(c) Suppose that L is a line tangent to the boundary of the golf green and parallel to the path of the ball. Let Q be the point where the line is tangent to the circle. Notice that there are two possible positions for Q. Find the possible x-coordinates of Q:

Answer:

In this case the equation is already in vertex form. The vertex of the parabola is the maximum point and the value of h(t) at that point is the maximum height.

Since the equation is h(t) = -16t² + 70.56, the maximum height is 70.56 feet.

Uday Tahlan

Answer: The height of an object can be determined using the relationship between the height of an object, the length of its shadow, and the length of a reference shadow. This relationship is given by the formula:

Height of object = (Height of reference object x Length of object's shadow) / Length of reference shadow

Given that a 4-ft vertical post casts a 10-in shadow at the same time a nearby cell phone tower casts a 125-ft shadow, we can use this formula to find the height of the cell phone tower:

Height of the cell phone tower = (4 ft x 10 in) / 125 ft

To find the height of the cell phone tower, we have to convert the 10 inches to feet, since the reference object's height is in feet.

10 inches = 10/12 ft = 5/6 ft

Height of the cell phone tower = (4 ft x 5/6 ft) / 125 ft

Height of the cell phone tower = 20/125 ft = 16/125 ft = 128/1025 ft = 128/1025 * 12/12 in = 128/85 ft

So the cell phone tower is 128/85 ft or (128/85) * 12 = 128/7 ft = 18.285714 ft tall.

The cell phone tower's height is 18.285714 ft.

Step-by-step explanation:

Answer: 6

12 divided by 2 is 6 or 6 + 6 = 12

The survey conducted by the fourth-grade class can provide an estimate of the opinions of the teachers in the district, but it is subject to sampling error and the sample is not random and may not be representative of the population of all teachers in the district.

The fourth-grade class' survey is a sample survey of a subset of teachers in the district, not a census of all teachers in the district. As such, it can provide an estimate of the opinions of all teachers in the district, but it is subject to sampling error. This means that if the class were to survey a different sample of teachers, the results might be slightly different. The sample size of 150 teachers may or may not be big enough to provide a reliable estimate of the population of the teachers.

Another thing to keep in mind is that the sample is not random and it's composed only of teachers who have children at the school, so the results may not be representative of the population of all teachers in the district. Also, because the survey indicates that the majority of those sampled were in favor of the club, it does not necessarily mean that the majority of all teachers in the district are in favor of the club.

Thus, In summary, The survey conducted by the fourth-grade class can provide an estimate of the opinions of the teachers in the district, but it is subject to sampling error and the sample is not random and may not be representative of the population of all teachers in the district.

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Answer:

Let G be Emily's gross pay.

Deductions:

FIT = 112

State Tax = 0.04G

City Tax = 0.015G

Social Security and Medicare

Net pay = Gross pay - Deductions

3,223 = G - 112 - 0.04G - 0.015G - Social Security - Medicare

We can then solve for G by isolating it on one side of the equation:

3,223 + 112 + 0.04G + 0.015G = G - Social Security - Medicare

3,223 + 0.055G = G - (Social Security + Medicare)

Now we can solve for G by dividing both sides by 1.055

G = 3223 / 1.055 + (Social Security + Medicare)

So we can find the gross pay but we don't have the exact amount for Social Security and Medicare that are being deduced.

The polynomial of degree 3 with the given zeros and a leading coefficient of 1 is:

P(x) = x^3 - 5x^2 - 14x

Remember to do one post per question, I will answer the first one.

We know that for a polynomial of degree N with the given N zeros:

{x₁, x₂, ..., xₙ}

We can write the polynomial as:

P(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)

Where the leading coefficient is a.

Here the degree of the polynomial is 3, and the 3 zeros are:

-2, 0, 7

And the leading coefficient is 1.

Then we can write it as:

P(x) = 1*(x + 2)*(x - 0)*(x - 7)

P(x) = (x^2 + 2x)*(x - 7)

P(x) = x^3 + 2x^2 - 7x^2 - 14x

P(x) = x^3 - 5x^2 - 14x

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The intersection of all of those intervals always be a closed interval if it is nonempty

Given that

for an arbitrary collection of closed intervals

the intersection of all of those intervals always be a closed interval if it is nonempty it's true

An arbitrary (finite, countable, or uncountable) intersection of

closed sets is closed.

Let C0 = [0, 1], C1 = [0, 1/3] ∪ [2/3, 1], and

C2 = [0, 1/9] ∪ [2/9, 1/3]∪ [2/3, 7/9] ∪ [8/9, 1]

In general, let

Cn =(1/3 [tex]C_{n-1}[/tex])U(1/3[tex]C_{n-1}[/tex] + 2/3)

Let C = ∩n>1Cn, called Cantor’s middle-third set. Show that C is

a closed set.

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The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y).

e(x+y)

e = expected

x = points earned on part 1

y = points earned on part 2

So, the expected recorded score is the total of points earned on both parts: e(x+y).

The expected recorded score in a grade book is the total amount of points earned on both parts of the assignment. This is written as e(x+y), where e stands for expected, x is the points earned on part 1, and y is the points earned on part 2. Therefore, the expected recorded score is the sum of the points earned on both parts, e(x+y). This formula is useful for quickly calculating the total score of an assignment, allowing the grade book to be updated quickly and accurately.

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When Kp = 1.00 at 300K, for X(g) + Y(g) <==> Z(g), where [X] = [Y] = [Z] = 1.0 M, the reaction is in equilibrium.

Therefore the answer is c)  reaction is at equilibrium.

Given the equilibrium constant Kp = 1.00 at 300K, this means that the reaction is already at equilibrium. Therefore, the net reaction will not proceed in any direction. The concentration of all the species X, Y, and Z in the reaction mixture will remain constant. So the answer is [c] reaction is at equilibrium.

It's important to note that the equilibrium constant Kp is the product of the concentration of the products raised to their stoichiometric coefficients divided by the product of the concentration of the reactants raised to their stoichiometric coefficients.

When Kp = 1, it means that the product of the concentrations of the products raised to their stoichiometric coefficients is equal to the product of the concentrations of the reactants raised to their stoichiometric coefficients. Therefore, the reaction is at equilibrium.

--The question is incomplete, answering to the question below--

"In which direction will the net reaction proceed.

X(g) + Y(g) <==> Z(g) … Kp = 1.00 at 300k

for each of these sets of initial conditions?

A) [X] = [Y] = [Z] = 1.0 M

[a] net reaction goes to the left [this one?]

[b] net reaction goes to the right

[c] reaction is at equilibrium"

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Yes, Charlie can finish the work by 4:30 pm

With Mr. Brown, he has an appointment for 1 × [tex]1^{1}[/tex] hour

[tex]1^{1}[/tex] = 1

∴ 1 × 1 = 1 hour

So if he starts work at 9:15 am, he will finish an appointment with Mr. Brown at 10:15 am

9:15 means 9 hours 15 minutes

9 hours 15 minutes + 60mins   [1 hour = 60 mins]

9 hours 75 mins ⇒ 10:15 am

With Mr Pryce he has an appointment for 1 hour 10 mins. He willl finish with him at 11:25 am

1 hour 10 minutes ⇒ 60 + 10 = 70 minutes

At 10:15am he starts work with Mr Pryce,

⇒10:15 + 70 minutes = 10:85 minutes = 11:25 am

Then if he takes a 45 minutes break,

11 hours 25 mins + 45 mins = 11 hours 70 mins = 12:10 pm

With Sam he has an appontment for 3 × [tex]1^{1}[/tex] hours. He will complete with him at 3:10 pm

⇒ 3 × 1 = 3 hours

At 12: 10 he starts with Sam,

12:10 means 12 hours 10 mins.

12 hours 10 mins + 3 hours = 15 hours 10 mins

⇒ 3:10 pm

Thus he finishes his work by 3:10 pm which is 1 hour 20 mins before 4:30 pm.

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Answer:

Step-by-step explanation:

The depth of the submarine after 6 minutes would be -182.9 ft. below sea level. This is calculated by taking the starting depth of -250 ft. and adding 12.1 ft. for each minute (6 minutes x 12.1 ft. = 72.6 ft.). Therefore, -250 + 72.6 ft. = -182.9 ft. below sea level.

The distributive property shows that (2x + 3)(4x - 5) will give a value of 8x² + 2x - 15.

The distributive property states that multiplying the sum of two or more addends by a number yields the same outcome as multiplying each addend separately by the number and combining the resulting products.

Here is an example of using the distributive property to expand:

(2x + 3)(4x - 5)

Using the distributive property, this can be expanded as:

2x * 4x + 2x * -5 + 3 * 4x + 3 * -5

Which simplifies to:

8x² - 10x + 12x - 15

Combining like terms:

8x² + 2x - 15

Note that your information wasn't well written and another example was issued for your understanding.

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Information organised in rows and columns, such as numbers and descriptions is known as table.

General tables and summary tables are the two broad types into which statistical tables can be divided.

General tables

General tables include a compilation of specific data that is all pertinent to the topic or theme. Such tables are typically included in the appendices of reports and serve the primary function of assembling all the information on a given issue for quick reference.

Summery tables

Summary tables are made to accomplish a number of distinct tasks. They are typically included into the text, smaller in size than regular tables, and focus on a particular component of the data. Because they are generated from the general tables, the summary tables are also known as derivative tables. The data in the summary table is intended for analysis and inference. They are also known as interpretative tables as a result.

