2 Use the Squeeze Theorem to compute the following limits: (a) (5 points) lim (1 – 2)°cos (221) (1 1+ (b) (5 points) lim xVez 5 (Hint: You may want to start with the fact that since x + 0-, we have

Answer:

Brainliest here!

Step-by-step explanation:

3 dozen cookies = 1.5 cups

one dozen cookies= 0.5 cups

5 dozen cookies = 2.5 cups of sugar

The angle of depression from the cruiser to the submarine is 63.43 degrees.

We can use the tangent function to find the angle of depression from the cruiser to the submarine.

The tangent function relates the opposite side (the vertical distance, or the depth) to the adjacent side (the horizontal distance) in a right triangle.

tan(angle of depression) = opposite/adjacent

In this case, the opposite side is the depth, or the vertical distance from the cruiser to the submarine, which is 2100 ft.

The adjacent side is the horizontal distance from the cruiser to the submarine, which is 900 ft.

tan(angle of depression) = 2100/900

Using a calculator we can find that tan(angle of depression) = 2.3333

Now we can use the inverse tangent function (arctan) to find the angle of depression:

the angle of depression = arctan (2100/900)

Using a calculator we can find that angle of depression = 63.43 degrees

Therefore, the angle of depression from the cruiser to the submarine is 63.43 degrees.

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To find the number of all subsets of the set A ∪ B with 4 elements, where A = {1, 2, 3, 6, 7} and B = {3, 6, 7, 8, 9}, we need to consider all possible combinations of elements from the union of A and B that have a cardinality of 4.

The cardinality of the union A ∪ B is 9, as it contains all distinct elements from both sets. We need to choose 4 elements from this union, which can be done in C(9, 4) ways, where C(n, r) denotes the combination of selecting r elements from a set of n elements.

Using the formula for combinations, C(n, r) = n! / (r! * (n - r)!), we can calculate the number of subsets.

C(9, 4) = 9! / (4! * (9 - 4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126.

Therefore, there are 126 subsets of the set A ∪ B with 4 elements.

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Answer:

Prism A

Step-by-step explanation:

formula for prism triangular prisms: V=1/2(bhl) so V=1/2(4 x 7 x 9) V=126 m

formula for rectangular prisms: V=b x h x l so V= 8 x 8 x 2 V=128

126 is less than (<) 128 so Prism A

Given:

The expression is given as,

The objective is to graph the function.

Explanation:

As the degree of the function is 1, the graph of the expression will be a straight line.

To obtain two coordinates to draw a straight line first consider x = 0 in the expression.

Thus, the obtained coordinate is (0,-3).

Now, consider y = 0 in the given expression.

Thus, the obtained coordinate is (-2,0)

To plot the graph:

Thus, the graph of the expression will be,

Hence, the graph of the equation is obtained.

Answer:

hgjkhkjkgvhbj,k

Step-by-step explanation:

Here, we are supposed to find the value of the stock. Let's begin by determining the expected dividends: Expected dividends1st year dividend (D1)

= $1.55(1 + 26.56%)

= $1.96Second-year dividend (D2) = $1.96(1 + 26.56%) = $2.48Third-year dividend (D3)

= $2.48(1 + 26.56%)

= $3.

= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4...∞Where r

= required rate of return Let us substitute the values now PV of the future dividends

= $1.96/(1 + 14.40%)^1 + $2.48/(1 + 14.40%)^2 + $3.14/(1 + 14.40%)^3 + $3.25/(1 + 14.40%)^4...∞PV of the future dividends = $1.96/1.1440^1 + $2.48/1.1440^2 + $3.14/1.1440^3 + $3.25/1.1440^4...∞PV of the future dividends

= $1.72 + $1.92 + $2.04 + $1.86...∞PV of the future dividends

= $7.54We know that the value of the stock is the present value of the expected dividends, so we can calculate it as follows: Value of the stock

= PV of the future dividends Value of the stock

= $7.54

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The solution to the systems of equations graphically is (2, 4)

From the question, we have the following parameters that can be used in our computation:

y = 2x

y = -x + 6

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

This points are located at (2, 4)

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The coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

The center of the coordinate system (where the lines intersect) is called the origin. The axes intersect when both x and y are zero. The coordinates of the origin are (0, 0). An ordered pair contains the coordinates of one point in the coordinate system.

The coordinates of the point on the first tree where the rope is attached are (10, 6, 8), and the coordinates of the point on the second tree where the rope is attached are (-5, 8, 5).

To find the distance between the points, we can use the distance formula:

distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Plugging in the coordinates from part 1, we get:

distance = √((-5 - 10)² + (8 - 6)² + (5 - 8)²)

distance = √(225 + 4 + 9)

distance = √(238)

Therefore, the distance between the points is √(238).

Since the food bag is hung at a point exactly halfway along the length of the rope, we can find its coordinates by taking the average of the coordinates of the points where the rope is attached.

The x-coordinate of the midpoint is: (10 + (-5)) / 2 = 2.5

The y-coordinate of the midpoint is: (6 + 8) / 2 = 7

The z-coordinate of the midpoint is: (8 + 5) / 2 = 6.5

Therefore, the coordinates of the point where the food bag is hung are (2.5, 7, 6.5).

To determine whether the food is safe from bears, we need to compare the height of the food bag to the maximum height that bears can reach. The food bag is hung at a height of 6.5 feet, and bears can reach a height of 7.5 feet when standing. Therefore, the food is not completely safe from bears, as they may be able to reach it if they stand up on their hind legs. However, hanging the food bag at this height does make it more difficult for the bears to reach, and may deter them from trying to get to it. It is also important to note that proper food storage techniques in bear country should involve using bear-resistant containers, in addition to hanging food bags.

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The explicit equation of the function is t(n) = 5 * 8^(n-1)

The function definition is given as:

t(1)=5

t(n+1)=8t(n)

Let n = 1

So, we have:

t(2) = 8t(1)

Divide through by t(1)

t(2)/t(1) = 8

The common ratio of the function is:

r = t(2)/t(1) = 8

The explicit rule is then calculated as:

t(n) = t(1) * r^(n-1)

So, we have:

t(n) = 5 * 8^(n-1)

Hence, the explicit equation of the function is t(n) = 5 * 8^(n-1)

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Step-by-step explanation:

I am not sure I understand the question with all the typos and potentially missing parts.

as I understand it, it will take her 4 hours to reach her destination when going 15 mph.

and the question is how long the trip will take, if she travels at 12 mph.

4 h × 15 m/h = 4 × 15 m = 60 miles

that is the distance of her trip.

when going slower, the distance is of course still the same, only the needed time changes :

x h × 12 m/h = 60 m

x × 12 m = 60 m

x = 60/12 = 5 hours

the trip would take her 5 hours to complete (instead of 4).

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

The probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie can be calculated by dividing the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
Step-by-step explanation:
1. Determine the number of ways to select two sugar cookies: There are 4 sugar cookies in the bag, so the number of ways to select the first sugar cookie is 4. After eating the first sugar cookie, there are 3 sugar cookies left, so the number of ways to select the second sugar cookie is 3. Therefore, there are 4 * 3 = 12 ways to select two sugar cookies.
2. Determine the total number of ways to select any two cookies: There are a total of 6 + 5 + 4 + 7 = 22 cookies in the bag. So, the number of ways to select any two cookies is calculated by choosing 2 cookies out of 22, which is denoted as 22C2.
3. Calculate the probability: To find the probability, divide the number of ways to select two sugar cookies by the total number of ways to select any two cookies.
  Probability = (Number of ways to select two sugar cookies) / (Total number of ways to select any two cookies)
  Probability = 12 / 22C2
So, the probability that Kwan randomly selects a sugar cookie from the bag, eats it, and then randomly selects another sugar cookie is 12 / 22C2.

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The extraction efficiency of liquid-liquid extraction (LLE) depends on the hydrophobicity (D) of the chemical to be extracted and the number of extractions. In this case, a water sample contaminated with PCB is being extracted using methylene chloride, with a partition coefficient (D) of 25.

To calculate the extraction efficiency, we need to consider two scenarios: one extraction with 30 mL of methylene chloride and three extractions with 10 mL each. The total volume of the water sample is 100 mL.

1. One extraction with 30 mL of methylene chloride:
  - The volume of methylene chloride used is 30 mL.
  - The extraction efficiency can be calculated using the formula:
    Extraction Efficiency = (Volume of Chemical Extracted / Total Volume of Chemical in the Water Sample) * 100
  - Volume of PCB extracted = D * Volume of Methylene Chloride used = 25 * 30 mL = 750 mL
  - Extraction Efficiency = (750 mL / 100 mL) * 100 = 750%

2. Three extractions with 10 mL each:
  - The volume of methylene chloride used in each extraction is 10 mL.
  - In each extraction, the volume of PCB extracted is given by D * Volume of Methylene Chloride used = 25 * 10 mL = 250 mL.
  - Total volume of PCB extracted in three extractions = 250 mL * 3 = 750 mL.
  - Extraction Efficiency = (750 mL / 100 mL) * 100 = 750%

Both methods of extraction, one with 30 mL and three with 10 mL each, result in the same extraction efficiency of 750%. Therefore, both methods are equally effective in extracting the PCB from the water sample.

In summary, the extraction efficiency depends on the hydrophobicity of the chemical and the number of extractions. In this case, both methods of extraction yield the same efficiency, indicating that the choice between one extraction with 30 mL or three extractions with 10 mL each does not affect the overall efficiency.

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The coefficient of p²s¹⁰ in binomial expansion of (2p-s)¹² is 66.

The binomial theorem states that for any binomial expression

(a + b)ⁿ,

the term with the general form

\(a^{n - k} * b^k * C(n, k)\)

where C(n, k) represents the binomial coefficient,

gives the coefficient of that term.

We are given (2p - s)¹².

We need the term with:

p² and

s¹⁰

Therefore, we need to find the coefficient of the term:

\(a^{12 - k} * b^k * C(12, k)\)

in the expansion.

Given:

a = 2p,

b = -s, and

n = 12.

We want to find the value of k that corresponds to p²s¹⁰.

The power of p in the term is (12 - k), and the power of s is k. So, we set up the equation:

12 - k = 2  (for the power of p)

k = 10   (for the power of s)

To find the coefficient, we can substitute these values into the binomial coefficient formula:

C(12, 10) = \(\frac{12!}{10! * (12 - 10)!}\)

= \(\frac{12!}{10! 2!}\)

Now, we can calculate the coefficient:

C(12, 10) = \(\frac{12 * 11 * 10!}{10! * 2}\)

         = 66

Therefore, the coefficient of p²s¹⁰ in the binomial expansion of (2p - s)¹² is 66.

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The mean of the sampling distribution of sample means for a sample of size 150 is approximately 81, and the standard deviation is approximately 2.0.

In order to compute the mean and standard deviation of the sampling distribution, we can use the properties of the Central Limit Theorem (CLT). The CLT states that for a large enough sample size, the sampling distribution of the sample means will be approximately normally distributed, regardless of the shape of the population distribution. The mean of the sampling distribution will be equal to the mean of the population, which in this case is 81.

The standard deviation of the sampling distribution, also known as the standard error, can be calculated by dividing the standard deviation of the population by the square root of the sample size. In this case, the standard deviation of the population is 25, and the sample size is 150. Therefore, the standard deviation of the sampling distribution is 25 / √150, which is approximately 2.0.

This means that if Mary takes multiple random samples of size 150 from the population of similar businesses and calculates the mean startup costs for each sample, the distribution of those sample means will have a mean of 81 and a standard deviation of 2.0. By comparing the mean of her sample to the mean of the sampling distribution, Mary can assess how her online startup costs compare to the known population mean.

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1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer: 390

Step-by-step explanation:

65 x 6 = 390

78 x 5 = 390

Answer:

12

Step-by-step explanation:

30 is 3x larger than 10

4 x 3 = 12

The main answer to your question is "interchanging". To find the inverse of a function, we interchange the numbers in each ordered pair of the function. This means that we switch the x and y values of each point in the function.

For example, if we have a function f(x) = 2x + 3, the ordered pairs would be (1,5), (2,7), (3,9), etc. To find the inverse function, we would switch the x and y values of each point to get ordered pairs such as (5,1), (7,2), (9,3), etc.

The explanation for why we interchange the numbers is that the inverse function "undoes" the original function. If we apply the original function to a number, the inverse function will take us back to the original number. By switching the x and y values, we make sure that the inverse function will undo the original function.

In conclusion, to find the inverse of a function, we interchange the numbers in each ordered pair of the function. This ensures that the inverse function will undo the original function.
Hi! I'm happy to help you with your question.

Main answer: The inverse of a function can be found by interchanging the numbers in each ordered pair of the function.

Explanation: When finding the inverse of a function, you are essentially swapping the input and output values in each ordered pair (x, y) to create a new ordered pair (y, x). This process is called interchanging the numbers in the ordered pair.

Conclusion: To find the inverse of a function, you need to interchange the numbers in each ordered pair of the function, which essentially swaps the input and output values.

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The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

What is the probability?

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

To fill in the blanks, we need to use the given information to complete the probability distribution table.

We can see that there were 3 dogs (out of the 60) that did not use any toys, and the probability of a dog not using any toys is 0.05 or 5%. There were 12 dogs (out of the 60) that used 1 toy, and the probability of a dog using 1 toy is 0.2 or 20%. Similarly, there were 15 dogs that used 2 toys, 21 dogs that used 3 toys, and 9 dogs that used all 4 toys. The corresponding probabilities for these outcomes are 0.25, 0.35, and 0.15, respectively.

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Answer:

126 centimeters squared

Step-by-step explanation:

Answer: Angle 1= 32 degrees

Angle 2=90 degrees

Angle 3=58 degrees

Angle 4=32 degrees

Step-by-step explanation:

Simple

Total no of marbles = 6 + 4 + 8 = 18

Probability of red marble = 6 / 18 = 1/ 3

Answer:

7 / 1

Step-by-step explanation:

0.¯7 = 0.7777.....

10x = 7.7777.....

9x = 0.7777.....

(-) (-)

___________

1x = 7

x = 7 / 1

Simplified fraction = 7 / 1.

Dilation factor is 3/2.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. According to Math Bits Notebook, the scale factor is equal to the ratio of these distances.

Given,

OQ = 10

OQ' = 15

Let dilation factor be r

OQ ×r = OQ'

10× r = 15

r = 3/2

Dilation factor is 3/2.

Coordinates of P  = (-4, -3)

Coordinates of P' = (-6, -4.5)

b) ΔOPQ ≅ ΔOP'Q'

Congruent,

\(\frac{OQ}{OQ'}\) = \(\frac{PQ}{P'Q'}\)

\(\frac{10}{15}\) = \(\frac{PQ}{11.2}\)

PQ = 7.46

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Answer:

Same side interior angles theorem

Step-by-step explanation:

 Same-Side Interior Angles Theorem: Sum of the same side of interior angles of parallel lines are supplementary

Answer:

I think it is A

Step-by-step explanation:

Hope this helped have an amazing day!

Main Answer:

Height decreased in 1 second is 80 cm

Explanation:

The total amount of height decreased is 120.

Total amount of time taken is 1.5 s.

Height decreased in 1 second = \(\frac{120}{1.5}\)

⇒ \(\frac{1200}{15}\)

⇒ 80 cm

Therefore, height decreased in 1 second is 80 cm.