Refer to Interactive Solution 17.45 to review a method by which this problem can be solved. The fundamental frequencies of two air columns are the same. Column A is open at both ends, while column B is open at only one end. The length of column A is 0.504 m. What is the length of column B?

Answer:

Choice A

Step-by-step explanation:

a=-6           (1st term)

ar=             (2nd term)

ar^2=         (3rd term)

ar^3           (4th term)

ar^4=         (5th term)

ar^5=-1458 (6th term)

a=-6 so -6r^5=-1458

divide both sides by -6 giving r^5=243 so to obtain r you do the fifth root of 243 which is 3.

The common ratio is 3.

so ar=6(-3)=-18 (2nd term)

Only choice A fits this.

Answer:

Step-by-step explanation:

Let's start by making up as many teams as we can with the 32 student. Given that each team is different, we can make 10 teams of 3 each. (we still have 23 more teams to make).

The last two people make a team of only 2. No matter which student from the 30 other students is picked, the team of two and the one the student is coming from will have one student in common. Though there are more borrowings that take place (many more), the results remain as stated. At least 2 teams will have 1 person in common.

The method is called the pigeon hole method.

By applying the Pigeonhole Principle in combinatorics, in a scenario where 32 students are assigned to 33 teams of 3 students each, there must exist two teams that share exactly one student.

This problem can be solved by using the principles of Combinatorics and the Pigeonhole Principle. The Pigeonhole Principle states that if you try to distribute n items into m containers and n > m, then at least one container must contain more than one item.

In the given scenario, we have 32 students that are being assigned to 33 teams, with each team consisting of 3 students. That means a total of 96 (3 x 32) places in teams.

If each student is a 'pigeon' and each 'place' in a team is a 'pigeonhole', the Pigeonhole Principle tells us that at least two pigeons must share at least one pigeonhole. Since each student can't be in more than one place at a time nor in the same team more than once, there must exist two teams that share exactly one student.

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The curl of the vector field F is 2i + 2j + 2k. The dot product of F and dr along the closed path C is -60√3.

To find the curl of vector field F, we need to compute the partial derivatives of its components with respect to x, y, and z. In this case, F = (z-y)i + (x-z)j + (y-x)k. Taking the partial derivatives, we get curlF = 2i + 2j + 2k.

The dot product of F and dr along the closed path C can be calculated using Stokes' Theorem. By evaluating the dot product and integrating over C, we find that F · dr = -60√3.

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The shop sells 216 "I LOVE NY" T-shirts each day. Therefore, over the course of one week, the shop sells 1512 T-shirts.

The shop in Times Square is open from 9 am to 9 pm, which means the shop operates for 12 hours. Since there are 60 minutes in an hour, this shop is open for a total of 720 minutes each day.

Three "I LOVE NY" T-shirts are sold every 10 minutes. So, in 720 minutes, the number of T-shirts sold would be 720 ÷ 10 = 72 sets of three T-shirts. Therefore, 72 sets x 3 shirts = 216 T-shirts are sold per day.

Finally, to calculate the weekly total, it is necessary to multiply the daily total by 7 (the number of days in a week). So, 216 T-shirts x 7 days = 1512 T-shirts sold in one week.

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Answer:

Step-by-step explanation:

Let n represent the number of 42-cent stamps Sabrina bought. Then 52-n is the number of 22-cent stamps she bought. Her total expense was ...

  0.42n +0.22(52 -n) = 16.24 . . . . total price of stamps

  0.20n + 11.44 = 16.24 . . . . . . . . . simplify

  0.20n = 4.80 . . . . . . . . . . . . . . . . subtract 11.44

  n = 24 . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of n

  52-n = 28 . . . . . . . . . . . . . . . . . . . find the number of 22-cent stamps

She bought 24 42-cent stamps and 28 22-cent stamps.

She bought 24-42 cent stamps

And, 28-22 cent stamps.

Here we assume  n be the number of 42-cent stamps

The equation should be

0.42n +0.22(52 -n) = 16.24

0.20n + 11.44 = 16.24

0.20n = 4.80

n = 24

Now

= 52 - n

= 52 - 24

= 28

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Answer:

Quotient will be 1.25

Step-by-step explanation:

First we convert decimal numbers to fractions. So write down the decimal divided by 1 and then multiply both top and bottom with 10 for every number after decimal point.

Here we found for  .4375  = [tex]\frac{4375}{10000}[/tex]

and .35 =   [tex]\frac{35}{100}[/tex]

Now we divide both the numbers as

= [tex]\frac{\frac{4375}{1000} }{\frac{35}{100} }[/tex]

= [tex]\frac{4375}{1000}[/tex] × [tex]\frac{100}{35}[/tex]

= [tex]\frac{125}{100}[/tex]

= 1.25

Quotient will be 1.25

Final answer:

The quotient of 0.4375 divided by 0.35 is 1.25, which rounded to the tenths place is 1.3.

Explanation:

The student is asking to find the quotient of two decimal numbers, which is a basic arithmetic operation involving division. The numbers are 0.4375 and 0.35. To find the quotient, simply divide 0.4375 by 0.35.

Using a calculator or performing the division manually, you would proceed as follows:

Adjust the decimals by multiplying both numbers by 100 to make them whole numbers, resulting in 43.75 divided by 35.

Perform the division to get the preliminary result: 43.75 / 35 = 1.25.

Since we need to round the final answer to the tenths place based on the least precise number given (35.5 g), round 1.25 to one decimal place, which is 1.3 (1.25 rounds up because the next digit, 5, is equal to or greater than 5).

Therefore, the quotient of 0.4375 divided by 0.35, rounded to the tenths place, is 1.3.

The alternative hypothesis would state that the proportion of Republicans who favor a bill to make gun ownership easier is not equal to the proportion of Democrats who favor the same.

The question was regarding how to construct an alternative hypothesis for a study on political beliefs and opinions on firearm ownership. In this case, the alternative hypothesis statement goes against the null hypothesis. The null hypothesis would be that there's no significant difference between the proportions of Republicans and Democrats that favor a bill making gun ownership easier. So, the alternative hypothesis can be written as: 'The proportion of Republicans (Group A) who favor a bill making it easier for someone to own a firearm is not equal to the proportion of Democrats (Group B) who favor the same.'

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The alternative hypothesis can be written as: H_A: The proportion of Republicans who favor a bill to make it easier for someone to own a firearm differs from the proportion of Democrats who favor the same.

The alternative hypothesis can be written as:

HA: The proportion of Republicans who favor a bill to make it easier for someone to own a firearm differs from the proportion of Democrats who favor the same.

Alternatively, it can be written as:

HA: pA ≠ pB

where pA is the proportion of Republicans who favor the bill and pB is the proportion of Democrats who favor the bill.

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Answer:

22 minutes after 7:00 P.M. they will be closest.

Step-by-step explanation:

A boat heading south travelling for t hours at the rate of 20 km/h, so the distance x = 20t

The another boat will reach the dock after travelling another 1-t hours at the rate of 15 km/h, so the distance =

y = 15 - 15t

D = d²  = x² + y²

D = (20t)² + (15 - 15t)²

dD/dt = -2(15² )( 1-t ) +2 × 20² × t

dD/dt = 2 (15² + 20²) × t -2 ( 15 )² = 0

t = [tex]\frac{2(15)^{2}}{(2\times15^{2}+2\times20^{2})}[/tex]

t = 0.36 hours = 0.36 × 60 = 21.6 minutes ≈ 22 minutes

Therefore, the distance is minimized 22 minutes after 7 pm.

The two boats were closest together 12 minutes after 7:00 PM.

To find the time when the two boats were closest together, we can first determine the position of each boat at 8:00 PM. The boat traveling south will have traveled for 1 hour at a speed of 20 km/h, so it would be 20 km south of the dock. The boat traveling east will have traveled for 1 hour at a speed of 15 km/h, so it would be 15 km east of the dock. We can then calculate the distance between the two boats by using the Pythagorean theorem. The distance is the square root of the sum of the squares of the distances traveled south and east, which is approximately 25 km. Since both boats started at the dock at 7:00 PM, to find the time when they were closest together, we can subtract the time traveled by the boat heading south until it reaches the closest point to the other boat from 60 minutes. The boat heading south will have traveled (20/25) * 60 minutes, which is 48 minutes. So, the two boats were closest together 12 minutes after 7:00 PM.

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Answer:  0.3936

Step-by-step explanation:

Given: Mean : [tex]\mu =1387 \text{ grams}[/tex]

Standard deviation : [tex]\sigma = 161 \text{ grams}[/tex]

The formula to calculate z is given by :-

[tex]z=\dfrac{x-\mu}{\sigma}[/tex]

For x= 1,425 grams

[tex]z=\dfrac{1425-1387}{161}=0.23602484472\approx0.27[/tex]

The P Value =[tex]P(X>1425)=P(z>0.27)=1-0.6064198=0.3935802\approx0.3936[/tex]

Hence, the  probability that a randomly selected broiler weighs more than 1,425 grams =0.3936

Final Answer:

There is approximately a 40.66% chance that a randomly selected broiler weighs more than 1,425 grams.

Explanation:

To solve this problem, you will need to apply the properties of the normal distribution. We want to find out the probability that a broiler weighs more than 1,425 grams.
Given:
- Mean (μ) = 1387 grams
- Standard deviation (σ) = 161 grams
- X = 1425 grams (the value we're interested in)

Step 1: First, we compute the z-score for the weight of 1425 grams. The z-score is a measure of how many standard deviations an element is from the mean. It can be calculated using the formula:

[tex]\[ z = \frac{(X - \mu)}{\sigma} \][/tex]

where X is the value for which we're finding the probability, μ is the mean, and σ is the standard deviation.

Step 2: Insert the values into the formula to compute the z-score for 1425 grams:

[tex]\[ z = \frac{(1425 - 1387)}{161} \\\\\[ z = \frac{38}{161} \\\\\[ z \approx 0.236 \][/tex]
Step 3: Once we have the z-score, we can use the z-table (a standard normal distribution table) to find out the probability of a z-score being less than 0.236. However, since we want the probability that the broiler weighs more than 1425 grams, we are interested in the probability of a z-score being greater than 0.236.

Step 4: Look up the corresponding probability for z = 0.236 on the z-table. The z-table gives us the area under the normal curve to the left of the z-score.

Let's assume the z-table gives us a probability of P(Z < 0.236). The value would typically be around 0.5934, which means there is a 59.34% chance that a random broiler will weigh less than 1425 grams.

Step 5: To find the probability that a broiler weighs more than 1425 grams, we subtract the value found in the z-table from 1 because the total area under the curve equals 1 (which corresponds to the probability of all possible outcomes).

[tex]\[ P(Z > 0.236) = 1 - P(Z < 0.236) \\\\\[ P(Z > 0.236) = 1 - 0.5934 \\\\\[ P(Z > 0.236) \approx 0.4066 \][/tex]

Answer:

  16

Step-by-step explanation:

Moment of inertia of a disk is proportional to its mass and to the square of its radius. For two disks with the same mass, the larger one will have a moment of inertia that is (4R/R)^2 = 16 times that of the smaller one.

It will take 16 smaller disks to make the systems have the same moment of inertia.

Answer:

V = x³ + 20x² + 124x + 240

Step-by-step explanation:

Volume of a rectangular prism is width times length times height.

V = wlh

Given w = x+4, l = x+10, and h = x + 6:

V = (x + 4)(x + 10)(x + 6)

V = (x + 4)(x² + 16x + 60)

V = x²(x + 4) + 16x(x + 4) + 60(x + 4)

V = x³ + 4x² + 16x² + 64x + 60x + 240

V = x³ + 20x² + 124x + 240

Final answer:

The volume of the rectangular aquarium is given by the function V = x²t + 6x² + 14xt + 84x + 40t + 240, representing the product of its length, width, and height with given dimensions.

Explanation:

To determine a simplified function that represents the volume of the aquarium with given dimensions, we need to use the formula for the volume of a rectangular prism, which is length × width × height. The problem provides expressions for these dimensions: length is (x + 10), width is (x + 4), and height is (t + 6).

Therefore, the volume V of the aquarium can be calculated as follows:

V = (x + 10) × (x + 4) × (t + 6)

To simplify this, we multiply the expressions:

V = (x² + 14x + 40)(t + 6)

Expanding this, we get:

V = x²t + 6x² + 14xt + 84x + 40t + 240

This is the simplified function for the volume of the aquarium in terms of x and t.

Answer:

2nd answer.

Step-by-step explanation:

see attached.

Answer with Step-by-step explanation:

We have to find the solution of the equation:

[tex]x^4+6x^2+5=0[/tex]

Let u=x²

Then, above equation is transformed to:

[tex]u^2+6u+5=0[/tex]

it could also be written as:

[tex]u^2+5u+u+5=0[/tex]

u(u+5)+1(u+5)=0

(u+1)(u+5)=0

either  u+1=0 or u+5=0

either u= -1 or u= -5

Putting u=x²

x² = -1 or x² = -5

On taking square root both sides

x= ± i  or  x= ± i√5

Hence, roots of the equation [tex]x^4+6x^2+5=0[/tex] are:

i , -i , i√5 and -i√5

Answer:

= (x+5)² = x² + 10x + 25

= (x-2)² = x² - 4x + 4

= (x² + 10x + 25) - (x² - 4x + 4)

 = x² + 10x + 25 - x² + 4x - 4

 = 14x + 21  square units

The area of the shaded region is found by subtracting the area of the inner square, (x-2)², from the area of the outer square, (x+5)², resulting in the expression 14x + 21.

The area of the shaded region in this problem represents the difference between the area of the outer square and the inner square.

To find this, we calculate the area of each square individually and then subtract one from the other.

First, the area of the outer square is (x+5)² and the area of the inner square is (x-2)².

Now, we find the difference between these two areas to isolate the shaded region:

Area of shaded region = (x+5)² - (x-2)²

To expand this, we use the binomial expansion:

Now we subtract the smaller area from the larger area:

Shaded region = (x² + 10x + 25) - (x² - 4x + 4)

Shaded region = x² + 10x + 25 - x² + 4x - 4

Shaded region = 14x + 21

This expression represents the area of the shaded region in terms of x.

Answer:

Nico invest [tex]\$2,100[/tex] at 7% and [tex]x=\$900[/tex] at 3%

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]I=P(rt)[/tex]

where

I is the Final Interest Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

At 7%

[tex]t=1\ years\\ P=\$x\\r=0.07[/tex]

substitute in the formula above

[tex]I1=x(0.07*1)[/tex]

[tex]I1=0.07x[/tex]

At 3%

[tex]t=1\ years\\ P=\$(x-1,200)\\r=0.03[/tex]

substitute in the formula above

[tex]I2=(x-1,200)(0.03*1)[/tex]

[tex]I2=0.03x-36[/tex]

The total interest is equal to

I=I1+I2

I=$174

substitute

[tex]174=0.07x+0.03x-36[/tex]

[tex]0.10x=174+36[/tex]

[tex]0.10x=210[/tex]

[tex]x=\$2,100[/tex]

[tex]x-1,200=2,100-1,200=\$900[/tex]

therefore

Nico invest [tex]\$2,100[/tex] at 7% and [tex]x=\$900[/tex] at 3%

Answer:

The face value would be $75,000

Step-by-step explanation:

Maturity value = $76,386.99

Time = 90 days

Rate of interest = 7.5%

Let face value be 'x'

By using the formula [tex]A=P(1+\frac{RT}{100})[/tex]

                      $76,386.99 = [tex]x(1+\frac{7.5\times \frac{90}{365}}{100})[/tex]

Time in years = [tex]\frac{90}{365}[/tex]

⇒ $76,386.99 = x( 1 + 0.01849315 )

⇒ x = [tex]\frac{76,386.99}{1.01849315}[/tex]

x = $75,000

The face value would be $75,000

Answer:  The required result is 15.

Step-by-step explanation:  We are given to evaluate the following :

"6 choose 4".

Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.

We know that

the formula for the combination of n different things chosen r at a time is given by

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}.[/tex]

For the given situation, n = 6  and  r = 4.

Therefore, we get

[tex]^6C_4=\dfrac{6!}{4!(6-4)!}=\dfrac{6!}{4!2!}=\dfrac{6\times5\times4!}{4!\times2\times1}=15.[/tex]

Thus, the required result is 15.

Answer: Hence, the distance covered in a straight line from the starting point is 13 miles.

Step-by-step explanation:

Since we have given that

Distance between AB = 5 miles

Distance between BC = 12 miles

We need to find the distance covered from the starting point.

We will use "Pythagorean Theorem":

[tex]H^2=P^2+B^2\\\\AC^2=AB^2+BC^2\\\\AC^2=5^2+12^2\\\\AC^2=25+144\\\\AC^2=169\\\\AC=\sqrt{169}\\\\AC=13\ miles[/tex]

Hence, the distance covered in a straight line from the starting point is 13 miles.

Step-by-step explanation:

[tex]x-\text{the number}\\\\\text{Nine times the difference of a number and 3}:\\\\\boxed{9\times(x-3)=9(x-3)}[/tex]

[tex]9(x-3)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\=9x+(9)(-3)\\\\=9x-27[/tex]

Answer:

After the 6th day, beginning with the 7th day, he is walking less than 0.5 km.

Step-by-step explanation:

To find a percent of a number, change the percent to a decimal and multiply by the number. To find 90% of a number, change 90% to a decimal and multiply by the number.

90% = 0.9

He first walks 1 km. The next day, he walks 90% of 1 km. To find 90% of 1 km, multiply 0.9 by 1 km. It is 0.9 km. For the next day, he walks 90% of 0.9 km, which is 0.9 * 0.9 km = 0.81 km. To find how much he walks each day, multiply what he walked on the previous day by 0.9.

Now you can find out how much he walks each day until you see he walks less than 0.5 km.

Day 1: 1 km

Day 2: 1 km * 0.9 = 0.9 km

Day 3: 0.9 km * 0.9 = 0.81 km

Day 4: 0.81 km * 0.9 = 0.729 km

Day 4: 0.729 km * 0.9 = 0.6561

Day 5: 0.6561 km * 0.9 = 0.59049 km

Day 6: 0.59049 km * 0.9 = 0.531441 km

Day 7: 0.531441 km * 0.9 = 0.4782969 km

On the 6th day, he is still walking more than 0.5 km, but by the 7th day, he is walking less than 0.5 km.

Answer: After the 6th day, beginning with the 7th day, he is walking less than 0.5 km.

After the 6th day, beginning with the 7th day, he exists walking less than 0.5 km.

To find a percent of a number, change the percent to a decimal and multiply by the number. To discover 90% of a number, change 90% to a decimal and multiply by the number.

90% = 0.9

He first walks 1 km. The next day, he walks 90% of 1 km.

To discover 90% of 1 km, multiply 0.9 by 1 km. It is 0.9 km.

For the subsequent day, he walks 90% of 0.9 km, which exists

0.9 [tex]*[/tex] 0.9 km = 0.81 km.

To find how much he walks each day, multiply what he walked on the last day by 0.9.

Now find out how much he walks each day until sees he walks less than 0.5 km.

Day 1: 1 km

Day 2: 1 km [tex]*[/tex] 0.9 = 0.9 km

Day 3: 0.9 km [tex]*[/tex] 0.9 = 0.81 km

Day 4: 0.81 km [tex]*[/tex] 0.9 = 0.729 km

Day 4: 0.729 km [tex]*[/tex] 0.9 = 0.6561

Day 5: 0.6561 km [tex]*[/tex] 0.9 = 0.59049 km

Day 6: 0.59049 km [tex]*[/tex] 0.9 = 0.531441 km

Day 7: 0.531441 km [tex]*[/tex] 0.9 = 0.4782969 km

On the 6th day, he stands still walking more than 0.5 km, but by the 7th day, he exists walking less than 0.5 km.

Answer: After the 6th day, beginning with the 7th day, he exists walking less than 0.5 km.

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Answer:

160/1001, 175/1001

Step-by-step explanation:

i) There are:

₈C₁ ways to choose 1 new camera from 8 new cameras

₆C₃ ways to choose 3 refurbished cameras from 8 refurbished cameras

₁₄C₄ ways to choose 4 cameras from 14 cameras

The probability is:

P = ₈C₁ ₆C₃ / ₁₄C₄

P = 8×20 / 1001

P = 160 / 1001

P ≈ 0.160

ii) At most one new camera means either one new camera or no new cameras.  We already found the probability of one new camera.  The probability of no new cameras is the same as the probability of choosing 4 refurbished cameras:

P = ₆C₄ / ₁₄C₄

P = 15 / 1001

So the total probability is:

P = 160/1001 + 15/1001

P = 175/1001

P ≈ 0.175

To find the probability that one new camera will be selected, use the binomial coefficient and calculate the probability of selecting one new camera and three cameras that are not new. To find the probability of at most one new camera, calculate the probabilities of selecting zero new cameras and one new camera and add them together.

To find the probability that one new camera will be selected, we need to calculate the probability of selecting one new camera and three cameras that are not new. The total number of ways to select four cameras from 14 without replacement is given by the binomial coefficient 14 choose 4, which is equal to 14!/(4!(14-4)!). The probability of selecting one new camera is given by the product of the probability of selecting one new camera (8/14) and the probability of selecting three cameras that are not new (6/13 * 5/12 * 4/11). To find the probability that at most one new camera will be selected, we need to calculate the probabilities of selecting zero new cameras and one new camera and add them together.

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[tex]\bf \sqrt{xy}=y\implies \left( xy \right)^{\frac{1}{2}}=y\implies \stackrel{\textit{chain rule~\hfill }}{\cfrac{1}{2}(xy)^{-\frac{1}{2}}\stackrel{\textit{product rule}}{\left(y+x\cfrac{dy}{dx} \right)}}=\cfrac{dy}{dx} \\\\\\ \cfrac{1}{2\sqrt{xy}}\left(y+x\cfrac{dy}{dx} \right)=\cfrac{dy}{dx}\implies \cfrac{y}{2\sqrt{xy}}+\cfrac{x}{2\sqrt{xy}}\cdot \cfrac{dy}{dx}=\cfrac{dy}{dx}[/tex]

[tex]\bf \cfrac{x}{2\sqrt{xy}}\cdot \cfrac{dy}{dx}=\cfrac{dy}{dx}-\cfrac{y}{2\sqrt{xy}} \implies \cfrac{x}{2\sqrt{xy}}\cdot \cfrac{dy}{dx}-\cfrac{dy}{dx}=-\cfrac{y}{2\sqrt{xy}} \\\\\\ \stackrel{\textit{common factor}}{\cfrac{dy}{dx}\left( \cfrac{x}{2\sqrt{xy}}-1 \right)}=-\cfrac{y}{2\sqrt{xy}} \implies \cfrac{dy}{dx}=-\cfrac{y}{\left( \frac{x}{2\sqrt{xy}}-1 \right)2\sqrt{xy}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \cfrac{dy}{dx}=-\cfrac{y}{x-2\sqrt{xy}}~\hfill[/tex]

[tex]f(x_1,\ldots,x_n)=x_1+\cdots+x_n=\displaystyle\sum_{i=1}^nx_i[/tex]

[tex]{x_1}^2+\cdots+{x_n}^2=\displaystyle\sum_{i=1}^n{x_i}^2=4[/tex]

The Lagrangian is

[tex]L(x_1,\ldots,x_n,\lambda)=\displaystyle\sum_{i=1}^nx_i+\lambda\left(\sum_{i=1}^n{x_i}^2-4\right)[/tex]

with partial derivatives (all set equal to 0)

[tex]L_{x_i}=1+2\lambda x_i=0\implies x_i=-\dfrac1{2\lambda}[/tex]

for [tex]1\le i\le n[/tex], and

[tex]L_\lambda=\displaystyle\sum_{i=1}^n{x_i}^2-4=0[/tex]

Substituting each [tex]x_i[/tex] into the second sum gives

[tex]\displaystyle\sum_{i=1}^n\left(-\frac1{2\lambda}\right)^2=4\implies\dfrac n{4\lambda^2}=4\implies\lambda=\pm\frac{\sqrt n}4[/tex]

Then we get two critical points,

[tex]x_i=-\dfrac1{2\frac{\sqrt n}4}=-\dfrac2{\sqrt n}[/tex]

or

[tex]x_i=-\dfrac1{2\left(-\frac{\sqrt n}4\right)}=\dfrac2{\sqrt n}[/tex]

At these points we get a value of [tex]f(x_1,\cdots,x_n)=\pm2\sqrt n[/tex], i.e. a maximum value of [tex]2\sqrt n[/tex] and a minimum value of [tex]-2\sqrt n[/tex].

Answer:

C. 153.84 mL

Step-by-step explanation:

Let's say x is the volume of 75% solution and y is the volume of 10% solution.

Sum of the volumes:

x + y = 500

Sum of the alcohol amounts:

0.75x + 0.10y = 0.30(500)

0.75x + 0.10y = 150

Solve the system of equations using either substitution or elimination.  I'll use substitution.

y = 500 - x

0.75x + 0.10 (500 - x) = 150

0.75x + 50 - 0.10x = 150

0.65x = 100

x = 153.84

You need 153.84 mL of 75% solution.

"153.84 mL" of 75% alcohol should be added. A further explanation is provided below.

Let,

then,

→ [tex]x+y = 500[/tex]

         [tex]y = (500-x)[/tex]

now,

→ [tex]75(x)+10(500-x) = 500\times 30[/tex]

                [tex]65x+5000=15000[/tex]

                           [tex]65x=15000-5000[/tex]

                           [tex]65x=10000[/tex]

                               [tex]x = \frac{10000}{65}[/tex]

                                  [tex]= \frac{2000}{13}[/tex]

                                  [tex]= 153.84 \ mL[/tex]

Thus the above response i.e., "option c" is correct.

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Answer:

3/15 or 0.2

Step-by-step explanation:

Answer: There is a probability of 40% of getting a school or district uses digital content and uses it as part of their curriculum.

Step-by-step explanation:

Since we have given that

Probability that schools or districts in a country use digital content = 80%

Probability that schools uses digital content as a part of their curriculum out of 80% = [tex]\dfrac{5}{10}[/tex]

So, the probability that a selected school or district uses digital content and uses it as  a part of their curriculum is given by

[tex]\dfrac{80}{100}\times \dfrac{5}{10}\\\\=0.8\times 0.5\\\\=0.4\\\\=40\%[/tex]

Hence, there is a probability of 40% of getting a school or district uses digital content and uses it as part of their curriculum.

The probability that a randomly selected school or district uses digital content and uses it as part of their curriculum is 40%.

To find the probability that a randomly selected school or district uses digital content and uses it as part of their curriculum, we need to multiply the probabilities of these events occurring.

Given that 80% of K-12 schools or districts use digital content and 5 out of 10 of these schools use it as part of their curriculum, we can calculate the probability as:

P(Uses digital content and uses it as part of curriculum) = P(Uses digital content) x P(Uses it as part of curriculum | Uses digital content)

Substituting the values, we have:

P(Uses digital content and uses it as part of curriculum) = 0.80 x 0.50 = 0.40 or 40%

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Answer:

a. The two events are dependent.

b. [tex]P(A\cap B)[/tex]= [tex]\frac{1}{220}[/tex].

Step-by-step explanation:

Given

Total coins =220

Number of Indian pennies= 6

A: When one of the 220 coins is randomly selected, it is one of the Indian pennies.

Therefore , the probability of getting an  Indian pennies=[tex]\frac{6}{220 }[/tex]

By using formula of probability=[tex]\frac{Number \; of\; favourable\; cases}{total\; number \; of \;cases}[/tex]

Probability of getting an  Indian pennies=[tex]\frac{3}{110}[/tex]

B: When another one of the 220 coins is randomly selected( with replacement) , It is also one of the Indian pennies.

Therefore, probability of getting an Indian pennies=[tex]\frac{6}{220}[/tex]

Probability of getting an Indian pennies =[tex]\frac{3}{110}[/tex]

[tex]A\cap B[/tex]: 1

[tex]P(A\cap B)=\frac{1}{220}[/tex]

If two events are independent. Then

[tex]P(A\cap B)= P(A)\times p(B)[/tex]

P(A).P(B)= [tex]\frac{3}{110} \times \frac{3}{110}[/tex]=[tex]\frac{9}{12100}[/tex]

Hence, [tex]P(A\cap B)\neq P(A).P(B)[/tex]

Therefore, the two events are dependent.

b. Probability that events A and B both occur

Number of favourable cases when both events A and B occur=1

Total coins=220

Probability=[tex]\frac{Number \; of\; favourable \; cases}{Total\; number\; of\; cases}[/tex]

[tex]P(A\cap B)=\frac{1}{220}[/tex]

Answer:

30 degrees

Step-by-step explanation:

u dot v=1*4+1*4+1*4+0*4=4+4+4+0=12

|u|=sqrt(1^2+1^2+1^2+0^2)=sqrt(3)

|v|=sqrt(4^2+4^2+4^2+4^2)=sqrt(4*4^2)=2*4=8

cos(theta)=u dot v/(|u||v|)

cos(theta)=12/(sqrt(3)*8)

cos(theta)=3/(sqrt(3)*2)

cos(theta)=sqrt(3)/2

theta=30 degrees

Step-by-step explanation:

[tex]3n-7\\\\\text{The difference between three times the number n and seven.}[/tex]

An expression is a set of numbers, variables, and mathematical operations. The Variable Expression 3n -7 into Verbal Expression​ can be written as expression 7 less than 3 times a number 'n'.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The expression that is given to us is 3n -7, this expression can be written as a verbal expression 7 less than 3 times a number 'n' or 7 subtracted from  3 times of number 'n'.

Hence, the Variable Expression 3n -7 into Verbal Expression​ can be written as expression 7 less than 3 times a number 'n'.

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Answer: 5\times10

Step-by-step explanation:

We know that the scientific notation is a representation of a very large or a very small number in the product of a decimal form of number (commonly between 1 and 10) and powers of ten.

Given : There are red blood cells contained in 50 cubic millimeters of blood .

The representation of 50 cubic millimeters in scientific notation is given by :-

[tex]5\times10\ \text{cubic millimeters }[/tex]

Answer:

b. (-3, -4) and (2, 6)

Step-by-step explanation:

By the transitive property of equality, if y equals thing 1 and y also equals thing 2, then thing1 and thing 2 are also equal.  So we will set them equal to each other and factor to solve for the 2 values of x:

[tex]2x+2=x^2+3x-4[/tex]

Get everything on one side of the equals sign, set the whole mess equal to 0, and combine like terms to get:

[tex]0=x^2+x-6[/tex]

Because this is a second degree polynomial, a quadratic to be precise, it has 2 solutions.  We need to find those 2 values of x and then use them in either one of the original equations to solve for the y values that go with each x.  

Factoring that polynomial above gives you the x values of x = -3 and 2.  Sub in -3 first:

y = 2(-3) + 2 and

y = -6 + 2 so

y = -4

Therefore, the coordinate is (-3, -4).

Onto the next x value of 2:

y = 2(2) + 2 and

y = 4 + 2 so

y = 6

Therefore, the coordinate is (2, 6)