Which linear system has this matrix of constants? `[[12],[11],[4]]` a, b, c or d
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Divide the interval [3, 5] into [tex]n[/tex] subintervals of equal length [tex]\Delta x=\frac{5-3}n = \frac2n[/tex].

[tex][3,5] = \left[3+\dfrac0n,3+\dfrac2n\right] \cup \left[3+\dfrac2n,3+\dfrac4n\right]\cup\left[3+\dfrac4n,3+\dfrac6n\right]\cup\cdots\cup\left[3+\dfrac{2(n-1)}n, 3+\dfrac{2n}n\right][/tex]

The right endpoint of the [tex]i[/tex]-th subinterval is

[tex]r_i = 3 + \dfrac{2i}n[/tex]

where [tex]1\le i\le n[/tex].

Then the definite integral is given by the Riemann sum

[tex]\displaystyle \int_3^5 \sqrt{8+x^2} \, dx = \lim_{n\to\infty} \sum_{i=1}^n \sqrt{8+{r_i}^2} \Delta x = \boxed{\lim_{n\to\infty} \frac2n \sum_{i=1}^n \sqrt{17 + \frac{12i}n + \frac{4i^2}{n^2}}}[/tex]

Answer:

36

Step-by-step explanation:

[tex]\sqrt{24a}=12\sqrt{6} \\ \\ 24a=864 \\ \\ a=36[/tex]

Answer:

x=3/2 y=1/2

Step-by-step explanation:

Answer:

  |-3| = 3 and -|-4| = -4

Step-by-step explanation:

The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.

|-3| = 3 (true) and -|-4| = -4 (true)   ⇒ this statement is true

|-3| = 3 (true) and |-4| = -4 (false)   ⇒ this statement is false

-|3| = 3 (false) and |4| = 4 (true)   ⇒ this statement is false

|-3| = 3 (true) and -|4| = 4 (false)   ⇒ this statement is false

__

Additional comment

A compound "and" statement is only true if all of the parts of it are true.

Answer:

Step-by-step explanation:

I am going to be honest here. I know the answer is 22 but I cant really explain it you kinda just have to trust I'm right.

The length of the trip at a distance of 300 miles and the given times are

The distance is given as:

d = 300

The formula is represented as:

d = r * t

Make t the subject

t = d/r

Substitute 300 for d

t = 300/r

When r = 50 mph,

t = 300/50

Evaluate

t = 60

When r= 70 mph, we have

t = 300/70

Evaluate

t = 30/7

When r = x, we have

t = 300/x

When r = x + 10, we have

t = 300/x + 10

When r = x - 5, we have

t = 300/x - 5

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Complete question

A train traveled 300 miles. How long did the trip take if the train was traveling at a rate of:

Note * Use the d=rt formula (distance = rate * time). NOTE: You may not be able to solve for the variable. If you do not have enough information to solve for the variable then write the equation.

The cost of goods sold using LIFO is $99.

Using this formula

Cost of goods sold=(March 3 Purchased units × March 3 Purchase price)+ [(March 3 Purchased units -March 9 sold units)×March 1 Beginning inventory cost]

Let plug in the formula

Cost of goods sold=(15 units×$3.90)+[(22 units-15 units)×$5.80]

Cost of goods sold=$58.5+(7 units×$5.80)

Cost of goods sold=$58.5+$40.6

Cost of goods sold=$99.1

Cost of goods sold=$99 (Approximately)

Therefore the cost of goods sold using LIFO is $99.

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Answer:

  x = 3

Step-by-step explanation:

Maybe you want the value of x such that ...

  4(6^x) = 864

Dividing by 4 gives ...

  6^x = 216

You may know that 216 = 6^3. Using that, we can equate exponents:

  6^x = 6^3

  x = 3

Alternatively, we can use logarithms to find x. Taking logs gives ...

  x·log(6) = log(216)

  x = log(216)/log(6) = 3

If (-1, -1) is an extremum of [tex]f[/tex], then both partial derivatives vanish at this point.

Compute the gradients and evaluate them at the given point.

[tex]\nabla f = \left\langle y - \dfrac1{x^2}, x - \dfrac1{y^2}\right\rangle \implies \nabla f (-1,-1) = \langle-2,-2\rangle \neq \langle0,0,\rangle[/tex]

[tex]\nabla f = \langle 2x+2,0\rangle \implies \nabla f(-1,-1) = \langle0,0\rangle[/tex]

[tex]\nabla f = \langle y, x-2y\rangle \implies \nabla f(-1,1) = \langle-1,1\rangle \neq\langle0,0\rangle[/tex]

[tex]\nabla f = \left\langle y + \frac1{x^2}, x + \frac1{y^2}\right\rangle \implies \nabla f(-1,1) = \langle0,0\rangle[/tex]

The first and third functions drop out.

The second function depends only on [tex]x[/tex]. Compute the second derivative and evaluate it at the critical point [tex]x=-1[/tex].

[tex]f(x,y) = x^2+2x \implies f'(x) = 2x + 2 \implies f''(x) = 2 > 0[/tex]

This indicates a minimum when [tex]x=-1[/tex]. In fact, since this function is independent of [tex]y[/tex], every point with this [tex]x[/tex] coordinate is a minimum. However,

[tex]x^2 + 2x = (x + 1)^2 - 1 \ge -1[/tex]

for all [tex]x[/tex], so (-1, 1) and all the other points [tex](-1,y)[/tex] are actually global minima.

For the fourth function, check the sign of the Hessian determinant at (-1, 1).

[tex]H(x,y) = \begin{bmatrix} f_{xx} & f_{xy} \\ f_{yx} & f_{yy} \end{bmatrix} = \begin{bmatrix} -2/x^3 & 1 \\ 1 & -2/y^3 \end{bmatrix} \implies \det H(-1,-1) = 3 > 0[/tex]

The second derivative with respect to [tex]x[/tex] is -2/(-1) = 2 > 0, so (-1, -1) is indeed a local minimum.

The correct choice is the fourth function.

Answer:

38°

Step-by-step explanation:

EFGH is an isosceles trapezoid (a trapezoid with two congruent legs is isosceles)

∠HGF=70° (base angles of an isosceles trapezoid are congruent)

∠EGH=32° (angles in a triangle add to 180°)

∠FGE=38° (angle subtraction postulate)

The constant of proportionality between the cost and the number of pounds is: A. 0.59.

The constant of proportionality of a relationship between two variables X and Y can be defined as the ratio between of X and Y at a constant value. This means that the ratio or product of X and Y will give us a constant if both are in a proportional relationship.

Thus, the constant of proportionality for the  relationship between two variables X and Y would be calculated as:

Constant of proportionality (k) = Y/X. [this is the proportional between the two quantities, X and Y].

Given the table of values, using a pair of points on the table, say, (5, 2.95), we can calculate the constant of proportionality as:

X = 5

Y = 2.95

Constant of proportionality (k) = Y/X = 2.95/5

Constant of proportionality (k) = 0.59 pounds per dollar.

Therefore, the constant of proportionality between the cost and the number of pounds is: A. 0.59.

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Answer: [tex]4x^3 -29x^2 +10x-21[/tex]

Step-by-step explanation:

[tex](4x^2 -x+3)(x-7)\\\\=4x^3 -28x^2 -x^2 +7x+3x-21\\\\=4x^3 -29x^2 +10x-21[/tex]

The angles in degrees to radian is as follows:

-54 degrees = -3π / 10 radian

The measurement is in degrees. Let's convert it to radian with respect to π.

Therefore,

180 degrees = π radian

-54 degrees = ?

cross multiply

Hence,

angle in radian = -54 × π / 180

angle in radian = - 54π / 180

angle in radian = - 6π / 20

angle in radian = -3π / 10 radian

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The probability of obtaining a success is 0.010935.

Given that the probability of obtaining success is P(X>=5),n=6,p=0.3.

We are required to find the probability of obtaining a success if the probability is P(X>=5).

Probability is basically likeliness of happening an event among all the events possible.

Binomial distribution is basically the discrete probability distribution of the number of successes in a sequence of n independent experiments.

[tex](a+b)^{n} =nC_{0}p^{0} (1-p)^{n-0}+-----------nC_{n} p^{n} (1-p)^{0}[/tex]

We have to just put n=6 anr r=6 and 5 one by one to get the probability.

P(X>=5)=[tex]6C_{5}(0.3)^{5} (0.7)^{1} +6C_{6}(0.3)^{6} (0.7)^{0}[/tex]

=6!/5!1!8*0.00243*0.7+0.000729

=6*0.00243*0.7+0.000729

=0.010206+0.000729

=0.010935

Hence the probability of obtaining a success if the probability is P(X>=5) is 0.010935.

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Answer:

Răspuns: 88=>rezultatul

Explicație pas cu pas:

a+2b =18/×3

b+3c=17/×2

3a+6b =54 ^

2b+6c=34 | +

3a+(6b+2b)+6c=54+34

3a+8b+6c=88

Step-by-step explanation:

there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

Remember that for a rectangle of length L and width W, the area is given by:

A = L*W

In this case, we know that the area is:

[tex]A = 4x^2 + 12x[/tex]

We can factorize that expression into:

[tex]A = x*(4x + 12)[/tex]

So there are two expressions that can represent the length of the rectangle, these two expressions are:

L = x

or

L = (4x + 12)

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Hello and Good morning/afternoon:

Let's take this problem step-by-step:

What does the problem want:

 ⇒ unit rate ⇒ price per gallon

What does the problem give us:

  ⇒ price of all three milk

  ⇒ number of gallons of milk bought

Therefore

   [tex]\hookrightarrow \text {unit rate} = \text{total amount of money spent} / \text {total amount of milk bought}\\\\\hookrightarrow\text{unit rate} = 9.75 / 3 = 3.25 _. \text {dollar per gallon}[/tex]

Answer: 3.25 dollars per gallon

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Answer:

[tex]t = \cfrac{1}{2}[/tex]

Step-by-step explanation:

Given equation:

[tex]4(t+\cfrac{1}{4})=3[/tex]

Divide both sides by 4:

[tex]t+\cfrac{1}{4}=\cfrac{3}{4}[/tex]

Subtract 1/4 from both sides:

[tex]t = \cfrac{3}{4}- \cfrac{1}{4}[/tex]

[tex]t = \cfrac{2}{4}[/tex]

Simplify:

[tex]t = \cfrac{1}{2}[/tex]

Answer:

[tex]t = \frac{1}{2} [/tex]

Step-by-step explanation:

[tex]4(t + \frac{1}{4} ) = 3[/tex]

Divid the whole equation by 4.

[tex] \frac{4(t + \frac{1}{4} )}{4} = \frac{3}{4} [/tex]

[tex](t + \frac{1}{4} ) = \frac{3}{4} [/tex]

[tex]t + \frac{1}{4} = \frac{3}{4} [/tex]

Take 1/4 to right side.

[tex]t = \frac{ 3}{4} - \frac{1}{4} [/tex]

[tex]t= \frac{2}{4} [/tex]

To simplify the answer more divide the numerator and denominator by 2.

[tex]t = \frac{1}{2} [/tex]

The linear equations are y - 25 = 0.89(x - 20) and y  = 0.89x + 7.2

The complete question is added as an attachment

The two points from the graph are (20, 25) and (38, 41)

The slope of the line is calculated using

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (41 - 25)/(38 - 20)

Evaluate

m =0.89

This is calculated as:

y - y1 = m(x - x1)

Substitute the known values in the above equation

y - 25 = 0.89 * (x - 20)

Evaluate

y - 25 = 0.89(x - 20)

We have:

y - 25 = 0.89(x - 20)

Expand

y - 25 = 0.89x - 17.8

Add 25 to both sides

y  = 0.89x + 7.2

Hence, the linear equations are y - 25 = 0.89(x - 20) and y  = 0.89x + 7.2

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Answer:

49°

Step-by-step explanation:

The circumference of a circle measures 360 degrees, so arc XW is 98°.

So, angle XWY is 49°.

Using equivalent angles, the solutions are given as follows:

a) [tex]x = \frac{15\pi}{23}[/tex].

b) [tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex].

c) [tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

For item a, we have to find the equivalent angle on the 2nd quadrant, where the sine is also positive.

Hence:

[tex]\pi - \frac{8\pi}{23} = \frac{23\pi}{23} - \frac{8\pi}{23} = \frac{15\pi}{23}[/tex]

Hence [tex]x = \frac{15\pi}{23}[/tex].

For item b, if two angles are complementary, the sine of one is the cosine of the other.

Complementary angles add to 90º = 0.5pi, hence:

[tex]x + \frac{11\pi}{31} = \frac{\pi}{2}[/tex]

[tex]x = \frac{31\pi}{62} - \frac{22\pi}{62}[/tex]

[tex]x = \frac{9\pi}{62}[/tex]

The equivalent angle on the second quadrant is:

[tex]\pi - \frac{9\pi}{62} = \frac{62\pi}{62} - \frac{9\pi}{62} = \frac{53\pi}{62}[/tex]

Hence the solutions are:

[tex]x = \frac{9\pi}{62}, x = \frac{53\pi}{62}[/tex]

For item c, the angles are also complementary, hence:

[tex]x + \frac{\pi}{8} = \frac{\pi}{2}[/tex]

[tex]x = \frac{4\pi}{8} - \frac{\pi}{8}[/tex]

[tex]x = \frac{3\pi}{8}[/tex]

The tangent is also positive on the third quadrant, hence the equivalent angle is:

[tex]x = \pi + \frac{3\pi}{8} = \frac{8\pi}{8} + \frac{3\pi}{8} = \frac{11\pi}{8}[/tex]

Hence the solutions are:

[tex]x = \frac{3\pi}{8}, \frac{11\pi}{8}[/tex]

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Answer:

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

Step-by-step explanation:

You have to move the variables (r and t) with u to isolate s.

[tex]rs+t=u[/tex]

   [tex]-t[/tex]       [tex]-t[/tex]

------------------------

[tex]rs=u-t[/tex]

÷ [tex]r[/tex]       ÷ [tex]r[/tex]

------------------------

[tex]s=\frac{u}{r} -\frac{t}{r}[/tex]

The amount add to the borrower's monthly payment is $313.33.

Given that lender requires PMI that is 0.8% of the loan amount of $470,000.

A loan's PMI, or personal mortgage insurance, is a type of mortgage insurance used by lenders when making traditional loans such as home loans. A PMI helps cover the loss to the lender (bank) if the borrower stops making monthly mortgage payments on their home loan. Therefore, the PMI can be described as a kind of risk mitigation tool for the bank when the borrower defaults on their EMIs (monthly mortgage payments). So, PMI for a borrower is an additional cost or payment for the borrower on top of his monthly payments i.e. EMI.

Thus, the additional amount of dollars that the borrower has to pay for the PMI on his loan along with his monthly mortgage payments

= Principal Loan amount × (PMI/12)

= $470,000 × (0.8%/12)

= $470,000 × (0.008/12)

= $470,000 × 0.0006666667

=$313.333349

Hence, the additional monthly payment for PMI where lender requires PMI that is 0.8% of the loan amount of $470,000 is $313.33.

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Answer:

shift left 3

Step-by-step explanation:

(x+3)²

x = -3

therefore translation by (-3,0)

The negative number shows it move to the left

The number of solutions to the system is 1

A linear equation is a equation that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

y = 4x + 8

4y = 4x - 8

Substitute y = 4x + 8 in 4y = 4x - 8

4(4x + 8) = 4x - 8

Expand the equation

16x + 32 = 4x - 8

Evaluate the like terms

12x = - 40

Divide by 12

x = -10/3

The above means that the number of solutions to the system is 1

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The number of specimens should be tested is 1352.

According to the statement

we have to given that the in testing of wine specimens, lead levels ranging from 47 to 660 parts per billion were recorded. and we have to find the number specimen should be tested.

so,

Using the uniform and the z-distribution, it is found that 1353 specimens should be tested.

For an uniform distribution of bounds a and b, the standard deviation is given by:

σ = [tex]\sqrt{\frac{(b-a^{2})}{12} }[/tex]

and put the values a= 50 and b= 700 then the

standard deviation is 187.64

And here the critical value become 1.6 then

We want the sample for a margin of error of 10, thus, we have to solve for n with the help of value of m is 100.

Then n is 1352.

So,  The number of specimens should be tested is 1352.

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The value of the probability P(A and B) is 0.20

The given parameters about the probability are

P(A or B) = 0.9

P(A) = 0.5

P(B) = 0.6

To calculate the probability P(A and B), we use the following formula

P(A and B) = P(A) + P(B) - P(A or B)

Substitute the known values in the above equation

P(A and B) = 0.5 + 0.6 - 0.9

Evaluate the expression

P(A and B) = 0.2

Hence, the value of the probability P(A and B) is 0.20

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Step-by-step explanation:

First thing first, let find the x value of where P and Q both meet y=5, we know that y=5, and y=2x^2+7x-4, so using transitive law,

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]2 {x}^{2} + 7x - 9[/tex]

[tex]2 {x}^{2} - 2x + 9x - 9[/tex]

[tex]2x(x - 1) + 9(x - 1)[/tex]

[tex](2x + 9)(x - 1) = 0[/tex]

[tex]x = 1[/tex]

[tex]2x + 9 = 0[/tex]

[tex]x = - \frac{9}{2} [/tex]

Now, to find the gradient of the curve let take the derivative of both sides

[tex]5 = 2 {x}^{2} + 7x - 4[/tex]

[tex]0 = 4x + 7[/tex]

[tex]4x + 7[/tex]

Plug in -9/2, let call that point P

[tex]4( \frac{ - 9}{2} ) + 7 = - 11[/tex]

Plug in 1, let call that point Q

[tex]4(1) + 7 = 11[/tex]

So the gradient of the curve at point P (-9/2,5) is -11

The gradient of the curve at point Q (1,5) is 11.