What is the formula for the nth partial sum of the series?.

Answers

Answer 1

The formula for the nth partial sum of the series is Sn=a1(1−rn)1−r.

The initial term a1 and the common ratio r can be used to determine the nth partial sum of a geometric sequence is given by Sn equals to a1(1−rn)1−r, where a1 denotes the first term in the partial sum and a the nth (final) term.

One of a number of sums of items in a particular sequence, starting with the first sum, which is the first element, going on to the second sum, which is the first element plus the second element, and so forth. This is the concept of partial sum.

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Related Questions

please help me
[tex] \sqrt[4]{ - 81} [/tex]

Answers

Answer:

3 ⁴√-1

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

How do you find the sum of the given polynomial?.

Answers

The sum of the polynomial is obtained by adding the terms with the same power and variable together.

The steps to determine the sum of the polynomial :

Step 1: Arrange each polynomial with the term with the highest degree first then

in decreasing order of degree.

Step 2: Group the like terms : Like terms are defined as the terms whose variables and exponents are the same. For example 2x² and 3x² are like terms.

Step 3: Simplify by combining like terms.

For example, (2x² + 6x +5) +(-2x + 3x²- 1)

and we have determine sum of polynomial. Follows the above steps :

Arrange the polynomials are in decreasing order of degree.

=> (2x² + 6x +5) + ( 3x²– 2x – 1)

Group the like terms.

2x² + 3x² + 6x – 2x + 5 -1

Simplify by combining the like terms

= 2x² + 3x² + 6x – 2x + 5 -1

= 5x² + 4x + 4

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What is the scale factor in the dilation if the coordinates of A are (-7, 6) and the coordinates of Care (-4, 3)?
D
B
d
21
OLE
18-
45-
42-
9-
B'6
Dº 6'3-
-24-21-18-15-12-9-6-33- 3 6 9 12 15 18 x
-6-
60325
-9
42

Answers

The scale factor in the dilation can be found by comparing the coordinates of the original image (A) and the new image (B). The coordinates of A and B must be provided in order to determine the scale factor.

What is the scale factor in the dilation if the coordinates?The scale factor in the dilation can be found by comparing the coordinates of A and B. The x-coordinate of A is -7 and the x-coordinate of B is -4, which means that the x-coordinate of B is 3 units closer to the origin than the x-coordinate of A. Similarly, the y-coordinate of B is 3 units closer to the origin than the y-coordinate of A. Therefore, the scale factor in the dilation is 3. This means that the image of A is 3 times larger than the preimage, and the image of B is 3 times closer to the origin than the preimage of A. The scale factor can be found by dividing the distance between the coordinates of A by the distance between the coordinates of B. For example, if the coordinates of A are (4,5) and the coordinates of B are (8,10), the scale factor would be 2, as the distance between the coordinates of B is twice the distance between the coordinates of A. It is important to note that the scale factor applies to both the x and y coordinates and is the same value for both.

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What is the product of A & B?.

Answers

The cross product of A & B (A × B) is |A| |B| Sin θ, where θ is the angle between A and B.

The vector product or cross product of two vectors, A and B, is denoted by A × B, and its resultant vector is perpendicular to the vectors A and B.

The cross product is mostly used to determine the vector, which is perpendicular to the plane surface spanned by two vectors, whereas the dot product is used to find the angle between two vectors or the length of the vector.

The cross product of two vectors, say A × B, is equal to another vector at right angles to both, and it happens in the three dimensions.

If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:

|A| |B| Sin θ

--The given question is incorrect; the correct question is

"What is the cross product of A & B?"--

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How do you find the properties of a 30 60 90 triangle?.

Answers

A 30-60-90 triangle has one right angle, with the other two angles measuring 30 and 60 degrees. The shortest side is half as long as the hypotenuse, while the middle side is equal to the shortest side multiplied by the square root of 3. The area can be found using (1/2) x base x height, with the perimeter equal to the sum of all three sides.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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why is paying back along with a nominal interest rate of 13.62% if the interest is compounded quarterly, how much greater is white effective interest rate than his nominal interest rate

Answers

The required white effective interest rate is 0.71% more than his nominal interest rate.

What is compound interest?

Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.

Here,

White Effective interest R,
[tex]R=(1+i/m)^m)-1\\R=(1+0.1362/4)^4)-1\\R =0.1433*100=[/tex]
R = 14.33 percent

So

Difference in interest = 14.33%-13.62%
                                    =0.71%

Thus, the required white effective interest rate is 0.71% more than his nominal interest rate.

