Find the value of this expression and show ur work

The expressions for the lengths of the segments obtained using vectors notation are;

a. i. \(\overrightarrow{LA}\) = q - (1/2)·p  ii. \(\overrightarrow{AN}\) = (2/7)·(p - q)

b. The expressions for \(\overrightarrow{MN}\), \(\overrightarrow{LA}\), and \(\overrightarrow{AN}\) indicates;

\(\overrightarrow{MN}\) = (1/84)·(46·q - 11·p)

A vector is a quantity that has magnitude and direction and are expressed using a letter aving an arrow in the form, \(\vec{v}\)

a. i. \(\overrightarrow{LA}\) = \(\overrightarrow{BA}\) - \(\overrightarrow{LB}\) =  \(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\)

\(\overrightarrow{BA}\) - (1/2) × \(\overrightarrow{CB}\) = q - (1/2)·p

\(\overrightarrow{LA}\) = q - (1/2)·p

ii. \(\overrightarrow{AC}\) = \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{AC}\)

\(\overrightarrow{AN}\) = (2/7) × \(\overrightarrow{BC}\) - \(\overrightarrow{BA}\)

\(\overrightarrow{AN}\) = (2/7) × (p - q)

b. \(\overrightarrow{MN}\) = \(\overrightarrow{MA}\) + \(\overrightarrow{AN}\)

\(\overrightarrow{MA}\) = (5/6) × \(\overrightarrow{LA}\)

\(\overrightarrow{LA}\) = q - (1/2)·p

\(\overrightarrow{AN}\) = (2/7) × (p - q)

Therefore;

\(\overrightarrow{MN}\) = (5/6) × ( q - (1/2)·p) + (2/7) × (p - q)

\(\overrightarrow{MN}\) = (1/84) × ( 70·q - 35·p + 24·p - 24·q) = (1/84)(46·q - 11·p)

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Answer:

y = 2/3 x + 6

Step-by-step explanation:

I do not see a point C, so I guess you get to make your own point C.  I will make it at (06,)

The equation of the line seen is

y = 4/6x + 5  If you start at A and count up, you will get 4 unit and then count right you will be 6 units.  This is the slope 4/6.  the 5 is where the line crosses the x axis (0,5)

We can simplify  4/6 to 2/3

y = 2/3 x + 5

When lines are parallel, they have the same slope, but different y intercept.  

Since I made C (0,6)  The equation of this parallel line would be

y = 2/3 x + 6

Draw a line parallel to AB but make sure that it goes through the point (0,6)

The maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

The revenue function R(x) represents the amount of money the company earns from selling x units of lab equipment. It is given by the equation:

R(x) = -0.32x^2 + 270x

The costs function C(x) represents the expenses incurred by the company for producing and selling x units of lab equipment. It is given by the equation:

C(x) = 70x + 52

To determine the company's profit, we subtract the costs from the revenue:

Profit = Revenue - Costs

P(x) = R(x) - C(x)

Substituting the given revenue and costs functions:

P(x) = (\(-0.32x^2 + 270x)\) - (70x + 52)

Simplifying the equation:

P(x) = -0.32x^2 + 270x - 70x - 52

P(x) = -\(0.32x^2\)+ 200x - 52

The profit function P(x) represents the amount of money the company makes from selling x units of lab equipment after deducting the costs. It is a quadratic function with a negative coefficient for the x^2 term, indicating a downward-opening parabola. The vertex of the parabola represents the maximum profit the company can achieve.

To find the maximum profit and the corresponding number of units sold, we can use the vertex formula:

x = -b / (2a)

For the profit function P(x) = -\(0.32x^2 + 200x\)- 52, a = -0.32 and b = 200.

x = -200 / (2 * -0.32)

x = 312.5

Therefore, the maximum profit is achieved when approximately 312.5 units of lab equipment are sold.

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Answer:

Step-by-step explanation:

B

The y-intercept of the function f(x) = 2(0.5)^x is 2. This means that the graph of the function intersects the y-axis at the point (0, 2).

To find the y-intercept of the function f(x) = 2(0.5)^x, we need to determine the value of f(x) when x is equal to 0.

