Consider the recurrence relation that arose in Example 11.3.7: E1 = 0 and Ek = Ek−1 + k + 1 + 2, for all integers k ≥ 2.
a. Use iteration to find an explicit formula for the sequence.

The calculated value of the angle x is 58 degrees

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

The triangle

Using the sum of opposite external angles, we have the following equation

114 = 56 + x

When the like terms are evaluated, we have

x = 114 - 56

Evaluate

x = 58

Hence, the value of x is 58

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The equation of the linear graph is y = x-2

A linear equation is an algebraic equation of the form y=mx+c. involving only a constant and a first-order (linear) term, where m is the slope and c is the y-intercept. Linear equation can also be defined as an equation with the highest power of the variable to be 1.

on the graph, the y intercept is the point where the graph line crosses the y axis. Therefore the y intercept is -2

The slope of the line = 0-(-2)/2-0

slope = 2/2 = 1

therefore the equation of the graph is ;

y = mx+c

y = x+(-2)

y = x-2

therefore the equation of the linear graph = y = x-2

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Answer:

1/6

Step-by-step explanation:

gradient= change in y/ change in x

-4--5/2--4= 1/6

1/6 is the gradient

The gradient of the line segment in its simplest form is: 1/6.

Given the following points, (-4,-5) and (2,-4) are on a line segment:

Gradient (m) = change in y / change in x

Gradient (m) = (-4 -(-5))/(2 -(-4))

Gradient (m) = 1/6

Therefore, the gradient of the line segment in its simplest form is: 1/6.

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Let

S = 1 + 2 + 3 + … + (n - 2) + (n - 1) + n

Reversing the order of terms, we have

S = n + (n - 1) + (n - 2) + … + 3 + 2 + 1

and we observe that terms in the same position on the right side add up to n + 1.

2S = (1 + n) + (2 + (n - 1)) + (3 + (n - 2)) + … + (n + 1)

There are n terms in the sum, so each the right side is simply n copies of n + 1, and

2S = n (n + 1)

S = n (n + 1)/2

Now,

17 + 18 + 19 + … + 41 + 42 + 43

= (1 + 2 + 3 + … + 41 + 42 + 43) - (1 + 2 + 3 + … + 14 + 15 + 16)

= (S with 43 terms) - (S with 16 terms)

= 43 (43 + 1)/2 - 16 (16 + 1)/2

= 810

Answer:

3,6,9,12,15,18,21}

B={4,8,12,16,20}

C={2,4,6,8,10,12,14,16}

D={5,10,15,20}

(i) A−B={3,6,9,15,18,21}

(ii) A−C={3,9,15,18,21}

(iii) A−D={3,6,9,12,18,21}

(iv) B−A={4,8,16,20}

(v) C−A={2,4,8,10,14,16}

(vi) D−A={5,10,20}

(vii) B−C={20}

(viii) B−D={4,8,12,16}

(ix) C−B={2,6,10,14}

(x) D−B={5,10,15}

(xi) C−D={2,4,6,8,12,14,16}

To determine the number of smaller boxes that would contain the same amount of cereal as a larger box, we set the expressions representing the cereal content equal to each other. Solving the equation, we find that 15 smaller boxes are required to match the cereal quantity in the larger box.

To find the number of smaller boxes that equal the same amount of cereal in a larger box, we need to equate the two expressions and solve for n.

Setting the expressions equal to each other:

10 + 6.3n = 7 + 6.5n

Simplifying the equation:

6.3n - 6.5n = 7 - 10

-0.2n = -3

Dividing both sides by -0.2:

n = -3 / -0.2

n = 15

Therefore, 15 smaller boxes would equal the same amount of cereal as the larger box.

The problem states that the expressions 10 + 6.3n and 7 + 6.5n represent the amount of cereal in the new larger box. The variable n represents the number of smaller boxes.

To find how many smaller boxes are equivalent to the larger box, we need to set the two expressions equal to each other and solve for n. This equation represents the balance between the amount of cereal in the larger box and the combined amount of cereal in the smaller boxes.

By simplifying the equation and solving for n, we find that 15 smaller boxes are needed to equal the same amount of cereal as the larger box.

