12. A rectangle has a perimeter of 12y² - 2y +18 and has a width of 4y²-y + 6. What is the length of the rectangle?​

Answer:

320 miles.

Step-by-step explanation:

we can use following the formula to solve this:

Distance = Speed*Time

We need to calculate the distance Paige travelled for each leg of her journey and then add them together to get the total distance.

For the first leg of her journey from Swansea to Chichester:

speed = 60 mph

time = 3 hours and 30 minutes =3.5 hours

distance = speed*time=60*3.5= 210 miles

For the second leg of her journey from Chichester to Dover:

speed = 55 mph

time = 2 hours

distance = speed*time=55*2=110 miles

Therefore, the total distance Paige travelled is:

Total distance = distance from Swansea to Chichester + distance from Chichester to Dover

Therefore, Paige travelled a total of 320 miles.

Answer:

total distance = 320 miles

Step-by-step explanation:

The question tells us the average speeds and time taken for two separate journeys made by Paige and asks us to calculate the total distance of the two journeys.

In order to calculate the distance travelled, we have to use the following formula for average speed:

[tex]\boxed{\mathrm{Average \ speed = \frac{ distance\ travelled}{time \ taken}}}[/tex].

Rearranging the above formula to make distance travelled the subject of the equation, we get:

distance travelled = average speed × time taken

Therefore, for the first journey:

• distance travelled = 60 m/h × 3.5 h

                                 = 210 miles

And for the second journey:

• distance travelled = 55 m/h × 2

                                = 110 miles

Hence, the total distance travelled by Paige = 210 + 110

                                                                          = 320 miles

The value of x for the given value of y in the equation y = x + 2 - 1 is 1

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

y = x + 2 - 1

Also, we have the value of y to be

y = 0

When the equation is evaluated, we have

y = x - 1

substitute the known values in the above equation, so, we have the following representation

x - 1 = 0

Add 1 to both sides

x = 1

Hence, the value of x for the given value of y is 1

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Step-by-step explanation:

20÷40

=0'5×60min

30min

80÷120

=0,6666666667×60

=40mins

john will arrive earlier

The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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The simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

To simplify the expression (2⁵ x 5²² - 2 x 5²¹) / 25¹⁰.

we can use the properties of exponents and the fact that 25 = 5².

First, let's simplify the numerator:

(2⁵ x 5²² - 2 x 5²¹)

Using the distributive property, we can factor out 5²¹ from both terms:

= 5²¹ x (2⁵ x 5 -2)

= 5²¹ (32 x 5- 2)

= 5²¹ (160-2)

= 5²¹ x 158

Now, let's simplify the denominator: 25¹⁰

Since 25 = 5², we can rewrite it as (5²)¹⁰, which gives us:

=  (5²)¹⁰

= 5²⁰

Using the quotient rule of exponents [tex](a^m / a^n = a^{(m-n)})[/tex], we can simplify further:

=  5²¹ x 158 / 5²⁰

= 5²¹⁻²⁰ x 158

= 5 x 158

= 790

Therefore, the simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.

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Answer:

To estimate the value of sec 195° using the graph of y = sec x, you would need to locate the point on the graph where x = 195°. However, since you have not provided the graph, I am unable to estimate the value of sec 195°.

Alternatively, you can calculate the value of sec 195° using the definition of the secant function. The secant function is defined as the reciprocal of the cosine function: sec x = 1 / cos x. Therefore, to find the value of sec 195°, you can calculate the cosine of 195° and take its reciprocal:

sec 195° = 1 / cos 195°

        ≈ 1 / (-0.9063)

        ≈ -1.103

Rounded to the nearest tenth, sec 195° is approximately -1.1.

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The expression for the quotient of 78k and 40 without any spaces would be:

78k/40

The quotient of two numbers refers to the result obtained from dividing one number by another. In this case, you are dividing 78k by 40. In mathematical notation, division is often represented by the slash (/) symbol.

So when we say "the quotient of 78k and 40", we mean "78k divided by 40", which can be written as "78k/40".

