Suppose that for a function g (x), g (4) = 7. Select all of the statements that are true.
A. 4 is in the range of g.
B. For a value a, it is possible that g (a) = 4.
C. For a value y, it is possible that g (4) = y.
D. The point (4,7) is on the graph of y = g (x).
E. The point (7,4) is on the graph y = g (x).

1. The possible amounts of time for which the chemistry club could rent the meeting room are 1 to 5 hours.

2. Solving the inequality for t is 39 + 6.80t ≤ 73, where the maximum time is 5 hours.

Inequality is a mathematical statement that two or more mathematical expressions are unequal.

Inequalities are depicted using the following symbols:

The total budget of the chemistry club for renting a meeting room = $73.60

The reservation fee charged by the college = $39

The additional fee (variable cost) per hour = $6.80

The number of hours the club can rent the meeting room = t

The inequality representing the situation is:

39 + 6.80t ≤ 73.

39 + 6.80t ≤ 73

6.8t ≤ 73 - 39

6.8t ≤ 34

t ≤ 5 (34/6.8)

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Explanation:

The ratio of orange juice to pineapple juice is:

And the function can be written as:

To choose one graph we have to identify one point in each of them and check if the expression above is true for that point. This chosen point cannot be (0,0).

Answer:

The first series,

\(\displaystyle \sum_{k=2}^\infty \frac{\cos(k)}{k^2}\)

is convergent. By comparison, using the fact that |cos(x)| ≤ 1 for all real x,

\(\displaystyle \sum_{k=2}^\infty \frac{\cos(k)}{k^2} \le \sum_{k=2}^\infty \frac1{k^2}\)

and the bounding series is a convergent p-series (with p = 2).

The second series,

\(\displaystyle \sum_{k=2}^\infty \frac{e^k}{\left(2+\frac1k\right)^k}\)

is divergent by the limit test. We have

\(\dfrac{e^k}{\left(2 + \frac1k\right)^k} = \dfrac{e^k}{2^k\left(1+\frac1{2k}\right)^k} = \left(\dfrac e2\right)^k \cdot \dfrac1{\left(1+\frac1{2k}\right)^k}\)

By definition,

\(e = \displaystyle \lim_{k\to\infty}\left(1+\frac1k\right)^k\)

so that

\(\displaystyle \lim_{k\to\infty}\left(1+\frac1{2k}\right)^k = \lim_{k\to\infty}\sqrt{\left(1+\frac1{2k}\right)^{2k}} = \sqrt{\lim_{k'\to\infty}\left(1+\frac1{k'}\right)^{k'}} = \sqrt{e}\)

so that the limit of the summand is

\(\displaystyle \lim_{k\to\infty} \frac{e^k}{\left(2+\frac1k\right)^k} = \frac1{\sqrt{e}} \lim_{k\to\infty} \left(\frac e2\right)^k\)

but e > 2, so the limit is ∞.

Step-by-step explanation:

xy/5

.........

....................

Answer:

Smallest element in the set of range is -3

Step-by-step explanation:

From the given set of ordered pairs,

x-value of each pair represents the Domain of the relation.

y-value of the pair represents the Range of the relation.

Set of domain:

{0, 1, 2, 3, 4, 5, 6}

Set of Range:

{1, 3, 2, 5, 2, -3, 2}

Smallest number in the set of range = -3.

Therefore, smallest element in the set of range is -3.

The factors of the expression x^2 - 49 = 0 are as follows

(x + 7) (x - 7) = 0

The number 49 is a perfect square, and therefore the roots are either a negative 7 or a positive 7.

So the factores would be x + 7 or x - 7. That is,

When x + 7 = 0

Then x = -7

When x - 7 = 0

Then x = 7

The factors of the expression therefore are

(x + 7) and (x - 7)

Answer:

D.) there is 9a and 6b ,3c and 1 thats four different terms

Step-by-step explanation:

Have a nice day! :D

Answer:

Jason - 9.375 miles per hour

Kevin -7.875 miles per hour

Step-by-step explanation:

Let Jason’s running speed be x miles per hour

Kevin runs 1.5 miles per hour less;

so his running speed will be (x-1.5) miles per hour

At any point, distance = speed * time

Their running time is same here;

Jason’s running time will be 5/x

Kevin’s running time will be 4.2/(x-1.5)

These times are equal;

So;

5/x = 4.2/(x-1.5)

5(x-1.5) = 4.2x

5x - 7.5 = 4.2x

5x-4.2x = 7.5

0.8x = 7.5

x = 7.5/0.8

x = 9.375 miles per hour

So kevin’s speed will be 9.375 - 1.5 = 7.875 miles per hour

The coordinates of point B are (-3, 17).

The given equation is M = I₁ + I₂ = 31 + 32.

Now let's substitute in our given values:

(-2, 2) = ((-5 + x₂) / 2, (-5 + 2 + y₂) / 2)

We will now set up two equations to solve for our two unknowns, x₂ and y₂:

Equation 1: (-5 + x₂) / 2 = -4

Multiply both sides by 2:

-5 + x₂ = -8

Add 5 to both sides:

x₂ = -3

This gives us the x-coordinate of point B.

Equation 2: (-5 + 2 + y₂) / 2 = 7

Simplify:

(-3 + y₂) / 2 = 7

Multiply both sides by 2:

-3 + y₂ = 14

Add 3 to both sides:

y₂ = 17

This gives us the y-coordinate of point B.

Therefore, the coordinates of point B are (-3, 17).

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There will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

To calculate the amount in Nathan's daughter's RESP after 25 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount (amount in the account after 25 years)

P = Principal amount (amount deposited every 2 months)

r = Annual interest rate (in decimal form)

n = Number of times the interest is compounded per year

t = Number of years

In this case, Nathan deposits $940 every 2 months, so the principal amount (P) is $940. The annual interest rate (r) is 3.99% or 0.0399 in decimal form. Since the interest is compounded quarterly, the compounding frequency (n) is 4. The number of years (t) is 25.

Since Nathan deposits every 2 months, we need to calculate the total number of deposits made over 25 years. There are 12 months in a year, so in 25 years, there will be 25 * 12 = 300 months. However, since Nathan deposits every 2 months, the number of deposits (m) is 300 / 2 = 150.

Now, we can substitute these values into the formula:

A = 940(1 + 0.0399/4)^(4*25)

Calculating the exponent first:

(1 + 0.0399/4)^(4*25) ≈ 2.703236

Now, substituting the calculated exponent and the number of deposits into the formula:

A = 940 * 2.703236 * 150 ≈ $594,311.34

Therefore, there will be approximately $594,311.34 in Nathan's daughter's RESP after 25 years of depositing $940 every 2 months with a 3.99% annual interest rate compounded quarterly.

It's important to note that this calculation assumes Nathan makes the same $940 deposit every 2 months consistently over the 25-year period and does not make any withdrawals from the account during that time. Additionally, the actual amount may vary slightly due to rounding and any potential changes in interest rates over the years.

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The correct answer is C. It is the graph of f(x) translated 11 units to the left.

The correct answer is:

C. It is the graph of f(x) translated 11 units to the left.

When we have a function of the form g(x) = f(x - a), it represents a horizontal translation of the graph of f(x) by 'a' units to the right if 'a' is positive and to the left if 'a' is negative.

In this case, g(x) = f(x - 11), which means that the graph of f(x) is being translated 11 units to the right. However, the answer options do not include this specific transformation. The closest option is option C, which states that the graph of g(x) is translated 11 units to the left.

The graph of f(x) = x is a straight line passing through the origin with a slope of 1. If we apply the transformation g(x) = f(x - 11), it means that we are shifting the graph of f(x) 11 units to the right. This results in a new function g(x) that has the same shape and slope as f(x), but is shifted to the right by 11 units.

Therefore, the correct answer is C. It is the graph of f(x) translated 11 units to the left.

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The solutions for the quadratic equation:

x^2 - 8x = -3

Are:

Here we want to solve the quadratic equation:

x^2 - 8x = -3

First we can move all the terms to the left side so we get:

x^2 - 8x + 3 = 0

Using the quadratic formula (or Bhaskara's formula) we can get the solutions for x as:

\(x = \frac{8 \pm \sqrt{(-8)^2 - 4*¨1*3} }{2*1} \\\\x = \frac{8 \pm 7.2 }{2}\)

Then the two solutions for the quadratic equation are:

x = (8 + 7.2)/2 = 7.6

x = (8 - 7.2)/2 =0.4

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The cost of a soda is $2.50. By solving the system of equations formed from the given information, the value of S is determined to be 2.50.

To find the cost of the soda, let's set up a system of equations using the given information. Let's assume the cost of a candy bar is represented by 'C' and the cost of a soda is represented by 'S.'

From the first statement, we can write the equation:

3C + 2S = 14.00 ----(Equation 1)

From the second statement, we can write the equation:

4C + 3S = 19.50 ----(Equation 2)

To solve the system of equations, we can use a method called substitution. Rearranging Equation 1, we get:

S = (14.00 - 3C) / 2

Substituting this expression for S into Equation 2, we have:

4C + 3((14.00 - 3C) / 2) = 19.50

Simplifying this equation, we get:

4C + (42.00 - 9C) / 2 = 19.50

8C + 42.00 - 9C = 39.00

-C + 42.00 = 39.00

-C = 39.00 - 42.00

-C = -3.00

C = 3.00

Now we can substitute the value of C back into Equation 1 to find the value of S:

3(3.00) + 2S = 14.00

9.00 + 2S = 14.00

2S = 14.00 - 9.00

2S = 5.00

S = 5.00 / 2

S = 2.50

Therefore, the cost of a soda is $2.50.

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Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].

The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).

In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.

So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.

In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].

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According to the table given, the rate of change is of 9.

The rate of change is given by the change in the output divided by the change in the input.

In this problem:

Taking two of the points, (3,27) and (5,45), we have that:

\(m = \frac{45 - 27}{5 - 3} = \frac{18}{2} = 9\)

Hence, the rate of change is of 9, which would be verified taking any pair of two points.

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Answer: Answer below

Step-by-step explanation: So you would simply have to divide 8 into 72 which would be 9.

we can verify our answer by doing 9x8 which equals 72.

Answer: 9

Step-by-step explanation:

bears divided by shelves = number of bears per shelf

72 bears divided by 8 shelves= 9 bears per shelf

Answer:

\(\huge\boxed{\sf \frac{2\sqrt{7}-4 }{3}}\)

Step-by-step explanation:

This is a rationalizing denominator question.

\(= \displaystyle \frac{2}{2+\sqrt{7} } \\\\Multiply \ and \ divide \ by \ conjugate \ 2 - \sqrt{7} \\\\= \frac{2}{2+\sqrt{7} } \times \frac{2-\sqrt{7} }{2-\sqrt{7} } \\\\\underline{\sf Using \ formula:}(a+b)(a-b)=a^2-b^2\\\\= \frac{2(2-\sqrt{7}) }{(2)^2-(\sqrt{7})^2 } \\\\= \frac{4-2\sqrt{7} }{4-7} \\\\= \frac{4-2\sqrt{7} }{-3} \\\\= \frac{-(4-2\sqrt{7}) }{3} \\\\= \frac{2\sqrt{7}-4 }{3} \\\\\rule[225]{225}{2}\)

Answer:

the absolute value of -5 is 5, and the absolute value of 5 is also 5. ∣ a + b i ∣ = a 2 + b 2 . |a+bi| = \sqrt{a^2 +b^2}

please give me heart

Answer:

A

Step-by-step explanation:

(2,1) - only one in the table. Remember (x,y)

Answer:

The depreciation tax shield for this project in year 4 is $178.24.

Explanation:

To calculate the depreciation tax shield for this project in year 4, we need to first determine the depreciation expense for year 4 using the MACRS three-year class life category and the double-declining balance (DDB) method.

From Table 12.8 on page 415 of the textbook, we can see that the depreciation rate for year 1 is 33.33%, for year 2 it is 44.45%, for year 3 it is 14.81%, and for year 4 it is 7.41%.

Using the DDB method, we can calculate the depreciation expense for each year as follows:

Year 1: Depreciation expense = $14,000 x 33.33% = $4,667

Year 2: Depreciation expense = ($14,000 - $4,667) x 44.45% = $3,554

Year 3: Depreciation expense = ($14,000 - $4,667 - $3,554) x 14.81% = $830

Year 4: Depreciation expense = ($14,000 - $4,667 - $3,554 - $830) x 7.41% = $557

The total depreciation expense over the four years is the sum of the individual year's depreciation expenses, which is:

$4,667 + $3,554 + $830 + $557 = $9,608

Now, we can calculate the depreciation tax shield in year 4. The depreciation tax shield is the amount of the depreciation expense that reduces the firm's taxable income, multiplied by the tax rate. In year 4, the depreciation tax shield is:

Depreciation tax shield = Depreciation expense in year 4 x Tax rate

Depreciation tax shield = $557 x 32% = $178.24

Therefore, the depreciation tax shield for this project in year 4 is $178.24.

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U thought this was a professional answer?!!!!??????

You're wrong!!!!!!!!!!!!!!!!!

But the answer is correct though...

:))

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Bing Chilling

It's over...

No more to read

Happy birthday if it's ur birthday...

Have a nice day my king:)

Answer: d = 14/5

Step-by-step explanation:

14 + d = 6d

14 = 5d

14/5 = d

Check Work:

14 + (14/5) = 6(14/5)

16.8 = 16.8

The function m(x) = 2tan(3x+4) is obtained by applying a sequence of transformations to the parent tangent function.

To determine the sequence of transformations, let's break down the given function:

1. Inside the tangent function, we have the expression (3x+4). This represents a horizontal compression and translation.

2. The coefficient 3 in front of x causes the function to compress horizontally by a factor of 1/3. This means that the period of the function is shortened to one-third of the parent tangent function's period.

3. The constant term 4 inside the parentheses shifts the function horizontally to the left by 4 units. So, the graph of the function is shifted to the left by 4 units.

4. Outside the tangent function, we have the coefficient 2. This represents a vertical stretch.

5. The coefficient 2 multiplies the output of the tangent function by 2, resulting in a vertical stretch. This means that the graph of the function is stretched vertically by a factor of 2.

In summary, the sequence of transformations applied to the parent tangent function to create the function m(x) = 2tan(3x+4) is a horizontal compression by a factor of 1/3, a horizontal shift to the left by 4 units, and a vertical stretch by a factor of 2.

Example:
Let's consider a point on the parent tangent function, such as (0,0), which lies on the x-axis.

After applying the transformations, the corresponding point on the function m(x) = 2tan(3x+4) would be:
(0,0) -> (0,0) (since there is no vertical shift in this case)

This example helps illustrate the effect of the transformations on the graph of the function.

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The set (A U B) n (A U C) is {2, 5, 7, 10}. A.

To find the set (A U B) n (A U C), we first need to calculate the union of sets A and B, and then calculate the union of that result with set C. Finally, we find the intersection of these two sets.

Set A U B:

The union of sets A and B, denoted as A U B, is the combination of all elements from both sets without any repetitions.

A contains the elements 2, 5, 7, and 10, while B contains the elements 1, 2, and 3.

A U B consists of the elements {1, 2, 3, 5, 7, 10}.

Set (A U B) U C:

Next, we calculate the union of the set (A U B) with set C, denoted as (A U B) U C. A U B contains the elements {1, 2, 3, 5, 7, 10} and C contains the elements {1, 2, 3, 4, 5}.

Taking the union of these two sets results in {1, 2, 3, 4, 5, 7, 10}.

Finding the intersection:

Finally, we find the intersection of (A U B) U C with A U C. A U C consists of the elements {2, 5, 7, 10}.

The intersection of these two sets is the combination of common elements.

The common elements are {2, 5, 7, 10}.

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Answer:

100x100=10,000

A short and easy trick is to multiply only the first number since the rest are zero. So, multiply 1 and 1: 1 x 1. What do you get? 1, of course. Then, add the rest of the zero's after that. In 100, there are two zero's. In 100, there are two zero's. What is two plus two? Well: 2 + 2 = 4 so, four zero's. After that, add the 4 zero's after the 1. One is extremely important in this problem. 1, one zero, 10, two zero's, 100, three zero's, 1,000, and finally, four zero's, 10,000. So, the trick is to multiply the one by the other one, get 1, and add the zero's in the other numbers. This can work as long as it is something like: 10 x 10, 100 x 100, 1,000 x 1,000, or even beyond. Just remember to add the zero's!

Note: This only works with digits similar to the ones listed below.

Notice that they all have a 1 at the front and zero('s) behind them.

1) 10 x 10

2) 100 x 100

3) 1,000 x 1,000

This can continue to over 100 zero's per digit!

The solution to the expression is A = 10000

Given data ,

Let the expression be represented as A

Now , the value of A is

Let the first number be represented as p

The value of p = 100

Let the second number be represented as q

The value of q = 100

So, A = pq

On simplifying the equation , we get

A = p multiplied by the value of q

And , A = 100 x 100

A = 10000

Therefore , the value of A is 10000

Hence , the expression is A = 10000

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Answer:

84x

Step-by-step explanation: