given that $x$, $\frac{1}{x}$, $y$, $\frac{1}{y}$, $z$ and $\frac{1}{z}$ are all integers, how many distinct values of $x y z$ are possible?

Answers

Answer 1

Distinct value of x, y, z are will be 3

Consider the function will be f(x) = x3 - x2 - 2x +2 = ( x - 1 ) (x2 - 2 )

we have three real roots and ,

x + y + z = - 1/ (-1)

= 1 ,

1/x + 1/y + 1/z = -2 /(-2)

= 1

Consider the function

f(x) = x3 - x2 - 40 + 20.

Set the derivation equal 0 we get x = 4 and x = -10/3

are two local extrema. When x= 4 , f(x)<0,when x = -10/3 . f(x) >0 there are three real roots . we have x + y + z = 1 and 1/x + 1/y + 1/z = - (-40)/ 20 = 2

consider the function

f(x) = x3 - x2- 40x + 40/3 .

we still have same local extrema as (2) and we have x= 4 , f(x) < 0 and we

x= -10/3 , f(x) > 0 so there are three real roots. We have x+ y + z = 1 and 1/x + 1/y + 1/z = -(-40)/40/3 = 3

So, there are 3 distinct values

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Related Questions

if 17% of men are bald, what is the probability that at most 140 in a random sample of 900 men are bald? use normal to binomial

Answers

If 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

In the given question, if 17% of men are bald, then we have to find the probability that at most 140 in a random sample of 900 men are bald.

As given that; 17% of men are bald.

So,p=0.17

Let X=Number of men that are bald

Sample size, n=900

Here X follows binomial distribution with parameters n= 900 and p =0.17

Since np≥5 and n(1-p)≥5, We can use normal approximation to the binomial with continuity correction.

So,Binomial can be approximated to normal with;

mean, μ=np

μ = 900*0.17

μ = 153

Standard deviation, σ = √np(1-p)

σ = √900*0.17*(1-0.17)

σ = √153*0.83

σ = √126.99

σ = 11.269

So, X→Normal (μ = 153, σ = 11.269)

Then, X= (X-μ)/σ

X=(X-153)/11.269

We need to find the probability that at most 140 in a random sample of 900 men are bald i.e. we need to find P(X≤140)

P(X≤140) =P(X<140+0.5)  [using continuity correction factor]

P(X≤140) =P(X<140.5)

P(X≤140) =P(z<(X-153)/11.269)

P(X≤140) =P(z<(140.5-153)/11.269)

P(X≤140) =P(Z<-1.11)  [z score rounded to 2 decimal places]

P(X≤140)  =0.1335

Hence, if 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.

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What is the equation of a line that has a
3/4
slope of and an x-intercept of 0?

A y=0
B y=3/4
C y=3/4x
D y=x+3/4

Answers

Answer: C

Step-by-step explanation: This is because there is no y - intercept. But since there is still a slope an x but be next to the 3/4. Which represents the rate of change.

A particle of mass mm moves in the plane with coordinates ( x ( t ) , y ( t ) )(x(t),y(t)) under the influence of a force that is directed toward the origin and has magnitude k / \left( x ^ { 2 } + y ^ { 2 } \right)k/(x 2 +y 2 )—an inverse-square central force field.

Answers

An inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

From Newton's second law of motion,

mass × acceleration = Force acting on the mass

Resolving the force F along x and y directions and applying Newton's second law of motion,

Using,

[tex]r = \sqrt{x^2+y^2}[/tex]

Therefore,

[tex]m\frac{d^2x}{dt^2} =-|F|cos \theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and cos⁡θ = [tex]\frac{x}{\sqrt{x^2+y^2} }[/tex]

Similarly using,

[tex]r = \sqrt{x^2+y^2}[/tex]

we get,

 [tex]m\frac{d^2y}{dt^2} = -|F|sin\theta[/tex]

[tex]mx^{''} = -\frac{k}{x^2+y^2} \frac{x}{\sqrt{x^2+y^2} } \\\\mx^{''} = - \frac{kx}{(x^2+y^2)^\frac{3}{2} }\\ \\mx^{''} = - \frac{kx}{r^3}[/tex]

Where [tex]r = \sqrt{x^2+y^2}[/tex]

​ and sinθ = [tex]\frac{y}{\sqrt{x^2+y^2} }[/tex]

Therefore we showed that holds

[tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex]

Hence the answer is an inverse-square central force field is  [tex]mx^{''} = -\frac{kx}{r^3}\\ \\mx^{''} = -\frac{ky}{r^3}\\[/tex].

