- Use an appropriate formula to calculate how many terms there are in the sequence
2, 10, 50, ...31250.

*please put full solution

Answer:

Both of them work

Step-by-step explanation:

by multiplying the first equation by 2 it creates the same coefficient in front of "p" for both equations. same for the second equation and "q".

Both strategies works since we can easily eliminate a variable from both equations.

Given the simultaneous equation solved by Tyler

4p + 2q = 62

8p - q = 59

In order for him to eliminate a variable to solve the system of equations, he must ensure that the coeffiecient of the variable to be eliminated are equations in both expressions. To do that;

8p + 4g = 124

8p - q = 59

Subtract

4q + q = 124 + 59

5q = 183

The second required strategy is  to Multiply 8p-q=59 by 2, then add the result to 4p + 2q = 62, to have:

16p-2q=118

4p + 2q = 62

Adding up

16p + 4p = 118 + 62

20p = 180

p = 9

We can see that both strategies works since we can easily eliminate a variable from both equations.

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A) If Mari travels 2 ft, Anya travels for a distance of 4 ft

B) If Mari travels M ft, Anya travels for a distance of 2M ft

D)  D represents the varying distance in (feet) between Mari and Anya. D = 160 - 3M

E) If Anya walks 25% faster than Mari, Anya's travel if Mari walks M feet is M + 0.25M

A) If Mari travels 2 ft Anya will travel 4ft because Anya is jogging, and travels twice as fast as Mari.

Anya travels twice as fast as Mari

Mari travels = 2ft

Anya travel = 2 × 2

Arya travels = 4 ft

B) If Mari travels M ft, Anya travels 2M ft because Anya is jogging, and travels twice as fast as Mari.

Anya travels twice as fast as Mari

Mari travels = M ft

Anya travel = 2 × M

Arya travels = 2M ft

C)Refer to diagram

D) Total distance = 160

Distance between them = D

Distance between = total distance - total distance covered by Anya and Mari  

D = 160 -(2M +M)

D = 160 - 3M

E) Anya walks 25% faster than Mari

Anya travel = Mari walks + 25% Mari walks

Anya travel if Mari walks: 4 feet

= 4 +0.25(4)

= 5 feet

Anya travel if Mari walks: 5 feet

= 4 +0.25(5)

= 5.25 feet

Anya travel if Mari walks: M feet

=  M + 0.25(M)

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Answer:

\(-16/5 < s < 4\)

Step-by-step explanation:

\(|5s-2|-6 < 12 \\ |5s-2| < 18 \\-(5s-2) < 18 \\ -5s+2 < 18 \\ -5s < 16 \\ -s < (16/5) \\ s > -(16/5) \\(5s-2) < 18 \\ 5s < 20 \\ s < 4 \\= -16/5 < s < 4\)

Answer:

75 over 100

Step-by-step explanation:

To find the probability of "no blue," we need to find the probability of drawing two white marbles. The probability of drawing a white marble in one draw is 5/7. So, the probability of drawing two white marbles is (5/7) * (5/7) = 25/49.

Therefore, the probability of "no blue" is 25/49 = 25/100 = 25%.

So, the answer is D. 75 over 100.

Answer: 27/100 or twenty-seven over one hundred

Step-by-step explanation:

We are trying to find the outcome that does not contain blue. The only one that does not contain blue is (White, White) (27)

Therefore 27/100 is the right answer because it does not have any blue.

Answer:

The number is 42.

The given fractions have equal value, so Liam is correct.

Equivalent fractions are defined as fractions that have different numerators and denominators but the same value. For example, 2/4 and 3/6 are equivalent fractions because they are both equal to 1/2. A fraction is part of a whole. Equivalent fractions represent the same part of a whole.  

Liam is claiming that the fraction -(5/12) is equivalent to 5/-12.

Thus, we can say that:

The fraction  -(5/12) can be described as the opposite of a positive number divided by a positive number. A positive number divided by a positive number always results in a positive quotient and its' opposite is always negative.

The fraction 5/-12 can be described as a positive number divided by a negative number which always results in a negative quotient

The fractions have equal value, so Liam is correct

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Answer:

Step-by-step explanation:

4,800 cm Units

Answer:

10.7 + 2 + 10.9 10.9 x 30.9 is 336.81

Step-by-step explanation:

BIG BRAIN POWER

The correct answer is C) The initial population at the time of the estimation

Explanation:

A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.

Answer:

yes the 3ed answer in correct on ENG 2022

To design ac to meet the specifications in problem 1c, we need to determine the desired closed-loop pole location. Once we have the desired pole location, we can design the PD compensator to place one of the poles at that location.

To design a PID compensator to meet the specifications in problem 1b, we need to consider both the desired pole location and zero location. The pole location determines the system's transient response, while the zero location affects the steady-state response. By adjusting the locations of the pole and zero, we can achieve the desired performance specifications.

To sketch the , we plot the loci of the closed-loop poles as we vary the compensator gain. We include the effect of the compensator in the open-loop transfer function and analyze how the poles move in the complex plane. The sketch helps us understand the stability and transient response characteristics of the system with the compensator

To obtain MATLAB plots of the step and ramp responses for the PD and PID compensators, we can use the `step` and `lsim` functions in MATLAB. By simulating the response of the system with different compensator gains, we can observe the system's performance in terms of settling time (Ts), maximum overshoot (Mp), and steady-state error. We can adjust the compensator parameters until the desired performance specifications are met. Overall, designing the PD and PID compensators involves determining the desired closed-loop pole and zero locations, sketching the compensated root locus, and simulating the system's response using MATLAB to fine-tune the compensator parameters and meet the given specifications.

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The number line shows the yards gained or lost by a team during a football game.

To find the difference in yards between the third down and first down, we need to look at the positions of the markers for these downs on the number line. If we assume that the team started at the 0 yard line, we can use the number line to determine the yards gained or lost on each play. For example, if the team gains 5 yards on first down, the marker would move to the right 5 units on the number line. If they lose 3 yards on second down, the marker would move 3 units to the left. We can continue this process until we reach the marker for the third down. Then, we can calculate the difference in yards between the third down and first down by subtracting the position of the third down marker from the position of the first down marker. This difference will be the number of yards gained or lost by the team during these downs. It is difficult to provide a specific answer without a visual representation of the number line and the positions of the markers, but this method can be used to find the difference in yards between any two downs.

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Answer:

0

Step-by-step explanation:

A tangent line is a line that touches the circle's circumference at only one point.

Given two concentric circles one with radius \(r_1\) and the second with radius \(r_2\), and \(r_1>r_2\). SInce \(r_2\) is inside the smaller circle, there is no way it would intersect with the tangent line t.

Therefore, there are no points of intersection between the tangent line t and    \(r_2\) .

Answer: The unit value of a cubic centimeter (cm^3) is the same as the metric measurement of a milliliter (mL).

This is because 1 milliliter is equal to 1 cubic centimeter. In other words, if you have a cube that measures 1 centimeter on each side, its volume would be 1 cubic centimeter, which would also be equivalent to 1 milliliter of volume.

This relationship between cm^3 and mL is commonly used in scientific and medical measurements involving liquids and gases.

The unit value of a cubic centimeter (cc) is equivalent to one milliliter (mL) in the metric system. Both cubic centimeters and milliliters are used to measure volume, and their conversion is straightforward: 1 cc = 1 mL.

The metric system uses base units such as meters, liters, and grams, and applies prefixes like kilo-, centi-, and milli- to indicate larger or smaller units of measurement.
Cubic centimeters are often used to measure the volume of solid objects or the capacity of containers, while milliliters are more commonly used to measure the volume of liquids. However, both units represent the same volume and can be used interchangeably.
It is important to understand the difference between volume measurements and other metric measurements, such as length or mass. For instance, meters are used to measure length or distance, and grams are used to measure mass or weight. These units cannot be directly converted to cubic centimeters or milliliters, as they represent different physical properties.
In summary, a cubic centimeter (cc) is a unit of volume in the metric system that is equivalent to one milliliter (mL). Both units can be used to measure volume, and they have a simple conversion of 1 cc = 1 mL. Understanding the relationship between these units and other metric measurements is essential for accurately quantifying and comparing different physical properties.

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Answer:

16

Step-by-step explanation:

you back track the numbers such as 4 goes back to 2 and 28 goes back to 22 then again and you get x as 9 and y as 16

The distance from the origin to the line given by the parametric equations x = 1 + t, y = 2 - t, z = -1 + 2t is 3/√6.

To find the distance from the origin to the line, we can use the formula for the distance between a point and a line in 3D space. The formula is given by d = |AP × n| / |n|, where AP is the vector from any point on the line to the origin, n is the direction vector of the line, and |.| denotes the magnitude of a vector.

We can choose the point (1, 2, -1) on the line and the direction vector n = (1, -1, 2).

Calculating the cross product AP × n, we have:

AP = (-1, -2, 1) and AP × n = (-5, -3, -3).

The magnitude of AP × n is |AP × n| = √((-5)^2 + (-3)^2 + (-3)^2) = √43.

The magnitude of the direction vector n is |n| = √(1^2 + (-1)^2 + 2^2) = √6.

Substituting these values into the distance formula, we get:

d = |AP × n| / |n| = √43 / √6 = (3√6) / 2√6 = 3 / √6.

Therefore, the distance from the origin to the line is 3/√6.

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If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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In the fraction form, each friend ate 1/2 out of 2 total pizzas, or 1/4 of a pizza per pizza.

To solve this problem, we need to use fractions. The part we are interested in is the fraction of a pizza each friend ate.

Since each friend ate half of a pizza, we can write this as 1/2. This means that each friend ate one-half of a pizza, which is one part out of two equal parts that make up a whole pizza.

To find out what fraction of the total two pizzas each friend ate, we need to add up the fractions for each friend. Since there are two friends, we need to add the fraction 1/2 twice:

1/2 + 1/2 = 2/2

When we add these two fractions together, we get a total of 2/2. This fraction simplifies to 1, which means that each friend ate one whole pizza.

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Answer:

B. The graph on the first row that is in the middle.

Step-by-step explanation:

4/5 Rise/run. That means it goes up 4 units for every 5 units it goes right.

Answer:

I believe it is the first one. I know it isn't the second one

The interval that contains the median 25.5 is

(5 - 10)

The median is the value that's exactly in the middle of a dataset when it is ordered.

We have a histogram as given below.

We need to make a table of class intervals and their frequency:

class interval      frequency

0-5                       22

5-10                       5

10-15                       9

15-20                      9

20-25                      5

25-30                      1

We also need to find the cumulative frequency.

class interval      frequency    cumulative frequency

0-5                       22                 22

5-10                       5                   22 + 5 = 27

10-15                       9                  27 + 9 = 36

15-20                      9                   36 + 9 = 45

20-25                      5                   45 + 5 = 50

25-30                      1                      50 + 1 = 51

Now,

The number of questions = 50 ( even number)

Median:

= (50 + 1) / 2

= 51 / 2

= 25.5

We need to select the cumulative frequency where it is greater than the median.

So we have 27 which is at the interval (5 - 10).

Thus the interval that contains the median 25.5 is (5 - 10)

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The possible dimensions for the smallest perimeter of the given rectangle are 4inches each and smallest perimeter is 16inches.

As given in the questions,

Area of the rectangle = 16 square inches

Let x and y be the length and width of the rectangle

Factors of 16 are 2, 4, 8, 16

16 = 2 × 8  or 4 × 4 or 16 × 1

Perimeter of the rectangle using this dimensions are

= 2( x + y)

When x = 2 , y =8

Perimeter = 20 inches

When x = 4 and y =4

Perimeter = 16inches

When x = 1 and y = 16

Perimeter = 34inches

Smallest perimeter is 16inches

Dimensions are 4 inches each

Therefore, the dimensions and smallest perimeter for the given area of rectangle is equal to 4 inches each and 16inches respectively.

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The minimized SOP expression for F(A,B,C,D,E) using a five-variable Karnaugh map is D'E' + BCE'. A five-variable Karnaugh map is a graphical tool used to simplify Boolean expressions.

The map consists of a grid with input variables A, B, C, D, and E as the column and row headings. The cell entries in the map correspond to the output values of the logic function for the respective input combinations.

To find the minimized SOP expression, we start by marking the cells in the Karnaugh map corresponding to the minterms given in the function: 2m(4,5,6,7,9,11,13,15,16,18,27,28,31). These cells are identified by their binary representations.

Next, we look for adjacent marked cells in groups of 1s, 2s, 4s, and 8s. These groups represent terms that can be combined to form a simplified expression. In this case, we find a group of 1s in the map that corresponds to the term D'E' and a group of 2s that corresponds to the term BCE'. Combining these groups, we obtain the expression D'E' + BCE'.

The final step is to check for any remaining cells that are not covered by the combined terms. In this case, there are no remaining cells. Therefore, the minimized SOP expression for the given logic function F(A,B,C,D,E) is D'E' + BCE'.

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Answer:

13

Step-by-step explanation:

39/3

Answer:1 4 2

Step-by-step explanation:

In the 2012 Gallup survey, a random sample of 474,195 U.S. adults was interviewed by phone to gather information about their work status, height, and weight.

The objective was to determine the prevalence of obesity (defined as having a body mass index greater than 30) among different work status groups. The survey found that 24.9% of the participants who were employed (either full-time or part-time by choice) were classified as obese. In contrast, 28.6% of the participants who were unemployed and actively seeking work were also found to be obese. This indicates that there may be a relationship between employment status and obesity rates in the U.S. adult population.

However, it is important to note that correlation does not necessarily imply causation, and various factors could contribute to these findings. Further research may be necessary to determine the underlying causes behind the differences in obesity rates among employed and unemployed individuals.

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Area of semicircle is 76.93 \(units^{2}\).

Given,

Diameter = 14 units

Radius = r = 14/2

                 = 7 units

Area of semicircle = \(\frac{1}{2}\pi r^{2}\)

                               = (3.14*7*7)/2

                               = 153.86/2

                               = 76.93

Hence, Area of semicircle is 76.93 \(units^{2}\).

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Answer:

x = 122°

Step-by-step explanation:

There is remote angle( non- adjecent angle) and their sum equal to the exterior angle .

Exterior angle is an angle formed from one side of the polygone and the extended side so

<A and <B are remot angle and <BCD is exterior angle .

And we write the equetion as

<A + <B = <BCD

58° + 64° = x°

122° = X°

so the exterior angle ( x ) measures 122° .

Since triangles abc and xyz are similar, their corresponding sides are proportional.

Let's label the sides of triangle xyz as a, b, and c. We know that the smallest side of xyz (side a) is 52 cm. We need to find the length of the longest side of xyz (which we can label as side c).
We can set up a proportion to solve for c:  121/52 = 105/b = 98/c
Solving for b, we get:  121/52 = 105/b
b = (105*52)/121
b ≈ 45.6
Now we can set up a new proportion to solve for c:  121/52 = 98/c
Multiplying both sides by c, we get:  121c/52 = 98
Solving for c, we get:
c = (98*52)/121
c ≈ 42.3
Therefore, the length of the longest side of xyz is approximately 42.3 cm.

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B = -9/2

Hopefully this helps and this is what you're looking for.