below is the graph of a trigonometric function it has a maximum point at (-pi , 7.7) and a minimum point at (- 1/3 pi, -6.7)
what is the period of the function? give an exact value

Below Is The Graph Of A Trigonometric Function It Has A Maximum Point At (-pi , 7.7) And A Minimum Point

Answers

Answer 1

The period of the trigonometric function is -2π/3.

What is the period of the function?

To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.

Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.

The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.

The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:

Δx = -1/3π - (-π) = π/3π - π = -π/3

Since the full period is twice this distance, we multiply by 2:

2 * (-π/3) = -2π/3

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Related Questions

Como se llama un ángulo de 192 grados?

Answers

Answer:

reflex angle

Step-by-step explanation:

the angle of 192 degrees is called a reflex angle

.

At a meat packing plant in Green Bay, the owners want to begin a continuing education program so their 186 employees can get a college education online if they desire. The following table represents an incomplete picture of the results. Use the following two-way frequency table for the questions below:




Men Women Total
No College Credit 28 A B
Some College C D 81
College Graduate 15 22 E
Total 79 F 186

a. Fill in the missing data in the table for values A through F. Explain the strategies you used to get each answer.

b. Describe a few pieces of data in terms of joint relative frequency. Explain why these data are both joint and relative.

c. Explain a few ways we can summarize pieces of this table using conditional relative and marginal relative frequency.

d. Are the data independent or dependent? Why?

Answers

Answer:

a. To fill in the missing data in the table, we can use the information given in the table along with the fact that the total number of employees is 186.

For value A: Since the total number of employees with no college credit is 28, and the total number of men is 79, we can subtract the number of men with some college (C) and college graduates (15) from the total number of men to find the missing value A. So A = 79 - C - 15.

For value B: Since the total number of women is 186, we can subtract the number of women with some college (D) and college graduates (22) from the total number of women to find the missing value B. So B = 186 - D - 22.

For value C: Since the total number of employees with some college is 81, and we have already determined the values A and D, we can subtract A and D from the total number of employees with some college to find the missing value C. So C = 81 - A - D.

For value D: Similarly, we can subtract B and E from the total number of women to find the missing value D. So D = 186 - B - E.

For value E: Since the total number of college graduates is 37 (15 men + 22 women), we can subtract the number of college graduates among men (15) from the total to find the missing value E. So E = 37 - 15.

For value F: Since the total number of employees is 186, we can subtract the total number of men (79) from the total to find the missing value F. So F = 186 - 79.

b. Joint relative frequency refers to the proportion of individuals that fall into a particular combination of categories. For example, the joint relative frequency of men with no college credit is the number of men with no college credit divided by the total number of employees (28/186). These data are joint and relative because they represent the proportion of individuals in a specific category combination relative to the total population.

c. To summarize the data using conditional relative frequency, we can calculate the proportion of individuals in each category given a specific condition. For example, we can calculate the conditional relative frequency of women who are college graduates by dividing the number of women who are college graduates (22) by the total number of women (186). Similarly, we can calculate the conditional relative frequency of men with some college by dividing the number of men with some college (C) by the total number of men (79).

To summarize the data using marginal relative frequency, we can calculate the proportion of individuals in each category by dividing the number of individuals in that category by the total number of individuals. For example, we can calculate the marginal relative frequency of men by dividing the total number of men (79) by the total number of employees (186). Similarly, we can calculate the marginal relative frequency of college graduates by dividing the total number of college graduates (37) by the total number of employees (186).

d. The data in the table can be analyzed to determine if there is an association or relationship between the variables. If the values in the table change depending on the categories of the other variable, then the variables are dependent. In this case, the data is dependent because the number of individuals with certain educational levels (no college credit, some college, college graduate) varies based on their gender. For example, there are different proportions of men and women in each educational category, indicating a relationship between gender and education level.

Step-by-step explanation:

Final answer:

The missing values in the two-way frequency table are filled based on the given values and the composition of the table. The table represents joint relative frequency, which is the proportion of specific groups in the total population. We can summarize the data using marginal and conditional relative frequencies, and the data are considered dependent because an employee's education level depends on their gender.

