What type of symmetry is shown in this picture (point, line, or rotational)? Explain your answer and identify the line of symmetry or the point of rotation.

Answer:

Problem 1: [tex]r=4[/tex]

Problem 2: [tex]r=-2\sin(\theta)[/tex]

Problem 3: [tex]r\sin(\theta)=3[/tex]

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

[tex]x=r \cos(\theta)[/tex]

[tex]y=r \sin(\theta)[/tex]

[tex]\frac{y}{x}=\tan(\theta)[/tex]

So if we make those substitution into the first equation we get:

[tex]x^2+y^2=16[/tex]

[tex](r\cos(\theta))^2+r\sin(\theta))^2=16[/tex]

[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)=16[/tex]

Factor the [tex]r^2[/tex] out:

[tex]r^2(\cos^2(\theta)+\sin^2(\theta))=16[/tex]

The following is a Pythagorean Identity: [tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex].

We will apply this identity now:

[tex]r^2=16[/tex]

This implies:

[tex]r=4 \text{ or } r=-4[/tex]

We don't need both because both of include points with radius 4.

Problem 2:

[tex]x^2+y^2+2y=0[/tex]

[tex](r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0[/tex]

[tex]r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0[/tex]

Factoring out [tex]r^2[/tex] from first two terms:

[tex]r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0[/tex]

Apply the Pythagorean Identity I mentioned above from problem 1:

[tex]r^2(1)+2r\sin(\theta)=0[/tex]

[tex]r^2+2r\sin(\theta)=0[/tex]

or if we factor out r:

[tex]r(r+2\sin(\theta))=0[/tex]

[tex]r=0 \text{ or } r=-2\sin(\theta)[/tex]

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

[tex]y=3[/tex]

[tex]r\sin(\theta)=3[/tex]

A Cartesian equation can be converted to a polar equation using trigonometric relations. For example, the equations [tex]x^2 + y^2 = 16, x^2 + y^2 + 2y = 0,[/tex]  and y = 3 can be transformed into the polar forms r = 4, r = -2sin(θ), and r = 3/cos(θ) respectively. The TI-84 calculator is recommended for these conversions.

In Mathematics, specifically in the conversion of Cartesian equations to polar equations, we have two basic formulas from trigonometry. These are r2 = x2 + y2 and tan(θ) = y/x. But for regions where x might be zero, it is advisable to remember the Cartesian-polar relations which are x = rcos(θ), y = rsin(θ).

For x2 + y2 = 16, by substituting the first relation r2 = x2 + y2 we can get the polar equation r = 4. For x2 + y2 + 2y = 0, we complete the square on the left side then apply our formulas, resulting in a polar equation of r = -2sin(θ). For y = 3, this is a horizontal line in the Cartesian coordinate system, so we use y = rsin(θ) and solve for r to give the polar equation r = 3/cos(θ).

As for a suitable calculator, the TI-84 would be a good option for these conversions as it has the functionality to convert between these forms easily.

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Answer:

Step-by-step explanation:

yes 30

Answer:

See below.

Step-by-step explanation:

Average rate of change =( R(1008) - R(1001) ) / (1008 - 1001)

=[ 12(1008) - 0.005(1008)^2 - (12(1001) - 0.005(1001)^2) ] / 7

Answer:

2

Step-by-step explanation:

Average rate of change is just the slope.

You want to find the slope of the line that goes through x=1001 and x=1008 while on R(x)=12x-0.005x^2.

So y=R(x)... R(x) will give your corresponding y values for the x's mentioned.

Just plug them in.

R(1001)=12(1001)-0.005(1001)^2=7001.995

R(1008)=12(1008)-0.005(1008)^2=7015.68

So now the question just becomes find the slope of the line that goes through

(1001,7001.995) and (1008,7015.68).

To find the slope of a line given two points: I just lined the points up and subtract vertically.  Afterwards I put the second number on top of the first number.

So let's do that!

(1008 ,  7015.68)

-(1001,    7001.995)

------------------------------

      7       13.685

So the slope also known as the average rate of change here is 13.685/7.

Putting 13.685 divided by 7 into my calculator returns the value 1.955.

This rounded to the nearest integer is 2.

