A ball is launched from a 69.92-foot tall platform. The equation for
the ball's height h at time t seconds after launch is h (t) = -16t2 +
6.4t+69.92, where h is in feet. When does the object strike the
ground?

Answer:A

Step-by-step explanation:

they are alternate exterior angles so, x+y=180

The fewest number of whole years the Banks family would need to include in the mortgage agreement in order to have a monthly payment of no more than $720 is 25 years.

Let's denote the number of years by y. Then the total number of monthly payments will be 12y.

The formula to calculate the monthly payment for a mortgage loan is:

M = P * (r/12) * (1 + r/12)^(12y) / ((1 + r/12)^(12y) - 1)

where:

M = monthly payment

P = principal (the amount borrowed)

r = annual interest rate

Plugging in the given values, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(12y) / ((1 + 0.048/12)^(12y) - 1)

To solve for y, we can use trial and error or a numerical solver. Using trial and error, we can start with a few values of y and check if the monthly payment is less than or equal to $720.

Trying y = 20, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1220) / ((1 + 0.048/12)^(1220) - 1)

This results in a monthly payment of $753.81, which is higher than $720.

Trying y = 25, we get:

720 = 120000 * (0.048/12) * (1 + 0.048/12)^(1225) / ((1 + 0.048/12)^(1225) - 1)

This results in a monthly payment of $715.48, which is lower than $720.

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Answer:

Step-by-step explanation:

If WY and XZ are the diagonals (I think they are), then the equation to find it is 16x + 2 = 36x - 6 --> 8 = 20x --> x = 0.4

16(0.4) + 2 = WY = XZ --> 6.4 + 2 = 8.4 are the diagonal lengths.

Let a and b be two independent events, if p (a) = 0. 4 and p (a ∪ b) = 0. 64 then the value of the p(b) = 0.4

In this question, we will utilise the notion of independent events and the probability addition rule to determine the probability of event B. The product of the individual probabilities will represent the intersection of independent events.

p(a) = 0.4

p(a∪b) = 0.64

p (a ∩ b) = p(a) x p(b)

p (a ∪ b) = p(a) + p(b) - p(a) x p(b)

0.64 = 0.4 + p(b) - 0.4 x p(b)

p(b) = 0.4

Therefore, the value of the p(b) = 0.4

Independent occurrences are ones whose occurrence is unrelated to any other event. For example, suppose we flip a coin in the air and receive the result Head, then we flip the coin again and obtain the result Tail. The occurrences occur independently of one another in both circumstances. It is one of the several kinds of occurrences in probability.

Let us now look at the whole description of independent events, including a Venn diagram, examples, and how they vary from mutually exclusive events.

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He equation that rightly shows the Commutative Property of addition is

10 x3/10 = 3/10 x 10

The Commutative Property of Multiplication states that changing the order of the factors doesn't change the product. In other words, when you multiply two figures, it doesn't count which number comes first. The equation 10 x3/10 = 3/10 x 10 is an illustration of this property, as both sides of the equation represent the same value, indeed though the order of the factors is different.

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The probability that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1 is approximately 0.012 or 1.2%.

To solve this problem, we need to count the number of ways to choose 10 cards from a deck of 52 cards and then divide by the total number of ways to put these cards into 4 piles.

Step 1: Count the total number of ways to choose 10 cards from a deck of 52 cards using the combination formula:

C(52, 10) = 52! / (10! × 42!) = 158,200,242,880 / (3,628,800 × 99,884,160) = 1,787,671

Step 2: Count the total number of ways to put 10 cards into 4 piles. We can think of each card as having 4 choices, one for each pile. Therefore, the total number of ways to put the cards into piles is:

[tex]4^{10}[/tex] = 1,048,576

Step 3: Count the number of ways to put 10 cards into 4 piles such that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1.

First, we need to choose 4 cards from the 10 cards to go into the largest pile. This can be done in C(10,4) ways:

C(10,4) = 10! / (4! × 6!) = 210

Then, we need to choose 3 cards from the remaining 6 cards to go into the next largest pile. This can be done in C(6,3) ways:

C(6,3) = 6! / (3! × 3!) = 20

Next, we need to choose 2 cards from the remaining 3 cards to go into the next largest pile. This can be done in C(3,2) ways:

C(3,2) = 3! / (2! × 1!) = 3

Finally, the remaining card goes into the smallest pile. Therefore, there is only one way to put the card into the smallest pile.

Therefore, the total number of ways to put 10 cards into 4 piles such that the largest pile has 4 cards, the next largest has 3, the next largest has 2, and the smallest has 1 is:

C(10,4) × C(6,3) × C(3,2) × 1 = 210 × 20 × 3 × 1 = 12,600

Step 4: Calculate the likelihood by dividing the number of ways in Step 3 by the number of ways in Step 2:

P = 12,600 / 1,048,576 = 0.012 or 1.2%.

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The percent discount for a student ticket is C. 40%

Percent Discount is a kind of discount that is offered on a product or service in the form of an amount per hundred.

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

Original price of the ticket = $50

Price of ticket on Monday = $35

Additional discount = $5

To determine the percentage discount, we make use of the following equation

Discount = 1 - (Price of ticket on Monday - Additional discount)/Original price of the ticket * 100%

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

Discount = 1 - (35 - 5)/50 * 100%

Evaluate

Discount = 40%

Hence, the percentage discount is 40%

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We need to add (t - 2πr) units of rope.

We have,

Let's call the radius of the hula hoop "r" and the distance from the center of the hula hoop to the rope "d".

We want to find the length of the rope we need to add in order to create a circle with radius "d" that is tangent to the hula hoop.

The distance between the center of the hula hoop and the center of the tangent circle is (r + d), so the diameter of the tangent circle is

2(r + d), and the length of the circle is 2π(r + d).

We want to find the value of d that will make the circle just touch the person's toes, so the radius of the tangent circle is equal to the length of the person's toes, which we'll call t.

So we have the equation:

2π(r + d) = t

Solving for d.

d = (t/2π) - r

The amount of rope we need to add is:

2πd = 2π((t/2π) - r) = t - 2πr

Thus,

We need to add (t - 2πr) units of rope.

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Answer:

You can drink it thank u for asking

The binomial probability formula calculates the probability of obtaining a specific number of successes in a fixed number of independent trials, each with the same probability of success

The binomial probability formula is used to calculate the probability of obtaining a certain number of successes in a fixed number of independent trials, each with the same probability of success.

The formula is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:

P(X=k) is the probability of obtaining k successes

n is the total number of trials

p is the probability of success in each trial

(n choose k) represents the number of ways to choose k successes from n trials, and is calculated as n! / (k! * (n-k)!)

Therefore, the uses of binomial probability formula has been explained

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The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.

The binomial probability formula is used to calculate the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In other words, it helps us determine the likelihood of achieving a certain outcome in a series of experiments, where each experiment can result in one of two possible outcomes (success or failure).
The formula is given by P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where P(X=k) represents the probability of getting exactly k successes, n is the total number of trials, p is the probability of success in a single trial, and (n choose k) is the binomial coefficient.
For example, let's say you flip a fair coin 10 times and want to know the probability of getting exactly 7 heads. In this case, n = 10 (number of trials), k = 7 (number of successes), and p = 0.5 (probability of heads). Plugging these values into the binomial probability formula will give you the desired probability.
The binomial probability formula is widely used in various fields, including statistics, probability theory, and genetics, to analyze and predict outcomes in situations with binary events.

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No, the probability be found by using the binomial probability formula with x counting the number who are left-handed. The correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

The binomial distribution assumes that the trials are independent, meaning that the outcome of one trial does not affect the outcome of any other trial. However, in this case, the 100 adults were selected without replacement, which means that the outcome of one selection affects the probability of the next selection. Therefore, the trials are dependent, and the binomial probability formula cannot be used.

Instead, we can use the hypergeometric distribution to calculate the probability of at least 30 left-handed adults in a sample of 100 adults selected without replacement from the U.S. population. The hypergeometric distribution takes into account the fact that the selections are dependent and is appropriate for this type of problem.

Therefore, the correct option is (c) No, because the 100 adults were selected without replacement, the selections are dependent.

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Answer:4

Step-by-step explanation:

In this situation, interval measurement is being employed as the measurement level.

As the height of each student can be measured on a continuous scale with equal intervals between the values. It's important to note that the teacher may have rounded the measurements to the nearest unit, which would make it a discrete measurement.

Interval measurement is a level of measurement in which the values are measured on a continuous scale and have equal intervals between them, but there is no true zero point. This means that the difference between any two values on the scale is meaningful and consistent, but it is not possible to say that one value is "zero" or has no quantity of the measured attribute.

For example, measuring temperature in degrees Celsius or Fahrenheit is an example of interval measurement. In this case, the difference between 10 and 20 degrees is the same as the difference between 20 and 30 degrees, but there is no true zero temperature - a temperature of 0 degrees does not mean the absence of heat.

Another example of interval measurement is measuring time in minutes or hours. The difference between 10 minutes and 20 minutes is the same as the difference between 20 minutes and 30 minutes, but there is no "zero" point in time - even if nothing is happening, time continues to pass.

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Answer: 21

Step-by-step explanation: Evaluate the first expression which is the cube root of 216. 6^3 equals 216 so the cube root of it is equal to six. Multiply it by 4 because thats what's its there for and you get 24. Subtract by 3 to get the final answer, 21.

Answer:32 (Irrational)

Step-by-step explanation:

Basically, just do it

Answer:  In trigonometry, the unit circle has a radius of 1 and is centered at the origin. It’s useful for learning ratios like sine and cosine. It also illustrates the relationship between angles in degrees and radians.

Step-by-step explanation:

The mode of the sample can be larger, smaller, or equal to the mode of the population.

The correct answer is A.

The mode is the most frequent value in a dataset. In a random sample, the mode can differ from the mode of the population because random sampling is subject to sampling variability. In other words, each random sample is likely to have different sample statistics than the population parameters. Therefore, it is possible for the mode of the sample to be larger, smaller, or equal to the mode of the population.

However, as the sample size increases, the mode of the sample becomes more likely to approach the mode of the population. This is because larger samples provide more information about the population and therefore reduce the impact of sampling variability.

Option B is incorrect because even if the sample is truly random, it is still subject to sampling variability, which means that the mode of the sample may not be equal to the mode of the population.

Option C is also incorrect because the mean of the population is a different statistic than the mode, and it is not necessarily related to the mode of the sample.

Option D is clearly incorrect, as the mode of a sample cannot be equal to the population size.

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The minimum number of minutes that Lydia still needs to practice is 105 minutes to meet her coach's requirement.

To find the minimum number of minutes that Lydia still needs to practice, we first need to solve the inequality:

3.75 + h ≥ 5.5

Subtracting 3.75 from both sides, we get:

h ≥ 1.75

This means that Lydia still needs to practice for at least 1.75 hours to meet her coach's requirement of practicing for at least 5.5 hours per week.

To find the minimum number of minutes, we can multiply 1.75 by 60, since there are 60 minutes in an hour:

1.75 × 60 = 105 minutes

So, Lydia still needs minimum 105 minutes to practice.

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The missing side length of the triangle is:

UT = 54

Here we can assume that the two triangles are similar triangles, that means that the quotient between the correspondent sides must be equal.

That means that:

KL/UV = ML/UT

And we know that:

KL = 130

ML = 117

UV = 60

UT = ?

Replacing that we can write:

130/60 = 117/?

Solving for the missing value we will get:

? = 117*(60/130) = 54

That is the missing side length.

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Answer:

1y is your answer, 1:y

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think it could be any number only if they gave you the number for y

The the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches.

volume for a rectangular prism is calculated using:

length × width × height

the rectangular prisms can be divided into bigger and smaller prism and their volumes calculated separately and then added to get the total volume as follows:

1). volume of bigger rectangular prism = 7ft × 7ft × 3ft = 147ft³

volume of smaller rectangular prism = 7ft × 2ft × 2ft = 28ft³

volume of object = 147ft³ + 28ft³ = 175ft³

2). volume of bigger rectangular prism = 6m × 3m × 3m = 54m³

volume of smaller rectangular prism = 3m × 3m × 1m = 6m³

3). volume of bigger rectangular prism = 7m × 6m × 3m = 126m³

volume of smaller rectangular prism = 7m × 2m × 1m = 14m³

volume of object = 126m³ + 14m³ = 140m³

4). volume of bigger rectangular prism = 12in × 4in × 4in = 192in²

volume of smaller rectangular prism = 4in × 3in × 2in = 24in³

volume of object = 192in³ + 24in³ = 216³

Therefore, the rectangular prisms have their volumes as:

1). 175 cubic feet

2). 60 cubic metres

3). 140 cubic metres

4). 216 square inches

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SRRC is a pulse shaping filter used in digital communications to minimize intersymbol interference and improve the signal-to-noise ratio.

The square root raised cosine (SRRC) is a famous heartbeat molding channel utilized in computerized correspondences, especially in applications like advanced tweak and demodulation. It is intended to limit intersymbol obstruction (ISI) by restricting the data transmission of the sent sign while keeping a consistent envelope.

The SRRC channel is described by a reaction that is like the raised cosine channel, yet with a square root capability applied to the recurrence reaction. This outcomes in a smoother change between the passband and stopband, which assists with decreasing ISI and work on the sign to-clamor proportion.

The SRRC channel is usually utilized in correspondence frameworks that utilization quadrature sufficiency regulation (QAM) or stage shift keying (PSK) tweak plans, as it gives great ghastly control and heartbeat molding properties that are appropriate to these kinds of signs.

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Answer:

The probability of drawing a red marble then a yellow marble out of the bag is probably 0.48(Decimal) or 12/25(Fraction).

4 lbs is approximately equal to 1.8143 kg  ( rounded to four decimal places )

The conversion factor to convert lbs to kilogram is 0.453592

1 lbs = 0.453592 kg

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in kg = The mass in lbs × conversion factor

Substitute the values in the equation

1 lbs = 0.453592 kg

4 lbs = 4 × 0.453592

Multiply the numbers

= 1.8143 kg  ( rounded to four decimal places )

Therefore, 180lbs is 1.81437 kg

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Answer:

Jessica rode her bike 16 miles per week and Pablo rode his bike 17 miles per week.

Step-by-step explanation:

Answer:

Jessica's and Pablo's statement both are correctly comparing the number of miles they rode per week.

Step-by-step explanation:

You are told that Jessica rode her bicycle for 128 miles in 8 weeks and equally the same distance each week.

Therefore you can easy tell how much she rode her bicycle for 8 weeks by dividing 128 by 8 which is 16miles per week

While in Pablo's statement tell us the same as Jessica's statement since you can divide it like Jessica's statement 95 divided by 5 equals 19miles per week

Answer:

The solutions to the equation cos(x + 3π/2) = √2/2 on the interval [0, 2π] are x = π/4 + 2kπ, k ∈ {0, 1, 2, 3}.

A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables. The null hypothesis is rejected for both parts A and B of the question.

A sample's null hypothesis indicates that no statistical relationship exists in a set of provided single observed variables.

Part A: The conclusion to be reached at the 5% level of significance-

The p value for the z score in the right tailed or upper test can be obtained from the z table, which is,

p-value=0.125=0.125

The p value of 0.125 is greater than the significance level of 0.06. As a result, the effect is not significant, and the null hypothesis cannot be rejected.

Part B: If the alternative hypothesis is Ha: p 0.6, the conclusion to reach at the 5% level is-

The unequal sign 2-test is carried out here. The p value for the 2-test is as follows:

The p-value is 0.25=0.25.

In this case, the p value of 0.25 is greater than the significance level of 0.05. As a result, the effect is not significant, and the null hypothesis cannot be rejected.

As a result, the null hypothesis fails to be rejected for both parts A and B of the question.

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Answer:

30√5 + 7√2

Step-by-step explanation:

To simplify this expression, we can first use the fact that the square root of a product is equal to the product of the square roots. We can also simplify any perfect squares under the square root sign.

5√180 + 4√18 - √50

= 5√(36 × 5) + 4√(9 × 2) - √(25 × 2)

= 5√36 × √5 + 4√9 × √2 - √25 × √2

= 5 × 6√5 + 4 × 3√2 - 5√2

= 30√5 + 12√2 - 5√2

= 30√5 + 7√2

Therefore, the simplified form of the expression is [30√5 + 7√2.]

Answer:

Ms. Perry needs to make an additional 1/24 kg of fudge.

Step-by-step explanation:

Ms. Perry has a total of 8/8 + 1/6 = 13/6 kg of fudge. She needs 1 1/8 kg of fudge for the brownies, which is equivalent to 9/8 kg. To find how much more fudge she needs to make, we can subtract the amount of fudge she already has from the amount she needs:

9/8 - 13/6 = 27/24 - 26/24 = 1/24

Therefore, Ms. Perry needs to make an additional 1/24 kg of fudge.