Find the remainder when f(x)=2x3−x2+x+1 is divided by 2x+1.

Step-by-step explanation:

given,

base( b) = 6cm

height (h)= 11cm

now, area of parallelogram (a)= b×h

or, a = 6cm ×11cm

therefore the area of parallelogram (p) is 66cm^2.

hope it helps...

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}.

Answer:

x = -2 , -1

Step-by-step explanation:

Set the equation equal to 0. Add 2 to both sides:

x² + 3x = -2

x² + 3x (+2) = - 2 (+2)

x² + 3x + 2 = 0

Simplify. Find factors of x²  and 2 that will give 3x when combined:

x²  + 3x + 2 = 0

x               2

x               1

(x + 2)(x + 1) = 0

Set each parenthesis equal to 0. Isolate the variable, x. Note that what you do to one side of the equation, you do to the other.

(x + 2) = 0

x + 2 (-2) = 0 (-2)

x = 0 - 2

x = -2

(x + 1) = 0

x + 1 (-1) = 0 (-1)

x = 0 - 1

x = -1

x = -2 , -1

~

Answer:

x = -2       OR      x = -1

Step-by-step explanation:

=> [tex]x^2+3x = -2[/tex]

Adding 2 to both sides

=> [tex]x^2+3x+2 = 0[/tex]

Using mid-term break formula

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

=> x(x+1)+2(x+1) = 0

=> (x+2)(x+1) = 0

Either:

x+2 = 0    OR     x+1 = 0

x = -2       OR      x = -1

P.S. Ummmm maybe...... Because he usually reports absurd answers! So, Won't it be better that he could directly delete it. And one more thing! He's Online 24/7!!!!!

Answer:

C and D

Step-by-step explanation:

khan acedemy

An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the given equation v²=25/81 can be found as shown below.

v²=25/81

Taking the square root of both sides of the equation,

√(v²) = √(25/81)

v = √(25/81)

v = √(5² / 9²)

v = ± 5/9

Hence, the solutions of the given equation are A, B, and C.

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Answer:

[tex]\dfrac{1}{7}[/tex]

Step-by-step explanation:

There are 7 days in a week.

For the first person, we select one day out of the 7 days. The first person has 7 options out of the 7 days.

Let Event A be the event that the first person was born on a day of the week.

Therefore:

[tex]P(A)=\dfrac{7}{7}=1[/tex]

The second person has to be born on the same day as the first person. Therefore, the second person has 1 out of 7 days to choose from.

Let Event B be the event that the second person was born.

Therefore, the probability that the second person was born on the same day as the first person:

[tex]P(B|A)=\dfrac{1}{7}[/tex]

By the definition of Conditional Probability

[tex]P(B|A)=\dfrac{P(B \cap A)}{P(A)} \\$Therefore:\\P(B \cap A)=P(B|A)P(A)[/tex]

The probability that both were born on the same day is:

[tex]P(B \cap A)=P(B|A)P(A) = \dfrac{1}{7} X 1 \\\\= \dfrac{1}{7}[/tex]

Answer:

7 + 5(x - 3) = 22

5(x - 3) = 15

x - 3 = 3

x = 6

Answer:

x = 6

Step-by-step explanation:

Step 1: Distribute 5

7 + 5x - 15 = 22

Step 2: Combine like terms

5x - 8 = 22

Step 3: Add 8 to both sides

5x = 30

Step 4: Divide both sides by 5

x = 6

Answer:

Option (A).

Step-by-step explanation:

The function f(x) = x² + 4 is defined over the interval (-2, 2)

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, height of the right endpoint of each rectangle = [tex]\frac{5}{n}[/tex]

Height of the endpoint of the k rectangles = [tex]k.\frac{5}{n}[/tex]

Therefore, height of the endpoint of the kth rectangle = Height of first rectangle + height of k rectangles

= -2 + [tex]k.\frac{5}{n}[/tex]

Option (A). will be the answer.

The height of the right endpoint of the kth rectangle h = -2 + k (5/n)

The height is a vertical distance between two points. In the case of the triangle, the height will be the distance between the base and the top vertex of the triangle.

The function f(x) = x² + 4 is defined over the interval) (-2, 2 )

Total number of equal parts between this interval = 5

If the interval is divided into n equal parts, the height of the right endpoint of each rectangle = (5/n)

Height of the endpoint of the k rectangles = k (5/n)

The height of the endpoint of the kth rectangle:-

= Height of first rectangle + height of k rectangles

= -2   +  k (  5/n )

Therefore the height of the right endpoint of the kth rectangle h = -2 + k (5/n)

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Answer:

Step-by-step explanation:

Since there are  2 red and 5 white balls in the box, the total number of balls in the bag = 2+5 = 7balls.

Probability that at least 1 ball was​ red, given that the first ball was replaced before the second can be calculated as shown;

Since at least 1 ball picked at random, was red, this means the selection can either be a red ball first then a white ball or two red balls.

Probability of selecting a red ball first then a white ball with replacement = (2/7*5/7) = 10/49

Probability of selecting two red balls with replacement = 2/7*2/7 = 4/49

The probability that at least 1 ball was​ red given that the first ball was replaced before the second draw= 10/49+4/49 = 14/49

If the balls were not replaced before the second draw

Probability of selecting a red ball first then a white ball without replacement = (2/7*5/6) = 10/42 = 5/21

Probability of selecting two red balls without replacement = 2/7*2/6 = 4/42 = 2/21

The probability that at least 1 ball was​ red given that the first ball was not replaced before the second draw = 5/21+4/21 = 9/21 = 3/7

The probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

Since two balls are drawn in succession out of a box containing 2 red and 5 white balls, to find the probability that at least 1 ball was red, given that the first ball was A) replaced before the second draw; and B) not replaced before the second draw; the following calculations must be performed:

Therefore, the probability that at least 1 ball was red, given that the first ball was replaced before the second draw is 28.5%; and the probability that at least 1 ball was red, given that the first ball was not replaced before the second draw is 22.5%.

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Answer:

The probability plot of this distribution shows that it is approximately normally distributed..

Check explanation for the reasons.

Step-by-step explanation:

The complete question is attached to this solution provided.

From the cumulative probability plot for this question, we can see that the plot is almost linear with no points outside the band (the fat pencil test).

The cumulative probability plot for a normal distribution isn't normally linear. It's usually fairly S shaped. But, when the probability plot satisfies the fat pencil test, we can conclude that the distribution is approximately linear. This is the first proof that this distribution is approximately normal.

Also, the p-value for the plot was obtained to be 0.541.

For this question, we are trying to check the notmality of the distribution, hence, the null hypothesis would be that the distribution is normal and the alternative hypothesis would be that the distribution isn't normal.

The interpretation of p-valies is that

When the p-value is greater than the significance level, we fail to reject the null hypothesis (normal hypothesis) and but if the p-value is less than the significance level, we reject the null hypothesis (normal hypothesis).

For this distribution,

p-value = 0.541

Significance level = 0.05 (Evident from the plot)

Hence,

p-value > significance level

So, we fail to reject the null or normality hypothesis. Hence, we can conclude that this distribution is approximately normal.

Hope this Helps!!!

Answer:

x < 11.5

Step-by-step explanation:

2x + 9 < 32

(2x + 9) - 9  < 32 - 9

2x < 23

2x/2 < 23/2

x < 11.5

Answer:

x < 11 1/2

Step-by-step explanation:

2x+9<32

Subtract 9 from each side

2x+9-9 < 32-9

2x<23

Divide by 2

2x/2 <23/2

x < 11 1/2

X is any number less than 11 1/2

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)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:

Answer:

5x + 10 = 25

Subtract 10 on each side to make x alone

5x = 15

divide by 5 on each side

x=3 so x=3

3x + 12 = 48

48-12=36

3x=36

divide by 3

x=12

4x + 8 = 16

4x = 8

x=2

2x + 15=25

2x=10

x=5

5x + 20 = 50

5x=30

x=6

hope this helps

1. 3

2.12

3.2

4.5

5.6

Step-by-step explanation:

Answer:

Step by step explanation

First:

Solution,

1. 5x + 10 = 25

Move constant to the R.H.S and change its sign:

5x = 25 - 10

Calculate the difference

5x = 15

Divide both sides by 5

5x/5 = 15/5

calculate

X = 3

2. 3x + 12 = 48

or, 3x = 48 - 12

or, 3x = 36

or, 3x/x = 36/3

x = 12

3. 4x + 8 = 16

or, 4x = 16 - 8

or, 4x = 8

or, 4x/x = 8/4

x = 2

4. 2x + 15 = 25

or, 2x = 25 - 15

or, 2x = 10

or, 2x/x= 10/2

x = 5

5. 5x + 20 = 50

or, 5x = 50-20

or, 5x = 30

or, 5x/x = 30/5

x = 6

Hope this helps...

Good luck on your assignment...

Answer:

Step-by-step explanation:

Least common denominator = a²b²

[tex]\frac{3}{a^{2}}+\frac{2}{ab^{2}}=\frac{3*b^{2}}{a^{2}*b^{2}}+\frac{2*a}{ab^{2}*a}\\\\=\frac{3b^{2}}{a^{2}b^{2}}+\frac{2a}{a^{2}b^{2}}\\\\=\frac{3b^{2}+2a}{a^{2}b^{2}}[/tex]

Answer:

0.007

Step-by-step explanation:

We were told in the above question that a random sample of 51 households is monitored for one year to determine aluminum usage

Step 1

We would have to find the sample standard deviation.

We use the formula = σ/√n

σ = 12.2 pounds

n = number of house holds = 51

= 12.2/√51

Sample Standard deviation = 1.7083417025.

Step 2

We find the z score for when the sample mean is more than 61

z-score formula is z = (x-μ)/σ

where:

x = raw score = 61 pounds

μ = the population mean = 56.8 pounds

σ = the sample standard deviation = 1.7083417025

z = (x-μ)/σ

z = (61 - 56.8)/ 1.7083417025

z = 2.45852

Finding the Probability using the z score table

P(z = 2.45852) = 0.99302

P(x>61) = 1 - P(z = 2.45852) = 0.0069755

≈ 0.007

Therefore,the probability that the sample mean will be more than 61 pounds is 0.007

Answer:

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

Answer:  width = 300

Step-by-step explanation:

Area (A) = Length (L) x width (w)

Given: A = 268,500

           L = 3w - 5

           w = w

268,500 = (3w - 5) x (w)

268,500 = 3w² - 5w

            0 = 3w² - 5w - 268,500

            0 = (3w + 895) (w - 300)

   0 = 3w + 895        0 = w - 300

  -985/3 = w             300 = w

Since width cannot be negative, disregard w = -985/3

So the only valid answer is: w = 300

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

Answer:

-10, 40, -240, 1,920 and -19, 200

Step-by-step explanation:

Given the recurrence relation of the sequence defined as aₙ₊₁ = -2naₙ for n = 1, 2, 3... where a₁ = 5, to get the first five terms of the sequence, we will find the values for when n = 1 to n =5.

when n= 1;

aₙ₊₁ = -2naₙ

a₁₊₁ = -2(1)a₁

a₂ = -2(1)(5)

a₂ = -10

when n = 2;

a₂₊₁ = -2(2)a₂

a₃ = -2(2)(-10)

a₃ = 40

when n = 3;

a₃₊₁ = -2(3)a₃

a₄ = -2(3)(40)

a₄ = -240

when n= 4;

a₄₊₁ = -2(4)a₄

a₅ = -2(4)(-240)

a₅ = 1,920

when n = 5;

a₅₊₁ = -2(5)a₅

a₆ = -2(5)(1920)

a₆ = -19,200

Hence, the first five terms of the sequence is -10, 40, -240, 1,920 and -19, 200

Answer:

A. y=-1/4x

Step-by-step explanation:

We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.

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)  

Answer:

k = -6

Step-by-step explanation:

hello

saying that (x-2) is a factor of [tex]x^2+x+k[/tex]

means that 2 is a zero of

[tex]x^2+x+k=0 \ so\\2^2+2+k=0\\<=> 4+2+k=0\\<=> 6+k =0\\<=> k = -6[/tex]

and we can verify as

[tex](x^2+x-6)=(x-2)(x+3)[/tex]

so it is all good

hope this helps

Answer:

Step-by-step explanation:

Length of an arc is expressed as [tex]L = \frac{\theta}{2\pi } * 2\pi r\\[/tex]. Given;

[tex]\theta = \frac{5\pi }{6} rad\\ radius = 24in\\[/tex]

The length of the minor arc SV is expressed as:

[tex]L = \frac{\frac{5\pi }{6} }{2\pi } * 2\pi (24)\\L = \frac{5\pi }{12\pi } * 48\pi \\L = \frac{5}{12} * 48\pi \\L = \frac{240\pi }{12} \\L = 20\pi \ in[/tex]

Hence, The length  of the arc SV is 20π in

Answer:

20 pi

Step-by-step explanation:

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]

Answer:

a. 0.34885

b. 0.04651

c. 0.02404

d. 36

e. 14.7, say 15 trials

Step-by-step explanation:

Q17070205

Note:  

1. In order to be applicable to established probability distributions, each roll is considered a Bernouilli trial, i.e. has only two outcomes, success or failure, and are all independent of each other.

2. use R to find the probability values from the respective distributions.

a) the chance that the first 6 appears before the tenth roll

This means that a six appears exactly once between the first and the nineth roll.

Using binomial distribution, p=1/6, n=9, x=1

dbinom(1,9,1/6) = 0.34885

b) the chance that the third 6 appears on the tenth roll

This means exactly two six's appear between the first and 9th rolls, and the tenth roll is a six.

Again, we have a binomial distribution of p=1/6, n=9, x=2

p1 = dbinom(2,9,1/6) = 0.27908

The probability of the tenth roll being a 6 is, evidently, p2 = 1/6.

Thus the probability of both happening, by the multiplication rule, assuming independence  

P(third on the tenth roll) = p1*p2 = 0.04651

c) the chance of seeing three 6's among the first ten rolls given that there were six 6's among the first twenty roles.

Again, using binomial distribution, probability of 3-6's in the first 10 rolls,

p1 = dbinom(3,10,1/6) = 0.15504

Probability of 3-6's in the NEXT 10 rolls

p1 = dbinom(3,10,1/6) = 0.15504

Probability of both happening  (multiplication rule, assuming both events are independent)

= p1 *  p1 = 0.02404

d) the expected number of rolls until six 6's appear

Using the negative binomial distribution, the expected number of failures before n=6 successes, with probability p = 1/6

=  n(1-p)/p

Total number of rolls by adding n  

= n(1-p)/p + n = n(1-p+p)/p = n/p = 6/(1/6) = 36

e) the expected number of rolls until all six faces appear

P1 = 6/6 because the firs trial (roll) can be any face with probability 1

P2 = 6/5 because the second trial for a different face has probability 5/6, so requires 6/5 trials

P3 = 6/4 ...

P4 = 6/3

P5 = 6/2

P6 = 6/1

So the total mean (expected) number of trials is 6/6+6/5+6/4+6/3+6/2+6/1 = 14.7, say 15 trials

Answer:

  C)  42

Step-by-step explanation:

The parallel lines divide the transversals proportionally.

  x/35 = 30/25

  x = 35(6/5) . . . . multiply by 35, reduce the fraction

  x = 42

Answer:

it we'll be 0.3

Step-by-step explanation:

trust me man I like to explain but it's long

Answer:

0.3 meter or 3/10 meter

Step-by-step explanation:

As there are 100cm in 1 meter and you want to find 30cm in terms of meters.

It will be as

100cm = 1 meter     (rule/lax)

100/100 cm = 1/100  meter   (divide both sides of equation with 100)

1 cm = 1/100 meter

1 *30 cm = (1/100)*30  meter    (multiply both sides with 30)

30 cm = 30/100 meter

30/100 more shortly can be written as  3/10 meter or in decimals 0.3 meter.

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

Answer:

100%

Step-by-step explanation:

Start with x.

x = x/1

Increase the numerator by 60% to 1.6x.

Decrease the numerator by 20% to 0.8.

The new fraction is

1.6x/0.8

Do the division.

1.6x/0.8 = 2x

The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.

The increase is 100%.

Answer:

33%

Step-by-step explanation:

let fraction be x/y

numerator increased by 60%

=x+60%ofx

=8x

denominator increased by 20%

=y+20%of y

so the increased fraction is 4x/3y

let the fraction is increased by a%

then

x/y +a%of (x/y)=4x/3y

or, a%of(x/y)=x/3y

[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]

therefore a=33

anda%=33%

━━━━━━━☆☆━━━━━━━

▹ Answer

0.25 = 1/4 because 25/100 = 1/4

▹ Step-by-Step Explanation

0.25 to a fraction → 25/100

25/100 = 1/4

Therefore, this statement is true. (0.25 = 1/4 because 25/100 = 1/4)

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]

Step-by-step explanation:

Critical points:

The critical points of a function f(x) are the values of x for which:

[tex]f'(x) = 0[/tex]

For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.

The critical points help us find these intervals.

In this question:

[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]

So

[tex]P'(x) = -0.008x + 6[/tex]

Critical point:

[tex]P'(x) = 0[/tex]

[tex]-0.008x + 6 = 0[/tex]

[tex]0.008x = 6[/tex]

[tex]x = \frac{6}{0.008}[/tex]

[tex]x = 750[/tex]

We have two intervals:

(0, 750) and [tex](750, \infty)[/tex]

(0, 750)

Will find P'(x) when x = 1

[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]

Positive, so increasing.

Interval [tex](750, \infty)[/tex]

Will find P'(x) when x = 800

[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]

Negative, then decreasing.

Answer:

Increasing: [tex](0, 750)[/tex]

Decreasing: [tex](750, \infty)[/tex]