Explanation:

To fill in the missing values of the two-way frequency table, we need to use the given numbers and the rules of the two-way frequency table. Here are the strategies used for filling in the values for A through F:

A = Total number of women - Total number of women with some college and college graduate education (in this case A = F - D - 22, because we know the number of total women F and the number of women college graduates 22, but D is still unknown).B = Total number of employees - Total number of men - Total number of women (B = 186 - 79 - F).C = Total number of some college - Number of women with some college (C = 81 - D)D = Total number of some college - Number of men with some college (D = 81 - C).E = Total number of employees - Total of men and women with and without college (E = 186 - B - 81 - 37F = Total number of employees - Total number of men (F = 186 - 79).

The table will also represent joint relative frequency because each cell represents the joint occurrence of two categories (gender and education level). For example, the number of male employees with no college credit (28) divided by the total number of employees (186) is a joint relative frequency.

We may summarize the table data using conditional relative frequency and marginal relative frequency. The marginal relative frequency is the total of each row or column divided by the grand total. The conditional relative frequency would be, for example, the proportion of women among those with no college credit.

The data are dependent because the education level depends on whether the employee is a man or a woman.

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50 Points! Multiple choice geometry question. Photo attached. Thank you!

Answers

The length of the segment AD found using the triangle proportionality theorem is the option (B)

(B) = 4 1/2

What is the triangle proportionality theorem?

The triangle proportionality theorem states that if a line drawn parallel to a side of a triangle, intersecting the other two points at two distinct point, then it will divide the two sides intersected in the same ratio.

The arrow markings indicates that the segment DE and ACV are parallel, therefore, according to the triangle proportionality theorem, we get;

8/12 = 3/AD

AD/3 = 12/8

AD = 3 × (12/8) = 4.5

AD = 4 1/2

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52 divided by 7 = 6r3
A. Incorrect
OB. Correct

Answers

Answer:

incorrect

Step-by-step explanation:

as 7 * 6 = 42 and r is 10

so 6r3 is incorrect

and 7 * 7 = 49 and r is 3

so 7r3 is correct

need help please see attacged

Answers

The domain of f(x) is (0, +∞), and the range is (0, +∞). The graph of the function will have a vertical asymptote at x = 0 and will continuously increase as x approaches positive infinity.

To graph the given logarithmic function f(x) based on the table, we can use the information provided. The table presents pairs of values (x, y), where x represents the input and y represents the output of the function.

From the table, we can observe that the input values (x) are positive and non-zero. This indicates that the domain of the function is x > 0, meaning x is greater than zero. In interval notation, the domain would be written as (0, +∞).

Looking at the output values (y) in the table, we see that they are all positive. This suggests that the range of the function is y > 0, meaning y is greater than zero. In interval notation, the range would be expressed as (0, +∞).

Graphically, the function f(x) is logarithmic and will have a vertical asymptote at x = 0. As x approaches positive infinity, the function increases without bound. The graph starts at y = 125 when x = 1, and it intersects the y-axis at y = 5 when x = 1.5. The graph of the function will resemble a curve that approaches but never touches the x-axis.

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please help I'm losing braincells ​

Answers

Answer:h equals 12

Step-by-step explanation:

Help, please!

Brianna predicted that 16 puppies would be sold at the pet store on Saturday. However, only 9 were sold. What was Brianna's percent error?

Answers

Answer:

Percent error is calculated using the formula:

   Percent Error = ( |Predicted Value - Actual Value| / Actual Value ) * 100%

Plugging in Brianna's prediction and the actual number of puppies sold:

   Percent Error = ( |16 - 9| / 9 ) * 100%

The absolute value of (16 - 9) is 7, so the calculation becomes:

   Percent Error = ( 7 / 9 ) * 100%

This is approximately 77.78%, which is Brianna's percent error in her prediction.

Reduce this fraction to lowest terms 64/72

Answers

Answer: 8/9

Step-by-step explanation:

64/72            Divide both the top and bottom by 8

8/9

8/9 divide both top and bottom and which will give u 8/8

Which of the rays or segments below is a chord of circle O?

A) ->
TC
B)—
SO
C)—>
TU
D)—
FC

Answers

The ray or segment that is a chord is (d) segment FC

How to determine the ray that is a chord

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

The circle

By definition, a chord is a straight line that joins points of the circle without passing through the center

The ray that has the above properties is ray FC

Hence, the segments that is a chord is (d) FC

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find the critical numbers of the function.
f(x)=x^2(x-3)^2

Answers

To find the critical numbers of the function f(x) = x^2(x-3)^2, we need to find the values of x where the derivative of f(x) is zero or undefined.

First, we find the derivative of f(x) using the product rule:

f'(x) = 2x(x-3)^2 + x^2(2(x-3))

Simplifying, we get:

f'(x) = 2x(x-3)(2x-6+x) = 2x(x-3)(3x-6)

Setting f'(x) = 0, we get:

2x(x-3)(3x-6) = 0

This equation is zero when x = 0, x = 3, and x = 2.

Now we need to check if these values make the derivative undefined. None of these values make the derivative undefined.

Therefore, the critical numbers of the function f(x) = x^2(x-3)^2 are x = 0, x = 3, and x = 2.

how do i get 0.225 in fraction form while showing my work

Answers

0.225 can be expressed as the fraction  1/200.

To convert 0.225 to a fraction, we need to understand the place value of each digit. In this case, the digit 2 is in the hundredths place (2/100), the digit 2 is in the thousandths place (2/1000), and the digit 5 is in the ten-thousandths place (5/10000).

Next, we can simplify the fraction by finding the greatest common divisor (GCD) of the numerator and denominator. In this case, the GCD of 2, 100, 1000, and 10000 is 2.

Now, we divide both the numerator and denominator by 2 to simplify the fraction. The numerator becomes 1 (2 divided by 2) and the denominator becomes 5000 (10000 divided by 2).

Further simplification is possible by dividing both the numerator and denominator by 5. The numerator becomes 1 (1 divided by 1) and the denominator becomes 1000 (5000 divided by 5).

Again, we can divide both the numerator and denominator by 5. The numerator remains 1 and the denominator becomes 200 (1000 divided by 5).

Therefore, 0.225 can be expressed as the fraction 1/200.

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f(x)=-4x+7 and g(x)=x^3 choose the expression for (fog)(x)

Answers

Answer:

(fog)(x) = -4x^3 + 7.

Step-by-step explanation:

We can think of (f o g)(x) as f(g(x)).  This shows that we plug in the entire g(x) function for x in f(x) and simplify:

f(x^3) = -4(x^3) + 7

f(x^3) = -4x^3 + 7

Thus, (f o g)(x) = -4x^3 + 7

One more question thank you

Answers

Answer:

Step-by-step explanation:

n=30

r=12

Plug into formula

you get:

1.7 in²

If the coordinates of point E are (-4,y), what is the value of y ?

Answers

-8 because point F is four units below the CD line, so E has to be four units below it too since the lines are parallel

consider the graph function below ​

Answers

The equation of the red graph is g(x) = f(x) - 5

How to calculate the equation of the red graph

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

The functions f(x) and g(x)

Where, we have

f(x) = -x

i.e.. the parent equation of the function

From the graph, we can see that

The function is shifted down by 5 units

This means that

g(x) = f(x) - 5

This means that the equation of the red graph is g(x) = f(x) - 5

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find x using the trigonometric function

Answers

The value of x in the diagram given in the question is 6

How do i determine the value of x?

From the question given above, the following data were obtained:

Angle (θ) = 60Adjacent = 3Hypotenuse = x =?

The value of x can be obtained using cos ratio.

Cos θ = Adjacent / Hypotenuse

Cos 60 = 3 / x

Cross multiply

x × Cos 60 = 3

Divide both sides by Cos 60

x = 3 / Cos 60

= 3 / 0.5

= 6

Thus, the value of x is 6

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SOMEINE GELP IYS DUE IN HOURS

Answers

Answer: the answer is use ur ai in Brainly, it helped me a lot

Step-by-step explanation:

Write and solve an inequality that represents the number of gigabytes of data . G . You can use to stay under your budget of $130

Answers

Answer:

Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:

```

cost_per_gb * G <= budget

```

where:

* cost_per_gb is the cost of data per gigabyte, which is $10 in this case

* G is the number of gigabytes of data

* budget is your budget, which is $130 in this case

To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:

```

G <= budget / cost_per_gb

```

We can then plug in the values for cost_per_gb and budget to get:

```

G <= 130 / 10

```

```

G <= 13

```

This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.

