5.99 is greater less or equal 5.990

Answer:

The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side.

Step-by-step explanation:

The solution in terms of a and b is x=(-a/6)+(b/6) and y=(2a/3)-(b/3).

To find the solution to the systems using the inverse of the matrix, we can use the formula:
[xy]=[A^-1][b]
where [A] is the coefficient matrix, [b] is the constant matrix, and [A^-1] is the inverse of the coefficient matrix.

For system (a), we have:
[A]=[21​41​]
[b]=[12​]
To find the inverse of [A], we can use the formula:
[A^-1]=1/(ad-bc)[d -b​-c a​]
where a=2, b=1, c=4, and d=1.
So, [A^-1]=1/(-6)[1 -1​-4 2​]=[-1/6 1/6​2/3 -1/3​]
Now, we can find the solution by multiplying [A^-1] and [b]:
[xy]=[-1/6 1/6​2/3 -1/3​][12​]=[-1/6+1/6 2/3-1/3​]=[-1/3​]
So, the solution to system (a) is x=-1/3 and y=1/3.

For system (b), we have:
[A]=[21​41​]
[b]=[20​]
We can use the same inverse of [A] that we found for system (a) and multiply it by [b] to find the solution:
[xy]=[-1/6 1/6​2/3 -1/3​][20​]=[-2/6+0 4/3-0​]=[-1/3​2​]
So, the solution to system (b) is x=-1/3 and y=2.

For the system [21​41​][xy​]=[ab​], we can use the same inverse of [A] and multiply it by [ab]:
[xy]=[-1/6 1/6​2/3 -1/3​][ab​]=[-a/6+b/6 2a/3-b/3​]
So, the solution in terms of a and b is x=(-a/6)+(b/6) and y=(2a/3)-(b/3).

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B-girls are more commonly found in towns with military bases.

The term "B-girls" is used to refer to women who are in bars and whose role is to entertain customers and motivate them to spend more money.

This term is often a synonym of "bar girls" or "hostess"; moreover, depending on the type of bar these girls offer different services including sexual services.

Besides this, b-girls are more common in towns or areas with a higher number of possible male customers. This includes towns with military bases because these are related to a high number of men and many of them are bar customers, which makes it profitable to have b-girls in these areas.

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Answer:

for for A,

16+7+5+12 = 40

the probability of throw the darts is 5/40

if there were 80 people doing it, an estimate of 10 people would do throw the darts

x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.

General process of solving for an unknown angle.

1. Determine the type of angle: Determine whether the angle is a right angle (90 degrees), acute (less than 90 degrees), or obtuse (greater than 90 degrees).

2. Use geometric properties: If there are geometric properties or relationships given in the problem, such as angles formed by parallel lines or within a triangle, apply those properties to find the value of x.

3. Apply trigonometric functions: If the problem involves trigonometry, use sine, cosine, or tangent functions along with the given information to solve for x.

4. Apply algebraic equations: If there is an algebraic equation involving x, set up the equation and solve for x by isolating it on one side of the equation.

To find the value of x in the given triangle, we can use the inverse tangent function, which is tan^-1.

tan(x) = opposite/adjacent

tan(x) = 5/14

To isolate x, we take the inverse tangent of both sides:

x = tan^-1(5/14)

Using a calculator, we can find that x is approximately 20.5 degrees when rounded to the nearest degree. Therefore, x ≈ 21 degrees.

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Answer: -30r + 15

Step-by-step explanation:

first, we multiply the parenthesis by 20.

-20 x 1.5r + 20 x 0.75

then, we multiply/calculate.

-30r + 15

Answer: Brainliest? Need One More!

Step-by-step explanation:

20*(-1.5r)

+

20*(0.75)

-30r+15

Answer:

25

Step-by-step explanation:

$50

Cost=$6

Selling price=$8

Profit=$8-$6=$2

50/2=25

To maximize the expression Σ pi' (1 - bi') given the lists bi and Pi, we can use a greedy algorithm.  The algorithm works as follows:

1. Sort the lists bi and Pi in descending order based on the values of Pi.

2. Initialize two empty lists, bi' and pi'.

3. Iterate through the sorted lists bi and Pi simultaneously.

4. For each pair (bi, Pi), append bi to bi' and Pi to pi'.

5. Calculate the sum of pi' (1 - bi') to obtain the maximum value.

The greedy expression selects the elements with the highest Pi values first, ensuring that the products pi' (1 - bi') contribute the most to the overall sum. By sorting the lists in descending order based on Pi, we prioritize the higher Pi values, maximizing the sum.

It's important to note that this greedy algorithm may not guarantee an optimal solution in all cases, as it depends on the specific values in the lists. However, it provides a simple and efficient approach to maximize the given expression based on the provided lists bi and Pi.

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The sum of the values of k for which the area of the triangle is a minimum is 10.

To find the sum of the values of k for which the area of the triangle is a minimum, we need to determine the possible values of k.

Given that the area of the triangle is 10, we can use the formula for the area of a triangle:

Area = 1/2 * base * height

We can choose any two sides of the triangle as the base and height. Let's consider the sides formed by the points (1,7) and (13,16) as the base.

The length of the base is the distance between these two points:

base = sqrt((13-1)^2 + (16-7)^2) = sqrt(144 + 81) = sqrt(225) = 15

Since the area is 10, we can substitute the values into the formula:

10 = 1/2 * 15 * height

Simplifying the equation, we find:

height = 20/3

Now, let's find the equation of the line passing through the points (1,7) and (13,16) to determine the possible values of k.

The slope of the line is given by:

m = (16-7)/(13-1) = 9/12 = 3/4

Using the point-slope form of a linear equation, we have:

(y - 7) = (3/4)(x - 1)

Rearranging the equation, we find:

4y - 28 = 3x - 3

Simplifying, we get:

4y = 3x + 25

Substituting x = 5 (since the point (5,k) lies on the line), we can solve for k:

4k = 3(5) + 25

4k = 15 + 25

4k = 40

k = 10

Therefore, the sum of the values of k for which the area of the triangle is a minimum is 10.

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Answer: x = -12

Step-by-step explanation:

-1/2x=6

Divide by -1/2

x = -12

Hope it helps <3

The conditions on the parameter 'a' determine whether the poles of the exponential functions are in the LHP or RHP.

In the Laplace transform analysis, the poles of a function are the values of 's' that make the denominator of the Laplace transform expression equal to zero. The location of the poles provides important insights into the system's behavior.

For the exponential functions x₃(t) = e^(at), x₆(t) = te^(at), and x₇(t) = t^2e^(at), the Laplace transform expressions will contain poles. The poles will be in the LHP if the real part of 'a' is negative, meaning a < 0. This condition indicates stable behavior, as the exponential functions decay over time.  

On the other hand, if the real part of 'a' is positive, a > 0, the poles will be in the RHP. This implies unstable behavior since the exponential functions will grow exponentially over time.

If the real part of 'a' is zero, a = 0, then the pole lies on the jω-axis. The system is marginally stable, meaning it neither decays nor grows but remains at a constant amplitude.

By analyzing the sign of the real part of 'a', we can determine whether the poles of the Laplace transforms are in the LHP, RHP, or on the jω-axis, thereby characterizing the stability of the system.

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Parallel Lines

Given the equation of a line as:

y = mx + c

The variable m represents the slope or the gradient of the line, and c represents the y-intercept of the line.

If two lines are parallel, they have the same gradient, i.e., their value of m is equal for both and c is different. Note if c was equal also, both lines would be exactly the same, not parallel.

We are given a number of pairs of lines and we must identify which pairs are parallel lines.

a) y = 3x + 4, y = 3x - 8

Comparing the values of m (the coefficient of x) in both equations, we conclude they are parallel lines since m=3 for both and c is different.

b) y = 2x - 17 , y - 2x = 17

We must express the second equation with the y isolated at the left side:

y = 2x + 17

Both lines have the same value of m=2 and different values of c, so they are parallel.

c) y = x - 4 , y = -2x - 4

The first gradient is m=1 and the second gradient is m=-2, thus these lines are not parallel

d) 3y + 3x = 9 , y = x + 3/2

Divide the first equation by 3:

y + x = 3

And solve for y:

y = -x +3

The gradient of this line is -1 and the gradient of the other line is m=1, thus these lines are not parallel.

e) 2x = y + 8 , 2y = x + 8

Solving for y both equations:

y = 2x - 8

y = x/2 + 4

The gradients are m=2 and m=1/2 respectively, thus these lines are not parallel.

f) 3 - x = 3y , y - 3x = 5

Solving for y:

y = -x/3 + 1

y = 3x + 5

The gradients are, respectively m=-1/3 and m=3, thus these lines are not parallel.

g) 4y + 8x = 0 , y = 22 - 2x

Solving for y and rearranging:

y = -2x , y = -2x + 22

The gradients are m=-2 for both lines and the values of c are different, thus these lines are parallel.

h) y = 2x - 8 , 8y + 8x = 9

Solving the second equation for y:

y = -x + 9/8

The gradients are, respectively m=2 and m=-1, thus these lines are not parallel.

The following image summarizes the results by circling the pairs of parallel lines as required.

heres a trick

to find 25 - 35, multiply the result of subtracting 25 from 35 by -1

35 - 25 = 10

25 - 35 = -1(10)

= -10

Answer:

the answer is -10

Step-by-step explanation:

For conservative forces, force can be fouind as being the negative of the deriviation of potential energy.

It should be noted that a conservative force simply means the force in moving a particle from a particular point to another. In this case, the force is independent of the path that's taken by the particle.

It should be noted that F = du/dr as u is the potential energy. Therefore, force is the negative derivative of the potential energy.

Therefore, for conservative forces, force can be fouind as being the negative of the deriviation of potential energy.

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Complete question

For conservative forces, force can be fouind as being the negative of the deriviation of?

momentum

kinetic energy

impulse

work

potential energy

Step-by-step explanation:

first we notice that the line RS makes a diagonal in the circle.Since we are given ROP we can find SOP by:

180⁰-125⁰=55⁰

since they are in each others opposite point they are equal so that means that if we try the equation we did before: SOQ =ROP and QOR=SOP

Step-by-step explanation:

step 1. mPOS = 180 - 125 = 55°. (supplementary angles)

step 2. mQOS = 125° (vertical angles)

step 3. mQOR = 180 - 125 = 55° (supplementary angles).

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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Answer:

Your answer will be x= -1

Step-by-step explanation:

have a nice day:)

Answer:

y=−x2+6x+16

explanation

Willard should interpret the 95% prediction interval for percent potassium when nitrogen is 18 ppm as a range of values within which the true value of percent potassium is likely to fall with a 95% probability.

Specifically, the prediction interval (0.87%, 1.02%) suggests that if Willard were to measure the percent potassium in a large number of soil samples with a nitrogen level of 18 ppm and calculate the prediction interval for each sample, then 95% of the prediction intervals would contain the true value of percent potassium.

The lower and upper limits of the prediction interval correspond to the lower and upper bounds of the plausible range for percent potassium, given the observed nitrogen level. In this case, the interval (0.87%, 1.02%) indicates that Willard can be 95% confident that the true value of percent potassium for a soil sample with nitrogen level 18 ppm falls between 0.87% and 1.02%. However, it is important to note that the prediction interval is based on statistical assumptions and may not capture all sources of uncertainty or variability in the data. Therefore, it is important to interpret the prediction interval with caution and in the context of the specific statistical model and assumptions used to derive it.

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Answer:

6×12 has the product of 72

And

-11-11 has the sum of -22

Answer:

y = -4/1x + 28

Step-by-step explanation:

y=Mx +b

slope (m): -4/1

Y intercept (b): 28

We are required to know if the point (4,10) is a solution of the equation

5x + 10y = 120

If a point is a solution of the given equation, then when we replace x = 4 and y = 10 in the equation, the condition must stand, that is:

5(4) + 10(10) should be equal to 120

Evaluating the operations, we have:

20 + 100 = 120

Note the result of the operations equals the right side of the equation, thus we conclude the point (4,10) is a solution of 5x + 10y = 120

Answer:

Find the GCF and put it outside parentheses...then put the rest of digits in parentheses.

Step-by-step explanation:

1. 2a(b+c-1)

2. y^3(y^2+1)

3. 4(5x^2-3)

We can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26.

Based on the given information, we can calculate a 95% confidence interval for the mean amount that women in the population spend dining out per week. With a sample size of 25 and a standard error of $4, we can use the formula:

95% CI = sample mean +/- (critical value x standard error)

To find the critical value, we need to look up the t-distribution with degrees of freedom (df) = n-1 = 24 and a significance level of alpha = 0.05/2 = 0.025 (since we are interested in a two-tailed test). From a t-table or calculator, we find that the critical t-value is approximately 2.064.

Plugging in the values, we get:

95% CI = $100 +/- (2.064 x $4)
95% CI = $100 +/- $8.26
95% CI = ($91.74, $108.26)

Therefore, we can say with 95% confidence that the true mean amount that women in the population spend dining out per week lies within the range of $91.74 to $108.26. This means that if we were to repeatedly take random samples of 25 women and calculate their mean amount spent dining out, about 95% of the intervals we construct using this method would contain the true population mean.

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The margin of error at a 99% confidence level is 8.36.

The margin of error at a 99% confidence level based on a larger sample of 275 observations is 4.14.

a. Yes, the condition that X−X− is normally distributed is satisfied for a sample size of 69 by the central limit theorem.

b. The margin of error at a 99% confidence level can be computed using the formula:

Margin of error = z* (sigma / sqrt(n))

where z* is the z-score corresponding to a 99% confidence level, sigma is the known standard deviation, and n is the sample size.

The z-score for a 99% confidence level is 2.576 (from the z table).

Substituting the given values, we get:

Margin of error = 2.576 * (27.5 / sqrt(69)) = 8.36

c. The margin of error at a 99% confidence level based on a larger sample of 275 observations can be computed using the same formula:

Margin of error = z* (sigma / sqrt(n))

where z* is the z-score corresponding to a 99% confidence level, sigma is the known standard deviation, and n is the sample size.

The z-score for a 99% confidence level is still 2.576 (from the z table).

Substituting the given values, we get:

Margin of error = 2.576 * (27.5 / sqrt(275)) = 4.14

d. The margin of error is inversely proportional to the square root of the sample size. As the sample size increases, the margin of error decreases. Therefore, the margin of error with n = 275 will be smaller than the margin of error with n = 69, leading to a narrower confidence interval.

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The orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

To find the orthogonal complement w⊥ of w, we need to find the set of all vectors that are orthogonal (perpendicular) to w.

Given w = (x, y, z) = (12t, -12t, 6t), we can find a vector v = (a, b, c) that is orthogonal to w by taking their dot product equal to zero:

w · v = 0

Substituting the values of w and v:

(12t, -12t, 6t) · (a, b, c) = 0

(12t)(a) + (-12t)(b) + (6t)(c) = 0

12at - 12bt + 6ct = 0

Now, we can solve this equation to find the values of a, b, and c that satisfy the orthogonal condition for all values of t.

12at - 12bt + 6ct = 0

Factor out t:

t(12a - 12b + 6c) = 0

For this equation to hold true for all values of t, the expression inside the parentheses must equal zero:

12a - 12b + 6c = 0

Divide by 6:

2a - 2b + c = 0

This equation represents a plane in three-dimensional space. To find a basis for w⊥, we can express this equation in the form of a linear combination of vectors. Let's solve for c:

c = 2b - 2a

Now, we can express the basis vectors for w⊥ in terms of a and b:

v = (a, b, 2b - 2a)

We can choose any values for a and b to get different vectors in the orthogonal complement w⊥. For example, we can set a = 1 and b = 0:

v1 = (1, 0, 0)

Or we can set a = 0 and b = 1:

v2 = (0, 1, 2)

These two vectors, v1 and v2, form a basis for w⊥.

Therefore, the orthogonal complement w⊥ of w has a basis given by {v1, v2} = {(1, 0, 0), (0, 1, 2)}.

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Let's begin by finding the mean of the data

Mean = 48.9

Next, we calculate the absolute value of the difference between each data value and the mean, we have:

|data value – mean|

|46 - 48.9| = 2.9

|47 - 48.9| = 1.9

|56 - 48.9| = 7.1

|48 - 48.9| = 0.9

|46 - 48.9| = 2.9

|52 - 48.9| = 3.1

|57 - 48.9| = 8.1

|52 - 48.9| = 3.1

|45 - 48.9| = 3.9

Next, we sum up the absolute values of the differences (from above) & divide by the number of data values, we have:

MOD = 8 (to the nearest whole number)

Answer:

Y = 4

Step-by-step explanation:

To find the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1, we can use definite integration.

The area of the region bounded by the given graphs is approximately 25 square units.

To find the area, we need to integrate the given function over the interval [0, 1]. The integral represents the area under the curve between the limits of integration. Since the region is bounded by the x-axis, we integrate the function with respect to x.

∫[0, 1] (32 / (x² - 17x + 72)) dx

Evaluating this integral gives us the area of the region bounded by the graphs. Using numerical integration methods, we find that the area is approximately 25 square units.

The integral calculation involves finding the antiderivative of the function and then evaluating it at the upper and lower limits of integration. The resulting value represents the area between the curves and the x-axis within the specified interval.

Therefore, the area of the region bounded by the graphs of y = 32 / (x² - 17x + 72), y = 0, x = 0, and x = 1 is approximately 25 square units.

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