How do I solve this equation?

For a proper use of unit multipliers to convert 24 square feet per minute, the right choice is A.

The proper use of unit multipliers to convert 24 square feet per minute to square inches per second is:

24 ft²/1 min × 12 in/1 ft × 12 in/1 ft × 1 min/60 sec = (24 × 12 × 12)/(1 × 1 × 60) in²/sec

Thus, when these conversion factors are multiplied by the specified value of  24 ft²/1 min:

24 ft²/1 min . 12 in/1 ft . 12 in/1 ft . 1 min/60 sec

= (24 x 12 x 12) in² / (1 x 1 x 1) min x (1 x 1 x 60) sec

= 4,608 in²/sec

Therefore, the correct answer choice is:

24 ft²/1 min . 12 in/1 ft . 12 in/1 ft . 1 min/60 sec.

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For f(x) = sin(Tr), there exists at least one point 0 < c < 2 such that f (2) - f(0) = f'(c) (2 - 0)^2. However, for f(x) = |x|, there is no such c that satisfies f(1) - f(-1) = f'(c) (2). The Mean Value Theorem does not apply over the interval [-1, 1] for f(x) = |x|.

For f(x) = sin(Tr), we can apply the Mean Value Theorem which states that for a function f(x) that is continuous on the interval [a, b] and differentiable on (a, b), there exists at least one point c in (a, b) such that:

f(b) - f(a) = f'(c) (b - a)

Here, a = 0, b = 2, and f(x) = sin(Tr). Thus,

f(2) - f(0) = f'(c) (2 - 0)

sin(2T) - sin(0) = cos(cT) (2)

2 = cos(cT) (2)

cos(cT) = 1

cT = 2nπ, where n is an integer

0 < c < 2, so 0 < cT < 2π

Thus, cT = π/2, and c = π/4

Therefore, f'(π/4) satisfies the Mean Value Theorem condition.

For f(x) = |x|, we can find f'(x) for x ≠ 0:

f'(x) = d/dx|x| = x/|x| = ±1

However, at x = 0, the function f(x) is not differentiable because the left and right derivatives do not match:

f'(x=0-) = lim(h->0-) (f(0) - f(0-h))/h = -1

f'(x=0+) = lim(h->0+) (f(0+h) - f(0))/h = 1

Thus, the Mean Value Theorem does not apply over the interval [-1, 1] for f(x) = |x|.

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The value of the Nintendo after 35 years is $2455

Since the formula f(x) = 3x² - 40x + 180 predicts the value of the Nintendo x years after 1986.

Since we require the value in 2021, x years after 1986 is 2021 - 1986 = 35 years.

Substituting x = 35 into the equation, we have

f(x) = 3x² - 40x + 180

f(x) = 3(35)² - 40(35) + 180

f(x) = 3(1225) - 40(35) + 180

f(x) = 3675 - 1400 + 180

f(x) = 2275 + 180

f(x) = 2455

So, the value of the Nintendo after 35 years is $2455

Do you think this is a realistic prediction of the value of that Nintendo?

This is not a realistic prediction for the value of the Nintendo, because, it is too high.

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Answer:

= \(z^{11}\)

Step-by-step explanation

The function of the path of the punted ball is a quadratic function which

follows the path of a parabola.

The correct responses are;

Part A: The coordinates of the vertex is \(\underline {(59, \, 36.81)}\)

Part B: The maximum height of the punt is 36.81 ft.

Part C: The defensive player must reach up to 7.65 feet to block the punt.

Part D: The distance down the field the ball will go without being blocked is approximately 119.67 ft.

Reasons:

The function for the height of the punted ball is; h = -0.01·x² + 1.18·x + 2

Assumption; The distances are feet.

Part A: By completing the square, we have;

f(x) = -0.01·x² + 1.18·x + 2

100·f(x) = -x² + 118·x  + 200

-100·f(x) = x² - 118·x  - 200

x² - 118·x + (118/2)²= 200 + (118/2)²

(x - 59)² = 200 + (59)² = 3681

(x - 59)² - 3681

At the vertex, -3281 = -100·f(x)

∴ f(x) at the vertex = -3681/-100 = 36.81

\(\mathrm{\underline{Coordinate \ of \ the \ vertex = (59, \, 36.81)}}\)

Part B: The maximum height is given by the y-value at the vertex = 36.81 ft.

Part C: When x = 5, we have;

h = -0.01·x² + 1.18·x + 2

h = -0.01 × 5² + 1.18 × 5 + 2 = 7.65

The defensive player must reach up to 7.65 feet to block the punt

Part D: The distance the ball will go before it hits the ground is given by

the function, for the height as follows;

h = -0.01·x² + 1.18·x + 2 = 0

From the completing the square method, above, we get;

-0.01·x² + 1.18·x + 2 = 0

x² - 118·x  - 200 = 0

x² - 118·x + (118/2)²= 200 + (118/2)²

x² - 118·x + (59)²= 200 + (59)² = 3681

(x - 59)² = 3681

x - 59 = ±√3681

x = 59 ± √3681

x = 59 + √3681 ≈ 119.67

The distance down the field the ball will go without being blocked, x ≈ 119.67 ft.

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Percentage change = 10%

We can use the formula:

Percent change = \(\frac{New-Old}{Old}\) x 100

Percent change = \(\frac{77-70}{70}\)x100

Percent change = \(\frac{7}{70}\) x 100

Percent change = 0.1 x 100

Percent change = 10%

Answer: 53.9

Step-by-step explanation:

The numerical value of x in the given figure is 14.

Sum of angles on a straight line is equal to 180°.

From the figure in the diagram.

Angle ( 7x - 1 )° and angle ( 6x - 1 )° add up to 180° since they both on a straight line.

( 7x - 1 ) + ( 6x - 1 ) = 180

We solve for x

7x - 1 + 6x - 1 = 180

Collect like terms

7x + 6x -1 - 1 = 180

13x - 2 = 180

13x = 180 + 2

13x = 182

x = 182/13

x = 14

Therefore, the numerical value of x in the figure is 14.

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Statistical guidance should perform well in situations such as clinical trials and market research where rigorous data analysis and inference are necessary. Statistical methods provide a systematic approach to control biases, handle variability, and draw reliable conclusions, ensuring accurate decision-making and predictions based on the data.

Statistical methods are crucial in determining sample sizes, designing the study, and analyzing the data to draw valid conclusions about the effectiveness and safety of the treatment.

In this situation, statistical guidance should do well because it provides a systematic framework to control for biases, random variability, and confounding factors, ensuring robust and reliable results that can be generalized to a larger population.

One example where statistical guidance should perform well is in clinical trials for new drugs or treatments.

Another example is in market research and opinion polling. Statistical techniques can be used to collect and analyze data from a representative sample of the target population, allowing for accurate estimation and prediction of consumer preferences, market trends, or election outcomes.

Statistical guidance should do well in this situation because it provides methods for random sampling, hypothesis testing, and confidence interval estimation, which help minimize sampling errors and increase the reliability of the findings.

Additionally, statistical models can capture complex relationships and make accurate predictions based on the observed data.

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Answer:

this might take a while

Answer:

a rectangle

Step-by-step explanation:

The selling price of the game is (d) $111.80

The given parameters are:

Discount = 30%

Selling price = $86.00

Since the item is sold less, then the original price would be more.

So, we have:

Price = Selling price * (1 + Discount)

This gives

Price = $86.00 * (1 + 30%)

Evaluate

Price = $111.80

Hence, the selling price is (d) $111.80

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Answer:

Step-by-step explanation:

If point M is midpoint of ST then:

\(x_S-x_M=x_M- x_T\qquad\quad\ \wedge\qquad y_S-y_M=y_M - y_T\\\\S(x_S,\,y_S)\,,\quad T(0,\,2)\,,\quad M(4,\,-4)\,,\ \ so:\\\\x_S-4=4- 0\qquad\quad\ \wedge\qquad y_S-(-4)=-4-2\\\\x_S=4+4\qquad\quad\ \wedge\qquad\ y_S=-6-4\\\\{}\quad x_S=8\qquad\quad\ \wedge\qquad\ y_S=-10\)

Answer:

4 lawns

Step-by-step explanation:

Answer:

She has to mow 4 lawns to be able to buy the concert ticket although I would advise she mow 5 lawns cause it never pays to be broke.

