Given vectors: p=2i-j, q=-i+j
find: 1. p+q
2.p-q
3. 2p-3q

To count the number of different 6-letter strings that can be formed using the letters c, i, r, c, l, and e, we can use the permutation formula. There are 6 choices for the first letter, 5 choices for the second letter (since we can't use the same letter twice), and so on, giving us:

6 x 5 x 4 x 3 x 2 x 1 = 720

However, not all of these strings meet the condition that the two occurrences of the letter c are separated by at least one other letter. To count the number of strings that do meet this condition, we can use the complementary counting method.

First, let's count the number of strings in which the two c's are adjacent. There are 5 positions where the two c's could be (the first two, second and third, third and fourth, fourth and fifth, or last two positions), and once we place the c's, we have 4 letters left to fill in the remaining 4 positions. This gives us:

5 x 4 x 3 x 2 x 1 = 120

Now, let's count the total number of 6-letter strings that have at least one pair of adjacents c's. We can use the same method as above, but this time we can place the two c's anywhere in the string, giving us:

6 x 5 x 4 x 3 x 2 x 1 - 5 x 4 x 3 x 2 x 1 = 720 - 120 = 600

Finally, we can subtract this from the total number of 6-letter strings to get the number of strings in which the two c's are separated by at least one other letter:

720 - 600 = 120

Therefore, there are 120 different 6-letter strings that can be formed using the letters c, i, r, c, l, and e in which the two occurrences of the letter c are separated by at least one other letter.

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Answer: 82x^2-196x+136

hope it helps

Answer: 40%

Step-by-step explanation: To find what percentage of members voted for Hans simply multiply 32 by 100.

32 x 100 = 3200.

Then, divide that number, or 3200 by 80.

3200/80 = 40.

So, 40, or 40% of members voted for Hans.:)

Answer:  Theorem 4 says that the columns of B do NOT span R4. Further, using Theorem 4, since 4(c) is false, 4(a) is false as well, so Bx = y does not have a solution for each y in R4.

Step-by-step explanation:

Yes, the column b span r4. Yes, the equation has a solution for each y in r4.

Matrix is defined as a set of numbers consisting of rows and columns elements.

It consists of rows and columns.

The dimensions of the matrix are determined by m×n.

Given matrix,

\(\begin{bmatrix} &1 &3 &-2 &2\\ &0 &1 &1 &-5\\ &1 &2 &-3 &7\\ &-2 &-8 &2 &-1\\\end{bmatrix}\)

R3  → R1

R3→R4+2R1

\(\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-1 &1 &5 \\ &0 &-2 &-2 &3\\\end{bmatrix}\)

R3→R3+R2

R4→R4+2R2

\(\begin{bmatrix} &1 &3 &-2 &2 \\ &0 &1 &1 &-5 \\ &0 &-0 &2 &0 \\ &0 &-0 &0 &7\\\end{bmatrix}\)

This is the row echelon form of B. It has four independent columns and the dimension of r4 is 4.

column of B spans r4.

Row of matrix = 4

No of columns of matrix = No of rows of the matrix.

and the columns of B span r4.

thus we can conclude that the columns of b span r4 and the equation

bx =d y have a solution for each y in r4.

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Can you please show the triangle?

Answer:

Step-by-step explanation:

To find the standard form equation for a hyperbola, we can start by determining the center of the hyperbola. The center is the midpoint between the vertices, which in this case is at (0, 0).

The given asymptote equation is y = 2/3. Since the asymptotes of a hyperbola pass through the center, we can write the equation of the asymptotes in the general form as (y - k) = ±(a/b)(x - h), where (h, k) represents the center and a/b represents the ratio of the distance from the center to a vertex to the distance from the center to a co-vertex.

Using the given asymptote equation y = 2/3, we can substitute the values of the center (h, k) = (0, 0) and the ratio a/b = 8/2 = 4 into the equation:

(y - 0) = ±(4/2)(x - 0)

y = ±2x

Now, we can write the standard form equation for the hyperbola using the center (h, k) = (0, 0) and the values of a and b (which are equal since the hyperbola is symmetric):

(x - h)^2/a^2 - (y - k)^2/b^2 = 1

(x - 0)^2/4^2 - (y - 0)^2/4^2 = 1

x^2/16 - y^2/16 = 1

Therefore, the standard form equation for the hyperbola is x^2/16 - y^2/16 = 1.

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A standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

The probability is calculated by dividing the total number of outcomes by the total number of events.

Odds and probability are two different concepts.

Divide the probability of an event occurring by the probability that it won't happen to calculate chances.

The four main types of probability that mathematicians study are axiomatic, classical, empirical, and subjective.

So, the probability that a standard normal random variable will occur with a probability ranging from 0.3 to 3.2 must therefore be calculated.

First, a mean and standard deviation are introduced for a standard normal random variable.

The probability that a standard normal random variable will fall between 0.3 and 3.2 needs to be calculated.

Therefore, it should be more likely that:

P(0.3<z<3.2)=P(z<3.2)−P(z<0.3)

Using the usual value of z:

P(0.3<z<3.2)=0.9993−0.6179

Justify by saying:

P(0.3<z<3.2)=0.3814

Therefore, a standard normal random variable has a 0.3814 percent chance of falling between 0.3 and 3.2, according to the z table.

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6. Ashley

7. Points are represented by (x, y). Therefore, when proving that your answer is correct, you are to plug in the points into the corresponding values. With this problem, the original function was f(x) = -16x^2 + 96x

f(x) always means y, which means that whenever you plug in x into the other side of the function, you should get -112 because that is the y value in your given point. Ashley is correct because she plugged in -1 wherever x was in the function. In equations, solving the exponent comes before multiplying any numbers together, which is what she did: she squared the -1 and got 1. Now the equation reads to be -16(1)+96(-1)

-16 times 1 is just -16, and 96 times -1 is just -96, therefore when she added -16 and -96 together, she got -112, which is what she should’ve gotten since we were looking for the y value. That is why Ashley is correct.

According to property the diagonals are equal in rectangle

6x+19=9x-5

9x-6x=19+5

3x=24

x=24/3

x=8

Answer:

100n² - 1

Simplifying we get

(10n)² - 1

Hope this helps.

Answer:

(10n)² - 1²

Step-by-step explanation:

100 n² − 1= (10n)² - 1²

Answer:

i keep getting different stuff

Step-by-step explanation:

4 x − 5 + y = 0

x + 6 y = 5

6 x − 3 y =12

3 x + y = 16

6 x − 3 y = 12

3 x + 4 y = − 5

Answer:

y = -8/3x + 33

Step-by-step explanation:

y2 - y1 / x2 - x1

9 - 1 / 9 -12

8 / -3

= -8/3

y = -8/3x + b

1 = -8/3(12) + b

1 = -32 + b

33 = b

Answer:

This is an even function because u can see that the function graph has Oy as the symmetry axis

Step-by-step explanation:

Answer:

\(m\angle FGC =101\degree \)

Step-by-step explanation:

\(m\angle CBF = 46\degree\) (Given)

\(m\angle FIG = 55\degree\) (Given)

\(m\angle IFG = m\angle CBF\) (Corresponding angles)

\(\implies m\angle IFG = 46\degree\)

\(m\angle FGC =m\angle IFG+ m\angle FIG\)

(By exterior angle theorem)

\(m\angle FGC =46\degree+ 55\degree \)

\(m\angle FGC =101\degree\)

Here

Using the formula

sum of interiors=external

The probability that fewer than 4 are independent = 0.971

Let X be a random variable representing the number of independent people out of 12 people.

Then X follows binomial distribution.

A binomial distribution considers two possibilities in 'n' trials -  success or  failure. Here the case of success is being independent and the case of failure is being either republican or democrat.

The probability distribution function of a binomial distribution is,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ

Where n is the number of trials, p - the probability of success

Here, n = 12

Since 6% of voters are independent, probability of being an independent = 6/100 = 0.06

Probability that fewer than 4 are independent = P( X = 0 or 1 or 2 or 3)

                                                                             = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Now, P(X=0) = ¹²C₀ (0.06)⁰ (1-0.06)¹²⁻⁰

                      = 1 x 1 x 0.4759

                      = 0.4759

P(X = 1) = ¹²C₁ (0.06)¹ (1-0.06)¹²⁻¹

           = 12 x 0.06 x 0.94¹¹

           = 0.3645

P(X = 2) = ¹²C₂ (0.06)² (1-0.06)¹²⁻²

             = 66 x (0. 06)² x 0.94¹⁰

            = 0.128

P(X = 3) =  ¹²C₃ (0.06)³ (1-0.06)¹²⁻³

             = 22 x 0.000216 x 0.94⁹

             = 0.00272

Therefore, Probability that fewer than 4 are independent = P( X = 0) + P(X = 1) + P(X = 2) + P(X = 3) =  0.4759 + 0.3645 +  0.128 + 0.00272 = 0.971

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P-value =0.0108 , The true mean stay is longer than 4 days.

AS per the details given in the above question are as follow,

The details are,

The random sample size  of patient n=28

The sample sample mean time \($=\bar{x}=4.6$\)

The sample standard deviation is S.D. \($=S=1.3$\)

Where \($\alpha=0.05$\)

Degree of freedom =n-1

Substitute the value in above equation we get,

Degree of freedom =28-1=27.

Point estimate = n - α

substitute the value in above question we get,

Point estimate=1.3- 0.5 = 0.6

Standard error= sample standard deviation/ sample mean^α

Standard error=0.246

Test statistic = Point estimation / Standard error

Test statistic = 2.442

Critical value for right trailed = T. Inv(Level of significance X Point estimation)

Critical value for right trailed = 1.703

P value for right trailed = T. Div (Level of significance  X Degree of freedom)

p-value \($=0.0108$\)

p-value \($ < \alpha$\)

There is sufficient evidence to conclave that the true mean stay longer than 4 days.

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Note:- The correct question is ,

The president is concerned about the escalating costs of providing health care in the United States. One of the components contributing to the increasing cost is the length of the hospital stay of a patient. In a random sample involving 28 patients, the sample mean time was 4.6 days with sample standard deviation s=1.3 days. We would like to know if these results demonstrate that the true mean stay of a patient is significantly longer than 4 days, by carrying out a test using a significance level of \($\alpha=0.05$\) significance. Determine the P-value of the test, and what decision should be made?

a)P-value =0.0108, The true mean stay is longer than 4 days.

b)P-value =0.0073, The true mean stay is longer than 4 days.

c)P-value =0.9892, The true mean stay is not longer than 4 days.

d)P-value =0.0108, The true mean stay is not longer than 4 days.

Answer:

bellow the graph

Step-by-step explanation:

Answer:

Answer included in picture attachment

By calculating the volume of the pool and considering the cost per 1000 gallons of water, we determined that it would cost $286.70 to fill the pool.

Dimensions of rectangular pool: 25 yd by 25 yd

Depth of pool: 5.7 feet

Cost per 1000 gallons of water: $1.50

To find:

The cost of filling the pool

First, we need to find the volume of the pool. The volume of a rectangular pool is calculated by multiplying its length, breadth, and depth.

Volume of rectangular pool = length * breadth * depth = 25 yd * 25 yd * 5.7 feet

Since 1 yard is equal to 3 feet, we convert the dimensions from yards to feet:

25 yd = 25 * 3 = 75 feet

Now we can calculate the volume:

Volume of rectangular pool = 75 ft * 75 ft * 5.7 ft = 25537.5 cubic feet

Since 1 cubic foot is equal to 7.48052 gallons, we can convert the volume to gallons:

Volume of rectangular pool = 25537.5 * 7.48052 gallons = 191136.36 gallons

Next, we need to calculate the cost of filling the pool. Given that the cost per 1000 gallons of water is $1.50, we can determine the total cost.

Cost of filling 191136.36 gallons of water = (191136.36/1000) * $1.50 = $286.70

Therefore, the cost of filling the pool is $286.70.

In summary, by calculating the volume of the pool and considering the cost per 1000 gallons of water, we determined that it would cost $286.70 to fill the pool.

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Statistics are used to make estimates of population parameters. Therefore, the correct option is B.

Statistics are used for various purposes in data analysis. One important application of statistics is to make estimates of population parameters. Population parameters are characteristics or measures that describe an entire population. However, it is often impractical or impossible to collect data from the entire population, so statistics provide methods for estimating these parameters based on a sample of the population.

By collecting and analyzing data from a sample, statisticians can make inferences and draw conclusions about the larger population. These estimates help researchers understand the characteristics, patterns, and relationships within the population.

Additionally, statistics form the basis for analysis in many fields, including scientific research, business, social sciences, and more. They provide tools and techniques to summarize, interpret, and draw meaningful insights from data, enabling researchers and decision-makers to make informed choices and draw valid conclusions from their observations and experiments.

Therefore, the correct choice is option b. Statistics play a crucial role in estimating population parameters and providing insights for analysis and decision-making.

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The probability of a randomly selected person from this group visiting a physical therapist is 0.68.

The probability is the extent to which an event is likely to occur, measured by the ratio of the favourable cases to the whole number of cases possible. Let A denote the event that the person visits a physical therapist, and let B denote the event that the person visits a chiropractor. Now, we need to use the laws of probability to arrive at each individual probability i.e. P(A) and P(B).

Given: P(A∩B)=0.28

(ii) P(AC∩BC)=0.08

(iii) P(A)−P(B)=0.16

Required: P(A)

By the laws of inclusion/exclusion,

P(A∪B)=P(A)+P(B)−P(A∩B)

Therefore,

P(A)+P(B)=P(A∩B)+P(A∪B)

By DeMorgan's Law,

P(AC∩BC)=1−P(A∪B)

Therefore,

P(A)+P(B)=0.28+1−0.08=1.2

By adding the equation,

P(A)−P(B)=0.16

we get

2P(A)=1.36

Therefore, P(A)=0.68

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Answer:

the shape could be congruent or similar to its preimage. There are basically four types of transformations: Rotation; Translation; Dilation; Reflection; Definition of Transformations. Transformations could be rigid (where the shape or size of preimage is not changed) and non-rigid (where the size is changed but the shape remains the same).

Step-by-step explanation:

Answer:

I believe the graph would look like this.

The domain would be 2<x>8 and the range would be 1<y>3.5

The equations of the line parallel to the z-axis and passing through the midpoint (-3, 0.5, 4) are: x = -3;y = 0.5; z = t, where t is a parameter.

To find the equation of a line parallel to the z-axis, we know that the x and y coordinates will remain constant, while the z coordinate can vary. Given two points (0, -4, 3) and (-6, 5, 5), we can find the midpoint by averaging the corresponding coordinates: Midpoint = ((0 + (-6))/2, (-4 + 5)/2, (3 + 5)/2) = (-3, 0.5, 4). Since the line is parallel to the z-axis, the x and y coordinates will remain constant.

Therefore, the equation of the line passing through the midpoint is: x = -3; y = 0.5;  z = t (where t is a parameter). So, the equations of the line parallel to the z-axis and passing through the midpoint (-3, 0.5, 4) are: x = -3;y = 0.5; z = t, where t is a parameter.

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mark me brainlist pls im first

The numbers for which the graph of y = tan(x) has vertical asymptotes in the range -2π ≤ x ≤ 2π are -3π/2, -π/2, π/2, and 3π/2. The correct option is B: -3π/2, -π/2, π/2, 3π/2.

The tangent function, denoted as tan(x), has vertical asymptotes where the function approaches infinity or negative infinity. In other words, vertical asymptotes occur where the tangent function is undefined.

The tangent function is undefined at odd multiples of π/2. Therefore, the vertical asymptotes for the function y = tan(x) occur at x = -3π/2, -π/2, π/2, and 3π/2.

Considering the options:

A. -2, -1, 0, 1, 2: This set of numbers does not include the values -3π/2, -π/2, π/2, or 3π/2. Therefore, it does not represent the numbers for which the graph of y = tan(x) has vertical asymptotes.

B. -3π/2, -π/2, π/2, 3π/2: This set correctly includes the values where the graph of y = tan(x) has vertical asymptotes.

C. -2π, -π, 0, π, 2π: This set does not include -3π/2 or 3π/2, which are vertical asymptotes for y = tan(x).

D. None: This option is incorrect since we have already identified the vertical asymptotes in option B.

Therefore, the correct answer is option B: -3π/2, -π/2, π/2, 3π/2.

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Answer:

5x+2y<=30

Step-by-step explanation:

Inequalities help us to compare two unequal expressions. The graph for the inequality can be made as shown below.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.

As per the graph let the number of pounds of quinoa be represented by x and the number of pounds of rice Celeste can buy be represented by y.

Therefore, the expression that can represent the number of pounds that Celeste can buy is,

5x + 2y

Also, it is given that Celeste can spend no more than $30. Therefore, the inequality can be written as,

5x + 2y ≤ 30

Now the graph for the inequality can be made as shown below.

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Answer:

Step-by-step explanation:

Total no. of children = 366

let the number of boys be x

and the no. of girls be x + 28

According to the question,

x + x + 28 = 366

2x + 28 = 366

2x = 366 - 28

2x = 338

x = 338 / 2

x = 169

So the no. of boys = x = 169

and the no. of girls = x + 28 = 169 + 28 = 197

( you can also recheck it by adding the no. of boys and the no. of girls

that is, 169 + 197 = 366 which equal to the total no. of children )

Hope this helps

plz mark as brainliest!!!!!!

Let's calculate the products and check if they indeed have the same value:

Product of 32 and 46:

32 * 46 = 1,472

Reverse the digits of 23 and 64:

23 * 64 = 1,472

As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.

To find two other pairs of two-digit numbers that have this property, we can explore a few examples:

Product of 13 and 62:

13 * 62 = 806

Reversed digits: 31 * 26 = 806

Product of 17 and 83:

17 * 83 = 1,411

Reversed digits: 71 * 38 = 1,411

As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.

For example, let's consider the pair 25 and 79:

A = 2, B = 5, C = 7, D = 9

The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.

Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.