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How do you graph x+y= -1

Answers

Answer:

See the image attached.

Step-by-step explanation:

x    y

0    -1

1     -2

What is the value of K if ½ is a root of equation x² KX 5 4 0?.

Answers

So, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

A root of an equation is a value that satisfies the equation when it is set equal to zero. In other words, a root of an equation is a solution to the equation of the form x = constant.

The equation x^2 - kx - 5 = 0 is a quadratic equation, which can be factored into (x - r1)(x - r2) = 0 where r1 and r2 are the roots of the equation.

In this case, we can use the fact that 1/2 is a root of the equation x^2 - kx - 5 = 0

We can use the factored form of the equation and substitute x = 1/2

(x-1/2) (x-r2) = 0

Then, we can set each factor equal to zero and solve for r1 and r2:

x - 1/2 = 0 and x - r2 = 0

x = 1/2 and x = r2

We can use the quadratic formula to find the value of r2:

x = (-b ± √(b^2 -4ac) ) / 2a

We can substitute the values in the equation x^2 - kx - 5 = 0

x = (-(-k) ± √((-k)^2 - 41(-5)) ) / 2*1

x = (k ± √(k^2 + 20) ) / 2

x = (k ± √(k^2 + 20) ) / 2

r2 = (k + √(k^2 + 20) ) / 2

Now we have two values of x that satisfies the equation x^2 - kx - 5 = 0

x = 1/2 and x = (k + √(k^2 + 20) ) / 2

We can use the first value x = 1/2 and substitute it back into the original equation:

(1/2)^2 - k(1/2) - 5 = 0

1/4 - k/2 - 5 = 0

k/2 = 6 - 1/4

k = 12 - 1

k = 11

Therefore, the value of k that makes 1/2 a root of the equation x^2 - kx - 5 = 0 is 11.

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When using substitution to solve a linear system how do you know if the system is inconsistent?.

Answers

The first step in determining whether a linear system is inconsistent is to identify whether the lines are parallel. Check to see if the lines have a y-intercept in common, if so.

This result establishes an inconsistent system due to the fact that two parallel lines with distinct y-intercepts will never intersect.

If there is at least one solution to a linear equations system, it is said to be a consistent system. The system is regarded as inconsistent if there is no solution.

When the lines are parallel to one another, a system of linear equations cannot become inconsistent in any other way. The slope of parallel lines is the same. Therefore, comparing the slopes is a good way to ascertain whether the system is inconsistent. The comparison is simple if the linear equations are written in the point-slope or slope-intercept form. In order to determine the coefficient of x and compare slopes, it is a good idea to solve for y on all equations that are in a different form and express them in the slope-intercept form. The equation system is inconsistent if the slopes are equal to one another.

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Alex ran 4 1/2 kilometers in 3/4 of an hour. How many kilometers he ran per hour?

Answers

First convert the distance she ran from a mixed number to a improper fraction:

• 4-1/2 equals 9/2.

Since this a unit rate problem divide the km by the time traveled.

• 9/2 (km) ÷ 3/4 (hour). When you divide a number by a fraction use (Keep-Change-Flip).

• 9/2 × 4/3 = 36/6 miles/hour.

That's means 36/6 = 18/3 = 6 km/ hour.

MCD y mcm de 420,630,330

Answers

The GCD is 30 and the LCM is 13860 for the numbers 420, 630, and 330 .

What are LCM and GCD?

The highest factor among two or more numbers is the greatest common denominator (GCD).

The lowest common multiple (LCM) is another name for the least common multiple in mathematics. The least common multiple of two or more numbers is the smallest of all the common multiples of the numbers provided.

Take all three numbers and their factors to determine the greatest common divisor.

1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420 are the factors for 420.

The factors for 630 are as follows: 1, 2, 3, 5, 6, 7, 9, 10, 14, 15, 18, 21, 30, 35, 42, 45, 63, 70, 90, 105, 126, 210, 315, 630, and 330 are as follows: 1, 2, 3, 5, 6, 10, 11, 15, 22, 30, 33, 55, 66, 110, 165, 330.

Of the three, 30 is the common factor with the highest value.

Take all three numbers and their prime factors to determine the lowest common multiple.

