A bathtub can be filled in 8 min. it takes 12 min for the bathtub to drain. if the faucet is turned on but the drain is also left open, how long will it take to fill the tub?

Answers

Answer 1

Time taken to fill the bathtub is 8 min
time taken to drain the bathtub is 12 min
fraction of bathtub filled in 1 hour=1/8
fraction of bathtub drained in 1 hour=1/12
fraction that will be filled in a minute given that both taps are opened at he same time:
1/8-1/12
=1/24
thus time taken for the bathtub to be filled is 24 min

Answer 2

Final answer:

It will take 24 minutes to fill the tub when both the faucet is running and the drain is open. The calculation is done using rates and subtraction.

Explanation:

This problem can be approached with the concept of rates. The rate at which the bathtub fills is 1 tub per 8 minutes or 1/8 tubs/min. Similarly, the rate at which it drains is 1 tub per 12 minutes or 1/12 tubs/min. When the faucet is running and the drain is open, the net rate is the fill rate minus the drain rate.

So, (1/8 - 1/12) tubs/minute = 1/24 tubs/minute. Thus, it will take 24 minutes to fill the bathtub with both the faucet running and the drain open.

Learn more about Rates here:

https://brainly.com/question/30354032

#SPJ12

Related Questions

For a circle with a radius of 6 feet, find the arc length of a central angle of 45 degrees

Answers

The arc length formula is given below.

Arc Length, s = radius*theta where theta is in radians. First we need to convert theta from degrees to radians.

theta (radians) = 45 degrees * π radians / 180 degrees = 0.785 radians

radius = 6 ft
theta = 0.785 radians

s = arc length = 6 ft * 0.785 radians = 4.712 ft

a boy flies a kite with a 100 foot long string. the angle of elevation of the string is 48 degrees. how high is the kite from the ground?

Answers

we know that
in a right triangle
sin ∅=opposite side angle ∅/hypotenuse
opposite side angle ∅=hypotenuse*sin ∅

in this problem
angle ∅=48°
hypotenuse=100 ft
opposite side angle ∅=?----> height of the kite from the ground

opposite side angle ∅=100*sin 48°------> 74.31 ft

the answer is
74.31 ft

Three added to eight times a number is the same as three times the value of two times the number minus one

Answers

im sorry do not now i will try and help

Create a function to model the height of a firework when shot in the air. Explain whether the function will have a maximum or a minimum value.

Answers

The function would be h(t)=-16t²+v₀t+0, where v₀ is the initial velocity of the firework.

0 is the initial height, since you cannot hold one in your hand and safely set it off.

This will have a maximum; the firework will reach a highest point and fall back down. This is also evident from the equation; the negative in front of t² flips the parabola upside down, which gives it a maximum.

If the areas of two rhombi are equal, are the perimeters sometimes, always or never equal. explain your answer – you can use examples with actual numbers to do so.equalif the areas of two rhombi are equal

Answers

If the areas are equal then the perimeters are also equal.
The area of a rhombus = length of base * altitude. To keep the area the same we would have to keep the same base and move the opposite side so its parallel to the base. But doing this will lengthen the other 2 sides of the figure so its no longer a rhombus.

The perimeters of two rhombi with equal areas are sometimes equal, but not always.

Let's consider the formula for the area of a rhombus, which is given by [tex]$ A = \frac{1}{2} \times d_1 \times d_2 $, where $ d_1 $ and $ d_2 $[/tex] are the lengths of the diagonals. For the perimeter P, we have [tex]$ P = 4 \times s $[/tex], where s is the length of one side of the rhombus.

For two rhombi to have equal areas, the product of their diagonals must be the same. That is, if we have two rhombi with diagonals [tex]$ (d_1, d_2) $ and $ (d_1', d_2') $, then $ d_1 \times d_2 = d_1' \times d_2' $[/tex].

However, the perimeter depends only on the length of one side, s, and not on the diagonals. Therefore, two rhombi with the same area can have different side lengths and thus different perimeters.

Let's consider an example:

Rhombus 1:

[tex]- Diagonals $ d_1 = 8 $ units and $ d_2 = 4 $ units[/tex]

[tex]- Area $ A = \frac{1}{2} \times 8 \times 4 = 16 $ square units[/tex]

[tex]- Side length $ s $, using the Pythagorean theorem (since the diagonals bisect each other at right angles), is $ s = \sqrt{4^2 + 2^2} = \sqrt{16 + 4} = \sqrt{20} $ units[/tex]

[tex]- Perimeter $ P = 4 \times s = 4 \times \sqrt{20} $ units[/tex]

Rhombus 2:

[tex]- Diagonals $ d_1' = 10 $ units and $ d_2' = 3.2 $ units[/tex]

[tex]- Area $ A' = \frac{1}{2} \times 10 \times 3.2 = 16 $ square units (equal to the area of Rhombus 1)[/tex]

[tex]- Side length $ s' $, using the Pythagorean theorem, is $ s' = \sqrt{1.6^2 + 2.56^2} = \sqrt{2.56 + 6.5536} = \sqrt{9.1136} $ units[/tex]

[tex]- Perimeter $ P' = 4 \times s' = 4 \times \sqrt{9.1136} $ units[/tex]

Comparing the perimeters:

[tex]- $ P = 4 \times \sqrt{20} \approx 4 \times 4.472 = 17.888 $ units[/tex]

[tex]- $ P' = 4 \times \sqrt{9.1136} \approx 4 \times 3.0188 = 12.0752 $ units[/tex]

Clearly, the perimeters are not equal, even though the areas are the same.

However, it is possible for two rhombi with equal areas to have equal perimeters if their side lengths are the same. For instance, if Rhombus 1 and Rhombus 2 both had side lengths of s = s' = 4 units, then their perimeters would both be P = P' = [tex]4 \times 4 = 16 \)[/tex] units, regardless of the lengths of their diagonals, as long as the diagonals satisfy the area condition [tex]$ d_1 \times d_2 = d_1' \times d_2' $[/tex].

In conclusion, the perimeters of two rhombi with equal areas can sometimes be equal, specifically when the side lengths are the same, but they are not always equal, as demonstrated by the example above.

Find the determinant of G

Answers

the determinant is found by the formula ad-cb

where the letters are: a and b is the top row and c and d is the bottom row
so ad = 12*2 and cb = -6*0

12x2 = 24
-6x0 =0

24-0 = 24
the determinant = 24

if (x+1) is a factor of x^3+2x^2-x-2, find the remaining factors.

Answers

Using synthetic division to divide x³ + 2x² - x - 2. Since (x + 1) is the factor, we can divide by -1. See the attached file for the synthetic division. After that, we are left with x² + x - 2. This can easily be factored into (x + 2)(x - 1). The remaining factors are (x + 2) and (x - 1).

Answer:

The other factors are (x-1) and (x+2).

If an airplane travels 15 miles in 2 minutes what is the speed in miles per hour

Answers

15 miles = 2 minutes

1 hour = 60 minutes

60 ÷ 2 = 30

30 × 15 = 450

Answer = 450 miles in 1 hour

Hope this helped :)

How do I convert 2.4 x 10^21 formula units of magnesium hydroxide to grams?

Answers

Are you taking chemistry at the same time? If not, this is a pretty hard question.

Facts

1. As a formula unit, Magnesium Hydroxide has a chemical formula of Mg(OH)2
2. That means for every Magnesium, there are 2 oxygens and 2 hydrogens
3. The weights of these components are found on a periodic table. Since every periodic table is different, I'm going to approximate the results.

Mg = 24
O = 16
H = 1

4. One mole of anything has 6.02 * 10^23 (in this case) formula units associated with it.

Step One
Find the number of grams in 1 formula unit using the numbers from the periodic table.

1 Mg = 1 * 24 = 24
2 O = 2 * 16 = 32
2 H = 2 * 1 = 2
Total = 58 grams

So
1 mole of Mg(OH)2 = 58 grams

1 mole / 6.02 * 10 ^23 formula units = x mole / 2.4 * 10 ^ 21 formula units
Cross multiply

1 mole * 2.4 * 10^21 formula units = x mole * 6.02 * 10^23 formula units.
Divide both sides by 6.02 * 10^23

1 * 2.4 * 10^21 / 6.02 * 10 ^ 23 = x
x = 0.003987 moles

Now do this again for grams
1 mole / 58 grams = 0.003987 mole / x grams Cross multiply
1 mole * x = 0.003987 * 58 grams
x = 0.2232 grams <<<<< Answer

PLEASE ANSWER QUICKLY! Suppose that there were a strong correlation between the variables n and p. Which of these is a true statement?

A. n may cause p.

B. p must cause n.

C. n must cause p.

D. n must not cause p.

Answers

The correct answer will be option A.

Correlation does not imply Causation.
This means if two variables are strongly related, it is not a must thing that one is causing any occurrence or change in the other variable. For example, before and during an occasion or an event people buy new clothes and celebrate by having different drinks. So there will be a strong correlation between buying new clothes and having drinks.
Thus this mean, having different drinks is causing people to buy new clothes? The answer is NO.

However, it is possible that if two variables are correlated on might be causing the other. For example, more hours of work will help the worker to earn more. So more work is causing the salary to grow. So more work is Causing an increase in salary? The answer is YES

Therefore, the answer to this question will be option A

Simplify. x + 4.7 = −9.2 A. −13.9 B. 13.9 C. −12.9 D. 12.9

Answers

Note the equal sign. What you do to one side you do to the other.

Isolate the x, subtract 4.7 from both sides

x + 4.7 = - 9.2

x + 4.7 (-4.7) = - 9.2 (-4.7)

x = -9.2 - 4.7

x = -13.9

-13.9, or A, is your answer

hope this helps

What is the best estimate for the sum of 3/8 and 1/12?

Answers

the best estimate is 5/12

The best answer would be 0.458

look at the image then answer the question that goes with it

Answers

[tex]\sin(\theta) = \dfrac{\text{opp}}{\text{hyp}}[/tex]

[tex]\sin(60) = \dfrac{x}{8} [/tex]

[tex]x = 8\sin(60) [/tex]

[tex]x = \dfrac{8 \sqrt{3} }{2} [/tex]

[tex]x = 4 \sqrt{3} [/tex]

x = 8 x sin(60)
x = 4sqrt3

Anyone know the answer?

Answers

i think it is 3=4 i could be wrong though

How many distinct permutations are there of the letters of the word BOOKKEEPER?
There are __[blank]__ distinct permutations of the letters of the word BOOKKEEPER.

A group of 3 English majors, 2 anthropology majors, and 5
history majors are going out to dinner, where they will sit at a circular table. If students with the same major need to sit together, how many different ways can the students be seated around the table?

Answers

The letters of the word BOOKKEEPER can be arranged in 151,200 ways.

The group can be arranged in 8640 ways with all students of the same major together.

Explanation
There are 10 letters in the word bookkeeper. There is 1 B; 2 O's; 2 K's; 3 E's; 1 P; and 1 R.

An arrangement of n total objects where n₁ is one kind, n₂ is another, etc. is given by:
[tex]\frac{n!}{n_1!\times n_2!\times ... \times n_k!} \\ \\=\frac{10!}{1!2!2!3!1!1!} = \frac{10!}{2!2!3!} = 151,200[/tex]

Keeping all of the students of each major together makes each one essentially a "unit." With this in mind, there are 3 units, that can be arranged in 3!=6 ways.

Within the English unit, the students can be arranged in 3!=6 ways.
Within the anthropology unit, the students can be arranged in 2!=2 ways.
Within the history unit, the students can be arranged in 5!=120 ways.

This gives us 6(6*2*120) = 8640

Final answer:

The word BOOKKEEPER has 10 letters, but with repetitions. There are 30240 distinct permutations. On the circular table, with students of the same major sitting together, there are 1440 different ways to seat the students.

Explanation:

The word BOOKKEEPER has 10 letters, but the letter O appears twice, the letter K appears twice, and the letter E appears three times. To find the number of distinct permutations, we need to divide the total number of permutations by the repetitions. So, we have 10!/(2!2!3!) = 30240 distinct permutations.

In the second question, we need to consider the students with the same major sitting together as a single entity. We can treat the circular table as a linear arrangement by fixing one student in a position and arranging the rest. So, the total number of different ways the students can be seated around the table is (3!2!5!) × 2! = 1440.

Learn more about Permutations and Circular Arrangements here:

https://brainly.com/question/1216161

#SPJ3

Choose the example that correctly shows the mean population density of a region.

A. 678 people per cubic meter

B. 678 cubic meter per number of people

C. 678 people per square mile

D. 678 square mile per people

Answers

678 people per cubic meter - lol!! That would be a SQUash!!!

The answer is C

- 678 per square mile

The length of a rectangle is 4 feet shorter than its width. the area of the rectangle is 42 square feet. find the length and width. round your answer to the nearest tenth of a foot

Answers

Length is [tex]\boldsymbol{4.4}[/tex] feets and width is equal to [tex]\boldsymbol{8.8}[/tex] feets.

Area of a rectangle

The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.

A quadrilateral having four right angles is known as a rectangle.

Let [tex]\boldsymbol{w}[/tex] feets denotes width of a rectangle.

Length of a rectangle [tex]=\boldsymbol{w-4}[/tex] feets

Area of a rectangle [tex]=\boldsymbol{42}[/tex] square feet

Length [tex]\times[/tex] Width [tex]=42[/tex]

[tex]w(w-4)=42[/tex]

[tex]w^2-4w-42=0[/tex]

[tex]w=\frac{4\pm \sqrt{16+168}}{2}[/tex]

[tex]=2\pm \sqrt{46}[/tex]

As dimension can not be negative, [tex]2-\sqrt{46}[/tex] is rejected.

So,

[tex]w=2+ \sqrt{46}[/tex]

[tex]=\boldsymbol{8.8}[/tex] feets

Length [tex]=8.8-4[/tex]

[tex]=\boldsymbol{4.4}[/tex] feets

So, length is [tex]4.4[/tex] feets and width is equal to [tex]8.8[/tex] feets.

Find out more information about rectangle here:

https://brainly.com/question/10046743?referrer=searchResults

Find the values of b such that the function has the given maximum value. f(x) = −x2 + bx − 14; Maximum value: 86

Answers

[tex]f(x)=-x^2+bx-14\\\\y_{max}=86[/tex]
[tex]y_{max}\ \text{is in the vertex of the parabola}.[/tex]
[tex]\text{The coordinates of the vertex of the parabola}\ f(x)=ax^2+bx+c:\\\\V\left(\dfrac{-b}{2a};\ \dfrac{-(b^2-4ac)}{4a}\right)[/tex]
[tex]\text{We have:}\\\\f(x)=-x^2+bx-14\to a=-1;\ b=b;\ c=-14[/tex]
[tex]\text{Substitute:}\\\\\dfrac{-\left(b^2-4\cdot(-1)\cdot(-14)\right)}{4\cdot(-1)}=86\\\\\dfrac{b^2-56}{4}=86\ \ \ \ |\cdot4\\\\b^2-56=344\ \ \ \ |+56\\\\b^2=400\to b=\pm\sqrt{400}\\\\b=-20\ \vee\ b=20[/tex]
Answer: b = -20 or b = 20.

Final answer:

To find the value of 'b' that gives the maximum value of 86 for the function f(x) = -x² + bx - 14, substitute the x-coordinate of the vertex (-b/2a) into the function, equate it with 86 and solve for 'b'.

Explanation:

To find the values of b for which the quadratic function f(x) = -x² + bx - 14; Maximum value: 86 holds true, we need to utilize the properties of quadratic functions. In a quadratic function in the form f(x) = ax² + bx + c, the maximum value occurs at the vertex of the parabola. The x-coordinate of the vertex is given by -b/2a.

Given that our quadratic is a maximum (opens downwards since a=-1), the y-coordinate of the vertex, which is our maximum value, is 86. Substituting these into our function, we get f(-b/2a) = 86, replacing a=-1, this reduces to -b²/4 -14 = 86. Simplifying this equation will give you the value of b.

Learn more about Quadratic Function here:

https://brainly.com/question/35505962

#SPJ2

PLEASE HELP! - Caitlyn recorded the height of each plant after she exposed each plant to a set amount of darkness daily. The scatterplot shows her results after 2 weeks of exposing each plant to the amount of darkness.

(Graph Below)

Which statement about the scatterplot is true?
A. The point (17, 12) could cause the description of the data set to be overstated.
B. The point (17, 12) could cause the description of the data set to be understated.
C. The point (17, 12) shows that there is no relationship between the number of hours of darkness and the height of the plant.
D. Although (17, 12) is an extreme value, it should be part of the description of the relationship between number of hours of darkness and the height of the plant.

Answers

Answer:

I think it's b, please correct me if I'm wrong.

Step-by-step explanation:

I'm taking the test rn so I hope its right.

Answer:

its b i just did it

Step-by-step explanation:

can you please help me on this worksheet and try to show the work

Answers

For 13 and 14, the conversion factor is
180° = π radians

13. (105°)*(π radians)/180° = 7π/12 radians

14. 5π/6 radians * 180°/(π radians) = 150°

15. (The geometry shown cannot actually exist. The total of subtended arcs on any linked sprockets must be 360°.)
a.
The arc length on the smaller sprocket is (12 in)*(160/360) = 5 1/3 in.
The arc length on the larger sprocket is (20 in)*(185/360) = 10 5/18 in.
The total chain length is 5 6/18 +10 + 10 5/18 + 10 = 35 11/18 in. Rounded to the nearest tenth inch, the chain length is 10.3 inches.

b.
10.3/0.5 ≈ 20.6 ≈ 21
The chain has about 21 links. (There are no "teeth" on a chain.)

1. The radius can be found by looking at the distance between the origin and the line 8x+6y-48=0. That distance is |-48|/√(8²+6²) = 4.8.

Since the radius of the circle is 4.8, so its circumference is ...
9.6π cm, about 30.159 cm.

2. s = rθ
s = (12 cm)(π/3 radians) = 4π cm
The length of arc AB is 4π cm, about 12.566 cm.

The shorter leg of a right triangle is 7 inches shorter than the longer leg. The hypotenuse is 17 inches longer than the longer leg. Find the side lengths of the triangle.

Answers

Or round them all up.

a² + b² = c²

c² - a² = b²

17² - 7² = x² ↓

289 - 49 = √240

√240 = 15.49193338482967 (rounded 15.49 or 15.5)

Hope this helps,

♥A.W.E.S.W.A.N.♥

A man has 25 25 coins in his pocket, all of which are dimes and quarters. if the total value of his change is $ 4.45 $4.45, how many dimes and how many quarters does he have?

Answers

If all were dimes, the value would be $2.50. The man has $1.95 more than that amount. Trading a dime for a quarter increases the value by $0.15, so there must be
$1.95/$0.15 = 13
quarters.

The man has 12 dimes and 13 quarters.

_____
Check:
12*$0.10 +13*$0.25 = $1.20 +3.25 = $4.45 . . . (answer checks OK)

help me 15p for an answer and brainliest
help mme please
the true it is 20p

Answers

Option 4.
______________

Answer:

Option 4.

Step-by-step explanation:

Rachel enjoys exercising outdoors. Today she walked5 2/3 miles in2 2/3 hours. What is Rachel’s unit walking rate in miles per hour and in hours per mile

Answers

the answer to your question is

Unit walking rate in miles per hour = 5 2/3 / 2 2/3 = 17/3 / 8/3 = 17/3 x 3/8 = 17/8 = 2 1/8 miles per hour.

Unit walking rate in hours per mile = 1/ 17/8 = 8/17 hours per mile

Answer:

Rachel enjoys exercising outdoors. Today she walked 5 2/3 miles or 5.67 miles in 2 2/3 hours or 2.67 hours.

Rachel’s unit walking rate in miles per hour is = [tex]\frac{5.67}{2.67}[/tex] = 2.125 miles per hour or 2 1/8 miles per hour.

Rachel’s unit walking rate in hours per mile = [tex]\frac{2.67}{5.67}[/tex] = 0.47 hours per mile.

10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!

Answers

I find short work can be made of many limit problems simply by graphing them. Your limits appear to be:
1. 1
2. -1
3. 0
4. 1
5. 1 (x has been replaced by 1/x and the limiting value of x changed to 0)

describe the steps you would use to solve the following inequality

Answers

[tex] \frac{x + 1}{2x - 3} > 2 \\ x + 1 > 2(2x - 3) \\ x + 1 > 4x - 6 \\ - 3x + 1 > - 6 \\ - 3x > - 7x \\ x < \frac{7}{3} [/tex]

Answer:

Rewrite the inequality so there is a single rational expression on one side, and 0 on the other.

Combine under a common denominator.

Test points in the critical regions.

Construct the solution.

Step-by-step explanation:

Answer Above

What is the area of the parallelogram?

Answers

Area of the parallelogram is given by:

Area = Base x Height

Base = 8 cm

Height is the perpendicular distance between the base. 6 cm is not the height, but we can use 6 cm and the angle 60 to find the height. See the picture attached with.

The height x is the perpendicular side of the triangle as shown in figure and 6 is the hypotenuse.

So,we can write

cos 60 = x/6
⇒
x = 6 * cos 60 = 3 cm

So, now we can write:

Area of parallelogram = 8 x 3 = 24 cm²

The area of a parallelogram is base*height

or A = base*lateral side /cos(theta)

A = 8 * 6 / cos(60) = 96cm^2

The area of the parallelogram is 96 sq.cm

PLEASE HELP ME

If the maximum density of killer whales per cubic foot is 0.000011142, what is the maximum number of killer whales allowed in the main show tank at any given time? You must explain your answer using words, and you must show all work and calculations

Answers

a]
Given that the the tank has a radius of 70 ft;
The volume of the sphere will be:
V=1/4[4/3*pi*r^3]
v=1/4[4/3*3.14*70^3]
V=359,006.6675

b] The maximum number of whales will be given by:
density=mass/volume
thus
0.000011142=x/(359006.6675)
thus
x=0.000011142*359006.6675
x=4
thus the maximum number of whale would be 4

A certain company's main source of income is selling socks. The company's annual profit (in millions of dollars) as a function of the price of a pair of socks (in dollars) is modeled by: P(x)=-3(x-5)^2+12 . What sock price should the company set to earn a maximum profit?

Answers

For this case we have the following function:
P (x) = - 3 (x-5) ^ 2 + 12
We derive the function to obtain the maximum.
We have then:
P (x) = - 6 (x-5)
We match zero:
-6 (x-5) = 0
We clear x:
x-5 = 0
x = 5
Answer:
the company should set a sock price of 5 $ to earn a maximum profit

Final answer:

To obtain the maximum profit, the company should set the price of each pair of socks to $5. This answer is derived from the vertex of the given quadratic profit function.

Explanation:

The student question asks at which price the sock selling company should sell its product to earn a maximum profit, given the profit function: P(x)=-3(x-5)^2+12. This function is a standard form of a quadratic equation, and in such equation, the maximum value is achieved at the vertex.

In this case, the vertex (h,k) of the quadratic function is (5,12), where 'h' is the value of 'x' that gives the maximum profit 'k'. So the company should set the price at $5 to earn a maximum profit.

This economic model analysis' underlying principle relies on the assumption of maximizing total revenues and minimizing total costs to yield the maximum profit. Hence, recognizing the nature of the profit function is crucial.

Learn more about Profit Maximization here:

https://brainly.com/question/33809682

#SPJ3

Find the area of the shaded region.

Answers

1)
Area of bigger rectangle
A = (x+1)(x+1) = x^2 + 2x + 1

2)
Area of smaller rectangle
A = 5(x - 7) = 5x - 35

3)
The difference:
(x^2 + 2x + 1) - (5x - 35)
= x^2 + 2x + 1 - 5x +35
= x^2 - 3x + 36

area of the shaded region = x^2 - 3x + 36

Hello!

You first have to find the area of the bigger rectangle

You find this by multiplying the sides

(x + 1)(x + 1) = x^2 + 2x + 1

Next you have to find the area of the smaller rectangle

(x - 7) * 5 = 5x - 35

Subtract the two polynomials

(x^2 + 2x + 1) - (5x - 35) = x^2 - 3x + 36

The answer is [tex] x^{2} -3x + 36[/tex]

Hope this helps!

Other Questions

On a scatter plot what does it mean when both variables are increasing a blank is an electric circuit that produces a magnetic field.whats the blank? The most difficult part of the journey westward for settlers was The process of moving through a system and returning to the starting point Another development in social networking is the rise of __________, as it uses internet-based messages to share information simultaneously with a large number of people. An exoskeleton is found in ________; an endoskeleton is found in ________. One of the principal reasons the "noble experiment" of prohibition failed was that it led to an enormous increase in The three types of federal student aid are: A. grants, waivers, and loans. B. loans, grants, and work-study. C. scholarships, loans, and grants. D. scholarships, grants, and work-study. Two astronauts are playing catch with a ball in space. The first astronaut throws the ball; and A)the ball moves, but the astronaut doesnt. B)the ball moves, and so does the astronaut. C)the ball doesnt move, but the astronaut does. D)the ball doesnt move, and neither does the astronaut. A spring with a spring constant of 1.8 102 n/m is attached to a 1.5 kg mass and then set in motion.a.what is the period of the mass-spring system?b.what is the frequency of the vibration divide r+5/ r^2+5r-14 by r^2+4-21/r-2 The secretions of the bulbo-urethral glands neutralize traces of acidic urine in the urethra and serve as a lubricant during sexual intercourse. the secretions of the bulbo-urethral glands neutralize traces of acidic urine in the urethra and serve as a lubricant during sexual intercourse. a. True b. False Kelvin was released from prison before his entire sentence was served. however, he has to be supervised by an officer. this situation is commonly referred to as: In my last duchess by robert browning, how do the duke and the duchess differ? he is proud and suspicious, but she is open and trusting. he is ill-mannered, but she values courtesy. he is passionate and outgoing, but she is unemotional and quiet. he loves art, but she only enjoys nature. On a map, 1 inch equals 9.2 miles. two houses are 3.5 inches apart on the map. what is the actual distance between the houses? use pencil and paper. show how you can represent the scale with two different ratios. what ratio is more helpful for solving the problem? explain. What is the primary site of intracellular digestion? A. the endoplasmic reticulum B. the mitochondria C. the lysosome D. the nucleus in figure 33-6 what structure is labeled a> what is the role of the delicate network At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure ____. i really need help. please helpPart A: Explain why the x-coordinates of the points where the graphs of the equations y = 4^x and y = 8^(x1) intersect are the solutions of the equation 4^x = 8^(x1). (4 points)Part B: Make tables to find the solution to 4^x = 8^(x1). Take the integer values of x between 3 and 3. (4 points)Part C: How can you solve the equation 4^x = 8^(x1) graphically? (2 points) The sumerians were one of the first civilizations to make use of ______.