Ethan's class is handing out balloon arrangements consisting of 4 balloons each. Each balloon has an equally likely chance of being red, blue, or yellow. Ethan created a spinner to simulate this probability. Here is Ethan's data from 30 trials of 4 spins on the spinner (r = red, b = blue, y = yellow):



ybrr bybb rbbb rrry rbbb rryy yybb ryry ryyr rbyr ryyr rryy rrrr yrby bbyy byyr byyr byyb rbby ybry rryy rbrr rybb bbbr rrbr ybry ryrr rryb rrrb rryr



According to this data, what is the experimental probability that an arrangement will contain at least one yellow balloon?

0.75
0.23
0.767
0.233

The null and alternative hypothesis is represented by option A.

The test statistic is 0.153.

We want to test the claim that women and men have the same mean diastolic blood pressure.Let μ1 be the mean diastolic blood pressure for women and let μ2 be the mean diastolic blood pressure for men.

The t-statistic value will be:

= (69.81 - 69.53) / (✓10.46²/26 + 11.24²/26)

=0.153

Since p-value for two tail test=0.879 which is greater than =0.05(0.879>0.05) So we do not reject H0.

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Using Pythagorean's theorem we can see that the variables are:

t = 13.86

w = 12.81

Remember that for any right triangle, Pythagorean's theorem says that the sum of the squares of the legs is equal to the square of the hypotenuse, where the hypotenuse is the side opposite to the 90° angle.

Then for the first triangle we can write:

t² + 8² = 16²

Solving for t:

t = √(16² - 8²) = 13.86

For the second triangle we have:

10² + 8² = w²

Solving for w:

w = √(10² + 8²)

w = 12.81

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Answer:

Think about the PEMDAS rules for order of operations.

Multiplication comes before addition or subtraction, so first we have "the product of a number and 5" - that's 5x. Then "six more" than that would be 5x + 6. "Equals" means the "=" sign, so the final answer is 5x + 6 = 8.

Answer:B

Step-by-step explanation:i did the quiz

The radius of the sphere with a volume of 10000 m³ is approximately 13.4 meters.

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

Where r is the radius of the sphere and π is the mathematical constant pi (approximately equal to 3.14).

Given that the volume of the sphere is 10000 m³, we can set up the equation:

Volume =  (4/3)πr³

r³ = Volume / (4/3)π

r = ∛( Volume / (4/3)π )

r = ∛( 10000/ ( (4/3) × 3.14) )

r = 13.4 m

Therefore, the radius is 13.4 m.

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The equations that can be used to solve for y, the length of the room are y * (y - 5) = 750, y^2 - 5y = 750 and (y + 25)(y – 30) = 0

From the question, we have the following parameters that can be used in our computation:

Area = 750

Length = y

Width = y - 5

The area is the product of the length and the width

So, we have

y * (y - 5) = 750

When expanded. we have

y^2 - 5y = 750

Lastly, we have

(y + 25)(y – 30) = 0 -- when factored

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The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

The answer is 1/5

Step-by-step explanation:

5ft:25ft=5ft/25ft=1/5

Answer:

1/2

Step-by-step explanation:

The value that lie above 25% of the data of the box plot is 31 and the lower quartile (Q1) = 14 upper quartile (Q3) = 31

Given data ,

The minimum value, which is 14

Now , the lower quartile, which is 16 (25% of the data is below this value)

And , the median, which is 24 (50% of the data is below this value)

Now , the upper Quartile, which is 31 (75% of the data is below this value)

And , the maximum value is 32.

The upper and lower quartiles of a box plot, also known as the 75th percentile (Q3) and 25th percentile (Q1) respectively, represent the range within which the middle 50% of the data falls.

Lower quartile (Q1) = 14

Upper quartile (Q3) = 31

Hence , 25% of the data lie above 31, which is the upper quartile.

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The water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

We have

Number of students= 1200

Water consumption per student= 750 ml

So, Total water consumption

= Number of students × Water consumption per student

= 1200 × 750 ml

= 900000 ml

= 900 Liter

Now, the time cooler tank has to be filled to quench the thirst

= 900 / 50

= 18 times

Thus, the water cooler tank has to be filled 18 times to quench the thirst of 1200 students.

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The difference in the students who chose peach pie and apple pie is 46

From the question, we have the following parameters that can be used in our computation:

From the above, we have the percentage difference to be

Difference = 38% - 15%

When the given values are substituted, we have

Difference = 23%

This means that

Students = 23% * 200

Evaluate

Students = 46

Hence, the number of students is 46

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The triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

We have,

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given that YO = NZ.

Consider YO = NZ

Now Add OZ on both sides

YO + OZ = NZ + OZ

YZ = NO

Consider triangles Δ MNO and ΔXYZ.

M ≅ X

N ≅ Y

YO ≅ NZ

Δ MNO ≅ ΔXYZ by AAS postulate.

