When 58,511 is divided by 21, the quotient is 2,786 R ___.<br><br> Numerical Answers Expected!

A sample of baseball games shows that the mean length of the games is 179.83 minutes. (The data is given in BaseballTimes if you

Dmitriy789 [7]

Answer: Yes, This sample provide evidence that the length of time for baseball games is more than 170 minutes.

Step-by-step explanation:

Since we have given that

Mean length of the games = 179.83

Standard error = 3.75

We need to find the value of P(X>170).

So, it becomes,

$z=\dfrac{X-\mu}{s}=\dfrac{179-170}{3.75}\\\\z=2.4$

Let $z_{crict}=1.64$

Since z is greater than z(critical value).

So,Yes, This sample provide evidence that the length of time for baseball games is more than 170 minutes.

5 0

2 years ago

Jack bought seven tickets for a movie he paid seven dollars for each adult ticket and four dollars for each child ticket jack sp

Alja [10]

7x = 40

7x + 4y = 40

The first equation represents that in total, the 7 tickets whether they are for adults or children costs $40.

The second equation represents that x = adult and y = children tickets both add up to equal $40.

7 0

2 years ago

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

Nick billups is paid a salary of $ 900 a month, a 2 % commission on all sales, and 1.8 % more on monthly sales over $ 17,500. In

Trava [24]

June :
900 + 0.02(48,500) + 0.018(48500 - 17500) =
900 + 970 + 558 = 2428 <==

July :
900 + .02(50,200) + 0.018(50200 - 17500) =
900 + 1004 + 588.60 = 2492.60 <===

5 0

2 years ago

Read 2 more answers

A police officer, in her car, is watching a person in a sports car. Assume the locations of the cars are mapped onto the coordin

Paha777 [63]

is there and answers like mutipol choice

5 0

2 years ago

Read 2 more answers

When 58,511 is divided by 21, the quotient is 2,786 R ___. Numerical Answers Expected!