If an object is projected vertically upward with a velocity of 29.4 m/s from a height of 30 m, then its height h above the ground in meters after t seconds is given by h = 30 + 29.4t - 4.9t^2. What is the maximum height the object will reach?

If you could show work, that would be excellent. Thank you!

The angle of depression from the top of the hill to the bottom is 23.106°.

Angle of depression is the angle which is between a horizontal line and the line of sight which is pointed downwards.

The figure representing the situation is given below.

From the figure, we get a right angled triangle ABC, right angle at B.

AB = 300 feet

BC = 128 feet

tan x = BC / AB

tan x = 128 / 300

tan x = 0.4267

x = tan⁻¹ (0.4267)

x = 23.106°

Hence the angle of depression is 23.106°.

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The balance of the account will be 1500 in a period of 8.31 years.

Compound interest is defined as the amount of interest which has been calculated on the principal amount as well as the amount accumulated over the previous period is also included.

(a) The final amount in a compound interest is,

A = P(1 + [tex]\frac{r}{n}[/tex] )^ (nt), where,

A : Final amount

P : Principal amount

r : Rate of interest

t : Time in years

n : number of times compounded in a year

Given A = $1500, P = $1000, r = 0.05, n = 1

The equation is,

1500 = 1000 (1 + 0.05)^t

(b) 1500 = 1000 (1 + 0.05)^t

1500 / 1000 = (1.05)^t

1.5 = (1.05)^t

Taking logarithm on both sides,

㏒ (1.5) = t ㏒ (1.05)         [since ㏒ (a)ᵇ = b ㏒ (a)]

t = ㏒ (1.5) / ㏒ (1.05)

t = 8.31 years

Hence the amount will be $1500 in 8.31 years.

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Answer:

= x-24

Step-by-step explanation:

[tex] \frac{x}{1.2} - 18 - 2 \\ = 1.2 \times \frac{x}{1.2} - 1.2 \times 18 - 1.2 \times 2 \\ = x - 21.6 - 2.4 \\ = x - 24[/tex]

Explanation:

Here are all of the ways to factor 16 using positive whole numbers

Which of those add to 10? That would be 2+8 = 10

Now make each of those numbers negative

The order of the -2 and -8 doesn't matter. Use a number line to help see why -2 plus -8 = -10.

Answer:

No

Step-by-step explanation:

is it always true (Dm x Dn)(X) = Dmn(X)?

NO

(Dm x Dn)(x) = D²xmn

The image point after the translation would be (10, - 1).

Given is the coordinate point of (5, 1).

We can write the translation rule as -

(x, y) → (x + 5, y - 2)

We can write the image point as -

(5, 1) → (5 + 5, 1 - 2)

(5, 1) → (10, - 1)

Therefore, the image point after the translation would be (10, - 1).

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A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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The rate of change of the table is $0.8 per pencil

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

The table of values

Using the above as a guide, we have the following:

Rate of change = Cost/Pencils

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

Rate of change = 6.4/8

Evaluate

Rate of change = 0.8

Hence, the Rate of change is $0.8

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No, the equations 1/5 + 2 = 6 and 1/5(x + 2) = 6 do not represent the same situation.

To solve the first equation, we can subtract 2 from both sides to get 1/5 = 4, and then multiply both sides by 5 to get 1 = 20.

This equation is not true, so there is no solution. To solve the second equation, we can multiply both sides by 5 to get x + 2 = 30, and then subtract 2 from both sides to get x = 28.

This is the solution to the equation. So, while both equations contain the same numbers and operations, they represent different situations and have different solutions.

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The percentage of data between 20 and 50 is 25%

The boxplot in the complete question is added as an attachment

From the attached box plot, we have

From the given box plot it is clear that 20 is the median and 50 is the third quartile.

As a general rule:

There are 25% of data values between the median and the third quartile.

Hence, 25% of the data values are between 20 and 50.

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Answer:

x=46

Step-by-step explanation:

this is how you set up the problem

3x-6+x-2=180

then you combine like terms

4x-6-6=180

then combine like terms again

4x-4=180

then you have to get 4 to the other side

4x-4=180

+4 +4

which leaves you with 4x=184

which you then divide both sides by 4

which leaves you with

x=46

I hope this helps you!!!

Answer:

x=46 =))))))))))))))))))))))))))))))))))(((()((((()()(

The volume of the triangular solid is 128/3 cubic units.

The cross-sections of the triangular solid along the y-axis are equilateral triangles with side length equal to the width of the triangular base at that y-coordinate. The width of the triangular base at y = h is equal to 8 - 4h/4. So, the side length of the equilateral triangle at y = h is 8 - 4h/4.

