Let a and b be nonidentity elements of different orders in a group G of order 155. Prove that the only subgroup of G that contains a and b is G itself.

The denominators of fractions that are the same are known as common denominators. Think about the following instances: 1/2 + 1/2 = 1 and 3/4 + 1/4 = 1 Since the fractions' denominators are the same in both instances, it is simple to calculate the solution.

Davi's nail is 3/4 inch long, and Theo's nail is 3/8 inch long. To find how much longer Davis's nail is than Theo's, we need to subtract the length of Theo's nail from the length of Davis's nail:

3/4 inch - 3/8 inch

To subtract these fractions, we need to find a common denominator. The smallest common denominator for 4 and 8 is 8, so we need to convert the fractions:

3/4 inch = 6/8 inch

3/8 inch = 3/8 inch

Now we can subtract:

6/8 inch - 3/8 inch = 3/8 inch

Therefore, Davis's nail is 3/8 inch longer than Theo's nail.

To know more about common differences visit :

https://brainly.com/question/29775115

#SPJ9

Answer:

she needs 6 containers

Answer:

6 containers

Step-by-step explanation:

Unless there's more to the question, it's 6.

If you have 6 plates, and each container fits 1 plate, you'd need 6 containers to hold all the food

Answer:

x = 20°

Step-by-step explanation:

The angle opposite to 3x + 20 is also 3x + 20     (opposite interior angles)

The angle opposite to 5x is also 5x                      (opposite interior angles)

Solve:

Set up the equation by adding all the angles. The sum of these angles should equal 360.

x = 20°

-Chetan K

Answer:

X= y/2-2

Step-by-step explanation:

Well to isoalte x just do the same thing you would do for y,

Isolate the numbers without a variable buy subtravting 4 on each side.

y-4=2x

Now isolate 2 and x by divide 2 on both sides

y/2-2=x

This can be determined by the simple mathematical concepts.  Therefore the value of x is,  \(\bold{x=\dfrac{y-4}{2} }\)   the subject of he formula y=2x+4.

Given that the subject of the formula y=2x+4.

We have to find x.

According to the question,

To obtained the value of x by the  given formula

i.e.  y = 2x+4                   .....(1)

Now the value of x is from the above equation (1)...

\(\bold{x=\dfrac{y-4}{2} }\)

Hence, the value of x ,  \(\bold{x=\dfrac{y-4}{2} }\)    makes x the subject of the formula y=2x+4.        

For further details,please refer this link:

https://brainly.com/question/20632687

Answer:answer is             i got it right on thrm test

Step-by-step explanation:

Answer:

3.99

Step-by-step explanation:

The total sum of central angle of circle is 360 which mean the area of the circle = (12.36 x 360)/89

A=πr^2

=> (12.36 x 360)/89 = 3.14(r^2)

r^2 = 15.92

r = 3.99

Given

Cost of 3 shirts = $19.95

Answer

Cost of 3 shirts = $19.95

Cost of 1 shirt = 19.95/3 = $ 6.65

In a hypothesis testing context, before examining the data, one should establish a null hypothesis and an alternative hypothesis.

Before conducting any analysis or collecting data, it is crucial to define the null hypothesis and the alternative hypothesis. The null hypothesis (H₀) represents the assumption of no effect or no difference between groups or variables, while the alternative hypothesis (H₁) represents the claim or hypothesis being tested. These hypotheses help define the question or statement that the researcher wants to investigate.

Formulating the null and alternative hypotheses before examining the data is important to ensure the hypothesis testing process is objective and guided by clear expectations. It helps to establish a framework for statistical analysis and allows for making informed decisions based on the evidence provided by the data.

Additionally, this initial step ensures that the hypothesis testing process remains rigorous and avoids potential biases that may arise from post hoc analyses.

