Suppose the area of a region bounded by two curves is y = x² and y = x + 2 with a ≤ x ≤ a and a > 1 is 19/3 unit area. Determine the value of a² - 3a + 1

We will apply the percentage method to find that 48 students said red is their favourite colour.

Probability is a constituent part of computation that deals with the occurrence of a random event. The value is defined from zero to one. Probability is familiarised to predict how likely events are to happen. Probability is the degree to which something is possible to happen.

Total number of pupils in class 9 = 80

We need to calculate the number of students choosing red as their favourite colour.

We are given that 80 pupils are there in year 9.

Out of these, 3/5 of the pupils say that their favourite colour is red.

Let n be the number of pupils who say red is their favourite colour.

∴ n = (3/5) × 80

∴ n = 48

--The given question is incorrect; the correct question is

"3/5 of the pupils in a year 9 class say their favourite colour is red. There are 80 pupils in Year 9. How many students said red is their favourite colour?"--

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In your given situation, the distribution of grades is left-skewed, which indicates that the majority of the students scored higher grades, with fewer students receiving lower grades.

If the distribution of grades was left-skewed, it means that there were more students who scored higher grades than those who scored lower grades. This would result in a longer tail on the left side of the distribution curve. However, despite the skewness, the mean, median, and mode were all the same. This suggests that the majority of the grades fell around the same value, which is the central tendency of the distribution. The fact that the mean and median are the same suggests that the skewness was not significant enough to pull the mean away from the median. Therefore, in this case, the mean and median can be considered as representative of the typical grade achieved by the students.
. However, the mean, median, and mode are all the same, suggesting that the central tendency of the grades is consistent, and the overall distribution might be only slightly skewed.

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according to question the Laplace transform of f(t) is:

F(s) = 16/s^2 + 9/(s-1), defined for s > 1.

The Laplace transform of f(t) is defined by:

F(s) = L{f(t)} = ∫[0,∞) e^(-st) f(t) dt

Applying this definition to the given function:

F(s) = L{16t + 9e^t} = ∫[0,∞) e^(-st) (16t + 9e^t) dt

We can separate this integral into two parts and evaluate each part separately:

F(s) = ∫[0,∞) e^(-st) 16t dt + ∫[0,∞) e^(-st) 9e^t dt

To evaluate the first integral, we can use integration by parts:

u = 16t, dv/dt = e^(-st) -> du/dt = 16, v = -e^(-st)/s

∫[0,∞) e^(-st) 16t dt = [-16t e^(-st)/s] [0,∞) + ∫[0,∞) 16e^(-st)/s dt

= [16/s] ∫[0,∞) e^(-st) dt = [16/s] (1/s) = 16/s^2

To evaluate the second integral, we can use the fact that the Laplace transform of e^at is 1/(s - a):

∫[0,∞) e^(-st) 9e^t dt = 9 ∫[0,∞) e^(-(s-1)t) dt

= 9/(s-1)

Putting everything together, we have:

F(s) = 16/s^2 + 9/(s-1)

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Based on the given scenario, we have an automobile travelling at a speed of 20m/s approaching an intersection. At a distance of 100 meters from the intersection, a truck travelling at 40m/s crosses the intersection.

Approaching an intersection means that the automobile is getting closer to the intersection as it moves forward. This means that the distance between the automobile and the intersection is decreasing over time.

Travelling at a rate of 20m/s means that the automobile is covering a distance of 20 meters in one second. Therefore, the automobile will cover a distance of 100 meters in 5 seconds (since distance = speed x time).

When the automobile is 100 meters from the intersection, the truck travelling at 40m/s crosses the intersection. This means that the truck has already passed the intersection by the time the automobile reaches it.

In summary, the automobile is approaching the intersection at a speed of 20m/s and will reach the intersection 5 seconds after it is 100 meters away from it. The truck has already crossed the intersection and is no longer in the path of the automobile.

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Answer:

5x cm

Step-by-step explanation:

Total length of AE = 2x + 3x

= 5x cm

Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

Answer:

Deepika Deepika use 32% of his salary ^ housed and which is the amount of this is Monica is in driving on the monthly on the this is profit or loss we know don't don't know that we are what we do if x x is value of you don't know why I don't know it's your mistake I don't care

Answer:

x = 15

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

( leg of large Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )

x² = 9 × 25 = 225 ( take the square root of both sides )

x = \(\sqrt{225}\) = 15

Answer:117 feet

Step-by-step explanation:

There are 12 inches in 1 foot

Multiply 12 x 9 which equals 108

Since you have a decimal, you take 75% of 12 which is 9, and add that to your inches

108 + 9 = 117

\( \huge \boxed{Answer \hookleftarrow}\)

=》1² + 3²

=》1 + 9

=》10

The length of the shadow that is cast by the scaffold and the technician to the nearest inch is approximately 196 inches.

Recall that where two triangles are said to be proportional, it means that their perimeters are similar.

Therefore, to solve this, first, we convert all figures into inches.

AC  = 8ft 2in. = 98in

CE = 7ft 6in = 90in

AB = 6ft 3in = 75in

Second,

Recall that the height of the technician = 5ft 8in. In inches that will be 68inches.

The height of the scaffold is arrived at by saying 188 + 68 = 256Inc

Recall that the triangles are proportional. Therefore, we say

\(\frac{256}{98}\) = \(\frac{s}{75}\)

if we cross multiply we can then say

s = 75(\(\frac{256}{98}\))

s = 75 * 2.6122449

s = 195.918 or approximately 196 inches. Answer in Feet is 16ft 4in.


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The given statement "the probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring." is False.

The union of two events A and B represents the event that at least one of the events A or B occurs. The probability of the union of two events can be calculated using the formula:

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

On the other hand, the intersection of two events A and B represents the event that both events A and B occur. The probability of the intersection of two events can be calculated using the formula:

P(A and B) = P(A) * P(B|A)

where P(B|A) is the conditional probability of B given that A has occurred.

It is possible for the probability of the union of two events to be greater than the probability of the intersection of two events if the two events are not mutually exclusive.

In this case, the probability of both events occurring together (the intersection) may be relatively small, while the probability of at least one of the events occurring (the union) may be relatively high.

In summary, the probability of the union of two events occurring can sometimes be greater than the probability of the intersection of two events occurring, depending on the relationship between the events.

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Answer:

The formula for the area of a trapezoid is:

Area = (b1 + b2) / 2 x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height.

We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).

Substituting the given values into the formula for the area of a trapezoid, we get:

96 = (11 + b2) / 2 x 8

Multiplying both sides by 2 and dividing by 8, we get:

24 = 11 + b2

Subtracting 11 from both sides, we get:

b2 = 13

Therefore, the length of the other base is 13 ft.

The value of \(csc(\theta)\)  is  \(\frac{15}{12}\)

"It is a triangle in which one of the angle measures 90° "

"It is the longest side of the right triangle."

"For a right triangle, \(x^{2}+ y^{2}=z^{2}\), where z is the hypotenuse and x, y are other two sides of the right triangle."

"In a right triangle, csc of angle is the ratio of the hypotenuse to the opposite side of angle."

For given question,

First we find the hypotenuse of the right triangle.

Using Pythagoras theorem,

\(\Rightarrow 9^{2} + 12^{2}= r^{2}\\\\ \Rightarrow 81 + 144=r^2\\\\\Rightarrow r=\sqrt{225}\\\\ \Rightarrow r=15\)

so, the hypotenuse is r = 15

Now we find the csc of angle \(\theta\)

\(\Rightarrow csc(\theta)=\frac{hypotenuse}{opposite~side~of~\theta} \\\\\Rightarrow csc(\theta)=\frac{15}{12}\)

Therefore, the value of \(csc(\theta)\) is \(\frac{15}{12}\)

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h(0) show the initial height of the plane, that is 25 feet.

The given equation is h(t)=25+2.5t-1/2 t².

Here, h(0)=25+2.5(0)-1/2 (0)²

h(0)=25

This shows the initial height is 25 feet.

Therefore, h(0) show the initial height of the plane, that is 25 feet.

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"Your question is incomplete, probably the complete question/missing part is:"

A girl throws a paper airplane from her treehouse. The height of the plane is a function of time and can be modeled by the equation h(t)=25+2.5t-1/2 t². Height is measured in feet and time is measured in seconds.

Evaluate h(0) and explain what this value means in this situation.

Answer:

Sorry let me try to understand the question

Step-by-step explanation:

The domain of the function r(x) is (0, 200).

The revenue earned when the price is $30 is $20400.

The rule for the function r(x) is x(800 - 4x).

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

Demand:

d(x) = 800 - 4x

Price = x

Revenue = Price x demand

Revenue = r(x)

A)

The rule for r(x).

r(x) = x d(x) = x(800 - 4x)

The domain of r(x) is 0 < x < 200 i.e (0, 200).

B)

x = 30

r(x) = 30(800 - 4 x 30)

r(x) = 30(800 - 120) = 30 x 680 = 20400

C)

r(x) = x(800 - 4x)

Thus,

The answers are given above.

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Answer:

I believe it is 3rd one but not 100% sure

Step-by-step explanation:

hope this helps

Answer:

edg 2020

Step-by-step explanation:

-1 2 1 -1

3 4 5 5

Answer:  This is a linear equation. The graph is a diagonal line with a slope of +1. The y-intercept is -1

Step-by-step explanation: The line intersects the y-axis at -1 and the x-axis at +1

The calculated value of x in the trapezoid is 16

From the question, we have the following parameters that can be used in our computation:

The trapezoid

The area of the trapezoid is given as

Area = 187 square cm

And the area is calculated as

Area = 1/2 * Sum of parallel sides * Height

using the above as a guide, we have the following:

1/2 * (x + 6) * 17 = 187

So, we have

(x + 6) = 22

When solved for x, we have

x = 16

Hence, the value of x is 16

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The rectangular pice has a wide of 24 inches and 40 inches long so we can calculate the area of the rectangle:

Now they say that Lenna folds the piece of fabric along its diagonal so the triangle will have halve of the area of the triangle, so que so we can divide the area of the trangle by 2

So the triangle has an area o

Answer:

When x=4, ln x-ln y=y-4, so ln 4-ln 4=4-4, which is true. Therefore, when x=4, y=4, and dy/dx=0.

Step-by-step explanation:

So, when x = 4, the value of the differentiable function dy/dx is 0.

A differentiable function of one real variable is one that has a derivative at each point in its domain. In other words, a differentiable function's graph has a non-vertical tangent line at each interior point in its domain.

Here,

Given the equation ln x - ln y = y - 4, we can rearrange it to get ln(x/y) = y - 4. Taking the derivative of both sides with respect to x using the chain rule:

d/dx (ln(x/y)) = d/dx (y - 4)

(1/x) (dx/dx) - (1/y) (dy/dx) = dy/dx

dy/dx = (1/y) (dx/dx) + (1/x) (dy/dx) = (1/y) + (1/x) (dy/dx)

Rearranging and solving for dy/dx:

(x/y) (dy/dx) = (1/y) - (1/x)

dy/dx = (x/y^2) (1/x - 1/y) = (x/y^2) (1/x - 1/y)

We can substitute x = 4 and y = 4 into the expression to find the value of dy/dx when x = 4:

dy/dx = (4/16) (1/4 - 1/4) = 0

So, the value of differentiable function dy/dx when x = 4 is 0.

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Answer:

Double - 7 5/6

Explantion: 2 1/4 times 2 equal 4 1/2 for the pancake mix

1 2/3 times 2 equal 3 1/3 for the milk

So.....4 1/2 plus 3 1/3 equals 7 5/6

Triple- 11 3/4

Explantion: 2 1/4 times 3 equals 6 3/4 for the pancake mix

1 2/3 times 3 for the milk equals 5

So.... 5 plus 6 3/4 equal 11 3/4

Hope it help :)

Answer:

2

Step-by-step explanation

Rate of change is the slope, \(\frac{Y}{X}\)

The distance from our y values which are -1 and 5 is 6.

The distance from our x values which 4 and 7 is 3.

Since its \(\frac{Y}{X}\) The 6 would be over the 3 as 6/3 which simplifies to 2 or 2/1.

In the given scenario, the independent variable is the distance (0.5 miles, 1 mile, or 1.5 miles) that participants are instructed to walk every day to observe whether it reduces joint stiffness in people suffering from arthritis of the knee is the correct answer.

The independent variable is the variable that is manipulated or changed by the experimenter to observe its effects on the dependent variable. In the given study, the independent variable is walking, specifically, the distance walked by the participants. The dependent variable, on the other hand, is joint stiffness. It is the variable that is being observed and measured in response to the independent variable. The experiment's design suggests that the researcher is interested in measuring the effect of different walking distances on joint stiffness. By controlling the independent variable, the researcher can observe how changes in this variable affect the dependent variable's outcomes.

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A.) How many students participated in dance?

Based on the chart, 25% of the students participated in the dance. Let's determine the actual number out of 200 students:

Therefore, there are 50 Students that participated in the dance.

B.) How many more students participated in Dodgeball than in Basketball?

Therefore, there are 30 more students that participated in Dodgeball than in Basketball.

Answer:

Answer is 5 inches on edg

Step-by-step explanation:

Answer:

The correct answer would be 5 inches.

Step-by-step explanation:

Answer:

Top TUV

Bottom: UV, UT, TV

Step-by-step explanation:

The scale factor from the larger to the smaller is 3/4

24(3/4) = 18

12(3/4) = 9

16(3/4) = 12

The required answer is the double declining-balance method is $9,840.

To calculate the depreciation expense for 2020 using the double declining-balance method, we first need to determine the asset's straight-line depreciation rate. This is calculated by subtracting the residual value from the cost of the asset and dividing by the asset's useful life:

Depreciation base = $30,000 - $3,000 = $27,000
Annual depreciation expense (straight-line) = Depreciation base / Useful life = $27,000 / 5 = $5,400

Next, we need to determine the double declining-balance rate, which is twice the straight-line rate. Therefore:
Double declining-balance rate = 2 x (1 / Useful life) = 2 x (1 / 5) = 0.40 or 40%
Now we can calculate the depreciation expense for 2020:
Depreciation expense (2020) = Book value (beginning of year) x Double declining-balance rate

The book value at the beginning of 2020 would be the cost of the asset minus accumulated depreciation for the first year:
Book value (beginning of 2020) = $30,000 - ($5,400 x 1) = $24,600
As a result, depreciation increases during the initial year of possession and decreases thereafter.

Therefore:

Depreciation expense (2020) = $24,600 x 0.40 = $9,840

So the amount of depreciation expense for 2020, the second year of the asset's life,

using the double declining-balance method is $9,840.

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