I need help I need to show my work please help

The smallest positive integer n so that,

$$\renewcommand{\arraystretch}{1.5} \begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix}$$is a column matrix that contains integers,

we can write it as follows. $$\begin{pmatrix} -\frac{\sqrt{2}}{2} \frac{1}{n} \\ \frac{\sqrt{2}}{2} \frac{1}{n} \end{pmatrix} = \begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix} \frac{1}{n}.$$Since n has to be an integer, we have to find the smallest positive integer n for which the right-hand side is a column matrix containing integers. Since the left-hand side has a factor of 1/n, we can see that the smallest value of n must be a divisor of the denominator of the left-hand side. The denominator of the left-hand side is $\sqrt{2}/2$. If we multiply this by 100, we get 70.710678.

Therefore, the smallest positive integer n that satisfies the equation is the smallest divisor of 70.710678. This is 2, and it gives us the column matrix $$\begin{pmatrix} -\frac{1}{\sqrt{2}} \\ \frac{1}{\sqrt{2}} \end{pmatrix}.$$Therefore, the smallest positive integer n is 2.

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The area of the quadrilateral ABCD for this case is of 4 square units.

The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.

The lengths for each diagonal of the diamond are given as follows:

The product of the diagonal lengths is given as follows:

AC x BD = 2 x 4 = 8 square units.

Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:

0.5 x 8 square units = 4 square units.

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Answer:

-1/3

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

The 12 months of age) as percentiles of the CDC growth chart reference population.

The most likely description of Sarah's weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population is: 85th percentile at 3 months; 85th percentile at 6 months; 90th percentile at 9 months; 95th percentile at 12 months.What is percentile in statistics?In statistics, a percentile is a value below which a specific percentage of observations in a group falls. It is used to split up data into segments that represent an equal proportion of the entire group, resulting in a data set split into 100 equal portions, with each portion representing one percentage point. Sarah's weight is in the 85th percentile at 3 months, 85th percentile at 6 months, 90th percentile at 9 months, and 95th percentile at 12 months is a most likely description of her weights (at 3, 6, 9, and 12 months of age) as percentiles of the CDC growth chart reference population.

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The length of a side of the square is 8 cm.

What do you mean by perimeter of a rectangle and square?

When a wire is bent into the shape of a rectangle, its length becomes the perimeter of the rectangle. Similarly, when the wire is reshaped into a square, its length becomes the perimeter of the square.

The perimeter of a rectangle is given by the formula [tex]P=2(l+w)[/tex] , where [tex]l[/tex] is the length and [tex]w[/tex] is the width.

The perimeter of a square is given by the formula [tex]P=4s[/tex] , where [tex]s[/tex] is the length of a side.

Calculating the length of a side of the square:

The length of the rectangle is 11 cm and the width is 5 cm.

Therefore, the perimeter of the rectangle is [tex]P=2(11+5)=32[/tex] cm.

Since the wire is reshaped into a square, the perimeter of the square is also 32 cm.

Using the formula [tex]P=4s[/tex], we can solve for the length of a side of the square:

[tex]32 = 4s[/tex]

[tex]s = 32/4[/tex]

[tex]s = 8[/tex]

Therefore, the length of a side of the square is 8 cm.

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The probability of at least one of your 10 lottery tickets being a winner is approximately 0.638 or 63.8%.

The probability of winning on a single lottery ticket is 1/8, which means that the probability of not winning is 7/8. If you buy 10 of these lottery tickets, the probability of not winning on any of them is:

(7/8)^10 = 0.362

This means that there is a 36.2% chance that none of your tickets will be a winner. To find the probability that at least one of your tickets will be a winner, we can use the complementary probability:

P(at least one winner) = 1 - P(no winners)

P(at least one winner) = 1 - 0.362

P(at least one winner) = 0.638

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The types of inferences that will be made about population parameters are causation, estimation, and regression on the basis of relationship.

Causation is the process of showing the cause-and-effect relationship between two variables. In this case, one variable influences the other variable. This type of inference is significant when making decisions because it helps us understand how a change in one variable leads to a change in another variable.

Estimation: In statistical analysis, estimation refers to determining the possible value of an unknown population parameter. It is impossible to calculate the population parameters directly, and hence we use sample statistics to estimate them.

Regression analysis is the statistical technique used to identify the relationship between two variables. It involves estimating the coefficients of the model that best fit the data.

This type of inference helps us predict the value of a dependent variable based on an independent variable.

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Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same, he also know that he can earn 16 for each hour that he works at his aunt's store, therefore he needs to work 8 hours.

Mark needs a total amount of 215 to buy sneakers and we know that his aunt gave him 100 for the same,

therefore, we can say that 215 - 100 = 115

therefore, Mark now needs only 115 for him to buy sneakers and  now we need to find how many full hours do Mark need to work to buy sneakers:

therefore, we need to divide 115 by 16 to find out the hours he needs to work at his aunt's store:

115/16 = 7.2

we get 7.2 which also means 7 hours 20 mins but we need to find full hours Mark needs to work, that will be:

8 hours.

Therefore, we know that Mark needs to work 8 full hours for him to buy sneakers.

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Using central limit theorem, the probability that the class of 20 students will have a mean completion time greater than 60 minutes on the unit 5 test is 0.00017332

We can use the Central Limit Theorem (CLT) to approximate the distribution of the sample mean completion time for the class. According to CLT, the distribution of the sample mean is approximately normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

In this case, the population mean is given as 48 minutes, the population standard deviation is given as 15 minutes, and the sample size is 20. Therefore, the mean of the sample mean completion time is also 48 minutes, and the standard deviation of the sample mean completion time is 15/√20 ≈ 3.3541 minutes.

To find the probability that the class mean completion time is greater than 60 minutes, we can standardize the distribution of the sample mean completion time using the z-score formula:

z = (x - μ) / (σ / √n)

where x is the value we want to find the probability for (in this case, x = 60), μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values, we get:

z = (60 - 48) / (15 / √20) = 3.5777

Using a standard normal distribution table (or calculator), we can find the probability that a z-score is greater than 3.5777.

P = 0.00017332

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In Δ ABC and Δ PQR, if AB = PR, BC = RQ and AC = PQ, then Δ ABC is congruent to Δ PRQ, which means option D is the right answer.

The congruency theorem is used to determine the relation between two similar looking figures in two dimensional space. The word congruent itself means being in harmony. There are different rules which are used to determine the congruency between the triangles.

These rules are given as follows:

In the given question, it is given that sides AB = PR, BC = RQ and AC = PQ, this implies that the congruency can be setup using SSS rule, which if followed will suggest that Δ ABC will be congruent to Δ PRQ.

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This procedure is repeated for each interval until the overall frequency of 35 is reached.

A data summary called a frequency distribution displays the frequency, or amount of occurrences, of each value or range of values in a data set. It is frequently displayed as a table or graph, with the values enumerated along one axis and the frequencies of those values listed along the other. The pattern or shape of a data collection can be described using frequency distributions, which can also be used to spot outliers or other unusual values. They can also shed light on the data's central trend and variability.

given

To complete a cumulative frequency table:

Class interval Frequency Cumulative frequency

0-10               5                                   5

10-20       8                                  13

20-30       12                                 25

30-40        7                                 32

40-50         3                                35

Total        35                               35

The number of the first class interval is 5.

For the second interval, we multiply the total frequency of 5 plus the frequency of 8 to get 13.

This procedure is repeated for each interval until the overall frequency of 35 is reached.

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The missing value in the cumulative table is 36.

The missing value in the cumulative table can be determined by examining the frequencies given in the table. Let's analyze the frequencies step by step:

1. The frequency for scores less than 145 is given as 16.
2. The frequency for scores less than 150 is given as 26.
3. The frequency for scores less than 155 is given as 36.
4. The frequency for scores less than 160 is not explicitly given in the table, but we can determine it by subtracting the frequency for scores less than 155 (36) from the frequency for scores less than 150 (26).

This gives us a value of [tex]26 - 36 = -10.[/tex]

Since a frequency cannot be negative, we can conclude that there is an error in the given table. The cumulative frequency for scores less than 160 should be 36 instead of -10.

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Answer: 61 kg

Step-by-step explanation:

To find the average mass of the other 5 people, we need to subtract the mass of the lightest person from the total mass of all six people and then divide by 5 (since we're looking for the average of the other 5 people). Here are the steps:

   Find the total mass of all six people:

   To find the total mass of all six people, we can multiply the average mass by 6:

Total mass of all six people = 58 kg/person x 6 people = 348 kg

   Subtract the mass of the lightest person:

   We need to subtract the mass of the lightest person (43 kg) from the total mass of all six people:

Total mass of the other 5 people = Total mass of all six people - Mass of the lightest person

Total mass of the other 5 people = 348 kg - 43 kg = 305 kg

   Find the average mass of the other 5 people:

   Finally, we divide the total mass of the other 5 people by 5 to find the average mass:

Average mass of the other 5 people = Total mass of the other 5 people / 5

Average mass of the other 5 people = 305 kg / 5 = 61 kg

Therefore, the average mass of the other 5 people is 61 kg.

The solutions to the equation are x = -4 and x = 1.

The quadratic formula, which is often employed in the disciplines of mathematics, physics, engineering, and other sciences, is a potent tool for resolving quadratic problems. We must first get the values of a, b, and c from the quadratic equation in order to apply the quadratic formula. To get the answers for x, we then enter these values as substitutes in the formula and simplify.

The given equation is 4x² + 6x - 13 = 3x².

Rearranging the equation we have:

x² + 6x - 13 = 0

The quadratic formula is given as:

x = (-b ± √(b² - 4ac)) / 2a

Substituting the values of a = 1, b = 6, and c = -13.

x = (-6 ± √(6² - 4(1)(-13))) / 2(1)

x = (-6 ± √(100)) / 2

x = (-6 ± 10) / 2

x = -8/2 or x = 2/2

x = -4 or x = 1

Hence, the solutions to the equation are x = -4 and x = 1

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Answer:

I hope this helps please rate my answer

Step-by-step explanation:

2/5×60

2×12=24

A quadratic function in standard form that passes through the points (-8,0), (-5,-3), and (-2,0) is equals to the f(x) = (1/3)( x² + 10x + 16).

A quadratic function is a polynomial function with one or more variables, the highest degree of the variable is two. It is also called the polynomial of degree 2. The form of quadratic function is

f(x) = ax² + bx + c ----(1)

is determined by three points and must be a≠ 0. That is for determining the f(x) we have to determine value of three values a, b, and c. Now, we have three ordered pairs (-8,0), (-5,-3), and (-2,0) and we have to determine quadratic function passing through these points. So, firstly, plug the coordinates of point ( -8,0), x = -8, y = f(x) = 0 in equation (1),

=> 0 = a(-8)² + b(-8) + c

=> 64a - 8b + c = 0 --(2)

Similarly, for second point ( -5,-3) , f(x) = -3, x = -5

=> - 3 = a(-5)² + (-5)b + c

=> 25a - 5b + c = -3 --(3)

Continue for third point (-2,0)

=> 0 = a(-2)² + b(-2) + c

=> 4a -2b + c = 0 --(4)

So, we have three equations and three values to determine.

Subtract equation (4) from (2)

=> 64 a - 8b + c - 4a + 2b -c = 0

=> 60a - 6b = 0

=> 10a - b = 0 --(5)

subtract equation (4) from (3)

=> 21a - 3b = -3 --(6)

from equation (4) and (5),

=> 3( 10a - b) - 21a + 3b = -(- 3)

=> 30a - 3b - 21a + 3b = 3

=> 9a = 3

=> a = 1/3

from (5) , b = 10a = 10/3

from (4), c = 2b - 4a = 20/3 - 4/3 = 16/3

So, f(x)= (1/3)( x² + 10x + 16)

Hence, required values are 1/3, 10/3, and 16/3.

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Answer:

5/37

Step-by-step explanation:

There are 37 possible outcomes when rolling a 37-sided die, so the probability of rolling any one specific number is 1/37.

To find the probability of rolling any of the given numbers (35, 25, 33, 9, or 19), we need to add the probabilities of rolling each individual number.

Probability of rolling 35: 1/37

Probability of rolling 25: 1/37

Probability of rolling 33: 1/37

Probability of rolling 9: 1/37

Probability of rolling 19: 1/37

The probability of rolling any one of these numbers is the sum of these probabilities:

1/37 + 1/37 + 1/37 + 1/37 + 1/37 = 5/37

So the probability of rolling any of the given numbers is 5/37, which is approximately 0.1351 when rounded to four decimal places.

Answer:

1

Step-by-step explanation:

Given values are:

x1 y1=(2,4)

x2 y2=( 4,6)

slop=(6-4)divide (4-2)=1

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thanks

Step-by-step explanation:

a) Area=144m²

side²= 144

side=12m

b) perimeter=32m

4×side=32

side=32/4

side=8m

Answer:

A random sample of size 64 is used to test the null hypothesis that for certain age group the mean score on an achievement test is less than or equal to 40 against the alternative that it is greater than 40. The scores are assumed to be normally distributed with variance 0? 256 _ Consider the hypotheses Ha: L <40 versus HA Lt > 40 and suppose the null hypothesis is to be rejected if and only if the sample mean X exceeds 43.5. What is the size of this test? Compute the probability of type Il error at L = 42

Step-by-step explanation:

With respect to the average cost curves, the marginal cost curve: intersects both average total cost and average variable cost at their minimum points that is option B.

The fixed cost per unit of production is the average fixed cost (AFC). AFC will reduce consistently as output grows since total fixed costs stay constant. The variable cost per unit of production is known as the average variable cost (AVC). AVC generally declines until it reaches a minimum and then increases due to the growing and then lowering marginal returns to the variable input. The average total cost curve's (ATC) behaviour is determined by the behaviour of the AFC and AVC.

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Complete question:

With respect to the average cost curves, the marginal cost curve:

A) Intersects average total cost, average fixed cost, and average variable cost at their minimum point

B) Intersects both average total cost and average variable cost at their minimum points

C) Intersects average total cost where it is increasing and average variable cost where it is decreasing

D) Intersects only average total cost at its minimum point

Answer:

To indicate that we want both the positive and the negative square root of a radicand

Answer:

Because a negative number times a negative number has a positive answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

This can be solved by taking X as the magnification

8*x = 12cm *10

x= 120/8

x= 30/2= 15

the magnification = 15 times

If a customer purchases 3 of the products, the probability of getting at least one that is defective is 38.59%.

In order to determine the probability of getting at least one defective product if a customer purchases three products with a defective rate of 7.5%, we can use the concept of complementary probability.

The probability of getting at least one defective product can be calculated as the complement of the probability of getting none defective products.

So, the probability of getting no defective products is:

P(none defective) = (1 - 0.075)³ = 0.6141

Therefore, the probability of getting at least one defective product is:

P(at least one defective) = 1 - P(none defective) = 1 - 0.6141 = 0.3859 or 38.59%

.So, the probability of getting at least one that is defective is 38.59%.

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Answer:

yes it is right now you can write it

The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

An equation is a statement that shows the equality between two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, division, exponentiation, or roots. An equation can be solved by finding the value(s) of the variable(s) that make the equation true. Equations are used extensively in mathematics, science, engineering, and other fields to describe relationships between different quantities and to make predictions or solve problems.

Here,

Since line B is perpendicular to line A, the product of their gradients is -1. Therefore, the gradient of line B is 1/5.

a) To find the y-intercept of line B, we need to know a point on the line. Since we don't have one, we can use the fact that the y-intercept is the point where the line intersects the y-axis. To find this point, we can set x = 0 in the equation of line B:

y = (1/5)x + c

0 = (1/5)(0) + c

c = 0

Therefore, the y-intercept of line B is (0,0).

b) The equation of line B is y = (1/5)x + 0, which can be simplified to y = (1/5)x.

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Therefore, 15% of the beads on Tiana's necklace are blue.

Percentage is a way of expressing a fraction or a proportion out of 100. It is denoted by the symbol "%". For example, if we say that 50% of the students in a class are girls, it means that 50 out of every 100 students are girls.

Percentage can be calculated by dividing the given quantity by the total and multiplying by 100. For example, if there are 20 girls out of a total of 40 students in a class, the percentage of girls in the class can be calculated as follows:

Percentage of girls = (number of girls / total number of students) x 100%

= (20 / 40) x 100%

= 50%

by the question.

Tiana's necklace has a total of 3 + 17 = 20 beads.

To find the percentage of blue beads, we need to divide the number of blue beads by the total number of beads and then multiply by 100 to get the percentage:

percentage of blue beads = (number of blue beads / total number of beads) x 100

percentage of blue beads = (3 / 20) x 100

percentage of blue beads = 15

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Given: ,8^2x= 32^x+3

a: (2³)^2x = (2⁵)^x+3

b: Solving, we get

2^6x = 2^5x+15

Since bases are same, we have

=>6x=5x+15

=> x = 15

Answer:

Show that, the sum of an infinite arithmetic progressive sequence with a positive common difference

is +∞

Step-by-step explanation:

To show that the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞, we can use the formula for the sum of the first n terms of an arithmetic sequence:

Sn = n/2 [2a + (n-1)d]

where a is the first term, d is the common difference, and n is the number of terms in the sequence.

Now, if we let n approach infinity, the sum of the first n terms of the sequence will also approach infinity. This can be seen by looking at the term (n-1)d in the formula, which grows without bound as n becomes larger and larger.

In other words, as we add more and more terms to the sequence, each term gets larger by a fixed amount (the common difference d), and so the sum of the sequence increases without bound. Therefore, the sum of an infinite arithmetic progressive sequence with a positive common difference is +∞.

Answer:

Step-by-step explanation:

71/8*9 which it 639/8 feet long

To prepare a buffer solution with a given pH, we need to choose a weak acid and its conjugate base, such that the pKa of the weak acid is close to the desired pH.

The pKa is related to the Ka value as follows:

pKa = -log(Ka)

So, for each of the weak acids given, we can calculate the pKa:

Phosphoric acid (H3PO4): Ka = 7.5 x 10^-3, so pKa = -log(7.5 x 10^-3) = 2.12

Acetic acid (CH3COOH): Ka = 1.8 x 10^-5, so pKa = -log(1.8 x 10^-5) = 4.74

Formic acid (HCOOH): Ka = 1.8 x 10^-4, so pKa = -log(1.8 x 10^-4) = 3.74

Now, let's consider the desired pH values and choose the best components for buffer solutions:

For a pH of 2.5, the best choice would be phosphoric acid (pKa = 2.12).

For a pH of 4.5, the best choice would be formic acid (pKa = 3.74) or a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

For a pH of 6.5, the best choice would be a mixture of acetic acid and acetate ion (CH3COOH/CH3COO-, pKa = 4.76).

Note that a buffer solution can be prepared by mixing a weak acid and its conjugate base in roughly equal amounts, so the appropriate salt can be added to the acid to form the buffer solution. For example, to prepare an acetate buffer, one could mix acetic acid with sodium acetate.

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