a ball travel with the velocity of (2,1) with wind blowing in the direction (3,-4) with respect to some coordinates axes .find the size of the velocity of the ball in the direction of the wind?

The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.

Given that,

The central limit theorem is important in statistics because it allows us to use the Normal distribution to find probabilities involving the sample mean,

In layman's words, the theorem asserts that regardless of the form of the initial population distribution, the sampling distribution of the mean tends to resemble a normal distribution as the sample size rises.

Statistics benefits from the Central Limit Theorem because it makes it safe to assume that the sampling distribution of the mean will be typically normal. As we will see in the next section, this means that we can benefit from statistical methods that presume a normal distribution.

The distribution of people's heights within a population is one illustration of how the central limit theorem is put to use. Even though the population's distribution of heights is not normal, when we sample this population, the distribution of the sample averages will be roughly normal.

Therefore,

The central limit theorem's not needed when the original distribution is normal, the distribution of the sample mean is always normal in that case. So, option (a) is correct. If the sample size is reasonably large (for any population) is correct.

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The probability of selecting a white rabbit on the second draw, given that the first rabbit selected was a black rabbit is 3/5.

P(B∩W) = 1/4  getting a black and a white rabbit

P(B) = 5/12  getting a black rabbit

 P(W/B)

= P(B∩W) / P(B)

= (1/4) / (5/12)

= 12/20

= 3/5

Therefore, the conditional probability is 3/5.

Conditional probability is the chance of an event A occurring when another event B in relation to A has previously occurred. P(A|B) represents it. As seen in the picture above, S represents sample space, and A and B represent events.

The potential of an event or outcome occurring based on the existence of a preceding event or outcome is known as conditional probability. It is computed by multiplying the preceding event's probability by the renewed probability of the next, or conditional, occurrence.

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So, the ordered pair which lies on the graph of the function y = -2x + 1 is (3,-5)

We will use the substitution method and check for all the ordered pair which are given

If the ordered pair lies on the graph, then it should satisfy the function.

So,

Given,

y = -2x+1

First check for (0,-2)

x=0, y=-2

Substitute the values,

y = -2x+1

-2=-2(0)+1

-2=1

It is false.

Next check for (2,-2)

x=2, y=-2

Substitute the values,

y = -2x+1

-2=-2(2)+1

-2=-3

It is false.

Next check for (3,-5)

x=3, y=-5

Substitute the values,

y = -2x+1

-5=-2(3)+1

-5=-5

It is true.

Next check for (5,2)

x=5, y=2

Substitute the values,

y = -2x+1

2=-2(5)+1

2=9

It is false.

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c. A greater proportion of adolescent girls with anorexia nervosa live in the South than live in the other regions when compared to the general US population.

Null Hypothesis, [tex]H_{0}[/tex] : All proportions are the same  

Alternative Hypothesis, [tex]H_{1}[/tex]: At least two of the proportions are not the same

The alternative and null are both population-based assertions. The reason for this is that the purpose of hypothesis testing is to draw conclusions about a population from a sample.

The null and alternative hypotheses are two competing claims that researchers weigh the evidence for and against using a statistical test:

Null hypothesis: There’s no effect on the population.

Alternative hypothesis: There’s an effect on the population.

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I would select company 2 because it has lower cost and tax amount for complete fencing job.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Let, f = Total feet of the fence

For company 1 :

Given that 25 $

eq : (f-1)x25 + 2500

 =  (100 -1)25 + 2500

 =  99 x 25 = 2500

 =  4975 $

For company 2 :

Given that 39 $

Now if company 1 charges 7 % taxes then,

4975 x 7%

=  4975 + 348.25

=  5323.25$

and for company 2

39 x 7%

=  39 + 2.73

=  41.93 $

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Answer:

See below and attached graph

Step-by-step explanation:

If you are using a graphing calculator it is a breeze. You write down the equation as it is and it should plot it, depending on what calculator you use.

