Crannapple juice costs $4.40 for a 20 ounce bottle. Pineapple juice costs $7.10 for a 30 ounce bottle. Which is the better deal?

Answer:3.8

Step-by-step explanation:

3.8

The value of log₄(256) is 4

In order to solve logarithm with different bases change of base rule is used, according to which a logarithm operation can be rewritten as a fraction of logarithms having a new base

                                logₐb = (logₓb) / (logₓa)

log₄(256) = (log₁₀256) / (log₁₀4)

= (log₁₀4⁴) / (log₁₀4)

As per the power rule of logarithms, the logarithm of an exponential number is equal to exponent times of the logarithm it means when an logarithmic term has an exponent it is transferred to the front of the logarithm and the logarithm is multiplied with it.

                                 (∵ logₐMⁿ = n logₐM)

=(4log₁₀4) / (log₁₀4)

= 4

Hence, it is seen that the value of the above question, log₄256 is 4.

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Step-by-step explanation:

a 4.1565×10²

b 2.675×10°

c 5.4906×10¹

d 7.104×10¹

e 9.001×10°

f 1.0298×10¹

Answer: x=1308.8

Step-by-step explanation:

If you are aware of the line's length or have access to a ruler, bisecting (or cutting in half) a line is not difficult. However, you can still cut the line in half with a straightedge and compass even if you don't know how long it is.

Draw the section of the line you need to divide. You must use a straightedge to create the line segment if it is not already present. Put the compass needle on either terminal to accomplish this. Approximately half of the length should be covered by the compass when it is opened.

Using the compass, aim to keep the needle on the endpoint and refrain from changing the compass's setting. To do this, position your straightedge on the intersection of the arcs above the line and line them up with the intersection below the line. The line is bisected at a 90-degree angle by the line you draw connecting the two arc intersections.

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If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.

First step is to calculate first sets printed

Number of pages=(1222 copies×46 page article)

Number of pages=56,212

Second step is to calculate the second set printed

Number of pages=(485 copies×16 page article)

Number of pages=7,760

Third step is to calculate the total pages

Total pages=56,212+7,760

Total pages=63,972 pages

Therefore If in one week, a printing center made 1,222 copies of a 46 page article. The printing center also printed 485 copies of a 16 page essay. The number pages that the printing center print during the week is: 63,972 pages.

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I assume you mean the polynomial

[tex](ax^6 + bx^8 + cx^3 + d) (x^5 + ex^4 + f) (x^2 + gx + h)[/tex]

The degree of this polynomial is the exponent of the largest power of [tex]x[/tex] in the expansion of the product.

This term is the product of the largest power terms in each factor. These are

[tex]ax^6 + bx^8 + cx^3 + d \implies bx^8[/tex]

[tex]x^5 + ex^4 + f \implies x^5[/tex]

[tex]x^2 + gx + h \implies x^2[/tex]

So, the largest power term in the polynomial is

[tex]bx^8 \cdot x^5 \cdot x^2 = bx^{15}[/tex]

and the degree is 15.

Answer:

Step-by-step explanation:

Area of shaded region = Area of Square ABCD− Area of 4 quadrants of circle

Side of square =14cm

Area of Square =(side)

2=(14) 2=196cm 2Radius of circle  = half of the side of square = 214=7cmArea of quadrant of circle = 41πr 2

Area of 4 quadrants of circle =4( 41 πr 2)= 722×7×7=154cm 2  Area of shaded region =196−154=42cm 2

The answer for the given logarithmic function is 3

Logarithm is a mathematical tool used to make high value calculations simple.

It is the exponent to the power of which a number must be raised to give a certain result.

Some of the important formulas in logarithm are:

loga[tex]b^{n}[/tex] where a is considered as base of the logarithm and b is the argument

is given as nlogab

when base and the argument is same , log is given as 1

logabc where a is the base is given as logab+logc

loga b/c where a is the base is given as logab-logac

Now it is given to us to find the value of log₅125

where 5 is the base and 125 is the argument

125 = 5x5x5 which is [tex]5^{3}[/tex]

hence 125 can be written as 5^3

Thus the logarithmic function becomes

log₅125=log₅[tex]5^{3}[/tex]

thus it can be written as3log₅5

Now we know that log₅5 can also be written as log5/log5

And hence log5/log5 becomes 1

Thus 3log₅5 = 3*1 =3

Hence the answer to the given logarithm is 3

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The inverse for the function f (x) = 4√x will be f ⁻¹ (x) = x² / 16

We are given the function:

f (x) = 4√x

we need to find the inverse of the function.

First we will write the function in the form of x.

y = 4√x

y / 4 = √x

x = y² / 4²

x = y² / 16

So, the inverse function will be:

f ⁻¹ (x) = x² / 16

Therefore, the inverse for the function f (x) = 4√x will be f ⁻¹ (x) = x² / 16

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given coordinates                           dilated coordinates

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

Given data

p' ( 4, 6 )

Q' ( 2, 2 )

R' ( 6, 2 )

S' ( 6, 6 )

The given coordinates is gotten by ( x, y ) and the coordinates is gotten to be ( x, -y ). Applying the rule is solve as follows:

given coordinates                           dilated coordinates

( x, y )                                                     ( x, -y )

p' ( 4, 6 )                                               p'' ( 4, -6 )

Q' ( 2, 2 )                                              Q'' ( 2, -2 )

R' ( 6, 2 )                                               R'' ( 6, -2 )

S' ( 6, 6 )                                               S'' ( 6, -6 )  

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The rate which the mulch is being applied is 250,000 cm^3/cm^2

The statement is given as

Rita is applying 250,000 cm^3 of mulch per m^2 of the garden space

This means that the rate is

Rate = Volume of mulch/Area of garden space

Substitute the known values in the above equation

So, we have

Rate = 250,000 cm^3/cm^2

Hence, the rate which the mulch is being applied is 250,000 cm^3/cm^2

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Answer:

8 and 12

Step-by-step explanation:

Answer:

Step-by-step explanation:

it is - 2 3/4 or it would be -2.75

Answer: False, it's the other way around

Step-by-step explanation:hope it helps, brainliest? i could really use it

Step-by-step explanation:

42086

14

12

10+

4

2

422

+ 9

2 4 6

8 10 12 14 16 x

42595

Answer: 440-25h = m

Step-by-step explanation:

She makes 25 dollars per hour (25h=m)

If u subtract the amount that the console costs the equation becomes

440-25=m

Im assuming u are in 7th grade math which is what i was in last year so i hope this helps! :)

The area and perimeter of the figures are 7) area=544 cm² and perimeter = 120 cm (8)area = 90cm² and  perimeter =  46 cm .

Area is defined as the total surface occupied by a figure. The SI unit of area is m² .

Area of rectangle is given by the product of its two sides the  length and Width

Perimeter is the sum of all sides of a two-dimensional figure.

7) In the first figure we have to separate it into a square and a rectangle.

Area of the square on top = 16 × 16 = 256 cm²

Length of the longest side in the second rectangle = 16 + 8+12=36cm

Area of the second rectangle = 36 × 8 = 288 cm²

Total area of the figure = (288 + 256) cm² = 544 cm²

Perimeter = 16 + 16 + 8 + 8 + 36 + 8 + 12 + 16 = 120 cm (taking all sides anti-clockwise from the top.)

8)Here we separate the two figures into two rectangles .

Length of the rectangle = 12 cm

Area of the first rectangle = 12 × 5 = 60 cm²

Area of the second rectangle = (6 × 5) cm² = 30cm²

Total area = (60 + 30)cm² = 90cm²

Perimeter = (5 + 6 + 7 + 5 + 12 + 11) cm² = 46 cm

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The distance between points is 9.11 .

What is the Distance Between Two Points?

the distance between points V(1,3) and W(6, -1)

[tex]d = \sqrt{( x_{2}- x_{1})^{2} + ( y_{2} - y_{1})^{2} }[/tex]

so x₁ = 1 , x₂ = 3 and y₁ = 6 , y₂ = -1

[tex]vw = \sqrt{( 3-1 )^{2} + ( -1 - 6 )^{2} }[/tex]

[tex]vw = \sqrt{( 2 )^{2} + ( -7)^{2} }[/tex]

[tex]vw = \sqrt{4 + 79}[/tex]

[tex]vw = \sqrt{83}[/tex]

vw = 9.110433 ≈ 9.11

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Answer:

-1/2

Step-by-step explanation:

[tex]-\frac{1}{6}[/tex] ÷ [tex]\frac{2}{6}= -\frac{1}{6}[/tex] x [tex]\frac{6}{2} \\[/tex] = [tex]\frac{-6}{-12} =- \frac{1}{2}[/tex]

The value of the quotient is 2. 83

A fraction can be defined as the part of a whole.

The types of fractions are;

It is also important to note that quotient also mean division.

Now, let's convert the mixed fraction to improper fraction.

We then have;

= 17/6

Find the quotient

= 2. 83

Thus, the value of the quotient is 2. 83

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The values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

The figure that completes the question is added as an attachment

The opposite sides of a parallelogram are congruent

This means that

5x - 20 = 7x - 38

4y + 11 = 6x - 31

So, we have

5x - 20 = 7x - 38

Collect the like terms

7x - 5x = 38 - 20

Evaluate the like terms

2x = 18

Divide through by 2

x = 9

Substitute x = 9 in 4y + 11 = 6x - 31

So, we have

4y + 11 = 6 x 9 - 31

Evaluate the product

So, we have

4y + 11 = 23

This gives

4y = 12

So, we have

y = 3

Hence, the values of x and y that makes quadrilateral ABCD a parallelogram are x = 9 and y = 3

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If Melinda hit a total of 1,645 tennis balls and she hits 32 balls per minute, it means she has been in the tennis practice for 50 minutes

How many of the hits of 1645 are attributable to only practice?

Out of the 1645 tennis balls so far hit by Melinda only 1,600 are attributable to the tennis practice because she  has already hit 45 tennis balls before the tennis practice commenced

number of tennis balls in tennis practice=1645-45

number of tennis balls in tennis practice=1600

number of minutest at practice=1600/32

number of minutest at practice=50 minutes

In essence, Melinda has been at the practice for 50 minutes

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The perimeter of rectangular classroom with its length five times its width is 108 ft.

Rectangle is two - dimensional shape with four sides such that the pair of two opposite sides are equal and parallel to each other.

Given is the width of rectangular classroom which is 9 ft wide. Its length is five times its width. From this, we can write -

Width [W] = 9 ft

Length [L] = 5W = 5 x 9 = 45 ft

The perimeter of rectangle is the sum of the length of its sides. Therefore, the perimeter [P] of the rectangle will be -

[P] = 2(L + W) = 2(9 + 45) = 2 x 54 = 108 ft

Therefore, the perimeter of rectangle with its length five times its width is 108 ft.

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The simplest form of the expression is 3xy .

We have given an expression  ∛81 x⁵ y³ / ∛3 x² .

On simplifying , we get

   [tex]\frac{(81x^5y^3)^{1/3}}{(3x^2)^{1/3}} = \frac{(3^4x^5y^3)^{1/3}}{(3x^2)^{1/3}}\\\\= \frac{3^{4/3}x^{5/3}y}{3^{1/3}x^{2/3}} \\\\= 3xy[/tex]

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Answer:

If in the next 6 days she rides an average of 8 miles per day, she will meet her goal.

Step-by-step explanation:

What is the average number of miles she would have to ride each day to meet her goal?

We know that Mayerlin wants to ride her bicycle for 56 miles this week, and she already has ridden 8 miles, so the distance left is:

56mi - 8mi = 48mi

Now, to find the average distance that she needs to ride each day in order to meet her goal, we need to take the quotient between the distance left and the number days that she has left (6 days), then we will get:

D = 48mi/6 = 8mi

This means that if in the next 6 days she rides an average of 8 miles per day, she will meet her goal.

The value of expression log₃27-2 log₃3 is equal to 1.

Given that the expression is log₃27-2 log₃3.

We are told to find the value of the expression by finding the logarithmic functions.

Change of base theorem is basically used when we have the base of the number having different base from 10 as logarithm having 10 base is required to find the log value from table.

log₃27-2 log₃3=log₃27-log₃[tex](3)^{2}[/tex]

([tex]log_{b}a[/tex] is equal to log a/log b and m log a=log [tex]a^{m}[/tex])

=log₃27-log₃9

=log₃(27/9)

=log₃3

=log3/log3

=1

Hence the value of expression log₃27-2 log₃3 is equal to 1.

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