Solve the system of equations by using substitution. ​ \mathrm{y}=2\mathrm{x}+3\newline \mathrm{y}=\mathrm{x}+2y=2x+3 y=x+2 ​ \left(\mathrm{x},\mathrm{y}\right) =(x,y)=

Therefore, the 90% confidence interval for the mean height of the population of female runners is (64.77, 66.83) inches.

A confidence interval is a range of values that provides an estimate of the unknown population parameter with a certain level of confidence. The confidence level represents the percentage of times that the true population parameter will be contained within the interval, based on repeated sampling.

a) Using a t-distribution with 11 degrees of freedom (n-1), and a 90% confidence level, the t-value is 1.796.

The left boundary of the confidence interval is:

65.80 - (1.796 * (1.95 / √(12))) = 64.77 inches (rounded to two decimal places)

b) The right boundary of the confidence interval is:

65.80 + (1.796 * (1.95 / √(12))) = 66.83 inches (rounded to two decimal places)

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The method of proof used here is a proof by contradiction. We start by assuming that n2 + 3n + 2 is not an even integer, and show that it is not possible for this statement to be true. We then use this to conclude that our original assumption must be false, and thus n2 + 3n + 2 must be an even integer.

To begin, assume that n2 + 3n + 2 is not an even integer. We can represent this statement as "n2 + 3n + 2 = 2k+1, for some integer k." Since the left-hand side of this equation is clearly an even integer, we know that the right-hand side must also be an even integer. This leads to a contradiction, since the right-hand side of the equation is an odd integer.

Therefore, our initial assumption - that n2 + 3n + 2 is not an even integer - must be false. Since the negp-hat is the best estimator of the population mean. true falesation of this statement is true, we have proven that n2 + 3n + 2 must be an even integer.

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The number of cruise passengers must there have been in 2017 is  26.7 million.

The term "percentage" comes from the Latin phrase "per centum," meaning "by the hundred." Percentages represent fractions with a denominator of 100. In other terms, it is the relationship between portion and whole in which the value of the whole is always assumed to be 100.

Now according to the question;

Let x represent the total number for cruise passengers during 2017.

In 2018, a 6.7% rise in x results in 28.5 million cruise passengers.

So, 106.7 % of x = 28.5

\(\begin{aligned}&\frac{106.7}{100} * x=28.5 \\&\frac{106.7 x}{100}=28.5\end{aligned}\)

Multiplying both sides by 100;

\(\begin{aligned}&\frac{106.7 x}{100} * 100=28.5 * 100 \\&106.7 x=2850\end{aligned}\)

Dividing both sides by 106.7;

\(\frac{106.7 x}{106.7}=\frac{2850}{106.7}\)

x = 26.7

Therefore, the number of cruise passengers in 2017 must have ranged from 26.7 million.

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Answer:

Step-by-step explanation:

10+10+20

5+5=10

6+4=10

10+10=20

Answer:

the person above me is incorrect

To write an equation from a description given in words, you first have to identify and define the variable. Then you would identify the coefficient, constants, and operations between the terms. Finally, you can translate to write the equation.

\(\displaystyle\\\lim_{x\to\infty}\left(1-\dfrac{2}{3x}\right)^x=\lim_{x\to\infty}\left(\left(1+\left(-\dfrac{2}{3x}\right)\right)^{-3x/2}\right)^{-2/3}=e^{-2/3}=\dfrac{1}{e^{2/3}}\)

Evaluating at infinity, we have:

         \(\displaystyle \lim_{x \to \infty}{\left( 1 - \frac{2}{3x} \right)^x = \left(1 - \frac{2}{\infty} \right)^{\infty} = 1^{\infty}\)

Therefore, we must perform an algebraic manipulation to obtain an expression similar to the definition of e. To do so, we first modify the expression inside the parentheses (and denote the limit as L):

       \(\displaystyle L = \lim_{x \to \infty}{\left( 1 - \frac{2}{3x} \right)^x = \lim_{x \to \infty}{\left( 1 + \frac{2}{-3x} \right)^x = \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^x\)

So in the exponent we must have \(\bf{-\tfrac{3}{2}x }\) somehow. Note that this is achieved by doing:

                \(\displaystyle L = \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^x = \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^{\left(-\frac{2}{3}\right)\left(-\frac{3}{2}\right)x}\)

Then we use properties of exponents:

          \(\displaystyle L = \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^{\left(-\frac{2}{3}\right)\left(-\frac{3}{2}\right)x} = \left[ \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^{-\frac{3}{2}x} \right]^{-\frac{2}{3}}\)

We can now calculate the limit (noting that what is inside the square brackets is the definition of e with n = \(\bf{-\tfrac{3}{2}x}\)):

\(\displaystyle L = \left[ \lim_{x \to \infty}{\left( 1 + \frac{1}{-\frac{3}{2}x} \right)^{-\frac{3}{2}x} \right]^{-\frac{2}{3}} = e^{-\frac{2}{3}} = \frac{1}{e^{2/3}} = \frac{1}{\sqrt[3]{e^2}}\)

Yes, the implications of leaving farm fields unused for the economy's PPF diagram can be seen in the output of agricultural products.

The PPF diagram shows the maximum output of two products that an economy can produce at a given time, and it is shaped like a curve. When farm fields are left unused, the amount of agricultural products that can be produced is decreased, resulting in a shift in the PPF curve inwards. This means that the economy has to sacrifice other goods to maintain the same level of production of agricultural products, leading to an opportunity cost. Thus, leaving farm fields unused has implications for the economy's PPF diagram, as it reduces the output of agricultural products, resulting in a shift in the PPF curve inwards.

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The lac curve, also known as the envelope curve, is a curve that shows the maximum amount of work that can be done in a given period of time.

It is defined by the equation: W = min {W1 + W2, W3, W4, ..., Wn}, where W1, W2, W3, W4, ..., and Wn are the individual work tasks. The envelope curve is called such because it forms an envelope that encompasses all of the individual tasks on the graph, visually representing the maximum amount of work that can be done within the given timeline. This curve can be used to assess the efficiency of a task or project, as well as to analyze the impact of changes in the workload, deadlines, and resources.

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Answer: 1224

Step-by-step explanation: 153 x 8 = 1224

I could better answer the question with a picture.

The recursive formula for the given problem is W(n) = W(n-1) + 2 * W(n-1), with the base case W(0) = 1. This formula calculates the number of n-letter "words" that can be created from an unlimited supply of 'a's, 'b's, and 'c's,

To derive the recursive formula, we consider two cases for the first letter of the word: either it is an 'a' or it is not. If the first letter is 'a', we need to ensure that the remaining (n-1) letters form a word with an even number of 'a's. Therefore, the number of words in this case is equal to W(n-1), as we are recursively solving for the remaining letters.

If the first letter is not 'a', we have the freedom to ch

oose from 'b' or 'c'. In this case, we have two options for each of the remaining (n-1) letters, resulting in 2 * W(n-1) possibilities. By summing these two cases, we obtain the recursive formula W(n) = W(n-1) + 2 * W(n-1), which calculates the total number of n-letter words satisfying the given criteria.

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\({ \qquad \qquad \huge \rm \underline{ \underline{ \Répondre}}} \)

lets find the equation of line in two point form, considering points (0 , 0) and (-3 , 4)

\(\qquad \rm\dashrightarrow \:y - 0= \dfrac{4 - 0}{ - 3 - 0} (x -0)\)

\(\qquad \rm\dashrightarrow \:y = - \dfrac{4 }{ 3 } x \)

That's the required equation ~

You can also simply it as :

\(\qquad \rm\dashrightarrow \:3y= - 4x\)

\(\qquad \rm\dashrightarrow \:4x + 3y = 0\)

Answer:

x = - 1, y = 6

Step-by-step explanation:

Given the 2 equations

y = - 2x + 4 → (1)

y = 6x + 12 → (2)

Substitute y = 6x + 12 into (1)

6x + 12 = - 2x + 4 ( add 2x to both sides )

8x + 12 = 4 ( subtract 12 from both sides )

8x = - 8 ( divide both sides by 8 )

x = - 1

Substitute x = - 1 into either of the 2 equations and solve for y

Substituting into (2)

y = 6(- 1) + 12 = - 6 + 12 = 6

Solution is (- 1, 6 )

Answer:

y=sqrt(x+12)

i hope this helped and have a nice day/night :)

Answer:

Step-by-step explanation:

Two possible equations, depending on how you read the question.

1. Is there a shipping and handling per disc?

If so:

\(C = 13n + 1.95n\)

2. Shipping and handling is only charged once?

If so:

\(C=13n+1.95\)

The distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

Given: height of helicopter = 300√3 feet from the ground.

To find: Distance between zoo and library.

Finding:

(Refer to the image attached.)

Let the distance from the plane to the zoo and library be d1 and d2 respectively.

Then, with the help of concepts of applications of trigonometry,

\(tan(60) = \frac{300\sqrt{3}}{d1}\)

=> \(\sqrt{3}=\frac{300\sqrt{3}}{d1}\)

=> d1 = 300 feet

\(tan(30) = \frac{300\sqrt{3}}{d2}\)

=> \(\frac{1}{\sqrt{3}}=\frac{300\sqrt{3}}{d2}\)

=> d2 = 300 (3) = 900 feet

The distance between zoo and library = d2 - d1 = 900 - 300 = 600 feet.

Hence, the distance between the zoo and library is 600 feet, as seen with the help of concept of applications of trigonometry.

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The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

A collection of one or more linear equations containing the same variables is known as a system of linear equations (or linear system).

Formation of the linear equation for the drinks bought by Maria:

The total number of drinks bought by the Maria is 13.

Lets say 'm' represents the number of medium drink.

's' represents the number of small drink.

Total drinks comprises of medium drinks and small drinks.

Thus,

s + m = 13, is the first linear equation.

Now medium drinks cost $3.

Total cost for purchasing medium drinks = (price of one medium drink)×(total number of medium drinks)

Total price for medium drinks = 3×m

Similarly,

Total cost for purchasing small drinks = (price of one small drink)×(total number of small drinks)

Total price for small drinks = 2×s

Total cost = total cost of medium drink + total cost of small drink

          32  = 3×m + 2×s, is second linear equation.

From equation first substitute the value of 'm' in second equation to fine the total number of drink.

32 = 3×(13 - s) + 2×s

32 = 39 - 3s + 22

s = 7

Put s = 7 in first equation and calculate 'm'.

m = 13 -7

m = 6

Therefore, The total number of small drinks 's' bought by Maria is 7.

The total number of medium drinks 'm' drinks bought by Maria is 6.

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Answer:

7/12 chance

Step-by-step explanation:

(1 2 3 4 5 6)

(1 2 3 4 5 6)

All the possibilities:

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 18 odd sums.

(1, 1) (2, 1) (3, 1) (4, 1) (5, 1) (6, 1)

(1, 2) (2, 2) (3, 2) (4, 2) (5, 2) (6, 2)

(1, 3) (2, 3) (3, 3) (4, 3) (5, 3) (6, 3)

(1, 4) (2, 4) (3, 4) (4, 4) (5, 4) (6, 4)

(1, 5) (2, 5) (3, 5) (4, 5) (5, 5) (6, 5)

(1, 6) (2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

There are 3 possibilities whose sums add up to 10.

Since there are 36 total possibilities and 21 numbers that fit the rule of having an odd sum or a sum of 10. There is a 21/36 chance or simplified, 7/12 chance.

The value of the expression 12.7 / 8 + 9 / 10 + 6 / 5.239 / 40 is approximately 2.5161.

To determine how many chickens will lay 24 eggs in 24 hours, we can set up a proportion based on the given information.

Given:

- Two chickens lay 6 eggs in 24 hours.

Let's represent the number of chickens as "x" that will lay 24 eggs in 24 hours.

Proportion: (number of chickens)/(number of eggs) = (number of chickens)/(number of eggs)

We can set up the proportion as follows:

2/6 = x/24

To solve for x, we can cross-multiply:

2 * 24 = 6 * x

48 = 6x

Now, let's solve for x by dividing both sides of the equation by 6:

48/6 = x

8 = x

Therefore, 8 chickens will lay 24 eggs in 24 hours.

Now, let's evaluate the expression: 12.7 / 8 + 9 / 10 + 6 / 5.239 / 40

To simplify this expression, we'll follow the order of operations (PEMDAS/BODMAS):

1. Divide 12.7 by 8: 12.7/8 = 1.5875

2. Divide 9 by 10: 9/10 = 0.9

3. Divide 6 by 5.239: 6/5.239 = 1.1444

4. Divide 1.1444 by 40: 1.1444/40 = 0.0286

Now, let's add the results together:

1.5875 + 0.9 + 0.0286 = 2.5161

Therefore, the value of the expression 12.7 / 8 + 9 / 10 + 6 / 5.239 / 40 is approximately 2.5161.

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Answer:

Calculus and other mathematical domains that use these irrational numbers are used a lot in real life. Irrational Numbers are used indirectly.

Step-by-step explanation:

Given information: Mass of dolphin, m = 1800 N; Height of jump, h = 2.10 m.

The gravitational potential energy of the dolphin can be calculated as follows: Gravitational potential energy = mgh where, m is the mass of the dolphin, g is the acceleration due to gravity, and h is the height of the jump.

Given that the dolphin jumps from the water, its initial potential energy is zero. Hence, the total energy of the dolphin is equal to the potential energy at the highest point. At this point, the kinetic energy of the dolphin is also zero. Therefore, the energy conservation equation can be written as follows: mg h = (1/2)mv²where, v is the velocity of the dolphin just before it jumps out of the water.  

Solving for v, we get v = sqrt(2gh)where sqrt denotes the square root, g is the acceleration due to gravity, and h is the height of the jump. Substituting the given values, we get v = sqrt(2 x 9.8 x 2.10)v = 6.22 m/s Therefore, the dolphin must be moving at a speed of 6.22 m/s as it leaves the water in order to jump to a height of 2.10 m.

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The best estimate of the magnitude of the box's acceleration is equal to: B. 11 m/s².

In order to determine the magnitude of the acceleration of this box, we would first of all calculate the magnitude of the kinetic frictional force.

Mathematically, the kinetic frictional force that is acting on a physical body can be calculated by using this equation:

F = μkN = μk(mg)

Where:

Substituting the given parameters into the formula, we have;

F = 0.20 × 2.0 × 9.81

F = 3.924 Newton.

By applying Newton's second law of motion, the net force is given by:

∑Fx = Applied force - kinetic frictional force = ma

Acceleration, a = [Applied force - kinetic frictional force]/m

Acceleration, a = [25 - 3.924]/2

Acceleration, a = 21.076/2

Acceleration, a = 10.538 ≈ 11 m/s²

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\(\measuredangle A\cong \measuredangle E\implies 112=16x\implies \cfrac{112}{16}=x\implies \boxed{7=x} \\\\[-0.35em] ~\dotfill\\\\ \overline{MS}\cong \overline{NR}\implies 41=3x+5y\implies 41=3(7)+5y\implies 41=21+5y \\\\\\ 20=5y\implies \cfrac{20}{5}=y\implies \boxed{4=y}\)

Using tha basic multiplication and division, Stan will need 960 sprinkles to make 60 cookies.

In the branch of mathematics known as algebra, a situation is described using mathematical symbols, variables, and arithmetic operations like addition, subtraction, multiplication, and division that produce meaningful mathematical expressions.

The sprinkles needed for 1 cookie are given by

24 cookies need sprinkles = 384

1 cookie will need sprinkles = 384 ÷ 24

= 16 sprinkles

Now, sprinkles needed for 60 cookies are given by

1 cookie needs sprinkles = 16

60 cookies will need sprinkles = 16 × 60

= 960 sprinkles

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The correct question is:

"Stan's cookie recipe makes 24 cookies and calls for exactly 384 sprinkles. He is wondering how many sprinkles (p) he will need to make 60 cookies. He assumes each cookie will have the same number of sprinkles. How many sprinkles does Stan need to make 60 cookies?"

Answer:

20

Step-by-step explanation:

I'm pretty sure its 20 but I could be wrong but 20 is my best guess.

Answer:

16 of the 33 plays none.

Step-by-step explanation:

From the list, we get that 18 students play football, 1 basketball, and 7 both.

What we need to do here is add up 18 and 1

then we subtract 19 by 7 to cancel out the people who play both

and then subtract the total number of 33 by 17,

which gives you 16.

Answer:

1. 3/5

2. 4/5

3. 4/3

Answer: i think it is either A B C or D

Step-by-step explanation: So i know that there are 4 answers so that means one of the four answers are correct........ well i hope that one is correct

Answer: it equals A

Step-by-step explanation:

Answer:Me!" (stylized in all caps) is a song recorded by American singer-songwriter Taylor Swift featuring American singer Brendon Urie of Panic! at the Disco. It was released on April 26, 2019, through Republic Records, as Swift's first single after signing with the label. The song was revealed and released at the end of a thirteen-day countdown, as the lead single from her seventh studio album, Lover (2019). It was written by Swift, Joel Little and Urie, and produced by Swift and Little. The song was recorded at Electric Lady Studios, New York City and Golden Age West in Auckland, New Zealand in 2018. "Me!" is a cheery, campy bubblegum pop and synth-pop duet, driven by a marching band drumline. It is about embracing one's individuality, with lyrics on self-affirmation and self-love.

"Me!" debuted at number 100 on the US Billboard Hot 100, before surging up to number two the next week, breaking the record for the biggest single-week jump in the chart's history. The song reached the top five in several other countries. It broke several Amazon Music records, including the most first-day streams, most first-week streams and most on-demand voice requests with Alexa of a single debut on the platform. Upon release, the song received mixed reviews from music critics, who were favorable towards the bubbly production and the duo's vocal chemistry, but divided over the lyrics—some complimented the tongue-in-cheek songwriting, while others called it weak. "Me!" has since been certified double-platinum by Recording Industry As

Step-by-step explanation:

Answer:

D. Group A, because four children in the group have the least forearm length of 10 inches.

Step-by-step explanation:

It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A.

So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.

In order to verify the claim let us find the mean

Mean of Group A

Mean of Group B

So, group A has shorter average forearm length.

The purpose of this test is to evaluate the effects of rotational acceleration on the semicircular ducts and dynamic equilibrium. This test is called Rotational Acceleration Test.

The purpose of the rotational acceleration test is to assess how the semicircular ducts and the body's dynamic equilibrium respond to rotational movements. The semicircular ducts are part of the vestibular system, which is responsible for detecting changes in head position and rotational movements.

During the test, the individual is subjected to controlled rotational acceleration, usually in a specially designed chair or device. The rotational acceleration induces a sense of spinning or movement, stimulating the semicircular ducts.

By observing the individual's responses, such as eye movements or changes in body posture, healthcare professionals can gather information about the functioning of the vestibular system and the body's ability to maintain balance.

This test is particularly useful in diagnosing disorders of the vestibular system, such as vestibular dysfunction, vertigo, or balance disorders. It helps healthcare providers determine the extent of the impairment and develop appropriate treatment plans or interventions to improve balance and reduce symptoms.

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Answer:

\( \frac{dy}{dx} = 1,75\)

Certify Completion Icon Tries remaining: 3 A high school has 52 players on the football team. The summary of the players' weights is given in the box plot. The median weight of the players on the football team is 160 pounds.

The box plot shows that the median weight of the players is the middle value of the distribution. In this case, the median weight is halfway between the 26th and 27th players, which is 160 pounds.

The box plot also shows that the minimum weight of the players is 150 pounds and the maximum weight is 212 pounds. The interquartile range, which is the range of the middle 50% of the data, is 20 pounds.

In conclusion, the median weight of the players on the football team is 160 pounds. This means that half of the players on the team weigh more than 160 pounds and half of the players weigh less than 160 pounds.

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