Experimental Probability-Instruction-Level G

Mariana chooses a golf ball from a bucket at random, notes the color, and puts it back. After several
trials, she finds that she chose a yellow golf ball 8 times. Based on this, she predicts that if she
chooses a golf ball from the bucket 240 times, 160 will be yellow.
How many times did Mariana choose a golf ball
from the bucket?

12 times

Mariana chooses a golf ball from the bucket at
random 4 more times and none of the golf balls
are yellow. What is the experimental probability
of choosing a yellow golf ball based on all of
Mariana's trials?

This statement is true, as the test statistic represents the number of standard deviations between the observed sample proportion and the claimed value (po) under the null hypothesis.

- The large value of the test statistic means that our observed data are not surprising when the null hypothesis is true. This statement is false. A large test statistic implies that the observed data is surprising when the null hypothesis is true, which means there is evidence against the null hypothesis.
- The researcher should fail to reject the null hypothesis. This statement is false. A large test statistic suggests evidence against the null hypothesis, so the researcher should reject the null hypothesis in favor of the alternative hypothesis.

- When the null hypothesis is true, the test statistic comes from a standard normal distribution. This statement is true, as the test statistic follows a standard normal distribution when the null hypothesis is true.
- There is a 4.318% chance that the alternative hypothesis is true. This statement is false. The test statistic does not directly provide the probability of the alternative hypothesis being true. Instead, we can use the test statistic to calculate the p-value, which represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true.

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Answer:

6

Step-by-step explanation:

Answer:

6 students read 2 books

Answer:

B) 5V2

Step-by-step explanation:

5√2 is the simplified form of the 5 √8 - √18 -2√2. Therefore, the correct option is option B.

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. In order to help determine the sequence of operations and other features of logical syntax, mathematical symbols can be used to represent numbers, variables, operations, function, brackets, punctuation, or grouping.

Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators have to include the right amount of inputs in the right places, legal characters for these inputs, a clearly defined sequence of operations, etc.

5 √8 - √18 -2√2

10√2-3√2 -2√2

√2(10-3-2)

5√2

Therefore, the correct option is option B.

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\( \sf \: 1. \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 + ( - 5)}{ - 2 - 3} \bigg]\bigg[ \frac{14 + ( - 21)}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{4 - 5}{ - 2 - 3} \bigg]\bigg[ \frac{14 - 21}{ 2 - 8} \bigg] \\ \)

\( \sf \longrightarrow \: \bigg[ \frac{ - 1}{ - 5} \bigg]\bigg[ \frac{ - 7}{ - 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{1}{ 5} \times \frac{ 7}{ 6} \\ \)

\( \sf \longrightarrow \: \frac{7}{30} \\ \)

C) 7/30 ✅

________________________________

\( \sf \: 2. \bigg[ \frac{7+ ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 + ( - 6)}{ - 4 - 9} \bigg]\bigg[ \frac{20 + ( - 45)}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{7 - 6}{ - 4 - 9} \bigg]\bigg[ \frac{20 - 45}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 4 - 9} \bigg]\bigg[ \frac{ - 25}{ 8 - 2} \bigg] \\ \)

\( \sf \longrightarrow\bigg[ \frac{1}{ - 13} \bigg]\bigg[ \frac{ -25}{ 6} \bigg] \\ \)

\( \sf \longrightarrow \: \frac{ - 25}{ - 78} \\ \)

\( \sf \longrightarrow \: \frac{ 25}{ 78} \\ \)

A] 25 / 78 ✅

________________________________

\( \sf \: 3. \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4+ ( - 5)}{ - 2 - 4} \bigg]\bigg[ \frac{18 + ( - 36)}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4 - 5}{ - 2 - 4} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{18 - 36}{ 7 - 3} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{-1}{ - 6} \bigg]\bigg[ \frac{-18}{ 4} \bigg] \\ \)

\( \sf \longrightarrow \frac{18}{ - 24} \\ \)

\( \sf \longrightarrow -\frac{6}{ 8} \\ \)

\( \sf \longrightarrow -\frac{3}{ 4} \\ \)

C] -3/4 ✅

________________________________

\( \sf \: 4. \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7+ ( - 3)}{ - 6 - 2} \bigg]\bigg[ \frac{18 + ( - 6)}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{7- 3}{ - 6 - 2} \bigg]\bigg[ \frac{18 - 6}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 6 - 2} \bigg]\bigg[ \frac{12}{ 6- 7} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{4}{ - 8} \bigg]\bigg[ \frac{12}{ -1} \bigg] \\ \)

\( \sf \longrightarrow \frac{48}{ 8} \\ \)

\( \sf \longrightarrow \frac{6}{ 1} \\ \)

\( \sf \longrightarrow 6 \\ \)

D] 6 ✅

________________________________

\( \sf \: 5. \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8+ ( - 2)}{ - 5- 6} \bigg]\bigg[ \frac{40 + ( - 48)}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{8 - 2}{ - 5- 6} \bigg]\bigg[ \frac{40 - 48}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 5- 6} \bigg]\bigg[ \frac{-8}{ 9 - 8} \bigg] \\ \)

\( \sf \longrightarrow \bigg[ \frac{6}{ - 11} \bigg]\bigg[ \frac{-8}{ 1} \bigg] \\ \)

\( \sf \longrightarrow \frac{-48}{ - 11} \\ \)

\( \sf \longrightarrow \frac{48}{ 11} \\ \)

B] 48/11 ✅

________________________________

Answer:

False

Step-by-step explanation:

4/8 equals to 1/2 but 6/10 equals to 3/5. Correct would be if it was 5/10

Answer:

80%

Step-by-step explanation:

We need to find the percent of change from 3,545 pt to 709 pt.

Original value is 3,545

Changed value is 709

Percent change is given by :

\(\%=\dfrac{\text{difference in values}}{\text{original value}}\times 100\\\\\%=\dfrac{3545-709}{3545}\times 100\\\\\%=80\%\)

So, there is 80% of change from 3,545 pt to 709 pt.

Answer:

6

Step-by-step explanation:

you do 2/3 multiplied by 9

Answer:

it will be 1 : 3

Step-by-step explanation:

Answer:

Yes, these create an isosceles triangle, where two sides are equivalent

To find the probability that the average length of a randomly selected bundle of steel rods is greater than 242.9 cm, we need to calculate the z-score and use the properties of the normal distribution.

The formula for the z-score of the sample mean is:

z = (x - μ) / (σ / √n)

Where:

x = sample mean (242.9 cm)

μ = population mean (241.8 cm)

σ = population standard deviation (1.9 cm)

n = sample size (29)

Let's calculate the z-score:

z = (242.9 - 241.8) / (1.9 / √29)

z ≈ 1.672

Now, we need to find the probability of the z-score being greater than 1.672. This can be done by looking up the corresponding area under the standard normal distribution curve.

Using a standard normal distribution table or a calculator, we find that the probability of the z-score being greater than 1.672 is approximately 0.0466.

Therefore, P(x-bar > 242.9 cm) ≈ 0.0466 (rounded to 4 decimal places).

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To calculate the length of the curve defined by r(t) = 〈2 cos(t), 2 sin(t)〉 with the domain -π/2 ≤ t ≤ π/2, we need to find the arc length using the following formula:

Arc length = ∫(from a to b) ||r'(t)|| dt

First, let's find the derivative r'(t) of the given vector function r(t):

r(t) = 〈2 cos(t), 2 sin(t)〉
r'(t) = 〈-2 sin(t), 2 cos(t)〉

Next, find the magnitude ||r'(t)|| of the derivative vector:

||r'(t)|| = √((-2 sin(t))^2 + (2 cos(t))^2)
||r'(t)|| = √(4 sin^2(t) + 4 cos^2(t))

Factor out 4:

||r'(t)|| = √(4(sin^2(t) + cos^2(t)))

Since sin^2(t) + cos^2(t) = 1:

||r'(t)|| = √(4) = 2

Now, we can find the arc length by integrating ||r'(t)|| over the given domain:

Arc length = ∫(from -π/2 to π/2) 2 dt

To integrate, simply multiply the constant by the difference in t:

Arc length = 2(π/2 - (-π/2)) = 2(π) = 2π

So, the length of the curve is 2π.

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cos^2(x) - cos^4(x)

sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).

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The surface area of the composite figure is 714 sq. in.

Let, a be the edge of the cube.

Then, surface area of the cube = 6a² square unit

Let, length of the cuboid = l unit

Width of the cuboid = w unit

Height of the cuboid = h unit

Then, surface area of the cuboid = 2(lw+lh+hw) square unit

Given, edge of cube = 4 in.

∴ Surface area of cube = (6×4²) sq. in. = 96 sq. in.

Now, given, length of cuboid = 15 in.

Width of the cuboid = 10 in. & height of the cuboid = 7 in.

∴ Surface area of the cuboid = 2{(15×10)+(15×7)+(10×7)} sq. in.

                                                = 2{150+105+70} sq. in.

                                                = 2{325} sq. in. = 650 sq. in.

Here, we have to find the surface area of the composite figure.

We have to subtract the surface area from both of cube & cuboid, where they are attached.In that case, we have to subtract (4×4) from both.

So, we have to subtract 2(4×4) sq. in. = 32 sq. in.

∴ The surface area of the composite figure = (650+96-32) sq. in.

                                                                        = 714 sq. in.

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Answer:

125 = 1, 5, 25, 125

135= 1, 3, 5, 9, 15, 27, 45, 135

55= 1, 5, 11, 55

the common factor in all three numbers is 5

Answer:

7. Positive

8. negative

9. undefined

10. undefined

Step-by-step explanation:

Answer:

1) positive 2) negative 3) zero 4) zero

I think :3

Step-by-step explanation:

The sampling distribution of p is approximately normal with a mean of 0.80 and a standard error of 0.00309.

The sampling distribution of p can be determined using the formula for standard error.

Step 1: Calculate the standard deviation (σ) using the population proportion (p) and the sample size (n).
σ = √(p * (1-p) / n)
  = √(0.80 * (1-0.80) / 220)
  = √(0.16 / 220)
  ≈ 0.0457

Step 2: Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size.
SE = σ / √n
  = 0.0457 / √220
  ≈ 0.00309

Step 3: The sampling distribution of p is approximately normal, centered around the population proportion (0.80) with a standard error of 0.00309.

The sampling distribution of p is a theoretical distribution that represents the possible values of the sample proportion. In this case, we are interested in estimating the proportion of complaints settled for new car dealers. The population proportion of settled complaints is assumed to be the same as the overall proportion of settled complaints in 2016, which is 0.80.

To construct the sampling distribution, we calculate the standard deviation (σ) using the population proportion and the sample size. Then, we divide the standard deviation by the square root of the sample size to obtain the standard error (SE).

The sampling distribution is approximately normal, centered around the population proportion of 0.80. The standard error reflects the variability of the sample proportions that we would expect to see in repeated sampling.

The sampling distribution of p for the selected sample of new car dealer complaints has a mean of 0.80 and a standard error of 0.00309. This information can be used to estimate the proportion of complaints the Better Business Bureau is able to settle for new car dealers.

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Answer: -10 :))))

i hope this helps

Answer:

\(\displaystyle -1\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

h(x) = x² + 3x - 6

[-7, 3] → a = -7, b = 3

Step 2: Find Average

The X value corresponding to z = -2.25 is X = 56.

A z score is a statistical indicator that shows how far a raw score is from a distribution's mean. Give the z-score formula. The z-score is calculated using the formula z = (x -μ)/σ.

To find the corresponding X value for a given z-score, we use the formula:

X = µ + (z * σ)

Given µ = 65, σ = 4, and z = -2.25, we can calculate the X value:

X = 65 + (-2.25 * 4)

X = 65 - 9

X = 56

Therefore, the X value corresponding to z = -2.25 is X = 56.

The correct answer is b. X = 56.

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a) The simple harmonic motion of the bobber can be modeled by the equation:

y(t) = A sin(ωt + φ)

where y is the displacement of the bobber from its equilibrium position at time t, A is the amplitude of the oscillation, ω is the angular frequency, and φ is the phase angle.

From the given information, we know that the amplitude A of the oscillation is 1.5 inches and the period T is 3 seconds. The angular frequency is related to the period by the formula:

ω = 2π/T

Substituting the values, we get:

ω = 2π/3

The phase angle φ can be determined from the initial condition that the bobber is at its high point at t = 0. At the high point, the displacement is maximum and positive, so we have:

y(0) = A sin(φ) = A

Substituting the values, we get:

1.5 = 1.5 sin(φ)

Solving for φ, we get:

φ = sin⁻¹(1) = π/2

Substituting the values of A, ω, and φ in the equation for simple harmonic motion, we get:

y(t) = 1.5 sin(2πt/3 + π/2)

b) The midpoint between the high point and the low point of the bobber corresponds to a displacement of 0.5*A = 0.75 inches.

The bobber reaches this point twice during each period, once while going up and once while going down. We need to find the time t when the bobber is going down and reaches the midpoint for the first time.

At the midpoint, the displacement of the bobber is given by:

y(t) = 0.75

Substituting the equation for y(t), we get:

1.5 sin(2πt/3 + π/2) = 0.75

Simplifying, we get:

sin(2πt/3 + π/2) = 0.5

Using the identity sin(π/6) = 0.5, we can rewrite the equation as:

sin(2πt/3 + π/2) = sin(π/6)

The general solution for this equation is:

2πt/3 + π/2 = π/6 + 2πk or 2πt/3 + π/2 = 5π/6 + 2πk

where k is an integer.

Solving for t in each case, we get:

t = (π/18 - π/2)/ (2π/3) + k or t = (5π/6 - π/2)/ (2π/3) + k

Simplifying, we get:

t = 1/4 + k/3 or t = 5/4 + k/3

The first solution corresponds to the time when the bobber is going down and reaches the midpoint for the first time, so we have: t = 1/4 seconds.

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Since Jontorya's parents put $12,340 into a Florida prepaid account to start saving for her college, their interest rate is 14.9%.

Given the following data:

To find Jontorya's parents interest rate:

Mathematically, simple interest is given by the formula:

\(S.I = \frac{PRT}{100}\)

Where:

Making R the subject of formula, we have:

\(R = \frac{100S.I}{PT}\)

Substituting the given parameters into the formula, we have;

\(R = \frac{100 \times 5553}{12340 \times 3}\\\\R = \frac{555300}{37290}\)

Interest rate, R = 14.9%

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Answer:

16.75

Step-by-step explanation:

sorry for the wrong answer

Answer:

36

Step-by-step explanation:

Given:

1/6 of the marbles are red

1/3 of the marbles are blue

There are 18 green marbles in the jar

We can set up the following equations based on the given information:

Number of red marbles = 1/6 * x

Number of blue marbles = 1/3 * x

Number of green marbles = 18

Since the total number of marbles in the jar is "x", we can write the equation for the sum of all the marbles as:

(Number of red marbles) + (Number of blue marbles) + (Number of green marbles) = x

Substituting the values from the given information:

1/6 * x + 1/3 * x + 18 = x

Multiplying through by 6 to eliminate the fraction:

x/6 + 2x/6 + 18 = 6x/6

x + 2x + 108 = 6x

Combining like terms:

3x + 108 = 6x

Subtracting 3x from both sides of the equation:

3x + 108 - 3x = 6x - 3x

108 = 3x

Dividing both sides by 3 to solve for x:

108/3 = 3x/3

36 = x

Answer:

y = -6/7x - 3/7 or 7y = -6x - 3

Step-by-step explanation:

I'm guessing you mean line c: y = -6/7x - 1

Parallel lines have same slope => line d will have slope = -6/7

y = mx + b

-9 = -6/7(10) + b

-9 = -60/7 + b

b = 60/7 - 9 = 60/7 - 63/7 = -3/7

y = -6/7x - 3/7

or 7y = -6x - 3

The system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

A line process has three processing stages with the characteristics given below:

Stage A B C Unit processing time(minutes) 1 2 3 Number of machines 1 1 2 Machine availability 90% 100% 100% Process yield at stage 100% 100% 100%

To determine the system capacity and the bottleneck stage and utilization of Stage 3:

The system capacity is calculated by the product of the processing capacity of each stage:

1 x 1 x 2 = 2 units per minute

The bottleneck stage is the stage with the lowest capacity and it is Stage A. Therefore, Stage A has the lowest capacity and determines the system capacity.The utilization of Stage 3 can be calculated as the processing time per unit divided by the available time per unit:

Process time per unit = 1 + 2 + 3 = 6 minutes per unit

Available time per unit = 90% x 100% x 100% = 0.9 x 1 x 1 = 0.9 minutes per unit

The utilization of Stage 3 is, therefore, (6/0.9) x 100% = 666.67%.

However, utilization cannot be greater than 100%, so the actual utilization of Stage 3 is 100%.

Hence, the system capacity is 2 units per minute, the bottleneck stage is Stage A, and the utilization of Stage 3 is 100%.

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Answer:

19.25(miles?)

Step-by-step explanation:

Assuming 3.5 is the x value or input of the function

3.5 x 5.5 = 19.25

The area of the rhombus is 54 sq. units

Area of the trapizium is 115 sq. units.

A quadrilateral called a rhombus has four equal-length sides. The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

A parallelogram's general characteristics are as follows:

In American and Canadian English, a quadrilateral having at least one set of parallel sides is referred to as a trapezoid. It is referred to as a trapezium in British and other varieties of English. In Euclidean geometry, a trapezoid is a convex quadrilateral by definition. The bases of the trapezoid are the parallel sides.

The area of a rhombus = ½ x (product of the lengths of the diagonals)

= ½ *18*6 = 54 sq. units

Area of the trapizium = ½ x (sum of the lengths of the parallel sides) x perpendicular distance between parallel sides

=½ *(17 + 29) * 5 = 115 sq. units.

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The coordinates of G' after the rotation = (6, 5)

In this question we have been given a point G, located at (-5, 6) is rotated 270° counterclockwise.

We need to find the coordinates of G' after the rotation.

a point (-5, 6) is located in the second quadrant.

First 90° counterclockwise rotation gives (-6, -5)  because x & y are interchanged and in Quadrant III both coordinates will be negative.

Second 90° counterclockwise rotation yields (5,-6) because x & y are interchanged and in Quadrant IV the y coordinate will be negative.

Last 90° counterclockwise rotation yields (6, 5) because x & y are interchanged and in Quadrant I both coordinates will be positive.

Therefore, the coordinates of G' after the rotation = (6, 5)

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In linear equation, $200.62 is his average monthly expense for utilities.

What are a definition and an example of a linear equation?

Expenditure in December by Bill = $ 188.31

Expenditure in January by Bill = $192.80

Expenditure in February by Bill = $ 220.75

We have to find the average monthly expenses for Bill's utilities.

We know that,

Average monthly expense for utilities = (Expenditure in December + Expenditure in January + Expenditure in February)/3

Hence, using the data given in the question, we can write,

Average monthly expense for utilities = (188.31 + 192.80 + 220.75)/3

Average monthly expense for utilities = 601.86.01/3 =  $200.62

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