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If equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

The equation of the height h = -16[tex]t^2[/tex]+150

Where h is the height

t is the time taken

We have to find the time taken for the object to be 6 feet above the valley floor

The height = -150+6

= -144

Substitute the values in the equation

-16[tex]t^2[/tex]+150 = -144

-16[tex]t^2[/tex] = -144-150

-16[tex]t^2[/tex] = -294

[tex]t^{2}[/tex] = 18.375

t = 4.28 seconds

Hence, if equation of the height is h = -16[tex]t^2[/tex]+150, then the time taken for the object to be 6 feet above the valley floor is 4.28 seconds

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An accountant’s ethical code of conduct represents the moral values, principles, and rules that accountants should have.

The ethical codes of conduct of AICPA and IFAC are the two main codes most countries adopt to guide their members on how to deal with accounting information from an ethical perspective.

The fundamental principles within the Code – integrity, objectivity, professional competence and due care, confidentiality, and professional behavior – establish the standard of behavior expected of a professional accountant (PA) and it reflects the profession’s recognition of its public interest responsibility.

The common thing in all accounting codes of conduct is that "they all go into great detail on the responsibilities of accountants."

Therefore, the correct option is OPTION

Answer: 65$

Step-by-step explanation:

1. 40% of 150 is 60 so 60$ off of 150 is 90

2. total amount off is 85$. 60 is the 40% off and additional 25 for the rebate

3. final price will be 65$. 90-25=65

Given:

Required:

To find the domain of the given function.

Explanation:

Now consider

We have to indicate the steps to follow in order to evaluate:

(12.9-3.1) x 6.2-2 + 43

So FIRST: we solve for the operation indicated inside the parenthesis

12.9 - 3.1 = 9.8 (we subtract 3.1 from 12.9)

This is the answer you need to select.

Answer:

[tex] \csc(θ) = \frac{1}{ \sin(θ) } [/tex]

∠I ≅∠L

1) Given that the triangles are similar, then we can write:

Notice that the sides are proportional to k=3/2.

2) Since we need to prove that these triangles are similar under SAS -Side, Angle Side, examining the picture we can state that one of their corresponding angles are congruent so

3) Having one of these angles as congruent would fit to prove that these triangles are similar by SAS similarity.

Answer:

∠I ≅∠L

Step-by-step explanation:

We will apply the principle of similar triangles to solve this question

Given that

Method: Find side AC

We will use the Pythagoras theorem to evaluate AC

T

Answer:

21 cups

Step-by-step explanation:

This question tests on the the concept of Unit Conversion.

Unit Conversions involving converting values into per unit values.

Example: 15 apples in 3 days = (15 ÷ 3) apples per day = 5 apples per day

For this Question, we are given:

5 people per 3 cups of rice.

We are asked to find the number of cups of rice that 35 people can finish.

5 people = 3 cups

(5 ÷ 5) people = (3 ÷ 5) cups

1 person = 0.6 cups

(1 × 35) people = (0.6 × 35) cups

35 people = 21 cups

The vertex of the function is (1, -25) Correct

Because

f(x) = (x + 4)(x - 6)

Substitution

-25 = (1 + 4)(1 - 6)

Simplification

-25 = (5)(-5)

Result

-25 = -25 As both sides of the equation are equal this option is true

5) The graph is negative on the entire interval - 4 < x < 6 because the graph is below the x-axis

The volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4

A cylindrical drinking glass has radius 3 cm and height 8 cm.

The volume of a cylinder is 2πr²h

= 2 (3.14) 3² x 8

= 452.16cm³

The jug contains 1.5 litres of water

1 litre = 1000cm³

1.5 litre = 1500cm³

The volume of glass if it is filled upto a horizontal line 2 cm from the top.

volume =  2πr²h

= 2 (3.14) 3² x 6

= 339.12cm³

Number of glasses filled = 1500/339.12 = 4.42

4 glasses can be filled up to the line from the jug

Therefore, the volume of the glass is 454.16cm² and the number of glasses filled upto a horizontal line of 2 cm from top is 4

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The number of each type of coins are as follows:

q = 15 quarters.

d = 30 dimes.

n = 25 nickels.

In order to solve this word problem, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:

Let d represent the number of dimes.

Let q represent number of quarters.

Let n represent number of nickels.

Let T represent total number of coins.

Note: 1 quarter is equal to 0.25 dollar, 1 nickel is equal to 0.5 dollar, and 1 dime is equal to 0.1 dollar.

Translating the word problem into an algebraic equation, we have;

Dimes; d = 2q     .....equation 1.

Nickels; (70 - (q + 2q)) = (70 - 3q)     .....equation 2.

Total coins; T = n + d + q

0.5(70 - 3q) + 2q(0.1) + q(0.25) = 8.00

Multiplying all through by 100, we have:

5(70 - 3q) + 2q(10) + q(25) = 800

350 - 15q + 20q + 25q = 800

350 + 30q = 800

30q = 800 - 350

30q = 450

q = 450/30

q = 15 quarters.

For the number of dimes, we have:

Dimes, d = 2q

Dimes, d = 2(15)

Dimes, d = 30 dimes.

For the number of nickels, we have:

Nickels, n = (70 - 3q)

Nickels, n = (70 - 3(15))

Nickels, n = (70 - 45)

Nickels, n = 25 nickels.

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The area of the rectangle would be 4.90 units which is shown in the given graph.

The area of a rectangle is defined as the product of the length and width.

The rectangle is given which has:

verticals at  A(-4,0), B(-3,1) C(0,-2) and D(-1,-3)

The length of segment AB = √ (-3 - (-4))² + (1 - 0)² = √ (1 + 1) = √2

The length of segment BC = √ (-3 - 0)² + (1 - (-2))² = √ (9 + 3) = √12

The area of the rectangle = length of segment AB x length of segment BC

The area of the rectangle = √2 x √12

The area of the rectangle = √24

The area of the rectangle = 4.90 units

Thus, the area of the rectangle would be 4.90 units

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Let x be the minimum number of cars Ken has to wash to reach his goal, then we can set the following linear equation:

Solving the above equation for x, we get:

Rounding up to the nearest whole number we get:

121670000 different license plates are possible.

A license plate consists of 7 characters.

The first 4 characters are numerals from 0 to 9.

each character can be in 10 ways

so possible ways = 10 * 10 * 10 * 10  = 10000

The last 3 characters are letters excluding I, O, and X.

                    Each character can be in 26 - 3 = 23 Ways

                         Possible ways = 23 *23 * 23  = 12167

Number of possible different license plates  = 10000 * 12167

                                                                          = 121670000

Motor vehicle registration is the registration of a motor vehicle with a public authority, whether compulsory or otherwise. The purpose of registering a motor vehicle  is to establish a link between the vehicle and the owner or user of the vehicle. This link may be used for taxation or criminal investigations.

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Answer:

It has reflectional symmetry with four lines of symmetry.

Step-by-step explanation:

======================================================

Explanation:

Choice A is false since it does have rotational symmetry. See choice B.

Choice B is close, but the "90 degrees" needs to be "45 degrees". Each 45 degree rotation of the figure has the "before" and "after" be the same.

Choice C is one of the answers. There's a vertical line of symmetry, and a horizontal one as well.  Then there are two diagonal lines of symmetry. Each goes through the center. A line of symmetry is a mirror line to allow us to reflect one half over this line to get the other half.

Choice D is another answer. It has point symmetry since we can pick any point on the figure and reflect it over the center point, to land on a corresponding image point on the opposite side of the figure. For example, the northern most point reflects over the center to land on the southern most point.

Step-by-step explanation:

there is one item and it cannot be split.

the winning bid was $8,000.

that means the fair share for each one of the 5 participants is

8000/5 = $1,600

the winner is getting one item with a value greater than his fair share.

so, he has to pay the difference into the kitty :

8000 - 1600 = $6,400

Answer

Part A

(g o h)(x) = x - 1

Part B

Domain of (g o h) = (-∞, ∞)

Explanation

Part A

We are given that

g(x) = x² + 3

h(x) = √(x - 4)

We are then asked to find (g o h)(x)

To do that, we need to note that (g o h)(x) means we write g(x), but instead of x, we write h(x). That is,

(g o h)(x)

= g(h(x))

= [h(x)]² + 3

= [√(x - 4)]² + 3

= x - 4 + 3

= x - 1

Part B

To find the domain

The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists.

And for (g o h)(x) = x - 1, we know there will be an answer for all real number values of x. Hence,

Domain = (-∞, ∞)

Hope this Helps!!!

Answer:

one of the angles is 48 degrees the other is 42 degrees

Step-by-step explanation:

Complementary is 90

45 + 45 = 90

48 +42=90

SOLUTION

Consider the image given below.

From the image above,

To find the measures of each angle, we need to obtain the value of small x in the diagram.

Applying the rule: Sum of angle in a triangle is 180 degrees

Then substitute the given expression, we have

Collect like terms and add

Divide both sides by 6, we have

hence, x=30

Then substitute the value of x to obtain the measure of each angles.

Since the triangle is an issoceles triangle, then

Hence

Therefore

Answer : ∠V= 28°, ∠W=28°, ∠X=124°

Answer: 529.3 downloads

Explanation:

Standard version size = 2.1 MB

High quality version = 4.7 MB

The high-quality version was downloaded twice as often as the standard version

H = 2 S

The total size downloaded for the two versions = 3335 MB

H + S = 3335

We have the system:

H = 2 S (a)

H + S = 3335 (b)

Put A into B

(2S ) + S = 3335

3S = 3335

S= 3335/3

S= 1,111.67 MB

Divide the total MB of standard versions by the size of each standard version.

1,111.67 / 2.1 = 529.3 downloads

To solve the question we would need to state some facts.

1) In measurements, there are one thousand millimeters in a meter.

2) Also one thousand milligrams equals one gram

3) However one milligram is not equal to one milliliter

Answer: 1mg is equal to 1ml is not true

EXPLANATION

The equation of the function can be represented as shown as follows:

-This function is discrete.

-If we have 20 gallons, we can obtain the number of miles by plugging in the value into the equation, as shown as follows:

Dividing both sides by 12:

Simplifying:

We can make 1.67 miles with 20 gallons.

-The domain of the function are all the Real Numbers and the Range are also the Real numbers.

-Finally, drawing the graph of the function:

The points of the table are the following:

Gallons Miles

2 24

4 48

6 72

8 96

-We can get the number of gallons needed to, make 500 miles by plugging the value 500 into the equation, as shown as follows:

Isolating m:

Simplifying:

The number of gallons to make 500 miles is equal to 41.7 gallons

Finally, labeling the graph:

Formula to work out the Total surface area of half-cylinder = [tex]\pi rh + \pi r^{2} + 2rh[/tex]

To find:

Formula to work out the surface area of half a cylinder

Solution:

The surface area of ​​a semi-cylinder can be calculated by adding half the curved area of ​​the cylinder to the area of ​​the two semi-circles and the area of ​​the rectangular section below. The formula for the surface area of ​​a semi-cylinder is given by: Total surface area of ​​

Total surface area of a half-cylinder = (1/2) × curved area of ​​cylinder + 2 × area of ​​semi-circle + area of ​​base of cylinder.

total surface area of a half-cylinder = [tex]\pi rh+\pi r^{2} +2rh[/tex]

where r = radius of cylinder

[tex]\pi[/tex] = 3.14 or 22.7 cm

h = height of cylinder

(Or)  We can find Total surface area of half cylinder as, Total surface area of half cylinder ÷ 2

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The point estimate of the population mean is 9

The point estimate of the population standard deviation is 2.83

Part a

Point estimate of population mean:

Given the sample data is 5,8,10,7,10,14

Number of samples, n is 6

Population mean=[tex]\frac{\sum x }{n}[/tex]

                           =(5+8+10+7+10+14)/6

                           =54/6

                           =9

Point estimate of mean=9

Part b

Point estimate of population standard deviation:

Mean=9

Data (x)     (x-mean)^2

5                16

8                1

10               1

7                 4

10               1

14               25

Total           48

Standard deviation=√(x-mean)^2/n

                               =√48/6

                               =√8

                               =2.83

Hence, the point estimate of population standard deviation is 2.83

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The unknown angle in the triangle is as follows;

The angle H can be found using the exterior angle theorem.

The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.

In other words,  an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Hence,

∠DFG = ∠G + ∠H

∠DFG = 14x + 1

∠G  = 89°

∠H = 5x - 7

14x + 1 = 89 + 5x - 7

14x + 1 = 89 - 7 + 5x

14x - 5x = 89 - 7 - 1

9x = 81

divide both sides by 9

x = 81 / 9

x = 9

Therefore,

∠H = 5(9) - 7 = 45 - 7 = 38 degrees.

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The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

In this case we find a rational equation whose numerator and denominator are polynomials, which must be simplified by using algebra properties. The complete procedure is now shown:

(9 · x - 6)² / (2 · x⁴ + 4 - 2 · x⁴ - 1)                  Given

(81 · x² - 108 · x + 36) / (3)                             Perfect square binomial / Associative, commutative and modulative properties / Existence of additive inverse /Definition of subtraction

27 · x² - 36 · x + 12                                        Addition and subtraction of fractions with same denominator / Associative and commutative properties / Definition of division

The rational equation is equivalent to the polynomial 27 · x² - 36 · x + 12.

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Given:

a.) A person had 14,000 infested in two accounts.

b.) One paying 9% simple interest.

c.) One paying 10% simple interest.

Let,

x = the amount invested at 9% simple interest

y = the amount invested at 10% simple interest

1.) We know the total amount of money invested is $14,000. We get,

x + y = 14,000

2.) We know that the total interest for the year for the two accounts is $1432. We get,

0.09*x + 0.1*y = 1,339

Let's equate the two equations,

x = 14,000 - y (Substitute for x)

0.09*(14,000 - y) + 0.1*y = 1,339

1,260 - 0.09y + 0.1y = 1,339

0.1y - 0.09y = 1,339 - 1,260

0.01y = 79

0.01y/0.01 = 79/0.01

y = 7,900

Therefore, $7,900 was invested at the rate of 10% simple interest.

Let's determine x, substituting y = 7,900 in x + y = 14,000.

x + y = 14,000

x + 7,900 = 14,000

x = 14,000 - 7,900

x = 6,100

Therefore, $6,100 was invested at the rate of 9% simple interest.

Answer:

90%

Step-by-step explanation:

To find the percent of increase in the height of the tree, we need the change of the height and the original height (40 feet)

The change of height = 76 - 40 = 36 feet

Now, we need to divide the change by the original height to find the percent of increase.

36/40 = 9/10

9/10, which is then 90%.

1) How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?

In this case we can combine 30 types of candy bars in a set of 4 bars.

This can be calculated as a combination of 30 in 4 with no repetition:

Answer: 27,405 possible combinations (C).

2) How many ways can 13 students line up for lunch?

In this case we have a permutation of 13 in 13 with no repetition.

We can calculate this as:

Answer: 6,227,020,85)00 possible permutations (P).

3) How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID.

In the word we have 9 letters with no repetition, so we have to calculate a permutation (as order matters) of 9 letters in 3 places.

We can calculate this as:

Answer: 504 possible permutations (P).

4) How many ways can you choose 2 books from a shelf of 40 books.

In this case, the order does not matter, so it is a combination of 40 in 2.

This can be calculated as:

Answer: 780 possible combinations (C)

5) How many ways can 12 swimmers finish in first, second, and third place?

In this case, the order does matter, so we have a permutation of 12 in 3:

Answer: 1320 permutations (P)

6) How many ways can Mrs. Sullivan choose two students from 27 to help put away calculators at the end of class?

The order does not matter between the two students, so it is a combination of 27 in 2:

Answer: 351 combinations (C)