Therefore, the triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

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complete question:

The congruency of △MNO and △XYZ can be proven using a reflection across the line bisecting OZ. However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Given: M ≅ X

N ≅ Y

YO ≅ NZ

Prove: △MNO ≅ △XYZ

The distance between the areas of the two states is A = 1.727 x 10⁵ km²

Given data ,

Let the area of Nebraska = 2 x 10⁵ km²

Let the area of Massachusetts = 2.73 x 10⁴ km²

The difference between the areas of Nebraska and Massachusetts A =  the area of Nebraska - the area of Massachusetts

On simplifying the exponents , we get

A = 2 x 10⁵ km² - 2.73 x 10⁴ km²

Taking the common factor , we get

A = 10⁴ ( 20 - 2.73 )

A = 10⁴ ( 17.27 )

A = 1.727 x 10⁵ km²

Hence , the area is A = 1.727 x 10⁵ km²

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The solution to the given system of equations is a = 6, b = 4.

The system of equations is given as follows:

a + b = 10  .....(i)

a - b = 2    .....(ii)

To solve this system of equations, we can use the method of elimination.

Adding the two equations, we get:

(a + b) + (a - b) = 10 + 2

2a = 12

a = 6

Substituting a = 6 into one of the equations, we get:

6 - b = 2

b = 4

Therefore, the solution to the system of equations is:

a = 6, b = 4.

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Using the correct measure of center, the team that typically has the tallest players is C. The Champs, with a mean of about 66.4 inches.

The three typical measures of center are the mean, the median, and the mode.

The mean is the average value, obtained as the quotient of the total value of the data set divided by the number of items.

The median is the middle value of the data set arranged in descending or ascending order.

The mode refers to the value that occurs most in the data set.

66 66 66 = 198

63 63 63 = 189

65 65 65 = 195

64 64 64 = 192

58 58 58 = 174

Total =      948

Mean = 63.2 (948 ÷ 15)

Median = 64 (58, 58, 58, 63, 63, 63, 64, 64, 64, 65, 65, 65, 66, 66, 66)

62 69 65 = 196

68 60 70 = 198

70 58 67 = 195

66 75 70 = 211

69 67 60 = 196

Total = 996

Mean = 66.4 (996 ÷ 15)

Median = 67 (58, 60, 60, 62, 65, 66, 67, 67, 68, 69, 69, 70, 70, 70, 75)

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Answer:

Step-by-step explanation:

You want the amounts in each of two accounts, one earning 8% interest, and the other, with an initial balance that is $450 greater, earning 12% interest. The total interest earned is $176.

Let x represent the initial balance in the 12% account. Then the initial balance in the 8% account is (x -450). The total interest earned is ...

  0.08(x -450) +0.12(x) = 176

  0.20x - 36 = 176 . . . . . simplify

  0.20x = 212 . . . . . . add 36

  x = 1060 . . . . . .  divide by 0.2

  x -450 = 610

The 8% account had $610 invested; the 12% account had $1060 invested.

The net sales, =$20.98

The Goods available for sales= $2,045

The total cost of Goods sold=$1,955

Gross profit =$1,934.02

Net income = $1,395.98

The operating income (sales) = $7,240

The return on sales (ROS) = $345

The net sales (revenue generated) = ?

But ROS = operating income/net sales

Net sales = 7240/345;

= $20.98

The goods available for sale = beginning inventory+ new purchase = $725+$1320 = $2,045.

The total cost of Goods sold = Beginning inventory+goods available for sale - end inventory.

= 725+2,045- 815

= 2770-815

= $1,955

The gross profit = cost of goods sold (COGS) - total revenues.

= $1,955-$20.98

= $1,934.02

Net income = total operating expenses - gross profit

operating expenses = 1,750+1000+280+150+150 = $3,330

gross profit = $1,934.02

Net income = 3,330-1,934.02 = $1,395.98

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Investing could help you grow your funds over time. For example, if you were to invest $30 per month in a stock mutual fund that has a long-term average annual return of 8%, after 10 years, your investment could grow to about $5,000.

This could provide you with more financial security and give you the opportunity to reach your financial goals faster than keeping your money in a savings account.

Some investment products that you could consider are stocks, bonds, mutual funds, and exchange-traded funds (ETFs). You could also consider robo-advisors, which use algorithms to create and manage investment portfolios for you based on your goals and risk tolerance.

When it comes to choosing investments, there are a few things you can consider. First, think about your financial goals and your time horizon. This will help you determine how much risk you can afford to take on.

Thus, if you have a long-term goal, such as saving for retirement, you may be able to afford to take on more risk than if you have a short-term goal, such as saving for a down payment on a house.

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Step-by-step explanation:

5 000 gm = 5 kg

784kg  - 5kg=  779 kg  more than average

The x and y int for the equation are x = undefined and y-int = 1

From the question, we have the following parameters that can be used in our computation:

y = 4^x

Set the variable x to 0 to calculate the y-intercept

So, we have

y-int = 4^0

y-int = 1

Set the variable y to 0 to calculate the x-intercept

So, we have

4^x = 0

So, we have

x = ln(0)/ln(4)

Evaluate

x = undefined

Hence, the x-intercept is undefined

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Answer:

90 children's tickets and 200 adult tickets were sold.

Step-by-step explanation:

Let's use the variables c and a to represent the number of children's and adult tickets sold, respectively.

From the problem, we know that:

The total number of tickets sold is 290: c + a = 290

The total revenue from ticket sales is $2250: 5c + 9a = 2250

We now have two equations with two unknowns. We can use substitution or elimination to solve for c and a. Here's one way to use elimination:

Multiply the first equation by 5 to get 5c + 5a = 1450

Subtract the above equation from the second equation to eliminate c: 5c + 9a - (5c + 5a) = 2250 - 1450

Simplify: 4a = 800

Solve for a: a = 200

Substitute a = 200 into the first equation to solve for c: c + 200 = 290

Simplify: c = 90

Therefore, 90 children's tickets and 200 adult tickets were sold.

Answer:

The sample space describing all possible outcomes is:

{H1, H2, H3, H4, T1, T2, T3, T4}

The outcomes for the event that the coin toss is heads are:

{H1, H2, H3, H4}

Step-by-step explanation:

If it pertains to using the format H1 to mean that the coin toss is heads and the number chosen is 1.

The height of the rectangle is approximately 15.5 inches.

Let's call the height of the rectangle "h". We know that the width is 47 inches longer than the height, so the width can be expressed as "h + 47".

We can use the Pythagorean theorem to solve for the height. The Pythagorean theorem states that for a right triangle with legs of length "a" and "b" and hypotenuse of length "c", a^2 + b^2 = c^2.

In this case, we can consider the rectangle to be a right triangle, with the height as one leg, the width as the other leg, and the diagonal as the hypotenuse. So we can write:

h^2 + (h + 47)^2 = 65^2

Simplifying this equation gives:

2h^2 + 94h - 1476 = 0

We can solve for "h" using the quadratic formula:

h = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 2, b = 94, and c = -1476. Plugging these values into the quadratic formula gives:

h = (-94 ± sqrt(94^2 - 4(2)(-1476))) / 4

Simplifying this expression gives:

h = (-94 ± sqrt(10084)) / 4

h = (-94 ± 100.42) / 4

h = -48.6 or 15.42

Since the height of the rectangle cannot be negative, we can discard the negative solution. Therefore, the height of the rectangle is approximately 15.5 inches.

The volume of the pyramid is  9333 cubic centimetres

From the question, we have the following parameters that can be used in our computation:

Base dimensions = 40 cm by 20 cm

Height = 35 cm

The volume of the pyramid is calculated as

Volume = Product of Base dimensions and Height/3

substitute the known values in the above equation, so, we have the following representation

Volume = 40 * 20 * 35/3

Evaluate

Volume = 9333

Hence, the volume is 9333

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The volume of the sphere is 5,575.28 ft³.

The volume of the sphere is calculated by applying the following formula as shown below;

V = ⁴/₃ πr³

where;

The radius of the sphere is calculated as follows;

r = d/2

where;

r = 22 ft / 2

r = 11 ft

The volume of the sphere is calculated as;

V = ⁴/₃ π(11)³

V = 5,575.28 ft³

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If he business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344.12 were written, checkbook balance after checks and deposit are processed is $6613.25.

To find the checkbook balance, we need to add up the initial balance, subtract the amounts of the written checks, and add the deposit made by the store manager.

Starting with the initial balance of $7349.44, we subtract the amount of the first check for $1349.67, leaving a balance of $6000.77. Then we subtract the second check for $344.12, leaving a balance of $5656.65.

Finally, we add the deposit made by the store manager for $956.60, which gives us a final balance of $6613.25.

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The value of x is given as follows:

x = 13.1 ft.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

We have that the important parameters are given as follows:

Hence the value of x is obtained as follows:

sin(57º) = 11/x

x = 11/sine of 57 degrees

x = 13.1 ft.

The triangle is given by the image presented at the end of the answer.

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The equation of the line passing through the given points is y = -2x+1.

Given that is a line passing through two points (0, 1) and (2, -3) we need to find the equation of the line using them,

We know that the equation of a line passing through points (x₁, y₁) and (x₂, y₂) is =

y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)

Here (x₁, y₁) and (x₂, y₂) are (0, 1) and (2, -3),

Therefore, the required equation is =

y-1 = -3-1/2 (x-0)

y-1 = -2x

y = -2x+1

Hence, the equation of the line passing through the given points is y = -2x+1.

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