Let's call the height of the equilateral triangle at y = h as "x". Then, using the Pythagorean theorem, we can find the relationship between x and the side length:

x^2 = (8 - 4h/4)^2 - (x/2)^2

Expanding and simplifying the right-hand side:

x^2 = 64 - 16h + h^2/16 - x^2/4

Multiplying both sides by 4:

4x^2 = 256 - 64h + h^2 - x^2

Solving for x^2:

3x^2 = 256 - 64h + h^2

Taking the square root of both sides:

x = √(256 - 64h + h^2)/√3

So, the height of the equilateral triangle at y = h is equal to x = √(256 - 64h + h^2)/√3.

The volume of the triangular solid can be found by integrating the cross-sectional area over the height of the triangular base:

V = (1/3) ∫[0, 4] x^2(y) dy

= (1/3) ∫[0, 4] (√(256 - 64h + h^2)/√3)^2 dh

= (1/3) ∫[0, 4] (256 - 64h + h^2)/3 dh

Evaluating the definite integral:

V = (1/3) * [(256h/3 - 32h^2/2 + h^3/3) |_0^4]

= (1/3) * [(256/3 * 4 - 32/2 * 4^2 + 4^3/3) - (256/3 * 0 - 32/2 * 0^2 + 0^3/3)]

= (1/3) * (256 - 128 + 64/3)

= 128/3.

Correct Question :

The base of s is the triangular region with vertices (0, 0), (8, 0), and (0, 4). Cross-sections perpendicular to the y-axis are equilateral triangles. What is the volume of the triangular solid.

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A linear function is demonstrated by the line a.

Line a has a slope of one.

Y = x + 2 is the equation for the line a.

How do you calculate a line's slope?

Following points on line a (x,y) = (0,2) and are available in the figure (2,4)

Calculating the slope (m) involves using:

m= y^2-y^1/x^2-x^1

This results

m= 4-2/2-0

Analyze m = 1

Consequently, the line's slope is 1.

The formula for this is y = m(x - x1) + y1.

We thus have:

y = (x - 0) + 2

y = x + 2: Compare the difference and the result.

Consequently, y = x + 2 is the equation for the line a.

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B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

B. 5/12

Answer: B

Step-by-step explanation:

Here's how to subtract 3/12 from 4/6:

4/6−3/12

Step 1

We can't subtract two fractions with different denominators. So you need to get a common denominator. To do this, you'll multiply the denominators times each other... but the numerators have to change, too. They get multiplied by the other term's denominator.

So we multiply 4 by 12, and get 48.

Then we multiply 3 by 6, and get 18.

Next we give both terms new denominators -- 6 × 12 = 72.

So now our fractions look like this:

48/72−18/72

Step 2

Since our denominators match, we can subtract the numerators.

48 − 18 = 30

So the answer is:

30/72

Step 3

Last of all, we need to simplify the fraction, if possible. Can it be reduced to a simpler fraction?

To find out, we try dividing it by 2...

Are both the numerator and the denominator evenly divisible by 2? Yes! So we reduce it:

30/72÷ 2 =15/36

Let's try dividing by 2 again...

Nope! So now we try the next greatest prime number, 3...

Are both the numerator and the denominator evenly divisible by 3? Yes! So we reduce it:

15/36÷ 3 =5/12

Let's try dividing by 3 again...

Nope! So now we try the next greatest prime number, 5...

Nope! So now we try the next greatest prime number, 7...

No good. 7 is larger than 5. So we're done reducing.

There you have it! The final answer is:4.6−3/12=5/12

The angle -4π/3 in its standard position is added as an attachment

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

Angle = -4π/3

The coordinates of this point can be found by using the formula for converting from polar to rectangular coordinates:

x = cos(-4π/3)

y = sin(-4π/3)

So, we have

x = -0.5

y = 0.86

As an ordered pair, we have

(0.86, -0.5)

This means that we plot (0.86, -0.5)

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The term used to describe events that have no outcomes in common is called "Mutually Exclusive."

Probability is a measure of how likely an event is to occur. The probability of an event ranges from 0 to 1, where 0 means that an event will not occur, and 1 means that an event will certainly occur.

In Mutually Exclusive events, the probability of both events happening at the same time is 0, which means that the outcome of one event completely eliminates the possibility of the outcome of the other event. The probability of getting heads and tails at the same time is 0, as it is impossible for the coin to show both heads and tails at the same time.

In mathematical terms, Mutually Exclusive events are represented by

=> P(A) + P(B) = P(A or B),

where P(A) represents the probability of event A, P(B) represents the probability of event B, and P(A or B) represents the probability of either event A or B occurring.

To summarize, Mutually Exclusive events are events that have no outcomes in common and have a probability of 0 of occurring simultaneously.

