The distance s that an object falls is directly proportional to the square of the time t of the fall. If an object falls 16 feet in
second, how far will fall in 3 seconds? How long will it take an object to fall 400 feet?

Answer:

Step-by-step explanation:

2-A

3- trapezium

4 - perpendicular

6- A

The perimeter of the second park will be 320 feet. The correct option is C.

The perimeter is defined as the sum of all the sides of the object. For a rectangular park, the perimeter will be the sum of all the sides of the rectangular park.

Given that a  park has two rectangular, fenced playgrounds. The first playground has a perimeter of 160 feet.

The perimeter of the first park:-

160 = 2 ( L + W )

L + W = 80

The perimeter of the second park,

P = 2 ( 2L + 2W )

P = 4 ( L + W )

P = 4 x 80

P = 320 feet

Therefore, the perimeter will be 320 feet.

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The definite integral of a continuous function on an interval [a, b] represents the area under the graph of the function within that interval. It provides a mathematical way to measure the accumulation of change of the function over that interval.

The definite integral of a function f on the interval [a, b] is denoted by ∫f(x)dx over the interval [a, b]. This integral can be approximated by dividing the interval [a, b] into smaller subintervals and calculating the area under the graph of the function over each subinterval. The smaller the subintervals, the closer the approximation will be to the actual definite integral.

The definite integral is said to be a limit, meaning that as the size of the subintervals approaches zero, the sum of the areas under the graph over each subinterval approaches a definite value, which is the definite integral.

In mathematical terms, for each positive number e, there exists a positive number δ such that if the subintervals have width less than δ, then the difference between the sum of the areas under the graph and the definite integral will be less than e. This means that the definite integral provides a precise value for the area under the graph of the function over the interval [a, b].

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Answer:

k = 5.6

Step-by-step explanation:

[tex]\frac{10}{7} = \frac{8}{k}[/tex]

Cross-multiplication is applied:

(10)(k) = (8)(7)

   10k = 56

k needs to be isolated and made the subject of the formula:

k = [tex]\frac{56}{10}[/tex]

k = 5.6

The upper critical value to be used in constructing a 94% confidence interval is 1.88.

What is meant by confidence interval?

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. At a specified level of confidence, a confidence interval is calculated. The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval.

In statistics, confidence is another word for probability. The most typical level of confidence is 95%, however, higher levels, such as 90% or 99%, are occasionally employed.

The confidence interval is given as 94% = 0.94

Based on the normal population, a confidence interval for a population proportion is calculated, and a normal probability table is then used to determine the critical value.

So if the confidence interval is 94%, the rest 6% of the data will be present outside the given confidence interval.

Out of the 6%, 3% of data will be present on either side of the interval.

So the critical value will be the value of [tex]z_{\frac{\alpha }{2} } = z_{0.03 }[/tex] = 1.88.

Therefore the upper critical value to be used in constructing a 94% confidence interval is 1.88.

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Answer:

To solve this equation, we need to isolate the variable x on one side of the equation. To do this, we can start by adding 1/2 (12x - 2) to both sides of the equation:

-1/2 (12x - 2) + 1/2 (12x - 2) = -6x - 1 + 1/2 (12x - 2)

Combining like terms on the right side of the equation, we get:

0 = -6x + 12x - 1 + (12x - 2) / 2

Simplifying further:

0 = 6x - 1 + 6x

Combining like terms again:

0 = 12x - 1

Adding 1 to both sides:

1 = 12x

Finally, dividing both sides by 12:

x = 1/12

Step-by-step explanation:

Answer: No solution.

Step-by-step explanation:

1.) Distribute -1/2

-6x + 1 = -6x - 1

2.) Move over terms to combine

0 = -2

There is no solution to this equation.

Answer:

Let's call the number of magazines charged at £1.90 each "x".

So, the number of magazines charged at £1.70 each is "t=70-x".

The total cost of the x magazines is x * £1.90, and the total cost of the t magazines is t * £1.70.

The total bill for all 70 magazines is £124, so we can write an equation:

x * £1.90 + t * £1.70 = £124

x * £1.90 + (70-x) * £1.70 = £124

Expanding the equation, we get:

x * £1.90 + 70 * £1.70 - x * £1.70 = £124

x * £1.90 - x * £1.70 = £124 - 70 * £1.70

x * (£1.90 - £1.70) = £124 - 70 * £1.70

x * £0.20 = £124 - 70 * £1.70

x = (£124 - 70 * £1.70) / £0.20

Now that we have an expression for x, we can use a calculator to solve for it.

x = (124 - (70 * 1.70)) / 0.20 = 40.

So, 40 magazines were charged at £1.90 each and 70 - 40 = 30 magazines were charged at £1.70 each.

The monthly payment is ​$453.125.

If the initial amount (also called as principal amount) is P, and the interest rate is R% annually, and it is left for T years for that simple interest, then the interest amount earned is given by:

[tex]I = \dfrac{P \times R \times T}{100}[/tex]

Given;

Amount Financed (P) = $15,000

Annual Percentage Rate (R) = 5%

Number of Payments per Year (N) = 12

Time in Years (T) = 3

Now, monthly payment;

=(p*i*(1+i)^n)/((1+i)^n-1)

=15000(0.05/12)(1+0.05/12)^36/(1+0.05/12)^36-1

= 72.5/0.16

=453.125

Therefore, the monthly payment by 5% interest will be $453.125.

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Answer:

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5.

6.

7. imaginary number

Step-by-step explanation:

i think this is it I'm so sorry if its wrong

i cant figure out 5 and 6 so sorry

1. real rational decimal

2. real rational integer

3. real rational root, whole number

4. real rational

5. real irrational root

6. real ration root, whole number

7. imaginary number

Answer:

x²-2x-3 using factorisation method

Step-by-step explanation:

x²-3x+1x-3

x(x-3) 1(x-3)

(x+1) (x-3)

x=-1,x=+3

Answer:

The equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.

Step-by-step explanation:

Given the points (4, 2) and (2, 4), we can use the point-slope form of a line, which is given by:

y - y1 = m(x - x1)

where (x1, y1) is a point on the line, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.

To find the slope m, we can use the formula:

m = (y2 - y1) / (x2 - x1)

Plugging in the values for the two points, we get:

m = (4 - 2) / (2 - 4) = 2 / -2 = -1

Next, we'll substitute one of the points and the slope into the point-slope form:

y - 2 = -1 (x - 4)

Expanding the right-hand side, we get:

y - 2 = -x + 4

Adding x and 2 to both sides, we get:

y = -x + 6

So, the equation of the line passing through the points (4, 2) and (2, 4) is y = -x + 6.

Answer:

13.9873

Step-by-step explanation:

This problem can be solved using long division, use the picture for reference below.

First, change the divisor 6.3 to a whole number by moving the decimal point 1 places to the right. Then move the decimal point in the dividend the same, 1 places to the right.

We then have the equations:

881.2 ÷ 63 = 13.9873

and therefore:

88.12 ÷ 6.3 = 13.9873

For more information about long division involving decimals, I recommend looking at this video here: https://youtu.be/x48CYVaD0xE

The presented statement states that the economic profit at units has a numerical value of -512 dollars per unit.

A function is a collection of several statements that work together to complete a job. Every C program we use contains at least one function, which is main (). The programs can then declare a number of extra routines in a language.

Revenue function is R (q) = 7q² + 400q

Differentiate with respect to q

R'(q) = - 7(2q) + 400.......(1)

R'(q) = - 14q + 400

Substitute q = 8 in eqn.(1)

MR(8) = -14(8) + 400

= - 112 + 400

MR(8) = -512 $ per unit

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A) There are 100 * 99 * 98 * 97 ways to award the prizes, since there are 100 choices for the first prize, 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize..

What is the combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging objects, such as numbers, sets, and permutations.

B) If the person holding ticket 47 wins the grand prize, there are 99 * 98 * 97 ways to award the remaining prizes, since there are 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.

C) If the person holding ticket 47 wins one of the prizes, there are 100 * 99 * 98 * 97 ways to award the prizes.

D) If the person holding ticket 47 does not win a prize, there are 99 * 98 * 97 * 96 ways to award the prizes, since there are 99 choices for the first prize, 98 choices for the second prize, 97 choices for the third prize, and 96 choices for the fourth prize.

E) If the people holding tickets 19 and 47 both win prizes, there are 98 * 97 * 96 * 95 ways to award the remaining prizes, since there are 98 choices for the third prize, 97 choices for the fourth prize, 96 choices for the fifth prize, and 95 choices for the sixth prize.

F) If the people holding tickets 19, 47, 73, and 97 all win prizes, there are 96 * 95 * 94 * 93 ways to award the remaining prizes, since there are 96 choices for the fifth prize, 95 choices for the sixth prize, 94 choices for the seventh prize, and 93 choices for the eighth prize.

