Some data sets include values so high or so low that they seem to stand apart from the rest of the data. These data are called outliers. Outliers may represent data collection errors, data entry errors, or simply valid but unusual data values. It is important to identify outliers in the data set and examine the outliers carefully to determine if they are in error. One way to detect outliers is to use a box-and-whisker plot. Data values that fall beyond the limits

Lower limit: Q1 − 1.5 ✕ (IQR)
Upper limit: Q3 + 1.5 ✕ (IQR)

where IQR is the interquartile range, are suspected outliers. In the computer software package Minitab, values beyond these limits are plotted with asterisks (*). Students from a statistics class were asked to record their heights in inches. The heights (as recorded) were as follows:

65 72 68 64 60 55 73 71 52 63 61 74
69 67 74 50 4 75 67 62 66 80 64 65

Required:
Make a box-and-whisker plot of the data.

that log4x=2log16x. (ii)Show that log x=3logb³ x. (iii) Show that log₂x=(1+log₂3)logix

Answer:

Step-by-step explanation:

According to the distribution table, the percent values within the interval of [- 2, 2] are:

Add them together to get the required answer:

The answer is 0.6 or 60%.

The respective probabilities that lie in the interval [-2, 2] are 0.33, 0.16, and 0.11. Therefore, the probability it lies in the interval is equal to the sum of the probabilities.

Answer: -5

Step-by-step explanation:

-3x+9y=-57                x=4

-3(4)+9y=-57

-12+9y=-57

             +12

9y=-45

    9y

y=-5

Answer:

[tex]y + 6 = -1(x + 2).[/tex]

Step-by-step explanation:

Let's find the general equation of the given line:

[tex]y - x - 7 = 0\\\\y = x + 7.[/tex]

We can see that [tex]m = 1.[/tex]

Thus, the slope of any perpendicular line to the line [tex]y = x + 7[/tex] is [tex]-1.[/tex]

Given that the perpendicular line passes through (-2, -6), its point-slope form equation is as given:

[tex]y - y_1 = m(x - x_1)\\\\y - (-6) = -1(x - (-2))\\\\y + 6 = -1(x + 2).[/tex]

The dimensions are 7 inches by 17 inches.

What is the area of rectangle?

Let the length be l inches

Let the breadth be b inches

Area = l*b

We can find dimensions as shown below:

Let the length be x inches

Let the width be y inches

Area = 119 square inches

x=3+2y             (1)

Area = l*w

119 = x*y

Putting value of x

119 = (3+2y) *y

119 = 3y+2y^2

2y^2+3y-119=0

2y^2-14y+17y-119=0

2y(y-7) +17(y-7) =0

(y-7) (2y+17) =0

y=7, -17/2

y cannot be negative

so, y = 7

Putting in equation (1)

x=3+2(7)

= 3+14

= 17

Hence, the dimensions are 7 inches by 17 inches.

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The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

In this situation we assume that the loan does not accumulate interests continuously in time. Hence, the interest rate for paying the loan back 75 days later is:

575 = 525 · (1 + r/100)

50 = 525 · r /100

5000 = 525 · r

r = 9.524

The loan has an interest rate of 9.524 % for 75 days. Simple annual interest rate is determine by rule of three:

r' = 9.524 × 365/75

r' = 46.350

The simple annual interest rate for the $ 525 loan is equal to 46.35 %.

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The cost of one ounce of peanuts is $0.20

The cost of one ounce of cashew is $0.35

15p + 5c = 4.75 equation 1

5p + 15c = 6.25 equation 2

Where:

Multiply equation 2 by 3

15p + 45c = 18.75 equation 3

Subtract equation 1 from equation 3

40c = 14

c = 14/40

c = $0.35

Substitute for c in equation 1

15p + (5 x 0.35) = $4.75

15p + 1.75 = 4.75

15p = 4.75 - 1.75

15p = 3

p = 3/15

p = $0.20

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The interval where the function is increasing is (3, ∞)

Given the rational function shown below

g(x) = ∛x-3

For the function to be a positive function, the value in the square root  must be positive such that;

x - 3 = 0

Add 3 to both sides

x = 0 + 3

x = 3

Hence the interval where the function is increasing is (3, ∞)

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Someone may think this graph is misleading because it does not start from the origin

As a general rule, graphs are to begin from the origin

The origin of a graph is

(x, y) = (0, 0)

From the given graph, the origin is

(x, y) = (0, 60)

This means that someone may think this graph is misleading because it does not start from the origin

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[tex]\underset{\leftarrow \qquad \textit{\LARGE 4x}\qquad \to }{R\stackrel{4x-4}{\rule[0.35em]{7em}{0.25pt}} S\stackrel{2x}{\rule[0.35em]{20em}{0.25pt}}T} \\\\\\ RT~~ - ~~ST~~ = ~~RS\implies \stackrel{RT}{4x} - \stackrel{ST}{2x}~~ = ~~\stackrel{RS}{4x-4} \\\\\\ -2x=-4\implies x=\cfrac{-4}{-2}\implies \boxed{x=2}~\hfill \stackrel{4(2)~~ - ~~4}{RS=8}[/tex]

Using the Empirical Rule and the Central Limit Theorem, we have that:

It states that, for a normally distributed random variable:

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this problem, the standard deviation of the distribution of sample means is:

[tex]s = \frac{0.657}{\sqrt{50}} = 0.09[/tex]

68% of the means are within 1 standard deviation of the mean, hence the bounds are:

99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:

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Answer:

About 68% of the sample means fall within the interval $1.64 and $1.82.

About 99.7% of the sample means fall within the interval $1.45 and $2.01.

Step-by-step explanation:

To verify the given intervals, we need to calculate the standard error of the mean (SE) for a sample size of 50 using the population mean and standard deviation provided.

The standard error of the mean (SE) can be calculated as:

SE = population standard deviation / √(sample size)

Given that the population mean is $1.73 and the population standard deviation is $0.657, and the sample size is 50:

SE = $0.657 / √50 ≈ $0.09299 (rounded to 5 decimal places)

Now, we can calculate the intervals:

For the interval where about 68% of the sample means fall:

Interval = (Mean - 1 * SE, Mean + 1 * SE)

Interval = ($1.73 - $0.09299, $1.73 + $0.09299)

Interval ≈ ($1.63701, $1.82299)

So, about 68% of the sample means fall within the interval $1.64 and $1.82, which matches the given statement.

For the interval where about 99.7% of the sample means fall:

Interval = (Mean - 3 * SE, Mean + 3 * SE)

Interval = ($1.73 - 3 * $0.09299, $1.73 + 3 * $0.09299)

Interval ≈ ($1.54703, $1.91297)

So, about 99.7% of the sample means fall within the interval $1.55 and $1.91, which is different from the given statement.

The correct interval for about 99.7% of the sample means, rounded to the nearest hundredth, is $1.55 and $1.91, not $1.45 and $2.01 as mentioned in the statement.

Answer:

t + 3

Step-by-step explanation:

adding 3 years onto t amount of years

The containers must be spheres of radius = 6.2cm

We know that the shape that minimizes the area for a fixed volume is the sphere.

Here, we want to get spheres of a volume of 1 liter. Where:

1 L = 1000 cm³

And remember that the volume of a sphere of radius R is:

[tex]V = \frac{4}{3}*3.14*R^3[/tex]

Then we must solve:

[tex]V = \frac{4}{3}*3.14*R^3 = 1000cm^3\\\\R =\sqrt[3]{ (1000cm^3*\frac{3}{4*3.14} )} = 6.2cm[/tex]

The containers must be spheres of radius = 6.2cm

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Answer:

166 2/3 meters/sec.

Step-by-step explanation:

1/1 =1  12 inches/1 foot =1  you are looking for equivalents that will cancel out the unit until you can get to meters and seconds.  See work in the picture.

Answer:

v=-7

Step-by-step explanation:

13v-5v=-27-29

8v=-56

v=-56/8=-7

By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

Herein we have a quadratic equation, that is, a second order polynomial, of the form b² - a² = 0. By algebra we know that the polynomial of such form have the following equivalence:

b² - a² = (b - a) · (b + a), which means that the roots of the interval are x₁ = a and x₂ = - a.

If we know that a² = 9, then the roots of the second order polynomial are:

b² - 9 = (b - 3) · (b + 3)

By algebra, if one solution for the second order polynomial b² - 9 = 0 is 3, then the other solution to the expression is - 3.

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The number must be between 20 and 30.

The square of the whole number can be found as follows;

The square of the whole number is between 500 and 900. The number must be between 20 and 30.

The number is an whole number.

Therefore, the number will be between 20 and 30.

20² = 400

30² = 900

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Answer:

180°

cuz when a line (I forgot the name) and radius meet at the circumference they from an angle of 90°

The number of mice that didn't get a tumor is 9 mice out of the 25 mice.

Identify the total mice who did not have any effects or the effects did not include a tumor.

Repiratory failure: 9 mice

Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.

Note: This question is incomplete; here is the missing section:

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One tree is 31.044 m taller than the other one in height.

Given Information and Formula Used:

The distance between the trees, BC (from the figure) = 120 m

Elevation of angles to the top of the trees,

∠AMB = 52°

∠DMC = 36°

In a right angled triangle,

tan x = Perpendicular/Height

Here, x is the angle opposite to the Perpendicular.

Calculating the Height Difference:

Let's compute the height of the taller tree first.

In ΔAMB,

tan 52° = AB / BM

Now, since M is the point halfway between the trees,

BM = CM = BC/2

BM = CM = 60 m

⇒ 1.2799 = AB / 60

AB = 1.2799 × 60

Thus, the height of the taller tree, AB =  76.794 m

Now, we will compute the height of the smaller tree.

In ΔDCM,

tan 36° = DC / CM

⇒ 0.7625 = DC / 60

DC = 0.7625 × 60

Thus, the height of the smaller tree, DC = 45.75 m

The difference in the heights of the trees, AP = AB - DC

AP = (76.794 - 45.75)m

AP = 31.044m

Hence one tree is 31.044m taller in height than the other.

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Answer: option (2)

Step-by-step explanation:

The slanted line has a negative slope.

Also, the line is shaded below.

This leaves option (2) as the correct answer.

Using the Poisson distribution, it is found that:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

In this problem, the mean is:

[tex]\mu = 3.2[/tex]

The probability that the company will find 2 or fewer defective products in this batch is:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

In which:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

Then:

[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0408 + 0.1304 + 0.2087 = 0.3799[/tex]

There is a 0.3799 = 37.99% probability that the company will find 2 or fewer defective products in this batch.

The probability that 4 or more defective products are found in this batch is:

[tex]P(X \geq 4) = 1 - P(X < 4)[/tex]

In which:

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0408 + 0.1304 + 0.2087 + 0.2226 = 0.6025

[tex]P(X \geq 4) = 1 - P(X < 4) = 1 - 0.6025 = 0.3975[/tex]

There is a 0.3975 = 39.75% probability that 4 or more defective products are found in this batch.

For 5 or more, the probability is:

[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]

In which:

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4).

Then:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-3.2}3.2^{0}}{(0)!} = 0.0408[/tex]

[tex]P(X = 1) = \frac{e^{-3.2}3.2^{1}}{(1)!} = 0.1304[/tex]

[tex]P(X = 2) = \frac{e^{-3.2}3.2^{2}}{(2)!} = 0.2087[/tex]

[tex]P(X = 3) = \frac{e^{-3.2}3.2^{3}}{(3)!} = 0.2226[/tex]

[tex]P(X = 4) = \frac{e^{-3.2}3.2^{4}}{(4)!} = 0.1781[/tex]

P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0408 + 0.1304 + 0.2087 + 0.2226 + 0.1781 = 0.7806

[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.7806 = 0.2194[/tex]

Since [tex]P(X \geq 5) > 0.05[/tex], the company should not stop production it there are 5 defectives in a batch.

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The fraction of the remaining marbles in the bag will be blue is 6/17.

The first step is to determine the initial number of marbles in the bag:

Initial number of red marbles in the bag : (5/8) x 240 = 150

Initial number of blue marbles in the bag : (2/8) x 240 = 60

Initial number of green marbles in the bag : 240 - 150 - 60 = 30

Number of red marbles remaining after 1/3 is removed = (1 - 1/3) x 150

2/3 x 150 = 100

Number of green marbles remaining after 2/3 is removed = (1 - 2/3) x 30

1/3 x 30 = 10

Total number of marbles now in the bag : 100 + 10 + 60 = 170

Fraction of blue marbles = 60 / 170 = 6/17

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Answer: (0,1/3)

Step-by-step explanation:

Answer:

The y-intercept of the function f(x) = -2/9x + 1/3 is 1/3.

Step-by-step explanation:

Given, function is

f(x) = -2/9x + 1/3.

The y-intercept is the point where the graph intersects the y-axis.

The y-intercept of a graph is (are) the point(s) where the graph intersects the y-axis.

We know that the x-coordinate of any point on the y-axis is 0.

So the x-coordinate of a y-intercept is 0.

To find the y - intercept set x = 0.

f(0) = (2/9 . 0) + 1/3

f(0) = 0 + 1/3

f(0) = 1/3.

The adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

The matrix is given as:

[tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex]

For a matrix A be represented as:

[tex]A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]

The adjoint is:

[tex]Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right][/tex]

Using the above format, we have:

[tex]Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

Hence, the adjoint of the matrix [tex]\left[\begin{array}{cc}1&0\\2&-1\end{array}\right][/tex] is [tex]\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right][/tex]

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Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.

Given that;

To determine the length wall from the tip of the ladder to the ground level, we use trigonometric ratio since the scenario forms a right angle triangle.

Sinθ = Opposite / Hypotenuse

Sin( 71° ) = x / 17ft

x = Sin( 71° ) × 17ft

x = 0.9455 × 17ft

x = 16.1 ft

Given the length of the ladder and the angle it made with the ground, it will reach 16.7 ft up the wall.

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The measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines that are parallel to each other or p ll q

The angle made by transversal t is 136 degrees

The measure of the other angle = 180 - 136 = 44 degrees

Draw a line parallel to p and q and passes through the intersection point of line t and v

The angle made by the transversal and the line drawn is the same as 44 degrees.

The measure of the other angle = 121 - 44 = 77 degrees

Thus, the measure of the angle x is 77 degrees if two lines are parallel to each other or p ll q option (A) is correct.

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Answer:

+5

Step-by-step explanation:

There is a length of 5 between all numbers, meaning that 5 is added to each number to get the next one.

I hope this helps!