The prime factors for 420 = 2 × 2 × 3 × 5 × 7

The prime factors for 630 = 2 × 3 × 3 × 5 × 7

The prime factors for 330 = 2 × 3 × 5 × 11

The LCM of 420,630,330 = 2 × 2 × 3 × 3 × 5 × 7 × 11 = 13860.

Therefore, the GCD and LCM is 30 and 13860 respectively.

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What are the slope and the y-intercept of the linear function that is represented by the equation y?.

Answers

The slope of the line is -10, and the y-intercept is 1.

Linear equations can be written in the form y=mx+b, where:y is a y coordinate on the line m is the slope of the line.A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.

x is the x coordinate on the line that corresponds with the y coordinate in the equation,b is the y-intercept of the line

So for the equation y=-10x+1:

comparing the above equation with  y=mx+b we get,

m=-10 and b=1 so the slope of the line is -10, and the y-intercept is 1.

Thus, The slope of the line is -10, and the y-intercept is 1.

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Anybody know how to solve this??? Plsss

Answers

Answer:

12,34

Step-by-step explanation:

For 'a'

8x=(2x+72) [vertically opposite angle]

8x-2x=72

6x=72

x=72/6

x=12

For 'b'

4x+20+x-10=180° [ being straight angle ]

4x+x+20-10=180°

5x+10=180°

5x=180-10

x=170/5

x=34

2. *
5
A map is represented on a coordinate grid. Town A is located at (-8, 2) and Town B is located
at (10, 8). Town C is the midpoint between Town A and Town B.
If each unit represents 1 mile, the approximate distance from Town A to Town C is
1 point
miles.

Answers

The approximate distance from Town A to Town C is 12.5 miles.

What is the midpoint?

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

To find the midpoint of Town A and Town B, you need to find the average of the x-coordinates and the average of the y-coordinates.

The x-coordinate of Town A is -8 and the x-coordinate of Town B is 10, so the average is (10 - (-8))/2 = 9/2 = 4.5.

The y-coordinate of Town A is 2 and the y-coordinate of Town B is 8, so the average is (8 - 2)/2 = 6/2 = 3.

Therefore, Town C is located at (4.5, 3).

To find the distance from Town A to Town C, you can use the distance formula, which is the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The distance from Town A to Town C = √((4.5 - (-8))^2 + (3 - 2)^2) = √(12.5^2 + 1^2) = √(156.25 + 1) = √(157.25) = 12.5 miles

Hence, the approximate distance from Town A to Town C is 12.5 miles.

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Bowling Green middle school has 600 students. in Aiko’s class, 6 10 students prefer summer to spring. based on these results, how many students prefer summer

Answers

The number of students who prefer summer is equal to 60 students.

How to determine the number of students who prefer summer?

In order to determine the number of students who prefer summer, we would multiply the total number of students in Bowling Green middle school by the number of students in Aiko’s class who prefer summer to spring.

Mathematically, an expression which models the number of students who prefer summer is given by;

Number of students who prefer summer = 6/10 × 600

Number of students who prefer summer = 0.6 × 600

Number of students who prefer summer = 60 students.

Based on these results, we can logically conclude that 60 students in Aiko’s class who prefer summer to spring.

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Complete Question:

Bowling Green middle school has 600 students. in Aiko’s class, 6 out of 10 students prefer summer to spring. Based on these results, how many students prefer summer?

What is a 120 degree angle called?.

Answers

Answer:

Obtuse angle

Step-by-step explanation:

Angles greater than 90 degrees are obtuse angles, angles less than 90 degrees are acute angles, and angles at 90 degrees are right angles.

Noah earn 37 for 4 hr of babyitting. At thi rate how much more would he earn for 9 hr

Answers

The rate he would he earn for 9 h will be 83.25

Your pay for each hour of labor is expressed as an hourly rate. You might need to estimate your income for other applications or change your own budget after comparing the hourly and salaried pay rates.

The sum of money charged, received, or earned for each hour of work: Instead of paying for the things the advisers try to sell you, you pay a set or hourly charge for their time.

Noah earns 37 for 4 hr of babysitting.

so if you divide 37 by 4 you get the rate per hour

which is 9.25 so if you multiply 9 times 9.25

The rate he would earn for 9 h will be

you would get 83.25.

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Can a 9 12 15 form a triangle?.

Answers

Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(9cm + 12cm) =15cm

21cm = 15cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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Arc length of GH = 7pi cm
r =

Answers

The formula for a circle's arc length is L = r * θ, where L is the arc length, r is the circle's radius, and θ is the arc's central angle, expressed in radians.

What is the radius r in the given question?

We can calculate the radius of the circle by dividing the arc length by the central angle because we know the value of L (7 cm) and that can be calculated from the arc's measure (degrees or radians):

r = L / θ

It is crucial to keep in mind that in order to calculate the radius, you must first know the arc's central angle's measurement in radians.

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Given the experiment with the outcomes of the table

Answers

The experimental probability of spinning red and spinning blue is 4 and 2.8.

What is the experimental probability?

Experimental probability is a type of probability that is determined by conducting an experiment and observing the outcomes. It is also known as empirical probability.

It is calculated by counting the number of times an event occurs in a set of trials and then dividing that number by the total number of trials.

The experimental probability of spinning red.

P(red) = 20/5 = 4

The experimental probability of spinning blue

P(red) = 20/7 = 2.8

Hence, The experimental probability of spinning red and spinning blue is 4 and 2.8.

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A5=768 and a2=12; given two term in a geometric equence find the 8th term and the recurive formula

Answers

The recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.

What is geometric ?

A geometric sequence is a sequence of numbers such that the quotient between any two consecutive terms is always the same, this common ratio is denoted by "r" and the first term of the sequence is denoted by "a1". A geometric sequence can be represented by the following formula

a_n = a_1 * r^(n-1)

Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:

r = a5 / a2 = 768 / 12 = 64

To find the 8th term of the geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where a1 is the first term, r is the common ratio, and n is the position of the term.

Given the 8th term, we can substitute the values

a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7

To find the recursive formula, we can use the formula:

an = a(n-1) * r, where a(n-1) is the previous term of the sequence

So the recursive formula for this geometric sequence is , an = a(n-1) * 64, where a(n-1) is the previous term of the sequence.

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A geometric sequence is a set of numbers where any two consecutive terms' quotients are always the same. The first term in the series is indicated by the letter "a1," and the common ratio is indicated by the letter "r". The following formula can be used to describe a geometric sequence.

Given a5=768 and a2=12, we can find the value of the common ratio (r) by dividing the two terms:

r = a5 / a2 = 768 / 12 = 64

To find the 8th term of the geometric sequence, we can use the formula:

an = a1 * r^(n-1)

where a1 is the first term, r is the common ratio, and n is the position of the term.

Given the 8th term, we can substitute the values

a8 = a1 * r^(8-1) = a1 * 64^7 = a1 * 64^7

The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0

Answers

Answer: The area of a rectangular room is 750 square feet and the width of the room is 5 feet less than the length of the room.

Three equations that can be used to solve for y, the length of the room are:

y(y + 5) = 750: This equation uses the formula for the area of a rectangle, which is length x width. Since the width is 5 feet less than the length, we can substitute y-5 for the width.

750 – y(y – 5) = 0: This equation uses the same method as the first equation, but it is rearranged to solve for y.

(y + 25)(y – 30) = 0: This equation uses the quadratic formula to solve for the length of the room, this equation is also useful when the length is an irrational number.

Note that the fourth equation y(y – 5) + 750 = 0 is not valid because it is not possible to have negative area, hence y(y-5) should not be added to 750.

The fifth equation (y+25)(y-30)=0 is also not valid because it gives y = -25 and y = 30 as solutions but the length of the room can't be negative.

Step-by-step explanation:

simplify the expression
6(6- 2s)=

Answers

Answer:

36-12s=y

s=3

thats with it all the way simplified

find the value of f(3) + f(6)

Answers

Answer: The answer Is 9f

Step-by-step explanation:

The drawing below shows three squares joined at their vertices to form a right triangle. The area of square A is 9 ft2 and the area of
square B is 16 ft². What is the side length of square C?

25
7
8
5

Answers

The side length of square C is given as follows:

5 ft.

How to obtain the side length of square C?

The area of a square of side length is given as follows:

A = s².

Hence the side length of A and B are given as follows:

A = 3, as the square has area of 9 ft².B = 4, as the square has area of 16 ft².

Then the side length of square C is the hypotenuse of a right triangle, and applying the Pythagorean Theorem, it's length is obtained as follows:

C² = 3² + 4²

C² = 25

C = 5 ft.

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Somebody please help

Answers

The algebraic expression y = $2x + $10 represent the cost of each ATM transaction for the month where x is the cost of transaction during the month. And $20 is the total cost of 5 ATM transactions with the expression y = $2(5) + $10.