This means that if the cereal manufacturer wants to package the same amount of cereal as the larger box, they would need to use 15 smaller boxes instead. This calculation helps the manufacturer determine the number of smaller boxes needed to maintain the same quantity of cereal while changing the box size.

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Answer:

8x+8(y)/(x^(2))=x^(2)-(y^(2))/(x^(2))

x^(2)-(y^(2))/(x^(2)) = x^(2)-(y^(2))/(x^(2))

Step-by-step explanation:

Answer:C

Step-by-step explanation:

Answer:

Your answer should be A.

Step-by-step explanation:

3.50 is the base price but it adds 2.50 per mile that would make it 3.50 + 2.50x but you want it to be less than 4x so you'll put the inequality symbol with the open side facing the 4x because you want that to be the greater side.

this should be correct

Answer:

The mean is lower than the median which is lower than the mode.

Step-by-step explanation:

Answer:

48.

Step-by-step explanation:

12x4=48

Unit conversion converts one unit into another without changing its real value. The Four one-foot rulers laid end to end will have 48 inches.

Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimeter is equal to 10 mm,

though the real measurement is still the same the units and numerical values have been changed.

We know that the 1 foot has 12 inches in it, therefore, when the Four one-foot rulers laid end to end will have 4 feet in total, and since one foot has 12 inches, thus,

\(\begin{aligned}\rm 4\ feet &= 4 \times 12\ inches\\&=48\rm\ inches\end{aligned}\)

Hence, the Four one-foot rulers laid end to end will have 48 inches.

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Answer:

0.01949025487

Step-by-step explanation:

Answer:

If it's zero it's neither of them because zero is not a number to multiply with because it will always be zero when multiplying with zero

Answer:

(-2,-1)

Step-by-step explanation:

Don't mind the back

(x,y) = (-x,-y)

Answer:

1

Step-by-step explanation:

5÷1000=0.005

0.005 ≈ 1 (1 is the nearest whole number)

Hope this helps!

The number 5 divided by 1,000 is approximately 0 when rounded to the nearest whole number.

To divide 5 by 1,000, we simply perform the division:

5 ÷ 1,000 = 0.005

Now, to round the result to the nearest whole number, we examine the first decimal place. Since it is less than 5, we round down to the nearest whole number.

Thus, the rounded result is 0.

Rounding is a process used to simplify numbers to a certain level of precision. When rounding to the nearest whole number, we look at the digit to the right of the decimal point (the first decimal place). If this digit is 5 or greater, we round up to the next whole number. If it is less than 5, we round down to the current whole number.

In this case, 0.005 is less than 0.5, so we round down to 0.

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The end behavior of the given polynomial is that as x → -∞ or  x → ∞, then, f(x) → 5

We are given the polynomial;

f(x) = 5x/(x - 25)

Now, we want to find the limits as x → ±∞. Let us rearrange the given polynomial to get; f(x) = 5/(1 - (25/x))

Thus, applying limits we have;'

lim x → ±∞ [5/(1 - (25/x))]

From algebraic limit laws we know that;

If f(x) = k, then;

lim x → +∞ [f(x)] = k

Also, lim x → -∞ [f(x)] = k

Thus, applying limits at infinity to our polynomial gives;

lim x → ±∞ [5/(1 - (25/x))] = 5/(1 - 0) = 5

This is because lim x → ∞ for 1/x is 0.

Thus, f(x) has horizontal asymptotes at y = 5

Thus, we conclude that the end behavior is that as x → -∞ or  x → ∞, then, f(x) → 5

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Answer:

She will actually do it on the 35th day of gym

The correct answer for detecting nonrandomness in errors is E. control charts. Control charts are a statistical tool used to monitor processes and detect deviations from randomness or expected behavior. They are commonly used in quality control and process improvement to identify any systematic or nonrandom patterns in the data.

Control charts help visualize data over time and compare it to predetermined control limits. If the data falls within these limits and shows a random pattern, it suggests that the process is stable and operating within acceptable limits of variation. However, if the data exhibits nonrandom patterns, such as trends, cycles, or unusual points, it indicates the presence of special causes or systematic errors in the process. By analyzing the control chart, individuals can identify the sources of nonrandomness, investigate the underlying causes, and take corrective actions to improve the process and reduce errors. Therefore, control charts provide an effective method to detect nonrandomness and ensure the quality and consistency of processes.

