the state lottery board is examining the machine that randomly picks the lottery numbers. on each trial, the machine outputs a ball with one of the digits 0-9, the ball is then replaced in the machine. the lottery board tested the machine for 40 trailsround to the nearest thousandth A) assuming that machine is fair, compute the theoretical probability of getting a 9B) from these results, compute the experimental probability of getting a 9

The mean is 14.7, the median is 16, and the mode is 16.

To find the mean, we need to calculate the sum of all the data values and divide it by the total number of observations.

The sum of the data values is:

14 x 14 + 15 x 11 + 16 x 23 + 17 x 10 + 18 x 13 = 196 + 165 + 368 + 170 + 234 = 1043

The number of observations is:

14 + 11 + 23 + 10 + 13 = 71

The mean is calculated as follows,

1043 / 71 = 14.7 (rounded to one decimal place)

The median is the central value in the data collection. To find the median, we need to arrange the data values in ascending order and find the middle value. In this case, we have an odd number of observations, so the median is simply the middle value.

14, 14, 15, 15, 16, 16, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18

The median is 16.

The mode is the value that appears most repeatedly in the data set. In this case, the mode is 16 since it occurs the most (23 times).

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Answer:

C

Step-by-step explanation:

x^2 + 20^2 = 25^2

x^2 + 400 625

x^2 = 225

x = 15

Answer:

Male-19&Female-13

Step-by-step explanation:

See the image for solution

Hope it helps

Have a great day

Answer:

0.4 hours

Step-by-step explanation:

or 24 minutes :D

Answer:

4.2

Step-by-step explanation:

In a 45°45°90° triangle, the ratios of the sides to the hypotenuse is x : x√2

So if x√2 = 6, x = 3√2

3√2 is approximately 4.2

Hope this helps.

Answer:

$31.50

Step-by-step explanation:

42 x 0.25 = 10.5

42 - 10.50 = 31.50

$31.50

Explanation:

42 × 25% = 10.5

42 - 10.5 = 31.5

No, the trapezoids are not similar because their corresponding angles do not have the same measures.

The given trapezoids ABCD and EFGH can be analyzed to determine if they are similar. Similarity in geometric figures implies that their corresponding angles are congruent, and their corresponding sides are proportional.

Let's examine the angles of the trapezoids:

In trapezoid ABCD:

Angle A = 137 degrees

Angle B = 90 degrees

Angle C = 90 degrees

Angle D = 43 degrees

In trapezoid EFGH:

Angle E = 136 degrees

Angle F = 90 degrees

Angle G = 90 degrees

Angle H = 44 degrees

By comparing the angles, we can observe that angles B and F are both right angles (90 degrees) in both trapezoids. Additionally, angles C and G are also right angles (90 degrees) in both trapezoids.

However, angles A and E, as well as angles D and H, do not have the same measures. Angle A measures 137 degrees in trapezoid ABCD, while angle E measures 136 degrees in trapezoid EFGH. Similarly, angle D measures 43 degrees in trapezoid ABCD, while angle H measures 44 degrees in trapezoid EFGH.

Since the corresponding angles in the two trapezoids do not have the same measures, we can conclude that trapezoids ABCD and EFGH are not similar.

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Answer:

x = 12.5

Step-by-step explanation:

The three sides of the triangle have lengths 3x, 3x, and 15.

The perimeter of the triangle is the sum of the three lengths, and it is 90.

Perimeter = 3x + 3x + 15 = 6x + 15

3x + 3x + 15 = 90

6x + 15 = 90

6x = 75

x = 12.5

We can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

To determine the interval within which 95 percent of the sample means will fall, we need to calculate the margin of error using the standard deviation and the desired level of confidence.

The formula to calculate the margin of error is given by:

Margin of Error = Z * (Standard Deviation / √n)

Where:

Z is the critical value corresponding to the desired level of confidence

Standard Deviation is the standard deviation of the population

n is the sample size

Since the sample size is 41 and we want to find the interval at a 95 percent confidence level, we need to find the critical value corresponding to a 95 percent confidence level.

The critical value can be found using a standard normal distribution table or a calculator. For a 95 percent confidence level, the critical value is approximately 1.96.

Now we can calculate the margin of error:

Margin of Error = 1.96 * (0.0050 / √41)

Calculating this, we find:

Margin of Error ≈ 0.001624

To find the interval within which 95 percent of the sample means will fall, we need to subtract and add the margin of error to the true mean:

Interval = True Mean ± Margin of Error

Interval = 0.9550 ± 0.001624

Calculating this, we find:

Interval ≈ (0.9534, 0.9566)

Therefore, we can conclude that with 95 percent confidence, the sample means will fall within the interval of approximately (0.9534, 0.9566).

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Step-by-step explanation:

(1 + ax)⁴(2 - x)³ = (1 + 2ax + a²x²)²(8 - 12x + 6x² - x³) =

(1 + 4a²x² + a⁴x⁴ + 4ax + 2a²x² + 4a³x³)(8 - 12x + 6x² - x³) = ... 6x² + 32a²x² - 48ax² + 16ax² ...

= ... x²(6 + 32a² - 32a) ...

32a² - 32a + 6 = 6

32a(a - 1) = 0 → 32a = 0 → a = 0 OR a - 1 = 0 → a = 1

Answer:

G > F > H

Step-by-step explanation:

In a triangle, the largest side and largest angle are opposite eachother.   Similarly, the smallest side and smallest angle are opposite eachother.

