5. what rate (in mm/yr ) is the north american plate moving relative to the boundary? round your answer to 2 significant figures.

The computed value of the test statistic is 2.94.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

We have a sample size of n = 12, engine size (x) and emissions (y) are the two variables being correlated, and the sample correlation coefficient is r = 0.47.

The null hypothesis is that the population correlation is zero (H0: ρ = 0) and the alternative hypothesis is that the population correlation is positive (Ha: ρ > 0).

To compute the test statistic, we need to first calculate the degrees of freedom (df), which is (n-2) = 10 in this case.

We can then use the formula for the test statistic, which is:

t = (r√(df)) / √1 - r²

Substituting the values we have, we get:

t = (0.47 √10) / √(1 - 0.47²)

t = 2.94

Therefore, the computed value of the test statistic is 2.94.

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30 students needs to be added for the food to be enough for 75 days

A hostel contains 150 students

They have food that will last them for 90 days

If the food is supposed to last for 75 days, the number of students that will be added can be calculated as follows

150= 90

1= x

cross multiply

x= 150×90

x= 13,500

= 13500/75

= 180

180 students will be fed for 75 days

We initially had 150 students, subtract 150 from 180

180-150

= 30

Hence 30 students needs to be added so the food lasts for 75 days

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Three right angles are 270, the rest of two angle are 135 degree for each.

What is right angle triangle explain?

it is not a diamond shape. it is five angles, five sides.

sum of 5 angles is 540

three right angles are 270, the rest of two angle are 135 degree for each.

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a. The value of the swap to firm XYZ is -$23,225.33.

b. This would help to protect the firm against an increase in interest rates.

a. Calculation of the value of the swap to firm XYZ

The value of the swap to firm XYZ can be calculated using the following formula:

Value of Swap = Value of Fixed Leg - Value of Floating Leg

Where Value of Fixed Leg = VFL = (Coupon Rate * Principal * (1 - (1 + r)-n / r))

Value of Floating Leg = VFL = (Interest Rate * Principal * (1 - (1 + r)-n / r))

Where, Coupon Rate = 4% p.a. Principal = $20 million

Interest Rate = LIBOR + Spread, Spread = 0, therefore,

Interest Rate = 4.5% p.a.

Time to Maturity, n = 15 months

Remaining Time to Next Payment = 6 - 2 = 4 months

Therefore, the current six-month LIBOR rate is required to calculate the value of the swap as follows:

Current six-month LIBOR rate = 4.5% * (4/6) + x% * (2/6)x = ((Value of Swap/Principal + (1 - (1 + r)-n / r)) * r) / (1 - (1 + r)-n / r) = 0.0251%

Value of Fixed Leg = VFL = (0.04 * 20,000,000 * (1 - (1 + 0.05/2)-30 / (0.05/2))) = $1,328,816.76

Value of Floating Leg = VFL = (0.0451 * 20,000,000 * (1 - (1 + 0.05/2)-10 / (0.05/2))) = $1,352,042.09

Value of Swap = $1,328,816.76 - $1,352,042.09 = -$23,225.33

Therefore, the value of the swap to firm XYZ is -$23,225.33.

b. Suggest a reason why XYZ entered into the swap in the first place

Firm XYZ might have entered into the swap in the first place to mitigate the risk of a rise in interest rates in the future. By entering into a fixed-for-floating interest rate swap, the firm has fixed its borrowing cost for the duration of the swap at 4%, regardless of the future interest rate changes.

Therefore, this would help to protect the firm against an increase in interest rates.

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Answer:

Cube both sides tham solve the resulting quadratic

The correct statement is:

Cube both sides and then solve the resulting quadratic equation.

The cube root of a number is the factor that we multiply by itself three times to get that number.

Given:

∛(x² - 6) = ∛(2x + 2)

For solving the above equation we have to take cube on both side

x² - 6 = 2x +2

x² - 2x -8 = 0

Then we get the quadratic equation.

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Answer:

46.3cm

Step-by-step explanation:

Answer:

\(\frac{214}{6}\)cm

Step-by-step explanation:

To find the perimeter of a rectangle, add all its sides.

Length + Length + Width + Width

\(\frac{25}{2} + \frac{25}{2} + \frac{32}{3} + \frac{32}{3}\)

= \(\frac{50}{2} + \frac{64}{3}\)

Find the LCM. It will be 6. Multiply the denominators with 2 and 3, respectively to get similar denominators, and that you can add.

 = \(\frac{50}{2}\frac{X 3}{X 3}\) + \(\frac{32}{3} \frac{X2}{X2}\) (the X is the multiplication sign..)

 = \(\frac{150}{6}\) + \(\frac{64}{6}\)

Now that the denominators are both the same, you can add the fractions.

 = \(\frac{214}{6}\)cm ( or also 35.7cm (to 3 significant figures) or \(35\frac{4}{6}\))

Answer:

Step-by-step explanation:

To convert time to time, kernel time with 24 (number of time in a day).

To convert time to minutes, kernel with time with 1440 (number of minutes in a day = 24 * 60).

To convert s to seconds, multiply the time by 86400 (number of s in a day = 24 * 60 * 60).

Answer:

I'm not sure if it's right but I got -2455.15

Step-by-step explanation:

You would use PEMDAS,  

( 129 + 19 ) = 148

-18 ( 148 ) =  -2664

3/2.25 = 1.333333333

1.333333333 - 2664 = -2662.666667

0.9 ( -2662.666667 ) = -2396.4

-47/8 = -58.75

-2396.4 - 58.75 = -2455.15

The value of the given expression is -2357.953.

Given that, 0.9(3÷2.25− 1 8 (1 2 3 + 1 9 ))− 4 7 ÷0.8.

The Bodmas rule follows the order of the BODMAS acronym ie B – Brackets, O – Order of powers or roots, D – Division, M – Multiplication A – Addition, and S – Subtraction. The BODMAS rule states that mathematical expressions with multiple operators need to be solved from left to right in the order of BODMAS.

Now, 0.9(3÷2.25− 1 8 (1 2 3 + 1 9 ))− 4 7 ÷0.8.

=0.9(3÷2.25− 1 8×142)− 4 7 ÷0.8.

=0.9(1.33− 1 8×142)− 4 7 ÷0.8.

=0.9×(-2554.67)-58.75=-2357.953

Hence, the value of the given expression is -2357.953.

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Producing rDNA involves isolating and cleaving DNA, inserting fragments into a vector, and transforming host cells. rDNA can be introduced via transformation, transfection, or viral vectors. Clinical applications include protein production, gene therapy, vaccines, and diagnostics.

Producing a recombinant DNA (rDNA) vector involves several general steps. Here are the three main steps involved in the process:

Isolation and Cleavage of DNA:

The first step is to isolate the desired DNA fragments from the source organism. This can be done using various techniques such as PCR (Polymerase Chain Reaction) or restriction enzyme digestion. Restriction enzymes are enzymes that cut DNA at specific recognition sites. By using the appropriate restriction enzymes, the desired DNA fragment and a vector DNA can be cut at specific sites. The vector is usually a plasmid, which is a small circular DNA molecule.

Insertion of DNA Fragments into the Vector:

Once the DNA fragments and vector have been cut, they are mixed together and joined through a process called ligation. DNA ligase is used to catalyze the formation of covalent bonds between the ends of the DNA fragments and the vector. This creates a recombinant DNA molecule containing the desired DNA fragment within the vector. The recombinant DNA molecule is then introduced into host cells for replication.

Transformation of Host Cells:

The recombinant DNA molecules need to be introduced into host cells to produce multiple copies of the recombinant DNA. This is typically done using a process called transformation. Host cells, such as bacteria or yeast, are treated in a way that makes them more receptive to taking up the recombinant DNA. Methods for transformation include heat shock, electroporation, or using chemical agents. Once the host cells have taken up the recombinant DNA, they can be grown in culture to produce large quantities of the desired DNA fragment.

Introduction of rDNA into Cells:

Recombinant DNA can be introduced into cells using various methods, depending on the type of cells being targeted. Some common techniques include:

Transformation: As mentioned earlier, host cells, such as bacteria or yeast, can be treated to make them receptive to taking up the recombinant DNA. This can be achieved by exposing the cells to heat shock, electroporation, or using chemical agents.

Transfection: This method is used for introducing rDNA into eukaryotic cells, including animal cells. It involves the use of techniques such as calcium phosphate precipitation, liposome-mediated transfection, or electroporation.

Viral Vectors: Certain viruses, such as retroviruses, adenoviruses, or lentiviruses, can be modified to carry the recombinant DNA. These viral vectors can then infect target cells and deliver the rDNA into the host genome.

Clinical Applications of rDNA:

Recombinant DNA technology has revolutionized biomedical research and has led to numerous clinical applications. Some important applications include:

Production of Therapeutic Proteins: rDNA technology allows for the production of large quantities of therapeutic proteins, such as insulin, growth factors, clotting factors, and monoclonal antibodies. These proteins can be used to treat various diseases, including diabetes, cancer, and genetic disorders.

Gene Therapy: rDNA vectors can be used to deliver functional copies of genes into target cells to correct genetic defects. This holds promise for the treatment of inherited diseases caused by single gene mutations, such as cystic fibrosis and muscular dystrophy.

Vaccine Development: Recombinant DNA technology has been instrumental in the development of vaccines. By expressing specific antigens from pathogens, recombinant vaccines can be created to stimulate an immune response without causing disease.

Diagnostic Tools: Recombinant DNA techniques are used to produce specific DNA or RNA probes for diagnostic purposes. These probes can detect the presence of specific genes or mutations associated with diseases, aiding in early detection and personalized medicine.

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Let the numbers be 2x and 3x.

According to the Question,

⇒ 2x + 3x = 45

⇒ 5x = 45

⇒ x = 45/5

⇒ x = 9

Now finding the values of both the number,

⇒ 2x = 2 × 9

= 18

⇒ 3x = 3 × 9

= 27

Hence, the value of both the number is 18 and 27 respectively.

Now we have to,

find the both required numbers.

It is given that,

→ Two numbers are in the ratio 2:3.

→ Their sum is 45.

Now assume numbers as,

→ 2y and 3y

As per the given information,

→ 2y + 3y = 45

First we can find the value of y,

→ 2y + 3y = 45

→ 5y = 45

→ y = 45/5

→ [y = 9]

The given ratio is,

→ 2 : 3

Let's find the value of 2y,

→ 2y --- {y = 9}

→ 2 × (9)

→ 18

Let's find the value of 3y,

→ 3y --- {y = 9}

→ 3 × (9)

→ 27

Hence, the number is 18 and 27.

Answer:

4762 N/m^2

Step-by-step explanation:

Find area.

30x5.6=168

Convert to m^2

168cm^2=0.0168m^2

Use pressure formula to get answer

P=F/A

P=80/0.0168

P=4762 N/m^2

Answer:

The answer is ≈3 to the nearest whole number

Step-by-step explanation:

using SOH CAH TOA

BCA

sin0=opp/hyp

sin0=7.9/11

0=sin‐¹(7.9/11)

0=46 to the nearest degree

<A=<D

so,<EDF=46°

tan0=adj/hyp

tan46=x/3.3

x=tan46×3.3

x=3 to the nearest whole number

Answer:

Step-by-step explanation:

1256cm^2

Answer:

5 gallons

Step-by-step explanation:

If she can do 1/10 gallon per seconds, that means she can do 5/50.

You can write it as this ratio:

1/10 = x/50.

You know that 10 * 5 = 50.

Since it is a constant ratio, it has to be 1 * 5 = x

Since 1 * 5 = 5, Tiffany can fill the pool 5 gallons per 50 seconds.

Answer:

B

Step-by-step explanation:

We can determine the total miles run by the 10 students by adding all the miles run by each individual student:

A

1 student * 1/12 miles = 1/12 miles

2 students * 1/8 miles = 2/8 miles = 1/4 miles

1 student * 1/6 miles = 1/6 miles

2 students * 1/4 miles = 2/4 miles = 1/2 miles

1 student * 1/3 miles = 1/3 miles

3 students * 1/2 miles = 3/2 miles

We add all these fractions to obtain 17/6, which is approximately 2.83, which is not as the question describes.

B

2 students * 1/6 miles = 1/3 miles

2 students * 1/4 miles = 1/2 miles

2 students * 1/3 miles = 2/3 miles

3 students * 1/2 miles = 3/2 miles

1 student * 1 mile = 1 mile

We add all these fractions to obtain 4 miles, which is as the question describes.

Answer:

Given function:

\(q(x)=9x^2-24x+16\)

To factor a quadratic in the form \(ax^2+bx+c\),  find two numbers that multiply to \(ac\) and sum to \(b\):

\(ac=9 \cdot 16=144\)

Two numbers that multiply to 144 and sum to -24 are: -12 and -12

Rewrite \(b\) as the sum of these two numbers:

\(\implies q(x)=9x^2-12x-12x+16\)

Factorize the first two terms and the last two terms separately:

\(\implies q(x)=3x(3x-4)-4(3x-4)\)

Factor out the common term \((3x-4)\):

\(\implies q(x)=(3x-4)(3x-4)\)

Therefore:

\(\implies q(x)=(3x-4)^2\)

The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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The time it takes the ball to strike the ground after it is thrown, found using the kinematic equation, H = -16·t² - 24·t + 200 is approximately 2.86 seconds

We know  that,

A kinematic equation is an equation of the motion of an object moving with a constant acceleration.

The direction in which the ball is thrown = Downwards

Height of the building = 200 foot

Initial velocity of the ball = 24 ft./s

The kinematic equation that indicates the height of the ball after t seconds is, H = -16·t² - 24·t + 200

At ground level, H = 0, therefore;

H = 0 = -16·t² - 24·t + 200

-16·t² - 24·t + 200 = 0

-2·t² - 3·t + 25 = 0

t = (3 ± √((-3)² - 4 × (-2)×25))/(2×(-2))

t = (3 ± √(209))/(-4)

t =  (3 + √(209))/(-4) ≈ -4.36 and t =  (3 - √(209))/(-4)) ≈ 2.86

The time it takes the ball to strike the ground after it is thrown is approximately 2.86 seconds.

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Answer:

3240

Step-by-step explanation:

25% of 1620 is 405

Initial chocolate number is multiple 405 by 4 then add into 1620

405 *4 =1620

1620+1620 =3240

The number of chocolates that Tarquin had initially is 3240 and the calculation is below,

Tarquin ate 25% of his chocolate each day, so after 4 days, he had eaten 25% * 4 days = 100% of his chocolate.

Since he had 1620 chocolates left, this means that he initially had 1620 * 100% = 3240 chocolates.

Therefore, the answer is 3240.

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A. The approximate height of the building is 100 m

B. We can use the arc length formula to obtain an approximation of BC since angle A is small.

A.

The approximate height of the building is 100 m

To find the approximate height of the building, we consider the diagram.

From the diagram, we have that using trigonometry,

tanA = BC/AB

Now

So, making BC subject of the formua, we have

BC = ABtanA

Substituting the values of the variables into the equation, we have

BC = ABtanA

BC =2000tan0.05

BC = 2000 × 0.05

BC = 100 m

So, the approximate height of the building is 100 m

B.

We can use the arc length formula to obtain an approximation of BC since angle A is small.

We know that the arc length formula L = rФ where

Now BC = ABtanA

We know that Ф ≅ tanФ when Ф is small.

So, BC = AB × A which is the arc length formula with

So, we can use the arc length formula to obtain an approximation of BC since angle A is small.

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Answer:

  (a)  10x^2−x−21

Step-by-step explanation:

The area of a rectangle is given by the formula ...

  A = LW . . . . . where L is the length, and W is the width

__

The area of the given rectangle will be ...

  A = (2x -3)(5x +7)

This product is simplified using the distributive property to eliminate parentheses. Then like terms are combined.

  A = 2x(5x +7) -3(5x +7)

  = (2x)(5x) +(2x)(7) -3(5x) -3(7)

  = 10x^2 +14x -15x -21

  A = 10x^2 -x -21

The expression 10x^2 -x -21 represents the area of the rectangle in square inches.

Answer:

n/a

Step-by-step explanation:

how does it feel

The length of the arc is 2π units.

The area of a circle is 64πunits squared. The area of the sector is 8π. Therefore, the arc length can be found as follows:

area of a circle = πr²

64π = πr²

r = √64

r = 8 units

area of sector = ∅/ 360 × πr²

8π = ∅/ 360 × 8²π

8π = 64π∅ / 360

cross multiply

2880π = 64π∅

∅ = 2880π / 64π

∅ = 45 degrees

Therefore,

length of arc  = 45 / 360 × 2 × π × 8

length of arc  = 720 / 360 π

length of arc  = 2π units

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Answer:

x=-4,y=-3

Step-by-step explanation:

The sale price of the CD player, given a regular price of $3,600 and a sale discount of 20%, is $2,880.

To calculate the sale price, we need to apply the discount percentage to the regular price. In this case, the regular price is $3,600, and the sale discount is 20%.

To find the sale price, we can multiply the regular price by (100% - 20%) or 0.8 (since 20% is equivalent to 0.20 in decimal form).

Calculating the sale price, we get $3,600 * 0.8 = $2,880.

Therefore, the sale price of the CD player with a regular price of $3,600 and a 20% discount is $2,880.

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Answer:

A

Step-by-step explanation:

Answer:

Explanation:

Here, we want to get the diameter of one of the balls

Firstly, we need to get the size of one of the balls

We can get this by dividing the total volume of the three balls by 3

Mathematically, we have this as:

To get the diameter of one of the balls, we can get the radius first and multiply the value by 2 since the diameter is 2 times the radius length

A ball is spherical in shape

The volume of a sphere is:

Thus:

To get the diameter, we simply multiply this by 2