Find the range and the interquartile range of the data. Determine if there are outliers. 8, 9, 1, 5, 5, 7, 9, 12, 15

The number that belongs in the green box, using the law of cosines, is given as follows:

15.97º.

The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite to side c, the following equation is true to obtain the missing length:

c² = a² + b² - 2abcos(C)

For this problem, the parameters are given as follows:

c = 11, a = 12, b = 20.

Hence the missing angle measure is given as follows:

11² = 12² + 20² - 2 x 11 x 20cos(C)

440cos(C) = 423

cos(C) = 423/440

C = arccos(423/440)

C = 15.97º.

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Answer:

AB ≈ 8.1

Step-by-step explanation:

using the cosine ratio in the right triangle

cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{6.2}{AB}[/tex] ( multiply both sides by AB )

AB × cos40° = 6.2 ( divide both sides by cos40° )

AB = [tex]\frac{6.2}{cos49}[/tex] ≈ 8.1 ( to the nearest tenth )

Answer: number is the number so we can be a number

Step-by-step explanation:

Answer:

56,513,230

Step-by-step explanation:

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Answer: B

Step-by-step explanation:

English: 0.25^5=0.001

Science:0.5^7=0.008

English is harder to get 100% on, since the probability 0.001 is lower than 0.008.

[tex]1\cdot2^2+1\cdot2^1+1\cdot2^0=4+2+1=7\\\\111_2=7_{10}[/tex]

Answer:

Speed =distance divide by time

=200 kilometres divide by 5

=40km/h

Distance =speed multiple by time

=40 multiple by 7 hours

=280km

Answer:

$762.53

Step-by-step explanation:

think of 710.98 as the whole.

then 7.25% = an increase of 0.0725.

710.98 X (1 + 0.0725)

= $762.53 (to nearest cent)

The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, Functions are,

⇒ y = 2ˣ

And, Its inverse function is,

⇒ y = log₂ x

Thus, The graph of the exponential function y = 2ˣ and its inverse y = log₂ x are shown in figure.

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The fraction of the money the youngest boy does get is 5x/22.

Given that, three brothers share some money. The oldest 5/11 of the money.

Let the total money be x.

Share of oldest boy = 5/11 ×x

= 5x/11

Remainder = x-5x/11

Remainder = 6x/11

The next boy gets 7/12 of the remainder.

Share of next boy = 7/12 × 6x/11

= 7x/22

Share of youngest boy = 6x/11 - 7x/22

= (12x-7x)/22

= 5x/22

Therefore, the fraction of the money the youngest boy does get is 5x/22.

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The 90% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately (17.569, 18.831), rounded to three decimal places.To determine the 90% confidence interval for the number of chocolate chips per cookie in Big Chip cookies, we can use the sample mean and standard deviation along with the appropriate formula.

Given that Jose randomly selected a sample of 57 cookies and found a sample mean of 18.2 and a standard deviation of 2.9, we can calculate the confidence interval using the following formula:

Confidence Interval = Sample Mean ± (Z * (Standard Deviation / √Sample Size))

Since the data is assumed to be from a normally distributed population and we want a 90% confidence interval, we need to find the Z-value for a 90% confidence level. Using a standard normal distribution table or a calculator, the Z-value for a 90% confidence level is approximately 1.645.

Substituting the values into the formula:

Confidence Interval = 18.2 ± (1.645 * (2.9 / √57))

Calculating the values:

Confidence Interval = 18.2 ± (1.645 * 0.383)Confidence Interval ≈ 18.2 ± 0.631.

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The Y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.

The equation for the line of fit on the scatter plot, we need to determine the slope and y-intercept. Then, using the equation, we can predict the number of customers that will use the app after 12 months.

Given that we have a good line of fit, let's assume the equation of the line is in the form y = mx + b, where y represents the number of customers and x represents the number of months.

the scatter plot, we can determine two points on the line of fit. Let's say the coordinates of the first point are (x1, y1) and the coordinates of the second point are (x2, y2).

Next, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

the y-intercept (b), we can substitute one of the points into the equation y = mx + b and solve for b.

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cos 30° can be evaluated using the trigonometric identity: cos 30° = cos(π/6) = (√3)/2.

Therefore, the exact value of cos 30° is (√3)/2.