Here is a table that shows the cost of data for different amounts of data:

```

| Amount of data (G) | Cost (\$) |

|---|---|

| 1 | 10 |

| 2 | 20 |

| 3 | 30 |

| ... | ... |

| 13 | 130 |

| 14 | 140 |

| ... | ... |

```

Step-by-step explanation:

2.
Harry pours 650 cubic centimeters of water into cylindrical glass with a diameter of 10
centimeters. He then pours the water from the first glass to another cylindrical glass with a
diameter of 8 cm. How much higher did the water reach in the second glass than in the first
glass? Round to the nearest tenth of a centimeter.
agures of the

Answers

Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

Jerry tries to find the measure of ABC His work is shown. Which statement describes Jerry's error? The picture shows a circle with a center O. Two chords, BA and BC are drawn from the same internal point, B. The angle of A is 135 degrees and C is 119 degrees.

Answers

Jerry's error is that he incorrectly assumes that the measure of angle ABC is equal to the sum of the measures of angles A and C. Hence Statement B is answer.

This is not true because angle ABC is an inscribed angle, which means its measure is half the measure of the intercepted arc.

In this case, the intercepted arc is AC. Since angle A measures 135 degrees and angle C measures 119 degrees, the sum of their measures is 254 degrees. However, angle ABC is not equal to 254 degrees.

To find the measure of angle ABC, we need to find the measure of arc AC. Since arcs A and C are equal in measure, we can find the measure of arc AC by subtracting angle A's measure (135 degrees) from the full circle measure (360 degrees).

Therefore, the measure of arc AC is 360 - 135 = 225 degrees. Since angle ABC is an inscribed angle, its measure is half the measure of arc AC, which is 225/2 = 112.5 degrees.

Hence Statement B is answer.

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Order these from least to greatest.

Answers

Answer:

Least to greatest:

√143

√79 + √63

Step-by-step explanation:

√79 + √63 = 16.82

4π = 12.57

√143 = 11.96

Find the measure of UK
95°
T
99 °
U
87 R
S
?
K

Answers

99 i did it last night

Dylan's mom told him that she would replace each one of his dimes with a quarter. If he uses all of his coins, determine if Dylan would then have enough money to buy a game priced at $20.98 if he must also pay an 8% sales tax.

Answers

To determine if Dylan would have enough money to buy the game, let's calculate the total value of his coins after replacing each dime with a quarter.

First, we need to know the initial value of Dylan's dimes and the number of dimes he has. Since the value of a dime is $0.10, we'll assume that each dime is worth $0.10.

Let's say Dylan initially has "x" dimes. Therefore, the initial value of his dimes would be 0.10x.

Now, since his mom replaces each dime with a quarter, the value of each quarter is $0.25. So, the value of his quarters would be 0.25x.

The total value of his coins after the replacement would be the sum of the initial value of dimes and the value of quarters, which is 0.10x + 0.25x = 0.35x.

Now, to determine if Dylan has enough money to buy the game priced at $20.98, we need to consider the 8% sales tax. To calculate the total amount including tax, we multiply the game price by (1 + tax rate):

Total amount including tax = $20.98 * (1 + 0.08) = $22.65.

Now, we can set up an inequality to check if Dylan has enough money:

0.35x ≥ $22.65.

Dividing both sides of the inequality by 0.35, we get:

x ≥ $22.65 / 0.35.

x ≥ $64.71.

Therefore, Dylan would need to have at least $64.71 worth of dimes (before replacement) in order to have enough money to buy the game after his mom replaces each dime with a quarter.

Note: If Dylan has fewer dimes, the total value of his coins would be lower, and he would not have enough money to buy the game.

Guys i need help!! Im not understanding at all.

Answers

Answer:

H= [4 -1

      4 0]

Step-by-step explanation:

Find the probability that a randomly
selected point within the circle falls in the
red-shaded triangle.
12
12
P = [?]
Enter as a decimal rounded to the nearest hundredth.

Answers

Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases.

so, in this case it is the

area of the triangle / area of the circle.

as everything of the triangle is also a part of the circle.

and so, that fraction of the area of the whole circle that is the area of the triangle in refutation to the area of the whole circle is the probability that a random point inside the circle would be also inside the triangle.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case

12 × 12 / 2 = 72 units²

the area of a circle is

pi × r²

in our case that is

pi × 12² = 144pi units²

the requested probability is

P = 72 / 144pi = 1/2pi = 0.159154943... ≈ 0.16

GEOMETRY 50POINTS

find x to the nearest hundredth.

TYSM​

Answers

Answer:

It's 18.37

Step-by-step explanation:

I'm smart trust me.

peter is 24 years younger than his father. In 5 years time, his father will be 3 times as old as peter? a). how old is peter. b). how old will peter's father be in 25 year's time?​

Answers

Step-by-step explanation:

Let Peter's present age be "p" and his father's age be "x"

So, p = x-24 ;

5 years from now,

Peter's age will be (x-24) + 5 = x-19

His father's age will be x+5.

It is given that 3(x-19)= x+5.

3x - 57 = x + 5 => 2x = 62.

On solving, his father's present age (x) is 31.

So Peter's present age is (p) is x - 24 = 31 - 24 = 7.

Now going in the reverse oder to check the answer.

Peter's present is 7.

5 years from now, it will be 12.

His father's age is 31.

5 years from now, his age will be 36 (which is 3x12).

Hence , the answer to the given problem is 7

Joe worked 2 hours and packed 3 cartons. Bob worked 3 hours and packed 4 cartons. Who packed the most cartons per hour?

Answers

Answer:

bob

Step-by-step explanation:

The base of a triangle is 3 inches more than two times the height. If the area of the triangle is 7 in.² find the base and height.

Answers

Answer:

Let's denote the height of the triangle as "h" inches.

According to the given information, the base of the triangle is 3 inches more than two times the height. Therefore, the base can be expressed as (2h + 3) inches.

The formula to calculate the area of a triangle is:

Area = (1/2) * base * height

Substituting the given values, we have:

7 = (1/2) * (2h + 3) * h

To simplify the equation, let's remove the fraction by multiplying both sides by 2:

14 = (2h + 3) * h

Expanding the right side of the equation:

14 = 2h^2 + 3h

Rearranging the equation to bring all terms to one side:

2h^2 + 3h - 14 = 0

Now, we can solve this quadratic equation. We can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:

h = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, the values are:

a = 2

b = 3

c = -14

Substituting these values into the quadratic formula:

h = (-3 ± √(3^2 - 4 * 2 * -14)) / (2 * 2)

Simplifying:

h = (-3 ± √(9 + 112)) / 4

h = (-3 ± √121) / 4

Taking the square root:

h = (-3 ± 11) / 4

This gives us two possible solutions for the height: h = 2 or h = -14/4 = -3.5.

Since a negative height doesn't make sense in this context, we discard the negative solution.

Therefore, the height of the triangle is h = 2 inches.

To find the base, we substitute this value back into the expression for the base:

base = 2h + 3

base = 2(2) + 3

base = 4 + 3

base = 7 inches

Hence, the base of the triangle is 7 inches and the height is 2 inches.

Step-by-step explanation:

-The answer for the height is 5.5 units.

-The base of the triangle is aproximately 2.5454 units.

To answer this problem, you have to set an equation with the information you're given. If you do it correctly, it should look like this:

7=1/2(3+2h)

-Now, you have to solve for h:

7=1.5+h

7-1.5=h

5.5=h

-Now that you have the height, you plug it in into the triangle area formula to solve for the base:

7=1/2(b)5.5

7=2.75b

7/2.75=b

b≈2.5454

-To make sure that the corresponding values for the base and height are correct, we plug the values in and this time we are going to solve for a(AREA):

A(triangle)=1/2(2.5454)(5.5)

A=1/2(13.9997)

A=6.99985 square units

-We round the result to the nearest whole number and we get our 7, which is the given value they gave us.

1. The initial odometer reading of a cab is 369 km. It travelled for 2 hours and the final odometer reading showed 469 km. Find the approximate average speed of the cab. ​

Answers

The approximate average speed of the cab is 50 km/h.

To find the approximate average speed of the cab, we can use the formula:

Average Speed = Total Distance / Total Time

Given that the initial odometer reading is 369 km and the final reading is 469 km, the total distance covered by the cab is:

Total Distance = Final Odometer Reading - Initial Odometer Reading

Total Distance = 469 km - 369 km

Total Distance = 100 Km.

