Figure 1 shows a paperweight made from a hollow hemisphere and a hollow cone. The paperweight contains sand so that the sand exactly fills the hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 15cm and the volume of the cone is 180π cm3 Figure 2 below shows the paperweight after it has been turned upside down. Diagram NOT accurately drawn h cm Figure 2 The height of the sand in the cone is h cm. Find, to 3 significant figures, the value of h.

Answer:

n ≤103

Step-by-step explanation:

The product of a number n and 1 is expressed as  n

Six less than the number is n - 6

If the result is no more than 97, then;

n - 6 ≤ 97

n ≤ 97 + 6

n ≤103

Hence the value of n is no more than 103

Answer:

Step-by-step explanation:

The formula for this particular problem is

[tex]x^2=2(2+16)[/tex] and

x² = 2(18) and

x² = 36 so

x = 6

Scale factor = (image)/(preimage)

[tex]AC=8\\\\A'C'=12[/tex]

So, the scale factor is [tex]\frac{12}{8}=\boxed{1.5}[/tex]

Answer:

y= -1/2x+4

Step-by-step explanation:

slope = rise/run on the graph. the graph is going down, so it's negative. find where the line intersects the graph at a point and then count the squares up and over until it meets again. the line meets at (6,1), you count up one square and over 2 and it meets again. this gives you your rise/run = 1/2. the y intercept is where the line intersects the y axis. here the y intercept is 4 because the like goes through 4 at the y axis.

Answer:

Step-by-step explanation:

let angle p be x

x+27=56 degree (sum of two opposite interior angle is equal to the exterior angle formed)

x=56-27

x=29 degree

therefore p is 29 degree.

Answer:

Step-by-step explanation:

The roots of the quadratic equation below using the quadratic formula are option A. [-9 ± √105 ] / 6.

Given is a quadratic equation,

3x² + 9x - 2 = 0

Quadratic formula to find the roots of a general quadratic equation ax² + bx + c is,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex] ] / 2a

Here a = 3, b = 9 and c = -2.

Substituting the values,

x = [-9 ± [tex]\sqrt{9^2-(4)(3)(-2)}[/tex] ] / (2 × 3)

  = [-9 ± [tex]\sqrt{81+24}[/tex] ] / 6

  =  [-9 ± √105 ] / 6

So the roots are [-9 ± √105 ] / 6.

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Answer:

3 : 7 : 5

Step-by-step explanation:

Given

12 : 28 : 20 ← divide each part by 4 ( the LCM of 12, 28, 20 )

= 3 : 7 : 5

Answer:

Step-by-step explanation:

[tex]28y^{7} *x^{4} *u^{3} \\8x^{4} *u^{5}[/tex]

rewrite those 2 terms to better see what they have in common

[tex]4*7 *x^{4} *u^{3} *y^{7} \\4*2*x^{4}*u^{3} *u^{2}[/tex]

because, 4*7 =28, 4*2=8, u³*u² =u^5, and multiplication is commutative

The greatest common factor is:

[tex]4x^{4} u^{3}[/tex]

Answer:

C) 80

Step-by-step explanation:

triangles always add up to 180 degrees, so 80+20=100 the missing angle is 80 degrees

Answer:

28

Step-by-step explanation:

Answer:

DE ≈ 16.1, ∠E ≈ 60.3°, ∠D ≈ 29.7°

Step-by-step explanation:

use pythagorean theorem:

DE² = 8² + 14² => DE = √8² + 14² ≈ 16.1

use inverse tangent function:

∠E =  [tex]tan^{-1}[/tex](14/8) ≈ 60.3°

∠D =  [tex]tan^{-1}[/tex](8/14) ≈ 29.7°

Answers:

The "units" and "degrees" portions of the answers are likely to be left out.

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

Explanation:

Since we have a right triangle, we can use the pythagorean theorem to find the hypotenuse DE

a^2+b^2 = c^2

c = sqrt(a^2+b^2)

c = sqrt(8^2+14^2)

c = 16.124515496597

c = 16.1 is the approximate length of side DE

----------------------------------

We'll use the tangent ratio to find angle E

tan(angle) = opposite/adjacent

tan(E) = FD/FE

tan(E) = 14/8

E = arctan(14/8)

E = 60.2551187030578

E = 60.3 degrees

The notation arctan is the same as inverse tangent. You should have a [tex]\tan^{-1}[/tex] button on your calculator to help compute the inverse tangent.

-------------------------------------

We could use the tangent ratio to solve for angle D, by noting that

tan(D) = 8/14

or we could use the idea that D+E = 90 which solves to D = 90-E

D = 90-E

D = 90-60.3

D = 29.7 degrees

Note how arctan(8/14) = 29.74488 which rounds to 29.7

Answer:

y = 2x + 5

Step-by-step explanation:

We have two points,

(-2,1) and

(4,13)

from which we can find the slope, m, where

m = (13-1)/(4--2) = 12/6 = 2

take any of the two points to form the point-slope form

y-y1 = m(x-x1)

y-13 = 2 (x-4)

y = 2x - 8 + 13 =2x+5

Check:

when x = -2, y = 2(-2)+5 = 1 checks.

Answer:

0.88

Step-by-step explanation:

We would consider the first case second column....

So 14/16 will be the probability that comes out be approximately 0.88.

Answer:

D

Step-by-step explanation:

Answer:

Hello! answer: 30

Step-by-step explanation:

Triangle area can be found be doing base × height × 1/2 or base × height ÷ 2

So...

12 × 5 = 60 60 ÷ 2 = 30 therefore the area is 30 hope that helps!

The area of the following right-angled triangle is 30 sq units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

By the concept of Pythagoras' theorem,

13² = 5² + h².

h² = 13² - 5².

h² = 144.

h = 12.

Now, We have the height and we can find the area of the triangle,

= (1/2)×5×12.

= 30 sq units.

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Answer:

1. 345,600 seconds

2. 432,000 seconds

3. 1 day

4. 7500 meters

Hope that this helps!

Answer:

4 days=345600sec

5 days=432000

86400=24 hours

7.5km = 4.6miles

Step-by-step explanation:

60sec * 60= 1hour * 24 * 4=4 days  if one day = 86400 sec than 4 days is 345600 and we know one day is 86400 seconds so just add that for one day

to convers km to mils you multiply the km value by .6214

Answer:

70%

Step-by-step explanation:

He should round the percentage to the nearest 10 which will give him a more reasonable prediction. Hope this helps!

Answer:

C. every rhombus is a parallelogram

Answer:

every rhombus is also a parallelogram....

Answer:

A(-1,1) B(-3,2) C(-3,4) D(-1,5)

Step-by-step explanation:

when the shape is rotated 270° it will be in quadrant 2(top left). the x coordinates will be negative. the y coordinates will still be positive. basically if you move your paper so the shape in in the top left corner, you will find your coordinates.

Answer:

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

20² - 16² = x²

400 - 256 = x

400 - 256 = 144

√144 = 12

Answer:

8.06

Step-by-step explanation:

Answer:

$30.92

Step-by-step explanation:

Answer:

$23 I hope this helps :)

Step-by-step explanation:

Answer:

14.13 units

Step-by-step explanation:

Semicirle is half the circumferene of a full circle. A full circle has a circumfence of 28.26 units.

Answer:

Step-by-step explanation:

1 = 1/16 (one chance on 16

2 = 7/16 (the non shaded parts are 7, while the total parts are 16)

3 = 11/16 ( 11 is unshaded + even)

4 = 4/16 = 1/4 (the favourable possibilities are: 13, 14, 15, 16)

So you basically get 104% of your Savings Account every two months for Plan A.

Plan B makes it 110% of your Savings Account every 6 months. Now we just calculate it...I'm sure your allowed a calculator, so just do 110% of it till 5 years.

If you still don't understand I can explain it more.

Answer:

its none

Step-by-step explanation:

Answer:

none of these answers are correct.

Answer:

AC = 15.6

Step-by-step explanation:

AC = AE + EC

By he Pythagorean theorem,

A² + B² = C²

12² + 5² = AE²

144 + 25 = AE²

AE = √169

AE = 13

Find Angle AED

tan Angle AED = 12/5

Angle AED = tan-1 (12/5)

= 67.38°

Angle AED = Angle BEC

tan (67.38°) = BC/1

BC = 2.4

1² + 2.4² = EC²

6.76 = EC²

EC = √6.76

EC = 2.6

AC = 13 + 2.6

AC = 15.6

Answer:

Step-by-step explanation:

scale factor=3/2

(8,6)

(12,6)

(12,10)

use formula

(x,y)=(kx,ky)  (k means scale factor)

(8,6)=(3/2*8 , 3/*6)

=(24/2 , 18/2)

=(12 , 9)

(12,6)=(3/2*12 , 3/2*6)

=(36/2 , 18/2)

=(18 , 9)

(12,10)=(3/2*12 , 3/2*10)

=(36/2 , 30/2)

=(18 , 15)

Answer:

18 ,15

Step-by-step explanation:

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Answer:

h = -50

Step-by-step explanation:

- 3/10h = 15

Multiply each side by -10/3 to isolate h

-10/3 * - 3/10h = 15 * -10/3

h = -150/3

h = -50

Answer:

h = -50

Step-by-step explanation: