2. Ron lives in Seattle, but he is going to be in Hawaii for 13 days during the month of
March. There are 30 days in March. What would you subtract to find out how many days
in March Ron will be in Seattle?

Answer:

A. 90.5 cubic meters pet second.

B. 3.77 square meters per second.

C.  [tex]\frac{dV}{dS} = \frac{r}{2}[/tex]

Step-by-step explanation:

The radius of a sphere is increasing at a constant rate of 0.05 meters per second.

Therefore, [tex]\frac{dr}{dt} = 0.05[/tex] ......... (1)

A. Now, volume of the sphere is given by  

[tex]V = \frac{4}{3}\pi  r^{3}[/tex]

Now, differentiating both sides with respect to t we get,

[tex]\frac{dV}{dt} = \frac{4}{3}\pi (3r^{2}) \frac{dr}{dt} = 4\pi r^{2} \frac{dr}{dt}[/tex]

Then at r = 12 meters, the rate of increase in volume will be

[tex]\frac{dV}{dt} = 4 \times (\frac{22}{7}) \times 12^{2} \times 0.05 = 90.5[/tex] cubic meters pet second. {From equation (1)}

B. When the volume of the sphere is 36π cubic meters, then  

[tex]\frac{4}{3}\pi r^{3} = 36\pi[/tex]

⇒ [tex]r^{3} = 27[/tex]

⇒ r = 3 meters.

Now, surface area of a sphere is given by  

S = 4πr² .......... (2)

Differentiating both sides with respect to time (t) we get,

[tex]\frac{dS}{dt} = 8\pi r\frac{dr}{dt} = 8 \times (\frac{22}{7}) \times 3 \times 0.05 = 3.77[/tex] square meters per second. {From equation (1)}

C. Now, [tex]V = \frac{4}{3}\pi  r^{3}[/tex] and S = 4πr²

⇒ [tex]V = \frac{1}{3} (4\pi r^{2})r = \frac{Sr}{3}[/tex]

Now, differentiating with respect to S both sides we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{S}{3} \frac{dr}{dS}[/tex] ......... (3)

Now, we have, S = 4πr²

Differentiating with respect to S both sides, we get

[tex]1 = 8\pi r\frac{dr}{dS}[/tex]

⇒ [tex]\frac{dr}{dS} = \frac{1}{8\pi r }[/tex] ......... (4)

Now, from equations (2), (3) and (4) we get,

[tex]\frac{dV}{dS} = \frac{r}{3} + \frac{4\pi r^{2} }{3} \times \frac{1}{8\pi r }[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{3} + \frac{r}{6}[/tex]

⇒ [tex]\frac{dV}{dS} = \frac{r}{2}[/tex] (Answer)

Question:

C. Express the rate at which the volume of the sphere changes with respect to the surface are of the sphere (as a function of r)

Step-by-step explanation:

Here's how you solve part C of this question.

Start with what you know:

dV/dt = 4pir^2 x (dr/dt)

(dr/dt) = 0.05

S(r) = (Surface Area) = 4pir^2

So, since S(r) is equal to 4pir^2, we replace 4pir^2 with S(r). We also know that (dr/dt) = 0.05, so we replace (dr/dt) with 0.05.

Now the equation should look like this:

dV/dt = 0.05 x S(r) <----- (your answer).

Hope this helped!! :)

√12x^3÷√6x

Factor 6 out of both the numerator and denominator:

√2x^3÷√x

Cancel out common factors to get:

√2x^2

Pull the terms out from under the radical to get:

D. x√2

Answer:

48 units cubed

Step-by-step explanation:

length × height × width

4 × 6 × 2 = 48

Answer:

Let's find out!

Step-by-step explanation:

15 ounces / 2.49 dollars

≈ 6.024 ounces per dollar

20 ounces / 3.32 dollars

≈ 6.024 ounces per dollar

Your answer is:

C) The unit rates are equal

The amount of ounces per dollar is the same, so your answer MUST be C).

Answer:

C) The unit rates are equal.

Step-by-step explanation:

It will take you 2 hours since ur going 70 mph divide the 140 mph by 70mph . Hope this helps :)

Each student worked on 115 math problems.

Step-by-step explanation:

Given,

Problems solved in 4 hours = 8970

Number of students in competition = 78

As each student solved same number of problems, we will divide the total problems solved by number of students to find the amount of problems solved by one student.

Problems solved by one student = [tex]\frac{8970}{78}[/tex]

Problems solved by one student = 115

Each student worked on 115 math problems.

Keywords: division

Learn more about division at:

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Each student works 115 problems.

Explanation:

I'm going to copy and paste the question here, and bold important info.

"Rayville Elementary sponsors a math competition for 78 students. During the competition, the students work a total of 8,970 math problems in 4 hours. Each student works the same number of problems. How many problems does each student work?"

Now everything not bolded? Forget about it. All you need to know is that there are 78 students. They all do 8,970 # of problems. And all the students do the same amount. Now you just have to divide the # of probs. by the amount of students in the competition, and you have your answer.

8970÷78=115

Hope that helped!

===============================================

How I got that answer:

r = radius

h = height

LA = lateral surface area of cylinder

LA = 2*pi*r*h

Let's find the lateral surface area of each silo. The smallest lateral surface area will lead to the lowest total cost.

-------------

Silo A

LA = 2*pi*r*h

LA = 2*pi*6*60

LA = 720pi

-------------

Silo B

LA = 2*pi*r*h

LA = 2*pi*8*50

LA = 800pi

-------------

Silo C

LA = 2*pi*r*h

LA = 2*pi*10*34

LA = 680pi

-------------

Silo D

LA = 2*pi*r*h

LA = 2*pi*12*20

LA = 480pi

-------------

If we ignore the "pi" terms for each of the four answers above, we see that 480 is the smallest value. Silo D has the smallest lateral surface area at 480pi square feet.

-------------

Side note: to determine the total cost, you multiply the surface area by the cost per square foot ($1.20)

For example, the total cost to paint silo D is

cost = (surface area)*(price per square foot)

cost = (480*pi)*(1.20)

cost = 1809.557

cost = 1809.56

This section is optional as your teacher isnt requiring you to find the actual costs, but rather just the silo with the least amount of area. You could go the longer route to find each surface area, compute the total cost, and then compare the total costs. You should find that silo D's cost is the lowest.

Answer:

1/3

Step-by-step explanation:

Answer:

Step-by-step explanation:

X={0,12,23}

Y={3,12,15}  

X \ Y = { 0 , 23}

X/Y means the element should be only in X. We have remove the element in X if it is in Y

In this 0 and 23 is only in X

12 is X and Y. So it wont come in X/Y

The set X \ Y represents the difference of two sets, indicating all the elements that are in set X but not in set Y. For X={0, 12, 23} and Y={3, 12, 15}, the elements that are in X but not in Y are '0' and '23', so X \ Y = {0, 23}.

In set theory, the notation X \ Y represents the difference of two sets. This indicates all the elements that are in set X but not in set Y. In this case:

X={0, 12, 23}, Y={3, 12, 15}

So the elements that are in X but not in Y are '0' and '23'.

Therefore, X \ Y = {0, 23}.

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Answer:

53.33%

Step-by-step explanation:

(16/30)*100=0.5333333333*100=53.33%

Answer:53.3%

Step-by-step explanation:

Answer:

-13x + 6y

Step-by-step explanation:

combine like terms

-7x + 6y - 6x

-7x - 6x = -13x

-13x + 6y

Answer:

Step-by-step explanation:

-7x+6y-6x

Solution:

Put like terms together from left to right; that is the equation will assume a new order from -7x+6y-6x to

-7x-6x+6y

Sum the figures with like terms

= -13x+6y (answer)

Answer:

Option A does not give the right expression.

Step-by-step explanation:

On the number line if there are two points P(a) and Q(b) given by coordinates a and b, then the distance between those two points will be given by  

d = |a - b| ......... (1)

which is independent of the position of the points.

Therefore, if point A is at - 3.5 and point B is at 7.5, then the distance between point A and point B will be given by  |7.5+3.5| or |- 3.5-7.5| or |7.5-(-3.5)|, but not by  |7.4-3.5|.

Hence, option A does not give the right expression. (Answer)

Answer: 301

Step-by-step explanation:

the least amount one of the wrestlers could weigh is 301.

The term standard deviation refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

Given that,

Mean μ = 265,

Standard deviation σ = 28 lbs.

Let the least amount one of the wrestlers could weigh is x.

To find x such that P(X≥x) = 0.10

1 - P(X<x) = 0.10

P(X<x) = 1 - 0.10

P(X<x) = 0.90

z for area = 0.90 in equal to 1.28 in statistical table,

z = 1.28

Use  formula, to find the value of x,

x = μ + z × σ

x = 265 + 1.28 × 28

x = 265 + 35.84

x = 300.84

x = 301(Rounded to the nearest integer)

The required value of x is 301.

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Answer:

x<103/40

Step-by-step explanation:

-13(6x-15)+6x>8x-11

-78x+195+6x>8x-11

-78x-8x+6x+195>-11

-78x-2x>-11-195

-80x>-206

80x>206

x>206/80

x>103/40

x<103/40

Answer: 96mm²

Step-by-step explanation:

c=31 mm

m=6mm

b=8mm

d=10mm

l=24 mm

-----------------------

c=31 mm

a=24+6=30 mm

b=8mm

A of ΔM=30*8/2=

120 mm²

A of ΔS=b*m/2=8*6/2=24mm²

Area od shaded triangle is=area of ΔM-area ofΔS=120-24=96mm²

Answer:

d.) 81

Step-by-step explanation:

f(2) would be 27 and 27x3 is 81.

81/3=27

27/3=9

Answer:

81

Step-by-step explanation:

For the recursive function, f(n+1) = one-half(n)

Thus, when n = 2,

f(3) = 9

If n = 1,

f(2) = 9×3

f(2) = 27

If n = 0,

f(1) = 27 ×3

f(1) = 81

Answer: -9r+3

Step-by-step explanation:

In order to simplify this expression, all you have to do is combine the like terms. However, because there is an addition and a subtraction sign next to each other, we have to multiply them together to find which sign will stay.

Positive x Positive = Positive

Positive x Negative = Negative   <---

Negative x Negative = Positive

Because we know that multiplying a negative sign by a positive sign will give us negative, we have to keep the subtraction sign and remove the addition sign. This leaves us with 4-9r-1. All that is left to do is simplify.

Combine the like terms: 4-1 = 3

Answer: -9r+3

Hope this helps!

Answer:

Step-by-step explanation:

Group Like Terms:

A: -9r + 4 - 1,

Add/Subtract numbers:

If you have any questions feel free to comment below.

Best of Luck to you.

Answer:

4.94

Step-by-step explanation:

Subtract

9.03 - 4.09 = 4.94

Hope this helps :)

Answer:

4.94

Step-by-step

9.03 - 4.09= 4.94

Answer:

OPTION A: [tex]$ \frac{1}{2^{15}} $[/tex]

Step-by-step explanation:

We should know that:

[tex]$ (a^b)^c = a^{b . c} $[/tex]

So, [tex]$ (2^3)^{-5} = 2^{3 . (-5)}} $[/tex]

[tex]$ = 2^{-15} $[/tex]

This is equivalent to [tex]$ \frac{1}{2^{15}} $[/tex]

Hence, OPTION A is the answer.

Answer:

Total price of the glass is = $904.78

Step-by-step explanation:

Let's start by finding what is the surface area (in square meters) of the circular piece of glass. The information we have is that the radius of it is 8.0 meters. So we recall the formula for the area of the circle in terms of its radius (the product of the number [tex]\pi[/tex] times the square of the circle's radius):

Area of circle = [tex]\pi \,r^2[/tex]

Therefore, since the circle we need to investigate has radius 8 meters, the formula now becomes:

Area of circle = [tex]\pi \,r^2=\pi\,\,(8\,m)^2=201.062\,m^2[/tex]

Now, since they charge the glass per square meter ($4.50 per square meter), we just multiply the number of square meters we found for the glass' surface times the price per square meters, and get:

Total price = $4.50 * 201.062 = $904.78

Answer:

P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

"What is p? 4 1/2 + p = -5 3/4" was the question you have asked

So basically, in this equation we are looking for what the variable, P, is.

We already know that P plus 4[tex]\frac{1}{2}[/tex] equals -5[tex]\frac{3}{4}[/tex].

Now here's how you solve it:

So when trying to find the value a variable has, you should use inverse operations. What are inverse operations? Well let's look at this example:

453-T=56

How you would solve this is that you would subtract 56 from 453, removing 56 on the other side by subtracting it from the other side. *When performing inverse operations you always do it on BOTH sides*

We subtracted because 56 is positive and when performing operations on both sides of an equation, you do the inverse operation in both which in this case is to subtract.

453-T=56

-56      -56

↓

397-T=0

Now you may wonder 'What now? The other side is just 0! That didn't solve for T.' This is true. We have not solved for T just yet. But after this we will

397-T=0

     +T  +T

        ↓

397 = T

Tada! T is solved! We added T to both sides as T was negative and the opposite of negative is positive.

There are a few other ways to solve this equation like for example you could of subtracted 453 from both sides instead and have made it look like this:

453-T=56

-453    -453

↓

-T = -397

(Multiply both sides by negative 1 to make the -T and the -397 positive)

-1 (-T) = (-397) -1

↓

T = 397

----------------------------

Now that we've explained the basics of how that works let's now *actually* solve the problem:

4 1/2 + p = -5 3/4  

-4 1/2          -4 1/2

↓

P = -41/4

(4 1/2 is positive so the inverse operation was to subtract)

(A negative number subtracted by a negative number is a negative number that is even more negative than before)

--

ITS DONE!

Anyways let's check the equation to make sure it is right!

This is not needed but it is helpful to know how to check when you doubt that the value you got for a variable is correct.

You check by simply just pluging in the number you got into the variable and solving the equation to see if makes sense.

Here is how you would check this:

4 1/2 + p = -5 3/4

becomes

4 1/2 -[tex]\frac{41}{4}[/tex] = -5 3/4

subtract 41 fourths from 4 1/2

[tex]\frac{18}{4}[/tex]-[tex]\frac{41}{4}[/tex]= -[tex]\frac{23}{4}[/tex]

↓

-[tex]\frac{23}{4}[/tex] = -[tex]\frac{23}{4}[/tex]

Because the sides are equal, it is correct!

So, P = -[tex]\frac{41}{4}[/tex] or -10 [tex]\frac{1}{4}[/tex]

The value of p in the given algebraic equation 4 1/2 + p = -5 3/4 is -10.25. This is found by isolating p.

To resolve this algebraic equation, you need to subtract 4 1/2 (which is 4.5 in decimal form) from each side of the equation, in order to isolate p. Hence, the equation then becomes p = -5 3/4 - 4 1/2.

First, convert -5 3/4 and 4 1/2 to decimal form. -5 3/4 becomes -5.75 and 4 1/2 becomes 4.5.

Secondly, subtract 4.5 from -5.75. Therefore, p is equal to -5.75 - 4.5 = -10.25.

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Answer:

Draw a line on you paper, go to the start of the line and place your Protractor. Look for the 40 degree mark and place a little slash there. Take away the protractor and draw a line going through the slash. (Use a ruler too)

Step-by-step explanation:

For this you need a protractor

Joanie used a protractor to draw the angle 40° that Joanie will use on her map​ can follow the steps provided here.

An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.

Steps of Construction:

1. Draw ∠BAC=40° using protractor. By taking A as Centre draw an arc which cuts AB and AC at P and Q.

2. Now take O as centre on another line segment EF and taking the same radius PQ draw an arc which cuts OF at R. Now again take R as Centre and draw the arc which cut at S.

3. Join O to S which is the required ∠ROS=40°.

Therefore, Joanie used a protractor to draw the angle 40° that Joanie will use on her map​ can follow the steps provided here.

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when rounding up, decimals tend to lose accuracy, thus the rounding, due to that, fractions will always be the most accurate to represent the value, but let's go ahead

3/5 = 0.6 <- rounded up to one decimal

3/4 = 0.75

      = 0.8 <- rouned up to one decimal as well

if we add them up 0.6 + 0.8 = 1.4.

[tex]\bf \cfrac{3}{5}+\implies \cfrac{3}{4}\implies \stackrel{\textit{using an LCD of 20}}{\cfrac{(4)3+(5)3}{20}}\implies \cfrac{12+15}{20}\implies \cfrac{27}{20} \\\\\\ 1.35\implies \stackrel{\textit{rounded up}}{1.4}[/tex]

in this case, rounding up each result to 1 decimal, we end up with the same value, mind you that the instructions never said to round it to a certain amount of decimal places, if we do round it to two decimal places, the value will be 1.35 for both cases, and accurate on each.

Answer:2³*3²

Step-by-step explanation:

Answer:

[tex]\displaystyle x - 3y = 6\:OR\:y = \frac{1}{3}x - 2[/tex]

Step-by-step explanation:

First, find the rate of change [slope]:

[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{3 + 2}{3 + 12} = \frac{5}{15} = \frac{1}{3}[/tex]

Then plug these coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula since you get it swiftly that way. It does not matter which ordered pair you choose:

2 = ⅓[12] + b

4

[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

[tex]\displaystyle x - 3y = 6[/tex]

_______________________________________________

−3 = ⅓[−3] + b

−1

[tex]\displaystyle -2 = b \\ \\ y = \frac{1}{3}x - 2[/tex]

If you want it in Standard Form:

y = ⅓x - 2

- ⅓x - ⅓x

_________

−⅓x + y = −2 [We do not want fractions in our standard equation, so multiply by the denominator to get rid of it.]

−3[−⅓x + y = −2]

[tex]\displaystyle x - 3y = 6[/tex]

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.

The volume of Duante's bedroom is 1080 cubic feet.

Given that, the area of the floor is 90 square feet, and the height of the bedroom is 12 feet.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same.

Volume of a rectangular prism = Area of a base × Height.

Here, volume of a rectangular prism = 90 × 12

= 1080 cubic feet

Therefore, the volume of Duante's bedroom is 1080 cubic feet.

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Answer:

1/3

Step-by-step explanation:

The slope of a line in slope-intercept form, y=mx+b, is m.

This means the slope of y=-3x-2 is -3.

If a line is perpendicular to the one given, it will have the opposite reciprocal slope.

The opposite of -3 is 3.

The reciprocal of 3 is 1/3.

Therefore, the opposite reciprocal of -3 is 1/3.

Answer:

b.18

Step-by-step explanation:

18/4=4.5

Answer: The answer would be b, or 18. 4x4.5 is 18, but you are not multiplying it by a whole number. so it CAN'T be B.

Hope this helps!

Answer:

There will be no pieces of paper left over. Each student will receive 15 pieces of paper.

Step-by-step explanation:

If you divide the 345 pieces of paper between the 23 classmates, you will end up with 15. There is no remainder or decimal, just 15, a whole number. That means that there will be no pieces of paper left over.

Answer:

$1.40

Step-by-step explanation:

40 times 30% = 28 because 30% of 40 is 12 so 40-12 =28

28 times .05= 1.40 which  is the tax of  the final total

Answer:140

Step-by-step explanation: