determine whether the sequence converges or diverges. if it converges, find the limit. (if an answer does not exist, enter dne.) an = cos(n/2)

Answer:

5n is your answer hope this help

Step-by-step explanation:

Four friends all give each other presents. The total cost of the presents is £80.52. We need to find the mean cost of a present in pounds. So, the mean cost of a present is equal to 20.13 .

12*14=168

Hope this helps!

The statement 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value' is True.

In this question, we have been given a statement - 'when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.'

We need to state whether it is true or false.

We know that, the minimum value of the objective function Z = ax + by in a linear programming problem can also occur at more than one corner points of the feasible region.

Therefore, when finding a minimum in a linear programming problem, it is possible to find more than one minimum value.

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If a fair coin is flipped, the probability that the third head appears on the eight trial, ninth and tenth trial are as follows; Third head appears on the eighth trial; The first seven flips can be either heads or tails. There are 2⁷ = 128 possible outcomes. Since the coin is fair, each of these outcomes is equally likely.

There are C(7,2) = 21 ways to choose two of the seven flips to be heads. The other five must be tails. Thus there are 21 ways that the third head can occur on the eighth trial. Therefore, the probability of the third head appearing on the eighth trial is 21/128. Third head appears on the ninth trial: Similarly, the first eight flips can be any combination of heads and tails. There are 2⁸ = 256 possible outcomes.

There are C(8,2) = 28 ways to choose two of the eight flips to be heads. The other six must be tails. Thus there are 28 ways that the third head can occur on the ninth trial. The probability of the third head appearing on the ninth trial is 28/256. Third head appears on the tenth trial: Similarly, there are 2⁹ = 512 possible outcomes. There are C(9,2) = 36 ways to choose two of the nine flips to be heads. The other seven must be tails. Thus, there are 36 ways that the third head can occur on the tenth trial. Therefore, the probability of the third head appearing on the tenth trial is 36/512.
To find the probability of the third head appearing on a specific trial, we need to consider the previous trials.

For the third head to appear on the 8th trial, there must be 2 heads in the first 7 trials, and the 8th trial is a head. The probability is (7 choose 2) * (1/2)⁷ * (1/2) = 21/128.

For the third head to appear on the 9th trial, there must be 2 heads in the first 8 trials, and the 9th trial is a head. The probability is (8 choose 2) * (1/2)⁸ * (1/2) = 28/256.

For the third head to appear on the 10th trial, there must be 2 heads in the first 9 trials, and the 10th trial is a head. The probability is (9 choose 2) * (1/2)⁹ * (1/2) = 36/512.

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AC is 30.

Here it is given that AB = 4x-1 and BC = 2x + 7

Since it is given that a line m is perpendicular bisector of line segment AC. Hence, B is the mid-point of AC.

Therefore

AB = BC

4x-1 = 2x + 7

2x = 8

x = 4

As AC is the line and B is the mid-point

So AC = AB + BC

           = 4x - 1 + 2x +7

           = 6x + 6

           = 6×4 + 6

           = 24 + 6

           = 30

Therefore the value of AC is 30.

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Answer:

5

Step-by-step explanation:

Kendall has 45 dolphins.

15 shark stickers

20 whale stickers

The greatest common factor amount the three stickers is 5

45/5. , 15/5= 3. , 20/5= 4

= 9

Hence Kendall can put 5 stickers each in a bag

Answer: 8

Step-by-step explanation:

We have to complete the operation in the parenthesis first. 8-2 is 6. Now we have to take 4(6) which is 24. Now we have 6^2-24. 6^2 is 36. So 36-24 is 12. 16-12 is 4. Now 2 times 4 is 8.

Point P(6,6)

Point P'(2, 2)

To determine the dilation:

The dilation of this image is 1/3.

Answer:

C. 2

Step-by-step explanation:

2 can go into 36 and 60.

36/2 = 18

60/2 = 30

The other answers cannot go into 36 or 60.

Answer:

0.9452

Step-by-step explanation:

Answer for Khan academy

The proportion of bicycle prices that are lower than the price of the sports bicycle is approximately 94.52%.

A Z-score is defined as the fractional representation of data point to the mean using standard deviations.

We can start by standardizing the sports bicycle price using the formula:

z = (x - μ) / σ

where x is the sports bicycle price, μ is the mean, and σ is the standard deviation.

Substituting the values, we get:

z = (380 - 300) / 50 = 1.6

Now, we can use a standard normal distribution table or calculator to find the proportion of values below 1.6.

From the z-table, we find that this proportion is approximately 0.9452.

Therefore, the proportion of bicycle prices that are lower than the price of the sports bicycle is approximately 94.52%.

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The value r², called the coefficient of determination, measures the proportion of variability in one variable that can be determined from its relationship with the other variable.

The higher the value of r2, the more of the variation in the dependent variable can be attributed to the independent variable(s), and therefore the better the relationship between the two variables is. Overall, the coefficient of determination is an important statistical measure that is used to evaluate the strength and fit of regression models. It allows researchers to determine how much of the variation seen in the dependent variable can be explained by the independent variable(s), which can help in making predictions and drawing conclusions from the data.

It represents the strength and direction of the correlation between two variables, helping to quantify their linear association. A higher r² value indicates a stronger relationship between the variables, while a value close to zero signifies a weak or no relationship.

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Answer:

20cm

Step-by-step explanation:

We know that on the map, 3 cm represents 150 m.

To find how far apart two points are on the map when they are 1 km (1000 m) apart in reality, we can set up a proportion using the given scale:

(3 cm) / (150 m) = (x cm) / (1000 m)

We can cross-multiply and solve for x:

3 cm * 1000 m = 150 m * x cm

3000 cm * m = 150 m * x cm

The unit "m" cancels out, leaving us with:

3000 cm = 150 * x cm

Divide both sides by 150 cm:

3000 cm / 150 cm = x

20 = x

Therefore, the two points are 20 cm apart on the map.

Answer:

a) 8 groups

b) 5 boys per group and 7 girls per group

Step-by-step explanation:

School trip has 40 boys and 56 girls.

We solve the above question using the Greatest Common Factor Method

We find the factors of 40 and 56

The factors of 40 are: 1, 2, 4, 5, 8, 10, 20, 40

The factors of 56 are: 1, 2, 4, 7, 8, 14, 28, 56

Then the greatest common factor is 8.

a) What is the greatest number of groups that can be formed?

The greatest number of groups that can be formed is 8 groups

b)How many boys and how many girls will be in each group?

For boys.

The number of boys in each group is calculated as:

40 boys/8 groups = 5 boys per group

For girls

For 56 boys.

The number of boys in each grouo is calculated as:

56 girls /8 groups = 7 girls per group

Answer:

Step-by-step explanation:

16.5

Answer: 240ft

Step-by-step explanation:

Width:

10(15) + 10

= 150 + 10

= 160

Length:

4(15) + 20

= 60 + 20

= 80

L x W

= 160 + 80

= 240

Answer:

The equation is standard form is 2x + y = 11.

The equation is standard form is 2x - 3y = 18  

Step-by-step explanation:

Standard form: Ax + By = C

You need to solve the equation so that it is in that form.

y - 5 = -2(x - 3)

y - 5 = -2(x)  - 2(- 3)             Distributive property

y - 5         = -2x + 6             Simply . remember -2(-3) = 6

y - 5 + 2x = 2x + 6            Adding 2x to both sides of the equation

2x + y - 5      =     6             Now the x-term and the y-term are on one side

2x + y - 5 + 5 =   +5            Adding +5 to both sides of the equation

2x + y           =  11

Now the equation is standard form is 2x + y = 11

2.   y + 4 = 2/3 (x - 3)

       y + 4 = 2/3(x) + 2/3(- 3)        Distributive property

        y + 4         =  2/3x  - 2           Simply : 2/3(-3) = -6/3  = -2

    y  + 4 - 2/3x = -2/3x                 Adding -2/3x to both sides  

     y + 4 -2/3x =             -2      

        -4          =              -4            Adding -4 to both sides

     y - 2/3x  =   -  6

   -y  + 2/3x = 6                              x- term is positive so multiply by -1 will

      2/3x - y = 6                             change the sign in the equation      

     3(2/3x) -3(y) =  3(6)                You do not want a fraction in the x-term so

                                                     multiply by 3. Each term by 3.

        2x - 3y = 18                           3(2/3) = 6/3  = 2        

Answer:

-2 leis.

Step-by-step explanation:

212 * 14 = 2,968 leis

2,968/30 = 99 boxes

99*30=2970

2968-2970=-2

There is a problem with the wording of this question. There isn't a total so it's really confusing...

Answer:

20,000

Step-by-step explanation:

To round numbers to the nearest ten thousand, make the numbers whose last four digits are 0001 through 4999 into the next lower number that ends in 0000. For example 54,424 rounded to the nearest ten thousand would be 50,000.

There are no blue crayons in the box, so the probability of picking two blue crayons is 0. Therefore, the answer is none of the options provided.

Alternatively, we can use basic probability rules to calculate the probability of picking two crayons with a specific color. Since there are 12 crayons in total, Frieda has 12 choices for her first pick. After she picks one crayon, there are 11 crayons left in the box, so she has 11 choices for her second pick. The total number of ways to pick two crayons from the box is the product of these two numbers: 12 x 11 = 132.

To calculate the probability of picking two crayons with a specific color, we need to count the number of ways that Frieda can pick two crayons of that color. In this case, there are no blue crayons in the box, so the number of ways to pick two blue crayons is 0. Therefore, the probability of picking two blue crayons is 0/132 = 0.

In general, the probability of picking two crayons with the same color is the product of the probability of picking the first crayon with that color and the probability of picking the second crayon with that color, given that the first crayon was already picked. For example, the probability of picking two red crayons is (2/12) x (1/11) = 1/66, since there are 2 red crayons in the box on the first pick, and if one red crayon is picked, there is only 1 red crayon left in the box for the second pick. Similarly, the probability of picking two green crayons is (3/12) x (2/11) = 1/22.

The answer is none of the options provided.

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The determinant of an image matrix can only be equal to 1 or -1.

If we have an image matrix with the property that images, its determinant can only be equal to 1 or -1.

To understand why, let's first define what we mean by an image matrix. An image matrix is a square matrix A of size n x n, where each entry a_ij is either 0 or 1. We say that A is an image matrix if for every row i and column j, the sum of the entries in that row and column is odd. In other words, the row and column sums of A are all odd.

Now, let's consider the determinant of an image matrix A. The determinant of a matrix is a scalar value that can be calculated from its entries. Without loss of generality, let's assume that the first row of A has an odd sum, since we can always permute the rows and columns of A to achieve this.

We can expand the determinant of A along the first row to obtain:

det(A) = a_11 det(A_11) - a_12 det(A_12) + a_13 det(A_13) - ... + (-1)^(n+1) a_1n det(A_1n)

where A_ij is the matrix obtained by deleting the ith row and jth column of A. Each of the determinants det(A_ij) can be computed recursively using the same formula. Since each entry of A is either 0 or 1, the determinant det(A_ij) is either 0, 1, or -1.

Now, consider the ith term in the expansion of det(A). This term is of the form a_i1 det(A_i1), where a_i1 is either 0 or 1. Since the sum of the entries in the first row of A is odd, we know that there are an odd number of entries in that row that are equal to 1. Let k be the number of such entries. Then, det(A_i1) is the determinant of a (n-1) x (n-1) matrix in which each row and column sum is even, since we have deleted one row and one column that contained a 1. Therefore, det(A_i1) is either 1 or -1, since the determinant of a matrix with even row and column sums is always a square.

If k is odd, then the term a_i1 det(A_i1) is equal to either 1 or -1, depending on the value of a_i1. If k is even, then the term a_i1 det(A_i1) is equal to 0. Therefore, we have:

det(A) = ± 1

since the sum of an odd number of odd terms is odd, and the sum of an even number of odd terms is even (i.e., equal to 0 or ±2). Thus, the determinant of an image matrix can only be equal to 1 or -1.

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Answer:

Part 1:

Domain= {2,3,8,9}

Range = {7,9,14}

Part 2: Yes it is not a function

Step-by-step explanation:

Domain is the first number

Range is the second.

Domain= {2,3,8,9}

Range = {7,9,14} ( Notice that 14 is noted twice so just put it as once and this is not part of the answer)

Function: Is any of the domain numbers the same: Answer Yes it's a function.

Answer:

m∠T = 60°

m∠U = 60°

TS = 13 cm

SU = 13 cm

Step-by-step explanation:

The diagram shows that 2 sides, UT and TS, are equal, so it is an isosceles triangle. Since it is an isosceles triangle, the two angles opposite the equal sides are also congruent to each other, so m∠S = m∠U = 60°.

Now we know the measure of 2 angles, we can find the measure of the third angle, by subtracting the 2 known angles from 180°.

m∠T = 180° - m∠S - m∠U

m∠T = 180° - 60° - 60°

m∠T = 60°

Since all 3 angles are congruent, it is an equilateral triangle, therefore all the sides must be congruent too. So UT = TS = SU = 13 cm.

The opposite side and the adjacent side of angle I are GH and HI, respectively.

The opposite side and the adjacent side are dependent on the angle that is being referenced

Take for instance, the angle of reference is:

Angle G

The side opposite angle G is side HI and the side adjacent angle G is GH

So, the opposite side and the adjacent side of angle G are HI and GH, respectively.

Also if the angle of reference is:

Angle I

The side opposite angle I is side GH and the side adjacent angle G is HI

So, the opposite side and the adjacent side of angle I are GH and HI, respectively.

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The perimeter of the shaded shape is 30 cm.

The area of the shaded shape is 50 cm².

The perimeter of the shaded shape is calculated as follows;

A square has equal sides, that is all the sides of a square are equal.

A rhombus is also a type of parallelogram with equal sides.

If the length of the square joined with rhombus = 5 cm, then length of the rhombus is also equal to 5 cm.

The perimeter of the shaded shape is calculated as follows;

P = 4L + 2L

P = 6L

P = 6 x 5 cm

P = 30 cm

The area of the shaded shape is calculated as follows;

A = (L + L) x L

A = 2L x L

A = 2L²

A = 2 x ( 5 cm )²

A = 50 cm²

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The set of inequalities that expresses the given relationships are -6 < -2 and -2 > -4. The correction is second option -6 < -2 and -2 > -4

From the question, we are to determine the set of inequalities that expresses the relationships

From the given information,

The given relationships are:

A score of -6 is lower than a score of -2. A score of -2 is higher than a score of -4.

First, we will write the first relationship as an inequality

A score of -6 is lower than a score of -2

This means that -6 is less than -2.

Using inequalities symbols, we can write that

-6 < -2

Now,

For the second relationship :

A score of -2 is higher than a score of -4

This means, -2 is greater than -4

Using inequalities symbols, we can write that

-2 > -4

Hence,

The inequalities that express the relationships are -6 < -2 and -2 > -4

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Answer:

#1

Use Pythagorean:

Apply to given and find c:

#2

#3

We have:

We know that:

Find b:

So

#4

Given

We know that:

Find b:

So

#5

Given

We know:

From the cot we have:

Hypotenuse is:

So,

The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

It is a symbol standing in for an unknown numerical value in an equation.

The general form of a one variable linear equation is given by

ax+b = 0

where a and b are two integers, and x is the variable

The one-variable linear equation has only one solution.

Hence, the equation in the form ax+b = 0 is known as a one-variable linear equation.

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