(0, 3) and (-2, -1)
Write an equation in slope intercept from of the line that passes through the given points.

Answers

Answer 1

Answer:

y = 2x + 3

Step-by-step explanation:

Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Slope-Intercept Form: y = mx + b

Step 1: Find slope m

m = (-1 - 3)/(-2 - 0)

m = -4/-2

m = 2

y = 2x + b

Step 2: Rewrite equation

y = 2x + 3

*You are given y-intercept (0, 3), so simply add it to your equation.


Related Questions

Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).

Answers

This is not the complete question, the complete question is:

P18-1 (LO2,3) (Allocate Transaction Price, Upfront Fees)

Tablet Tailors sells tablet PCs combined with Internet service, which permits the tablet to connect to the Internet anywhere and set up a Wi-Fi hot spot. It offers two bundles with the following terms.

1. Tablet Bundle A sells a tablet with 3 years of Internet service. The price for the tablet and a 3-year Internet connection service contract is $500. The standalone selling price of the tablet is $250 (the cost to Tablet Tailors is $175). Tablet Tailors sells the Internet access service independently for an upfront payment of $300. On January 2, 2017, Tablet Tailors signed 100 contracts, receiving a total of $50,000 in cash.

2. After 2 years of the 3-year contract, Tablet Tailors offers a modified contract and extension incentive. The extended contract services are similar to those provided in the first 2 years of the contract. Signing the extension and paying $90 (which equals the standalone selling of the revised Internet service package) extends access for 2 more years of Internet connection. Forty Tablet Bundle A customers sign up for this offer.

INSTRUCTION

a) Prepare the journal entries when the contract is signed on January 2, 2019, for the 40 extended contracts. Assume the modification does not result in a separate performance obligation.

b) Prepare the journal entries on December 31, 2019, for the 40 extended contracts (the first year of the revised 3-year contract).

Answer:

Step-by-step explanation:

(A)

Date        Particulars                               Debit                     Credit

2-Jan-19        Cash                                        3600  

                      Unearned Service Revenue                               3600

40 * 90 = 3600

services in the extended period are the same as the services that were provided in the original contract period. As they are not distinct hence the modifications will be considered as part of the original contract.

(B)

Date           Particulars                                    Debit           Credit

31-Dec-19 Unearned Service Revenue            2413  

                       Service revenue                                             2413

internet = 300, price = 550, connection service = 500

(300/550) * 500 = 273

so

Original internet service contract = 40 * 273 = 10,920

Revenue recognized in 1st two years = 10,920 * 2/3 = 7280

Remaining service at original rates = 10920 - 7280 = 3640

Extended service = 3600

3640 + 3600 = $7240  

7240 / 3 = $2413

The problem is: On a Map, 3 inches represents 40 miles, How many inches represents 480 miles?

Answers

Answer: 36

480/40=12
12x3=36

You spend 6,380.00 a year for rent. This is 22% of your income. What is your income?

Answers

Answer: 29,000.00

Step-by-step explanation:

Let the income=x.  22%=0.22.

So 6380/x=0.22

x=6380/0.22=29,000.00

A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent. The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle? 2 cm 2 StartRoot 2 EndRoot cm 4 cm 4 StartRoot 2 EndRoot cm

Answers

Answer:

The leg measures 2 I believe

Step-by-step explanation:

Since the squares of the legs equal C ([tex]A^{2} +B^{2} = C^{2}[/tex]) the square root of 16 would be 4.

The Pythagorean theorem is a basic relationship between the three sides of a right triangle. The length of one leg of the triangle is 2√2 cm.

What is the Pythagoras theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between the three sides of a right triangle in Euclidean geometry. The size of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, according to this rule.

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

Let the length of the perpendicular be x.

Given the length of the hypotenuse is 4 centimeters, while the length of the other two sides is the same, therefore, the length of the other two sides is x. Therefore, using the Pythagorus theorem we can write,

[tex]\rm (Hypotenuse)^2 =(Perpendicular)^2 + (Base)^2[/tex]

[tex]4^2 = x^2+x^2\\\\16=2x^2\\\\8=x^2\\\\x= 2\sqrt2[/tex]

Hence, the length of one leg of the triangle is 2√2 cm.