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suppose a department store wants to estimate the average age of the customers of its contemporary apparel department, correct to within 2 years, with level of confidence equal to 0.95. management believes that the standard deviation is 8 years. the sample size they should take is .

Answers

By using the formula for sample size, it can be calculated that the sample size is 62

What is sample?

At first it is important to know about population.

Population is the group of items from where samples are taken for study and research and for statistical purpose

A subset of population is called sample.

Here, margin of error E = 2

Value of z for 95 % confidence interval = 1.96

Standard deviation = 8

Sample size  = [tex](\frac{1.96 \times 8}{2})^2[/tex] [tex]\sim[/tex] 62

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Please answer! Question is below! Thanks!

Answers

Answer:

y=4x+4

Step-by-step explanation:

slope intercept form is y=mx+b

m is slope

B is y intercept

To find slope we use y2-y1/x2-x1

16-(-4)/3-(-2)

20/5

4 is the slope

We can fill this in

y=4x+b

To find b we fill in any coordinates

-4=4(-2)+b

-4=-8+b

+8. +8

4=b

Now we can fill it in

y=4x+4

Hopes this helps please mark brainliest

Elouise and Marcus are 20km apart.
There is a lake due west of Elouise that is also 10√3 km due north of Marcus.
Work out the bearing of Marcus from Elouise

Answers

Elouise and Marcus are 20 km apart. There is a lake due west of Elouise that is also 10√3 km due north of Marcus, so 22.36 km distance the bearing of Marcus from Elouise.

What is Pythagoras theorem?

According to the Pythagoras theorem, the square of the hypotenuse of a right-angled triangle equals the sum of the squares of the other two sides. The formula for this theorem is c² = a² + b², where c is the hypotenuse and a and b are the triangle's two legs. Pythagoras theory triangles are another name for these triangles.

At first assume a triangle, In the triangle, assume Elouise at the point A and Marcus at the point B, and the lake at the C point.

Given that,

Elouise and Marcus are 20 km apart (AB)

There is a lake due west of Elouise that is also 10√3 km due north of Marcus (BC)

Now, according to a Pythagoras theorem,

(AC)² + (AB)² = (BC)²

or, (AC)² = (BC)²- (AB)²

or, (AC)² = (10√3)² - (20)²

or, AC = [tex]\sqrt{500}[/tex]

or, AC = 22.36 km

So, distance bearing of Marcus from Elouise is 22.36 km.

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1. A local zoo had 750 visitors on Saturday. If
20% of the guests traveled from out of town,
how many local guests visited the zoo on
Saturday?

Answers

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

The number of local guests who visited the zoo is 600.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Total number of visitors = 750

The percentage that visited the zoo.

= 100% - 20%

= 80%

Now,

The number of local guests who visited the zoo.

= 80% of 750

= 80/100 x 750

= 600

Thus,

The number of local guests who visited the zoo is 600.

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Determine which integer in the solution set will make the equation true. 8x − 4 = 2(2x + 4)

S: {−4, 0, 3, 12}

Answers

Solving the equation 8x − 4 = 2(2x + 4) the required integer to make the equation true is 3

How to find the integer

The integer required to be found is solved as follows

The given equation is  8x − 4 = 2(2x + 4)

solving for x

8x − 4 = 2(2x + 4)

8x - 4 = 4x + 8

collecting like terms

8x - 4x = 8 + 4

4x = 12

dividing through by 4

x = 3

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I got the rest of the answers just stuck on these two

Answers

The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

There are two table is shown in figure.

Now,

For first table;

Two points are,

⇒ (x, y) = (3, -6)  (0, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and

(x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for first table;

⇒ m = (- 2 - (-6)) / (0 - 3)

⇒ m = (- 2 + 6) / (-3)

⇒ m = - 4/3

And, For second table;

Two points are,

⇒ (x, y) = (0, -3)  (4, - 2)

Since, The slope of the line passing through the points  (x₁ , y₁) and (x₂, y₂) will be;

⇒ m = (y₂ - y₁) / (x₂ - x₁)

Hence, Slope for second table;

⇒ m = (- 2 - (-3)) / (4 - 0)

⇒ m = (- 2 + 3) / (4)

⇒ m = 1 / 4

Thus, The slope for the first table will be;

⇒ m = - 4/3

The slope for the second table will be;

⇒ m = 1 / 4

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A
Given:
O HA
ZC, ZF are rt. Z's; AC= DF, BC= EF
O LA
OLL
B D.
OHL
F
E

Answers

Answer: your question is not very clear

Step-by-step explanation:

what is the remainder when the positive integer n is divided by the positive integer k, where k > 1 ? (1) n

Answers

n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1

What is Remainder?

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.

For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.

As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.

As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.

[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]

[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).

The remainder will be n= (K+1)^3

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An arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students. How many students does the academy have per​ teacher? Per​ tutor? How many tutors does the academy need if it has ​60 students?

Answers

1. The students that the academy have per teacher is 18.

2. The students per tutor will be 10.

3. The tutors that the academy need if it has 60 students is 6 tutors.

How to calculate the number of students?

Given that the arts academy requires there to be 4 teachers for every 72 students and 3 for every 30 students.

The students that the academy have per teacher will be:

= Number if students / Teacher

= 72/4

= 18 students per teacher.

The students per tutor will be:

= 30/3

= 10 students per tutor

The number of tutors for 60 students will be:

= 60 / 10

= 6 tutors.

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Fill in the table using this function rule.
y=3x+1
X
2
3
6
7
X
y
0
0
0
S

Answers

Answer:

y={7,10,19,22}

Step-by-step explanation:

3(2)+1 = 6+1 = 7

3(3)+1 = 9+1 = 10

3(6) + 1 = 18+1 = 19

3(7) + 1 = 21+1 = 22

let m be the number of five-element subsets that can be chosen from the set of the first 14 natural numbers so that at least two of the five numbers are consecutive. find the remainder when m is divided by 1000.

Answers

We have (123) different possibilities. Therefore, we can derive from the multiplication principle that there are 13(123) ways.

What is probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.

An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

The likelihood that an event will occur increases with its probability. A straightforward illustration is tossing a fair (impartial) coin.

The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half .

According to our question-

Let n be the maximum number of subsets of five elements that can be selected from the first 14 natural numbers,

with at least two of the five numbers being consecutive.

I have made a block of two consecutive numbers (like (1,2),(2,3),(13,14) etc.).

Now we can choose this block in 13 ways. Now we have to choose 3 numbers from the rest 12 numbers.

Hence,  multiplication principle we come to know that there are  13×(123).

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5pts and who ever get this right gets brainliest ​

Answers

Answer:D is incorrect

Step-by-step explanation:

D is the only one that is incorrect because D is 9x-81

Answer:

  (d)  9(x -9)

Step-by-step explanation:

You want the expression that is not equivalent to the other three.

Simplified expressions

The simplified versions of the expressions are ...

9(x -1) = 9x -99x -92x -4 +7x -5 = (2+7)x +(-4 -5) = 9x -99(x -9) = 9x -81 . . . . . . . not equivalent to the others

The expression not equivalent to the other three is 9(x -9).

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Equations with variables on both sides that equal 19

Answers

An equation with variables on both sides that equal 19 is x - 2 = 17.

What is an equation?

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign

Based on the information, the equation will be:

x - 2 = 17

Collect like terms

x = 17 + 2

x = 19

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What is the color red?

Answers

Answer:

red im pretty sure

Can someone help? Solve for a given that the height of the triangle is 3 centimeters and each of the legs are 6 centimeters. I also need the centimeters please !!

Answers

Answer:

6√3 centimeters

Step-by-step explanation:

This is an isosceles triangle because two of the sides are the same. We can divide this into two triangles to make two right triangles, and use the Pythagorean theorem. The base (a) will be divided by 2.

Pythagorean theorem: a^2 + b^2 = c^2

a and b are the legs of the triangle. c is the hypotenuse.

Let's replace the variables with the given information we know.

The hypotenuse is 6. One of the legs is 3. the other leg is a/2.

3^2 + b^2 = 6^2

9 + b^2 = 36

b^2 = 27

b = √27 = 3√3

Since this was for half of the base, we will multiply it by 2.

3√3 x 2 = 6√3

That is our answer.

I hope this helps.

What is the distance between the points (11,19) and (11,-6) in the coordinate plane?

Answers

Answer: 25 units

Step-by-step explanation:

distance with negatives is still an addition but you have to turn the negative into a positive to get the answer.

576,000 in science notation

Answers

Answer: 5.76 x 10 to the 5th

please help me due in 10 min

Answers

Answer: A = 2(x+3y)+2z=2z+4x+2y

B=2(x+3y)=4x+2y

c=x+3y=2x+y

d=2y=x

Step-by-step explanation:

Answer:

2y=x:D

x+3y=2x+y:C

2(x+3y)=4x+2y:B

2(x+3y)+2z=2z+4x+2y

Step-by-step explanation:

D is the only possibility for 2y=x because it has 3 total. Similarly for C. B only has two different types, so it must be 2(x+3y)=4x+2y.

Which equation could generate the curve in the graph below?

Answers

Answer:

(Not accurate because I'm estimating amounts) y = ((x-2)/2)^2 + 4

Step-by-step explanation:

Scales horizontally by 2, Shifts up 4, right 2

(9 * 6) * 1 = 3 operations

Answers

Answer:

53

Step-by-step explanation:

PEMDAS

Parenthesis

multiply the numbers

Divide

Add

Subtract

In a city with an 8.5% tax rate, what would be the total cost for a $66.00

Answers

I got the answer of 71.61 because I took the % moved the decimals multiplied then added it to 66

we want to construct a 99% confidence interval for the proportion of people who will vote 'yes' on a ballot question in the next election. how many people should we sample to construct such an interval with a margin of error of 3%?

Answers

The sample size should be 1843 at 99% confidence level with margin of error of 3%.

What is Inferential statistics?

By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.

Given, Margin of error (m) = 0.03

           z (at 99% confidence level)=2.576

We know that, Sample size(n) = (z/m)^2 p (1-p)

In order to find the sample size, we must know the value of proportion.

here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.

Now, we've p = 0.5

Sample size = (z/m)^2 p (1-p)

                        = (2.576/0.03)^2 × 0.5 × (1-0.5)

                        = 1843 (approx).

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Ernesto guesses there are 69 marbles in a jar, but there are actually 60.

What is the percent error in Ernesto's guess?

Answers

Answer:

15%

Step-by-step explanation:

Since the problem is to find how much 69 is as a percent if 60 is 100%, we can use a rule of three, simple, direct proportion to do it:

60 = 100%

68 = x

x = 69x100/60

x = 115

That means 69 is 115% of 60, which means that the error is of:

115 - 100 = 15%

Hope this helps, have a great day! :D

what is the sum of the infinite geometric series?25 minus 10 plus 4 minus eight fifths plus continuing the series diverges.

Answers

Answer:

Geometric Sequence

Finding the sum

The sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Solution:

Geometric Series Sum Formula: S = a₁/1 - r

Given: a₁ = 3/4

          a₂ = -9/16

          a₃ = 27/64

          a₄ = -81/256

1. Find the common ratio.

      a_n = a₁r ⁿ ⁻ ¹

       a₂  = a₁r ⁿ ⁻ ¹

  -9/16 = 3/4 r ² ⁻ ¹

  -9/16 = 3/4 r

2. Divide both sides of the equation by 3/4 to find r.

   -9/16/3/4 = 3/4 r/3/4

 (-9/16)(4/3) = r

       -36/48 = r

           -3/4 = r

3. Using r = -3/4, find the sum of the infinite geometric series 3/4 -9/16 +27/64 -81/256+ ...

   S = a₁/1 – r

   S = 3/4/1 – (-3/4)

   S = 3/4/1 + ¾

   S = 3/4/4/4  + 3/4

   S = 3/4/7/4

   S = (3/4)(4/7)

   S = 12/28

   S = 3/7

4. Therefore, the sum of the infinite geometric series 3/4 -9/16+27/64 -81/256+ ...is 3/7.

Definition:

     A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant while the sum of an infinite number of terms in a geometric sequence is called sum to infinity.

Code: 10.3.1.1

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Step-by-step explanation:

Donnie, Karim, and Shawn run on the cross-country team. At yesterday’s practice, Donnie ran 200% as far as Karim. The ratio of the distance that Karim ran to the distance that Shawn ran is 4 : 3.

If you add the distance that all three boys ran, you get a sum of 45 miles. How far did each boy run individually?



this is ratio problem

Answers

The distance that each boy ran is as follows:

Donnie = 24 miles

Karim = 12miles

Shawn = 9 mile.

What is ratio?

Ratio is defined as an expression that is used to represent the part of a whole entity or structure.

The total distance covered by the three boys = 46miles.

Distance covered by Donnie = 200% of Karim (ratio 4)

That is;

200/100×4 = 8

Now the ratio of the three boys = 8:4:3

To calculate the distance of each boy is by finding the total ratio of the whole boys such as:

= 8+4+3 = 15

For Donnie = 8/15×45 = 24 miles

For Karim = 4/15×45 = 12 miles

For Shawn = 3/15 × 45 = 9 miles

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A car is sold for $80, 000. Every year it loses 1/4 of its value.

a. Write an equation to represent the value of the car after 1 year.

b. Write an equation to represent the value of the car after t years.
A=P(1+ r/n)^n•t

Answers

An equation to represent the value of the car after 1 year is P(t) = 80,000(1 - 0.25)¹.

An equation to represent the value of the car after t years is P(t) = 80,000(1 - 0.25)^t.

How to write this equation?

Generally speaking, a physical asset that loses its value at specific period of time represent an exponential decay. Therefore, a mathematical model for any physical asset (car) that decreases by r percent per unit of time is an exponential equation of this form:

P(t) = I(1 - r)^t

Where:

P(t ) represents the value of car in dollars.t represents the time or number of years.I represents the initial value of car.r represents the decay rate.

Note: 1/4 is equal to 0.25.

For a car that loses 1/4 of its value annually, after 1 year its value is given by;

P(t) = 80,000(1 - 1/4)^1

P(t) = 80,000(1 - 0.25)¹

For a car that loses 1/4 of its value annually, after t year its value is given by;

P(t) = 80,000(1 - 0.25)^t

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The sum of 4 times a number and 2 is two times the number minus 8. What is the number?

Answers

Answer:

Step-by-step explanation:

The word "Sum" = addition.

"A number" = the unknown, aka 'x'.

"Is equal to" is =.

Go piece by piece. I will set your equation exactly as it is worded as you read it. Follow along:

4x + (-2) = 5x + (-2)

Imagine there is a "1" infront of the parenthesis around the -2. A positive * a negative always = negative. So.

Other Questions
While marching, a drum major tosses a baton into the air and catches it. The height h (in feet) of the baton after t seconds can be modeled by h =16t2+32t+6. How long is the baton in the air? Were the colonies the only market for England manufactured goods Directions: Select and label the topic sentence (TS) in the group below. Then, number the supporting detail sentences in the correct order. ___ Initially, students gain a solid foundation at the sentence-level. ___ Since writing can be difficult and overwhelming, The Hochman Method provides a scaffolded approach. ___ After students have had ample practice planning and revising single paragraphs, they learn to develop a Multiple-Paragraph Outline (MPO) to plan a composition. ___ At the single-paragraph level, students learn a variety of revision strategies to improve the substance of their writing. ___ When students are ready to write a paragraph, they learn to use a Single-Paragraph Outline (SPO). the oldest and most common justification for punishment used today is: a. deterrence. b. incapacitation. c. rehabilitation. d. retribution. N. Scott Momaday connects his personal history with that of the Kiowa tribe, indicating that both personal and cultural experience have a role in forming his identity.How does the culture of the Kiowa tribe affect Momadays personal identity? Use textual evidence to support your answer. What other examples (in literature or life) can you think of in which personal and cultural identity are intertwined? Ill give branniest f(x)= Tessa has t times as many comic books as Joseph. Joseph has 14 comic books. Write an expression that shows how many comic books Tessa has Which of the images represents mitosis and why? on the map of utopian communities in the mid-nineteenth century, identify the state in which the community of oneida was established. this is also the state where the very first shaker community was established. A nurse is teaching a parent of an infant who has a pavlik harness for the treatment of development dysplasia of the hip. The nurse should identify that which of the following statements by the parent indicates an understanding of the teaching? 10. The cell wall... *OIs where photosynthesis happensOIs where cellular respiration happensOIs found in plant cells but not animal cellsO Produces energy Why does it make sense that acetyl-coa stimulates the activity of pyuruvate carboxylase?. which of the following statements is not true? group of answer choices the dom for a web page is built as the page is loaded by the web browser. the dom is a hierarchical collection of nodes in the web browser's memory. you can modify the dom using the properties and methods that are defined by the dom core specification. to display changes made to the dom, you must refresh the web page. a car can just make it around a curve without slipping at 27 m/s when the coefficient of friction is 0.7. find the radius of the curve. in a study to evaluate a test as a screen for the presence of a disease, 235 of the 250 people with the disease had a positive test and 600 of the 680 people without the disease had a negative test. based on this data, the specificity of the test for the disease is (check one) If agreement of either party is obtained by fraud, misrepresentation, mistake, undue influence, or duress, or if the contract is one of adhesion, or is unconscionable, a(n):a. voidable contract resultsb. void contract resultsc. valid contract resultsd. executed contract results Bach created masterpieces in every baroque form except ______.Multiple Choiceconcertosonataoperafugue write the y(x,t) equation for a wave travelling in the positive x-direction with a wavelength of 50.0 cm, speed of 4.00 m/s, and amplitude of 5.00 cm. be sure to include units where appropriate. The sales philosophy and process that emphasizes a commitment to maintaining customer relationships over the long term and investing in opportunities that are mutually beneficial to all parties is known as ________ selling. how can discussing issues of equality in sports help you ou understand general issues of equality