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Anna71 [15]
3 years ago
7

Lisa is standing on a dock beside a lake. She drops a rock from her hand into the lake. After the rock hits the surface of the l

ake, the rock's distance from the lake's surface changes at a rate of −5 inches per second. If Lisa holds her hand 5 feet above the lake's surface, how far from Lisa's hand is the rock 4 seconds after it hits the surface?
Mathematics
1 answer:
Mariana [72]3 years ago
5 0
5ft and 4 in??? I'm not sure but check tho
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Solve this a interval notation. 5 greater than or equal to |4-2x|
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5≥|4-2x|
5≥4-2x≥-5
-1≤2x≤9
-0.5≤x≤4.5
x∈[-0.5;4.5]

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2 years ago
Samantha buys a pair of sneakers that were originally $60. They were on sale for 25%
Alex_Xolod [135]

Answer:

$47.70

Step-by-step explanation:

60.00 x .25 = 15  ( so $15.00 off the shoes )

60.00-15.00 = 45.00

45.00 x .06 = 2.70 (2.70 is your sales tax so add that to you sale price )

$45.00 + $2.70 =$47.70 Total

3 0
3 years ago
Is this an inequality or equation?
romanna [79]

Answer:

Equation

Step-by-step explanation:

A statement that the values of two mathematical expressions are equal (indicated by the sign =).

^^ This is the definition of equation

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^^ This is the definition for Inequality

The question moves more toward equation than inequality.

3 0
3 years ago
Read 2 more answers
Use the rule for order of operations to simplify the expression as much as possible 30-2(4*9-26)=
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3 years ago
preliminary sample of 100 labourers was selected from a population of 5000 labourers by simple random sampling. It was found tha
VladimirAG [237]

Answer:

n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79  

n=369

Step-by-step explanation:

1) Notation and definitions

X=40 number of the selected labourers opt for a new incentive scheme.

n=100 random sample taken

\hat p=\frac{40}{100}=0.4 estimated proportion of the selected labourers opt for a new incentive scheme.

p true population proportion of the selected labourers opt for a new incentive scheme.

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".  

The population proportion have the following distribution

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

2) Solution tot he problem

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)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.4(1-0.4)}{(\frac{0.05}{1.96})^2}=368.79  

And rounded up we have that n=369

8 0
3 years ago
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