G) If none of the people holding tickets 19, 47, 73, and 97 wins a prize, there are 96 * 97 * 98 * 99 ways to award the prizes, since there are 96 choices for the first prize, 97 choices for the second prize, 98 choices for the third prize, and 99 choices for the fourth prize.

H) If the grand prize winner is a person holding ticket 18, 47, 73, or 97, there are 3 * 99 * 98 * 97 ways to award the remaining prizes, since there are 3 choices for the grand prize winner (18, 47, or 73), and 99 choices for the second prize, 98 choices for the third prize, and 97 choices for the fourth prize.

I) If the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes, there are 98 * 97 * 96 * 95 ways to award the prizes, since there are 98 choices for the first prize, 97 choices for the second prize, 96 choices for the third prize, and 95 choices for the fourth prize.

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Answer:

reflection  over the x axis

vertical stretch of 2

vertical translation down 1 unit

Step-by-step explanation:

-2 [tex]\sqrt[3]{x}[/tex] -1

The negative in front is a reflection  over the x axis

The 2  is a vertical stretch of 2

The subtraction of 1 at the end is  a vertical translation down 1 unit

Statements about the mean that are true-It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.

It is also known as the arithmetic mean, arithmetic average, or simply average. The mean measure of central tendency is also known as these terms.

When there are even numbers of data points rather than odd numbers, there might be more than one median when the two middle numbers are divided by two.

When there are scores that are uncertain, it can be located: With uncertain scores, the median can be discovered.

The mode is a real number in the data that occurs more frequently than other values, hence it correlates to an actual score in the data.

There can be more than one: there are multiple modes (bimodal, trimodal, and multimodal) where two or more values appear the same number of times.

Hence, the statements that are true about means are -It is commonly referred to as the arithmetic average, it is easily influenced by extreme scores, there can be more than one.

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The homeowner will need 43 packages of flooring material and it will cost him $388.29.

What is the arithmetic?

Arithmetic is a branch of mathematics that deals with the study of numbers, including their properties, operations, and calculations. It involves performing basic mathematical operations, such as addition, subtraction, multiplication, and division, on numbers to solve mathematical problems.

The first room requires 24 ft * 15 ft = 360 square feet of flooring.

The second room requires 12 ft * 13 ft = 156 square feet of flooring.

So, the total amount of flooring material required is 360 + 156 = 516 square feet.

The homeowner will need 516 square feet / 12 square feet per package = 43 packages of flooring material.

So, the cost will be 43 packages * $9.03 per package = $388.29.

Hence, The homeowner will need 43 packages of flooring material and it will cost him $388.29.

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a)  v(t) = -32t + 80 feet/second  and a(t)= -32 feet/second²

b. t = 3 seconds.

c. 24 feet/second > 0).

d.  the time at which the rock reaches its highest height is 2.5 seconds and 80 feet respectively.

e. the acceleration is given by a(2.5) = -32 feet/second²

The velocity, v(t), of the rock is given by the derivative of the position function s(t) with respect to time,

v(t) = ds(t)/dt = -32t + 80 feet/second.

The acceleration, a(t) = dv(t)/dt = -32 feet/second²

b) v(3) = -32*3 + 80 = 24 feet/second.

This quantity represents the velocity of the rock at t = 3 seconds.

c) At t = 3 seconds, the rock is rising up because the velocity is positive (v(3) = 24 feet/second > 0).

d) the time at which the rock reaches its highest height,

v(t) = 0, we get -32t + 80 = 0, so t = 80/32 = 2.5 seconds.

The height of the rock will be found using the position function s(t), so s(2.5) = -16(2.5)^2 + 80(2.5) = 80 feet.

e) At the highest height, the velocity of the rock is 0, so the acceleration is given by a(2.5) = -32 feet/second².

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The coordinates of the vertex will be (-1/12, 23/24).

ax²+bx+c=0, with a not, equals 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

Given, a quadratic equation F( x )=6 x²+ x +1

Compared with the general formula of the quadratic equation ax²+bx+c=0,

a = 6

b = 1

c = 1

Solving the equation:

F( x )=6 x²+ x +1

F( x ) - 1 =6 x²+ x

f(x) - 1 = 6(x² + x/6)

f(x) -1 = 6(x² + x/6 + 1/144 - 1/144)

f(x) - 1 = 6(x + 1/12)² - 1/24

f(x) = 6(x + 1/12)² - 1/24 + 1

f(x) = 6(x + 1/12)² + 23/24

From the general formula of a quadratic equation to vertex form will be

F(x) = a(x-h)² + k

h will be -1/12 and k  will be  23/24

therefore, The coordinates of the vertex will be (-1/12, 23/24).

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I identified the Atmospheric conditions such as air pressure, temperature, and relative humidity conditions that cause snow, rain, thunderstorms, fog, and clear sky in the lab. I discovered that low-pressure zones typically have snow, rain, and stormy weather, and high-pressure areas typically have foggy or bright weather.

Atmospheric conditions, such as temperature, pressure, humidity, wind direction, and the presence of fronts, greatly influence weather patterns.

Changes in air pressure result in winds, which can transport warm or cold air, moisture, and storms. High humidity leads to clouds and precipitation, while low humidity often results in clear skies.

Note that temperature differences between different air masses can create fronts, which are boundaries separating different air masses, leading to changes in weather.

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Full Question:

"How do atmospheric conditions influence weather patterns?

In the image you can see some rectangles with different dimensions, to scale.

A rectangle is a geometric figure that is characterized by:

To find the perimeter of a rectangle we must add all its sides. In this case we must illustrate a 20 m rectangle so we can draw the following variants:

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The equation of the line perpendicular to 5x - 3y = 12 is y = -3/5x + 64.

Given that two lines are perpendicular, their slopes are negative reciprocals of each other.

The equation 5x - 3y = 12 can be rearranged to find the slope:

y = (5/3)x - 4

So the slope of the line is 5/3.

The slope of a line perpendicular to it would be the negative reciprocal of 5/3:

-3/5

Since both lines intersects at x = 30, find a point on both lines by substituting x = 30 into 5x - 3y = 12:

5(30) - 3y = 12

150 - 3y = 12

-3y = 12 - 150

-3y = -138

y = 46

Write the equation of the perpendicular line by substituting (a, b) = (30, 46) and m = -3/5 into y - b = m(x - a):

y - 46 = -3/5(x - 30)

Rewrite in Slope-intercept form:

y - 46 = -3/5x + 18

y = -3/5x + 18 + 46

y = -3/5x + 64

The equation is: y = -3/5x + 64

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Answer:

254in^2

Step-by-step explanation:

(SA)=2lw+2lh+2hw

L -> 9 W ->4 H -> 7

2(9)(4)+2(9)(7)+2(7)(4)

18*4+18*7+14*

72+126+56

198+56

254

The required explanation for hypothesis test is described.

When the null hypothesis is true in this setting, it means that the true proportion of students at Mr. Tabor's school who completed their math homework last night is equal to 0.75, or 75%. This is the value that Mr. Tabor initially believed, but the sample data suggests that only 68% of the students completed their homework.

A PP-value is the probability of observing a sample proportion as extreme or more extreme than the sample proportion, given that the null hypothesis is true. In this case, the PP-value of 0.1265 is not small enough to reject the null hypothesis. A commonly used significance level is 0.05, which means that if the PP-value is less than 0.05, the null hypothesis would be rejected.

So, given the PP-value of 0.1265, which is greater than 0.05, we cannot reject the null hypothesis and must conclude that there is not enough evidence to suggest that the true proportion of students who completed their homework is less than 0.75. This means that, based on the sample data, the null hypothesis that the true proportion is equal to 0.75 is not ruled out, and there is not enough evidence to support the alternative hypothesis that the true proportion is less than 0.75.

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Value of angle x = 70°

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size. There are two different types of alternate angles, alternate interior angles and alternate exterior angles.

Given,

ACD = 35

BCE = 105

ABC = x

By, the figure

BA || CD

⇒ ACD = BAC (alternate angles on AC)

⇒ BAC = 35°

BCE = 105

Exterior angle is equal to sum of two opposite interior angles in the triangle.

BCE = BAC + ABC

105 = 35 + x

x = 105 - 35

x = 70°

Hence,

70° is measure of x.

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Answer:

[tex]\displaystyle y=\frac{1}{1-4e^{-x}}[/tex]

Step-by-step explanation:

[tex]\displaystyle y=\frac{1}{1+C_1e^{-x}}\\\\-\frac{1}{3}=\frac{1}{1+C_1e^{-0}}\\\\-\frac{1}{3}=\frac{1}{1+C_1}\\ \\ 3=-1-C_1\\\\4=-C_1\\\\-4=C_1[/tex]

Thus, the specific solution to the IVP given the initial condition is [tex]\displaystyle y=\frac{1}{1-4e^{-x}}[/tex]