Step-by-step explanation:

Answer:

4*4

Step-by-step explanation:

since 4 times 4 is 16 then if you add 8 its 24

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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The insurance company will pay $25,000.00.

Kevin will have to pay $7,000.00 out of his own pocket.

A company that offers financial protection or reimbursement to people, businesses, or other organizations in exchange for premium payments is known as an insurance company.

The insurance provider will only pay up to the policy maximum of $25,000 because Kevin has $25,000 in property damage insurance and the damage he caused is $32,000.

Therefore, the insurance company will pay $25,000.00.

Kevin will be responsible for paying the remaining balance, which is $32,000.00 - $25,000.00 =  $7,000.00.

Therefore, Kevin will have to pay $7,000.00 out of his own pocket.

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The cοrrect statement is the segment GC is transversal tο segments KG and QC.

A line that crοsses twο οr mοre lines in the same plane at different lοcatiοns is said tο be transversal. Accοrding tο the fundamental prοpοrtiοnality theοrem (alsο knοwn as Thales' theοrem), if three οr mοre parallel lines crοss acrοss twο transversals, they prοpοrtiοnally cut οff the transversals.

We have given the statements are:

A). KG QC.

B) KG and QC intersect at a right angle.

C) KQ || GC.

D) GC is transversal tο KG and QC.

Therefοre, here in the figure, segment GC intersects segments KG and QC in the same plane at different lοcatiοns.

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The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

The slope of the tangent line to the graph of the function y = x^4 - 10x^2 + 9 at x = 1 can be found by taking the derivative of the function and evaluating it at x = 1. The equation of the tangent line can then be determined using the point-slope form.

Taking the derivative of the function y = x^4 - 10x^2 + 9 with respect to x, we get:

dy/dx = 4x^3 - 20x

To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative:

dy/dx (at x = 1) = 4(1)^3 - 20(1) = 4 - 20 = -16

Therefore, the slope of the tangent line is -16.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Given that the point of tangency is (1, y(1)), we substitute x1 = 1 and y1 = y(1) into the equation:

y - y(1) = -16(x - 1)

Expanding the equation and simplifying, we have:

y - y(1) = -16x + 16

Rearranging the equation, we obtain the equation of the tangent line:

y = -16x + (y(1) + 16)

To find the slope of the tangent line, we first need to find the derivative of the given function. The derivative represents the rate of change of the function at any point on its graph. By evaluating the derivative at the specific value of x, we can determine the slope of the tangent line at that point.

In this case, the given function is y = x^4 - 10x^2 + 9. Taking its derivative with respect to x gives us dy/dx = 4x^3 - 20x. To find the slope of the tangent line at x = 1, we substitute x = 1 into the derivative equation, resulting in dy/dx = -16.

The slope of the tangent line is -16. This indicates that for every unit increase in x, the corresponding y-value decreases by 16 units.

To determine the equation of the tangent line, we use the point-slope form of a linear equation, which is y - y1 = m(x - x1). We know the point of tangency is (1, y(1)), where x1 = 1 and y(1) is the value of the function at x = 1.

Substituting these values into the point-slope form, we get y - y(1) = -16(x - 1). Expanding the equation and rearranging it yields the equation of the tangent line, y = -16x + (y(1) + 16).

The equation of the tangent line represents a straight line that passes through the point of tangency and has a slope of -16.

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Answer:

0.54

Step-by-step explanation:

sin 105 / 2 = sin 15 / b

b = sin 15 / 0.48296

b = 0.54

Answer:

x = 5   z = 94

Step-by-step explanation:

12x + 26 = 86

12x = 60

x = 5

360 - 172 = 188

z = 188 : 2 = 94

The ladder is 8ft in length and is leaning against the wall at an angle. The base of the ladder is 5.5ft from the wall. To determine the height of the wall, we need to find the length of the ladder that is touching the wall.

We have the base of the ladder (5.5ft), and the length of the ladder (8ft), and we are looking for the height of the wall.Using the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides, we can determine the height of the wall.   {Hypotenuse}^2={Base}^2+{Height}^2        

where the hypotenuse is the ladder length (8ft), the base is the distance between the ladder and the wall (5.5ft), and the height is what we are looking for.

Let's plug in the values we know and solve for the height of the wall.{8}^2={5.5}^2+{Height}^2 64=30.25+{Height}^2 {Height}^2=33.75 Height

≈ 5.8ft

Therefore, the wall is about 5.8ft tall.

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The final expression for the integral is:

∫ x f''(x) dx = x f'(x) - f(x) - ln|x-1| + 5 ln|2-x| + 3 ln|x-4| - ln|1-x| + 3

We can use integration by parts to evaluate the integral:

∫ x f''(x) dx

Let u = x and dv = f''(x) dx, then we have du = dx and v = f'(x).

Using integration by parts formula:

\(∫ u dv = u v - ∫ v du\)

Applying the formula, we get:

\(∫ x f''(x) dx = x f'(x) - ∫ f'(x) dx\)

Since we are given that f'(1) = 5 and f'(4) = 3, we can evaluate the integral as follows:

∫ x f''(x) dx = x f'(x) - ∫ f'(x) dx

= x f'(x) - f(x) + C (where C is the constant of integration)

Now, we need to find the value of the constant C. We can use the given values of f(1) and f(4) to find C as follows:

f(1) = 2, therefore C = 1*5 - 2 = 3

f(4) = 7, therefore 7 = 4f'(4) - f(4) + 3

Simplifying, we get:

f"(x) = [f'(x) - f'(1)]/(x-1) + [f'(x) - f'(4)]/(x-4)

Now, we can substitute the expression for f"(x) into the integral we found earlier:

∫ x f''(x) dx = x f'(x) - f(x) + C

= x f'(x) - ∫ [f'(x) - f'(1)]/(x-1) dx - ∫ [f'(x) - f'(4)]/(x-4) dx + 3

Evaluating the two integrals, we get:

∫ [f'(x) - f'(1)]/(x-1) dx = ln|x-1| - 5 ln|2-x|

∫ [f'(x) - f'(4)]/(x-4) dx = -3 ln|x-4| + ln|1-x|

Therefore, the final expression for the integral is:

∫ x f''(x) dx = x f'(x) - f(x) - ln|x-1| + 5 ln|2-x| + 3 ln|x-4| - ln|1-x| + 3

Note that the constant of integration, C, is included in the last term of the expression.

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Answer:

B) USA

Step-by-step explanation:

USA is in North America

Answer:

You need to look at the graph and find an ordered pair.  Once you find an ordered pair divide the x value by the y value to get the unit rate.

Step-by-step explanation:

Let y1, y2, y3 be iid beta(2, 1) random variables, the probability of 0.4 < y(2) < 0.6 is 0.32.

To find the probability of 0.4 < y(2) < 0.6, we first need to find the distribution of y(2). Since y1, y2, and y3 are independent and identically distributed beta(2,1) random variables, the distribution of y(2) is also beta(2,1). We can use this fact to find the probability we are looking for:
P[0.4 < y(2) < 0.6] = P[y(2) < 0.6] - P[y(2) < 0.4]
= F(0.6) - F(0.4)
where F is the cumulative distribution function of the beta(2,1) distribution.
Using a calculator or software, we can find that F(0.6) = 0.84 and F(0.4) = 0.52. Substituting these values, we get:
P[0.4 < y(2) < 0.6] = 0.84 - 0.52
= 0.32
Therefore, the probability of 0.4 < y(2) < 0.6 is 0.32.

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The events are mutually exclusive events, so P(A|B) is 0.

In this question,

If two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then

⇒ A ∩ B = 0

Now the conditional probability, P(A|B) = \(\frac{P(A \cap B )}{P(B)}\)

⇒ \(\frac{0}{0.10}\)

⇒ 0.

Hence we can conclude that the events are mutually exclusive events, so P(A|B) is 0.

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