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So, on solving the provided question we can say that the rate of change of the volume with respect to radius = [tex]1770 = 4/3 \pi r^3S = 4 \pi r^2[/tex] [tex]dS/dt = 8 \pi r dr/dt[/tex]

The length of a circle or sphere, in more contemporary use, is the same as its radius in classical geometry, which is one of the line segments from its center to its circumference. The Latin word radius, which also refers to the spokes of a wagon wheel, gave rise to the term. The distance a circle's center is from any point on its perimeter is its radius. Usually, "R" or "r" is used to indicate it. A radius is a line segment that has one endpoint in the center and one on the circumference of a circle. Circular diameter equals radius The diameter of a circle is the segment that traverses its center and has ends that are on the circle.

Taking the derivative of the volume formula

[tex]DV/dt = 4\pi r*2 dr/dt\\5471 = 4 \pi r*2 dr/dt[/tex]

This equation  r and dr/dt

We can solve for r...

sphere is 1770 cubic inches

[tex]1770 = 4/3 \pi r^3S = 4 \pi r^2dS/dt = 8 \pi r dr/dt[/tex]

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On solving the provided question we can say that the value of the equation will be 20-15=5 B

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Girls 4/(4+3)* 35= 20

Boys: 35-20= 15

Ans 20-15=5 B

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Five positive three-digit integers have a remainder of 2 when divided by 6, a remainder of 7 when divided by 11, and a remainder of 5 when divided by 9.

Looking at the values, we notice that,

11-7=4,  9-5=4 and 6-2=4

This means we are looking for a value that is four less than a multiple of

11, 9, 6

The least common multiple of these numbers is 198

we can write 198k - 4 ,where k is a positive integer.

This value is only a three-digit integer when k is 1, 2, 3, 4, 5 giving us 194, 392, 590, 788, 986.

The quantity that is "left over" after conducting a calculation is referred to as the remnant in mathematics. The residual is the integer that remains after dividing one integer by another to create an integer quotient in mathematics (integer division).

The polynomial that remains after dividing one polynomial by another is known as the "remainder" in algebra of polynomials. When a dividend and a divisor are provided, the modulo operation is the one that results in such a remainder.

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Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

To make a 75% sugar syrup, Anton will need 75% sugar and 25% water by weight. To find out how much sugar and how much water he needs, we can use the following formulas:

Sugar weight = 5lbs x 75% = 3.75lbs

Water weight = 5lbs x 25% = 1.25lbs

So Anton needs 3.75 lbs of sugar and 1.25 lbs of water to make 5 lbs of 75% sugar syrup.

It's important to note that syrup with 75% sugar content is heavy syrup, it is mostly used for preservation and not as a sweetener.

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Answer:

30.144 or 3.14 if rounded.

Step-by-step explanation:

First you need to find the area of the table top

a = [tex]\pi r^{2}[/tex]

a = (3.14) ([tex].8^{2}[/tex])    The radius is the half of the diameter 1.6/2 = .8

a = 3.14(.64)

a = 2.0096

The area is 2.0096 [tex]m^{2}[/tex]

the cost will be

2.0096 x 15 = 30.144 rupees

Doe you round rupees to the nearest hundredths' place?  I am not sure. Rounded the number would be 30.14

On solving the provide question, we can say that by linear equation the value  2000 times

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.When an equation has the formula y=mx+b, with m denoting the slope and b the y-intercept, it is referred to as being linear.

[tex]8*10^6/(4*10^3)\\=(8/4)*(10^6/10^3)\\=2*(10^3)\\=2*1000\\=2000 times[/tex]

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A light-year is the distance light can travel in one year. It is equal to 9.46 trillion kilometers or 5.88 trillion miles. This is equal to about 6 trillion kilometers (3.7 trillion miles). It is the most common unit used to measure interstellar distances.

1. One light-year is equal to the distance light can travel in one year.

2. Distance light can travel in one year = speed of light x time

3. Speed of light = 300,000 km/sec

4. Time = 1 year

5. Distance light can travel in one year = 300,000 km/sec x 1 year

6. Distance light can travel in one year = 9.46 trillion km

7.The annual distance that light can cover is 5.88 trillion miles.

A light-year is a unit of distance used to measure interstellar distances. It is equal to 9.46 trillion kilometers, or 5.88 trillion miles. This is equal to approximately 6 trillion kilometers (3.7 trillion miles). This is calculated by multiplying the speed of light (300,000 km/sec) by one year (365.25 days). Light-years are commonly used to measure distances between stars and galaxies.

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The three anti-fraud measures associated with the largest reduction in median losses are proactive data monitoring/analysis, management review, and hotline.

The ACFE claims that one of the primary characteristics of fraud is the deliberate attempt to conceal evidence and that many instances of fraud go undetected because of this. In order to reduce the likelihood of fraud occurring, businesses are urged to develop internal anti-fraud measures like a Code of Ethics.

The first step in deciding which internal controls to put in place is to gain an understanding of how occupational fraud is committed.

Asset misappropriation, bribery, and financial statement fraud are the three main types of occupational fraud schemes identified by the research. In addition, a crucial step in creating an efficient control environment across the company that may help in avoiding and detecting fraud is to gain an in-depth understanding of and analyze each of these categories.

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By the Pythagorean theorem, [tex]y=\sqrt{6^2-3^2}=3\sqrt{3}[/tex].

By the geometric mean theorem, [tex]y^2=3x \implies x=9[/tex].

Answer:

a)

x+y=24---1

y= 2x ---2

subs 2 in 1

x+2x=24

3x=24

x=8

when x=8 subs in 2

y=2(8)

y=16

b)

2x+y=100---1

y=2(x-10)---2

subs 2 in 1

2x+2(x-10)=100

2x+2x-20=100

2x+2x=100+20

4x=120

x=30

when x=30 subs in 2

y=2(30-10)

y=2(20)

y=40

c)

x+y=26---1

3x+y=56---2

from 1

x+y=26

y=26-x---3

subs 3 in 2

3x+26-x=56

3x-x=56-26

2x=30

x=15

when x=15 subs in 3

y=26-15

y=11

Answer:

h(g)x)) = - 6x + 1

Step-by-step explanation:

to find h(g(x)), substitute x = g(x) into h(x) , that is

h(g(x))

= h(2x)

= - 3(2x) + 1

= - 6x + 1

If a unit vector lies in the xy plane, at an angle of 158 degrees from the x-axis, with a positive y component. The unit vector is ( -0.927,  0.374).

The unit vector is defined as a vector that points in the same direction as our vector (158 degrees from the x-axis) and has a magnitude of 1.

As we know that for a radius R and an angle A, the rectangular coordinates can be written as:

x = R × cos(A)

y = R × sin(A)

And if we want that the magnitude/modulus of our vector to be 1, then R = 1, and we know that A = 158°

x = 1 × cos(158°) = -0.927

y = 1 × sin(158°) = 0.374

Then the unit vector is: ( -0.927,  0.374)

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Answer:

other leg ≈ 7.5 cm

Step-by-step explanation:

using Pythagoras' identity in the right triangle

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let x represent the other leg , then

x² + 13² = 15²

x² + 169 = 225 ( subtract 169 from both sides )

x² = 56 ( take square root of both sides )

x = [tex]\sqrt{56}[/tex] ≈ 7.5 cm ( to the nearest tenth )

The value of f(4) is -122.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(1) = 5

f(n) = -3 x f(n - 1) + n

Now,

For n = 4,

f(4) = -3 x f(4 - 1) + 4

f(4) = -3 x f(3) + 4

f(4) = -3 x f(3) + 4 ______(1)

We need to find f(3).

For n = 3,

f(3) = -3 x f(3 - 1) + 3

f(3) = -3 x f(2) + 3 _____(2)

We need to find f(2).

For n = 2,

f(2) = -3 x f(2- 1) + 2

f(2) = -3 x f(1) + 2

f(2) = -3 x 5 + 2

f(2) = -15 + 2

f(2) = -13

Substituting f(2) = -13 in (2)

f(3) = -3 x -13 + 3

f(3) = 39 + 3

f(3) = 42

Substituting f(3) = 42 in (1)

f(4) = -3 x f(3) + 4

f(4) = -3 x 42 + 4

f(4) = -126 + 4

f(4) = -122

Thus,

f(4) = -122.

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The value of angle A = 57°

angle B = 33°

c = 7.16

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then asin/A=bsin/B=csin/C.

using Pythagoras theorem, c² = 3.96² + 5.96²

c² = 15.682+35.522

c²= 51.204

c = √51.204

c = 7.16 ( nearest hundredth)

c/sinC = b/sin B

7.16 /sin90 = 3.96/sinB

sinB = (3.96× sin90)/7.16

sinB = 3.96/7.16

sinB = 0.55

B = sin^-1 0.55

B = 33° ( nearest degree)

Therefore A = 180-(90+33)

A = 57°

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If the absolute value is greater than or greater than or equal to a negative number, the solution is all real numbers.

If the absolute value is less than zero, there is no solution.

If the absolute value is less than or equal to zero, there is one solution.

If the absolute value is greater than zero, the solution is all real numbers

except for the value which makes it equal to zero. This will be written as a union.

The absolute value is always a positive value and not a negative number. so those numbers are called absolute values.

It is represented as |a|, which defines the magnitude of any integer ‘a’.

Absolute value is a term used in mathematics to indicate the distance of a point or number from the origin of a number line or coordinate system.

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