How to evaluate the total cost of 5 ATM transaction

We shall represent the total cost of ATM transaction in a the month with the letter y and the cost of a transaction with the letter x so that we have an algebraic expression as follows:

y = $2x + $10

using the algebraic expression to evaluate for the total cost of 5 ATM transaction, we have;

y = $2(5) + $10

y = $10 + $10

y = $20

Therefore, the algebraic expression y = $2x + $10 can be used to represent the cost of each ATM transaction for the month. And the expression y = $2(5) + $10 with the result $20 represent the total cost of 5 ATM transaction during the month.

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Help someone tell me what’s x??

Answers

The length of the rectangle side x is equal to 35.33 cm approximately to 2 decimal place using the trigonometric ratio of tangent.

What are trigonometric ratios

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

We shall represent the intercept of the diagonal lines in the rectangle with O so that we consider the right triangle ∆AOx, then we solve for the length of Ax and multiply the result by 2 to derive the value of x as follows:

angle 54 and m∠AOD are supplementary so;

m∠AOx = (180 - 54)/2 {m∠AOD/2}

m∠AOx = 63°

tan 63° = (x/2) ÷ 9

tan 63° = x/2 × 1/9 {change division to multiplication}

tan 63° = x/18

x = 18 × tan 63° {cross multiplication}

x = 35.3270

Therefore, 35.33 cm approximately to 2 decimal place is the length of the rectangle side x using the trigonometric ratio of tangent.

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Figure 1 and figure 2 are right triangles.

two right triangles labeled figure 1 and figure 2, where the legs of figure 1 are 3 units long and the legs of figure 2 are 5 units long

What scale factor was used to produce Figure 2 from Figure 1?

3 over 5
5 over 3
3
5

Answers

The scale factor used to produce the second triangle is 5/3.

What is a scale factor?

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size. For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Given that, a triangle with base length of 3 units is transformed into a second triangle with a base length of 5 units,

Therefore, the scale factor = 3/5

Therefore, to produce Figure 2 from Figure 1 we will multiply it by 5/3

Hence, the scale factor used to produce the second triangle is 5/3.

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Answer:

If ur options are  one sixth

6

one half

2

then the correct answer is 2

Step-by-step explanation:

I took the quiz and got it right.

Answer the following question in the picture

Answers

#2. 25b^4/a^3
……………………..

1. Draw a proportional line with a slope of 3/2

Answers

*desmos graphing calculator*

Other Questions
what are your thoughts on gender inequality? ever experienced it or witnessed it? do you believe that it's a major problem in society? how should a democratic society respond to terrorism the shaded region under a normal distribution with mean 0 and standard deviation 1 (standard normal distribution) is shown. which of the following is the best choice that corresponds to the shaded region? select one. The belief in what type of rights influenced Thomas Jefferson as he wrote the Declaration of Independence ? explain how the inegumentary system, skeletal, muscular systems work together to maintain good health I need help on this question What type of figurative language literary device is line 1 I Wandered Lonely as a Cloud?. QuestionSolve x 4 or x -6 and write the solution in interval notation. A random number generator assigned each pepper to one of two groups. The weights of the peppers in each group, given three randomizations, appear in the tables.First randomizationgroup a13.612.115.911.29.7group b9.28.211.513.814.6 who would like to become a nurse? a. daniel b. ana c. angela d. gabriela What is the SI unit of gravitational force and gravity?. The sides of a triangle are 24, 10, and 26. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse. medication order reads: rocephin 0.7 g im q 12 h. supply on hand: rocephin 1 g, reconstitute the 1 g vial by adding 2.1 ml of sterile water for injection. yields 350 mg/ml. give ml which is attacks do security professionals expose themselves to, if they do not salt passwords with a random value? What are the three parts of a proof?. A meteorologist drew the accompanying graph to show the changes in relative humidity during a 24 hour period in New York City. What is the range of this set of data? 0 one way to avoid impaired drivers is to stay away from the parts of town where the bars and nightclubs are located. an amendment to the international treaty on climate change designated to reduce the amount of greenhouse gases emitted by specific countries is called ? Calculate the resultant of two forces that act on a point, as indicated in the diagram. (193 N 355") F. - 200 N 40 F = 150 N 25 Imagine that you are a Christian observer transported back in time to the afterlife of the ancient Egyptians. In 75 total words or less, describe what you see there and how Egyptian religious beliefs differs from the Christian doctrine that you have been taught.