The diagram shows a sketch of the curve y = sin xº.
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a) Write down the coordinates of the point P.
b) Write down the coordinates of the point Q.
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Answer:

Step-by-step explanation:

Answer:

\(\boxed{\sf \ \ \ x^3-2x^2-19x+20 \ \ \ }\)

Step-by-step explanation:

hello,

by definition we can write

\((x-5)(x+4)(x-1)\)

as 5,-4,1 are the zeroes

now we have to write it in the standard form, let's do it

\((x-5)(x+4)(x-1)=(x^2+4x-5x-20)(x-1)\\=(x^2-x-20)(x-1)=x^3-x^2-20x-x^2+x+20\\=x^3-2x^2-19x+20\)

hope this helps

According to the standard deviation, the company should offer a warranty period that covers at least 65,895 miles to ensure that 96% of the tires sold will outlast the warranty.

To do this, we use a z-score table, which gives the probability of getting a z-score less than or equal to a given value. The z-score is a measure of how many standard deviations a data point is from the mean.

To find the z-score for the top 4% of the tires, we first subtract 96% from 100% to get 4%. Then we divide this by 2 to get 2%, as we are interested in the area under the normal distribution curve in the right tail. Using the z-score table, we find that the z-score corresponding to a 2% area under the curve is approximately 2.05.

Next, we use the formula for converting a z-score to a data value:

z = (x - μ) / σ

where z is the z-score, x is the data value, μ is the mean, and σ is the standard deviation. Solving for x, we get:

x = z x σ + μ

Plugging in the values, we get:

x = 2.05 x 2700 + 60000

x ≈ 65,895

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Question:

Which expressions are equivalent to ½ + 3c + ⅘.

Check all that apply.

Answer:

½ + 3c + ⅘ is equivalent to

1. ⅒(30c + 13)

2. 3c + 13/10

Step-by-step explanation:

The options are not well presented.

However, I'll give simplify the given expression in the question above.

Given: ½ + 3c + ⅘.

Required: Simplify

We start by collecting like terms

3c + ½ + ⅘

From this point, the expression can be solved in two ways

1. Solve fractions

This gives [Find LCM]

3c + (5 + 8)/10

3c + 13/10

3c + ⅒(13)

This can still be solved further [Find LCM]

(30c + 13)/10

⅒(30c + 13)

Hence ⅒(30c + 13) is equivalent to ½ + 3c + ⅘.

2. Convert fractions to decimal

½ + 3c + ⅘ becomes

0.5 + 3c + 0.8

Collect like terms

3c + 0.5 + 0.8

3c + 1.3

Convert decimal to fraction

3c + 13/10

3c + ⅒(13)

This can still be solved further [Find LCM]

(30c + 13)/10

⅒(30c + 13)

Hence ⅒(30c + 13) is equivalent to ½ + 3c + ⅘.

This is as far as the expression can be evaluated

Answer:

1,3.and 5

Step-by-step explanation:

Infinite discontinuity

The given equation is:

The function will be undefined at the point x + 1 = 0

x = -1

This means that x = -1 is a point of discontinuity

Substituting x = -1 into the equation:

This is an infinite discontinuity

21. (x+2)(x+9)

22. (x-2)(x+8)

23. \((x-4)^{2}\)

24. (x+3)(x+7)

25. (x-11)(x-2)

26. (x-7)(x-5)

27. (x-15)(x-2)

28. (x-1)(x-8)

29. (x-8)(x-4)

30. (x-8)(x+1)

31. (x-5)(x+7)

32. (x-6)(x+8)

33. (x-7)(x+5)

34. (x-16)(x+3)

35. (x-2)(x+24)

36. (x-2)(x+9)

Answer:

If the perimeter of a square picture frame is 12 inches, then each side of the square frame must be 3 inches long, since 4 x 3 = 12.

To find the area of the picture frame, we need to subtract the area of the picture from the area of the frame. Since the frame is a square with 3-inch sides, its area is 3 x 3 = 9 square inches.

However, we don't know the size of the picture, so we can't calculate its area directly. Instead, we can use the fact that the picture and the frame together form a larger square with sides that are 12 inches long (since the perimeter of the whole thing is 12 inches).

The area of this larger square is 12 x 12 = 144 square inches.

Since the area of the frame is 9 square inches, the area of the picture must be 144 - 9 = 135 square inches.

Therefore, the area of the picture frame is 9 square inches, and the area of the picture is 135 square inches.

Answer:

201495

Step-by-step explanation:

You can reverse this by multiplying 101 by 1995 which will give you that.

not good at explaining, am sorry.

Answer:

490.87 cm^2 or 491 cm^2

Step-by-step explanation:

by adding up the 2.5s from the center till the outer boundary, we can get the radius of the target. So= 2.5+2.5+2.5+2.5+2.5 which is = to 12.5 cm

12.5cm is the radius of the target

now by using the formula for area of a circle and by plugging in the 12.5 as radius we can get the area.

so,

A=πr^2

A=\(a=\pi *(12.5)^2\)

that gives us 490.87 cm^2

which after rounding is

491 cm^2

Answer:

Rational

Step-by-step explanation:

Rational numbers have terminating decimals

Answer: rational

Step-by-step explanation: 4.680 is a rational number because it can be written as a fraction. Irrational numbers are fractions that can’t be written as a fraction, which isn’t the case for 4.680.

Answer:

750 miles

Step-by-step explanation:

25+0.05x=40+0.03x

0.02x=15

x=750

In total, Menaha traveled 97km 1000m (97.1km).

Distance is a numerical measurement of how far apart two objects, points, or places are in space. Distance can be measured in linear units such as meters, kilometers, feet, miles, etc. It can also be measured in angular units such as degrees or radians.

Distance can also refer to the space between two points in time, such as the time between two events. Distance can be used to measure physical distance, time, or even emotional distance.
To calculate this, the two distances must be added together.
The train distance is =86km 520m (86.52km)

and the car distance is =11km 480m (11.48km).
When added together, =86km 520m+11km 480m = 97.52km.
However, since the distances are measured in km and m,
it is necessary to convert the measurements into a single unit of measurement.
To do this, the measurements must be converted into metres.
The train distance is 86,520 metres

And the car distance is 11,480 metres.
When added together,

the total distance is 97,000 metres (97km).

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The total materials cost before sales tax is $297.21.

The total materials cost is the result of the addition of the total cost of posts, wire mesh, gate, and staples, as follows.

The length of the rectangular space = 6 meters

The width of the space = 10.5 meters'

The perimeter of the space = 33 meters [2(6 + 10.5)]

The space between posts = 1.5 meters

The number of posts = 22 (33 ÷ 1.5)

The cost per post = $2.69

a) The cost of the posts = $59.18 ($2.69 x 22)

The cost of wire mesh:

Cost per meter = $5.96

The number of meters of wire mesh = 33 meters

b) Total cost of the wire mesh = $196.68 ($5.96 x 33)

c) Cost of the gate = $25.39

Cost of Staples:

The number of staples per post = 7

The total number of staples required = 154 (22 x 7)

The number of boxes of staples = 4

The cost per box = $3.99

d) The total cost of staples = $15.96 (4 x $3.99)

The total cost of materials = $297.21 ($59.18 + $196.68 + $25.39 + $15.96)

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Answer:

0.6763154335

Step-by-step explanation:

because. 10%is the same as 10 over 100 .because percent means 100. so you say 100÷10=10. then you say 10×14.786. this is how I got the answer.

Answer:

Step-by-step explanation:

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

Let's say that the very first figure is x and the next is y.

x - y = 3 -----> y=x-3 .........(i)

xy=88 .......(ii)

Substitute (i) to (ii)

xy=88

x(x-3)=88

x\(x^{2} - 3x = 88\\x^{2} - 3x - 88 = 0\)

(x+8)(x-11)=0

x+8=0 or x-11=0

x=-8 or x=11

Substitute x=-8 to (i)

y=x-3

y=-8-3=-11

Substitute x=11 to (i)

y=x-3

y=11-3=8

Thus, x = -8 and y =- 11 or x = 11 and y = 8

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

A 2nd equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0.  For instance, if school administration decides to build a chapel with a floor size of 400 sq metres and a length that is two meters longer than its width, we will need the aid of a quadratic equation to determine the length and breadth. 

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The number of spanning trees of a connected graph can be proven to be the product of the number of spanning trees of each of its blocks.

Here are the steps-

1. Consider a connected graph G with blocks B1, B2, ..., Bk. Each block is a maximal connected subgraph with no cut-vertex.

2. The number of spanning trees of G can be denoted as T(G), and the number of spanning trees of each block Bi can be denoted as T(Bi).

3. To prove the given statement, we need to show that\(T(G) = T(B1) * T(B2) * ... * T(Bk).\)

4. We can start by considering a single block B1. Since B1 is a maximal connected subgraph with no cut-vertex, it is a connected graph on its own.

5. The number of spanning trees of B1, T(B1), can be calculated using any method such as Kirchhoff's theorem or counting the number of spanning trees directly.

6. Now, consider the original graph G. We can remove block B1 from G, which leaves us with a graph G' that consists of the remaining blocks B2, B3, ..., Bk.

7. G' is still a connected graph, but it may have cut-vertices. However, the removal of B1 does not affect the connectivity between the other blocks, as each block is a maximal connected subgraph.

8. The number of spanning trees of G', denoted as T(G'), can be calculated using the same method as step 5.

9. Since G' is the remaining part of G after removing B1, the number of spanning trees of G can be expressed as T(G) = T(B1) * T(G').

10. We can repeat this process for the remaining blocks B2, B3, ..., Bk. For each block Bi, we remove it from G and calculate the number of spanning trees of the remaining graph.

11. By repeating steps 6-10 for all blocks, we can express the number of spanning trees of G as-

\(T(G) = T(B1) * T(G')\)

\(= T(B1) * T(B2) * T(G'')\)

= ...

\(= T(B1) * T(B2) * ... * T(Bk).\)

12. Therefore, we have proved that the number of spanning trees of a connected graph G is the product of the number of spanning trees of each of its blocks.

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Answer:

A. 2

Step-by-step explanation:

\( \int_0^1 \: 5x \sqrt x \: dx \\ \\ = \int_0^1 \: 5x . \: {x}^{ \frac{1}{2} } \: dx \\ \\ = 5\int_0^1 \: {x}^{ \frac{3}{2} } \: dx \\ \\ = 5 \bigg( \frac{ {x}^{ \frac{3}{2} + 1 } }{ \frac{3}{2} + 1 } \bigg)_0^1\\ \\ = 5 \bigg( \frac{ {x}^{ \frac{5}{2} } }{ \frac{5}{2}} \bigg)_0^1 \\ \\ = 5 \times \frac{2}{5} \bigg({x}^{ \frac{5}{2} } \bigg)_0^1 \\ \\ = 2 \bigg( {1}^{ \frac{5}{2} } - {0}^{ \frac{5}{2} } \bigg) \\ \\ = 2(1 - 0) \\ \\ = 2\)

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

\(\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx \)

Here 5 is a constant so it can come out . So that,

\(\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx \)

Now we can write √x as ,

\(\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx \)

Simplify ,

\(\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx \)

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

\(\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) \)

On simplifying we will get ,

\(\longrightarrow \underline{\underline{ I = 2 }}\)

There is a significant difference between the mean verbal score for Littlewood Regional High School seniors and the statewide mean.

To determine if there is a significant difference, we need to perform a hypothesis test.

Our null hypothesis is that the mean verbal score for Littlewood Regional High School seniors is equal to the statewide mean of 453.

Our alternative hypothesis is that the mean verbal score for Littlewood Regional High School seniors is greater than the statewide mean of 453.

We can use a one-sample t-test to test this hypothesis. The formula for the t-test is:

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.

Plugging in the values from the problem, we get:

t = (502 - 453) / (95 / √137) = 7.20

Using a t-table or a calculator, we find the p-value for a one-tailed test with 136 degrees of freedom to be less than 0.0001.

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is a significant difference between the mean verbal score for Littlewood Regional High School seniors and the statewide mean.

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1. i^4 = 1.

2. (-i)^15 = -i.

3. (4 - i)(5 + 3i) = 17 + 17i.

4. (1 - i)^3 = -4 - 4i.

5. (2 - 3i)(4 + i) + (6 - 5i) = 19 - 15i.

A. Graphing on a complex plane:

The result of i^4 = 1 is represented by the point (1, 0) on the complex plane.

The result of (-i)^15 = -i is represented by the point (0, -1) on the complex plane.

The result of (4 - i)(5 + 3i) = 17 + 17i is represented by the point (17, 17) on the complex plane.

The result of (1 - i)^3 = -4 - 4i is represented by the point (-4, -4) on the complex plane.

The result of (2 - 3i)(4 + i) + (6 - 5i) = 19 - 15i is represented by the point (19, -15) on the complex plane.

B. Arithmetic expressions in the form a + bi:

1. i^4 = 1 + 0i.

2. (-i)^15 = 0 - i.

3. (4 - i)(5 + 3i) = 17 + 17i.

4. (1 - i)^3 = -4 - 4i.

5. (2 - 3i)(4 + i) + (6 - 5i) = 19 - 15i.

C. When graphing the results from B on the same complex plane as A, we can observe that each point representing the complex number is plotted accordingly. A complex plane is a 2-dimensional plane where the real part represents the horizontal axis (x-axis) and the imaginary part represents the vertical axis (y-axis). The points on the graph correspond to the real and imaginary parts of the complex numbers obtained from the arithmetic expressions. Each point represents a unique complex number, and by plotting them together, we can visually see their positions and relationships on the complex plane.

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Answer:

  all real numbers

Step-by-step explanation:

The domain of any polynomial function is "all real numbers."

Answer:

Step-by-step explanation:

a.  2415

b.  3124

c. 627

d. 8

Answer:

Rate of Change = Slope

Step-by-step explanation:

"Rate of Change" is used commonly in real-world problems to refer to "slope."

y = mx + b, where "mx" is "slope."

So, the rate of change/slope of the equation would be 5.

Answer: why is it wrong

Step-by-step explanation:i said so

\(1 < 4\\and\\1 > 2\\equals\\3\)

Hope it helps! ♣

Answer:

it 5.5⋅10−^8m

Step-by-step explanation:

Unless I'm missing something important here, you can find the difference between the two wavelengths by subtracting one from the other. Since you're interested in finding how much longer the wavelength associated with the orange light is, subtract the wavelength of the green light from the wavelength of the orange light. You know that the two measured wavelengths are 6.15 ⋅ 10 − 7 m → orange light 5.6 ⋅ 10 − 7 m → green light Therefore, the difference between the two wavelengths will be Δ wavelength = 6.15 ⋅ 10 − 7 m − 5.6 ⋅ 10 − 7 m = 5.5 ⋅ 10 − 8 m

Given the relation r with four attributes abcd, let's analyze each set of functional dependencies (FDs) and answer the following questions:

a) c-->d, c-->a, b-->c
i) To identify the candidate key(s) for r, we need to find the minimal set of attributes that uniquely determines all other attributes. In this case, the candidate key(s) for r are ab.
ii) To identify the best normal form that r satisfies, we need to consider the highest normal form satisfied by all the FDs. In this case, r satisfies 2NF, as all non-prime attributes (c and d) are fully functionally dependent on the candidate key (ab).
iii) Since r is already in 2NF, it is also in BCNF. Therefore, no decomposition is required.

b) b-->c, d-->a
i) The candidate key(s) for r are bd, as they can uniquely determine all other attributes.
ii) The best normal form that r satisfies is 2NF, as all non-prime attributes (a and c) are fully functionally dependent on the candidate key (bd).
iii) Since r is already in 2NF, it is also in BCNF. Therefore, no decomposition is required.

c) abc-->d, d-->a
i) The candidate key(s) for r are abc, as it can uniquely determine all other attributes.
ii) The best normal form that r satisfies is 3NF, as all non-prime attributes (d) are fully functionally dependent on the candidate key (abc).
iii) Since r is already in 3NF, it is also in BCNF. Therefore, no decomposition is required.

d) ab-->c, ab-->d, c-->a, d-->b
i) The candidate key(s) for r are ab, as it can uniquely determine all other attributes.
ii) The best normal form that r satisfies is 3NF, as all non-prime attributes (c and d) are fully functionally dependent on the candidate key (ab).
iii) Since r is already in 3NF, it is also in BCNF. Therefore, no decomposition is required.

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Answer:

7918

Step-by-step explanation:

If you round Earth's diameter, I believe that it is 7,918 miles.

I apologize, I am unable to create tables or upload scanned documents. However, I can assist you in calculating the amount each investor will receive in each year based on the given information.

To calculate the amount received by each investor in each year, we need to follow these steps:

Calculate the total profit earned by the bank in each year by subtracting the loss values from zero.

Year 1: 0 - (-78,000) = 78,000

Year 2: 0 - (-23,000) = 23,000

Year 3: 29,000

Year 4: 63,000

Year 5: 103,500

Calculate the total profit to be distributed among the investors in each year, which is 60% of the total profit earned by the bank.

Year 1: 0.6 * 78,000 = 46,800

Year 2: 0.6 * 23,000 = 13,800

Year 3: 0.6 * 29,000 = 17,400

Year 4: 0.6 * 63,000 = 37,800

Year 5: 0.6 * 103,500 = 62,100

Calculate the profit share for each investor based on their respective share of the investment.

Year 1:

Fahad: (30/100) * 46,800

Yashara: (50/100) * 46,800

Saud: (20/100) * 46,800

Fariha: (40/100) * 46,800

Younus: (25/100) * 46,800

Asif: (35/100) * 46,800

Similarly, calculate the profit share for each investor in the remaining years using the same formula.

By following the calculations above, you can determine the amount each investor will receive in each year based on their share of the investment.

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