work out the area of this shape

Answer:

n = 112/13 = 8.615

Step-by-step explanation:

(3/8) n + 5n - 30 = (17/8)n - 2

(3/8)n +5n - (17/8)n = 30-2

(13/4)n = 28

n = 28 * 4/13

n = 112/13

n = 8.615

9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

Answer:

n=4

Step-by-step explanation:

f(x+n)=3(x+n)^2-7=3x^2+24x+41

3x^2+3n^2+6xn-7=3x^2+24x+41

Comparing and we will get, n=4

Answer:

t = 70 tons/1.5 tons/min = 46.7 min = 2800 sec before boat sinks

S = V * t

V = S / t = 20 mi * 5280 ft/mi / 2800  sec  = 37.7 ft/sec

Since 88 ft/sec = 60 mph

the speed is 60 * 37.7 / 88 = 25.7 mph

Answer:

Step-by-step explanation:

Let L represent the length of the triangle.

Let W represent the width of the triangle.

The length of a rectangle is four more than three times the width. This means that

L = 3W + 4

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

If the perimeter of this rectangle is at least 70 square centimeters, an inequality that can be solved to find the width of the rectangle is

2(L + W) ≥ 70

L + W ≥ 70/2

L + W ≥ 35

Answer:

6w +8 ≥70

Step-by-step explanation:

Let w be the width

The length is then 3w+4 ("the length is 4 more than 3 times the width")

Since a rectangle has opposite sides equal, the perimeter would be 2(l+w) or 2(w+3w+4) which would be 6w +8.  If the perimeter is at least 70, that is, 70 or more, the inequality would be

  6w + 8 ≥ 70.  

The units, however, would not be SQUARE centimeters, just centimeters.  If the question were asking for area, the units would be square units, but since perimeter is a linear measurement,  the units would have to be linear.

I think its A) (f+g)(z)=|2x+4|-2

Step-by-step explanation:

Answer:

95% provides more information

Step-by-step explanation:

The confidence interval is obtained by using the relation :

Xbar ± Zcritical * σ/√n

(Xbar - (Zcritical * σ/√n)) = 5.22 - - - (1)

(Xbar + (Zcritical * σ/√n)) = 5.98 - - (2)

Adding (1) and (2)

2xbar = 5.22 + 5.98

2xbar = 11.2

xbar = 11.2 / 2 = 5.6

Margin of Error :

Xbar - lower C.I = Zcritical * σ/√n

Zcritical at 90% = 1.645

5.6 - 5.22 = 1.645 * (σ/√n)

0.38 = 1.645 * (σ/√n)

(σ/√n) = 0.38 / 1.645 = 0.231

Therefore, using the se parameters to construct at 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * σ/√n

Margin of Error = 1.96 * 0.231 = 0.45276

C.I = xbar ± margin of error

C. I = 5.6 ± 0.45276

C.I = (5.6 - 0.45276) ; (5.6 + 0.45276)

C. I = (5.147 ; 6.053)

Hence, 95% confidence interval provides more information as it is wider.

Answer:

200 kilometers and 150 kilometers

Answer:

2 3/10

Step-by-step explanation:

3/5x2=6/10

6/10-3/10=3/10

Answer:

i) pi×4500 cm³

ii) pi×600 cm²

iii) 14 liters

Step-by-step explanation:

in general : the diameter is 30 cm, the radius is half of that (15 cm)

i)

the volume of a cylinder is base area times height.

Vc = pi×r²×h = pi×15²×20 = pi×225×20 = pi×4500 cm³

ii)

similar to volume, the side "mantle" area of the cylinder is the circumference of the base area times height.

surface area of the cylinder mantle is

Scm = 2×pi×r×h = 2×pi×15×20 = pi×30×20 = pi×600 cm²

iii)

for this we need now to do the multiplication with pi and then convert the cm³ to liters.

1 liter = a cube of 10 cm side length = 10×10×10 = 1000 cm³

pi×4500 = 14137.17 cm³ = 14.13717 liters or rounded 14 liters

Answer: About 21.98 cm²

Step-by-step explanation:

First, find the area of the large shaded circle:

[tex]r^{2} \pi =3^{2} \pi =9\pi[/tex]

Find the area of the two small unshaded circles:

[tex]1) r^{2} \pi =1^{2} \pi =1\pi \\2) r^{2} \pi =1^{2} \pi=1\pi[/tex]

Subtract the area of the small circle from the large circle:

[tex]9\pi -1\pi -1\pi =9\pi -2\pi =7\pi[/tex]

Therefore, the area of the shaded region is:

[tex]7\pi =7*3.14=21.98[/tex]

Answer:

It has 1 term and a degree of 4.

Step-by-step explanation:

3j⁴k-2jk³+jk³-2j⁴k+jk³

= 3j⁴k-2j⁴k-2jk³+jk³+jk³

= j⁴k

So, in this expression, there is 1 term, and it has a degree of 4.

Answer:          

35/5 (if you mean 10.6)    

1000000 (if you mean 10 to the sixth power)      

0.000001 (if you mean 10/6)

Answer:

There are 126 inches in 10'6

Step-by-step explanation:

take our feet and multiply the value by 12

Answer:

1600

Step-by-step explanation:

multiply the volume value by 1000

Answer:

1.6 ft

Step-by-step explanation:

If you use the Pythagorean Theorem to solve for x, you get:

[tex]x=\sqrt{2.1^2-1.4^2}[/tex]

[tex]x=\sqrt{2.45} = 1.56524758425[/tex]

Rounded to the nearest tenth, the answer is 1.6

Answer:

average of the two observations in the center of the data array

Step-by-step explanation:

When there is an odd number, we use the middle

Example

1,5,9

The median is 5

When there is an even number

1,3,5,7

The middle is between the 3 and 5 so we average the middle number

(3+5)/2 = 4

Answer:

the answer is => observation in the center of the data array

Step-by-step explanation:

[tex]\sf{}[/tex]

no the square root of 113 is rounded to 56x2

Answer:

theres no question....

Step-by-step explanation:

???

can you zoom in on my pic more or no does it say 1/z

Answer:

Option A. Reciprocal

Answered by GAUTHMATH

Answer: about 40.54°

Step by step explanation:

7^2 =  5^2 + 10^2  - 2(5)(10)cos(B)

cos(B)  = (7^2 - 5^2 - 10^2) / (-2(5)(10) )

B = cos-1 [ (7^2 - 5^2 - 10^2) / (-2(5)(10) ]  =  cos-1 (.76) = about 40.54°

Answer:

7:50 am

Step-by-step explanation:

Clara took 2 hours to reach, and she took a 20 min break, so she left at 7:50 and arrived at 10:10.

Answer:

7:50

Step-by-step explanation:

50 miles per hour/50 miles per 60 min.

50 miles + 50 miles = 100 miles.

if 50 miles takes 1 hour, 100 miles would equal to 2 hours.

considering clara took a 20 min break, thats 2 hours and 20 minutes.. subtract that from the time she arrived and you would get 7:50

Answer:

X * 0.8 = $64

x = $80

Step-by-step explanation:

Answer:

$80 (D)

Step-by-step explanation:

If Richard is getting a discount and his final price is $64 that means the answer must be above 64. That eliminates A, B, and C.

Use the formula: 20% of x = $64 and substitute the other two options. 20 percent of 84 is 16.8. 84-16.8=67.2 (not the correct answer). 20 percent of 80 is 16. 80-16=64(The Correct Answer).The answer must be $80 (D)    

lim ( sinx-1)/(x-1)

x=>0

apply x=0

(sin(0)-1)/(0-1)

(0-1)/(-1)

=1

Answer:

x^2 - 7x - 30 = 0

Step-by-step explanation:

since solutions are 10 and -3

a factorised quad eqn can be formed:

(x-10)(x+3)=0

expand the eqn

x^2-7x-30 = 0 is the answer