The cab traveled for 2 hours, so the total time is:

Total Time = 2 hours

Now, we can substitute the values into the average speed formula:

Average Speed = Total Distance / Total Time

Average Speed = 100 km / 2 hours

Average Speed = 50 km/h

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What is the range of the projectile? (Answer in Meter) 4. A process (including valve and sensor-transmitter) has the approximate transfer function, G(s) = 2e-0.2s with time constant and time delay in minutes. s+1 Determine PI controller setting (Hint: find Kc, assume t-0.5 min) and the corresponding gain margin if the phase margin is required to achieve 40. A skateboard of mass m slides from rest over a largespherical boulder of radius R. The skateboard gains speed as itslides, eventually falling off at a maximum angle.a. Determine the Kinetic Energy An increase in the MPCa. decreases the multiplier, so that changes in government expenditures have a smaller effect on aggregate demand.b. increases the multiplier, so that changes in government expenditures have a smaller effect on aggregate demand.c. decreases the multiplier, so that changes in government expenditures have a larger effect on aggregate demand.d. increases the multiplier, so that changes in government expenditures have a larger effect on aggregate demand. For each of the major body cavities below, list an organ or two located in that cavity: o Cranial: o Spinal: o Thoracic: o Abdominal: o Pelvic: For each of the membranes listed below, list what major cavity(les) it is located in and which organ(s) it encloses: o Fibrous Meninges: o Serous Pleura: o Serous Pericardium: ; o Serous Peritoneum: Learn and use the directional and relational terminology to describe the relationships below: to the abdomen. o The cranium is o The abdomen is The digits are The carpal region is The ears are o o to the cranium. to the carpal region. to the digits. to the nose. o o The nose is o The liver is to the skin. o The skin is to the liver. Study and review the body region terminology provided in the lab manual and in our lecture. to the ears. is disrupted sleep a risk factor for alzheimer's disease? evidence from a two-sample mendelian randomization analysis These substances typically exert their effects through either causing the release of neurotransmitters or inhibiting the re-uptake of neurotransmitters, particularly epinephrine and norepinephrine.a.Steroidsb.Selective estrogen receptor modulatorsc.Stimulantsd.Peptide hormones Question 2 (1 point)Which one of the following is true of the mean?1) one of the less common averages2) equals some whole numberobservations must be ordered from least to most before calculating the3)mean4) equals the sum of all observations divided by the number of observations (3 points) how many bit strings of length 7 are there? 128 how many different bit strings are there of length 7 that start with 0110? 8 how many different bit strings are there of length 7 that contain the string 0000? A number, N is increased by 10% to obtain P. The number P is reduced by 10% to get Q. Write down Q in terms of N. A. Q=1.10N B. Q=N C. Q=0.99N D. Q=0.90N Galway Travels organizes tours to a number of cities in Ireland. The manager of the company examines a spreadsheet which is an annual record of airfares to different cities from Dublin. The contents of the spreadsheet will be used to determine the difference between peak season and off-season airfares. The spreadsheet application, data, the computer the manager is using, and the process of recording the data, in this case, representsa systeman analysisa surveydatainformation Consider the transformation.2 trapezoids have identical angle measures but different side lengths. The first trapezoid has side lengths of 4, 2, 6, 2 and the second trapezoid has side lengths of 8, 4, 12, 4.Which statement about the transformation is true? An arrow is shot horizontally from a height of 6.2 m above the ground. The initial speed of the arrow is 43 m/s. Ignoring friction, how long will it take for the arrow to hit the ground? Give your answer to one decimal place. You have an idea for a vaccine to prevent Group A Strep (GAS) infections. You know that Streptococcus bacteria are fastidious organisms, and you don't expect to be able to produce your protein of interest in large quantities in S. pyogenes. Based on your knowledge of GAS, design a recombinant vaccine candidate to protect against GAS infection using E. coli as your recombinant protein production organism. Your choice of GAS antigen should be something produced by GAS that is not produced by humans. Your GAS protein(s) of choice will be expressed in E. coli and then purified for use in vaccine production. To express your protein in E. coli, you need to clone the gene(s) of interest into a plasmid under the control of the Plac promoter. Create and upload a diagra that shows each step of your design strategy and cloning process. Start with getting your gene of interest out of S. pyogenes and end with your selection and screening process in E. coli. Be sure to include all of the following: - What GAS protein(s) will be expressed by your recombinant E. coli? - Show all components that need to be present on your plasmid for replication, selection, screening, and for regulation by the Plac promoter. How do all of the parts come together? - A selection mechanism to ensure that only recombinant E. coli expressing your plasmid can grow. - Any selection mechanism is ok. Indicate what media needs to be used and what you expect to see. - A screening mechanism to show that your gene(s) of interest is being expressed. Indicate what media needs to be used and what you expect to see.