What are the 5 types of inequality math?

Answers

Answer 1

The four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.

What is meant by inequality?

In mathematics, an inequality displays the connection between two values in an unbalanced algebraic statement. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.

There are four ways to depict an inequality: solution graph, interval notation, set notation, and equation notation.

A comparison of any two values, known as an inequality, demonstrates whether one value is less than, larger than, or equal to the value on the opposite side of the equation. A relationship in a real-world scenario can be demonstrated by writing an inequality.

To learn more about inequality refer to;

brainly.com/question/25275758

#SPJ4


Related Questions

a. How many integers from 1 through 999 do not have any repeated digits?
b. How many integers from 1 through 999 have at least one repeated digit?
c. What is the probability that an integer chosen at random from 1 through 999 has at least one repeated digit?

Answers

a. There are 648 integers from 1 through 999 that do not have any repeated digits.

b. There are 351 integers from 1 through 999 that have at least one repeated digit.

c. The probability that an integer chosen at random from 1 through 999 has at least one repeated digit is approximately 0.351.

How many integers from 1 through 999 have unique digits?

Learn more about the count of integers without repeated digits from 1 to 999.In a range from 1 through 999, there are 900 integers in total. To determine the number of integers without repeated digits, we need to consider the possible combinations. For the hundreds place, there are 9 options (1-9) since zero cannot be used as the first digit. For the tens place, there are 9 options again (0-9 excluding the digit already used in the hundreds place). Similarly, for the units place, there are 8 options available (0-9 excluding the two digits already used in the hundreds and tens places). Multiplying these options together, we get 9 * 9 * 8 = 648 integers without repeated digits.To calculate the number of integers with at least one repeated digit, we can subtract the count of integers without repeated digits from the total count of integers in the range. Therefore, 900 - 648 = 252 integers have at least one repeated digit.

To find the probability, we divide the count of integers with at least one repeated digit by the total count of integers in the range, resulting in 252 / 900 ≈ 0.351. Therefore, the probability that a randomly chosen integer from 1 through 999 has at least one repeated digit is approximately 0.351.

Among the three-digit integers from 100 to 999, how many of them have at least one digit repeated?

Out of the three-digit integers from 100 to 999, there are 351 integers that have at least one repeated digit. To determine this count, we subtract the number of unique-digit integers (648) from the total count of three-digit integers (900). Hence, 900 - 648 = 252 integers have at least one digit repeated.

If a three-digit integer is selected randomly from the range 100 to 999, what is the probability that it will have at least one repeated digit?

If a three-digit integer is randomly selected from the range 100 to 999, the probability that it will have at least one repeated digit is approximately 0.39 or 39%. This probability is calculated by dividing the count of integers with repeated digits (351) by the total count of three-digit integers (900). Therefore, the probability is 351 / 900 ≈ 0.39 or 39%.

Learn more about combinatorics

brainly.com/question/31293479

#SPJ11

A dress pattern calls for 1 1/8 yards of fabric for the top and 2 5/8 yards for the skirt. Mia has 3 1/2 yards of fabric. Does she have enough fabric to make the dress? Explain

Answers

To find out whether Mia has enough fabric to make the dress, you need to add the amount of fabric required for the top and skirt. Then compare it with the amount of fabric she has.

So, let's do that.To make the dress, we need 11/8 yards of fabric for the top2 5/8 yards of fabric for the skirt Total fabric required

= 1 1/8 + 2 5/8

= 3 3/4 yards

Mia has 3 1/2 yards of fabric

So, Mia does not have enough fabric to make the dress because she needs 3 3/4 yards of fabric to make it.

To know more about yards visit :-

https://brainly.com/question/24487155

#SPJ11

Edgar decided to add a second gate. He removes 2 yards t foot of fencing from his section of 13 yards. How much fencing is left?

Answers

11 yards of fencing left.

Given that Edgar decided to add a second gate. He removes 2 yards of fencing from his section of 13 yards.

Therefore, the total length of the fencing was 13 yards.We have to remove 2 yards of fencing from the section.Therefore, the total fencing remaining will be=

Total fencing - Fencing Removed Fencing Removed = 2 yardsTotal fencing = 13 yards We can substitute the values in the above equation.Fencing remaining= 13 - 2 = 11 yards  In total, 11 yards of fencing are left.

Edgar had 13 yards of fencing. He had to remove 2 yards of fencing from it. Thus, he could not use the removed fencing for the gate. We need to calculate the remaining length of the fencing.Edgar had to remove 2 yards of fencing to add a second gate.

