what causes standard deviations between people to be different, and what might it suggest about motor ability?

Answer:

do it yourself what do you do while teacher is teaching

Answer:

A: FG = ½GC

Step-by-step explanation:

Since AD, BC and CD are medians concurrent at G, it means G is the centroid.

Now, when median passes through the centroid, the centroid divides the median in the ratio of 2:1.

Also,that the median touches the side of the triangle at their midpoints.

Thus,by inspection, we can say that;

GD = ⅓AD

GC/FG = 2/1

Thus, GC = 2FG and FG = ½GC

BG = ⅔BE

Tbus,looking at the options given and what we have gotten in proof, we can say only FG = ½GC is correct.

"The revenue is always more than the cost," is the incorrect statement in relation to the profit business model. It is untrue that the revenue is always greater than the cost since the cost of manufacturing and providing the service must be considered as well.

The profit business model is a business plan that helps a company establish how much income they expect to generate from sales after all expenses are taken into account. It outlines the strategy for acquiring customers, establishing customer retention, developing the sales process, and setting prices that enable the business to make a profit.

It is important to consider that the company will only make a profit if the total revenue from sales is greater than the expenses. The cost of manufacturing and providing the service must be considered as well. The revenue from selling goods is reduced by the cost of producing those goods.

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Answer:

£3.15 (nearest pence)

Step-by-step explanation:

If the price of a coffee has increased by 7% then the final price of the coffee is:  100% + 7% = 107% of the original price.

Therefore, to find the original price of the coffee:

  original price ÷ 107 × 100

= 3.37 ÷ 107 × 100

= £3.15 (nearest pence)

Answer:

Step-by-step explanation:

Use the law of sines:

Find the missing angle:

Use the law of sines to find the length of b:

Synthetic division is a method used to divide a polynomial by a linear factor. It is a simplified form of polynomial long division and is particularly useful when dividing by linear factors of the form (x - c).

Here are the steps to perform synthetic division:

Step 1: Write down the polynomial in descending order of powers. If there are missing terms, insert a placeholder with a coefficient of zero for that term.

Step 2: Identify the linear factor of the form (x - c), where 'c' is the divisor. Set up the division problem by writing 'c' on the outside of a division symbol and the coefficients of the polynomial on the inside.

Step 3: Bring down the first coefficient of the polynomial (the coefficient of the highest power).

Step 4: Multiply the divisor 'c' by the value you brought down and write the result below the next coefficient of the polynomial.

Step 5: Add the result from the previous step to the next coefficient and write the sum below the line.

Step 6: Repeat steps 4 and 5 until you have gone through all the coefficients.

Step 7: The number in the bottom row, at the right end, is the remainder. The numbers in the other positions represent the coefficients of the quotient polynomial.

Let's go through an example to illustrate these steps:

Example: Divide the polynomial P(x) = 3x^3 - 4x^2 + 2x - 1 by (x - 2).

Step 1: P(x) = 3x^3 - 4x^2 + 2x - 1

Step 2: Divisor: (x - 2)

  --------------

  2  |  3   -4   2   -1

       |  

Step 3: Bring down the first coefficient: 3

       --------------

  2  |  3   -4   2   -1

       |   6

Step 4: Multiply the divisor (2) by the value brought down (3): 2 * 3 = 6

       --------------

  2  |  3   -4   2   -1

       |   6

Step 5: Add the result to the next coefficient: -4 + 6 = 2

        --------------

  2  |  3   -4   2   -1

       |   6    2

Step 6: Repeat steps 4 and 5 for the remaining coefficients:

        --------------

  2  |  3   -4   2   -1

       |   6    2   8

Step 7: The remainder is 8, and the coefficients of the quotient polynomial are 6, 2, and 8. Therefore, the quotient is 6x^2 + 2x + 8, and the remainder is 8.

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The size of angle x is 54 degrees.

Let O be the complete angle,

<O = 360

Angle between diagonals = 360/5 = 72 degrees.

All diagonals of regular pentagon are equal and their opposite angles are equal .

With angle center O it forms a triangle:

sum of angles = 180

x + x + 72 = 180

2x + 72 = 180

2x = 180 - 72

2x = 108

divide by 2 on both sides

2x/2 = 108/2

x = 108/2

x = 54 degrees.

Therefore the size of angle x is 54 degrees.

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Answer:

hmmm.

Step-by-step explanation:

times it by 12,000

like 12,000 being half a day

hahaha I dont know

Answer:

the answer is 1.88 using cosine =adj/hyp

Answer: 2584

Step-by-step explanation:

We can find N with 2584 and 4181.

4181 - 2584

= 1597

We can also check our answer by adding 1597 and 987

1597 + 987

= 2584

A sequence can be arithmetic, geometric or neither.

The value of N is 1597

The partial sequence is given as:

.... 987, N, 2584, 4181......

From the question, the current term is the sum of two previous terms.

This means that:

\(\mathbf{987 + N = 2584}\) and

\(\mathbf{N + 2584 = 4181}\)

Make N the subject in both equations

\(\mathbf{N = 2584 - 987}\)

and

\(\mathbf{N = 4181 - 2584 }\)

So, we have:

\(\mathbf{N = 1597}\)

and

\(\mathbf{N = 1597}\)

Hence, the value of N is 1597

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The expected loss per game is approximately -$0.31.

The terms we need to consider in this problem are: standard 52-card deck, face cards, and expected gain or loss.
To find the expected gain or loss per game, follow these steps:

1. Determine the probability of drawing a face card.
There are 12 face cards (Kings, Queens, and Jacks) in a standard 52-card deck. So the probability of drawing a face card is \(\frac{12}{52}\), which simplifies to \(\frac{3}{13}\).

2. Determine the probability of drawing a non-face card.
There are 40 non-face cards in the deck (52 cards - 12 face cards). So the probability of drawing a non-face card is \(\frac{40}{52}\), which simplifies to \(\frac{10}{13}\).

3. Calculate the expected gain or loss per game.
Expected gain or loss = (Probability of drawing a face card x gain from drawing a face card) + (Probability of drawing a non-face card x loss from drawing a non-face card)

4. Simplify the equation.
Expected gain or loss = \((\frac{3}{13} (2))  +  (\frac{10}{13} (-1))\)
Expected gain or loss = \(\frac{-4}{13}\)

Your expected loss per game is approximately -$0.31 (rounded to two decimal places).

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The weakest correlation is represented by the value of c. 0.11.

The weakest correlation is represented by the value that is closest to zero, as it indicates a weaker relationship between the variables. In this case, the answer is: c. 0.11

A correlation coefficient of 0.11 is closer to zero than the other options provided, indicating a weaker correlation compared to the rest. The negative values (-0.75 and -0.27) represent negative correlations, but their magnitudes are larger than 0.11, making them stronger correlations (although still considered weak in general). The positive value of 0.54 represents a moderate positive correlation.

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Answer:

The building has a height of 14 feet.

Step-by-step explanation:

At first we construct the geometrical diagram respective to the person-building system, whose result can be seen in the attached image. We proceed to describe each variable:

\(h\) - Height of the eye level above the ground, measured in feet.

\(H\) - Height of the building, measured in feet.

\(\alpha\) - Angle of elevation, measured in sexagesimal degrees.

\(\beta\) - Angle of depression, measured in sexagesimal degrees.

\(r\) - Distance between eye level and the bottom of the building, measured in feet.

\(r'\) - DIstance between eye level and the top of the building, measured in feet.

By using trigonometric ratios and functions we find that height of the building is represented by the following formula:

\(H = r\cdot \sin \beta + r'\cdot \sin \alpha\) (Eq. 1)

But \(r\) and \(r'\) can be obtained by these expressions:

\(r = \frac{h}{\sin \beta}\) (Eq. 2)

\(r' = \frac{r\cdot \cos \beta}{\cos \alpha}\) (Eq. 3)

By (Eq. 2) in (Eq. 3):

\(r'= \frac{h}{\cos \alpha \cdot \tan \beta}\) (Eq. 3b)

Now, we expand (Eq. 1) by (Eqs. 2, 3b):

\(H = h + h \cdot \tan \alpha \cdot \tan \beta\)

\(H = h\cdot (1+\tan \alpha \cdot \tan \beta)\) (Eq. 4)

If we know that \(h = 11\,ft\), \(\alpha = 22^{\circ}\) and \(\beta = 34^{\circ}\), the height of the building is:

\(H = (11\,ft)\cdot (1+\tan 22^{\circ}\cdot \tan 34^{\circ})\)

\(H = 13.998\,ft\)

The building has a height of 14 feet.

Answer:

3637, 3638, 3639?

Step-by-step explanation:

i just drew 4 boxes and then worked it out

Answer:

-2.6

Step-by-step explanation:

Answer:

ranalllldooo

Step-by-step explanation:

suiiiiiii

Then,

Answer:

a.

\(f(t) = 21000( {.918}^{t} )\)

b.

\(f(4) = 21000( {.918}^{4}) = 14913.86\)

New car prices to fall within is $18,300 - $41,900

Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.

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Percent : 60%
Decimal : 0.6
Fraction : 3/5

Answer:

fourth

Step-by-step explanation:

Angle X is the inscribed angle of the two arcs that measure 122 and 64 so

\(x = \frac{1}{2} (122 + 64)\)

\(x = \frac{1}{2} (186) = 93\)

A cyclic quadrilateral states that the opposite angles add up to 180

so

\(y = 18 0 - 83 = 97\)

The correct answer is the fourth option

For the sample (a) Mean is 30.8, the median is 31 and the standard deviation is 3.96, (b) the coefficient of skewness using Pearson's method is -0.151, and (c) the coefficient of skewness using the software method is 0.075.

Given values,

36, 26, 33, 28, 31

no. of values, n = 5

(a)

Mean, μ = Σx/n

= (36+26+33+28+31)/5 = 30.8

Now, Median, M = (n+1)/2th value

M = (5+1)/2 th = 3rd value

M = 31

Standard deviation(s) = \(\sqrt{ }\)Σ(x-μ)²/n-1

= \(\sqrt{ \frac{(36-30.8)^{2}+(26-30.8)^2+(33-30.8)^2+(28-30.8)^2+(31-308)^2 }{4} }\)

s = 3.96

(b) the coefficient of skewness using Pearson’s method

= 3(μ-M)/s = 3(30.8-31)/3.96 = -0.151

(c) the coefficient of skewness using the software method

= 1/s³(n-1)Σ(x-μ)³ = \(\frac{(36-30.8)^{3}+(26-30.8)^3+(33-30.8)^3+(28-30.8)^3+(31-30.8)^3 }{4(3.96)^3}\)

= 0.075

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This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

What is the standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a wider range.

Standard deviation determines how far numbers deviate from the mean. The Standard deviation of the two sets will be the same if the numbers from the respective means are placed in the same order.

This is what 10, 15, and 20 will be on a number line

10_ _ _ _15 _ _ _ _20

(15 is the mean and 10 and 20 are 5 steps away from the mean)

i) Z - X = 10

This is what Z and X will be on the number line

X _ _ _ _ _ Z

ii) Z - Y = 5

This is what Z and Y will on the number line.

Y_ _ _ _ _ Z

Together, their relative placement on the number line:

X _ _ _ _ _  Y  _ _ _ _ _  Z

This matches the placement of 10, 15, and 20 and hence the standard deviation will be the same in the two cases.

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The rate of change for the line that goes through the ordered pairs (2.5, -6) and (1, 9) is -10.

The rate of change (or slope) of a line is a measure of how steep the line is and the direction it is going.

Given the ordered pairs (2.5, -6) and (1, 9), we can use the slope formula to find the rate of change for the line that goes through these points:

slope = (y₂ - y₁)/(x₂ -x₁ )

slope = (9 - (-6)) / (1 - 2.5)

slope = 15 / -1.5

slope = -10

This means that for every 1 unit change in the x-coordinate, the y-coordinate changes by -10 units.

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Matrix multiplication satisfies the associativity rule A. We have (PQ)R = P(QR).

B. We have (P+Q)R = PR + QR.

C. We have PQ ≠ QP in general.

D. We have P I = IP = P.

E. 1/51 [-29 12 17; 10 -3 -2; 25 -10 -7]

(a) We have:

(PQ)R = ([5 1; -2 4] [0 -4; 7 9]) [3 8; 8 -6]

= [(-14) 44; (28) (-20)] [3 8; 8 -6]

= [(-14)(3) + 44(8) (-14)(8) + 44(-6); (28)(3) + (-20)(8) (28)(8) + (-20)(-6)]

= [244 112; 44 256]

P(QR) = [5 1; -2 4] ([0 7; -4 9] [3 8; 8 -6])

= [5 1; -2 4] [56 -65; 20 -28]

= [5(56) + 1(20) 5(-65) + 1(-28); -2(56) + 4(20) -2(-65) + 4(-28)]

= [300 -355; 88 -134]

Thus, we have (PQ)R = P(QR).

(b) We have:

(P+Q)R = ([5 1; -2 4] + [0 -4; 7 9]) [3 8; 8 -6]

= [5 -3; 5 13] [3 8; 8 -6]

= [5(3) + (-3)(8) 5(8) + (-3)(-6); 5(3) + 13(8) 5(8) + 13(-6)]

= [-19 46; 109 22]

PR + QR = [5 1; -2 4] [3 8; 8 -6] + [0 -4; 7 9] [3 8; 8 -6]

= [5(3) + 1(8) (-2)(8) + 4(-6); (-4)(3) + 9(8) (7)(3) + 9(-6)]

= [7 -28; 68 15]

Thus, we have (P+Q)R = PR + QR.

(c) We have:

PQ = [5 1; -2 4] [0 -4; 7 9]

= [5(0) + 1(7) 5(-4) + 1(9); (-2)(0) + 4(7) (-2)(-4) + 4(9)]

= [7 -11; 28 34]

QP = [0 -4; 7 9] [5 1; -2 4]

= [0(5) + (-4)(-2) 0(1) + (-4)(4); 7(5) + 9(-2) 7(1) + 9(4)]

= [8 -16; 29 43]

Thus, we have PQ ≠ QP in general.

(d) The 2×2 identity matrix is given by:

I = [1 0; 0 1]

For any square matrix P, we have:

P I = [P11 P12; P21 P22] [1 0; 0 1]

= [P11(1) + P12(0) P11(0) + P12(1); P21(1) + P22(0) P21(0) + P22(1)]

= [P11 P12; P21 P22] = P

Similarly, we have:

IP = [1 0; 0 1] [P11 P12; P21 P22]

= [1(P11) + 0(P21) 1(P12) + 0(P22); 0(P11) + 1(P21) 0(P12) + 1(P22)]

= [P11 P12; P21 P22] = P

Thus, we have P I = IP = P.

(e) The system of linear equations can be written in matrix form as:

[1 1 1; 0 2 5; 2 5 -1] [x; y; z] = [6; -4; 27]

We can solve for [x; y; z] using matrix inversion:

[1 1 1; 0 2 5; 2 5 -1]⁻¹ = 1/51 [-29 12 17; 10 -3 -2; 25 -10 -7]

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The utility function u(x) = 0.25**(x/200) is consistent with Pablo's preferences.

To determine which utility function, represented by u(x), is consistent with Pablo's preferences, we need to compare the utility values for different prospects.

Pablo's certain equivalent for a deal with a 0.8 chance at $500 and a 0.2 chance at $100 is $300. We can calculate the expected value of this prospect:

Expected value = (0.8 * $500) + (0.2 * $100) = $400 + $20 = $420

Now let's evaluate the utility values for the given utility functions and compare them to $300 and $420.

a) u(x) = 10 - 10x^4 - x/200

If we substitute x = $420 into this utility function, we get:

u($420) = 10 - 10($420)^4 - $420/200 ≈ -1.06 x 10^18

b) u(x) = 1 - 0.25 - x/200

If we substitute x = $420 into this utility function, we get:

u($420) = 1 - 0.25 - $420/200 = 1 - 0.25 - 2.1 ≈ -1.35

c) u(x) = 5 - 2x^4 + x/300

If we substitute x = $420 into this utility function, e get:

u($420) = 5 - 2($420)^4 + $420/300 ≈ -1.59 x 10^16

d) u(x) = 0.25**(x/200)

If we substitute x = $420 into this utility function, we get:

u($420) = 0.25**(420/200) ≈ 0.063

Comparing the utility values to Pablo's certain equivalent ($300) and the expected value ($420), we find that option d) u(x) = 0.25**(x/200) is consistent with Pablo's preferences, as it yields a utility value (0.063) closer to the expected value than the others.

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(a) The 92nd percentile of the number of calories is 524.3.

(b) The 30th percentile of the number of calories is 466.4.

(c) The third quartile of the number of calories is 502.1.

To find percentiles in a normally distributed population, we use the standard normal distribution and the z-score formula:

z = (x - μ) / σ

where;

To find the 92nd percentile of the number of calories:

We want to find the value x such that 92% of the servings have fewer calories than x.

This means that we need to find the z-score such that the area to the left of z is 0.92.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.92 is approximately 1.41.

Then, we use the z-score formula to solve for x:

1.41 = (x - 482) / 30

x - 482 = 42.3

x = 524.3

To find the 30th percentile of the number of calories:

We want to find the value x such that 30% of the servings have fewer calories than x.

This means that we need to find the z-score such that the area to the left of z is 0.30.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.30 is approximately -0.52.

Then, we use the z-score formula to solve for x:

-0.52 = (x - 482) / 30

x - 482 = -15.6

x = 466.4

To find the third quartile of the number of calories:

The third quartile, denoted Q3, is the value such that 75% of the servings have fewer calories than Q3.

This means that we need to find the z-score such that the area to the left of z is 0.75.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to an area of 0.75 is approximately 0.67.

Then, we use the z-score formula to solve for x:

0.67 = (x - 482) / 30

x - 482 = 20.1

x = 502.1

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False. The expected cell frequency in statistical analysis, specifically in the context of contingency tables and chi-square tests, is not based on the researcher's opinion. Instead, it is determined through mathematical calculations and statistical assumptions.

In contingency tables, the expected cell frequency refers to the expected number of observations that would fall into a particular cell if the null hypothesis of independence is true (i.e., if there is no relationship between the variables being studied). The expected cell frequency is calculated based on the marginal totals (row totals and column totals) and the overall sample size.

The expected cell frequency is computed using statistical formulas and is not influenced by the researcher's opinion or subjective judgment. It is a crucial component in determining whether the observed frequencies in the cells significantly deviate from what would be expected under the null hypothesis.

By comparing the observed cell frequencies with the expected cell frequencies, statistical tests like the chi-square test can assess the association or independence between categorical variables in a data set.

Thus, the statement "the expected cell frequency is based on the researcher's opinion" is false. The expected cell frequency is derived through statistical calculations and is not subject to the researcher's subjective input.

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