PLEASE HELP ME.... PLEASEEEE.... ​

Answer:

f(2) = 1/8

Step-by-step explanation:

f(2) = (3 - (2))/((2)2 + 4)

f(2) = 1/8

Answer:

8 thousand

Step-by-step explanation:

The length and width of the plot that will maximize the area is 60 meters by 120 meters. The largest area that can be enclosed is 7200 square meters.

To maximize the area of the rectangular plot, Farmer Ed must use 9000 meters of fencing to enclose three sides of the plot. The fourth side, which borders the river, does not need to be fenced. To find the length and width of the plot that will maximize the area, the 9000 meters of fencing must be divided into two sides of equal length, with the remaining fencing used for the third side. This results in a length of 120 meters and a width of 60 meters, which maximizes the area of the plot. The largest area that can be enclosed is 7200 square meters.

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Answer:

6

Step-by-step explanation:

5x+12=42

subtract 12

5x=30

divide by 5

x=6

Answer:

Step-by-step explanation:

Conclusion:

Therefore, the answer is 'x = 6'.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

k = -11

Step-by-step explanation:

Let \(p(x) = x^3-6x^2+kx+10\)

And x+2 is a factor of p(x)

Let x+2 = 0 => x = -2

Putting in p(x)

=> p(-2) = \((-2)^3-6(-2)^2+k(-2)+10\)

By remainder theorem, Remainder will be zero

=> 0 = -8-6(4)-2k+10

=> 0 = -8-24+10-2k

=> 0 = -22-2k

=> -2k = 22

Dividing both sides by -2

=> k = -11

The required answer is the y = 80

The best fit line equation in a scatter plot represents the relationship between two variables. It is also known as the regression line or the line of best fit. The equation of the best fit line is typically represented as y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

To find the best fit line equation in a scatter plot,

1. Plot the data points on a scatter plot.
2. Visualize the trend or pattern in the data points.
3. Determine whether the relationship between the variables is linear, meaning that the data points roughly form a straight line pattern.
4. Use a statistical method, such as the least squares method, to find the line that minimizes the distance between the data points and the line.
5. Calculate the slope (m) and the y-intercept (b) of the best fit line.
6. Write the equation of the line using the values of m and b.

Using the least squares method, determine that the slope of the best fit line is 2 and the y-intercept is 70.

Therefore, the equation of the best fit line would be:

y = 2x + 70

This equation represents the expected test score (y) based on the number of hours studied (x). For example, if a student studies for 5 hours, estimate their test score by substituting x = 5 into the equation:

y = 2(5) + 70
y = 10 + 70
y = 80

So, according to the best fit line equation, if a student studies for 5 hours,  expect their test score to be around 80.

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Answer:

7.04 yards

Step-by-step explanation:

644 centimeters is 7.04287 yards that rounded to the nearest hundredth is 7.04 yards

Answer:

7.04

Step-by-step explanation:

It just is...

9514 1404 393

Answer:

  RT = 75 yards

Step-by-step explanation:

Triangle TCB is congruent to triangle TCR by ASA. (Side TC is between angles T and C.)

Then RT = BT = 75 yards.

The set of data that represents the interquartile range and the maximum, in that order, is (80 - 70, 95), which simplifies to (10, 95).

Looking at the box plot, we can see that the box spans from approximately 65 to 85, with the median at around 75. To find the values for the interquartile range and maximum, we need to determine the exact values for Q1, Q3, and any outliers.

From the box plot, we can estimate that Q1 is around 70 and Q3 is around 80.

The median of the lower half of the data is the middle value between the smallest value and the median, which is approximately 68.

The median of the upper half of the data is the middle value between the median and the largest value, which is approximately 83.

To find the maximum value, we look for the highest data point that is not an outlier. From the box plot, we can see that there are no outliers, so the maximum value is the highest value in the data set, which is approximately 95.

Therefore, the set of data that represents the interquartile range and the maximum, in that order, is (80 - 70, 95), which simplifies to (10, 95).

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By using what we know about right triangles, we will see that the height is 11.7 m.

We can view this as a right triangle, such that the wire is the hypotenuse of said triangle.

We know that the hypotenuse measures 14 m, and the angle between the ground and the wire si 57°. The height would be the opposite cathetus to that angle, so we can use the rule:

Sin(a) = (opposite cathetus)/hypotenuse

Replacing the values we get:

Sin(57°) = H/14m

Sin(57°)*14m = H = 11.7m

The height of the tower is 11.7 meters.