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Answer:

Step-by-step explanation:

Answer:

\(\displaystyle \frac{28}{15}\; \text{radians}\), which is approximately \(107^{\circ}\).

Step-by-step explanation:

In a given circle, the angle of a sector is proportional to the length of the corresponding arc:

\(\displaystyle \frac{\text{angle of sector $1$}}{\text{angle of sector $2$}} = \frac{\text{length of arc of sector $1$}}{\text{length of arc of sector $2$}}\).

For the circle in this question, \(r = 15\; \rm cm\), and the circumference would be:

\(2\, \pi \, r = 30\, \pi\; \rm cm\).

The full circle itself is like a sector with an angle of \(2\, \pi\), with the arc length equal to the circumference of the circle.

\(\displaystyle \frac{\text{angle of sector}}{\text{angle of full circle}} = \frac{\text{length of arc of sector}}{\text{circumference of circle}}\).

\(\displaystyle \frac{\text{angle of sector}}{2\,\pi\; \rm rad} = \frac{28\; \rm cm}{30\, \pi\; \rm cm}\).

Rearrange the equation to find the angle of the sector:

\(\begin{aligned} & \text{angle of sector} \\ =\; & (2\,\pi\; \rm rad) \cdot \frac{28\; \rm cm}{30\, \pi\; \rm cm} \\ =\; & \frac{28}{15}\; \rm rad\end{aligned}\).

In other words, the angle of this sector would be \(\displaystyle \frac{28}{15}\; \rm rad\). Multiply that measure in radians by \(\displaystyle \frac{360^{\circ}}{2\,\pi\; \rm rad}\) to find the value of the angle measured in degrees:

\(\begin{aligned} & \frac{28}{15}\; \rm rad \times \frac{360^{\circ}}{2\,\pi\; \rm rad} \approx 107^{\circ}\end{aligned}\).

If 16 ounce bottle of orange juice contain 200 milligram was 250% from total of daily recommended amount , then 100% or recommended vitamin C to daily consume is 80 milligram.

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The Equation of circle is (x-2)² +(y+ 8)² = 7²

The standard form of a circle with center (h, k) and radius r is given by the equation:

(x-h)²  + (y-k)² = r²

In this equation, (h, k) represents the coordinates of the center of the circle, and r represents the radius of the circle.

In this case, the center of the circle is (2, -8) and the radius is 7.

Plugging these values into the equation, we have:

(x- 2)² + (y- (-8))² = 7²

Simplifying further:

(x-2)² +(y+ 8)² = 7²

So, the equation in standard form for the circle with center (2, -8) and radius 7 is:

(x-2)² +(y+ 8)² = 7²

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Answer:

y=3x+8

2y=6x+16

2(3x+8)=6x+16

6x+16=6x+16

Infinite Many Solutions

Step-by-step explanation:

Let the other rational number be represented by "x". We know that the difference of the two rational numbers is 17/28, which can be written as:

x - (-9/14) = 17/28

Simplifying the left-hand side:

x + 9/14 = 17/28

Multiplying both sides by the least common multiple of 14 and 28, which is 28, we get:

28(x + 9/14) = 28(17/28)

Simplifying:

4(2x + 9) = 17

Expanding:

8x + 36 = 17

Subtracting 36 from both sides:

8x = -19

Dividing by 8:

x = -19/8

Therefore, the other rational number is -19/8.

Answer:

1) 26mm

2) 2mm x (years of age) = 26

Step-by-step explanation:

Answer:

answer is 1

Step-by-step explanation:

Answer:

(-4)-(-2)-{(-5)-[(-7)+(-3)-(-8)]}

=-4+2-{-5-[-7-3+8]

=2-{-5-[-2]}

=2-{-5+2}

=2+3

=5

Step-by-step explanation:

Answer: Graph D

Step-by-step explanation:

The slope is 2

x goes after the slope in graph functions

The line goes through 3 on the y-axis so that’s where + 3 comes in.

2x + 3

Answer:

y = -1x + 5

Step-by-step explanation: