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3 years ago

Negative 2 1/3 minus negative 5

2 answers:

4 0

Subtracting a negative number from a negative number—when you see the subtraction (minus) sign followed by a negative sign, turn the two signs into a plus sign. Thus, instead of subtracting a negative, you are adding a positive.

andrew11 [14]3 years ago

4 0

The answer to your question is 16/3

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Oil leaks out of a tanker at a rate of r=f(t) liters per minute, where t is in minutes. If f(t) = A e^{-k t}, write a definite i

8_murik_8 [283]

Answer:

$V_{total} = \displaystyle\int_0^{60} A e^{-k t}~dt$

Step-by-step explanation:

We are given the following in the question:

Oil leaks out of a tanker at a rate of r = f(t) liters per minute, where t is in minutes.

$f(t) = A e^{-k t}$

Let V be the volume, then we are given that rate of leakage is:

$\displaystyle\frac{dV}{dt} = f(t) = A e^{-k t}$

Thus, we can write:

$dV = f(t).dt = A e^{-k t}~dt$

We have to find the a definite integral expressing the total quantity of oil which leaks out of the tanker in the first hour.

Thus, total amount of oil leaked will be the definite integral from 0 minutes to 60 minutes.

$dV =A e^{-k t}~dt\\V_{total} = \displaystyle\int_a^b f(t)~dt\\\\a = 0\text{ minutes}\\b = 60\text{ minutes}\\\\V_{total} = \displaystyle\int_0^{60} A e^{-k t}~dt$

The units of integral will be liters.

5 0

3 years ago

A company loses $780 as a result of shipping delay. The 6 owners of the company must share the loss equally. Write an expression

Stels [109]

C that’s the answer very easy there u go

3 0

4 years ago

Someone please please help me with this ! I would really appreciate it

STALIN [3.7K]

Answer:

Both volumes are the same

Step-by-step explanation:

Volume of cylinder = $\pi$ $r^{2} h$

r = radius

h = height

Since area of the circle is given on top,

Area of a circle = $\pi$ $r^{2}$

We know the area is 12

12 = $\pi$ $r^{2}$ (we need to find r)

r = $\sqrt{\frac{12}{\pi} }$

r = 1.954

Now we can find the cylinder's volume:

Volume of cylinder = $\pi$ $(1.954)^{2}$ (6)

Volume of cylinder = 72

To find the volume of the cuboid, we use

Volume of cuboid = lwh

l = length

w = width

h = height

Volume of cuboid = 6 x 4 x 3

Volume of cuboid = 72

This proves that both the volumes are the same.

3 0

3 years ago

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

i have alot of work to do so this would make me go faster if u help me with this question In the picture

Lera25 [3.4K]

I think it’s $1.35 sorry if I’m not correct

7 0

3 years ago

Read 2 more answers