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3 years ago

7

a scuba diver descended at a rate of 2 1/4 per second. If 0 represents the surface of the water and distances below the surface

are negative,which expression represents one way to calculate the location of the diver after 12 1/2 seconds?

1 answer:

Shtirlitz [24]3 years ago

6 0

Answer:

The location will be at $- 28\frac{1}{8}$ units.

Step-by-step explanation:

A scuba diver descended at a rate of $2\frac{1}{4}$ units per second.

Now, if 0 represents the surface of the water and distances below the surface are negative, then after $12\frac{1}{2}$ seconds the location of the diver will be given by the followings :

In one second the diver descends by 2.25 units depth.

So, in 12.5 seconds the diver will descend by $(2.25 \times 12.5) = 28.125$ units i.e. $28\frac{1}{8}$ units depth.

Therefore, the location will be at $- 28\frac{1}{8}$ units. (Answer)

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Three assembly lines are used to produce a certain component for an airliner. To examine the production rate, a random

Katyanochek1 [597]

Answer:

a) Null hypothesis: $\mu_A =\mu_B =\mu C$

Alternative hypothesis: $\mu_i \neq \mu_j, i,j=A,B,C$

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667$

And we have this property

$SST=SS_{between}+SS_{within}$

The degrees of freedom for the numerator on this case is given by $df_{num}=df_{within}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=3*6-3=15$ .

And the total degrees of freedom would be $df=N-1=3*6 -1 =15$

The mean squares between groups are given by:

$MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166$

And the mean squares within are:

$MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544$

And the F statistic is given by:

$F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326$

And the p value is given by:

$p_v= P(F_{2,15} >11.326) = 0.00105$

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

b) $(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}$

The degrees of freedom are given by:

$df = n_B +n_C -2= 6+6-2=10$

The confidence level is 99% so then $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ and the critical value would be: $t_{\alpha/2}=3.169$

The confidence interval would be given by:

$(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321$

$(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345$

Step-by-step explanation:

Previous concepts

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"

Part a

Null hypothesis: $\mu_A =\mu_B =\mu C$

Alternative hypothesis: $\mu_i \neq \mu_j, i,j=A,B,C$

If we assume that we have $3$ groups and on each group from $j=1,\dots,6$ we have $6$ individuals on each group we can define the following formulas of variation:

$SS_{total}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x)^2 =20.5$

$SS_{between}=SS_{model}=\sum_{j=1}^p n_j (\bar x_{j}-\bar x)^2 =12.333$

$SS_{within}=SS_{error}=\sum_{j=1}^p \sum_{i=1}^{n_j} (x_{ij}-\bar x_j)^2 =8.16667$

And we have this property

$SST=SS_{between}+SS_{within}$

The degrees of freedom for the numerator on this case is given by $df_{num}=df_{within}=k-1=3-1=2$ where k =3 represent the number of groups.

The degrees of freedom for the denominator on this case is given by $df_{den}=df_{between}=N-K=3*6-3=15$ .

And the total degrees of freedom would be $df=N-1=3*6 -1 =15$

The mean squares between groups are given by:

$MS_{between}= \frac{SS_{between}}{k-1}= \frac{12.333}{2}=6.166$

And the mean squares within are:

$MS_{within}= \frac{SS_{within}}{N-k}= \frac{8.1667}{15}=0.544$

And the F statistic is given by:

$F = \frac{MS_{betw}}{MS_{with}}= \frac{6.166}{0.544}= 11.326$

And the p value is given by:

$p_v= P(F_{2,15} >11.326) = 0.00105$

So then since the p value is lower then the significance level we have enough evidence to reject the null hypothesis and we conclude that we have at least on mean different between the 3 groups.

Part b

For this case the confidence interval for the difference woud be given by:

$(\bar X_B -\bar X_C) \pm t_{\alpha/2} \sqrt{\frac{s^2_B}{n_B} +\frac{s^2_C}{n_C}}$

The degrees of freedom are given by:

$df = n_B +n_C -2= 6+6-2=10$

The confidence level is 99% so then $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ and the critical value would be: $t_{\alpha/2}=3.169$

The confidence interval would be given by:

$(43.333 -41.5) - 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}= 0.321$

$(43.333 -41.5) + 3.169 \sqrt{\frac{0.6667}{6} +\frac{0.7}{6}}=3.345$

7 0

3 years ago

What is equal to 14.1.

VLD [36.1K]

A lot of numbers, equations, etc equal 14.1. Be more specific in your questions. I’m sorry this doesn’t really help but just use this for future reference

3 0

3 years ago

Maya has 120 caramel apples to sell. Each caramel apple is covered with one

mylen [45]

Answer:

peanuts=2/5

chocolate chips=1/8

coconut=3/10

rest=sprinkles

2/5+1/8+3/10

lcm=40

<u>16 + 5 + 12</u>

60

=33/60

60/60 -33/60

=27/60

=9 /20 apples are covered with sprinkles

9/20 x 120

<h2>=63 apples are covered with sprinkles</h2>

Step-by-step explanation:

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2 years ago

Santo paid $16.25 to buy 5 children tickets and 1 adult ticket. Hulda paid $24.00 to buy 4 children tickets and 3 adult tickets.

jenyasd209 [6]

Answer:

The price of an adult ticket it $5

Step-by-step explanation:

To solve this, we would find the system of equations. We would set up two equations that will represent the situation.

Let c = price per children ticket

Let a = price per adult ticket

Santo:

5c + 1a = 16.25

Hulda:

4c + 3a = 24

5c + 1a = 16.25 -> a = 16.25 - 5c

4c + 3a = 24

4c + 3(16.25 - 5c) = 24

4c + 48.75 - 15c = 24

-11c + 48.75 = 24

-48.75 -48.75

-11c = -24.75

/-11 /-11

c = 2.25

5c + a = 16.25

5(2.25) + a = 16.25

11.25 + a = 16.25

-11.25 -11.25

a = 5

a = $5 , c = $2.25

5 0

3 years ago

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A random sample of 100 students was taken. Of the 100 students, 50 liked vanilla ice cream, 37 liked chocolate ice cream, and 13

tino4ka555 [31]

Answer:

444

Step-by-step explanation:

since 37/100 students liked chocolate you need to scale that data to the new data size and find thirty seven percent of 1200 which is 444

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3 years ago