Is it possible to form a triangle with side lengths , , and ? If so, will it be scalene, isosceles, or equilateral?A.Yes; scaleneB. Yes; isoscelesC. Yes; equilaterald. no

Every quadratic nonresidue of p is a primitive root of p, when p = 2^k + 1 is primeIf p = 2^k + 1 is a prime number, we want to show that every quadratic nonresidue of p is a primitive root of p.

In other words, we aim to prove that if an element x is a quadratic nonresidue modulo p, then it is also a primitive root of p.

Let's assume p = 2^k + 1 is a prime number. To prove that every quadratic nonresidue of p is a primitive root of p, we can use the properties of quadratic residues and quadratic nonresidues.

A quadratic residue modulo p is an element y such that y^((p-1)/2) ≡ 1 (mod p), while a quadratic nonresidue is an element x such that x^((p-1)/2) ≡ -1 (mod p).

Now, let's consider an element x that is a quadratic nonresidue modulo p. We want to show that x is a primitive root of p.

Since x is a quadratic nonresidue, we know that x^((p-1)/2) ≡ -1 (mod p). By Euler's criterion, this implies that x^((p-1)/2) ≡ -1^((p-1)/2) ≡ -1^2 ≡ 1 (mod p).

Since x^((p-1)/2) ≡ 1 (mod p), we can conclude that the order of x modulo p is at least (p-1)/2. However, since p = 2^k + 1 is a prime, the order of x modulo p must be equal to (p-1)/2.

By definition, a primitive root of p has an order of (p-1). Since the order of x modulo p is (p-1)/2, it follows that x is a primitive root of p.

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1. For the data set with Mean 79, Median 84, and Mode 83:

The best description for this data set would be moderately positively skewed because the mean (79) is lower than the median (84), indicating the presence of some lower values that pull the mean down.

2. For the data set with Mean 10, Median 8, and Mode 3:

The best description for this data set would be highly positively skewed because the mean (10) is higher than the median (8), suggesting the presence of a few higher values that pull the mean up.

3. For the data set with Mean 46, Median 52, and Mode 80:

The best description for this data set would be slightly negatively skewed because the mean (46) is lower than the median (52), indicating the presence of some higher values that pull the mean down.

For the data set with Mean 79, Median 84, and Mode 83:

The best description for this data set would be that it is moderately positively skewed.

This is because the mean (79) is lower than the median (84), indicating that there are some lower values that pull the mean down.

The mode (83) being close to the median suggests that it is a relatively common value in the data set.

Overall, this data set is slightly skewed to the left, but not excessively so.

For the data set with Mean 10, Median 8, and Mode 3:

The best description for this data set would be that it is highly positively skewed.

The mean (10) is higher than the median (8), which suggests the presence of a few higher values that pull the mean up.

The mode (3) being significantly lower than the median indicates that 3 is the most frequently occurring value in the data set.

The skewness towards the right indicates that there are some extreme values that are significantly higher than the rest of the data.

For the data set with Mean 46, Median 52, and Mode 80:

The best description for this data set would be that it is moderately negatively skewed.

The mean (46) is lower than the median (52), implying the presence of some higher values that pull the mean down.

The mode (80) being higher than both the mean and median indicates that 80 is the most common value in the data set.

This data set shows a slight skewness to the left, but not as pronounced as the first example.

There may be a few outliers on the lower end, but the majority of the data is centered around the higher values.

In summary, the best descriptions for the data sets are based on the relationship between the mean, median, and mode.

Analyzing these measures helps us understand the central tendency and the shape of the distribution, whether it is symmetric or skewed.

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Answer:

192

Step-by-step explanation:

2x9=18

18x12=192

1.)  Probabilities range from 0 to 1, denoting impossibility and certainty, respectively.

2.) The sum of probabilities of all possible outcomes is equal to 1.

1.) Individual probabilities will always have values between 0 and 1. This property is known as the "probability bound." Probability is a measure of uncertainty or likelihood, and it is represented as a value between 0 and 1, inclusive.

A probability of 0 indicates impossibility or no chance of an event occurring, while a probability of 1 represents certainty or a guaranteed outcome.

Any probability value between 0 and 1 signifies varying degrees of likelihood, with values closer to 0 indicating lower chances and values closer to 1 indicating higher chances. In simple terms, probabilities cannot be negative or greater than 1.

2.) The sum of the probabilities of all individual outcomes must equal 1. This principle is known as the "probability mass" or the "law of total probability." When considering a set of mutually exclusive and exhaustive events, the sum of their individual probabilities must add up to 1.

Mutually exclusive events are events that cannot occur simultaneously, while exhaustive events are events that cover all possible outcomes. This property ensures that the total probability accounts for all possible outcomes and leaves no room for uncertainty or unaccounted possibilities.

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h = 11.9 cm

cos = adjacent/ hypotenuse

therefore:

cos(24) = h/ 13

rearrange:

h = 13cos(24)

put into calculator:

h = 11.8760...

rounded to one decimal point:

h = 11.9cm

The answer is:

8 miles

Answer:

11.25 miles

Step-by-step explanation:

To figure out how many miles John will travel in 1/2 an hour, we can use the following formula:

distance = rate x time

We know the rate, which is the number of miles John can travel per hour. We can find this by dividing the total distance by the total time:

rate = distance / time

rate = 45 miles / 2 hours

rate = 22.5 miles per hour

Now we can use this rate and the given time of 1/2 an hour to find the distance:

distance = rate x time

distance = 22.5 miles per hour x 1/2 hour

distance = 11.25 miles

Therefore, John will travel 11.25 miles in 1/2 an hour at this rate.

There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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There are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

In this problem, we want to find the number of ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

Since every man must be diametrically opposite a woman, we can pair each man with one woman. There are 5 men and 9 women, so there are 5 pairs. We need to find the number of ways to seat these 5 pairs of people in a circle.

To do this, we can first seat one pair in any position. Then, we can seat the second pair anywhere but opposite the first pair. This gives us 11 positions for the second pair. Continuing in this way, we see that there are 11 * 6 * 5 * 4 * 3 = 7920 ways to seat the 5 pairs of people in a circle.

So, there are 7920 ways to seat 14 people in a circle such that every man is diametrically opposite a woman.

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Assuming 14 people, 5 men and 9 women, how many ways can they sit in a circle such that every man is diametrically opposite a woman?

The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.

Given that, 2.3p – 10.1 = 6.5p – 4 – 0.01p.

We need to find which equations have the same solution as the given equation.

Equivalent equations are algebraic equations that have identical solutions or roots. Adding or subtracting the same number or expression to both sides of an equation produces an equivalent equation. Multiplying or dividing both sides of an equation by the same non-zero number produces an equivalent equation.

Now, 2.3p - 10.1 = 6.5p - 4 - 0.01p can be simplified as follows:

To add or subtract terms of algebraic equations group like terms add numerals and keep the variables the same.

That is, 2.3p - 10.1 = (6.5p - 0.01p) - 4  

⇒2.3p - 10.1 =6.49p - 4

The equivalent equation for the given equation is 2.3p - 10.1 =6.49p - 4. Therefore, option B is the correct answer.

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The population of a district in 2005 was 35,700 with a continuous annual growth rate of approximately 4%. the population in 2030 will be approximately 97,209 according to the exponential growth function.

The formula for the continuous exponential growth is given by the formula:

P = Pe^(rt)

where,P is the population in the future.

P0 is the initial population.

t is the time.

r is the continuous interest rate expressed as a decimal.

e is a constant equal to approximately 2.71828.In this problem, the initial population P0 is 35,700. The rate r is 4% or 0.04 expressed as a decimal. We want to find the population in 2030, which is 25 years after 2005.

Therefore, t = 25.We will now use the formula:

P = Pe^(rt)P = 35,700e^(0.04 × 25)P = 35,700e^(1)P = 35,700 × 2.71828P = 97,209.09.

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Answer: I got 97,042.7

Step-by-step explanation:

Answer:

They have the most sales on Thursdays, and the least sales on Friday, so they might want to have specials on Friday to get more people.

The value of x from the given linear function is -48

Linear equations are equation that has a leading degree of 1. For instance the equation y = mx + b is a linear equation.

Given the equation below

-x/3 + 4 =20

We are to determine the value of x

Subtract 4 from both sides to have;

-x/3 + 4 - 4 = 20 - 4

-x/3 =20 - 4

-x/3 = 16

Multiply both sides by 3 to have

-x = 3(16)

-x = 48

x = -48

Hence the value of x from the given linear function is -48

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Answer:

1.) P = 8g + 50

2.) Find the attached file for the graph.

Step-by-step explanation:

Let the profit = P

And g = good sold.

Given that each yo-yo sells for $8.00

The rate or the slope of the equation will be 8

Also, it is given that they must pay a clerk $50.00 a day to sell them. A flat rate of 50 dollars is an intercept of the equation.

Using the general linear equation of

Y = mX + C

The equation for the profit the store will make in a day will be.

P = 8g + 50

Please find the attached file for the graph

To deduce if two line segments are parallel, we need to examine their corresponding angles. Therefore,  "none." is correct.

According to the information given, we have a missing value represented by m7. To find if any line segments are parallel, we can use the following rules:

1. If two lines are intersected by a transversal, and corresponding angles are congruent, then the lines are parallel.

2. If two lines are intersected by a transversal, and alternate interior angles are congruent, then the lines are parallel.

3. If two lines are intersected by a transversal, and alternate exterior angles are congruent, then the lines are parallel.

Let's consider each statement one by one:

Statement 1: m7 = 90 degrees. This statement represents a right angle. However, knowing that one angle is right does not provide enough information to deduce the lines' parallelism.

Statement 2: m7 = 135 degrees. This statement represents an angle greater than 90 degrees. Similarly, having this information alone is insufficient to deduce the lines' parallelism.

Statement 3: m7 = 45 degrees. This statement represents an angle less than 90 degrees. Again, having this information alone is not enough to deduce the lines' parallelism.

Given the information provided, we cannot deduce the parallelism of any line segments. Therefore,  "none." is correct.

In summary, without additional information about the relationships between angles formed by the line segments, we cannot determine whether the line segments are parallel or not.

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Answer:

55%

Step-by-step explanation:

We need to first find the total length of the side.

let remaining length be x

perimeter= 40cm

4 (s)=perimeter

4(7+x)=40

28+4x=40

4x=40-28=12

4x=12

x=12/4=3

total length= 7+3= 10cm

4+y= 10=

y=6

therefore, area of square= s*s= 10*10=100cm²

find areas of the two triangles (unshaded).

1/2*3*10= 15cm²

1/2*6*10= 30 cm²

15/100*100= 15%

30/100*100= 30%

shaded percentage= 100-(15+30)

= 100-45

= 55%

The critical numbers of the function h(p) = (p - 1) / (p^2 - 5) are "dne" (does not exist).

To find the derivative of h(p), we can apply the quotient rule. Taking the derivative, we have:

h'(p) = \([(p^2 - 5)(1) - (p - 1)(2p)] / (p^2 - 5)^2\)

Simplifying this expression, we get:

h'(p) = \((p^2 - 5 - 2p^2 + 2p) / (p^2 - 5)^2\)

= \((-p^2 + 2p - 5) / (p^2 - 5)^2\)

To find the critical numbers, we set h'(p) equal to zero and solve for p:

\(-p^2 + 2p - 5 = 0\)

However, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

p = (-2 ± √\((2^2 - 4(-1)(-5))) / (-1)\)

p = (-2 ± √(4 - 20)) / (-1)

p = (-2 ± √(-16)) / (-1)

Since the discriminant is negative, the equation has no real solutions. Therefore, the critical numbers of the function h(p) = (p - 1) / (\(p^2\) - 5) are "dne" (does not exist).

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Answer:

Negative 12

Step-by-step explanation:

-10 ≥ 2x + 14

-24 ≥ 2x [subtract 14 from both sides]

2x ≤ -24 [read right to left]

x ≤ -12  [divide both sides by 2]

When the speed of the body is doubled, it will travel a distance of 2 times the original distance d.

When the speed of a body moving on a rough surface is doubled, the distance it will travel can be calculated using the equation for distance traveled with constant deceleration. The initial speed of the body is doubled, so the final speed will be 2u. The deceleration on the rough surface remains the same. Let's denote the original distance traveled as d1 and the distance traveled after doubling the speed as d2.

To calculate d2, we can use the equation:

d2 = (v_f^2 - u^2) / (2a)

where:

v_f is the final speed (2u, in this case)

u is the initial speed

a is the deceleration

Since the body stops after traveling a distance d1, the final speed v_f will be 0. Substituting the values into the equation, we have:

0 = (2u)^2 - u^2 / (2a)

Simplifying the equation:

0 = 4u^2 - u^2 / (2a)

0 = 3u^2 / (2a)

Now, let's solve for d2:

d2 = (2u)^2 / (2a)

d2 = 4u^2 / (2a)

d2 = 2u^2 / a

Therefore, when the speed of the body is doubled, it will travel a distance of 2 times the original distance d.

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If the speed of a body moving on a rough surface is doubled, how far will it travel?

Answer:

n= 3

Step-by-step explanation:

3(n+3)= -4n+30

3n+9= -4n +30 expand

7n+9 = 30 +4n to both sides

7n = 21 -9 from both sides

n= 3 divide by 7 on both sides

your answer is going to be 100 and how you do that is you're going to estimate which means you're taking an educated guess and is it 70 closer to zero or 100 70 is only 20 numbers away and how you find that is by subtracting 100 from 70 which equals 20 and how you do that to see if it's up or down is 50 is in your middle okay so it's going to go from 0 to 50 to 100 on a number line 70 is in between 50 and 100 so that means that you'll be going up now if you did 30 instead of 70 in your equation rounding by 10 then it would be in between the zero and the 50 which that means that you're going down

The riddle mentioned in the question is about a farmer who is traveling along with a sack of rye, a goose, and a mischievous dog.

He comes to a river that he must cross from east to west, and there is a boat available to do so.  Therefore, the farmer takes the goose back to the east side and leaves it there. He then takes the sack of rye across the river, drops it off with the dog, and goes back to the east side to pick up the goose. In this manner, all of the farmer's possessions can be safely transported across the river without any of them being lost to the dog or the goose.This riddle is a classic example of a type of logical puzzle known as a "transport problem."

The goal of a transport problem is to determine how to transport one or more objects from one location to another while satisfying certain constraints, such as the size of the transport vehicle or the safety of the objects being transported.

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Answer:

3 squares

Step-by-step explanation:

Firstly, you have to count the number of squares in the shape. As it can been seen from the diagram, there are a total 18 squares (i.e 6 squares on each row × 3 squares on each column).

Secondly you have to find 1/6 of the total number of the squares in the shape. 1/6 of the total number of the square in the shape = 1/6 × 18 = 3 squares

Therefore 3 squares would have to be shaded so that 1/6 of the shape is shaded

Answer:

1

Step-by-step explanation:

1 part

i m sorry my small brother wrote it

Answer:

Step-by-step explanation:

1. 2x>-6

2.  x-4<7

3. -x-5<=-2

4. 6+x<=3

hope this helps!

Answer:

1 2x>-6

2 x-4<-7

4 6+x _<_

3-x-5 _<_-2

Step-by-step explanation:

The equation of the line that is parallel to y=-5x+6 and passes through the point (-4,-1) is y = -5x-21.

Given data :

Here, given equation of line is y = -5x+6

Required line is parallel to this given line, so we can say that the slope is same for the lines.

General equation of a line be y = mx+c ,  where m is the slope

Comparing given equation with this equation we get,

m = -5

The required line also passes through the point (-4, -1)

Now, we know that,

m = (y2-y1)/(x2-x1).

⇒ -5 = (-1 - Y ) / ( -4 - x )

⇒ -5 = y + 1 / x + 1

⇒ y+1 = -5x-20

⇒ y = -5x-21

Hence the equation proved.

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Answer:

C = 7.72 ~ 7.7

Step-by-step explanation:

So when you solve this equetion you must 1st find x then c

we can find x by using cos(60)

cos(60) = x/14

x = cos(60) × 14

x = 1/2 ×14

x = 7

so after we find x we are going to solve c by using cos (25)

cos (25) = X/C = 7/c

cos(25) × C = 7

C = 7/cos (25)

C = 7.72 ~ 7.7

so the solution is 7.7

The row vectors of the matrix are [-2 -3 1 0], and the column vectors are:

In a matrix, row vectors are the elements listed horizontally in a single row, while column vectors are the elements listed vertically in a single column. In this case, the given matrix is a 1x4 matrix, meaning it has 1 row and 4 columns. The row vector is [-2 -3 1 0], which represents the elements in the single row of the matrix. The column vectors, on the other hand, can be obtained by listing the elements vertically. Therefore, the column vectors for this matrix are -2, -3, 1, and 0, each listed in a separate column.

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The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Answer:

uihuvbuh ufsghiusgu 8y39 8y3yy894y87y48jhfjhjbvhjjavjlh ailhli

Step-by-step explanation: