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1 year ago

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The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V

and five-sevenths represent?
the radius of the rubber ball when the volume equals five-sevenths cubic feet
the volume of the rubber ball when the radius equals five-sevenths feet
that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet

2 answers:

enot [183]1 year ago

5 0

Answer:

5/7

Step-by-step explanation:

the volume of the rubber ball when the radius equals five-sevenths feet

Nat2105 [25]1 year ago

4 0

Corrected Question

The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V(5/7) represent?

Answer:

(B)the volume of the rubber ball when the radius equals five-sevenths feet

Step-by-step explanation:

The Volume of a sphere of radius r can be found using the formula:

$V(r)=\dfrac43 \pi r^3$

Therefore comparing the expression: $V(\dfrac57)$ with V(r):

$Radius, r=\dfrac57$

Thus, $V(\dfrac57)$ is the volume of a ball of radius $\dfrac57$ feet.

The correct option is B.

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Mark and Sofia walk together down a long, straight road. They walk without stopping for 4 miles. At this point Sofia says their

Marina CMI [18]

Answer:

Sofia is correct.

Step-by-step explanation:

Mark's statement depends on the starting point. He can be correct if they started at the 0 mile, but in this case we don't know where they started. They could had started at the 12 mile and their current position after the walking would be 16 miles.

On the other hand, Sofia's statement doesn't depend on where they started. She refers to how much they walked, not to where they are after the walking. Since they stopped after 4 non-stopping miles, their displacement was exactly 4 miles. So Sofia is correct.

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1 year ago

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

nikitadnepr [17]

Answer:

a) Reject H₀

b) [0.31; 3.35]

Step-by-step explanation:

Hello!

a) The objective of this example is to compare if the population means of the production rate of the assembly lines A, B and C. To do so the data of the production of each line were recorded and an ANOVA was run using it.

The study variable is:

Y: Production rate of an assembly line.

Assuming that the study variable has a normal distribution for each population, the observations are independent and the population variances are equal, you can apply a parametric ANOVA with the hypothesis:

H₀ μ₁= μ₂= μ₃

H₁: At least one of the population means is different from the others

Where:

Population 1: line A

Population 2: line B

Population 3: line C

α: 0.01

This test is always one-tailed to the right. The statistic is the Snedecor's F, constructed as the MSTr divided by the MSEr if the value of the statistic is big, this means that there is a greater variance due to the treatments than to the error, this means that the population means are different. If the value of F is small, it means that the differences between populations are not significant ( may differ due to error and not treatment).

The critical region is:

$F_{k-1;n-k; 1-\alpha } = F_{2;15; 0.99} = 6.36$

If F ≥ 3.36, the decision is to reject the null hypothesis.

Looking at the given data:

$F= \frac{MSTr}{MSEr}$ = 11.32653

With this value the decision is to reject the null hypothesis.

Using the p-value method:

p-value: 0.001005

α: 0.01

The p-value is less than the significance level, the decision is to reject the null hypothesis.

At a level of 5%, there is significant evidence to say that at least one of the population means of the production ratio of the assembly lines A, B and C is different than the others.

b) In this item, you have to stop paying attention to the production ratio of the assembly line A to compare the population means of the production ratio of lines B and C.

(I'll use the same subscripts to be congruent with part a.)

The parameter to estimate is μ₂ - μ₃

The populations are the same as before, so you can still assume that the study variables have a normal distribution and their population variances are unknown but equal. The statistic to use under these conditions, since the sample sizes are 6 for both assembly lines, is a pooled-t for two independent variables with unknown but equal population variances.

t= (X[bar]₂ - X[bar]₃) - ( μ₂ - μ₃) ~t $_{n_2+n_3-2}$

Sa√(1/n₂+1/n₃)

The formula for the interval is:

(X[bar]₂ - X[bar]₃) ± $t_{n_2+n_3-2; 1 - \alpha /2}$ * $Sa\sqrt{*\frac{1}{n_2} + \frac{1}{n_3} }$

$Sa^{2} = \frac{(n_2-1)*S_2^2+ (n_3-1)*S_3^2}{n_2+n_3-2}$

$Sa^{2} = \frac{(5*0.67)+ (5*0.7)}{6+6-2}$

$Sa^{2} = 0.685$

Sa= 0.827 ≅ 0.83

$t_{n_2+n_3-2;1-\alpha /2}= t_{10;0.995} = 3.169$

X[bar]₂ = 43.33

X[bar]₃ = 41.5

(43.33-41.5) ± 3.169 * $*0.83\sqrt{*\frac{1}{6} + \frac{1}{6} }$

1.83 ± 3.169 * 0.479

[0.31; 3.35]

With a confidence level of 99% you'd expect that the difference of the population means of the production rate of the assemly lines B and C.

I hope it helps!

8 0

1 year ago

Sophia was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a $5 bill

borishaifa [10]

The first thing we will do in this case is to define variables:
x = number of individual tickets.
y = number of tickets per couple.
We have then that the system of equations that represents the problem is:
10x + 15y = 590
x + 2y = 68
Solving the system we have:
x = 32
y = 18
Substituting we have:
10 (32) + 15 (18) = 590
320 + 270 = 590
590 = 590
Equality is met, therefore the $ 5 bill belongs to the box.
Answer:
the $ 5 bill belong inside the cash box

4 0

2 years ago

Ari is designing a patio that will be 20 feet long and 16 feet wide. He makes a scale drawing of the patio using a scale of 1 in

lara31 [8.8K]

Wouldnt it be four? id its 1/4

6 0

1 year ago

Read 2 more answers

F⃗ (x,y)=−yi⃗ +xj⃗ f→(x,y)=−yi→+xj→ and cc is the line segment from point p=(5,0)p=(5,0) to q=(0,2)q=(0,2). (a) find a vector pa

DerKrebs [107]

a. Parameterize $C$ by

$\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath$

with $0\le t\le1$ .

b/c. The line integral of $\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath$ over $C$ is

$\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt$

$=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt$

$=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt$

$=\displaystyle10\int_0^1\mathrm dt=\boxed{10}$

d. Notice that we can write the line integral as

$\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)$

By Green's theorem, the line integral is equivalent to

$\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy$

where $D$ is the triangle bounded by $C$ , and this integral is simply twice the area of $D$ . $D$ is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

4 0

1 year ago