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a) This situation represents exponential growth, as the number of bacterial cells is doubling every hour.

b) Let N be the number of bacterial cells on the petri dish at time t in hours. The equation to model the situation is:

N = 30 x 2^t

This equation represents exponential growth, as the number of bacterial cells is doubling every hour. The initial number of bacterial cells is 30 (when t = 0), and the number of bacterial cells at any time t is given by multiplying the initial number by 2 raised to the power of t.

c) After 5 hours, the number of bacterial cells on the petri dish is:

N = 30 x 2⁵ = 30 x 32 = 960

So there are 960 bacterial cells on the petri dish after 5 hours.

The math subject that is relevant to the case above is exponential growth and exponential decay. These are mathematical concepts that describe the behavior of quantities that increase or decrease at a constant percentage rate over time.

Exponential growth refers to a situation where a quantity grows at a constant percentage rate over time. In the case above, the number of bacterial cells doubles every hour, which is an example of exponential growth.

Exponential decay, on the other hand, refers to a situation where a quantity decreases at a constant percentage rate over time. An example of exponential decay could be the decay of a radioactive substance.

In summary, the case above involves the mathematical concept of exponential growth, which is a key concept in the field of mathematics and has important applications in fields such as biology, economics, and finance.

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Answer:

My friend didn't factorise the x in 4xy out.

Step-by-step explanation:

15x-20xy= 5x(3-4y)

To grow 80000 bacteria, it will take 4.152 hours.

An exponential function is a Mathematical function in the form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0. The most commonly used exponential function base is the transcendental number e, which is approximately equal to 2.71828.

Given,

Initial number of bacteria = 4500

Number of bacteria get doubled each hour

Function for population growth of bacteria is given by

N = 4500(2ˣ)

x is time in hours

Future population is N = 80000

Then

80000 = 4500(2ˣ)

800 = 45 . 2ˣ

taking log on both sides

log 800 = log (45 . 2ˣ)

log(mn) = log m + log n and log mⁿ = nlogm

log800 = log45+ x log2

2.9030 = 1.653 + x . 0.3010

x = (2.9030 - 1.653)/0.3010

x = 4.152

Hence, it will take 4.152 hours to grow 80000 bacteria.

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The area of this rectangular figure is equal to 52 1/2 feet.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Substituting the given points into the area of rectangle formula, we have the following;

Area of rectangular figure = 5 × 10 1/2

Area of rectangular figure = 5 × 21/2

Area of rectangular figure = 105/2

Area of rectangular figure = 52 1/2 feet.

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B. y = 5x² represents a proportional relationship.

In a proportional relationship, the ratio of the dependent variable (y) to the independent variable (x) is constant. In this equation, as x increases, y also increases by a constant factor (5 times x). This indicates that the two variables are proportional to each other.

In A. y = 4x + 1 and C. y = 9, there is no constant ratio between y and x, so they do not represent proportional relationships.

The weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

A commission is the extra pay to the person in the form of incentives.

Given that, an employee who receives a weekly salary of $300 and a 4% commission is paid according to the equation y = 0.04s + 300, where s represents the total weekly sales.

We are asked to find and make a table for employee's weekly salary for weekly sales of $3,000, $2,340, and $4,675.

We are given values of s,

so, weekly salary for weekly sales of $3,000

y = 0.04(3000)+300

= $420

Weekly salary for weekly sales of $2,340

y = 0.04(2340)+300

= $393.6

Weekly salary for weekly sales of $4,675

y = 0.04(4675)+300

= $487

Hence, the weekly salary for weekly sales of $3,000, $2,340, and $4,675 of the employee is $420, $393.6 and $487 respectively.

Table is attached

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The transformations and the order are a shift of 8 units left and 5 units up

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

f(x) = (x - 8)^2 + 5

The parent function is given as

y = x^2

When these functions are compared, we  have

y = x^2 is shifted right by 8 units and shifted up by 5 units to get f(x)

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The maximum index of refraction of the fluid that will still cause total internal reflection within the prism is nf = n/sinΘc.

Total internal reflection is a phenomenon in which light passes through a medium with a higher index of refraction and bounces back into the same medium instead of exiting it. This is possible when the angle of incidence is greater than the critical angle of the material.

In the case of a prism surrounded by a fluid, the maximum index of refraction of the fluid that will still cause total internal reflection within the prism can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two materials.

The critical angle of the prism can be calculated as the angle at which the sine of the angle of refraction becomes equal to 1. The critical angle can be calculated using the equation:

sinΘc = 1/n

where n is the index of refraction of the prism.

The maximum index of refraction of the fluid can then be found by rearranging Snell's law and substituting the critical angle into the equation:

nf = n/sinΘc

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The required quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
A quadratic function can be written in the general form:

f(x) = ax² + bx + c

where a, b, and c are constants.

Given a leading coefficient of 3 and a constant term of -12, we can write the quadratic function as,

f(x) = 3x² + bx - 12

Therefore, a quadratic function having a leading coefficient of 3 and a constant term of –12 is f(x) = 3x^2 + bx - 12.

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There are a total of 198 numbers with three digits in monotone order.

For non-decreasing order, we can choose any three digits from 0-9, and arrange them in increasing order. The total number of ways to do this is 10 choose 3, which is 120. For non-increasing order, we can choose any three digits from 1-9, and arrange them in decreasing order. The total number of ways to do this is 9 choose 3, which is 84. However, we have double counted the numbers that are all the same digit, such as 111, 222, etc. There are 9 of these numbers, so we need to subtract them from our total.

So the total number of numbers with three digits in monotone order is 120 + 84 - 9 = 198.

Therefore, there are 198 numbers with three digits in monotone order.

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Slope of lines 3x - 5y = 2 and 3x + 5y = -2 are m₁ = 3/5 and m₂ = -3/5 respectively.

The slope of a line is defined as the change in y-coordinate with respect to the change in x-coordinate of the line. The net change in the y coordinate is Δy and the net change in the x coordinate is Δx. Therefore, the change in y-coordinate for a change in x-coordinate can be written as

Line slope is a measure of the steepness or direction of a line in the coordinate plane.  

m = Δy/Δx

where,m is the slope

Given,

equations of the line

3x - 5y = 2

Moving 3x to RHS
-5y = -3x + 2

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

comparing with slope intercept equation of the line y = mx + c

slope m₁ = 3/5

Now, equation

3x + 5y = -2

moving 3x to RHS

5y = -3x - 2

y = (-3/5)x - 2

comparing with slope intercept equation of the line y = mx + c

slope m₂ = -3/5

Hence, m₁ = 3/5 and m₂ = -3/5 are slope of lines 3x - 5y = 2 and 3x + 5y = -2 respectively.

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The median of the given standard data set 9, 3, 10, 12, 4, 5, 12, 2 will be calculated approximately to 7. So , the median of the dataset is 7.

The median is a measure of central tendency that gives us an idea of where the "middle" of a data set lies. In other words, it gives us a value that separates the data set into two equal parts, with half of the values being above the median and the other half being below the median.

To find the median of a data set, the first step is to arrange the values in ascending or descending order. This makes it easier to identify the middle value(s) in the data set.

If the data set has an odd number of values, then there is a single middle value and that value is the median. For example, if we have the data set: 1, 2, 3, 4, 5, the median would be 3 because it is the middle value in the ordered set.

If the data set has an even number of values, then there are two middle values and the median is the average of those two values. For example, if we have the data set: 1, 2, 3, 4, 5, 6, the median would be the average of 3 and 4, which is (3 + 4) / 2 = 3.5.

So, in the case of the data set: 9, 3, 10, 12, 4, 5, 12, 2, we arrange the values in ascending order: 2, 3, 4, 5, 9, 10, 12, 12. Since there are 8 values, which is an even number, there are two middle values: 5 and 9. The median is the average of these two values, which is (5 + 9) / 2 = 7.

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The coefficient of the term x⁴y⁴ as required to be determined in the task content is; Choice C; 70.

By observation, since the expansion is to the eighth power, it follows that the number of terms in the expansion would be 9.

On this note, the x⁴y⁴ term would be the 5th term whose coefficient would be; ⁸C⁴.

Therefore, the coefficient of the x⁴y⁴ as required would be; 70.

Ultimately, Choice C is correct.

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Sam travels on the highway for approximately 1.4 hours.

We know that Sam's total travel time is 1.5 hours plus the time he spends on the highway, which we'll call "x" hours. So his total travel time can be represented as:

Total travel time = 1.5 + x

We also know that the total distance he travels is 140 miles. We can use the formula:

distance = rate x time

to set up two equations, one for his travel on city roads and one for his travel on the highway. Let's start with the city roads:

distance = rate x time

distance = 35 mph x 1.5 hours

distance = 52.5 miles

So Sam travels 52.5 miles on city roads, which means he still has to travel:

140 miles - 52.5 miles = 87.5 miles

on the highway. Now we can set up an equation for his travel on the highway:

distance = rate x time

87.5 miles = 65 mph x x hours

Solving for x, we get:

x = 87.5 miles / (65 mph)

x ≈ 1.35 hours

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I have solved the question in general, as the given question is incomplete:

The complete question is:

Sam is driving a distance of 140 miles from his house to visit Melissa. Sam takes city roads , on which can he travel an average of 35 mph for a total of 1.5 hours . Sam also takes the highway , on which he travels an average of 65 mph for a total of x hours . approximately how long does Sam travels on the highway , to the nearest tenth of an hour ?