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4 years ago

Graph the solution set for this inequality: -6x - 3y greater than or equal to -18

Mathematics

1 answer:

Lisa [10]4 years ago

4 0

9514 1404 393

Answer:

y-intercept: (0, 6)
x-intercept: (3, 0)

Step-by-step explanation:

In this form, it is not difficult to find the intercepts. Eliminate the term that has a zero value, and divide by the coefficient in the other term.

Y-intercept:

for x = 0, the equation is ...

-3y = -18

y = 6 . . . . . . divide by -3

X-intercept:

for y = 0, the equation is ...

-6x = -18

x = 3 . . . . . divide by -6

_____

Solid vs Dashed

The boundary of the shaded area is a solid line through these points. (It is solid because the symbol ≤ includes the "or equal to" case, meaning that points equal to those on the line are in the solution set.)

Above vs Below

The negative signs can make it a little tricky to figure out the shading. If we multiply the equation by -1, we get ...

6x +3y ≥ 18 . . . . . note the reversal of the comparison symbol

Now, both x and y have positive coefficients. The solution form ...

ky ≥ ( ) . . . . for positive k indicates shading above the line

kx ≥ ( ) . . . . for positive k indicates shading to the right of the line

The boundary line has negative slope, so "above" and "to the right" are both on the same side of the line (a good check of the answer).

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write an equation in point-slope form of the line that passes through the point (3, 5) and has a slope or -1

frez [133]

Answer:

y = -x + 8

Step-by-step explanation:

m = -1 ; x1 = 3 ; y1 = 5

Slope point form: y - y1 = m(x -x1)

y - 5 = -1(x - 3)

y - 5 = -1x - 3 *(-1)

y - 5 =-x + 3

y = -x + 3 + 5

y = -x + 8

3 0

3 years ago

What is the value of -3|15 - s| + 2s^3 when s = -3?

Scilla [17]

-3|15 - s| + 2s^3
=-3|15 - (-3)| + 2(-3)^3
= -3|18| -54
= -54 - 54
= -108

3 0

3 years ago

2. Find the probability of a batting average greater than 0.261.

Ludmilka [50]

Answer:

0.1044738

Step-by-step explanation:

6 0

3 years ago

Give the numerical value of the parameter p in the following binomial distribution scenarioA softball pitcher has a 0.721 probab

Igoryamba

Answer:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19)$

$P(X=16)=(19C16)(0.721)^{16} (1-0.721)^{19-16}=0.112$

$P(X=17)=(19C17)(0.721)^{17} (1-0.721)^{19-17}=0.051$

$P(X=18)=(19C18)(0.721)^{18} (1-0.721)^{19-18}=0.015$

$P(X=19)=(19C19)(0.721)^{19} (1-0.721)^{19-19}=0.002$

And replacing we got:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19) =0.112+0.051+0.015+0.002= 0.1801$

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

Solution to the problem

For this case our random variable is given by:

$X \sim Binom(n = 19, p = 0.721)$

For this case we want this probability:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19)$

$P(X=16)=(19C16)(0.721)^{16} (1-0.721)^{19-16}=0.112$

$P(X=17)=(19C17)(0.721)^{17} (1-0.721)^{19-17}=0.051$

$P(X=18)=(19C18)(0.721)^{18} (1-0.721)^{19-18}=0.015$

$P(X=19)=(19C19)(0.721)^{19} (1-0.721)^{19-19}=0.002$

And replacing we got:

$P(X>15)= P(X=16)+P(X=17)+P(X=18)+P(X=19) =0.112+0.051+0.015+0.002= 0.1801$

$P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668$

3 0

3 years ago

Sally is having a party and she has invited nine of her friends.

Alexeev081 [22]

Answer:

1) 5 limes, 5 lemons, 1,000 mL of pineapple juice, 2,000 mL of lemonade, 1,000 of orange juice

2) Limes = $2, Lemons = $2.5, Lemonade = $1.60, Orange Juice = 80c, Pineapple Juice = 90c

Step-by-step explanation:

1/2 limes · 10 = 5

1/2 lemons · 10 = 5

100 mL of pineapple juice · 10 = 1,000 mL

200 mL of lemonade · 10 = 2,000 mL

100 mL of orange juice · 10 = 1,000 mL

Cost:

5 limes · 0.4 = $2

5 lemons · 0.5 = $2.5

mL to L

1,000 mL of pineapple juice = 1 L, this costs 90¢

2,000 mL of lemonade = 2 L, this costs $1.60

1,000 mL of orange juice = 1 L, this costs 80¢

Overall:

5 limes for $2

5 lemons for $2.5

1 L of of pineapple juice for 90¢

2 L of lemonade for $1.60

1 L of orange juice for 80¢

3 0

4 years ago