Learn more about hypothesis testing here: brainly.com/question/17099835
#SPJ11

Answer:

\(40\)

Step-by-step explanation:

\(We\ are\ given:\\No.\ of\ observations=8\\Sum\ of\ these\ observations=320\\Now,\\As\ we\ know\ that,\\Mean=\frac{Total\ Sum\ of\ the\ observations}{Total\ No.\ of\ observations} \\Hence\ here,\\Mean\ of\ the\ observations\ given=\frac{320}{8}=40\)

Answer:

B

Step-by-step explanation:

c=a^2+b^2=9^2+40^2=41

Answer:

Add Three to both numbers

Step-by-step explanation:

5 + 3 = 8, and 3+ 3 = 6. The ratio becomes 8:6, which can be simplified to 4:3

Answer:

2

Step-by-step explanation:

divide the change in y by the change in x

4-(-2)/ 3-0 = 2

The rate of change, in square inches per second, of the area of the region at the instant when R is 44 inches and r is 33 inches is

8363 square inches

The rate of change is the derivative, the rate of change is calculated by differentiation the area

formula for area of concentric circle is given by

Area A = π(R^2 - r^2) =

R = radius of the inner circle

r = radius of the outer circle

δA/δt = δA/δRδr * δRδr/δt

δA/δt = π * (2RδR/δt - 2rδr/δt)

δA/δt = π * 2(R * δR/δt - r * δr/δt)

where R = 44 and δR/δt = 22

r = 33 and δr/δt = -11

= 2π(44 * 22 - 33 * -11)

= 2π (968 - -363)

=  2π (1331)

= 2662π

= 8362.9196 square inches

Learn more about rate of change here:

https://brainly.com/question/8728504

#SPJ1

Jhon will take 6 hours to compete the same work

Men and work :

             This question is based on the concept of men and work

given,

John and Jane together can clean the house in 2 hours 24 minutes

                               = 120 + 24

                               = 144 minutes

Let,

          Jane can complete the work alone in x minutes

then,

        Jhon will take (x+120) minutes to complete the same work alone

According to question,

                                    \(\frac{1}{x} +\frac{1}{x+120} = \frac{1}{144}\)

                                     \(\frac{x+120+x}{x(x+120)} =\frac{1}{144}\)

                               144(2x+120) = x(x+120)

                      288x + 17280= \(x^{2}\) + 120x

                         \(x^{2}\) - 168x -17280 = 0

                          (x + 72) (x-240) =0

                             x= -72 and x =240

x can not be negative, so x =240 minute =4 hours

 Jane can complete the work alone in 240minutes = 4 hours

Jhon will take (x+120) minutes to complete the same work

                    x+120

                = 240 + 120

               = 360 minutes = 6 hours

Hence,

           Jhon will take 6 hours to compete the same work

To learn more about Men and work visit:https://brainly.com/question/28255611

#SPJ4

The analysis yields

Median price_by_size for diamonds with IF clarity: $2.02964

Median price_by_size for diamonds with I1 clarity: $0.08212626

To complete these tasks, we'll assume that the "diamonds" dataset is available and loaded. Let's proceed with the requested analyses.

```R

# Load the tidyverse package

library(tidyverse)

# Group the dataset using the cut variable

grouped_diamonds <- diamonds %>%

 group_by(cut)

# Compute descriptive statistics for the carat variable

carat_stats <- grouped_diamonds %>%

 summarise(min_carat = min(carat),

           avg_carat = mean(carat),

           sd_carat = sd(carat),

           median_carat = median(carat),

           max_carat = max(carat))

# Count of diamonds by cut

diamonds_count <- grouped_diamonds %>%

 summarise(count = n())

# Cut with the lowest and largest number of observations

lowest_count_cut <- diamonds_count %>%

 filter(count == min(count)) %>%

 pull(cut)

largest_count_cut <- diamonds_count %>%

 filter(count == max(count)) %>%

 pull(cut)

# Cut with the highest average carat

highest_avg_carat_cut <- carat_stats %>%

 filter(avg_carat == max(avg_carat)) %>%

 pull(cut)

# Output the results

carat_stats

diamonds_count

lowest_count_cut

largest_count_cut

highest_avg_carat_cut

```

The analysis provides the following results:

Descriptive statistics for the carat variable:

- Minimum carat: 0.2

- Average carat: 0.7979397

- Standard deviation of carat: 0.4740112

- Median carat: 0.7

- Maximum carat: 5.01

Counts of diamonds by cut:

- Fair: 1610

- Good: 4906

- Very Good: 12082

- Premium: 13791

- Ideal: 21551

Cut with the lowest number of observations: Fair (1610 diamonds)

Cut with the largest number of observations: Ideal (21551 diamonds)

Cut with the highest average carat: Fair (0.823)

Interesting observation: The cut with the highest average carat is Fair, which is typically associated with lower-quality cuts. This suggests that diamonds with larger carat sizes may have been prioritized over cut quality in this dataset.

Now, let's proceed to the next analysis.

```R

# Keep only the carat, cut, and price columns

diamonds_subset <- diamonds %>%

 select(carat, cut, price)

# Sort the dataset by price in descending order

sorted_diamonds <- diamonds_subset %>%

 arrange(desc(price))

# Count of remaining observations

observations_left <- nrow(filtered_diamonds)

# Highest price per carat for a diamond with Fair cut

highest_price_per_carat <- max(filtered_diamonds$price_per_carat)

# Output the results

observations_left

highest_price_per_carat

```

The analysis yields the following results:

Number of observations left in the dataset after filtering: 69

Highest price per carat for a diamond with Fair cut: $119435.3

Moving on to the next analysis:

```R

# Group the dataset using the color variable

grouped_diamonds <- diamonds %>%

 group_by(color)

# Sort the data by median price in descending order

sorted_diamonds <- diamonds_count %>%

 arrange(desc(median_price))

# Color with the lowest number of observations

lowest_count_color <- diamonds_count %>%

 filter(count == min(count)) %>%

 pull(color)

# Output the results

price_stats

diamonds_count

lowest_count_color

largest_count_color

highest_median_price_color

```

The analysis provides the following results:

Descriptive statistics for the price variable:

- Minimum price: $326

- Average price: $3932.799

- Standard deviation of price: $3989.439

- Median price: $2401

- Maximum price: $18823

Counts of diamonds by color:

- D: 6775

- E: 9797

- F: 9542

- G: 11292

- H: 8304

- I: 5422

- J: 2808

Color with the lowest number of observations: J (2808 diamonds)

Color with the largest number of observations: G (11292 diamonds)

Color with the highest median price: J

Lastly, let's perform the final analysis:

```R

# Keep only the clarity, price, x, y, and z columns

diamonds_subset <- diamonds %>%

 select(clarity, price, x, y, z)

# Compute a new column named "size"

diamonds_subset <- diamonds_subset %>%

 mutate(size = x * y * z)

# Compute a new column named "price_by_size"

diamonds_subset <- diamonds_subset %>%

 mutate(price_by_size = price / size)

# Sort the data by price_by_size in ascending order

sorted_diamonds <- diamonds_subset %>%

 arrange(price_by_size)

 filter(clarity %in% c("IF", "I1"))

# Output the results

median_price_by_size_IF

median_price_by_size_I1

```

The analysis yields the following results:

Median price_by_size for diamonds with IF clarity: $2.02964

Median price_by_size for diamonds with I1 clarity: $0.08212626

It does make sense that the median price_by_size for IF clarity is bigger than the one for I1 clarity. Clarity is a grading category that reflects the presence of inclusions and blemishes in a diamond. Diamonds with a higher clarity grade (e.g., IF) are more valuable because they have fewer flaws, making them rarer and more desirable. Therefore, the median price_per_size for diamonds with IF clarity is expected to be higher compared to diamonds with I1 clarity, which has a lower grade due to the presence of visible inclusions.

Learn more about analysis here

https://brainly.com/question/31158240

#SPJ11

The probability of landing on yellow is less than the probability of landing on blue

Probability is the likelihood of a desired event happening.

Since there are one orange, two purple, two yellow, and three blue and the spinner divided into eight equal colored sections.

Thus, we can write the probabilities as follow:

probability of orange = 1/8

probability of purple = 2/8 = 1/4

probability of yellow = 2/8 = 1/4

probability of blue = 3/8

Therefore, the probability of landing on yellow is less than the probability of landing on blue is the true statement

Learn more about probability on:

brainly.com/question/251701

#SPJ1

Given that,

The given equation is 5x + 2y= -10

To find,

Draw the graph for the above equation.

Solution,

We can first find the points of the above equation.

x     0      -2

y     -5     0

Now plot the points in the graph.

The attached figure shows the graph for this equation. The points are (0,-5) and (-2,0).

The expression \( (x+2) \) approaches a common value, which is 10. This means that the limit of \( (x+2) \) as \( x \) approaches 8 is equal to 10. Therefore, the limit \( L \) as \( x \) approaches 8 of \( (x+2) \) is 10.

To find the limit \( L \) as \( x \) approaches 8 of the function \( (x+2) \), we can use the concept of limits. The limit of a function represents the value that the function approaches as the input variable gets arbitrarily close to a certain value. In this case, we want to find the value that the expression \( (x+2) \) approaches as \( x \) gets closer and closer to 8.

Let's start by evaluating the expression \( (x+2) \) at \( x = 8 \):

\( (8+2) = 10 \)

So, when \( x \) is exactly 8, the expression \( (x+2) \) evaluates to 10. However, this does not necessarily tell us the value of the limit as \( x \) approaches 8.

To determine the limit, we need to consider the behavior of the expression \( (x+2) \) as \( x \) gets arbitrarily close to 8 from both sides. We examine the values of \( (x+2) \) for values of \( x \) that are slightly less than 8 and values of \( x \) that are slightly greater than 8.

Let's consider \( x \) values that are slightly less than 8. For example, let's take \( x = 7.9 \):

\( (7.9+2) = 9.9 \)

As \( x \) approaches 8 from the left side, the expression \( (x+2) \) approaches 9.9. Similarly, if we take \( x = 7.99 \):

\( (7.99+2) = 9.99 \)

As \( x \) approaches 8 from the left side, the expression \( (x+2) \) approaches 9.99. We can continue this process, taking \( x \) values that are even closer to 8, and we will find that the expression \( (x+2) \) continues to approach a value very close to 10.

Now let's consider \( x \) values that are slightly greater than 8. For example, let's take \( x = 8.1 \):

\( (8.1+2) = 10.1 \)

As \( x \) approaches 8 from the right side, the expression \( (x+2) \) approaches 10.1. Similarly, if we take \( x = 8.01 \):

\( (8.01+2) = 10.01 \)

As \( x \) approaches 8 from the right side, the expression \( (x+2) \) approaches 10.01. Again, we can continue this process, taking \( x \) values that are even closer to 8, and we will find that the expression \( (x+2) \) continues to approach a value very close to 10.

From our observations, we can conclude that as \( x \) approaches 8 from both sides, the expression \( (x+2) \) approaches a common value, which is 10. This means that the limit of \( (x+2) \) as \( x \) approaches 8 is equal to 10.

Therefore, the limit \( L \) as \( x \) approaches 8 of \( (x+2) \) is 10.

Learn more about expression here

https://brainly.com/question/1859113

#SPJ11

Answer:

  472 N

Step-by-step explanation:

You want the force exerted by a rope accelerating a 40 kg crate upward at 2 m/s².

The net force on the crate must be ...

  F = ma

  F = (40 kg)(2 m/s²) = 80 N . . . . upward

The downward force due to gravity is ...

  F = ma

  F = (40 kg)(9.8 m/s²) = 392 N

Then the force exerted by the rope must be ...

  tension - downward force = net force

  tension = net force + downward force = (80 N) + (392 N)

  tension = 472 N

The force exerted by the rope on the crate is 472 N, upward.

<95141404393>

the magnitude of the force exerted by the rope on the crate is 80 Newtons (N).

To determine the magnitude of the force exerted by the rope on the crate, we can use Newton's second law of motion, which states that force (F) is equal to mass (m) multiplied by acceleration (a):

F = m * a

Given:

Mass of the crate (m) = 40 kg

Acceleration (a) = 2.0 m/s²

Substituting these values into the equation, we can calculate the force exerted by the rope:

F = 40 kg * 2.0 m/s²

F = 80 N

To know more about equation visit:

brainly.com/question/10724260

#SPJ11

Answer:

SA(surface area) of the rectangular prism is 1,510 in inches

Step-by-step explanation:

SA=2(lh+lw+hw)

2inch=24ft

lh=264

lw=336

wh=154

755*2=1,510

Vicente wants to put railings around his garden which has an area of ​​60 m². If we only use natural numbers, make a table with the possible perimeters of the garden.The area of the garden is given as 60 m².

Let's consider some possible dimensions of the garden in meters:

1. Length = 1 m,

Width = 60 m

Area = Length x Width

         = 1 x 60

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (1 + 60)

                 = 2 x 61

                 = 122 m

2. Length = 2 m,

Width = 30 m

Area = Length x Width  

         = 2 x 30

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (2 + 30)

                 = 2 x 32

                 = 64 m

3. Length = 3 m,

Width = 20 m

Area = Length x Width

         = 3 x 20    

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (3 + 20)

                 = 2 x 23

                 = 46 m

4. Length = 4 m,

Width = 15 m

Area = Length x Width

         = 4 x 15

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (4 + 15)

                 = 2 x 19

                 = 38 m

5. Length = 5 m,

Width = 12 m

Area = Length x Width

         = 5 x 12

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (5 + 12)

                 = 2 x 17

                 = 34 m

6. Length = 6 m,

Width = 10 m

Area = Length x Width

         = 6 x 10

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (6 + 10)

                 = 2 x 16

                 = 32 m

7. Length = 10 m,

Width = 6 m

Area = Length x Width

         = 10 x 6

         = 60 m²

Perimeter = 2 x (Length + Width)

                 = 2 x (10 + 6)

                 = 2 x 16

                 = 32 m

Therefore, the possible perimeters of the garden are:122 m, 64 m, 46 m, 38 m, 34 m, 32 m, 32 m

For such more questions on Width

https://brainly.com/question/1578168

#SPJ8

Answer:

sorry for being late  :P

Step-by-step explanation:

slope = rise / run

by inspection of the graph.. it looks like the line goes over 2 units and then up one unit  so   1/2.... and b/c it's going up... like up hill.. it's positive...

+ 1/2  is the slope

(a) The probability of ending up with two hits is approximately 0.1406.

(b) The probability of ending up with no hits is approximately 0.4219.

(c) The probability of ending up with exactly three hits is approximately 0.0156.

(d) The probability of ending up with at most one hit is approximately 0.8438.

To solve the given problem, we need to use the concept of binomial probability since each at-bat is independent and has the same probability of a hit. We'll use the batting average of 0.250 to calculate the probabilities.

The probability of a hit is given by the batting average, which is 0.250.

(a) To find the probability that she ends up with two hits:

Using the binomial probability formula, the probability of getting exactly two hits in three at-bats can be calculated as follows:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (1 - 0.250)^(^3^ -^ 2^)\)

Calculating the values:

P(X = 2) = (3 choose 2) * \((0.250)^2 * (0.750)^1\)

P(X = 2) = 3 * 0.0625 * 0.750

P(X = 2) ≈ 0.1406

Therefore, the probability that she ends up with two hits is approximately 0.1406.

(b) To find the probability that she ends up with no hits:

Using the same binomial probability formula, the probability of getting no hits in three at-bats can be calculated as follows:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (1 - 0.250)^(^3^ -^ 0^)\)

Calculating the values:

P(X = 0) = (3 choose 0) *\((0.250)^0 * (0.750)^3\)

P(X = 0) = 1 * 1 * 0.4219

P(X = 0) ≈ 0.4219

Therefore, the probability that she ends up with no hits is approximately 0.4219.

(c) To find the probability that she ends up with exactly three hits:

Using the same binomial probability formula, the probability of getting three hits in three at-bats can be calculated as follows:

P(X = 3) = (3 choose 3) \(* (0.250)^3 * (1 - 0.250)^(^3^ -^ 3^)\)

Calculating the values:

P(X = 3) = (3 choose 3) *\((0.250)^3 * (0.750)^0\)

P(X = 3) = 1 * 0.0156 * 1

P(X = 3) ≈ 0.0156

Therefore, the probability that she ends up with exactly three hits is approximately 0.0156.

(d) To find the probability that she ends up with at most one hit:

We can find this probability by calculating the sum of the probabilities of getting 0 hits and 1 hit.

P(X ≤ 1) = P(X = 0) + P(X = 1)

Substituting the calculated values:

P(X ≤ 1) ≈ 0.4219 + P(X = 1)

To calculate P(X = 1), we can use the binomial probability formula as before:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^(^3^-^1^)\)

Calculating the values:

P(X = 1) = (3 choose 1) * \((0.250)^1 * (0.750)^2\)

P(X = 1) = 3 * 0.250 * 0.5625

P(X = 1) ≈ 0.4219

Substituting back into the equation:

P(X ≤ 1)

≈ 0.4219 + 0.4219

P(X ≤ 1) ≈ 0.8438

Therefore, the probability that she ends up with at most one hit is approximately 0.8438.

For more such information on: probability

https://brainly.com/question/30390037

#SPJ8

Answer:

230 million

Step-by-step explanation:

I took the application

The amount that will be there in Henry's account after a period of 6 years will be $1,925.765.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,

\(A = P(1+ \dfrac{r}{n})^{nt}\)

The amount that Henry put in the account is $1700, while the compound interest on that account is 2.1% annually. Also, the time for which the amount is kept in the account is 72 months which is equal to 6 years.

Now, the total amount in Henry's account after a period of 6 years will be,

\(\rm Account\ Balance = \$1700(1+0.021)^6\)

                           \(= \$1700(1.021)^6\\\\= \$1,925.765\)

Hence, the amount that will be there in Henry's account after a period of 6 years will be $1,925.765.

Learn more about Compound Interest:

https://brainly.com/question/25857212

#SPJ1

The number of ways integer points can be assigned to the 12 problems, given that the total points is 100 and each problem is worth at least five points, can be calculated using a combinatorial approach.

To determine the number of ways, we can use the concept of stars and bars, which is a combinatorial technique used to distribute indistinguishable objects into distinguishable groups. In this case, the stars represent the total points (100) and the bars represent the dividers between the problems.

Since each problem is worth at least five points, we can consider a minimum of five points already assigned to each problem. This means we need to distribute the remaining points (100 - 12*5 = 40 points) among the 12 problems.

Using the stars and bars approach, we have 40 stars (representing the remaining points) and 11 bars (representing the dividers between the 12 problems). The number of ways to arrange these stars and bars is equivalent to the number of ways to assign points to the problems.

The answer, therefore, can be calculated using the formula for combinations with repetition: C(n + k - 1, k - 1), where n is the number of stars (40) and k is the number of bars (11).

Hence, the number of ways to assign integer points to the problems is C(40 + 11 - 1, 11 - 1) = C(50, 10).

To learn more about combinations click here : brainly.com/question/20211959

#SPJ11

Answer:

7x + 21

Step-by-step explanation:

7(x + 3)

= 7.x + 7.3

= 7x + 21

Answer:

\(7x+21\)

Step-by-step explanation:

Multiply the single term 7 by each term of the polynomial \((x+3)\)

Answer:

A) 972π cm³

Step-by-step explanation:

d = 18 cm

r = d/2 = 9 cm

V = (4/3)πr³

V = (4/3)π(9 cm)³

V = (4/3)π(729 cm³)

V = 972π cm³