What is the sum of (49p2 – 25) + (16p4 - 32p2 + 16)?

The number of  combinations of random samples  of 5 students can be selected is 56, here, the correct answer is 60.

To find the number of combinations of selecting a random sample of 5 students from a group of 12 students, you can use the formula for combinations which is:

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

where C(n, k) represents the number of combinations, n is the total number of students (12 in this case), and k is the number of students to be selected (5 in this case). The exclamation mark (!) represents a factorial, which means the product of all positive integers up to that number.

Using the formula, we can calculate the number of combinations:

C(12, 5) = 12! / (5!(12-5)!)
= 12! / (5!7!)
= (12×11×10×9×8) / (5×4×3×2×1)
= 95,040 / 1,680
= 56.52 (rounded)

Since the number of combinations must be a whole number, the correct answer is 56, which is not among the given answer choices. However, the closest answer choice to 56 is 60.

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Answer:

x=-1/6

I luv u

Answer:

y = - \(\frac{3}{5}\) x - \(\frac{14}{5}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = \(\frac{5}{3}\) x + 1 ← is in slope- intercept form

with slope m = \(\frac{5}{3}\)

Given a line with slope m then the slope of a line perpendicular to it is

\(m_{perpendicular}\) = - \(\frac{1}{m}\) = - \(\frac{1}{\frac{5}{3} }\) = - \(\frac{3}{5}\) , thus

y = - \(\frac{3}{5}\) x + c ← is the partial equation

To find c substitute (- 8, 2) into the partial equation

2 = \(\frac{24}{5}\) + c ⇒ c = 2 - \(\frac{24}{5}\) = - \(\frac{14}{5}\)

y = - \(\frac{3}{5}\) x - \(\frac{14}{5}\) ← equation of perpendicular line

For the polygon the individual value of the interior angles.

a) 15 sides is 145°

b) 20 sides is 108°

c) 3 sides is 60°

d) 4 sides is 90°

e) 100 sides is 18°

A regular polygon is one where all sides are the same length and all interior angles are the same. The number of sides of a regular polygon can affect the value of its interior angles.

a) 15 sides: The sum of the interior angles of a regular polygon with 15 sides is equal to 2180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2180 / 15 = 145 degrees per angle.

b) 20 sides: The sum of the interior angles of a regular polygon with 20 sides is equal to 2160 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 2160 / 20 = 108 degrees per angle.

c) 3 sides: The sum of the interior angles of a regular polygon with 3 sides is equal to 180 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 180 / 3 = 60 degrees per angle.

d) 4 sides: The sum of the interior angles of a regular polygon with 4 sides is equal to 360 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 360 / 4 = 90 degrees per angle.

e) 100 sides: The sum of the interior angles of a regular polygon with 100 sides is equal to 1800 degrees. To find the individual value of each angle, divide the sum by the number of sides. In this case,

=> 1800 / 100 = 18 degrees per angle.

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If you mean "factor over the rational numbers", then this cannot be factored.

Here's why:

The given expression is in the form ax^2+bx+c. We have

a = 3

b = 19

c = 15

Computing the discriminant gives us

d = b^2 - 4ac

d = 19^2 - 4*3*15

d = 181

Note how this discriminant d value is not a perfect square

This directly leads to the original expression not factorable

We can say that the quadratic is prime

If you were to use the quadratic formula, then you should find that the equation 3x^2+19x+15 = 0 leads to two different roots such that each root is not a rational number. This is another path to show that the original quadratic cannot be factored over the rational numbers.

The magnitude of the electric field at the origin due to the given charges is 2.98×10^4 N/C, and its direction is 139.5 degrees counterclockwise from the positive x-axis. The magnitude of the instantaneous acceleration of a proton placed at the origin is 5.97×10^14 m/s^2, and its direction is 139.5 degrees counterclockwise from the positive x-axis.

To determine the electric field at the origin, we need to calculate the contributions from each charge and then sum them up. The electric field due to a point charge can be found using Coulomb's law, which states that the electric field magnitude (E) is equal to the charge (Q) divided by the distance squared (r^2), multiplied by a constant (k) equal to 8.99×10^9 Nm^2/C^2. Considering the first charge, the distance from the origin (0, 0) to (0, -2) is 2 cm. Using the formula, we find that the electric field magnitude due to this charge is 1.12×10^4 N/C, pointing along the positive y-axis.

For the second charge, the distance from the origin to (3, 0) is 3 cm. Calculating the electric field magnitude for this charge yields 3.32×10^4 N/C, pointing along the positive x-axis. Lastly, the third charge at (3, 4) creates an electric field magnitude of 2.24×10^4 N/C, directed at an angle of 53.13 degrees from the positive x-axis.

To determine the net electric field at the origin, we must vectorially add the electric field contributions from each charge. By adding the x-components and y-components separately, we find that the resultant electric field magnitude is 2.98×10^4 N/C, at an angle of 139.5 degrees counterclockwise from the positive x-axis.

Now, let's calculate the instantaneous acceleration of a proton at the origin. Since the proton has a positive charge, it will experience a force in the opposite direction to the electric field. We can use Newton's second law, F = ma, where F is the force experienced by the proton, m is its mass, and a is its acceleration. The force experienced by the proton is given by the electric field strength multiplied by its charge. The mass of a proton is approximately 1.67×10^-27 kg, and its charge is 1.6×10^-19 C. Substituting these values, we find that the acceleration of the proton is approximately 5.97×10^14 m/s^2, pointing at an angle of 139.5 degrees counterclockwise from the positive x-axis, which is the same as the direction of the electric field at the origin.

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Answer:

x = -5

Step-by-step explanation:

add 14 to both sides:

x = -19 + 14

x = -5

Answer:

y = 2x + 8

Step-by-step explanation:

To find the line, use the equation y = mx + b.

Plug in the slope and given point, then solve for b:

y = mx + b

2 = 2(-3) + b

2 = -6 + b

8 = b

Plug in the slope and b into the equation:

y = 2x + 8

So, the equation of the line is y = 2x + 8

Answer:

m

Step-by-step explanation:

Based on the given data, there are a total of 13 packets and 5 of them are spicy. Therefore, the probability that the next packet Cooper pulls out of the box will be spicy is 5/13 or approximately 0.385 (rounded to three decimal places).

To calculate the probability of the next packet being spicy, we need to know how many packets of each flavor are in the box. Assuming that Cooper doesn't put back the packets he has pulled out, we can count the number of spicy packets and divide it by the total number of packets he pulled out.

In this case, out of the 13 packets he pulled out, 5 were spicy. Therefore, the probability of the next packet being spicy is 5/13, or approximately 0.38, or 38%. However, if the box is refilled with packets of different flavors, this probability may not hold.

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Answer: 4/13

Step-by-step explanation: i did this IXL and this was the correct answer

Answer:

Exponents =

\(\textsf y^{\frac{2}{5}} \textsf{equivalent} \sqrt[5]{y^2}\)

Solution :

\(\textsf{When} \ a^{\frac{m}{n}} = \sqrt[n]{a^m}\)

\(\textsf{And} \ y^{\frac{2}{5}} = \sqrt[5]{y^2}\)

.

Based on the given options, the displacement could be either 0 km or 6 km, depending on the specific details of Dr. Siva's route.

To determine the displacement, we need to consider the net change in position or the straight-line distance between the initial and final positions. Let's analyze the information given:

Dr. Siva walked from home to school, then from the school to the park, and finally walked back home.

The displacement is not determined by the total distance traveled but rather by the straight-line distance between the starting and ending points. We don't have specific information about the distances or directions between the locations, so we cannot calculate the exact displacement.

However, we can make some assumptions based on the given options:

If the distances from home to school and from the school to the park are the same, and Dr. Siva returns directly from the park back home, the displacement would be 0 km. This implies that the final position is the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 10 km from the school to the park, and finally walks 10 km back home, the displacement would be 0 km. This is because the final position would be the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 2 km from the school to the park, and finally walks 6 km back home, the displacement would be 6 km. This implies that the final position is 6 km away from the initial position in the direction of home.

