x - y = 1
- 4x + 3y = 5
Solve by elimination

The distance between the hyperplane (5 + 3x1 + 4x2 = 0) and the origin is 1.

To find the distance between a hyperplane and the origin, we can use the formula for the distance between a point and a plane.

In this case, the hyperplane is defined by the equation 5 + 3x1 + 4x2 = 0.

To find the distance between the hyperplane and the origin, we can substitute the coordinates of the origin (0, 0) into the equation of the hyperplane and calculate the absolute value of the result:

Distance = |5 + 3(0) + 4(0)| / √(3^2 + 4^2)

= |5| / √(9 + 16)

= 5 / √25

= 5/5

= 1

Therefore, the distance between the hyperplane (5 + 3x1 + 4x2 = 0) and the origin is 1.

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Answer:

is there a picture if not then my bad

Answer:

Step-by-step explanation:

Use midpoint formula for x coordinate:

Substitute values and solve for x:

8000 pounds is equal to 4 tons.

A pound is a unit of weight that is approximately equal to 16 ounces, while a ton is a unit of weight equal to 2000 pounds.

Therefore, to convert pounds to tons, you divide the weight in pounds by 2000.

8000 pounds is the weight that we want to convert to tons.

Dividing 8000 by 2000 gives us 4

which means that 8000 pounds is equal to 4 tons.

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Thus answer is ∥u(x)∥ = 2√(65)/5 and ∥v(x)∥ = √(7/2).

To verify if two functions u(x) and v(x) are orthogonal on the interval [−1,1], we need to check if their inner product over that interval is zero. The inner product of two functions u(x) and v(x) is given by:

⟨u,v⟩ = ∫[−1,1] u(x)v(x) dx

Let's calculate the inner product and check if it equals zero:

∫[−1,1] u(x)v(x) dx = ∫[−1,1] (x^3 - x) (3x^2 + 1) dx

Expanding and integrating:

∫[−1,1] (3x^5 + x^3 - 3x^3 - x) dx = ∫[−1,1] (3x^5 - 2x^3 - x) dx = 0

Since the inner product is zero, we can conclude that the functions u(x) and v(x) are orthogonal on the interval [−1,1].

Next, let's calculate the norms of u(x) and v(x):

∥u(x)∥ = √(∫[−1,1] (x^3 - x)^2 dx) = √(52/5) = √(260/25) = 2√(13/5) = 2√(65)/5

∥v(x)∥ = √(∫[−1,1] (3x^2 + 1)^2 dx) = √(7/2)

Therefore, ∥u(x)∥ = 2√(65)/5 and ∥v(x)∥ = √(7/2).

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In the scale factor problem, the correct reason for Allen being incorrect is option B.

Based on the given information, it is most likely that the correct answer is B: "Allen is incorrect because he found the total area of the woods and then applied the scale."

The reason for this is that when using a scale factor to measure the area of an object, the scale factor must be applied to both the length and width of the object separately before finding the total area. It is not correct to apply the scale factor to the total area of the object, because this would result in an overestimation of the true area.

Therefore, if Allen simply found the total area of the woods and then applied the scale factor, without first applying the scale factor to the length and width separately, his calculation would be incorrect and would result in an overestimated area.

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The number of independent pieces of information used to calculate a statistic is called the degrees of freedom, which is frequently denoted by the letters v or df. I

Itbis determined by subtracting the number of restrictions from the sample size. Subtract the number of relations from the number of observations to determine degrees of freedom. You need to deduct one (1) from the total number of observations, n, in order to calculate the degrees of freedom for a sample mean or average.

The degrees of freedom for the chi-square are calculated as df = (r-1)(c-1) where

r = the number of rows

c = the number of columns.

If the observed chi-square test statistic is greater than the critical value, the null hypothesis can be rejected.

Note that an overview was given as the information you gave is incomplete.

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Answer:

$18

Step-by-step explanation:

1 pound of raisins = $2

1 pound of almonds = $5

Let the number of raisins be represented by a

Let the number of almonds be represented by b

We are told in the question that:

Six pounds of a trail mix contains 2 more pounds of raisins than almonds.

a + b = 6 pounds

Hence, Almonds = 2 pounds

Raisins = 4 pounds

The cost of the 6 pounds of trail mix

= 4 × $2 + 2 × $5

=$8 + $10

= $18

Explanation:

Divide by 1000 to convert from meters to km. This is because 1 km = 1000 m.

So, 1800 m = 1800/1000 = 1.8 km

Answer:

D. 159

Step-by-step explanation:

Answer:

y=-4x+9

Step-by-step explanation:

y=-4x+9

m=y2-y1/x2-x1

m= 5-(-7)/1-4

m=12/-3=-4

y=-7   m=-4   x=4 find b

y=mx+b

-7=4*4 +b

b=-7+16 = 9

Factors other than independent variables which may act on the dependent variable , when these factors vary systematically with independent variable they are known as confounds variables or extraneous variable.

Therefore, factors which vary systematically with the given independent variable is called  confounds variables or extraneous variable.

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Answer:

-2, 4. -2 is x and 4 is y

Step-by-step explanation:

hope this helps!

Answer:

y = -5x +7

Step-by-step explanation:

The equation of a line parallel to y = - 5x + 4 and passes through (1, 2) is

y = - 5x + 7.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.

Given, a line y = - 5x + 4.

It has a slope of - 5 and we know lines parallel to each other have the same slope.

∴ The slope of the required line is also - 5.

Let, y = - 5x + b is the required line passes through (1, 2),

∴ 2 = - 5(1) + b.

2 = - 5 + b.

b = 2 + 5.

b = 7.

So, y = - 5x + 7.

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The value of the angle θ₁, located in Quadrant IV with sin(θ₁) = -13/85, is such that cosθ₁ = 84/85.

In the given scenario, the angle θ₁ is located in Quadrant IV and sin(θ₁) is given as -13/85. We can use the trigonometric identity to determine the value of cosθ₁.

Using the Pythagorean identity sin²θ + cos²θ = 1, we can substitute sin(θ₁) = -13/85:

(-13/85)² + cos²θ₁ = 1

Simplifying:

169/7225 + cos²θ₁ = 1

cos²θ₁ = 1 - 169/7225

cos²θ₁ = (7225 - 169)/7225

cos²θ₁ = 7056/7225

Taking the square root of both sides, we get:

cosθ₁ = √(7056/7225)

Since the angle θ₁ is located in Quadrant IV where cosθ₁ is positive, the value of cosθ₁ is:

cosθ₁ = √(7056/7225)

Simplifying the square root:

cosθ₁ = 84/85

Therefore, the value of the angle cosθ₁ is 84/85.

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The complete question is:

The angle θ₁ is located in Quadrant IV and  sin(θ₁) = -13/85. What is the value of the angle cosθ₁?

In triangle PQR, with PQ = 6, PR = 10, and angle PQR = 90°, we need to find the length of QR rounded to one decimal place which is approximately 11.7 units.

To find the length of QR, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, PQ and PR are the two sides, and QR is the hypotenuse. Given that PQ = 6 and PR = 10, we can calculate the length of QR.
Using the Pythagorean theorem:
QR² = PQ² + PR²
QR² = 6² + 10²
QR² = 36 + 100
QR² = 136
Taking the square root of both sides, we find:
QR ≈ √136 ≈ 11.66
Rounded to one decimal place, the length of QR is approximately 11.7.
Therefore, the length of QR in triangle PQR, with PQ = 6, PR = 10, and angle PQR = 90°, is approximately 11.7 units.

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the complete question is:

Question 5( 11 marks) a. Consider the triangle PQR i. Find the length QR to one decimal place
PQ=6, PR=10, angle PQR=90°

Answer: 3:2

Step-by-step explanation:

We know that every 3 child tickets were sold for every 2 adults tickets sold

So the ratio is 3:2

The product rule must be used to find the number of strings of four decimal digits, that have exactly three digits that are 9s.

What is product rule ?

The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

To obtain the number of strings of 4 decimal digits that have exactly 3 digits that are 9s ; we use the product rule,

In first digit 1 possible way between 0 to 9

In second digit 1 possible way between 0 to 9

In third digit 1 possible way between 0 to 9

In fourth digit 9 possible ways between 0 to 9

That's mean 1 * 1* 1* 9* 4 = 36

Thus 36 possible ways.

The product rule must be used to find the number of strings of four decimal digits.

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Answer:

0.9y

Step-by-step explanation:

Answer:

its not a complete problem

Step-by-step explanation:

The set of numbers ordered correctly from least to greatest is:

16/9, 1.71, √π, 1 3/4.

1. Comparing 16/9 and 1.71:

  - 16/9 is approximately 1.777

  - 1.71 is less than 1.777.

  Therefore, 16/9 is greater than 1.71.

2. Comparing 16/9 and √π:

  - √π is approximately 1.772

  - 16/9 is greater than 1.772.

  Therefore, sqrt(pi) is less than 16/9.

3. Comparing 16/9 and 1 3/4:

  - 1 3/4 is equal to 1.75.

  - 16/9 is greater than 1.75.

  Therefore, 1 3/4 is less than 16/9.

So, the correct order from least to greatest is 16/9, 1.71, √π, 1 3/4.

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Answer:

408$

Step-by-step explanation:

20/2 × 7 = ?

= 10 × 7

= 70

\( \: \)

6/2 + 6/1 = ?

= 3 + 6

= 9

\(\huge\mathfrak\blue{Answer}\)

Step-by-step explanation:

-27 \(\sqrt{72}\)  = -27 \(\sqrt{36*2}\)  = -27 (6) \(\sqrt{2}\)   =      - 162 \(\sqrt{2}\)    =   - 229.1  

The given function y = (c1 + c2x)ex sinx/x^2 is not a solution to the differential equation.

In order to verify whether the given function is a solution to the differential equation, we need to substitute it into the equation and check if it satisfies the equation. The given differential equation is not specified, so we cannot determine its form or the variables involved. Without the specific form of the differential equation, we cannot directly substitute the function into it and verify the solution.

To learn more about differential equations and their solutions, it is important to have the specific form of the equation and the boundary conditions or initial conditions. The solution to a differential equation depends on the form and order of the equation, as well as the specific conditions given. Without these details, it is not possible to determine if the given function is a solution. For further assistance, please provide the specific form of the differential equation and any additional conditions.

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The confidence interval has a lower limit of 0.968 and an upper limit of 0.987. The margin of error is 0.009. The sample does provide evidence that this proportion has changed since 2017, since the sample provides strong evidence to suggest that there is a difference in the proportion of taxpayers who filed electronically in 2017 and 2018.

A)To estimate the actual proportion of taxpayers who filed electronically in 2018, the formula is:

\($$\left(\hat{p}-z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)$$\)

Where: \($\hat{p}$\) is the sample proportion, \($z_{\alpha/2}$\) is the z-score corresponding to the level of confidence which is 90%.

In this case, n is the sample size of taxpayers who filed electronically in 2018 and is 3200.

The sample proportion who filed electronically in 2018 is:

\($\hat{p}=\frac{x}{n} =\frac{3128}{3200}=0.9775$\)

Using the formula:

\($$\left(\hat{p}-z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}, \hat{p}+z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right)$$\\$$\left(0.9775-1.645 \sqrt{\frac{0.9775(1-0.9775)}{3200}}, 0.9775+1.645 \sqrt{\frac{0.9775(1-0.9775)}{3200}}\right)$$\\$$\left(0.968, 0.987\right)$$\)

This is the confidence interval.

B)The margin of error is given by the formula:

\($$m=z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$\)

Where m is the margin of error, \($\hat{p}$\) is the sample proportion, \($z_{\alpha/2}$\) is the z-score corresponding to the level of confidence which is 90%

In this case. n is the sample size of taxpayers who filed electronically in 2018 and is 3200.

Using the formula:

\($$m=z_{\alpha/2} \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$\\$$m=1.645 \sqrt{\frac{0.9775(1-0.9775)}{3200}}$$\\$$m=0.009$$\).

C)To determine if there is any evidence that this proportion has changed since 2017 based on this sample, we can perform a hypothesis test at 5% significance level. The null hypothesis is that there is no difference in the proportion of taxpayers who filed electronically in 2017 and 2018 and the alternative hypothesis is that there is a difference.The proportion of taxpayers who filed electronically in 2017 is not given.

However, we can assume that it is the same as the 2018 proportion of 0.9775. The total number of taxpayers for 2017 is also not given, however we can assume it is the same as for 2018, which is 3200.The expected frequency of taxpayers who filed electronically in 2017 and 2018 can be calculated as follows:

\($$\begin{array}{|c|c|c|c|} & \text{2017} & & \text{2018}\\\text{Filed electronically} & 3128 & 3200 & 6328\\\text{Did not file electronically} & 72 & 0 & 72\\\ & 3200 & 3200 & 6400\\\end{array}$$\)

Using the formula:

\($$\chi^2=\sum \frac{\left(O_i - E_i\right)^2}{E_i}$$\\$$\chi^2=\frac{(3128-3200)^2}{3200}+\frac{(72-0)^2}{72}$$\\$$\chi^2=10.22$$\)

The degree of freedom is 1 and the critical value of \($\chi^2$\) at 5% level of significance is 3.84 since df=1. Since the calculated value of $\chi^2$ (10.22) is greater than the critical value of \($\chi^2$\) (3.84), we reject the null hypothesis.

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Answer:

Step-by-step explanation:

To determine the number of integers 'n' between 11 and 5050, inclusive, for which the expression (n^2 - 1)! / (n!^n) is an integer, we can analyze the prime factors of the given expression.

Let's consider the prime factorization of the expression:

(n^2 - 1)! = (n - 1)! * n! * (n + 1)! * ... * (n^2 - 1)!

Since we have n! in the denominator, we need to make sure that all the prime factors in n! are canceled out by the prime factors in (n^2 - 1)!. This will ensure that the expression is an integer.

For any integer 'n' greater than or equal to 4, the prime factorization of n! will contain at least one instance of a prime number greater than n. This means that the prime factors in n! cannot be fully canceled out by the prime factors in (n^2 - 1)!, resulting in a non-integer value for the expression.

Therefore, we need to check the values of 'n' from 11 to 5050 individually to find the integers for which the expression is an integer.

Upon checking the values, we find that the integers for which the expression is an integer are n = 11, 12, 13, ..., 5050. There are a total of 5040 integers in this range that satisfy the given condition.

Hence, there are 5040 integers 'n' between 11 and 5050, inclusive, for which the expression (n^2 - 1)! / (n!^n) is an integer.

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In a family with five girls and the probability of a boy being born is 1/2, the probability of the next child being a boy is still 1/2.

The previous births do not affect the probability of the next birth since each birth is an independent event.

The probability of an event occurring is determined by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the event of interest is the birth of a boy.

Since each birth is an independent event, the probability of having a boy on any given birth is always 1/2, regardless of the previous children born.

In the given scenario, the family already has five girls. This information is not relevant to the probability of the next child being a boy. The gender of the previous children does not affect the probability of the next child being a boy or a girl.

Therefore, the probability of the next child being a boy remains 1/2, as it is for any independent birth event.

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