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2 years ago

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Bud's cheeseburger and fries contained 1310 milligrams and 350 milligrams of sodium, respectively. Together they contained 66.4%

of the recommended daily intake of sodium for
diet. What is the daily recommended intake of sodium for a 2,000 calorie diet?

1 answer:

Serhud [2]2 years ago

5 0

Answer:

The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.

Step-by-step explanation:

In order to calculate the daily intake of sodium we first need to calculate the mass of sodium present in both snacks, this is given by their sum.

$\text{total sodium} = 1310 + 350 = 1660 \text{ mg}$

We can now apply a rule of three for which the total sodium from the snacks is related to 66.4% in the same proportion as "x" mg, which is the value we want to know, is related to 100%. So we have:

$\frac{1660}{x} \frac{mg}{mg} = \frac{66.4\%}{100\%}$

$66.4*x = 1660*100\\x = \frac{166000}{66.4} = 2500 \text{ mg}$

The recommended daily intake of sodium for a 2000 calorie diet is 2500 mg.

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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) (

aalyn [17]

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form $y/x=k$ or $y=kx$

in this problem we have

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

so

Find the constant of proportionality k

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

the equation is

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

Remember that

If a point is on the line of direct variation

then

the point must satisfy the equation of direct variation

we're proceeding to verify each point

<u>case A)</u> point $(0,0)$

$x=0\ y=0$

Substitute the value of x and y in the direct variation equation

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

$0=0$ -------> is true

therefore

the point $(0,0)$ is on the line of direct variation

<u>case B)</u> point $(2.5,6)$

$x=2.5\ y=6$

Substitute the value of x and y in the direct variation equation

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

$6=6$ -------> is true

therefore

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

<u>case C)</u> point $(3,10)$

$x=3\ y=10$

Substitute the value of x and y in the direct variation equation

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

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

therefore

the point $(3,10)$ is not on the line of direct variation

<u>case D)</u> point $(7.5,18)$

$x=7.5\ y=18$

Substitute the value of x and y in the direct variation equation

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

$18=18$ -------> is true

therefore

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

<u>case E)</u> point $(12.5,24)$

$x=12.5\ y=24$

Substitute the value of x and y in the direct variation equation

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

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

therefore

the point $(12.5,24)$ is not on the line of direct variation

<u>case F)</u> point $(15,36)$

$x=15\ y=36$

Substitute the value of x and y in the direct variation equation

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

$36=36$ -------> is true

therefore

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

therefore

<u>the answer is</u>

$(0,0)$

$(2.5,6)$

$(7.5,18)$

$(15,36)$

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Answer:

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Therefore, $11,890 money will she borrow in an auto loan.

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Now, Monthly Auto payment(M) be :

P=$11,890, Monthly Car payment per $1000 borrowed at 2.6% for 48 months = $21.958

∴ $M=$11,890\cdot \frac{21.958}{1000}$

On solving we get, M=$261.082

Therefore, $261.082 will be her monthly auto payment.

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Total amount of interest(A) she will pay ,

A=total payment in 4 years-total loan amount= $(\$261.082\cdot 48)-11,890$

=$12,531.936-$11,890=$641.936

So, the total amount of interest she will pay is, $641.936

(d)

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Answer: $x+y=45\\\\1000 x + 500y = $2500$

Step-by-step explanation:

Let x = Number of employees taking technology training

y= Number of employees taking customer service training

Given, The technology training costs $1,000 per person. The customer service training costs $500 per person.

Total cost = 1000 x + 500y

Since, Total cost = $25,000 and total employee to attend training= 45 .

That means , the required equations are:

$x+y=45\\\\1000 x + 500y = $2500$

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Emily is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. Emily will earn $

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Answer:

(6,2)

Step-by-step explanation:

Variable Definitions:

x= the number of commercials

y= the number of movies

Each commercial earns Emily $50, so x commercials would earn her 50x dollars in royalties. Each movie earns Emily $150, so y movies would earn her 150y dollars in royalties. Therefore, the total royalties 50x+150y equals $600:

50x+150y=600

Since Emily's songs were played on 3 times as many commercials as movies, if we multiply 3 by the number of movies, we will get the number of commercials, meaning x equals 3y.

x=3y

Write System of Equations:

50x+150y=600

x=3y

Solve for y in each equation:

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150y=−50x+600

y=-1/3x+4

2) x=3y

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The x variable represents the number of commercials and the yy variable represents the number of movies. Since the lines intersect at the point (6,2) we can say:

Emily's songs were played on 6 commercials and 2 movies.

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Answer:

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Step-by-step explanation:

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