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2 years ago

What is the volume of this box? 4 in long 12in high 3in wide

Mathematics

2 answers:

Natali5045456 [20]2 years ago

6 0

Answer:

Step-by-step explanation:

Multiply the length, width and height to find the volume of the box

blagie [28]2 years ago

3 0

Volume= length x width x height
Then, 4 x 12 x 3 = 144
Now since volume is measured in cubic units. The answer is 144 in^3
(Inches because the box is measured in inches)

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Bethany and her family are attending the Funville Town Fall Festival, and the first thing they do is get in line for the Maize (

erik [133]

Answer:

Part 1: 31.4 feet

Part 2: 61 feet

Part 3: 99,000 stalks of corn

Step-by-step explanation:

Diagram attached.

You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.

The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.

Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2

Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:

$h^2 = 31^2 + 5^2\\h=\sqrt{31^2 + 5^2} \\h=31.4$

Hence Bethany has to walk 31.4 feet

See 2nd diagram attached.

The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.

We use Pythagorean Theorem twice on the two triangles and add up the results.

<u>Left Triangle:</u>

If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:

$h^2=30^2 + 10^2\\h=\sqrt{30^2 + 10^2} \\h=31.62$

<u>RightSide triangle:</u>

two legs are 25 and 15 respectively, so we use the pythagorean theorem again:

$h^2=25^2 + 15^2\\h=\sqrt{25^2 + 15^2} \\h=29.15$

Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)

The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].

Area of Maze:

100 * 100 = 10,000 sq. yd.

Area of Path = 1.5 * 3000 = 4,500 sq. yd.

Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.

Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:

18 * 5,500 = 99,000 stalks of corn

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7 0

3 years ago

Find an equation of the line containing the centers of the two circles whose equations are given below.

Anna35 [415]

Answer:

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1 =0 and x²+y²+4x+2y+4 =0, to get the centre of both circles,<em> we will compare both equations with the general form of the equation above as shown;</em>

For the circle with equation x²+y²−2x+4y+1 =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4 =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

<em>Hence the equation of the line containing the centers of the two circles is 3y+x = -5</em>

5 0

3 years ago

Please help me it’s a formative grade

sergejj [24]

Answer:

Step-by-step explanation: 800/x=100/17

(800/x)*x=(100/17)*x - we multiply both sides of the equation by x

800=5.88235294118*x - we divide both sides of the equation by (5.88235294118) to get x

800/5.88235294118=x

136=x

x=136

83% of 800=664

5 0

3 years ago

In a survey of adults who follow more than one sport, 30% listed football as their favorite sport. You survey 15 adults who foll

maxonik [38]

Answer: 0.5

Step-by-step explanation:

Binomial probability formula :-

$P(x)=^nC_x\ p^x(q)^{n-x}$ , where P(x) is the probability of getting success in x trials , n is the total trials and p is the probability of getting success in each trial.

Given : The probability that the adults follow more than one game = 0.30

Then , q= 1-p = 1-0.30=0.70

The number of adults surveyed : n= 15

Let X be represents the adults who follow more than one sport.

Then , the probability that fewer than 4 of them will say that football is their favorite sport,

$P(X\leq4)=P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)\\\\=^{15}C_{0}\ (0.30)^0(0.70)^{15}+^{15}C_{1}\ (0.30)^1(0.70)^{14}+^{15}C_{2}\ (0.30)^2(0.70)^{13}+^{15}C_{3}\ (0.30)^3(0.70)^{12}+^{15}C_{4}\ (0.30)^4(0.70)^{11}\\\\=(0.30)^0(0.70)^{15}+15(0.30)^1(0.70)^{14}+105(0.30)^2(0.70)^{13}+455(0.30)^3(0.70)^{12}+1365(0.30)^4(0.70)^{11}\\\\=0.515491059227\approx0.5$

Hence, the probability rounded to the nearest tenth that fewer than 4 of them will say that football is their favorite sport =0.5

4 0

3 years ago

A right triangle with side legs of length 13 and 12 what is the value of x enter your answer in the box

Y_Kistochka [10]

Step-by-step explanation:

$x = \sqrt{ {12}^{2} + {13}^{2} } \\ = \sqrt{ 144 + 169 } \\ = \sqrt{313} \\ = 17.69 \\$

4 0

3 years ago

Read 2 more answers