33 1/3 of 21 (finding the percent of a number)

Which graph shows the following system of equations and its solutions? -0.1x-0.3y=1.2 and 0.2x-0.5y=2

Vera_Pavlovna [14]

Answer:

Option b is the correct answer as both the equations are true for given solution.

Step-by-step explanation:

Given equations are:

-0.1x-0.3y=1.2

0.2x-0.5y=2

We can observe each graph and find the point that is the solution and put the point in the equations to know if that point is the solution

For option A:

(0,4)

Putting x=0 and y = 4 in both equations

$-0.1(0)-0.3(4)=1.2\\0-1.2 =1.2\\-1.2 \neq 1.2\\0.2(0)-0.5(4)=2\\0-2 = 2\\-2 \neq 2$

This is not the correct answer as both equations are not true with this solution

For Option B:

(0,-4)

Putting x = 0 and y = -4 in both equations

$-0.1(0)-0.3(-4)=1.2\\0+1.2 = 1.2\\1.2 = 1.2\\0.2x-0.5y=2\\0.2(0)-0.5(-4) = 2\\2 = 2$

Both equations are true for (0,-4) hence it is the solution of the system.

For Option C:

(4,0)

$-0.1(4)-0.3(0)=1.2\\-0.4-0 = 1.2\\-0.4 \neq 1.2\\0.2x-0.5y=2\\0.2(4)-0.5(0) = 2\\0.8 \neq 2$

Not true for both equations

Hence,

Option b is the correct answer.

7 0

2 years ago

Find the length of side x in simplest radical form with a rational denominator.

SSSSS [86.1K]

Answer:

2 $\sqrt{5}$

Step-by-step explanation:

this is a 30-60-90 Δ and the ratio of the sides are 1 : $\sqrt{3}$ : 2

1 / 2 = $\sqrt{5}$ / x

cross-multiply: x = 2 $\sqrt{5}$

3 0

2 years ago

Solve for n: c= 6n−5g /11t

qwelly [4]

Answer: $\frac{11tc+5g}{66t}=n$

Step-by-step explanation:

You have the equation $c=6n-\frac{5g}{11t}$ .

Then, to solve for the variable $n$ from the equation you need:

Make the subtraction of the right side of the equation:

(As the denominators are 1 and $11t$ , the least common denominator is $11t$ )

$c=\frac{(6n)(11t)-5g}{11t}\\\\c=\frac{66nt-5g}{11t}$

Multiply $11t$ to both sides:

$(11t)c=(\frac{66nt-5g}{11t})(11t)\\\\11tc=66nt-5g$

Add $5g$ to both sides:

$11tc+5g=66nt-5g+5g\\\\11tc+5g=66nt$

And finally divide both sides by $66t$ :

$\frac{11tc+5g}{66t}=\frac{66nt}{66t}\\\\\frac{11tc+5g}{66t}=n$

3 0

2 years ago

MATH HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

sveta [45]

So the first one, 1.2 >11/5. and the second one 1/3> 1/2

6 0

2 years ago

Read 2 more answers

It is estimated % of all adults in United States invest in stocks and that % of U.S. adults have investments in fixed income ins

katovenus [111]

Complete question :

It is estimated 28% of all adults in United States invest in stocks and that 85% of U.S. adults have investments in fixed income instruments (savings accounts, bonds, etc.). It is also estimated that 26% of U.S. adults have investments in both stocks and fixed income instruments. (a) What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to decimal places. (b) What is the probability that a randomly chosen U.S. adult invests in stocks, given that s/he invests in fixed income instruments?

Answer:

0.929 ; 0.306

Step-by-step explanation:

Using the information:

P(stock) = P(s) = 28% = 0.28

P(fixed income) = P(f) = 0.85

P(stock and fixed income) = p(SnF) = 26%

a) What is the probability that a randomly chosen stock investor also invests in fixed income instruments? Round your answer to decimal places.

P(F|S) = p(FnS) / p(s)

= 0.26 / 0.28

= 0.9285

= 0.929

(b) What is the probability that a randomly chosen U.S. adult invests in stocks, given that s/he invests in fixed income instruments?

P(s|f) = p(SnF) / p(f)

P(S|F) = 0.26 / 0.85 = 0.3058823

P(S¦F) = 0.306 (to 3 decimal places)

3 0

2 years ago