Determine whether the set S spans R2. If the set does not span R2, then give a geometric description of the subspace that it does span.
S = {(-1, 2), (2, -1), (1, 1)}
A. S spans R2.
B. S does not span R2. S spans a line in R2.
C. S does not span R2. S spans a point in R2.

The coordinate of P that divides line AB in the ratio 4:1 is (6.6, 3.8)

An equation is an expression that shows the relationship between numbers and variables.

If a point O(x, y) divides line segment AB with endpoints A(x₁, y₁) and B(x₂, y₂) in the ratio of n:m. The coordinates of O is:

[tex]x = \frac{n}{n+m}(x_2-x_1)+x_1 \\\\y = \frac{n}{n+m}(y_2-y_1)+y_1[/tex]

Given that P(x, y) divides line AB in the ratio 4:1. The coordinates are A(1, 3) and B(8, 4). Therefore:

[tex]x=\frac{4}{4+1}(8-1) +1=6.6\ unit\\\\y=\frac{4}{4+1}(4-3) +3=3.8\ unit[/tex]

The coordinate of P is (6.6, 3.8)

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Answer:

Part a: Answer is 1/2

78-3/1500 = 75/150

= 1/2

Part b: Answer is -1/2

3-78/300-150

=-75/150

= -1/2

Part c: No, the two rates aren't the same,

because one is positive and the other is

negative.

Part d: The rate of change of the function

determined by using the two pairs of

coordinates is not the same. So, the

function modeling the movement of the

ball is a nonlinear function

The ordered pair that lies on the graph of the equation is (1, 2)

From the question, we have the following parameters that can be used in our computation:

y = 2x

The point in the ordered pair lies on the graph of the equation is the solution set

Take for instance, we set x = 2

So, we have

y = 2 * 1

Evaluate the product

This gives

y = 2

When repesented as an ordered pair, we have

(1, 2)

Hence, the point is (1, 2)

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Answer: the diameter of the circle is about 19.8

Step-by-step explanation:

Since the length of the square is 14 units, we can use the Pythagorean theorem to find the diagonal:

14^2 + 14^2 = c^2

196 + 196 =c^2

392 = c^2

c = about 19.8

Answer:

19.8

Step-by-step explanation:

The diameter of the base of the cylinder is equal to the diagonal of the inscribed square and is equal to the hypotenuse of an equilateral triangle into which the square is divided by diagonals ... By the Pythagorean theorem, the diameter (hypotenuse) is equal to the square root of the sum of the squares of the legs and is equal to 19.8

Answer: Let's call the price of an advance ticket "a" and the price of a same-day ticket "s". We know that the combined cost of one advance ticket and one same-day ticket is 60, so we can set up the equation: a + s = 60.

We also know that 40 advance tickets and 15 same-day tickets were sold for a total of 1400 dollars. So we can set up the equation: 40a + 15s = 1400

We have a system of two equations with two variables. We can use substitution or elimination method to solve for the unknowns.

Using substitution:

Solve the first equation for s, s=60-a

substitute it into the second equation, 40a + 15(60-a) = 1400

Expanding the second equation: 40a + 900 - 15a = 1400

25a = 500

a = 20

substitute a back into the first equation: s = 60 - 20 = 40

So the price of an advance ticket is $20, and the price of a same-day ticket is $40.

Step-by-step explanation:

When Jeremy's sample is being compared to the sample collected by Morgan and Maddy by the left, about 6 Jeremy samples ranges from 81-10 while only 2 samples ranges from 81-100 in Morgan's and Maddy's.

A histogram is defined as one of the graphical way of representation of data for an easy analysis, comparison and interpretation of results.

From the two histogram given above, the comparison of both results shows that about 6 Jeremy samples ranges from 81-10 while only 2 samples ranges from 81-100 in Morgan's and Maddy's.

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Answer:

6

Step-by-step explanation:

since x=8, 8-2 equals 6

The probability (a) 6! ways; (b) 3! ways; (c) 3!2! ways. 6! = 6 x 5 x 4 = 120, 3! = 3 x 2 x 1 = 6, 3!2! = 3 x 2 x 1 x 2 x 1 = 12.

(a) In this instance, the three novels, two volumes on mathematics, and one book on chemistry can be arranged on the bookshelf in any sequence. By multiplying the number of things in each category, you can arrive at the answer: 3 novels x 2 math books x 1 chemistry book = 6. These things can be arranged in 6! (6 factorial) different ways, which is equal to 120 when multiplied by 6 x 5 x 4.

(b) In this instance, both the novels and the mathematical books must be in the same location. You can figure this out by multiplying the number of things in each category; for example, 3 novels times 1 collection of math books is 3. These things can be arranged in 3! (3 factorial) different ways, which is equal to 3 x 2 x 3.

(c) The other books may be put in any sequence, but the novels in this instance must be together. By multiplying the amount of items in each category, you can arrive at the answer: 3 novels x 2 math books and 2 x 2 chemistry books = 6. These objects can be arranged in 3!2! (3 factorial x 2 factorial) ways, which is equal to 12 when multiplied by 3 x 2 x 1 x 2 x 1.

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The perimeter of a rectangle can be represented by a polynomial expression. The expression will consist of two terms, one representing the width and one representing the length. Each term will contain a variable, which is to the power of one, multiplied by a coefficient. The sum of the two terms produces the perimeter of the rectangle.

For example, if the width of the rectangle is w and the length is l, then the polynomial expression for the perimeter would be: P = w + l. This expression can also be written in expanded form as: P = w + w + l + l.

By adding more terms to this polynomial expression, the perimeter of more complex rectangles can be found. For example, if the rectangle is not a perfect square, then two additional terms can be added to the polynomial expression. One term will represent the extra width and one term will represent the extra length. By adding these two additional terms, the perimeter of the rectangle can be calculated.

In conclusion, the perimeter of a rectangle can be represented as a polynomial expression, which consists of terms that have variables raised to the power of one and are multiplied by coefficients. By adding more terms to the expression, the perimeter of more complex rectangles can be found.

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Based on the information provided, Mason can cut four pieces of ribbon.

Based on the information provided, Mason has 2/3 of a foot ribbon, which is equivalent to 0.66.

To know the answer, use a division with the following formula:

Total ribbon/ size of the desired pieces

0.66 / 2/3 or 0.166 (2/3 = 0.166)

0.66 / 0.166

4 pieces

Based on this, it can be concluded that Mason will be able to get 6 1/6 feet long pieces.

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The value of x and y in the parallel lines are 14 and 60 respectively.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate exterior angles, alternate interior angle, linear angles, vertically opposite angles etc.

Therefore, let's find the values of x and y in the parallel lines as follows:

4x + 12 = 68 (vertically opposite angles)

Vertically opposite angles are congruent.

Hence,

4x + 12 = 68

4x = 68 - 12

4x = 56

divide both sides by 4

x = 56 / 4

x = 14

Therefore, let's find the value of y.

68 + 2y - 8 = 180(same side interior angles)

Same side interior angles are supplementary

68 + 2y - 8 = 180

2y = 180 - 68 + 8

2y = 120

y = 120 / 2

y = 60

Therefore,

x = 14

y = 60 degrees

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The total number of elephants in the herd is 24.

This is a math problem that can be solved using algebra. To start, let x be the total number of elephants in the herd.

From the first part of the problem, we know that:

x/3 = a herd of elephants seen on a mountain slope

From the second part of the problem, we know that:

3 * √(x - x/3) = a herd of elephants seen on a mountain slope

From the third part of the problem, we know that:

1 + 3 = 4 = the ultimate remainder of the herd seen in a lake.

We can then use these equations to solve for x.

x/3 + 3 * √(x - x/3) + 4 = x, where x is the total number of elephants in the herd.

x = 3 * (1 + √(x - x/3) + 4)

Solving for x, we get x = 24

So, the total number of elephants in the herd is 24.

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Answer:

C)  30 and 38

Step-by-step explanation:

In a normal distribution, 95% of the data points fall within two standard deviations of the mean.

