) As an ice cube melts its surface area is decreasing at a rate of 6cm2/sec. Find the rate at which the length of each side is decreasing at the moment when each side has length 2 cm. [Hint: a cube has 6 sides and each side has area x 2 where x is the side length]

Answer:

C/5

Step-by-step explanation:

This is because there are 2 people in the 3| part, and 3 people under 6 in the 4| part.

The sequence is geometric with first term  

a

1

=

100

and common ratio  

r

=

0.5

Explanation:

a

1

=

100

,

a

2

=

50

,

a

3

=

25

,

a

4

=

25

2

,

a

5

=

25

4

...

50

100

=

0.5

,

25

50

=

0.5

,

25

2

25

=

0.5

,

25

4

25

2

=

0.5

∴

a

2

a

1

=

a

3

a

2

=

a

4

a

3

=

a

5

a

4

=

0.5

The ratio of successive term and preceeding term is constant

(

r

=

0.5

)

. Therefore the sequence is geometric whose first

term is  

a

1

=

100

and common ratio is  

r

=

0.5

[Ans]

Answer:

Answer: 60.

Step-by-step explanation:

30 percent (calculated percentage %) of what number equals 18?

Answer:

12180

Step-by-step explanation:

Answer:

n

Step-by-step explanation:

Answer:

1360 inches.

Step-by-step explanation:

Equation: 40 × (40-6) Since 40 inches is the width :)

40-6= 34

34*40=1360

Taun's canvas is 1360 inches :)

Answer: 9 adults 7 children

Step-by-step explanation:

Answer:

Step-by-step explanation:

take theta as reference angle

tan theta=opposite/adjacent

=15/8

Answer:

option B

Step-by-step explanation:

First find opposite side using Pythagoras theorem:

[tex]17^2 = 8^2 + opposite^2 \\\\opposite^2 = 289 - 64 = 225\\\\opposite = 15[/tex]

Therefore,

          [tex]tan \theta = \frac{opposite}{adjacent} = \frac{15}{8}[/tex]

Answer:

(0,-2)

Step-by-step explanation:

Answer:

A percentage is out of 100.

85/100

in lowest terms this is

17/20

Hope this helps :)

Step-by-step explanation:

Answer:

(95.215 ; 100.785)

(95 ; 101) (nearest whole number)

Step-by-step explanation:

To obtain the confidence interval :

Mean ± margin of error

Mean = 98 hours

Margin of Error = Tcritical * (s/√n)

samole standard deviation, s = 5.6 hours

df = n - 1 = 18 - 1 = 17

Tcritical at (0.05, df = 17) = 2.110

Hence ;

Margin of Error = 2.110 * (5.6/√18) = 2.785

Confidence interval :

98 ± 2.785

Lower boundary = 98 - 2.785 = 95.215

Upper boundary = 98 + 2.785 = 100.785

(95.215 ; 100.785)

The answer goes here,

a) We have to tell the time and day which simone has to tell her sister, for picking her up from airport.

b) We have given the day (monday), time(7:00 pm) and total time to reach the destination(18 hours).

c) No such formula will be used here, we will just use our mental ability to solve this question.

d) She will leave at 7:00 pm, day has 24 hours. So, she will be in the flight on monday:

= 24 - (12 + 7) ----------- [12 here means the time of rest of the day,(morning to noon)]

= 24 - 19

= 5 hours

So, she will complete 5 hours of her destination on monday,now the time left is:

= 18 - 5

= 13

= (12 + 1 )hours

So, on tuesday, she will be in the flight for 12 hours (noon) and then on 1:00 pm she will reach the airport, as she needs and extra hour to plane so, the final time is 1:30 pm. And finally, the time she should tell her sister is 1.30 pm.

Answer:

735 mm³

Step-by-step explanation:

49 x 15 = 735

Answer:

735mm

Step-by-step explanation:

Answer:

BD ≈ 2.8 units

Step-by-step explanation:

By angle bisector theorem,

"If a segment bisects an angle of a triangle, then it divides the opposite side  into the segments which are proportional to the other two sides"

Here, AD is the bisector of the ∠BAC,

[tex]\frac{BD}{CD}=\frac{AB}{AC}[/tex]

[tex]\frac{8.1}{5.9}= \frac{BD}{2}[/tex]

BD = [tex]\frac{2\times 8.1}{5.9}[/tex]

BD = 2.75

BD ≈ 2.8 units

Given:

The geometric sequence is:

25.5, 5.1, 1.02, 0.204, ...

To find:

The explicit rule for the given geometric sequence.

Solution:

We have,

25.5, 5.1, 1.02, 0.204, ...

Here, the first term is 25.5 and the common ratio is:

[tex]r=\dfrac{a_2}{a_1}[/tex]

[tex]r=\dfrac{5.1}{25.5}[/tex]

[tex]r=\dfrac{1}{5}[/tex]

The explicit rule for a geometric sequence is:

[tex]a_n=ar^{n-1}[/tex]

Where, a is the first term and r is the common ratio.

Putting [tex]a=25.5,\ r=\dfrac{1}{5}[/tex] in the above formula, we get

[tex]a_n=25.5(\dfrac{1}{5})^{n-1}[/tex]

Therefore, the correct option is B.

Answer:

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 27 - 1 = 26

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 26 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0518

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

In this question:

[tex]n = 27, s = 21.4[/tex]. So

[tex]M = 2.0518\frac{21.4}{\sqrt{27}}[/tex]

[tex]M = 8.45[/tex]

The margin of error for the 95% confidence interval for the mean score of all such subjects is of 8.45.

Answer:

[tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

Step-by-step explanation:

From the question we are told that:

Radius [tex]r=5ft[/tex]

Height [tex]H=15ft[/tex]

Rate [tex]R=15ft/3sec =5ft/s[/tex]

Surface Radius [tex]R_{surf}=2.2ft[/tex]

Generally the equation for Volume is mathematically given by

 [tex]V=\frac{1}{3}\pi*r^2h[/tex]

Since radius to height ratio gives

 [tex]\frac{r}{h}=\frac{5}{15}[/tex]

 [tex]\frac{r}{h}=\frac{1}{3}[/tex]

 [tex]h=3r[/tex]

Therefore

 [tex]V=\frac{1}{3}\pi*r^2(3r)[/tex]

 [tex]V=\pi r^3[/tex]

Generally the equation for Change of Volume is mathematically given by

 [tex]\frac{dv}{dt}=\pi \frac{d}{dt}(r^3)[/tex]

 [tex]\frac{dv}{dt}=\pi 3*r^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dv}{dt}=\pi 3*(2.2)^2 \frac{dr}{dt}[/tex]

 [tex]\frac{dr}{dt}=\frac{5}{45.62}[/tex]

 [tex]\frac{dr}{dt}=0.11062ft/sec[/tex]

Answer:

y = mx + b

m =(-2--4)/(-6--7)

m = 2

-2 = 2(-6) +b

b = 10

y= 2x + 10

Answer:

C

Step-by-step explanation:

Answer:

6750J

Step-by-step explanation:

30^2=900 900x15=13500 13500/2=6750

Answer:

K=6750[J]

Step-by-step explanation:

[tex]Kinetic \:Energy=\frac{1}{2} mv^2\\\\K=\frac{1}{2} (15)(30)^2\\\\K=6750[J][/tex]

Answer:

Solution given:

Area of parking space [parallelogram]=290ft²

base*height=290

base=290/29

base:10ft

Area of rectangular dimensions=11*7.4=81.4ft²

yes

The truck can not fit in the space because the length and breadth is less than that of the parallelogram parking area.

Area of truck bid 81.4ft².

Answer:

Step-by-step explanation:

D.all citizens; registered voters

Answer:

(x-5)(x+5)

Step-by-step explanation:

x^2 -25

We can rewrite this as the difference of squares

x^2 - 5^2

(x-5)(x+5)

Answer:

.08

Step-by-step explanation:

Answer:

Hi, there your answer is 0.08

Step-by-step explanation:

Given :

A function f(x) for different range of x.

To Find :

The value of f( -3 ) .

Solution :

We have to find the value of function at x = -3.

Now, in the given figure -3 lies in range x ≤ -2 and definition of function at that range is :

[tex]f(x) = \dfrac{2}{x}[/tex]

So, putting value of x = -3 in above equation, we get :

[tex]f(-3) = \dfrac{2}{-3} \\\\f(-3) = \dfrac{-2}{3}[/tex]

Hence, this is the required solution.

Answer:

Yes they are all right

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1/4 bczz its not saying about the highest its about average and the average is 1/4