if the nth term of a number sequence is n squared-3 if the first 3 terms and the 10th term

Answers

Answer 1

Answer:

First three terms: -2, 1, 6

Tenth term: 97

Step-by-step explanation:

Given

[tex]T_n =n^2 -3[/tex]

Required

The first three terms and the tenth

So, we have:

First term: n =1

[tex]T_1 = 1^2 - 3 = 1 - 3 = -2[/tex]

Second term: n = 2

[tex]T_2 = 2^2 - 3 = 4 - 3 = 1[/tex]

Third term: n = 3

[tex]T_3 = 3^2 - 3 = 9 - 3 = 6[/tex]

Tenth term: n = 10

[tex]T_{10} = 10^2 - 3 = 100 - 3 = 97[/tex]


Related Questions

Which of the following is a subspace of R^3? (A) All vectors of the form(0, a, a^2), (B) All vectors of the form(a+2, a, 0), (C) All vectors of the form (a, b, 2), (D) All vectors of the form(a, b, a-2b)

Answers

All vectors of the form(a, b, a - 2b) is a subspace of R³. So, the correct option is option(D).

Subspace:

If W is a set of one or more vectors from a vector space V, then W is a subspace of V if and only if

If u and v are vectors in W, then u + v in W. ku is in W if k is any scalar and u is any vector in W.

Now, check the options and find out the option which satisfy the subspace conditions.

A) All the vectors are of form (0, a,a²)

let (0,1,1) = u and v=(0,2,4) and both are belongs to { 0, a,a² : a∈R }, (0,0,0)∈ {0, a,a² : a∈R }.

u + v = (0,1,1) + (0,2,4) = (0,3, 5) not belongs to

{ 0, a,a² : a∈R }. So, this is not correct option.

B) Here, (0,0,0) does not belongs to

{0, a, a+2 : a∈R } because if a= 0 then a+2 =/ 0 .

So, it is also not subspace.

C) All vectors of the form (a, b, 2)

The third tuple is 2 which never be equal to zero. Hence, (0,0,0) does not belongs to (a, b, 2) and it is not form subspace.

D) All vectors of the form (a, b, a - 2b)

When a = 0 , b = 0 => (0,0,0) ∈(a, b, a - 2b)

let u = ( a1, b1 , a1- 2b1) and v = ( a₂, b₂ , a₂ - 2b₂)

and α∈R

u + v = ( a₁, b₁ , a₁- 2b₁ ) + ( a₂, b₂ , a₂ - 2b₂)

= ( a₁ +a₂ , b₁+b₂ , a₁+a₂ -2(b₁ - b₂)) €(a, b, a - 2b)

αu = α(a₁ , b₁ , a₁- 2b₁)

=( αa₁ , αb₁ , α(a₁ - 2b₁))∈(a, b, a - 2b)

both the conditions are satisfied, so it is Subspace of R³.

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b) What number is 10% text more than 40?

Answers

Answer:

it might be 4

Step-by-step explanation:

that's all I have

what is a acute angle

Answers

Answer: Measure less 90 degrees

Step-by-step explanation: Less than 90 degrees measure acute angle. 90 degrees in right corner. Obtuse corners are larger than 90 degrees

A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?

Answers

following algorithms correctly updates the values, If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.

What is algorithm ?An algorithm is a process used to carry out a computation or solve a problem. In either hardware-based or software-based routines, algorithms function as a detailed sequence of instructions that carry out predetermined operations sequentially.

The game records the highest and lowest scores that were earned. This indicates that the game already has the highest and lowest score stored in its memory.

Now, if a new score, num, is achieved, the game must compare num with the minimum and maximum scores in order to update the minimum and maximum scores. The minimum score is updated to the score, num if the most recent score, num, is lower than the minimum score.

Additionally, the maximum score is updated to the score, num if the most recent score, num, is higher than the maximum score.

Complete Question :

A certain game keeps track of the maximum and minimum scores obtained so far. If num represents the most recent score obtained, which of the following algorithms correctly updates the values of the maximum and the minimum?

If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num.If num is less than the minimum, set the minimum equal to num. Otherwise, if num is greater than the maximum, set the maximum equal to num. If num is less than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num. If num is greater than the minimum, set the minimum equal to num. Otherwise, if num is less than the maximum, set the maximum equal to num.​

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It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the expected number of republicans ? It is known that 25 % percent of Americans identify themselves as republican . In a random sample of n=20 Americans , what is the standard deviation of the number of republicans ? ( Round to 2 decimal places )

Answers

Using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

What is the percentage?

A percentage is a figure or ratio stated as a fraction of 100 in mathematics.

We must divide the value by the entire value to find the percentage, and then multiply the resulting number by 100.

As an illustration, 1% of 1,000 chickens is equal to 1/100 of 1,000, or 10 birds, and 20% of the quantity is equal to 20% of 1,000, or 200.

So, we have a random sample of 20 people.

n = 20

And we also know that 25% of Americans identify themselves as republicans.

Then the number of republicans in 20 people would be:

20/100 * 25

.2 * 25

5


Therefore, using percentages, we know that out of 20 people, 5 people that is 25% of the random sample consider themselves as republicans.

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A quiz team of 5 children is to be selected from a class of 25 children. There are 15 girls and 10 boys in the class. (a) How many teams made up of 3 girls and 2 boys can be selected? (b) How many teams can be selected with at least 3 girls?

Answers

Using combination we get  20475 teams can made up of 3 girls and 2 boys and 37128  teams can be selected with at least 3 girls.

Why does combination mean?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.

Since this is just a team of 5 children,

we have   no of girls = 15

No of boys = 10

teams made up of 3 girls and 2 boys

girls out of 3 girls can be selected in  ¹⁵C₃ ways and

2 boys out of 10 boys can be selected in  ¹⁰C₂  ways.

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂

= 455*45 =20475 Ways

Teams can be selected with at least 3 girls

It is the probability of at least 3 girls which means P(3 girls,2 boys) or P(4 girls,1 boy) or P(5 girls, 0 boys)

[tex]\implies[/tex] ¹⁵C₃ X  ¹⁰C₂  + ¹⁵C₄ X  ¹⁰C₁ + ¹⁵C₅ X  ¹⁰C₀

= 455 * 45 +1365*10+3003*1

=20475 +13650 +3003

=37128 ways

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Angel wants to invest $4,000.00 in a savings account.

Determine the simple interest rate required for Angel's investment to grow to $13,400.00 in 25 months.

Round your answer to the nearest tenth of a percent and don't forget to include a percent sign, %, in
your answer.

The interest rate required to grow the investment to $13,400.00 is ______

Answers

The interest rate required to grow the investment to $13,400.00 would be = 35%

What is simple interest?

Simple interest is the amount of money that is received for a particular period of time due to an investment made to an account.

The principal amount = $4,000.00

The time for investment = 25 months = 2 years

The simple interest = 13,400 - 4000= $9400

The rate (R) = X

The formula for simple interest=

p×t×r/100

9400= 13,400× 2×r/100

Make R the subject of formula;

R = 9400×100/13400×2

R = 940000/ 26800

R= 35%

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The graphs below have the same shape. f(x)=x². What is the equation of the graph of g(x) ?
A. g(x)=(x-2)²
B. g(x)=(x+2)²
C. g(x)=x²+2
D. g(x)=x²-2

Answers

The equation of the graph of the function g(x) is A. g(x) = (x - 2)²

How to determine the equation of the graph of the function g(x)?

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

f(x) = x²

Also, we have the given graph

From the graph, we can see that the graph f(x) is shifted right y 2 units

This means that

g(x) = f(x - 2)

So, we have

g(x) = (x - 2)²

Hence, the equation is (a) g(x) = (x - 2)²

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A hospital director is told that 54% of the emergency room visitors are insured. The director wants to test the claim that the percentage of insured patients is under the expected percentage. A sample of 120 patients found that 60 were insured. Find the value of the test statistic. Round your answer to two decimal places.

Answers

According to question,

Given data,

A hospital director is told that 54% of the emergency room visitors are insured.

A sample of 120 patients  found that 60 were insured.

We know that,

To determine the percentage,

we have to divide the value by the total value and then multiply the resultant by 100,

Percentage formula

Is /of=%?100

Or

Part/whole=%/100

With the help of formula,

Part/sample of patient=%/100

60×100/120=50%

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A fast food chain decides to decrease the size of its soft drink cups by 10%. If the new soft drink
cup holds 27 oz, how much did the original cup hold?

Answers

Answer:

30 oz

Step-by-step explanation:

x = size of original cup

x - (0.10)x = 27 oz

(0.90)x = 27 oz

x = 27 / 0.90 = 30 oz

Two friends, Andrew and Liz, are playing a game using this spinner. If the spinner lands on region 1, Andrew wins. If it lands on region 2, Liz wins. If it lands on region 3, nobody wins. Is this a fair game?​

Answers

Answer:

Based on the information provided, it does not seem like this game is fair. Since region 1 and region 2 are the same size, each player has an equal chance of winning, but since region 3 is significantly larger than the other regions, neither player has a high chance of winning. This means that one player could potentially win multiple times in a row just by luck, without the other player having a chance to catch up. In order for the game to be considered fair, the relative sizes of the regions should be such that each player has a roughly equal chance of winning.

Answer:

yes. they both have ⅓ chance of winning

Step-by-step explanation:

For each diagram below, work out whether AB is a tangent to the circle, is not a
tangent to the circle, or if it is not possible to tell.
Justify your answers.
13 cm
5 cm
12 cm
10 cm
4 cm
11 cm
18 cm
18 cm
25 cm
Not drawn accurately

Answers

The tangent AB is for circle in figure (a).The correct option is (a).

What is the relation between the tangent and a circle?

For a given circle there can only be one tangent at one point.

The tangent and the circle has only one point in common.

The tangent to a circle is always perpendicular to the radius at that point.

The tangent drawn to a circle is always at right angle to the radius at that point.

The given figures are examined one by one as follows,

(a) The sides of the triangle are given as 5, 12 and 13.

And, 13² = 5² + 12²

Which implies it is a right triangle by Pythagoras theorem.

(b) The sides of the triangle are given as 4, 10 and 11.

And, 11² ≠ 10² + 4²

Which implies it is not a right triangle by Pythagoras theorem.

(c) The sides of the triangle are given as 18, 25 and 18.

And, 25² ≠ 18² + 18²

Which implies it is not a right triangle by Pythagoras theorem.

Thus, only for figure (a) the criteria for the tangent satisfies.

Hence, the line segment AB is tangent to the circle given in figure (a).

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Please help!!!!!!!!!!!!

Answers

The value of variable x in the equation is x = -3y + 5/ 2

How to solve an equation for a variable?

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Therefore, the equation 2x + 3y = 5 can be solved for x as follows:

We have to make x the subject of the formula in the equation.

Subject of the formula is the variable which is expressed in terms of other variables involved in the formula.

Hence,

2x + 3y = 5

subtract 3y from both sides of the equation

2x + 3y = 5

2x + 3y  - 3y = 5 - 3y

2x = 5 - 3y

divide both sides by 2

Therefore,

x = 5 - 3y / 2

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NO LINKS!!!
Find the sum of the finite arithmetic sequence.
Sum of the first 150 positive integers

Answers

Answer:

11325

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[a+l]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $l$ is the last term.\\\phantom{ww}$\bullet$ $n$ is the number of terms.\\\end{minipage}}[/tex]

A positive integer is a whole number that is greater than zero.

Therefore:

The first term, a, of the first 150 positive integers is 1.The last term, l, of the first 150 positive integers is 150.The number of terms, n, is 150.

Substitute the values into the formula to find the sum of the first 150 positive integers:

[tex]\implies S_{150}=\dfrac{1}{2}(150)\left[1+150\right][/tex]

[tex]\implies S_{150}=75 \cdot 151[/tex]

[tex]\implies S_{150}=11325[/tex]

I need help that's all if you cN helpe please do I'm beginning you

Answers

The slope of y = 7x - 10 is 7 while the y-intercept is -10 thus it has a high slope but a lower y-intercept so option (D) is correct.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear function with slope m and y-intercept c is given as y = mx + c.

Compare the given function y = 7x - 10

Slope m  = 10

y-intercept = -10

Hence "Y = 7x - 10 has a slope of 7 and a y-intercept of -10, meaning it has a high slope but a low y-intercept".

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Suppose we roll a fair die four time. What is the probability that a 6 occurs on exactly one of the rolls?

Answers

The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

What are the 3 types of probability?

The Three Kinds of Probability

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

What is the formula to find out probability?

Formula used to find probability

The probability is often defined as the proportion of positive outcomes to all outcomes in the sample space. It is written as, the likelihood of an event

P(E) = (Number of favorable outcomes) ÷ (Sample space).

As die is rolled 4 times ,

X≈ binomial(4, 1/6)

P(X=r) = nCr (p)^r (q)^(n-r)

P(X = 1) = 4C1 × (1/6)^1 × (5/6)^3

           = 4 × 1/6 × (5/6)^3

∴P(X = 1) = 0.257

The probability that a 6 occurs on exactly one of the rolls after rolling a fair die four times is 0.385.

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Complete the following.
(a) Consider the following statement.
The water temperature is 70.
Check all the statements below that are negations of this statement.

The water temperature is less than 80.

It is not the case that the water temperature is 70.

The water temperature is not 70.

(b) Consider the following conditional statement.
If the dress is red, then Keisha likes the dress.
What is the conclusion of this statement?

It is not true that Keisha owns a dress.

Keisha likes the dress.

The dress is red.

Keisha loves the dress.

The dress likes Keisha.

Answers

a) The option that is a negation of the given statement is; The water temperature is not 70.

b) The conclusion of the given conditional statement is; Keisha likes the dress.

How to Interpret Conditional Statements?

In mathematics, a conditional statement is defined as a statement that can be written in the form “If P then Q,” where P and Q are sentences.

a) We are given the statement as;

The water temperature is 70.

Now, negation is a false/opposite form of the given statement and as such among the options, the only one that is a negation is that

"The water temperature is not 70."

b) We are given the conditional statement as;

If the dress is red, then Keisha likes the dress.

Thus, the conclusion of this is that likes the dress.

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Solve:(6x^2+5x+1)÷(x+2)​

Answers

Answer:

6x+6x2+3

Step-by-step explanation:

6x2+5x+1+x+2

Combine 5x and x to get 6x.

6x2+6x+1+2

Add 1 and 2 to get 3.

6x2+6x+3

Question 1-28
What is the range of possible values for x?
B
A
8.2
11.7
(11x-4)
D
84°
C

Answers

The range of possible values for x is 4/11 < x < 8

How to determine the range of possible values for x?

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

Triangles = 2

On these triangles, we have the following angles

Angle 1 = 11x - 4

Angle 2 = 84

Angle 1 cannot exceed angle 2

So, we have

11x - 4 < 84

Add 4 to both sides

11x < 88

Divide

x < 8

Angle 1 cannot exceed be negative or 0

So, we have

11x - 4 > 0

Add 4 to both sides

11x > 4

Divide

x > 4/11

Hence, the range is 4/11 < x < 8

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An account executive receives a base salary plus a commission. On $50,000 in monthly sales, the account executive receives $6500. On $60,000 in monthly sales, the account executive receives $6800.
(a) Determine a linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x.


(b) Use this model to determine the account executive's compensation for $90,000 in monthly sales.
$

Answers

A)  A linear function that will yield the compensation y of the sales executive for a given amount of monthly sales x is;

B) The account executive's compensation for $90,000 in monthly sales is; $300

How to model a linear equation?

The general equation of a line in slope intercept form is;

y = mx + b

where;

m is slope

b is y-intercept

x and y are provided in the problem: x = monthly sales and y = compensation

We will have to find m (Slope), which represents the commission percentage, and b (y-intercept), which represents the the base salary.

    x₁        y₁         x₂        y₂      

(50000, 6500) (60000, 6800)

Slope;

m = (y₂ - y₁) / (x₂ - x₁)

m = (6800 - 6500) / (60000 - 50000)  

m = 300/10000

m = 3/100 = 0.03 = 3%

To find b, we have to take one of our ordered pairs [ (50000, 6500) or (60000, 6800) ] and plug it into the equation, y=mx+b.

Let's use (60000, 6800)

6800 = 0.03(60000) + b

6800 = 1200 + b  

b = 6800 - 1200

b = $5600

The base salary = $5600

The equation is y = 0.03x + 5600

b) For $90000 in monthly sales, the executive's compensation is;

y = 0.03(90000) + 5600

y = 2700 + 5600

y = $300

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Rory is an independent filmmaker and has great ideas for several movies. For each short film or full-length movie she makes, she has to raise money. She figures that it will take 7 months to raise money for each short film and 7 months to raise money for each full-length movie. She has given herself at most 49 months to raise money for the films before she abandons the project.
1
While Rory is raising money, she also has to write the scripts. It will take her of a month to write each short film script and 2 months to write each full-length movie script. She is committed to spending at most 13 months on writing scripts.
a. What is the system of inequalities that models this scenario?
b. What is the graph of the solutions?
continued

Answers

The required inequality expressions are 7x + 7y ≤ 49 and x + 2y ≤ 13 an the graph has been plotted with clarity.

How to write an expression for linear inequality?

The expression for inequality can be written by taking the suitable sign for the given problem and then relating the variable part to the constant terms.

(a) Suppose the number of short film and full movie are x and y respectively.

Then, the inequality expression for the given case can be written as follows,

The inequality for money raised is,

7x + 7y ≤ 49

And, the inequality for script writing is,

x + 2y ≤ 13

(b) These inequalities can be graphed as follows,

Hence, for the given case the required system of inequalities is 7x + 7y ≤ 49 and x + 2y ≤ 13 and the graph for the solution is drawn properly.

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Last week Scott ran 43 miles less than James. Scott ran 5 miles. How many miles did James run?
A. 35
B. 44
C. 38
D. 48

Answers

Answer:

D) 48

Step-by-step explanation:

Let s = Scott

Let j - James

s = 5

s + 43 = j  Substitute 5 for s

5 + 43 = j

48 = j

(Graphing Proportional Relationships MC)

The table shows a proportional relationship between x and y

x 4.5 // 8.2 // 2.4
----------------------------------------
y 13.5 // 24.6 // 7.2

Which of the following correctly describes the graph of the relationship?

A line that goes through (0, 0) and (13.5, 4.5)
A line that goes through (4.5, 13.5) and (24.6, 8.2)
A line that goes through (13.5, 4.5) and (8.2, 24.6)
A line that goes through (0, 0) and (4.5, 13.5)

Answers

The option that  correctly describes the graph of the relationship is; D: A line that goes through (0, 0) and (4.5, 13.5)

How to find the slope between two coordinates?

The formula for the slope between two coordinates is;

Slope = (y₂ - y₁)/(x₂ - x₁)

Let us take two coordinates from the table which are;

(2.4, 7.2) and (4.5, 13.5)

Thus;

Slope = (13.5 - 7.2)/(4.5 - 2.4)

Slope = 3

Now, looking at the options, the first 3 cannot be correct because they have mixed up x-coordinate values with y-coordinate values.

Let us check the last option which is a line that goes through (0, 0) and (4.5, 13.5). Thus;

Slope = (13.5 - 0)/(4.5 - 0)

Slope = 13.5/4.5

Slope = 3

Thus, we conclude that it is correct.

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I need help these problems

Answers

Step-by-step explanation:

she made shots = 34%of 54

=50*34/100

=17

he made 17 shots

Construct a cumulative frequency distribution
765-799| 22

Answers

The steps to construct a cumulative frequency distribution table are mentioned above.

What is cumulative frequency distribution? What is a mathematical function, equation and expression?                cumulative frequency : A cumulative frequency is defined as the total of frequencies, that are distributed over different class intervals. function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.

Given is to construct a cumulative frequency distribution table.

Since the data is not given, we can write the steps to construct a frequency distribution table. The steps to create a cumulative frequency distribution table are mentioned below -

find the individual frequencies for each distinct value or category.arrange the obtained data in ascending order.the cumulative frequency of a distinct category is calculated by finding the sum of a category’s frequency and the total frequencies of all categories below it. the cumulative frequency of the first category equals the category’s individual frequency.

Therefore, the steps to construct a cumulative frequency distribution table are mentioned above.

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if the circumference of a circle is 5cm, then the diameter is ____cm.
a. 5 cm
b. 31.4 cm
c. 15.7 cm
d. 1.57 cm

Answers

Let’s start with the circumference of a circle formula and solve for “d” (diameter):

C=2πr

The circumference, “C,” is 5cm

5=2πr

Let’s rewrite the formula using the commutative property of multiplication so we can solve for “d:”

5=π2r

The order in which numbers are multiplied does not affect the product. Since the diameter is double the radius, 2r will equal the diameter since 2r equals r+r. So, we can substitute “d” in for 2r:

5=πd

Now, let’s solve for d

Divide both sides by pi:

5/π=d

1.591=d

We can check this back into the formula:

C=π(1.591)

C=4.998


So, your answer is 1.57 since it is the closest.

2. The width, w, of a rectangular garden is x-2. The area of the garden is ³-2x-4. What is
an expression for the length of the garden?
Ox²-2x-2
Ox²+2x-2
Ox²-2x+2
Ox²+2x+2

Answers

Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]

option D is correct

what is area?

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. Surface area refers to an open surface or the perimeter of a three-dimensional object, whereas plane region or plane area refers to a shape or planar lamina.

given

the width(w) of the rectangular garden= [tex]x[/tex][tex]-2[/tex]

area of the rectangular garden = [tex]x^{3} -2x-4[/tex]

The area of a rectangle is,

area = length × width(w) ,

If l is the rectangle's length,

w is the width of the rectangle,

By substituting values,

[tex]x^{3}-2x-4[/tex] = ([tex]x-2[/tex]) *  length ( l )

[tex]l=\frac{x^{3}-2x-4 }{x-2}[/tex] = [tex]x^{2} +2x+2[/tex]   (by long division method)

Consequently, the rectangular garden's length is [tex]x^{2} +2x+2[/tex]

option D is correct

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Neglecting air resistance and the weight of the propellant, determine the work done in propelling a 10-ton satellite to a height of 200 miles above Earth. Assume that the Earth has a radius of 4000 miles. O 4.190.48 mi-ton 1,142.86 mi-ton O 1,904.76 mi-ton 2,857.14 mi-ton 1,523.81 mi-ton

Answers

Therefore ,the the  the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.

Analyze the equation.

An expression is composed of a number, a variable, both, or neither, and specific operation symbols. An equation is made up of two expressions, which are separated by an equal sign.

Here,

Use F(x) = C/[tex]x^{2}[/tex]

Where c is a constant and x is the radius of the earth

F(x) is satellite weight

We have to find c.

thus,

=> 10 = c /[tex]4000^{2}[/tex]

=> c =160000000

Therefore,

=> F(x) =  160000000/  [tex]x^{2}[/tex]

Workdone ,

=> W = [tex]\int\limits^{4200}_{4000} {F(x)} \, dx[/tex]

=>W = [tex]\int\limits^{4200}_{4000} {160000000 /x^{2} } \, dx[/tex]

=>W =[tex]\left \{ {{4200} \atop {4000}} \right. \frac{-160000000 }{x}[/tex]

=> W =1904.7619 million ton

Therefore ,the the  the work done in propelling a 10-ton satellite to a height of 200 miles above Earth is 1904.7619 million ton.

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Data collected on the discharge of the Colorado River and the speed are given in the table:


Discharge (ft3) Speed
1.3 2.3
2.2 0.99
5.8 3.5
11 5
12 16
14 22
16 27
21 14
49 33
51 35


What is the value of the correlation coefficient and its interpretation?
0.76; There is a strong, positive association between discharge and speed.
0.87; There is a strong, positive association between discharge and speed.
−0.76; There is a strong, negative association between discharge and speed.
−0.87; There is a strong, negative association between discharge and speed.

Answers

Answer:

The value of the correlation coefficient is 0.87, which means there is a strong, positive association between discharge and speed. A positive correlation means that as one variable increases, the other variable also increases. In this case, as the discharge of the Colorado River increases, the speed of the river also increases. The strength of the association is indicated by the magnitude of the correlation coefficient, which ranges from -1 to 1. A value of 0.87 is considered a strong positive correlation, indicating that there is a strong relationship between the two variables.

In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat.

What percentage of times at bat did Emerson actually hit the ball?

%

Answers

Emerson actually hit the ball 32% of times at bat.

What is percentage ?

In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Rather than being expressed as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You divide the part of the whole by the whole and multiply the result by 100 to get the percentage.

Since in Game 1, Emerson struck out 30 times in 90 times at bat;

in Game 2, he struck out 40 times in 120 times at bat;

in Game 3, Emerson struck out 42 times in 140 times at bat;

To determine what percentage of times at bat did Emerson actually hit the ball, the following calculation must be performed:

(30 + 40 + 42) / (90 + 120 + 140) = X

112/350 = X

0.32 = X

Therefore, Emerson actually hit the ball 32% of times at bat.

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