(6CQ) Evaluate the limit, or state that the limit does not exist. 2n+7n/13n

Answer:

Step-by-step explanation:

Answer:

Option b (4,1)

Step-by-step explanation:

The region given by the system of inequalities is shown in the graph. We must look within this region for the point that minimizes the objective function [tex]f(x, y) = 8x + 8y[/tex]

The minimum points are found in the lower vertices of the region.

These vertices are found by equating the equations of the lines::

[tex]3x+2y=14\\-5x +5y=10[/tex]

-------------------

[tex]x = 2\\y = 4[/tex]

[tex]-8x + 3y = -29\\3x + 2y = 14[/tex]

---------------------

[tex]x = 4\\y = 1[/tex]

The lower vertices are:

(4, 1) (2, 4)

Now we substitute both points in the objective function to see which of them we get the lowest value of [tex]f(x, y)[/tex]

[tex]f(4, 1) = 8(4) +8(1) = 40\\f(2, 4) = 8(2) + 8(4) = 48[/tex]

Then the value that minimizes f(x, y) is (4,1).

Option b

let's not forget that a function and its inverse have a domain <-> range relationship, namely, if the original function has a point of say (3 , 7 ), then its inverse function will have a point of (7 , 3 ), the same pair just flipped sideways.

[tex]\bf (g\circ f^{-1})(x)\implies g(~~~f^{-1}(x)~~~) \\\\\\ (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~) \\\\[-0.35em] ~\dotfill\\\\ \textit{so let's firstly find out what is }f^{-1}(2)[/tex]

we don't have an f⁻¹(x), darn!! but but but, we do have an f(x) on the left-hand-side graph, and it has a pair where y = 2, namely ([ ] , 2), so then, f⁻¹(x) will have the same pair but sideways, let's inspect f(x).

hmmmmmm when y = 2, x = 0, notice the y-intercept on the graph, ( 0, 2 ).

so then, that means that f⁻¹(x) has a pair sideways of that, namely ( 2, 0), or f⁻¹(2) = 0.

so then, g(  f⁻¹(2)  ), is really the same as looking for g(  0  ), well then, what is "y" when x = 0 on g(x)?  let's inspect the right-hand-side graph.

hmmmmmmmmmmm  notice, the point is at ( 0 , 2 ), namely when x = 0, y = 2.

[tex]\bf (g\circ f^{-1})(2)\implies g(~~~f^{-1}(2)~~~)\implies g(0)\implies 2[/tex]

Answer:

  [tex]v\sqrt[28]{v^{13}}[/tex]

Step-by-step explanation:

The exponent rules that apply are ...

[tex](a^b)(a^c)=a^{b+c}\\\\a^{\frac{b}{c}}=\sqrt[c]{a^b}[/tex]

Using these rules for your product, we have ...

[tex]v^{\frac{3}{4}}\times v^{\frac{5}{7}}=v^{\frac{3}{4}+\frac{5}{7}}\\\\=v^{\frac{41}{28}}=v\cdot v^{\frac{13}{28}}=v\sqrt[28]{v^{13}}[/tex]

Answer:6

Step-by-step explanation: 1,000 divided by 7 is 994 with a remainder of six. Which means the principal had six left

Answer:

2.25 hours for the man and 1.83 hours for the woman.

Step-by-step explanation:

We first find the number of calories consumed by both the man and the woman.

The man's calories are:

750+400+225 = 1375

The woman's calories are:

370+400+0 = 770

The man burns 610 calories per hour.  This means to find the number of hours, we divide the number of calories by the rate burned per hour:

1375/610 = 2.25 hours

The woman burns 770 calories per hour.  This means to find the number of hours, we divide the number of calories by the rate burned per hour:

770/420 = 1.83 hours

A 190-pound man needs to shovel snow for approximately 2.25 hours, and a 130-pound woman needs to shovel for approximately 1.83 hours to burn off the calories from their Burger King meal.

The question involves calculating the time it takes for a 190-pound man and a 130-pound woman to burn off the calories consumed from a meal at Burger King through the physical activity of shoveling snow. The man consumed a total of 1375 Calories (750 Cal for BK Big Fish sandwich, 400 Cal for medium french fries, and 225 Cal for a large Coke). The woman consumed a total of 770 Calories (370 Cal for a basic hamburger, 400 Cal for medium french fries, and 0 Cal for a diet Coke).

