Amy's penny bank is 1/2 full. After she adds 360 pennies, it is 5/6 full. How many pennies can Amy's bank hold?

Answer:

  3 cm

Step-by-step explanation:

The volume of a cube is the cube of the side dimension, hence the side dimension is the cube root of the volume.

  ∛(27 cm³) = 3 cm

_____

Problems like this are worked readily if you memorize the cubes of small integers. I suggest 1–5 at least, perhaps 1–10.

Answer:

B. Square root

Step-by-step explanation:

using distance formula:

x = √z^2 - y^2

y = √z^2 - x^2

=> z = √x^2 + y^2

Answer:

Option B. square root

Step-by-step explanation:

An incoming airplane is x miles due North at A from the control tower and a second airplane is y miles East at B of the same control tower.

The shortest distance between the two airplanes is z miles.

By Pythagoras Theorem

z² = x² + y²

z = √(x² + y²)

So function which models the situation best is "square root".

Therefore, option B. square root is the answer.

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

It’s the first one t(10t-29)=-10

Answer:

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

Step-by-step explanation:

I got it right!

Answer:

Part 1) The volume of the cylinder is [tex]V=108\ units^{3}[/tex]

part 2) The volume of the sphere is [tex]V=144\ units^{3}[/tex]

Step-by-step explanation:

step 1

Find the radius of the cone

we know that

the volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2} h[/tex]

we have

[tex]V=36\ units^{3}[/tex]

[tex]h=r\ units[/tex]

substitute and solve for r

[tex]36=\frac{1}{3}\pi r^{2} (r)[/tex]

[tex]108=\pi r^{3}[/tex]

[tex]r^{3}=108/ \pi[/tex] ------> equation A

step 2

Find the volume of the cylinder

we know that

the volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=r\ units[/tex]

substitute

[tex]V=\pi r^{2} (r)[/tex]

[tex]V=\pi r^{3}\ units^{3}[/tex]

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\pi (108/ \pi)\ units^{3}[/tex]

[tex]V=108\ units^{3}[/tex]

step 3

Find the volume of the sphere

we know that

The volume of the sphere is equal to

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

substitute the equation A in the formula above

[tex]r^{3}=108/ \pi[/tex] ----> equation A

[tex]V=\frac{4}{3}\pi (108/ \pi)[/tex]

[tex]V=144\ units^{3}[/tex]

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

Answer:

a circle with a circumference of 34π

Step-by-step explanation:

The circumference is given by ...

C = 2πr

so the circle with a radius of 16 has a circumference of ...

C = 2π·16 = 32π

The area is proportional to the square of the circumference, so the circle with a larger circumference will have a larger area.

The circle with the circumference of 34π has the largest area.

➷ First find the angle on the opposite side of x.

We can find this using the rule that angles on a straight line equal 180 degrees

180 - (90 + 47) = 43

Vertically opposite angles are equal

Therefore, x would also be 43 degrees.

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

x=43

Step-by-step explanation:

The angle between x and 47 is a right angle because it is a vertical angle to the right angle and vertical angles are equal.

Starting with x, we add x + the right angle +47 and we have a straight line.  We know straight lines are 180 degrees

x + 90 + 47 = straight line

x+ 137 = 180

Subtract 137 from each side

x+137-137 = 180-137

x = 43

Values that do not satisfy the inequality -2x - 6 ≤ 1 are those which are less than -3.5. This is found by isolating x and solving the inequality.

The question asks which values do not satisfy the inequality -2x - 6 ≤ 1. To solve this, first, let's isolate x on one side of the inequality. We follow these steps:

This means that all values of x that are greater than or equal to -3.5 satisfy the inequality. Thus, values that do not satisfy the inequality are those less than -3.5.

Answer:

o

Step-by-step explanation:

the median is obvi zero

Answer:

0

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.

https://brainly.com/question/31166734

#SPJ12

$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

B'(0,-7)

C'(0,-9)

D'(-4,-7

E'(-4.-2)

Answer:

Domain: (-∞ , 8) ∪ (8, +∞)

Step-by-step explanation:

Since denominator is x - 8 so x ≠ 8

If x = 8 then y = 8/0  : undefined.

Hence, the domain is all real numbers except  8

So

Domain: (-∞ , 8) ∪ (8, +∞)

Answer:

The correct answer is A) x does not equal 8

Step-by-step explanation:

In order to find gaps in the domain, we look for two things. The first we look for is negatives under square roots (which are not an issue here since there are none) and then we look for 0, denominators. So to find the gap, we set the denominator equal to 0 and see what the x value cannot be.

x - 8 = 0

x = 8

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)

___

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)

2 centimeters per hour

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:

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: 90 pounds.

Step-by-step explanation:

Let's call:

A: pounds of type A coffee.

B: pounds of type B coffee.

Based on the information given in the problem you can set up the following system of equations:

[tex]\left \{ {{A+B=153} \atop {4.25A+5.45B=758.25}} \right.[/tex]

You can use the Elimination method:

- Multiply the first equation by -4.25.

- Add both equations.

- Solve for B.

Then, you obtain:

[tex]\left \{ {{-4.25A-4.25B=-650.25} \atop {4.25A+5.45B=758.25}} \right.\\----------\\1.2B=108\\B=90[/tex]

He used 90 pounds of type B coffee.

Answer:

B = 90 pounds

Step-by-step explanation:

We know that Han's Coffee shop uses coffee A at $4225 per pound and coffee B at $5.45 per pound and this month it made 153 pounds of blend for a total cost of $758.25.

We are find the number of pounds for coffee B used.

[tex]A+B=153[/tex]

[tex]A=153-B[/tex] --- (1)

[tex]4.25A+5.45B =758.25[/tex] --- (2)

Substituting equation (1) in (2) to get:

[tex]4.25(153-B)+5.45B=758.25[/tex]

[tex]650.25-4.25B+5.45B=758.25[/tex]

[tex]1.2B=758.25-650.25[/tex]

[tex]1.2B=108[/tex]

B = 90 pounds

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!

Final answer:

To find the missing height of a cone with a given diameter of 6 cm and volume of 84.78 cm³, the volume formula for a cone is used, and after plugging in the known values, solving for the height gives an approximate value of 3.0 cm when rounded to the nearest tenth.

Explanation:

The student is asking for the missing height of a cone given the diameter and the volume. The formula to calculate the volume of a cone is V = (1/3)πr²h, where V is the volume, r is the radius, and h is the height of the cone. Since the diameter is given as 6 cm, the radius is half of that, which is 3 cm. The known volume of the cone is 84.78 cm³. Plugging these values into the formula gives:

84.78 cm³ = (1/3)π(3 cm)²h

After solving for h, we get:

h = ³ × 84.78 cm³ / (π × (3 cm)²)

h = 84.78 cm³ / (9π cm²)

h = 84.78 / (9 × 3.14159)

Now calculating h and rounding to the nearest tenth:

h = 84.78 / 28.27431

h ≈ 3.0 cm

Therefore, the height of the cone is approximately 3.0 cm.

Answer:

  |x -23| = 0

Step-by-step explanation:

In order for there to be one x-intercept, the x-intercept must be the vertex. The vertex of your form will be (b, c), and you want that to be (23, 0). Hence your equation is ...

  |x -23| = 0

An absolute value equation with the single solution set x=23 can be expressed as |x-23|=0, where b=23 and c=0 in the formula |x-b|=c.

To write an absolute value equation with the solution set x=23, we need to express this in the form |x-b|=c. The value of c must be positive, as the absolute value is always non-negative, and b will be the number that x is being compared to within the absolute value.

In this case, since we only have a single solution, this means that b=23 and c=0 because we want the equation to be true only when x is exactly 23. Thus, the absolute value equation that has only the solution set x=23 is |x-23|=0.

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: 14 centimeters.

Step-by-step explanation:

You need to use the formula for calculate the volume of a sphere:

[tex]V=\frac{4}{3}(3.14r^3)[/tex]

Where the radius of the sphere is "r".

As you know the volume of the ball, you can susbtitute it into the formula [tex]V=\frac{4}{3}(3.14r^3)[/tex], and solve for the radius "r":

[tex]1437=\frac{4}{3}(3.14r^3)\\\\3( 1437)=4(3.14r^3)\\\\4311=12.56r^3\\\\r=\sqrt[3]{\frac{4311}{12.56}}\\\\r=7.0cm[/tex]

The diameter of the ball can be calculated with:

[tex]D=2r[/tex]

Where r is the radius of the ball.

Substituting the radius of the ball into  [tex]D=2r[/tex], you get that the diameter of the ball that she should purchase, rounded to the nearest whole number, is:

[tex]D=2(7.0cm)\\D=14.0cm\\D=14cm[/tex]

Final answer:

To solve for the diameter of the ball, the volume of a sphere formula is used. The calculated diameter is rounded to the nearest whole number, and Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

Explanation:

To find the diameter of the ball that can hold 1437 cubic centimeters of treats, we need to use the formula for the volume of a sphere: V = (4/3) π r^3, where V is the volume and r is the radius. We will solve for r and then multiply by 2 to find the diameter. Given that the volume, V, is 1437 cubic centimeters, the formula becomes:

1437 = (4/3) × 3.14 × r^3

To isolate r, we first divide both sides of the equation by (4/3) × 3.14:

r^3 = 1437 / ((4/3) × 3.14)

Calculating the right side gives us the approximate value of r^3. Then, we take the cube root of both sides to solve for r:

r = ∛(1437 / ((4/3) × 3.14))

Once we find r, we can calculate the diameter, D, by:
D = 2 × r

Calculating the above with the given volume, we find:

r ≈ ∛(1437 / ((4/3) × 3.14)) ≈ 6.83 cm

D ≈ 2 × 6.83 cm ≈ 13.66 cm

So, rounding the diameter to the nearest whole number, Martha should purchase a treat ball with a diameter of approximately 14 centimeters.

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.

Answer:

Step-by-step explanation:

The answer is D)

Best regards

Answer:

$0.55

Step-by-step explanation:

2x36= 72

39.60/ 72

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:

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.