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3 years ago

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A butterfly is flying 8 3/4 feet above the ground. It descends at a steady rate to a spot 6 1/4 feet above the ground in 1 2/3 m

inutes. What is the butterfly’s change in elevation each minute?

1 answer:

trasher [3.6K]3 years ago

7 0

Answer:

Step-by-step explanation:

6¼ ft - 8¾ ft = -2½ ft

(-2½ ft)/(1⅔ min) = (5/2 ft)/(5/3 min)

= (5/2)/(5/3) ft/min

= (5/2 × 3/5 ft)/min

= 1.5 ft /min

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Describe a real-world situation that the graph could represent. Then describe the possible values for each variable

Alex777 [14]

Answer:

$Speed=distance/time$ i.e. relation between speed-distance-time is one such situation that can be modeled using graph

Step-by-step explanation:

There are many real world examples that can be modeled using graph. Graphs are represented on co-ordinate planes, so any real world example that can be represented by use of linear equation can be represented onto a graph.

One such example, is speed-distance-time relation. Uniform speed can be represented on a graph as shown in figure.

So, the equation for speed is represented by equation as follows:

$Speed=distance/time$

So, if we take distance on y axis and time on x axis with points as (distance,time)

(0,0) ==> $v=0/0=0$

(1,2) ==> $v=1/2=0.5$

(2,2) ==> $v=2/2=1$

the following points 0,0.5,1 will be plotted on graph. Similarly, more values can be plotted by assuming values for distance and time.

8 0

3 years ago

A random sample of size n1= 25, taken from a normal population with a standard deviation σ1= 5, has a mean X1= 80. A second rand

sesenic [268]

Answer:

The 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

Step-by-step explanation:

Previous concepts

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".

$\bar X_1 =80$ represent the sample mean 1

$\bar X_2 =75$ represent the sample mean 2

n1=25 represent the sample 1 size

n2=36 represent the sample 2 size

$\sigma_1 =5$ sample standard deviation for sample 1

$\sigma_2 =3$ sample standard deviation for sample 2

$\mu_1 -\mu_2$ parameter of interest.

The confidence interval for the difference of means is given by the following formula:

$(\bar X_1 -\bar X_2) \pm z_{\alpha/2}\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$ (1)

The point of estimate for $\mu_1 -\mu_2$ is just given by:

$\bar X_1 -\bar X_2 =80-75=5$

Since the Confidence is 0.94 or 94%, the value of $\alpha=0.06$ and $\alpha/2 =0.03$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.03,0,1)".And we see that $z_{\alpha/2}=1.88$

The standard error is given by the following formula:

$SE=\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2}}$

And replacing we have:

$SE=\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=1.118$

Confidence interval

Now we have everything in order to replace into formula (1):

$5-1.88\sqrt{\frac{5^2}{25}+\frac{3^2}{36}}=2.898$

$5+1.8\sqrt{\frac{6^2}{36}+\frac{7^}{49}}=7.102$

So on this case the 94% confidence interval would be given by $2.898 \leq \mu_1 -\mu_2 \leq 7.102$

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3 years ago

The weight of 10 identical samples of a substance is 0.01 pound. What is the weight of 1000 samples?

lys-0071 [83]

The weight would be 10 pounds

7 0

3 years ago

Read 2 more answers

L want to know the sum result.10+67×2=?<br>

Volgvan

Answer:

$144$

Step-by-step explanation:

<u>Step 1: Multiply </u>

$10 + (67 * 2)$

$10 + 134$

<u>Step 2: Combine </u>

$10 + 134$

$144$

Answer: $144$

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3 years ago

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Gcf using prime factorization of 52 and 65

Leto [7]

<span>25: 2 × 2 × 13 65: 5 × 13</span>

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4 years ago