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Approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.  

The velocity function for a sky diver falling near the Earth's surface is given by the exponential function \(v(t) = 71 - 71e^(-0.19t)\), where t represents the time after diving measured in seconds.

To find the number of seconds after diving when the sky diver's velocity is 59 meters per second, we need to solve the equation:

\(59 = 71 - 71e^{(-0.19t)}\)

Let's solve it step by step:

Subtracting 71 from both sides:

\(-12 = -71e^{(-0.19t)}\)

Dividing both sides by -71:

\(e^{(-0.19t)} = \frac{12}{71}\)

Taking the natural logarithm (ln) of both sides to eliminate the exponential:

\(ln(e^{(-0.19t)}) = ln(\frac{12}{71})\\-0.19t = ln(\frac{12}{71})\)

Now, we can solve for t by dividing both sides by -0.19:

\(t =\frac{ln(\frac{12}{71})}{-0.19}\)

Using a calculator or a software, we find:

t ≈ 9.356 seconds (rounded to three decimal places)

Therefore, approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.  

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Answer:

Third option is the correct choice.

Step-by-step explanation:

\(a_1\) is the first term of the sequence which is given to be 1.

\(r\) is the common ration which can be found as:

\(r=\frac{3}{1}=3\quad r=\frac{9}{3}=3\)

Best Regards!

Answer:

1

Step-by-step explanation:

I got it right

We know that

< means smaller than

≤ means smaller or equal to

> means greater than

≥ means greater or equal to

We want to find a number (let's call it x), greater than -34

Since, > means greater than, we use this symbol:

y > -34

To find the equation of the tangent plane to the given equation 2(x-2)^2 (y-1)^2 (z-3)^2=10, we need to find the gradient of the function and use the point-slope form of a plane.

First, we find the gradient of the function by taking the partial derivatives with respect to x, y, and z:

∂f/∂x = 4(x-2)(y-1)^2(z-3)^2

∂f/∂y = 4(x-2)^2(y-1)(z-3)^2

∂f/∂z = 4(x-2)^2(y-1)^2(z-3)

Next, we find the point on the surface where we want to find the tangent plane. For simplicity, let's choose the point (2,1,3), which is on the surface because 2(2-2)^2(1-1)^2(3-3)^2=0=10.

Now we plug in the point into the gradient to find the normal vector to the plane:

∂f/∂x(2,1,3) = 4(2-2)(1-1)^2(3-3)^2 = 0

∂f/∂y(2,1,3) = 4(2-2)^2(1-1)(3-3)^2 = 0

∂f/∂z(2,1,3) = 4(2-2)^2(1-1)^2(3-3) = 0

So the normal vector is <0,0,0>.

Finally, we use the point-slope form of a plane to find the equation of the tangent plane:

0(x-2) + 0(y-1) + 0(z-3) = 0

Simplifying, we get:

0 = 0

This means that the tangent plane is the entire xyz-space, since any point satisfies this equation.

Therefore, the equation of the tangent plane to the given equation at the point (2,1,3) is 0 = 0.

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Let the number be x

5 times of x=5x

And 7 means add 7=5x+7

Their sum = 5x+7=22

Therefore 5x=22–7=15

5x=15 dividing by 5

x=3

Verification

5x+7=22

5*3+7=22

15+7=22

22=22

L.H.S.= R.H..S

Ans The number is 3

Or.

(x)*(7+5) ≥ 22

(a) The 95% confidence interval for the population mean of the treatment group is [7.02, 10.98].

(b) To calculate Cohen's d, we need the standard deviation of the sample. Using the given sample scores, the standard deviation is approximately 2.68. Cohen's d is then (9 - 8.31) / 2.68 = 0.26, indicating a small effect size.

(c) To perform a hypothesis test, we compare the sample mean of 8.31 (obtained from the given sample scores) with the population mean of 9. Using a t-test, assuming a significance level of 0.05 and a two-tailed test, we calculate the t-value as (8.31 - 9) / (2.68 / sqrt(6)) = -0.57. The critical t-value for a 95% confidence level with degrees of freedom of 5 (n-1) is 2.571. Since |-0.57| < 2.571, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.