Therefore, the total fencing remaining will be= Total fencing - Fencing RemovedFencing Removed = 2 yardsTotal fencing = 13 yardsWe can substitute the values in the above equation.

Fencing remaining= 13 - 2 = 11 yards

Thus, Edgar has only 11 yards of fencing left to use. This will be less fencing available to Edgar to use for his purpose. With a smaller area to work with, Edgar will have to ensure that the fencing is placed appropriately.

Edgar had a total of 13 yards of fencing before removing 2 yards of fencing to add a second gate. Therefore, he had only 11 yards of fencing left.

To know more about length visit:

brainly.com/question/32060888

#SPJ11

A farmer had 4/5 as many chickens as ducks. After she sold 46 ducks, another 14 ducks swam away, leaving her with 5/8 as many ducks as chickens. How many ducks did she have left?

Answers

Let's assume the number of ducks the farmer initially had as 'd' and the number of chickens as 'c'.

Given:

The farmer had 4/5 as many chickens as ducks, so c = (4/5)d.

After selling 46 ducks, the number of ducks becomes d - 46.

After 14 ducks swam away, the number of ducks becomes (d - 46) - 14.

The farmer was left with 5/8 as many ducks as chickens, so (d - 46 - 14) = (5/8)c.

Now we can substitute the value of c from the first equation into the second equation:

(d - 46 - 14) = (5/8)(4/5)d.

Simplifying the equation:

(d - 60) = (4/8)d,

d - 60 = 1/2d.

Bringing like terms to one side:

d - 1/2d = 60,

1/2d = 60.

Multiplying both sides by 2 to solve for d:

d = 120.

Therefore, the farmer initially had 120 ducks.

After selling 46 ducks, the number of ducks left is 120 - 46 = 74.

After 14 more ducks swam away, the final number of ducks left is 74 - 14 = 60.

So, the farmer is left with 60 ducks.

Learn more about linear equation here:

https://brainly.com/question/2030026

#SPJ11

need help understanding this question

Answers

The exponential function for the table is given as follows:

[tex]y = 0.02(4)^x[/tex]

The simple radical form of the expression is given as follows:

[tex]\sqrt{8} = 2\sqrt{2}[/tex]

How to define an exponential function?

An exponential function has the definition presented as follows:

[tex]y = ab^x[/tex]

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

The parameter values for the exponential function in this problem are given as follows:

a = 0.02, as when x = 0, y = 0.02.b = 4, as when x is increased by one, y is multiplied by 4.

Hence the exponential function for the table is given as follows:

[tex]y = 0.02(4)^x[/tex]

For the simple radical form, we have that 8 = 2 x 4, hence:

[tex]\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}[/tex]

More can be learned about exponential functions at brainly.com/question/2456547

#SPJ1

How many decimal strings are there with length at least 4 and at most 7?

Answers

Answer: To find the number of decimal strings of length at least 4 and at most 7, we can count the number of strings of length 4, 5, 6, and 7 and add them together.

Number of strings of length 4: There are 10 possible digits for each of the 4 positions, so there are 10^4 = 10,000 possible strings.

Number of strings of length 5: There are 10 possible digits for each of the 5 positions, so there are 10^5 = 100,000 possible strings.

Number of strings of length 6: There are 10 possible digits for each of the 6 positions, so there are 10^6 = 1,000,000 possible strings.

Number of strings of length 7: There are 10 possible digits for each of the 7 positions, so there are 10^7 = 10,000,000 possible strings.

Therefore, the total number of decimal strings of length at least 4 and at most 7 is:

10,000 + 100,000 + 1,000,000 + 10,000,000 = 11,110,000.

So there are 11,110,000 decimal strings with length at least 4 and at most 7.

To answer your question, we need to first understand what a decimal string is.

A decimal string is a sequence of digits, 0 through 9.

So, for example, 123 and 987654 are both decimal strings.

Now, we need to find how many decimal strings there are with length at least 4 and at most 7. This means that we need to count all the decimal strings that have a length of 4, 5, 6, or 7.

To find the number of decimal strings with length 4, there are 10 options for the first digit, 10 options for the second digit, 10 options for the third digit, and 10 options for the fourth digit. So, there are 10 x 10 x 10 x 10 = 10,000 decimal strings with length 4.

To find the number of decimal strings with length 5, there are also 10 options for each digit, so there are 10 x 10 x 10 x 10 x 10 = 100,000 decimal strings with length 5.

To find the number of decimal strings with length 6, there are again 10 options for each digit, so there are 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 decimal strings with length 6.

Finally, to find the number of decimal strings with length 7, there are 10 options for each digit, so there are 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 decimal strings with length 7.

So, to find the total number of decimal strings with length at least 4 and at most 7, we add up the number of decimal strings with each length:

10,000 + 100,000 + 1,000,000 + 10,000,000 = 11,110,000

Therefore, there are 11,110,000 decimal strings with length at least 4 and at most 7.

To Know more about decimal string refer here

https://brainly.com/question/31841719#

#SPJ11

What is one way that adding and subtracting polynomials is similar to adding and subtracting whole numbers and integers?

Answers

One way that adding and subtracting polynomials is similar to adding and subtracting whole numbers and integers is that both operations follow the same basic rules for combining like terms.

In both cases, you add or subtract the coefficients (numbers) of the same type of term or same variable with the same exponent.

Just like adding and subtracting integers, you also need to consider the signs (+ or -) when combining the terms.

To Know more about polynomials  refer here

https://brainly.com/question/20121808#

#SPJ11

Add


3/5+7/8+3/10

Enter your answer in the box as a mixed number in simplest form.

Answers

The gcf of the denominators is 40, so after making that change to each fraction, the answer is 1 31/40
LCM of 5, 8, and 10 = 40, so

3/5 turns into 24/40
7/8 into 35/40
3/10 into 12/40

24/40 + 35/40 + 12/40 = 71/40

71/40 = 1 31/40

Answer: 1 31/40

Have a good day ^^

Let p equal the proportion of letters mailed in the Netherlands that are delivered the next day Suppose that y= 142 out of a random sample of n = 200 letters were delivered the day after they were mailed. (a) Give a point estimate of p (b) Use Equation 73-2 to find an approximate 90% confidence interval for p (7.3-2) (c) Use Equation 73-4 to find an approximate 90% interval for p. 7.3-4) (d) Use Equation 73-5 to find an approximate 90% confidence interval for p. 7.35

Answers

For the sample population

(a) The point estimate of p is 0.71.

(b) Using Equation 73-2, the approximate 90% confidence interval for p is obtained by calculating 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/200).

(c) Using Equation 73-4, the approximate 90% interval for p is found by calculating 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/(200 - 1)).

(d) Using Equation 73-5, the approximate 90% confidence interval for p is obtained by calculating 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/(200 + 1.645^2/4)).

(a) To obtain a point estimate of p, we divide the number of letters delivered the next day (y = 142) by the sample size (n = 200):

Point estimate of p = y/n = 142/200 = 0.71

(b) Using Equation 73-2, we can find an approximate 90% confidence interval for p. The formula is given by:

Point estimate ± Z * sqrt((p * (1 - p))/n)

Since the confidence level is 90%, the Z-value for a 90% confidence level is approximately 1.645. Substituting the values into the equation:

Confidence interval = 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/200)

Simplifying the expression:

Confidence interval = 0.71 ± 1.645 * sqrt(0.21/200)

(c) Using Equation 73-4, we can find an approximate 90% interval for p. The formula is given by:

Point estimate ± Z * sqrt((p * (1 - p))/(n - 1))

Applying the formula with the given values:

Confidence interval = 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/(200 - 1))

Simplifying the expression:

Confidence interval = 0.71 ± 1.645 * sqrt(0.21/199)

(d) Using Equation 73-5, we can find an approximate 90% confidence interval for p. The formula is given by:

Point estimate ± Z * sqrt((p * (1 - p))/(n + Z^2/4))

Substituting the values into the equation:

Confidence interval = 0.71 ± 1.645 * sqrt((0.71 * (1 - 0.71))/(200 + 1.645^2/4))

Simplifying the expression:

Confidence interval = 0.71 ± 1.645 * sqrt(0.21/200.5084)

To know more about sample proportion refer here:

https://brainly.com/question/29912751

#SPJ11

Solve: 7(s + 1) + 21 = 2(s - 6) - 20

Answers

7s + 7 +21= 2s -12 -20
7s -2s= -12-20-21-7
5s=-60
S = -12

What is the probability that either event will occur?

Answers

Answer:

0.67

Step-by-step explanation:

Estimate the sum of 192 and 91 by rounding both values to the nearest ten. what is the best estimate of the sum?

280

290

300

310

Answers

To estimate the sum of 192 and 91 by rounding both values to the nearest ten, we round 192 to 190 and 91 to 90.

190 + 90 = 280

Therefore, the best estimate of the sum is 280.

