Find the median of the data.
Length (cm) of fish in tank:
7, 2, 1, 4, 5, 2, 3
Median: [?] cr

Answer:

1798 and 32798

Step-by-step explanation:

31000/100=310

310x5.8=1798

Answer:

Common ratio = 12.

Step-by-step explanation:

2nd term = a1r and 3rd = a1r^2

So (a1)^2 r^3 = 972

a1 = 3/4, so

(3/4)^2 r^3 = 972

r^3 = 972 / 9/16

r^3 = 972*16/9 = 1728

r = 12.

The probability that a teenager has exactly 3 pairs of shoes in their closet is 0.38, or 38%.

To find the probability that a teenager has exactly 3 pairs of shoes in their closet, we need to calculate the relative frequency of this event. The relative frequency is obtained by dividing the frequency of the event by the total number of observations.

Given the distribution of pairs of shoes and their respective frequencies:

Pairs of Shoes: 1 2 3 4 5

Frequency: 18 30 57 30 15

To calculate the total number of observations, we sum up the frequencies:

Total observations = 18 + 30 + 57 + 30 + 15 = 150

The frequency for 3 pairs of shoes is 57, so the relative frequency is:

Relative frequency of having 3 pairs of shoes = 57 / 150 = 0.38

Therefore, the probability that a teenager has exactly 3 pairs of shoes in their closet is 0.38, or 38%.

The concept of probability is used to quantify the likelihood of an event occurring. In this case, we are interested in the probability of a teenager having exactly 3 pairs of shoes based on the given distribution. By calculating the relative frequency, we are able to estimate the probability of this specific event.

It is important to note that the accuracy of the probability estimate depends on the representativeness and reliability of the data used to construct the distribution.

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If any doubt leave a comment

Answer:35

Step-by-step explanation:

The volume of a cylinder is calculated by multiplying the area of its base by its height. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base and h is the height.

The volume of a cone is calculated by multiplying the area of its base by its height and then dividing by 3. The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height.

Since Sonequa’s two containers have equal radii and equal heights, it can be concluded that the volume of the cylinder is three times the volume of the cone. This means that if Sonequa fills the cone with water and pours it into the cylinder, she will need to repeat this process three times to fill the cylinder completely.

So, the claim that is most likely to be supported using the result of Sonequa’s investigation is: “The volume of a cylinder with the same radius and height as a cone is three times greater than the volume of the cone.”

Solution:

The equation of a line that passes through a point is expressed as

Two lines A and B are said to be perpendicular if the slope of line A is equal to the negative reciprocal of the slope of line B.

Thus, lines A and B are perpendicular if

Let the line equation

represent the line A.

step 1: Evaluate the slope of line A.

Comparing the equation of line A with equation 1, we can conclude that the slope of the line A is

step 2: Evaluate the slope of line B.

Since lines A and B are perpendicular, we have

step 3: Evaluate the line B.

Since the line B passes through the points (-3,2), recall from equation 1

where

Substitute these values into equation 1.

Thus,

Hence, the equation of the line is

The correct option is A

Answer:

\(\frac{y^2}{4x^5}\)

Step-by-step explanation:

Used Exponents Properties :

\(\blacksquare \left( a\times b\right)^{n} =a^{n}\times b^{n}\\\blacksquare \left( a^{n}\right)^{m} =a^{n\times m}\\\blacksquare \left( \frac{a}{b} \right)^{n} =\frac{a^{n}}{b^{n}}\)

==========================

\(\begin{aligned}\left(\frac{256 \times x^{20}}{y^8}\right)^{-\frac{1}{4}} & =\left(\frac{y^8}{2^8 \times x^{20}}\right)^{\frac{1}{4}} \\& =\frac{\left(y^8\right)^{\frac{1}{4}}}{\left(2^8 \times x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{8 \times \frac{1}{4}}}{\left(2^8\right)^{\frac{1}{4}} \times\left(x^{20}\right)^{\frac{1}{4}}} \\& =\frac{y^{\frac{8}{4}}}{2^{\frac{8}{4}} \times x^{\frac{20}{4}}} \\& =\frac{y^2}{2^2 x^5}\\& =\frac{y^2}{4 x^5}\end{aligned}\)

a) 58^-8 is the same as 1/58^8. we can also simplify the expression by applying the rule for negative exponents to the entire fraction.

To evaluate this expression, we can use the rule that any number raised to a negative exponent is equal to the reciprocal of the same number raised to the same positive exponent. In other words, x^-n = 1/x^n.

Applying this rule to the expression 1/58^8, we get:

1/58^8 = 1/(58^8) = 58^-8

Therefore, the correct answer is 58^-8.

It is important to note that the exponentiation operator (^) has higher precedence than the division operator (/), so we need to use parentheses to indicate that the exponent should be applied to the entire denominator before the division is performed. In this case, we can also simplify the expression by applying the rule for negative exponents to the entire fraction:

1/58^8 = (1/58)^8 = 58^-8

This simplification shows that the correct answer is still 58^-8.

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Answer: A B C

Step-by-step explanation:

Answer:

Step-by-step explanation:

The probability P(Z>1.28) represents the area under the standard normal distribution curve to the right of the z-score 1.28.

Using a standard normal distribution table or a calculator, we find that the area to the right of 1.28 is approximately 0.1003.

Therefore, the answer is closest to option (b) 0.10. there is a 10% chance of obtaining a value above 1.28 in a standard normal distribution.

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The three major chords built on white notes without accidentals are:

1. C major chord (C, E, G)

2. F major chord (F, A, C)

3. G major chord (G, B, D)

These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.

Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.

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Answer:

$12.5

Step-by-step explanation:

Since prize is split equally.

So, money received by each person

= 75/6

= $12.5

Answer:

The 1st one

Step-by-step explanation:

I would explain but you said u need help fast

Answer:

A) A1 A2 A3 B1 B2 B3

B) 3 paths from A

C) 1 out of 6 or 1/6

D) 2 out of 6 or 2/6 (simplified would be 1/3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(a) A1, A2, A3, B1, B2, B3

(b) 6

(c) 0.5 x 0.33 = 0.1665 0r 16.7%

(d) 0.5 x 0.66 = 0.33 or 33%

Answer:

213

Step-by-step explanation:

the equations for this is y=2x+13

just plug in x to find y

y=2(100)+13

y=213

The average annual return on this investment from 2011 to 2015 is approximately 0.8%.

To calculate the value of a $1 investment made at the beginning of 2011 and its average annual return by the end of 2015, we need to multiply the successive annual returns and calculate the cumulative value.

The successive annual returns on small U.S. stocks from 2011 to 2015 are:

-3.80%, 19.15%, 45.91%, 3.26%, and -3.80%.

To calculate the cumulative value, we multiply the successive returns by the initial investment value of $1:

(1 + (-3.80%/100)) * (1 + (19.15%/100)) * (1 + (45.91%/100)) * (1 + (3.26%/100)) * (1 + (-3.80%/100))

Calculating this expression, we find that the cumulative value is approximately $1.044, rounded to three decimal places.

Therefore, a $1 investment made at the beginning of 2011 would have been worth approximately $1.044 at the end of 2015.

To calculate the average annual return, we need to find the geometric mean of the annual returns. We can use the following formula:

Average annual return = (Cumulative value)^(1/number of years) - 1

In this case, the number of years is 5 (from 2011 to 2015).

Average annual return = (1.044)^(1/5) - 1

Calculating this expression, we find that the average annual return is approximately 0.008 or 0.8% per year, rounded to two decimal places.

Therefore, the average annual return on this investment from 2011 to 2015 is approximately 0.8%.

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Answer:

The greatest common factor is 4

Step-by-step explanation:

1)     12x3+4x2-8x

2)    (12x3)+(4x2)-8x

3)     36+(4x2)-8x

4)     36+8-8x

5)     44-8x

6)     4(11-2x)

The product of the two matrices Q₁Q₂ is orthogonal

In linear algebra, an orthogonal matrix, or orthonormal matrix, is a real square matrix whose columns and rows are orthonormal vectors. ... {\displaystyle Q^{\mathrm {T} }Q=QQ^{\mathrm {T} }=I,} where QT is the transpose of Q and I is the identity matrix.

It is said to be an orthogonal matrix if its transpose is equal to its inverse matrix, or when the product of a square matrix and its transpose gives an identity matrix of the same order.

If A is an n*n orthogonal matric, then A*A¹ = A¹*A

Therefore A*A¹ = A¹*A  = 1

This implies that the product Q₁O₂ is orthogonal.

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The function represented in the table changes over equal intervals of 10 for each increase in x. This means that the change in f(x) is constant over these intervals. In other words, the function has a constant rate of change over equal intervals of x.

This tells us that the function is a linear function. Linear functions have a constant rate of change, which means that the change in the output variable (f(x) in this case) is proportional to the change in the input variable (x in this case).

In this specific table, we can see that for every increase in x by 10, f(x) also increases by a constant factor of 5. This indicates that the function is of the form f(x) = 5x + c, where c is a constant.

Overall, the fact that the function changes over equal intervals in a constant manner tells us that it is a linear function, which can be described by a simple equation that relates the input variable (x) to the output variable (f(x)).
Hi! To analyze the function represented in the table, we will look at the changes in the input (x) and output (f(x)) values over equal intervals. By doing so, we can determine the type of function.

Step 1: Identify the interval between the x-values.
In the table, x values are increasing by 10: 14, 24, 34, and 44.

Step 2: Examine the changes in the f(x) values.
For f(x) values, we have: 5, 10, 20, and 40.

Step 3: Analyze the relationship between the changes in x and f(x).
As x increases by 10, the f(x) values double each time:
- From 5 to 10 (10 = 5 * 2)
- From 10 to 20 (20 = 10 * 2)
- From 20 to 40 (40 = 20 * 2)

Step 4: Determine the type of function.
Since the output is doubling for each equal interval of the input, we can conclude that the function is an exponential function.

In summary, the function in the table changes over equal intervals by doubling the output (f(x)) values as the input (x) values increase by 10. This behavior indicates that the function is an exponential function.

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Therefore, Kim still owes $294.06 on her credit card account.

Addition is a basic mathematical operation that combines two or more numbers or quantities to give a total or a sum. In other words, it is the process of finding the total when two or more values are combined. It is denoted by the plus symbol (+). For example, in the expression 5 + 3, 5 and 3 are the addends, and the sum or total is 8. Addition is one of the four basic arithmetic operations, the others being subtraction, multiplication, and division. It is widely used in many areas of mathematics, as well as in everyday life situations such as counting objects or adding up a shopping bill.

Here,

Starting balance on the credit card account = $810.00

Return 1: $37.66

Return 2: $120.00

Total credits from returns = $37.66 + $120.00 = $157.66

Adjusted balance after returns = Starting balance - Total credits from returns

Adjusted balance after returns = $810.00 - $157.66 = $652.34

Purchase 1: $86.50

Purchase 2: $10.00

Purchase 3: $10.00

Total purchases = $86.50 + $10.00 + $10.00 = $106.50

Adjusted balance after purchases = Adjusted balance after returns + Total purchases

Adjusted balance after purchases = $652.34 + $106.50 = $758.84

Payment = $500.00

Adjusted balance after payment = Adjusted balance after purchases - Payment

Adjusted balance after payment = $758.84 - $500.00 = $258.84

Finance charge = $35.22

Total amount owed = Adjusted balance after payment + Finance charge

Total amount owed = $258.84 + $35.22 = $294.06

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Answer:

Step-by-step explanation:

7y-3y= 4y

4y=8

Here when its like this we need y by itself, so you take out 4 by dividing 8 by 4.

y= 2

Answer:

56

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

A=hb/2

b = 20

h=45

The type of measurement, the nature of the comparison, and the number of groups to be compared influence the statistical choice is true.

The choice of statistical test depends on several factors, including the type of measurement (nominal, ordinal, interval, or ratio), the nature of the comparison (independent or dependent), and the number of groups being compared.

For example, different statistical tests are used for comparing means between two groups, three or more groups, or paired observations within the same group. It is important to select the appropriate statistical test that matches the research question and the data being analyzed to ensure accurate and valid results.

Hence, The type of measurement, the nature of the comparison, and the number of groups to be compared influence the statistical choice is true.

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Answer:

h-2

Step-by-step explanation:

-2x5=-10

8-10=-2

=h-2

Amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

Let amount of one tin of paint = x

Let the total amount Mr. Chong  having = y

On buying 18 tins of paint, he will need another $80. This can we mathematically represented as,

18x = y + 80            

On rearranging this equation can be written as,

18x - y = 80                                         equation 1

On buying 10 tins of paint, he will will have $32 left. This can we mathematically represented as,

10x = y - 32

On rearranging this equation can be written as,

-10x + y = 32                                      equation 2

On adding equation 1 and equation 2, we get

18x - y -10x + y = 80 + 32

8x = 112

x = (112/8) = 14

On substituting x = 14 in equation 2 , we get

-140 + y = 32

y = 172

So, amount of one tin of paint is $14 and the total amount Mr. Chong  have is $172.

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The situation in which it is safe to employ t-procedures is described by option (c) where both samples are approximately normal.

option (c) is identified as the situation where it is safe to use t-procedures.

t-procedures are appropriate when certain assumptions are met, including the assumption of normality of the population or sample distributions. Option (c) states that both samples are approximately normal, which fulfills this requirement. This means that the data in both samples have a symmetric bell-shaped distribution, allowing t-procedures to be used for hypothesis testing or confidence interval estimation.

Options (a), (b), and (d) describe scenarios where either one or both samples are moderately skewed or contain outliers, which violates the assumption of normality. Skewness and outliers can impact the validity of t-procedures, making them less reliable. Therefore, these options do not fulfill the requirement for safely employing t-procedures.

Option (e) states that it is safe to use t-procedures in more than one of the situations above. However, based on the analysis provided, only option (c) meets the criteria of having both samples approximately normal, making it the only situation where t-procedures can be safely employed.

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Step-by-step explanation:

no.

15/20 = 3/4

10/15 = 2/3

A set is called denumerable if it is either finite or has the same cardinality as the set of natural numbers.

Let a1, a2, a3, … be the elements of A since A is a denumerable set. We can enumerate the elements of A as: a1, a2, a3, …Using the same method, we can enumerate the elements of B as: b1, b2,That is, B can be written in the form B = {b1, b2, …}.

Then, we can write down A × B as follows:(a1, b1), (a1, b2), (a2, b1), (a2, b2), (a3, b1), (a3, b2), …

Let's now associate every element of A × B with a natural number in the following way: For (a1, b1), associate with the number 1.

For (a1, b2), associate with the number 2.

For (a2, b1), associate with the number 3.

For (a2, b2), associate with the number 4.

For (a3, b1), associate with the number 5.

For (a3, b2), associate with the number 6.…We can repeat this process for each element of A × B.

We see that every element of A × B can be associated with a unique natural number.Therefore, A × B is denumerable and we can list its elements as (a1, b1), (a1, b2), (a2, b1), (a2, b2), (a3, b1), (a3, b2), … which can be put into a one-to-one correspondence with the natural numbers, proving that it is denumerable. The statement is hence proved.

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