If the subspace of all solutions of Ax 0 has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A

The length of BC is approximately 4.58 cm when AB is 5.9 cm.

To find the length of BC in triangle ABC, we can use the Law of Sines. The Law of Sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In triangle ABC, we know that angle A is 40°, angle B is 30°, and side AB is 5.9 cm. We want to find the length of side BC.

Let's denote the length of side BC as x. According to the Law of Sines:

sin(A) / AB = sin(B) / BC

Substituting the known values:

sin(40°) / 5.9 = sin(30°) / x

To find x, we can cross-multiply and solve for x:

x = (5.9 * sin(30°)) / sin(40°)

Using a calculator:

x ≈ (5.9 * 0.5) / 0.6428

x ≈ 2.95 / 0.6428

x ≈ 4.58 cm

Therefore, the length of BC is approximately 4.58 cm when AB is 5.9 cm.

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We can conclude that it is extremely unlikely to obtain a sample mean greater than 904.8 minutes if the design engineer's claim about the population variance and mean is true.

We can use the Central Limit Theorem to approximate the distribution of the sample means.

Under the given assumptions, the mean of the sampling distribution of the sample means is equal to the population mean, which is 886886 minutes, and the standard deviation of the sampling distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size, which is\(\sqrt{84648464/145145} = 41.77\) minutes.

Therefore, we can standardize the sample mean using the formula:

\(z = (\bar{x} - \mu) / (\sigma / \sqrt{n } )\)

where \(\bar{x}\)  is the sample mean, \(\mu\)  is the population mean, sigma is the population standard deviation, and n is the sample size.

Plugging in the values we get:

z = (904.8 - 886886) / (41.77) = -21115.47

The probability of getting a sample mean greater than 904.8 minutes can be calculated as the area under the standard normal curve to the right of z = -21115.47.

This probability is essentially zero, since the standard normal distribution is symmetric and nearly all of its area is to the left of -6.

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Answer:

the 3 in the 10ths place would be "worth" more as it's in front of the decimal

To find various values related to the vectors (u, v) and (kv, w), such as cos, ||v||, d(u, v), and ||u - kv||, within the range C[-1,1].

(i) To find cos, we need to compute the dot product of the vectors (u, v) and divide it by the product of their magnitudes.
(ii) To determine kv, we scale the vector v by a factor of k, and then calculate the dot product with w.
(c) Since C[-1,1], we can infer that the cosine of the angle between the two vectors is within the range [-1, 1].
(iii) Adding the vectors (u + v) results in a new vector.
(iv) The magnitude of vector v, denoted as ||v||, can be found using the Pythagorean theorem.
(v) The distance between vectors u and v, represented as d(u, v), can be calculated using the formula for the Euclidean distance.
(vi) To find the magnitude of vector u - kv, we subtract kv from u and compute its magnitude using the Pythagorean theorem.

The angle between the vectors f(x) = x + 1 and g(x) = x² can be determined by finding the angle between their corresponding direction vectors. The direction vector of f(x) is (1, 1), while the direction vector of g(x) is (1, 2x). By calculating the dot product of these vectors and dividing it by the product of their magnitudes, we can find the cosine of the angle.


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Answer:

eu não entendo seu idioma vale

Answer:

1/9

Step-by-step explanation:

If it’s a negative exponents you just use the reciprocal and multiply that by the power. In this case its, 1/3(1/3)=1/9

1/9

No negative signs since it’s multiplying by the reciprocal to the power

Given a sample mean is 82, the sample size is 100, 90% confidence level and the population standard deviation is 20, the margin of error is 3.29.

To calculate the margin of error, we need to use the formula:

Margin of error = Z-score * (population standard deviation / square root of sample size)

Where the Z-score corresponds to the confidence level. Since we have a 90% confidence level, the Z-score is 1.645.

Plugging in the given values, we get:

Margin of error = 1.645 * (20 / sqrt(100))
Margin of error = 1.645 * 2
Margin of error = 3.29 (rounded to 2 decimals)

Therefore, the margin of error is 3.29.

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Answer:

$9,750.00

Step-by-step explanation:

By algebra properties, the solution to the system of linear equations is (x, y) = (1 / 3, 2 / 3).