If you are doing this manually here are the steps
We are given y - 2 = 3(x-2)

Expand the brackets on the right hand side
3(x - 2) = 3x - 6

So the original equation becomes
y - 2 = 3x - 6

Adding 2 to both sides
y - 2 + 2 = 3x -6 + 2

y = 3x - 4   [1]

This form of equation is known as a slope-intercept form of the line

We need two points to plot a line. This can be done by choosing a value for x, finding the y value which gives one point. Then repeat for another value of x to get y for that value giving another point. Draw a straight line through both points

Point 1
Let's choose x = 2 and plug this into the equation [1]
y = 3·2 - 4 = 6- 4 = 2.
So (2, 2) is one point on the graph

Point 2

Choose another value for x, say x = 4

y = 3·4 - 4

y = 12-4

y = 8

So (4, 8) is another point

Draw a line through these two points

The value of y(0.4) is 1.04384484247985 using  Runge-Kutta method of fourth order .

What is  Runge-Kutta method of fourth order ?

The RK4 method, also known as the fourth-order Runge-Kutta method, is the Runge Kutta technique most frequently employed to get the answer to a differential equation. For a given point x, the Runge-Kutta technique returns an approximation of the value of y. The Runge Kutta RK4 method can only be used to solve first order ODEs.

The step size is h = 0.1

f(x,y) = (x²+y²)/10

Step 1:

x₁ = 0 + 0.1 = 0.1

k₁ =f(0,1) = 0.1

k₂ = f(1/20, 1.005) = 0.1012525

k₃ = f(1/20, 1.005062625) =0.101265088017189

k₄ = f(1/10, 1.01012650880172) = 0.103035556378395

y₁ = 1+ (1/10)/6 +(0.1 + 2⋅0.1012525 + 2⋅0.101265088017189 + 0.103035556378395) = 1.01013451220688

Step 2:

x₂ = x₁ + h = 1/5

k₁ =f(1/10,1.01013451220688)=0.103037173275143

k₂ = f(3/20,1.01528637087064) = 0.105330641487567

k₃ = f(3/20, 1.01540104428126) = 0.105353928072747

k₄ = f(1/5, 1.02066990501415) = 0.10817670550016

y₂ =1.01013451220688 + (1/10)/6 +(0.103037173275143 + 2⋅0.105330641487567 + 2⋅0.105353928072747 + 0.10817670550016) = 1.02067756250514

Step 3:

x₃ = x₂ + h = 3/10

k₁ =f(1/5, 1.02067756250514)=0.108178268660144

k₂ = f(1/4,1.02608647593815)=0.111535345610318

k₃ = f(1/4, 1.02625432978566)=0.111569794940382

k₄ = f(3/10, 1.03183454199918)=0.115468252206266

y₃ =1.02067756250514 + (1/10)/6 (0.108178268660144 + 2⋅0.111535345610318 + 2⋅0.111569794940382 + 0.115468252206266) = 1.03184184253794

Step 4:

x₄ = x₃ + h = 2/5

k₁ =f(3/10, 1.03184184253794) = 0.115469758801209

k₂ = f(7/20,1.037615330478)=0.119914557404297

k₃ = f(7/20, 1.03783757040816)=0.119960682255071

k₄ = f(2/5, 1.04383791076345)=0.1249597583947

y₄ = 1.03184184253794 + (1/10)/6 (0.115469758801209 + 2⋅0.119914557404297 + 2⋅0.119960682255071 + 0.1249597583947) = 1.04384484247985

y(0.4) ≈ 1.04384484247985

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Answer:x+19-x+10 is equal to 29.

The correct statements regarding the transformations to the volumes are given as follows:

1. A cone's radius increases x 3: -> The cone's volume will increase x 9.

2. A cone's height increases x 3: -> The cone's volume will increase x 3

3. A sphere's radius increases x 3 -> The sphere's volume will increase x 27.

4. A cylinder's radius increases x 6 -> The cylinders volume will increase x 36.

The volume of a cone of radius r and height h is given as follows:

V = πr²h/3.

Then the scale factors are considered as follows:

The volume of an sphere of radius r is given as follows:

V = 4πr³/3.