Learn more about estimate here:

https://brainly.com/question/30870295

#SPJ11

determine whether the series converges or diverges. [infinity] n2 4n3 − 3 n = 1

Answers

The given series is divergent.

Does the series ∑n=1∞ n^2 / (4n^3 - 3) converge or diverge?

To determine whether the series converges or diverges, we can use the divergence test, which states that if the limit of the nth term of a series does not approach zero as n approaches infinity.

Then the series must diverge.

Let's find the limit of the nth term of the given series:

lim n → ∞ n^2 / (4n^3 - 3n)

= lim n → ∞ n^2 / n^3 (4 - 3/n^2)

= lim n → ∞ 1/n (4/3 - 3/n^2)

As n approaches infinity, the second term approaches zero, and the limit becomes:

lim n → ∞ 1/n * 4/3 = 0

Since the limit of the nth term approaches zero, the divergence test is inconclusive. Therefore, we need to use another test to determine whether the series converges or diverges.

We can use the limit comparison test, which states that if the ratio of the nth term of a series to the nth term of a known convergent series approaches a nonzero constant as n approaches infinity.

Then the two series must either both converge or both diverge.

Let's compare the given series to the p-series with p = 3:

∑ n = 1 ∞ 1/n^3

We have:

lim n → ∞ (n^2 / (4n^3 - 3n)) / (1/n^3)

= lim n → ∞ n^5 / (4n^3 - 3n)

= lim n → ∞ n^2 / (4 - 3/n^2)

= 4/1 > 0

Since the limit is a nonzero constant, the two series either both converge or both diverge. We know that the p-series with p = 3 converges, therefore, the given series must also converge.

The correct series should be:

∑ n = 1 ∞ n / (4n^3 - 3)

Using the same tests as above, we can show that this series is divergent. The limit of the nth term approaches zero, and the limit comparison test with the p-series with p = 3 gives a nonzero constant:

lim n → ∞ (n / (4n^3 - 3)) / (1/n^3)

= lim n → ∞ n^4 / (4n^3 - 3)

= lim n → ∞ n / (4 - 3/n^4)

= ∞

Therefore, the given series is divergent.

Learn more about divergence test

brainly.com/question/30098029

#SPJ11

-2+-6 in absolute value minus -2- -6 in absolute value

Answers

`-2+-6` in absolute value minus `-2--6` in absolute value is equal to `4`.

To solve for `-2+(-6)` in absolute value and `-2-(-6)` in absolute value and subtract them, we first evaluate the two values of the absolute value and perform the subtraction afterwards.

Here is the solution:

Simplify `-2 + (-6) = -8`.

Evaluate the absolute value of `-8`. This gives us: `|-8| = 8`.

Therefore, `-2+(-6)` in absolute value is equal to `8`.

Next, simplify `-2 - (-6) = 4`.

Evaluate the absolute value of `4`.

This gives us: `|4| = 4`.

Therefore, `-2-(-6)` in absolute value is equal to `4`.

Now, we subtract `8` and `4`. This gives us: `8 - 4 = 4`.

Therefore, `-2+-6` in absolute value minus `-2--6` in absolute value is equal to `4`.

To know more about absolute value minus visit:

https://brainly.com/question/31140452

#SPJ11

Find the area of the given triangle. Round your answer to the nearest tenth. Do not round any Intermediate computations. 36° 12 square units​

Answers

The area of the triangle is 52.32 square units

Finding the area of the triangle

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

The triangle

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

Read more about area at

https://brainly.com/question/24487155

#SPJ1

The area of the right triangle is approximately 52.3 square units.

What is the area of the triangle?

The area of triangle is expressed as:

Area = 1/2 × base × height

The figure in the image is a right triangle.

Angle θ = 36 degrees

Adjacent to angle θ ( height ) = 12

Opposite to angle θ ( base ) = ?

To determine the area, we need to find the opposite side of angle θ which is the base.

Using trigonometric ratio:

tanθ = opposite / adjacent

tan( 36 ) = base / 12

base = 12 × tan( 36 )

base = 8.718510

Now, area will be:

Area = 1/2 × 8.718510 × 12

Area = 52.3 square units

Therefore, the area of the triangle is 52.3 square units.

Learn more about trigonometric ratio here: brainly.com/question/28016662

#SPJ1

for an experiment with three conditions with n = 15 each, find q

Answers

Answer:

The number of ways to allocate the total sample size of 45 into three conditions with n = 15 each is q ≈ 1.276 × 10^38

Step-by-step explanation:

o find q, we need to know the number of all possible ways to allocate the total sample size (n = 45) into the three conditions with equal sample sizes (n = 15 each). This is given by the multinomial coefficient:

q = (n choose n1, n2, n3) = (n!)/(n1! * n2! * n3!)

where n1, n2, and n3 represent the sample sizes for each of the three conditions.

Since each condition has the same sample size, we have n1 = n2 = n3 = 15, so:

q = (45!)/(15! * 15! * 15!)

To simplify this expression, we can use the fact that:

n! = n * (n-1) * (n-2) * ... * 2 * 1

Therefore:

45! = 45 * 44 * 43 * ... * 2 * 1

15! = 15 * 14 * 13 * ... * 2 * 1

Substituting these into the expression for q, we get:

q = (45 * 44 * 43 * ... * 2 * 1) / [(15 * 14 * 13 * ... * 2 * 1) * (15 * 14 * 13 * ... * 2 * 1) * (15 * 14 * 13 * ... * 2 * 1)]

Simplifying the denominator, we get:

q = (45 * 44 * 43 * ... * 2 * 1) / (15!)^3

Using a calculator or computer program to evaluate this expression, we get:

q = 1.276 × 10^38

Therefore, the number of ways to allocate the total sample size of 45 into three conditions with n = 15 each is q ≈ 1.276 × 10^38.

To know more about multinomial coefficient refer here

https://brainly.com/question/10787369#

#SPJ11

given the following equation, find the value of y when x=3. y=−2x 15 give just a number as your answer. for example, if you found that y=15, you would enter 15.

Answers

Answer:

Step-by-step explanation:

To find the value of y when x = 3 in the equation y = -2x + 15, we substitute x = 3 into the equation and solve for y:

y = -2(3) + 15

y = -6 + 15

y = 9

Therefore, when x = 3, y = 9.

ONLY ANSWER IF YOU KNOW. What is the probability that either event will occur?

Answers

Answer:

0.67

Step-by-step explanation:

Given Rhombus ABCD, find x, y and z. Then find the perimeter

Answers

The perimeter of the rhombus is 34 units.

Given rhombus ABCD, the figure is represented as:

Rhombus ABCD, x= 7y+3, z= 4y-3

Find the value of y

First, we need to find the value of y. Since, the opposite angles of a rhombus are congruent, so,

∠DAB= ∠DCB

Now, x = 7y+3z = 4y-3

Adding both, x+z= 11y

By solving the above equation, we get,

y= (x+z)/11

On substituting the value of x and z in terms of y, we get,

x= (7(x+z)/11)+3z

= (4(x+z)/11)-3

On substituting x and z values in the given equations,

x= 17y/11+3z= 10y/11-3

Find the perimeter

Perimeter of a rhombus is given by,

Perimeter= 4a, where a is the side of the rhombus.

Since opposite sides of a rhombus are parallel and all sides are equal, hence AB= CD and AD= BC.

So,AB= 17y/11+3, CD= 17y/11+3AD= 10y/11-3, BC= 10y/11-3

On substituting the value of y in the above equations, we get,

AB= 4, CD= 4AD= 13, BC= 13

Therefore,

Perimeter = AB+ CD+ AD+ BC

Perimeter = 4+ 4+ 13+ 13

Perimeter = 34 units.

To know more about perimeter  please visit :

https://brainly.com/question/397857

#SPJ11

The curve of the equation y^2 = x^2(x 3) find the area of the enclosed loop.

Answers

The area of the enclosed loop of the curve y^2 = x^2(x 3) is 56√3/15.

To find the area of the enclosed loop of the curve y^2 = x^2(x 3), we need to first sketch the curve to see what it looks like. The equation can be rewritten as y^2 = x^2(x-3), which means that the curve is symmetric about the x-axis and passes through the origin.

Next, we can find the x-intercepts of the curve by setting y=0: 0^2 = x^2(x-3), which simplifies to x=0 and x=3. So the curve intersects the x-axis at (0,0) and (3,0).

To find the area of the enclosed loop, we need to integrate the curve from x=0 to x=3 and subtract the area below the x-axis. We can do this by setting up the integral as follows:

A = ∫[0,3] y dx - ∫[0,3] -y dx

We can solve for y by taking the square root of both sides of the equation y^2 = x^2(x-3):

y = ± x√(x-3)

To find the bounds of the integral, we can set the two functions equal to each other and solve for x:

x√(x-3) = -x√(x-3)
x=0 or x=3

So our integral becomes:

A = ∫[0,3] x√(x-3) dx - ∫[0,3] -x√(x-3) dx

We can simplify the integral by making the substitution u = x-3, which gives us:

A = ∫[0,3] (u+3)√u du - ∫[0,3] -(u+3)√u du

Simplifying further, we get:

A = 2∫[0,3] (u+3)√u du

This integral can be evaluated using integration by parts, which gives us:

A = 2/3 [2(u+3)(2u+3)√u - ∫(2u+3)√u du] from 0 to 3

Simplifying, we get:

A = 2/3 [(54√3/5) - (2/5)(18√3) + (2/3)(4√3)]

A = 56√3/15 DETAIL ANS

Therefore, the area of the enclosed loop of the curve y^2 = x^2(x 3) is 56√3/15.

Learn more about enclosed loop of the curve

brainly.com/question/30174664

#SPJ11

use the alternating series test, if applicable, to determine the convergence or divergence of the series. [infinity] n = 7 (−1)nn n − 6

Answers

To apply the Alternating Series Test, we need to check two conditions:

The terms of the series must alternate in sign.

The absolute values of the terms must decrease as n increases.

Let's analyze the given series: ∑ (-1)^n (n - 6) from n = 7 to infinity.

Alternating Signs: The series has alternating signs because of the (-1)^n term. When n is even, (-1)^n becomes positive, and when n is odd, (-1)^n becomes negative.

Decreasing Absolute Values: Let's examine the absolute values of the terms: |(-1)^n (n - 6)| = |n - 6|.

As n increases, the absolute value |n - 6| also increases. Therefore, the absolute values of the terms do not decrease.

Since the terms do not meet the decreasing absolute values condition, we cannot conclude convergence or divergence using the Alternating Series Test. The Alternating Series Test does not apply in this case.

To determine the convergence or divergence of the series, we need to use other convergence tests, such as the Ratio Test or the Comparison Test.

Learn more about divergence here: brainly.com/question/32386596

#SPJ11

Determine whether the series converges or diverges.
[infinity]
Σ 3 / ( 4n + 5 )
n=1

Answers

Answer:

This series diverges--compare it to the harmonic series.

Choose all the fractions whose product is greater than 2 when the fraction is multiplied by 2.

Answers

Answer:

n

Step-by-step explanation:

Consider the following. {(0, −1, 4), (−1, 4, 1), (−17, −4,−1)} (a) Determine whether the set of vectors in Rn is orthogonal. orthogonal not orthogonal (b) If the set is orthogonal, then determine whether it is also orthonormal. orthonormal not orthonormal not orthogonal (c) Determine whether the set is a basis for Rn. a basis not a basis

Answers

a. the dot product of every pair of vectors is zero, the set of vectors is orthogonal. b. the set is not orthonormal. c. we cannot determine whether the set is a basis for Rn without knowing the dimension of Rn.

(a) To determine whether the set of vectors in Rn is orthogonal, we need to check if the dot product of every pair of vectors is zero.

Taking dot products:

(0, -1, 4) • (-1, 4, 1) = 0 + (-4) + 4 = 0

(0, -1, 4) • (-17, -4, -1) = 0 + 4 + (-4) = 0

(-1, 4, 1) • (-17, -4, -1) = 17 + (-16) + (-1) = 0

Since the dot product of every pair of vectors is zero, the set of vectors is orthogonal.

(b) To determine whether the set is also orthonormal, we need to check if each vector has length 1.

Calculating the length of each vector:

|| (0, -1, 4) || = sqrt(0^2 + (-1)^2 + 4^2) = sqrt(17)

|| (-1, 4, 1) || = sqrt((-1)^2 + 4^2 + 1^2) = sqrt(18)

|| (-17, -4, -1) || = sqrt((-17)^2 + (-4)^2 + (-1)^2) = sqrt(292)

Since none of the vectors have length 1, the set is not orthonormal.

(c) Since the set is orthogonal and has three vectors in Rn, it is a basis for Rn if and only if n = 3. Therefore, we cannot determine whether the set is a basis for Rn without knowing the dimension of Rn.

Learn more about orthogonal here

https://brainly.com/question/30772550

#SPJ11

.Let Y1 ∼ Poi(λ1) and Y2 ∼ Poi(λ2). Assume Y1 and Y2 are independent and let U = Y1 + Y2.
a) Find the mgf of U.
b) Identify the "named distribution" of U and specify the value(s) of its parameter(s)
c) Find the pmf of (Y1|U = u), where u is a nonnegative integer. Identify your answer as a named distribution and specify the value(s) of its parameter(s).

Answers

a) The moment generating function[tex](mgf)[/tex] of U is M(t) = exp((λ1+λ2)(e^t-1)) b) U follows a named distribution known as Poisson distribution with parameter λ1+λ2. c) The [tex]pmf[/tex]of (Y1|U = u) is a binomial distribution with parameters u and λ1/(λ1+λ2).

a) The[tex]mgf[/tex]of U can be found using the fact that the [tex]mgf[/tex]of the sum of independent random variables is the product of their individual [tex]mgfs[/tex]. Thus,

M(t) = E[tex][e^(tU)][/tex] = E[e^(t(Y1+Y2))] = E[e^(tY1)]E[e^(tY2)] = exp(λ1(e^t-1))[tex]exp(λ2(e^t-1)) = exp((λ1+λ2)).[/tex]

b) The sum of independent Poisson random variables is a Poisson distribution with parameter equal to the sum of the individual parameters. Therefore, U follows a Poisson distribution with parameter λ1+λ2.

c) To find the[tex]pmf[/tex]of (Y1|U = u), we use Bayes' theorem:

P(Y1=[tex]k|U=u) = P(Y1=k, Y2=u-k)/P(U=u)[/tex]

= [tex]P(Y1=k)P(Y2=u-k)/(λ1+λ2)^u e^-(λ1+λ2)\\= (λ1^k/k!)(λ2^(u-k)/(u-k)!) / (λ1+λ2)^u e^-(λ1+λ2)[/tex]

This simplifies to a binomial distribution with parameters u and p=λ1/(λ1+λ2), as the probability of success (i.e., Y1=k) is p and the number of trials is u. Thus, the [tex]pmf[/tex] of (Y1|U = u) is a binomial distribution with parameters u and λ1/(λ1+λ2).

Learn more about binomial distribution here:

https://brainly.com/question/29137961

#SPJ11

The cones below are similar. Work out the radius, r, of the larger cone.

Answers

The radius, r, of the larger cone is equal to 24 mm.

How to calculate the volume of a cone?

In Mathematics and Geometry, the volume of a cone can be calculated by using this formula:

Volume of cone, V = 1/3 × πr²h

Where:

V represent the volume of a cone.h represents the height.r represents the radius.

Since both the large and small cones are similar, we can logically deduce the following proportion based on their side lengths;

19,008/704 = (r/8)³

19,008/704 = r³/512

r³ = 19,008/704 × 512

Radius of larger cone = 24 mm.

Read more on cone here: https://brainly.com/question/27604827

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

In a given hypothesis test, the null hypothesis can be rejected at the 0.10 and the 0.05 level of significance, but cannot be rejected at the 0.01 level. The most accurate statement about the p- value for this test is: A. p-value = 0.01 B. 0.01 < p-value < 0.05 C. 0.05 value < 0.10 D. p-value = 0.10

Answers

Option B is correct. The most accurate statement about the p-value for this test is: B. 0.01 < p-value < 0.05.

How to interpret the p-value?

In hypothesis testing, the null hypothesis is a statement that assumes there is no significant difference between the observed data and the expected outcomes.

The p-value is a measure that helps to determine the statistical significance of the results obtained from the test. When the null hypothesis can be rejected at the 0.10 and 0.05 levels of significance, but not at the 0.01 level, it means that the test results are significant but not highly significant. In this case, the p-value must be greater than 0.01 but less than 0.05.

Therefore, option B is the most accurate statement about the p-value for this test. It implies that the results are statistically significant at a moderate level of confidence.

Learn more about hypothesis testing

brainly.com/question/30588452

#SPJ11

(07. 04 MC)


An observer (O) is located 660 feet from a tree (T). The observer


notices a hawk (H) flying at a 35° angle of elevation from his line of


sight. How high is the hawk flying over the tree? You must show all


work and calculations to receive full credit. (10 points)

Answers

Height of hawk eye at a distance of 660 feet from tree is 462.1 feet .

Given,

An observer (O) is located 660 feet from a tree (T). The observer

notices a hawk (H) flying at a 35° angle of elevation from his line of sight.

Here,

Let x be the height of the hawk.

The tangent ratio expresses the relationship between the sides of a right triangle depicted above as:

tanФ = opposite side/adjacent side

tan35° = x / 660

x = 660 (tan35° )

x = 462.1 feet .

Thus the height of hawk eye is 462.1 feet .

Know more about angle of elevation,

https://brainly.com/question/29008290

#SPJ12

f(x) = 8 1 − x6 f(x) = [infinity] n = 0 determine the interval of convergence. (enter your answer using interval notation.)

Answers

Answer:

The interval of convergence is (-∞, ∞).

Step-by-step explanation:

Using the ratio test, we have:

| [tex]\frac{1 - x^6)}{(1 - (x+1)^6)}[/tex] | = | [tex]\frac{(1 - x^6) }{(-6x^5 - 15x^4 - 20x^3 - 15x^2 - 6x) }[/tex] |

Taking the limit as x approaches infinity, we get:

lim | [tex]\frac{(1 - x^6) }{(-6x^5 - 15x^4 - 20x^3 - 15x^2 - 6x) }[/tex] | = lim | [tex]\frac{(1/x^6 - 1)}{(-6 - 15/x - 20/x^2 - 15/x^3 - 6/x^4)}[/tex] |

Since all the terms with negative powers of x approach zero as x approaches infinity, we can simplify this to:

lim | [tex]\frac{(1/x^6 - 1) }{(-6)}[/tex] | = [tex]\frac{1}{6}[/tex]

Since the limit is less than 1, the series converges for all x, and the interval of convergence is (-∞, ∞).

To know more about convergence refer here

https://brainly.com/question/31756849#

#SPJ11

use the formula for the sum of a geometric series to find the sum or state that the series diverges (enter div for a divergent series). ∑=3[infinity]710

Answers

The given series ∑=3[infinity]710 is a geometric series with the first term a=3 and the common ratio r=7/10. Therefore, the sum of the given geometric series is 10, and the series is convergent.

To determine whether the series converges or diverges, we can apply the formula for the sum of an infinite geometric series, which is S = a / (1 - r). Plugging in the values for a and r, we get:

S = 3 / (1 - 7/10) = 3 / (3/10) = 10

Therefore, the sum of the infinite geometric series is 10. This means that as we add up more and more terms of the series, the sum gets closer and closer to 10. In other words, the series converges to a finite value of 10.

In conclusion, the sum of the given geometric series is 10, and the series is convergent.

To learn more about “geometric series” refer to the https://brainly.com/question/24643676

#SPJ11

Other Questions
what temperature, in c , is a blackbody whose emission spectrum peaks at 460 nm ?express your answer in degrees celsius. what economic concept do the fourth and fifth amendments to the constitution identify? A soccer player is running down the field at the speed of 5 m/s. To get the soccer ball from his opponent he accelerates to 10 m/s in. 5 seconds. What is the soccer players rate of acceleration? an empty hash table hashtable has 10 buckets and a hash function of key 0. the following operations are performed in order. select which operations cause a collision. an apparently voluntary agreement may in fact not be voluntary if A car wash gives every 5th custmer a free tire wash and every 8th custermer. A free coffe mug. Which customer will be the firstt to recive both a free tire wash and free coffe mug the percent composition by mass of phosphorus in phosphoric acid (h3po4) is An equation is shown: 3x^3+5/x+1 = Ax^2+Bx+C+ R(x)/Q(x)Determine the values of B, R(x), and Q(x) that make the equation true the ethics & compliance initiative found more than half of global workers reported pressure to compromise their standards. (True or False) Choose from the following list of terms and phrases to best complete the following statements is a set of approvals and procedures used to control the acceptance of liabilities and cash payments summarizes the projected cash payments and cash receipts category includes currency, coins, and deposits in bank accounts A spinner has sections that are numbered 1 through 5. Melanie spins the spinner 15 times andrecords her results in the dot plot.Use the results to predict the number of timesthe spinner will land on an even number in 300 trials 300 trials. was the current entering the battery equal to the current leaving the battery? use your results in data table 2 and photo 1 to explain your answer. The time required to build a house varies inversely as the number of workers. It takes 8 workers 25 days to build a house. How long would it take 5 workers? how did the free speech movement change Harvard ? until the 18th century, what was thought to be the cause of criminal behavior? How much agarose, in grams, would you need to prepare a 130 mL of a 1.6% agarose gel for gel electrophoresis? O 1.3 g 2.08 g 1.6 g 20.8 8 16 B the concept ""bird"" could be represented in a persons mind as an average of all the birds the person has encountered. this would be an example of fill in the blank. steppes are generally considered a ____ separating savannas and deserts. a company that engages in global purchasing activities that are integrated across worldwide locations and functional groups is at which level of global purchasing? 1 point) The growth of Guernsey cows can be approximated by the equation dtdW=0.016(476W) where W is the weight in kg after t weeks.in the long run, how much does a guernsey cow weigh?