(5-t-t^4)(9t+t^2)pls help

Paragraph 1: Spring is the most beautiful time of the year - the Authors opinion and not fact.

Paragraph 2: Birds love the spring - Nobody knows how a bird is feeling, this is just based off of the Author trying to make a scenery for you.

Hoped this helped :)

Answer:

N would equal anything lower than -4 for example, -5 or -6

Step-by-step explanation:

yw

The value of length ZY in nearest 10th place is 1,240.8 units.

The value of length ZY is calculated as follows;

Considering triangle XYZ;

tan 60 = ZY/XY

tan 60 = (ZY)/(240 + n)

ZY = 1.732(240 + n)   ------ (1)

Considering triangle WYZ;

tan 69 = ZY/WY

tan 69 = ZY/n

n = ZY/tan69

n = 0.384(ZY) ---------- (2)

The length ZY is calculated as;

Substitute the value of n into equation (1)

ZY = 1.732(240 + 0.384ZY)

ZY = 415.68 + 0.665ZY

0.335ZY = 415.68

ZY = 415.68 / 0.335

ZY = 1,240.8 units

From equation (2);

n = WY = 0.384 (1,240.8)

WY = 476.5 units

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The probability that a teenager has exactly 4 pairs of shoes in their closet is given as follows:

P(4) = 1/5 = 0.2 = 20%.

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

The total number of outcomes in this problem is given as follows:

18 + 30 + 57 + 30 + 15 = 150.

30 of the students have exactly 4 pairs, hence the probability is given as follows:

P(4) = 30/150

P(4) = 1/5 = 0.2 = 20%.

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∇f · dr = (3/2)(0) + (4)(0) + (3)(0) = 0

Therefore, C∇f · dr along the given curve C is 0.

Consider F and C below.

F(x, y, z) = yz i + xz j + (xy + 14z)   kC is the line segment from (3, 0, −1) to (6, 4, 2)

(a) Find a function f such that F = ∇f.f(x, y, z) = x y z + 7 z2

(b) Use part (a) to evaluate C∇f · dr along the given curve C.(a) Given F(x, y, z) = yz i + xz j + (xy + 14z) k, we need to find a function f such that F = ∇f.

Let F = ∇f

Then ∂f/∂x = yz, ∂f/∂y = xz and ∂f/∂z = xy + 14z

∴ Integrating ∂f/∂x = yz w.r.t x,

we get f = xyz + g(y, z).

Here, g(y, z) is an arbitrary function of y and z.

Differentiating f w.r.t y and equating it to xz, we get

∂f/∂y = xz + ∂g/∂y

∴ Integrating ∂g/∂y = 0 w.r.t y, we get g(y, z) = h(z).

Here, h(z) is an arbitrary function of z.

Thus, we get f(x, y, z) = xyz + h(z).

Differentiating f w.r.t z and equating it to xy + 14z, we get

∂f/∂z = xy + 14z

∴ f = x y z + 7 z2

Thus, f(x, y, z) = x y z + 7 z2

(b) Now, we need to evaluate C∇f · dr along the given curve C.Curve C is the line segment from (3, 0, −1) to (6, 4, 2).

Let C(t) be a parametrization of the curve C, where C(0) = (3, 0, −1) and C(1) = (6, 4, 2)

Given that f(x, y, z) = x y z + 7 z2

Thus, ∇f(x, y, z) = yz i + xz j + (2xy + 14z) k

At the point (3, 0, −1), we have ∇f(3, 0, −1) = 0 i + 0 j + 0 k = 0

Similarly, at the point (6, 4, 2), we have ∇f(6, 4, 2) = 32 i + 24 j + 64 k

Now, dr = C′(t) dt = (dx/dt) i + (dy/dt) j + (dz/dt) k dt

⇒ dr = 3/2 i + 4 j + 3 k dt along the given curve C.

Then, ∇f · dr = (3/2)(0) + (4)(0) + (3)(0) = 0

Therefore, C∇f · dr along the given curve C is 0.

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Answer:

(5):  Missing side:  x = 13.9

(6):  Missing side:  x = 8.5

(7):  Measure of indicated angle: ? = 46°

(8):  Measure of indicated angle:  ? = 35°  

Step-by-step explanation:

Because all four triangles are right triangles, we're able to find the side lengths and angles using trigonometry.

(5):  When the 44° is the reference angle:

Thus, we can find x using the cosine ratio, which is given by:

cos (θ) = adjacent / hypotenuse, where

Thus, we plug in 44 for θ, 10 for the adjacent side, and x for the hypotenuse and solve for x:

(cos (44) = 10 / x) * x

(x * cos (44) = 10) / cos (44)

x = 13.90163591

x = 13.9

Thus, x is about 13.9 units.

(6):  When the 23° angle is the reference angle:

Thus, we can find x using the tangent ratio, which is given by:

tan (θ) = opposite / adjacent, where

Thus, we plug in 23 for θ, x for the opposite side, and 20 for the adjacent side and solve for x:

(tan (23) = x / 20) * 20

8.489496324 = x

8.5 = x

Thus, x is about 8.5 units.

Since problems (7) and (8) require to find angles in a right triangle, we will need to use inverse trigonometry.

(7):  When the unknown (?) angle is the reference angle:

Thus, we can find the measure of the unknown (?) angle in ° using the inverse sine ratio which is given by:

sin^-1 (opposite / hypotenuse) = θ, where

Thus, we plug in 25 for the opposite side and 35 for the hypotenuse to solve for θ, the measure of the unknown angle:

sin^-1 (25 / 35) = θ

sin^-1 (5/7) = θ

45.5846914 = θ

46 = θ

Thus, the unknown angle is about 46°.

(8):  When the unknown (?) angle is the reference angle:

Thus, we can find the measure of the unknown (?) angle in ° using the inverse cosine ratio which is given by:

cos^-1 (adjacent / hypotenuse) = θ, where

Thus, we plug in 23 for the adjacent side and 28 for the hypotenuse to solve for θ, the measure of the unknown angle:

cos^-1 (23 / 28) = θ

34.77194403 = θ

35 = θ

Thus, the measure of the unknown angle is about 35°.

Answer:

Hello! answer: 250

Step-by-step explanation:

10 × 5 = 50

10 × 5 = 50

10 × 5 = 50

10 × 5 = 50

5 × 5 = 25

5 × 5 = 25

50 × 4 = 200

200 + 25 + 25 = 250 the total surface area is 250 hope that helps!

Answer:

I'm gonna go with b to be honest sorry if I'm wrong

Verifying that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c = 2  such that f'(c) = 0.

Given:

Consider the function f(x) = x2 - 4x + 8 on the interval 0, 4. Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval f(x) is f(x) is and f(0) on [0, 4] on (0, 4) f(4) Then by Rolle's theorem, there exists at least one value c such that f'(c) = 0.

f(x)=x^2−4x+8, [0,4]

when, x = 0

f(x) = x^2 -4x +8

f(0) = y = 0 - 0 + 8 = 8

when, x=4

f(5) = y = 16 - 16+8 =

thus, we have 2 points (0, 8) ; (4, 8)

slope,m = {8-(8)} / {4-0} = 0

hence, we have to calculate all the points,x where 0<x<8 and slope=0

f '(x) = 2x - 4 = 0

or, f '(c) = 2c - 4 = 0

c = 4/2 =2 ( 0<x<4)

hence, the there is only one solution c=2 which satisfies Rolle's theorem.

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By empirical rule, 99.7% of the students have a grade point average which is between 1.38 and 3.84.

Suppose that the grade point average of undergraduate students at one university has a bell-shaped distribution with a mean of 2.61 and a standard deviation of 0.41.

Here, μ = 2.61 , σ = 0.41

Using the empirical rule :

The first part of the empirical rule states that 68% of the data values will fall within 1 standard deviation of the mean. To calculate "within 1 standard deviation," you need to subtract 1 standard deviation from the mean, then add 1 standard deviation to the mean. That will give you the range for 68% of the data values.

2.61 − 0.41 = 2.2

2.61 + 0.41 = 3.02

The range of numbers is 2.2 to 3.02

The second part of the empirical rule states that 95% of the data values will fall within 2 standard deviations of the mean. To calculate "within 2 standard deviations," you need to subtract 2 standard deviations from the mean, then add 2 standard deviations to the mean. That will give you the range for 95% of the data values.

2.61 − 2(0.41) = 1.79

2.61 + 2(0.41) = 3.43

The range of numbers is 1.79 to 3.43

Finally, the last part of the empirical rule states that 99.7% of the data values will fall within 3 standard deviations of the mean. To calculate "within 3 standard deviations," you need to subtract 3 standard deviations from the mean, then add 3 standard deviations to the mean. That will give you the range for 99.7% of the data values.

2.61 − 3(0.41) = 1.38

2.61+3(0.41) = 3.84

The range of numbers is 1.38 to 3.84.

Hence, 99.7% of the students have a grade point average which is between 1.38 and 3.84.  

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The standard form is given by(As highest degree is 2 we will take till degree 2 i.e quadratic)

So

#1

Multiply 4

Here

#2

Already in standard form

Answer:

\(\dfrac{5}{2}x^3-\dfrac{9}{4}x^2+\dfrac{7}{2}x-\dfrac{3}{2}\)

Step-by-step explanation:

The product of the two expressions is:

\(\left(\dfrac{1}{2}x-\dfrac{1}{4}\right)(5x^2-2x+6)\)

\(=\dfrac{1}{2}x(5x^2-2x+6)-\dfrac{1}{4}(5x^2-2x+6)\)

\(=\dfrac{5}{2}x^3-\dfrac{2}{2}x^2+\dfrac{6}{2}x-\dfrac{5}{4}x^2+\dfrac{2}{4}x-\dfrac{6}{4}\)

\(=\dfrac{5}{2}x^3-x^2-\dfrac{5}{4}x^2+3x+\dfrac{1}{2}x-\dfrac{3}{2}\)

\(=\dfrac{5}{2}x^3-\dfrac{9}{4}x^2+\dfrac{7}{2}x-\dfrac{3}{2}\)

The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

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

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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(A) If Two independent events, A and B, are such that P(A) = 0. 2 P(A U B) = 0. 8, then probability P(B) =  5/8.

The possibility of the result of any random event is referred to as probability. This term refers to determining how likely an event is to occur. What are the chances of getting a head when we toss a coin in the air, for instance? The quantity of outcomes depends on the response to this question. Here, the outcome could be either head or tail. Thus, there is a 50% chance that the result will be a head.

The probability serves as a gauge for the likelihood that an event will occur. It gauges how likely an event is to occur. The probability equation is given by;

P(E) = Number of Favourable Outcomes/Number of total outcomes

We know that

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = P(A) + P(B) - P(A).P(B)

0.8 = 0.2 + P(B) - 0.2.P(B)

0.5 = P(B)  - 0.2.P(B)

0.5 = 0.8.P(B)

P(B) = 0.5/0.8

P(B) = 5/8

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Answer:

Step-by-step explanation:

b/(2 - g) = T

(2 - g)(b/(2-g) = T)

b = T(2 - g)

Answer:

90 degrees

90 degreesPerpendicular lines are lines that intersect at a right (90 degrees) angle.

Answer:

400 students

Step-by-step explanation:

We can rewrite the problem using the words is and of:

240 is 60% of the total number of students in the graduating class.

A simple formula for percentage problems is Px = y, where P is the percentage.  

In this case, we only know that 240 is 60% of some number, so we must find x:

\(0.60x=240\\x=400\)

The answer is b) n - 1. When constructing a confidence interval for the population mean using the standard deviation of the sample, we use the t-distribution.

The degrees of freedom for the t-distribution is given by n - 1, where n is the sample size. This is because we estimate the population mean using the sample mean, and we lose one degree of freedom in the process. Degrees of freedom refer to the number of independent pieces of information available for estimating a parameter.

Since one piece of information is used to estimate the sample mean, we subtract one from the sample size to get the degrees of freedom for the t-distribution. Therefore, the correct option is b) n - 1.

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Answer:

\(x =12\ or\ -8\)

Step-by-step explanation:

Given

\((x_1,y_1) = (6,5)\)

\((x_2,y_2) = (8,2)\)

\((x_3,y_3) = (x,11)\)

\(Area = 15\)

Required

Find x

The area is calculated as thus:

\(Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|\)

Substitute values

\(15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|\)

\(15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|\)

\(15 = \frac{1}{2}|-54 + 48 + 3x|\)

\(15 = \frac{1}{2}|-6 + 3x|\)

Multiply through by 2

\(2 * 15 = \frac{1}{2}|-6 + 3x| * 2\)

\(30 = |-6 + 3x|\)

Remove absolute sign

\(30 = -6 + 3x\ or\ -30 = -6 + 3x\)

Add 6 to both sides

\(36 = 3x\ or\ -24 = 3x\)

Divide by 3

\(12 = x\ or\ -8 = x\)

\(x =12\ or\ -8\)

So, the coordinates are (-8, 11) or (12,11)

Given an LTI system that has an output y = 2te^-ul for the input x(t) = -(t). Here, e^-ul is the decay constant and is a real positive constant. The impulse response of the system can be found by considering the impulse input x(t) = δ(t).

