How much leather is needed to cover a basketball with a diameter of 14 inches?​

Answer:

5.(345)=1,780/333

Step-by-step explanation:

5.(345)=(5,345-5)/999=5,340/999=1,780/333

The fraction corresponds to given decimal is 1780/333.

What is fraction form?

A fraction is used to show how much of something is left over. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction.

Let x=5.345

The repeating number is 345

Multiply both sides by 1000

1000x=5345.345

Subtract x=5.345 from the obtained equation,

999x=5340

Solve for x,

x=5340/999

x=1780/333

Therefore, the fraction corresponds to given decimal is 1780/333.

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The vector v (-6, 6, -5) points in the direction of itself, so we start there.

We can capture all points on the line through the origin and the point (-6, 6, -5) by scaling v by an arbitrary real number t.

The line through point P and pointing in the same direction as v is parallel to the other line that passes through the origin. Then the line we want can be obtained by translating the line through the origin by a vector p that points to (-4, 5, 2), so the vector equation for this line is

r (t ) = p + t v

r (t ) = (-4, 5, 2) + t (-6, 6, -5)

r (t ) = (-4 - 6t, 5 + 6t, 2 - 5t )

To get the parametric equations, simply take out the components:

x (t ) = -4 - 6t

y (t ) = 5 + 6t

z (t ) = 2 - 5t

Answer:

1) 943.895 mm3

2) 144 cm3

Step-by-step explanation:

1)

First we need to find the volume of the rectangular prism:

Volume_1 = 9 * 11 * 6 = 594 mm3

Then, we can find the volume of the half cylinder above the prism:

Volume_2 = 0.5*(pi * (4.5^2) * 11) = 349.895 mm3

So the volume of the figure is the sum of both volumes:

Volume_total = Volume_1 + Volume_2 = 943.895 mm3

2)

The volume of a pyramid is one third of the base area multiplied by the height, so we have:

Volume = (1/3) * 6 * 8 * 9 = 144 cm3

Answer:

1. Volume of the composite figure is 943.89 mm³

2. The volume, of the is 144 cm³

Step-by-step explanation:

1. The composite figure comprises of a cube and a half cylinder;

Volume of a cube = 9 mm × 11 mm × 6 mm = 594 mm³

Volume of the half cylinder = area of base × length = (π·r²)/2 × l

Where:

r = (Diameter of base)/2 = 9/2 = 4.5 mm

l = 11 mm

Therefore, plugging the values, gives;

Volume of the half cylinder = (π × 4.5²)/2 × 11 = 349.89 mm³

Hence, volume of the composite figure = Volume of the cube + Volume of the half cylinder

Volume of the composite figure = 594 mm³ + 349.89 mm³ = 943.89 mm³

2. The volume, V of a pyramid is given by the following relation;

[tex]V = \frac{l \times w \times h}{3}[/tex]

Where:

l = Length of base = 8 cm

w = Width of the base = 6 cm

h = Height of the pyramid = 9 cm

[tex]V = \frac{8 \times 6 \times 9}{3} = 144 \ cm^3[/tex]

Here we have that a cube of side x, therefore, the area = x·x, integrating we have;

[tex]\int\limits^x_0 {x \cdot x} \, dx = \frac{x^3}{3}[/tex]

Where:

Length, height width of the pyramid = x

It can therefore be shown, that for a pyramid of length, l, width, w, and height, h, the volume, [tex]V = \frac{l \times w \times h}{3}[/tex] .

Answer:

t/16

•The correct algebraic expression is StartFraction t Over 16 EndFraction

Step-by-step explanation:

Quotient of a number and 16

Let the number=t

Quotient represent division

The expression can be written as t/16

•Replace "a number" with a variable, like t.

•Quotient represents division.

•The correct algebraic expression is StartFraction t Over 16 EndFraction

Answer:

t/16

•The correct algebraic expression is StartFraction t Over 16 EndFraction

Step-by-step explanation:

Quotient of a number and 16

Let the number=t

Quotient represent division

The expression can be written as t/16

•Replace "a number" with a variable, like t.

•Quotient represents division.

•The correct algebraic expression is StartFraction t Over 16 EndFraction

Give the other persn credit to :D

Multiplying a negative number by a negative number will give you a positive product.

When multiplying two negative integers, it comes out as positive.

For example, we are given the equation -4 * -4.

Using the rule [ -(-a) = a ], the answer for the equation is 16.

Best of Luck!

Answer:

11 cm

Step-by-step explanation:

The strip of paper is 66 cm and it is folded into 6 different parts. It is used to form a model of a honeycomb cell.

To find the length of one side of the model, all we have to do is divide 66 cm by 6. That is:

66 / 6 = 11 cm

The length of one side of the model is 11 cm.

Answer:

The answer is sandy

Step-by-step explanation:

18/3= 6 why? because each glass of lemonade he drink he puts 3 table spoons, and a table spoon is the big spoon

hope this helped <3

I hope this helps you

Answer:

18 gallons containing 20% solvent and 6 gallons containing 60% solvent

Step-by-step explanation:

the painter needs 24 gallons of paint containing 30% solvent = 7.2 gallons of solvent

let a = 20% solvent paint

let b = 60% solvent paint

a + b = 24

0.2a + 0.6b = 7.2

(replace a = 24 - b in the second equation)

a + b = 24

0.2(24 - b) + 0.6b = 7.2

4.8 - 0.2b + 0.6b = 7.2

0.4b = 7.2 - 4.8 = 2.4

b = 2.4 / 0.4 = 6

a = 24 - 6 = 18

Answer:

The result for the equation is [tex]x = -8[/tex] .

Step-by-step explanation:

-Solve the equation:

[tex]0.75x -0.5 =x +1.5[/tex]

-Subtract [tex]x[/tex] from [tex]0.75x[/tex] :

[tex]0.75x -0.5-x =x -x+1.5[/tex]

[tex]-0.25x -0.5 = 1.5[/tex]

-Add both sides by 0.5 :

[tex]-0.25x -0.5 +0.5 =1.5 +0.5[/tex]

[tex]-0.25x = 2[/tex]

-Divide both sides by 0.25 :

[tex]\frac{-0.25x}{-0.25} =\frac{2}{-0.25}[/tex]

[tex]x = -8[/tex]

So, the answer for the equation is [tex]x = -8[/tex] .

Answer:

B represents area of the right triangle

Step-by-step explanation:

Given;

Area of a triangle is A = 0.5bh

where;

b is the base of the triangle

h is the height of the triangle

Given, formula for the volume of a prism is V = Bh

For a right triangle prism, the formula for the volume is, V = Bh

Where;

B is the area of the right triangle

h is the height of the prism

Therefore, B represents area of the right triangle

Answer:

314.97

Step-by-step explanation:

Answer:

x = -2.67

Step-by-step explanation:

6.8x + 9.3 = -9.4 + 3.4(-3x)

6.8x + 10.2x = -9.4 - 9.3

17x = -18.7

x = -2.67

Answer:

The initial amount of money Tyra has is $90

Step-by-step explanation:

Let the initial money Tyra has be equal to y

She spent ⁴/₅ of her initial money on gas for her car = ⁴/₅ of y

She spent ¹/₂ of the remainder on sandwiches;

the remainder = 1 -  ⁴/₅  = ¹/₅

¹/₂ of the remainder = ¹/₂ x ¹/₅ = ¹/₁₀

Thus, she spent ¹/₁₀ of her money on sandwiches = ¹/₁₀ of y

Amount she spent on sandwiches = $9 = ¹/₁₀ of y

[tex]\frac{y}{10} = \$ 9\\\\y = \$ 90[/tex]

Therefore, the initial amount of moneyTyra has is $90

Answer:

x >5       or        x < -1

Step-by-step explanation:

This has 2 solutions one positive and one negative

x-2 > 3   or x-2 < -3

Add 2 to each side

x-2+2 > 3+2   or x-2+2 < -3+2

x >5       or        x < -1

Answer:

20 %

Step-by-step explanation:

$10/100%    $2/?

10/ what to get 2 so you do 10/5=2 so 100/5= 20.

Answer:

D

Step-by-step explanation:

-4 x 3/2 = -12/2; which equals -6

so -6x.

-4 x -1/2 = 4/2; which equals 2

This means that:

-6x + 2 = 15; so 'D' is the answer

Answer:

D

Step-by-step explanation:

The distributive property states that a(b+c)=ab+ac. In this problem -4 is a, 3/2x is b, and -1/2 is c. -4(3/2) is 6, and -4(-1/2) is 2. So we have -6x+2=-15.

Answer:

30.113

Step-by-step explanation:

r(t) = (t³, 2 sin t)

The distance traveled is the length of the path (arc length):

L = ∫ₐᵇ √((dx/dt)² + (dy/dt)²) dt

L = ∫₁ᵖⁱ √((3t²)² + (2 cos t)²) dt

L = ∫₁ᵖⁱ √(9t⁴ + 4 cos²t) dt

Using a calculator:

L ≈ 30.113

Notice that distance is not the same as displacement.  If we wanted to find the displacement:

r(π) = (π³, 0)

r(1) = (1, 2 sin 1)

Δr = √((π³ − 1)² + (0 − 2 sin 1)²)

Δr ≈ 30.053

Answer:

A point on either side of the line

Step-by-step explanation:

To determine which side to shade, you look at a point on each side of the line.  One will make the inequality true  and one will not.  Shade on the side that will make the inequality true

Answer:

The scale factor to transform DEF to D'E'F' is 1/2

Step-by-step explanation:

DEF is

D(-8, 6), E(-8, 14), F(2, 3)

D'(-3, 6), E'(-3, 10), F'(2, 4.5)

Therefore;

DE = √((-8-(-8))²+(6-14)²) = 8

D'E' = √((-3 -(-3))² + (6 - 10)²) = 4

Similarly,

EF = √((-8 - 2)² + (14 - 3)²) = √(100 + 121) = √221

E'F' = √((-3 - 2)² + (10 - 4.5)²) = √(100/4 + 121/4) = (√221) × 1/2

Also

DF = √(-8 - 2)² + (6 - 3)² = √(100 + 9 =√109

D'F' = √(-3 - 2)² + (6 - 4.5)² = √(5² + 3²) = √((10/2)² + (3/2)²) = √(100/4 + 9/4) = (√109)×1/2

Therefore the ratio of DEF to D'E'F' = DE/D'F' = EF/E'F' = DF/D'F' = √221/(√221) × 1/2 = 2

That is the scale factor of DEF to D'E'F'  = 1/2.

Answer:

17 is added to both numerator and denominator.

Step-by-step explanation:

Given:

Fraction = 1/10

New fraction = 2/3

Find:

Number added to both numerator and denominator.

Computation:

Assume,

a is added to both numerator and denominator.

[tex]\frac{1+a}{10+a}=\frac{2}{3}\\\\3 + 3a=20+2a\\\\3a-2a=20-3\\\\a=17[/tex]

Therefore, 17 is added to both numerator and denominator.

Answer:

The answer is 66 ways .

Step-by-step explanation:

You have to use Combination because it says choosing 10 out of 12 as the position is not important :

12C10 = 66 ways of arrangements

The number of different 10-person teams are 66.

A combination is a mathematical technique for determining the number of potential arrangements in a set of objects where the order of the selection is irrelevant. You can choose the components in any order in combinations. Permutations and combinations are often mistaken.

We have out of the 12 girls who tried out for the softball team, 10 will be chosen for the team.

Using Combination

C(n, r) = n!/ r! (n- r)!

Here n = 12, r= 10

So, C(12, 10)= 12! / 10! (12- 10)!

