<1 and <2 form a linear pair.
if m<1 (4 x + 12)° and m <2 = (6x - 2)°, find the measure of each angle.

Answer:

To calculate the edge length, take the cube root of the total volume of the cube.

Step-by-step explanation:

hope this helps ! :)

The formula that shows the dependence of the edge length 'a' on volume V of a cube will be a = ∛V.

All the edges of the cube are congruent with each other. Suppose that: The side length of the considered cube is 'a' units. Then, we get:

Volume of that cube = a³ cubic units.

Solve the equation for 'a', then we have

V = a³

a³ = V

a = ∛V

More about the volume of the cube link is given below.

https://brainly.com/question/26136041

#SPJ2

(a) No conditions. (b) The playlist must consist of exactly 3 songs from each artist. (c) The playlist must consist of at least 2 songs from each artist.

Working:

To build a playlist of 6 songs from 25 unique songs, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of songs and r is the number of songs we want to include in the playlist.

So the number of ways to build the playlist is:

25C6 = 25! / 6!(25-6)! = 177,100

Therefore, there are 177,100 ways to build the playlist without any conditions.

(b) The playlist must consist of exactly 3 songs from each artist.

To build a playlist of 6 songs with exactly 3 songs from each artist, we can use the formula for combinations again:

nCr = n! / r!(n-r)!

We need to choose 3 songs from artist A and 3 songs from artist B, so we can calculate the number of ways to do this separately:

Number of ways to choose 3 songs from artist A:

10C3 = 10! / 3!(10-3)! = 120

Number of ways to choose 3 songs from artist B:

15C3 = 15! / 3!(15-3)! = 455

To get the total number of ways to build the playlist, we can multiply these two numbers together:

120 * 455 = 54,600

Therefore, there are 54,600 ways to build the playlist with exactly 3 songs from each artist.

(c) The playlist must consist of at least 2 songs from each artist.

To build a playlist of 6 songs with at least 2 songs from each artist, we can break this down into cases:

Case 1: 2 songs from artist A and 4 songs from artist B

Number of ways to choose 2 songs from artist A:

10C2 = 10! / 2!(10-2)! = 45

Number of ways to choose 4 songs from artist B:

15C4 = 15! / 4!(15-4)! = 1,386

Total number of ways for case 1:

45 * 1,386 = 62,370

Case 2: 3 songs from artist A and 3 songs from artist B

We already calculated the number of ways for this case in part (b):

54,600

Case 3: 4 songs from artist A and 2 songs from artist B

Number of ways to choose 4 songs from artist A:

10C4 = 10! / 4!(10-4)! = 210

Number of ways to choose 2 songs from artist B:

15C2 = 15! / 2!(15-2)! = 105

Total number of ways for case 3:

210 * 105 = 22,050

Total number of ways to build the playlist with at least 2 songs from each artist:

62,370 + 54,600 + 22,050 = 139,020

Therefore, there are 139,020 ways to build the playlist with at least 2 songs from each artist.

Visit here to learn more about Total brainly.com/question/30883537

#SPJ11

The speed of sound at the coldest place on Earth. Temperatures on the East Antarctic Plateau can reach -100° C is B. 231 m/s

In this equation, v signifies the pace of sound measured in meters per second, while T represents the temperature expressed in Celsius degrees; and 273.15 denotes the standardized temperature in Kelvin.

When substituting T value as -100°C into our function implies that:

v = 331.3 * ✓(-100)/273.15)

v = 231 m/s

Thus, select option indicating 231 m/s.

Learn more about speed on

https://brainly.com/question/13943409

#SPJ1

The measure of the shorter base is approximately 28.85.

To solve this problem, we need to use the fact that the line segment joining the midpoints of the diagonals of a trapezoid is parallel to the bases and has a length equal to half the sum of the bases. Let's call the shorter base "x".

We know that the longer base is 97, so the sum of the bases is x + 97.

We also know that the line segment joining the midpoints of the diagonals has a length of 3. Since this line segment is parallel to the bases, it divides the trapezoid into two smaller trapezoids that are similar to the original trapezoid.

Using the similar triangles, we can set up the following equation:

3/x = (x + 97)/97

Cross-multiplying and simplifying, we get:

3*97 = x^2 + 97x

Multiplying out the right side and rearranging, we get:

x^2 + 97x - 291 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac))/2a

Plugging in a=1, b=97, and c=-291, we get:

x = (-97 ± sqrt(97^2 - 4(1)(-291)))/2(1)

x = (-97 ± sqrt(9429))/2

x = (-97 ± 97)/2 or x = (-97 ± sqrt(9429))/2

Since we're looking for the shorter base, we can discard the negative solution:

x = (-97 + sqrt(9429))/2

x ≈ 28.85

Learn more about Similar Triangles here: brainly.com/question/14926756

#SPJ11

There are 128 students who do not like any of these vegetables.

To solve this problem, we can use the principle of inclusion-exclusion. We start by adding up the number of students who like each vegetable:

Number who like brussels sprouts = 64

Number who like broccoli = 94

Number who like cauliflower = 58

Next, we subtract the number of students who like more than one vegetable once:

Number who like both brussels sprouts and broccoli = 26

Number who like both brussels sprouts and cauliflower = 28

Number who like both broccoli and cauliflower = 22

We can't just subtract the number who like all three vegetables once, since we have now subtracted them twice (once for each pair of vegetables). So we need to add them back in once:

Number who like all three vegetables = 14

Now we can calculate the number of students who like at least one vegetable:

Number who like at least one vegetable = 64 + 94 + 58 - 26 - 28 - 22 + 14

Number who like at least one vegetable = 154

Finally, to find the number of students who do not like any of these vegetables, we subtract this from the total number of students:

Number who do not like any of these vegetables = 282 - 154

Number who do not like any of these vegetables = 128

Therefore, there are 128 students who do not like any of these vegetables.

Learn more about vegetables

brainly.com/question/11972819

#SPJ11

The value of angle s is determined as 22.5 ⁰.

The value of angle s is calculated by applying intersecting chord theorem as shown below;

The missing arc angle is calculated as;

arc LI = 360 - (125 + 95)

arc LI = 140⁰

The value of angle s is calculated as follows;

∠s = ¹/₂ (arc LI - arc KI) (intersecting chord theorem)

∠s =  ¹/₂ ( 140 - 95 )

∠s =  ¹/₂ ( 45 )

∠s = 22.5 ⁰

Thus, the value of the missing angle s (tangent angle) is determined by applying intersecting chord theorem.

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

Answer: I don't know, sorry!

Step-by-step explanation:

A slope field is a graphical representation of the slopes of the tangent lines to the solutions of a first-order differential equation, dy/dx = f(x, y).

The goal of a slope field is to provide a visual representation of the behavior of the solutions to the differential equation, without necessarily solving the equation analytically.

To create a slope field, follow these steps:

1. Write down the given first-order differential equation, dy/dx = f(x, y).

2. For each point (x, y) in the field, calculate the slope f(x, y) using the differential equation.

3. At each point (x, y), draw a short line segment with the slope calculated in step 2.

4. Repeat steps 2 and 3 for various points on the field to get a complete visual representation.

5. Observe the overall behavior of the slopes in the field, which can help you understand the behavior of the solution curves.

In summary, a slope field is a useful tool to visualize the behavior of solutions to differential equations. By analyzing the slopes of tangent lines at various points, you can gain insights into the characteristics of the solution curves without solving the equation analytically.

Learn more about slope field here:

https://brainly.com/question/29678428

#SPJ11

Total number of people = (4 classes x 23 students x 3 adults) = 276 people
Number of buses = 5
So, the numbers of people on each bus = 276/5 = 55.2
Since the number of people on each bus must be a whole number, we need to round up to the nearest whole number, which is 56. Therefore, there will be 56 people on each bus.

First, let's find the total numbers of people going on the field trip:

There are 4 classes with 23 students and 3 adults each, so there are 26 people per class (23 students + 3 adults). Since there are 4 classes, we have a total of 4 * 26 = 104 people.

Now, let's divide the total number of people by the number of buses to find out how many people will be on each bus:

104 people / 5 buses = 20.8 people per bus

However, we cannot have a fraction of a person on a bus, so the solution must belong to the set of natural numbers. In this real-world context, having 20.8 people on each bus is not a valid solution, as it is not a natural number.

Therefore, the correct answer is:
C. Because of the real-world context, the solution must belong to the set of all natural numbers. Therefore, the solution is unacceptable.  The statement that must be true about the solution is C. Because the real-world context involves a group of 4th-grade students and their teachers, the solution must be a whole number, since we cannot have a fraction of a person and the solution must belong to the set of all natural numbers, and any solution that is not a natural number would be unacceptable.

Learn more about numbers:

brainly.com/question/17429689

#SPJ11

Therefore, we can conclude that 98% of the sample means will fall within the interval (0.9565, 0.9615).

We are given that the true mean of the bio/total carbon ratio is 0.9590 and the standard deviation is 0.0080. We want to find the interval within which 98% of the sample means will fall.

Since we are dealing with a sample, we will use the standard error of the mean (SEM) to calculate the interval. The formula for SEM is:

SEM = σ/√n

where σ is the population standard deviation, and n is the sample size. In this case, we are given σ = 0.0080, and n = 44. Therefore,

SEM = 0.0080/√44

SEM = 0.00120

Next, we need to find the critical z-value for a 98% confidence interval. We can do this using a standard normal distribution table or a calculator. Using a calculator, we get:

z = invNorm(0.99)

z = 2.3263

Finally, we can find the interval using the formula:

CI = X ± z*SEM

where X is the sample mean, z is the critical z-value, and SEM is the standard error of the mean.

Plugging in the given values, we get:

CI = 0.9590 ± 2.3263*0.00120

Simplifying, we get:

CI = (0.9565, 0.9615)

To know more about mean,

https://brainly.com/question/30094057

#SPJ11

Answer: The general form of a sine function is:

y = A sin (Bx + C) + D

Where:

A = amplitude

B = 2π/period

C = phase shift

D = vertical shift or midline

Given the values in the problem, we can substitute and simplify:

A = 3

midline = 2, so D = 2

period = 8π/7, so B = 2π/(8π/7) = 7/4

y = 3 sin (7/4 x + C) + 2

To find the phase shift, we need to use the fact that the sine function is at its maximum when the argument of the sine function is equal to π/2. That is:

Bx + C = π/2

We can solve for C:

C = π/2 - Bx

C = π/2 - (7/4) x

Substituting back the value of C in the equation, we get:

y = 3 sin (7/4 x + π/2 - 7/4 x) + 2

y = 3 sin (7/4 x - 7π/8) + 2

Therefore, the sine function with an amplitude of 3, a midline of y=2, and a period of 8π/7 is:

y = 3 sin (7/4 x - 7π/8) + 2

Answer:

Step-by-step explanation:

The length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.

A central angle is an angle with its vertex at the center of a circle and its rays extending out to the edge of the circle, creating an intercepted arc.

The length of the arc intercepted by a central angle of 1.1 radians can be found by using the formula:

Length of arc = (central angle / 2π) × 2πr

where r is the radius of the circle.

Plugging in the given values, we get:

Length of arc = (1.1 / 2π) × 2π(6)

Length of arc = 1.1 × 6

Length of arc = 6.6 cm

Therefore, the length of the arc intercepted by a central angle of 1.1 radians is 6.6 cm.

To learn more about central angle visit: https://brainly.com/question/15698342

#SPJ11

We have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge

To prove that xn ≤ zn ≤ yn for all n ∈ N, we just need to compare the values of xn, yn, and zn for any given n. We have xn = -1, yn = 1, and zn = (-1)^n+1, so we need to show that -1 ≤ (-1)^n+1 ≤ 1.

For n even, we have (-1)^n+1 = -1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

For n odd, we have (-1)^n+1 = 1, so -1 ≤ (-1)^n+1 ≤ 1 holds.

Therefore, we have xn ≤ zn ≤ yn for all n ∈ N.

Next, we will prove that (xn) converges to -1 and (yn) converges to 1.

Since xn = -1 for all n ∈ N, (xn) is a constant sequence and converges to -1. Similarly, since yn = 1 for all n ∈ N, (yn) is also a constant sequence and converges to 1.

Finally, we will prove that (zn) does not converge.

Suppose (zn) converges to some limit L. Then, for any ε > 0, there exists N ∈ N such that |zn - L| < ε for all n > N.

Let ε = 1. Then, there exists N such that |zn - L| < 1 for all n > N.

Consider the cases when n is even and odd separately.

When n is even, we have zn = -1. So, we have |-1 - L| < 1, which implies L - 1 < -1 and L < 0.

When n is odd, we have zn = 1. So, we have |1 - L| < 1, which implies L - 1 < 1 and L > 0.

Thus, we have L < 0 and L > 0, which is a contradiction. Therefore, (zn) does not converge.

Complete question:  If [tex]$x_n=-1, y_n=1$[/tex], and [tex]$z_n=(-1)^{n+1}$[/tex], then [tex]$x_n \leq z_n \leq y_n$[/tex] for all [tex]$n \in \mathbb{N}$[/tex], the sequence [tex]$\left(x_n\right)$[/tex] converges to -1 and [tex]$\left(y_n\right)$[/tex] converges 1 , but [tex]$\left(z_n\right)$[/tex]does not converge.

As once consequence, we show that we can take absolute values inside limits.

To learn more about show visit:

https://brainly.com/question/4026666

#SPJ11

Answer: 20

Step-by-step explanation:

With 2 secants, it's the inside of the secant times the whole secant for one line = same on other side but for other secant

EF(EF+GF)=ED(ED+CD)       EF=18; GF=3+CD; ED=19; CD=CD

18(18+3+CD)=19(19+CD)    substitute and simplify and distribute

18(21+CD)=361+19CD

378+18CD=361+19CD

CD=17

GF=3+CD      substitute

=3+17

=20

The length of diagonal of square is 141.14 m.

We have,

Area of square = 100 square meter

So, the side of square is

Side = √Area

side= √100

side= 10 m

Now, the diagonal of square

= √2 a

= 10√2

= 14.14 m

Learn more about Area here:

https://brainly.com/question/27683633

#SPJ1

a) The total amount of money earned is 7.30 dollars.

b) Max is wrong, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

a) To find the total amount of money earned, we need to convert the number of quarters and dimes to dollars.

6 quarters = 6 * 0.25 = 1.50 dollars

8 dimes = 8 * 0.10 = 0.80 dollars

The total amount of money earned is:

5 dollars + 1.50 dollars + 0.80 dollars = 7.30 dollars

b) Max is incorrect. The total amount of money earned is an odd number ($7.30), which means it is impossible to divide it equally between two people in whole dollar amounts. However, it is possible to divide the total amount equally if we allow for fractions of a dollar.

For example, if we split the money equally, Gwen and Max would each get $3.65. This means that Gwen would get 3 dollars and 65 cents, while Max would also get 3 dollars and 65 cents.

Therefore, it is possible to divide the money equally between Gwen and Max, even though the total amount is an odd number.

To learn more about money click on,

https://brainly.com/question/14865967

#SPJ1

Using Xbar/s charts, we can analyze the data to determine if any of the indicated events influenced the part weights. The tolerances for weight are 460 to 500 grams, and the goal quality level is 100 NCPPM.

Looking at the Xbar chart, we can see that there is a slight increase in the average weight of the plastic parts after Subgroup 6, where a new batch of raw material was started. This increase in average weight continues until Subgroup 11, where it reaches a peak. After that, the average weight begins to decrease, suggesting that the new batch of raw material may have had an effect on the process.

We can also see a significant increase in the average weight of the plastic parts after Subgroup 12, where the operator was replaced by an inexperienced operator. This increase continues until Subgroup 18, where it reaches a peak. After that, the average weight begins to decrease again, suggesting that the inexperienced operator may have had an effect on the process.

Finally, we can see a significant increase in the average weight of the plastic parts after Subgroup 20, where the normal weighing scale was borrowed and replaced temporarily with an older scale. This increase continues until Subgroup 24, where it reaches a peak. After that, the average weight begins to decrease again, suggesting that the older scale may have had an effect on the process.

Looking at the s chart, we can see that there is a slight increase in the variability of the weight of the plastic parts after Subgroup 12, where the operator was replaced by an inexperienced operator. This increase continues until Subgroup 18, where it reaches a peak. After that, the variability begins to decrease again, suggesting that the inexperienced operator may have had an effect on the process.

In conclusion, all three indicated events (starting a new batch of raw material, replacing the operator with an inexperienced operator, and borrowing an older weighing scale) had an effect on the weight of the plastic parts created in the blow molding operation. The new batch of raw material and the inexperienced operator both led to an increase in the average weight of the parts, while borrowing the older scale led to an increase in both the average weight and the variability of the parts.

Learn more about weights here:

https://brainly.com/question/31527377

#SPJ11

The future value of the annuity due is $1,848.20, rounded to the nearest cent.

To find the future value of an annuity due of $1,000 paid at the beginning of each 6-month period for 5 years, we can use the formula:

[tex]FV = Pmt x ((1 + r/m)^n - 1) x (1 + r/m)[/tex]

where:

Pmt is the payment amount, which is $1,000 in this case

r is the interest rate per year, which is 6%

m is the number of compounding periods per year, which is 2 since interest is compounded semiannually

n is the total number of compounding periods, which is 10 since there are 5 years and interest is compounded semiannually

(1 + r/m) is the interest factor

Substituting the values, we get:

[tex]FV = $1,000 x ((1 + 0.06/2)^10 - 1) x (1 + 0.06/2)[/tex]

= $1,000 x [tex](1.06^{10[/tex] - 1) x 1.03

= $1,000 x 1.79155 x 1.03

= $1,848.20

Therefore, the future value of the annuity due is $1,848.20, rounded to the nearest cent.

To learn more about compounded visit:

https://brainly.com/question/19458442

#SPJ11

Answer:

A. [tex](x-3)^{2}[/tex]

Step-by-step explanation:

Find 2 numbers who's sum is -6 and product is 9

-3 and -3

sum = -6

(-3) * (-3) = 9

product = 9

You can also calculate each option individually

A.

[tex](x -3)^{2} = (x-3)(x-3)[/tex]

Use FOIL... then

[tex]x^{2} -6x+9[/tex]

Answer:

Step-by-step explanation: The answer to this problem would be A . You would first see if the first and third numbers were perfect squares and if they were you would put the value of the perfect squares in parentheses and add a 2 at the top of the answer after the parentheses

Answer:

  8√23 ≈ 38.37

Step-by-step explanation:

You want the length of a chord 10 units from the center of a circle when a chord 12 units from the center has length 36 units.

The radius OA completes the right triangle OBA. The hypotenuse (OA) is found using the Pythagorean theorem:

  OA² = OB² +BA²

  OA² = 12² +18² = 468

Radius OF is the same length, so we can use the Pythagorean theorem to find FE.

  OF² = OE² +FE²

  FE² = OF² -OE² = 468 -10² = 368

  FD = 2·FE = 2√368 = 8√23

  FD ≈ 38.37

The product of 10 by 2 = 20 because when 10 is multiplied twice(2) the result would be = 20.

Multiplication is defined as one of the major arithmetic operations used in solving mathematical questions which involves the duplication of a value.

Other arithmetic operations include addition, subtraction and Division.

The multiplication of a value can also be the product of the value and another value.

That is 10×2 is the product of 10 and 2 which should be = 20.

Learn more about multiplication here:

https://brainly.com/question/28768606

#SPJ1

To solve (2b) to the 4th power, we need to raise the entire quantity of 2b to the power of 4.

This can be done by multiplying the quantity (2b) by itself 4 times using the power rule of exponents, which states that (a^m)^n = a^(m*n).

So we have:

(2b)^4 = (2b) x (2b) x (2b) x (2b)

Expanding this expression, we get:

(2b)^4 = 2 x 2 x 2 x 2 x b x b x b x b

Simplifying further, we can multiply the 2's together to get:

(2b)^4 = 16b^4

Therefore, the expression (2b) to the 4th power simplifies to 16b^4.

learn more about exponent,

https://brainly.com/question/13669161

#SPJ11

Answer:

B. 27 Units

Step-by-step explanation:

To find the perimeter of the figure, we simply add up the lengths of all the sides.

So, the perimeter of the figure with sides of length 8, 6, 4, and 9 units is:

P = 8 + 6 + 4 + 9 = 27 units

Therefore, the answer is B. 27 units.

The probability that a person will wait for more than 9 minutes is approximately 0.0228, or 2.28% when rounded to four decimal places

To find the probability that a person will wait for more than 9 minutes, we'll use the z-score formula and a standard normal distribution table (Z-table).

First, calculate the z-score using the formula:
z = (X - μ) / σ

Where X is the value we're interested in (9 minutes), μ is the mean (5 minutes), and σ is the standard deviation (2 minutes).

z = (9 - 5) / 2
z = 4 / 2
z = 2

Now, look up the probability for a z-score of 2 in a Z-table. You'll find a value of 0.9772, which represents the probability of waiting less than or equal to 9 minutes. To find the probability of waiting more than 9 minutes, subtract this value from 1:

Probability of waiting more than 9 minutes = 1 - 0.9772 = 0.0228

Know more about probability here:

https://brainly.com/question/30034780

#SPJ11

.

The sum of all these probabilities is equal to 1, which is the total probability of all possible outcomes.

To solve this problem, we need to consider all the possible outcomes that result in at most four successes. These outcomes are:

0 successes

1 success

2 successes

3 successes

4 successes

The probability of each of these outcomes can be calculated using the binomial distribution formula:

P(k) = (n choose k) [tex]* p^k * (1-p)^(n-k)[/tex]

where n is the number of trials, k is the number of successes, and (n choose k) is the binomial coefficient, which is equal to n!/(k!*(n-k)!).

To find the probability of at most four successes, we need to add up the probabilities of all these outcomes. So the expression that would provide the answer is:

P(0 successes) + P(1 success) + P(2 successes) + P(3 successes) + P(4 successes)

This expression includes all the possible outcomes that correspond to having at most four successes in five trials. Note that it does not include the probability of having five successes, since we are only interested in the probability of at most four successes.

For example, if the probability of success in each trial is 0.3, then the probability of having zero successes is:

P(0 successes) = (5 choose 0)[tex]* 0.3^0 * 0.7^5 = 0.168[/tex]

Similarly, the probability of having one success is:

P(1 success) = (5 choose 1) [tex]* 0.3^1 * 0.7^4 = 0.360[/tex]

We can calculate the probabilities of having two, three, and four successes in a similar way. Then, we can add up all these probabilities to get the probability of at most four successes:

P(at most 4 successes) = P(0 successes) + P(1 success) + P(2 successes) + P(3 successes) + P(4 successes)

In this example, we get:

P(at most 4 successes) = 0.168 + 0.360 + 0.308 + 0.132 + 0.032 = 1.000

Note that the sum of all these probabilities is equal to 1, which is the total probability of all possible outcomes.

To learn more about probability visit:

https://brainly.com/question/30034780

#SPJ11

The final amount after 2 years of continuous compounding at a 5% annual interest rate is $11.05.

Step By Step Calculation:

Step 1: Convert the annual interest charge from a percent to a decimal. In this case, the yearly interest rate is 5%, so we have:

r = 5% = 0.05

Step 2: Use the formulation for continuous compounding to calculate the final amount A, where P is the initial principal and t is the time in years:

[tex]A = Pe^{(rt)}[/tex]

Substituting the given values, we get:

[tex]A = 10e^{(0.05*2)}[/tex]

Step 3: Simplify the exponential expression through elevating the natural number e to the power of 0.1:

[tex]A = 10e^{0.1}[/tex]

Step four: examine e^0.1 the use of a calculator or by means of the use of the Taylor series expansion for [tex]e^x[/tex]:

[tex]e^x = 1 + x + (x^2/2!) + (x^3/3!) + ...[/tex]

when x = 0.1, we get:

[tex]e^0.1 = 1 + 0.1 + (0.1^2/2!) + (0.1^3/3!) + ... = 1.10517092...[/tex]

Step 5: Multiply the preliminary most important by means of the calculated cost of e^0.1 to get the final quantity:

[tex]A = 10 * 1.10517092 = $11.05[/tex]

Consequently, the final amount after 2 years of continuous compounding at a 5% annual interest rate is $11.05.

Learn more about continuous compounding:-

https://brainly.com/question/14303868

#SPJ4

a. Both samples were randomly selected from their populations and c. Individual observations in each sample can be considered independent, and the samples themselves are independent.

Explanation: To use a two-sample interval to estimate the difference between the proportion of each type of fruit that has the disease, the following conditions must be met:
a. Both samples were randomly selected from their populations (this ensures that the samples are representative of their respective populations)
b. The observed counts of successes and failures are sufficiently large in each sample (this ensures that the normal approximation can be used)
c. Individual observations in each sample can be considered independent, and the samples themselves are independent (this ensures that the samples are not related to each other in any way)

In this scenario, Kumari took separate random samples of each type of fruit, meeting the conditions of random selection and independence for both samples. Additionally, the observed counts of successes and failures are sufficiently large (3 of 10 oranges and 1 of 15 tangerines), meeting the condition of large enough counts. Therefore, conditions a and c are both met.
Based on the information provided, Kumari's samples met the following conditions for a two-sample interval estimation:

a. Both samples were randomly selected from their populations
c. Individual observations in each sample can be considered independent, and the samples themselves are independent.

The observed counts of successes and failures (condition b) are not sufficiently large in each sample, as a general rule of thumb is to have at least 10 successes and 10 failures in each sample. In this case, the numbers of diseased and healthy fruits in each sample do not meet this criterion.

Visit here to learn more about populations brainly.com/question/27991860

#SPJ11

We need to use a different test, such as the ratio test or the root test, to make a conclusion.

For the first series, we have:

∑[infinity]k=1 (2+k)/(3-k²)

Using the divergence test, we consider the limit of the general term as k approaches infinity:

lim (k→∞) (2+k)/(3-k²)

We can see that the denominator, k², grows much faster than the numerator, k. Therefore, as k approaches infinity, the term approaches zero. However, the denominator approaches infinity, meaning that the terms do not go to zero fast enough for the series to converge. Therefore, we can conclude that the series diverges.

For the second series, we have:

∑[infinity]k=1 (2e^k)/(3+k)

Using the divergence test, we consider the limit of the general term as k approaches infinity:

lim (k→∞) (2e^k)/(3+k)

We can see that the denominator, 3+k, grows much faster than the numerator, e^k. Therefore, as k approaches infinity, the term approaches zero. However, the denominator approaches infinity, meaning that the terms do go to zero fast enough for the series to converge. Therefore, we cannot conclude anything about the convergence or divergence of the series using only the divergence test. We need to use a different test, such as the ratio test or the root test, to make a conclusion.

To learn more about limit visit:

https://brainly.com/question/12207558

#SPJ11