5. Name the side included by

AB
AC
BC
none of these.

The table is an illustration of a linear function

9. The student's rate

Take any two points from the table

\((x,y) =\{(1,644)\ (4,500)\}\)

The rate is then calculated using:

\(Rate = \frac{y_2 -y_1}{x_2 -x_1}\)

This gives

\(Rate = \frac{644 -500}{1-4}\)

\(Rate = \frac{144}{-3}\)

\(Rate = -48\)

The statement that the student reads at a rate of 48 pages per hour is true

10. The pages in the novel

From the table, there are 644 pages left, after the student read for 1 hour.

This means that there are more than 644 pages in the novel.

The statement that the number of pages in the novel is 644 is false

11. The linear equation

This is calculated as:

\(y = Rate(x -x_1) + y_1\)

So, we have:

\(y = -48(x -1) + 644\)

\(y = -48x +48 + 644\)

\(y = -48x +692\)

The statement that the situation can be represented by the  equation y = -48x + 692 is true

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Answer:

Step-by-step explanation:

Answer:

102.5, 103.5

Step-by-step explanation:

a+a+1=206

2a+1=206

2a=205

a=102.5

103.5

I think there is a bug here. They can't be whole numbers.

Answer:

There are no two consecutive whole numbers that sum to 206 (See proof below)

Step-by-step explanation:

let the first number be x

since the numbers are whole and consecutive, the second number must be (x + 1)

we are given that the number sum to 206

hence,

x + (x+1) = 206

x + x + 1 = 206

2x + 1 = 206  (subtract 1 from both sides)

2x = 206 - 1

2x = 205  (divide both sides by 2)

x  = 205/2 = 102.5  (NOT A WHOLE NUMBER)

if x = 102.5, then the second number must be

x + 1 = 102.5 + 1 + 103.5 (ALSO NOT A WHOLE NUMBER)

Answer:

x = -2 hope it helped

As per question,

\(19x+15=8x−7\)

Solving it,

\(19x - 8x = - 7 - 15\)

\( = > 11x = - (7 + 15)\)

\( = > 11x = - 22\)

\( = > x = - \frac{22}{11}\)

\( = > x = - 2\)

Hence, Value of x is -2

-------------------☆-------------------

( If it shows that the answer isn't -2, then it is some technical error with the system. The answer will however come as -2 only. )

Answer:

Each term in pattern B is 9 less than the corresponding term in pattern A.

Ans

c=9

Step-by-step explanation:

2 x 9 = 18 +9 = 27

Answer:

see below

Step-by-step explanation:

A = {8, 9, 10, 11, 12, 13, 14} and   B = {2, 4, 6, 8, 10, 12, 14, 16, 18}

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

(i) List down the elements of A’ and B’

{8, 9, 10, 11, 12, 13, 14, 2, 4, 6, 8, 10, 12, 14, 16, 18} - this is the elements of both sets

----------

(ii) Are sets A - B and B - A equal sets?

A-B= {9, 11, 13}

B-A= {2, 4, 6, 16, 18}

These are not equal as we can see

----------

(iii) Find and compare the sets (AUB)’ and A’∩B’ and share your observations

A∪B= {2, 4, 6, 8, 9, 10, 11, 12, 13, 14, 16, 18}- union included all elements of both sets

A∩B= {8, 10, 12, 14} - intersection only includes common elements

Answer:

D on edge

Step-by-step explanation:

\(\longrightarrow \sf Slope = -7 \)

\(\longrightarrow \sf y-intercept = 2\)

The equation of any straight line can be written as in slope intercept form as -

\(\green{ \underline { \boxed{ \sf{y=mx+c}}}}\)

where,

\(\leadsto\)Comparing the equation y = -7x+2 with the standard form of the equation, we get -

Hence,

Answer:

What is

Step-by-step explanation:

What is it

The hundreds place is the 0

Answer:

-1 1/2,-1,-1/2,0,1/2,1

Step-by-step explanation:

negatives always go to the least, even if they have a bigger number

Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3

A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.

r = 1 − cosθsin3θ

Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.

The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.

The figure attached shows the bounded region of the two graphs. The red curve is  r=4cos⁡(θ) and the blue curve is r=2.

The points of intersection of the two curves are

θ = π/3 and 5π/3

The area is calculated as follows:

Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.

A = 2 \(\(\int_{0}^{\pi /3}\) ½ (4 cos (θ)² − ½ (2)² dθ

  =  \(\(\int_{0}^{\pi /3}\) 16 cos2 (θ) − 4dθ

  = \(\(\int_{0}^{\pi /3}\) 8 (1+cos(2θ)) − 4dθ

  =\(\(\int_{0}^{\pi /3}\) 4 + 8 cos (2θ) dθ

  = [4θ + 4sin (2θ)] \(\(\int_{0}^{\pi /3}\)

  = 4π/3 + 2√3

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The early finish time for activity t is unknown and needs to be determined.  It cannot be determined from the given information as only the early finish times for activities l, m, and p are given.

To determine the early finish time for activity t, the following steps should be taken:

1. Review the activities that are related to activity t and note their durations.

2. Identify the activities that must be completed before activity t can begin.

3. Calculate the early start time for activity t by adding the duration of all preceding activities.

4. Calculate the early finish time for activity t by adding the early start time and the duration of activity t.

5. Compare the early finish times of activities l, m, and p to the early finish time of activity t.

6. If the early finish time for activity t is greater than any of the other activities, then activity t is the critical activity.

7. If the early finish time for activity t is less than any of the other activities, then activity t is not the critical activity.

8. If the early finish time for activity t is equal to any of the other activities, then activity t could be the critical activity and further investigation is required.

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The area of a regular hexagon can be calculated using the formula A = (3√3/2) * s^2, where A is the area and s is the length of each side.

In this case, the hexagon has a radius of 5 inches, so the length of each side can be found by multiplying the radius by 2 and dividing it by the square root of 3. Substituting the side length into the formula gives the area of the regular hexagon.

The formula for calculating the area of a regular hexagon is derived from its relationship to an equilateral triangle. The regular hexagon can be divided into six equilateral triangles, where the side length of the hexagon is equal to the base of each equilateral triangle.

The formula A = (3√3/2) * s^2 is a result of the area formula for an equilateral triangle, where s is the length of each side. In this case, the radius of the hexagon is given as 5 inches. To find the length of each side, we multiply the radius by 2 and divide it by the square root of 3. Substituting this value into the formula gives us the area of the regular hexagon.

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Answer:

True

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer

Area = 324π ft²

Explanation

The area of a circle is given as

Area = πr²

where

π = pi

r = radius of the circle = 18 ft.

Area = πr²

Area = π (18²)

Area = 324π ft²

Hope this Helps!!!

Answer:

118%

Step-by-step explanation:

weight at first visit = 550g

weight at 2nd visit = 550 + 350 = 900g

weight at 3rd visit = 900 + 300 = 1200g

Percentage increase = \(\frac{1200-550}{550} \times100=118.181818...\) = 118%

To solve this problem, we need to use the Central Limit Theorem (CLT) since we have a large number of independent images (80) and we want to calculate the probability of the total size falling within a certain range.

The CLT states that the sum of a large number of independent and identically distributed random variables approaches a normal distribution, regardless of the shape of the original distribution.

In this case, the sum of the sizes of the 80 images will also follow a normal distribution. The mean of the sum is the product of the average size of one image (0.6 megabytes) and the number of images (80), which is 48 megabytes (0.6 * 80).

The standard deviation of the sum is the product of the standard deviation of one image (0.4 megabytes) and the square root of the number of images (square root of 80), which is approximately 3.5777 megabytes (0.4 * sqrt(80)).

Now we can standardize the range of interest using the formula for standardizing a variable:

Z = (X - μ) / σ

where Z is the standardized value, X is the value of interest, μ is the mean, and σ is the standard deviation.

For the lower bound of 47 megabytes:

Z1 = (47 - 48) / 3.5777

For the upper bound of 50 megabytes:

Z2 = (50 - 48) / 3.5777

Now, we can use a standard normal distribution table or a calculator to find the probabilities associated with these standardized values.

P(47 ≤ X ≤ 50) = P(Z1 ≤ Z ≤ Z2)

By looking up the values of Z1 and Z2 in the standard normal distribution table or using a calculator, we can find the corresponding probabilities.

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Firstly, the student's graph is not a correct representation of the piecewise function, We would consider each function.

1. f(x) = x + 3 for x ≤ - 2

The graph is correct but the interval was not represented correctly. To correct it, the circle at x = 2 should be solid

2) f(x) = x^2 - 1 for - 2 < x < 1

The graph is correct but the interval was not represented correctly. To correct it, the circles at x = - 2 and x = 1 shouldn't be solid

3) f(x) = log2(- x + 3) for 1 ≤ x < 3

The graph is not correct. To correct it, values of x should be substituted into the function and the correct values of y or f(x) would be calculated for. These values of x and y should be used to plot the graph again. For the intervals, the circle at x = 1 should be solid while the circle at x = 3 shouldn't be solid

Answer:

c

Step-by-step explanation:

Answer: yellow box

Step-by-step explanation:

Answer:

3rd Option

Step-by-step explanation:

5^2 = 25

2^5 = 32

3^3 = 27

6^4 = 2196

Answer:

Let's call the number of soldiers that should leave the group as x.

We know that the group of 30 soldiers has enough food for 40 days. And we want to find the number of soldiers that should leave the group so that the food is enough for 100 days for remaining soldiers.

We can use the proportion of soldiers to days of food to find the number of soldiers needed for 100 days of food.

30/40 = (30-x) / 100

We can cross-multiply and then solve for x:

1200 = 30x - x^2

x^2 + 30x -1200 = 0

x = 20 or x = -40

20 is the valid solution, so 20 soldiers should leave the group.

So, 20 soldiers should leave the group so that the food is enough for 100 days for remaining soldiers.

Let's calculate the interest he will accumulate in 1 year:

1.5% of 1600

Note: 1.5% = 1.5/100 = 0.015

So,

0.015 * 1600 = $24 (in 1 yr)

Thus, in 17 years, he will get:

17 * 24 = $408 [total simple interest in 17 years]

Now,

So, total amount he will accumulate after 17 years is the initial amount PLUS interest. That would be:

1600 + 408 =

Answer: 70%

Step-by-step explanation:

First, add 5.25 with 2.25 = 7.5 MB

7.5 MB is the total that can be downloaded

We know that it used 5.25 MB

So take 5.25 divided by 7.5, then times 100% = 70%

Answer:

x=4

Step-by-step explanation:

9+x=13

x=4

Answer:

The number is 4

Step-by-step explanation:

Let the number = x

Nine more than a number: x +9

x + 9 = 13

Subtract 9 from both sides

x + 9 -9 = 13 - 9

x = 4

Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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y =\((x/2)^2 + 1 or y = (x/2)^2 + 1\)

The curve represents a parabola opening upwards. It is symmetric about the y-axis.

Let's eliminate the parameter t and sketch the curves for each exercise:

1. x = t^2 + 2t, y = t + 1

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 + 2t = x

t = -1 ± √(x + 1)

Substituting the expression for t into the equation y = t + 1, we get:

y = (-1 ± √(x + 1)) + 1

y = -√(x + 1) or y = √(x + 1)

The curve represents two branches of a parabola opening upwards. It is symmetric about the y-axis.

2. x = cos(t), y = sin(t), (0, 2π]

Eliminating the parameter t, we obtain:

\(x^2 + y^2 = cos^2(t) + sin^2(t) \\= 1\)

The curve represents a circle centered at the origin with a radius of 1. It covers a full revolution (360 degrees or 2π) in the counterclockwise direction.

3. x = 2t + 4, y = t - 1

By eliminating the parameter t, we have:

t = (x - 4) / 2

Substituting this expression into the equation for y, we get:

y = ((x - 4) / 2) - 1

y = (x - 6) / 2

The curve represents a line with a slope of 1/2 and a y-intercept of -3. It is inclined upwards from left to right.

4. x = 3 - t, y = 2t - 3, 1.5 ≤ t ≤ 3

Eliminating the parameter t, we have:

t = 3 - x

Substituting this expression into the equation for y, we get:

y = 2(3 - x) - 3

y = 6 - 2x - 3

y = -2x + 3

The curve represents a line with a slope of -2 and a y-intercept of 3. It is inclined downwards from left to right.

\(5. x = 2t^2, y = t^4 + 1\)

To eliminate the parameter t, we can solve the first equation for t and substitute it into the second equation:

t^2 = x/2

t = ±√(x/2)

Substituting the expressions for t into the equation y = t^4 + 1, we get:

y = (√(\(x/2))^4\) + 1 or y = (-√\((x/2))^4\) + 1

\(y = (x/2)^2 + 1 or y = (x/2)^2 + 1\)

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Answer:

hence the value of x is either 5 or 2

x=5 or x=2

Answer:

the hundredth place value

Answer:the hundredth place value

Step-by-step explanation: