a. The number 86,362,575 rounded to the nearest hundred is

Answer:

(a). Σx= 108, Σx^2 = 4984, Σy^2 = 2,157.

(b). 10.8, 0.1.

(C) and (d) => check explanation.

Step-by-step explanation:

To Calculate for Σx we will have to add all the values for x that is the summation of x-values.

Σx = 11 + 0 + 36 + 22 + 34 + 24 + 25 + -11 + -11 + -22 = 108.

Σx^2 = 11 × 11 + 0 × 0 + 36 × 36 + 22 × 22 + 34 × 34 + 24 ×24 + 25 × 25 + -11 × -11 + -11 × -11 + -22 × -22 = 4984.

Σy^2 = 9× 9 + -3 × -3 + 28 ×28 + 14 × 14 + 23 × 23 + 16 × 16 + 14× 14 + -3 ×-3 + -4 × -4 + -9 × -9= 2,157.

(b). Sample mean for x = 108/10 = 10.8.

Variance for x:

11 - 10.8 = 0.3

0 - 10.8 = -10.8

36 - 10.8 =25.2.

22 - 10.8=11.2.

34 - 10.8 = 23.2

24 -10.8 = 13.2.

25 - 10.8= 14.2

-11 - 10.8 = -21.8.

-11 - 10.8 = - 21.8

-22 -10.8 = -32.8.

Total=0.1

Standard deviation for x = √ s^2 = 0.3162

This can be done for y too

(c). 75% Chebyshev interval around the mean for x values = 10.8 + 2 (0.3162); 10.8 - 2(0.3162).

=> (11.4324, 10.1676).

(d). The coefficient of variation= (0.3162)/10.8 × 100 = 2.92%.

The sample means for annual returns of the Vanguard Total Stock Index (x) and Vanguard Balanced Index (y) have been computed as 10.8 and 8.5 respectively. The inclusion of bonds in a portfolio can lower overall return slightly while also reducing the risk.

The student's task revolves around the subject of statistical analysis, here applied to investment portfolio management. Their goal is to compute the sample mean (average) for two variables - x and y - which each represent annual returns for certain types of portfolios.

Portfolio x represents a 100% stock holding in the Vanguard Total Stock Index, while y represents a 60% stock and 40% bond holding in the Vanguard Balanced Index. Such portfolios carry varying degrees of risk, with all-stock portfolios generally accepted to be more volatile, yet offering higher potential returns than mixed portfolios.

In order to calculate the sample means for x and y, you simply add together all the annual returns for each, then divide by the number of years.

For x: (11 + 0 + 36 + 22 + 34 + 24 + 25 - 11 - 11 - 22)/10 = 10.8 (rounded to the nearest tenth)

For y: (9 - 3 + 28 + 14 + 23 + 16 + 14 - 3 - 4 - 9)/10 = 8.5 (rounded to the nearest tenth)

As seen, stocks did yield a higher average return over the period in consideration, though the range of returns was also much wider. By adding bonds to the portfolio (shown by y), the overall return reduced slightly, but so did the risk (variability) of returns.

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To calculate the surface area, the formula is the sum of the areas of all faces in a shape.

Back Prism:

1 base: 8 by 8.

4 lateral faces: 8 by 2.

One shared base: 64 – 32 = 32 square units.

Front Prism:

1 base: 8 by 4.

2 lateral faces: 8 by 2.

2 lateral faces: 2 by 4.

Therefore, one shared base: an area covered by another prism.

Total surface area: 240 square units.

A surface area is the outer part of the uppermost layer of something. This is known in maths as the amount of space covering the outside of a three-dimensional shape.

Hence, we can see that to calculate, the formula is the sum of the areas of all faces in a shape which sums up to 240 square units.

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Final answer:

Davide's age is determined by first calculating the total age of the four individuals and then subtracting the total age of the remaining three. With the given averages, Davide is found to be 10 years old.

Explanation:

The question asks us to find the age of Davide given that the average age of Aldo, Bruno, Carlo, and Davide is 16 years, but without Davide, the average age of the remaining three is 18 years.

First, we calculate the total age of all four by multiplying the average age by the number of people: 16 years × 4 = 64 years.

Next, we calculate the total age of Aldo, Bruno, and Carlo by multiplying the new average age by three: 18 years × 3 = 54 years.

Now, we can determine Davide's age by subtracting the total age of the three from the total age of all four: 64 years - 54 years = 10 years.

Therefore, Davide is 10 years old.

Answer:

1 1/2 cups

Step-by-step explanation:

2/4 = 1/2

(1/2) cups * 3 =  1.5 cups

Answer:

1 1/2 or 3/2 cups of flour

Step-by-step explanation:

2/4 + 2/4 + 2/4= 6/4

to simplify:

divide 6/4 by 2/2 to get 3/2

3/2 =1 1/2

Answer:

a) 256 m^2

Step-by-step explanation:

Area of a Trapezoid = (a+b)/2×h

*where a and b are the "top" and "bottom" lengths and h is the height

So: (13+19)/2×16= 32/2×16= 16×16 = 256 m^2

Answer:

if its length then its cm

if its area then its cm²

if its volume then its cm³

Step-by-step explanation:

Answer:

All of them

Step-by-step explanation:

Answer:

A,B,C,D,E,F

Step-by-step explanation:

to sum it up all of them !

Answer:

The weight of pears is 3.08 kg

Step-by-step explanation:

A farmer sells 7.7 kilograms of apples and pears.

3/5 of this weight is apples.

This means that the weight of apples is:

3/5 of 7.7

=> [tex]\frac{3}{5} * 7.7 = 4.62kg[/tex]

The weight of apples is 4.62 kg.

The weight of pears will therefore be:

[tex]7.7 - 4.62 = 3.08 kg[/tex]

The weight of pears is 3.08 kg.

Answer:

6

Step-by-step explanation:

Answer:

100-x represents the distance that Serena hit with her 9-iron. 2(100-x) represents the distance she can hit using her driver.

When the distance is given for the 9-iron, use the distributive property to find the simplified equation, so it will be much easier to solve after you are given the information on the 9-iron. Unsolvable without 9-iron distance.

Step-by-step explanation:

Hence, it is unsolvable without [tex]9[/tex] iron distance.

What is the yards?

A yard is a unit of length in both US Customary and British Imperial Systems of Measurement.

It is equivalent to [tex]3[/tex] feet or [tex]36[/tex] inches. Its symbol is yd. It is often used to measure the length of medium-sized objects.

Here, [tex]100-x[/tex] represents the distance that Serena hit with her [tex]9[/tex]-iron, and [tex]2(100-x)[/tex]  represents the distance she can hit using her driver.

Now using the distributive property, it will be easier to solve about the information of nine-iron.

Hence, it is unsolvable without [tex]9[/tex] iron distance.

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Answer:

-2097152

Step-by-step explanation:

(-8)(-8)(-8)(-8)(-8)(-8)(-8) =

-2097152

Answer: -2097152

Step-by-step explanation:

(-8)(-8)(-8)(-8)(-8)(-8)(-8)=

(-8)^7

=-2097152

Answer:

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis: [tex]\mu =10.6[/tex]

Alternative hypothesis: [tex]\mu \neq 10.6[/tex]

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

Step-by-step explanation:

For this case we are trying to proof if the mean number of sick days this year is different from the mean number of sick days last year (10.6 days). And that would represent the alternative hypothesis. And the complement would represent the null hypothesis.

Then the system of hypothesis are:

Null hypothesis: [tex]\mu =10.6[/tex]

Alternative hypothesis: [tex]\mu \neq 10.6[/tex]

And the best option would be:

H0:μ=10.6Ha:μ≠10.6 B

And the data from the sample is:

[tex]\bar X = 12.9[/tex] represent the sample mean

[tex]n =40[/tex] the sample size

Answer:

See explaination

Step-by-step explanation:

Please kindly check attachment for the detailed step by step solution of the given problem.

To find the closest point to y in subspace W, see the projection of y onto W. Solve the appropriate equations to find the scalars for v1 and v2. The sum of these scaled vectors will yield the closest point.

The closest point to y in the subspace W spanned by v1 and v2 can be determined using the projection formulas. First, find a and b such that a*v1 + b*v2 equals the projection of y onto W. To do this, set up the equations a*(v1 . v1) + b*(v1 . v2) = y . v1 and a*(v1 . v2) + b*(v2 . v2) = y . v2. Solve these equations for a and b. The solution will give you the scalars for v1 and v2, respectively. The vector a*v1 + b*v2 will be the closest point in W to y.

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Answer:

a) 1,518,000

b) 2,284,880

c) 60,720

Step-by-step explanation:

a) a. if the first letter must be Upper C comma Upper X comma Upper T comma or Upper M and no letter may be​ repeated?

We draw 5 boxes, and based on that we will see the total possible cases. There are 26 alphabets

The first box should have C or X or T or M .No letter may be repeated.

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   25 alphabets   24 alphabets   23 alphabets   22 alphabets

Therefore; total possible call letters = 5 × 25 × 24 × 23 × 22 = 1,518,000

b)

The first box should have C or X or T or M Repeats as allowed

Any                    Any             Any                 Any                    Any

5 alphabets    of the            of the              of the                 of the

C,X , T , M      remaining     remaining       remaining          remaining

                   26 alphabets   26 alphabets   26 alphabets   26 alphabets

Therefore Total possible call letters = 5 × 26 × 26 × 26 × 26 = 2,284,880

c)   The first box should have   C,X , T , M  and end with S

So the last place if fixed, and we now have 25 alphabets. The first box can go in 5 ways. The next box then will have only 24 letters to choose from, as the first box has taken a letter and the last box already has S in it. Repetition not allowed

Any                    Any             Any                 Any                       S

5 alphabets    of the            of the              of the                  is fixed

C,X , T , M      remaining     remaining       remaining           here

                   24 alphabets   23 alphabets   22 alphabets  

Therefore Total possible call letters = 5 × 24 × 23 × 22  × 1 =  60,720

a. 30,240 different call letters can be made if the first letter must be C, X, T, or M and no letter may be repeated. b. 11,881,376 different call letters can be made if repeats are allowed. c. 22,464 different call letters can be made if the call letters start with C, X, T, or M, have no repeats, and end with S.

a. If the first letter must be C, X, T, or M, and no letter may be repeated, the options for the first letter are 4. For the remaining 4 positions, we can choose from 25 letters (all except the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 4 * 25 * 24 * 23 * 22 = 30,240.

b. If repeats are allowed, including the first letter being C, X, T, or M, we still have 26 options for each position (including the possibility of repeating the first letter chosen). Therefore, the total number of different 5-letter radio station call letters is 26 * 26 * 26 * 26 * 26 = 26^5 = 11,881,376.

c. To have no repeats and end with the letter S, we have 24 options for the first position (all letters except C, X, T, or M) and 1 option for the last position (the letter S). For the remaining 3 positions, we can choose from 24 letters (all except the first and last position chosen). Therefore, the total number of different 5-letter radio station call letters starting with C, X, T, or M and ending with S is 4 * 24 * 24 * 24 * 1 = 22,464.

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Answer: People will pay about $5 for a ticket if 50 are sold.

Step-by-step explanation:

What we can deduce from this graph is the more expensive the tickets are, the less tickets are sold.

So far, the greatest number of tickets sold are 40 with a price of around $10.

Now, if people were to sell 50 tickets, following with the graph, it

would mean that the price would have to be less than 10.

Only one of the options is less than 10, and that is 5, so therefore, the answer is 5.

Answer: 21

Step-by-step explanation: If you lost the numbers in order from creates to least, and cross the least and the greatest the number in the middle or median is 21

Answer:

D

Step-by-step explanation:

There is more than one way to solve this; the easiest way is to plug in some numbers for x. We can see the roots are (3,0) and (7,0) and the lowest point is (5,0). So when we plug in 3 or 7, we should get zero.

B: (3-3)(3-7)=0

D: 3(3-3)(3-7)=0

So we have two possible solutions, So to check, let's find a point where we can easily find the y value.

When x is equal to 4,5, or 6, there is an integer value for y. so let's plugin 5:

(5-3)(5-7)=-4

We can see when x is five, y has to be -12, so that is not the answer, thus d is the final answer.

Answer: 45

Explanation: Remember that dividing by a fraction is the same thing as multiplying by the reciprocal of that fraction or that fraction flipped.

Also, think of the 15 in this problem as 15/1.

So we can rewrite 15/1 ÷ 1/3 as 15/1 · 3/1.

Multiplying across the numerators and the denominators,

we find that our answer is 45/1 or just 45.

15 divided by 1/3 is equal to 45.

To divide 15 by 1/3, we can interpret it as finding how many groups of 1/3 can be made from 15.

To begin, we can convert the division of 15 by 1/3 into a multiplication problem by taking the reciprocal of 1/3, which is 3/1 or simply 3.

So, we have:

15 ÷ (1/3) = 15 x 3

Multiplying 15 by 3, we get:

15 x 3 = 45

Therefore, 15 divided by 1/3 is equal to 45.

In other words, 15 can be divided into 45 equal parts of size 1/3. Each of these parts represents the quotient when dividing 15 by 1/3.

When we multiply 1/3 by 45, we get 15. This confirms that 15 divided by 1/3 is indeed equal to 45.

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Answer:

(See explanation for further details)

Step-by-step explanation:

A. [tex]x^{3} + 3\cdot x^{2} - 2\cdot x + 7[/tex] : V. Four terms.

B. [tex]3\cdot a \cdot b^{6}[/tex] : I . 9th Degree Monomial (Instead, 7th Degree Monomial)

C. [tex]3\cdot x^{4} - 9 \cdot x^{3} + 5\cdot x^{8}[/tex] : VII - Equivalent to [tex]5\cdot x^{8} + 3\cdot x^{4} - 9 \cdot x^{3}[/tex]

D. [tex]7\cdot a^{3}\cdot b^{2} + 18\cdot a \cdot b^{2}\cdot c - 9\cdot a^{3}[/tex] : III - 7th degree polynomial.

E. [tex]2\cdot x^{5} - 9\cdot x^{3} + 8\cdot x[/tex] : VI - 5th degree polynomial.

F. [tex]4\cdot x^{8} - 7\cdot x^{2} + 9[/tex] : IV - Leading coefficient of 4.

G. [tex]x^{2} - 7[/tex] : II - Constant term of -7.

The question is missing informations. The complete question is:

Find the (a) mean, (b) median, (c) mode, and (d) midrange for the given sample data. An experiment was conducted to determine whether a deficiency of carbon dioxide in the soil affects the phenotype of peas. Listed bellow are the phenotype codes where 1 = smooth-yellow, 2 = smooth-green, 3 = wrinkled-yellow and 4 = wrinkled-green. Do these results make sense?

4 3 3 1 3 4 1 1 1 4 2 3 1 1

(a) The mean phenotype code is _____

(b) The median phenotype code is _____

(c) Select the correct choice bellow and fill in any answer boxes within your choice

(A) The mode phenotype code is ___

(B) There is no mode

(d) The midrange of the phenotype code is ___

Do the measures of center make sense?

A. Only the mode makes sense since the data is nominal.

B. All the measures of center make sense since the data is numerical

C. Only the mean, median and midrange make sense since the data is nominal

D. Only the mean, median and midrange make sense since the data is numerical.

Answer: (a) mean = 2.285

(b) median = 2.5

(c) A) The mode phenotype code is 1

(d) midrange = 2.5 and A. Only the mode makes sense since the data is nominal.

Step-by-step explanation: Mean and Median are the average value of a data set, however, median is the value in the middle of the set while mean is the average value a data set must be if all the values were the same.

(a) To calculate mean:

mean = [tex]\frac{4+3+3+1+3+4+1+1+1+4+2+3+1+1}{14}[/tex]

mean = 2.285

(b) To find median: The set has an even number of elements (14), so, in this case, to determine the middle term:

median = [tex]\frac{7th + 8th}{2}[/tex]

median = [tex]\frac{2+3}{2}[/tex]

median = 2.5

(c) Mode is the value which has the highest frequency. For this data set, mode = 1, since the number 1 appears 6 times.

Mode = 1

(d) Midrange is the average of the smallest and largest on the set.

midrange = [tex]\frac{1+4}{2}[/tex]

midrange = 2.5

Nominal variable is a type of variable used to name, categorize or label attributes that are being measured. Mode is the most common used measure of central tendency and with it, it is possible to determine if the set is unimodal (one mode) or multimodal (two or more modes). In conclusion, mode makes sense because data is nominal.

The mean, median, and midrange of the given phenotype codes are all 2.5.

1. Mean

The mean is the average of the data set. We sum all the phenotype codes and divide by the number of observations.

2. Median

The median is the middle value of an ordered data set. For an even number of observations, it's the average of the two middle values.

3. Mode

The mode is the value that occurs most frequently. Here, each code appears only once, so there is no mode.

4. Midrange

The midrange is the average of the highest and lowest values in the data set.

Since each code represents a distinct phenotype, the measures provide a way to summarize the data set but don't hold biological significance independently. They mainly help to understand the distribution of phenotype observations numerically.

Answer:

x=8,3

Step-by-step explanation:

Move  

24  to the left side of the equation by adding it to both sides.

x 2−11x+24=0

Factor x2−1 1x+ 24

using the AC method.

(x−8)(x−3)=0

If any individual factor on the left side of the equation is equal to  

0 , the entire expression will be equal to 0

x−8=0   x−3=0

Set the first factor equal to  

0  and solve.

x =8

Set the next factor equal to  0  and solve.

x  = 3

The final solution is all the values that make  

( x− 8)(x−3)=0 true.

x =8,3

Solving:

Move constants to the left

[tex]x^2-11x=24\\[/tex]

write as a difference

[tex]x^2-11x+24=0[/tex]

factor

[tex]x^2-3x-8x-+24=0[/tex]

factor again

[tex]x(x-3)-8(x-3)=0[/tex]

separate

[tex](x-3)(x-8)=0[/tex]

solve all possible equations.

[tex]x-3=0\\x-8=0[/tex]

therefore, our answers are:

[tex]x=3,x=8[/tex]

Answer:63.6 units

Step-by-step explanation:

Theta=90°

Radius =9

area of sector=(theta)/360 x π x r x r

area of sector=90/360 x 3.14 x 9 x 9

area of sector=(90x3.14x9x9)➗360

area of sector=22890.6 ➗ 360

area of sector=63.535

area of sector=63.6 approximately

Answer:

It's 63.62

Step-by-step explanation:

Answer:11.5

Step-by-step explanation:

distance=6 2/5 + 2 3/4 + 2 1/3

d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3

d=32/5 + 11/4 + 7/3

d=(12x32+15x11+20x7) ➗ 60

d=(384+165+140) ➗ 60

d=689 ➗ 60

d=11.5

The total distance  did she run is 11.5 miles.

It is required to find the total distance.

The distance of an object can be defined as the complete path travelled by an object .Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion.

Given:

Melissa ran 6 2/5 miles north ,2 3/4 west and 2 1/3 south.

According to given question we have,

Total distance=6 2/5 + 2 3/4 + 2 1/3

d=(5x6+2)/5 + (4x2+3)/4 + (3x2+1)/3

d=32/5 + 11/4 + 7/3

d=(12x32+15x11+20x7) /60

d=(384+165+140) / 60

d=689 / 60

d=11.5 miles.

Therefore, the total distance  did she run is 11.5 miles.

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Answer:

In order for the statement to be true, the value of x has to be 19.

Step-by-step explanation:

3(x - 3) - 16 = 2(x - 8) + 10

3x - 9 - 16 = 2x - 16 + 10

3x - 25 = 2x - 6

x - 25 = - 6

x = 19

Answer:

b) 19

Step-by-step explanation:

Let's solve the problem,

→ 3(x - 3) - 16 = 2(x - 8) + 10

→ 3x - 9 - 16 = 2x - 16 + 10

→ 3x - 25 = 2x - 6

→ 3x - 2x = -6 + 25

→ [ x = 19 ]

Hence, option (b) is correct.

First we have to figure out how much 3 bags cost using the total cost of $8.25

That means. we would do 8.25/3 and 8.25 divide by 3 equals 2.75.

Now we know that each bag costs approximately $2.75

All we have to do now is multiply 2.75 by 4 to get the cost for the total of 4  bags.

4 times 2.75 is exactly 11 dollars, if might change if theres tax.

But, the answer would be 4 bags costs $11.

Answer:

∠AGB and ∠EGD are vertical angles.

∠DGC and ∠CGB are supplementary angles.

m∠EGD = 30

m∠AGF = 50

m∠EGF = 100

Step-by-step explanation:

Answer:

veryical

Step-by-step explanation:

Answer:

The weight of a box is 10 kg.

Step-by-step explanation:

Weight of each book is 2 kg

So, the weight of 3 books is 6 kg.

Weight of a container is 4 kg

3 books and one container is in a box. We need to find the weight of the box.

It is equal to the sum of weights of 3 books and one container. So,

Total weight = 6 kg + 4 kg

W = 10 kg

So, the weight of a box is 10 kg.

Answer:

y = (-5/3)x + 3

Step-by-step explanation:

slope intercept form: y = mx + b

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other.

First, add 9 to both sides:

3y - 9 (+9) = -5x (+9)

3y = -5x + 9

Next, divide 3 from both sides:

(3y)/3 = (-5x + 9)/3

y = (-5/3)x + 3

y = (-5/3)x + 3 is your answer.

~

Answer: 8 senior tickets, 12 normal tickets.

Step-by-step explanation:

You can find the answer to this by creating two equations: one for the amount of tickets sold and the other for how much money was collected.

I will represent the variables as A for normal tickets and C for senior tickets.

[tex]A + C = 20\\12A + 6C = 192[/tex]

To solve this, you can solve for one of the variables. I will solve for A in the first equation:

[tex]A = 20-C\\12A + 6C = 192[/tex]

Then, you can substitute the new value of A in the second equation:

[tex]12(20-C) + 6C = 192\\240-12C+6C=192\\240-6C=192\\-6C=-48\\C=8[/tex]

Knowing that there were 8 senior tickets sold and 20 tickets sold total, we know that there were 12 normal tickets sold.

Answer:

The painting area is approximately 28980 years old.

Step-by-step explanation:

The model for the amount of carbon-14 after t years is given by:

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

In which A(0) is the original amount.

The paint contained 3% of the original carbon-14.

This means that [tex]A(t) = 0.03A(0)[/tex]. This means that we have to find t.

[tex]A(t) = A(0)e^{-0.000121t}[/tex]

[tex]0.03A(0) = A(0)e^{-0.000121t}[/tex]

[tex]e^{-0.000121t} = 0.03[/tex]

[tex]\ln{e^{-0.000121t}} = \ln{0.03}[/tex]

[tex]-0.000121t = \ln{0.03}[/tex]

[tex]t = -\frac{\ln{0.03}}{0.000121}[/tex]

[tex]t = 28980[/tex]

The painting area is approximately 28980 years old.