Given:

To find the two values between which 95% of the data lies, subtract and add two standard deviations to the mean:

⇒ μ - 2σ = 34 - 2(2) = 34 - 4 = 30

⇒ μ + 2σ = 34 + 2(2) = 34 + 4 = 38

Therefore, 95% of the data lies between the values:

The Maximum value of the function is  5.71 and the Minimum value of the function is  -2.71. To find the maximum and minimum values of the function y=3x-4sin3x, 0x2π, we used a graphing calculator.

first, we set the range of x from 0 to 2π and graphed the function. By looking at the graph, I could identify the maximum and minimum values of the function. The maximum value was 5.71 and the minimum value was -2.71. This can be seen at the peak and trough of the graph respectively.   I then used the calculator to find the exact values of the maximum and minimum.

To do this, I used the 'maximum' and 'minimum' functions on the graphing calculator. This allowed me to input the function and the range of x and the calculator was able to output the exact maximum and minimum values. The output was 5.71 and -2.71.   The calculator used was able to identify the maximum and minimum values of the function by using a process called calculus.

Calculus is the study of how functions change and by using the maximum and minimum functions, the calculator can identify the peak and trough of the graph.

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Answer:

$4,200,000

Step-by-step explanation:

let x = total sales

(1/6)x = 700,000

x = 700,000(6/1) = 4,200,000

**dividing by 1/6 is the same as multiplying by 6

No, there is not. We do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

To test the hypothesis that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000, we can use a two-proportion z-test. The null hypothesis is that the proportion of U.S. adults who are aware of the investment's outcome is equal to or greater than 40%, and the alternative hypothesis is that the proportion is less than 40%.

The test statistic is calculated as:

z = (p1 - p2) / √(p(1-p)(1/n1 + 1/n2))

where p1 is the proportion of U.S. adults in the sample who are aware of the investment's outcome (374/1010), p2 is the proportion assumed in the null hypothesis (0.4), and n1 and n2 are the number of observations in the sample and population, respectively.

Using these values, the test statistic is:

z = (0.369 - 0.4) / √(0.4(1-0.4)(1/1010)) = -1.08

Using a two-sided test with a significance level of 0.05, we can look up the critical value in a standard normal table or using software and find that the critical value is ±1.96. Since -1.08 is between -1.96 and 1.96, we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that less than 40% of U.S. adults are aware that such an investment would result in a sum of over $100,000.

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the probability exactly five heads may be obtained is 77%.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

twelve people each spin a coin.

n = number of trials = 12

x = number of successes(head) among n trials = 5

p = probability of success(head) in any one trial = 1/2

probability of failure in any one trial (q = 1 - p) = 1/2

exactly five heads may be obtained 12 C 5 * (1/2)[tex].{5}[/tex] *(1/2)[tex].{5}[/tex] = 792/1024 =0.77

Hence the probability exactly five heads may be obtained is 77%.

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The quote that "Human beings only use ten percent of their brains. Ten percent! Can you imagine how much we could accomplish if we used the other sixty percent?" was made by Ellen DeGeneres.

The representation of an utterance in oral speech that is preceded by a quotative marker, such as a verb of saying, is known as a paraphrase. When doing a brainstorming exercise, quotes can help spark ideas that then influence the ideas for the piece.

Through the presentation of other people's ideas, they can steer you in new directions. Finally, using short quotes that won't keep a writer from writing for too long can help them as they put a piece together.

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lim [f(x) - g(x)] is9.

Generally, In mathematics, a limit is a value that a function "approaches" as the input of the function "approach" some value.

More formally, given a function f(x) and a value L, we say that "the limit of f(x) as x approaches a is L" if the values of f(x) can be made arbitrarily close to L by taking x sufficiently close to a, but not equal to a.

In other words, the limit of a function describes the behavior of the function as the input gets arbitrarily close to a particular value, but doesn't necessarily equal that value

The limit of the difference between the two functions is the difference of their individual limits. So,

lim [f(x) - g(x)] = lim f(x) - lim g(x)

= 7 - (-2)

= 9.

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Answer:

To find out how much interest you will earn, you need to multiply the bond principal amount ($1,000) by the interest rate (5%) and the number of years the bond matures (5).

The interest rate is expressed as a percentage, so you need to convert it to a decimal by dividing it by 100.

Interest = Principal x Interest Rate x Time

Interest = $1,000 x 0.05 x 5

Interest = $1,000 x 0.05 x 5 = $250

So, you will earn $250 in interest over the 5-year period.

Answer:

108 sorry there no more explanation!

Answer:

Step-by-step explanation:

180

The number 480,000 in scientific notation is 4.8 * 10⁵

From the question, we have the following parameters that can be used in our computation:

Number = 480,000

Multiply the number by 1

So, we have the following representation

Number = 480000 * 1

Express 1 as 10⁵/10⁵

Som we have

Number = 480000 * 10⁵/10⁵

This gives

Number = 4.8 * 10⁵

Hence, the expression is 4.8 * 10⁵

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According to the question rate at which the volume is dV/dt = dV/dm * dm/dt + dV/dθ * dθ/dt.

The space covered within an object's borders in three dimensions is referred to as its volume. It is refereed as the object's capability on occasion.

Volume, which is measured in cubic units, is the three dimensional volume occupied by matter or encircled by a surface. The cubic centimeter (m3), a derived unit, is the Standard unit of volume.

Substituting in the given information, we have:

V(m, θ) = sqrt(θ) * ln(m)

m(t) = t^2 + 3

θ(t) = e^t

Therefore:

dV/dm = (1/m) * sqrt(θ)

dm/dt = 2t

dV/dθ = (1/2sqrt(θ)) * ln(m)

dθ/dt = e^t

plugging in the values of m(t) = t^2 + 3 and θ(t) = e^t

dV/dt = (1/(t^2+3)) * sqrt(e^t) * 2t + (1/2sqrt(e^t)) * ln(t^2+3) * e^t

So the rate at which the volume is changing at time t is given by dV/dt

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The ratio table can be completed as follows :

The ratio table shows that every flower would have 5 petals.

2 flowers would therefore have ;

= 2 flowers x 5 petals

= 10 petals

4 flowers would have :

= 4 flowers x 5 petals

= 20 petals

15 petals would belong to :

= 15 / 5 petals per flower

= 3 flowers

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Answer:

Four hundred thirdy seven and six hundred and eight thousandths.

437.068

Step-by-step explanation:

Hope it helps! =D

The number formed by these terms is 437.068.

To solve this problem, we first need to understand the place value system and what each term represents.

As per the place value system used in decimals:

- Hundreds: It is the third digit to the left of the decimal point and each unit represents 100.
- Tens: It is the second digit to the left of the decimal point and each unit represents 10.
- Ones: It is right next to the decimal point, all the digits to the left of it are the ones. Each unit represents 1.
- Hundredths: It is the second digit to the right of the decimal point and each unit represents 0.01.
- Thousandths: It is the third digit to the right of the decimal point and each unit represents 0.001.

In the given context, we know that there are 4 hundreds, 3 tens, 7 ones, 6 hundredths, and 8 thousandths.

To start, we calculate each term separately:

- 4 hundreds = 4 x 100 = 400
- 3 tens = 3 x 10 = 30
- 7 ones = 7 x 1 = 7
- 6 hundredths = 6 x 0.01 = 0.06
- 8 thousandths = 8 x 0.001 = 0.008

After evaluating each term separately, we sum them up together for the final answer:

- Sum = 400 + 30 + 7 + 0.06 + 0.008 = 437.068

Hence, the number formed by these terms is 437.068.

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Average velocity between the interval t = 10 min to t = 15 min is; 52.5 miles per hour

The expression showing  Di's average velocity, in miles per hour, t minutes after entering the interstate highway is;

v(t) = ¹/₂₀₀t³ + ³/₂₀t² - ³/₈t + 60

At t = 10 minutes, we have;

v(10) = ¹/₂₀₀(10³) + ³/₂₀(10²) - ³/₈(10) + 60

v(10) = 5 + 15 - 7.5 + 60

v(10) = 52.5 miles per hour

At t = 15 minutes, we have;

v(15) = ¹/₂₀₀(15³) + ³/₂₀(15²) - ³/₈(15) + 60

v(15) = 16.875 + 33.75 - 5.625 + 60

v(15) = 105 miles per hour

Thus;

Average velocity between the interval t = 10 min to t = 15 min is;

v(15) - v(10) = 105 - 52.5

= 52.5 miles per hour

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By applying the definite integral, it can be concluded that the velocity at time t is v(t) = t² + 6t - 16, and the distance traveled during the given time interval is 36.67 meters.

Definite integral is the integral of a function whose values of the independent variables have a certain interval.

This kind of integral is frequently used for calculating the acceleration and velocity of a moving object.

a(t) = dv/dt

v(t) = ds/dt

To find the velocity at time t, we look at the given acceleration function:

    a(t) = dv/dt

2t + 6 = dv/dt

     dv = (2t + 6) dt

    v(t) = ∫(2t + 6) dt

          = t² + 6t + C

Knowing that v(0) = -16, we put this into the previous equation so we get C = -16

Now we have the velocity at the time t as follows:

v(t) = t² + 6t - 16

To find the distance traveled, we look at the velocity function:

           v(t) = ds/dt

t² + 6t - 16 = ds / dt

            ds = (t² + 6t - 16) dt

              s = ∫(t² + 6t - 16) dt

                 = 1/3t³ + 3t² - 16t + C

Then we calculate the distance traveled during 0 ≤ t ≤ 5:

s = s(5) - s(0)

  = (1/3 * 5³) + (3 * 5²) - (16 * 5) + C - 0 - 0 + 0 - C

  = 125/3 + 75 - 80

  = 125/3 - 5

  = 125/3 - 15/3

  = 110/3

  ≈ 36.67 meters.

Thus, the velocity at time t is v(t) = t² + 6t - 16, and the distance traveled during the given time interval is 36.67 meters.

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If the calculated value is less than the table value, we fail to reject the null hypothesis.

What is the null hypothesis?

The null hypothesis is a statement or assumption that there is no statistically significant difference or relationship between two variables or groups being studied. It is usually denoted by the symbol H₀. It serves as a starting point for a statistical hypothesis test, and it is the opposite of the alternative hypothesis, which states that there is a statistically significant difference or relationship between the variables or groups being studied.

for the given sample :

mean=6.6

S.D=2.31

n=10

Mean of population:6

t0=(6.6-6)/2.31/sqrt(10)=0.82

for 95% confidence and 9 df

t value is:2.26

Hence, if the calculated value is less than the table value, we fail to reject the null hypothesis.

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So, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is 80π mm^2/min and the rate at which the height is decreasing with respect to time is  -2 mm/min.

Part A: The area of the circular surface of the cookie dough is given by A = πr^2, where r is the radius of the dough. The rate at which the area is changing with respect to time is given by dA/dt = 2πr*dr/dt. At time t, the radius is 20 mm and the rate at which it is increasing is 2 mm/min. Therefore, the rate at which the area of the circular surface of the cookie dough is increasing with respect to time is dA/dt = 2π(20 mm)(2 mm/min) = 80π mm^2/min.

Part B: The height of the dough is given by h, and the rate at which the height is decreasing with respect to time is given by dh/dt. Since the dough is retaining its cylindrical shape, the decrease in the height of the dough is exactly the opposite of the increase in the radius. At time t, the rate at which the radius is increasing is 2 mm/min, so the rate at which the height is decreasing with respect to time is dh/dt = -2 mm/min.

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The following pair of angles are corresponding congruent angles of these quadrilaterals:

∠G ≅ ∠T

∠F ≅ ∠R

∠H ≅ ∠Q

∠E ≅ ∠S

A quadrilateral in geometry is a four-sided polygon with four edges and four corners.

Given:

Quadrilateral GFHE and quadrilateral TRQS are similar.

The figures are given in the attached image.

The following pair of angles are corresponding congruent angles of these quadrilaterals:

∠G ≅ ∠T

∠F ≅ ∠R

∠H ≅ ∠Q

∠E ≅ ∠S

Therefore, all the pairs are given above.

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