Answer:

(x - 1)²/4² - (y - 2)²/2² = 1 ⇒ The bold labels are the choices

Step-by-step explanation:

* Lets explain how to solve this problem

- The equation of the hyperbola is x² - 4y² - 2x + 16y - 31 = 0

- The standard form of the equation of hyperbola is

  (x - h)²/a² - (y - k)²/b² = 1 where a > b

- So lets collect x in a bracket and make it a completing square and

  also collect y in a bracket and make it a completing square

∵ x² - 4y² - 2x + 16y - 31 = 0

∴ (x² - 2x) + (-4y² + 16y) - 31 = 0

- Take from the second bracket -4 as a common factor

∴ (x² - 2x) + -4(y² - 4y) - 31 = 0

∴ (x² - 2x) - 4(y² - 4y) - 31 = 0

- Lets make (x² - 2x) completing square

∵ √x² = x

∴ The 1st term in the bracket is x

∵ 2x ÷ 2 = x

∴ The product of the 1st term and the 2nd term is x

∵ The 1st term is x

∴ the second term = x ÷ x = 1

∴ The bracket is (x - 1)²

∵  (x - 1)² = (x² - 2x + 1)

∴ To complete the square add 1 to the bracket and subtract 1 out

   the bracket to keep the equation as it

∴ (x² - 2x + 1) - 1

- We will do the same withe bracket of y

- Lets make 4(y² - 4y) completing square

∵ √y² = y

∴ The 1st term in the bracket is x

∵ 4y ÷ 2 = 2y

∴ The product of the 1st term and the 2nd term is 2y

∵ The 1st term is y

∴ the second term = 2y ÷ y = 2

∴ The bracket is 4(y - 2)²

∵ 4(y - 2)² = 4(y² - 4y + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out

   the bracket to keep the equation as it

∴ 4[y² - 4y + 4) - 4]

- Lets put the equation after making the completing square

∴ (x - 1)² - 1 - 4[(y - 2)² - 4] - 31 = 0 ⇒ simplify

∴ (x - 1)² - 1 - 4(y - 2)² + 16 - 31 = 0 ⇒ add the numerical terms

∴ (x - 1)² - 4(y - 2)² - 16 = 0 ⇒ add 14 to both sides

∴ (x - 1)² - 4(y - 2)² = 16 ⇒ divide both sides by 16

∴ (x - 1)²/16 - (y - 2)²/4 = 1

∵ 16 = (4)² and 4 = (2)²

∴ The standard form of the equation of the hyperbola is

   (x - 1)²/4² - (y - 2)²/2² = 1

Answer:

Refer to attachment below.

Final answer:

To convert Fahrenheit (F) to Celsius (C), subtract 32 from the Fahrenheit value, then multiply by 5/9 to get the Celsius value; the formula is C = (5/9)(F - 32).

Explanation:

Converting Fahrenheit to Celsius

To solve the formula for converting temperature from degrees Fahrenheit (F) to degrees Celsius (C), we are given the formula F = (9/5)C + 32. The student needs to find the value of C. To do this, we'll follow these steps:

Isolate the term containing C by subtracting 32 from both sides of the equation, which gives us F - 32 = (9/5)C.

Then, to solve for C, multiply both sides of the equation by the reciprocal of (9/5), which is (5/9), resulting in (5/9)(F - 32) = C.

Therefore, the converted equation for Celsius is C = (5/9)(F - 32), which can be used to find the Celsius temperature corresponding to a given Fahrenheit temperature.

Answer:

The answer is 27 on edge as well!

Step-by-step explanation:

The answer is 27

This is because 15x15 is 225 plus 8x8 is 64 which is 289 and the square root of that is 17 and that is the diameter of the circle and the hypotenuse of the triangle and since the kite has two congruent sides which are both radii or half of a diameter times two would be the same as the length of the diameter which is 17 plus the two bottom sides which are both 5 and 5 plus 5 is 10 and 10 plus 17 is 27 or the perimeter of the kite.

Your Welcome!

Answer:

27

Step-by-step explanation:

im taking the test right now on edg. 2020

Answer:

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Step-by-step explanation:

Since each number is the sum of it's 2 preceding numbers thus mathematically it can be written as

[tex]F_{k^{th}}=F_{(k-2)^{th}}+F_{(k-1)^{th}}[/tex]

Fibonacci Series can be written as

1,1,2,3,5,8,13...

Answer: The following statements are true:

It is symmetrical.

The first diagonal is all 1’s.

The second diagonal is the counting numbers.

Any number in the triangle is the sum of the two numbers directly above it.

Each row adds to a power of 2.

Answer:

They are all correct

Step-by-step explanation:

Answer:

The side length is multiplied by [tex]\sqrt{2}[/tex]

Step-by-step explanation:

we know that

The area of the original square is equal to

[tex]A=9^{2}=81\ in^{2}[/tex]

If the area is doubled

then

The area of the larger square is

[tex]A1=(2)81=162\ in^{2}[/tex]

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z ----> the scale factor

x ----> the area of the larger square

y ---> the area of the original square

so

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]x=162\ in\^{2}[/tex]

[tex]y=81\ in\^{2}[/tex]

[tex]z^{2}=\frac{162}{81}[/tex]

[tex]z^{2}=2[/tex]

[tex]z=\sqrt{2}[/tex] ------> scale factor

therefore

The side length is multiplied by [tex]\sqrt{2}[/tex]

Answer:

sq root of 2

Step-by-step explanation:

that's how Mr. Burger says it is, lol.

because the area is doubled then both side lengths are multiplied by the sq root of 2.

Answer:

B

Step-by-step explanation:

In step 1, we found ∠GAC ≅ ∠AFD.

In step 2, we found ∠GAC ≅ ∠AFE.

Therefore, by transitive property of equality, ∠AFD ≅ ∠AFE.

Answer:

0.0952  or 9.52%.

Step-by-step explanation:

The standard deviation = √(40,000) = 200.

Z-scores are  917 - 800  / 200 = 0.585 and

980 - 800 / 200 = 0.90..

From the tables the required probability =

0.81594 - 0.72072

= 0.09522 (answer).

The probability of the steer's weight falling between 917lbs and 980lbs can be determined by first calculating their respective z-scores based on given mean and variance. The difference in probabilities associated with these z-scores will give the desired probability.

In this case, we are dealing with a normal distribution which is important when we are considering mean and variance. To find the probability that the weight of the steer falls between 917lbs to 980lbs, we need to first convert these weights into z-scores, because a z-score helps us understand if a data point is typical or atypical within a distribution.

Z-score is given by z = (x - μ) / σ, where μ is the mean and σ is the standard deviation, which is the square root of variance. Given that the mean (μ) is 800lbs and variance is 40,000, the standard deviation (σ) is √40,000=200.

So, the z-scores for 917 and 980 lbs are z1 = (917 - 800) / 200 = 0.585 and z2 = (980 - 800) / 200 = 0.90 respectively.

The probability that the weight of a randomly selected steer is between 917lbs and 980lbs is the probability that the z-score is between 0.585 and 0.90. We can find these values using a z-table or statistical software. The difference between these probabilities will give us the probability of a steer's weight falling between 917 and 980 lbs.

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Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square.  

Step-by-step explanation:

Answer:

The quadratic formula is derived from a quadratic equation in standard form when solving for x by completing the square. The steps involve creating a perfect square trinomial, isolating the trinomial, and taking the square root of both sides. The variable is then isolated to give the solutions to the equation.

Step-by-step explanation:

Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

i got it right on plato

Answer:

c. 172.54 pi cm^3

Step-by-step explanation:

PLATO

Answer:

Pr(the sum of the numbers rolled is either a multiple of 3 or an even number)=[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

Let A be the event "sum of numbers is multiple of 3"

and B be the event "sum is an even number".

As our dice has six sides, so the sample space of two dices will be of 36 ordered pairs.

|sample space | = 36

Out of which 11 pairs have the sum multiple of 3 and 18 pairs having sum even.

So Pr(A)= [tex]\frac{11}{36}[/tex]

and Pr(B)= [tex]\frac{18}{36}[/tex]

and Pr(A∩B) = [tex]\frac{5}{36}[/tex], as 5 pairs are common between A and B.

So now Pr(A or B)= Pr(A∪B)

                            = Pr(A)+Pr(B) - Pr(A∩B)

                            = [tex]\frac{11}{36}[/tex] + [tex]\frac{18}{36}[/tex] - [tex]\frac{5}{36}[/tex]

                            = [tex]\frac{24}{36}[/tex]

                            = [tex]\frac{2}{3}[/tex]

Answer:

2/3 and NOT mutually exclusive

Step-by-step explanation:

plato

Answer:

cos(x) = square root 2 over 2; tan(x) = 1

Step-by-step explanation:

[tex]\frac{\sqrt{2} }{2}[/tex]

was, before it was rationalized,

[tex]\frac{1}{\sqrt{2} }[/tex]

Therefore,

[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]

The side opposite the reference angle measures 1, the hypotenuse measures square root 2.  That makes the reference angle a 45 degree angle.  From there we can determine that the side adjacent to the reference angle also has a measure of 1.  Therefore,

[tex]cos(x)=\frac{1}{\sqrt{2} }=\frac{\sqrt{2} }{2}[/tex] and

since tangent is side opposite (1) over side adjacent (1),

tan(x) = 1

Answer:

Approximately 56.7%.

Step-by-step explanation:

Choose two people at random from the crowd and there will be two cases:

There's no third possible outcome. In other words, the two cases are mutually exclusive. Either the first or the second event is expected to happen. The sum of their probabilities shall equal to 1.

66 out of that 100 were rooting for the champion. The probability that both were rooting for the champion will be easier to find. The probability that the first person is rooting for the champion is equal to [tex]66/100[/tex].

After that first person was chosen from the crowd, the 65 out of the remaining 99 person in the crowd were chanting. The probability that the second person is rooting as well will equal to [tex]65/100[/tex].

Both event shall take place. The probability that both were rooting for the champion will equal to

[tex]\displaystyle \frac{66}{100} \times \frac{65}{99}[/tex].

The probability that one or zero out of the two persons were rooting will equal to

[tex]\displaystyle 1 - \frac{66}{100} \times \frac{65}{99} \approx \frac{17}{30} = 56.7\%[/tex].

Answer:

56.7% is correct.

Step-by-step explanation:

Answer:

125 minutes of calling

It will cost $32.25 when the plans cost the same.

Step-by-step explanation:

The first plan's expression would be:

11+.17x       x being the number of minutes

The second plan's expression would be:

16+.13x

You must set the expressions equal to one another. So:

11+.17x=16+.13x

Then solve for x:

.17x=5+.13x

.04x=5

x=125

So the plans will cost the same after 125 minutes. To find the cost of the plans at that time, substitute 125 in for the x in one of the equations.

11+.17(125)=y        y being the overall cost of the plan

11+21.25=y

32.25=y

To check your answer, you can substitute again in the other equation:

16+.13(125)=y

16+16.25=7

32.25=7

Answer:

Step-by-step explanation:

  (2x +3)² = (2x)² + 2(2x)(3) +(3)²

  = 4x² +12x +9

Comparing that to ax² +bx +c, we can identify ...

The values of a, b, and c are:

a   =  4

b  =  12

c  =  9

The given quadratic equation is:

y  =   (2x  +  3)²

A quadratic equation is of the form:

y  =  ax²  +  bx   +  c

Expand the equation y = (2x  +  3)²

y  =  (2x  +  3)(2x  +  3)

y   =  4x²  +  6x  +  6x   +  9

y  =  4x²  +  12x   +  9

Comparing y = 4x²  +  12x  +  9   with  y  =  ax²  +  bx  +  c

a   =  4

b  =  12

c  =  9

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Answer:

  Converges; 51 3/7

Step-by-step explanation:

The common ratio is -10/60 = (5/3)/-10 = (-5/18)/(5/3) = -1/6.

Then the sum of the sequence is given by ...

  S = a1/(1 -r) = 60/(1 -(-1/6))

  S = 60/(7/6) = 360/7

  S = 51 3/7

_____

If you erroneously evaluate the formula for the sum using +1/6 as the common ratio, then you will get S=60/(1-1/6) = 60·6/5 = 72.

Answer:

  f(x) = x^2

Step-by-step explanation:

The square root function is defined to have a non-negative range only. That corresponds to restricting the domain of f(x) = x^2 to positive values of x.

_____

The attached graph shows the domain-restricted f(x)=x² in solid red and the corresponding f⁻¹(x) = √x in solid blue. The other halves of those curves are shown as dotted lines (and are inverse functions of each other, too). The dashed orange line is the line of reflection between a function and its inverse.

Answer:

OH NANANA

Step-by-step explanation:

Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.Find all real numbers $x$ such that $3x - 7 \le 5x +9$. Give your answer as an interval.

Answer:

amount of total cash payment is $5450

Step-by-step explanation:

Given data

amount = $15000

principal = $5000

rate = 3% = 0.03

to find out

the amount of total cash payment

solution

we know according to question is Each yearly installment will include both principal repayment of​ $5,000 and interest payment for the preceding​ one-year period

so first we calculate interest i.e.

interest = rate × amount

interest = 0.03 × 15000

interest = 450

so interest is $450 for 1 year

now we calculate the amount of total cash payment i.e.

interest + principal

so the amount of total cash payment = 450 +5000 = 5450

amount of total cash payment is $5450

Mandy will make total cash payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

Further explanation:

Mandy issued a 3% long-term notes payable for [tex]\$\text{ }15000[/tex] over a 3-year term in [tex]\$\text{ }5000[/tex] principal installments on March 1 each year.

Then the interest payment for the first year will apply on total amount of [tex]\$\text{ }15000[/tex].

The formula for simple interest at principal value [tex]P[/tex] and rate percentage of [tex]R[/tex] in the time of [tex]T[/tex] years is,

[tex]\fbox{\begin{minispace}\\ \math{I}=\dfrac{P\times R\times T}{100}\\\end{minispace}}[/tex]

So, the interest amount payable at the end of one year is calculated as,

[tex]I=\dfrac{15000\times 3\times 1}{100}\\I=150\times 3\\I=450[/tex]

The total cash payment to be done by Mandy after a year on March 1, 2019, is the sum of the principal installment of [tex]\$\text{ }5000[/tex] and the interest applied on the total amount.

Hence the total cash payment is obtained as,

[tex]\fbox{\begin{minispace}\\\text{Total cash payment}=5000+450=5450\end{minispace}}[/tex]

Therefore, Mandy has to make a total payment of [tex]\fbox{\begin{minispace}\\\$\text{ }5450\end{minispace}}[/tex] on March 1, 2019.

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Answer details  

Grade: High school  

Subject: Mathematics  

Chapter: Simple Interest

Keywords: installments, one year, Mandy, principal, long-term, payable, March 1, amount, total cash, total cash payments, each year, payments, simple interest, rate percentage, sum, total amount, time, interest applied.

A.) Yes. The input and output are both possible.

In this problem, a dentist sees patients each day to clean their teeth. So we represent this function as [tex]g(x)[/tex] where:

x: Represents the number of people who saw the dentist.

g(x): Represents the number of teeth cleaned.

So we are given a point that is solution to our function, which is [tex](20, 20)[/tex] but what does this point represent? This tells us that the dentist saw 20 patients and cleaned 20 teeth, that is, he cleaned an only teeth per patient. So this will make sense under the conditions that make it possible, for example, a volunteer dentist can see more people than a common dentist and it is likely that that volunteer person sees fewer teeth. However, it's very difficult that that dentist finds 20 people with an only tooth each. So this situation is possible, but not realistic in the real world.

Answer:

Mr Johnson will receive 1024 mL IV in 8 hours.

Step-by-step explanation:

Mr Johnson has an IV that is infusing at 32 gtt per minute.

So in 1 hour patient will get the drug = 32×60 = 1920 gtt

Now in 8 hours drug received by the patient = 1920 × 8

= 15360 gtt

Since IV tube is calibrated for 15 gtt per mL which means in 1 mL amount of drug is 15gtt.

Therefore, total volume of infusion (in mL) will be

= [tex]\frac{\text{Total drug infused}}{\text{Total drug in 1 mL}}[/tex]

= [tex]\frac{15360}{15}[/tex]

= 1024 mL.

Therefore, 1024 mL IV will be infused in 8 hours.

Answer:

14

Step-by-step explanation:

An isosceles triangle has two sides that are the same.  If one side is 7 and another is 14, then the two possibilities are 7, 7, and 14, or 14, 14, and 7.

It can't be 7, 7, and 14, because the sum of the shortest sides of a triangle must be greater than the longest side.

Therefore, it must be 14, 14, and 7.  So the third leg is 14.

The length of third side of the isosceles triangle is 14.

An isosceles triangle is a triangle that has two sides of equal length. Also the property of isosceles triangle states that the base angle of the isosceles triangle subtends angle of equal measure.

It is given that the two sides of the triangle have lengths 7 and 14.

Thus for the triangle to be isosceles, the third side of the triangle will have the length as 7 or 14.

We know that the sum of any two sides of a triangle must be greater than the third side.

Thus if the third side is 7, then the sum of the sides will be (7 + 7) = 14 which is not greater than the other side. So, third side will not be of length 7 units.

The third side of the isosceles triangle is of 14 units .

Therefore, the length of third side of the isosceles triangle is 14.

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Answer:

C. greater than or equal to

Step-by-step explanation:

For example,

  ceiling(5) =  5

ceiling(5.1) =  6

 ceiling(-5) = -5

ceiling(-5.1) = -5

Answer:0.68

Step-by-step explanation:

Given

Total of 600 employees out of which 400 had college degree ,100 are single

and 60 were single graduates

therefore out of 100, 60 were single and rest 40 are single undergraduate

and out of 400, 60 were single graduates thus 340 are married graduate.

Now out of 600, 100 were single i.e. 500 is married

thus Probability that an employee is married and has a college degree is

=[tex]\frac{Favourable outcome }{Total outcome}[/tex]

P=[tex]\frac{340}{500}[/tex]=0.68  

Answer:

Step-by-step explanation:

a. We assume the appropriate equation for ballistic motion is ...

  h = -4.9t^2 +1

Then h = 0 when ...

  0 = -4.9t^2 +1

  49t^2 = 10 . . . . . add 4.9t^2, multply by 10

  7t = √10 . . . . . . . take the square root

  t = (√10)/7 . . . . . . divide by the coefficient of t

The marble will be in the air about (√10)/7 ≈ 0.451754 seconds.

__

b. The average velocity is the ratio of distance to time:

  v = (1 m)/((√10)/7 s) = 0.7√10 m/s ≈ 2.214 m/s

__

c. Under the influence of gravity, the velocity is linearly increasing over the time period, so its instantaneous value when the marble hits the ground will be twice the average value:

  When it hits, the marble's velocity is 1.4√10 m/s ≈ 4.427 m/s.

Answer:

Step-by-step explanation:

very interesting question. The temptation is to say that n should be 11 and that likely is divisible by 11 but it may not be the smallest.

100 + 100^2 = 100 + 10000 = 10100

The pattern of the series goes 101010101 ... 00...

100 / 11 = The remainder is 1/11

10100 / 11 = the remainder is 2/11

1010100 /11 the remainder is 3/11

The pattern suggests that the remainder will be 0 then n = 11

There might be other ways of doing this, but I don't know them.

Answer:

Lowest score needed=4.92

Step-by-step explanation:

Using the standard normal distribution table we find the value of standard normal deviate corresponding to area of 15%

For area of 15% we have Z= -1.04

Thus we have

[tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}\\\\[/tex]

Applying values we get

[tex]X=-1.04\times 2+7\\\\X=4.92[/tex]

Thus lowest score needed = 4.92

Answer:

He should word his statement as "Free replacement for tires that wear before 30875 miles."

Step-by-step explanation:

If he is willing to replace 10% of tires he should find the life of tires that gives an area of 10% in the normal distribution graph.

Now for 10% of area standard normal deviate Z can be obtained from normal distribution table

Using normal distribution table for 10% area we have Z = -1.28

Thus we have [tex]Z=\frac{X-\overline{X}}{\sigma }\\\\\therefore X=\sigma Z+\overline{X}[/tex]

Applying given values we get

[tex]X=-1.28\times 2500+34000\\\\X=30875miles[/tex]

The mechanic would replace the tires that spoil without covering up to 30800 miles.

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

For a mean of 34000 miles and standard deviation of 2500. The probability of 10% correspond with a z score of -1.28. Hence:

-1.28 = (x - 34000)/2500

x = 30800

The mechanic would replace the tires that spoil without covering up to 30800 miles.

Find out more on z score at: https://brainly.com/question/25638875