Asalad made such that the difference between twice the ounces of greens and the ounces of carrots is at least 3. also, the sum of the ounces of greens and twice the ounces of carrots is less than 4. which graph represents the system of equations for this scenario?

The graph is in the attached image

Explanation:

Assume that the number of ounces of the greens is y and that the number of ounces of the carrots is x

We are given that:

1- The difference between twice the ounces of greens and the carrots is at least 3. This means that the difference could be equal to or more than 3

This means that:

2y - x ≥ 3 ..............> first inequality to graph

2- sum of ounces of greens and twice the ounces of carrots is less than 4

This means that:

y + 2x < 4 ...........> second inequality to graph

Using a graphing tool, we can plot the two inequalities as shown in the attachment

Hope this helps :)

Let x be the number of ounces of greens and y be the number of ounces of carrots,

Since, the difference between twice the ounces of greens and the ounces of carrots is at least 3,

⇒ 2x + y ≥ 3,

Also, the sum of the ounces of greens and twice the ounces of carrots is less than 4,

⇒ x + 2y < 4,

Thus, the system of equations that represents the given situation is,

2x + y ≥ 3 ------(1)

x + 2y < 4 -----(2),

Related equation of inequality (1),

2x + y = 3

Having x-intercept = (1.5, 0)

y-intercept = (0, 3),

2(0) + 0 ≥ 3 ( false )

The shaded region of inequality (1) does not contain the origin,

Also, ≥ sign shows the solid line,

Now, the related equation of the inequality (2),

x + 2y = 4

Having x-intercept = (4, 0)

y-intercept = (0, 2),

0 + 2(0) < 4 ( true )

The shaded region of inequality (2) contains the origin,

Also, < sign shows the dotted line,

Thus, by the above explanation we can plot the system of the inequalities ( shown below )

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;