(d) Bayesian factor (BF) represents the strength of evidence for one hypothesis over another. Without specific information about the alternative hypothesis, we cannot compute a Bayesian factor in this case.

(a) To compute a 95% confidence interval for the population mean of the treatment group, we can use the formula:

Confidence Interval = sample mean ± (t-value * standard error)

From the given sample scores, the sample mean is (10 + 7 + 9 + 6 + 10 + 12) / 6 = 8.31. The t-value for a 95% confidence level with degrees of freedom 5 (n-1) is 2.571. The standard error can be calculated as the sample standard deviation divided by the square root of the sample size.

Using the sample scores, the sample standard deviation is approximately 2.68. The standard error is then 2.68 / sqrt(6) ≈ 1.09.

Plugging in the values, the 95% confidence interval is 8.31 ± (2.571 * 1.09), which gives us [7.02, 10.98].

(b) Cohen's d is a measure of effect size, which indicates the standardized difference between the sample mean and the population mean. It is calculated by subtracting the population mean from the sample mean and dividing it by the standard deviation of the sample.

In this case, the population mean is given as 9. From the sample scores, we can calculate the sample mean and standard deviation. The sample mean is 8.31, and the standard deviation is approximately 2.68.

Using the formula, Cohen's d = (sample mean - population mean) / sample standard deviation, we get (8.31 - 9) / 2.68 ≈ 0.26. This suggests a small effect size.

(c) To perform a hypothesis test, we can compare the sample mean of the treatment group (8.31) with the mean of the general population (9) using a t-test. The null hypothesis assumes that the population mean of the treatment group is equal to the mean of the general population.

Using the sample scores, the standard deviation is approximately 2.68, and the sample size is 6. The t-value is calculated as (sample mean - population mean) / (sample standard deviation / sqrt(sample size)).

Plugging in the values, the t-value is (8.31 - 9) / (2.68 / sqrt(6)) ≈ -0.57. The critical t-value for a 95% confidence level with 5 degrees of freedom (n-1) is 2.571.

Since |-0.57| < 2.571, we fail to reject the null hypothesis. This means there is not enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.

(d) Bayesian factor (BF) represents the strength of evidence for one hypothesis over another based on prior beliefs and data. However, to compute a Bayesian factor, we need specific information about the alternative hypothesis, which is not provided in the given question. Therefore, we cannot calculate a Bayesian factor in this case.

(a) The 95% confidence interval for the population mean of the treatment group is [7.02, 10.98].

(b) Cohen's d suggests a small effect size, with a value of approximately 0.26.

(c) The hypothesis test does not provide enough evidence to suggest a significant difference between the population mean of the treatment group and the mean of the general population.

(d) A Bayesian factor cannot be computed without information about the alternative hypothesis.

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The formulated Linear Program aims to minimize the objective function, which is the sum of production and inventory costs minus the revenue from selling the end-of-period inventory at month 4.

In this problem, we need to determine the optimal production and inventory levels over the four-month period to minimize costs and maximize revenue. We can formulate this as a linear programming problem with the following decision variables:

Let x1, x2, x3, x4 represent the production quantities for months 1, 2, 3, and 4, respectively.

Let y1, y2, y3, y4 represent the end-of-month inventory levels for months 1, 2, 3, and 4, respectively.

The objective function we want to minimize is:

Minimize: (5x1 + 8x2 + 4x3 + 7x4) + (2y1 + 2y2 + 2y3) - (15y4)

Subject to the following constraints:

1. Initial inventory: y1 = 15 (given)

2. Production capacity constraints:

  x1 <= 90 (month 1 capacity)

  x2 <= 75 (month 2 capacity)

  x3 <= 80 (month 3 capacity)

  x4 <= 50 (month 4 capacity)

3. Inventory balance equations:

  y1 + x1 - 50 = y2 (month 1)

  y2 + x2 - 65 = y3 (month 2)

  y3 + x3 - 100 = y4 (month 3)

  y4 + x4 - 70 = 0 (month 4, no carryover inventory)

4. Non-negativity constraints:

  x1, x2, x3, x4, y1, y2, y3, y4 ≥ 0

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Answer:

120 grams of 20% sugar and 480 grams of 10% sugar

Step-by-step explanation:

The reason that the answer is what it is is because the total of the sugar syrup must be 600 grams. It is 12% which means that its 1/5 20% and 4/5 10% and if you divide 600 by 5 you get 120 therefore 120 grams of 20% sugar is correct and for the rest just subtract 120 from 600 the get the answer.

There are 120 g of 20% sugar syrup and 480 grams of 10% of sugar syrup.

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

Given that;

A 20% sugar syrup is mixed with 10% sugar syrup.

And, The result is 600 g of 12% sugar syrup.

Now,

It is 12% which means that its 1/5 of 20%.

Hence, Amount of sugar grams = 600 / 5

                                                  = 120 grams

And,  It is 12% which means that its 4/5 of 10%.

Hence, Amount of sugar grams = 600 / (4/5)

                                                  = 480 grams

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The graphs of the modulus functions are just a pair of lines drawn simultaneously.

A modulus function is a function which gives the absolute value of a number or variable. It produces the magnitude of the number of variables. It is also termed as an absolute value function. The outcome of this function is always positive, no matter what input has been given to the function.

Given here ; The modulus functions y=|x|-2 , y=|x-1|+1 , y=|x-3|

To plot these, we’ll use the definition of a modulus function, just like for |x|. Let’s start with the first one.

|x–3|={x,, when x≥3

           {  −x  when x<3

That  means, to plot the graph of y = |x – 3|, we have to plot the graph of

y = x – 3, when x ≥ 3

y = 3 – x, when x < 3

That is, for x ≥ 3, we’ll draw a line whose slope is 1 and y-intercept is –3. For x < 3, we’ll draw a line whose slope is –1 and y-intercept is -3.

Similarly for  y=|x|-2 and y=|x-1|+1 we can use the definition of modulus function to plot the pair of  lines (y=x-2 & y=-x-2) & (y=-x+2 & y=x)

as shown in the graph attached.

Hence, The graphs of the modulus functions are just a pair of lines drawn simultaneously.

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458 fishes

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The answer is in the picture. Click on it.

Answer: g(f(10)) = g(√2x+5) = 6x-3

We need to substitute x = √2*10 + 5 into g(x) = 6x - 3

g(f(10)) = 6(√2*10 + 5) - 3 = 6√20 + 30 - 3 = 6√20 + 27

So g(f(10)) = 6√20 + 27.

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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n=196

x=26,2

s=6,2

CL=99%

then z= 2.576

we use the following formula to find the confidence interval

Thus the 1st answer is: 25.1 < u < 27.3

now comparing the 2 intervals we find the answer to the second question

Are the results very differts?

the answers is

A. No, because the confidence interval limits are similar

The probability of a simple event to occur is this:

In the question given, the favorable outcomes are either 8 or diamond.

In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.

Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:

The probability, in fraction, is 4/13.

In decimal form, it is 0.3077.

In percentage form, it is 30.77%

Set up a proportion!

40 minutes / 5 holes = m minutes / 20 holes

Cross multiply.

800 = 5m

m = 160.

It will take him 160 minutes to dig 20 post holes.

Good luck Fabian!

Hope this helps

Answer:

64

Step-by-step explanation:

(2x + 3y)^2 = 4

xy = -5

4x^2 + 9y^2

===========

(2x + 3y)^2 = 4                   [Start here]

4x^2 +12xy + 9y^2 = 4       [Expand]

4x^2 +12(-5) + 9y^2 = 4     [Substitute xy = -5]

4x^2 -60 + 9y^2 = 4            

4x^2 + 9y^2 = 4 + 60       [Rearrange]

4x^2 + 9y^2 = 64              [64 is the value of 4x^2 + 9y^2]

Let's solve for x

Y=x-5

step 1:flip the equation

x-5=y

step 2:Add 5 to both sides

x-5+5=y+5

x=y+5

answer :x=y+5

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