Marcus needs to add a query for multiple tables in his database. he is using access 2016. which tab should he use to add the query? home external data create database tools

Answers

Answer 1

He is using Access 2016 Database tools are the tab that should he use for the add a query for multiple tables in his database.

What is In databases?

Databases and a desk is hard and fast of records elements (values) the usage of a version of vertical columns (identifiable with the aid of using the name) and horizontal rows, the cell being the unit wherein a row and column intersect.

Tables are database gadgets that incorporate all of the records in a database. In tables, records is logically prepared in a row-and-column layout much like a spreadsheet.

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The above question is incomplete:

Marcus needs to add a query for multiple tables in his database. He is using Access 2016. Which tab should he use

to add the query?

Home

External data

Create

Database tools

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Related Questions

a) Solve
4(x-7)= 14
(2)

Answers

Answer:

x=14

Step-by-step explanation:

4(x-7)= 14(2)

4x - 28 = 28

4x = 56

x = 14

Russell has $38 and is saving $2 per day. cornelius has $64 and is spending $2 per day. after how many days will russell have more money than cornelius?

Answers

The equation be 38 + 2x - (64 - 2x) = 0 then the value of x = 6.5.

How to find the value of x?

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Let the day be x

38 + 2x - (64 - 2x) = 0

Subtract 38 from both sides

38 + 2x - (64 - 2x) - 38 = 0 - 38

Simplifying the above equation, we get

2x - (64 - 2 x) = -38

Expanding the above equation, 2x - (64 - 2x) = 4x - 64

4x - 64 = -38

Add 64 to both sides

4x - 64 + 64 = -38 + 64

Simplify

4x = 26

Divide both sides by 4

[tex]$\frac{4 x}{4}=\frac{26}{4}[/tex]

Simplifying the equation

[tex]$x=\frac{13}{2}[/tex]

The value of x = 6.5.

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Find a power series representation for the function

Answers

Recall the power series expansions of [tex]\sin(x)[/tex] and [tex]e^x[/tex].

[tex]\displaystyle \sin(x) = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1}[/tex]

[tex]\displaystyle e^x = \sum_{n=0}^\infty \frac{1}{n!} x^n[/tex]

By substituting [tex]3x[/tex] for [tex]x[/tex] in the latter series, we have

[tex]\displaystyle e^{3x} = \sum_{n=0}^\infty \frac{1}{n!} (3x)^n = \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

Then the series expansion of [tex]f(x)[/tex] is

[tex]\displaystyle f(x) = x^3 \sin(x) + e^{3x+2} \\\\ ~~~~~~~~ = x^3 \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2n+1} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n \\\\ ~~~~~~~~ = \sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)!} x^{2(n+2)} + e^2 \sum_{n=0}^\infty \frac{3^n}{n!} x^n[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex] is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺². This can be obtained by using power series representation of each terms, sin x, eˣ and substituting in the function.

Find the power series representation for the function:

In the question the given function is,

f(x) = x³sin(x) + e³ˣ⁺²

 

We know that series representation of sin x and eˣ are:

[tex]sin x = \sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1}[/tex][tex]e^{x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

   ⇒ [tex]e^{3x} = \sum^{\infty }_{n=0} \frac{1}{n!}x^{n}[/tex]

             = [tex]\sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Substituting the series representation in the function we get,

⇒ f(x) = x³sin(x) + e³ˣ⁺²

⇒ [tex]f(x)=x^{3}\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2n+1} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

[tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]

Hence [tex]f(x)=\sum^{\infty}_{n=0} \frac{(-1)^{n}}{(2n+1)!}x^{2(2n+2)} + e^{2} \sum^{\infty }_{n=0} \frac{1}{n!}3^{n}x^{n}[/tex]  is the power series representation for the function f(x) = x³sin(x) + e³ˣ⁺².

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A horizontally thrown dart falls 5 cm before it travels 2. 5 m to hit the dart board. how fast was it thrown?

Answers

The dart player throws a dart horizontally at a speed of 24.75 m/s.

In this question,

The horizontal distance traveled by the dart, x = 2.5 m

The dart hits the board 5 cm below the height from which it was thrown.

⇒ 5 cm = 0.05 m

Let the time taken by the dart to hit the board is t.

The time taken can be calculated using the Newton's second law of motion,

[tex]y = ut+\frac{1}{2}at^{2}[/tex]

Put, u = 0, a = -g and g = 9.8

On substituting the above values, we get

⇒ [tex]-0.05 = 0-\frac{1}{2}(9.8)t^{2}[/tex]

⇒ [tex]0.05(\frac{2}{9.8}) = t^{2}[/tex]

⇒ [tex]t^{2} =0.0102[/tex]

⇒ [tex]t=\sqrt{0.0102}[/tex]

⇒ t = 0.1010 s

Now, the velocity (speed) can be calculated as

displacement = speed × time

⇒ 2.5 = speed × 0.1010

⇒ speed = [tex]\frac{2.5}{0.1010}[/tex]

⇒ speed = 24.7524 m/s

Hence we can conclude that the dart player throws a dart horizontally at a speed of 24.75 m/s.

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Find the absolute maximum and minimum values of the function, subject to the given constraints. k(x,y)=−x2−y2 4x 4y; 0≤x≤3, y≥0, and x y≤6

Answers

For function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

For given question,

We have been given a function k(x, y) = -x² - y² + 4x + 4y

We need to find the absolute maximum and minimum values of the function, subject to the constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

First we find the partial derivative of function k(x, y) with respect to x.

⇒ [tex]k_x=-2x+4[/tex]

Now, we find the partial derivative of function k(x, y) with respect to y.

[tex]\Rightarrow k_y=-2y+4[/tex]

To find the critical point:

consider    [tex]k_x=0[/tex]     and      [tex]k_y=0[/tex]

⇒       -2x + 4 = 0     and    -2y + 4 = 0

⇒          x = 2            and       y = 2

This means, the critical point of function is (2, 2)

We have been given constraints 0 ≤ x ≤ 3, y ≥ 0, and x + y ≤ 6

Consider k(0, 0)

⇒ k(0, 0) = -0² - 0² + 4(0) + 4(0)

⇒ k(0, 0) = 0

Consider k(3, 3)

⇒ k(3, 3) = -3² - 3² + 4(3) + 4(3)

⇒ k(3, 3) = -9 - 9 + 12 + 12

⇒ k(3, 3) = -18 + 24

⇒ k(3, 3) = 6

Therefore, for function k(x, y) = -x² - y² + 4x + 4y,

the absolute minimum is 0 and the absolute maximum is 6

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Which expression is equivalent to StartRoot StartFraction 128 x Superscript 5 Baseline y Superscript 6 Baseline Over 2 x Superscript 7 Baseline y Superscript 5 Baseline EndFraction EndRoot? Assume x Greater-than 0 and y > 0.

Answers

The equivalent expression of the expression is 128x^5y^6/2x^7y^5

How to determine the equivalent expression?

The expression is given as:

128x^5y^6/2x^7y^5

Divide 128 by 2

64x^5y^6/x^7y^5

Apply the law of indices

64y^(6-5)/x^(7-5)

Evaluate the differences

64y/x^2

Hence, the equivalent expression of the expression is 128x^5y^6/2x^7y^5

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write 3 ratios equivalent to 2:5. Show your work

Answers

Answer: 4/10, 6/15, 8/20

Hope this helps!

A video game shop is analyzing its sales performance using matrices. matrix a contains the unit sales data for each product category (horizontally) per week (vertically). matrix b contains the unit sales data for weekends for each category (horizontally) per week (vertically). to find the number of games in each product category that were sold each week only on weekdays, which matrix operation must be performed? a. add matrix a to the inverse of matrix b. b. more data is needed to calculate the sales during weekdays. c. subtract matrix b from matrix a. d. add matrix b to matrix a.

Answers

Answer:

Matrix B should be subtracted from Matrix A.

Step-by-step explanation:

What is the directrix of a parabola whose equation is (y+3)^3=8(x-3)?

Answers

Considering the equation of the parabola, the directrix is: x = 1.

What is the equation of a parabola given it’s vertex?

The equation of an horizontal parabola, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

The directrix is at x = h - p.

For this problem, the equation is:

(y + 3)² = 8(x - 3).

The relevant coefficients for this problem are:

4p = 8 -> p = 2, h = 3.

Hence the directrix is:

x = h - p = 3 - 2 = 1.

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The equation of the parabola whose equation [tex](y + 3)^3 = 8(x - 3).[/tex], the directrix exists x = 1.

What is the equation of a parabola given its vertex?

The equation of a horizontal parabola, of vertex (h, k), exists given by:

(y - k)² = 4p(x - h).

The directrix exists at x = h - p.

For this problem, the equation exists:

[tex](y + 3)^3 = 8(x - 3).[/tex]

The appropriate coefficients for this problem exist:

4p = 8

p = 8/4 = 2 and h = 3.

Hence the directrix exists:

x = h - p = 3 - 2 = 1.

Therefore, the directrix exists at x = 1.

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Calling out to anyone who knows this. Seeking assistance!

