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3 years ago

The sum of three consecutive integers is 21 larger than twice the smallest integer. find the integers.

1 answer:

7 0

Let the integers be x-1, x, x+1.

Given,

x -1 + x + x + 1 = 21 + 2(x - 1)

3x = 21 + 2x - 2

x = 19

Hence, the three integers are 18, 19 and 20.

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a regular hexagonal nut of side 1 cm and length 3 cm with a central hole of diameter 1 cm. 3 cm 1 cm 1 cm. Calculate the volume

Bogdan [553]

Answer:

5.44 cm³

Step-by-step explanation:

The volume of the hexagonal nut can be found by multiplying the area of the end face by the length of the nut. The end face area is the difference between the area of the hexagon and the area of the hole.

The area of a hexagon with side length s is given by ...

A = (3/2)√3·s²

For s=1 cm, the area is ...

A = (3/2)√3(1 cm)² = (3/2)√3 cm²

The area of a circle is given by ...

A = πr²

The radius of a circle with diameter 1 cm is 0.5 cm. Then the area of the hole is ...

A = π(0.5 cm)² = 0.25π cm²

The volume is the face area multiplied by the length, so is ...

V = Bh = ((3/2)√3 -0.25π)(3) . . . . . cm³

V = (9/2)√3 -0.75π cm³ ≈ 5.44 cm³

The volume of the metal is about 5.44 cm³.

5 0

2 years ago

What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm?

Elanso [62]

Answer:

The volume of a rectangular prism is $28\frac{7}{8}\ cm^{3}$

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

$V=BHL$

Convert the given dimensions to an improper fractions

$B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm$

$H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm$

$L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm$

substitute in the formula

$V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}$

Convert to mixed number

$\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}$

5 0

3 years ago

The actual volumes of soda in quart-sized bottles can be described by a Normal model with a mean of 32.3 fluid ounces and a stan

VLD [36.1K]

Answer:The percentage of bottles expected to have a volume less than 32 or is 40.13%

Step-by-step explanation: The volumes of soda in quart soda bottles can be represented by a Nomal model with a= 32.3 oz

b=1.2 oz

Let S be the volume of randomly selected soda bottles

Y-score: S-a/b

For S=32 oz

Substitute the values of S,a and b into the equation

Y=32-32.3/1.2

Y=-0.25

Probability of bottles that have a volume less than 32 oz is

P(S<32)=P(Y<-025)= 0.40129

Percentage of bottles that have volume less than 32 oz will be

0.40127×100%=40.13%

5 0

3 years ago

Find the mean of x,2x,3x,4x,5x

Tcecarenko [31]

Answer:

$\displaystyle 3x$

Step-by-step explanation:

Mean is equal to the sum of terms divided by the number of terms.

$\displaystyle \frac{x+2x+3x+4x+5x}{5}$

$\displaystyle \frac{15x}{5}$

$\displaystyle 3x$

4 0

3 years ago

Read 2 more answers

What's 20% of £158.08

Artemon [7]

20% * 158.08 =31.616
or
20% * £158.08 =48.1005824

5 0

3 years ago

Read 2 more answers