one half cubed − 6 ÷ square root of 64

negative five eighths
negative 47 over 64
five eighths
47 over 64

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour.

Sample Mean: = (29 + 27 + 34 + 40 + 22 + 28 + 14 + 35 + 26 + 35 + 12 + 30 + 23 + 18 + 11 + 22 + 23 + 33) / 18

= 480 / 18

≈ 26.667

Sample Standard Deviation (s):

= ✓((Σ(29 - 26.667)² + (27 - 26.667)² + ... + (33 - 26.667)²) / (18 - 1))

≈ ✓(319.778 / 17)

≈ ✓(18.81)

≈ 4.336

Confidence level = 99%

Sample Size (n) = 18

Sample Mean = 26.667

Sample Standard Deviation (s) = 4.336

Degrees of Freedom (df) = n - 1 = 18 - 1 = 17

Using a t-table or statistical software, we find that the critical value for a 99% confidence level with 17 degrees of freedom is approximately 2.898.

Margin of Error (E) = 2.898 * (4.336 / ✓18))

≈ 3.748

Confidence Interval = (26.667 - 3.748, 26.667 + 3.748)

= (22.919, 30.415)

We can be 99% confident that the true mean healing rate of newts falls within the interval of 22.919 to 30.415 micrometers per hour. This means that if we were to repeat the study multiple times and construct confidence intervals, approximately 99% of those intervals would contain the true mean healing rate of the population.

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Answer:

[6, 8).

Step-by-step explanation:

When we are looking for the range of a function by just looking at the graph, we have to define from what point to what point the graph move vertically. On the other hand, if we were looking for the domain, we would state from where to where the graph moves horizontally.

In this case we have to analyze the graph vertically, since we are looking for the range of the function. Therefore, if we take a look at the line we can notice that it goes from y=6 to y=8. Therefore the range should be from 6 to 8.

Now, this result must be expressed in interval notation, meaning that we have to state whether the values of each end are contained or not by the function. The graph already tells us about it., because it marks it with the closed or open dots. In the case of the number 6, we have a closed dot, means that the function contains the number 6. For the other end we have an open dot, means that the function doesn't contain the number 8.

Applying internal notation, the range of this function is:

[6, 8).

Learn more about interval notation here:

1. https://web.nmsu.edu/~kberver/Unit1/Unit18.html#:~:text=An%20interval%20is%20closed%20if,used%20for%20an%20open%20endpoint.

2. https://brilliant.org/wiki/interval-notation/#:~:text=Interval%20notation%20is%20a%20way,inequality%20or%20system%20of%20inequalities.

There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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Answer:

Step-by-step explanation:

Answer:

26880 ways

Step-by-step explanation:

Given

\(Crust = 4\)

\(Toppings = 10\)

\(Cheese = 8\)

Required

Determine the number of ways 3 toppings and 3 cheese can be selected

The number of crusts to be selected was not stated. So, I'll assume 1 crust to be selected from 4.

This can be done in \(^4C_1\) ways

For the toppings:

3 can be selected from 10 in \(^{10}C_3\) ways

For the cheeses:

3 can be selected from 8 in \(^{8}C_3\) ways

Total number of selection is:

\(Total = ^4C_1 * ^{10}C_3 * ^{8}C_3\)

Apply combination formula:

\(Total = \frac{4!}{(4-1)!1!} * \frac{10!}{(10-3)!3!} * \frac{8!}{(8-3)!3!}\)

\(Total = \frac{4!}{3!1!} * \frac{10!}{7!3!} * \frac{8!}{5!3!}\)

\(Total = \frac{4*3!}{3!*1} * \frac{10*9*8*7!}{7!*3*2*1} * \frac{8*7*6*5!}{5!*3*2*1}\)

\(Total = \frac{4}{1} * \frac{10*9*8}{3*2*1} * \frac{8*7*6}{3*2*1}\)

\(Total = 4 * \frac{720}{6} * \frac{336}{6}\)

\(Total = 4 * 120* 56\)

\(Total = 26880\)

Hence, there are 26880 ways

Answer:

7/2=3.5 each of them got 3 and half

Answer:

16.25 acres

Step-by-step explanation:

If corn is 1/4 of the land and we have 65 acres, we merely multiply 1/4 to 65.

You get 16.25 acres.

Answer:

16.25acres

Step-by-step explanation:

65/4=16.25 or 16 and 1/4

Answer:

40%

Step-by-step explanation:

6/15 * 100 = 0.4 * 100 = 40%

Answer:

40% of the pieces of fruit in the Bowl are apples.    

Step-by-step explanation:

Given the statement:- There are 15 pieces of fruit in a bowl and six of them are apples.

Total number of pieces of fruit  in a bowl = 15 pieces

Number of pieces of apple in a bowl = 6 pieces.

Therefore, 40% of the pieces of fruit in the Bowl are apples.

One characteristic of a well-defined probability density function of a continuous random variable X is that the area under the curve, f(x) over all values of x is equal to one.

Probability density functions are a group of functions commonly used in statistical theory to describe the behavior of theoretical probability distributions. A function satisfies a criterion like the function if its values are always positive for all horizontal axes and its primitives are probability distributions. This means that this function is non-negative for all abscissa values and its definite integral product in the range -∞ to +∞ is equal to 1. Apart from being called the probability density function, it is also called the probability density function or probability density function in the literature.

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A possible starting point:

Split up the limit as

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} \times \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = 54\)

Consider the first limit,

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}}\)

Refer to the Stolz-Cesàro theorem, which says

\(\displaystyle \lim_{n\to\infty} \frac{a_n}{b_n} = \lim_{n\to\infty}\frac{a_{n+1}-a_n}{b_{n+1}-b_n}\)

where \(a_n\) and \(b_n\) are two real sequences, with \(b_n\) monotone and divergent. In this case,

\(a_n = 1+\sqrt[3]{2}+\sqrt[3]{3}+\cdots+\sqrt[3]{n}\)

\(b_n = n^{4/3}\)

Applying S-C, we get

\(\displaystyle \lim_{n\to\infty} \frac{\sqrt[3]{n+1}}{(n+1)^{4/3} - n^{4/3}} = \lim_{n\to\infty} \frac{(n+1)^{1/3}}{(n+1)^{4/3} - n^{4/3}}\)

Recalling the difference of cubes identity,

\(a^3 - b^3 = (a - b) (a^2 + ab + b^2)\)

we can rewrite the limit as

\(\displaystyle \lim_{n\to\infty} \frac{(n+1)^3 + (n+1)^{5/3} n^{4/3} + (n+1)^{1/3} n^{8/3}}{(n+1)^4 - n^4}\)

and dividing uniformly through the limand by (n + 1)³ yields

\(\displaystyle \lim_{n\to\infty} \frac{1 + \left(\frac n{n+1}\right)^{4/3} + \left(\frac n{n+1}\right)^{8/3}}{(n+1) - \frac{n^4}{(n+1)^3}}\)

Now,

\(n^4 = (n+1)^4 - 4n^3 - 6n^2 - 4n - 1\)

\(\implies \dfrac{n^4}{(n+1)^3} = (n+1) - \dfrac{4n^3+6n^2+4n+1}{(n+1)^3}\)

so the denominator in the limit reduces to a degree-1 polynomial with leading coefficient +4. The numerator converges to 1 + 1 + 1 = 3, so this first limit evaluates to

\(\displaystyle \lim_{n\to\infty} \frac{1 + \sqrt[3]{2} + \cdots + \sqrt[3]{n}}{n^{4/3}} = \frac34\)

It remains to determine the value of a such that

\(\displaystyle \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} = \frac43\times54 = 72\)

We have a natural choice of lower and upper bounds for the sum in the denominator:

\(\displaystyle \frac1{(an+n)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \\\\ ~ ~ ~ ~ ~ ~ ~ ~ \le \frac1{(an+1)^2} + \cdots + \frac1{(an+1)^2}\)

\(\implies \displaystyle \frac{n}{(an+n)^2} \le \frac1{(an+1)^2} + \cdots + \frac1{(an+n)^2} \le \frac{n}{(an+1)^2}\)

and

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+n)^2} = \frac1{(a+1)^2}\)

\(\displaystyle \lim_{n\to\infty} n\times\frac{n}{(an+1)^2} = \frac1{a^2}\)

so that by the squeeze/sandwich theorem,

\(\displaystyle \frac1{(a+1)^2} \le \lim_{n\to\infty} n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right) \le \frac1{a^2}\)

\(\implies \displaystyle a^2 \le \lim_{n\to\infty} \frac1{n \left(\frac1{(an+1)^2} + \frac1{(an+2)^2} + \cdots + \frac1{(an+n)^2}\right)} \le (a+1)^2\)

and if the middle limit is supposed to evaluate to 72, solving the inequality for a puts it in the interval [6√2 - 1, 6√2] ≈ [7.48528, 8.48528].

Checking against a computer, the solution appears to be a = 8, which agrees with the analysis above. Just not sure how to bridge the gap yet...

We are asked to determine the probability of landing on an odd number and then landing on a 6.

To do that we will use the product rule of probabilities:

Where:

To determine the value of the probability of A we need to have into account that there is only 1 odd number (7) out of 3 possible numbers, therefore, the probability is:

Now, to determine the value of the probability of "B" we need to have into account that there is only one number 6 out of 3 numbers therefore, we have:

Now, we substitute the values:

Now, we solve the operations:

Therefore, the probability is 1/9

The lengths of the missing sides in the triangle and the angles can be written as ; y= 3,   x =3√3 , 60°

We were given a right triangle. where the lenghts is required to be found, however this can be seen as a triangle with 30-60-90 triangle however the lengths of the sides of a 30-60-90 triangle  can be expressed in the ratio  1 :√3 : 2

We can represent the side opposite to 30 degree as n,  which then means that the side opposite to 60 degree angle  becomes √3n then the last side(hypothenus)  will be 2n, given that corresponding sides to hypotenuse= 6, then we can say that

2n = 6

n=3

Therefore, corresponding side that can be attributed to 30 degree angle = 6/2 = 3 which implies that y=3, then x =3√3 (side corresponding to 60 degree angle)

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Step-by-step explanation:

13080dollars.................

The 3 sets of data with the same median but different mean are given as follows:

The mean of a data-set is calculated as the sum of all values in the data-set divided by the number of values in the data-set.

The median of a data-set is the middle value of the data-set, the value which 50% of the data-set is less than and 50% of the data-set is more than.

Hence, for a data-set of five elements, which is an odd cardinality, the median is the third element of the ordered data-set.

Then the three data-sets can be constructed with five elements, in which the third element is the same but the sum of the five elements is different.

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Answer:

27

Step-by-step explanation:

3*3=9*3=27

Answer: 27

Step-by-step explanation: What 3 ^ 3 mean is when you multiply 3x3x3. Hope this was helpful.

The output value of f( -3 ) in the function f(x) = x³ + 3x + 17 is -19.

Given the function in the question:

f(x) = x³ + 3x + 17

To evaluate f(-3) for the function f(x) = x³ + 3x + 17, we simply substitute -3 for x in the expression and calculate the result.

f(x) = x³ + 3x + 17

Plug in x = -3

f(-3) = (-3)³ + 3(-3) + 17

First, let's calculate (-3)³, which means raising -3 to the power of 3:

(-3)³ = -3 × -3 × -3 = -27

Next, let's calculate 3(-3):

3(-3) = -9

Now, we can substitute these values into the expression:

f(-3) = -27 + (-9) + 17

Simplifying further:

f(-3) = -27 - 9 + 17

f(-3) = -36 + 17

f(-3) = -19

Therefore, the output value of f(-3) is -19.

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Answer:

b ≤ 3/8

Step-by-step explanation:

Let the unknown number be b.

Translating the word problem into an algebraic expression, we have;

8b + 23 ≤ 26

Rearranging the equation, we have;

8b ≤ 26 - 23

8b ≤ 3

Dividing both sides by 8, we have;

b ≤ 3/8

First it is important ot remember the folllowing:

1) "hm" is hectometre.

2) "dm" is decimetre.

In order to solve the exercise you also need to remember that, by definition:

Knowing the above, you can make the conversion from hectometre (hd) to decimetre as following:

Therefore, you get that the answer for the question is:

The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

It is given that:

The side length of the triangle is shown in the option:

As we know,

Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

Using Pythagoras' theorem:

From option(D):

3, 4 and 5

(3)² + (4)² = 5²

9 + 16 = 25 (True)

Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.

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A) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

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Answer:

Step-by-step expA) The type of triangles are congruent triangles

B) By the use of SAS Congruency Postulate

C) The distance across for the sink hole is: 52.2 ft

D) The perimeter of triangle ABC is: 172.2 feet.

How to solve congruent triangles?

A) Congruent triangles are defined as the triangles created because of the phrasing "you recreate the same triangle" mentioned in the instructions. Congruent triangles are basically identical carbon copies of each other.

B) If we knew the measure of angle ACB, and then mad use of it to form angle ECD, then we would have enough information to know that triangle ACB was congruent to triangle ECD. Therefore, it would be useful to do the SAS (side angle side) congruence rule.

C) We know that:

AB = ED = 52.2

AB is the distance across the sink hole. Thus, it is 52.2 feet

D) AB = 52.2

BC = 70

AC = 50

Thus:

Perimeter of triangle ABC = AB + BC + AC

Perimeter of triangle ABC = 52.2 + 70 + 50

Perimeter of triangle ABC = 122.2 + 50

Perimeter of triangle ABC = 172.2

The perimeter of triangle ABC is 172.2 feet.

lanation:

The end behavior of the graph of f(x) = x⁵ – 8x⁴ + 16x³ does not cross the x-axis at x = 4 and crosses the x-axis at x = 0. This is about the end behavior of a graph of a function at the end of the x-axis. Also, f(x) => -∞ as x => -∞; f(x) => +∞ as x => +∞.

We are given the function;

f(x) = x⁵ - 8x⁴ + 16x³

A) As x approaches negative infinity -∞, x⁵ will also approach negative infinity -∞. This is because when we raise a negative number to the power of an odd number, the result remains negative.

B) As x approaches positive infinity +∞, x⁵ will also approach positive infinity -∞. This is because when we raise a positive number to the power of an odd number, the result remains positive.

Let's now find the roots of this function;

f(x) = x⁵ - 8x⁴ + 16x³

Let's factorize it first to get;

f(x) = x³(x² – 8x + 16)

(x² – 8x + 16) is a perfect square trinomial and can be expressed as (x – 4)(x - 4).

Thus;

f(x) = x³ (x – 4)(x - 4)

C) Since we have found the factorized form to be;

f(x) = x³ (x – 4)(x - 4)

The roots are at f(x) = 0;

The roots are; x³ = 0; (x – 4) = 0 ; (x - 4) = 0

This means the roots of f(x) are; x=0 and x=4.  x = 4

This means the graph has a repeated root and so it will touch the x-axis but not at the repeated root of x=4.

D) Since, 0 is a root and it does not cross at x = 4, the graph will cross at x = 0.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

9/10

Step-by-step explanation:

3/5 gallon paint = 2/3 of wall

if you divide 3/2 each side then...

9/10 gallon of paint = 1 wall

Answer:

1/5 of a wall

Step-by-step explanation:

if you take 3/5 and divide it by 2/3 then you get 1/5

Answer:25.13

Step-by-step explanation:

I took a test that had that question hope it helps :)

Answer:

\( \frac{7}{9} \times 5 \frac{2}{5} \\ = 4 \frac{1}{5} \)

The result of 7/9 × 5 2/5 as a fraction is 21/5.

Given the expression in the question:

7/9 × 5 2/5

To multiply 7/9 by 5 2/5 as a fraction, first, convert the mixed number 5 2/5 to an improper fraction.

5 2/5 ⇒ ( 5 × 5 + 2 )/5 = ( 25 + 2 )/5 = 27/5

Hence, we have:

7/9 × 27/5

To multiply fractions, multiply the numerators together and then multiply the denominators together:

( 7 × 27 )/( 9 × 5 )

( 189 )/( 9 × 5 )

189/45

Simplifying, we get:

21/5

Therefore, the simplified form is 21/5.

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