(Chapter 13) Different parametrizations of the same curve result in identical tangent vectors at a given point on the curve.

Answer:

  10

Step-by-step explanation:

You want a number such that the square root of the sum of it and 8 is 3 times the square root of 2.

The relation in the problem statement is ...

  √(x +8) = 3√2

Squaring both sides, we have ...

  x +8 = 3²·2 = 18

  x = 10 . . . . . . . . . subtract 8

The number is 10.

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Answer:

  A, B, E are irrational

Step-by-step explanation:

You want to know which expressions result in an irrational number from the given expressions involving rational and irrational numbers.

  M + N = √2 +√5 . . . . irrational

  MN = (√2)(√5) = 10 . . . . irrational

  S + T = 2 + 5 = 7 . . . . rational

  ST = 2·5 = 10 . . . . rational

  N + T = √5 + 5 . . . . irrational

  N² = (√5)(√5) = 5 . . . . rational

__

Additional comment

When in doubt, you can use your calculator to evaluate these expressions. If the decimal fraction uses all available digits, the number is likely irrational.

If the number cannot be expressed exactly without using symbols (√, ∛, π, e), then it is irrational. The attached calculator display shows this nicely.

The discount percentage that has been offered to Sydney if after the discount she has to pay $20.79 for an item marked at $21 is 1%

Discount refers to a reduction in price offered on articles and items in order to increase sales. It is a marketing technique.

Listed price =$21

After discount price = $20.79

Discount offered = 21 - 20.79

= $0.21

Discount percentage = [tex]\frac{LP - DP}{LP}*100[/tex]

where LP is Listed Price

DP is Discount Price

Discount percent = [tex]\frac{21-20.79}{21}*100[/tex]

= [tex]\frac{0.21}{21}*100[/tex]

= 0.01 * 100

= 1%

Therefore, the discount she gets is equal to 1% after she uses her loyalty card at her local hardware store.

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Using a z-table or calculator, we can find that the probability of getting a z-score less than -3.14 is approximately 0.0008 (rounded to four decimal places as requested).

Using the Empirical Rule and the concept of probability, I can help you find the requested probability. The Empirical Rule, also known as the 68-95-99.7 rule, states that for a normal distribution:

- Approximately 68% of the data falls within 1 standard deviation (SD) of the mean
- Approximately 95% of the data falls within 2 SDs of the mean
- Approximately 99.7% of the data falls within 3 SDs of the mean

You are asked to find the probability P(z < -3.14). Since -3.14 is slightly beyond -3 SDs from the mean, we know that less than 0.15% of the data falls in that area, as 99.7% of the data is within ±3 SDs.

However, to get a more precise probability, we need to use a standard normal (Z) table or calculator. When looking up z = -3.14, we find that the probability P(z < -3.14) is approximately 0.0008.

So, the probability you are looking for is 0.0008.

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The measures of angles are m∠A = 80°, m∠B = 50°, and m∠C = 50°, concluding that the triangle is an isosceles triangle.

Based on the given information, we can start by using the fact that the angles in a triangle sum to 180 degrees. Let's label the unknown angles as m∠A, m∠B, and m∠C:

m∠A + m∠B + m∠C = 180

We also know that m∠1 = m∠2, which means that triangle ABD is similar to triangle CBD by the Angle-Angle (AA) similarity theorem. This implies that the ratios of corresponding sides in these triangles are equal:

AB/BD = BD/DC

Since BD = DC, we have AB = DC.

Therefore, triangle ABC is isosceles with AB = AC. This means that m∠B = m∠C.

Now let's use the given information that BD = DC and m∠BDC = 100° to find the measure of m∠B. We can draw the perpendicular bisector of BC to point D, which will bisect angle BDC into two equal angles of measure x degrees.

Since triangle BDC is isosceles, we know that:

m∠DBC = m∠DCB

= (180 - m∠BDC)/2

= 40°.

Therefore, m∠B = m∠DBC + m∠DCB = 40° + x.

Now we can use the fact that the angles in triangle ABC sum to 180 degrees to solve for m∠A:

m∠A + m∠B + m∠C = 180

m∠A + 2m∠B = 180 (since m∠B = m∠C)

m∠A + 2(40° + x) = 180 (since m∠B = 40° + x)

m∠A + 80° + 2x = 180

m∠A = 100° - 2x

We also know that m∠BDC = 100°, so m∠DBC = m∠DCB = (180 - m∠BDC)/2 = 40°. Therefore, we can write:

m∠A + m∠B + m∠C = 180

m∠A + 2m∠B = 180 (since m∠B = m∠C)

m∠A + 2(40° + x) = 180 (since m∠B = 40° + x)

m∠A + 80° + 2x = 180

m∠A = 100° - 2x

Now we can solve for x by using the fact that m∠A, m∠B, and m∠C must be positive:

m∠A > 0, m∠B > 0, m∠C > 0

100° - 2x > 0

x < 50°

Therefore, the possible values of x are 10°, 20°, 30°, 40°, and 49°. We can use these values to find the measures of m∠A, m∠B, and m∠C:

If x = 10°, then m∠A = 80°, m∠B = 50°, and m∠C = 50°.

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A: Liam is correct. The graph shows a positive correlation between ice cream sales and temperature. As the temperature increases, ice cream sales also increase.

B: Armonte is not correct. There are a few reasons why the graph represents a correlation and not causation:

Correlation does not imply causation. Just because two variables are correlated, it does not mean that one variable causes the other.

There could be other variables that are affecting both ice cream sales and temperature. For example, if the graph was plotted over a long period of time, there may be seasonal factors that affect both variables, such as summer months having higher temperatures and more ice cream sales.

The graph only shows a relationship between ice cream sales and temperature, but it does not prove causation. To establish causation, a controlled experiment would need to be conducted to show that changes in temperature cause changes in ice cream sales.

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For part (a), we use the product rule and chain rule of differentiation:

y = x^2 sin(8x)

dy/dx = (2x sin(8x)) + (x^2 cos(8x) * 8)

dy/dx = 2x sin(8x) + 8x^2 cos(8x)

So, the differential of y = x^2 sin(8x) is dy = (2x sin(8x) + 8x^2 cos(8x)) dx.

For part (b), the differential is simply the derivative of y with respect to x, since y is not a function of x in this case:

y = 4+

dy/dx = 0

So, the differential of y = 4+ is dy = 0 dx.

To find the differential of each function, we will use the derivative rules. Let's solve each part step-by-step:

(a) y = x^2 sin(8x)

To find the differential (dy) of this function, we will need to find the derivative of y with respect to x (dy/dx). In this case, we will use the product rule, which states that if y = uv, where u and v are functions of x, then:

dy/dx = u(dv/dx) + v(du/dx)

Let u = x^2 and v = sin(8x).

Now, we need to find du/dx and dv/dx:

du/dx = 2x (by using the power rule)
dv/dx = 8*cos(8x) (by using the chain rule)

Now apply the product rule:

dy/dx = x^2 * 8*cos(8x) + sin(8x) * 2x
dy/dx = 8x^2*cos(8x) + 2x*sin(8x)

So, the differential of the function y = x^2*sin(8x) is dy/dx = 8x^2*cos(8x) + 2x*sin(8x).

(b) y = 4

To find the differential (dy) of this function, we will find the derivative of y with respect to x (dy/dx).

Since y is a constant function (it doesn't depend on x), its derivative is simply:

dy/dx = 0

So, the differential of the function y = 4 is dy/dx = 0.

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To solve this problem, we need to first find the average number of shoppers in the new store at any time.

We know that during business hours, 90 shoppers per hour enter the store and each stays an average of 12 minutes.

To find the average number of shoppers at any time, we need to convert the time each shopper spends in the store to hours:

12 minutes = 0.2 hours

So, on average, each shopper takes up 0.2 hours in the store.

Therefore, the average number of shoppers in the new store at any time is:

90 shoppers/hour x 0.2 hours/shopper = 18 shoppers

Now we can find the percent less that the average number of shoppers in the new store is compared to the original store:

Percent less = (Original - New) / Original x 100%

Percent less = (45 - 18) / 45 x 100%

Percent less = 27 / 45 x 100%

Percent less = 60%

So the answer is A. 60.
To find the average number of shoppers in the new store at any time, we can use the formula:

Average number of shoppers at any time = (Number of shoppers per hour * Average time spent in store) / 60

For the new store:
Average number of shoppers at any time = (90 shoppers per hour * 12 minutes) / 60
Average number of shoppers at any time = 1080 / 60 = 18 shoppers

Now we will find the percentage difference between the average number of shoppers in the original store (45 shoppers) and the new store (18 shoppers):

Percentage difference = ((Original store shoppers - New store shoppers) / Original store shoppers) * 100
Percentage difference = ((45 - 18) / 45) * 100
Percentage difference = (27 / 45) * 100 = 60%

So the average number of shoppers in the new store at any time is 60% less than the average number of shoppers in the original store at any time. Your answer: A. 60

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If "exponential-function" is "5ˣ + 6", then (a) Domain: All real numbers

Range: All real numbers greater than 6.

The "Domain" of an exponential function is all real numbers, since any real number can be raised to a power. The range, depends on the value of the base and any vertical shift that is applied to the function.

In the given function F(x) = 5ˣ + 6, the base is 5 which is greater than 1. Therefore, as x approaches negative infinity, F(x) approaches 6, and as x approaches positive infinity, F(x) grows without bound.

It means that the range of the function is all real-numbers greater than 6.

Therefore, the correct option is (a).

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The given question is incomplete, the complete question is

What are the domain and range of the exponential function below?

F(x) = 5ˣ + 6,

(a) Domain: All real numbers

Range: All real numbers greater than 6

(b) Domain: All real numbers greater than 0

Range: All real numbers greater than 0

(c) Domain: All real numbers greater than 0

Range: All real numbers greater than 6

(d) Domain: All real numbers

Range: All real numbers greater than 0

Step-by-step explanation:

solve for y

x-4y =24

-4y = 24-x

 y = x/4 - 6    slope = 1/4, the coefficient of the x term

a perpendicular line has the negative inverse,  change the sign and flip the fraction upside down to get -4/1 or -4

y=-4x + b.  plug in the point x=-2, y=7 to calculate b the y intercept

7=-4(-2) + b

b = 7-8 =-1

y=-4x -1 is the perpendicular line through (-2,7)

general equation in slope intercept form is y=mx +b.  m=-4,  b=-1

The critical values of x are 31.319, 18.475, and 28.869 for each case respectively.

To find the critical values of x (x₂), we'll use the chi-square distribution table. The critical values depend on the degrees of freedom (df) and the significance level (α).

1. For n=14 and α=0.005:
  Degrees of freedom (df) = n - 1 = 14 - 1 = 13
  From the chi-square table, x₂ (13, 0.005) ≈ 31.319

2. For n=8 and α=0.01:
  Degrees of freedom (df) = n - 1 = 8 - 1 = 7
  From the chi-square table, x₂ (7, 0.01) ≈ 18.475

3. For n=18 and α=0.02:
  Degrees of freedom (df) = n - 1 = 18 - 1 = 17
  From the chi-square table, x₂ (17, 0.02) ≈ 28.869

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The correct surface area of the cylinder is  878.06 sq. cm.

From the net of the cylinder we have the diameter of the circular bases of the cylinder.

So, the radius of the circle would be,

r = 13/2

Using the formula for area of circle the surface area of two circular bases would be,

A₁ = 2 × π × r²

A₁ = 2 × π × (13/2)²

A₁ = π × 169/2

A₁ = 265.46 sq. cm.

The length of the rectangle would be equal to the circumference of the circle.

So, the length of the rectangle would be,

l = 2× π × r

l = 2× π × (13/2)

l = 13 × π

l = 40.84 cm

Using the formula for the area of rectangle,

A₂ = l × w

A₂ = 40.84 × 15

A₂ = 612.6 sq. cm.

So, the total surface area of the cylinder would be,

A = A₁ + A₂

A = 265.46 +  612.6

A = 878.06 sq. cm.

This means that the surface area claimed by Talia is incorrect.

Therefore, the correct surface area of the cylinder =  878.06 sq. cm.

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The values of the trigonometry are as follows

8. cos x = 9/17

10. sin x = 0.8

12. cos x = 4/5

From trigonometry: cos² x + sin² x = 1

Let the angle be x

8.

cos² x + sin² x = 1

cos² x + (4√13)/17 = 1

cos² x = 1 - (4√13)/17

cos² x = 81 / 289

cos x = √(81 / 289)

cos x = 9/17

10.

sec x = 5/3 and sec x = 1 / cos x, therefore

cos x = 3/5

x = arc cos 3/5

x = 53.1301

sin x = 0.8

12.

sec x = 5/4 and sec x = 1 / cos x, therefore

cos x = 4/5

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The Pacific Northwest region of america is located within the upper northwest corner of the united states of america, bordering to the Pacific Ocean. The state this is most generally located in this place is Washington,

That's home to numerous fundamental cities which include Seattle and Olympia. Oregon, that's located simply south of Washington, is also taken into consideration to be part of the Pacific Northwest.

The vicinity is thought for its various geography, which incorporates lush forests, rugged coastlines, and towering mountains such as Mount Rainier and Mount Hood.

The Pacific Northwest is likewise domestic to a vibrant tradition and economy, with industries which include generation, aerospace, and outside pastime gambling massive roles within the place's boom and development.

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x = -1 and x = 3 are the solutions to the equation [tex]-x^2+2x+3=0[/tex].

To solve the quadratic equation[tex]-x^2+2x+3=0[/tex], we can use the quadratic formula:

[tex]x = \frac{(-b \pm \sqrt{b^2 - 4ac)} }{2a}[/tex]

In this case, a = -1, b = 2, and c = 3, so we can substitute these values into the formula:

[tex]x = \frac{(-2 \pm \sqrt{2^2 - 4*1*3)} }{2*-1}[/tex]

x = (-2 ± sqrt(16)) / (-2)

x = (-2 ± 4) / (-2)

Simplifying this expression, we get:

x₁ = (-2 + 4) / (-2) = -1

x₂ = (-2 - 4) / (-2) = 3

Therefore, the solutions to the equation [tex]-x^2+2x+3=0[/tex] are x = -1 and x = 3.

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Answer:

1ab

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

1ab or just ab

Step-by-step explanation:

All 3 parts of the equation have the variables ab at the end, meaning that the solution will also end with ab.

Let's first solve by doing the first property, subtraction:

3ab-9ab=-6ab

Now, we add that sum to 7ab:
-6ab+7ab=1ab

Depending on what they ask, you can either write 1ab or ab, they are the exact same thing.

The given problem is a hypothesis testing problem, specifically a one-sample proportion test.

The null hypothesis is that the proportion of stuffed animals sold is 0.7, and the alternative hypothesis is that it is greater than 0.7. The sample proportion is 400/500=0.8, and we need to test whether this result is statistically significant at a 1% level of significance. We assume a normal distribution for the sample proportion and use a one-tailed z-test to calculate the p-value and make a conclusion about the null hypothesis.

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Answer:

No solution

Step-by-step explanation:

How many solutions does 5 = -5 ?

5 ≠ -5

So, there is no solution

Given that P(Xi > 0), we can infer that the probability of Xi being positive has implications on the convergence properties of the sequence and the limiting constant 'a'.

Based on the information given, we can say that the probability of xi being greater than zero is positive, i.e., p(xi > 0) > 0. This means that xi has a positive probability of taking values greater than zero.

Moreover, since the sequence of random variables converges in probability to a constant a, we can say that for any ε > 0,

lim P(|xi - a| > ε) = 0

This implies that as n approaches infinity, the probability that xi deviates from a by more than ε approaches zero.

Thus, we can conclude that the sequence of random variables xi is "almost surely" bounded away from zero as n approaches infinity, and the limit of the sequence is the constant a.
. Considering a sequence of random variables X1, X2, ..., Xn that converges in probability to a constant 'a', we can say that the probability of each Xi being greater than 0, denoted as P(Xi > 0), is relevant to understanding the limiting behavior of the sequence.

As the sequence converges in probability to 'a', it means that for any given ε > 0, the probability that the absolute difference between Xi and 'a' is greater than ε approaches 0 as n approaches infinity:

lim (n→∞) P(|Xi - a| > ε) = 0

Given that P(Xi > 0), we can infer that the probability of Xi being positive has implications on the convergence properties of the sequence and the limiting constant 'a'.

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The perfect square trinomial for this problem would be 5(x - (7/5))^2.

The given quadratic equation is:

5x^2 - 14x + 8

To complete the square and find the perfect square trinomial, follow these steps:

1. Make sure the coefficient of x^2 is 1. Divide the entire equation by the coefficient of x^2 (in this case, 5):

  x^2 - (14/5)x + 8/5

2. Find the term to complete the square. Take half of the coefficient of the x term, square it, and add it to both sides:

  x^2 - (14/5)x + (14/10)^2 = -8/5 + (14/10)^2

3. Rewrite the left side of the equation as the perfect square trinomial:

  (x - 7/5)^2 = -8/5 + 49/25

Now, the perfect square trinomial for the given problem is (x - 7/5)^2.

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Euler's method is useful for providing an approximate solution to ODEs that may not have an easily obtainable closed-form solution for differential equations.

Euler's method is a numerical technique for solving first-order ordinary differential equations (ODEs) with an initial value. Here's a step-by-step explanation:

1. Start with a given initial value problem (IVP): dy/dx = f(x, y), with an initial condition y(x0) = y0.

2. Choose a step size, h, which represents the interval between consecutive points in your solution.

3. Apply Euler's method formula to find the approximate value of y at the next point: y1 = y0 + h * f(x0, y0).

4. Continue this process, using the previously calculated value as the new initial condition, to find the approximate solution at other points. For the nth point, use the formula: yn = yn-1 + h * f(xn-1, yn-1).

5. Compare your approximate solution to the exact solution, if available, to evaluate the accuracy of Euler's method.

Keep in mind that the accuracy of Euler's method depends on the step size, h. Smaller values of h will generally yield more accurate results, but require more calculations.

Euler's method is useful for providing an approximate solution to ODEs that may not have an easily obtainable closed-form solution. It's a simple and easy-to-understand method, which is why it's often covered in introductory differential equations courses, such as the one you mentioned.

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The base angles of the isosceles triangle is A = 50°

Given data ,

Let the isosceles triangle be represented as ΔABC

Now , the measure of ∠ABC = 80°

So , the measure of ∠ACB = ∠BAC = A°

And , In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. The angle opposite the base is called the vertex angle

So , A° + A° + 80° = 180°

Subtracting 80 on both sides , we get

2A° = 100°

Divide by 2 on both sides , we get

A = 50°

Hence , each base angle measures 50°

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To find the probability that a customer has to wait more than 4 minutes, we need to use the normal distribution and standard deviation.

If the manager knows the standard deviation, we can use it to calculate the z-score and find the probability using a standard normal distribution table. However, since the standard deviation is not given in this question, we will assume that the distribution of waiting times is approximately normal and use the empirical rule.
The empirical rule states that for a normal distribution, approximately 68% of the values lie within one standard deviation of the mean, approximately 95% lie within two standard deviations, and approximately 99.7% lie within three standard deviations.
Since the average time that customers wait is 3 minutes, and we want to find the probability that a customer waits more than 4 minutes, we need to calculate how many standard deviations away from the mean 4 minutes is.
z = (x - μ) / σ
where x = 4, μ = 3, and σ is the standard deviation. Since we don't know the value of σ, we can't calculate the z-score directly. However, we can make a reasonable assumption that the standard deviation is around 1 minute. This is based on the empirical rule which states that approximately 68% of the values lie within one standard deviation of the mean.
So, σ = 1 minute, and
z = (4 - 3) / 1 = 1
Now we can use a standard normal distribution table to find the probability of a z-score of 1 or greater. From the table, we can see that the probability of a z-score of 1 or greater is approximately 0.1587.
Therefore, the probability that a customer has to wait more than 4 minutes is approximately 0.1587 or 15.87%.

To find the probability that a customer at the fast-food restaurant has to wait more than 4 minutes, we'll use the exponential distribution.
1. First, let's find the rate parameter, which is the reciprocal of the average waiting time: λ = 1 / average waiting time. In this case, λ = 1 / 3 ≈ 0.3333.
2. Now, we'll use the cumulative distribution function (CDF) of the exponential distribution to find the probability of waiting less than or equal to 4 minutes: P(X ≤ 4) = 1 - e^(-λx) = 1 - e^(-0.3333 × 4) ≈ 0.7364.
3. To find the probability of waiting more than 4 minutes, subtract the CDF value from 1: P(X > 4) = 1 - P(X ≤ 4) = 1 - 0.7364 ≈ 0.2636.
So, the probability that a customer at the fast-food restaurant has to wait more than 4 minutes is approximately 0.2636 or 26.36%.

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Once the issue is resolved, the seller can try to create or match the product with an ASIN again.

This error message is related to Amazon's Global Trade Item Number (GTIN) requirements. Amazon requires that sellers provide valid GTINs (such as UPC, EAN, or ISBN) for their products. The error message indicates that the SKU (Stock Keeping Unit) provided by the seller does not match any existing ASIN (Amazon Standard Identification Number) and contains invalid attribute values required for the creation of a new ASIN.

To fix this error, the seller should check that the SKU and attribute values are correct and that the product has a valid GTIN. The seller may need to obtain a valid GTIN for their product or correct any errors in the attribute values. Once the issue is resolved, the seller can try to create or match the product with an ASIN again.

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The solution to the exponential equation 64^a = 8^(a + 2) is given as follows:

a = 2.

The exponential equation in this problem is defined as follows:

64^a = 8^(a + 2)

64 is the second power of 8, hence:

64 = 8².

Applying the power of power rule, we have that:

64^a = 8^2a.

Hence:

8^2a = 8^(a + 2)

The exponential function is one to one, hence we can obtain the value of a as follows:

2a = a + 2

a = 2.

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Answer: x=-4

Step-by-step explanation:

i'm assuming that you meant 92-17x=24 instead of -24 because that gives the answer -4

the goal of these equations is to get all the x variables on one side and all of the constants on the other side.

92-17x=-24

92-17x -92 =24 -92

-17x=-68

divide both sides by -17

x = -4

The value of x is -4

When an integer by itself , the product obtained is a perfect square. Examples of perfect squares are 25 from 5×5, 36 from 6×6

The square root of the perfect square will give the original number.

Solving 4(x+7)^2-49=-13

collecting like terms

4( x+7)^2 = -13+49

4(x+7)² = 36

divide both sides by 4

(x+7)² = 9

Square both sides

x+7 = √9

x+7 = 3

x = 3-7

x = -4

therefore the value of x is -4

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Step-by-step explanation:

Joe is about 10 times more likely to bowl at least three strikes out of four tries than to bowl zero strikes out of four tries.

To find the probability of Joe bowling at least three strikes out of four tries, we need to consider the different combinations of strikes and non-strikes he can get.

There are four possible outcomes:
- strike, strike, strike, non-strike
- strike, strike, non-strike, strike
- strike, non-strike, strike, strike
- non-strike, strike, strike, strike

The probability of getting a strike is 0.6, and the probability of not getting a strike (a non-strike) is 0.4. So for each outcome, we can calculate the probability as follows:

- Probability of strike, strike, strike, non-strike = 0.6 x 0.6 x 0.6 x 0.4 = 0.0864
- Probability of strike, strike, non-strike, strike = 0.6 x 0.6 x 0.4 x 0.6 = 0.0864
- Probability of strike, non-strike, strike, strike = 0.6 x 0.4 x 0.6 x 0.6 = 0.0864
- Probability of non-strike, strike, strike, strike = 0.4 x 0.6 x 0.6 x 0.6 = 0.0864

To find the probability of Joe bowling at least three strikes, we need to add up the probabilities of the last three outcomes, since they all have at least three strikes:

0.0864 + 0.0864 + 0.0864 = 0.2592

So the probability of Joe bowling at least three strikes out of four tries is 0.2592, or about 26% (rounded to the nearest whole number).

To find the probability of Joe bowling zero strikes, we can use the same approach:

- Probability of non-strike, non-strike, non-strike, non-strike = 0.4 x 0.4 x 0.4 x 0.4 = 0.0256

So the probability of Joe bowling zero strikes out of four tries is 0.0256, or about 3% (rounded to the nearest whole number).

To find how many times more likely it is for Joe to bowl at least three strikes than to bowl zero strikes, we can divide the probability of the first outcome by the probability of the second outcome:

0.2592 / 0.0256 = 10.125

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Tatum earns more than Real.

We have,

Real works 36 hours a week and makes $612.

Tatum works 34 hours a week and makes $663

So, per hour earning of Real is

= 612 / 36

= $17

and, per hour earning of Tatum is

= 663 / 34

= $19.5

Thus, Tatum earns more than Real.

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