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Answer:

Step-by-step explanation:

Let the length be L

Formula

SA = 2Lw + 2Lh + 2wh

Givens

h = 15 cm

w = 6 cm

L = ?

SA = 684 cm^2

Solution

Substitue what you know into the given formula

2*6*L + 2*15*L + 2 * 6 * 15 = 684         Combine

12*L + 30*L + 180 = 684                         Combine again

42L + 180 = 684                                     Subtract 180 from both sides.

42L +180 -180 = 684 - 180            

42L = 504                                               Divide by 42

Answer: L = 12

Answer:

Step-by-step explanation:

Answer:

24.1 is a possibility for the perimeter

Step-by-step explanation:

The third side between 12+0.5 and 12-0.5, or 12.5 and 11.5.

The third side is between 11.5 and 12.5.

Simce it isn't isosceles third side can't be 12.

So it's asking you to choose a number between 11.5 and 12.5 with the exclusiion of 12 for the third side measurement in meters.

So let's choose 11.6.

So the perimeter is just the sum of all side measurements.

11.6+12+0.5

11.6+0.5+12

12.1+12

24.1

24.1 is a possibility for the perimeter

Answer: Below

Step-by-step explanation:

7 1/5 - 6 2/5 = 4/5

Hope this helped!

Prime polynomials cannot be factorized in smaller degree polynomials. The prime polynomials out of the considered option are:

Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called prime polynomial.

(it is necessary that no factors exists having their coefficients are still integers and they're of lower degree)

Checking all the options for them being prime or not:

Take \((x+a)(x+b) = x^2 + 9\)

Then, expanding it gives:

\(x^2 + (a+b)x + ab = x^2 + 9 \implies a+b = 0, ab = 9\)

or we get: \(a = -b, ab = -b^2 = 9, b^2 = -9\)

Square of a real number doesn't exist, so this factor doesn't exist. Thus, it is prime polynomial.

We have the identity \((a+b)(a-b) = a^2 - b^2\)

and since 9 is square of 3, therefore, we get:

\(x^2 -9 = x^2 -3^2 = (x+3)(x-3)\)

So it got factorized. Thus, not a prime polynomial.

Take \((x+a)(x+b) = x^2 + 3x + 9\)

Then, expanding it gives:

\(x^2 + (a+b)x + ab = x^2 + 3x + 9 \implies a+b = 3, ab = 9\)

That gives:

\(a = 3-b\\ab = b(3-b) = 3b - b^2 = 9\\b^2 -3b + 9 = 0\)

Solving this quadratic equation by root formula gives:

\(b = \dfrac{-(-3) \pm \sqrt{(-3)^2 -4(1)(9)} }{2}\\\\b = \dfrac{-(-3) \pm \sqrt{-27} }{2}\\\)

this makes 'b' a complex number and it doesn't remain a real number as its expression contains square root of a negative number.

Thus, this polynomial cannot be factorized in terms of smaller degree polynomials. Thus, its a prime polynomial.

Taking -2 common out, we get:

\(-2(x^2 - 4) = -2(x^2 - 2^2) = -2(x-2)(x+2)\)

Thus, it got factorized, and therefore not a prime polynomial.

Thus, the prime polynomials out of the considered option are:

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Answer:

A) x2 + 9

C) x2 + 3x + 9

☆
EDGE2022; Good Luck :D!!!

Answer:

B. P(A and B) = 0.14

Step-by-step explanation:

To determine if events A and B are independent, we need to check if the probability of their intersection, P(A and B), is equal to the product of their individual probabilities, P(A) and P(B).

If A and B are independent events, then P(A and B) = P(A) * P(B).

Given that P(A) = 0.70 and P(B) = 0.20, let's calculate their product:

P(A) * P(B) = 0.70 * 0.20 = 0.14

Now, let's evaluate the answer choices:

A. P(A or B) = 0.90:

This does not provide information about the intersection of A and B, so it doesn't help determine if A and B are independent.

B. P(A and B) = 0.14:

This matches the product of P(A) and P(B) calculated earlier. If this option is true, then A and B are independent events.

C. P(A or B) = 0.14:

This is the same value as the product of P(A) and P(B), but it represents the probability of their union (A or B). It doesn't provide information about their intersection, so it doesn't help determine if A and B are independent.

D. P(A and B) = 0:

This does not match the product of P(A) and P(B) calculated earlier. If this option is true, it would imply that A and B have no common outcomes, making them independent.

Therefore, based on the calculations, the correct option is:

B. P(A and B) = 0.14

If P(A and B) equals the product of P(A) and P(B), then events A and B are independent.

The total force acting on the floor when completely filled with water is 11.5 kN and the pressure that this bed exerts on the floor is 3.5 kPa.

A student decides to set up her waterbed in her dormitory room.

The bed measures 220 cm x 150 cm, and its thickness is 30 cm. The bed without water has a mass of 30 kg.

The total force of the bed acting on the floor when completely filled with water and the pressure that this bed exerts on the floor are calculated below:

Given, Dimensions of the bed = 220 cm x 150 cm

Thickness of the bed = 30 cm

Mass of the bed without water = 30 kg

Total force acting on the floor can be found out as:

F = mg Where, m = mass of the bed

g = acceleration due to gravity = 9.8 m/s²

The mass of the bed when completely filled with water can be found out as follows:

Density of water = 1000 kg/m³

Density = mass/volume

Therefore, mass = density × volume

When the bed is completely filled with water, the total volume of the bed is:

(220 cm) × (150 cm) × (30 cm) = (2.2 m) × (1.5 m) × (0.3 m) = 0.99 m³

Therefore, mass of the bed when completely filled with water = 1000 kg/m³ × 0.99 m³ = 990 kg

Therefore, the total force acting on the floor when completely filled with water = (30 + 990) kg × 9.8 m/s²

= 11,514 N

≈ 11.5 kN.

The pressure that the bed exerts on the floor can be found out as:

Pressure = Force / Area

The entire bed makes contact with the floor, therefore the area of the bed in contact with the floor = (220 cm) × (150 cm) = (2.2 m) × (1.5 m) = 3.3 m²

Therefore, Pressure = (11,514 N) / (3.3 m²) = 3,488.48 Pa ≈ 3,490 Pa ≈ 3.5 kPa

Therefore, the total force acting on the floor when completely filled with water is 11.5 kN and the pressure that this bed exerts on the floor is 3.5 kPa.

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t distributions tend to be flatter and more spread out than the normal distribution.

This is due to the fact that in the formula, the denominator is s rather than σ.

The distribution of the sample mean is normal if some samples are taken from a normal population with known variance. However, if the population variance is unknown, the distribution is not normal but Student-t with long tails. This means that sample means tend to be extreme when the population variance is unknown. Using the normal distribution instead of the t distribution to test the hypothesis increases the chance of error.

Note that there is a different t-distribution for each sample size. That is, the class of distributions. When talking about a particular t-distribution, we need to specify the degrees of freedom. The degrees of freedom for this t-statistic is given by the sample standard deviation s in the denominator of Equation 1. The spread is larger than the standard normal distribution. This is because the denominator of equation (1) is s, not σ. Because s is a random variable that changes from sample to sample, t becomes more volatile and more spread out.

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If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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For this question, since we need to show that Eric and Nancy contributes the same amount to their monthly income, we just need to equate both expressions with each other, and then solve for the value of x.

In order to check if we got the right answer, we just need to substitute the value of x to both equations.

Therefore, we can conclude that Eric and Nancy has to sell 6 fish tanks each.

Sample size is inversely related to the tolerable deviation rate, a larger sample size is needed to provide a more accurate estimate of the population parameter.

Step-by-step explanation:
1. Sample size refers to the number of observations or units included in a study or analysis to represent a population.
2. Desired level of confidence refers to the degree of certainty that the estimate obtained from the sample accurately represents the population parameter. It is directly related to sample size, as a higher level of confidence generally requires a larger sample.
3. Expected population deviation rate refers to the anticipated rate of deviation or error in a population. It is also directly related to sample size, as a higher expected deviation rate requires a larger sample to ensure accuracy.
4. Tolerable deviation rate, on the other hand, is the maximum rate of deviation that can be accepted in the sample without affecting the overall conclusions. This is inversely related to sample size because as the tolerable deviation rate decreases, a larger sample size is needed to provide a more accurate estimate of the population parameter.

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The length ||x||2 is positive, we must have λ

is positive. It follows that every eigenvalue λ

of A is real.

Recall that the eigenvalues of a real symmetric matrix are real.

Let λ be a (real) eigenvalue of A and let x be a corresponding real eigenvector. That is, we have

Ax=λx.

Then we multiply by xᵀ on left and obtain

xᵀAx = λxᵀx = λ || x || 2.

The left hand side is positive as A is positive definite and x is a nonzero vector as it is an eigenvector.

Since the length ||x||2 is positive, we must have λ

is positive. It follows that every eigenvalue λ

of A is real.