To find out how long each person needs to shovel snow to burn off the lunch calories, we divide the total number of calories consumed by the rate at which they burn calories while shoveling snow.

For the man: 1375 Calories / 610 Cal/h = approximately 2.25 hours.

For the woman: 770 Calories / 420 Cal/h = approximately 1.83 hours.

Answer:

Sample mean for solution 1:  19.27; sample mean for solution 2:  10.32

Step-by-step explanation:

To find the sample mean, find the sum of the data values and divide by the sample size.

For solution 1, the sum is given by:

9.7+10.5+9.4+10.6+9.3+10.7+9.6+10.4+10.2+10.5 = 192.7

The sample size is 10; this gives us

192.7/10 = 19.27

For solution 2, the sum is given by:

10.6+10.3+10.3+10.2+10.0+10.7+10.3+10.4+10.1+10.3 = 103.2

The sample size is 10, this gives us

103.2/10 = 10.32

The sample mean for Solution 1 is 10.05 mils per minute, while the sample mean for Solution 2 is 10.32 mils per minute. These figures represent the average etch rates of each solution in the semiconductor manufacturing process. So here the sample mean should be calculated.

To calculate the sample means of Solution 1 and Solution 2, we first sum up the etch rates of each solution, and then divide by the number of samples in each solution.

For Solution 1, the etch rates sum up to 100.5 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.05 mils per minute.

For Solution 2, the etch rates sum up to 103.2 mils per minute. Dividing this by 10 (number of samples), we get a sample mean of 10.32 mils per minute.

So, the sample means for Solution 1 and Solution 2 are 10.05 and 10.32 mils per minute respectively. These means are useful to compare the average efficiency of these two solutions as a part of normal distribution analysis in the semiconductor manufacturing process.

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Answer:

$386794

Step-by-step explanation:

To be able to find how much we get in 5 years, we need to base it off the initial salary value.

So in the first year we get.

$70,000

To get how much we get in the 2nd year we add the extra 5%.

2nd year salary = (1.05)70000

2nd year salary = 73500

Now we continue to do that until the 5th year

3rd year = (1.05)73500

3rd year = 77175

4th year = (1.05) + 77175

4th year = 81033.75

5th year = (1.05) + 81033.75

5th year = 85085.44

Now we add them all up to get the total.

70000 + 73500 + 77175 + 81033.75 + 85085.44 = $386794.19 or $386794

Reflection over x-axis, shift down 5 units.

Answer:

Option B is correct.

Step-by-step explanation:

Given Parent Function, f(x) = |x|

Transformed function, f(x) = - |x| + 5

In transformed function, f(x) = -|x|

Represent that parents function is first reflected ove x - axis.

then in transformed function, f(x) = -|x| + 5

represent that after reflection function is shifted 5 unit in upward direction.

Therefore, Option B is correct.

Answer: 22 feet.

Step-by-step explanation:

Note that there are two right triangles in the figure attached: ACD and BCD. Where "h" is the height of the chimeney  from John's eye level to the top of the chimney.

You need to use the trigonometric identity [tex]tan\alpha=\frac{opposite}{adjacent}[/tex] for this exercise.

[tex]tan(45\°)=\frac{h}{x}[/tex]

Solve for h:

[tex]h=xtan(45\°)\\h=x[/tex]

[tex]tan(30\°)=\frac{h}{x+16}[/tex]

Substitute [tex]h=x[/tex] and solve for h:

[tex]tan(30\°)=\frac{h}{h+16}\\\\(h+16)(tan(30\°))=h\\\\0.577h+9.237=h\\\\9.237=h-0.577h\\\\9.237=0.423h\\\\h=\frac{9.237}{0.423}\\\\h=21.836ft[/tex]

Rounded to the nearest foot:

[tex]h=22ft[/tex]

Answer:

The total area of the side of the house in the drawing is [tex]1.4\ in^{2}[/tex]

Step-by-step explanation:

step 1

Convert the actual dimensions of the side view of a house to the dimensions of the drawing

The scale of the drawing is [tex]\frac{1}{20}\frac{in}{ft}[/tex]

so

[tex]20\ ft=20/20=1\ in[/tex]

[tex]24\ ft=24/20=1.2\ in[/tex]

[tex]8\ ft=8/20=0.4\ in[/tex]

The total area is equal to the area of rectangle plus the area of triangle

so

[tex]A=(1)(1.2)+\frac{1}{2}(1)(0.4)=1.4\ in^{2}[/tex]

Answer:

[tex]\large\boxed{S.A.=368\ cm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a rectagular prism:

[tex]S.A.=2(lw+lh+wh)[/tex]

l - length

w - width

h - height

We have the dimensions 6cm × 14cm × 5cm. Substitute:

[tex]S.A.=2(6\cdot14+6\cdot5+14\cdot5)=2(84+30+70)=2(184)=368\ cm^2[/tex]

The surface area of the rectangular prism is 368 cm²

To calculate the surface area of the prism, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The surface area of the rectangular prism is 368 cm².

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Answer:

The length of the third side could be 9 ft

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

so

In this problem

Let

c-----> the length of the third side, in feet

Applying the Triangle Inequality Theorem

1) [tex]6+10>c[/tex] -------> [tex]c<16\ ft[/tex]

2) [tex]c+6>10[/tex] -----> [tex]c>4\ ft[/tex]

so

The length of the third side must be greater than 4 ft and less than 16 ft

Remember that

The scalene triangle has three different sides

therefore

The length of the third side could be 9 ft

Check the picture below.

Answer:

[tex]10.8 units[/tex]

Step-by-step explanation:

To find the answer, we need to use the distance formula.

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

Let us look at our points. We have:

[tex](-2, 5)[/tex] and [tex](-6, -5)[/tex]

Now, let's identify our x's and y's:

x₁ = -2

y₁ = 5

x₂ = -6

y₂ = -5

Plug it in to the distance formula and simplify:

[tex]d=\sqrt{(-6+2)^2+(-5-5)^2}[/tex]

[tex]d=\sqrt{(-4)^2+(-10)^2}\\d=\sqrt{16 +100} \\d=\sqrt{116}\\[/tex]

[tex]d=2\sqrt{29}[/tex] OR [tex]10.77032961...[/tex]

We kinda need the graph

Answer:

4 : 24 or 1 : 6

Step-by-step explanation:

There are 4 bananas and 24 fruits so we just make that a ratio of 4 : 24.

We can then simplify that ratio to 1 : 6.

Answer:

the answer is 1:3

i did the test

Step-by-step explanation:

Assuming the question is "at what rate did the chemist heat the solution," the answer is the chemist heated the solution at +4.5 degrees Celsius per minute.

75-21=54

54/12=4.5

Answer:

If the angle is in degrees, when taking the tangent, make sure your calculator is in Degree mode.

I hope this helps.

Answer:

35

Step-by-step explanation:

First, we will define range.

The difference between the highest and lowest values in a data is called range. To find the range, first the highest and lowest values are found from data, then the lowest value is subtracted from the highest value.  

In the above data,

Highest Value=71  

Lowest Value=36  

Range=Highest value-lowest value  

=71-36  

=35  

The range in the number of fish across the 12 large aquariums is 35, calculated by subtracting the minimum number of fish, 36, from the maximum number, 71.

The question asks us to calculate the range in the number of fish across 12 large aquariums at a zoo. To find the range, we need to identify the largest and smallest numbers in the given data set and then subtract the smallest from the largest.

Here is the list of the numbers of fish in each aquarium: 37, 58, 62, 36, 42, 71, 56, 58, 69, 66, 47, 68.

First, we find the maximum and minimum values:

Maximum (the largest number of fish in an aquarium): 71

Minimum (the smallest number of fish in an aquarium): 36

Next, we calculate the range by subtracting the minimum value from the maximum value:

Range = Maximum - Minimum

Range = 71 - 36

Range = 35

Therefore, the range in the number of fish across the 12 aquariums is 35.

Answer:

9 miles.

Step-by-step explanation:

We have been given that Yi is told that the item that she wants to buy is still available at a store that is 3/4 inch on a map from her current location. The scale of the map is 1 inch= 12 miles.

To find the actual distance between Yi and store we will multiply 3/4 by 12 as:

[tex]\text{The distance between Yi and store}=\frac{3}{4}\text{ inch}\times \frac{\text{12 miles}}{\text{inch}}[/tex]

[tex]\text{The distance between Yi and store}=\frac{3}{4}\times \text{12 miles}[/tex]

[tex]\text{The distance between Yi and store}=3\times \text{3 miles}[/tex]

[tex]\text{The distance between Yi and store}=9\text{ miles}[/tex]

Therefore, Yi is 9 miles away from the store.

Answer: True, the measure of the angle formed by two intersecting perpendicular lines should be 90 degrees.

Answer:

True.

Step-by-step explanation:

You can see it with the cartesian plane. The cartesian plane are two intersecting perpendicular lines. The intersection point is the (0,0) and each cuadrant is 90°. 90°(4 cuadrants) = 360° .

Answer:

We know that [tex]\triangle ACE[/tex] is isosceles, that means [tex]\angle A \cong \angle E[/tex], by definition.

Also, [tex]\angle BDC \cong \angle DBC[/tex], because [tex]BD \parallel AE[/tex].

Then, we have [tex]115\° + \angle BDC = 180\°[/tex], by sumpplementary angles.

[tex]\angle BDC = 180 -115 = 65\° = \angle DBC[/tex]

Which means,

[tex]\angle C= 180 - 65 - 65[/tex], by definition.

[tex]\angle C= 50[/tex]

Then,

[tex]\angle A + \angle E + 50 = 180\\2\angle A = 180 - 50\\\angle A= \frac{130}{2}=65 = \angle E[/tex]

Therefore, the measures of vertex angles are 65 for the base angles of triangle and 50 for the different angle.

Answer:

2.8 putts in average on any given green

Step-by-step explanation:

To calculate how many putts Madison will need on any given green, we need to calculate the weighted average of his putts.

We use a global sample of 100 puts and factor in the fact he had a one-putt performance 15% of the time, two-putts 20% of the time and so on.

So, the calculation goes like this:

[tex]\frac{1 * 15 + 2 * 20 + 3 * 35 + 4 * 30}{100}  = \frac{280}{100}  = 2.8[/tex]

So, he'll need an average of 2.8 putts in average on any given green.

Which makes sense since 65% of the time, he needs 3 putts or more on the green.

The expected number of putts Madison will need for any given green is 2.85. This is calculated by multiplying each possible outcome by its probability and then summing these values.

The subject of this question is the calculation of an expected value in the context of a game of golf. The expected value is a weighted average, taking into account the probability of each event. Expected value calculations are common in probability and statistics.

In Madison's case, the expected number of putts can be calculated with the following formula:

E(X) = Σ [x * P(X = x)], where x is the outcome (number of putts) and P(X = x) is the probability of that outcome.

Applying the probabilities and outcomes given: E(X) = 1(0.15) + 2(0.20) + 3(0.35) + 4(0.30) = 2.85

So, the expected value of the number of putts Madison will need for any given green is 2.85.

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The false statement among the options given is 'None of the other 3 statements here are false', because all the other three statements about the geometric series are actually true.

The question presents a geometric series: 1, 2, 4, ... Each term is double the previous term, which means that for this series, the common ratio (r) is 2. Now let us analyze the statements given:

S600 > a600: The sum of the first 600 terms of the series will be greater than the 600th term.

This is true, since the sum of a geometric series to n terms is given by the formula Sn = a1(1 - rn)/(1 - r) for r > 1, where Sn is the sum of the first n terms, a1 is the first term, and r is the common ratio.

Since the sum involves multiple terms and all terms are positive, it will be bigger than the last term.

S600 > S599: The sum of the first 600 terms will be greater than the sum of the first 599 terms.

This is also true, since each term added to the series is positive, so the sum will increase.

S1 = a1: The sum of the first term equals the first term itself.

This is true because the first term of the series is 1, and the sum of just one term (i.e., the first term) is the term itself.

Therefore, the false statement is 'None of the other 3 statements here are false' because actually, none of the other three statements provided are false.

Final answer:

The presented geometric series has a common ratio greater than 1, so the sum of the first 600 terms is greater than the 600th term; similarly, the sum of 600 terms is greater than the sum of 599 terms. Since all provided statements are true, the answer is that 'None of the other 3 statements here are false'.

Explanation:

The question presents a geometric series with the first term 1 and a common ratio of 2. This series is 1+2+4+8+... and so on. We are asked to identify which of the given statements is false regarding the series.

S600 > a600: This statement says that the sum of the first 600 terms is greater than the 600th term. In a geometric series where the common ratio is greater than 1, the sum of the first n terms is indeed greater than the nth term, so this statement is true.S600 > S599: This statement indicates that the sum of the first 600 terms is greater than the sum of the first 599 terms. Since each term in the series is positive, adding another term will always increase the sum, thus this statement is also true.

S1 = a1: This statement equates the sum of the first term to the first term itself. Since there's only one term involved, they are the same. Therefore, this statement is true.

By process of elimination, since the other statements are true, the correct answer would be 'None of the other 3 statements here are false'.

Answer:

L = 18 and w = 16

Step-by-step explanation:

The area of a rectangle is found by A = l*w. Since the length here is 2 more than the width or 2 + w and the width is w, substitute these values and A = 288 to solve for w.

[tex]A = l*w\\288 = w(2+w)\\288 = w^2 + 2w[/tex]

To solve for w, move 288 to the other side by subtraction. Then factor and solve.

[tex]w^2 + 2w  - 288 = 0 \\(w +18)(w-16) = 0\\[/tex]

Set each factor equal to 0 and solve.

w - 16 = 0 so w = 16

w + 18 = 0 so w = -18

Since w is a side length and length/distance cannot be negative, then w = 16 is the width of the rectangle.

This means the length is 16 + 2 = 18.

First we must subtract 25 in 18 because we are doing percentages.

So we do [tex]25 - 18  = 7[/tex]

So we get 7.

Now we need to do [tex]7/25 * 100% = 28%[/tex]

We would get a total of 18% of on the discount.

Answer:

The answer is 1D , 2A , 3C , 4B ⇒ answer (c)

Step-by-step explanation:

* Lets talk about the transformation

- If the function f(x) reflected across the x-axis, then the new

 function g(x) = - f(x)

- If the function f(x) translated horizontally to the right  

 by h units, then the new function g(x) = f(x - h)

- If the function f(x) translated horizontally to the left  

 by h units, then the new function g(x) = f(x + h)

* Lets explain each function

∵ y = tan(x)

∵ y = -tan(x - π/2)

# (x - π/2) means the graph translated horizontally to

  the right π/2 units

# -tan(x - π/2) means the graph reflected across the x-axis

∴ The graph is (D)

* 1) y = -tan(x - π/2) ⇒ (D)

∵ y = tan(x + π/2)

# (x + π/2) means the graph translated horizontally to

  the left π/2 units

∴ The graph is (A)

* 2) y = -tan(x - π/2) ⇒ (A)

∵ y = -cot(x - π/2)

# (x - π/2) means the graph translated horizontally to

  the right π/2 units

# -cot(x - π/2) means the graph reflected across the x-axis

∴ The graph is (C)

* 3) y = -cot(x - π/2) ⇒ (C)

∵ y = cot(x + π/2)

# (x + π/2) means the graph translated horizontally to

  the left π/2 units

∴ The graph is (B)

* 4) y = -tan(x - π/2) ⇒ (B)

∴ The answer is 1D , 2A , 3C , 4B answer (c)

Answer:

A = 50.29 units²

Step-by-step explanation:

See attached photo

Answer:

The analysis of your expresson is given in the images below.

Please see attached pictures.

Answer:

(x + 12)² + (y + 32)² = 1031  

Step-by-step explanation:

137 + 64y = -y² - x² - 24x

Arrange the terms in descending powers of x and y.

x² + 24x  + y² + 64y = -137

Complete the squares  for x and y

(x² + 24x  + 144) + (y² + 64y + 1024) = -137 + 144 + 1024

Write the equation as the  squares of binomials of x and y

(x + 12)² + (y + 32)² = 1031

This is the equation of a circle with centre at (-12, -32) and radius r = √1031.