A square sheet of paper has area $15. The front side is white and the back side is black. A corner of the sheet is lifted and placed so that the crease is at a $45 angle. If the fold is such that the visible black area is equal to the visible white area, how many centimeters long is the crease?

The vector with norm 2 and the direction opposite to vector a is option (a) -2/√26 (i + 3j - 4k).

To find the vector with norm 2 and with a direction opposite to the direction of a= i+3j-4k, we need to normalize the given vector a, as the direction of vector a is known. The formula for normalizing the vector a is as follows;

Normalization of vector a =  a / ||a||

where ||a|| is the norm of vector a.

Now, ||a|| = √(1^2 + 3^2 + (-4)^2)

               =√(1 + 9 + 16)

               = √(26)

Normalization of vector a = a / √(26)

Normalized vector of a = a / ||a||= (i + 3j - 4k) / √(26)

As the required vector is opposite to the direction of a, multiply the normalized vector with -2, so the vector will point in the opposite direction.

Now, Required vector = -2 * Normalized vector of a

                                     = -2/√(26) (i + 3j - 4k)

Hence, option (a) is the correct answer: -2/√26 (i +3j − 4k)

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Answer:

The bench mark values might be 10/120 - 30/80

Step-by-step explanation

Using the law of cosines, it is found that the measure of angle Y is of 64º.

The problem is incomplete, hence we research it on a search engine, and we have that we have a triangle in which:

The law of cosines states that we can find the side c of a triangle as follows:

c² = a² + b² - 2abcos(C)

In which:

For this problem, the parameters are given as follows:

a = 12, b = 17, c = 16, C = Y.

Hence:

c² = a² + b² - 2abcos(Y)

16² = 12² + 17² - 2(12)(17)cos(Y)

408cos(Y) = 177

cos(Y) = 177/408

Y = arccos(177/408)

Y = 64º.

The measure of angle Y is of 64º.

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Answer:

2.15

Step-by-step explanation:

I will assume that "−1/4(−8.6)" is telling us to multiply (-8.6) times -(1/4):

(-1/4)*(-8.6)

= (8.6/4)

= 2.15

The exact values of all angles in the interval [0, 360°) that satisfy the given equations are:

data = 45°, 135°, 315°.

To solve the given trigonometric equations, we will consider each equation separately.

tan²(data) - 1 = 0:

First, let's rewrite tan²(data) as (sin(data)/cos(data))²:

(sin(data)/cos(data))² - 1 = 0

Now, we can factor the equation:

(sin²(data) - cos²(data)) / cos²(data) = 0

Using the Pythagorean identity sin²(data) + cos²(data) = 1, we can substitute sin²(data) with 1 - cos²(data):

((1 - cos²(data)) - cos²(data)) / cos²(data) = 0

Simplifying further:

1 - 2cos²(data) = 0

Rearranging the equation:

2cos²(data) - 1 = 0

Now, we solve for cos(data):

cos²(data) = 1/2

cos(data) = ± √(1/2)

cos(data) = ± 1/√2

cos(data) = ± 1/√2 * √2/√2

cos(data) = ± √2/2

From the unit circle, we know that cos(data) = √2/2 corresponds to angles 45° and 315° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 315°.

cos(data)sin(data) = 1:

Since cos(data) ≠ 0 (otherwise the equation wouldn't hold), we can divide both sides by cos(data):

sin(data) = 1/cos(data)

sin(data) = 1/√2

From the unit circle, we know that sin(data) = 1/√2 corresponds to angles 45° and 135° in the interval [0, 360°). Therefore, the solutions for data are:

data = 45° and data = 135°.

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The sampling probability refers to the property of an element of a given population in its given probability to become a part of a sample during the drawing of a single sample.

It is a defined and distinguished technique that is based on the principle of random selection to study a certain part of a concerning population. Furthermore, in this specific method, every member of the population has the possibility of having an equal chance of being chosen for the sample.

One backlash in the field of using sampling probability is it's very time-consuming and has a higher expenditure in comparison to other methods.