Then when the radius is multiplied by 3, the volume is multiplied by 27, as 3³ = 27, and the radius is cubed in the equation.

The volume of a cylinder of radius r and height h is given as follows:

V = πr²h.

Then if the radius is multiplied by 6, the volume is multiplied by 36, as the variable r is squared in the equation for the volume.

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The equivalent expression for the given expression is 29/3.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given mixed fraction [tex]9\frac{2}{3}[/tex].

There are equivalent improper fractions for all mixed numbers. By multiplying the integer by the denominator and then adding the numerator, they are transformed. The numerator will not change.

Convert mixed fraction to improper fraction as follows

Improper fraction = [(Numerator × Denominator)+Numerator]/Denominator

[(9×3)+2]/3

=[27+2]/3

= 29/3

Therefore, the equivalent fraction for the given mixed fraction is 29/3.

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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : [tex]8x^{3}-1[/tex]

Degree of polynomial =3

The expression is a Cubic Expression.

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Observing the nature of the provided equation and the degree of the polynomial , The answer is Cubic.

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The highest degree of a polynomial's monomials (individual terms) with non-zero coefficients is referred to as the polynomial's degree in mathematics.

Expression : 8x³ - 1

Degree of polynomial =3

The expression is a Cubic Expression.

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We know that the required value of y is -17 using the slope formula.

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

The slope of a line can be used to gauge how steep it is.

The slope is theoretically determined as "rise over run" (change in y divided by change in x).

So, we have the slope 5/2.

The points are: (−6, y) and (4, 8)

The slope formula: m = y2 - y1/x2 - x1

Now, insert the values and calculate y as follows:

m = y2 - y1/x2 - x1

5/2 = 8 - y/4 + 6

5/2 = 8 - y/10

5/2 * 10 = 8 - y

25 = 8 - y

-y = 25 - 8

-y = 17

y = -17

Therefore, we know that the required value of y is -17 using the slope formula.

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After doing the equation the original price of the tie is $20.

What do you mean by algebraic expression?

An algebraic expression is the idea of ​​using letters or alphabets to represent numbers without specifying the actual values. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here. An algebraic expression can be a combination of variables and constants. Anything that is prepended to a variable and multiplied by it is a coefficient.

It is given that Duke bought the shirt and tie at half off rate.

Cost of shirt = $24

Total money paid by Duke = $22

Let cost of tie be x

According to question:

[tex]24\times \frac{1}{2}+ x\times \frac{1}{2}=22[/tex]

12 + [tex]x\times \frac{1}{2}[/tex] = 22

[tex]x\times \frac{1}{2}[/tex] = 22 - 12

x = 10 × 2

x = 20

Therefore , cost of tie is $20.

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The probability that the other side of the card is not green is 60%

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

P(green) = 40%

Using the complement rule of probabilities, we have

P(not green) = 1 - P(green)

Substitute the known values in the above equation, so, we have the following representation

P(not green) = 1 - 40%

Evaluate

P(not green) = 60%

Hence, the probability is 60%

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Complete question

The probability of a green face is 40%. If you're shown a card with a green face showing what is the probability that the other side of the card is not green

Answer:

Hope this helps!

It is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].

When two variables are added, we have that:

The variances for each variable are given as follows:

Then the standard deviation of the total income, which is the combination of the income of the husband and of the wife, is calculated as follows:

[tex]\sigma = \sqrt{\sigma_x^2 + \sigma_y^2}[/tex]

The variance is the square root of the variance, hence it is obtained as follows:

[tex](\sigma)^2 = (\sqrt{\sigma_x^2 + \sigma_y^2})^2 = \sigma_x^2 + \sigma_y^2[/tex]

Which means that it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].

The problem asks if it is reasonable to take the variance of the total income to be [tex]\sigma_x^2 + \sigma_y^2[/tex].

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In the case where a=78, b=716, c=0.8, and d=14, the simplest form of a mixed number is -117/640.

The smallest equivalent fraction of the number is the form that is the simplest. How to find the most basic form: In the numerator and denominator, look for shared factors. Examine the fraction to see if one of the numbers is a prime number.

The term "reduced form" refers to the fraction's simplest form. As an illustration, the simplest form of a fraction with a common component of 1 is 34 However, while 2/4 can be further condensed and expressed as 12, it is not the most basic form.

When the top and bottom of a fraction cannot be any smaller while remaining whole numbers, it is said to be in its simplest form.

b a + c d

b= -7/16

a= 7/8

c= 08.(4/5)

d= 1/4

It can therefore be calculated as follows.

-7/16×7/8 + 4/5×1/4

-49/128 + 1/5

-246+128/640

= -117/640

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The two equations that equal Willie's number are given as follows:

Jennie's number is unknown, hence we use the variable x to refer to her number.

Robbie picked a number that is nine more than four times Jennie's number, hence:

y = 9 + 4x.

(using y to refer to Robbie's number).

Willie picked a number that is two less than three times Robbie's number, hence:

n = 3y - 2.

(using n to refer to Willie's number).

Considering the expression for y, the second expression that describes Willie's number is given as follows:

n = 3(9 + 4x) - 2

n = 12x + 25.

The problems asks foir the two expressions that equals Willie's number.

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Step-by-step explanation:

for question 1, the change in y is the highest value takeaway the lowest value.

change in y = 10 - 1 = 9

change in x = 6 - (-3) = 9

9/9 = 1

therefore m = 1, this works for all the questions

The number of country A forces in country B decreased to approximately 34,000 in 2014 from a high of about 10,000 in 2008. X represents the number of years after January 2007, this means that the amount of funding was approximately $10.5 billion in the year 2.135 years after January 2007, or approximately September 2009.

Generally, To find the year in which the amount of funding was approximately $10.5 billion, we need to solve the equation:

f(x) = 10.5

Substituting the given function for f(x), we get:

-1.384x^{2} + 5.253x + 5.517 = 10.5

We can solve this quadratic equation by using the quadratic formula:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]

where a = -1.384, b = 5.253, and c = 5.517.

Substituting these values into the formula, we get:

[tex]x = \frac{5.253 \pm \sqrt{5.253^2 - 4(-1.384)(5.517)}}{2(-1.384)}[/tex]

Simplifying this expression gives us:

[tex]x = \frac{5.253 \pm \sqrt{27.747029}}{-2.768}[/tex]

Since x represents the number of years after January 2007, we are only interested in the positive solution. Therefore, we can ignore the negative solution.

[tex]x = \frac{5.253 + \sqrt{27.747029}}{-2.768}[/tex]

Simplifying this expression further gives us:

x = 2.135

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Answer:

Step-by-step explanation:

a) 1012⁵ can be written as:

1012⁵ = 15¹² + 05¹¹ + 1*5¹º

= 5¹² + 5¹º

= 3125 + 625

= 3750

(b) 101⁵ can be written as:

101⁵ = 15⁴ + 05³ + 1*5²

= 5⁴ + 5²

= 625 + 25

= 650

(c) 1.1⁵ can be written as:

1.1⁵ = 15¹ + 15º

= 5¹ + 5º

= 25 + 5

= 30

(d) 10.21⁵ can be written as:

10.21⁵ = 15² + 05¹ + 25º + 15⁻¹

= 5² + 2*5º + 5⁻¹

= 25 + 10 + 0.2

= 35.2

(e) 210⁵ can be written as:

210⁵ = 25⁴ + 15²

= 2*625 + 25

= 1250 + 25

= 1275

According to Trigonometric Identity , tan(theta) = -5 / 13

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. The relationship between a triangle's side length and angle is expressed by a variety of specific trigonometric identities.

Sin, cos, and tan are the three fundamental trigonometric ratios. The reciprocals of sin, cos, and tan are represented by the three additional trigonometric ratios sec, cosec, and cot in trigonometry, respectively.

According to the given information

We know that

tan(theta) = 1/cot(theta)

                = 1 / -2.6

                = -1 / 2.6

                = -10 / 26

                = -5 / 13

According to Trigonometric Identity , tan(theta) = -5 / 13

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The interest accrued in the first four years is $1.69 and a half years is $0.21.

What is interest rate?

The amount that the lender charges the borrower above and beyond the principal amount is referred to as the interest rate. A person who deposits money in a bank or other financial institution also earns additional income in terms of the recipient, known as interest, taking into account the time value of money.

Given:

Jeff took out a 15 year unsubsidized loan for $9.800 to attend four years of college.

The rate is 4.3%.

We have to find the interest accrued in the first four-and-a-half years.

First to find the interest for first four years.

p = $9.800,  r  = 4.3% = 0.043,  t = 4

⇒ I = P x r x t

   I = 9.800 x 0.043 x 4

   I = 1.6856

   I = $1.69

Now to find the interest for a half years.

p = $9.800 ,  r = 4.3% = 0.043,  t = 1/2

I = p x r x t

I = 9.800 x 0.043 x 1/2

I = 0.2107

I = $0.21

Hence, the interest accrued in the first four years is $1.69 and a half years is $0.21.

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Answer:

½

pa brainliest po thanks

Answer:

Step-by-step explanation:

6 small rectangles, 3 are shaded and three are not, so half,

your answer is 1/2 (one half)

Using the two column proof, we have been able to prove that;

ΔPQR ≅ ΔTSR by AAS Congruency Postulate

A two-column proof is defined as a geometric proof that consists of a list of statements, and the reasons that we know those statements are true.

Thus, the two column proof required is as follows;

Statement 1: PR ≅ TR

Reason 1: Given

Statement 2: ∠PQR ≅ ∠TSR

Reason 2: Given

Statement 3: ∠PRQ ≅ ∠TRS

Reason 3: Opposite angles

Statement 4: ΔPQR ≅ ΔTSR

Reason 4: AAS Congruency postulate

AAS congruency postulate is one of the 5 major triangle congruency postulates that is defined as Angle-Angle-Side. This tells us that two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

We can also say that Opposite angles are defined as the angles that are directly opposite each other where two lines cross. The intersection point in this regards is called the vertex, which is the point where the lines connect to form the angle. Opposite angles are also referred to as vertical angles

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To determine if the mean reduction in blood pressure is different between the two groups, you can use a statistical test such as a two-sample t-test. This test compares the means of two groups and determines whether the difference between the means is statistically significant.

To conduct the t-test, you will need the following information:

Once you have this information, you can use a statistical software or calculator to perform the t-test and determine the p-value. The p-value is a measure of the probability that the difference between the means is due to chance.

If the p-value is less than the level of significance (5% in this case), then the difference between the means is statistically significant and you can conclude that there is a significant difference in the mean reduction in blood pressure between the two groups.

If the p-value is greater than the level of significance, then the difference between the means is not statistically significant and you cannot conclude that there is a difference in the mean reduction in blood pressure between the two groups.

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Answer:

Y=6x-12

Step-by-step explanation:

whenever the X is at zero the number across from it is the Y-intercept. and to find the slope just count how much they are increasing or decreasing by.

9 pounds of the $50 coffee should be used

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

let's let p = the pounds of coffee we need.

50p + 80(20) = 6(p+ 20)

The total price of the $50 coffee is going to be the pounds x price per pound. The total amount of coffee is the number of pounds of each added together.

From the equation above 50p + 80(20) = 60(p+ 20)

expanding the brackets and collecting like terms

50p + 1600 = 6p + 120

50p - 6p = 1200 - 1600

44p= 400

p= 9

Therefore, 9 pounds of  $50 coffee should be used

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Answer:

The answer is (x + 10)

Step-by-step explanation:

(9x + 6) - (8x - 4)

9x + 6 - 8x + 4

Rearrange it

9x - 8x + 6 + 4

Combine like terms

x + 10

Thus, The answer is (x + 10)

Answer:m

Step-by-step explanation: