Use the organized list which shows the possible outcomes of flipping a fair coin three times, where H is heads and T is tails.

Answer:

The formula for the volume of a cone is V = (1/3)πr^2h,

r is the base radius

h is the height.

Substituting the given values, we get:

V = (1/3)π(4 yards)^2(9 yards)

V = (1/3)π(16 yards^2)(9 yards)

V = (1/3)π(144 yards^3)

V = 48π cubic yards

Therefore, the volume of the cone is 48π cubic yards.

Answer:

$6.81 or 681 US Cents

Step-by-step explanation:

100 - 19 = 81

7 - 1 = 6

$7.00 - .19 = $6.81

or 681 US Cents.

To calculate the number of years it will take to finish paying the debt, we need to determine the total number of monthly installments required.

Loan amount: ₦90,000

Monthly installment: ₦2,500

Total number of installments: Loan amount / Monthly installment

Total number of installments: ₦90,000 / ₦2,500 = 36

Therefore, it will take the man 36 months to finish paying the debt. To convert this into years, we divide the number of months by 12 since there are 12 months in a year.

Number of years: 36 months / 12 months/year = 3 years

Hence, it will take him approximately 3 years to finish paying the debt.

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The expression 1.05h correctly represents the total amount Sylvia will pay for the hat if it costs h dollars.

Sylvia knows that the price of the hat will increase by 5% when she pays sales tax. Let's break down the expressions to understand them better.

Expression 1: h + 0.05h

In this expression, h represents the cost of the hat. Adding 0.05h to h accounts for a 5% increase. However, this expression does not accurately represent the total amount Sylvia will pay because it only considers the increase due to sales tax, not the original cost of the hat.

Expression 2: 1.05h

In this expression, 1.05 represents the total cost multiplier, which includes the original cost of the hat and the 5% increase. Multiplying h by 1.05 accounts for both the original cost and the sales tax increase. This expression correctly calculates the total amount Sylvia will pay for the hat.

Therefore, the expression 1.05h is the correct representation of the total amount Sylvia will pay for the hat if it costs h dollars.

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Answer:

Surface area = 408.2cm²

Volume = 628cm²

Step-by-step explanation:

r = radius

h = height

Surface Area

A = 2xπxrxh+2xπxr²

A = 2 x 3.14 x 5 x 8 + 2 x 3.14 x 25

A = 251.2 + 157

A = 408.2cm²

Volume

V = πr²h

V = 3.14 x 5 x 5 x 8

V = 628cm²

The perimeter of trapezium, is 0.92 meters. And 0.92 meters in millimeters is 920 mm. Therefore, option B is the answer.

Let's name the trapezium as ABCD.

AB= 0.41m

BD= 0.21m

CD= 0.18m

AC= 0.12m

∴ AB and CD are parallel sides and AC and BD are oblique sides.

The perimeter of trapezium = Sum of parallel sides + Sum of oblique sides

The perimeter of trapezium = (AB+CD) + (AC+BD)

                                                = (0.41+0.18) + (0.12+0.21)

                                                = 0.59 + 0.33

∴ The perimeter of trapezium ABCD = 0.92 meters.

Converting 0.92 meters into millimeters (mm)

0.92 × 1000 = 920 millimeters (mm)

Therefore, the perimeter of trapezium in millimeters is 920 mm.

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The probabilities for this problem are given as follows:

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The total number of regions is given as follows:

12.

One of these 12 regions is a six, hence:

p(6) = 1/12.

Six of these numbers are prime numbers, hence:

p(prime number) = 6/12 = 1/2.

Six of the numbers are odd, while 4, 6 and 9 are unshaded even numbers, hence:

p(odd or unshaded) = 9/12 = 3/4.

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Answer:

Step-by-step explanation:

principle=1000

time= 2 years

rate = 2×12=24/100=0.24%

simple intrest= p×r×t

= 1000 × 0.24 × 2

=480 rupees

total amount will be 1000 + 480= 1480

The coordinates of the midpoint M of segment JK are (-0. 3). The distance between the endpoints of JK is sqrt(104) or approximately 10.198.

To find the coordinates of the midpoint M of segment JK, we can use the midpoint formula, which states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints. So, for segment JK with endpoints J(3, -6) and K(-3, 2), the x-coordinate of the midpoint is (-3+3)/2 = 0 and the y-coordinate of the midpoint is (-6+2)/2 = -2. Therefore, the coordinates of the midpoint M are (0, -2).

To find the distance between the endpoints of JK, we can use the distance formula, which states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by the square root of [(x2-x1)^2 + (y2-y1)^2]. So for segment JK with endpoints J(3, -6) and K(-3, 2), the distance is sqrt[(-3-3)^2 + (2-(-6))^2] = sqrt[36 + 64] = sqrt(100) = 10. Therefore, the distance between the endpoints of JK is approximately 10.198.

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The length of side a is approximately 6.0 in the triangle. The correct option is (b) 6.0.

To find the length of side a in triangle ABC, we can use the Law of Sines.

The Law of Sines states that the ratio of a side length to the sine of its opposite angle is constant for all sides of a triangle.

In this case, we have:

a/sin(A) = b/sin(B) = c/sin(C)

Given that angle A has a measure of 29°, we can substitute the known values:

a/sin(29°) = 13.5/sin(B) = 8.9/sin(C)

Solving for side a, we have:

a = sin(29°) × 13.5 / sin(B)

To find sin(B), we can use the fact that the sum of the angles in a triangle is 180°:

B = 180° - A - C = 180° - 29° - 90° (since angle C is 90° in a right triangle)

B = 61°

Now we can calculate side a:

a = sin(29°) × 13.5 / sin(61°)

a ≈ 6.0

Therefore, the length of side a is approximately 6.0. The correct option is (b) 6.0.

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Answer:

The null hypothesis (H0) is that the average time spent studying is 2 hours or less, while the alternative hypothesis (H1 or Ha) is that the average time spent studying is more than 2 hours.

The null hypothesis (H0) is a statement of no effect or no difference, while the alternative hypothesis (H1 or Ha) is a statement of the opposite, suggesting that there is an effect or a difference.

In this case, the professor does not believe that his students spend 2 hours on average studying for the final exam and thinks they spend more time than that.

The null hypothesis (H0) would be that the average time spent studying for the final exam is indeed 2 hours or less:

H0: μ ≤ 2

The alternative hypothesis (H1 or Ha) would be that the average time spent studying for the final exam is more than 2 hours:

Ha: μ > 2

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The lateral area for the regular pyramid is 18√91 sq. units

The base of the pyramid has a side length of 6 units

Hypotenuse of triangle is the lateral edge

base = 6 and height = 8

Lateral edge  = 10

To find the slant height

The height of triangle with base  3 and hypotenuse 10 is Slant height

Slant height  = √91

To find the area of single face

Area = bh/2

b = 6 and h =  √91

Area = (6×√91)/2 = 3√91

To find the lateral area of pyramid

Lateral area = 6×face area = 6×3√91 = 18√91 square units

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The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.

To find the zeros of the function F(x) = -(x+6)^2 - 49, we need to find the values of x when F(x) = 0.
Step 1: Set the function equal to 0.
0 = -(x+6)^2 - 49
Step 2: Isolate the squared term.
49 = -(x+6)^2
Step 3: Divide both sides by -1 to remove the negative sign.
-49 = (x+6)^2
Step 4: Take the square root of both sides.
√(-49) = x+6
Since the square root of a negative number is a complex number (involving an imaginary unit 'i'), there are no real zeros for this function. The zeros are complex and can be written as:
Lesser x = -6 - 7i
Greater x = -6 + 7i
Your answer: The zeros of the function F(x) = -(x+6)^2 - 49 are -6 - 7i and -6 + 7i.

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The unconditional expectation of y (E(y)) equals β0 + (β1 * E(x)), derived using the Law of Iterated Expectations.

To simplify the expression for the unconditional expectation E(y), we can apply the properties of expected value and the Law of Iterated Expectations. The Law of Iterated Expectations states that the unconditional expectation of a conditional expectation is equal to the unconditional expectation itself.

Starting with the expression for E(y):

E(y) = E(β0 + β1x + u)

We can break down this expression using the linearity of expectation:

E(y) = E(β0) + E(β1x) + E(u)

Since β0 and β1 are constants, their expected values are equal to themselves:

E(y) = β0 + β1E(x) + E(u)

Now, since u is the error term and it is assumed to have a mean of zero (E(u) = 0), the expression simplifies to:

E(y) = β0 + β1E(x)

Therefore, we can conclude that the unconditional expectation of y (E(y)) is equal to the constant term β0 plus the product of the slope coefficient β1 and the unconditional expectation of x (E(x)). This result follows from the Law of Iterated Expectations, which allows us to simplify the expression by considering the expected values of the individual terms separately.

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Answer:

The correct answer is: A. If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.

Step-by-step explanation:

A confidence interval is a range of values that is likely to contain the true value of a population parameter. In this case, the population parameter is the proportion of voters who favor a tax on e-commerce. The confidence interval is constructed from a sample of voters, and it is based on the assumption that the sample is representative of the population.

The 99% confidence interval means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion. This does not mean that there is a 99% chance that the true value of the population proportion lies between 0.113 and 0.171. It means that if we were to take many different samples of size 250 and construct a confidence interval for each sample, 99% of the confidence intervals would contain the true value of the population proportion.

The other answer choices are incorrect because they do not correctly interpret the meaning of a confidence interval.

Answer:

$9.25

Step-by-step explanation:

One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.

We have,

We are given that the cost C of buying three boxes of popcorn and a fountain drink is represented by the equation C = 3x + 1.75.

Where x is the number of popcorn.

Now,

We want to find the cost of one box of popcorn when the cost is $9.70.

Let's first substitute C = 9.70 into the equation:

9.70 = 3x + 1.75

Next, we'll isolate x by subtracting 1.75 from both sides:

9.70 - 1.75 = 3x

7.95 = 3x

Finally, we'll solve for x by dividing both sides by 3:

x = 7.95/3 = 2.65

Therefore,

One box of popcorn costs $2.65 while the total cost of three boxes of popcorn and a fountain drink is $9.70.

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The volume of the recycling bin when the length is doubled is 3,600 cubic feet.

To find the volume of the recycling bin when the length is doubled, we first need to determine the original volume of the bin.

The formula for the volume of a rectangular prism is V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length is 15 ft, the width is 12 ft, and the height is 10 ft. So the original volume of the recycling bin is:

V = lwh = 15 ft × 12 ft × 10 ft = 1,800 cubic feet

To find the volume when the length is doubled, we simply need to multiply the original length by 2, and then calculate the new volume using the same formula:

New length = 15 ft × 2 = 30 ft

New volume = lwh = 30 ft × 12 ft × 10 ft = 3,600 cubic feet

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The value of the acute angles are 67.4° and 22.6° respectively

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

sin(tetha) = opp/hyp

cos( tetha) = adj/hyp

tan(tetha) = opp/adj

Here the longest side which is the hypotenuse is 13 and the other legs of the right triangle are 12 and 13.

Represent the acute angle by A and B. If 12 is that opposite and 5 is the adjascent

sin A = 12/13

A = sin^-1( 0.923)

A = 67.4°

sinB = 5/13

B = sin^-1( 0.385)

B = 22.6°

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The order of Candice and her friends in terms of who was more consistent would be :

Candice is judged to be the least consistent of the friends because of her range which is:

= Largest laps - least laps

= 8 - 5

= 3 laps

Malaya and Zoe the same range so this cannot be used to show which of them was more consistent. Instead, we will use the mode. The person that has the mode which appears more times is more consistent.

Zoe has a mode of 8 laps which appears 3 times as opposed to the mode of 3 laps for Malaya which only appears twice. Zoe is therefore most consistent.

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Answer:

32.5

Step-by-step explanation:

if it completes a pack per second then it’s 32.5 g per second but this question does not have much detail on what you need to do

The equation of the line in Slope-intercept form is y = -3x - 3.

The equation of the line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to solve for y.

Starting with the given equation:

9x + 3y = -9

We can isolate y by subtracting 9x from both sides:

3y = -9x - 9

Now we can simplify the equation by dividing both sides by 3:

y = (-9/3)x - 3

Simplifying the fraction, we get:

y = -3x - 3

Therefore, the equation of the line in slope-intercept form is y = -3x - 3.

The slope of the line is -3, which means that for every 1 unit increase in x, y decreases by 3 units. The y-intercept is -3, which means that the line crosses the y-axis at the point (0, -3).

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Answer:

To tell if a polynomial is constant, linear, quadratic, cubic or quartic, you must first look at the highest power of the variable in the polynomial. If the highest power is 0, then the polynomial is a constant. If the highest power is 1, then it is a linear polynomial. If the highest power is 2, then it is a quadratic. If the highest power is 3, then it is a cubic and finally, if the highest power of the variable is 4, then the polynomial is a quartic.

Step-by-step explanation:

No, Jenna and Henry cannot both be correct. Jenna’s answer of 614 hours is incorrect, as it is much too long for a school day. Henry’s answer of 6.25 hours is also incorrect, as it is much too short for a school day.

The part of the length of the school day that is the same in all three ways the time is given is the hours. In the first way, the school day is given as 6 hours and 15 minutes.

In the second way, the school day is given as 6.25 hours. In the third way, the school day is given as 375 minutes. In each case, the number of hours in the school day is the same: 6 hours. However, the way that the minutes are expressed differs, leading to different numerical values.

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Answer:

x = 19

Step-by-step explanation:

Let's use the following variables:

Let x be the number of coach seats sold.

Let y be the number of first-class seats sold.

We know that there are 29 seats in total, so:

x + y = 29

We also know that the total amount collected for the flight was $21,900, so:

600x + 1050y = 21,900

We can solve this system of equations by substitution or elimination. Let's use elimination.

Multiplying the first equation by 600, we get:

600x + 600y = 17400

Subtracting this equation from the second equation, we get:

450y = 4500

Dividing both sides by 450, we get:

y = 10

Substituting this value into the first equation, we get:

x + 10 = 29

x = 19

Therefore, the airline sold 19 coach seats and 10 first-class seats.

The inverse of f(x) = 11x - 8 include the following: C. [tex]f^{-1}(x) = \frac{x+8}{11}[/tex]

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In this exercise, you are required to determine the inverse of the function f(x). This ultimately implies that, we would have to swap (interchange) both the independent value (x-value) and dependent value (y-value) as follows;

f(x) = y = 11x - 8

x = 11y - 8

11y = x + 8

By dividing both sides of the equation by 11, we have:

y = x/11 + 8/11

f⁻¹(x) = (x + 8)/11

[tex]f^{-1}(x) = \frac{x+8}{11}[/tex]

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To find the test statistic for a test to show that the population mean height of the school district is lower than 59 inches, we can perform a one-sample t-test.

The test statistic is calculated using the sample mean, sample standard deviation, sample size, and the hypothesized population mean.

Given the sample heights of the 11 fifth-grade boy students: 59.0, 57.2, 57.1, 58.0, 57.0, 50.1, 52.3, 55.6, 57.8, 53.9, 57.8, we can calculate the sample mean () and sample standard deviation (s).

= (59.0 + 57.2 + 57.1 + 58.0 + 57.0 + 50.1 + 52.3 + 55.6 + 57.8 + 53.9 + 57.8) / 11

Next, calculate the sample standard deviation:

s = sqrt(((59.0 - )^2 + (57.2 - )^2 + ... + (57.8 - )^2) / (11 - 1))

Once you have the sample mean and sample standard deviation, you can calculate the test statistic (t):

t = ( - μ) / (s / sqrt(n))

where μ is the hypothesized population mean (in this case, 59 inches), and n is the sample size (11).

By substituting the values into the formula, you can calculate the test statistic rounded off to the first decimal place.

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