a A hole in the shape of a hemisphere is carved into each face of a cube. The holes are identical and centered at the centre of each face. The holes touch their neighbours at only one point. The cube has side 2. What is the diameter of each hole?​

The diameter of a sphere with a volume of 397 meter cube to the nearest tenth of a meter is 9.1 meters

volume of a sphere = 4 / 3 πr³

where

Therefore,

volume = 397m³

Diameter = radius  × 2

Hence,

volume of a sphere = 4 / 3 πr³

volume of a sphere = 4 / 3 × 3.14 × r³

397 = 12.56 / 3 r³

cross multiply

397 × 3 = 12.56 r³

1191 = 12.56 r³

divide both sides by 12.56

r³ = 1191 / 12.56

r = ∛94.8248407643

r = 4.56009658

Hence,

diameter = 4.56009658 × 2 = 9.12 = 9.1 meters

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Brent estimates that the model's circumference is about 3 times the measure of the circle's diameter, with this, he can estimate the area.

A circle is the locus of a point, such that the distance from a fixed point (center) is always constant.

The circumference of a circle is given by:

Circumference = π * diameter

Brent estimates that the model's circumference is about 3 times the measure of the circle's diameter, with this, he can estimate the area.

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By solving a simple linear equation, we conclude that the length of the second lawn is 10 meters.

We know that one of the lawns is 5 meters long and 4 meters wide, then its area is:

A = 4m*5m = 20m^2

The other is two times as big, so its area is 40m^2 and has the same width as the first one (4 meters), so if we define the length as L we can write:

40m^2 = 4m*L

Solving for L we get:

(40 m^2)/4m = L = 10m

The length is 10 meters.

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Answer:

C. (5, 8, 9)

Step-by-step explanation:

Put the triples into the Pythagorean Theorem and see if they come out true.

a² + b² = c²

5² + 12² = 13²

25 + 144 = 169

169 = 169

5, 12, and 13 are a Pythagorean Triple.

a² + b² + c²

8² + 15² = 17²

64 + 225 = 289

289 = 289

8, 15, and 17 are a Pythagorean Triple.

a² + b² = c²

5² + 8² = 9²

25 + 64 = 81

89 ≠ 81

5, 8, and 9 are NOT a Pythagorean Triple.

a² + b² = c²

6² + 8² = 10²

36 + 64 = 100

100 = 100

6, 8, and 10 are a Pythagorean Triple.

The amount of plastic covering needed to cover the window is 25.71.

The window consists of a semi circle and a rectangle. The circumference and the perimeter of the semi circle and a rectangle has to be determined.

Circumference of the semi circle = 1/2πd + d

Where:

π = 3.14

d = diameter = 3

1/2 x 3.14 x 3 + 3 = 7.71

Perimeter of the rectangle = 2(length + width)

2x (6 + 3) = 18

18 + 7.71 = 25.71

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Answer:

30.7%, 0.3, or 4/13

Step-by-step explanation:

The correct procedure for this problem is:

Answer:

3

Step-by-step explanation:

these are 2 similar triangles (all 3 pairs of corresponding angles are equal in their pair, and the lengths of corresponding sides have the same ratio in every pair of corresponding sides and other lengths).

and they are also right-angled triangles.

so, what else do we know about them ?

PQ = 18

RT = 6

ST = QT + 9

therefore

QT = ST - 9

and

QR = QT + RT = ST - 9 + 6 = ST - 3

due to the principles of cumulative triangles

PQ/ST = QR/RT = 18/ST = (ST - 3)/6

108/ST = (ST - 3)

108 = (ST - 3)ST = ST² - 3ST

ST² - 3ST - 108 = 0

we can the write

x² - 3x - 108 = 0

and the solution for such a squared equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -3

c = -108

x = (3 ± sqrt(9 - 4×1×-108))/2 = (3 ± sqrt(441))/2 =

= (3 ± 21)/2

x1 = (3+21)/2 = 24/2 = 12

x2 = (3-21)/2 = -18/2 = -9

a negative solution for real lengths is not valid, so we know

x = ST = 12

so,

QR = ST - 3 = 12 - 3 = 9

and then

QT = QR - RT = 9 - 6 = 3

Answer:

she saves $40

Step-by-step explanation:

first of all, you find 20% of $50, that is,

(20/100) * $50

then you get: $10

next step is to subtract this answer from the $50, that is: $50 - $10 = $40

have a great day!!

We get the amount of price removed as a result of free coupon as below:

[tex] \frac{20}{100 } \times 50 = \frac{1000}{100} = 10 \\ coupon = 10dollars[/tex]

Therefore, Sonya saved $10

Answer:

4000 meters

Step-by-step explanation:

Shortest run was 5 laps (2000 meters), and longest was 15 (6,000 meters)

Answer:

21,42/2,-(42/-2)

Step-by-step explanation:

please mark me as brainlest

Answer: 200 students gave their speeches.

Explanation;

240 ÷ 6 = 40

40 x 5 = 200

Answer:

get better maybe

Step-by-step explanation:

just pay attention in class

Answer:

(B) is the answer of your question

Answer:

The answer is 270

Step-by-step explanation:

5×54=270

The true statement about h(x) is: The function is increasing on the interval [0, ∞).

A linear function can be represented by a line. The standard form for this equation is: ax+b , for example, y=2x+7. Where:

a= the slope.If:

             a> 0 , the function is increasing;

             a< 0 , the function is decreasing;

b=the constant term that represents the y-intercept.

The domain of a function is the set of input values for which the function is real and defined. In other words, when you define the domain, you are indicating for which values x the function is real and defined.

While the domain is related to the values ​​of x, the range is related to the possible values ​​of y that the function can have.

You should convert the text of the question into a math expression.

[tex]h(x)=3*\sqrt{x}[/tex]

Like the coefficient a is greater than zero (a>0), the function is increasing.

The equation has a square root, so, the values of x can not present negative values. Therefore, x≥0. Consequently, the values of y (range) for this function will be greater than or equal to zero (y≥0). See the attached image.

The range is:

[tex]{Solution:}\:&\:f\left(x\right)\ge \:0\:\\Notation:}&\:[0,\:\infty \:)\end{bmatrix}[/tex]

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Answer:

√20 which can be written as 2√5

Answer:

Area of right angle triangle is axb/2

3x4/2 = 6 sq. Cm

Area of parallelogram = bxh

20x21.5 = 430 in2

Answer:

Area of the triangle: 6 cm
Area of the parallelogram: 430 in²

Step-by-step explanation:

Area of a triangle formula is base * height * 1/2, in this case 4 * 3 * 1/2, which equals 6.

Area of a parallelogram formula is base * height, in this case 21.5 * 20 which equals 430.

Answer:

SW = 130

Step-by-step explanation:

[tex]2(2x+5)=5x-20[/tex]

This is what the equation should be because this is a rectangle.

[tex]4x+10=5x-20[/tex]

Once you finish simplifying, move the numbers and variables over to get this.

[tex]x=30[/tex]

Then do multiplication and addition to get 130.

Answer: 42.0

Step-by-step explanation:

Let's see

Area

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}\times Base\times Height [/tex]

[tex]\\ \rm\rightarrowtail \dfrac{1}{2}(6xy^5)(4x^2y)[/tex]

[tex]\\ \rm\rightarrowtail 3xy^5(4x^2y)[/tex]

[tex]\\ \rm\rightarrowtail 12x^3y^6[/tex]

[tex]\text{Area of triangle} = \dfrac 12 \times \text{Height} \times \text{Base} \\\\~~~~~~~~~~~~~~~~~~~~~~=\dfrac 12 \cdot 6xy^5\cdot 4x^2y\\\\~~~~~~~~~~~~~~~~~~~~~~=12x^3y^6 ~ \text{units}^2[/tex]

Sorry but no speek English

Answer:

3 and 4

Step-by-step explanation:

3.5 ounces is 7/2 so if they eat the same amount they would both eat 3.5 ounces.

Answer:

You are right

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve as requested in the question, round each number:

The sum is:

Answer:

8000

Step-by-step explanation:

⇒ 3008 + 5243 ≈ 3000 + 5000

⇒ 3000 + 5000 = 8000

Answer:

44 campers chose basketball

Answer:

The rule for this question should be an=10*(-3)^(n-1)

Step-by-step explanation:

Because 10, -30, 90, and -270 divide (for example -30/10, 90/-30 and -270/90 which means the ratio equals -3) To find the ratio, you must divide by its previous term.

Then, the equation for the ratio would be a1 (first term in the sequence) multiplied by the ratio, then to the power of the number subtracted by 1. an=a1*r^(n-1) This is the formula to find the nth term of a geometric sequence.

Hope this helped!

Answer: you literally said it yourself. its 36°

Step-by-step explanation:

Answer:

42cm³

Step-by-step explanation:

7*2*3=42

7*2=14

14*3=42

42

Answer: 0.15

Step-by-step explanation:

Answer:

0.15

Step-by-step explanation:

3/20=15% so that means its 0.15