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2 years ago

13

One gallon is approximately 3.875 liters. Mario buys 1.5 gallons of gasoline for his lawn trimmer. How many liters of gasoline,

to the nearest tenth, did Mario buy?

1 answer:

lara [203]2 years ago

8 0

Answer:

Ф∵∴∵Hello wonderful person∵∴∵Ф

Your answer should be:

5.8

Step-by-step explanation:

First answer!!!

Brainliest please! It would be appreciated!

Thanks for your time!

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A cardboard box without a lid is to have a volume of 16,384 cm3. Find the dimensions that minimize the amount of cardboard used.

Reika [66]

Answer:

The dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

Step-by-step explanation:

Volume of the cardboard = 16,384 $cm^{3}$

The function that represents the area of the cardboard without a lid is given by

$f (x,y,z) = xy + 2xz + 2yz$ ------ (1)

Volume of the cardboard with sides x, y & z is

$xyz = 16384$

$z = \frac{16384}{xy}$

Put this value of z in equation (1) we get

$f (x,y,z) = xy + 2x(\frac{16384}{xy} ) + 2y(\frac{16384}{xy} )$

$f (x,y,z) = xy + \frac{32768}{y} + 2y(\frac{32768}{x} )$

Differentiate above equation with respect to x & y we get

$f_{x} = y - \frac{32768}{x^{2} }$

$f_{y} = x - \frac{32768}{y^{2} }$

Take $f_{x} = 0 \ and \ f_{y} = 0$

$y - \frac{32768}{x^{2} } = 0$

$y = 32768 \ x^{-2}$ ------ (2)

$x - \frac{32768}{y^{2} } = 0$

$x = 32768 \ y^{-2}$ ------- (3)

By solving equation (2) & (3) we get

$x^{3} = 32768$

x = 31 cm

From equation 2

$y = 32768 \ x^{-2}$

y = 32768 ( $31^{-2}$ )

y = 34 cm

$z = \frac{16384}{xy}$

$z = \frac{16384}{(34)(31)}$

Z = 15.54 cm

Thus the dimensions that minimize the amount of cardboard used is

x = 31 cm , y = 34 cm & Z = 15.54 cm

6 0

2 years ago

El producto de dos números consecutivos es 552 cuáles son esos números?

lara31 [8.8K]

Answer: 23 y 24 ( ó -23 y -24)

Step-by-step explanation:

Dos números consecutivos se escriben como:

n y (n + 1)

done n es un numero entero.

Entonces "El producto de dos números consecutivos es 552"

Se escribe como:

n*(n + 1) = 552

n^2 + n = 552

n^2 + n - 552 = 0

Tenemos una cuadrática, las posibles soluciones son obtenidas con la formula de Bhaskara.

$n = \frac{-1 +- \sqrt{1^2 - 4*1*(-552)} }{2} = \frac{-1 +- 47}{2}$

Las dos soluciones son.

n = (-1 - 47)/2 = -48/2 = -24

n = (-1 + 47)/2 = 46/2 = 23

Si tomamos la primer solución, n = -24

Entonces los dos números consecutivos son:

n = -24

(n + 1) = -23

Si n = 23 entonces

n + 1 = 24

Lo cual tiene sentido, por que lo único que cambia son los signos, los cuales se cancelarían en la multiplicación.

7 0

2 years ago

Suppose a certain airline uses passenger seats that are 16.2 inches wide. Assume that adult men have hip breadths that are norma

Pachacha [2.7K]

Answer:

Each adult male has a 5.05% probability of having a hip width greater than 16.2 inches.

There is a 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

$Z = \frac{X - \mu}{\sigma}$

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem

Assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. This means that $\mu = 14.4, \sigma = 1.1$ .

What is the probability that any one of those adult male will have a hip width greater than 16.2 inches?

For each one of these adult males, the probability that they have a hip width greater than 16.2 inches is 1 subtracted by the pvalue of Z when X = 16.2. So:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16.2 - 14.4}{1.1}$

$Z = 1.64$

$Z = 1.64$ has a pvalue of 0.9495.

This means that each male has a 1-0.9495 = 0.0505 = 5.05% probability of having a hip width greater than 16.2 inches.

For the average of the sample

What is the probability that the 110 adult men will have an average hip width greater than 16.2 inches?

Now, we need to find the standard deviation of the sample before using the zscore formula. That is:

$s = \frac{\sigma}{\sqrt{110}} = 0.1$ .

Now

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{16.2 - 14.4}{0.1}$

$Z = 18$

$Z = 18$ has a pvalue of 0.9999.

This means that there is a 1-0.9999 = 0.0001 = 0.01% probability that the 110 adult men will have an average hip width greater than 16.2 inches.

7 0

2 years ago

Area of parallelogram

Aliun [14]

The formula for the area of a parallelogram is base times height or bh.

There's a formula sheet on Khan Academy:
https://www.khanacademy.org/math/basic-geo/basic-geo-area-and-perimeter/parallelogram-area/a/area-of...

5 0

2 years ago

Read 2 more answers

What is the answer? The glee club has 120 cupcakes to sell. they have decided to arrange the cupcakes in the shape of a rectangl

grin007 [14]

<span>Find the number of columns and rows of the cupcake in a rectangle shape with 120 pieces.
=> The row must ne even and the column must be add
=> 120 = 2 x 2 x 2 x 15
=> 120 = 8 x 15
=> 120 = 120
Thus, the glee club will need to arrange the row of the rectangle shaped cupcake as 8 rows and the column as 15 columns.
That gets the total of 120 cupcakes in all.

</span>

8 0

2 years ago