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Alekssandra [29.7K]
3 years ago
12

A circular garden has a circumference of 88 yards. Lars is digging a straight line along a diameter of the garden at a rate of 7

yards per hour. How many hours will it take him to dig across the garden? Use 3.14 for π and round the diameter to the nearest whole number, if necessary.
Mathematics
1 answer:
ankoles [38]3 years ago
4 0

Answer:

It will take 4 hours to dig in the garden

Step-by-step explanation:

First we have to calculate the diameter, for this we will use the formula to calculate the circumference of a circle and we will clear the diameter

d = diameter

π = 3.14

c = circumference

c = π * d

d = c / π

d = 88yd / 3.14

d = 28.025yd

round to the nearest whole number

28.025 = 28

d = 28yd

To know how many hours it takes, we divide the diameter by the speed

t = time

v = velocity

t = d / v

t = (28yd) / (7yd/h)

t = 4h

It will take 4 hours to dig in the garden

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Vikki [24]
Think it's no solution might be wrong though

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3 years ago
The equation is 12m+12=15-1
Fudgin [204]

Answer:

1/6

Step-by-step explanation:

Solve-

Subtract the numbers:

12m+12=15 - 1

12m+12 = 14

Subtract 12 form both sides of the equation:

12m+12= 14

12m+12-12 =14-12

Simplify:

Subtract 1: 12m+12-12=14-12

12m=14-12

then 2; 12m=14-12

12m=2

Divide both sides of the equation by the same term:

12m=2

12m/12=2/12

Simplify again:

Cancel out the terms:

12m/12=2/12

m=2/12

Divide the numbers:

m=2/12

m=1/6

Soulution= 1/6

6 0
2 years ago
Determine the following:
dolphi86 [110]

Answer:

a) P(X = 0) = 0.5997

b) P(X = 9) = 0.0016

c) P(X = 8) = 0.0047

d) P(X = 5) = 0.4018

Step-by-step explanation:

These following problem are examples of the binomial probability distribution.

Binomial probability

Th binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And \pi is the probability of X happening.

(a) for n = 4 and π = 0.12, what is P(X = 0)?

P(X = 0) = C_{4,0}.(0.12)^{0}.(0.88)^{4} = 0.5997

(b) for n = 10 and π = 0.40, what is P(X = 9)?

P(X = 9) = C_{10,9}.(0.4)^{9}.(0.6)^{1} = 0.0016

(c) for n = 10 and π = 0.50, what is P(X = 8)?

P(X = 8) = C_{10,8}.(0.5)^{8}.(0.5)^{2} = 0.0047

(d) for n = 6 and π = 0.83, what is P(X = 5)?

P(X = 5) = C_{6,5}.(0.83)^{5}.(0.17)^{1} = 0.4018

3 0
3 years ago
Which is greater 0.25 or 0.025
storchak [24]

Answer:

0.25

Step-by-step explanation:

0.25*100=25

0.05*100=5.25

25 is greater than 5.25 so 0.25 is your answer

Hope this helps :) and pls give brainliest

3 0
3 years ago
Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by
11111nata11111 [884]

Answer:

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is 8.217 cubic inches.

Step-by-step explanation:

Given : The open rectangular box of maximum volume that can be made from a sheet of cardboard 11 in. by 7 in. by cutting congruent squares from the corners and folding up the sides.

To find : The dimensions and the volume of the open rectangular box ?

Solution :

Let the height be 'x'.

The length of the box is '11-2x'.

The breadth of the box is '7-2x'.

The volume of the box is V=l\times b\times h

V=(11-2x)\times (7-2x)\times x

V=4x^3-36x^2+77x

Derivate w.r.t x,

V'(x)=4(3x^2)-2(36x)+77

V'(x)=12x^2-72x+77

The critical point when V'(x)=0

12x^2-72x+77=0

Solve by quadratic formula,

x=\frac{18+\sqrt{93}}{6},\frac{18-\sqrt{93}}{6}

x=4.607,1.392

Derivate again w.r.t x,

V''(x)=24x-72

Now, V''(4.607)=24(4.607)-72=38.568>0 (+ve)

V''(1.392)=24(1.392)-72=-38.592 (-ve)

So, there is maximum at x=1.392.

The length of the box is l=11-2x

l=11-2(1.392)=8.216

The breadth of the box is b=7-2x

b=7-2(1.392)=4.216

The height of the box is h=1.392.

The dimension of the open rectangular box is 8.216\times 4.216\times 1.392.

The volume of the box is V=l\times b\times h

V=8.216\times 4.216\times 1.392

V=48.217\ in.^3

The volume of the box is 8.217 cubic inches.

5 0
3 years ago
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