The volume of a right cylinder is V = πr²h, where r is the radius of the base and h is the height of the cylinder. If the volume of a cylinder is 72π cubic inches and the height of the cylinder is 2 inches, then what is the radius of the cylinder in inches?

Answer: (-3, 18) and (-1, 18)

Step-by-step explanation:

Solve the system of equations. [tex]x^{2}[/tex] - 2x + 3 = -6x. [tex]x^{2}[/tex] + 4x + 3 = 0. (x+1)(x+3) = 0. x = -1, -3. Then plug it in. f(x) = 18.

There is a 20% chance that a risky stock investment will end up in a total loss. If you invest in 25 independent risky stocks, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

Given data:

Probability of getting a total loss in one investment = 20% = 0.20

Probability of not getting a total loss in one investment = 1 - 0.20 = 0.80

Number of investments = 25

We need to find the probability that fewer than six out of these 25 risky investments end up in total losses.

We will use the binomial distribution formula here:P(X < 6) = Σp(x) (from x = 0 to x = 5)

Here, Σ is the summation signp(x) = probability of x successes in 25 trials, which is given by the formula:

p(x) = [ nCx * p^x * (1-p)^(n-x)]

Where, n = number of trial

s = 25

p = probability of success = 0.80

q = probability of failure = 1 - p = 0.20n

Cx = n! / (x! × (n-x)!) = combination of n items taken x at a time

We need to substitute these values in the formula and calculate the probability:

P(X < 6) = Σp(x) (from x = 0 to x = 5)

P(X < 6) = p(0) + p(1) + p(2) + p(3) + p(4) + p(5)

P(X < 6) = [tex][25C0 * (0.80)^0 * (0.20)^25] + [25C1 * (0.80)^1 * (0.20)^24] + [25C2 * (0.80)^2 * (0.20)^23] + [25C3 * (0.80)^3 * (0.20)^22] + [25C4 * (0.80)^4 * (0.20)^21] + [25C5 * (0.80)^5 * (0.20)^20][/tex]

P(X < 6) ≈ 0.91

Therefore, the probability that fewer than six of these 25 stocks end up in total losses is approximately 0.91.

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The terminal ray of α falls in the third quadrant (where cosine is negative), we can conclude that: cos(α) = -3/5.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides and angles in triangles, and to solve problems involving angles, distances, and heights. The three primary trigonometric functions are sine, cosine, and tangent, which describe the ratios of the sides of a right triangle. Other trigonometric functions include cosecant, secant, and cotangent, which are the reciprocals of the primary trig functions. Trigonometry has many applications in science, engineering, and technology, including astronomy, physics, navigation, and surveying.

Here,

Since the reference angle of α has a sine value of 4/5, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find the cosine of the reference angle:

cos²(θ) = 1 - sin²(θ)

= 1 - (4/5)²

= 1 - 16/25

= 9/25

Taking the square root of both sides gives us:

cos(θ) = ± √(9/25)

= ± (3/5)

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The volume of a cone that has the same base area and the same height as the cylinder is 116.25pi cubic units. This is because the volume of a cone is one-third the volume of a cylinder with the same base area and the same height. Therefore, the volume of the cone is 116.25pi cubic units.

The volume of a cylinder is equal to the area of the base, multiplied by the height. The volume of a cylinder with a base area of 465pi and a height of h is therefore 465pi*h. For a cone, the volume is equal to a third of the area of the base multiplied by the height. Since the cone and cylinder have the same base area and height, the volume of the cone is one third of the volume of the cylinder. Therefore, the volume of the cone is 155pi cubic units (465pi/3). A cone has one third the volume of a cylinder with the same base and height.

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The surface area of the larger sphere is 64π cm². therefore option A. 64π cm² is correct.

To find the surface area of the larger sphere, given the volumes of two spheres and the surface area of the smaller sphere, follow these steps:

1. Determine the ratio of the volumes of the spheres:

Volume ratio = Volume of larger sphere / Volume of smaller sphere

                     = (64π cm³) / (8π cm³)

                     = 8

2. Find the cube root of the volume ratio to get the ratio of their radii:

Radii ratio = cube root of volume ratio = cube root of 8 = 2

3. Since the surface area of a sphere is proportional to the square of its radius, find the ratio of the surface areas by

squaring the radii ratio:

Surface area ratio = (Radii ratio)² = (2)² = 4

4. Finally, multiply the surface area of the smaller sphere by the surface area ratio to get the surface area of the larger

sphere:

Surface area of larger sphere = Surface area of smaller sphere × Surface area ratio

                                                 = 16π cm² × 4

                                                = 64π cm²

So, the surface area of the larger sphere is 64π cm² (Option A).

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Answer:

5.9

Step-by-step explanation:

im assuming 5.9

not sure what your answer choices are but, its before 6, and way after 5.5, its like counting 123456789. hope this helps.

The correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

What is the median?

The median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in numerical order. It is the value separating the higher half from the lower half of a sample or a population.

To compare the measures of center in the two sets of data, we need to find their respective medians.

For Plot A, we can see that the median is between 5 and 6, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

For Plot B, we can see that the median is between 5 and 6 as well, since there are 5 values below 5 and 5 values above 6. We can estimate the median as approximately 5.5 hours.

Therefore, the correct statement that compares the measures of center in the two sets of data is:

The medians of the number of hours ten girls and ten boys watched television over a one-week period are approximately equal.

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The perimeter of Felicia's playhouse is 60ft, and its area is 144ft².

In order to determine the perimeter and area of Felicia's playhouse, we must first analyze the provided diagram:

There are two rectangles and a triangle, therefore we must calculate the area of each shape, and then add the areas together to get the total area.

Area of Rectangle A = lw = 8ft x 10ft = 80ft²

Area of Rectangle B = lw = 4ft x 10ft = 40ft²

Area of Triangle C = (1/2)bh = (1/2)(8ft)(6ft) = 24ft²

Total Area = Area of Rectangle A + Area of Rectangle B + Area of Triangle C = 80ft² + 40ft² + 24ft² = 144ft²

To determine the perimeter, we must add up the lengths of all four sides of the rectangle and the three sides of the triangle.

P = 2l + 2w + a + b + c

P = 2(10ft) + 2(8ft) + 6ft + 10ft + 8ft

P = 20ft + 16ft + 6ft + 10ft + 8ft

P = 60ft

Therefore, the perimeter of Felicia's playhouse is 60ft, and its area is 144ft².

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Question

Felicia created a floor plan for a playhouse, as shown below. 2 ft 23 ft 7 ft 8 ft 844 What will be the perimeter and area of Felicia's playhouse?

The probability that a randomly selected quartz timepiece will have a replacement time less than 11.9 years is 0.0007 or 0.07%.

The given information is that a company XYZ knows that the replacement times for the quartz timepieces it produces are normally distributed with a mean of 16 years and a standard deviation of 1.4 years. We need to calculate the probability that a randomly selected quartz timepiece will have a replacement time of less than 11.9 years. Let us solve this problem using the standard normal distribution.
The standard normal distribution has a mean of 0 and a standard deviation of 1. We can convert the given distribution into the standard normal distribution using the formula:
z = (x - μ)/σ
Where x is the replacement time, μ is the mean and σ is the standard deviation.

Putting the given values, we get:
z = (11.9 - 16)/1.4
z = -3.21
We need to find the probability that the replacement time is less than 11.9 years. This can be calculated as the area under the standard normal distribution curve to the left of z = -3.21.

Using the standard normal distribution table, we find that the area to the left of

z = -3.21 is 0.0007.
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Answer: To solve this problem, we need to first find the average number of shoppers in the new store at any time and the average number of shoppers in the original store at any time, and then calculate the percent difference between the two.

Let's start by finding the average number of shoppers in the new store at any time. We know that 90 shoppers enter the store per hour, and each shopper stays for an average of 12 minutes, which is 0.2 hours. So the number of shoppers in the store at any time is:

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

Now let's find the average number of shoppers in the original store at any time. We don't have any information about the original store, so let's call the average number of shoppers in the original store "x". We want to find the percent difference between x and 18, so we need to calculate:

percent difference = |x - 18| / x × 100%

To solve for x, we need to use some algebra. We know that the number of shoppers entering the original store per hour is equal to the number of shoppers leaving the store per hour (assuming the store has a steady flow of shoppers and no one stays for more than an hour). So if we let t be the average amount of time each shopper stays in the original store, we can write:

x/t = shoppers entering the store per hour = shoppers leaving the store per hour = x/t

We can then solve for t:

x/t = x/t

x = x × t/t

x = t

So the average number of shoppers in the original store at any time is equal to the average amount of time each shopper stays in the store.

We don't know the average amount of time each shopper stays in the original store, but we can make an estimate based on the information we have about the new store. We know that the average amount of time each shopper stays in the new store is 12 minutes, or 0.2 hours. If we assume that the shopping behavior is similar in both stores, we can use this estimate for the original store as well.

So we have:

x = t = 0.2 hours

Now we can calculate the percent difference between x and 18:

percent difference = |x - 18| / x × 100%

percent difference = |0.2 - 18| / 0.2 × 100%

percent difference = 8800%

This means that the average number of shoppers in the new store at any time is 8800% less than the average number of shoppers in the original store at any time. However, this answer seems implausible, since a percent difference greater than 100% means that the new store has a negative number of shoppers!

It's possible that there was an error in the problem statement, such as a typo or a missing decimal point. If we assume that the average number of shoppers in the new store is actually 18 per hour (instead of 90 per hour), we get a more reasonable answer:

x = t = 0.2 hours

percent difference = |x - 18| / x × 100%

percent difference = |0.2 - 18| / 0.2 × 100%

percent difference ≈ 98%

So the average number of shoppers in the new store at any time is approximately 98% less than the average number of shoppers in the original store at any time.

Step-by-step explanation:

The double integral ∬D(x2+6y)dA can be evaluated using the properties of integration. The value of the double integral is 53/60.

The given function is (x2+6y). Here, we will find the limits of integration for x and y. Given that D is bounded by y = x, y = x3, and x ≥ 0, we can represent this region in the x-y plane as follows: We see that the lower limit of y is x and the upper limit of y is x3. The lower limit of x is 0 and the upper limit of x is given by the line y=x.

Hence, the limits of integration can be written as follows:0 ≤ x ≤ yx ≤ y ≤ x3

Now, we can substitute these limits in the double integral and integrate first with respect to y and then with respect to x.

∬D(x2+6y)dA = ∫₀¹⁰∫x^x³(x2+6y)dydx

On integrating, we get

∬D(x2+6y)dA = ∫₀¹⁰(x³ - x^7/3 + 3x⁴)dx= [(1/4)x⁴ - (1/12)x^10/3 + (3/5)x⁵] from 0 to 1∬D(x2+6y)dA = (1/4 - 1/12 + 3/5) - (0 + 0 + 0) = 53/60

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The derivative of f(x) of (2√x+1){(2-x)/(x^2+3x)}, is f'(x) = (-x^3+5x+6)/[x(x+3)^2√x].

To find the derivative of the function f(x) = (2√x+1){(2-x)/(x^2+3x)}, we can use the product rule and the quotient rule.

First, let's find the derivative of (2-x)/(x^2+3x):

f1(x) = (2-x)/(x^2+3x)

f1'(x) = [(-1)(x^2+3x)-(2-x)(2x+3)]/(x^2+3x)^2

  = (-x^2-3x-4x+6)/(x^2+3x)^2

  = (-x^2-x+6)/(x^2+3x)^2

Next, let's find the derivative of 2√x+1:

f2(x) = 2√x+1

f2'(x) = 2(1/2√x) = 1/√x

Using the product rule, we get:

f'(x) = f1(x)f2'(x) + f2(x)f1'(x)

 = [(2-x)/(x^2+3x)](1/√x) + (2√x+1)(-x^2-x+6)/(x^2+3x)^2

 = (2-x)/(x^2√x+3x√x) - (x^2+4x-6)/(x^2+3x)^2√x

 = (2-x)/(x(x+3)√x) - (x^2+4x-6)/(x^2+3x)^2√x

Simplifying the expression, we get:

f'(x) = [(2-x)(x^2+3x) - (x^2+4x-6)x]/[x(x+3)^2√x]

 = (-x^3+5x+6)/[x(x+3)^2√x]

Therefore, the derivative of f(x) is:

f'(x) = (-x^3+5x+6)/[x(x+3)^2√x]

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Answer: 30, 30%, 8181

Step-by-step explanation:

Step 1: I looked at the question and saw that it was asking which of the given options had the same value as 30%30 and 81 8181.

Step 2: I looked at the list of options and saw that 30, 30%, and 8181 all had the same value as the given numbers.

Step 3: I chose those three options as my answer.

Answer:

32,40 in

Step-by-step explanation:

please

give brainliest

The volume of the image after the dilation for given scale factor are:

a. k = 1/2: V = 4 cubic units

b. k = 0.6: V = 2.4 cubic units

c. k = 1: V = 8 cubic units

d. k = 1.5: V = 12 cubic units

The ratio between comparable analyses of an object and an identification of that object is known as a scale factor in mathematics. The copy will all be larger if the scaling factor is a complete number. A fractional scaling factor means that the duplicate will be smaller.

Volume of solid: 8 cubic units

a. k = 1/2

volume of the image : 1/2 *8 = 4 cubic units

b. k = 0.6

volume of the image : 0.6*8 = 2.4  cubic units

c. k = 1

volume of the image : 1*8 = 8 cubic units

d. k = 1.5

volume of the image : 1.5*8 = 12 cubic units

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A sample space is a collection or a set of possible outcomes of a random experiment and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.

A sample space is a collection or a set of possible outcomes of a random experiment.

The sample space is represented using the symbol, “S”.

The subset of possible outcomes of an experiment is called events.

A sample space may contain a number of outcomes that depends on the experiment.

So, Let X = a number of times the sum of the two numbers on two cubes is 5.

Two numbered cubes are rolled n = 180 times.

The event of getting a sum of 5 in independent of the other results.

The random variable X follows a Binomial distribution with parameters n = 180 and n = 1/9.

Then,

E(X) = np

Calculate how many times Tamara expects the two dice to sum to 5 as follows:

= E(X) = np

= 180 * 1/9

= 20

Therefore, a sample space is a collection or a set of possible outcomes of a random experiment, and using it we know that Tamara should assume that the sum of the two dice is 5 x 20.

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Complete question:

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible combinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?

The cost of repairing the car was $360 after selling the car at a profit of

16⅔ % on the cost of buying and repairing the car.

Profit is the financial gain that is earned by a business or an individual after all the expenses have been subtracted from the revenue. In simple terms, profit is what remains after all costs, including the cost of goods sold, operating expenses, taxes, and other charges, have been deducted from the revenue generated from the sale of goods or services.

Let's call the cost of repairing the car "x". We know that Mr. Peterson bought the car for $1200, spent x dollars on repairing it, and sold it for $2100 at a profit of 16⅔ % on the cost of buying and repairing the car.

We can start by calculating the total cost of buying and repairing the car, which is the sum of the initial cost and the cost of repairs:

Total cost = $1200 + x

Next, we can calculate the profit that Mr. Peterson made on this total cost, which is given as 16⅔ %:

Profit = (16⅔ %) × Total cost

Profit = (16⅔ / 100) × ($1200 + x)

We know that Mr. Peterson sold the car for $2100, so we can set up an equation for the profit:

Profit = Selling price - Total cost

(16⅔ / 100) × ($1200 + x) = $2100 - ($1200 + x)

Simplifying and solving for x, we get:

(5/6) x = $2100 - $1200 - (5/6)($1200)

(5/6) x = $450

x = $360

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Answer:

The angles are supplementary.

Step-by-step explanation:

Let's first draw a diagram to better visualize the problem:

* T (top of incomplete tower)

/|

/ |

/ |

/ | h (height of incomplete tower)

/ |

/ |

/θ1 |

/___ | M (man's position, height = 6 feet)

d

We can see that we have a right triangle with the tower's height as the opposite side, the distance between the man and the tower as the adjacent side, and the angle of elevation θ1 as 30°. We can use trigonometry to find the height of the incomplete tower:

tan(30°) = h / d

h = d * tan(30°)

We don't know the value of d, but we can use the fact that the man's height plus the height of the incomplete tower equals the distance from the man to the top of the incomplete tower:

d = h / tan(30°) + 6

Now we can use trigonometry again to find the height of the complete tower. Let's call this height H and the new angle of elevation θ2:

* T (top of complete tower)

/|

/ |

/ |

/ | H (height of complete tower)

/ |

/ |

/θ2 |

/___ | M (man's position, height = 6 feet)

d

We have another right triangle, this time with the height of the complete tower as the opposite side, the same distance between the man and the tower as the adjacent side, and the new angle of elevation θ2 as 60°. We can use the tangent function again:

tan(60°) = H / d

H = d * tan(60°)

