Find the numerical value of the area under the normal curve that is above the mean.

A building in the shape of a square pyramid is being built in Las Vegas. The height of the building will be 309 feet, and a size

finlep [7]

Answer: 51.5 cubic feet.

Step-by-step explanation:

Since, The height of the building will be 309 feet, and a size of the base measures 250 feet.

And, we know that the volume of the square pyramid = $(size of the base)^2\times \frac{height}{3}$

Here, size of the base of the square pyramid = 250 feet.

And, height = 309 feet.

Therefore, the volume of the given square pyramid,

$V=(250)^2\times\frac{309}{3}$

⇒ $V=62500 \times\frac{309}{3}$

⇒ $V= \frac{19312500}{3}$ = 6437500 cubic feet.

Again according to the question,

The scale model that is displayed at a convention is one fiftieth the size of the actual building.

Therefore, Volume of the scale model = the volume of the given square pyramid/125000

= 6437500/125000= 51.5 cubic feet.

Thus, the volume of the scale model is 51.5 cubic feet.

6 0

4 years ago

C=1/21.22.23+1/22.23.24+................+1/200.201.202 . = là dấu nhân

Aneli [31]

It looks like you have to find the value of the sum,

$C = \displaystyle \frac1{21\times22\times23} + \frac1{22\times23\times24} + \cdots + \frac1{200\times201\times202}$

so that the n-th term in the sum is

$\dfrac1{(21+(n-1))\times(21+n)\times(21+(n+1))} = \dfrac1{(n+20)(n+21)(n+22)}$

for 1 ≤ n ≤ 180.

We can then write the sum as

$\displaystyle C = \sum_{n=1}^{180} \frac1{(n+20)(n+21)(n+22)}$

Break up the summand into partial fractions:

$\dfrac1{(n+20)(n+21)(n+22)} = \dfrac a{n+20} + \dfrac b{n+21} + \dfrac c{n+22}$

Combine the fractions into one with a common denominator and set the numerators equal to one another:

$1 = a(n+21)(n+22) + b(n+20)(n+22) + c(n+20)(n+21)$

Expand the right side and collect terms with the same power of n :

$1 = a(n^2+43n+462)+b(n^2+42n+440) + c(n^2+41n + 420) \\\\ 1 = (a+b+c)n^2 + (43a+42b+41c)n + 462a+440b+420c$

Then

a + b + c = 0

43a + 42b + 41c = 0

462a + 440b + 420c = 1

==> a = 1/2, b = -1, c = 1/2

Now our sum is

$\displaystyle C = \sum_{n=1}^{180} \left(\frac1{2(n+20)}-\frac1{n+21}+\frac1{2(n+22)}\right)$

which is a telescoping sum. If we write out the first and last few terms, we have

C = 1/(2×21) - 1/22 + 1/(2×23)

… … + 1/(2×22) - 1/23 + 1/(2×24)

… … + 1/(2×23) - 1/24 + 1/(2×25)

… … + 1/(2×24) - 1/25 + 1/(2×26)

… … + … - … + …

… … + 1/(2×198) - 1/199 + 1/(2×200)

… … + 1/(2×199) - 1/200 + 1/(2×201)

… … + 1/(2×200) - 1/201 + 1/(2×202)

Notice the diagonal pattern of underlined and bolded terms that add up to zero (e.g. 1/(2×23) - 1/23 + 1/(2×23) = 1/23 - 1/23 = 0). So, like a telescope, the sum collapses down to a simple sum of just six terms,

C = 1/(2×21) - 1/22 + 1/(2×22) + 1/(2×201) - 1/201 + 1/(2×202)

which we simplify further to

C = 1/42 - 1/44 - 1/402 + 1/404

C = 1,115/1,042,118 ≈ 0.00106994

4 0

3 years ago

The grocery store carries diapers for children. Each diaper container has 48 diapers. Two dozen babies each need a container of

charle [14.2K]

Answer:

1152 diapers are needed

Step-by-step explanation:

2 dozen babies is equall to 24 babies

-(1 dozen is 12 babies)

If 24 babies need a package of diapers which includes 48 diapers, we need to multiply 24x48 which equals 1152 diapers

7 0

3 years ago

Read 2 more answers

The lengths of the sides of a triangle are in the extended ratio 44 : 55 : 77. the perimeter of the triangle is 6464 cm. what

joja [24]

44x + 55x + 77x = 6,464 centimeters.
x = 36.7272727273 

Therefore the sides are
44*36.7272727273 = 1,616 
55*36.7272727273 = 2,020
77* 36.7272727273 = 2,828

OR maybe that's another of those infamous Brainly typos.

4x + 5x + 7x = 64 centimeters.
x = 8

Therefore the sides are
4*8 = 32
5*8 = 40 and
7*8 = 56 centimeters

6 0

3 years ago

In a packet of 40 skittles,30% are red .How Many are not red?

elena55 [62]

Answer:

28 skittles

Step-by-step explanation:

30% of 40 is 12

subtract 12 from 40 and that is 28

6 0

3 years ago