We have 3 sides of length 6 cm, 11 cm, and 12 cm.  The angle opposite the 6 cm side is the smallest (H).  The angle opposite the 14 cm side is the largest (G).

Hi, there!

 ______

\(\begin{tabular}{c|1} \boldsymbol{Things \ to \ Consider} \\\cline{1-3} \end{tabular}\)

(1)

 - The slopes of parallel lines are identical.

{The line \(\sf{y=7x-1}\) has a slope of 7}

Thus,

{The slope of the line that is parallel to the aforementioned line (whatever its equation happens to be) is \(\sf{7}\).}

(2)

 - The slopes of perpendicular lines are negative inverses of each other.

The negative inverse of 7 is

\(-\dfrac{1}{7}\).

Therefore,

\(\textsc{Answers:\begin{cases} \bf{7} \\ \bf{-\dfrac{1}{7}} \end{cases}}\)

Hope the answer - and explanation - made sense,

happy studying!!                                                                 \(\tiny\boldsymbol{Frozen \ melody}\)

Answer:

$2.99 per pound of cherries

Step-by-step explanation:

$14.95 / 5 pounds of cherries = $2.99 per pound of cherries

Answer:

4 and a half nights

Answer:

1. Triangles HIJ and KML

2. Triangles RST and YXZ

3. Reflexive property and Congruent Property

Step-by-step explanation:

Step-by-step explanation:

for 1 and 2 to find which ones are congruent you have to look at the lines on the angles which show congruence

Step 1: Concept

Since it has a maximum

You multiply by negative

Then we have

Answer:

hope this helps

Step-by-step explanation:

To determine its end behavior, look at the leading term of the polynomial function. Because the power of the leading term is the highest, that term will grow significantly faster than the other terms as x gets very large or very small, so its behavior will dominate the graph

Answer:

the equation is (2x^9y^n)(4x^2y^10)=8x^11y^20

Step-by-step explanation:

,

Answer:

sorry about that that was my sister . the correct answer is yes

Step-by-step explanation:

please mark as brainliest

Answer:

5

Step-by-step explanation:

i think i dont know

Answer:

e = 2

Step-by-step explanation:

7(2e - 1) - 3 = 6 + 6e

14e - 7 - 3 = 6 + 6e

14e - 10 = 6 + 6e

14e - 6e - 10 = 6

8e - 10 = 6

8e = 6 + 10

8e = 16

8e/8 = 16/8

e = 2

Recheck:

7(2e - 1) - 3 = 6 + 6e

7(2(2) - 1) - 3 = 6 + 6(2)

7(4 - 1) - 3 = 6 + 12

7(3) - 3 = 18

21 - 3 = 18

18 = 18 ✅

The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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Answer:

the dean bought more of swiss than cheddar because hee only bought  1.5 pounds of cheddar and 1.7 of swiss

Step-by-step explanation:

Using Gaussian elimination, the solution to the given system of equations is given as follows:

x = 5, y = -11, z = 3.

A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.

For this problem, the variables are x, y and z, and the system is given as follows:

There are multiple ways in which a system can be solved, and for this one, Gaussian elimination will be used.

The first step is writing the augmented matrix of the system, as follows:

\(\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right]\)

Then, the first column, which is equivalent to be coefficient of y, has to be of zero on the second and on the third row, hence:

The updated matrix will be given by:

\(\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right]\)

Then, the second column, equivalent to the coefficient of y, on the third row has to be zero, hence:

R3 -> 11R2 + 5R3.

Then the matrix is:

\(\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right]\)

From each row of the system, from bottom up, we find the variables, as follows:

40z = 120

z = 120/40

z = 3.

5y - 10z = -85

5y - 30 = -85

5y = -55

y = -11.

2x - y + 4z = 33

2x + 11 + 12 = 33

2x = 10

x = 5.

Hence the solution for the system is:

x = 5, y = -11, z = 3.

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Answer:

B-log(x-4)

Step-by-step explanation:

Have a nice day lol i just know things

The equation as a single logarithm is:

\(log[(x^2 - 16)/(x + 4)].\)

Option C is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

Using the logarithmic identity,

log a - log b = log (a/b)

We can simplify the given expression as:

\(=log(x^2 - 16) - log(x + 4) \\= log[(x^2 - 16)/(x + 4)]\)

Therefore,

The equation as a single logarithm is:

\(log[(x^2 - 16)/(x + 4)].\)

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The principal in this scenario is $ 8000.

Simple Interest can be defined as the sum paid back for using the borrowed money, over a fixed period of time.

Compound Interest can be defined as when the sum principal amount exceeds the due date for payment along with the rate of interest, for a period of time.

It is Given that:

Priscilla invested 20,000 that means the total amount she invested.

Amount= $ 20,000

Rate of interest=12%

Time= 5 year

Interest= $12,000.

By the formula;

Amount =  principal + Interest

Principal = Amount - Interest

Principal= $ 20,000- $12,000

Principal=$ 8000

Hence, the principal in this scenario is $ 8000.

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Answer

Option D is correct.

c - 2 = 25 + c + 10√c

Explanation

The equation is

√(c - 2) - √c = 5

√(c - 2) = 5 + √c

Square both sides

[√(c - 2)]² = [5 + √c]²

c - 2 = 25 + 10√c + c

c - 2 = 25 + c + 10√c

Hope this Helps!!!

Answer:

X is always positive and y is always negative.

Step-by-step explanation:

Quadrant IV is the bottom right area, which is under the x axis (meaning y is less than y=0) and right of the y axis (meaning x is greater than x=0).