In this problem we find a system of two linear equations with two variables, whose solution should be found. This can be done by means of algebra properties. First, write the entire system:

2 · x + 5 · y = 4

7 · x - 5 · y = - 1

Second, clear variable x in the first expression:

2 · x + 5 · y = 4

x + (5 / 2) · y = 2

x = 2 - (5 / 2) · y

Third, substitute on second expression:

7 · [2 - (5 / 2) · y] - 5 · y = - 1

Fourth, simplify the expression:

14 - (35 / 2) · y - 5 · y = - 1

14 - (45 / 2) · y = - 1

15 = (45 / 2) · y

30 = 45 · y

y = 30 / 45

y = 2 / 3

Fifth, compute the variable x:

x = 2 - (5 / 2) · (2 / 3)

x = 2 - 5 / 3

x = 1 / 3

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Answer:

Part a
\(m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}\)

\(y = \boxed{70}x\)

Part b.
The heart's resting rate is \(\boxed{70}\) beats each minute

Step-by-step explanation:

Q6

Part a

The slope-intercept form of an equation is y = mx + b

where m is the slope and b the y-intercept ie the value of y when x is 0

Here we see when x = 0, y = 0 so the value of b is 0 and the equation is simply

y = mx

To compute m, all we have to do is take 2 points on the graph, find the difference in y values(called rise) and divide by the difference in x values(called run)

This would be \(\dfrac{y2-y1}{x2-x1}\)

We are given y2 as 280(on the numerator). The corresponding x2 value from the graph is 4

We are given x1(on the denominator) as 2. The corresponding y1 value is 140 from the graph

So just fill in the missing values to get

\(m = \dfrac{280-\boxed{140}}{\boxed{4} - 2} = \dfrac{\boxed{140}}{\boxed{2}}\)

The above simplifies to 70

So the equation is

\(y = \boxed{70}x\)

Part b
The interpretation is:

The heart's resting rate is \(\boxed{70}\) beats each minute

Answer:

Y= -3x + 11

Step-by-step explanation:

Y= -3x + 11 (-3x is your slope and 11 is your y intercept)

It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.

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Answer:

The answer is below

Step-by-step explanation:

The volume of box = width * length * height

120 = x * x * y

120 = x²y

y=120/x²

The surface area (SA) = sum of the area of all faces side

SA = x² + x² + xy + xy + xy + xy

SA = 2x² + 4xy

substitute y =120/x²

SA = 2x² + 4x(120/x²)

SA = 2x² + 480/x

Taking the derivative:

SA' = 4x - 480/x²

making SA' = 0:

0 = 4x - 480/x²

480/x² = 4x

4x³ = 480

x³ = 120

x = 4.93 feet

y = 120 / x² = 120 / 4.93² = 4.93

Hence the width, length and height is 4.93 feet.

An expression which represents the perimeter of a rectangle is \(P =(36V+2w)\) centimeters.

Given the following data:

Mathematically, the perimeter of a rectangle is given by the formula;

\(P =2(L+W)\)

Where:

Substituting the parameters into the formula, we have;

\(P =2(9v+6w+(9v -5w) )\\\\P =2(9v+6w+9v-5w)\\\\P =2(18v+w)\\\\P=(36V+2w)\;centimeters\)

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the answer

155

324

5/9 (87/3(1/12)= 155/324

The team had at least one of them playing for a total of 48 minutes.

To calculate the total minutes in which at least one of them was playing, we need to consider the individual playing time and the time when they played together.

Sue played for 15 minutes, Ann played for 20 minutes, and John played for 18 minutes. This accounts for a total of 53 minutes. However, we have to subtract the time when they played together. Each pair played for 6 minutes, which means that we subtract 12 minutes from the total. Now, the combined playing time is 41 minutes.

But there's an additional factor to consider: the 5 minutes when all three of them played together. These minutes should not be subtracted, as they are part of the total playing time. Therefore, we add these 5 minutes back to the 41 minutes, resulting in a total of 46 minutes.

So far, we have accounted for the playing time of Sue, Ann, and John individually, the time when they played together in pairs, and the time when all three played together. However, we have not considered the overlapping minutes when Sue and Ann played together with John. Since each pair played together for 6 minutes, this means that Sue and Ann played with John for 6 minutes as well.

To calculate the final total, we add these 6 minutes to the previous total of 46 minutes. The team had at least one of them playing for a total of 52 minutes.

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The number of people who like a particular video online triples every day after the day the video is posted and 15 people like the video on the day it is posted.

We need to find an inequality which can be used to find the number of days, t, it takes for the number of people who have liked the video to reach more than 3000. The inequality which can be used to find the number of days, t, it takes for the number of people who have liked the video to reach more than 3000 is: 15 + 3t > 3000

The above inequality is correct because the number of people who like a particular video online triples every day after the day the video is posted. This means that on the 2nd day, 3 * 15 people like the video. On the third day, 3 * 3 * 15 people like the video, which is equal to 9 * 15 people.

Therefore, the total number of people who like the video on the 1st, 2nd and 3rd day is:

15 + 3 * 15 + 9 * 15 = 15 + 45 + 135 = 195

We can see that the number of people who like the video on the 1st day itself is only 15, which is very less. We need to get the number of people who have liked the video to reach more than 3000. Therefore, the above inequality is used.

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15) The height of the hotel is given as follows: 250 foot.

16) A reasonable estimate would be for the height of the building to be taller than the height of the tower, as it casts a larger shadow.

The height of the hotel is obtained applying the proportions in the context of the problem.

The proportions are applied by a rule of three, between the height of the building and it's shadow, as follows:

x foot - 25 feet

120 foot - 12 feet

The height of the building is the height of the shadow multiplied by 10, hence the height is given as follows:

25 x 10 = 250 foot.

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Answer:

x = -1/2

Step-by-step explanation:

4x^2 + 4x + 1 = 0

Factor

(2x+1)(2x+1) =0

Using the zero product property

2x+1 = 0 2x+1 =0

2x = -1  2x=-1

x = -1/2   x = -1/2

An angle in standard position is an angle whose vertex is at the origin and whose initial side is along the positive x-axis. An angle of 180° is a straight angle, which means that it measures 180 degrees.

To sketch an angle of 180° in standard position, we start by drawing a ray along the positive x-axis. Then, we rotate the ray 180° counterclockwise. The terminal side of the angle will then lie along the negative x-axis.

As you can see, the angle starts at the origin and rotates 180° counterclockwise. The terminal side of the angle lies along the negative x-axis.

Note that an angle of 180° can also be written as -180°. This is because angles can be measured in positive or negative degrees, and a positive angle of 180° is the same as a negative angle of -180°.

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Answer:

Try 150

Step-by-step explanation:

I'm not sure but it might work.

Answer:

150

Step-by-step explanation:

180-30 = 150 degrees

The probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes is 2/1 or simply 1, which means it is certain that the cycle time exceeds 60 minutes if it exceeds 55 minutes.

Given that the cycle time for trucks hauling concrete to a highway construction site is uniformly distributed over the interval 50 to 70 minutes, we know that the probability density function is:

f(x) = 1 / (70 - 50) = 1/20, for 50 <= x <= 70

To find the probability that the cycle time exceeds 60 minutes given that it exceeds 55 minutes, we need to use conditional probability:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

We can simplify this by noticing that if X is greater than 55, then it must be between 55 and 70, and therefore:

P(X > 55) = P(55 <= X <= 70) = (70 - 55) / (70 - 50) = 1/4

Similarly, we can rewrite the numerator as:

P(X > 60 and X > 55) = P(X > 60)

since if X is greater than 60, it is also greater than 55.

Now, to find P(X > 60), we integrate the density function from 60 to 70:

P(X > 60) = ∫60^70 (1/20) dx = (1/20) × (70 - 60) = 1/2

Putting it all together:

P(X > 60 | X > 55) = P(X > 60 and X > 55) / P(X > 55)

= P(X > 60) / P(X > 55)

= (1/2) / (1/4)

= 2

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Answer:

Thomas draws a triangle with side lengths of 5 centimeters and 12 centimeters and one angle of 90°.  The length of the longest side of the triangle is not known.

How many different triangles can be drawn with these dimensions? Explain your reasoning.

Step-by-step explanation:your weclome

The number of triangles that can be drawn with these dimensions will be one.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Thomas draws a triangle with side lengths of 5 centimeters and 12 centimeters and one point of 90° The length of the longest side of the triangle isn't known.

The longest side of the triangle is given as,

H² = P² + B²

H² = 12² + 5²

H² = 144 + 25

H² = 169

H = 13 cm

If the three dimensions of the triangle are known, then the number of possible triangles is only one.

The number of triangles that can be drawn with these dimensions will be one.

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Answer:

4 roots: 2 , -3, 1+√2, 1 - √2

Step-by-step explanation:

x⁴ − x³ − 9x² + 11x + 6 = 0    leading: 1 (x⁴)    Trailing: 6 (1,2,3,6)

possible roots: trailing/leading (±1 , ±2, ±3, ±6)

Test: x = 2     (2)⁴ - (2)³ - 9*(2)² + 11*(2) + 6 = 0

        x = -3    (-3)⁴ - (-3)³ - 9*(-3)² + 11*(-3) + 6 = 0

By rational roots test: possible roots (x-2)(x+3) are factors

Long division:  (x⁴ − x³ − 9x² + 11x + 6) / (x-2)(x+3) = x²-2x-1

roots of x²-2x-1: x= (-b±√b²-4ac) / 2a

x = (2 ± √4+4) / 2 = (2 ± 2√2) / 2 = 1 ± √2

Hey there!

The answer to your question is, yes, it is

Given:

\(\frac{8}{5}\) \(and\) \(\frac{24}{15}\)

To see if they are equal, we can use cross products (see below for information about this, if you don't know what it is). Let us assume they are equal. This would mean that:

\(8*15=24*5\)

Let's solve it and see if it is true:

\(8*15=24*5\)

\(120=120\)

Therefore, they are proportional.

Cross products

WORD DEFINITION:

Given two fractions, you can take the numerator of the first fraction multiplied by the denominator of the second fraction and it should equal the denominator of the first fraction multiplied by the numerator of the second fraction.

ALGEBRAIC DEFINITION:

Given two fractions, \(\frac{a}{b}\) \(and\) \(\frac{c}{d}\), \(a*d\) should equal to \(b*c\)

Hope it helps, and have a terrificly amazing day!

Answer:

2.63274768567

Step-by-step explanation:

First, note that 3.1415... is p, so 2(3.1415...) is 2pi and 4(3.1415...) is 4pi.

2pi and 4pi are full rotations, which will lead to the same cosine (i.e. cos(x) = cos (x+2pi) = cos(x+4pi) = ... = cos (x+2k*pi)).

So, the expression equals cos0.5 + cos 0.5 + cos0.5 = 3cos0.5 = 3(0.87758256189) = 2.63274768567

I hope this helps! :)

Answer:

a.) perimeter: 48 yards      area: 96 sq. yds

b.) perimeter: 39 feet     area: 74.36 ft. sq.

Step-by-step explanation:

a.) perimeter: 16 + 20 + 12 = 48          area: height * base / 2 = 96

b.) perimeter: (14.3 * 2) + (5.2 * 2) = 39        area: Length * Width = 74.36

Answer:

Area = 96 yd

Perimeter = 48 yd,

Area = 74.36 yd

Perimeter = 39 yd

Step-by-step explanation:

so the probability will be: p(red)=2652=0.5 or 50% as we could guess immediatelly.

(a) The time (in h) will the plane take to reach the city is 7.09 hours or 7.1 hours.

(b) The plane flies through a constant tailwind blowing at 53.5 km/h, the time (in h) will it take to reach the city is 3.58 hours or 3.6 hours.

(c) The plane flies through a constant crosswind blowing east at 53.5 km/h, the time (in h) will it take to reach the city is infinite.

(a) To find the time it will take for the plane to reach the city with a headwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by subtracting the speed of the headwind from the plane's airspeed.

Ground speed = Airspeed - Headwind speed

Ground speed = 163 km/h - 53.5 km/h

Ground speed = 109.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 109.5 km/h

Time = 7.09 hours or 7.1 hours

(b) To find the time it will take for the plane to reach the city with a tailwind, we need to first find the plane's ground speed. The ground speed is the speed of the plane relative to the ground. We can find the ground speed by adding the speed of the tailwind to the plane's airspeed.

Ground speed = Airspeed + Tailwind speed

Ground speed = 163 km/h + 53.5 km/h

Ground speed = 216.5 km/h

Now that we know the ground speed, we can use the formula:

Time = Distance ÷ Speed

Time = 776 km ÷ 216.5 km/h

Time = 3.58 hours or 3.6 hours

(c) To find the time it will take for the plane to reach the city with a crosswind, we need to first find the component of the crosswind that is perpendicular to the plane's direction of travel. This component will not affect how long it takes for the plane to reach its destination.

Component of crosswind = Crosswind speed × sin(angle between direction of travel and crosswind)

Component of crosswind = 53.5 km/h × sin(90°)

Component of crosswind = 53.5 km/h

Now we can find the ground speed of the plane relative to its direction of travel:

Ground speed = Airspeed × cos(angle between direction of travel and crosswind)

Ground speed = 163 km/h × cos(90°)

Ground speed = 0 km/h

Since the ground speed is 0 km/h, the plane will not make any progress towards its destination. Therefore, it will take an infinite amount of time to reach the city with a crosswind.

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