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11 days ago

8

Arlene is showing her work in simplifying −7.9 + 8.2 − 3.4 + 2.1. Identify any errors in her work or in her reasoning. Write fee

dback to Arlene explaining the mistake she made and how to correct her work.

1 answer:

PIT_PIT [9.1K]11 days ago

8 0

Response:

Steps 1 and 5

Detailed explanation:

To amend the work, the following issues must be addressed

In step 1, an additive inverse is mentioned; however, it actually does not represent an additive inverse, since it pertains to the opposite in relation to a number, yet there is no opposing number present

Moreover, the correction needed in step 5 indicates simplification, but in reality, it should not be simplified

These are the corrections that should be made

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Utilize the! operation to determine the count of combinations.

8!/5! = 40,320/120 = 336

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1 day ago

My cupcake recipe makes $12$ cupcakes and requires $1\frac12$ sticks of butter. I can only buy whole sticks of butter. How many

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Answer:

According to my cupcake recipe, it yields $12$ cupcakes and calls for $1\frac{1}{2}$ sticks of butter. I can only purchase whole sticks of butter.

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9 days ago

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A grocery store receives deliveries of corn from two farms, one in Iowa and the other in Ohio. Both farms produce ears of corn w

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Answer:

The number of standard deviations above the mean is $z_o = 1.4607$

Step-by-step explanation:

The question indicates that:

The average weight of the corn ears from each farm is $\mu=1.26$

The standard deviation for the corn ears from Iowa is $\sigma_1$

The standard deviation for the corn ears from Ohio is

$\sigma_2= 0.01 + \sigma_1$

A randomly chosen ear of corn from Iowa weighs x = 1.39 pounds

The standardized score is z = 1.645

The weight of a randomly chosen ear of corn from Ohio measures $x_1 = 1.39\ pound$

In general, the standardized score of corn weight from Iowa can be mathematically defined as:

$z = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $1.645 = \frac{ 1.39 - 1.26 }{\sigma_1 }$

=> $\sigma_1 = \frac{ 1.39 - 1.26 }{ 1.64 5}$

=> $\sigma_1 = 0.0790$

Conversely, the standardized score of corn weight from Ohio is expressed as:

$z_o = \frac{ 1.39 - 1.26 }{\sigma_2 }$

=> $z_o= \frac{ 1.39 - 1.26 }{0.01 + \sigma_1 }$

=> $z_o = \frac{ 1.39 - 1.26 }{ 0.089}$

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1 month ago

What other points are on the line of direct variation through (5, 12)? Check all that apply. (0, 0) (2.5, 6) (3, 10) (7.5, 18) (

Inessa [9000]

It is established that

A correlation between two variables, x and y, demonstrates a direct variation if it can be written in the format $y/x=k$ or $y=kx$

For this question, we have

the point $(5,12)$ lies on the direct variation line

therefore

Determine the constant of proportionality k

$y/x=k$ -------> substitute ------> $k=12/5$

The equation is

$y=\frac{12}{5}x$

Keep in mind that

If a point is located on the direct variation line

then

the point has to fulfill the direct variation equation

we will now validate each point

case A) point $(0,0)$

$x=0\ y=0$

Insert the values of x and y into the direct variation equation

$0=\frac{12}{5}*0$

$0=0$ -------> is valid

thus

the point $(0,0)$ lies on the direct variation line

case B) point $(2.5,6)$

$x=2.5\ y=6$

Insert the values of x and y into the direct variation equation

$6=\frac{12}{5}*2.5$

$6=6$ -------> is valid

thus

the point $(2.5,6)$ lies on the direct variation line

case C) point $(3,10)$

$x=3\ y=10$

Insert the values of x and y into the direct variation equation

$10=\frac{12}{5}*3$

$10=7.2$ -------> is not valid

thus

the point $(3,10)$ does not lie on the direct variation line

case D) point $(7.5,18)$

$x=7.5\ y=18$

Insert the values of x and y into the direct variation equation

$18=\frac{12}{5}*7.5$

$18=18$ -------> is valid

thus

the point $(7.5,18)$ lies on the direct variation line

case E) point $(12.5,24)$

$x=12.5\ y=24$

Insert the values of x and y into the direct variation equation

$24=\frac{12}{5}*12.5$

$18=30$ -------> is not valid

thus

the point $(12.5,24)$ does not lie on the direct variation line

case F) point $(15,36)$

$x=15\ y=36$

Insert the values of x and y into the direct variation equation

$36=\frac{12}{5}*15$

$36=36$ -------> is valid

thus

the point $(15,36)$ lies on the direct variation line

ultimately

the solution is

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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24 days ago

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