The output of the system with an impulse input is given by y(t) = h(t), where h(t) is the impulse response of the system.We have,x(t) = -(t)..........(1)Applying derivative on both sides of the above equation, we get,y(t) = 2te^-ul, Applying derivative on both sides of the above equation, we get,

Plot of frequency response and Impulse response of the system Hence, the plot of frequency response and the impulse response of the LTI system is shown in the figure below:, the frequency response is given by H(jω) = (2/(-jω + ul)^2) where ω is the angular frequency. The impulse response of the system is given by h(t) = (2/ul^2)t.e^-ul.

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Answer: C

Step-by-step explanation:

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

          = (2 - 4) / (-1 - 3)

          = -2 / -4

          = 1/2

Answer:

g[f(-2)] = 7

Step-by-step explanation:

f(x) = x^2

g(x) = 3x – 5

g[f(-2)]

First find f(-2) = (-2)^2 = 4

Then find g(4) = 3(3) -5 = 12-5 = 7

\(f(x)=x^2;g(x)=3x-5\\\\g[f(-2)]=3\times (f(-2))^2-5=3\times(-2)^2-5=3\times4-5=7\)

Answer: c

hope it helps

Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

Answer:

This is a negative slope.

Step-by-step explanation:

When plotting the numbers on a graph, the slope goes downhill from left to right.

Answer:

In the pic

Step-by-step explanation:

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below ;)

answer:

provided in the explanation.

step-by-step explanation:

the graph would contain the points (0,0), (1,10), (2,20), etc. the slope is 10, which represents the number of coordinate video games practiced in x number of hours. the representation for the slope depends on whether coordinate video game or hours practiced is on the x or y axis. hope that helps!

Answer:

I think the answer will be 18

The TCF associated with the purchase of this machine is -$32,000, indicating a net cash outflow of $32,000 over the 5-year period.

We need to take into account the initial cost, depreciation, salvage value, inventory increase, and the effect on earnings before depreciation and taxes (EBDT) when calculating the Total Cash Flow (TCF) associated with the purchase of the new machine.

Information provided:

New machine cost: $90,000

Deterioration period: 5 years

Assessed rescue worth of new machine following 5 years: Cost of the current machine: $25,000 $60,000

Deterioration time of current machine: Current machine's salvage value in five years: $36,000 More of the new machine's stock: $3,000

Expanded EBDT yearly because of new machine: The marginal tax rate is $56,000. 34 percent Now let's figure out the TCF:

Ascertain the devaluation cost for the two machines:

Depreciation costs for the new machine are as follows: (Cost - Salvage value) / Life; depreciation costs for the current machine are as follows: (Cost - Salvage value) / Life; depreciation costs for the new machine are as follows: (90,000 - $25,000) / 5 = $13,000; depreciation costs for the current machine are as follows: (60,000 - $36,000) / 5 = $4,800.

The annual increase in earnings before depreciation and taxes (EBDT) can be calculated by multiplying the tax savings for the new machine by the depreciation expense, multiplied by the tax rate, and the tax savings for the current machine by the depreciation expense, multiplied by the tax rate.

The net cash inflow resulting from the increased EBDT can be calculated as follows: EBDT increase = Increased EBDT - Tax savings for the current machine EBDT increase = $56,000 - $1,632 = $54,368

The net cash inflow is equal to the EBDT increase minus the tax rate. The net cash inflow is equal to $35,899.52 minus the 0.34 percent figure.

Absolute money surge = Cost of new machine + Expanded stock

Absolute money surge = $90,000 + $3,000 = $93,000

Compute the rescue worth of the ongoing machine toward the finish of its 5-year life:

The machine's salvage value is $36,000. At the end of five years, the total cash inflow will be as follows:

All out cash inflow = Rescue worth of new machine + Rescue worth of current machine

All out cash inflow = $25,000 + $36,000 = $61,000

Ascertain the TCF:

The TCF associated with the purchase of this machine is -$32,000, indicating a net cash outflow of $32,000 over the course of the five years. TCF = Total cash inflow - Total cash outflow TCF = $61,000 - $93,000 = -$32,000

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