A certain small country has $10 billion in paper currency in circulation, and each day $50 million comes into the country's banks. The government decides to introduce new currency by having the banks replace old bills with new ones whenever old currency comes into the banks. Since both old bills and new bills will come into the banks while the new currency is gradually introduced, we will need to solve a differential equation to track the amount of new currency in circulation at a given time. Let x (t) denote the amount of new currency, in billions of $, in circulation after t days. We've shown that new currency is introduced at the rate 10 - x (t) / 10 0.05, which simplifies to 0.005 (10 - x (t)). This justifies that x (t) satisfies the differential equation dx / dt = 0.005 (10 - x). (a) Solve the differential equation to find x (t). (b) At what time t will new bills make up 90% of the currency in circulation?

Answers

Answer 1

(a) The solution to the differential equation isx(t) = 10(1 - e^(-0.005t))

To solve the differential equation dx/dt = 0.005(10 - x), we can use separation of variables:

dx / (10 - x) = 0.005 dt

Integrating both sides:

-ln|10 - x| = 0.005t + C

where C is the constant of integration. Solving for x:

|10 - x| = e^(-0.005t - C)

Since x cannot be negative, we can drop the absolute value sign and solve for C using the initial condition that x(0) = 0:

C = -ln(10)

Therefore, the solution to the differential equation is:

x(t) = 10 - e^(-0.005t - ln(10))

Simplifying:

x(t) = 10(1 - e^(-0.005t))

(b) New bills will make up 90% of the currency in circulation after approximately 461 days.

We want to find the value of t such that x(t) = 0.9(10) = 9. Plugging this into our solution from part (a):

9 = 10(1 - e^(-0.005t))

Dividing both sides by 10 and taking the natural logarithm:

ln(0.1) = -0.005t

Solving for t:

t = 200 ln(10) = 460.51

Therefore, new bills will make up 90% of the currency in circulation after approximately 461 days.

For more questions like Equation click the link below:

https://brainly.com/question/16663279

#SPJ11


Related Questions

please help I need this complete

Answers

Answer: [tex]c-34=21[/tex]; 55 cups of lemonade.

Step-by-step explanation:

We are given the amount sold and the amount leftover so we need to figure out how many cups were there at the start. Since you are subtracting the amount of cups you sold from the amount you start with and it equals an end amount, the cups can be modeled by the equation [tex]c-34=21[/tex] rather than [tex]21+c=34[/tex].

Now to solve for c

[tex]c-34=21\\[/tex]

add 34 to both sides

[tex]c=55[/tex]

Use Lagrange multiplier techniques to find shortest and longest distances from the origin to the curve x2 + xy + y2 = 3. shortest distance longest distance

Answers

The shortest distance from the origin to the curve x2 + xy + y2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

We have to find the shortest and longest distances from the origin to the curve x^2 + xy + y^2 = 3. This can be done using the Lagrange multiplier technique.

Given, x^2 + xy + y^2 = 3.

We have to minimize and maximize the distance of the origin from the given curve. The distance of the origin from the point (x, y) is given by √(x²+y²).

Therefore, we have to minimize and maximize the function f(x, y) = √(x²+y²) subject to the constraint x^2 + xy + y^2 = 3.

Now, we have to form the Lagrange function.

L(x, y, λ) = f(x, y) + λ(g(x, y))

where, g(x, y) = x2 + xy + y2 - 3L(x, y, λ) = √(x²+y²) + λ(x2 + xy + y2 - 3)

Now, we have to find the partial derivatives of L with respect to x, y, and λ.

∂L/∂x = x/√(x²+y²) + 2λx+y = 0 ............. (1)

∂L/∂y = y/√(x²+y²) + λx+2λy = 0 ............. (2)

∂L/∂λ = x² + xy + y² - 3 = 0 ............. (3)

Solving equations (1) and (2), we get x/√(x²+y²) = 2y/x.

Since x and y cannot be equal to 0 simultaneously, we can say that x/y = ±2.

Substituting x = ±2y in equation (3), we get y²(5±2√7) = 9.

Now, we can solve for x and y to get the values of (x, y) at which the minimum and maximum value of the distance of the origin occurs.

Using x = 2y, we get y²(5+2√7) = 9 ⇒ y = ±3/√(5+2√7)

Using x = -2y, we get y²(5-2√7) = 9 ⇒ y = ±3/√(5-2√7)

Therefore, the four points at which the distance is minimum and maximum are {(2/√(5+2√7), 1/√(5+2√7)), (-2/√(5+2√7), -1/√(5+2√7)), (2/√(5-2√7), -1/√(5-2√7)), (-2/√(5-2√7), 1/√(5-2√7))}.

To find the minimum and maximum distances, we can substitute these points in f(x, y) = √(x²+y²).

After substituting, we get the minimum distance as √(6-2√7) and the maximum distance as √(6+2√7).

Therefore, the shortest distance from the origin to the curve x^2 + xy + y^2 = 3 is √(6-2√7) and the longest distance is √(6+2√7).

To know more about the shortest distance and longest distance: https://brainly.com/question/30985130

#SPJ11

Find the Volume of the given cylinder. Round your answer to the nearest tenth. 3 m 3 m​

Answers

Answer: The volume of the cylinder is approximately 21.2 cubic meters

Step-by-step explanation:

To find the volume of a cylinder, we use the formula:

V = πr^2h

where:

V = volume

r = radius

h = height

In this case, we are given that the cylinder has a height of 3m, but we need to determine the radius.

Since we are not given the radius directly, we can estimate it from the diameter. If the cylinder has a diameter of 3m, then the radius would be half of that, or 1.5m.

So, substituting the values into the formula, we get:

V = π(1.5)^2(3)

V ≈ 21.2 m^3

Rounding to the nearest tenth, the volume of the cylinder is approximately 21.2 cubic meters.

Hanna has a bag of 20 sweets and eats 7 of them what fraction of the sweets does she eat?

Answers

The fraction of sweets that does she eat is 7/20

In this case, we will be using fractions to describe the portion of sweets that Hanna eats from her bag of 20.

Hanna has a bag of 20 sweets, and she eats 7 of them. To find out what fraction of the sweets she eats, we need to determine the ratio of the number of sweets she eats to the total number of sweets in the bag.

So in this case, Hanna eats 7 sweets, and there are 20 sweets in the bag. Therefore, the fraction of sweets she eats can be written as:

=> 7/20

To know more about fraction here

https://brainly.com/question/10354322

#SPJ4

a retired potter can produce china pitchers at a cost of $5 each. she estimates her price function to be where p is the price at which exactly x pitchers will be sold per week. find the number of pitchers that she should produce and the price that she should charge in order to maximize profit. also find the maximum profit.

Answers

The number of pitchers that she should produce and the price that she should charge in order to maximize profit is 0 and $5, respectively, and the maximum profit is $0.


Given that a retired potter can produce china pitchers at a cost of $5 each. She estimates her price function to be where p is the price at which exactly x pitchers will be sold per week.

The formula for the profit is given by,

Profit = Revenue - Cost

The revenue for selling x pitchers at a price p is xp.

The total cost of producing x pitchers is 5x.

Therefore, Profit [tex]= xp - 5x[/tex]

Profit can be expressed as a function of x using the formulae of the function,

[tex]y = xp - 5x= (p - 5)x[/tex] .............(1)

Now, the number of pitchers that she should produce and the price that she should charge in order to maximize profit can be found by finding the maximum value of the profit function (1).

Let the maximum profit be P. Maximize P with respect to x. To find the maximum of a function of x, we can find its derivative and equate it to zero.

[tex]dP/dx = 0P = (p - 5)x[/tex]

Differentiate P with respect to x again to determine whether it is a maximum or minimum.

[tex]d^2P/dx^2 = -5 < 0[/tex]

Since [tex]d^2P/dx^2[/tex] is negative, the value of P is a maximum.

Substitute the value of x from equation (1) in terms of P to find

[tex]p.P = (p - 5)*P/(p - 5) \\\\p = 5[/tex]

Therefore, the price to maximize profit is $5 and the number of pitchers to produce is,

[tex]x = P/(p - 5) = P/0 =[/tex] undefined

Maximum profit is [tex]P = (p - 5)x = (5 - 5)x = $0[/tex]

Learn more about profit here:

https://brainly.com/question/1078746

#SPJ11

If a large bag of the same candy has 75 pieces, which of the 5 colors is likely to appear the most? justify your answer.

Answers

If a large bag of the same candy has 75 pieces, then the expected average for each color is 15 pieces.

Now, let's apply this concept to our candy problem. If the bag of candy has 75 pieces, we can assume that each color makes up approximately 1/5 or 20% of the total. That means each color should have an equal chance of appearing, with an expected average of 15 pieces per color (75 pieces divided by 5 colors).

However, this is only an expected average. In reality, there may be some variation in the number of pieces of each color that we actually find in the bag. This variation can be caused by a variety of factors, such as the manufacturing process, the mixing of different batches of candy, or even random chance.

To determine which color is likely to appear the most, we can look at the range of variation for each color. If the range of variation for a particular color is higher than the expected average of 15 pieces, then that color is more likely to appear more often than the others. On the other hand, if the range of variation is lower than the expected average, then that color is less likely to appear as often.

To know more about average here

https://brainly.com/question/16956746

#SPJ4

Use the factorization A PDP 1 to compute Ak, where k represents an arbitrary integer. a 7(b-a) 17 a 017

Answers

If A = [tex]PDP^{-1}[/tex], Then [tex]A^{k}[/tex] = [tex](PDP^{-1}) ^{k}[/tex] = [tex]PDP^{-1}[/tex][tex]PDP^{-1}[/tex] .....[tex]PDP^{-1}[/tex] = [tex]PD^{k} P^{-1}[/tex]since [tex]P^{-1}[/tex] P = I, the identity matrix.

Further, the representation can be made as in the following attachment.

To learn more about integers, refer to:

https://brainly.com/question/929808

#SPJ4

pls answer this!!!!


<333

Answers

A is geometric sequence
B is arithmetic sequence
C is arithmetic sequence
D is geometric sequence
Geometric sequence because the next terms are gotten by multiplying the previous terms by certain numbers and the common ratio may be derived by dividing the next term by the previous term.
Arithmetic sequence because the next terms are gotten by adding a certain number to the previous number and the common difference may be found by subtracting the preceding term from next term.

1+3=?



i don't know
im not very smart

Answers

Answer:

4

Step-by-step explanation:

count 3 what comes next

I think its aaaaaaaaaa i think its a carot yea a carot
* its 4 :(

A cruise ship compartment can hold 440 pieces of luggage. If a ship had 42 compartments,how many pieces of luggage can it hold?

Answers

Answer: 18480

i used a calculator :)

the answer i need is Another pair it could be (_,10)

and every y value is _ every x value

Answers

Answer:

Another order pair could be (30,10).

Every y value is "one-third of" every x value.

Let P be some predicate. Check the box next to each scenario in which ∀n ∈ N, P(n) must be true.
a) For every natural number k > 0 , if P(i) holds for every natural number i < k, then P(k) holds.
b) P(0) holds and for every natural number k > 0, if P(i) does not hold, then there is some natural number i < k such that P(i) does not hold.
c) For every natural number k, if P(i) holds for every natural number i < k, then P(k) holds.
d) For every natural number k, if P(k) does not hold, then there is a smaller natural number i < k such that P(i) does not hold.

Answers

Answer:

A

Step-by-step explanation:

a) ✔️

This is the principle of mathematical induction. If P holds for the base case k=1 and we can show that if it holds for any arbitrary k (e.g. k=n) then it must also hold for the next value (e.g. k=n+1), then we have shown it holds for all natural numbers.

b) ❌

There is no guarantee that P holds for all natural numbers from the statement alone. It only guarantees that for any k where P does not hold, there exists a smaller number i where P does not hold.

c) ❌

This is the principle of weak mathematical induction. It only shows that if P holds for a given k and for all smaller values i then it must hold for k+1. It does not guarantee that P holds for all natural numbers.

d) ❌

This statement is the negation of the principle of mathematical induction. It is known as the "strong induction" principle, which assumes that if P does not hold for k, then there exists a smaller i where P does not hold. However, this principle is not sufficient to prove that P holds for all natural numbers k.

if there is a sample, the standard error is used in the denominator of the z stat or t stat formula. group of answer choices true false

Answers

It is correct to state that if there is a sample, the standard error is used in the denominator of the z stat or t stat formula.

What is the formula for the test statistic?

The t-distribution is used when we have the standard deviation for the sample instead of the population, hence the equation is given as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.

The standard error is modeled as follows:

[tex]s_e = \frac{s}{\sqrt{n}}[/tex]

Which is the denominator of the formula for the test statistic, hence the statement is true.

When we have the standard deviation for the population, we use the z-distribution, however the formula for the standard error is similar.

More can be learned about the z-distribution at https://brainly.com/question/25890103

#SPJ1

Victor spent $61 on some sandpaper for his model
cars. He bought 2 packages of the smallest-grain
sandpaper and spent the rest on the largest-grain
sandpaper. How many packages of the largest-
grain sandpaper did he buy?
Size of
Grain (cm)
0.003
0.011
0.001
Cost per
Package (S)
13
7
20

Answers

Answer:

3 packages

Step-by-step explanation:

61 - 20 * 2 (small grain sandpaper) = $21 remain. The largest grain costs $7, so 21/7 = 3 packages of the largest grain sandpaper was bought.

Hope this helped!

I need help with these 2 please ​

Answers

Question 7. C (rectangular pyramid)

Question 8. 17 cm

Answer:

Question 7:C rectangular pyramid

Question 8: C 120 in

A=2(wl+hl+hw)=2·(10·2+5·2+5·10)=160

Step-by-step explanation:

● Thornton
1 centimeter =
50 kilometers
Peter's mother is a pilot. She often makes deliveries
near their community. Peter and his mother flew from
Charlton to Thornton to make a mail delivery. Then they
continued on to Avon and Ashton and returned to Charltc
How many kilometers did Peter and his mother
travel in all?

Answers

The answer is 250 kilometers. Peter and his mother traveled a total distance of 250 kilometers on their mail delivery.

What is distance?

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter is equal to 0.01 kilometers, so 50 kilometers would be equal to 5,000 centimeters. The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

Charltc to Thornton is 1,000 centimeters, Thornton to Avon is 1,500 centimeters, Avon to Ashton is 1,000 centimeters, and Ashton to Charltc is 1,500 centimeters. This gives us a total of 5,000 centimeters, or 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times, since they flew from Charltc to Thornton, then to Avon, then to Ashton, and then back to Charltc). This gives us 250 kilometers, which is the answer to the question.

For more questions related to magnitude

https://brainly.com/question/28047791

#SPJ1

Peter and his mother traveled a total distance of 250 kilometers on their mail delivery. The answer is 250 kilometers.

What is distance?

Distance is a numerical measurement of how far apart two objects or points are. It is a scalar quantity, meaning that it is only expressed as a magnitude, or numerical value, without any direction.

1 centimeter =  0.01 kilometers,

so 50 kilometers = 5,000 centimeters.

Charlton to Thornton= 1,000 centimeters,

Thornton to Avon= 1,500 centimeters,

Avon to Ashton= 1,000 centimeters,

and Ashton to Charlton= 1,500 centimeters.

Total distance= 1,000+1,500+1,000+1,500

= 5,000 centimeters, or 50 kilometers.

The total distance between the four cities is 5,000 centimeters, which is equal to 50 kilometers.

This can be calculated by multiplying the total distance between the four cities (50 kilometers) by the number of times they traveled the route (5 times.

=50*5

=250

Since they flew from Charlton to Thornton, then to Avon, then to Ashton, and then back to Charlton.

250 kilometers is the answer to the question.

For more questions related to magnitude

https://brainly.com/question/28047791

#SPJ1

Question:

Peter's mother is a pilot. She often makes deliveries near their community. Peter and his mother flew from Charlton to Thornton to make a mail delivery. Then they continued on to Avon and Ashton and returned to Charlton. How many kilometers did Peter and his mother travel in all?

What is one possibility for the price of Carlotta’s charges per person

Answers

$50 is one estimate for the cost of Carlotta's fees per individual. This is based on information from the article, which claims that some consumers pay $50 a session for Carlotta's services,

which are less expensive than conventional therapy. The precise price, however, is not stated and may change based on the client's financial status and the services rendered. Carlotta's services are priced in the article, although the details are not totally apparent. It states that Carlotta charges less than conventional therapy, indicating that her costs are reasonable and competitive. The article also mentions that some clients pay $50 for each session, which gives a particular pricing range. However, it is crucial to remember that the precise cost may change .

learn more about price  here:

https://brainly.com/question/19091385

#SPJ4

Use the given information below to answer the questions. Show ALL your work.The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches.LetM = the height of a randomly selected young manW = the height of a randomly selected young woman1. Describe the shape, center, and spread of the distribution of M-W.2. Find the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman.

Answers

We have that, The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is 0.709

How do we find the probability?

1. The shape, center, and spread of the M-W distribution are:Shape: NormalCenter: 4.8 inches (69.3 - 64.5)Spread: The standard deviation of the difference between two normally distributed variables is given by the formula:

[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]

Let us define [tex]Z = (M - W - 2)/3.64[/tex]. So the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is:

[tex]P(M > W + 2) = P((M - W - 2)/\sigma(M-W) > (- 2)/\sigma (M-W)) = P(Z > -0.55) = 1 - P(Z \leq  - 0.55)[/tex]

Using a standard normal table or a calculator, we find that [tex]P(Z \leq  -0.55) \approx 0.291[/tex]. Therefore, the probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx  1 - 0.291 = 0.709[/tex].

The shape, center, and spread of the M-W distribution are:

Shape: Regular Center: 4.8 inches (69.3 - 64.5)

Dispersion: The standard deviation of the difference between two normally distributed variables is given by the formula:

[tex]\sigma (M-W) = \sqrt{(\sigma_1^2 + \sigma_2^2)} = \sqrt{(2.8^2 + 2.5^2)} \approx 3.64[/tex]

The probability that a randomly selected young man is at least 2 inches taller than a randomly selected young woman is: [tex]P(M > W + 2) \approx 0.709[/tex].

See more information about probability in: https://brainly.com/question/24756209

#SPJ11

which one do you think is the correct Triangle Congruence Theorem?

Answers

These theories are all true and can be used to demonstrate the congruence of two triangles.

what is triangle ?

Three straight sides and three angles define the two-dimensional geometric form known as a triangle. It is created by joining three non-collinear plane lines. The three places where a triangle's sides intersect are known as the triangle's vertices, and the line segments that make up the triangle's sides are known as its edges or sides. A triangle's inner angles are always added up to 180 degrees. Triangles can be categorised according to their edges and side lengths.

given

Many triangular congruence theorems exist, and they are all true.

The two triangles are congruent if their two sides and included angles match those of another triangle, according to the Side-Angle-Side (SAS) congruence theory.

The Angle-Side-Angle (ASA) congruence theory states that two triangles are congruent if their included sides and two angles are congruent with one another.

The two triangles are congruent if all three sides of one triangle are congruent with all three sides of the other triangle, according to the Side-Side-Side (SSS) congruence theory.

The right triangles are congruent if their hypotenuses and legs are congruent with those of another right triangle, according to the Hypotenuse-Leg (HL) congruence theory.

These theories are all true and can be used to demonstrate the congruence of two triangles.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

Can someone help me with this

Answers

Answer:

they bought 62 item from noodles and 51 items from hot chips

the two sides of a right triangle opposite the non-right angles are called

Answers

The two sides of a right triangle opposite the non-right angles are called as adjacent and opposite angle or Legs.

A triangle is a three-sided regular polygon in which the total of any two sides is always larger than the sum of the third side.

A right-angled triangle is one with one of its internal angles equal to 90 degrees, or any angle is a right angle. As a result, this triangle is also known as the right triangle or the 90-degree triangle. In trigonometry, the correct triangle is very significant.

A right-angled triangle is a triangle in which one of the angles is 90 degrees. The total of the other two angles is 90 degrees. The sides that include the right angle are perpendicular and form the triangle's base. The third side is known as the hypotenuse, and it is the longest of the three sides.

The three sides of the right triangle are connected. Pythagoras' theorem explains this relationship. This theorem states that in a right triangle,

Perpendicular² + Base² = Hypotenuse²

Learn more about Right angle triangle:

https://brainly.com/question/64787

#SPJ4

there are 30 aaa batteries in a box and 9 are defective. two batteries are selected without replacement. what is the probability of selecting a defective battery followed by another defective battery

Answers

Therefore, the probability of selecting a defective battery followed by another defective battery is about 12/145 or 8.28%.

What is the probability?

The probability of selecting a defective battery on the first draw is 9/30, or 3/10, since there are 3 defective batteries out of 30 total.

Since one battery has already been drawn, there are now 29 batteries left in the box, and 8 defective batteries remaining. The probability of selecting another defective battery on the second draw, without replacement, is 8/29.

To find the probability of both events happening (selecting a defective battery followed by another defective battery), we multiply the probabilities of each event:

P(defective battery and then another defective battery) = P(defective battery on first draw) × P(defective battery on second draw)

P(defective battery and then another defective battery) = (3/10) × (8/29)

P(defective battery and then another defective battery) = 24/290 = 0.0828 or 8.28%

Therefore, the probability of selecting a defective battery followed by another defective battery out of 30 AAA batteries in a box where 9 are defective and two batteries are selected without replacement is 0.0828 or 8.28%.

Learn more about Probability here:

https://brainly.com/question/9793303

#SPJ11

If x is a positive integer , 4x^1/2 is equivalent to

Answers

If x is a positive integer , 4x^1/2 is equivalent to product of 2 and square root of x, wherein it would surely be a positive value greater than 2.

Positive integers are the numbers on the number line which are greater then zero and extend on the right hand side of the number line till infinity. These numbers are also whole numbers in itself such as 1, 2, 3...,∞. When 4x^1/2 is calculated, it is assumed that 4x is raised to power half, which will provide the answer as 2√x.

It is because square root of 4 will be 2 and that of x will be √x. Square roots are the numbers obtained by multiplying a specific number by the number itself. For example: 3×3 = 9 or square root of 9 is 3.

If some positive integer is fixed in the equation, the desired outcome would be obtained as follows:

If x=4, (4×4)^1/2 = 4

Learn more about positive integers at:

brainly.com/question/1367050

#SPJ4

a researcher compares the effectiveness of two different instructional methods for teaching anatomy. a sample of 116 students using method 1 produces a testing average of 50.3. a sample of 151 students using method 2 produces a testing average of 68.6. assume that the population standard deviation for method 1 is 15.62, while the population standard deviation for method 2 is 17.21. determine the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2. step 3 of 3 : construct the 99% confidence interval. round your answers to one decimal place.

Answers

The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 is [15.8, 20.8].

The 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2 can be calculated using a two-sample t-test.

First, calculate the sample difference in means. Subtract the mean for method 1 (50.3) from the mean for method 2 (68.6) to get 18.3.

Next, calculate the pooled standard deviation, which is the weighted average of the standard deviations for each sample:

Pooled standard deviation = [tex]√(((n1-1)×s12 + (n2-1)×s22)/ (n1+n2-2))[/tex]

n1=116, s12=15.62, n2=151, s22=17.21

Pooled standard deviation = [tex]√(((116-1)×15.62 + (151-1)×17.21)/ (116+151-2))[/tex]
Pooled standard deviation = [tex]√(1422.3788/265)[/tex]

Pooled standard deviation = 4.89

Finally, calculate the 99% confidence interval for the true difference between testing averages for students using method 1 and students using method 2:

99% Confidence Interval = Sample Difference in Means ± (Critical Value) × (Pooled Standard Deviation/√(n1+n2))

99% Confidence Interval =[tex]18.3 ± (2.58) × (4.89/√(116+151))[/tex]

99% Confidence Interval = 18.3 ± 2.50

for such more questions on standard deviation
https://brainly.com/question/475676

#SPJ11

At the local pet store, zebra fish cost $2.00 each and neon tetras cost $2.30 each. If Yumi bought 13 fish for a total cost of $27.50, not including tax, how many of each type of fish did she buy?​

Answers

If Yumi bought 13 fish for total then yumi bought 8 zebra fish and 5 neon tetras.

What is substitution?

Substitution is a mathematical operation that involves replacing a variable or expression in an equation, function, or formula with another variable, expression, or value.

According to question:

Let's assume Yumi bought x zebra fish and y neon tetras.

x + y = 13 (equation 1)

2x + 2.3y = 27.5 (equation 2)

Using equation 1, we can solve for one variable in terms of the other:

x = 13 - y

Then, change x in equation 2 to the following expression:

2(13 - y) + 2.3y = 27.5

Simplifying and solving for y:

26 - 2y + 2.3y = 27.5

0.3y = 1.5

y = 5

So Yumi bought 5 neon tetras. To find how many zebra fish she bought, we can substitute y = 5 into equation 1:

x + 5 = 13

x = 8

Therefore, Yumi bought 8 zebra fish and 5 neon tetras.

To know more about substitution visit:

https://brainly.com/question/13058734

#SPJ1

Solve for x,
using the tangent lines.
X
42°
x = [?]

can someone pls help explain how they got the answer? i’m having a hard time understanding, ty :)

Answers

Answer:

  138°

Step-by-step explanation:

You want the measure of the angle at two tangents when they intercept an arc of 42°.

Supplementary angles

The short answer is that the exterior angle x is the supplement of the measure of the arc:

  x = 180° -42°

  x = 138°

Exterior angle

An exterior angle where secants meet is half the difference of the arcs of the circle they intercept. Here, the secants have been located so the corresponding chord length between the near and far circle intercept points have degenerated to zero. That is, they are tangents.

The angle relation still holds:

  x = (long arc - short arc)/2 = ((360° -42°) -42°)/2 = (360° -2·42°)/2

  x = 180° -42° = 138°

Quadrilateral

The tangents, together with their associated radii form a quadrilateral. The angles at the tangents are 90°, and the total of all angles is 360°. This gives us the relation ...

  x + 90° +42° +90° = 360°

  x +42° = 180° . . . . . . . . . . . . . subtract 180°

  x = 180° -42° = 138°

(We solved this with an extra step, so you could see the same "supplementary angles" relationship between x and 42°.)

I need help on this ! Please

Answers

Answer: Infinitely many solutions

Step-by-step explanation:

On the graph I have attached, you can see the two lines overlap each other. This means the linear equations have an infinite amount of solutions.

a crime reporter was told that on average, 3000 burgalries per month occured in the city, write null hypothesis

Answers

A crime reporter's null hypothesis is:H0: The actual number of burglaries per month is 3000.

A null hypothesis is a hypothesis that claims that there is no significant relationship between two variables. The term "null" implies that no effect exists or that the effect is negligible. The null hypothesis is typically utilized in scientific research and experiments. It is also utilized in statistical studies, such as those investigating cause-and-effect relationships or the effects of a treatment or intervention.

The null hypothesis of a crime reporter regarding 3000 burglaries per month is that there is no significant difference between the observed results and what is expected or hypothesized. This is because 3000 burglaries per month is the average, and the null hypothesis aims to verify whether this is the actual result.

Therefore, a crime reporter's null hypothesis is:H0: The actual number of burglaries per month is 3000.

To learn more about null hypothesis refer :

https://brainly.com/question/16261813

#SPJ11

Given the right triangle below, what is the measure of angle G

Answers

Therefore, the measure of angle G in the right triangle is approximately 31.0 degrees.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to study the properties and behavior of triangles, and is also widely used in fields such as engineering, physics, surveying, and navigation. The three main trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions relate the ratios of the sides of a right triangle to the angles of the triangle.  Trigonometry also involves other concepts such as the Pythagorean theorem, which relates the sides of a right triangle, and the unit circle, which is a circle of radius 1 used to define trigonometric functions of angles beyond 90 degrees. Trigonometry is widely used in a variety of applications, such as calculating the heights of buildings and mountains, designing bridges and other structures, and predicting the motion of objects in physics and engineering.

Here,

In a right triangle, the tangent of an acute angle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.

Using this formula, we can find the tangent of angle G:

tan(G) = opposite / adjacent

tan(G) = 6 / 10

tan(G) = 0.6

To find the measure of angle G, we need to take the inverse tangent (or arctangent) of 0.6:

G = tan⁻¹(0.6)

G ≈ 31.0 degrees

To know more about trigonometry,

https://brainly.com/question/26719838

#SPJ1

can you guys help me with this

Answers

Answer:

b all real numbers are greater then or equal-2

Other Questions
what is the function of the promoter in a bacterial transcription unit? One of the stable isotopes of lithium has 3 protons and 4 neutrons, so its atomic mass is 7. Assume that a lithium atom initially at rest radiates a photon of energy 1.8488 eV and recoils.How long does it take for the recoiling atom to travel 1 mm? Assume that the lithium atom travels in a straight line without any collisions.Note: 1 amu = 1.66 10-27 kgt = The cost of capital for two mutually exclusive projects that are being considered is 8%. Project K has an IRR of 20% while Project R's IRR is 15%. The projects have the same NPV at the 8% current cost of capital. However, you believe that money costs and thus your cost of capital will also increase. You also think that the projects will not be funded until the cost of capital has increased, and their cash flows will not be affected by the change in economic conditions. Under these conditions, which of the following statements is CORRECT?a. You should recommend Project R, because at the new cost of capital it will have the higher NPV.b. You should delay a decision until you have more information on the projects, even if this means that a competitor might come in and capture this market.c. You should reject both projects because they will both have negative NPVs under the new conditions.d. You should recommend Project K because it has the higher IRR and will continue to have the higher IRR even at the new cost of capital.e. You should recommend Project K, because at the new cost of capital it will have the higher NPV. -2,1,4,7 general term See worksheet bellow!!! Social control can best be described as the techniques and strategies for preventing ______ behavior in any group or society. What conditioning technique have psychologists used to promote personal growth? A. operant conditioning B. counterconditioning C. discrimination D. observational learning the chain ganglia of the question blank 1 of 1 type your answer... division of the autonomic nervous system lie near the spinal cord. a uniform meter stick is in static rotational equilibrium when a mass of 220 g is suspended from the 5 cm mark, a mass of 120 g is suspended from the 90 cm mark, and the support stand is placed at the 40 cm mark. what is the mass of the meter stick? what is the hybridization of the oxygen atom in a water molecule? an aqueous solution is known to contain pb2 , cu2 , and na ions. treatment of the sample with both naoh and licl solution produces a precipitate. which of the metal cations does the solution contain? explain your response According to Schaie's research, the cross-sectional approach shows a ______ in inductive reasoning with age; while the longitudinal approach shows a ______ of inductive reasoning in middle adulthood. why does tom attack myrtle at the end of the party Why is pi important in math? a cell with two complete sets of chromosomes is a cell. what are the relation between point and circle assume a marketing campaign targets the market of consumers who have already purchased their product. which market segment is the company targeting? Place the steps of the marketing research approach in the correct order. NOTE: The first step should be the top item in your list.1. Define the problem2. Develop the research plan3. Collect relevant information4. Develop findings5. Take marketing actions Alice holds a small battery operated device used for tuning instruments that emits the frequency of middle C (262 Hz) while walking with a constant speed of 4.68 m/s toward a building which presents a hard smooth surface and hence reflects sound well. (Use343 m/s as the speed of sound in air.)(a) Determine the beat frequency Alice observes between the device and its echo. (Enter your answer to at least 1 decimal place.)(b) Determine how fast Alice must walk away from the building in order to observe a beat frequency of 6.19 Hz. jem is changing and growing up and trying to live up to the idea of being a gentlemen, what does this idea mean?