                   = 12 x 11 x 10! / 10! x 2

                   = 6 x 11

                   = 66

There are 66 10-person teams.

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Answer:

2083.33 trouts

Step-by-step explanation:

Total population of fish in the pond is unknown, therefore, let's us represent this using letter Z

The ratio of banded , caught and released trout to the total trout population is represented as 250 : Z

We can solve this type of problem with a proportion:

Total number of fishes that was tagged and caught/ Total number of fishes that was caught = Total number of tagged fishes in the pond/ Total number of fishes in the pond.

In the question, we were given this values:

Total number of banded trout's that was caught and released into the pond = 250

Total number of trouts that was caught and had bands in the lake= 30

Total number of trouts that was caught in the lake = 250

Total number of fishes in the pond = Z

Hence we have:

30/250 = 250/ Z

We cross mulitply

30× Z = 250 × 250

30Z = 62500

We divide both sides by 30

30Z/ 30 = 62500/30

Z = 2083.33

Therefore, the expected population of trout is 2083.33 trouts

Answer: So, an Engineer will use a topography while working to locate the elevation for a given region. They provide the numerical value of an elevation. So from the list of options the closest to it is to determine the best location for a new road.

I hope this is helpful.

Answer:

B

Step-by-step explanation:

The quadratic has one root with multiplicity 2 if the discriminant is 0, which is

[tex](2m+4)^2-4(4-m)(8m+1)[/tex]

(That is, for a quadratic [tex]ax^2+bx+c[/tex], the discriminant is [tex]b^2-4ac[/tex].)

Set the discriminant equal to 0 and solve for [tex]m[/tex]:

[tex](2m+4)^2-4(4-m)(8m+1)=0[/tex]

[tex]4m^2+16m+16+32m^2-124m-16=0[/tex]

[tex]36m^2-108=0[/tex]

[tex]36m(m-3)=0[/tex]

[tex]\implies m=0\text{ or }m=3[/tex]

Answer:

A

Step-by-step explanation:

The rule for negative exponents is:

[tex]a^{-n} = \frac{1}{a^n}[/tex]

We have:

[tex]5^{-2}[/tex]

So, we can create a fraction with 1 as the numerator, and our exponent raised to a positive number as the denominator, and rewrite it as:

[tex]\frac{1}{5^2}[/tex]

Evaluate the exponent in the denominator

[tex]\frac{1}{5*5}\\\frac{1}{25}[/tex]

Therefore, choice A, 1/25 is correct.

Answer:

225

Step-by-step explanation:

first the square

9*9 = 81

then the triangle

a is 8

triangles are l*w/2 so 8*4.5/2

8*4.5 = 36/2 = 18

There are 8 of these triangles

18*8 is 144

144+81 = 225

The surface area of the square pyramid is approximately `196` square cm.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

We can use the Pythagorean theorem to find the slant height of the pyramid:

[tex]$$l = \sqrt{a^2 + \left(\frac{b}{2}\right)^2} \\= \sqrt{8^2 + \left(\frac{9}{2}\right)^2} \\= \sqrt{64+\frac{81}{4}} \\= \frac{\sqrt{433}}{2}$$[/tex]

So, the lateral area of the pyramid is the area of the four triangles with base `b` and height `l`, which is:

[tex]$$A_{lat} = 4\cdot\frac{1}{2}b\cdot l \\= 4\cdot\frac{1}{2}\cdot 9 \cdot \frac{\sqrt{433}}{2} \\= 27\sqrt{433}$$[/tex]

So, The area of the base of the pyramid is a² then

[tex]$$A = A_{lat} + a^2$$[/tex]

=  = 27√433 + 8²

= 27√{433} + 64

= 196.4 cm²

Therefore, the surface area of the square pyramid is approximately `196` square cm.

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Answer:

1. B

2. A

3. B

4. ???

5. A

6 ???

7. I can't see it

Step-by-step explanation:

Answer:

y' = y

Step-by-step explanation:

The slopes are independent of x.  So the only possible answer is y' = y.