determine the number of linearly independent vectors needed to span m2,3. the basis for m2,3 has linearly independent vectors.

There are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

The multiplication principle states that if there are m ways to perform one task and n ways to perform another task, then there are m x n ways to perform both tasks together.

To find the number of ways to choose 3 men from the 12 men, we can use the formula for combination, which is: ⁿCᵣ = n! / (r! (n-r)!).

where n is the total number of men and r is the number of men chosen

so, the number of ways to choose 3 men from the 12 men = ¹²C₃ = 1.

Similarly, we evaluate the number of ways to choose 2 women from the 8 women

as = ⁸C₂ = 14

Now, using the multiplication principle, we can find the total number of ways 3 men and 2 women be chosen if they are equally considered.

220 x 14 = 3080

Therefore, there are 3080 ways 3 men and 2 women can be chosen if they are equally considered, using the multiplication principle of counting

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Answer:

1

Step-by-step explanation:

\(\\ \sf\longmapsto 3x-8=-2x+\dfrac{9}{3}\)

\(\\ \sf\longmapsto 3x-8=-2x+3\)

\(\\ \sf\longmapsto 3x+2x=3+8\)

\(\\ \sf\longmapsto 5x=11\)

\(\\ \sf\longmapsto x=\dfrac{11}{5}\)

Answer: false

Step-by-step explanation:

To evaluate the integral ∫tan^4(x) cos^5(x) dx, we can use trigonometric identities to simplify the integrand.

We'll use the power-reducing formula for tan^4(x) and the power-reducing formula for cos^5(x) to simplify the integrand:

∫tan^4(x) * cos^5(x) dx

= ∫(tan^2(x))^2 * (cos^2(x))^2 * cos(x) * cos^2(x) dx

= ∫[(sec^2(x) - 1)^2] * [(1 - sin^2(x))^2] * cos(x) * cos^2(x) dx

Expanding the square terms, we get:

= ∫[(sec^4(x) - 2sec^2(x) + 1)] * [(1 - 2sin^2(x) + sin^4(x))] * cos(x) * cos^2(x) dx

Multiplying the terms together, we have:

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

Now, let's integrate each term separately:

∫sec^4(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 + u^2)^2 * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(1 + 2u^2 + u^4 - u^4 - u^6) du

= u + 2/3 u^3 + 1/5 u^5 - 1/7 u^7 + C

Substituting back u = sin(x), we have:

= sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x) + C

∫-2sec^2(x) * cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫-2(1 + u^2) * (1 - u^2) du

Expanding the expression and integrating, we get:

= ∫(-2 + 2u^2 - 2u^2 + 2u^4) du

= -2u + 2/3 u^3 - 2/5 u^5 + 2/7 u^7 + C

Substituting back u = sin(x), we have:

= -2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x) + C

∫cos^3(x) dx:

Using the substitution u = sin(x), we have:

∫(1 - u^2) du

Integrating, we get:

= u - 1/3 u^3 + C

Substituting back u = sin(x), we have:

= sin(x) - 1/3 sin^3(x) + C

Putting it all together, the complete result of the integral is:

∫tan^4(x) * cos^5(x) dx

= ∫[sec^4(x) - 2sec^2(x) + 1 - 2sin^2(x) + 4sin^4(x) - 2sin^6(x)] * cos^3(x) dx

= ∫sec^4(x) *

cos^3(x) dx - 2∫sec^2(x) * cos^3(x) dx + ∫cos^3(x) dx

= (sin(x) + 2/3 sin^3(x) + 1/5 sin^5(x) - 1/7 sin^7(x)) - 2(-2sin(x) + 2/3 sin^3(x) - 2/5 sin^5(x) + 2/7 sin^7(x)) + (sin(x) - 1/3 sin^3(x)) + C

= sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

Therefore, the final result is:

∫tan^4(x) * cos^5(x) dx = sin(x) + 4/3 sin^3(x) - 8/5 sin^5(x) + 20/7 sin^7(x) + C

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To determine which independent variables are significantly related to traffic at the .05 level of significance, you would need to perform a statistical test such as regression analysis.

In a regression analysis, each independent variable is tested to see if it has a statistically significant relationship with the dependent variable (traffic in this case) at a given level of significance (in this case, 0.05).

Here are the steps to perform regression analysis and determine the significant independent variables:

1. Gather your data: Collect data on the dependent variable (traffic) and the independent variables of interest.

2. Choose a regression model: Select the appropriate regression model based on the nature of your data and research question. Common regression models include linear regression, multiple regression, logistic regression, etc.

3. Run the regression analysis: Input your data into the chosen regression model and run the analysis. The output will provide you with coefficients and p-values for each independent variable.

4. Interpret the results: Look at the p-values associated with each independent variable. The p-value represents the probability of observing a relationship as strong as the one found in the sample, assuming there is no true relationship in the population. A p-value less than the chosen level of significance (in this case, .05) indicates a significant relationship between the independent variable and the dependent variable.

5. Identify the significant independent variables: If the p-value for an independent variable is less than .05, then that independent variable is considered significantly related to traffic at the .05 level of significance.

Therefore, to determine which independent variables are significantly related to traffic at the .05 level of significance, you would need to perform a regression analysis and examine the p-values associated with each independent variable.

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Answer: $30

Step-by-step explanation:

Your question isn't well written. Here's the complete question:

Susan buys the item listed below at a grocery store. 2 packages of chicken priced at $12.36 per package. 1/2 pound of broccoli priced at $1.98 per pound. 1gallon of milk priced at $3.49 per gallon. There is no sales tax on the food she buys. Susan pays for the items and recevies $0.80 in change. What amount of money does Susan use to pay for the items?

2 packages of chicken priced at $12.36 per package will cost:

= 2 × $12.36

= $24.72

1/2 pound of broccoli priced at $1.98 per pound will cost:

= 1/2 × $1.98

= $0.99

1 gallon of milk priced at per $3.49 per gallon will be:

= 1 × $3.49

= $3.49

We are then told that Susan pays for the items and receives $0.80 in change. The amount of money does Susan use to pay for the item will be:

= $24.72 + $0.99 + $3.49 + $0.80

= $30

Answer:

a=11

Step-by-step explanation:

So, the line that (9a+6) and 75 are sharing is straight, meaning that it is 180 degrees. Also, (9a+6) and 75 are sharing the line. Even though we don't know there exact measurements, when know that by adding them together we will get 180 degrees.

1. (9a+6) + 75 = 180

2. 9a + 81 = 180

3. 9a = 99

4. a = 11

Hope this helped!

Answer:

(0, 1)

Step-by-step explanation:

So, the spot on the graph where they cross.

Answer:

the Solution is 0,1

Step-by-step explanation:

Because the place where the two lines intersect are the two numbers that are the answer to the system.

The cost of 11 cans of dog food will be equal to $10.12.

What is unitary method ?

The unitary method is a method in which , you first determine the value of a single unit before determining the value of the required quantity of units.

It is given that the cost of 20 cans of dog food at store B is $18.40.

We need to find cost of 1 can of dog food and that can be calculated by dividing the cost of cans of dog food by total no. of cans.

i.e.,

Cost of 1 can of dog food = $ 18.40 ÷ 20

So ,

The cost of 1 can of dog food will be :

= $0.92

Now , the cost of 11 cans of dog of food will be calculated by multiplying cost of 1 can of food to 11 cans of dog food which will be :

= 11 × $ 0.92

= $10.12

Therefore , the cost of 11 cans of dog food will be equal to $10.12 .

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Her rate at the end of the summer is 20 miles per hour.

We can define the rate in this case as the change in position as a function of the time.

So, the rate would be something like a speed (exactly a speed, actually).

Initially, the camper travles at a rate of 10mi/h in 2 hours, so the total distance is:

d = (10mi/h)*2h = 20mi

And at the end of the sumer, the camper travels that distance in one hour, so the rate at the end of the summer is:

R = 20mi/1h = 20mi/h

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The area of a shape is the amount of space it occupies

The area of the regular pentagon is 58.1 square centimeters

The given parameters are:

\(a = 4cm\) -- the apothem

\(l = 5.81cm\) --- the side length

\(n=5\) --- the number of sides of a pentagon

The area (A) of the pentagon is then calculated using:

\(A = \frac {nal}2\)

This gives

\(A = \frac {5 \times 4cm \times 5.81cm}2\)

Divide 4 cm by 2

\(A = 5 \times 2cm \times 5.81cm\)

Multiply the factors

\(A = 58.1cm^2\)

Hence, the area of the regular pentagon is 58.1 square centimeters

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There is a 20 percent chance the relationship being studied is real.  Option D

If a study shows a result with a P value of 0.2, it means that there is a 20 percent chance that the observed relationship being studied is due to random chance or sampling variability.

