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3 years ago

11

1. Part A: Solve the inequality. Show work for full credit. 2x+3<7

2 answers:

LiRa [457]3 years ago

7 0

Answer:

x<2

Step-by-step explanation:

2x+3<7

Subtract 3 from both sides:

2x<4

Divide both sides by 2:

x<2

Harman [31]3 years ago

5 0

Answer:

x < 2

Step-by-step explanation:

If 2x + 3 is less than 7, then 2x alone must be less than 4.

2x + 3 < 7

2x < 4

If 2x is less than 4, then x must be less than 2.

2x < 4

x < 2

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vitfil [10]

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2 years ago

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We are interested in conducting a study to determine the percentage of voters of a state would vote for the incumbent governor.

Vladimir [108]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

Step-by-step explanation:

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

The estimated proportion for this case is $\hat p=0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

4 0

3 years ago

mrs. henein is purchasing cupcakes for her homeroom class. of each cupcake costs $2.25 and she has 31 students in her homeroom c

Luda [366]

Answer:

$69.75

Step-by-step explanation:

Multiply $2.25 by 31 students

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3 years ago

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4> Solve by using Laplace transform: y'+5y'+4y=0; y(0)=3 y'(o)=o

harina [27]

Answer:

$y=3e^{-4t}$

Step-by-step explanation:

$y''+5y'+4y=0$

Applying the Laplace transform:

$\mathcal{L}[y'']+5\mathcal{L}[y']+4\mathcal{L}[y']=0$

With the formulas:

$\mathcal{L}[y'']=s^2\mathcal{L}[y]-y(0)s-y'(0)$

$\mathcal{L}[y']=s\mathcal{L}[y]-y(0)$

$\mathcal{L}[x]=L$

$s^2L-3s+5sL-3+4L=0$

Solving for $L$

$L(s^2+5s+4)=3s+3$

$L=\frac{3s+3}{s^2+5s+4}$

$L=\frac{3(s+1)}{(s+1)(s+4)}$

$L=\frac3{s+4}$

Apply the inverse Laplace transform with this formula:

$\mathcal{L}^{-1}[\frac1{s-a}]=e^{at}$

$y=3\mathcal{L}^{-1}[\frac1{s+4}]=3e^{-4t}$

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3 years ago

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