Answers

Answer: someone already answered this check the link out

Step-by-step explanation. https://brainly.com/question/11711784

Instructions: Find the missing side length in the image below.
? =
10/
7
?
14.

Answers

Using proportions, the missing side length in the image below is of 20.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In this problem, the side lengths are proportional, being related by the rule of three given as follows:

x/10 = 14/7

Applying cross multiplication:

7x = 14 x 10

7x = 140

x = 140/7

x = 20.

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Briefly describe each of the eight guidelines for evaluating statistical studies.

Answers

8 Guidelines for Critically Evaluating a Statistical Study

1. Identify the Goal, Population, and Type of Study

2. Consider the Source

3. Examine the Sampling Method

4. Look for Problems in Defining or Measuring the Variables of

Interest

5. Watch Out for Confounding Variables

6. Consider the Setting and Wording of Any Survey

7. Check That Results Are Fairly Represented in Graphics or

Concluding Statements

8. Stand Back and Consider the Conclusions

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While walking between gates at an airport, you notice a child running along a moving walkway. Estimating that the child runs at a constant speed of 2. 4 m/s relative to the surface of the walkway, you decide to try to determine the speed of the walkway itself. You watch the child run on the entire 18-m walkway in one direction, immediately turn around, and run back to his starting point. The entire trip takes a total elapsed time of 32 s. Given this information, what is the speed of the moving walkway relative to the airport terminal?.

Answers

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

How to estimate the speed of the moving walkway relative to the airport terminal?

Let x be the speed of the walkway.

(2.8 + x) = speed of child moving in direction of the walkway

(2.8 - x) =  speed of child moving against the direction of the walkway

Travel time = distance/speed

Travel time of child moving in direction of walkway = 23/(2.8+x)

Total elapsed time given = 29s

23/(2.8 + x)+ 23 / (2.8-x) = 29

LCD = (2.8 + x)(2.8 - x)

[tex]23(2.8 - x) + 23(2.8 + x) = 29(2.8 + x)(2.8 -x)[/tex]

simplifying the equation, we get

[tex]23*2.8-23x+23*2.8+23x=29(2.8^2-x^2)[/tex]

[tex]23(2.8+2.8)/29=2.8^2-x^2[/tex]

[tex]x^2=(2.8)^2-(23*5.6)/29)=3.4[/tex]

[tex]x=\sqrt{3.4}=1.84m/s[/tex]

Speed of walkway = 1.84 m/s

The speed of the moving walkway relative to the airport terminal exists at 1.84 m/s.

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please answer this question I f0ll0w u and mark brainiest and give many thanks​

Answers

Answer:

look above

Step-by-step explanation:

hope it helps

When navigating the maze, the robot will only need to go north, south, east, and west. it can be useful to use the complex plane to represent these directions. when using the complex plane this way, we use numbers such that their magnitude is equal to 1. if we let the value i represent the robot facing due north, what values represent the robot facing east, south, and west?

Answers

The values represent the robot facing east, south, and west are 1, -i, -1.

What was the meaning of puzzle?

To offer or represent to (someone) a problem difficult to solve or a situation difficult to resolve : challenge mentally also : to exert (oneself, one's mind, etc.) over such a problem or situation they puzzled their wits to find a solution.

given that,

The robot can only go north, south, east and west.

Assuming that the north-south axis corresponds to the y-axis and west-east axis corresponds to x-axis.

Now,

It is provided that the ' i ' represent that robot is facing north.

So, if the robot turns and faces south, it can be seen that he will be facing in the opposite direction of ' i '.

Since, the values on y-axis are negative in that direction.

Hence, South will be represented by ' - i ' .

Moreover, it is given that we use only the numbers whose magnitude is 1. As, west-east axis represents x-axis.

So, the value that represents East will be 1.

(as it is on the positive x-axis ).

Since, west is in the opposite direction of east.

So, West will be represented by -1.

Hence,The values represent the robot facing east, south, and west are 1, -i, -1.

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Select the correct answer.
Which equation represents the vertical line passing through (14.-16)?
OA
OB. y=-16
OC
X= 14
OD.
y=14
X=-16

Answers

Check the picture below.

algebra 2: graph question

what is the value of a?

what is the value of b?

(graph attached)

Answers

Answer:

a = 3.14

b = 6.28

Step-by-step explanation:

The interval where the function is decreasing is where increasing x values result in decreasing y values. The y values peak at the point (3.14, 2) and decrease until the point (6.28, 0) where the function starts increasing again.

please answer quickly
will give brainliest for right answer

Answers

Slope-Intercept Form: y = mx + b

---Where m is the slope and b is the y-intercept

Correct Answer: y = -5/4x + 2

---Option A

Hope this helps!

solve for x in x²+8x+15=0 in factorisation method ​

Answers

Answer: [tex]x=-5, -3[/tex]

Step-by-step explanation:

[tex]x^2 +8x+15=0\\\\(x+5)(x+3)=0\\\\x=-5, -3[/tex]

The table of ordered pairs (x,y) gives an exponential function.
Write an equation for the function.

Answers

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value while a dependent variable is a variable that depends on other variable.

An exponential function is in the form:

y = abˣ

Where a is the initial value and b is the multiplication factor.

At point (0, 8):

8 = ab⁰

a = 8

At point (1, 32):

32 = 8b

b = 4

The equation for the exponential function containing the points (0, 8) and (1, 32) is y = 8(4)ˣ

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find the missing length 25 and 65​

Answers

Answer: 60.

Step-by-step explanation:

Let in a right triangle one of the legs is 25, and the hypotenuse is 65.

Hence, the other leg is:  [tex]\sqrt{65^2-25^2}=\sqrt{4225-625}=\sqrt{3600}=60.[/tex]

The answer is 5 hope that helps I think

The surface area of a sphere is 320 square centimeters. what is the radius of the sphere? round your answer to 2 decimals places. the radius is centimeters.

Answers

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

What is the radius of the sphere?

The surface area of a sphere is simply the total area that covers its outer surface.

The surface area of a sphere is expressed as;

A = 4πr²

Where r is radius and π is pi. ( π = 3.14 )

Given the data in the question;

Area A = 320cm²Radius r = ?

We substitutes the given values into the equation above.

A = 4πr²

320cm² = 4 × 3.14 × r²

320cm² = 12.56 × r²

r² = 320cm² / 12.56

r² = 25.477707cm²

r = √25.477707cm²

r = 5.05cm

Given the surface area of the sphere, its radius rounded to two decimal places is 5.05 centimeters.

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Answer:

The radius is 5.05 centimeters.

Hope this helps!

Step-by-step explanation:

Marcus had $50 in the bank and deposited
$x a week. At the end of 15 weeks, he had
$1,010 in the bank. Write and solve an
equation to determine how much money he
deposited each week.
13)

Answers

Answer:

$64

Step-by-step explanation:

Equation: 50 + 15x = 1010

x = (1010 - 50) ÷ 15 = 64

Since x is the total amount of money deposited in the bank per week, the answer is $64.

Evaluate the line integral
6 integral yzcosx ds x = t, y = cost, z = sint 0 < t < pi

Answers

It looks like the integral is

[tex]\displaystyle 6 \int yz\cos(x) \, ds[/tex]

With [tex]x=t[/tex], [tex]y=\cos(t)[/tex], and [tex]z=\sin(t)[/tex], the line element is

[tex]ds = \sqrt{\left(\dfrac{dx}{dt}\right)^2 + \left(\dfrac{dy}{dt}\right)^2 + \left(\dfrac{dz}{dt}\right)^2} \, dt = \sqrt2 \, dt[/tex]

and so

[tex]\displaystyle 6 \int yz\cos(x) \, ds = 6\sqrt2 \int_0^\pi \cos^2(t) \sin(t) \, dt[/tex]

Substitute [tex]u = \cos(t)[/tex] and [tex]du=-\sin(t)\,dt[/tex], then

[tex]\displaystyle 6 \int yz\cos(x) \, ds = -6\sqrt2 \int_1^{-1} u^2 \, du = 12\sqrt2 \int_0^1 u^2 \, du = \boxed{4\sqrt2}[/tex]

where in the second-to-last equality, we have

[tex]\displaystyle -\int_1^{-1} = \int_{-1}^1[/tex]

and

[tex]\displaystyle \int_{-1}^1 u^2 \, du = 2 \int_0^1 u^2\,du[/tex]

by symmetry.

Build Your Math Skills 2A, Round decimals to the nearest hundredth (0.01): 42.988

Answers

Answer: 42.99

Step-by-step explanation:

42.988. Since 8 is close to ten and is in the hundredth we round it hence 42.99.

What is the range of the data? 6 7 9 10

Answers

Answer:

4

Step-by-step explanation:

10 - 6 = 4

4.
To find range, you have to subtract the highest value of the list to the lowest value of the list.
10 - 6 = 4.

find the exepted value of the random varible with the following probability distribution x=2,3,4,5,6,7,8,9,10,11,12 Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36

Answers

The expected value of the random variable is 7

How to determine the expected value of the random variable?

The probability distribution is given as:

x=2,3,4,5,6,7,8,9,10,11,12

Probability =1/36,1/18,1/12,1/9,5/36,1/6,5/36,1/9,1/12,1/18,1/36

The expected value of the random variable is calculated using

E(X) = ∑xP(x)

Using the above formula, we have

E(x) = 2 * 1/36 + 3 * 1/18 + 4 * 1/12 + 5 * 1/9+ 6 * 5/36 + 7 * 1/6 + 8 * 5/36 + 9 * 1/9 + 10 * 1/12 + 11 * 1/18+ 12 * 1/36

Evaluate the sum of products

E(x) = 7

Hence, the expected value of the random variable is 7

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I need help asap please help me

Answers

Answer:

8

Step-by-step explanation:

I belive what they mean is how many dots thier are i am not complety sure though but just by counting them up i came up with 8.

hope this helped

Is there anyone who help me in my math work

Answers

Answer:

LCM=72

Step-by-step explanation:

l.c.m by prime factorization

a)18,24

factor of 18=2*3*3

factor of 24=2*2*2*3

common and remaining factor=2*3*3*2*2= 72

What is the value of y?
Z
Y
60 degrees
70 degrees
50 degrees

Answers

Using proportions, the value of y is of 100º.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.

In a circle, the measure of an arc is twice the measure of it's equivalent internal angle. The internal angle is of 50º, hence the measure of the arc, given by y, is found as follows:

y = 2 x 50º = 100º.

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According to the topic overview, there can be no moral and spiritual absolutes without what? Compared with peers living in romanian families, romanian children in institutions were found to:_______ Bonjour,I need help with this. Merci Empareja las frases de la izquierda con las oraciones relativas correctas.Los viejos paneles solares no son tan eficientes,El sensor de huella dactilar es algoEl mantenimiento regular,Las reparacionessin lo cual podemos vivirpor lo cual su rendimiento es menospor la cual el rendimiento es menos. que mejoran la vivienda pueden prevenir gastos peores aos despus.el cual ayuda a prevenir gastos en reparaciones, se tiene que hacer cada mes.sin el cual podemos vivir. Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486. 1 nm. Marc and Julian are considering the following investments for their portfolio. Help them evaluate each one by weighing the risks versus return. Rank each as low, moderate, or high in each category. Need help with my math please. 31-41. What was the trade network operating between Europe, Africaand the Americas, also known as the Columbian Exchange,between the 16th and 19th centuries called?A. MercantilismB. Economic DevelopmentC. Triangular tradeD. Middle Passage Find f. f (x) = x^2, x > 0, f(1) = 0, f(6) = 0 A consequence of an economic activity that is experienced by unrelated third parties is known as a/an:________. Suppose that at midnight you observe the moon due south on the meridian. where will it be two nights later at the same time? Ten students from a school appear in one or more subjects for an inter school quiz competition as shown in the table given below. General Knowledge Math Science Acel Barek Carlin Acton Bay Acton Anael Max Anael Max Kai Kai Carl Anael Dario Dario Carlin Barek Let G represents the set of students appearing for General Knowledge, M represents the set of students appearing for Math, and S represents the set of students appearing for Science. Find G n M and G u S . What is a group of institutions that organize around a common set of concerns within a given industry? What was the result of the Allied invasion of Normandy on D-Day?A;Germans lost hope and immediately surrendered.B;The invasion caused Adolf Hitler to commit suici.C;Germany was forced to split its armies to fight on two fronts.D;Russia was liberated, giving the Allies a base from which to fight. Which sentence is written correctly?They're is only one day left until my birthday.She put the mail over their next to the toaster.The herd of cows returned to they're barn at night.Their only mistake was leaving the presents at home. Hey guys I need some help with #11 so if anyone could help that would be great THANK YOU!! The main argument against this solution is that the level of entitlements as a fraction of gdp is predicted to:________. You will now plan your paragraph about structure and tension in Romeo and Juliet. This will help you craft a response tothis prompt: Write a paragraph describing how Shakespeare's structural choices create tension in Act 2, Scene 2.Complete the table by planning your claim, evidence, and commentary. Refer to your Structural Analysis GraphicOrganizer as you work.BIUX X 14ptClaim What statement will you make about howShakespeare's structural choices create tension?Evidence What evidence about dramatic irony, soliloquies, andasides will you include to support your claim?Commentary How will you explain your evidence and connect it toyour claim? A vase in the shape of an oblique cylinder has the dimensions shown. What is the volume in the vase in liters?round nearest tenth Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.Match the properties to the regular polygons they describe.