Answer:

cos30 = √3 / 2

or cos30 ≈ 0.8660254037

The measure of each arc is calculated as: 16. m(MN) = 72°;  17. m(NQR) = 180°; 18. m(NQ) = 108°; 19. m(MRP) = 265°; 20. m(QR) = 72°; 21. m(MR) = 108°; 22. m(QMR) = 288°; 23. m(PQ) = 13°.

To determine the measures of each of the arcs, note that the central angle will have the same measure as the arc.

16. m(MN) = m<QRN [vertical angles are equal}.

m(MN) = 72°.

17. m(NQR) = 180° [half of a circle is 180 degrees]

18. m(NQ) = 180 - 72 = 108°

19. m(MRP) = 180 + (180 - 95)

m(MRP) = 180 + 85 = 265°

20. m(QR) = 72°

21. m(MR) = 180 - 72 = 108°

22. m(QMR) = 360 - 72 = 288°

23. m(PQ) = 180 - 95 - 72 = 13°

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A graph and table for the linear equation y = 2x/5 - 2 in slope-intercept form is shown in the image attached below.

In Mathematics, a graph is a type of chart that is typically used for the graphical representation of data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis respectively.

Next, we would rearrange and simplify the given given linear equation in slope-intercept form in order to enable us plot it on a graph;

2x - 5y = 10

5y = 2x - 10

y = 2x/5 - 2

In conclusion, we would use an online graphing calculator to plot the given linear equation in slope-intercept form as shown in the graph attached below.

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The external circumference of the metal pipe is approximately 31.4 centimeters.

We know that the circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We are given that  internal radius is 5cm and the thickness of the metal is 6mm.

The circumference of the external circle = 2πr

= 2 x 3.14 x 5

= 31.4

The circumference of the metal pipe is approximately 31.4 centimeters.

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the next two terms in the sequence would be 12 and 17.

Step-by-step explanation:

y= rad(x+3)

y²=x+3

x= y²-3

change the variables

y= x²-3

The inverse of the functions are solved

Given data ,

Let the inverse of the function be represented as f⁻¹ ( x )

a)

f(x) = 5x - 1

y = 5x - 1

x = 5y - 1

x + 1 = 5y

y = (x + 1)/5

Inverse: f⁻¹(x) = (x + 1)/5

b)

f(x) = (1/5)x

y = (1/5)x

x = (1/5)y

y = 5x

Inverse: f⁻¹(x) = 5x

c)

f(x) = x - 5

y = x - 5

x = y - 5

y = x + 5

Inverse: f⁻¹(x) = x + 5

d)

f(x) = 7x + 1

y = 7x + 1

x = 7y + 1

x - 1 = 7y

y = (x - 1)/7

Inverse: f⁻¹(x) = (x - 1)/7

Hence , the inverse of the functions are solved

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The y-intercept of the line is 2. the equation of the line in the form y=mx+b is y = 2x + 2.

To find the equation of the line in the form y=mx+b, we need to first find the slope (m) and the y-intercept (b).
Looking at the table:
x | y
--|--
1 | 4
2 | 6
3 | 8
We can use the formula for slope:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1, 4) and (2, 6):
m = (6 - 4) / (2 - 1)
m = 2 / 1
m = 2
So the slope of the line is 2.
To find the y-intercept, we can use the formula:
b = y - mx
Let's use the first point (1, 4) and the slope we just found:
b = 4 - (2)(1)
b = 4 - 2
b = 2
So the y-intercept of the line is 2.
Putting it all together, the equation of the line in the form y=mx+b is:
y = 2x + 2.

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The standard deviation for this set of data is approximately 2.85.

To find the standard deviation, we first need to take the square root of the variance. Therefore, the standard deviation for the given data set is the square root of 8.1, which is approximately 2.846.
To find the standard deviation of a set of data when the variance is given, you simply need to take the square root of the variance. In this case, the variance equals 8.1.
Step 1: Identify the variance, which is 8.1.
Step 2: Take the square root of the variance.
Standard Deviation = √(Variance) = √(8.1)
Step 3: Calculate the square root of 8.1.
Standard Deviation ≈ 2.85
So, the standard deviation for this set of data is approximately 2.85.

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The simplified expression for (x+6)^2 is x^2 + 12x + 36.

The expression (x+6)^2 represents the square of the sum of x and 6. To simplify this expression, we need to use the formula for expanding a binomial squared, which is (a+b)^2 = a^2 + 2ab + b^2.

Applying this formula to our expression, we get:

(x+6)^2 = x^2 + 2(x)(6) + 6^2

Simplifying further:

(x+6)^2 = x^2 + 12x + 36

In summary, to simplify the expression (x+6)^2, we use the formula for expanding a binomial squared and simplify the resulting terms to get the simplified expression x^2 + 12x + 36.

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Answer:

6

Step-by-step explanation:

To find the mean you've got to add 7, 9,4,3,9 and 4 (which gives you 36) and divide that by the number of figures/numbers (which is 6 numbers in total) and it gives you 6

Answer:

m = 25 + 6n

Step-by-step explanation:

To write a function for the amount of money Makayla spent going to the movies during the club, you need to consider two things: the annual registration fee and the discounted ticket price. The annual registration fee is a fixed amount that does not depend on the number of movie tickets Makayla purchases. The discounted ticket price is a variable amount that depends on the number of movie tickets Makayla purchases. You can use a letter, such as n, to represent the number of movie tickets Makayla purchases. Then, you can write an expression for the amount of money Makayla spent on movie tickets, which is 6 times n, or 6n. To find the total amount of money Makayla spent going to the movies during the club, you need to add the annual registration fee and the amount of money spent on movie tickets. This gives you the expression 25 + 6n. You can use another letter, such as m, to represent the total amount of money Makayla spent going to the movies during the club. Then, you can write an equation that relates m and n, which is m = 25 + 6n. This equation is a function that models the amount of money Makayla spent going to the movies during the club as a function of the number of movie tickets she purchased.

Answer: 8

Step-by-step explanation:

      We see that each term is 5 less than the previous one. We will subtract 5 from 13 to find the next term in the sequence.

                    13 - 5 = 8

Answer:

150°

Step-by-step explanation:

Measure of and interior angle of 12-gon:

  [tex]\sf \boxed{\text{\bf Sum of all angles of n-polygon = (n -2) * 180}}[/tex]

n is the number of sides.

  Sum of all angles of 12-gon     = (12 - 2) * 180

                                                     = 10 *180

                                                     = 1800°

In a regular 12-gon, all the interior angles will be equal.

    [tex]\text{\bf Measure of each interior angle = $\bf \dfrac{Sum \ of \ all \ the \ angles}{number \ of \ sides}$}[/tex]

                                                            [tex]\sf = \dfrac{1800}{12}\\\\=150^\circ[/tex]

The value of the x is 31.4 mm

Surface area = 282.6  

According to the given figure,

Radius of circle = 5 mm

The length of x is the circumference of the circle,

⇒ x = 2πr

Here r is the radius of the circle,

Therefore, r = 5

Then put it into the circumference expression,

⇒ x =  2x3.14x5

       = 31.4 mm

Total surface area,

= 2 x area of circle + area of rectangle

= 2(πr²) + (LxW)

= 2xπx5² + 10xπx4

= 50π + 40π

= 90 π

= 90x3.14

= 282.6

Hence,

Surface area = 282.6 mm³

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Answer: x = 11

Step-by-step explanation:

     We know that vertical angles are congruent to each other. We will create an equation to help us solve. Then, will isolate the x-variable with inverse operations.

128° = 8x + 40°

8x + 40° = 128°

8x = 88°

x = 11

The median will be greater than the mean in a left-skewed distribution

We have,

In statistics, skewness is a measure of the asymmetry of a probability distribution around its mean.

A distribution is said to be skewed left if it has a long tail on the left side and the bulk of the data is on the right side.

When the data is skewed left, it means that the distribution is being pulled towards the left side.

This is because there are a few extreme values on the left side that are pulling the mean in that direction.

In contrast, the median is the middle value of the dataset, and it is not influenced by outliers.

For a left-skewed distribution,

The median will be greater than the mean because the mean is being pulled towards the left by the few extreme values.

In a data distribution that is skewed left, the mean will be less than the median.

This is because the mean is sensitive to outliers and is pulled towards the direction of the skewness, while the median is not affected by extreme values and is a more robust measure of central tendency.

Therefore,

The median will be greater than the mean in a left-skewed distribution

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