A movie theater has a seating capacity of 323. The theater charges $5. 00 for children, $7. 00 for


students, and $12. 00 of adults. There are half as many adults as there are children. If the total ticket


sales was $ 2348, How many children, students, and adults attended?


_____children attended.


_____students attended.


_____adults attended.

The solution of the given system of equations is x = 3.2 and y = 1.5.

To solve this system of equations, we can use the method of elimination, where we eliminate one of the variables by adding or subtracting the equations.

First, let's eliminate y by multiplying the first equation by 2 and the second equation by 15:

12x/5 + 2y/15 = 4.6 (multiply the first equation by 2)

3x/2 - 10y = 18 (multiply the second equation by 15)

Now we can eliminate y by multiplying the first equation by 5 and adding it to the second equation:

12x + y/5 = 23 (multiply the first equation by 5 and simplify)

12x - y = 54 (subtract the second equation from the previous equation)

Adding the two equations, we get:

24x = 77

Therefore, x = 77/24.

Substituting x = 77/24 into the first equation, we get:

6(77/24)/5 + y/15 = 2.3

Simplifying this equation, we get:

y = 1.5

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Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700

Mato will pay more in interest because he has a higher interest rate and a shorter repayment period. To calculate the amount of interest each will pay, we can use the formula:

Interest = (Loan amount) x (Interest rate) x (Time in years)

For Kika:
Interest = $5,000 x 0.052 x 5
Interest = $1,300

For Mato:
Interest = $5,000 x 0.075 x (2/12)
Interest = $625

Therefore, Mato will pay about $700 more in interest than Kika ($625 - $1,300 = $675, which rounds to $700). The answer is C: Mato; $700.

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The probability of getting a number less than 5 or greater than 9 is:

P = 0.583

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are less than 5 or greater than 9 are:

{1, 2, 3, 4, 10, 11, 12}

So 7 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 7/12 = 0.583

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b. <2 ≅ < 3; corresponding angles are equal

d. < 1 + < 2 = 180 degrees; sum of angles on a straight line

To determine the reasons, we need to know about transversals

Transversals are lines that passes through two lines at the given plane in two distinct points.

It intersects two parallel lines

It is important to note the following;

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the MAXIMUM area that can be enclosed is 900 m²

To find the maximum area that can be enclosed, we need to find the vertex of the parabolic function A(x) = -4x^2 + 120x. The vertex represents the maximum point on the parabola.

The x-coordinate of the vertex can be found using the formula x = -b/2a, where a is the coefficient of the x^2 term and b is the coefficient of the x term. In this case, a = -4 and b = 120, so x = -120/(2*(-4)) = 15.

To find the y-coordinate of the vertex, we can substitute x = 15 into the function: A(15) = -4(15)^2 + 120(15) = 900. Therefore, the maximum area that can be enclosed is 900 square meters.

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The area of S is:

[tex]A(S) = 16\pi \sqrt{(500/11)}= 128.8[/tex]

The surface S can be described in terms of cylindrical coordinates by setting:

x = r cos(θ)

y = r sin(θ)

z = z

Using these coordinates, we can rewrite the equation for C as:

r² = 22/100(x² + y²) = 22/100r²

Simplifying this equation, we get:

[tex]r = \sqrt{(500/11)}[/tex]

Thus, the surface S is the portion of the cylinder of radius [tex]\sqrt{(500/11)}[/tex] between z = 1 and z = 5.

To calculate the area of S, we can use the formula:

A(S) = ∫∫∂S ||n|| [tex]dA[/tex]

where ||n|| is the magnitude of the normal vector to the surface, and [tex]dA[/tex] is the area element on the surface.

For the cylinder, the normal vector is simply the radial unit vector pointing outward from the origin:

n = (cos(θ), sin(θ), 0)

The magnitude of the normal vector is ||n|| = 1, so we can simplify the formula for the area to:

A(S) = ∫∫∂S [tex]dA[/tex]

To evaluate this integral, we need to parameterize the surface S. We can use the cylindrical coordinates we defined earlier:

x = r cos(θ)

y = r sin(θ)

z = z

with 0 ≤ θ ≤ 2π and 1 ≤ z ≤ 5.

The area element in cylindrical coordinates is given by:

[tex]dA = r \ dz\ d\theta[/tex]

Substituting in our parameterization of S, we get:

A(S) = ∫∫∂S r [tex]dz[/tex] dθ

[tex]= \int\limits^{2\pi }_0 \int\limits^5_1 {\sqrt{(500/11)} dz d\theta}\\= \sqrt{(500/11)} \int\limits^{2\pi }_0 {(5 - 1) d\theta}\\= 16\pi \sqrt{(500/11)[/tex]

Therefore, the area of S is:

[tex]A(S) = 16\pi \sqrt{(500/11)}= 128.8[/tex]

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Answer:

2 7/24 gallons

(sorry if its wrong)

The value of x that will make a parallel to b is 30. We solved the equation 4x + 2x = 180 and obtained x = 30.

According to the definition of interior consecutive angles, when a transversal intersects two parallel lines, the sum of the measures of the two interior consecutive angles formed on the same side of the transversal is always 180°.

In this case, we are given that lines A and B are parallel, and line q intersects these lines at two distinct points, forming two interior consecutive angles with measures 4x and 2x, respectively.

Since the two angles are consecutive and on the same side of the transversal, their sum is equal to 180°. Therefore, we can set up the following equation

4x + 2x = 180

Simplifying the equation, we get

6x = 180

Dividing both sides by 6, we get

x = 30

Therefore, the value of x that will make a parallel to b is 30.

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--The given question is incomplete, the complete question is given

" Find the value of x that will make a parallel to b.

Lines A and B are parallel lines and a transverse line is intersecting these lines at two distinct points, making the angle 4x and 2x

x= "--

The total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.

What is Kilometer ?

Kilometer (km) is a metric unit of length or distance, commonly used in many countries around the world. It is equal to 1000 meters, or approximately 0.62 miles.

To find the shortest route back to Port X from Port Y, the ship needs to sail in a straight line. This means that it needs to sail due south for 20 kilometers and then due east for 25 kilometers.

We can now use the Pythagorean theorem to find the total distance traveled by the ship:

total distance = √(400+ 625 + 400+ 625)

total distance = √(1200 + 625)

total distance = √1825

total distance ≈ 42.73 kilometers (rounded to the nearest kilometer)

Therefore, the total distance traveled by the ship, including the trip from Port X to Port Y and the return trip, is approximately 42 kilometers.

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We can express the limits of integration as follows:

For z between 0 and 5/√2, x and y range from 0 to √(25 - [tex]z^2[/tex]).

For z between 5/√2 and 5/2, x and y range from 0 to √(3[tex]z^2[/tex] - 25).

For z between 5/2 and 5, x and y range from 0 to √(25 - z

Find the equation of the sphere.

The equation of a sphere with center (0,0,0) and radius r is

[tex]x^2 + y^2 + z^2 = r^2.[/tex]

In this case, we have r = 5, so the equation of the sphere is

[tex]x^2 + y^2 + z^2 = 25.[/tex]

Find the equations of the cones.

The equation of a cone with half-aperture angle θ and vertex at the origin is given by [tex]x^2 + y^2 = z^2 tan^2[/tex](θ). In this case, we have two cones: one with θ = π/4 and one with θ = π/3.

Their equations are x^[tex]2 + y^2 = z^2 tan^2(\pi /4) = z^2[/tex] and [tex]x^2 + y^2 = z^2 tan^2(\pi /3) = 3z^2.[/tex]

Find the intersection points of the sphere and the cones.

To find the intersection points, we substitute the equation of the sphere into the equations of the cones: [tex]x^2 + y^2 + z^2 = 25, x^2 + y^2 = z^2,[/tex] and x^2 + [tex]y^2 = 3z^2[/tex]. This gives us two sets of equations:

[tex]x^2 + y^2 = z^2 and x^2 + y^2 + z^2 = 25:[/tex]

Substituting [tex]x^2 + y^2 = z^2[/tex] into[tex]x^2 + y^2 + z^2 = 25[/tex], we get [tex]2z^2 = 25[/tex],

which gives z = ±5/√2.

[tex]x^2 + y^2 = 3z^2 and x^2 + y^2 + z^2 = 25:[/tex]

Substituting[tex]x^2 + y^2 = 3z^2[/tex]into [tex]x^2 + y^2 + z^2 = 25[/tex], we get [tex]4z^2 = 25[/tex],

which gives z = ±5/2.

So we have four intersection points: (±5/√2, ±5/√2, ±5/√2) and (±5/2, ±5/2, ±5/2√3).

Find the part of the ball that lies between the cones.

To find the volume of the part of the ball that lies between the cones, we

need to integrate the volume element dV = dx dy dz over the region

enclosed by the cones and the sphere. Since the region is symmetric

about the z-axis, we can integrate over a quarter of the region and

multiply the result by 4.

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Question

Express the volume of the part of the ball that lies between two cones: one with a half-aperture angle of π/4 and the other with a half-aperture angle of π/3.

Emily's homework will take approximately 9 hours to complete.

Emily has 6 pages of homework and she can finish 3/8 of a page in one hour, we can calculate the total number of hours required to complete her homework.

To find the number of hours, we divide the total number of pages by the number of pages she can finish in one hour:

Number of hours = Total number of pages / Pages finished in one hour

Number of hours = 6 pages / (3/8) pages per hour

To divide by a fraction, we can multiply by its reciprocal:

Number of hours = 6 pages * (8/3) pages per hour

Simplifying the multiplication:

Number of hours = 48/3

Number of hours = 16

Therefore, Emily's homework will take approximately 16 hours to complete.

Hence, the answer is that Emily's homework will take approximately 9 hours to complete.

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The value of x that maximizes the volume of the box is x=11 cm.

Let x be the length of the side of each square cut from the corners of the paper.

The height of the box will be x cm, and the length and width of the base of the box will be (88-2x) cm and (82-2x) cm, respectively.

The volume of the box is given by V(x) = x(88-2x)(82-2x).

Expanding this expression and simplifying, we get V(x) = 4x^3 - 340x^2 + 7040x.

To find the maximum volume, we take the derivative of V(x) with respect to x and set it equal to 0. We get dV/dx = 12x^2 - 680x + 7040 = 0.

Solving this quadratic equation using the quadratic formula, we get x = (680 ± sqrt(680^2 - 4127040))/(2*12).

Simplifying this expression, we get x = (680 ± 120)/24.

Therefore, the two possible values of x are x = 25/3 cm and x = 11 cm.

To determine which value of x maximizes the volume of the box, we evaluate V(x) at both values of x and compare them. We find that V(25/3) ≈ 5757.04 cm^3 and V(11) = 5808 cm^3.

Therefore, the value of x that maximizes the volume of the box is x = 11 cm.

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The random variable in this scenario is the number of cars held up at the intersection (option d).

The data provided in the table shows the number of cars held up at the intersection during specific time intervals, ranging from 12:00 p.m. to 9:00 p.m. Based on this information, it is clear that the random variable in this scenario is the number of cars held up at the intersection.

To put it in mathematical terms, let X be the random variable representing the number of cars held up at the intersection during a specific time interval. The data provided in the table represents a sample of X, with each time interval being a different observation. The values of X can range from 0 to 25, with 17 being the threshold for intervention by a traffic officer.

Therefore, the answer to the question is d. the number of cars held up at the intersection. It is important to note that this random variable is discrete, as it takes on specific integer values.

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No, the relationship between the number of additional boxes of candles purchased. C = 14.00 + 10.00b. The person would spend $34.00 on 3 boxes of candles.

a. No, the relationship between the number of additional boxes of candles purchased and the total money spent is not linear. This is because the cost of the first box is $14.00 and the cost of each additional box is $10.00.

A linear relationship implies that the change in the dependent variable (total money spent) is proportional to the change in the independent variable (number of additional boxes purchased), but in this case, the cost does not change at a constant rate.

b. The equation that relates the total money spent on boxes of candles, C, to the number of additional boxes purchased, b, is:

C = 14.00 + 10.00b

This equation takes into account the cost of the first box, which is $14.00, and the cost of each additional box, which is $10.00.

c. If someone buys 3 boxes of candles, they are purchasing 2 additional boxes (since the first box is already included in the $14.00). Using the equation from part (b), the total money spent by a person who bought 3 boxes of candles for the fundraiser would be:

C = 14.00 + 10.00(2) = $34.00

Therefore, the person would spend $34.00 on 3 boxes of candles.

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14.33% of the lifetime cost of Hillary's laptop was interest.

Since Hillary paid off her laptop in two and a half years, and kept it for six years, we need to calculate the compound interest over six years. Accounting for two leap years, there were 365 * 6 + 2 = 2192 days over the period that Hillary kept the laptop. Therefore, the total cost of electricity over that period was 2192 * 0.27 = $592.64.

Plugging in the values, we get:

A = 804 * (1 + 0.1127/12)³⁰= 1003.94

Hillary paid $1003.94 for her laptop, including interest. Subtracting the original cost of the laptop, we get:

Interest = 1003.94 - 804 = 199.94

So Hillary paid $199.94 in interest on her credit card over two and a half years. To calculate what percentage of the lifetime cost of the laptop was interest, we need to divide the interest paid by the total cost of the laptop and electricity:

Lifetime cost = 804 + 592.64 = 1396.64

Percentage of lifetime cost that was interest = (199.94 / 1396.64) * 100% = 14.33%

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For the following probabilities:

7. Theoretically, if the spinner is spun 400 times, you would expect to get blue 100 times since blue has a probability of 1/4 or 25% of being selected on each spin.

8. Based on the experiment, if the spinner is spun 400 times, you would expect to get blue around 95-105 times, depending on the margin of error in the experiment. This is based on the observed experimental probability of blue being selected in the given number of spins.

9. a) P(club) = 13/52 or 1/4

b) P(red card) = 26/52 or 1/2

c) P(not a heart) = 39/52 or 3/4

10. a) P(club) = 5/30 or 1/6 in the experiment, which is close to the theoretical probability of 1/4 or 0.25.

b) P(red card) = 13/30 in the experiment, which is close to the theoretical probability of 1/2 or 0.5.

c) P(not a heart) = 27/30 in the experiment, which is close to the theoretical probability of 3/4 or 0.75.

11. Theoretically, if a card is drawn at random 500 times, you would expect to get a spade around 125 times since spades have a probability of 1/4 or 25% of being selected on each draw.

12. Based on the experiment, if a card is drawn at random 500 times, you would expect to get a spade around 110-140 times, depending on the margin of error in the experiment. This is based on the observed experimental probability of spades being selected in the given number of draws.

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Image transcribed:

7. Theoretically, if the spinner is spun 400 times, how many times would you expect to get blue?

8. Based on the experiment, if the spinner is spun 400 times, how many times would you expect to get blue?

9. A card is drawn from a standard deck of cards. Find each probability.

a) P(club)

b) P(red card)

c) P(not a heart)

10. The table below shows the results of an experiment in which a card was drawn at random 30 times. Find each probability based on the experiment and compare to the theoretical probability.

Result | Frequency

Heart | 3

Diamond | 10

Club | 5

Spade | 12

a) P(club)

b) P(red card)

c) P(not a heart)

11. Theoretically, if a card is drawn at random 500 times, how many times would you expect to get a spade?

12. Based on the experiment, if a card is drawn at random 500 times. how many times would you expect to get a spade?

To use the Limit Comparison Test, we need to find a series whose behavior is well-known and similar to the given series. Let's consider the series aₙ = n². We have:

limₙ→∞ (aₙ / (n² - 5naₙ - 6)) = limₙ→∞ (n² / n²) = 1

Since this limit is finite and positive, and aₙ is a convergent series (by the p-series test with p = 2), we can apply the Limit Comparison Test and conclude that the given series is convergent.
To determine if the series ∑(n² - 5n) from n=1 to infinity is convergent or divergent using the Limit Comparison Test, we need to find a comparable series and then calculate the limit of the ratio between the two series as n approaches infinity.

Let's compare the given series to a simpler series ∑n² (n=1 to infinity). Now, we'll find the limit of the ratio:

Limit (n→∞) [(n² - 5n) / n²]

As n approaches infinity, the -5n term becomes insignificant compared to the n² term. So, the limit becomes:

Limit (n→∞) [n² / n²] = 1

Since the limit is a finite, nonzero value (1 in this case), the given series and the comparison series will have the same convergence behavior. We know that the series ∑n² (n=1 to infinity) is a divergent series, as it is a p-series with p=2 (less than or equal to 1). Therefore, the given series ∑(n² - 5n) from n=1 to infinity is also divergent.

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Answer:

Nicole has 9 dimes and 19 nickels.

The value of the [tex]5000^{th}[/tex] term in the given arithmetic sequence K is 44995.

The sequence that is given in the question is said to be an arithmetic sequence which means the consecutive elements in the series will have common differences.

To find any term in the series first, we need to find the first term and the common difference that the series follows.

Here we know that the first and the second term of the series are 4 and 13 so from this we can find the common difference which is:

13-4=9

so the first term (a) = 4

the common difference (d) = 9

To find the [tex]n^{th}[/tex] term of the series we can use the formula:

[tex]a_n=a_1+(n-1)*d[/tex]

where [tex]a_n[/tex] is the nth term in the sequence, [tex]a_1[/tex] is the first term of the series, n is the no.of term, and d is the common difference.

So to find the 5000th term in the series

[tex]a_{5000}=4+(5000-1)*9\\a_{5000}=4+(4999*9)\\a_{5000}=4+ 44991\\a_{5000}= 44995\\[/tex]

The value of the [tex]5000^{th}[/tex] term is 44995

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(A) The length that beats 80 seconds is 256 cm.

(B) The time of a pendulum with length 36 cm is 30 seconds.

(A) According to the given information, the time of a pendulum varies as the square root of its length. Let's denote time as T and length as L. Therefore, T ∝ √L. To find the constant of proportionality, we can use the provided data: T1 = 15 seconds and L1 = 9 cm. So, we have T1 / √L1 = k, where k is the constant. Now, let's find k: k = 15 / √9 = 15 / 3 = 5.

Now, we want to find the length (L2) of a pendulum that beats 80 seconds (T2). We can use the formula T2 = k * √L2. Substituting the values, we get 80 = 5 * √L2. To find L2, we can rearrange and solve for it: L2 = (80 / 5)² = 16² = 256 cm.

(B) To find the time (T3) of a pendulum with a length of 36 cm (L3), we can use the same formula with the known constant k: T3 = k * √L3. Substituting the values, we get T3 = 5 * √36 = 5 * 6 = 30 seconds.

In conclusion, the length of a pendulum that beats 80 seconds is 256 cm, and the time of a pendulum with a length of 36 cm is 30 seconds.

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The height of the base of the statue, structured in rectangular prism shape with stated measure of dimension is 4 feet.

The volume of the rectangular prism will be given by the formula -

Volume = length × width × height

Keep the values in formula to find the value of height of the base of the statue

60 = 5 × 3 × height

Rearranging the equation in terms of height

Height = 60 × (5 × 3)

Multiplying the denominator on Right Hand Side

Height = 60/15

Divide the values

Height = 4

Hence the height is 4 feet.

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The newspaper should increase its subscription price by $2.19 to maximize its weekly income and the new subscription price would be  $8.19 per week.

To maximize the newspaper's income, we need to find the price that will result in the highest revenue. Let's assume that the newspaper increases the subscription price by x dollars.

Then the revenue R(x) can be expressed as:
R(x) = (700 - 40x) * (6 + 0.75x)

Expanding the expression, we get:

R(x) = 4200 + 1050x - 240x^2

To find the price that maximizes revenue, we need to find the value of x that maximizes R(x). We can do this by taking the derivative of R(x) with respect to x and setting it equal to 0:

dR/dx = 1050 - 480x = 0

Solving for x,

x = 1050/480 = 2.1875

Therefore, the newspaper should increase its subscription price by $2.19 to maximize its weekly income. The new subscription price would be:

6 + 2.19 = $8.19 per week.

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The area of the regular hexagon is 509.2 square units (to the nearest tenth).

The formula for the area of a regular polygon is:

[tex]\boxed{\text{Area}=\frac{\text{r}^2\text{n sin}\huge \text(\frac{360^\circ}{\text{n}}\huge \text) }{y} }[/tex]

where:

From inspection of the given regular polygon:

Substitute the values into the formula and solve for area:

[tex]\text{Area}=\dfrac{14^2\times6\times\text{sin}\huge \text(\frac{360^\circ}{6}\huge \text) }{2}[/tex]

        [tex]=\dfrac{196\times6\times\text{sin} (60^\circ)}{2}[/tex]

        [tex]=\dfrac{1176\times\frac{\sqrt{3} }{2} }{2}[/tex]

        [tex]=\dfrac{588\sqrt{3} }{2}[/tex]

        [tex]=294\sqrt{3}[/tex]

        [tex]=509.2 \ \text{square units (nearest tenth)}[/tex]

Therefore, the area of the regular hexagon is 509.2 square units (to the nearest tenth).

The sample space for this experiment contains a total of 12 possible outcomes.

The sample space for this experiment is the set of all possible outcomes. In this case, we have two independent events: flipping a coin and rolling a number cube.

The possible outcomes for flipping a coin are H (heads) and T (tails).

The possible outcomes for rolling a number cube are 1, 2, 3, 4, 5, and 6.

To determine the sample space for the experiment, we need to consider all possible combinations of these outcomes. Therefore, the sample space consists of all possible pairs of outcomes:

Sample space = {(H, 1), (H, 2), (H, 3), (H, 4), (H, 5), (H, 6), (T, 1), (T, 2), (T, 3), (T, 4), (T, 5), (T, 6)}

So the sample space for this experiment contains a total of 12 possible outcomes.

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We conclude that the data are consistent with Mendel's prediction of a 3:1 ratio of smooth to wrinkled peas.

To carry out a chi-square goodness-of-fit test, we need to calculate the expected number of smooth and wrinkled peas based on Mendel's prediction of a 3:1 ratio.

The total number of peas observed in the experiment is:n = 423 + 133 = 556The expected number of smooth peas is 3/4 of the total number of peas, and the expected number of wrinkled peas is 1/4 of the total number of peas.

Therefore, we have: Expected number of smooth peas = 3/4 × 556 = 417Expected number of wrinkled peas = 1/4 × 556 = 139

We can now calculate the chi-square statistic as follows:chi-square = Σ[(observed - expected)² / expected]where the sum is taken over the two categories (smooth and wrinkled).

For the observed values of 423 smooth and 133 wrinkled peas, we have: chi-square = [(423 - 417)^2 / 417] + [(133 - 139)^2 / 139]= 0.84 + 0.84= 1.68

The degrees of freedom for this test are (number of categories - 1), which is 2 - 1 = 1.

Using a significance level of 0.05 and a chi-square distribution table with 1 degree of freedom, we find that the critical value of chi-square is 3.84.

Since our calculated chi-square value of 1.68 is less than the critical value of 3.84, we fail to reject the null hypothesis that the observed frequencies do not differ significantly from the expected frequencies based on Mendel's prediction.

Therefore, we conclude that the data are consistent with Mendel's prediction of a 3:1 ratio of smooth to wrinkled peas.

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The expected population proportion,  with 95% confidence, that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

Based on the survey results, we know that 58% of the sample respondents prefer to shop at places with loyalty cards. If the margin of error is 3.4%, we can calculate the expected range of the population proportion as follows:

Upper bound: 58% + 3.4% = 61.4%
Lower bound: 58% - 3.4% = 54.6%

Therefore, we can say with 95% confidence that the expected population proportion that prefers to shop at places with loyalty cards is between 54.6% and 61.4%.

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If John bought stock for $350 then A year later, he sold it for $385. So John's Return on investment is 10%.

To find John's gain in dollars, we need to subtract the purchase price from the selling price i.e. Gain = Selling price - The purchase price. So John's Return on investment is 10%.

Gain = $385 - $350

Gain = $35

So John's gain in dollars is $35.

To find John's return on investment (ROI), we need to use the formula:

ROI = (Gain / Investment) x 100%

We already know the gain is $35, and the investment is $350. Substituting these values into the formula, we get:

ROI = ($35 / $350) x 100%

ROI = 0.1 x 100%

ROI = 10%

So John's Return on investment is 10%. Rounded to the nearest whole percent, the answer is also 10%.

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Answer:

p=3

Step-by-step explanation:

The probability that the woman would have done at least as well if she had no ability to recognize: the difference between the two methods is 0.117.

Let's assume that the woman has no ability to recognize the difference between the two methods. In that case, the probability of guessing the correct answer for each trial is 0.5 (since there are only two options).

The number of correct answers in 10 trials follows a binomial distribution with parameters n = 10 and p = 0.5. We want to calculate the probability of getting at least 7 correct answers.

Using a binomial distribution calculator or a standard normal distribution table, we can find that the probability of getting 7 or more correct answers is 0.117 (rounded to three decimal places).

Therefore, if the woman had no ability to recognize the difference between the two methods, there would still be a 0.117 probability that she would have gotten at least 7 correct answers by chance. Since 0.117 is not a small probability, we cannot reject the null hypothesis that the woman has no ability to recognize the difference between the two methods based solely on this experiment.

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