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If a smaller square of side length 17 feet is cut out of a square board , then the approximate area of remaining board in square feet is x² - 289 square feet  .

le the side length of the big square board be = "x" ft ;

the side length of smaller square is = 17 ft ;

So , the area of the smaller square is = (side length) × (side length)

= 17 × 17

= 289 ft² .

and , the area of the larger square is = (x) × (x) ;

= x²  .

So , the approximate area of the remaining board is calculated as :

= x² - 289  ;

Therefore , area of remaining board is "x² - 289" .

The given question is incomplete , the complete question is

A smaller square of side length 17 feet is cut out of a square board. What is the approximate area of the remaining board in square feet ?

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In interpreting effect size, the meaning of effect size at 0.3 is small effect size. So, the correct answer is A).

In interpreting effect size, an effect size of 0.3 is typically considered to be a small effect size. This means that there is a small but still measurable difference or relationship between two variables.

The interpretation of effect size can vary depending on the context and the discipline in which it is being used, but as a general rule, effect sizes of 0.2 or smaller are considered small, effect sizes of 0.5 are considered medium, and effect sizes of 0.8 or larger are considered large. Therefore, an effect size of 0.3 falls in the small effect size range. So, the correct option is A).

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The arrangement  from least to greatest)= is: -20, -9, -5, -2, 2.2, 2.5, 2.7

The absolute value of  the term 34 = 34.

Since Tyrese has scored +6,  that is greater than -4 and Whitney have scored -16 that is the lowest score hence, Whitney  has won the tournament.

January 25th was known to be warmer due to the fact that the high temperature was 48 °F, but on February 2nd, the high temperature was known to be 24 °F.

Lastly, Chicken Salad is said to costs more than the price of Hamburger. Hence, the inequality that tells more this is:

=  Chicken Salad > Hamburger

= $4.49 > $4.30.

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See text below

THE NUMBER SYSTEM (6.NS.7)

Class

Score

Understand ordering and absolute value of rational numbers.

1.

Write the numbers in order from least to greatest.

-2,-5,-9, 2.2, 2.7,-20, 2.5

2. What is the absolute value of 34?

3. At a golf tournament, Tyrese scored +6, Whitney scored -16, and Maxwell scored -4. One of these three players was the winner of the tournament. Who won the tournament? The winner will be the player with the lowest score.

4. On January 25th, the high temperature in Portland, Oregon, was 48 °F. On February 2nd, the high temperature was 24 °F. Which day was warmer?

5. Which costs more, a hamburger or chicken salad? Use the given prices to write an inequality that shows your answer.

Hamburger   $4.30

Hot Dog    $2.35

Chicken Salad $4.49

Pizza    $2.49

Answer:

Not totally sure if this will help,

The answer is a: "The population of this town is approximately 46,609"

I just took the test and This was the correct answer. Hope this helps!

Answer:.

The population of this town is approximately 46,609

Step-by-step explanation:

a

Creating a discussion question, evaluating prospective solutions, and brainstorming and evaluating possible solutions are steps in problem-solving.

What is problem-solving?

Problem-solving is the method of examining, analyzing, and then resolving a difficult issue or situation to reach an effective solution.

Problem-solving usually requires identifying and defining a problem, considering alternative solutions, and picking the best option based on certain criteria.

Below are the steps in problem-solving:

Step 1: Define the Problem

Step 2: Identify the Root Cause of the Problem

Step 3: Develop Alternative Solutions

Step 4: Evaluate and Choose Solutions

Step 5: Implement the Chosen Solution

Step 6: Monitor Progress and Follow-up on the Solution.

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Answer:

45 percent were brownies :)

0.375 cups lemon juice, 0.75 cups sugar, 3 cups water. Instructions Malanie makes lemonade using 1:2:8 lemon juice, sugar, and water.

This is further explained below.

Generally, The act of quantifying the characteristics of an item or event so that they may be compared to those of other things or occurrences is what we mean when we talk about measurement.

To put it another way, measuring is the act of estimating the size of a physical amount in relation to a fundamental reference quantity of the same sort in order to get an accurate reading.

In conclusion, The needed quantities of lemon juice, sugar, and water are equal to 0.375 cups, 0.75 cups, and 3 cups, respectively. Explanation in detail step by step: Malanie is preparing lemonade, and she discovers a recipe that calls for the juice of one lemon, two tablespoons of sugar, and eight ounces of water.

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The given integral expression is \(3(x - 4)\sqrt{x}\). We are required to integrate it using the substitution u = √x. Let's begin by using the chain rule of differentiation to find dx in terms of du.\(dx/dx = 1 => dx = du / (2\sqrt{x} )\)Substituting the value of dx in the integral expression,

we get:\(3(x - 4)\sqrt{x} dx = 3(x - 4)\sqrt{x}  (du / 2\sqrt{x} ) = 3/2 (x - 4)\)duUsing the substitution u = √x, we can write x in terms of u: \(u = \sqrt{x}  \\=> x = u^2\)Substituting the value of x in terms of u in the integral expression, we get:3/2 (x - 4) du = 3/2 (u^2 - 4) duNow we can integrate this expression with respect to u:\(\int3/2 (u^2 - 4) du = (3/2) * \int(u^2 - 4) du= (3/2) * ((u^3/3) - 4u) + C= (u^3/2) - 6u + C,\) where C is the constant of integration.

Substituting the value of u = √x, we get:\(\int3(x - 4)\sqrt{x}  dx = (u^3/2) - 6u + C= (\sqrt{x} ^3/2) - 6\sqrt{x}  + C\)This is the final answer in terms of x, obtained by substituting the value of u back in the integral.

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Answer:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

The given trianagle FAN is an acute triangle.

Step-by-step explanation:

There are three types of triangles on the basis of angle:

(As shown in image attached)

Given:

A triangle FAN with an angle measurement of each angke.

To find:

The name adjoining triangle FAN on the  basis of angle.

Solution:

In ΔFAN

∠A=55°, ∠F=85° ,and ∠C=45​°

∠A<90°, ∠F<90° ,and ∠C<90°

All the given three angles of triangle FAN are less than 90°, which imolies that the given trianagle FAN is an acute triangle.

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Answer:

5x-7

Step-by-step explanation:

:According to the question:You are working with a population of crickets. Before the mating season you check to make sure that the population is in Hardy-Weinberg equilibrium, and you find that the population is in equilibrium.

During the mating season you observe that individuals in the population will only mate with others of the same genotype (for example Dd individuals will only mate with Dd individuals). There are only two alleles at this locus ( D is dominant, d is recessive), and you have determined the frequency of the D allele =0.6 in this population. Selection acts against homozygous dominant individuals and their survivorship per generation is 80%. After one generation the frequency of DD individuals will decrease in the population.

According to the Hardy-Weinberg equilibrium equation p² + 2pq + q² = 1, the frequency of D (p) and d (q) alleles are:p + q = 1Thus, the frequency of q is 0.4. Here are the calculations for the Hardy-Weinberg equilibrium:p² + 2pq + q² = 1(0.6)² + 2(0.6)(0.4) + (0.4)² = 1After simplifying, it becomes:0.36 + 0.48 + 0.16 = 1This means that the population is in Hardy-Weinberg equilibrium. This is confirmed as the frequencies of DD, Dd, and dd genotypes

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The line of intersection formed by the two planes 2x - y + z = 5 and x + y - z = 1 can be represented by the vector equation r = <x, y, z> = <2, 3, 4> + t<3, 4, 1>, where t is a parameter.

To find the vector equation for the line of intersection, we need to determine the direction vector and a point on the line.

First, we'll find the direction vector by taking the cross product of the normal vectors of the two planes. The normal vector of the first plane is <2, -1, 1>, and the normal vector of the second plane is <1, 1, -1>. Taking the cross product of these two vectors, we get the direction vector <3, 4, 1>.

Next, we'll find a point on the line of intersection by solving the system of equations formed by the two planes. Subtracting the second plane equation from the first, we get 3x - 2y + 2z = 4. Solving this system along with the original plane equation, we find x = 2, y = 3, and z = 4.

Combining the direction vector and the point on the line, we obtain the vector equation r = <x, y, z> = <2, 3, 4> + t<3, 4, 1>, where t is a parameter. This equation represents the line of intersection formed by the two given planes.

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Proficiency in statistics is a vital skill for a data analyst because it helps in analyzing and interpreting data and thereby making informed decisions based on the analyzed data.

Data analysts are responsible for ensuring that an organization's data is correct, and they do this by collecting and analyzing data. Statistics is a branch of mathematics that provides a way to systematically collect and analyze data. Statistical analysis provides a framework for identifying trends, patterns, and relationships in data and helps to understand the underlying mechanisms that produce them. It is important for a data analyst to have a good understanding of statistical methods because they need to use these techniques to analyze and interpret data. Furthermore, the statistical techniques used in data analysis help to identify patterns, relationships, and trends that may not be immediately apparent from the data. In conclusion, proficiency in statistics is an essential skill for a data analyst as it helps to make informed decisions based on data and ensures that an organization's data is accurate.

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To find the probability that the mean of the sample would be greater than 48.83 months, we will use the central limit theorem.

We will first find the z-score for the given values using the formula: `z = (x - μ) / (σ / √n)` where `x` is the sample mean, `μ` is the population mean, `σ` is the population standard deviation and `n` is the sample size.

Then we will find the probability using a standard normal distribution table.

Given,The mean lifetime of a tire, μ = 48 monthsStandard deviation of the lifetime of a tire, σ = 7Sample size, n = 147Sample mean, x = 48.83 months

We need to find the probability that the mean of the sample would be greater than 48.83 months.

Using the formula for z-score,z = (x - μ) / (σ / √n)z = (48.83 - 48) / (7 / √147)z = 0.83 / 0.577 = 1.44

Using a standard normal distribution table, the probability corresponding to a z-score of 1.44 is 0.9251.Approximately, the probability that the mean of the sample would be greater than 48.83 months is 0.9251.

Summary: The probability that the mean of the sample would be greater than 48.83 months is 0.9251.

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Answer:

4

Step-by-step explanation:

First, the numbers should be in ascending or descending order . Since, 4 numbers are in ascending order we don't have to do that .

Second, find the "middlest" of them . If there were total of odd numbers it would have been easier but, here is total of even number(4) and mean of 2 middlest number would be its median: (4+4)/2=4 .

Answer: - 3 1/4

Step-by-step explanation:

- 3 3/4 + 1/2

Get a common denominator

-3 3/4 + 2/4

-3 1/4

The volume of the solid below the paraboloid z = 75 - 3x² - 3y² and above the xy-plane, in terms of polar coordinates, is given by V = Rθ(75 - 3R²).

To find the volume of the solid below the paraboloid z = 75 - 3x² - 3y² and above the xy-plane using polar coordinates, express the equation of the paraboloid in terms of polar coordinates.

In polar coordinates:

x = r cos(theta)

y = r sin(theta)

Substituting these values into the equation of the paraboloid:

z = 75 - 3(r cos(theta))² - 3(r sin(theta))²

z = 75 - 3r² cos²(theta) - 3r² sin²(theta)

z = 75 - 3r² (cos²(theta) + sin²(theta))

z = 75 - 3r²

Finding the volume above the xy-plane, integrate the expression z = 75 - 3r² with respect to z over the region where z is positive.

The region in polar coordinates can be defined as:

0 <= r <= R

0 <= theta <= 2pi

To calculate the volume, integrate the expression z = 75 - 3r² with respect to z over the region defined above:

V = ∫∫∫ (75 - 3r²) dz dr d(theta)

To simplify the integration, note that the expression (75 - 3r²) does not depend on z or theta. Therefore, pull it out of the integral:

V = (75 - 3r²) ∫∫∫ dz dr d(theta)

Integrating dz over the positive range of z gives us z evaluated from 0 to (75 - 3r²):

V = (75 - 3r²) ∫∫ (75 - 3r²) dr d(theta)

Integrating dr over the range 0 to R and d(theta) over the range 0 to 2pi, we get:

V = (75 - 3r²) ∫[0 to R] ∫[0 to 2pi] dr d(theta)

Now, perform the integration:

V = (75 - 3r²) ∫[0 to R] [r] d(theta)

V = (75 - 3r²) [rθ] evaluated from 0 to R

V = (75 - 3R²) (Rθ) - (75 - 3R²) (0)

V = Rθ(75 - 3R²)

Therefore, the volume of the solid below the paraboloid z = 75 - 3x² - 3y² and above the xy-plane, in terms of polar coordinates, is given by V = Rθ(75 - 3R²).

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C. The probability of the type I error best defines the notion of the significance position of a thesis test.

The significance position, denoted by alpha( α), is the probability of rejecting the null thesis(H_o) when it's actually true. This is also known as a type I error, which occurs when we inaptly reject a true null thesis.

Option a isn't correct because the probability of rejecting H_o, whether it's true or not, isn't fixed and depends on the sample and the chosen significance position.

Option b isn't correct because it describes the p- value, which is a affiliated conception but not the significance position. The p- value is the probability of observing a sample statistic as extreme or more extreme than the one actually attained, assuming the null thesis is true.

Option d is also not correct because it describes the probability of a type II error, which occurs when we fail to reject a false null thesis. The probability of a type II error is denoted by beta( β) and is told by factors similar as sample size and effect size.

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Answer:

Step-by-step explanation:

look at the png

Based on the total number of pages in the textbook, and the total thickness, the average thickness per page is 0.0047 cm.

The average thickness per page of the textbook can be found by the formula:

= Total thickness of textbook / Number of pages

Solving gives:

= 3.86 / 820

= 0.0047 cm

In conclusion, the average thickness per page is 0.00470 cm.

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The probability of tossing at least one head in three tosses of a fair coin is 7/8 i.e seven eighths.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

The probability of an event A is denoted as P(A)

Here we have

A fair coin is tossed three times

When a coin is tossed number of outcomes = 2

Number of outcomes that we get 1 tail = 1

The probability of getting a tail = 1/2

Hence,

The probability of getting tails on the 1st toss = 1/2

The probability of getting tails on the 2nd toss = 1/2

The probability of getting tails on the third toss = 1/2

The probability of getting at least one head is equal to 1 minus the probability of getting all tails, which is:

=> 1 - (1/2) x (1/2) x (1/2) = 7/8

=> 1 - 1/8 = 7/8

Therefore,

The probability of tossing at least one head in three tosses of a fair coin is 7/8 i.e seven eighths.

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Answer/Exaplantion:

Given, a coin is tossed 3 times.We have to find the probability of getting at least one head.The possible outcomes areT H HH T HH H TT T HT H TH T TT T TH H HWe observe that there is only one scenario in throwing all coins where there are no heads.The chances for one given coin to be heads is 1/2.The chance for all three to have the same result would be (1/2)3= (1/2)(1/2)(1/2)= 1/8So, the probability to have atleast one head is 1 - 1/8= (8 - 1)/8= 7/8Therefore, the probability of getting at least one head is 7/8.

Answer:

a) Only the first one is an identity.

Step-by-step explanation:

1). 8 cos O tan O csc O = 8   simplifies to:

cos O tan O csc O = 1

cos O * (sin O / cos O) * (1 /sin O)

=  cos O sin O / cos O sin O

= 1

So it is identity.

2) 13 sec^2 O/ cos^2 O - tan^2 O / cos^2O

= 13 sec^2 O - tan^2 O / cos^2 O

Now  sec^2 O = 1 + tan^2 O, so we have:

(13( 1 + tan^2 O) - tan^2 O) / cos^2 O

= (12 tan^2 O + 13) / cos^2 O

This is not always = 2 so its not an identity.