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Aleksandr-060686 [28]
4 years ago
7

Bob can run 5 miles in 1.25 hours. Stan can run 3 miles in 50 minutes. Who can run faster?

Mathematics
1 answer:
emmasim [6.3K]4 years ago
6 0

Speed of Bob = 5/1.25 = 4miles/h

Speed of Stan = 3/ (5/6) = 3 * 6 / 5 = 18/5 = 3.6 miles/ h#

Bob runs faster than Stan

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The volume of a cone is represented by the formula V = 1 T?n. If the volume of a cone is 30rt and the height is 2.5, what is the
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Answer:

radius is 3.38cm

Step-by-step explanation:

Note: the volume of a cone is given as

V= 1/3 \pi r^2 h

Step one:

Given Information

volume= 30cm^3

height= 2.5cm

Required

The radius of the cone

Step two:

substituting our data into the expression for the volume of a cone we can then solve for the radius r

30=1/3 *3.142*r^2 * 2.5\\\\30=1/3*7.855r^2\\\\30=2.62r^2\\\\

divide both sides by 2.62

30/2.62= r^2\\\\11.45= r^2\\\\r=\sqrt{11.45} \\\\r=3.38cm

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Assume that you have a sample of n 1 equals 6​, with the sample mean Upper X overbar 1 equals 50​, and a sample standard deviati
tigry1 [53]

Answer:

t=\frac{(50 -38)-(0)}{7.46\sqrt{\frac{1}{6}+\frac{1}{5}}}=2.656

df=6+5-2=9

p_v =P(t_{9}>2.656) =0.0131

Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.

Step-by-step explanation:

Data given

n_1 =6 represent the sample size for group 1

n_2 =5 represent the sample size for group 2

\bar X_1 =50 represent the sample mean for the group 1

\bar X_2 =38 represent the sample mean for the group 2

s_1=7 represent the sample standard deviation for group 1

s_2=8 represent the sample standard deviation for group 2

System of hypothesis

The system of hypothesis on this case are:

Null hypothesis: \mu_1 \leq \mu_2

Alternative hypothesis: \mu_1 > \mu_2

We are assuming that the population variances for each group are the same

\sigma^2_1 =\sigma^2_2 =\sigma^2

The statistic for this case is given by:

t=\frac{(\bar X_1 -\bar X_2)-(\mu_{1}-\mu_2)}{S_p\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}

The pooled variance is:

S^2_p =\frac{(n_1-1)S^2_1 +(n_2 -1)S^2_2}{n_1 +n_2 -2}

We can find the pooled variance:

S^2_p =\frac{(6-1)(7)^2 +(5 -1)(8)^2}{6 +5 -2}=55.67

And the pooled deviation is:

S_p=7.46

The statistic is given by:

t=\frac{(50 -38)-(0)}{7.46\sqrt{\frac{1}{6}+\frac{1}{5}}}=2.656

The degrees of freedom are given by:

df=6+5-2=9

The p value is given by:

p_v =P(t_{9}>2.656) =0.0131

Since the p value is higher than the significance level given of 0.01 we don't have enough evidence to conclude that the true mean for group 1 is significantly higher thn the true mean for the group 2.

4 0
3 years ago
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