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The mean monthly car payment for 123 residents of the local apartment complex is $624. What is the best point estimate for the mean monthly car payment for all residents of the local apartment complex?

Answers

Answer:

The best point estimate for the mean monthly car payment for all residents of the local apartment complex is $624.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

In this question:

We apply the inverse Central Limit Theorem.

The mean monthy car payment for 123 residents of the local apartment complex is $624.

So, for all residents of the local apartment complex, the best point estimate for the mean monthly car payment is $624.

The length of a rectangle is 5M more than twice the width and the area of the rectangle is 63M to find the dimension of the rectangle

Answers

Answer:

width = 4.5 m

length = 14 m

Step-by-step explanation:

okay so first you right down that L = 5 + 2w

then as you know that Area = length * width so you replace the length with 5 + 2w

so it's A = (5 +2w) * w = 63

then 2 w^2 + 5w - 63 =0

so we solve for w which equals 4.5 after that you solve for length : 5+ 2*4.5 = 14

Simplify the expression (5j+5) – (5j+5)

Answers

Answer:

0

Step-by-step explanation:

multiply the negative thru the right part of the equation so, 5j+5-5j-5. The 5j and the 5 than cancel out with each other. Hope this helps!

Answer:

0

Explanation:

step 1 - remove the parenthesis from the expression

(5j + 5) - (5j + 5)

5j + 5 - 5j - 5

step 2 - combine like terms

5j + 5 - 5j - 5

5j - 5j + 5 - 5

0 + 0

0

therefore, the simplified form of the given expression is 0.

Find the indicated conditional probability
using the following two-way table:
P( Drive to school | Sophomore ) = [?]
Round to the nearest hundredth.

Answers

Answer:

0.07

Step-by-step explanation:

The number of sophmores is 2+25+3 = 30.

Of these sophmores, 2 drive to school.

So the probability that a student drives to school, given that they are a sophmore, is 2/30, or approximately 0.07.

Answer:

[tex]\large \boxed{0.07}[/tex]

Step-by-step explanation:

The usual question is, "What is the probability of A, given B?"

They are asking, "What is the probability that you are driving to school if you are a sophomore (rather than taking the bus or walking)?"

We must first complete your frequency table by calculating the totals for each row and column.

The table shows that there are 30 students, two of whom drive to school.

[tex]P = \dfrac{2}{30}= \mathbf{0.07}\\\\\text{The conditional probability is $\large \boxed{\mathbf{0.07}}$}[/tex]

Evaluate the expression.........

Answers

Answer:

9

Step-by-step explanation:

p^2 -4p +4

Let p = -1

(-1)^1 -4(-1) +4

1 +4+4

9

Given a right triangle with a hypotenuse length of radical 26 and base length of 3. Find the length of the other leg (which is also the height).

Answers

Answer:

  √17

Step-by-step explanation:

The Pythagorean theorem can be used for the purpose.

  hypotenuse² = base² +height²

  (√26)² = 3² +height²

  26 -9 = height²

  height = √17

The length of the other leg is √17.

At 95% confidence, how large a sample should be taken to obtain a margin of error of 0.05 for the estimation of a population proportion

Answers

Answer:

A sample of 385 is needed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

How large a sample:

We need a sample of n.

n is found when M = 0.05.

We dont know the true proportion, so we work with the worst case scenario, which is [tex]\pi = 0.5[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.96*0.5[/tex]

[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]

[tex](\sqrt{n})^{2} = (\frac{1.96*0.5}{0.05})^{2}[/tex]

[tex]n = 384.16[/tex]

Rounding up

A sample of 385 is needed.

4
The equation of a circle is x2 + y2 + x + Dy+ E= 0. If the radius of the circle is decreased without changing the coordinates of the center point, how are the coefficients CD,
and E affected?
O A CD, and E are unchanged.​

Answers

Answer:

Step-by-step explanation:

in x²+y²+2gx+2fy+c=0

center=(-g,-f)

radius=√((-g)²+(-f)²-c)

if center is not changed ,then c will change .

Here only coefficients of  E will change.

2{ 3[9 + 4(7 -5) - 4]}

Answers

Answer:

2{3[9+4(7-5)-4]}

2{3[9+4(2)-4]}

2{3[13(2)-4]}

2{3[26-4]}

2{3[22]}

2{66}

132

Step-by-step explanation:

Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter: 116 meters

Answers

Answer:

Length = 29 m

Width = 29 m

Step-by-step explanation:

Let x and y be the length and width of the rectangle, respectively.

The area and perimeter are given by:

[tex]A=xy\\p=116=2x+2y\\y=58-x[/tex]

Rewriting the area as a function of x:

[tex]A(x) = x(58-x)\\A(x) = 58x-x^2[/tex]

The value of x for which the derivate of the area function is zero, is the length that maximizes the area:

[tex]A(x) = 58x-x^2\\\frac{dA}{dx}=0=58-2x\\ x=29\ m[/tex]

The value of y is:

[tex]y = 58-29\\y=29\ m[/tex]

Length = 29 m

Width = 29 m

In a survey, 205 people indicated they prefer cats, 160 indicated they prefer dots, and 40 indicated they don’t enjoy either pet. Find the probability that if a person is chosen at random, they prefer cats

Answers

Answer: probability =  0.506

Step-by-step explanation:

The data we have is:

Total people: 205 + 160 + 40 = 405

prefer cats: 205

prefer dogs: 160

neither: 40

The probability that a person chosen at random prefers cats is equal to the number of people that prefer cats divided the total number of people:

p = 205/405 = 0.506

in percent form, this is 50.6%

Which proportion would convert 18 ounces into pounds?

Answers

Answer:

16 ounces = 1 pound

Step-by-step explanation:

You would just do 18/16 = 1.125 pounds. There are always 16 ounces in a pound, so it always works like this

16 ounces to 1 pound

Christopher collected data from a random sample of 800 voters in his state asking whether or not they would vote to reelect the current governor. Based on the results, he reports that 54% of the voters in his city would vote to reelect the current governor. Why is this statistic misleading?

Answers

Answer:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

Step-by-step explanation:

The statistic is misleading because Christopher collects his sample from a population (voters in his state) and make inferences about another population (voters in his city).

He should make inferences about the population that is well represented by his sample (voters in his state), or take a sample only from voters from his city to make inferences about them.

Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year. Which of the following choices is the correct function? a p(s) = 114000• 0.985x b p(s) = 114000x c p(s) = 114000x + 0.985 d None of these choices are correct.

Answers

Answer: D

Step-by-step explanation:

According to the question, Silver Lake has a population of 114,000. The population is decreasing at a rate of 1.5% each year

The initial population Po = 114000

Rate = 1.5% = 0.015

The declining population formula will be:

P = Po( 1 - R%)x^2

The decay formula

Since the population is decreasing, take away 0.015 from 1

1 - 0.015 = 0.985

Substitutes all the parameters into the formula

P(s) = 114000(0.985)x^2

P(s) = 114000× 0985x^2

The correct answer is written above.

Since option A does not have square of x, we can therefore conclude that the answer is D - non of the choices is correct.

Suppose a random variable X is best described by a uniform probability distribution with range 1 to 5. Find the value of that makes the following probability statements true.
a) P(X <-a)= 0.95
b) P(X c) P(X d) P(X ->a)= 0.89
e) P(X >a)= 0.31

Answers

Answer:

a) 4.8

b) 2.96

c) 4.4

d) 1.44

e) 3.76

Step-by-step explanation:

What we will do is solve point by point, knowing the following:

Fx (x) = P (X <= x) = (x - 1) / 4

a) P (X <-a) = 0.95

Fx (a) = 0.95

(a -1) / 4 = 0.95

a = 1 + 0.95 * 4

a = 4.8

b) P (X <a) = 0.49

Fx (a) = 0.49

(a -1) / 4 = 0.49

a = 1 + 0.49 * 4

a = 2.96

c) P (X <a) = 0.85

Fx (a) = 0.85

(a -1) / 4 = 0.55

a = 1 + 0.85 * 4

a = 4.4

d) P (X> a) = 0.89

P (X <a) = 1 - 0.89 = 0.11

Fx (a) = 0.11

(a -1) / 4 = 0.11

a = 1 + 0.11 * 4

a = 1.44

e) P (X> a) = 0.31

P (X <a) = 1 - 0.31 = 0.69

Fx (a) = 0.69

(a -1) / 4 = 0.69

a = 1 + 0.69 * 4

a = 3.76

the ellipse is centered at the origin, has axes of lengths 8 and 4, its major axis is horizontal. how do you write an equation for this ellipse?​

Answers

Answer:

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

Step-by-step explanation:

The standard equation of the ellipse is described by the following expression:

[tex]\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}} = 1[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the horizontal and vertical semi-axes, respectively. Given that major semi-axis is horizontal, [tex]a > b[/tex]. Then, the equation for this ellipse is written in this way: (a = 8, b = 4)

[tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex]

The equation for this ellipse is [tex]\frac{x^{2}}{64} + \frac{y^{2}}{16} = 1[/tex].

if a varies inversely as the cube root of b and a=1 when b=64, find b​

Answers

Answer:

  b = 64/a³

Step-by-step explanation:

Using the given information, we can only find a relation between a and b. We cannot find any specific value for b.

Since a varies inversely as the cube root of b, we have ...

  a = k/∛b

Multiplying by ∛b lets us find the value of k:

  k = a·∛b = 1·∛64 = 4

Taking the cube of this equation gives ...

  64 = a³b

  b = 64/a³ . . . . . divide by a³

The value of b is ...

  b = 64/a³

show that 7 1/2 - 4 2/3 = 2 5/6

Answers

You have to make the denominator common before subtracting 2 fractions.

Since the end fraction has a denominator of 6 try and multiply both of the ones on the LHS to get 6 as a denominator.

First though convert the improper fractions into fractions solely.

7 1/2 goes to 15/2

While

4 2/3 goes to 14/3

Now

15/2 multiply both numerator and denominator by 3 gives you 45/6

14/3 multiply both numerator and denominator by 2 gives you 28/6

Subtract 45/6 by 28/6= 17/6

Highest multiple of 6 in 17 is 12
12/6 + 5/6 = 2 5/6

Equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The given equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex]

We need to check whether the left hand side is equal to right hand side.

These are in the form pf mixed fraction we can convert them to the improper fraction.

[tex]7\frac{1}{2}=15/2[/tex]

[tex]4\frac{2}{3}=\frac{14}{3}[/tex]

So Let us subtract 24/3 from 15/2

15/2-14/3

LCM of 2 and 3 is 6

45-28/6

17/6

This can be written as mixed fraction [tex]2\frac{5}{6}[/tex]

Hence, equation is [tex]7\frac{1}{2} -4\frac{2}{3}=2\frac{5}{6}[/tex] is true.

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Jeremy makes $57,852 per year at his accounting firm. How much is Jeremy’s monthly salary? (There are 12 months in a year.) How much is Jeremy’s weekly salary? (There are 52 weeks in a year.)

Answers

Answer:

Monthly: $4,821

Weekly: $1112.54

Step-by-step explanation:

Monthly

A monthly salary can be found by dividing the yearly salary by the number of months.

salary / months

His salary is $57,852 and there are 12 months in a year.

$57,852/ 12 months

Divide

$4,821 / month

Jeremy makes $4,821 per month.

Weekly

To find the weekly salary, divide the yearly salary by the number of weeks.

salary / weeks

He makes $57,852 each year and there are 52 weeks in one year.

$57,852 / 52 weeks

Divide

$1112.53846 / week

Round to the nearest cent. The 8 in the thousandth place tells use to round the 3 up to a 4 in the hundredth place.

$1112.54 / week

Jeremy makes $1112.54 per week

The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 7/8 inches and a standard deviation of 1/16 inch. Assume independence. a. Determine the mean and standard deviation of the difference between the width of the casing and the width of the door. b. What is the probability that the width of the casing minus the width of the door exceeds 1/4 inch? c. What is the probability that the door does not fit in the casing?

Answers

Answer:

a) Mean = 0.125 inch

Standard deviation = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25) = 0.18673

c) Probability that the door does not fit in the casing = P(X < 0) = 0.18673

Step-by-step explanation:

Let the distribution of the width of the casing be X₁ (μ₁, σ₁²)

Let the distribution of the width of the door be X₂ (μ₂, σ₂²)

The distribution of the difference between the width of the casing and the width of the door = X = X₁ - X₂

when two independent normal distributions are combined in any manner, the resulting distribution is also a normal distribution with

Mean = Σλᵢμᵢ

λᵢ = coefficient of each disteibution in the manner that they are combined

μᵢ = Mean of each distribution

Combined variance = σ² = Σλᵢ²σᵢ²

λ₁ = 1, λ₂ = -1

μ₁ = 24 inches

μ₂ = 23 7/8 inches = 23.875 inches

σ₁² = (1/8)² = (1/64) = 0.015625

σ₂ ² = (1/16)² = (1/256) = 0.00390625

Combined mean = μ = 24 - 23.875 = 0.125 inch

Combined variance = σ² = (1² × 0.015625) + [(-1)² × 0.00390625] = 0.01953125

Standard deviation = √(Variance) = √(0.01953125) = 0.1397542486 = 0.13975 inch

b) Probability that the width of the casing minus the width of the door exceeds 1/4 inch = P(X > 0.25)

This is a normal distribution problem

Mean = μ = 0.125 inch

Standard deviation = σ = 0.13975 inch

We first normalize/standardize 0.25 inch

The standardized score of any value is that value minus the mean divided by the standard deviation.

z = (x - μ)/σ = (0.25 - 0.125)/0.13975 = 0.89

P(X > 0.25) = P(z > 0.89)

Checking the tables

P(x > 0.25) = P(z > 0.89) = 1 - P(z ≤ 0.89) = 1 - 0.81327 = 0.18673

c) Probability that the door does not fit in the casing

If X₂ > X₁, X < 0

P(X < 0)

We first normalize/standardize 0 inch

z = (x - μ)/σ = (0 - 0.125)/0.13975 = -0.89

P(X < 0) = P(z < -0.89)

Checking the tables

P(X < 0) = P(z < -0.89) = 0.18673

Hope this Helps!!!

1. Growth of Functions (11 points) (1) (4 points) Determine whether each of these functions is O(x 2 ). Proof is not required but it may be good to try to justify it (a) 100x + 1000 (b) 100x 2 + 1000

Answers

Answer:

See explanation

Step-by-step explanation:

To determine whether each of these functions is [tex]O(x^2)[/tex], we apply these theorems:

A polynomial is always O(the term containing the highest power of n)Any O(x) function is always [tex]O(x^2)[/tex].

(a)Given the function: f(x)=100x+1000

The highest power of n is 1.

Therefore f(x) is O(x).

Since any O(x) function is always [tex]O(x^2)[/tex], 100x+1000 is [tex]O(x^2)[/tex].

[tex](b) f(x)=100x^ 2 + 1000[/tex]

The highest power of n is 2.

Therefore the function is [tex]O(x^2)[/tex].

Answer:

i think its 2000

Step-by-step explanation:

whats 1/2 + 2/4 - 5/8?

Answers

Answer:

3/8

Step-by-step explanation:

Step 1: Find common denominators

1/2 = 4/8

2/4 = 4/8

Step 2: Evaluate

4/8 + 4/8 - 5/8

8/8 - 5/8

3/8

Alternatively, you can just plug this into a calc to evaluate and get your answer.

Answer:

3/8

Step-by-step explanation:

Look at the denominator:

2, 4, 8. The LCM (Lowest Common Multiple) is 8.

So this equation becomes

4/8+4/8-5/8=3/8

I got the answer but I really don’t know if it’s correct or not, please help this is due today

Answers

Answer: x=2

Explanation: 180-52 = 128

So we have an equation:

2^3x+1=128 ( cuz they are in the same position)

Now we need to find what number that 2 raise to the power of that number is 128

And the answer is 2^7=128

Let’s go back to our equation:

2^3x+1=128
And we know that 2^7=128
Now we just have to make 3x+1=7:
3x+1=7
x=(7-1)/3
x=2

And there you have it x=2

Suppose 150 students are randomly sampled from a population of college students. Among sampled students, the average IQ score is 115 with a standard deviation of 10. What is the 99% confidence interval for the average IQ of college students? Possible Answers: 1) A) E =1.21 B) E = 1.25 C) E =2.52 D) E = 2.11 2) A) 112.48 < μ < 117.52 B) 113.79 < μ < 116.21 C) 112.9 < μ < 117.10 D) 113.75 < μ < 116.3

Answers

Answer:

99% confidence interval for the mean of college students

A) 112.48 < μ < 117.52

Step-by-step explanation:

step(i):-

Given sample size 'n' =150

mean of the sample = 115

Standard deviation of the sample = 10

99% confidence interval for the mean of college students are determined by

[tex](x^{-} -t_{0.01} \frac{S}{\sqrt{n} } , x^{-} + t_{0.01} \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

Degrees of freedom

ν = n-1 = 150-1 =149

t₁₄₉,₀.₀₁ =  2.8494

99% confidence interval for the mean of college students are determined by

[tex](115 -2.8494 \frac{10}{\sqrt{150} } , 115 + 2.8494\frac{10}{\sqrt{150} } )[/tex]

on calculation , we get

(115 - 2.326 , 115 +2.326 )

(112.67 , 117.326)  

The dimensions of a closed rectangular box are measured as 96 cm, 58 cm, and 48 cm, respectively, with a possible error of 0.2 cm in each dimension. Use differentials to estimate the maximum error in calculating the surface area of the box.

Answers

Answer:

161.6 cm²

Step-by-step explanation:

Surface Area of the rectangular box = 2(LW+LH+WH)

L is the length of the box

W is the width of the box

H is the height of the box

let dL, dW and dH be the possible error in the dimensions L, W and H respectively.

Since there is a possible error of 0.2cm in each dimension, then dL = dW = dH = 0.2cm

The surface Area of the rectangular box using the differentials is expressed as shown;

S = 2{(LdW+WdL)+(LdH+HdL)+(WdH+HdW)]

Also given L = 96cm W = 58cm and H = 48cm, on substituting this given values and the differential error, we will have;

S = 2{(96*0.2+58*0.2) + (96*0.2+48*0.2)+(58*0.2+48*0.2)}

S = 2{19.2+11.6+19.2+9.6+11.6+9.6}

S = 2(80.8)

S = 161.6 cm²

Hence, the surface area of the box is 161.6 cm²

¿Cuál serie numérica tiene como regla general Xn = 2n +1?
a. 3, 5, 7, 9
b. 2, 4, 5, 8
c. 4, 6, 8,10
d. 2, 3, 4, 5

Answers

Answer:

The series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

Step-by-step explanation:

We are given with the following series options below;

a. 3, 5, 7, 9

b. 2, 4, 5, 8

c. 4, 6, 8,10

d. 2, 3, 4, 5

And we have to identify what number series has a general rule as [tex]X_n=2n+1[/tex].

For this, we will put the values of n in the above expression and then will see which series is obtained as a result.

So, the given expression is ; [tex]X_n=2n+1[/tex]

If we put n = 1, then;

[tex]X_1=(2\times 1)+1[/tex]

[tex]X_1 = 2+1 = 3[/tex]

If we put n = 2, then;

[tex]X_2=(2\times 2)+1[/tex]

[tex]X_2 = 4+1 = 5[/tex]

If we put n = 3, then;

[tex]X_3=(2\times 3)+1[/tex]

[tex]X_3 = 6+1 = 7[/tex]

If we put n = 4, then;

[tex]X_4=(2\times 4)+1[/tex]

[tex]X_4 = 8+1 = 9[/tex]

Hence, the series of numbers that correspond to the general rule of  [tex]X_n=2n+1[/tex] is {3, 5, 7, 9}.

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