in exercises 25–30, find the distance between points p1 and p2. p1(1, 1, 1),p2(3, 3, 0) p1(−1, 1, 5),p2(2, 5, 0) p1(1, 4, 5),p2(4, −2, 7) p1(3, 4, 5),p2(2, 3, 4) p1(0, 0, 0),p2(2, −2, −2) p1(5, 3, −2),p2(0, 0, 0) find the distance from the point (3, −4, 2) to the xy-plane yz-plane xz-plane find the distance from the point (−2, 1, 4) to the plane x

Answer:

The answer would be B.

Because if you multiply all the numbers of ABC then go through the list of the A'B'C' options only B matches up

Answer:

im gonna assume the 10 - 20 is what the equation is = to if not x wouldnt be = to anything x = -1.5

Step-by-step explanation:

-2.25x + 8.75x = 10-20

-2.25x+ 8.75x = -10

6.50x = -10 divide both sides by 6.5

x = -1.5

(a) To determine the convergence or divergence of the sequence given by n = n * e^n * cos(n), we can apply the Limit Test. We'll find the limit as n approaches infinity:
lim (n→∞) [n * e^n * cos(n)]
As n becomes very large, e^n grows faster than any polynomial term (n, in this case), making the product n * e^n very large as well. Since cos(n) oscillates between -1 and 1, the product of these terms also oscillates and does not settle down to a specific value.
Therefore, the limit does not exist, and the sequence is divergent.
(b) To analyze the convergence of the sequence given by a_n = n^3 / 5, we again apply the Limit Test:
lim (n→∞) [n^3 / 5]
As n approaches infinity, the numerator (n^3) grows much faster than the constant denominator (5). This means the ratio becomes larger and larger without settling down to a specific value.
Thus, the limit does not exist, and the sequence is divergent.

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Therefore, the Laplace transform of d. f(t) = et² is $ \frac{1}{2} \sqrt{\frac{\pi}{s}} e^{s^{2}/4} $, the Laplace transform of e. f(t) = 3e4t – e-2t is $ \frac{3}{s-4} - \frac{1}{s+2} $ and the Laplace transform of f. f(t) = sinh(kt) is $ \frac{k}{s^{2}-k^{2}} $.

a. Laplace transform of

f(t) = et²

can be calculated as follows:

$$ \mathcal{L} \{ f(t) \} = \int_{0}^{\infty} e^{-st} e^{t^{2}} dt = \int_{0}^{\infty} e^{-(s-2t^{2}/s)} dt = \frac{1}{2} \sqrt{\frac{\pi}{s}} e^{s^{2}/4} $$

b. Laplace transform of

f(t) = 3e4t – e-2t

can be calculated as follows:

$$ \mathcal{L} \{ f(t) \} = 3 \mathcal{L} \{ e^{4t} \} - \mathcal{L} \{ e^{-2t} \} = \frac{3}{s-4} - \frac{1}{s+2} $$c.

Laplace transform of

f(t) = sinh(kt)

can be calculated as follows:

$$ \mathcal{L} \{ f(t) \} = \int_{0}^{\infty} e^{-st} \sinh(kt) dt = \frac{k}{s^{2}-k^{2}} $$.

Therefore, the Laplace transform of d. f(t) = et² is $ \frac{1}{2} \sqrt{\frac{\pi}{s}} e^{s^{2}/4} $, the Laplace transform of e. f(t) = 3e4t – e-2t is $ \frac{3}{s-4} - \frac{1}{s+2} $ and the Laplace transform of f. f(t) = sinh(kt) is $ \frac{k}{s^{2}-k^{2}} $.

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Answer:

51.33 cm

Step-by-step explanation:

154cm / π = 51.33 cm

The matrix M is: M = [2/9 -8/27 , 4/9 -8/27 ]

Let's say that M is a 2 x 2 matrix that satisfies M × [3 -2 , 6 -8 ] = [-2 16]. This means that the product of matrix M and matrix [3 -2 , 6 -8 ] will give us the result matrix [-2 16].  We know that the product of two matrices is equal to the sum of the products of their corresponding elements.  We can use this knowledge to solve for the unknown elements in matrix M. Let us assume that M = [a b , c d] so that we can solve for its elements.

a(3) + b(6) = -2 ... (1) c(3) + d(6) = 16 ... (2) a(-2) + b(-8) = -2 ... (3) c(-2) + d(-8) = 16 ...

(4)Simplifying equations (1) to (4),  we get:

3a + 6b = -2 ... (5) 3c + 6d = 16 ... (6) -2a - 8b = -2 ... (7) -2c - 8d = 16 ... (8)

Solving for a, b, c, and d, we get:a = 2/9 b = -8/27 c = 4/9 d = -8/27.

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The required value of k will the system of linear equations has infinite number of solutions is 8.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given set of equations is

kx + 4y = k - 4 ...(i)

16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)

= k² - 64

= (k + 8) (k - 8)

D1 = k (k - 4) - 4k

= k² - 4k - 4k

= k² - 8k

= k (k - 8)

D2 = k² - 16 (k - 4)

= k² - 16k + 64

= (k - 8)²

= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,

since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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Answer:

Its a square....please dont' eat my cookie D:

Step-by-step explanation:

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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The given problem involves analyzing a cost function and finding the average cost and marginal cost functions. Specifically, we need to determine the values of average and marginal cost when x = a and interpret their meanings.

To find the average cost function, we divide the cost function, denoted as C(x), by the quantity x. This gives us the expression C(x)/x. The average cost represents the cost per unit of x.

To find the marginal cost function, we take the derivative of the cost function C(x) with respect to x. The marginal cost represents the rate of change of the cost function with respect to x, or in other words, the additional cost incurred when producing one more unit.

Once we have obtained the average cost function and the marginal cost function, we can substitute x = a to find their values at that specific point. This allows us to determine the average and marginal cost when x = a.

Interpreting the values obtained in part (b) involves understanding their significance. The average cost at x = a represents the cost per unit of production when units are being produced. The marginal cost at x = a represents the additional cost incurred when producing one more unit, specifically at the point when a unit have already been produced.

These values are crucial in making decisions regarding production and pricing strategies. For instance, if the marginal cost exceeds the average cost, it suggests that the cost of producing additional units is higher than the average cost, which may impact profitability. Additionally, knowing the average cost can help determine the optimal pricing strategy to ensure competitiveness in the market while covering production costs.

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Answer:

yes

Step-by-step explanation:

5 is more than or equal to 3

3 makes the inequality true

plz mark me brainliest

Answer:

No the answer would be x  ≥ 5

Answer:

Step-by-step explanation:

Let n represent the unknown number.

1) The sum of a number and 5 is less than 7 becomes n + 5 < 7

2) The product of a number and 8 is at least 25 becomes 8n ≥ 25

3) Six less than a number is greater than 54 becomes n - 6 > 54

4) the quotient of a number and 12 is no more than 6 becomes n/12 ≤ 6

A scalar potential function f(x,y), the vector field f(x,y) = x^2 i + y j is conservative.

To show that the vector field f(x,y) = x^2 i + y j is conservative, we need to find a scalar potential function f(x,y) such that grad f(x,y) = f(x,y).

So, let's first calculate the gradient of a potential function f(x,y):

grad f(x,y) = (∂f/∂x) i + (∂f/∂y) j

Assuming that f(x,y) exists, then f(x,y) = ∫∫ f(x,y) dA, where dA = dx dy, the double integral is taken over some region in the xy-plane, and the order of integration does not matter.

Now, we need to find f(x,y) such that the partial derivatives of f(x,y) with respect to x and y match the components of the vector field:

∂f/∂x = x^2

∂f/∂y = y

Integrating the first equation with respect to x gives:

f(x,y) = (1/3)x^3 + g(y)

where g(y) is a constant of integration that depends only on y.

Taking the partial derivative of f(x,y) with respect to y and comparing it to the y-component of the vector field, we get:

∂f/∂y = g'(y) = y

Integrating this equation with respect to y gives:

g(y) = (1/2)y^2 + C

where C is a constant of integration.

Therefore, the scalar potential function is:

f(x,y) = (1/3)x^3 + (1/2)y^2 + C

where C is an arbitrary constant.

Since we have found a scalar potential function f(x,y), the vector field

f(x,y) = x^2 i + y j is conservative.

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Answer:

See attachment

Step-by-step explanation:

Answer:

(7 a - 8y^2) x (3-y)

Step-by-step explanation:

21a+8xy^3 −24y^2−7axy

factor out 3 from the expression

3( 7 a - 8 y^2) + 8y^3 - 7 a y

3(7 a - 8 y^2) - y x (-8y^2 + 7 a)

Factor out 7 a - 8y^2 from the expression

(7 a - 8y^2) x (3-y)

= (7 a - 8y^2) x (3-y)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

0 (none).  Just bc their is no exact value therefore when u compare them all they equal 0 equivalents

Answer: The probability of getting two red marbles is P = 0.141

Step-by-step explanation:

We know that in the bag there are 3 blue marbles and 5 red marbles, then there is a total of 8 marbles in the bag.

The probability of taking at random a red marble is equal to the quotient between the number of red marbles and the total number of marbles, this is:

p = 3/8

Suppose we got a red marble:

Now we replace the red marble we took, so in the bag there are again 3 red marbles and 8 total marbles, then the probability of getting another red marble is again:

q = 3/8

The joint probability (this is, the probability of both events happening) is equal to the product of the individual probabilities, with gives us:

P = p*q = (3/8)*(3/8) = 9/64 = 0.141

Answer:

93%

Step-by-step explanation:

divide 1395 by 1500

0.93

0.93=93%

Answer:

93%

Step-by-step explanation:

This problem can be best solved with a proportion! First, we can set up one side of the proportion with the two values that are given to us. It will look something like this:

\(\frac{1395}{1500}\)

Next, we need to set up the other side. Since we are solving for a percent, we know that our x will be out of 100. This side will look something like this:

\(\frac{x}{100}\)

Next, we need to set them equal to each other and solve for x.

\(\frac{1395}{1500} = \frac{x}{100}\)

To solve, just cross multiply and divide. Multiply 1395 by 100 to get 139,500. Next, divide 139,500 by 1500 to get a final answer of 93%! Hope this helps!

For part A. One way to know if there is a correlation between the data is to graph the data set, like this

Then, as can you see the data presents a positive linear correlation.

For part B. You can take the coordinates of two points and find the slope of the line using the formula

If you take

Now, using the slope formula, you can find the equation of the line in its slope-intercept form

Therefore, the function that best fits the data is

For part C. The slope of the plot is 10 and indicates that for every hour students spend time studying, they get 10 more points on the science test.

The y-intercept of the plot is 57 and indicates that if students study 0 hours for the science test, they will obtain 57 points as a grade.

The inequality which represents the given situation will be 2.25x + 2y ≤ 25.

A mathematical phrase in which the sides are not equal is referred to as being unequal. In essence, a comparison of any two values reveals whether one is less than, larger than, or equal to the value on the opposite side of the equation.

Suppose the cost of an apple is x and the cost of one mango is y.

2.25x + 2y = total cost

2.25x + 2y ≤ 25

Hence "The inequality which represents the given situation will be 2.25x + 2y ≤ 25".

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Answer:

5.(x+7)(4x2+7)

6.(b−3x)(3x2−1)

Answer:

1.99

Step-by-step explanation:

Swiss chard: $0.49 per kg

Chinese lettuce: $0.52 per kg =

= 3 kg Swiss chard + 1 kg Chinese lettuce

= 3 kg * $0.49/kg + 1 kg * $0.52/kg

= $1.47 + $0.52

= $1.99

Answer: 1.99

Answer:

125º

Step-by-step explanation:

An exterior angle of a triangle is equal to the sum of its opposite interior angles.

In this case, 146º is the exterior angle and 21º and xº are the interior angles.

We can set up an equations 146=21+x

By subracting 21, we find that x=125

Answer:

\(\boxed{\boxed{\tt x=125^{\circ}}}\)

Step-by-step explanation:

To solve this problem we need to apply the triangle exterior angle property.

*Exterior angle of a triangle is equal to the sum of its two opposite interior angles.*

146 °  here, is an exterior angle of the triangle, and 21 °/x are opposite interior angles.

\(\tt 146^{\circ}=21^{\circ}+x\)

Switch sides:

\(\longmapsto\tt 21^{\circ}+x=146^{\circ}\)

Subtract 21 from both sides:

\(\longmapsto\tt 21^{\circ}+x-21^{\circ}=146^{\circ}-21^{\circ}\)

\(\longmapsto\tt x=125^{\circ}\)

Answer:

f=-\(\frac{x}{5}\)+\(\frac{3}{5}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

f(10) = -2(10) + 6 = -20 + 6 = -14

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. the expression.343 ^ { 4 / 3 } is 7,625

In order to evaluate the expression, we must first understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 = 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.The expression 343^ {4/3} can be broken down into 343 to the power of 4 divided by 3. Before we evaluate the expression, we must understand the order of operations. The ^ symbol indicates an exponential, which takes precedence over division. Therefore, we will first calculate 343^4 and then divide the result by 3. 343^4 can be calculated using the formula 343 x 343 x 343 x 343. This results in 7,741,675. 7,741,675 divided by 3 is equal to 2,580,558.33. When rounded to the nearest whole number, the answer is 7,625.

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Answer:

2.537 x 10¹⁵ miles

Step-by-step explanation:

We are given the following:

1 light year = 5.9 x 10¹² miles

Distance of the star = 4.3 x 10² light years

To get this we just convert the distance of the star in light years into miles.

We cancel out the light years and then we are left with:

In dealing with scientific notation, when we multiply them we can treat the coefficients and exponents of 10 separately.

Coefficients:

4.3 x 5.9 = 25.37

Exponents of 10:

10² x 10¹² = 10⁽²⁺¹²⁾=10¹⁴

Then we combine them again to form a scientific notation:

25.37 x 10¹⁴

But since the standard in writing a scientific notation, the coefficient needs to be a number from 1-9, we need to move the decimal. When we move the decimal to the right or left, we change the exponent of the power of 10. Since we will move it once to the left, we add 1.

The answer will then be:

2.537 x 10¹⁵ miles

Hope I helped! If you really thought I did a great job answering this question please rate, thanks, and award brainliest.

Yours,

Fellow Brainiac

Answer:    318,600

Step-by-step explanation:

This is what I got hope it helped:)

The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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The change in Ms Smith's saving account balance each month due to her car payments is of:

-$267.75.

A proportion is a fraction of a total amount, and this fraction is used along with the basic arithmetic operations, especially multiplication and division, to find the desired measures in the context of a problem.

In this problem, the monthly balance change is obtained as follows:

Monthly balance change = Yearly balance change / 12.

(as an year is composed by 12 months).

As stated in the text, the yearly balance change of Ms. Smith's account is given as follows:

-$3,213.

The payments are equal each month, hence the monthly change is of:

Monthly balance change = -3213/12 = -$267.75.

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