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2 years ago

Carl draws a square with the side lengths of 7 centimeters what is the area of the square

Mathematics

2 answers:

abruzzese [7]2 years ago

7 0

49 would be your answer

Anton [14]2 years ago

3 0

The area of the square that he drew would be 49 square centimeters.

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A sequence has a common ratio of Three-halves and f(5) = 81. Which explicit formula represents the sequence? f(x) = 24(Three-hal

Ede4ka [16]

Answer:

$f(x)=16\, (\frac{3}{2} )^{x-1}$

Step-by-step explanation:

Since we are given the common ratio (3/2), all we need to find to define the geometric sequence, is its multiplicative factor ( $a$ ) that corresponds to the first term of the sequence - remember that all consecutive terms will be generated by multiplying this first value repeatedly by the common ratio (3/2) as shown below:

$f(1)=a\\f(2)=a\,*\,(\frac{3}{2} )\\f(3)=a\,*\,(\frac{3}{2} )^2\\f(4)=a\,*\,(\frac{3}{2} )^3\\f(5)=a\,*\,(\frac{3}{2} )^4$

Since we are given the information that $f(5)=81$ we can use this to find the value of the first term:

$f(5)=\,a\,*\,(\frac{3}{2} )^4\\81=\,a\,*(\frac{81}{16} )\\a\,*\,81=\,81\.*\,16\\a\,=\,16$

Notice as well that the first term doesn't contain the common ratio, the second term contains the common ration (3/2) to the power one, the third one contains the common ratio to the power two, the fourth one contains it to the power three, and so forth. So the exponent at which the common ratio appears is always one unit less than the order (x) of the term in question. This concept helps us finalize the expression for the sequence's formula:

$f(x)=16\,*\,(\frac{3}{2} )^{x-1}$

6 0

2 years ago

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The national average for mathematics SATs in 2011 was 514 and the standard deviation was approximately 40. a) Within what bounda

blondinia [14]

Answer:

$0.75 = 1-\frac{1}{k^2}$

If we solve for k we can do this:

$\frac{1}{k^2}= 1-0.75=0.25$

$\frac{1}{0.25}= k^2$

$k^2 =4$

$k =\pm 2$

So then we have at last 75% of the data withitn two deviations from the mean so the limits are:

$Lower = \mu -2\sigma = 514- 2*40=434$

$Upper = \mu +2\sigma = 514 + 2*40=594$

Step-by-step explanation:

We don't know the distribution for the scores. But we know the following properties:

$\mu = 514 , \sigma =40$

For this case we can use the Chebysev theorem who states that "At least $1 -\frac{1}{k^2}$ of the values lies between $\mu -k\sigma$ and $\mu +k\sigma$ "

And we need the boundaries on which we expect at least 75% of the scores. If we use the Chebysev rule we have this:

$0.75 = 1-\frac{1}{k^2}$

If we solve for k we can do this:

$\frac{1}{k^2}= 1-0.75=0.25$

$\frac{1}{0.25}= k^2$

$k^2 =4$

$k =\pm 2$

So then we have at last 75% of the data withitn two deviations from the mean so the limits are:

$Lower = \mu -2\sigma = 514- 2*40=434$

$Upper = \mu +2\sigma = 514 + 2*40=594$

4 0

2 years ago

1. A certain truck traveling at 55 miles per hour gets 4.5 miles per gallon of diesel fuel consumed. Traveling at 60 miles per h

Lena [83]

Answer:

Step-by-step explanation:

I don’t know, can I get help answering this

7 0

2 years ago

A giraffe measures 17 feet tall . A gorilla mesures 63 inches tall. How many feet taller is the giraffe than the gorilla

9966 [12]

Answer:

11.75 feet

Step-by-step explanation:

17 times 12 = 204 inches

204 - 63 = 141 inches

141/12 = 11.75 feet

4 0

2 years ago

A cube with side length 2f is stacked on another cube with side length 3g2. Choose the expression that represents the total volu

Reil [10]

The expression that represents the total volume of both cubes is $8f^3+27g^6$ .

The volume of a cube is found by multiplying its length, width, and height; for the first cube, this is
V=(2f)(2f)(2f)=8f³.

For the second cube, this is
V=(3g²)(3g²)(3g²)=27g⁶.

The total area is their sum, so 8f³+27g⁶.

4 0

2 years ago

Read 2 more answers