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The expression is an illustration of the summation notation

The expanded form of the summation notation \(\sum\limits^{4}_{i = 0} i^4\) is  0^4 + 1^4 + 2^4 + 3^4+4^4

The summation notation is given as:

\(\sum\limits^{4}_{i = 0} i^4\)

The above summation notation represents the sum of the numbers raise to the power of 4, from 0 to 4

So, we have:

\(\sum\limits^{4}_{i = 0} i^4 = 0^4 + 1^4 + 2^4 + 3^4+4^4\)

Hence, the expanded form of \(\sum\limits^{4}_{i = 0} i^4\) is  0^4 + 1^4 + 2^4 + 3^4+4^4

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4 , 7 , 14 , 19 , 21 , 23 , 23 , 26 , 27 , 30

Step-by-step explanation:

HOPE IT'S HELP ;)

We have the ratio of students that are from Florida and the ones that are not. For every 3 students from florida, 1 isn't. Therefore we can create the following ratio:

Where x is the number of Florida's students and y is the number of students that are not from that place. We can rewrite the equation as follows:

The sum of "x" and "y" must be equal to the number of students in the university. So we have:

If we replace the value of the first equation on the second, we can solve for y.

Therefore, we can determine the number of students from Florida, by using the first equation:

There are 9000 students from Florida.

Answer:

16

Step-by-step explanation:

Remark

Linear Pair means two angles add to 180. They have a base and a transversal in common.

Equation

1/3(27x - 6) + 1/2(6x  - 20) = 180                Remove the brackets

Solution

9x - 2 + 3x - 10 = 180                                 Collect like terms

12x - 12 = 180                                             Add 12

12x - 12 + 12 = 180 + 12                              Combine

12x = 192                                                    Divide by 12

12x/12/ = 192/12

x = 16

\(slope = \frac{rise}{run}\\\\m = \frac{y2 - y1}{x2 - x1}\)

Answer:

B. f(x) = -x + 2

Step-by-step explanation:

First, you find the point on the y-axis which is (0,2) in this problem.

This will be your b in y = mx+ b

Then, you'll find how many blocks you are moving or rise over run. Which is -1/1 or -1.

This will be your m in y = mx + b

But we don't write the 1 so it will just be -x

Now add all your numbers in the standered form (y = mx + b) to get y = -x + 2 or f(x) = -x + 2

Answer:

6x2 + 16x = 672

Reorder the terms:

16x + 16x2 = 672

Solving

16x + 16x2 = 672

Solving for variable 'x'.

Reorder the terms:

-672 + 16x + 16x2 = 672 + -672

Combine like terms: 672 + -672 = 0

-672 + 16x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '16'.

16(-42 + x + x2) = 0

Factor a trinomial.

16((-7 + -1x)(6 + -1x)) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying

-7 + -1x = 0

Solving

-7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '7' to each side of the equation.

-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0

0 + -1x = 0 + 7

-1x = 0 + 7

Combine like terms: 0 + 7 = 7

-1x = 7

Divide each side by '-1'.

x = -7

Simplifying

x = -7

Subproblem 2

Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying

6 + -1x = 0

Solving

6 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-6' to each side of the equation.

6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0

0 + -1x = 0 + -6

-1x = 0 + -6

Combine like terms: 0 + -6 = -6

-1x = -6

Divide each side by '-1'.

x = 6

Simplifying

x = 6

Solution

x = {-7, 6}

Step-by-step explanation:

The given quadratic function models the projectile of the object as it is

launched off the top of the building.

The interpretation of the function values are;

The appropriate domain is 0 ≤ x ≤ 7

Reasons:

The given function for the height of the object is f(x) = -16·x² + 16·x + 672

The domain is given by the values of x for which the value of y ≥ 0

Therefore, when -16·x² + 16·x + 672 = 0, we get;

-16·x² + 16·x + 672 = 0

16·(-x² + x + 42) = 0

-x² + x + 42 = 0

x² - x - 42 = 0

(x - 7)·(x + 6) = 0

x = 7, or x = -6

The minimum value of time, x is 0, which is the x-value at the top of the

building, and when x = 7, the object is on the ground.

Therefore;

The maximum value of f(x) = a·x² + b·x + c, is given at \(x = -\dfrac{b}{2 \cdot a}\)

Therefore;

We have;

\(x = -\dfrac{16}{2 \times (-16)} = \dfrac{1}{2}\)

Which gives;

\(f \left(\frac{1}{2} \right) = -16 \times \left(\dfrac{1}{2} \right)^2 + 16 \times \left(\dfrac{1}{2} \right)+ 672 = 676\)

The height of the building is given when the time, x = 0, as follows;

Height of building, f(0) = -16 × 0² + 16 × 0 + 672 = 672

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