0. A pill has the shape of a cylinder with a hemisphere at each end. The height of the cylindrical portion 11
mm and the overall height is 18 mm.
(a) Find the volume of the pill in cubic millimeters. Round to the nearest cubic
millimeter.

(b) If the pill is to contain 1,000 milligrams of vitamin C, then how much vitamin C does the pill contain per
cubic millimeter? Round to the nearest tenth of a cubic millimeter.
(c) Another pill that is entirely spherical has a diameter of 10 millimeters and contains 1.5 milligrams of
vitamin C per cubic millimeter. How much less vitamin C does this second pill contain, rounded to the
nearest milligram, than the one pictured?​

Answer:

24 and 8

Step-by-step explanation:

The formula for the perimeter of the rect. is P = 2W + 2L.

Here, L = 2W + 8, so the area formula becomes:

P = 2W + 2(2W + 8) = 64

Dividing all terms by 2 reduces this to:

         W + 2W + 8 = 32, or 3W = 24, or W = 8.

Then:  L = 2W + 8 = 2(8) + 8 = 24

Check:  does 2W + 2L = 64 when these values for W and L are substituted?

              Is 2(8) + 2(24) = 64   true?  Yes

The length and width are 24 and 8 respectively.

The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is eight more than twice the width.

The perimeter is 64.

Now,

Let the width of rectangle = x

Then, The length of rectangle = 2x + 8

Here, The perimeter is 64.

So, We get;

2 (length + width) = 64

2 (2x + 8 + x) = 64

2 (3x + 8) = 64

3x + 8 = 64/2

3x + 8 = 32

3x = 32 - 8

3x = 24

x = 8

Thus, The width of rectangle = x

                                            = 8

Then, The length of rectangle = 2x + 8

                                              = 2 × 8 + 8

                                              = 24

Therefore, The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

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Answer:

[tex]x^3+x^2-5x+28[/tex]

Step-by-step explanation:

since a=lw, the area is (x^2-3x+7)(x+4)

1. distribute parentheses [tex]\left(x^2-3x+7\right)\left(x+4\right)=x^2x+x^2\cdot \:4+\left(-3x\right)x+\left(-3x\right)\cdot \:4+7x+7\cdot \:4[/tex]

2. apply +(-a)=-a rule [tex]x^2x+4x^2-3xx-3\cdot \:4x+7x+7\cdot \:4[/tex]

3. Simplify

    Steps to simplify:

[tex]x^2x=x^3[/tex]

[tex]3xx=3x^2[/tex]

[tex]3\cdot \:4x=12x[/tex]

[tex]7\cdot \:4=28[/tex]

[tex]x^3+4x^2-3x^2-12x+7x+28[/tex]

4. Add like terms [tex]=x^3+4x^2-3x^2-5x+28[/tex]

5. Add like terms [tex]=x^3+x^2-5x+28[/tex]

the area of the rectangle as a single polynomial in simplest form is  x³+x²-5x+28.

Area is the space occupied by a plane object.

To calculate the area of a rectangle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the rectangle as a single polynomial in simplest form is  x³+x²-5x+28.

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B) is the answer because 22+22+18+18 will equal 80 and 22-18 is five

1095 to the second power is what google told me!

Answer:

y=x^2-3x

Step-by-step explanation:

Final answer:

A fourth degree polynomial with real roots at 0, 3 and a double real root at -1 passes through the point (2, 12). The equation for the function is -2x(x - 3)(x - 3)(x + 1).

Explanation:

A fourth degree polynomial with real roots at 0, 3 and a double real root at -1 can be expressed as:

f(x) = a(x - 0)(x - 3)(x - 3)(x + 1)

To find the value of 'a', we can substitute the point (2, 12) into the equation:

12 = a(2 - 0)(2 - 3)(2 - 3)(2 + 1)

12 = -6a

a = -2

So, the equation for the function is:

f(x) = -2x(x - 3)(x - 3)(x + 1)

the value effects it by now much they have so you can determine who has the most and who has the least

Answer:

A: [tex]y=-3sin(2(x+\pi))+2[/tex]

Step-by-step explanation:

As all of the functions are sin functions, the option must be negative due to the shape of the graph.

This narrows down the options to A and B

When looking at b, it has a period of [tex]2\pi[/tex] which is not equivalent to the given graph that has a period of [tex]\pi[/tex]

Function A has a period of [tex]\pi[/tex] and is negative, so it is the correct option

Answer:

[tex]y=-3\sin(2(x+\pi)+2[/tex]

Step-by-step explanation:

The graph completes two cycles on the interval [tex][-\pi,\pi][/tex].

This implies that, the graph has a period of [tex]\pi[/tex].

The functions is a sine function that is reflected in the x-axis and shifted up by 2 units.

The range of the graph is -1 to 5.

This means that the amplitude is 6/2=3

The graph is also shifted to the right [tex]\pi[/tex] units

The function is

[tex]y=-3\sin(2(x+\pi)+2[/tex]

Answer:

The value of x is 6 and -6. The smallest value of x is -6

Step-by-step explanation:

2/3 x² = 24

solving this equation for finding the value of x.

Multiply both sides by 3/2

x² = 24 * 3/2

x² = 72/2

x² = 36

Now, to find the value of x taking square root on both sides

√x² = √36

x= ±6

So, the value of x is 6 and -6. The smallest value of x is -6

Answer:

a. 13,2 in.

Step-by-step explanation:

66 : 2.5 = 26.4

0.5 x 26.4 = 13.2

By creating a proportion based on the heights shown in the photo and Alice's actual height, we can calculate that Alice's dog's actual height is 13.2 inches, which is option A.

To find out how tall Alice's dog is in reality, we need to use the ratio of their heights in the photograph to determine the dog's actual height. In the photograph, Alice's height is 2.5 inches and her dog's height is 0.5 inches, while her actual height is 66 inches. This creates a ratio that we can use to calculate the dog's actual height.

First, we set up a proportion where the height of Alice in the photo is to her actual height as the height of the dog in the photo is to the dog's actual height:

2.5 inches / 66 inches = 0.5 inches / x inches

Now we solve for x, which represents the dog's actual height:

x = (0.5 inches * 66 inches) / 2.5 inches

After performing the multiplication and division, we get:

x = 13.2 inches

Therefore, the height of Alice's dog in reality is 13.2 inches, which corresponds to option A.

32

1024/2=528(~512)/2=256/2=128/2=64/2=32

Answer:

x^2 + y^2 = 32

Step-by-step explanation:

The fact that the circle's center is at (0,0) tells you that the circles equation is of the form x^2 + y^2 = radius^2

radius = 4*sqrt(2)       Given

r^2 = (4sqrt(2) )^2

r^2 = 16 * 2

r^2 = 32

So the entire equation is

x^2 + y^2 = 32

Answer:

3) y = 50 * 2¹²ˣ

2) y = 80 * 2⁸ˣ

Step-by-step explanation:

1 day = 24 hours

Number of 2-hour periods in 1 day = 24 ÷ 2 = 12

Number of 3-hour periods in 1 day = 24 ÷ 3 = 8

Colby's experiment:

y = 50 * 2¹²ˣ

Jaquan's experiment:

y = 80 * 2⁸ˣ

Answer:

$2,239.66

Step-by-step explanation:

To find the amount of reimbursement, convert miles to km by multiplying 1564 by 1.609 since 1 mile = 1.609 km.

He drive 1564(1.609)=2,516.476 km.

Multiply this distance by $0.89 per km.

2516.476(0.89)=$2,239.66

Answer:

0.025

Step-by-step explanation:

First you need to figure out the common pattern you see. What I saw was that we are dividing something.

I looked at the 16 and -8 and thought of -2. To make sure, you can use a calculator.

So -8 is the 4th term you can go back dividing -8 with -2 until you've reached the 11th term.

I don't know if my answer is right. I wasn't being organized as I could be. It would be better if you do it again to make sure it's correct.

Answer:

B. Division

Step-by-step explanation:

Subtraction is closed for polynomials subtracting two polynomials will result in another polynomial. Same goes with multiplication. However, if you divide polynomials, you are able to get a result that is not always a polynomial. Therefore, division is the answer.

Answer: division

Step-by-step explanation: a p e x 2020

ANSWER

[tex]{ {6}{x}^{3} {y}^{ \frac{16}{3} } }[/tex]

EXPLANATION

We want to find the cube root of

[tex]216 {x}^{9} {y}^{16} [/tex]

This is the same as:

[tex] \sqrt[3]{216 {x}^{9} {y}^{16} } [/tex]

We rewrite as radical exponent to get;

[tex] {(216 {x}^{9} {y}^{16} )}^{ \frac{1}{3} } [/tex]

This implies that;

[tex] {( {6}^{3} {x}^{9} {y}^{16} )}^{ \frac{1}{3} } [/tex]

This simplifies to:

[tex]{ {6}^{ \frac{3}{3} } {x}^{ \frac{9}{3} } {y}^{ \frac{16}{3} } }[/tex]

Hence the cube root is:

[tex]{ {6}{x}^{3} {y}^{ \frac{16}{3} } }[/tex]

Answer:

The cube root of [tex]\sqrt[3]{216x^9y^{16}} \,\,is\,\,6x^3y^{16/3}[/tex]

Step-by-step explanation:

We need to find the cube root of 216x^9y^16

[tex]\sqrt[3]{216x^9y^{16}} \\can\,\, be\,\, written\,\, as\,\,\\=\sqrt[3]{216} \sqrt[3]{x^9} \sqrt[3]{x^{16}} \\=\sqrt[3]{6x6x6} \sqrt[3]{x^9} \sqrt[3]{x^{16}} \\we\,\, know\,\,\sqrt[3]{x} = x^{1/3}\\= (6^3)^{1/3} (x^9)^{1/3}(y^{16})^{1/3}\\= 6x^3y^{16/3}[/tex]

So, the cube root of [tex]\sqrt[3]{216x^9y^{16}} \,\,is\,\,6x^3y^{16/3}[/tex]

Answer: it should be 3 units down

Think if it on a graph in your mind and plot points then use every choice to see which makes sense

For this case we have:

Let k> 0:

To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

Let h> 0:

To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.

So, we have:

[tex]y = f (x) = \sqrt {x}\\h = 3\\y = f (x) = \sqrt {x + 3}[/tex]

It means that it was shifted 3 units to the left

Answer:

Option A

Answer:

$1.01

Step-by-step explanation:

To find the cost of one ounce of birdseed, first convert the weight to ounces (4 pounds equals 64 ounces) and then divide the total cost by the total number of ounces. The result is approximately $0.11 per ounce.

First, we need to convert the weight from pounds to ounces since there are 16 ounces in 1 pound. So, 4 pounds is equivalent to 4 × 16, which equals 64 ounces.

Now, if 4 pounds (or 64 ounces) of birdseed cost $6.95, we want to find the cost of one ounce. To do this, we divide the total cost by the total number of ounces:

$6.95 / 64{ ounces} = approximately $0.10859375 { per ounce}

This result is the cost per ounce. So, the approximation for the cost of 1 ounce of birdseed is roughly $0.11 (rounded to 2 decimal places).

Answer: 10

Step-by-step explanation:

15 - 5 is 10.

Answer: 10

Step-by-step explanation:

From the given box plot in the picture, we can see that the least observation  from the data = 4.5

The largest observation from the data = 14.5

We know that the range of data tells the difference between the largest observation and the lowest observation.

[tex]\text{ i.e. Range=Largest observation - Least observation}\\\\=14.5-4.5=10[/tex]

Therefore, the range of the data = 10

Clarice started with 12 tickets and added more (t) to it. She doesn't know how many tickets she used, fitting situation A.

The expression t + 12 implies that Clarice started with 12 tickets and then added some more tickets ( t ) to it.

Among the given options, situation A best fits this expression. Clarice knows she had 12 tickets to start with, but she doesn't know how many additional tickets ( t ) she has acquired or used since then.

So, the correct situation described by the expression is A.

From the equation given, each ticket costs 50 cents as expressed in 0.50x. Every time you increase x by one, the total cost increases by 50 cents

Answer

A) $10

Step-by-step explanation:

Answer:

$12 per dozen muffins

Step-by-step explanation:

3.00/3 = 1

1x = the price of one muffin

1(12) = 12

Step 1: Find what the price is per muffin. To do this you must divide $3.00 by 3 muffins (this will tell you dollar per muffin or $/muffin)

3 ÷ 3 = 1

This means that every muffin is $1

Since we know this, and we know that a dozen means 12 we can multiply 1 by 12 to find how much you would pay for a dozen muffins

12 × 1 = 12

It's $12 per dozen muffins

Hope this helped!

Answer:

B

Step-by-step explanation:

Margin of Error is simply a range, an amount that is allowed for in case of miscalculation or change of circumstances. The margin of error is 5%.

1. Find the 5% of 3.20 = .16

2. Subtract and add .16 to 3.20 to get rid of that margin of error

    3.20 + .16 = 3.36 and 3.20 - .16 = 3.04

3. 3.04 and 3.36

Answer:

b 3.04 to 3.36

Step-by-step explanation:

First we need to find 5% of 3.20

.05*3.20 = .16

To find the lower value, subtract 16 cents from 3.20

3.20-.16 = 3.04

To find the upper value, add 16 cent to 3.20

3.20 + .16 = 3.36

The range is 3.04 to 3.36

Answer:

D. should be the correct answer. Hope this helps.

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

took test

Answer:

See step-by-step

Step-by-step explanation:

A prism is named by the shape of its bases.  That makes this an octagonal prism

The shape of the bases are octagons.

The vertices are all the letters

The lateral edges are all the vertical lines connected by the vertices.  RQ, WN, VM, are all examples.

The rectangles making up the sides are called lateral faces.

The altitudes are the same as the lateral edges.  They all represent the height of the prism.

Answer:

The angles are m∠EQF=14°, m∠EFQ=90° and m∠QEF=76°  

Step-by-step explanation:

Given the figure in which m∠DFQ = 10°,  m∠EOF = 28°

we have to find the angles of △EFQ

m∠EOF = 28°

By theorem angle subtended at the centre is twice the angle subtended at the circumference

⇒ m∠EQF=14°

As angle ∠EFQ is the angle in the semicircle

∴ ∠EFQ=90°

In ΔEFQ, by angle sum property of triangle

m∠EFQ+m∠FQE+m∠QEF=180°

90°+14°+m∠QEF=180°

m∠QEF=180°-90°-14°=76°

Hence,  m∠EFQ=90° and m∠QEF=76°

To find the missing angle in triangle △EFQ, we used the fact that the sum of angles in a triangle is always 180°. Therefore, m∠EQF is found to be 142°, making the angles of the triangle 10°, 28°, and 142°.

This problem deals with finding the measurements of angles in a triangle. In this case, the triangle is △EFQ, and we are given that m∠DFQ = 10° and m∠EF = 28°. The sum of the angles in a triangle always equals 180°. So, the third angle, m∠EQF, can be found by subtracting the given angles from 180°.

To calculate, follow these steps:

Therefore, m∠EQF = 142°. So, the angles of triangle △EFQ are 10°, 28°, and 142°.

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Answer:

B and D

Step-by-step explanation:

Given

2a² + 8a - 15 = 3a - 3 ( subtract 3a - 3 from both sides )

2a² + 5a - 12 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the product of the a² term and the constant term which sum to give the coefficient of the a term, that is

product = 2 × - 12 = - 24 and sum = + 5

The factors are + 8 and - 3

Use these factors to split the a- term

2a² + 8a - 3a - 12 = 0 ( factor the first/second and the third/fourth terms )

2a(a + 4) - 3(a + 4) = 0 ← factor out (a + 4) from each term

(a + 4)(2a - 3) = 0 ← in factored form

Answer:

Characteristics of the axis of symmetry include the following: It is the line of symmetry of a parabola and divides a parabola into two equal halves that are reflections of each other about the line of symmetry. It intersects a parabola at its vertex. It is a vertical line with the equation of x = -b/2a.

Step-by-step explanation:

Answer: i need a pic to know what your asking for.

Answer:

x = 4, y = 2

Step-by-step explanation:

Given the 2 equations

5x + 2y = 24 → (1)

5y = x + 6 → (2)

Rearrange (2) expressing x in terms of y by subtracting 6 from both sides

x = 5y - 6 → (3)

Substitute x = 5y - 6 into (1)

5(5y - 6) + 2y = 24 ← distribute and simplify left side

25y - 30 + 2y = 24

27y - 30 = 24 ( add 30 to both sides )

27y = 54 ( divide both sides by 27 )

y = 2

Substitute y = 2 into (3) for corresponding value of x

x = (5 × 2) - 6 = 10 - 6 = 4

ANSWER

Converges

[tex]S_{ \infty } = 68[/tex]

EXPLANATION

The guy sequence is

17 + 12.75 + 9.5625 + ...

The common ratio is:

[tex] \frac{9.5625}{12.75} = \frac{12.75}{17} = \frac{3}{4} = r[/tex]

Since

[tex] |r| < 1[/tex]

the series converges.

The sum to infinity of this sequence is :

[tex]S_{ \infty } = \frac{a}{1 - r} [/tex]

where a=17 is the first term of the series.

[tex]S_{ \infty } = \frac{17}{1 - \frac{3}{4} } [/tex]

[tex]S_{ \infty } = \frac{17}{ \frac{1}{4} } = 68[/tex]