Find the mean for the following frequency tables. (Round your answers to one decimal place.)
(a)
Grade Frequency
49.5–59.5 2
59.5–69.5 3
69.5–79.5 7
79.5–89.5 11
89.5–99.5 5


(b)
Daily Low Temperature Frequency
49.5–59.5 52
59.5–69.5 30
69.5–79.5 15
79.5–89.5 1
89.5–99.5 0


(c)
Points per Game Frequency
49.5–59.5 14
59.5–69.5 33
69.5–79.5 15
79.5–89.5 24
89.5–99.5 2

Answers

Answer 1

The mean for the given frequency tables is:

(a) Grade Frequency: 48.7

(b) Daily Low Temperature Frequency: 54.5

(c) Points per Game Frequency: 54.5

To find the mean for the given frequency tables, we need to calculate the weighted average. The mean is calculated by multiplying each value by its corresponding frequency, summing up these products, and then dividing by the total frequency.

(a) Grade Frequency:

To find the mean for the grade frequency table, we need to multiply the midpoints of each class interval by their respective frequencies and then divide by the total frequency.

The midpoints are:

54.5, 64.5, 74.5, 84.5, 94.5

The frequencies are:

2, 3, 6, 11, 5

Calculating the weighted sum: (54.52) + (64.53) + (74.56) + (84.511) + (94.5*5) = 1315

Calculating the total frequency: 2 + 3 + 6 + 11 + 5 = 27

Mean = 1315 / 27 ≈ 48.7

(b) Daily Low Temperature Frequency:

Since the frequency for the 49.5–59.5 class interval is 5 and for the other intervals is 0, we can conclude that the mean will be within the range of 49.5–59.5. The mean will be the midpoint of this class interval.

Mean = (49.5 + 59.5) / 2 = 54.5

(c) Points per Game Frequency:

Similarly to part (b), since the frequency for the 49.5–59.5 class interval is 1 and for the other intervals is 0, the mean will be within the range of 49.5–59.5.

Mean = (49.5 + 59.5) / 2 = 54.5

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Related Questions

what is 4.5x-100>125

Answers

Answer:

4,5x>225--> x>225:4,5

Step-by-step explanation:

The answer is:

x > 50

Work/explanation:

To solve this inequality, begin by adding 100 on each side:

[tex]\sf{4.5x-100 > 125}[/tex]

[tex]\sf{4.5x > 125+100}[/tex]

[tex]\sf{4.5x > 225}[/tex]

Now, divide each side by 4.5.

[tex]\sf{x > 50}[/tex]

Hence, the answer is x > 50.

How many combinations of poker hands are in a deck of cards?

Answers

2,598,960 distinct poker hands

Which of the following could be a real world description of 3x-15

Answers

Answer:

three times a number minus fifteen

or

fifteen is less than three times a number

1. Consider a simple random sample of 25 newts. The mean tail length of our sample is 5 cm. If we know that 0.2 cm is the standard deviation of the tail lengths of all newts in the population, then what is a 90% confidence interval for the mean tail length of all newts in the population ?

Answers

The 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

How to find 90% confidence interval for the mean tail length of all newts in the population

To calculate the 90% confidence interval for the mean tail length of all newts in the population, we can use the formula:

Confidence Interval = Sample Mean ± Margin of Error

Given:

- Sample size (n) = 25

- Sample Mean (xbar) = 5 cm

- Standard Deviation of the population (σ) = 0.2 cm

- Confidence level = 90% (which corresponds to a z-score of 1.645 for a two-tailed test at a 90% confidence level)

First, we need to calculate the margin of error:

Margin of Error = (Critical Value) * (Standard Deviation / √Sample Size)

In this case, the critical value for a 90% confidence level is 1.645. Let's substitute the values:

Margin of Error = 1.645 * (0.2 / √25)

Margin of Error = 1.645 * 0.04

Margin of Error ≈ 0.0658

Now, we can calculate the confidence interval:

Confidence Interval = Sample Mean ± Margin of Error

Confidence Interval = 5 ± 0.0658

Confidence Interval ≈ (4.9342, 5.0658)

Therefore, the 90% confidence interval for the mean tail length of all newts in the population is approximately (4.9342 cm, 5.0658 cm).

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Ray found the perimeter of his bedroom window to be 12 ft if the length of the window is 4 ft what is the width of his bedroom window ​

Answers

Step-by-step explanation:

Perimeter= 12ft

Length= 4ft

Width= ?

Bedroom window = rectangle

Rectangle= l×b

= 4× ?

12÷ 4=3

Therefore,The width of his bedroom window is 3ft

HELP ASAP IVE BEEN STUCK ONNTHIS 20 PTS

Answers

Answer:

[tex] \sqrt{ {( - 4 - 2)}^{2} + {(1 - 0)}^{2} } = \sqrt{ {( - 6)}^{2} + {1}^{2} } = \sqrt{36 + 1} = \sqrt{37} [/tex]

The number 37 goes beneath the radical symbol.

Create a table of values for the function graphed below using the plotted points. Remember, table of values are written with the x
-values in order from least to greatest (read the graph from left to right).
there are 5 rows for both problems x,y and 45 points for helping me with this

Answers

The table of values of the graphs are

x    -2    -1    0    1    2

y  -8   -6   -4   -2    0

and

x   -7    -2    2    3    4

y  1       -8   3      5   -5

Writing the table of values of the graphs.

from the question, we have the following parameters that can be used in our computation:

The graph

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

So, we have

y = mx - 4

Using the points, we have

2m - 4 = 0

This gives

2m = 4

So, we have

m = 2

This means that the equation is y = 2x - 4

So, we have the following table of values

x    -2    -1    0    1    2

y  -8   -6   -4   -2    0

For the second table, we have

x   -7    -2    2    3    4

y  1       -8   3      5   -5

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If the HCF of two numbers is 36 and their LCM is 1260 . If one number is 72 find the other one

Answers

Answer:  B   =   630

        Hence, The other Number is:   B   =  630

Step-by-step explanation:  EUCLIDS ALGORITHM

If the HCF of two numbers is 36 and their LCM is 1260. If one number is 72 find the other one:

PRIME FACTORS of 1260 are:

        2,   2,  3,   3,  7

PRIME FACTORS of 72 are:

        2,  2,  2,  3,  3

Write the formula  for  HCF  and  LCM:

        HCF  *   LCM   =   a  *  b

        HCF   =    2  *  2  *  3  *  3

                   =  36

Substitute  The Given Values:

        36  *   1260   =    72  *  b

        36  *  1260    =    72b

        45360           =    72b

Divide Both Sides by 36:

        1260            =   2  *  b

        45360 / 72  =   72b/72

                        b   =   630

Divide Both Sides by 2:

        B    =    630

Draw the conclusion:

        Hence, The other Number is:   B   =  630

I hope this helps you!

one year on venus is equivalent to 224.7 days on earth. How many days on earth, in decimal form are equivalent to 9 1/2 years on venus

Answers

9.5 Venus years is equal to 9.5 x 224.7 = 2134.65 Earth days.
Final answer:

9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth.

Explanation:

To find how many days on Earth are equivalent to 9 1/2 years on Venus, we need to use the ratio of 224.7 days on Earth to 1 year on Venus. First, we convert 9 1/2 years to a decimal form, which is 9.5 years. Then, we multiply 9.5 years by the conversion ratio: 9.5 years * 224.7 days/year = 2137.65 days on Earth. Therefore, 9 1/2 years on Venus is equivalent to approximately 2137.65 days on Earth in decimal form.

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Solve 5 ≥ -5x > 25 and graph the solution set on a number line

I need help please.

Answers

Answer:

false

Step-by-step explanation:

Its All Real Numbers

After college, you get a job with a starting salary of $37,000. You have a cousin that works at the same company, but he was hired three years before you. Your contract states you will receive a pay raise each year of 6%. Your cousin tells you that his starting salary three years ago was $50,000 and he has been guaranteed a 4% pay raise each year.
1. Make a table showing your salary for your first five years on the job


Answers

1. A table showing your salary for the first five years on the job is shown below.

2. Your cousin's salary would be $56243.2 in the year you started working.

3. A formula for your salary is [tex]P(t) = 37000(1.06)^t[/tex]

A formula for your cousin's salary is [tex]P(t) = 50000(1.04)^t[/tex]

4. A graph of your salary and your cousin's salary is shown below.

It would take about 16 years before your salary exceed your cousin's salary.

How to write an exponential function to model the situation?

In Mathematics and Geometry, an exponential function can be modeled by using this mathematical equation:

[tex]P(t) = I(1 + r)^t[/tex]

Where:

P(t) represent the future value.t represent the time or number of years.I represent the initial amount.r represent the exponential growth rate.

Part 1.

We can create a table of values to model your salary for the first five years on the job as follows;

Years               1                2               3                4                 5

Salary ($)    39,220    41,573.2    44,067.6    46,711.7     49,514.4

Part 2.

For your cousin's salary three years after, we have:

y = 50,000(1.04)³

y = $56243.2.

Part 3.

We can write a formula for your salary as follows;

[tex]P(t) = 37000(1 + 0.06)^t\\\\P(t) = 37000(1.06)^t[/tex]

For your cousin's salary, we have:

[tex]P(t) = 50000(1 + 0.04)^t\\\\P(t) = 50000(1.04)^t[/tex]

Part 4.

In order to plot a graph of your salary and your cousin's salary, we would use an online graphing tool with a scale of 1 units for 1 year on the x-axis and a scale of 50 units for 1000 dollars on the y-axis.

Since the lines representing both salaries intersect at 15.808, we can logically deduce that it would take approximately 16 years for your salary to exceed your cousin's salary.

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Can I get a help with the second one please!

Answers

Answer:

897

Explanation:
Start with replacing all the [tex]t[/tex] with 2.

[tex](t^{2} + 6t+7)(3t^{2} +3)[/tex]
[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]

Deal with the exponent before multiplying and adding.

[tex](2^{2} + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 6(2)+7)(((3)(2))^{2} +3)[/tex]
[tex](4 + 12+7)(((3)(2))^{2} +3)[/tex]
[tex](23)(((3)(2))^{2} +3)[/tex]

Now I believe here is where you made your mistake, you should first multiply 3 and 2 instead of evaluating the exponent straight away, because [tex]3t[/tex] was squared together.

[tex](23)(((3)(2))^{2} +3)[/tex]
[tex](23)(6^{2} +3)[/tex]
[tex](23)(36 +3)[/tex]

Then after adding, just multiply to get your answer, 897.

[tex](23)(36 +3)[/tex]
[tex](23)(39) = 897[/tex]

At the zoo for every six adore camel 05 baby camels there are a total of 44 adult and baby camels at the zoo

Answers

Using proportions, it is found that the table is completed as follows:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels     6                     24

Total camels     11                    44

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

At the zoo, for every 6 adult camels, there are 5 baby camels, hence, out of 11 camels, 5 are baby and 6 are adult.

Thus, out of 44 camels, we have that:

44/11 x 5 = 20, hence there are 20 baby camels.44/11 x 6 = 24, hence there are 24 adult camels.

The table is:

                        Original Ratio Number in the zoo

Baby camels     5                     20

Adult camels    6                     24

Total camels     11                     44

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Your question was incomplete, the complete question is-

At the zoo, for every 6 adult camels, there are 5 baby camels. There are a total of 44 adult and baby camels at the zoo.

Complete the table.

Original ratio Number in the zoo

Baby camels 5 ?

Adult camels 6 ?

Total camels ? 44

PLEASE HELP PLEASE HELP​

Answers

220 divided by 22 is equal to 10. You can check this by multiplying 22 by 10 to get 220.

Answer:

22

Step-by-step explanation:

You can do it by 220 divided by 10, which gives an answer of 22.

no explanation needed would be nice ytho thnks

Answers

The average rate of change in the population between 2002 and 2004 is one thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

Rate of change

To calculate the average rate of population change, we need to find the difference in population between the given years and divide it by the difference in years.

Between 2002 and 2004:

Population change = 80 - 82 = -2 (decrease of 2, as the population decreased)

Year difference = 2004 - 2002 = 2

Average rate of change = Population change / Year difference

Average rate of change = -2 / 2 = -1 (thousands per year)

Between 2002 and 2006:

Population change = 75 - 82 = -7 (decrease of 7, as the population decreased)

Year difference = 2006 - 2002 = 4

Average rate of change = Population change / Year difference

Average rate of change = -7 / 4 = -1.75 (thousands per year)

Therefore, the average rate of change of population between 2002 and 2004 is 1 thousand per year, and between 2002 and 2006 is 1.75 thousand per year.

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solve the following problem

Answers

a. The maximum population of the squirrels is 1800.

b. The number of squirrels that were introduced to the island are 200 squirrels.

What is an exponential function?

In Mathematics and Geometry, a logistic growth function can be represented by using the following mathematical equation:

[tex]f(x) = \frac{L}{1\;+\;e^{-k(x-x_0)}}[/tex]

Where:

L represents the carrying capacity, maximum value or supremum.x represents the x-value of midpoint.k represents the rate of change or growth rate.

Based on the information provided above, the population of squirrels can be modeled by the following logistic growth function;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}[/tex]

Part a.

By comparison, the maximum value or supremum population of the squirrels is 1800 squirrels.

Part b.

When t = 0, the initial number of squirrels that were introduced to this island can be calculated as follows;

[tex]P(t) = \frac{1800}{1\;+\;8e^{-0.3t}}\\\\P(0) = \frac{1800}{1\;+\;8e^{-0.3(0)}}[/tex]

P(0) = 1800/9

P(0) = 200 squirrels.

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Find the missing side. 42° Y y 18 y = [?] Round to the nearest tenth.​

Answers

Answer:

Step-by-step explanation: a = o/t

a = 18/tan(42)

a = 19.99

3
2
1
-1
-2
-3
Determine the period.
V
MAN
6 8 10 12 14
2 4

Answers

The period of the function in this problem is given as follows:

5 units.

How to obtain the period of the function?

A periodic function is a function that has the behavior repeating over intervals in the domain of the function.

Then the period of the function has the concept defined as the difference between two points in which the function has the same behavior.

The distance between peaks of the function in this problem is of 5 units, which represents the period of the function.

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An environmental group is tracking a fast-growing algae's coverage on a nearby pond. When
the group first measured the algae, it covered 3 square meters of the pond. They expect the
area of the pond covered by algae will double each day.
Write an exponential equation in the form = a(b)^x that can model the area of the pond
covered by algae, y, in x days.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y =

How much of the pond is expected to be covered by algae after 4 days?

Answers

Answer:

y = 3(2^x)48 m² after 4 days

Step-by-step explanation:

You want an exponential function of the form y = a(b^x) that models algae growth that initially covers 3 square meters of a pond and doubles in area each day.

Exponential function

The function y = a(b^x) has an initial value of 'a', which the problem statement tells us is 3 (square meters). The value 'b' is the growth factor, which the problem statement tells us is 2 each day.

The desired exponential equation is ...

  y = 3(2^x)

4 days

When x=4, the function evaluates to ...

  y = 3(2^4) = 3(16) = 48 . . . . square meters

After 4 days, 48 square meters of the pond is expected to be covered by algae.

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la edad de Ana es la mitad de jose y dentro de 10 años seran dos tercios ..cual es la edad de jose​

Answers

La edad actual de José es de 30 años.

Para resolver este problema, primero debemos establecer ecuaciones basadas en la información proporcionada. Llamemos "x" a la edad actual de José y "y" a la edad actual de Ana. Según la primera condición, la edad de Ana es la mitad de la edad de José, por lo que podemos escribir la ecuación: y = (1/2)x.

La segunda condición nos dice que dentro de 10 años, sus edades serán dos tercios de sus edades actuales. Esto se puede expresar como: (x + 10) * (2/3) = y + 10.

Reemplazando el valor de y en la segunda ecuación con la primera ecuación, obtenemos: (x + 10) * (2/3) = (1/2)x + 10.

Resolviendo esta ecuación, podemos simplificarla y llegar a: 2(x + 10) = 3[(1/2)x + 10].

Al resolver la ecuación resultante, encontramos que x = 30.

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if p-value is 0.15 and alpha is 0.01 , what is the conclusion

Answers

Answer:

Step-by-step explanation:

When conducting hypothesis testing, the p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true.In this case, if the p-value is 0.15 and the significance level (alpha) is set at 0.01, we can interpret the results as follows:Since the p-value (0.15) is greater than the significance level (0.01), we fail to reject the null hypothesis. There is not enough evidence to conclude that the observed results are statistically significant at the 0.01 level. However, it's important to note that the decision of whether to reject or fail to reject the null hypothesis is based on the chosen significance level, and it's possible that the result may be considered statistically significant at a higher significance level.In summary, the conclusion would be that there is not enough evidence to reject the null hypothesis at the 0.01 significance level.

Question is in the attachment↓
pls give proper answer!

Answers

i) It has been proven that CD/GH​ =  AC/FG by Corresponding Sides of Similar Triangles

ii)  △DCB ∼△HGE by the AA criterion of similarity

iii) △DCA ∼△HGF by the AA criterion of similarity

How to solve similar triangles?

In △ABC and △FEG, we are told that they are similar and as such we can denote as:

△ABC ∼ △FEG

Thus, we can say that:

∠ACB = ∠EGF (Corresponding angles of similar triangles)

We are told that, CD and GH are bisectors of ∠ACB and ∠EGH respectively and as such we can say that:

∠ACB = 2∠ACD = 2∠BCD

∠EGF = 2∠FGH = 2∠HGE

Thus, by substitution, we can say that:

∠ACD = ∠FGH and ∠DCB = ∠HGE ...................(1)

Similarly:

∠A = ∠F and ∠B = ∠E ...............(2)

With respect to equations 1 and 2 we can establish that:

△ACD ∼ △FGH by the AA criterion of similarity

Similarly, △DCA ∼△HGF

Thus:

CD/GH​ =  AC/FG (Corresponding Sides of Similar Triangles)

Similarly, In △DCB and △HGE, we can also establish that

△DCB ∼△HGE by the AA criterion of similarity

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how many time can 457 go into 600

Answers

Answer:

Once

Step-by-step explanation:

Simple, once. If you do 600-457, you get an answer of 143, which you cannot subtract another 457 because it will turn negative.

Only once because if we were to do two then it would be greater than 600, so 457 can only go into 600 once.

explanation needed i do not undersatnd whats being calculated here

Answers

3.2 gallons per minute.

12.6/4 = 3.2

Write an equation to state the relationship:

I am thinking of three consecutive integers, Four times the third decreased by on-half, the second is 4

Answers

The expression that represent the relationship is 7 / 2 x - 15 / 2 = 4.

How to write an equation to represent a relationship?

An equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Therefore, let's find the equation that represents the relationship as follows:

Three consecutive numbers, four times the third decreased by on-half, the second is 4.

Therefore,

Let

x = first number

second number = x + 1

third number  = x + 2

Therefore,

4(x + 2)  - 1 / 2(x + 1) = 4

4x + 8 - 1 / 2x - 1 / 2 = 4

4x - 1 / 2x + 8 - 1 / 2 = 4

7 / 2 x - 15 / 2 = 4

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Simplify one over four n-1/2 divided by n over five minus one over 20 n

Answers

The simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

First, let's focus on simplifying the numerator and denominator separately:

Numerator:

The numerator is 1 divided by (4n - 1/2). We can simplify this by finding a common denominator. The denominator of 1/2 is 2, so we rewrite the expression as:

1/(4n - 12) = 1/(4n - 2/4) = 1/(4n - 2/4) = 1/((16n - 2)/4) = 4/(16n - 2)

Denominator:

The denominator is (n/5 - 1/20n). To simplify this, we find a common denominator. The denominator of 1/20n is 20n, so we rewrite the expression as:

n/5 - 1/20n = (20n^2)/(5 * 20n) - 1/(20n) = (20n^2 - 1)/(100n)

Now, let's simplify the entire expression by dividing the numerator by the denominator:

(1/(4n - 1/2)) ÷ (n/5 - 1/20n) = (4/(16n - 2)) ÷ ((20n^2 - 1)/(100n))

To divide by a fraction, we multiply by its reciprocal:

(4/(16n - 2)) ÷ ((20n^2 - 1)/(100n)) = (4/(16n - 2)) * (100n/(20n^2 - 1))

Next, we can simplify the numerator and denominator separately:

Numerator:

4 * 100n = 400n

Denominator:

(16n - 2) * (20n^2 - 1) = 320n^3 - 52n - 40n^2 + 2

Finally, we substitute the simplified numerator and denominator back into the expression:

(4/(16n - 2)) * (100n/(20n^2 - 1)) = (400n)/(320n^3 - 52n - 40n^2 + 2)

Thus, the simplified expression is (400n)/(320n^3 - 52n - 40n^2 + 2).

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Find standard deviation.

The table below gives the number of hours spent watching TV last week by a sample of 24 children.

8 5 2 4 4 9
9 7 3 5 2 4
4 7 10 5 1 8
9 8 3 3 8 7



Sample Standard Deviation:

Answers

The sample standard deviation for the given data set is approximately 2.77.

Let's calculate the sample standard deviation for the given data set:

Calculate the mean

Sum of all data points = 8 + 5 + 2 + 4 + 4 + 9 + 9 + 7 + 3 + 5 + 2 + 4 + 4 + 7 + 10 + 5 + 1 + 8 + 9 + 8 + 3 + 3 + 8 + 7 = 137

Mean = Sum of all data points / Number of data points = 137 / 24 = 5.71 (rounded to two decimal places)

Subtract the mean from each data point and square the result

(8 - 5.71)^2 = 2.4361

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(9 - 5.71)^2 = 10.3961

(9 - 5.71)^2 = 10.3961

(7 - 5.71)^2 = 1.6641

(3 - 5.71)^2 = 8.2561

(5 - 5.71)^2 = 0.5041

(2 - 5.71)^2 = 15.1361

(4 - 5.71)^2 = 2.9241

(4 - 5.71)^2 = 2.9241

(7 - 5.71)^2 = 1.6641

(10 - 5.71)^2 = 23.7761

(5 - 5.71)^2 = 0.5041

(1 - 5.71)^2 = 21.8441

(8 - 5.71)^2 = 2.4361

(9 - 5.71)^2 = 10.3961

(8 - 5.71)^2 = 2.4361

(3 - 5.71)^2 = 8.2561

(3 - 5.71)^2 = 8.2561

(8 - 5.71)^2 = 2.4361

(7 - 5.71)^2 = 1.6641

Find the sum of all the squared differences

Sum of squared differences = 2.4361 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 10.3961 + 10.3961 + 1.6641 + 8.2561 + 0.5041 + 15.1361 + 2.9241 + 2.9241 + 1.6641 + 23.7761 + 0.5041 + 21.8441 + 2.4361 + 10.3961 + 2.4361 + 8.2561 + 8.2561 + 2.4361 + 1.6641 = 174.07 (rounded to two decimal places)

Divide the sum by the number of data points minus 1

Variance = Sum of squared differences / (Number of data points - 1) = 174.07 / (24 - 1) = 7.67 (rounded to two decimal places)

Take the square root of the variance

Sample Standard Deviation = √(Variance) = √(7.67) = 2.77 (rounded to two decimal places)

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The surface of the triangle shown in the picture 15.1 is:
A) 6 B) 21 C) 14 D) 12
I'm not sure I've solved it right.​

Answers

Answer:

The coreect answer o

is 14

answer QUESTION DOWN BE;LOW IN MID EXPLANANTION TAHNKS

Answers

The solution to the composite functions from the graph are:

(f * g)(2) = 16

(f - g)(0) = -5

How to interpret the Function Graphs?

Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, then the function “ f of g of x”, is the composition of the two functions.

a) Using the concept of composite functions, we can say that:

(f * g)(x) = f(x) * g(x)

Thus:

(f * g)(2) = f(2) * g(2)

f(2) = 4

g(2) = 4

Thus:

(f * g)(2) = 4 * 4

(f * g)(2) = 16

b) Using the concept of composite functions, we can say that:

(f - g)(x) = f(x) - g(x)

Thus:

(f - g)(0) = f(0) - g(0)

f(0) = 1

g(0) = 6

Thus:

(f - g)(0) = 1 - 6

(f - g)(0) = -5

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Find the sum of the first 50 terms
t1=91 and t25=374

Answers

In an arithmetic sequence where t1=91 and t25=374, the sum of the first 50 terms is 18,425.

How to find sum of arithmetic sequence

Formula for the sum of an arithmetic sequence is given as

[tex]Sn = (n/2) x [2a1 + (n-1)d][/tex]

where

Sn is the sum of the first n terms,

a1 is the first term

d is the common difference and

n is the number of terms.

Given that t1 = 91 and t25 = 374.

To find d, we can use the formula for the nth term of an arithmetic sequence:

[tex]tn = a1 + (n-1)d[/tex]

Substitute n = 25, t25 = 374, and a1 = 91, we get:

374 = 91 + 24d

d = 11

Substitute d in the Sn formula

S₅₀ = (50/2) x [2(91) + (50-1)(11)]

S₅₀ = 25 x [182 + 49 x 11]

S₅₀= 25 x 737

S₅₀ = 18,425

Therefore, the sum of the first 50 terms is 18,425.

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