PLS HELP
WHAT COULD BE THE LARGEST WHOLE NUMBER???

30 POINTSSSS

a. The ranges of g(x) and h(x) differ by a constant value of 1, since h(x) is simply g(x) shifted upward by 1 unit. Therefore, the range unit.

b.

Graph of g(x) = 2x + 1 and h(x) = 2x + 2 over the interval 0 < x < 5:

![Graph of g(x) over the interval 0 < x < 5 is (1, 11), while the range of h(x) is (2, 12). This confirms that the range of h(x) is equal to the range of g(x) shifted upward by 1 unit.

g(x) = 2x+1 h(x) = 2x + 2

for the domain 0 < x < 5.

These are two parallel lines where h(x) is 1 unit above g(x) Then, the range of h(x) over the given domain will have endpoints 1 unit greater.

g(0) = 2(0) + 1 g(0) = 0 + 1 g(0) = 1

Evaluating g(x) when x = 5 :

g(5) = 2(5) + 1

g(5) = 10 + 1

g(5) = 11

Then, we can graph g(x) by connecting the points (0, 1) and (5, 11).

Evaluating h(x) when x = 0 :

h(0) = 2(0) + 2 h(0) = 0 + 2 h(0) = 2

Evaluating h(x) when x = 5 :

h(5) = 2(5) + 2

h(5) = 10 + 2

h(5) = 12

Then, we can graph h(x) by connecting the points (0, 2) and (5, 12).

From the graph, the range of g(x) over the given domain is (1, 11) and of h(x) is (2,12)

Answer:

Option 2

Step-by-step explanation:

Recall the distance formula:

[tex]\sqrt{(x^1-x^2)+(y^1-y^2)}[/tex]

(note that this formula can be switched around. x^1 and x^2 can be switched and y^1 and y^2 can be switched and you could put the y's parentheses in front of the x's parentheses)

If we insert our numbers into our question we can see that they match option 2. (remember, two negatives make a positive)

Therefore, the answer is option 2.

The top of the ladder is dropping at a rate of -5/24 ft/s (approximately -0.208 ft/s) when the base is 5 feet from the wall.To answer your question, we'll use the Pythagorean theorem for the right triangle formed by the ladder, wall, and ground.

Let x be the distance from the base of the ladder to the wall, and y be the distance from the top of the ladder to the ground. The ladder's length (13 ft) is the hypotenuse of the triangle.
According to the Pythagorean theorem:
x² + y² = 13²
When the base is 5 feet from the wall:
5² + y² = 13²
y² = 144
y = 12 ft
Now, we'll differentiate the equation with respect to time (t):
2x(dx/dt) + 2y(dy/dt) = 0
Given that the base is being pulled away at 0.5 ft/s (dx/dt = 0.5 ft/s), we can find the rate at which the top of the ladder is dropping (dy/dt) when x = 5 ft and y = 12 ft:
2(5)(0.5) + 2(12)(dy/dt) = 0
5 + 24(dy/dt) = 0
dy/dt = -5/24

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The top of the ladder is dropping at a rate of [tex]5/\sqrt(119)[/tex]feet per second.

Let's begin by drawing a diagram of the situation:

           |\

           | \

           |  \   <-- ladder

           |   \

           |    \

           |     \

           |         \

           |______\

              wall

A right triangle formed by the ladder, the wall, and the ground.

Let's call the distance from the foot of the ladder to the wall "x" and the height of the ladder "y".

The ladder is 13 feet long and that the foot of the ladder is being pulled away from the wall at a rate of 0.5 feet per second.

The height of the ladder is changing when the foot of the ladder is 5 feet from the wall.

Using the Pythagorean theorem,

the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation

[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

[tex]x^2 + y^2 = 13^2[/tex]

Differentiating both sides with respect to time t, we get:

[tex]2x dx/dt + 2y dy/dt = 0[/tex]

We want to find. [tex]dy/dt[/tex] when [tex]x = 5[/tex], so, we need to substitute. [tex]x = 5[/tex] and [tex]dx/dt = 0.5[/tex] into the equation above:

[tex]2(5)(0.5) + 2y dy/dt = 0[/tex]

[tex]y dy/dt = -5[/tex]

[tex]dy/dt = -5/y[/tex]

Pythagorean theorem to solve for y when. [tex]x = 5[/tex]:

[tex]5^2 + y^2 = 13^2[/tex]

[tex]y^2 = 144 - 25[/tex]

[tex]y^2 = 119[/tex]

[tex]y = \sqrt(119)[/tex]

The foot of the ladder is 5 feet from the wall, the height of the ladder is:

[tex]y = \sqrt(119) feet[/tex]

And the rate of change of the height of the ladder is:

[tex]dy/dt = -5/y = -5/\sqrt(119) feet per second[/tex]

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The probability that the sample contains exactly two defective parts is 0.0058.

We may utilize the binomial probability formula to resolve this issue:

P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)

where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.

Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).

P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3

We calculate P(X = 2) = 0.0058 using a calculator.

As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.

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Answer: x=23±√609/10

Step-by-step explanation:

The 80% confidence interval is 1501 to 1599 square feet, indicating with 80% confidence that the true population mean of square feet per house falls within this range based on the sample data.

Based on the given information, we can calculate the 80% confidence interval for the true population mean of the number of square feet per house using the sample mean of 1550 square feet and the population standard deviation of 154 square feet. The interval is 1501 to 1599 square feet. This means that if we were to repeat the sampling process and construct confidence intervals in the same way for an infinite number of times, approximately 80% of these intervals would contain the true population mean. Therefore, we can estimate with 80% confidence that the true population mean falls within the range of 1501 to 1599 square feet.

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Identifying  the first term and common difference and writing a recursive rule:

a. an = an-1 - 5, n > 1

b.  an = an-1 + 12, n > 1

a) The first term is 1 and the common difference is -5. To write a recursive rule for this sequence, we can use the formula:

an = an-1 + d

where an is the nth term of the sequence, an-1 is the (n-1)th term, and d is the common difference.

Using this formula, we get the recursive rule:

a1 = 1

an = an-1 - 5, n > 1

b) The first term is 11 and the common difference is 12. To write a recursive rule for this sequence, we can use the same formula as above:

an = an-1 + d

Using this formula, we get the recursive rule:

a1 = 11

an = an-1 + 12, n > 1

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Answer:

B. 12x^2 + 31x + 20

Step-by-step explanation:

Use FOIL (First, Outer, Inner, Last)

(3x + 4)(4x + 5)

12x^2 + 15x +16x + 20

12x^2 + 31x + 20

Answer:

B

Step-by-step explanation:

You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x

The quotient function of f(x) and g(x) is given as follows:

(f/g)(x) = 3x^(3/4).

The functions in the context of this problem are defined as follows:

When we want to divide two functions, we just divide each other, hence:

(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).

When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:

x/x^(1/4) = x^(1 - 1/4) = x^(3/4).

Hence the function is:

(f/g)(x) = 3x^(3/4).

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The proportional relationship is y = 3x.

What is the proportional relationship?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

Here, we have

Given:

x:  2, 6, 8, 10

y:  6, 18, 24, 30

We have to find the proportional relationship between x and y.

So, we can see from inspection and visual observation that there is a proportional relationship between x and y.

6 = 3  2,  18 = 3  6, 24 = 3  8, 30 = 3  10.

Hence, The proportional relationship is y = 3x.

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The absolute deviation for the observation of 16 in the data-set is given as follows:

5.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the mean of the data-set in this problem is given as follows:

(19 + 16 + 4 + 9 + 7)/5 = 11.

The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:

16 - 11 = 5.

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Answer:

the angles which are formed in matching corners or corresponding corners with the transversal when two parallel lines are intersected by any other line

Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

The closest answer to the total amount of the mortgage is option D: $351,226.80.

What is percentage?

Percentage is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". The term "percent" comes from the Latin word "per centum", which means "per hundred".

To calculate the total amount of the mortgage, we need to first calculate the amount of each mortgage.

For the first (80%) mortgage, we can calculate the amount by multiplying the house price by 80%:

$175,000 x 0.80 = $140,000

For this mortgage, we have a 30-year fixed rate of 4.75%. We can use an online mortgage calculator or formula to calculate the monthly payment:

M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1]

where:

M = monthly payment

P = principal (amount of the loan)

i = interest rate per month (annual rate divided by 12)

n = total number of payments (number of years multiplied by 12)

Using this formula, we get:

M = $140,000 [ 0.0475/12 (1 + 0.0475/12)^360 ] / [ (1 + 0.0475/12)^360 – 1]

M = $755.67

For the second (20%) mortgage, we can calculate the amount by multiplying the house price by 20%:

$175,000 x 0.20 = $35,000

For this mortgage, we have a 30-year fixed rate of 7.525%. Using the same formula as above, we get:

M = $35,000 [ 0.07525/12 (1 + 0.07525/12)^360 ] / [ (1 + 0.07525/12)^360 – 1]

M = $250.09

To calculate the total amount of the mortgage, we simply add the two monthly payments:

$755.67 + $250.09 = $1,005.76

Finally, we multiply this monthly payment by the total number of payments (30 years multiplied by 12 months per year) to get the total amount of the mortgage:

$1,005.76 x 360 = $361,475.77

Therefore, the closest answer to the total amount of the mortgage is option D: $351,226.80.

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Answer:

x = 8, y = 3

Step-by-step explanation:

Assuming the figure is a parallelogram, opposite sides on a parallelogram are equal.

This means that 3x-2 = 2x+6 and 3y-5 = y+1.

To solve these equations:

3x-2 = 2x+6 (collect like terms)

3x-2x = 6+2

x = 8

3y-5 = y+1 (collect like terms)

3y-y = 1+5

2y = 6 (divide both sides by 2)

y = 3

∴ x = 8, y = 3

The first step is to find the mean number of incorrect answers. Since there are 11 questions, and each question has a 50/50 chance of being answered incorrectly, we can expect the student to get 5.5 questions wrong on average.

Next, we need to calculate the variance. To do this, we can use the formula:

Variance = p(1-p)n

Where p is the probability of getting a question wrong (0.5), and n is the number of questions (11).

Variance = 0.5(1-0.5)11 = 1.375

Finally, we can find the standard deviation by taking the square root of the variance:

Standard deviation = sqrt(1.375) = 1.17 (rounded to two decimal places)

Therefore, the standard deviation of the number of incorrect answers on the exam is 1.17.

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The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.

To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.

The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.

However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.

To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.

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We can use proportions to solve this problem. If 2 inches represent 75 miles, then we can set up a proportion:

2 inches / 75 miles = x inches / 11 miles

To solve for x, we can cross-multiply:

2 inches * 11 miles = 75 miles * x inches

22 inches = 75 miles * x inches

Divide both sides by 75 miles:

22 inches / 75 miles = x inches

Simplify:

0.2933 inches = x inches

Therefore, 11 miles on the map would be represented by approximately 0.2933 inches.

The opportunity of drawing a chocolate from the bag is 0.4, therefore, the answer is A. 0.4.

Steven has a bag of 20 pieces of candy, out of which 8 are chocolates. If he draws one piece of sweet at random, the opportunity of it being a chocolate may be calculated through dividing the wide variety of chocolates in the bag with the aid of the full quantity of chocolates inside the bag. In this situation, there are 8 chocolates out of 20 total candies.

The formulation to calculate the opportunity is:

P(chocolate) = number of candies / total range of candies

Substituting the given values, we get:

P(chocolate) = 8 / 20

Simplifying this fraction, we get:

P(chocolate) = 0.4

Consequently, the opportunity of drawing a chocolate from the bag is 0.4  

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In the event that a monopolistic firm takes over superbly competitive advertising, we would anticipate seeing the advertising cost of the great rise and the amount sold drop.

Be that as it may, when a monopolistic firm takes over the showcase, it picks up showcase control and the capacity to impact the cost. The monopolist can charge a better cost than the competitive advertising cost since there are no near substitutes for its item. As the monopolist raises the cost, the amount requested will drop, as customers switch to substitutes or decrease their utilization of the item.

we would anticipate seeing the advertising cost of the great rise and the amount sold fall as the monopolist tries to extend benefits by raising costs. This is often in differentiating from impeccably competitive advertising.

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The results are:

7a) Explicit = h(n) = [tex]0.87^{n-1}[/tex] * 200.

Recursive = h(0) = 200 and h(n) = 0.87 * h(n-1)

7b) Rebound height = 99.76 cm (rounded to the nearest hundredth).

8a) Explicit formula: A(n) = 575 + 47.50n

Recursive formula: A(0) = 575, A(n) = A(n-1) + 47.50

8b) 30 weeks to save $2000'

7a) Explicit: h(n) = [tex]0.87^{n-1}[/tex] * 200 (

where h(n) = height of the golf ball after n bounces,

0.87 is the rebound factor,

200 is the initial height)

h(n) = [tex]0.87^{n-1}[/tex] * 200

Recursive:  h(0) = 200

h(n) = 0.87 * h(n-1)

where h(n) = the height after n bounces,

h(n-1) = height after (n-1) bounces,

0.87 = rebound factor.

Apply given values:

h(0) = 200

h(n) = 0.87 * h(n-1)

7b) Rebound height, using recursive formula:

h(0) = 200

h(1) = 0.87 * 200 = 174

h(2) = 0.87 * 174 = 151.38

h(3) = 0.87 * 151.38 = 131.70

h(4) = 0.87 * 131.70 = 114.71

h(5) = 0.87 * 114.71 = 99.76 (rounded to the nearest hundredth)

8a)Explicit: A(n) = 575 + 47.50n,

where A(n) = amount of money Jessica has after n weeks,

575 = initial amount given by grandfather,

47.50 = amount Jessica adds each week.

Recursive: A(0) = 575, A(n) = A(n-1) + 47.50,

where A(n) = the amount of money Jessica has after n weeks,

A(n-1) = amount Jessica has after (n-1) weeks

47.50 = amount Jessica adds each week.

8b) Weeks to save $2000:

A(n) = 575 + 47.50n = 2000

Solving for n:

575 + 47.50n = 2000

47.50n = 2000 - 575

47.50n = 1425

n = 1425 / 47.50

= 30 weeks.

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The measurement of the sides of the equilateral triangle is 16 cm.

The perimeter of the rectangle,

Perimeter of rectangle = 2(length + width)

                                      = 2(15 + 9)

                                      = 2(24)

                                      = 48 cm

Since the perimeter of the equilateral triangle is equal to the perimeter of the rectangle, we have,

Perimeter of equilateral triangle = 48 cm

An equilateral triangle has all three sides equal, so let's call the length of each side "s". The perimeter of the equilateral triangle can also be expressed as:

Perimeter of equilateral triangle = 3s

Therefore, we have,

3s = 48

Solving for "s", we get,

s = 16

The length of sides of equilateral triangle is 16 cm.

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Answer: A: 4

Step-by-step explanation:

This is the number we will start the line, if we were to graph this example. We would then go up 1 page for every hour (1 y for every x), on the graph.

The best center is the mean because there are no outliers

To determine the best center, we need to examing the ages of the player withing the range of age.

The ages of the players are: 11, 10, 11, 11, 8, 11, 12, 11, 9, 10, 11, 12

In the above list of age, we can seee that there are no outliers are

When there are no outliers in a dataset, the best center to use is the mean

Hence, the best center is the mean

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Joel cannot make a right triangle with the current lengths of fencing.

A right triangle is a triangle that has one angle that measures exactly 90 degrees (a right angle). This means that the other two angles of the triangle are acute (measuring less than 90 degrees). The side opposite the right angle is called the hypotenuse, and it is always the longest side of the triangle. The other two sides are called the legs of the triangle.

To check if Joel can make a right triangle with the current lengths of fencing, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).

So, let's check if the measurements satisfy the Pythagorean theorem:

8²  + 15² = 64 + 225 = 289

20²  = 400

According to the Pythagorean theorem, a triangle with sides of length 8 ft, 15 ft, and 20 ft would be a right triangle if it satisfies the equation a²  + b²  = c² , where a and b are the shorter sides (legs) and c is the longest side (hypotenuse). However, in this case, we can see that the sum of the squares of the shorter sides (8²  + 15² ) is not equal to the square of the longest side (20² ), so the measurements cannot form a right triangle.

Therefore, Joel cannot make a right triangle with the current lengths of fencing.

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Chad drinks  389.28  fluid ounces of water in 6 days.

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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D) 8.25

E) 12

F) 13.5

G) 26

H) 28