We can substitute the value of d we found earlier:

H = (h / tan(30°) + 6) * tan(60°)

Simplifying:

H = h * sqrt(3) + 6 * sqrt(3)

(a) To find how high the tower must be raised, we subtract the height of the incomplete tower from the height of the complete tower:

raise = H - h

raise = h * (sqrt(3) - 1) + 6 * sqrt(3)

Substituting the value of h we found earlier:

raise = 24 * (sqrt(3) - 1) + 6 * sqrt(3)

raise ≈ 38.8 feet

(b) The height of the completed tower is simply the height of the incomplete tower plus the raise we found:

height = h + raise

height = 24 + 38.8

height ≈ 62.8 feet

Therefore, the height of the tower after completing its construction work is approximately 62.8 feet.

Step-by-step explanation:

See image and calcs below

Answer:

Mohsin could be first, Yousuf could be second and luke could be third it doesn't matter really wich way roun it could be that yousuf is first or luke thirst.

Step-by-step explanation:

Answer:

1/6

16.667%

well in simple terms 16.6

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

trust me

The triangles can be congruent if the corresponding sides of two triangles are congruent except their hypotenuse, and the angle between the congruent corresponding sides between the the two angle is same.

When two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent.

Congruent triangles are triangles that have identical dimensions and shape. Congruent figures have equal areas and corresponding sides that have the same lengths. They're exactly the same in terms of everything.

As a result, if two triangles are congruent, all of their corresponding sides and angles are equivalent to those in the other triangle.

A triangle with one 90-degree angle is referred to as a right-angled triangle. A right triangle has two legs and one hypotenuse.

The hypotenuse is the triangle's longest side, while the legs are the sides that make up the right angle.
The Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, is true for right triangles only.

The Side-Angle-Side (SAS) postulate is used to prove that two triangles are congruent. Two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle in this postulate.

Two triangles are congruent if and only if they have two corresponding sides and the included angle are equal.

Using the SAS postulate, we can only conclude that the two right triangles are congruent if we have two pairs of corresponding sides and the included angle between those sides.

As a result, if only two pairs of corresponding sides are congruent, it is not enough to demonstrate that the two triangles are congruent.

Hence when two pairs of corresponding sides of two right triangles are congruent, we cannot conclude that the triangles are congruent unless their hypotenuse are not equal and their angle between the congruent corresponding sides between the the two angle is same.

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So the minimum probability that a Yes respondent exercises for at least 1 hour is 6/(x+6), where x is the number of students who answered No.

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 indicating an impossible event and 1 indicating a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in various fields such as mathematics, statistics, science, economics, and finance to model and analyze uncertain situations.

Here,

Let the number of students who answered No be x. Then the number of students who answered Yes is x+12. The total number of students is then x + (x+12) = 2x + 12.

Suppose y of the students who answered Yes exercise for at least 1 hour. Then the probability that a Yes respondent exercises for at least 1 hour is y/(x+12).

Since we don't have the full frequency tree, we can't determine y or x directly. However, we do know that the total number of students who exercise for at least 1 hour is greater than or equal to 12 (since there are 12 more Yes respondents than No respondents). Therefore, the probability that a Yes respondent exercises for at least 1 hour is y/(x+12) is at least 12/(2x+12) = 6/(x+6).

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Answer:In a standard deck of 52 cards, there are 12 face cards (4 jacks, 4 queens, and 4 kings) and 40 non-face cards. To find the number of five card hands consisting of no face cards, we need to count the number of hands that include only non-face cards.

The number of ways to choose 5 non-face cards out of the 40 available non-face cards is:

C(40, 5) = (40!)/(5!35!) = 658,008

Therefore, there are 658,008 five card hands consisting of no face cards at all.

Step-by-step explanation:

If the cube and sphere both have volume as 512 cubic units, then the solid that has a greater surface area is Cube.

we first find the side length of the cube and the radius of the sphere.

The volume of the cube is 512 cubic units,

We have,

⇒ side³ = 512,

⇒ side = 8

So, the side length of the cube is 8 units.

Volume of sphere is also 512 cubic units,

We have,

⇒ (4/3)πr³ = 512,

On Simplifying,

We get,

⇒ r = 4.96 units.

So, radius of sphere is = 4.96 units.

Next we can find the surface area of each solid.

The surface-area of cube is = 6×(side)²,

⇒ 6(side²) = 6(8²) = 384 square units,

The surface area of the sphere is = 4πr²,

⇒ 4π(r²) = 4π(4.96²) ≈ 309 square units.

Therefore, the Cube has a greater surface area than the sphere.

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Answer:

10) -1.5

11) 1

Step-by-step explanation:

Hope this helps! Pls give brainliest!

The probability of incurring a loss when it rains is:P (loss | raining) = 80%So, there is a 20% chance that the food truck will not have incurred a loss when it rains.

The P (not raining | not loss) = 90% × 30% = 27%.Thus, the probability that it had not rained on that randomly selected day given that the food truck did not incur a loss is 27%.

The chance of not raining on a given day in Seattle can be calculated as follows:When it does not rain, there is a 10% probability that the food truck will incur a loss, as given in the statement. Similarly, when it rains, there is an 80% chance that the food truck will incur a loss on that day.

To calculate the probability that the food truck will not have incurred a loss on that day, we must first calculate the probability that the food truck will have incurred a loss on that day.Suppose the probability of rain is 70%, so the chance that it won't rain will be: P (not raining) = 100% - 70% = 30%When it rains, there is a 80% probability that the food truck will have incurred a loss, as given in the statement.

The probability of not incurring a loss when it does not rain is:P (not loss | not raining) = 100% - 10% = 90%The probability of not raining when the food truck does not incur a loss can be calculated as follows:P (not raining | not loss) = P (not loss | not raining) × P (not raining)P (not loss | not raining) = 90%P (not raining) = 30%

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The null hypothesis rejected represents there is evidence the proportion of members engaged in professional networking within last month is different from established percentage.

Using a hypothesis test we have,

Let p be the proportion of employees in the company who engage in professional networking within the last month.

The null hypothesis represents,

The proportion of employees who engage in professional networking within the last month is equal to the established percentage of 55%.

H0: p = 0.55

The alternative hypothesis represents ,

The proportion of employees who engage in professional networking within the last month is different from 55%.

Ha: p ≠ 0.55

Use a two-tailed z-test for the proportion to test this hypothesis, with a significance level of 0.05.

The test statistic is,

z = (p₁ - p) / √(p(1-p)/n)

p₁ is the sample proportion

p is the hypothesized proportion

And n is the sample size.

Here,

p = 0.55

n = 980

p₁ = 500/980

   = 0.51.

Substituting these values, we get,

z = (0.51 - 0.55) / √(0.55(1-0.55)/980)

  = -1.96

The critical values for a two-tailed test with a significance level of 0.05 are ±1.96.

Since the test statistic (-1.96) falls within the critical region.

Reject the null hypothesis

Therefore, there is evidence that the proportion of employees who engage in professional networking within the last month is different from the established percentage of 55%.

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The equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is: y = 4x² + 24x + 32.

What is an equation?

Since the parabola is symmetric with respect to the vertical line passing through the vertex (which is in the second quadrant), its axis of symmetry is the line x = -3.

Let's first find the vertex of the parabola. The x-coordinate of the vertex is simply the average of the x-coordinates of the two given points on the x-axis:

x = (-4 + (-2))/2 = -3

To find the y-coordinate of the vertex, we can use the fact that the vertex lies on the axis of symmetry. Therefore, it must also be the midpoint of the distance between the touch point (-3, -1) and the y-axis.

The distance between (-3, -1) and the y-axis is 3 units. Therefore, the y-coordinate of the vertex is:

y = -1 - 3 = -4

So the vertex of the parabola is V(-3, -4).

Since the parabola is open in the second quadrant and its vertex is in the second quadrant, its equation has the form:

y = a(x + 3)²- 4

where a is a positive constant that determines the "steepness" of the parabola.

To find the value of a, we can use one of the given points on the x-axis. Let's use (-2, 0):

0 = a(-2 + 3)² - 4

4 = a

Therefore, the equation of the parabola is:

y = 4(x + 3)² - 4

or

y = 4x² + 24x + 32

So the equation of the parabola that passes through (-4, 0) and (-2, 0) and has a touch point at (-3, -1) is:

y = 4x² + 24x + 32.

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Complete question is: The equation of the given parabola is: y = 4x^2 + 24x + 32.