Study the number line. Then choose the letters to complete the statement.

The fraction 1/3 is labeled ________ and the fraction 5/3 is labeled _________

Answer:

The 99% confidence interval for the mean germination time is (12.3, 19.3).

Step-by-step explanation:

The question is incomplete:

Recorded here are the germination times (in days) for ten randomly  chosen seeds of a new type of bean: 18, 12, 20, 17, 14, 15, 13, 11, 21, 17. Assume that the population germination time is normally distributed. Find the 99% confidence interval for the mean germination time.

We start calculating the sample mean M and standard deviation s:

\(M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(18+12+20+17+14+15+13+11+21+17)\\\\\\M=\dfrac{158}{10}\\\\\\M=15.8\\\\\\\)

\(s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((18-15.8)^2+(12-15.8)^2+(20-15.8)^2+. . . +(17-15.8)^2)}\\\\\\s=\sqrt{\dfrac{101.6}{9}}\\\\\\s=\sqrt{11.3}=3.4\\\\\\\)

We have to calculate a 99% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=15.8.

The sample size is N=10.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

\(s_M=\dfrac{s}{\sqrt{N}}=\dfrac{3.4}{\sqrt{10}}=\dfrac{3.4}{3.162}=1.075\)

The degrees of freedom for this sample size are:

df=n-1=10-1=9

The t-value for a 99% confidence interval and 9 degrees of freedom is t=3.25.

The margin of error (MOE) can be calculated as:

\(MOE=t\cdot s_M=3.25 \cdot 1.075=3.49\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=M-t \cdot s_M = 15.8-3.49=12.3\\\\UL=M+t \cdot s_M = 15.8+3.49=19.3\)

The 99% confidence interval for the mean germination time is (12.3, 19.3).

The regression line is yˆ = 4 + 1.891x , the coefficient of determination of two variables or the fraction of the variation in y that can be explained by the variation in the values of x is 0.51..

Here the fitted regression equation of y on x is

yˆ = 4 + 1.891x ---(*)

where, x --> Independent variable

yˆ --> predicted value of the dependent variable

Now, b₁ = slope cofficient = 1.891 ~ 1.91

(estimated from least squares method)

We have given that,

Standard deviations for X = 1.34 = sₓ say

Standard deviations for Y = 3.6 = sᵧ say

we know, b₁ = r₀( sₓ/sᵧ ) where ro is corr(X,Y)

=> 1.91 = r₀ (3.6/1.34)

=> 1.91×1.34/ 3.6 = r₀

=> r₀ = 0.71944

Defining, R² = cofficient of determination of two variables = Proportion of variation in Y , explained by the variation in the value of X, through the regression model.

= (r₀)² = (0.71944)² = 0.505442

R² = 0.505442 ~ 0.51 (in two decimals)

Hence, the cofficient of determination is 0.51..

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Complete question:

Using your favorite statistics software package, you generate a scatter plot which displays a linear form. You find a regression equation and the standard deviation for both variables. The standard deviation for x is 1.34 , and the standard deviation for y is 3.6 . The regression equation is reported as y = 4 + 1.891x . What fraction of the variation in y can be explained by the variation in the values of x? (Enter your answer as a decimal between 1 and 2.)

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

For brand A,

Mean, x1 = (34.36 + 31.26 + 37.36 + 28.52 + 33.14 + 32.74 + 34.34 + 34.33 + 34.95)/9 = 33.44

standard deviation, s1 = √(summation(x - mean)²/n

Summation(x - mean)² = (34.36 - 33.44)^2 + (31.26 - 33.44)^2 + (37.36 - 33.44)^2 + (28.52 - 33.44)^2 + (33.14 - 33.44)^2 + (32.74 - 33.44)^2 + (34.34 - 33.44)^2 + (34.33 - 33.44)^2 + (34.95 - 33.44)^2 = 49.6338

Standard deviation = √(49.6338/9

s1 = 2.35

For brand B,

Mean, x2 = (41.08 + 38.22 + 39.59 + 38.82 + 36.24 + 37.73 + 35.03 + 39.22 + 34.13 + 34.33 + 34.98 + 29.64 + 40.60 )/13 = 36.89

Summation(x - mean)² = (41.08 - 36.89)^2 + (38.22 - 36.89)^2 + (39.59 - 36.89)^2 + (38.82 - 36.89)^2 + (36.24 - 36.89)^2 + (37.73 - 36.89)^2 + (35.03 - 36.89)^2 + (39.22 - 36.89)^2 + (34.13 - 36.89)^2 + (34.33 - 36.89)^2 + (34.98 - 36.89)^2 + (29.64 - 36.89)^2 + (40.60 - 36.89)^2 = 124.5024

Standard deviation = √(124.5024/13

s2 = 3.09

The formula for determining the confidence interval for the difference of two population means is expressed as

Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)

For a 98% confidence interval, we would determine the z score from the t distribution table because the number of samples are small.

Degree of freedom =

(n1 - 1) + (n2 - 1) = (9 - 1) + (13 - 1) = 20

z = 2.528

x1 - x2 = 33.44 - 36.89 = - 3.45

Margin of error = z√(s1²/n1 + s2²/n2) = 2.528√(2.35²/9 + 3.09²/13) = 2.935

The 98% confidence interval is

- 3.45 ± 2.935

Answer:

Step-by-step explanation:

The solution is in the attached file

A sorting algorithm is defined as an algorithm that sorts the elements of a list. The most commonly used sequences are numerical sequence and lexicographical sequence, ascending or descending.

A sorting algorithm is used to reorder an array or list of elements according to an element comparison operator. Comparison operators are used to define a new order of elements in that data structure. Consider example, The above list of characters is sorted in ascending order by their value. That is, characters with lower values are placed before characters with higher values. It is important in real life because it supports the development of the scientific concept that things can be owned and organized into distinct groups (e.g. creatures, cars, weather types, etc.). We will now discuss some real-world examples of using sorting algorithms.

1) Your phone's contact list is sorted. This means that your data is organized in this way so you can easily access the contacts you want from your phone. That is, "I ordered."

2) Paper sorting : Imagine a teacher sorting students' work alphabetically by student name. This type of operation is similar to the functionality of sorting algorithms such as bucket sort. Sorting is more efficient process.

3) Traffic lights : Traffic lights are a good example of how algorithms are used in the real world around us. Next time you get stuck in a car at a red light, think about the algorithm that traffic lights run." Most traffic lights don't automatically switch between green, yellow, and red. This algorithm is a well-established turn-by-turn algorithm that directs traffic correctly. It's in order (it may not seem that way when you're sitting at a red light).

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7.22 mg of medicine is needed for the cat weighing 13lb.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Dosage of her medication is 1.8 mg for every 1 lb and her cat weighs 13lb.

∴ The amount of medicine the cat needs is (13/1.8) mg = 7.22 mg.

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Step-by-step explanation:

Hello!

For this you multiply the numbers that intersect at that box

Box A 2x and 4 intersect

2x * 4 = 8x

Box B 3 and 4 intersect

3 * 4 = 12

Box C 2x and x intersect

2x * x = \(2x^{2}\)

Box D 3 and x intersect

3 * x = 3x

To solve this we put all these together

\(2x^{2} +3x+8x+12\)

Combine like terms

\(2x^{2} +11x+12\)

Hope this helps!

Given:

The zeroes of the polynomial are -11 and 2.

The objective is to find a polynomial function P(x) with leading coefficient 1, least possible degree.

Consider the given zeroes as, x=-11 and x=2.

Now the zeroes can be written as,

Now, multiply the terms using algebraic identitites,

Here, the leading coefficient is 1. The real coefficients are 1, 9, -22.

Hence, the required polynomial is obtained.

Answer:

480 push-ups

Step-by-step explanation:

40 times 12 = 480

or

80 times 6 =480

Number of pushups that can be completed in 5 minutes = 40

Number of pushups that can be completed in 1 minute :-

\( = \frac{40}{5} \)

\( = 8\)

So , 8 pushups can be completed in one minute .

1 hour = 60 minutes

Number of pushups that can be completed in 1 hour :-

= 8 × 60

= 480 pushups .

Therefore , I can complete 480 pushups in one hour .

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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Answer:

green line or "b"

Step-by-step explanation:

we can set this up into the slope intercept form

y=mx+b

where m is the slope and b is y intercept

12=3x+4y

-3x -3x

-3x+12=4y

/4.  /4.  /4

-3/4x+3=y

we can see the only line with a negative slope and a y intercept at 3 is the green line or "b"

hopes this helps please mark rainliest

Answer:

x = -4/3 and x = 5/2.

Step-by-step explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

\(\frac{-b±\sqrt{b^2 - 4ac} }{2a}\)

In this case, a = 6, b = -7, and c = -20.

\(\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}\)

= \(\frac{7±\sqrt{49 + 80 * 6} }{12}\)

= \(\frac{7±\sqrt{49 + 480} }{12}\)

= \(\frac{7±\sqrt{529} }{12}\)

= \(\frac{7±23 }{12}\)

\(\frac{7 - 23 }{12}\) = \(\frac{-16 }{12}\) = -8 / 6 = -4 / 3

\(\frac{7 + 23 }{12}\) = \(\frac{30}{12}\) = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!  

Answer:

Step-by-step explanation:

\(6 {x}^{2} - 7x = 20\)

Move constant to the left and change its sign

\( {6x}^{2} - 7x - 20 = 0\)

Write -7x as a difference

\(6 {x}^{2} + 8x - 15x - 20 = 0\)

Factor out 2x from the expression

\(2x(3x + 4) - 15x - 20 = 0\)

Factor out -5 from the expression

\(2x(3x + 4) - 5(3x + 4) = 0\)

Factor out 3x + 4 from the expression

\((3x + 4)(2x - 5) = 0\)

When the product of factors equals 0 , at least one factor is 0

\(3x + 4 = 0\)

\(2x - 5 = 0\)

Solve the equation for X1

\(3x + 4 = 0\)

Move constant to right side and change its sign

\( 3x = 0 - 4\)

Calculate the difference

\(3x = - 4\)

Divide both sides of the equation by 3

\( \frac{3x}{3} = \frac{ - 4}{3} \)

Calculate

\(x = - \frac{4}{3} \)

Again,

Solve for x2

\(2x - 5 = 0\)

Move constant to right side and change its sign

\(2x = 0 + 5\)

Calculate the sum

\(2x = 5\)

Divide both sides of the equation by 2

\( \frac{2x}{2} = \frac{5}{2} \)

Calculate

\(x = \frac{5}{2} \)

\(x1 = - \frac{4}{3} \)

\(x2 = \frac{5}{2} \)

Hope this helps...

Best regards!!

Answer:

yes

Given a 2D line e.g. (3,10) -> (8.3,16.5), how can I find any point on that line that has has whole-number coordinates?

I can easily iteratively walk along one of the axis in integer steps, seeing if the value on the other axis is integer, but this is slow for very very long lines.

Answer:

19

Step-by-step explanation:

4 dozens = 4 × 12 = 48

48 pen = 576

x pen = 228

48 = 576

x = 228

x = (228 × 48)/576

x = 10,944/576

x = 19

Answer:

929

Step-by-step explanation:

this is very important to world

Answer:

Step-by-step explanation:

r =5sin i

r=5 cos i

divide

tan i=1=tan (π/4),tan(π+π/4)

or tan i=tan (π/4),tan(5π/4)

or  tan i=tan (2n π+π/4),tan (2nπ+5π/4)

or tan i=tan ((8n+1)π/4),tan((8n+5)π/4)

i=(8n+1)π/4,(8n+5)π/4

where n is an integer.

so we get infinite points of intersection.

Answer:

20% profit

Step-by-step explanation:

(1800-1500) / 1500 = 0.2

so 20% profit

Answer:

20% profit

Step-by-step explanation:

Hope this helps

Answer:

V = 460.68

Step-by-step explanation:

V=(lwh)/3

Answer:

B.!!!!!!!!!!!!!!

Step-by-step explanation:

have a good day =)

The measure of angle DEF is 37 degrees.

What is chord in circle

In geometry, a chord is a straight line segment that connects two points on the circumference of a circle. More specifically, a chord of a circle is a line segment whose endpoints lie on the circle.

Every circle has infinitely many chords, but some of the most commonly discussed chords are the diameter (a chord that passes through the center of the circle), and the secant (a chord that intersects the circle at two distinct points).

Chords play an important role in geometry, as they can be used to determine various properties of circles, such as their radius, diameter, and area.

Since G is the center of the circle, the angle DGE is a central angle of the circle.

Therefore, the angle DGE is equal to twice the inscribed angle DEF that subtends the same arc DE.

Let x be the measure of angle DEF. Then, we have:

2x = 74

x = 37

Hence, the measure of angle DEF is 37 degrees.

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The lower extreme price at Dealer 1 is higher than the median price at Dealer 2.

Price is the value of a product or service that an individual or business is willing to accept in exchange for a good or service. It is typically determined by the market forces of supply and demand. Prices are usually expressed in monetary terms, but can also be expressed in terms of labor time or other resources. Prices can vary widely depending on the availability of a good or service, the amount of competition, and other factors.
This conclusion can be drawn from the box-and-whisker plots of the prices of the sports cars at each of the two dealerships. The lower extreme price of the sports cars at Dealer 1 is represented by the lower whisker of the box-and-whisker plot and is higher than the median price of the cars at Dealer 2, which is represented by the horizontal line in the middle of the box-and-whisker plot. This means that the lower extreme price of the sports cars at Dealer 1 is higher than the median price of the cars at Dealer 2.

The higher prices of the sports cars at Dealer 1 could be due to several factors. It is possible that the cars sold at Dealer 1 are of a higher quality or have more features than those sold at Dealer 2. Additionally, Dealer 1 may simply be charging higher prices due to its location or reputation. Whatever the reason, it is clear that the lower extreme price of the sports cars at Dealer 1 is higher than the median price of the cars at Dealer 2.

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Answer: \(x=0, -\frac{3}{2}\)

Step-by-step explanation:

\(4x^2 +6x=0\\\\2x(2x+3)=0\\\\2x=0, 2x+3=0\\\\x=0, -\frac{3}{2}\)

Answer:

2c + 2 = 16

Hope this helps :)

Answer:

2

Step-by-step explanation:

2 is the y intercept of this line. y intercept is the point where the line intersects with y axis.

Answer:

b) LeBron is relatively taller because he has a larger z-score.

Step-by-step explanation:

Z-score:

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

LeBron James:

Height of 81 inches, while the average 30- to 39-year old man is 69.5 inches tall, with a standard deviation of 2.7 inches, which means that we have to find Z when \(X = 81, \mu = 69.5, \sigma = 2.7\)

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{81 - 69.5}{2.7}\)

\(Z = 4.26\)

Candace Parker:

Height of 76 inches, while the average 30- to 39-year old woman is 64.2 inches tall, with a standard deviation of 3.2 inches. This means that we have to find Z when \(X = 76, \mu = 64.2, \sigma = 3.2\)

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{76 - 64.2}{3.2}\)

\(Z = 3.69\)

Who is relatively taller?

Due to the higher z-score, LeBron James, and thus, the correct answer is given by option b.

Answer:

B

Step-by-step explanation:

the sum of the 3 angles in a triangle is 180° , so

∠ c + 56° + 38° = 180°

∠ c + 94° = 180° ( subtract 94° from both sides )

∠ c = 86°

Answer:

40.5

Step-by-step explanation:

if y varies jointly as the square of x and the cube of z and inversely as the square root of w, this is expressed as;

y ∝ x²z³/√w

y = kx²z³/√w

If x = 2, z = 2, y = 12 and w = 64

Substitute;

12 = k (2)²(2)³/√64

12 = 32k/8

12 = 4k

k = 12/4

k = 3

To get y when x = 1, z = 3, and w = 4.

y = 3 (1)²(3)³/√4

y = (3*27)/2

y = 81/2

y = 40.5

Hence the value of y is 40.5