Ask your teacher find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→1 [ln(x5 − 1) − ln(x3 − 1)]

The bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar

Feel great energy bars = Total cost / number of bars

= $18 / 12

= $1.5 per bar

Super power brand = Total cost / number of bars

= $21.75 / 15

= $1.45 per bar

Therefore, the bar which Adelina should buy is super power brand because it cost less than feel great energy bar at $1.45 per bar

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Answer: $4.50

Step-by-step explanation:

Original Price: $6

Discount: 25%

Discounted Price: 6*25%= $1.5

                              $6-$1.5= $4.5

Answer:

slope = 1

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (10, 3 ) and (x₂, y₂ ) = (7, 0 )

m = [tex]\frac{0-3}{7-10}[/tex] = [tex]\frac{-3}{-3}[/tex] = 1

Answer:

-7

Step-by-step explanation:

[tex]f(10) = 5-g(10)\\=5-(2(10)-8)\\=5-(20-8)\\=5-(12)\\=-7[/tex]

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

The value of the z score is 1.03.

According to the statement

we have given that the value of mean and standard deviation and we have to find the value of the z score.

So, For this purpose we know that the

Z-score indicates how much a given value differs from the standard deviation. The Z-score, or standard score, is the number of standard deviations a given data point lies above or below mean.

And the given values are:

mean value = 69 inches

s.d value = 2.8 inches

And the value of x is 71.9 inches.

So, The Z score is

z = x - mean / standard deviation

substitute the values in it then

z = 71.9 - 69 / 2.8

then

z = 2.9 /2.8

z  = 1.03

So, The value of the z score is 1.03.

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The summary of the given data is are as follows :-

Minimum: 11

Lower quartile:11

Median:24

Upper quartile:34

Maximum:45

Interquartile range:23

Given :- 9, 11, 11, 16, 16, 24, 28, 30, 34, 42, 45

Minimum = The smallest number of data

Thus Minimum = 11

Maximum = The largest number of data

Thus Maximum = 45

Median = The middle number of the data if data consists of odd number of elements

Thus Median = 45

Lower quartile = The median of the lower half of data

Thus Lower quartile = 11

Upper quartile = The median of the upper half of data

Thus Upper Quartile = 34

Interquartile range = The difference of upper and lower quartiles,

Thus Interquartile range = 34 -11 = 23

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The price x which will maximize the company's revenue is 904

The price x which will maximize the company's revenue is 240

Let

Price of the good = x

Number of goods sold = 2712- 3x

The formula for revenue is given as;

Revenue = Price × Quantity

= x( 2712 - 3x)

Expand the bracket

2712x - 3x^2

Therefore, the price x which will maximize the company's revenue will be:

2712x - 3x^2 =0

Collect like terms

3x² = 2712x

3x =  2712

Divide both side by 3

3x/3 = 2712/3

x = 904

Hence, the price x which will maximize the company's revenue is 904

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Answer:

[tex]y = - \frac{1}{4} x - 10[/tex]

Step-by-step explanation:

The negative reciprocal of 4 is -1/4.

Let's substitute in our values, to find the y-intercept:

[tex]y = - \frac{1}{4} x + c[/tex]

[tex] - 11 = - 1 + c[/tex]

[tex]c = - 10[/tex]

Finally, our full equation is:

[tex]y = - \frac{1}{4} x - 10[/tex]

Answer:

A perfect cube monomial must have three identical root , such that the product of the roots equal the perfect square monomial . The coefficient of the monomial must be divisible by 3 . Any monomial can be a perfect cube root .

Step-by-step explanation:

1.)1000=10 cube

2.) 729=9 cube

3.) 512=8 cube

4.) 343=7 cube

5.) 216=6 cube

6.) 125=5 cube

7.) 64=4 cube

8.) 27=3 cube

9.) 8=2cube

10.) 1=1 cube

When you have negative exponents, you flip it around. Let me give you two examples below.

[tex]x^{-5} = \frac{1}{x^{5} }[/tex]

[tex]10^{-2} = \frac{1}{10^{2} }[/tex]

Therefore you will be doing: [tex]\frac{4}{1} * \frac{1}{10^{2} } = \frac{4}{1} * \frac{1}{100} } = \frac{4}{100} = \frac{1}{25}[/tex]

Your final answer is 1/25.

Brainliest would make my day :)

The height of the ground from the base of the window is 144 inches.

One angle of a right angle triangle is equals to 90 degrees.

Therefore, the sides and angles of the right triangle can be found using trigonometric ratios.

tan x = WY / XY

tan x  = opposite / adjacent

tan x = 24 / 8

x = tan⁻¹ 3

x = tan⁻¹ 3

x = 71.5650511771

x = 71.60°

tan 71.60 = h / 48

cross multiply

h = 48 tan 71.60

h = 48 × 3

h = 144 inches

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Answer: B

Step-by-step explanation:

First, find the sum of the bottles, which is 6,235,168,989 which is not an estimate.

Rounding it to the nearest billion, the answer is 6,000,000,000 or B)

Answer: 2

Step-by-step explanation:

1) substitute

2) calculate the difference before the absolute value

3) calculate the absolute value

4) convert into whole numbers/reduce

5) subtract the whole numbers

this is what i think might be wrong

The height of the rectangular pyramid is 7 ft.

First, we know that the volume of a rectangular pyramid is given by:

[tex]V = B*H/3[/tex]

Where B is the base, H is the height.

First, we know that the volume is 56 ft³, and the base is 24ft², then we can replace these two in the volume equation to get:

[tex]56 ft^3 = 24ft^2*H/3[/tex]

Solving that for H, we get:

[tex]H = 3*(56ft^3/24ft^2) = 7ft[/tex]

The height of the rectangular pyramid is 7 ft.

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Answer:

Yes

Step-by-step explanation:

The given line is an average of the data points.

Answer:

  0.33 ⋅ 10^−15

Step-by-step explanation:

Scientific notation requires exactly one non-zero digit to the left of the decimal point.

The number ...

  0.33 ⋅ 10^−15

has no non-zero digits to the left of the decimal point. It is not in "scientific notation."

__

Additional comment

Expressed in scientific notation, it would be ...

     3.3 ⋅ 10^−16

Answer:

[tex]\dfrac{8y-43}{(y-1)(y-8)}[/tex]

Explanation:

[tex]\rightarrow \dfrac{5}{y-1} +\dfrac{3}{y-8}[/tex]

make the denominators similar

[tex]\rightarrow \dfrac{5(y-8)}{(y-1)(y-8)} +\dfrac{3(y-1)}{(y-8)(y-1)}[/tex]

Join both the fraction

[tex]\rightarrow \dfrac{5(y-8)+3(y-1)}{(y-1)(y-8)}[/tex]

simplify the expression

[tex]\rightarrow \dfrac{5y-40+3y-3}{(y-1)(y-8)}[/tex]

[tex]\rightarrow \dfrac{8y-43}{(y-1)(y-8)}[/tex]

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's simplify ~

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5}{y - 1} + \cfrac{3}{y - 8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5(y - 8) + 3(y - 1)}{(y - 1)(y - 8)} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{5y -40 + 3y - 3}{y {}^{2} - y - 8y + 8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: \cfrac{8y -43}{y {}^{2} - 9y + 8} [/tex]

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

A line plot can be defined as a type of graph that is used to graphically represent a data set above a number line, while using crosses, dots, or any other mathematical symbol.

Based on the data provided in the complete question, we can logically deduce the following points:

In conclusion, graph C shown in the image attached below is a line plot which correctly shows the data from the table above.

The most common length of ribbon is 11 1/4: True.

The sum of the longest and shortest lengths is 20 1/8: False.

Sum = 11 1/4 + 9 7/8

Sum = 21 9/8 ≠ 20 1/8.

The difference between the longest and shortest lengths is 2 1/8: False.

Difference = 11 1/4 - 9 7/8

Difference = 1 3/8 ≠ 2 1/8 .

The greatest amount of juice is equal to 3.

The least amount of juice is equal to 1 4/6.

The sum of the least and greatest amount of juice is:

Sum = 1 4/6 + 3

Sum = 4 4/6 = 4 2/3.

The difference between the greatest and least amount of juice is:

Difference = 3 - 1 4/6

Difference = 8/6 = 4/3.

If the children were to share the juice equally, the amount of juice each would get should be calculated by determining the mean:

Mean = [F(x)]/n

Mean = (1 4/6 + 2 + 2 + 2 + 2 2/6 + 2 5/6 + 2 5/6 + 3)/8

Mean = 18.7/8

Mean = 2.3375 = 2 27/80.

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Complete Question:

Katie recorded the length, in inches, of the ribbon pieces she was going to use for a project. Use this information for questions 1 and 2.

11 1/4, 11 1/4, 10 3/4, 10 1/2, 10 7/8, 10 5/8, 9 7/8,  11 1/4,

1. Which line plot correctly shows the data?

Answer:

C) (6 x 3) - 18 ÷ 9

Step-by-step explanation:

I'll solve this question by writing down every step and doing it one by one.

1. Multiply 6 by 3

--> This will be represented as 6 x 3.

2. Subtract the quotient of 18 and 9

--> The quotient is a number resulting in a division of another number. In this case, 18 is bigger than 9, so the quotient will be: 18 ÷ 9.

--> Since we are subtracting this from the equation we got earlier, it can be expressed as (6 x 3) - (18 ÷ 9)

This equation is the same as C) (6 x 3) - 18 ÷ 9, so C is our final answer.

The probability that the last marble removed is non-red is 2/3.

According to the given question.

Total number of marbles in a bucket = 3

And, a person arbitary pulls out each marble one at a time.

So, there are 6 possible sequences of removing 3 marbles.

Let R be the red marble, B be the blue marble and G be the green marble.

The possible sequences or sample space for removing marbles are: {RBG, RGB, BGR, BRG, GRB and GBR}.

Let A denotes the event of removing the non-red marbles at the last.

The favorable cases for event A are: RBG, RGB, BRG and GRB.

As, we know that probability of any event is calculated as by taking the ratio of total number of favorable outcomes to the total number of outcomes.

Thereofre,

The probability that the last marble removed is non-red

= 4/6

= 2/3

The probability that the last marble removed is non-red is 2/3.

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Answer:67 wins, 26 losses

Step-by-step explanation: They played 93 games. Let L = their losses and w = their wins. They won 15 more than twice as many games they lost so w =  2L + 15. So, 93 = 3L + 15. 93 - 15 = 78. 78 divided by 3 is 26 so they lost 26 games and won the rest of them or 93-26 = 67 wins and 26 losses.

The paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

In the question, we are asked to convert the given proof to the paragraph format, where the proof is already given to us.

The proof given to us is:

Statements________________________Reasons

1. AC, MN, and  DB intersect at O.______1. given

2. ∠AOM ≅ ∠NOC__________________2. vertical angles theorem.

3. ∠MOD ≅ ∠BON__________________3. vertical angles theorem.

4. ∠BON ≅ ∠NOC__________________4. given.

5. ∠AOM ≅ ∠MOD_________________5. transitive property of congruence.

To convert this proof to the paragraph format, we need to translate each statement along with its reason in the paragraph.

Thus, the paragraph looks like:

Since AC, MN, and DB intersect at O, ∠AOM ≅ ∠NOC and ∠MOD ≅ ∠BON by the vertical angles theorem. It is given that ∠BON ≅ ∠NOC, so by the transitive property of congruence, ∠AOM ≅ ∠MOD.

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The statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

Ordered pairs are known to be pairs of numbers that are used locate a point in the rectangular coordinate plane

They are written as (x ,y)

where

It is important to note that the location of the ordered pair in the quadrants determines the sign of the x and y coordinates.

The signs of the ordered pairs are given as;

When (x , y)  is in Quadrant I then both x and y are positive

Therefore, the statement that is true about two ordered pairs that are the same except for the signs of the numbers is their points are in different quadrants. Option D

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Using it's concept, the probability that a student plays basketball or soccer is given as follows:

B. 7/10.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

P(A or B) is the probability that a student plays basketball or soccer, hence, from the Venn diagram:

Hence the probability P(A or B), that is, the probability that a student plays basketball or soccer, is given as follows:

p = 7/10.

Which means that option B is correct.

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The probability of rolling a sum of six or two even numbers.

is P = 1/3

Here we are rolling two dice, and each dice has 6 possible outcomes, then the total number of outcomes is:

6*6 = 36

Now, the outcomes that given a sum of 6 are:

dice 1    dice 2.

1              5

5              1

2              4

4              2

3             3

We have 5 outcomes there.

The outcomes where both numbers are even are:

dice 1    dice 2.

2             2

2             4

4             2

4             4

4            6

6             2

6             4

6             6

We have 8 outcomes here (such that 2 are in the ones we counted before).

Then the total number of outcomes that either add to 6 or have both even numbers are:

5 + 8 - 2 = 12

Then 12 out of 36 outcomes either add to 6 or have both even numbers, this means that the probability is:

P = 12/36 = 1/3

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Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

According to the statement

we have given that the two rectangle which are similar to each other and we have to find the correct proportion for corresponding sides of rectangles.

So, we know that the

For the two rectangles to be similar, it means the ratio of their corresponding sides must be the same.

Looking at the two rectangles, the corresponding sides are pf the rectangles are:

4 m side corresponds to 8 m side in rectangle A

12m side corresponds to the 24 m side in rectangle B.

Then

The ratios of the both rectangles are:

In rectangle A is 8/4 = 2

In rectangle B is 24/12 = 2

From this it is clear that the ratios are equal.

Thus, the scale factor is 2

Since 8/4 = 24/12, we can rearrange to get;

12/4 = 24/8.

So, Option D is correct, the proportion for corresponding sides is 12/4 = 24/8.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

The two rectangles are similar with sides 4 m side corresponds to 8 m side in rectangle A and 12m side corresponds to the 24 m side in rectangle B.which is the correct proportion for corresponding sides?

A. 12/3 = 24/12.

B. 12/2 = 27/8.

C. 11/4 = 23/8.

D. 12/4 = 24/8.

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