The vertical height in feet of a projectile on a planet in our solar system at a given time t in seconds is represented by the function h(t) = -42t^2 +252t. Re-write h(t) in the form h (t) = a(t- h)^2 + k and determine the maximum height of the projectile. Show all work. ​

Answer:

$9.25

Step-by-step explanation:

Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:

6(x - 1.50)

We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:

6(x - 1.50) = 46.50

Simplifying this equation, we get:

6x - 9 = 46.50

Adding 9 to both sides, we get:

6x = 55.50

Dividing both sides by 6, we get:

x = 9.25

Therefore, the original price of each ticket was $9.25.

Answer:

9.25$

Step-by-step explanation:

Let x be the original price of each ticket before the discount was taken. The discount is $1.50 off each ticket, so the price they actually paid for each ticket is x - 1.50. Since there are 6 tickets, the total price they paid for all 6 tickets is:

6(x - 1.50)

We know from the problem that the total price they paid for all 6 tickets was $46.50, so we can set up the following equation:

6(x - 1.50) = 46.50

Simplifying this equation, we get:

6x - 9 = 46.50

Adding 9 to both sides, we get:

6x = 55.50

Dividing both sides by 6, we get:

x = 9.25

Therefore, the original price of each ticket was $9.25.

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The true statement about the function y = 40x is that it is a linear function

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

y = 40x

The given function is y = 40x, which represents the total number of dollars Mark earns depending on the number of lawns he mows.

Here are some properties of the function:

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As per military time, 4pm would be 1600 hours or 16:00. We can deduce this by also seeing the 24 hour clock.

A day is divided into 24 equal-length segments and runs from midnight to midnight on the modern 24-hour clock, also known as military time in the United States.

Many nations use a 12-hour clock or a 24-hour/12-hour time combination, especially those that speak English as their primary language. Some professions favor using the 24-hour clock in nations where the twelve-hour clock is most prevalent.

A 24-hour clock is used in military time instead of a 12-hour clock to measure time. To convert from the 12-hour clock to military time, just add 12 to any time that is after noon. For example, 1 PM would be 13:00 in military time. To convert from military time to a 12-hour clock, just deduct 12 from any time that is after 12 PM (noon).

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Answer: 57.153 kilograms

Step-by-step explanation:

126 lbs is equal to 57.15 kg.

To convert pounds (lbs) to kilograms (kg).

you can use the conversion factor of 1 lb = 0.453592 kg.

To convert 126 lbs to kg:

multiply the weight in pounds by the conversion factor:

126 lbs×0.453592 kg/lb

= 57.152712 kg

Therefore, 126 lbs is equal to approximately 57.15 kg.

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The point estimate that can be used to estimate the true mean population is 11.97 inches.

To find the point estimate that can be used to estimate the true population mean, we need to take the sample mean of the given observations. The formula for the sample mean is:

Mod(X)= (Σx) / n

where Mod(X)  is the sample mean, Σx is the sum of all the observations, and n is the size.

Using the given observations, we can calculate the sample mean as follows:

Mod(X) = (11.3 + 10.7 + 12.4 + 15.2 + 10.1 + 12.1 + 16.2 + 10.5 + 11.4 + 11.0 + 10.7 + 12.0) / 12

Mod(X) = 11.97

Therefore, the point estimate that can be used to estimate the true mean population is 11.97 inches.

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Answer:

1. No

2. Yes

3. No

Step-by-step explanation:

1.

We know that c = 7, so we plug it in to prove if the equation is true.

[tex]7+8=15[/tex]

The variable is not a solution.

2.

We know a = 30, so we plug it in to prove if the equation is true.

[tex]30-4=26[/tex]

The variable is a solution.

3.

We know y = 4.1, so we plug it in to prove if the equation is true.

[tex]12.6-4.1=8.5[/tex]

The variable is not a solution.

The solution is, The value of x is 21.4.

A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangle triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.

here, we have,

The height of the right-angle triangle is 11. The hypotenuse of the right-angle triangle is x.

The measure of the angle opposite to height is 31°.

The sine of an angle is the ratio of height to the hypotenuse.

Therefore,

sin 31° = height/hypotenuse

sin 31° = 11/x

Multiply x with both sides:

x sin 31° = 11

Divide sin 31° with both sides:

x = 11/ sin 31°

x = 21.35

x ≈ 21.4 units

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Answer: The missing side is 8

Step-by-step explanation: I hope this helps!

Answer:

43,560ft

Step-by-step explanation:

A unit can be used for measurement, and is commonly found in mathematics to describe length, size, etc.

Therefore, for every 1 acre it is equivalent to 43,560 feet.

205 lbs is approximately equal to 92.9864 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

205 lbs =  0.453592 × 205

Multiply the numbers

= 92.9864 kg  ( rounded to four decimal places )

Therefore, 205 lbs is 92.9864 kg

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Answer:

t = 13

Step-by-step explanation:

Solve for t

[tex]-6(t-12)=-6[/tex]

Simplify

[tex]-6(t+-12)=-6[/tex]

Distribute -6

[tex]-6t+72=-6[/tex]

Subtract 72 on both sides

[tex]-6t=-78[/tex]

Divide by -6

[tex]t=13[/tex]

Answer:

Step-by-step explanation:

3*6=18

Answer:

20 millilitres of oil

Step-by-step explanation:

You need to first find how much goes into 1 litre of oil and to do that we divide the two numbers

80/2 = 40

Now we know that for every 1 litre we need 40 millitres

Since .5 is half of 1 we just need to take half of 40

half of 40 = 20

20 millilitres of oil

Answer:

x = 88

Step-by-step explanation:

To find the value of x, we know that the sum of a quadrilateral's exterior angles are 360. We can use this information to create an algebraic expression and solve for x.

[tex]x+73+90+109=360[/tex]

Add like terms

[tex]x+272=360\\[/tex]

Subtract 272 on both sides

[tex]x=88[/tex]

To prove our work, we can add up all the angle measures and see if they add up to 360.

[tex]88+73+90+109=360[/tex]

So, our work is correct.

Knowing that a circle has a radius of 6 inches, the area of a sector with a central angle of 120º is 12π square inches.

The area of a sector can be found using the formula:
Area of sector = (Central angle/360°) × π × r²

Where "central angle" is the angle of the sector in degrees and "r" is the radius of the circle.

In this case, the central angle is 120° and the radius is 6 inches. Plugging these values into the formula, we get:
Area of sector = (120°/360°) × π × 6²
Area of sector = (1/3) × π × 36
Area of sector = 12π square inches

Therefore, the area of the sector bounded by a central angle measuring 120° in a circle with a radius of 6 inches is 12π square inches.

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The number [square] can divided exactly by six. and when [square] is divided by five, four is the number left over is:

12, 42, 72 o 102

The number [square] can be represented as 6x, where x is any positive integer, since it can be divided exactly by six. When [square] is divided by five, four is the number left over. Therefore, we can write the equation:

6x = 5y + 4

Where y is any positive integer. We can rearrange the equation to solve for x:

6x - 4 = 5y

2x - 2 = (5/3)y

2x - 2 = (5/3)(3x/5)

2x - 2 = (15/15)x

2x - 2 = x

x = 2

Therefore, the smallest possible value for [square] is 6(2) = 12. The next smallest possible value for [square] would be 6(2 + 5) = 42, since adding multiples of 5 to x will still satisfy the equation. The possible values for [square] are 12, 42, 72, 102, etc.

The possible values for [square] that are listed in the question are not provided, but the correct answer will be one of the numbers listed above.

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Answer:

Equation: 1,152.00 = 21.80x + 16.60y

21.80x + 16.60y = 1,152.00

x = 52 days

y = 69 days

This money will buy 121 days of food for Jasmine and Siri.

As per the unit conversion process, 4 meters is equal to 400 centimeters.

Unit conversion is a process of changing a given value from one unit of measurement to another. For example, converting meters to centimeters, or grams to kilograms. This skill is essential in science, engineering, and everyday life. In this article, we will learn how to convert 4 meters to centimeters.

First, we need to know the conversion factor between meters and centimeters. Since there are 100 centimeters in one meter, the conversion factor is 100 cm/m.

To convert 4 meters to centimeters, we need to multiply 4 meters by the conversion factor of 100 cm/m. This will give us the equivalent value in centimeters.

4 meters x 100 cm/m = 400 centimeters

It is essential to understand the conversion factor and the units of measurement involved in unit conversion. By doing so, we can accurately and efficiently convert values from one unit to another.

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Taking choices that benefit the world on a microeconomic or macroecomomic level.

Taking choices that benefit the environment, whether on an individual, national or international level.

Striving towards establishing inclusive and resilient forums that are broad-minded.

Establishing close connections with other nations to benefit global communities and address major societal issues like gender discrimination and marginalisation.

Sampling error refers to the difference between the results of a sample and the true characteristics of the population from which the sample was drawn.

In statistics, sampling error is a measure of the degree of uncertainty that arises when estimating the characteristics of a population based on a sample of that population. This error occurs due to the fact that it is not feasible to collect data from every individual in a population, so researchers must rely on samples.

Sampling error can arise from various sources, including biases in the sample selection process, variability in the characteristics of the population, and random chance. Understanding and quantifying sampling errors are important in order to assess the validity and reliability of statistical estimates and to draw accurate conclusions from data.

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Answer:

Benny the tiger costs more to feed each day because he eats 12.5 pounds of meat per day, which costs $38.75 ($3.10 x 12.5). Jasmine eats 200 pounds of hay and alfalfa, which costs $0.00, since hay and alfalfa are not typically purchased with money. Therefore, Benny the tiger costs more to feed each day.

Thus, the value displayed by Point K is roughly 373.

A number line in mathematics is a continuous straight line with numerals spaced equally apart along that line. Some stories will have a defined beginning and conclusion. We refer to these as closed number lines.

The distance between 367 and 377 can be split into five equal portions because the number line has 5 increments. Two components make up each section.

So, starting at 367, we must move 2 units to the right for each component until we reach Point K in order to determine the number represented by Point K.

We arrive at 369 by adding 2 units to the right of 367. From 369, we deduct another 2 units to arrive at 371. Following the same pattern, we arrive at 373, 375, and ultimately 377.

Point K is closest to 373 because it lies between 373 and 375. Thus, the value displayed by Point K is roughly 373.

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A circular diagram is a pie chart.

A pie chart is a circular statistical graph used to display data.

The chart is divided into slices, with each slice representing a category or proportion of the data.

Pie charts are commonly used to show percentages or fractions of a whole.

We have,

A circular diagram.

A circular diagram is commonly referred to as a pie chart.
It is a type of graph that represents data in a circular format, with each section of the chart representing a different category or value.

The size of each section is proportional to the value it represents, and the total sum of all sections is equal to 100%.

Example:

From the pie chart,

The total color is 100.

The number of each color.

Green = 25/100 x 100 = 25

Blue = 35/100 x 100 = 35

Red = 10/100 x 100 = 10

White = 15/100 x 100 = 15

Orange = 15/10 x 100 = 15

Thus,

A circular diagram is a pie chart.

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The complete question in Englsih.

What is a circular diagram.

Cluster Analysis is a statistical technique that is used to group a set of objects into clusters such that objects within the same cluster are similar to one another and objects in different clusters are dissimilar. This technique can be used to group traits such as being talkative, social, and adventurous with extroversion.

The cluster analysis is performed by assigning each trait to a group, or cluster, based on the similarity of the traits. For example, if two traits are very similar, they may be grouped together. The cluster analysis uses various algorithms to determine which traits should be grouped together. These algorithms can be based on Euclidean distance, correlation, or other measures of similarity. Once the clusters have been created, the researcher can then analyze the clusters to see how they are related to extroversion. For example, the researcher may find that traits such as talkativeness and socialness are strongly correlated with extroversion, while adventurousness is only weakly correlated. This allows the researcher to identify which traits are most strongly associated with extroversion.

Overall, Cluster Analysis is a powerful statistical technique that can be used to group traits such as being talkative, social, and adventurous with extroversion. This technique can help researchers understand the relationship between various traits and extroversion and can be used to develop better intervention strategies for individuals who exhibit certain personality traits.

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Answer:

Yes, 23 is a prime number, because its only factors are 1 and itself.

Answer: 9pi cm squared

Step-by-step explanation:

The radius is diameter divided by 2, so radius = 3cm.

Now, the equation for area is pi * r^2

3 squared is 9, so the area is 9pi cm squared.

Functional residual capacity (FRC) is the volume of air that remains in the lungs after a normal exhalation.

functional residual capacity  (FRC) is the volume of air that remaining parts in the lungs after a typical exhalation when the muscles of breath are loose. It is the equilibrium point between the outward flexible force of the chest wall and the internal versatile backlash of the lungs. At FRC, there is no air development and the tensions in the lungs and the climate are equivalent.

FRC is a significant estimation in pneumonic capability tests and can be utilized to analyze different respiratory circumstances like obstructive lung illnesses, prohibitive lung sicknesses, and neuromuscular illnesses that influence the respiratory framework.

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The correct answer is A. no; since np<5, the normal distribution should not be used.  This is because np<5, which violates the condition for using the normal distribution approximation to the binomial distribution. In this case, np=15 which is less than 5, and therefore, the binomial distribution should be used. If np is greater than or equal to 5, a normal approximation to the binomial distribution can be used.

The binomial distribution can be used to model the probability of a certain number of successes in a fixed number of independent trials, where the probability of success in each trial is the same. However, if the number of trials is large and the probability of success is small, the binomial distribution can be approximated by a normal distribution.

In this case, we have

n = 100 trials and p = 0.15

probability of success in each trial.

Therefore, np = 15, which is less than 5. According to the rule of thumb, if np < 5 or n(1-p) < 5, the normal distribution approximation is not valid, and the binomial distribution should be used.

Since the probability of success is small (0.15), and the number of trials is relatively large (100), we could use a normal approximation to the binomial distribution. However, since np < 5, we cannot use the binomial probability formula directly. Instead, we would need to use a continuity correction and the standard normal distribution to estimate the probability. Therefore, option A is the correct answer.

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Answer: 22 degrees !

Step-by-step explanation: angle ABD is a right, 90 degree angle. angle ABC is a 68 degree angle. CBD is left, so you would do 90-68 to find it, which equals 22 :)