20 COINS
Cylinder A has radius r and height h as shown in the diagram. Cylinder B has radius 2r and height 2h. How many times greater is the surface area of Cylinder B than the surface area of Cylinder A?

Answer:

14. 5log3(x) -2log3(y)

18. ln(x+1) -2ln(x)

Step-by-step explanation:

The relevant rules of logarithms are ...

log(ab) = log(a) +log(b)

log(a^b) = b·log(a)

___

14. Applying the first rule gives ...

log3(x^5) +log3(y^-2)

Applying the second rule gives ...

5·log3(x) -2·log3(y)

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18. The log of a sum cannot be simplified. We can make this be a simpler expression so that the log of it will be fairly simple.

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

Now, we can apply rule 1 to get ...

ln(x+1) +ln(1/x^2)

and applying rule 2 gives ...

ln(x+1) -2ln(x)

Answer:

y - 5 = -1(x + 3)

Step-by-step explanation:

Point slope form

y - y1 = m(x - x1) where m = slope and passing through point (x1 , y1)

In this case if the equation in point-slope form contains the point (–3, 5) and has slope –1 then the equation should be:

y - 5 = -1(x - (-3))

y - 5 = -1(x + 3)

The correct point-slope equation containing the point (–3, 5) with a slope of –1 is y - 5 = -1(x + 3).

The equation of a line in point-slope form is written as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line. Plugging in the point (–3, 5) and the slope –1, we get the equation y - 5 = -1(x + 3). None of the other options correctly use both the given point and the given slope in the point-slope form equation.

First you would need to add the amount of the increase to the old price , so that would be p +1.25.

Then to find the total amount he will spend, you need to multiply the total price by the number of games he buys.

The equation becomes:

t = n(p+1.25)

Answer:

  756 m²

Step-by-step explanation:

The ratio of areas is the square of the ratio of linear dimensions. Hence the area of the red solid is ...

  (6/4)²×336 m² = 756 m²

Answer:

3ft  by 6ft

Step-by-step explanation:

Area = l*w

P = 2(l+w)

We know that the area is the same as the perimeter

2 (l+w) = 18

Divide each side by 2

l+w =9

Our choices our 1,9

                           2,8

                            3,6

                            4,5

we know that they have to multiply to 18

1*9 =9

2,8 = 16

3,6=18

4,5=20

They only choice is 3 by 6

The tabletop can have dimensions of 6 feet by 3 feet.

Let's denote the length of the table as [tex]\( l \)[/tex] and the width as [tex]\( w \)[/tex]. We are given two equations based on the area and perimeter:

1. Area equation: [tex]\( A = l \times w = 18 \) square feet[/tex]

2. Perimeter equation: [tex]\( P = 2l + 2w = 18 \) feet[/tex]

From the perimeter equation, we can express [tex]\( l \)[/tex] in terms of [tex]\( w \)[/tex]:

[tex]\[ 2l + 2w = 18 \][/tex]

[tex]\[ l + w = 9 \][/tex]

[tex]\[ l = 9 - w \][/tex]

Now, we substitute [tex]\( l \)[/tex] into the area equation:

[tex]\[ (9 - w) \times w = 18 \][/tex]

[tex]\[ 9w - w^2 = 18 \][/tex]

[tex]\[ w^2 - 9w + 18 = 0 \][/tex]

[tex]\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]

where [tex]\( a = 1 \)[/tex], [tex]\( b = -9 \)[/tex], and [tex]\( c = 18 \)[/tex].

Plugging in the values, we get:

[tex]\[ w = \frac{9 \pm \sqrt{(-9)^2 - 4 \times 1 \times 18}}{2 \times 1} \][/tex]

[tex]\[ w = \frac{9 \pm \sqrt{81 - 72}}{2} \][/tex]

[tex]\[ w = \frac{9 \pm \sqrt{9}}{2} \][/tex]

[tex]\[ w = \frac{9 \pm 3}{2} \][/tex]

This gives us two possible solutions for [tex]\( w \)[/tex]:

[tex]\[ w_1 = \frac{9 + 3}{2} = \frac{12}{2} = 6 \][/tex]

[tex]\[ w_2 = \frac{9 - 3}{2} = \frac{6}{2} = 3 \][/tex]

Now we find the corresponding lengths for each width:

For [tex]\( w_1 = 6 \)[/tex] feet:

[tex]\[ l = 9 - w \][/tex]

[tex]\[ l = 9 - 6 \][/tex]

[tex]\[ l = 3 \][/tex]

For [tex]\( w_2 = 3 \)[/tex] feet:

[tex]\[ l = 9 - w \][/tex]

[tex]\[ l = 9 - 3 \][/tex]

[tex]\[ l = 6 \][/tex]

Answer:

  60 miles per hour

Step-by-step explanation:

Let s represent the speed in miles per hour during the first part of the trip. Then s-10 will be the speed during the last part of the trip.

For speed/time/distance problems, the appropriate relation is the one that is posted on every speed limit sign:

  speed = miles/hour = distance/time

Rearranging this relation gives you the expression for time:

  time = distance / speed

You are given time and distance and you need to find speed. The time you're given is the total for the two parts of the trip, so ...

  4 = 84/s + 130/(s-10) . . . . . . total time = time1 + time2

Multiplying by the product of the denominators, this becomes ...

  4s(s-10) = 84(s-10) +130s

  4s^2 -254s +840 = 0 . . . . . . subtract the right side to put in standard form

This can be solved using any of several methods for solving quadratic equations. Solutions are ...

  s = 60, s = 3.5 . . . . . only the first solution makes any sense in the problem

The speed during the first part of the trip is 60 miles per hour.

Answer:

Option B)

Step-by-step explanation:

The intersection of two sets M and N consists of all the elements that are in both M and N.

So if M = {5, 10, 15, 20, 25} and N ={10, 20, 30, 40, 50}, then M ∩ N = {10, 20}

Then, the union of two sets L and C is to add to L all the elements that are in C

Where: C = M ∩ N

So, if  L = {0, 20, 40, 80, 100} and  M ∩ N = {10, 20}, then:

L ∪ (M ∩ N) =  {0, 10, 20, 40, 80, 100}

Finally the correct option is B) {0, 10, 20, 40, 80, 100}

Answer:

B) {0, 10, 20, 40, 80, 100}

Step-by-step explanation:

The INTERSECTION of two sets is the set of elements which are in both sets.

The UNION of two sets is the set of elements which are in either set.

Answer:

Step-by-step explanation:

1. You have correctly written the relationship between the side lengths and the length of the hypotenuse for these isosceles right triangles.

For this problem, you simply need to multiply the side length by √2. The length of the hypotenuse is then ...

  x = 6√2

___

2. The side length multiplied by √2 is √6. You know

  √6 = √(2·3) = (√2)(√3) = (√2) · (side length)

so we know that x = √3.

Answer:

Step-by-step explanation:

First of all, the formulas need to be written correctly, and you need to understand what the variables mean. Usually, the variables have these meanings:

Usually, an annual interest rate is quoted and compounding is annual (n=1), quarterly (n=4) or monthly (n=12). In some formulas, r is the monthly rate and n is the number of months (there is no "t" in such formulas).

When we say "written correctly", we mean that parentheses are needed around exponents and denominators. In the formulas you have here, necessary parentheses are missing or misplaced, so you cannot use these formulas directly in your calculator or spreadsheet. If you're copying formulas from a question where they're typeset, be aware of the grouping effect of fraction bars and superscripts and use parentheses accordingly.

In the first two problems, you're not given P directly. Rather, the principal invested is to be computed as 10% of the amount given as "earnings."

___

1. P = $147; r = 0.035; n = 12; t = 25.

  A = P(1 + r/n)^(nt) = 147·(1 + .035/12)^(12·25) ≈ 147·1.002916667^300

  A ≈ 352.19 . . . . matches choice B

___

2. P = $3600; r = 0.0625; n = 4; t = 15.

  A = P(1 + r/n)^(nt) = 3600·(1 + .0625/4)^(4·15) ≈ 3600·1.01625^60

  A ≈ 9126.53 . . . . matches choice B

___

3. P = $208; r = 0.05/12; n = 300. Here, r is the monthly rate, n is the number of months. Please note the correction of the formula. The variable "S" refers to the Sum of payments and interest. This is effectively the sum of a geometric sequence, so the formula should look familiar on that basis.

  S = P((1 +r)^n -1)/r = 208·((1.004166667^300 -1)/0.004166667

  S ≈ 123,866.02 . . . . matches choice D

Answer:

B. $325.19

B. $9,126.53

D. $123,866.02

Step-by-step explanation:

Hope this helps! Have an amazing day/restful night!

Answer: 52

Step-by-step explanation:

Answer:  [tex]52^{\circ}[/tex]

Step-by-step explanation:

We know that the sum of a ll the angles of a quadrilateral is 360 degrees.

Then for the given trapezoid, applying the angle sum property of quadrilateral we get

[tex]\angle{A}+\angle{B}+\angle{C}+\angle{D}=360^{\circ}\\\\\Rightarrow\ 128^{\circ}+126^{\circ}+54^{\circ}\angle{D}=360^{\circ}\\\\\Rightarrow\ \angle{D}=360-128-126-54\\\\\Rightarrow\ \angle{D}=360-308\\\\\Rightarrow\ \angle{D}=52^{\circ}[/tex]

Hence, The measure of angle D = [tex]52^{\circ}[/tex]

A car's speed is a measure of velocity. One method for finding (final) velocity is using the formula v = u + at where u is initial velocity, a is acceleration, and t is time.

Answer:

{1;-2}

Step-by-step explanation:

[tex]...=\left \{ {{x=2y+5} \atop {7x-3y=13}} \right. =\left \{ {{x=2y+5} \atop {14y+35-3y=13}} \right.=\left \{ {{x=2y+5} \atop {y=-2}} \right.=\left \{ {{x=1} \atop {y=-2}} \right.[/tex]

It’s the first one t(10t-29)=-10

Answer:

(2t - 5)(5t - 2) = 0

Step-by-step explanation:

I got it right!

Answer:

Step-by-step explanation:

The answer is D)

Best regards

Answer:

Step-by-step explanation:

a) Apparently, you're to put the given values into a table. The first 5 entries of the table below are the given values. The next few are the result of using the recursive formula. (The formula bar shows the formula that is in the selected cell.)

__

b) The first differences of the terms of this sequence are ...

These are not constant, so the sequence is not arithmetic. The ratios of terms are not constant (2/-1 ≠ 10/2), so the sequence is not geometric.

The second differences are ...

These are constant, which tells us the sequence is a polynomial sequence of 2nd degree (since 2nd differences are constant).

In terms of the differences and second differences we can write the expression for the n-th term

  first difference with term before: a[n] -a[n-1]

  first difference between previous two terms: a[n-1] -a[n-2]

The difference between these two differences is 5, so we can write ...

  (a[n] -a[n-1]) -(a[n-1] -a[n-2]) = 5

Solving for a[n], we get ...

  a[n] = 5 + 2·a[n-1] -a[n-2] . . . . . the desired recursive relation

__

c) As indicated in part (b), this sequence is quadratic. As "proof", we offer that the sequence can be described by an explicit quadratic formula that can be derived from the first sequence term (d0) and the first and second differences (d1 and d2):

  f(n) = d0 + (n-1)(d1 +(n-2)/2·d2) = -1 +(n-1)(3 +(n-2)/2·5)

  f(n) = 5/2n² -9/2n +1

Answer:

81/π square cm

Step-by-step explanation:

Area can be expressed in terms of circumference by ...

A = C²/(4π)

Filling in the given dimension, you have ...

A = (18 cm)²/(4π) = 81/π cm²

Answer:

81/π

Step-by-step explanation:

If r is the radius of the circle, then the circumference is 2πr. Setting 2π r equal to 18 cm, we find r=9/π cm. The area of the circle is πr^2= π (9/π)^2 = 81/π square centimeters.

A solid has 6 faces

2 centimeters per hour

16 ounces = 1 pound, 8 ounces is half of 16, so 8 ounces = 1/2 pound.

1 pound of salmon cost 17.98.

Divide the cost for one pound in half:

8 ounces cost: 17.98 / 2 = $8.99

Answer:

y = 5 + 2.50x

Step-by-step explanation:

If no apples are picked, the cost is 5 (dollars). For each pound of apples (x) the cost goes up by 2.50x (dollars). The sum of the entry and per-pound costs is the total cost:

y = 5 + 2.50x

Answer:

y=2.5x+5

Step-by-step explanation:

The total payback for a $2500 loan at 9% annual interest for two years is $2,864.64.

To calculate the total payback for a $2500 loan at 9% annual interest for two years, we can use the formula M = P * [(1 + m)^na] / [(1 + m)^na - 1].

M represents the monthly payment, P is the principal (loan amount), m is the monthly interest rate (9% / 12), and na is the total number of payments (2 years * 12 months).

Substituting the values, the monthly payment becomes $119.32.

Multiplying this by the total number of payments gives us the total payback of $2,864.64.

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Answer:

1.

a) 357 inches³ of water more would be required to fill the tank

b) Riley is not correct, the volume of the larger aquarium is 27

   times larger than the volume of the smaller on

c) Riley is not correct, the surface area of the larger aquarium is 9

   times the surface area of the smaller one

2.

a) There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) The surface area of the shipping box is 567 inches²

Step-by-step explanation:

1.

a) * Lets study the first aquarium:

- The formula for volume is V = l × w × h

∴ It is a rectangular box of dimensions 16 in , 8.5 in , 10.5 in

∴ Its volume = 16 × 8.5 × 10.5 = 1428 inches³

* The full capacity of this aquarium is 1428 inches³

- Riley noticed that it 3/4 full of water, then still can fill with

 1/4 to be full

- Why 1/4 because 1 - 3/4 = 1/4

∴ The volume of 1/4 the aquarium = 1/4 × 1428 = 357 inches³

* There are 357 inches³ of water more would be required to fill the tank

b) * Lets talk about the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their volumes will be (3 : 1)³

- Because we will multiply each dimension by 3 and they

  are 3 dimensions, that means 3 × 3 × 3 ⇒ 3³

∴ The ratio between their volumes = 27 : 1

∴ Riley is not correct because the volume of the larger aquarium is 27

   times larger than the volume of the smaller aquarium

c) * Similar for the surface area of the larger aquarium

- Each dimension will be triple to construct the larger aquarium

- That means we will multiply each dimension of the small aquarium by 3

- That means the ratio between each dimension in the larger

  aquarium to the smaller aquarium is 3 : 1

∴ The ratio between their surface area will be (3 : 1)²

- Because we will multiply each dimension by 3 and to get the

 surface area we multiply each two dimensions for the six faces

 and then add them

∴ The ratio between their surface area = 9 : 1

∴ Riley is not correct because the surface area of the larger aquarium

  is 9 times larger than the surface area of the smaller aquarium

2.

a) * Lets think about this situation

- We want to fill some office supplies boxes of side length

 4.5 inches inside the shipping box of dimensions 18 in , 9 in , 4.5 in

- That means the volume of the shipping box is how many times

 the volume of the office supplies box

∴ The number of office supplies boxes = the volume of shipping box ÷ the volume of the office supplies box

∵ the volume of shipping box = 18 × 9 × 4.5 = 729 inches³

∵ the volume of the office supplies box = 4.5 × 4.5 × 4.5 = 91.125 inches³

∴ The number of office supplies boxes = 729 ÷ 91.125 = 8 boxes

* There are 8 boxes of office supplies can be packed into

   the larger box for shipping

b) Look to the Net of the shipping box

- The net has 6 faces shaped rectangles

- Each two faces are congruent

- To find the surface area we will add all the areas of the 6 faces

- Two faces with dimensions 18 in and 9 in

∴ Their areas = 2 (18 × 9) = 324 inches²

- Two faces with dimensions 18 in and 4.5 in

∴ Their areas = 2 (18 × 4.5) = 162 inches²

- Two faces with dimensions 4.5 in and 9 in

∴ Their areas = 2 (4.5 × 9) = 81 inches²

∴ The total surface area = 324 + 162 + 81 = 567 inches²

* The surface area of the shipping box is 567 inches²

Answer:

  The solids are similar.

Step-by-step explanation:

Each linear dimension of the larger solid is 3 times the corresponding linear dimension of the smaller one. Since the scale factor is the same in every direction, the solids are similar.

You get extract [tex] 2i [/tex] objects out of 97 object in this number of ways:

[tex] \displaystyle \binom{97}{2i} = \dfrac{97!}{(2i)!(97-2i)!} [/tex]

So, the number of all possible subsets is

[tex]\displaystyle \binom{97}{0} + \binom{97}{2} + \ldots + \binom{97}{96} = \sum_{i=0}^{48}\binom{97}{2i} = 79228162514264337593543950336[/tex]

Answer:

z = 0.33

Step-by-step explanation:

Mean = u = 500

Standard Deviation = s = 60

Scores of Jake = x = 520

Step 1: Finding the z score

In order to find the percentage who scored below Jake first we have to convert the scores of Jake to z scores. The formula to find z value is:

[tex]z=\frac{x-u}{s}[/tex]

Using the given values in this formula, we get the z scores:

[tex]z=\frac{520-500}{60}=0.33[/tex]

Thus, rounded of to two decimal places, the z-value for Jake's score is 0.33

Step 2: Find probability from the z-table

In the given table, from first column we will find the value 0.3. In the row across 0.3 we will find the value directly below 0.03 as 0.3 + 0.03 = 0.33

This value comes out to be 0.6293

The image attached below shows this process of finding the probability.

Step 3: Converting the probability to percentage

In order to convert this probability to percentage simply multiply it be 100.

So, 0.6293 = 62.93 %

62.93% rounded to nearest whole number will be 63%

This tells us that approximately 63% students scored below Jake i.e. below 520.

Answer:

o

Step-by-step explanation:

the median is obvi zero

Answer:

0

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Number of orange crayons = 2

Total number of crayons = 2 + 4 + 1 + 2 + 3 = 12

Probability is calculated as:

[tex]\frac{\text{Number of Favorable outcomes}}{\text{Total number of outcomes}}[/tex]

Here the favorable or desired outcome is picking up an orange crayon. So number of favorable outcomes will be 2 as 2 orange crayons are available.

Total number of outcomes is 12 which is the sum of all the crayons available.

So, the probability the crayon she pulls out will be orange = [tex]\frac{2}{12}=\frac{1}{6}[/tex]

The probability of Jill drawing an orange crayon from her bag is 1/6. This is calculated by dividing the number of desired outcomes (orange crayons) by the total number of outcomes (total crayons).

To solve this problem, we have to calculate the probability of picking an orange crayon from the bag. First, we calculate the total number of crayons Jill has in the bag. So Jill has 2 black, 4 blue, 1 yellow, 2 orange, and 3 purple crayons, which add up to a total of 12 crayons.

Probability is calculated by dividing the number of desired outcomes (in this case, drawing an orange crayon) by the total number of outcomes (the total number of crayons). Jill has 2 orange crayons, so the total number of desired outcomes is 2. As calculated earlier, the total number of outcomes is 12 crayons. So the probability of Jill drawing an orange crayon from her bag is 2 (orange crayons) divided by 12 (total crayons), or 1/6.

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Answer:

Step-by-step explanation:

Y is every x + 1, so for the first thingy magnify, it would had been -2+1 which is -1

$135

First, change the mixed number to an improper fraction.

2 1/4 = 9/4

Next, change $60 to an improper fraction.

$60 = 60/1

Then, multiply straight across on both the top and bottom to get 540/4.

Finally, simplify and get 135.

Hope this helped :)

For this case we have to:

[tex]2 \frac {1} {4}[/tex]is a mixed number that equals:

[tex]\frac {4 * 2 + 1} {4} = \frac {9} {4}[/tex]

If the price of the original ticket is $ 60, then the current price is:

[tex]\frac {60 * 9} {4} =\\\frac {540} {4} =\\135[/tex]

So, the price of the ticket is $ 135

Answer:

$ 135

Answer:

Step-by-step explanation:

The formula for the area of a circle is ...

  A = πr^2

where the radius (r) is half the diameter. For a circle with a diameter of 20 units, the radius is 10 units and the circle area is ...

  A = π·(10 units)^2 = 100π units^2 ≈ 314.16 square units

__

When there are 20 congruent sectors, each sector has an area of 1/20 of the circle area, so

  sector area = (1/20)·100π unit^2 = 5π units^2 ≈ 15.7 square units