If the sum of the first n terms of an AP is 1/2 (3n^2+7n),then find its nth term.Hence write its 20th term.​

Answer:

b. -1/6

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6

Answer:

m = -1/6 = B

Step-by-step explanation:

[tex]m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}[/tex]

Answer:

12345824.4

Step-by-step explanation:

I'm not really sure. I just did 1240x637x15.63=12345824.4

answer:

53,445.1 gallons of water

Step-by-step explanation:

im not exactly sure but i looked up how to calculate gallons in a container and the website i went to told me to measure the interior length, width, and height which was already done, then it told me to multiply the length by width by height to get the volume of the container then it told me to divide the volume by 231 to get the number of gallons in the container, so 1,240* 637= 789,880* 15.63= 12,345,824.4÷231= 53,445.127272727272727272727272727 which rounded to the nearest tenth is 53,445.1, i honestly hope that this is right and that it helps

Hi there!! (✿◕‿◕)

⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐

Hillsboro: 700 houses sold

Lowell: 100 houses sold

700 + 100 = 800

Hillsboro and Lowell: 800 houses sold

Other: 600

800 + 600 = 1,400

Clay County: 1,400 houses sold

800/1,400 = 4/7

Hope this helped!!  ٩(◕‿◕｡)۶

Answer:

4/7

Step-by-step explanation:

Well first we need to find the total amount of houses sold in Clay County.

700 + 100 + 600

= 1,400

Now we need to find the total of houses sold in Lowell and Hillsboro.

700 + 100

= 800

Now we can make the fraction,

800/1400

and simplify

400/700

200/350

20/35

4/7

Thus,

the fraction of houses sold in Hillsboro and Lowell in Clay County is 4/7.

Hope this helps :)

Answer:  21 ft³

Step-by-step explanation:

Let x represent the height of the box.

Then the 5 ft width of cardboard is (5 - 2x) when creating the box

and the 9 ft length of cardboard is (9 - 2x) when creating the box.

Volume = length x width x height

            = (9 - 2x)(5 - 2x)(x)

            = 45x - 28x² + 4x³

Using Calculus to solve for x, set the derivative equal to zero and use the quadratic formula to solve for x:

V' = 45 - 56x + 12x²

0 = 12x² - 56x + 45

x = 3.6, x = 1.0

Use those values to find the width, length, and volume:

height(x)   ×  width (5 - 2x)   ×  length (9 - 2x) = Volume

  3.63       ×       -2.26*                                            

     1          ×          3               ×         7              =    21

*width cannot be negative so the height cannot be 3.63

Answer:

see graph

Step-by-step explanation:

A reflection across the y-axis means the point is equal but opposite distance from the y-axis. This has no change on the y-value of the point, because no matter the y-value, the point will still be the same distance from the y-axis. Long story short, if you're reflecting across the y-axis, change the sign of the x-coordinate. If you're reflecting across the x- axis, change the sign of the y-coordinate.

In any coordinate pair, the first number is the x-value and the second number is the y-value.

To find the slope, simply take the difference of the y values and divide by the difference in the x values: (14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is -5/3.

It is find the slope of the line.

The slope of any line, ray, or line segment is the ratio of the vertical to the horizontal distance between any two points on it (“slope equals rise over run”).

The slope is always calculated from the rise divided by the run. Typically, the equation is presented as:

m = Rise/Run

If you have two points, the points should be [tex]P_{1} (x_{1} ,y_{1} )[/tex] and [tex]P_{2} (x_{2} ,y_{2} )[/tex]  So, the equation would be:

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

In any coordinate pair, the first number is the x-value and the second number is the y-value.

The difference of the y values and divide by the difference in the x values:

m=(14-9)/(1-4) is equal to -5/3.

The slope of the line that passes through (1, 14) and (4,9) is  -5/3.

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Answer:

The value of this expression when a = 3 and b = -2 is -1.

Step-by-step explanation:

The expression is:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

Compute the value of X for a = 3 and b = -2 as follows:

[tex]X=\frac{3a^{-2}b^{6}}{2a^{-1}b^{5}}[/tex]

    [tex]=\frac{3\cdot (3)^{-2}\cdot (-2)^{6}}{2\cdot (3)^{-1}\cdot (-2)^{5}}\\\\=\frac{(3^{-1})\times (-2)^{6}}{2\cdot (3^{-1})\cdot (-2)^{5}}\\\\=\frac{(-2)^{1}}{2}\\\\=-1[/tex]

Thus, the value of this expression when a = 3 and b = -2 is -1.

Answer:

x=0.2136

Step-by-step explanation:

Answer:

x=0.214 rounded to the thousandths

Step-by-step explanation:

2.35=11x

divide each side by 11 to isolate the x

x=0.214 rounded to the thousandths

Answer:

Total hectares needed = 13.3 billion hectares of ecological footprint.

Step-by-step explanation:

Country X's per capita ecological footprint = 3.2 hectares

Country Y's per capita ecological footprint = 0.6 hectares

Earth's population = 7 billion

Average footprint between the two nations = 1.9 (3.2 + 0.6) hectares

If everybody in the world (i.e. the earth's population) has an ecological footprint the size of the average footprint between these two countries, i.e. = 1.9 per capita of earth's population,

Therefore, the total hectares of ecological footprint needed will be equal to 7 billion x 1.9

= 13.3 billion hectares of ecological footprint.

Answer:

(4,0,-7)

Step-by-step explanation:

The initial position was (0,0,0) since it was the origin

Now, we have a movement of positive x at a distance of 4 units, with a distance of z a total of 7 units(negative since downward)

The current position is thus;

(4,0,-7)

Thus correlates to (x,y,z) and our y has remained zero as there is no movement along the y-axis

Answer:

perimeter = 56 in

area = 192 sq. in.

Step-by-step explanation:

area of a triangle = 0.5 * b * h

b = 12

h = 8

At = (0.5 * 12 * 8)  = 48

Area of a square

As = 12 * 12 = 144

total area = At + As

total area = 48 + 144

total area = 192 sq. in.

perimeter = add all sides

12 + 12 + 12 + 10 + 10 = 56 in

hope it helps

Answer:

Step-by-step explanation:

f(x)=3x+15

let  f(x)=y

y=3x+15

flip x and y

x=3y+15

3y=x-15

y=1/3 x-5

or f^{-1}x=1/3 x-5

The value of x from the diagram is 50 degrees. Vertical angles are angles that meets at a point of intersection.

Vertical angles are angles that meets at a point of intersection. From the given diagram 150 and 50+2x are vertical angles showing that they are equal to each other. Hence;

50 + 2x = 150

2x = 150 - 50

2x = 100

Divide both sides by 2

2x/2 = 100/2

x = 50

Hence the value of x from the diagram is 50 degrees

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Answer:

Its d [tex]x^{2} -6x+7=0[/tex]

Step-by-step explanation:

A= [tex]2+\sqrt{3\\}[/tex]

B= [tex]3\sqrt{2}[/tex]

C= [tex]-3+\sqrt{2}[/tex]

Answer:

D. x^2 - 6x + 7 = 0.

Step-by-step explanation:

The roots are 3 plus or minus sqrt(2). That means the equation is...

(x - [3 + sqrt(2)]) * (x - [3 - sqrt(2)])

= [x - 3 - sqrt(2)] * [x - 3 + sqrt(2)]

= x^2 - 3x - xsqrt(2) - 3x + 9 + 3sqrt(2) + xsqrt(2) - 3sqrt(2) - (sqrt(2))^2

= x^2 - 3x - 3x + 9 - 2 - xsqrt(2) + xsqrt(2) + 3sqrt(2) - 3sqrt(2)

= x^2 - 6x + 7.

Hope this helps!

If the path is perpendicular to the field it is zero.

If the path is along the field it is positive or negative depending on it's direction.

See the attached picture.

Answer:

$1116

Step-by-step explanation:

Answer:

cars are dum

Step-by-step explanation:

Answer:

They will find 69 viruses in 8 hours.

Step-by-step explanation:

The number of viruses after t hours is given by the following equation:

[tex]V(t) = V(0)(1-r)^{t}[/tex]

In which V(0) is the initial number of viruses and r is the decay rate, as a decimal.

They start with 500 viruses

This means that [tex]V(0) = 500[/tex]

Decay rate of 22% per hour.

This means that [tex]r = 0.22[/tex]

So

[tex]V(t) = V(0)(1-r)^{t}[/tex]

[tex]V(t) = 500(1-0.22)^{t}[/tex]

[tex]V(t) = 500(0.78)^{t}[/tex]

How many viruses will they find in 8 hours?

This is V(8).

[tex]V(t) = 500(0.78)^{t}[/tex]

[tex]V(8) = 500(0.78)^{8}[/tex]

[tex]V(8) = 68.51[/tex]

Rounding to the nearest whole number

They will find 69 viruses in 8 hours.

Answer:

The researchers will find 86 viruses.

Step-by-step explanation:

Identify the value of each variable in the formula. Be sure to put the percent in decimal form. Be sure the units match—the rate is per hour and the time is in hours.

A =?

A0 =  500

R= -0.22/hour

t= 8 hours

Substitute the values in the formula.

A= A0e^rt

A= 500e^-0.22x8

Compute the amount.

A ≈ 86.02

Round to the nearest whole number.

A ≈ 86

Answer:

The answer to your question is 24 cm³

Step-by-step explanation:

Data

Initial volume = 2/5

Additional volume = 42 cm³

Final volume = 4/7

the total volume of the glass = ?

Process

1.- Write a proportion to help you solve the problem

                  42 cm³  -------------------- 4/7 of the total

                   x            -------------------  7/7

2.- Solve the proportion

                  x = (7/7 x 42) / 4/7

3.- Simplification

                  x = 42 / 4/7

                  x = 168/7

                 x = 24 cm³                  

Answer:

y = mx + c

since m = 0

c = 9

Step-by-step explanation:

y = mx + c

since m = 0

c = 9

SLOPE THESE DAYS

Answer:

3 PM

350 miles

Step-by-step explanation:

Let's say t is the number of hours since 8 AM.

The distance traveled by Winston is:

w = 50t

The distance traveled by Alice is:

a = 70(t−2)

When w = a:

50t = 70(t−2)

50t = 70t − 140

140 = 20t

t = 7

Winston and Alice will be at the same place 7 hours after 8 AM, or 3 PM.

The distance they travel is 350 miles.

The approximate volume only applies when pi = 3.14

Use either answer, but not both of course.

===============================================

Work Shown:

V = volume of cylinder

V = pi*r^2*h

V = pi*2^2*8

V = pi*32

V = 32pi .... exact volume in terms of pi

V = 32*3.14

V = 100.48 .... approximate volume when we use pi = 3.14

Answer:

Number of dollar = 28.28 (Approx)

Step-by-step explanation:

Given:

176 dollar = 140 pound

1 pound = Rs.130

Find:

Number of dollars in Rs 2925

Computation:

1 pound = Rs.130

Number of pound = 2925 / 130

Number of pound = 22.5 pound

1 pound = 176 / 140

Number of dollar = [176 / 140]22.5

Number of dollar = 28.28 (Approx)

Answer:

3(sqrt42) ft

Step-by-step explanation:

If l is side length of square patio, then area of patio would be l^2.

l^2 = 378

l = sqrt378 = 3(sqrt42)

Answer:

Range of wages is £140 to £525.

Mean wage = £226

Step-by-step explanation:

Given:

Weekly wages paid to the staff are :

£245, £140, £525, £163, £195, £174 and £140.

To find:

Range of these wages = ?

Mean wage = ?

Solution:

First of all, let us learn about the range of wages and mean wage.

Range of wages has a minimum pay and a maximum pay.

Here, if we have a look £140 is the minimum pay and

£525 is the maximum pay.

So, range of wages is £140 to £525.

Mean wage means the average of all the wages given to the staff.

Mean is defined as the formula:

[tex]\text{Average/Mean =} \dfrac{\text{Sum of all the observations}}{\text{Number of observations}}[/tex]

Here, Sum of all observations mean sum of the wages of all the staff members.

Number of observations mean the number of staff members i.e. 7 here.

Applying the formula:

[tex]\text{Average/Mean =} \dfrac{\text{245+140+525+163+195+174+140}}{\text{7}} \\\Rightarrow \text{Average/Mean =} \dfrac{\text{1582}}{\text{7}}\\\Rightarrow \text{Average/Mean =} 226[/tex]

So, the answer is:

Range of wages is £140 to £525.

Mean wage = £226

Answer:

30% constituents=20 mL

10% constituents=180 mL

Step-by-step explanation:

x= 30% volume

y=10% volume

For our first equation, we know the total volume is 200 mL and is the sum

x+y=200

y=200-x (1)

For our second equation, we do a mass balance for 200 mL of final solution.

12% w/v = 0.12 g/mL

This means that in 1 mL of solution, we have 0.12 g of NaCl.

For any solution, concentration multiplied by volume will give the mass of NaCl:

Mass in x mL= C*V (g/mL) (mL)

So in 200 mL, we have

0.12*200 (g/mL) (mL)

=24g of NaCl

Cx*Vx + Cy*Vy=24

0.3x+0.1y=24 (2)

Substitute y=200-x into (2)

0.3x+0.1(200-x)=24

0.3x+20-0.1x=24

0.2x=24-20

0.2x=4

Divide both sides by 0.2

0.2x/0.2=4/0.2

x=20

Substitute x=20 into (1)

y=200-x

y=200-20

y=180

30% constituents=20 mL

10% constituents=180 mL

Answer:

Step-by-step explanation:

Given the population increasing according to the exponential function defined by y = 3e^0.04x, where y is in millions and x is the number of years, to determine when the population will reach 4 million, the following steps must be carried out.

Since y is in millions, we will first substitute y = 4 into the modeled equation as shown;

4 =  3e^0.04x

Therefore to calculate x, we need to solve the expression 3e^0.04x = 4 for the value of x and this is arrived at by simply substituting y = 4 into the given equation.

To get x;

3e^0.04x = 4

e^0.04x  = 4/3

taking the ln of both sides

lne^0.04x = ln1.333

0.04x = 0.287

x = 0.287/0.04

x≈ 3.59 years

Answer:

A) (3, 2)

Step-by-step explanation:

y = 4x - 10

y = 2

Substitute y with 2 in the first equation and solve for x.

y = 4x - 10

2 = 4x - 10

12 = 4x

3 = x

Solution: x = 3, y = 2

Answer: A) (3, 2)

Answer:

1.28

Step-by-step explanation:

Margin of error is also called confidence interval, and it shows how much the results from sample reflects the characteristics of the larger population.

The following steps are used to calculate margin of error.

- obtain population standard deviation (σ) and sample size (n)

- divide standard deviation by square root of sample size

- multiply result by z score consistent with the given confidence. In this case confidence is 80% and z score for it is 1.28

Margin of error= z * (σ ÷ √n)

Margin of error = 1.28 * (10 ÷ √100)

Margin of error= 1.28 * (10 ÷ 10) = 1.28

Answer:   90°

Step-by-step explanation:

As known ∡EGC=(arcEC+arcDF)/2

arcEC+arcDF=70°*2

5x+10+11x+2=140

16x+12=140

16x=128

x=128:16

x=8

So arcDF=11*x+2=11*8+2=90°

The measure of arc DF is 90°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the centre.

Given,  Circle A with chords EF and CD that intersect at point G,

arc EC = 5x + 10°

arc DF = 11x + 2°

∠EGC = 70°

The measure of the inner angle is the semi-sum of the arcs comprising it and its opposite

so

∠EGC=(1/2)[arc EC+arc DF]

substitute the values

70 = 1/2(5x + 10 + 11x + 2)

70 = 1/2(16x + 12)

140 = 16x + 12

16x = 128

x = 128/16 = 8

so ac DF = 11x + 2

arc DF = 11(8) + 2

arc DF= 88 + 2 = 90°

Hence the value of arc DF is 90°.

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