A certain shampoo is available in two sizes. A 14.2 ounce bottle costs $3.98. A 33.9 ounce bottle costs $9.98. Find the unit price for each size. Then state which size is the better buy based on the unit price. Round your answers to the nearest cent. Thank you!

Answer:

3166.7

Step-by-step explanation:

Volume=pi*r^2*h

=pi*12^2*7=3166.7

Answer:

3166.7

Step-by-step explanation:

Volume of a cylinder= pi × radius² × height

3.14 × 12² ×7 = 3166.7

Answer:

3/root8+root9

Step-by-step explanation:

3/root8+root9

Answer:

Hello,

Step-by-step explanation:

30°=π/6 (rad)

[tex]L=\theta*R=\dfrac{\pi}{6} *120\\\\=20*\pi\\\\\approx{20*3=60\ (cm)}[/tex]

Answer:

Hello,

p=0.1024

Step-by-step explanation:

The probability is the ratio of the areas of the 2 circles:

[tex]p=\dfrac{\pi*8^2}{\pi*25^2} =\dfrac{64}{625} =0.1024[/tex]

Answer:

64/625.

Step-by-step explanation:

Probability = area of small circle / area of the large one

= 8^2 / 25^2

= 64/625

Answer:

4

Step-by-step explanation:

The distance between the center are  the foci located 8 units.

It is required to find  the focus is c.

A closed plane curve generated by a point moving in such a way that the sums of its distances from two fixed points is a constant.

Given that:

The length of the major axis is 2a,  

length of the major axis

2a=10

a=5

The length of the minor axis is 2b.

Length of the minor axis

2b=6

b=3

The distance between the center and either focus is c,

c^{2} =a^{2} -b^{2}

c^{2} =5^{2} -3^{2}

c^{2} =25-9

c=8

So, the distance between the center are  the foci located 8 units.

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Answer:

absolute value

Step-by-step explanation:

Answer:

This shows the absolute value of an integer.

Step-by-step explanation:

When you see the lines | | around a number, it should always give you the answer of that number's positive integer. So lets say I out | -2 | the answer for this equation should be 2.

Answer:

[tex]{ \sf{ \int 4x \cos(2 - 3x) dx = {4x}^{2} \cos(2 - 3x) + c }}[/tex]

Step-by-step explanation:

From integration by parts:

[tex]{ \boxed{ \bf{ \int u \: \frac{dv}{dx} = uv - \int v \: \frac{du}{dx} }}}[/tex]

let u be cos(2-3x) and let dv/dx be 4x:

[tex]{ \sf{ \frac{du}{dx} = 3 \sin(2 - 3x) }} \\ \\ { \sf{ v = \int 4x = 2 {x}^{2} }}[/tex]

Substitute in formular box:

[tex]{ \sf{ = (2 {x}^{2} \times \cos(2 - 3x)) - \int 2 {x}^{2} .3 \sin(2 - 3x) dx}} \\ = { \sf{2 {x}^{2} ( \cos(2 - 3x) - 3 \int \sin(2 - 3x)dx }} \\ { \sf{ = 2 {x}^{2} ( \cos(2 - 3x) - 3( - \frac{1}{3} \cos(2 - 3x) ) + c}} \\ { \sf{ = {4x}^{2} \cos(2 - 3x) + c}}[/tex]

Answer:

Vertex is (-2.5, - 13.25) and x=(-5±sqrt(53))/2

Step-by-step explanation:

x^2+5x-7

x^2+5x+(2.5)^2-(2.5)^2-7

(x+2.5)^2-13.25. Vertex is (-2.5, - 13.25)

Solution of the functions are x=(-5±sqrt(53))/2

Answer:

don't understand....................

[tex]\\ \sf\longmapsto 8-6a-9a^2+27a^3[/tex]

[tex]\\ \sf\longmapsto 27a^30-9a^2-6a+8[/tex]

[tex]\\ \sf\longmapsto 3a(9a^2-3a-2)+8[/tex]

Answer:

4th option

Step-by-step explanation:

The range is the values of y covered by the graph

The lowest value is a solid dot at y = 2, indicating that y can equal 2.

The graph then increases upwards to infinity.

The range is all real numbers greater than or equal to 2

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

The range is all the y-values or outputs. That means that the answer is greater than or equal to 2.

Answer:

Its AA similaroty theorem

Answer:

23 and 25

Step-by-step explanation:

Integers are whole numbers that are either positive, negative, or zero. Fractions and decimals are not integers. Therefore, 24 is between 23 and 25.

Answer:

Positive 23 and positive 25

Step-by-step explanation:

Answer:

99 minutes

Brainliest, please!

Step-by-step explanation:

22/8 = x/36

11/4 = x/36

36(11)/4 = x

396/4 = x

x = 99

Answer:

BF = |4 – 1| = 3

FC = |4 – 0| = 4

Using the Pythagorean Theorem to find BC:

BC2  =  BF2 + FC2

BC2   =  32 + 42

BC2   =  9 + 16

BC  =  sqaure root 25

BC  =  5

Step-by-step explanation:

The length of BC is 5 unit.

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

|AC|^2 = |AB|^2 + |BC|^2    

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

We need to find the length of BC place point F at (4,4) and draw BF and FC now you have the right ∆BFC with BC as the hypotenuse find BC and FC using the coordinates of B,C, and,F then use the Pythagorean theorem to find BC.

Using the Pythagorean Theorem to find BC:

BC^2  =  BF^2 + FC^2

BC^2   =  32 + 42

BC^2   =  9 + 16

BC  =  √25

BC  =  5

So, BF = |4 – 1| = 3

FC = |4 – 0| = 4

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Answer:

[tex]\frac{2}{a-b}[/tex]

Step-by-step explanation:

Given

[tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] + [tex]\frac{2b}{a^2-b^2}[/tex] ← a² - b² is a difference of squares

= [tex]\frac{1}{a+b}[/tex] + [tex]\frac{1}{a-b}[/tex] = [tex]\frac{2b}{(a-b)(a+b)}[/tex] ← LCD is (a - b)(a+b)

= [tex]\frac{a-b+a+b+2b}{(a-b)(a+b)}[/tex]

= [tex]\frac{2a+2b}{(a-b)(a+b)}[/tex]

= [tex]\frac{2(a+b)}{(a-b)(a+b)}[/tex] ← cancel common factor (a + b) on numerator/ denominator

= [tex]\frac{2}{a-b}[/tex]

Step-by-step explanation:

(=) 1 ( x-5 ) > 6x-17

(=) x-5 > 6x -17

(=) -5x > -12

=> x < 12/5

Answer:

5

Step-by-step explanation:

This illustrates the Remainder Theorem. If a polynomial f(x) is divided by x−a , the remainder is the constant f(a) , and f(x)=q(x)⋅(x−a)+f(a) , where q(x) is a polynomial with degree one less than the degree of f(x) . Synthetic division is a simpler process for dividing a polynomial by a binomial.

Answer:

a)7, b)-40

Step-by-step explanation:

a) 5(x-1)=30

=>5x -5=30

=>5x=30+5

=>5x=35

=>x=35/5

so, x=7

b)3(x+10)-2(x-5)=0

=>3x+30-2x+10=0

=>x+40=0

so,x=-40

Answer:

5/12

frsjnjjuvvffklomjyyrx

Answer:

3(4p-2) + 3= 2p-5

12p-6 +3 = 2p-5

10p-3=-5

10p=-2

p=-1/5

There is one solution.

hope this helps!

Answer:

one solution

-0.2

Step-by-step explanation:

3(4p - 2) +3 = 2p - 5         Remove the brackets on the left

12p - 6 + 3 = 2p - 5           Combine

12p  - 3 = 2p -5                  Subtract 2p from both sides

12p - 2p - 3 = -5                Combine

10p - 3 = - 5                       Add 3 to both sides

10p = -5 + 3

10p = - 2                            Divide by 10

p = - 0.2

The area of most three-dimensional geometric shapes is

A = a · h

Area = area of the base · height of the figure.

In this case, the area of the base is the area of a circle, so a = πr²:

a = 10²π

a = 100π ≅ 314

Now, all we have to do is multiply the area of the base to the height:

A = 100π · 6

A = 600π                            ← In terms of "π"

A ≅ 1884                             ← Rounded answer

Answer:

[tex]8 \times \frac{15}{5} - (5 + 9) \\8 \times 3 - (14) \\ 24 - 14 \\ = 10[/tex]

I hope I helped you^_^

Answer: quit

Step-by-step explanation:

it’s really easy .

Answer:

[tex]n=10[/tex]

Step-by-step explanation:

[tex]\frac{4^8}{(4^2)^-^3}\ / 4^4=4^n[/tex]

Simplify, remember, an exponent raised to the power of another exponent is equal to the product of the two exponents,

[tex]\frac{4^8}{(4^2)^-^3}\ / 4^4=4^n[/tex]

[tex]\frac{4^8}{4^-^6}\ / 4^4=4^n[/tex]

Now bring the term in the denominator (number under the fraction bar) to the numerator (number over the fraction bar). This can be done by multiplying the exponent of the denominator by (-1).

[tex]\frac{4^8}{4^-^6}\ / 4^4=4^n[/tex]

[tex]4^8(4^(^-^1^)^(^-^6^))\ / 4^4=4^n[/tex]

Simplify,

[tex]4^8(4^6)\ / 4^4=4^n[/tex]

Remember, multiplying two numbers of the same base is the same as adding their exponents, apply this property here,

[tex]4^8(4^6)\ / 4^4=4^n[/tex]

[tex]4^1^4\ / 4^4=4^n[/tex]

Dividing two numbers of the same base is the same as subtraction their exponents,

[tex]4^1^4\ / 4^4=4^n[/tex]

[tex]4^1^0=4^n[/tex]

Thus, the following statement can be made,

[tex]4^1^0=4^n[/tex]

[tex]n=10[/tex]

Answer:

it is <

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Complementary means that they add to 90 degrees

<A + <B = 90  given

<B + <C = 90  given

<A + <B = <B + <C  substitution property of equality.

<A = <C  subtraction property of equality

Given the five number summary, christina has scored 70 marks which is equal to the median of the test scores, therefore about [tex]\frac{1}{2}[/tex] class scored higher than her and  [tex]\frac{1}{2}[/tex] class scored lower than her, making option (d) correct.

The five number summary is the descriptive summary of a data where in you are provided the lowest observation, first quartile, median, third quartile and the maximum observation.

Here, the first quartile is the observation which lies at a point in the ordered data that 25% observations are lesser than it and 75% are greater than it.

the median is the observation which lies at a point in the ordered data that 50% observations are lesser than it and 50% are greater than it.

the third quartile is the observation which lies at a point in the ordered data that 75% observations are lesser than it and 25% are greater than it.

As given in the data,

Christina's marks = 70

median marks = 70

christina's marks = median marks

therefore, by definition of median, about half class scored lower than christina and half more than her.  

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The complete question is given below:

Given the five number summary  as:

minimum = 2

first quartile = 50

median = 70

third quartile = 85

maximum = 96

Christina earned 70 on the test. Describe how the scores of Christina's

classmates compared to Christina's score.

A. about 1/4 scored higher, about 3/4 scored lower

B. about 314 scored higher, about 1/2 scored lower

C. about 3/4 scored higher, about 1/4 scored lower

D. about 1/2 scored higher, about 1/2 scored lower

___________________A

The function that represents the inequality of the given graph is;

Option A

From the given graph, the curve with the shaded dot shows less than or equal to because the dot indicates that the maximum input value of x is at that point.

Secondly, the curve without a shaded dot shows that the input function of x is only greater than 3.

Looking at the options, option A is right and we will prove it thus;

for y = x³ - 3

At x = 2, we see that;

y = 2³ - 3

y = 5

This corresponds with the given equation

For the second curve, for y = x² + 6;

At x = 2, we have;

y = 2² + 6

y = 4 + 6

y = 10

This corresponds with what is given and is thus correct.

Thus, option A is the correct answer

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