Let's substitute x = 0 into the equation:

f(0) = 2(0.5)^0

Since any number raised to the power of 0 is equal to 1, we have:

f(0) = 2(1)

Simplifying further, we get:

f(0) = 2

Therefore, the y-intercept of the function f(x) = 2(0.5)^x is 2. This means that the graph of the function intersects the y-axis at the point (0, 2).

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Answer:

(x - 2) / 2

Step-by-step explanation:

x = 2y + 2

2y = x - 2

y = (x - 2) / 2

Answer: (x-2)/2

Step-by-step explanation:

edg

Answer:

$8190

Step-by-step explanation:

So we know that were putting away $2 each month from  our allowance.

Jan-$2

Feb-$4

March-$8

April-$16

Ok so we already put away 4 months of our allowance from 12. So we need 8 more months to count how much.

So lets add: 2 + 4 + 8 + 16=30

Now we need to figure out how much in May and so on.

May- 16x2=32

June-32x2=64

July-64x2=128

August-128 x 2=256

September-256 x 2=512

October-512 x 2=1024

November-1024 x 2=2048

December-2048 x 2=4096

In total to add:

2 + 4 + 8 + 16 + 32 +64 + 128 + 256 + 512 + 1024 + 2048 + 4096 = 8190

Hope this helps :)

The dimensions of the outdoor enclosure with the most area is 250 feet and 125 feet.

One side of the store is 270 feet long

There are 500 feet of fencing available for the other three sides of the enclosure.

The Perimeter of rectangular outdoor storage = 2x + y

2x + y = 500

To maximize the area

y = 500 - 2x...............(1)

Area of rectangle;

A = xy

Now putting the value of y

A = x(500 - 2x)

Solve

A = 500x - 2x^2...................(2)

To finding the value of x differentiating on both side with respect to x.

dA/dx = 500 - 4x...................(3)

Equating dA/dx = 0

500 - 4x = 0

Subtract 4x on both side, we get

4x = 500

Divide by 4 on both side, we get

x = 125

Now putting the value of x in equation 1

y = 500 - 2(125)

y = 500 - 250

y = 250

Differentiating equation 3 again with respect to x

d^2A/dx^2 = -4 < 0 (Maximum)

Hence, for the maximum storage area

Length parallel to the store wall = 250 feet

Length perpendicular to the store wall = 125 feet

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yes, for your x to be positive and to make it remain on the left hand side you actually have to add 4x to both side to eliminate x from the right hand side.

a. Null hypothesis: H₀: µ ≤ 74

b. A t-test is appropriate here because the population standard deviation is not known, and the sample size is less than 30.

c. The value of Test statistic is -6.325

d. At a 0.05 significance level, the critical value for a right-tailed test is  -1.664.

e. The test statistic (-4.38) is less than the critical value (1.645). Hence we can reject the null hypothesis.

a. Null hypothesis, H0: µ = 74, alternative hypothesis, H1: µ > 74  (there is no significant difference in the mean job satisfaction scores of employees after the telecommuting policy is adopted).

b. A t-test is appropriate here because the population standard deviation is not known, and the sample size is less than 30. This is a one-tailed test because the alternative hypothesis is directional (i.e., it states that the mean level of satisfaction will increase with telecommuting).

c. The test statistic is calculated using the formula: t = (X - µ) / (s / √n), where X is the sample mean, µ is the population mean, s is the sample standard deviation, and n is the sample size.  Substituting the values given in the question: t = (56 - 74) / (8 / √80) = -6.325

d. The critical value for a one-tailed t-test with 79 degrees of freedom at the 0.05 level of significance is -1.664. Since the calculated t-value of -6.325 is less than the critical value of -1.664, we reject the null hypothesis.

e. Based on the calculated t-value and critical value, we reject the null hypothesis that the mean level of satisfaction is the same before and after telecommuting and accept the alternative hypothesis that telecommuting increases the mean level of satisfaction among employees.

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Answer:

Step-by-step explanation:

       56

Answer: \(\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6}\) if you want 3/6 in simplifed form it will be 1/2

Step-by-step explanation: Find the Least common denominator ( LCD). Then add the numerators.

Answer:

8

Step-by-step explanation:

Step-by-step explanation:

i think its A

Answer:

735mm³

Step-by-step explanation:

V=A of base×h

=49×15

=735mm³

The probability that the coin is fair given that it lands heads is 0.3571.

Given that a coin is picked from the box and flipped, the probability of the coin being fair is 1/3.

The probability of the coin being biased towards heads and the coin being biased towards tails is 1/3.

Therefore, the probability that the coin is fair and lands heads is (1/3) x 0.5

= 0.1667.

The probability that the coin is biased towards heads and lands heads is (1/3) x 0.8

= 0.2667.

The probability that the coin is biased towards tails and lands heads is (1/3) x 0.1

= 0.0333.

Therefore, the total probability that the coin lands heads is 0.1667 + 0.2667 + 0.0333

= 0.4667.

Using Bayes' Theorem, the probability of the coin being fair given that it lands heads is:

P(fair|heads)

= P(heads|fair) * P(fair) / P(heads)

= 0.5 * 1/3 / 0.4667

= 0.3571.

Thus, the probability that the coin is fair given that it lands heads is 0.3571.

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It will take approximately 15.61 years for $1,886 to grow to $8,156 with a 7.02 percent annual interest rate, compounded annually.

To determine the number of years it will take for $1,886 to grow to $8,156 with a 7.02 percent annual interest rate, we can use the compound interest formula:

A = P * (1 + r)^n,

where A is the future value, P is the principal amount, r is the interest rate per period, and n is the number of periods.

In this case, the principal amount is $1,886, the future value is $8,156, and the interest rate is 7.02 percent. We need to solve for n.

Dividing both sides of the equation by P:

(1 + r)^n = A / P,

Substituting the given values:

(1 + 0.0702)^n = 8,156 / 1,886.

Using logarithms to solve for n:

n = log(8,156 / 1,886) / log(1 + 0.0702).

Using a calculator, the approximate value of n is:

n ≈ 15.61.

Therefore, it will take approximately 15.61 years for $1,886 to grow to $8,156 with a 7.02 percent annual interest rate, compounded annually.

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The solution to the initial value problem is y = 9/2 * e^(2x) + 7x + 49 - 9/2 * e^(-14).

To solve the initial value problem, we need to find the function y(x) that satisfies the given differential equation and initial condition.

The given differential equation is dy/dx = 9e^(2x) + 7.

To solve this, we can integrate both sides of the equation with respect to x:

∫ dy = ∫ (9e^(2x) + 7) dx

Integrating, we get:

y = 9/2 * e^(2x) + 7x + C

where C is the constant of integration.

To find the specific value of C, we use the initial condition y(-7) = 0. Substituting x = -7 and y = 0 into the equation, we can solve for C:

0 = 9/2 * e^(2*(-7)) + 7*(-7) + C

0 = 9/2 * e^(-14) - 49 + C

C = 49 - 9/2 * e^(-14)

Now we have the complete solution:

y = 9/2 * e^(2x) + 7x + 49 - 9/2 * e^(-14)

Therefore, the solution to the initial value problem is y = 9/2 * e^(2x) + 7x + 49 - 9/2 * e^(-14).

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In the collection, there are 11 nickels and 23 dimes. If each nickel is replaced with a quarter, the value of the collection becomes $5.05. So, C is correct. By writing them in the system of equations, we get the required value.

The given units are nickels, dimes, and quarters. Their conversion into dollars is as follows:

1 nickel = $0.05

1 dime = $0.10

1 quarter = $0.25

Given a collection of nickels and dimes is worth $2.85.

And there are 34 coins in the collection.

So, consider the number of nickel coins = n and the number of dime coins = d.

Then, the equation for the given collection is

n + d = 34...(1)

0.05n + 0.10d = 2.85...(2)

On simplifying (2), we get

5n + 10d = 2.85 × 100

⇒ 5n + 10d = 285

From (1), n = 34 - d, we get

5(34 - d) + 10d = 285

⇒ 170 - 5d + 10d = 285

⇒ 5d = 285 - 170 = 115

∴ d = 115/5 = 23

Thus, the number of dime coins is 23.

So, from (1), we get n + 23 = 34 ⇒ n = 34 - 23 = 11

∴ n = 11

Thus, the number of nickel coins is 11.

If each nickel coin in the collection is replaced with a quarter, then the value of the collection is

q + d = 34 and 0.25q + 0.10d = Y

Here q = 11; d = 23

So, we get

0.25(11) + 0.10(23) = Y

⇒ 2.75 + 2.3 = Y

⇒ 5.05 = Y

∴ Y = $5.05

The value of the new collection becomes $5.05.

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Answer:

B. y = 30x

Step-by-step explanation:

Answer:

The answer to this problem is B)y = 30x

Step-by-step explanation:

Answer:

4 1/4

Step-by-step explanation:

Turn the mixed numbers in to improper fractions.

find least common denominator.

Subtract them.

Then turn your answer back into a mixed number and you have how much the plant is above the ground which is 4 1/4

Answer:

5.25 minutes

Step-by-step explanation:

7 * 0.75 = 5.25

Answer:

325

Step-by-step explanation:

Each of the darker dashes is 100 grams so each of the lighter dashes is representing a fourth of 100 or 25 grams so the weight shown on the scale is 325

Answer:

Im assuming you wrote a hypothesis or experimented or something, the "..." is where you write whatever your talking about I hope this helps :)

Step-by-step explanation:

My estimates would have changed to get a more accurate answer if I had previously known that.... would affect.... My estimate would have been...... because.....

A polynomial f(x) of degree 4 with real coefficients is P(x) = x³- 10x² + 36x - 40

A polynomial function is a mathematical expression that involves only non-negative integer powers or positive integer exponents of a variable in an equation.

Since 4 - 2i is a zero, 4 + 2i is also a zero.

Then by substitution, we have the following

x = 2, x = 4 - 2i, x = 4 + 2i

x - 2 = 0, x - 4 + 2i = 0, x - 4 - 2i = 0

P(x) = (x - 2)(x - 4 + 2i)(x - 4 - 2i)

P(x) = (x - 2)(x2 - 8x + 20)  

P(x) = x³- 10x² + 36x - 40

Therefore the polynomial function is P(x) = x³- 10x² + 36x - 40

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Answer:

16 yards of barbed wire

Step-by-step explanation:

Length=5 yards

Width=3 yards

Perimeter of the pasture=2(length + width)

=2(5 yards +3 yards)

=2(8 yards)

=16 yards

You should order 16 yards of barbed wire for fencing the pasture

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

The answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

Step-by-step explanation:

Numbers in order:

4,5,6,6,7,8,9,9,10,10,12,12,14,15

List into two equal parts:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Find middle numbers:

4,5,6,6,7,8,9 and 9,10,10,12,12,14,15

Lower quartile: 6

Upper quartile: 12

Thus the answer to your problem is, The difference of the values of the first and third quartiles of the data set is 12 - 6 = 6

y=-5x+5...(1)

2x+y=3...(2)

subt (1)into (2)

2x+(-5x+5)=3

2x-5x-5=3

2x-5x=3+5

-3x=8

divide by -3

x=-8/3

subt 2 into 1

y=-5(-8/3)+5

y=55/3

(a) To find all the least squares solutions of the linear system Ax = b, we need to solve the normal equation (A^T A)x = A^T b. Let's compute the necessary matrices:

A^T = [2 1; 1 2; A]  and A^T A = [6 4; 4 6; 4 4 + A²]

A^T b = [2 + A; 4 + 3A; 2 + 2A]

Substituting these values into the normal equation, we have:

[6 4; 4 6; 4 4 + A²]x = [2 + A; 4 + 3A; 2 + 2A]

Solving this system of equations will give us the values of x that satisfy the least squares criterion.

(b) To find the orthogonal projection projcol(A) b of b onto col(A), we can use the formula projcol(A) b = A(A^T A)^(-1) A^T b. We already have the matrices A^T A and A^T b from the previous step. Calculating (A^T A)^(-1) and substituting the values, we can compute projcol(A) b.

(c) The least squares error ||b - projcol(A) b|| can be found by subtracting the projection of b onto col(A) from b, and then calculating the norm of the resulting vector.

||b - projcol(A) b|| = ||b - A(A^T A)^(-1) A^T b||

Simplifying the expression using the matrices we computed in the previous steps, we can find the least squares error.

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