Here, no spaces are used between the numbers, variables, and the division symbol in the expression, as per your request.

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Axiom of Choice is also known to have some non-intuitive consequences, such as the Banach-Tarski paradox and the existence of non-measurable sets.

The Axiom of Choice is a fundamental principle in set theory that states that for any collection or family of nonempty sets, it is possible to select exactly one element from each set, creating a choice function.

In other words, given a family F of nonempty sets, the Axiom of Choice asserts the existence of a function called a choice function, which takes as input each set in the family and outputs a single element from that set. This choice function essentially "chooses" an element from each set in a consistent manner.

The Axiom of Choice is an important tool in mathematics and has significant implications in various areas, including analysis, topology and algebra.

It allows for the construction of mathematical objects that might not be easily defined without making explicit choices from infinitely many sets simultaneously.

As a result, its use is sometimes subject to scrutiny, and alternative set theories like constructive mathematics have been developed that do not rely on the Axiom of Choice.

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Given statement solution is :- Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

To determine which company will provide the lowest total cost for 12 lunches, let's calculate the costs for both Carla's Catering and Dan's Diner.

Carla's Catering:

Using the equation provided, y = 6.75x + 25, where x represents the number of lunches:

For x = 12:

y = 6.75(12) + 25

y = 81 + 25

y = 106

The total cost for 12 lunches from Carla's Catering is $106.

Dan's Diner:

We are given the following data points for Dan's Diner:

Number of Lunches (x) Total Cost (y)

5 $57.50

10 $100.00

15 $142.50

From this data, we can calculate the rate at which the cost increases per lunch:

Rate = (Change in Total Cost) / (Change in Number of Lunches)

Rate = (100 - 57.50) / (10 - 5)

Rate = 42.50 / 5

Rate = 8.50

Now, let's calculate the cost for 12 lunches using the rate:

For x = 12:

y = 100 + (8.50 * (12 - 10))

y = 100 + (8.50 * 2)

y = 100 + 17

y = 117

The total cost for 12 lunches from Dan's Diner is $117.

Comparing the costs:

Carla's Catering: $106

Dan's Diner: $117

Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

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1.  The velocity of the object is 1.25 m/s.

2. This indicates that the object is moving in the positive direction.

3. The total distance traveled by the object is 10 m.

4.  The displacement of the object is 10 m.

1.The velocity of an object can be determined by calculating the slope of the graph. Since velocity is the rate of change of position, it is equal to the change position- in position divided by the change in time.

By examining the graph, we can see that the change in position between the initial and final points is 14 m - 4 m = 10 m. The corresponding change in time is 10 s - 2 s = 8 s.

Therefore, the velocity of the object is:

Velocity = Change in position / Change in time = 10 m / 8 s = 1.25 m/s

2. Based on the position-time graph, we observe that the object's position is increasing with time. This indicates that the object is moving in the positive direction.

3. To find the total distance traveled, we need to consider the absolute values of the changes in position. In this case, the object moves from 4 m to 14 m, which results in a change of 10 m. Since the direction is not specified, we consider the magnitude of the change.

Therefore, the total distance traveled by the object is 10 m.

4.Displacement is the change in position of an object, taking into account both magnitude and direction. In this case, the object starts at a position of 4 m and ends at a position of 14 m.

Therefore, the displacement of the object is:

Displacement = Final position - Initial position = 14 m - 4 m = 10 m.

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a. The equation shows that a 11-pound turkey would need to be roasted for 335 minutes.

b. A turkey that takes 300 minutes to roast would weigh 14 pounds.

a. The rule for finding the time in minutes needed to roast a turkey is:

time in minutes = 15 + (pounds of turkey * 20)

So, to find the time needed to roast a 11-pound turkey, we would use the following formula:

time in minutes = 15 + (11 pounds * 20)

= 335 minutes

b. To find the weight of a turkey that takes 300 minutes to roast, we would use the following formula:

pounds of turkey = (300 minutes - 15 minutes) / 20 minutes

= 14 pounds

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The year that they will next be seen together is 2219.

Considering periodic events, they will repeat on the same day for the least common factor of the periods of each event.

The periods for this problem are given as follows:

The least common factor is obtained factoring 8 and 54 by prime factors as follows:

8 - 54|2

4 - 27|2

2 - 27|2

1 - 27|3

1 - 9|3

1 - 3|3

1 - 1.

Hence:

lcf(8, 54) = 2³ x 3³ = 216.

Then the next year is of:

2003 + 216 = 2219.

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Answer:

  B)  15/17

Step-by-step explanation:

You want the sine of acute angle A in the right triangle shown.

The sine of the angle is the ratio ...

  Sin = Opposite/Hypotenuse

We can go to the trouble to figure the hypotenuse, or we can choose the only suitable answer from the list provided. (It is the one marked already.)

The leg lengths of the triangle shown are 8 and 15, with leg 15 being opposite angle A. This is the first clue that the ratio will have 15 in the numerator. Only answer choice B matches.

The value of the sine function is never greater than 1, eliminating answer choices A, C, and E, leaving choices B and D.

Since the side opposite angle A is the longest of the two legs, we know that angle A is more than 45°, and its sine is more than √2/2. That means choice D can be eliminated, since it is less than 1/2.

The sine of angle A is 15/17.

<95141404393>

There are 3003 different arrangements of 5 people that can be chosen as winners out of 15 people.

The number of combinations of "n" objects taken "r" at a time is given by the formula:

C(n, r) = n! / (r! (n - r)!)

Where n! represents the factorial of "n" (the product of all positive integers up to "n").

We have 15 people entering the contest, and we want to choose 5 winners. Thus, we have:

C(15, 5) = 15! / (5! × (15 - 5)!)

15! = 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

5! = 5 × 4 × 3 × 2 × 1

(15 - 5)! = 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

Plugging these values into the formula:

C(15, 5) = (15×14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)

C(15, 5) = 3003

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Answer:

  7

Step-by-step explanation:

You want the constant q when 4x² -8x -24 = 0 is written as (x -p)² = q.

First, we can divide by 4:

  x² -2x -6 = 0

To make the left side a perfect square, the constant there needs to be +1. Adding 7 to both sides will make it so:

  x² -2x +1 = 7

  (x -1)² = 7 . . . . . . . (p, q) = (1, 7)

The value of q is 7.

__

Additional comment

The square of a binomial is ...

  (x +b)² = x² +2bx +b²

The constant term (b²) is the square of half the coefficient of x. In the above equation, the coefficient of x is -2, so the constant needs to be ...

  (-2/2)² = 1

<95141404393>

Answer:To find the original price of the sofa before the sale, we can use the formula:

sale price = original price * (1 - discount rate)

Substituting the given values, we get:

1680 = original price * (1 - 0.3)

Solving for the original price, we get:

original price = 1680 / (1 - 0.3) original price = 1680 / 0.7 original price = 2400

Therefore, the sofa cost £2400 before the sale.

Step-by-step explanation:

The lengths of the sides of the Triangle are 3 units, 10 units, and 12 units.

The length of the sides of a triangle are in the extended ratio 3:10:12. This means that the ratio of the lengths of the sides can be written as 3x:10x:12x, where x is a common factor.To determine the actual lengths of the sides, we need to assign a specific value to x. Let's assume x = 1 for simplicity.

Then, the lengths of the sides of the triangle become:

Side 1: 3(1) = 3 units

Side 2: 10(1) = 10 units

Side 3: 12(1) = 12 units

So, the lengths of the sides of the triangle are 3 units, 10 units, and 12 units.the extended ratio of the sides, 3:10:12, indicates the proportional relationship between the lengths. However, it doesn't provide information about the specific size or shape of the triangle.

For example, we can determine whether it is a right triangle or an equilateral triangle by comparing the ratios of its sides. However, additional information would be required to make further conclusions about angles, area, or other geometric properties of the triangle.

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For calculating a 95% confidence mean range for the typical number of visits for patients receiving physical therapy.

a. We employ a t-distribution to calculate the confidence interval.

b. The population mean number of visits per physical therapy patient is between 9.454 and 19.000 visits, with a 95% confidence interval.

c. If multiple groups of 11 randomly chosen physical therapy patients are examined, roughly 95% of these confidence intervals will contain the genuine population mean number of visits per patient, and around 5% will not.

a. T-distribution is used to calculate the confidence interval for the mean number of visits. This is so because the population standard deviation is unknown and the sample size is tiny (only 11). The t-distribution is used in place of the conventional normal distribution when certain conditions are satisfied.

b. We have two options for calculating the confidence interval: we can do it manually or with statistical software. We determine the sample mean to be 13.182 and the sample standard deviation to be 6.446 using the provided data (13, 6, 25, 11, 11, 10, 21, 20, 9, 20, 9). Given the limited sample size and a 95% level of confidence, we use the t-distribution to establish the critical value. Using a calculator or the t-distribution table, determine the critical value for a 95% confidence level with 10 degrees of freedom is approximately 2.228.

The formula for the confidence interval is:

Sample Mean (Critical Value) * (Standard Error) = Confidence Interval

Sample Standard Deviation / sqrt(sample size) gives the standard error.

By entering the values, we can determine the confidence interval using the formula below:

The confidence interval is equal to 13.182 (2.228) * (6.446 / sqrt(11)).

9.454 visits make up the lower bound and 19.000 visits make up the upper bound of the confidence interval. The population mean number of visits per physical therapy patient is therefore expected to range between 9.454 and 19.000 visits, with a 95% confidence interval.

c. Confidence intervals for each group of 11 randomly chosen physical therapy patients can be constructed, and roughly 95% of these intervals will contain the actual population mean number of visits per patient. This is due to the fact that we are employing a 95% confidence level, which indicates that over time, 95% of the confidence intervals created will accurately reflect the underlying population mean.

On the other hand, around 5% of these confidence intervals won't include the actual population mean for visits per patient. These intervals are referred to as Type I errors or "misses". The likelihood of rejecting the actual null hypothesis is represented by the significance level, or alpha, which is represented by the 5%.

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Answer :

We know that,

where r is radius

Volume = 4/3 × 3.14 × (14)²

= 4/3 × 3.14 × 2744

= 4/3 × 8616.16

= 34464.64/3

= 11488 m³ (approx)

Surface area of sphere = 4πr²

= 4 × 31.4 × (14)²

= 4 × 3.14 × 196

= 12.56 × 196

= 2461 m² (approx)

Answer:

8

Step-by-step explanation:

total number: 128+ 154 = 282

divide by number of buses

282/36 = 7.8333...

can't split girls so need extra bus

therefore answer is 8

[tex]u=(\sqrt{3}~~,~-1)\hspace{5em}v=(3~~,~-4) \\\\\\ u\cdot v\implies (\sqrt{3}\cdot 3)~~ + ~~(-1\cdot -4)\implies \stackrel{ \textit{dot product} }{3\sqrt{3}+4}[/tex]

The vertices of the image triangle N'M'O' are N'(-1, 2), M(-4, 1), and O'(-3, 3).

We may use the idea of reflection to get the vertices of the picture N'M'O' created when triangle NMO is reflected over the line x = -3.

The distance between each of the x-coordinates of the original positions and x = -3 must be calculated.

The distance (from -3 to -5) is 2 units for N(-5, 2).

The distance (from -3 to -2) is 1 unit for M(-2, 1).

Since the point is already on the line, the distance for O(-3, 3) is 0 units.

Then, maintaining the same vertical coordinate, we move each point the same distance to the opposite side of the line.

We move 2 units to the right of N(-5, 2) to obtain N'(-1, 2).

We move one unit to the left from M(-2, 1) to obtain M(-4, 1).

We don't need to move at all for O(-3, 3), as the point is already on the line. Thus, O'(-3, 3).

Hence the vertices of the image triangle N'M'O' are N'(-1, 2), M(-4, 1), and O'(-3, 3).

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Angle x is 110 degrees, angle y is 110 degrees, and angle z is 70 degrees.

Let's analyze the given information step by step. We are given that two lines intersect, creating four angles. One of these angles is 70 degrees. The other angles are labeled as x, y, and z.

First, we know that angles x and 70 degrees form a linear pair because they are adjacent angles and their sum is 180 degrees. Therefore, angle x must be 180 degrees minus 70 degrees, which equals 110 degrees.

Next, we are told that angles y and 70 degrees also form a linear pair. This means that angle y is also 110 degrees, as the sum of a linear pair is always 180 degrees.

Finally, angle z can be found by considering the angles around the point of intersection. The sum of the angles around a point is always 360 degrees. Since we already have angles x, y, and 70 degrees, we can find angle z by subtracting their sum from 360 degrees.

The sum of angles x, y, and 70 degrees is 110 degrees + 110 degrees + 70 degrees, which equals 290 degrees. Therefore, angle z is 360 degrees minus 290 degrees, resulting in 70 degrees.

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Hola !

1500/10 = 150

una rata tiene 150 nervios por bigote

Answer:

150

Step-by-step explanation:

We need to divide 1500 by 10 since the seal has 10 more than the rat

1500 ÷ 10 = 150

Therefore the answer is 150

Answer:

The correct equation is D)

Step-by-step explanation:

The answer is equation D)

To find how many [tex]\frac{1}{3}[/tex] inches are in [tex]\frac{5}{6}[/tex] of an inch, you must divide [tex]\frac{5}{6}[/tex] by [tex]\frac{1}{3}[/tex].  

When diving fractions, you find the reciprocal of the second fraction (flip the fraction) & then you multiply the fractions.

[tex]\frac{5}{6}[/tex] ÷ [tex]\frac{1}{3}[/tex]

In this case, [tex]\frac{1}{3}[/tex] is the second fraction you must find the reciporcal of.

Flipping the fraction will give you the reciprocal as 3.

Multiply [tex]\frac{5}{6}[/tex] by 3.

Cross-cancellation:

[tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]

As 3 can go into 6, you can divide both 3 by 3 & 6 by 3. The second fraction will be cancelled out ([tex]\frac{1}{1}[/tex]) and you will have [tex]\frac{5}{2}[/tex] left over (since anything multiplied by 1 will remain the same).

Simplification:

[tex]\frac{5}{6}[/tex] x [tex]\frac{3}{1}[/tex]

[tex]\frac{15}{6}[/tex]

Divide both numerator & denominator by 3 (the Greatest Common Factor) to simplify.

= [tex]\frac{5}{2}[/tex]

So, as a result, the correct equation is equation D).

Answer:

Step-by-step explanation:

First we need to calculate the price per kilogram of goat meat.

If 12 kg of goat meat is sold for R840, then the price per kilogram can be calculated as:

Price per kilogram = Total price ÷ Total weight

Price per kilogram = R840 ÷ 12 kg

Price per kilogram = R70

Therefore, Sam's claim that the goat meat is being sold at R60 per kilogram is incorrect. The actual price per kilogram is R70.

In conclusion, Mr Mlambo is selling the goat meat at R70 per kilogram, and Sam's claim is not valid.

Answer:

Let x be the nightly rate before tax.

We know that the total cost including tax is $200.02, which is 100% of the cost before tax plus 7% sales tax:

x + 0.07x = 200.02

Combining like terms on the left-hand side:

1.07x = 200.02

Dividing both sides by 1.07:

x = 186.91

Therefore, the nightly rate before tax is $186.91, rounded to the nearest cent.

The approximate x-values for the local maximum and the local minimum are given as follows:

D) max ≈ -0.3 , min ≈ 2.3.

Hence the critical points of the graphed function are given as follows:

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