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4 years ago

What is the solution the the system of equations graphed below?

Mathematics

2 answers:

castortr0y [4]4 years ago

4 0

First off, the solution is where the graphs intersect. You can find this by setting the equations equal to each other. 0.5 x + 2 = -2x -3. Solve this to get 2.5 x = -5. This equal x = -2. Plug in the x value into either of the two equations to get a y value of 1. Thus, the answer would be (-2, 1). B!
Hope this helps! :)

defon4 years ago

3 0

Answer:

Step-by-step explanation:

Its b because I'm gangsta

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A bank account has a starting balance of

Elza [17]

Answer:

$67.52

Step-by-step explanation:

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3 years ago

There were 48 peaches in a carton. The average mass of all the peaches was 0.17 kg. What was their total mass?

alexira [117]

Answer:

8.16 Kg

Step-by-step explanation:

average is calculated as

average = $\frac{sum}{count}$

here average = 0.17 and count = 48 , then

0.17 = $\frac{sum}{48}$ ( multiply both sides by 48 )

8.16 = sum

that is total mass = 8.16 Kg

4 0

2 years ago

A poll was taken of 1000 residents in county. The residents sampled were asked whether they think their local government did a g

prohojiy [21]

Answer:

a) (0.72, 0.78)

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Description in words of the parameter p

$p$ represent the real population proportion of all residents in that county who think their local government did a good job

$\hat p$ represent the estimated proportion of all residents in that county who think their local government did a good job

n=1000 is the sample size required

$z_{\alpha/2}$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Numerical estimate for p

In order to estimate a proportion we use this formula:

$\hat p =\frac{X}{n}$ where X represent the number of people with a characteristic and n the total sample size selected.

$\hat p=\frac{750}{1000}=0.75$ represent the estimated proportion of all residents in that county who think their local government did a good job

Confidence interval

The confidence interval for a proportion is given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.95=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.750 - 1.96 \sqrt{\frac{0.75(1-0.75)}{1000}}=0.72$

$0.750 + 1.96 \sqrt{\frac{0.75(1-0.75)}{1000}}=0.78$

And the 95% confidence interval would be given (0.72;0.78).

We are confident at 95% that the true proportion of people who think their local government did a good job is between (0.72;0.78).

a) (0.72, 0.78)

3 0

3 years ago

Help me please i need the equation of axis of symmetry

Anvisha [2.4K]

Answer:

x = -2

Step-by-step explanation:

It's a vertical line at x = -2

6 0

3 years ago

You drive 30 miles due east in a half hour. Then, you turn left and drive 30 miles north in 1 hour. What are your average speed

garri49 [273]

Original position: P1=(0,0)
<span>You drive 30 miles due east in a half hour: x=+30 miles, t1=1/2 hour=0.5 hours
</span><span>Then, you turn left and drive 30 miles north in 1 hour: y=+30 miles, t2=1 hour
Rectangular coordinates of final position: P2=(x,y)→P2=(30,30)
Total time: t=t1+t2=0.5 hours+1 hour→t=1.5 hours

Average speed: S ave=d/t
Total distance: d=x+y=30 miles+30 miles→d=60 miles
S ave = 60 miles / (1.5 hours)
S ave = 40 miles/hour

Velocity is a vector, the magnitude of this vector is the magnitude of the vector of change of position dividing by the total time t
The vector of change of position: s=P1-P2=(30,30)-(0,0)=(30-0,30-0)→
s=(30,30)
Magnitude of vector s=sqrt[30^2+30^2]=sqrt[30^2*2]=sqrt[30^2]*sqrt(2)
Magnitude of vector s=30*sqrt(2) miles

Magnitude of velocity vector = Magnitud of vector s / t
Magnitude of velocity vector = [30*sqrt(2) miles] / (1.5 hours)
Magnitude of velocity vector = 20*sqrt(2) miles / hour
Magnitude of velocity vector=20*1.4142 miles / hour
Magnitude of velocity vector=28.284 miles/hour

Polar coordinates of your position=(r, theta)
r=Magnitude of vector s=30*sqrt(2) miles
theta=tan^(-1) (y/x) = tan^(-1) [(30 miles) / (30 miles)]
theta=tan^(-1) (1)→theta=45°=Pi/4 (Pi=3.1416)
Polar coordinates of your position: ( 30*sqrt(2) miles, 45°)
Polar coordinate of your position: ( 30*sqrt(2) miles, Pi/4 )

Answers:
Average speed: 40 miles / hour
Velocity: 20*sqrt(2) miles / hour = 28.284 miles / hour
Rectangular coordinates of your position = (30,30)
Polar coordinates of your position=(30*sqrt(2) miles,45°)
Polar coordinates of your position=(30*sqrt(2) miles,Pi/4)</span>

4 0

3 years ago