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3 years ago

4x + y = 3 -2x + 3y = -19 what's the solution plz help

Mathematics

1 answer:

Rainbow [258]3 years ago

5 0

The solution to given system of equations is x = 2 and y = -5

Solution:

Given the system of equations are:

4x + y = 3 ---------- eqn 1

-2x + 3y = -19 ---------- eqn 2

We have to find the solution to above system of equations

We can solve the system by substitution method

From eqn 1,

4x + y = 3

Isolate y to one side

y = 3 - 4x ----------- eqn 3

Substitute eqn 3 in eqn 2

-2x + 3(3 - 4x) = -19

-2x + 9 - 12x = -19

Combine the like terms

-14x = -19 - 9

-14x = -28

Divide both sides of equation by -14

Substitute x = 2 in eqn 3

y = 3 - 4(2)

y = 3 - 8

Thus the solution is x = 2 and y = -5

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if you are dealt 6 cards from a shuffled deck of 52 cards, find the probability of getting 3 jacks and 3 aces.

steposvetlana [31]

There’s 4 jacks and 4 aces in a deck of cards so the probability would be 8:52 i think

4 0

3 years ago

So it’s the angle sun theory but i don’t understand it at all

DedPeter [7]

ANSWER

$30\degree$

EXPLANATION

The angle sum theory states that:

This implies that:

$x+x+60+60=180$

Solve for x in the equation above:

$\begin{gathered} 2x+120=180 \\ \Rightarrow2x=180-120=60 \\ x=\frac{60}{2} \\ x=30\degree \end{gathered}$

That is the value of x.

5 0

1 year ago

The Johnson family pays 1,783 per month for rent. If the cost of their rent remains the same, how much will they pay for rent ov

irinina [24]

Answer:

1 year= 12 months

1 months rent=1783

1783x12=21396

15 years = 180 months

the equation would be

1783x180=320940

21396x15= 320940

6 0

3 years ago

A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like to

Citrus2011 [14]

Answer:

We conclude that there is no difference in the two population proportions using α = 0.05.

Step-by-step explanation:

We are given that a corporation randomly selects 150 salespeople and finds that 66% who have never taken a self- improvement course would like to do so.

The firm did a similar study 10 years ago and found that 70% of a random sample of 160 salespeople wanted a self-improvement course.

Let $p_1 (\pi_1)$ = true proportion of workers who would like to attend a self-improvement course in the recent study.

$p_2 (\pi_2)$ = true proportion of workers who would like to attend a self-improvement course in the past study.

SO, Null Hypothesis, $H_0$ : $p_1=p_2$ {means that there is no difference in the two population proportions}

Alternate Hypothesis, $H_A$ : $p_1\neq p_2$ {means that there is a difference in the two population proportions}

The test statistics that would be used here Two-sample z test for proportions;

T.S. = $\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }$ ~ N(0,1)

where, $\hat p_1$ = sample proportion of salespeople who would like to attend a self-improvement course in recent study = 66%

$\hat p_2$ = sample proportion of salespeople who would like to attend a self-improvement course in past study = 70%

$n_1$ = sample of salespeople in recent study = 150

$n_2$ = sample of salespeople in past study = 160

So, the test statistics = $\frac{(0.66-0.70)-(0)}{\sqrt{\frac{0.66(1-0.66)}{150}+\frac{0.70(1-0.70)}{160} } }$

= -0.755

The value of z test statistics is -0.755.

Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.

Since our test statistic lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that there is no difference in the two population proportions.

5 0

3 years ago

Paulina swims 5 miles down a creek with a current for 2 hours. It takes her 4

Westkost [7]

Answer: her swimming speed = 1.875 mph

Speed of current = 0.625 mph

Step-by-step explanation:

Let x represent her swimming speed.

Let y represent the speed of the current.

Paulina swims 5 miles down a creek with a current for 2 hours. Since this is faster, it means that she swam with the current. Her total speed would be (x + y) mph

Distance = speed × time

Therefore,

5 = 2(x + y)

dividing both sides by 2, it becomes

2.5 = x + y- - - - - - -1

It takes her 4 hours to swim the same 5 miles back to her original destination against the

same current. It means that her total speed was (x - y) mph

Distance covered would be

5 = 4(x - y)

Dividing both sides by 4, it becomes

1.25 = x - y- - - - - - - 2

Adding equation 1 to equation 2, it becomes

3.75 = 2x

x = 3.75/2

x = 1.875

Substituting x = 1.875 into equation 1, it becomes

2.5 = 1.875 + y

y = 2.5 - 1.875

y = 0.625

4 0

3 years ago