P/n)}[/tex]

The exact formula used in the expression is quite different from the standard formula for calculating the standard error. We are supposed to find the root of the standard deviation but that is not the case as can be seen in the formula above.

So, the main issue with this formula is that the square root is not considered in the proportion formula used by the council, so it is not a valid estimate.

Learn more about sample errors here:

https://brainly.com/question/28008941

#SPJ1

Answer:

if two parallel lines are cut by a transversal,then, exterior angles on the same side of the transversal are supplementary!

Step-by-step explanation:

I don't really know how to explain it but I hope this helped!

Answer:

x=30 degrees, 2x=60 degrees, 3x=90 degrees

Step-by-step explanation:

in a triangle the sum of angles is 180 so

x+2x+3x=180

6x=180

x=180/6

x=30

so the angle x is 30 degrees, the angle that is 2x is 60 degrees and the angle the angle 3x is 90

The distance of the bicycle race is approximately 24.61 miles.

Let's assume the distance of the run is 'x' miles and the distance of the bicycle race is 'y' miles.

We know that average velocity is equal to the total distance divided by the total time taken.

We can use this information to form two equations based on the given average velocities and total time.

For the run:

Average velocity = Distance of the run / Time taken for the run

5 mph = x miles / T hours ---(Equation 1)

For the bicycle race:

Average velocity = Distance of the bicycle race / Time taken for the bicycle race

23 mph = y miles / (6 - T) hours ---(Equation 2)

Since the total time for the race is 6 hours, we can substitute (6 - T) for the time taken during the bicycle race.

Now, we can solve these equations simultaneously to find the values of 'x' and 'y'.

From Equation 1, we have:

5T = x

From Equation 2, we have:

23(6 - T) = y

Now, we substitute the value of 'x' in terms of 'T' from Equation 1 into Equation 2:

23(6 - T) = 5T

138 - 23T = 5T

138 = 28T

T = 138 / 28

T ≈ 4.93 hours

Substituting this value back into Equation 1, we can find 'x':

5(4.93) = x

x ≈ 24.65 miles

Therefore, the distance of the run is approximately 24.65 miles.

To find the distance of the bicycle race, we substitute the value of 'T' back into Equation 2:

23(6 - 4.93) = y

23(1.07) = y

y ≈ 24.61 miles

For similar question on distance.

https://brainly.com/question/30395212  

#SPJ8

Answer:

A. 6² + 11² = c²

Step-by-step explanation:

The correct equation to find the length of the hypotenuse in a right triangle is the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, if we assume that the length of one side is 6 and the length of the other side is 11, the correct equation would be:

A. 6² + 11² = c²

This equation can be simplified as follows:

36 + 121 = c²

157 = c²

Therefore, the correct equation to find the length of the hypotenuse in this case is A. 6² + 11² = c².

Reason:

Tangent is the ratio of opposite over adjacent.

The side 'a' is opposite reference angle 52, while c is adjacent to this angle.

Using a calculator, tan(52) = 1.27994 approximately.

Answer:

Tan 52°

Step-by-step explanation:

Since the Tangent of angle is given by the ratio of opposite to the adjacent.

So, Here

Tan 52°= opposite/adjacent

Tan 52°=a/c

Therefore, the ratio of a/c is Tan 52°

Answer:

1. x = 18

2. x = 31

Step-by-step explanation:

1. Angles in a quadrilateral sum to 360°.

360 -(60 +130 +70) = 360 -260 = 100

So, x +82 = 100. x = 100 -82 = 18

2. Angles in a triangle sum to 180°. 180 -(29 +75) = 180 -104 = 76.

So, -17 +3x = 76. 3x = 93. x = 93/3 = 31

Answer:

119in^2

Step-by-step explanation:

formula= 2(width×length+hight×length+hight×5

2×(5×8+3×8+3×5) = 119in^2

The length of the unknown side x using the concept of similar triangles is: x = 4

Similar triangles are referred to as triangles that have the same shape but different sizes. All equilateral triangles and squares of any side length are examples of similar objects. In other words, if two triangles are similar, their corresponding angles are the same and their corresponding side proportions are the same.

Now, we are told that triangle PQR is similar to Triangle STU and as such their corresponding sides are similar and therefore to find the missing side x, we have:

12/x = 15/5

x = (12 * 5)/15

x = 60/15

x = 4

Read more about similar triangles at: https://brainly.com/question/14285697

#SPJ1

The surface area of the given triangle is approximately 33.74 square centimeters.

To calculate the surface area of a triangle, we need the lengths of two sides and the included angle between them. However, in this case, you provided the lengths of all three sides (6 cm, 7 cm, and 12 cm).

To determine the surface area, we can use Heron's formula, which is applicable to triangles with all three side lengths known.

Heron's formula states that the surface area (A) of a triangle with side lengths a, b, and c is given by:

[tex]A = \sqrt(s \times (s - a) \times (s - b) \times (s - c))[/tex]

where s is the semi perimeter of the triangle, calculated as:

s = (a + b + c) / 2

Plugging in the given side lengths, we have:

s = (6 cm + 7 cm + 12 cm) / 2 = 25 / 2 = 12.5 cm

Now we can substitute the values into Heron's formula:

[tex]A = \sqrt(12.5 cm \times (12.5 cm - 6 cm) \times (12.5 cm - 7 cm) \times (12.5 cm - 12 cm))[/tex]

[tex]= \sqrt(12.5 cm \times 6.5 cm \times 5.5 cm \times 0.5 cm)[/tex]

= √(1137.5 cm^4)

≈ 33.74 cm^2

For more such questions on triangle

https://brainly.com/question/1058720

#SPJ8

Step-by-step explanation:

In a randomized block design blocked by gender, treatments should be assigned randomly within each gender block. The correct assignment maintains a distribution of one treatment for each gender. Looking at the given options, only one meets this criterion:

OA: (1f, 2f), B: (1m, 2m). C: (3f, 3m). D: (4f, 4m)

Each treatment group A, B, C, and D contains one male and one female, making the distribution of treatments blocked by gender.

Answer:168

Step-by-step explanation:Let's denote the total number of marks as "M."

Marks obtained = (84/100) * M

For example, if the total marks were 200, then:

Marks obtained = (84/100) * 200 = 168

Answer:

21

Step-by-step explanation:

If you got 84% then divide it by 100%. 100%/84%=21/25 check.

[tex] \frac{21}{25 } \times \frac{100}{1} = 84[/tex]

i) Probability of at least six patients wanting Brand-2: P(X ≥ 6)

ii) Probability of number of patients within 1 standard deviation of mean: P(μ - σ ≤ X ≤ μ + σ)

iii) Probability that all ten patients get their desired brand from current stock: (7/14) * (6/13) * ... * (1/5)

i) The probability of at least six patients wanting Brand-2 out of ten randomly selected patients can be calculated using the binomial distribution. We need to sum the probabilities of six, seven, eight, nine, and ten patients wanting Brand-2.

The probability can be calculated as P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10), where X follows a binomial distribution with n = 10 and p = 0.65. The answer is the sum of these individual probabilities.

ii) To calculate the probability of the number of patients who want the Brand-2 vaccine being within 1 standard deviation of the mean value, we need to find the range of values that fall within one standard deviation of the mean.

We can use the normal approximation to the binomial distribution since n = 10 is reasonably large. We calculate the mean (μ) and standard deviation (σ) using μ = n * p and σ = √(n * p * (1 - p)), where p = 0.65. Then we calculate the probability of the number of patients falling within the range μ - σ to μ + σ.

iii) Since there are seven vaccines of each brand in stock, the probability that all ten patients who want the vaccine can get the brand they want from the current stock is equal to the probability of the first patient getting their desired brand (7/14) multiplied by the probability of the second patient getting their desired brand (6/13), and so on until the tenth patient (1/5). The final probability is the product of these individual probabilities.

For more question on Probability visit:

https://brainly.com/question/25839839

#SPJ8

Answer:

the solution would be X=3 as 3.1 represents 3×1.

Answer:

To find the length of AB using the segment addition postulate , we need to add the lengths of segments AC and CB.

AC + CB = AB

Substituting the given lengths:

2x-3 + 24 = 5x+6

Simplifying and solving for x:

21 = 3x

x = 7

Now that we know x, we can substitute it back into the expression for AB:

AB = 2x-3 + 24 = 2(7)-3 + 24 = 14-3+24 = 35

Therefore, the length of AB is 35.

Step-by-step explanation:

Step-by-step explanation:

Part A: The graph of the system of inequalities consists of two lines and a shaded region.

The line 2x + 3y = 15 is a solid line (because of the "less than" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 5, and when x = 7.5, y = 0.

The line x + y = 3 is a solid line (because of the "greater than or equal to" symbol in the inequality) and is graphed using a straight line connecting two points. For example, when x = 0, y = 3, and when x = 3, y = 0.

The shaded region represents the solution set. It is the area below the line 2x + 3y = 15 and above or on the line x + y = 3. This shaded region satisfies both inequalities simultaneously.

Part B: To determine if the point (5, 1) is included in the solution area, we substitute x = 5 and y = 1 into both inequalities:

2x + 3y < 15:

2(5) + 3(1) < 15

10 + 3 < 15

13 < 15

Since 13 is less than 15, the point (5, 1) satisfies the first inequality.

x + y ≥ 3:

5 + 1 ≥ 3

6 ≥ 3

Since 6 is greater than or equal to 3, the point (5, 1) satisfies the second inequality.

Since the point (5, 1) satisfies both inequalities, it is included in the solution area for the system.

Part C: Let's choose the point (2, 2) as another example from the solution set.

Interpretation in real-world context:

When we have x = 2 and y = 2, it means Michael decides to buy 2 cupcakes and 2 pieces of fudge. This combination of sweets satisfies the conditions set in the inequalities, ensuring that he can feed at least three siblings.

The point (2, 2) represents a valid solution in which Michael spends a total of $10 (2 cupcakes * $2/cupcake + 2 fudges * $3/fudge = $4 + $6 = $10). With this choice, he can afford to buy enough treats to feed his three siblings while staying within his budget of $15.

The correct answer is option (b): Square root of 4x^2.

The standard deviation of a random variable Y is the square root of its variance. In this case, the variance of Y is given as 4x^2. Taking the square root of 4x^2, we get the standard deviation of Y as 2x.

Therefore, the correct answer is the square root of 4x^2, which is the standard deviation of Y.

The total length of electric wire in both rolls is 166.76 meters.

To find the total length of electric wire in both rolls, we need to add the lengths of the two rolls together.

The first roll contains 80m 20cm of wire. We can convert this to meters by noting that 1 meter is equal to 100 centimeters. Therefore, the length of the first roll is:

80m 20cm = 80 meters + (20 centimeters / 100) meters

= 80 meters + 0.20 meters

= 80.20 meters

Similarly, the second roll contains 86m 56cm of wire. Converting this to meters:

86m 56cm = 86 meters + (56 centimeters / 100) meters

= 86 meters + 0.56 meters

= 86.56 meters

To find the total length, we add the lengths of both rolls:

Total length = 80.20 meters + 86.56 meters

= 166.76 meters

Therefore, the total length of electric wire in both rolls is 166.76 meters.

for such more question length

https://brainly.com/question/20339811

#SPJ8

The distance from the given city to the South Pole is 125 degrees of latitude.

To determine the distance from the given city to various locations, we need to consider the latitude and longitude coordinates.

Distance to the North Pole:

The North Pole is located at 90°N latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the North Pole.

Distance to the North Pole = 90° - 35° = 55°

The distance from the given city to the North Pole is 55 degrees of latitude.

Distance to the Equator:

The Equator is located at 0° latitude. To determine the distance from the city to the Equator, we need to calculate the absolute value of the latitude of the city.

Distance to the Equator = |35°| = 35°

The distance from the given city to the Equator is 35 degrees of latitude.

Distance to the South Pole:

The South Pole is located at 90°S latitude. Since the given city is at 35°S latitude, we need to calculate the difference in latitude between the city and the South Pole.

Distance to the South Pole = 35° - (-90°) = 35° + 90° = 125°

The distance from the given city to the South Pole is 125 degrees of latitude.

for such more question on distance

https://brainly.com/question/12356021

#SPJ8

Answer:

36)

[tex]f(x) = \frac{1}{x + 3} - 1[/tex]

The equation of the function is y = 1/(x + 3) - 1

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

The reciprocal function shifted down one unit and left three units

The equation of the reciprocal function is represented as

y = 1/x

When shifted down one unit, we have

y = (1/x) - 1

When shifted left three units, we have

y = 1/(x + 3) - 1

Hence, the equation of the function is y = 1/(x + 3) - 1

Read more about transformation at

https://brainly.com/question/27224272

#SPJ1