In other words, the P value represents the probability of obtaining a result as extreme as, or more extreme than, the observed result if the null hypothesis were true.

The null hypothesis assumes that there is no real relationship or effect in the population being studied. The alternative hypothesis, on the other hand, suggests that there is a real relationship or effect. The P value helps determine the strength of evidence against the null hypothesis.

A P value of 0.2 means that if the null hypothesis were true (i.e., there is no real relationship), there would be a 20 percent chance of obtaining a result as extreme as, or more extreme than, the observed result by random chance alone.

This implies that the observed result is not statistically significant at conventional levels of significance (typically set at 0.05 or 0.01), which means there is not enough evidence to reject the null hypothesis.

Therefore, the correct answer is (D) There is a 20 percent chance the relationship being studied is real. It's important to note that the P value does not directly indicate the probability of the relationship being true or real, but rather the probability of obtaining the observed result under the assumption of no relationship. Option D

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Answer:

d

Step-by-step explanation:

Answer:

1. Angle forming a linear pair sum to 180°

2. Transitive property of equality

3. Algebra

4. Definition of congruency

Step-by-step explanation:

The given statement and reasons are presented as follows;

Statement      \({}\)                          Reason

1. m∠GKH + m∠HKI = 180°    \({}\) 1. Angle forming a linear pair sum to 180°

m∠HKI + m∠IKJ = 180°

2. m∠GKH + m∠HKI = m∠HKI + m∠IKJ \({}\)2. Transitive property of equality

3. m∠GKH = m∠IKJ  \({}\)              3. Algebra

4. m∠GKH ≅ m∠IKJ               4. Definition of congruency

The explanation are;

1. The sum of angles on a straight line is 180°

2. The transitive property of equality can be written as follows;

Given a = c and b = c, therefore, a = b

3. The addition property of equality states that given a + b = c + b, therefore a = c

4. Two geometric figures are said to be congruent when they are equal.

The angles in the range 0≤θ<360 that satisfy the equation sin(θ)=-4/7 are approximately θ1 = 214.8° and θ2 = 325.2°.

1. Identify the given value: sin(θ) = -4/7.
2. Determine the reference angle: arcsin(4/7).
3. Find the angles in the range 0≤θ<360 that have the same sine value but with a negative sign.
4. Round the angles to the nearest 10th of a degree.
1. The given value is sin(θ) = -4/7.
2. To find the reference angle, we take the arcsin of the absolute value of the given sine value: θ' = arcsin(4/7) ≈ 34.8°.
3. Since the sine value is negative, we need to find angles in the 3rd and 4th quadrants.

To do this, we subtract the reference angle from 180° and add it to 180°:
  - 3rd quadrant: θ1 = 180° + 34.8° ≈ 214.8°
  - 4th quadrant: θ2 = 360° - 34.8° ≈ 325.2°
4. The angles are already to the nearest 10th of a degree.

Summary:
The angles in the range 0≤θ<360 that satisfy the equation sin(θ)=-4/7 are approximately θ1 = 214.8° and θ2 = 325.2°.

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Answer:

about 17.21 feet

Step-by-step explanation:

Set your calculator to degree mode.

The figure is omitted--please sketch it to confirm my answer.

\( \sin(73) = \frac{h}{18} \)

\(h = 18 \sin(73) = 17.21\)

The coordinates of an undefined slope are points that are either the same or have no x-value. In both cases, the slope of a line between these points would be undefined because it would involve dividing by 0, which is not allowed in mathematics. This is because the slope of a line is calculated by dividing the difference in y-coordinates by the difference in x-coordinates, and if the x-coordinates are the same or do not exist, this division would result in an undefined value.

The surface area of the complex shape in the image shown is calculated as: 508 ft².

To Find the Surface Area of the Complex Shape, decompose the shape into two rectangular prism.

Rectangular prism 1 dimensions would be:

Length = 12 ft

Width = 5 ft

Height = 7 ft

Surface area (SA) = 2(wl + hl + hw)

= 2·(5·12 + 7·12 + 7·5) = 358 ft²

Rectangular prism 2 dimensions would be:

Length = 12 - 7 = 5 ft

Width = 5 ft

Height = 12 - 7 = 5 ft

Surface area (SA) = 2(wl + hl + hw)

= 2·(5·5 + 5·5 + 5·5) = 150 ft²

Therefore, surface area of the complex shape = 358 + 150 = 508 ft².

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Answer:

43 minutes

Step-by-step explanation:

Equations as per given, considering same distance in both cases:

We see that driving speed is 3 times greater than cycling speed

Then 8 minutes driving = 8*3= 24 minutes of cycling, or 10 minutes of driving = 10*3= 30 minutes of cycling:

0 ≤ x < 2, where x is an integer. Option C

The appropriate domain for the function f(x) = 42 - 15x in the given context can be determined by considering the constraints of the problem.

Tyson has a $50 gift card, and he wants to purchase a belt that costs $8 and x number of shirts that cost $15 each. The function f(x) represents the balance on the gift card after Tyson makes the purchases.

The number of shirts Tyson can purchase depends on the remaining balance on the gift card. Since each shirt costs $15, the maximum number of shirts he can buy is limited by the amount of money left on the gift card.

If we subtract the cost of the belt ($8) and the cost of x shirts ($15x) from the initial balance ($50), we should get a non-negative result, indicating that Tyson has enough money on the gift card to make the purchases.

Therefore, we can set up the inequality:

50 - 8 - 15x ≥ 0

Simplifying, we have:

42 - 15x ≥ 0

Now, we can solve for x:

-15x ≥ -42

Dividing by -15 (remembering to flip the inequality sign), we get:

x ≤ 42/15

x ≤ 2.8

Since x represents the number of shirts Tyson can buy, it should be a whole number. Therefore, the appropriate domain for the function f(x) is:

0 ≤ x ≤ 2, where x is an integer.

Option C.

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The equation of the line passing through the points (-3, -5) and (6, 1) can be expressed in the form y = (2/3)x - 3.

The equation of the line passing through the points (-3, -5) and (6, 1) can be expressed in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.

To find the slope of the line, we can use the formula:

\(m = (y2 - y1) / (x2 - x1)\)

Let's substitute the coordinates of the given points into the formula:

\(m = (1 - (-5)) / (6 - (-3))m = 6 / 9m = 2/3\)

So, the slope of the line is 2/3.

Now, let's find the y-intercept (b) by substituting the coordinates of one of the points into the equation y = mx + b. Let's use the point (-3, -5):

-5 = (2/3)(-3) + b

-5 = -2 + b

b = -5 + 2

b = -3

Therefore, the equation of the line passing through the points (-3, -5) and (6, 1) can be expressed in the form y = (2/3)x - 3.

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We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

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Answer:

y = -3x - 1

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Point (-1, 2) (1, -4)

We see the y decrease by 6 and the x increase by 2, so the slope is

m = -6 / 2 = -3

Y-intercept is located at (0, - 1)

So, the equation is y = -3x - 1

Based on the completed table, the 35th percentile is 43 and the 90th percentile is approximately 66.88.

The completed table is given below:

Class Interval | Frequency | Lower Class Boundary | Cumulative Frequency

91-100 | 8 | 91 | 8

81-90 | 7 | 81 | 15 (8 + 7)

71-80 | 1 | 71 | 16 (15 + 1)

61-70 | 4 | 61 | 20 (16 + 4)

51-60 | 9 | 51 | 29 (20 + 9)

41-50 | 17 | 41 | 46 (29 + 17)

31-40 | 5 | 31 | 51 (46 + 5)

21-30 | 6 | 21 | 57 (51 + 6)

To solve for the 35th and 90th percentiles, we will use the cumulative frequency column in the completed table.

35th Percentile:

The 35th percentile represents the value below which 35% of the data falls.

The cumulative frequency of 35 is between the class intervals "31-40" and "41-50."

Let's calculate the 35th percentile using linear interpolation:

Lower class boundary of the interval containing the 35th percentile = 31

Cumulative frequency of the previous class = 29

Frequency of the class interval containing the 35th percentile = 5

Formula for linear interpolation:

Percentile = Lower class boundary + (Percentile rank - Cumulative frequency of the previous class) * (Class width / Frequency)

Percentile = 31 + (35 - 29) * (10 / 5) = 31 + 6 * 2 = 31 + 12 = 43

90th Percentile:

The 90th percentile represents the value below which 90% of the data falls.

The cumulative frequency of 90 is between the class intervals "41-50" and "51-60."

Let's calculate the 90th percentile using linear interpolation:

Lower class boundary of the interval containing the 90th percentile = 41

Cumulative frequency of the previous class = 46

Frequency of the class interval containing the 90th percentile = 17

Percentile = 41 + (90 - 46) * (10 / 17) ≈ 41 + 44 * (10 / 17) ≈ 41 + 25.88 ≈ 66.88

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The standard deviation for the binomial distribution with n trials and success probability p is given by the formula σ = sqrt(np(1-p)).

In this case, n = 48 and p = 3/5. Plugging these values into the formula, we get σ = sqrt(48*(3/5)*(2/5)) ≈ 3.05. Therefore, the standard deviation for this binomial distribution is approximately 3.05.

The standard deviation measures the spread of a distribution. In the case of a binomial distribution, it tells us how much the number of successes varies around the mean. A smaller standard deviation indicates that the distribution is more concentrated around the mean, while a larger standard deviation indicates that the distribution is more spread out. In this case, the standard deviation of approximately 3.05 means that the number of successes is likely to vary by about 3 around the mean, which is np = 28.8.

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For part a, we know that b = ac - 1. We can rewrite this equation as ac = b + 1. So, all vectors of the form (a, b, c) can be written as (a, b, (b + 1)/a).

For part b, we are given that c = 0. So, all vectors of the form (a, b, 0) can be written simply as (a, b, 0).
For part c, we are given that ab = 7. So, all vectors of the form (a, b, c) for which ab = 7 can be written as (a, b, 7/a).
a. All vectors of the form (a, b, c), where b = a c 1:
These vectors are represented as (a, a*c + 1, c). To create such a vector, you can choose any values for 'a' and 'c', and then calculate the value of 'b' by using the given formula (b = a*c + 1).
b. All vectors of the form (a, b, 0):
These vectors are represented as (a, b, 0). To create such a vector, you can choose any values for 'a' and 'b', and the third component 'c' will always be 0.
c. All vectors of the form (a, b, c) for which a b = 7:
These vectors satisfy the condition a*b = 7. To create such a vector, you can choose any values for 'a' and 'b' that satisfy this equation (for example, a=1 and b=7, or a=7 and b=1), and then choose any value for 'c'. The resulting vector will be of the form (a, b, c).

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The greatest vertical length of the green section should be approximately 3.52 feet.

To determine the greatest vertical length of the green section, we can use the given information that the greatest horizontal length of the green section is 8.8 feet.

Since the ratio of the line segment is 5:2, we can set up a proportion using the horizontal and vertical lengths of the green section:

(horizontal length of green section) / (vertical length of green section) = (5/2)

Let's denote the greatest vertical length of the green section as y. We can rewrite the proportion as:

8.8 / y = 5 / 2

To solve for y, we can cross-multiply and then divide:

8.8 * 2 = 5 * y

17.6 = 5y

Dividing both sides by 5, we get:

y = 17.6 / 5

y ≈ 3.52 feet

Therefore, the greatest vertical length of the green section should be approximately 3.52 feet.

It's important to note that this calculation assumes a linear relationship between the horizontal and vertical lengths of the green section. If there are other factors or constraints involved in the scenario, such as angles or specific geometric properties, a more detailed analysis may be required to determine the exact vertical length.

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Answer:

Segment pr

Step-by-step explanation: hope this helps

By using function, it can be calculated that

The value of f(8, 9) is 73

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the function is

f(a, b) = ab - (a - b)

f(8, 9) = 8 \(\times\) 9 - (8 - 9)

f(8, 9) = 72 + 1

f(8, 9) = 73

So the value of f(8, 9) is 73

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