whats the measure of

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1] is the orthogonal basis for w using Gram-Schmidt process.

Given,

The set;

x₁ = [1  -4  0  1]

x₂ = [7  -7  -6  1]

We have to produce the orthogonal basis for w using the Gram-Schmidt process;

Here,

y₁ = x₁ =  [1  -4  0  1]

Now,

Solve for y₂

y₂ = x₂ - [x₂y₁ / y₁y₁] y₁

That is,

y₂ = [7  -7  -6  1] - ( [7  -7  -6  1] [1  -4  0  1] / [1  -4  0  1] [1  -4  0  1] ) × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - (7 + 28 - 0 + 1) / (1 + 16 + 0 + 1) × [1  -4  0  1]

y₂ = [7  -7  -6  1]  - 36/18 × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - 2  × [1  -4  0  1]

y₂ =  [7  -7  -6  1] - [2  8  0  2]

y₂ = [5  1  -6  -1]

That is,

The orthogonal basis for w using Gram-Schmidt process is,

y₁ =  [1  -4  0  1] and y₂ = [5  1  -6  -1]

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Answer:

B

Step-by-step explanation:

Answer:

0.19 50% 15/20 9/10 95%

Step-by-step explanation:

I know

Answer: The correct inequality that matches the graph is 6x + y < 3.

This inequality can be graphed by plotting the points (0,3) and (1,9) as the boundary of the solution set, and shading the area above the line. The graph will be a line with a negative slope that pass through the points (0,3) and (1,9) and the shaded area will be above the line, which match the graph you have described.

We can check this by plugging the points (0,3) and (1,9) into the inequality to see if they satisfy it:

6(0) + 3 < 3 => 3 < 3 which is true

6(1) + 9 < 3 => 6 + 9 < 3 which is false

This confirms that the inequality 6x + y < 3 matches the graph.

Step-by-step explanation:

According to the mathematical notations, we can say that in this case, Antonhy's reasoning is incorrect, because the expression abc is only one term and not three as he stated.

It corresponds to a term that has letters and numbers, which are separated only if there is a mathematical sign between them, such as the plus or multiplication sign, for example, to be an expression of three terms, the expression should be like this:

Therefore, we can consider that the term abc corresponds to a monomial, as it is only one term in an expression, and not three as supposed by Anthony.

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Answer: The divisor is the thing you are dividing by. The divident is what are dividing.

Step-by-step explanation:

(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Converting the force from newtons to pounds can help us determine the chances of a driver being able to stop a child. The conversion factor is 1 pound (lb) = 4.45 newtons (N).

To convert the force from newtons to pounds, we use the conversion factor of 1 lb = 4.45 N. If we have a force in newtons, we can divide it by 4.45 to obtain the equivalent force in pounds. For example, if the force is 20 N, we divide it by 4.45 to get approximately 4.49 lb.

Now, in order to assess the chances of the driver stopping the child, we need to consider various factors such as the mass and speed of the child, the friction between the driver's shoes and the ground, and the force applied by the driver. If the force applied by the driver, converted to pounds, is greater than or equal to the force exerted by the child, there is a higher chance of stopping the child.

However, it's important to note that other factors, such as the driver's reaction time and the coefficient of friction between the shoes and the ground, also play significant roles in determining the outcome. Thus, the chances of the driver stopping the child depend on a combination of these factors, making it essential to consider them comprehensively when evaluating the situation.

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The coordinates of the vertices after a rotation 180° counterclockwise around the origin are

Coordinates:

Coordinates means the set of values that show an exact position of the point in the graph. Basically, obtained using the x and y values.

Given.

Here we have the graph with four coordinate and they formed the parallelogram.

Now, we need to find the the coordinates of the vertices after a rotation 180° counterclockwise around the origin.

In order to find the rotation, first we have to identify the current coordinates of the graph,

They are J(1, 1), K(6, 1), L(10,4) and M(5, 4).

It can be obtained by writing the corresponding x and y values.

Now, we have to know that rule for the rotations,

"The rule for a rotation by 180° states that the origin is (x , y) then it can rewritten as (−x,−y) "

So, based on these rule the coordinates after 180° rotation in counterclockwise are,

J(1, 1) →  J'(-1, -1)

K(6, 1) →  K'(-6,-1)

L(10,4) →  L'(-10, -4)

M(5, 4) → M'(-5,-4)

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Answer:

69.2% or 18.8%

Step-by-step explanation:

Try it pls

Answer:

George

Step-by-step explanation:

The set of side length similar to the given one is 1.6 meters, 2 meters, 3.2 meters.

Option A.

Given is a side length of a triangle has side lengths of 8 meters, 10 meters, and 16 meters.

We know that the similar triangles has proportional side lengths,

8/1.6 = 5

10/2 = 5

16/3.2 = 5

Hence the set of side length similar to the given one is 1.6 meters, 2 meters, 3.2 meters.

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Answer:

2/9 * (-4 - 3) + 3

= 2/9 * (-7) + 3

= -14/9 + 3

= -14/9 + 27/9

= 13/9

After solving the question by Pythagorean theorem we have: OM = PR(cos(ß) - sin(ß)) = cos(a + ß)(cos(ß) - sin(ß)) as the expression for the length of segment OM.

You may determine the right angled triangle's missing length using Pythagoras' Theorem. The triangle has three sides: the adjacent, which doesn't touch the hypotenuse, the opposite, which is always the longest, and the hypotenuse. Pythagoras' formula is: \(a^{2} + b^{2} = c^{2}\)

There seems to be a typo in the question, as "segment ON =" is not followed by an expression or value. However, I will provide an explanation based on the given information.

We start with the point (1,0) on the unit circle and rotate it counterclockwise by an angle of a + ß. This brings us to the point P on the circle, which has coordinates (cos(a + ß), sin(a + ß)).

Next, we draw a perpendicular segment PN from point P to the line ON, where O is the origin (0,0) and N is the foot of the perpendicular from P to ON. We also draw another perpendicular segment PR from point P to the x-axis.

From the right triangle ONP, we see that ON = sin(a + ß) (since sin is the y-coordinate of a point on the unit circle) and NP = cos(a + ß) - 1 (since the x-coordinate of P is cos(a + ß) and we started with the point (1,0)).

Using the Pythagorean theorem, we have:

\(OM^2 + NP^2 = ON^2\)

where OM is the segment from point O to the foot of the perpendicular from P to the x-axis (which we called R). Since OR is perpendicular to PR, we have OR = PR cos(90 - ß) = PR sin(ß), and since OP is perpendicular to PR, we have OP = PR cos(ß).

Thus, OM = OP - OR = PR cos(ß) - PR sin(ß) = PR(cos(ß) - sin(ß)).

Substituting this into the Pythagorean theorem equation, we have:

(PR(cos(ß) - sin(ß))) + (cos(a + ß) - 1) = sin(a + ß)

This is the expression for the length of segment OM.

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Answer:

5 x (3 x Y - 2y^3)

x(15 x Y - 10 y^3)

5 (y^3 - 3x Y )^    -    5y^6

-----------------------------------

3Y                                3Y

X=  0       Y=  0

HOPE THIS HELPSS

Answer:157/10

Step-by-step explanation:

Make 15 into an improper fraction (every number is a fraction over 1) so multiply the numerator(15) and the denominator(1) by 10 to get 150/10 then add 150/10 to 7/10 to get 157/10

Answer:

\(\frac{157}{10}\)

Step-by-step explanation:

Step 1

Multiply the denominator by the whole number

10 × 15 = 150

Step 2

Add the answer from Step 1 to the numerator

150 + 7 = 157

Step 3

Write answer from Step 2 over the denominator \(\frac{157}{10}\)

As per the given information, the estimated increase in a patient's length of stay at the hospital if they contract a nosocomial infection is 9.5833 (rounded to 4 decimal places).

A nosocomial infection is an infection acquired in a hospital by a patient who was admitted for a reason other than that infection. The presence of a nosocomial infection indicates poor quality of care and unnecessary patient suffering. When patients are in a hospital, they may be exposed to microorganisms that can lead to infections. These microorganisms are often found on the skin or in the mouth or intestines of patients, healthcare workers, or visitors.

The estimated increase in a patient's length of stay at the hospital if they contract a nosocomial infection is calculated as follows: Estimate of the increased length of stay (days) = mean duration of hospital stay (with no infection) x rate of infection x (1 - rate of infection) [1]

Where, The mean duration of hospital stay (with no infection) = 5 days

The rate of infection = 0.1

Hence, putting these values in the above formula: Estimate of the increased length of stay (days) = 5 x 0.1 x (1 - 0.1) = 0.45 days = 9.5833 (rounded to 4 decimal places)

Thus, the estimated increase in a patient's length of stay at the hospital if they contract a nosocomial infection is 9.5833 (rounded to 4 decimal places).

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Answer:

No, that would cost more than $180.

Step-by-step explanation:

6(10)+60(3)≤$180

60+180 = $240

$240≤$180

Hope this helps!

Answer:

the answer is B

x = 1

Step-by-step explanation:

the symmetry is in the middle of the curve like a mirror and the equation of the mirror or symmetry line is x=1

Answer:

5.5

Step-by-step explanation:

180/3 =60 (60/1 hr)

330/60 =5.5

Therefore, the dimensions of the pool are 30 meters in length, 12 meters in width, and 3 meters in depth.

To find the dimensions of the rectangular pool, we first need to determine the ratio of the length, width, and depth. We are given that the ratio is 10:4:1. We can represent this ratio as:
Length = 10x
Width = 4x
Depth = x

Where x is a common factor that we will use to determine the actual measurements of the pool.
Now, we are given that the volume of the pool is 1,080 cubic meters. We can use the formula for the volume of a rectangular prism, which is:
Volume = Length x Width x Depth
Substituting the values we have for the length, width, and depth, we get:
1,080 = (10x) x (4x) x (x)
Simplifying the equation, we get:
1,080 = 40x^3
Dividing both sides by 40, we get:
27 = x^3
Taking the cube root of both sides, we get:
x = 3

Now that we know x is equal to 3, we can find the actual measurements of the pool by substituting x back into the original ratio we were given.
Length = 10x = 10(3) = 30 meters
Width = 4x = 4(3) = 12 meters
Depth = x = 3 meters

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Answer:

160%

Step-by-step explanation:

320 divided by 200, times 100 = 160%

Answer:

1. Correct

2. Incorrect

Step-by-step explanation:

( - 1 + 1 ) / - 1

= 0 / - 1

= 0

- 1 / 1 = - 1

Answer:

below

Step-by-step explanation:

1) correct

2) incorrect

Answer:

g(8)=17

Step-by-step explanation:

Given :
g(a)=a²+2a-63

Substitute a = 8 :

g(8)=8^2+2(8)-63

= 64+16-63

=17

Answer: 1/6

Step-by-step explanation:

Out of 30 students, 5 liked country music.

To find the fraction of students who liked country music, we need to divide the number of students who liked country music by the total number of students in the class.

Fraction of students who liked country music = (Number of students who liked country music) / (Total number of students)

Fraction of students who liked country music = 5/30

We can simplify this fraction to lowest terms by dividing both the numerator and denominator by the greatest common factor, which is 5.

5/30 ÷ 5/5 = 1/6

Therefore, the fraction in lowest terms that shows how many students liked country is 1/6.

Answer: 1/6

Step-by-step explanation:

Out of 30 students, 5 liked country music.

To find the fraction of students who liked country music, we need to divide the number of students who liked country music by the total number of students in the class.

Fraction of students who liked country music = (Number of students who liked country music) / (Total number of students)

Fraction of students who liked country music = 5/30

We can simplify this fraction to lowest terms by dividing both the numerator and denominator by the greatest common factor, which is 5.

5/30 ÷ 5/5 = 1/6

Therefore, the fraction in lowest terms that shows how many students liked country is 1/6.

Answer:

answer: 504 blooms <3

Step-by-step explanation:

if you add 72 and 72 then you get 144 so that means 72 blooms each week so if you multiply 72 x 7 you get 504!

The estimated amount of rust-proofer needed for the coat is approximately 21.95 ft³.

To estimate the amount of rust-proofer needed to coat a hemisphere-shaped dome, we can use differentials and the formula for the volume of a hemisphere.

The volume of a hemisphere with radius r is given by V = (2/3)πr³.

We are given that the radius of the dome is 55 ft and the coat is to be 0.01 in. thick. We need to estimate the additional volume of rust-proofer required to create this thin coat.

First, we convert the coat thickness to feet. Since 1 inch is equal to 1/12 feet, the thickness in feet is 0.01/12 = 0.000833 ft.

Next, we calculate the differential of the volume, dV, using the differential of the volume formula:

dV = (4/3)πr² dr.

Substituting the given values, we have:

dV = (4/3)π(55)² (0.000833) ≈ 21.95 ft³.

It's important to note that this is an estimate, and the actual amount of rust-proofer required may vary based on factors such as the surface texture and the application process.

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The  probability that a product will operate properly within an expected time frame is the dimension of quality known as reliability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes. The value of the probability is varies from zero to one

Here, the product will operate properly within an expected time frame is the dimension of quality

Reliability is expressed as the probability that a given item will perform its intended function with no failures for a given period of time under a given set of conditions that means the reliability is the complementary to the failure of probability

Therefore, the given statement is know as the reliability

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