Alyssa is 1. 65 meters tall. At 11 a. M. , she measures the length of a tree's shadow to be 27. 75 meters. She stands 23. 5 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Therefore, the dresser will now be sold for $295

Answer:

3x

Step-by-step explanation:

The general solution of the partial differential equation is:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

The partial differential equation (PDE) is given as:

Uxx = (1/2)Ut with the boundary and initial conditions as 0< X <3 with U(0,t) = U(3, t)=0, U(0, t) = 5sin(4πx)

Assume that the solution can be written as a product of two functions:

U(x, t) = X(x)T(t)

Substituting this into the PDE, we have:

X''(x)T(t) = (1/2)X(x)T'(t)

Dividing both sides by X(x)T(t), we get:

(X''(x))/X(x) = (1/2)(T'(t))/T(t)

Since the left side only depends on x and the right side only depends on t, both sides must be equal to a constant, denoted as -λ²:

(X''(x))/X(x) = -λ²

(1/2)(T'(t))/T(t) = -λ²

Simplifying the second equation, we have:

T'(t)/T(t) = -2λ²

Solving the second equation, we find:

T(t) = Ce^(-2λ²t)

Applying the boundary condition U(0, t) = 0, we have:

U(0, t) = X(0)T(t) = 0

Since T(t) ≠ 0, we must have X(0) = 0.

Applying the boundary condition U(3, t) = 0, we have:

U(3, t) = X(3)T(t) = 0

Again, since T(t) ≠ 0, we must have X(3) = 0.

Therefore, we can conclude that X(x) must satisfy the following boundary value problem:

X''(x)/X(x) = -λ²

X(0) = 0

X(3) = 0

The general solution to this ordinary differential equation is given by:

X(x) = Asin(λx) + Bcos(λx)

Applying the initial condition U(x, 0) = 5*sin(4πx), we have:

U(x, 0) = X(x)T(0) = X(x)C

Comparing this with the given initial condition, we can conclude that T(0) = C = 5.

Therefore, the complete solution for U(x, t) is given by:

U(x, t) = Σ [Aₙsin(λₙx) + Bₙcos(λₙx)]*e^(-2(λₙ)²t)

where:

Σ represents the summation over all values of n

λₙ are the eigenvalues obtained from solving the boundary value problem for X(x).

To find the eigenvalues λₙ, we substitute the boundary conditions into the general solution for X(x):

X(0) = 0: Aₙsin(0) + Bₙcos(0) = 0

X(3) = 0: Aₙsin(3λₙ) + Bₙcos(3λₙ) = 0

From the first equation, we have Bₙ = 0.

From the second equation, we have Aₙ*sin(3λₙ) = 0. Since Aₙ ≠ 0, we must have sin(3λₙ) = 0.

This implies that 3λₙ = nπ, where n is an integer.

Therefore, λₙ = (nπ)/3.

Substituting the eigenvalues into the general solution, we have:

U(x, t) = Σ [Aₙ*sin((nπ/3)x)]*e^(-(nπ/3)²t)

where Aₙ are the coefficients that can be determined from the initial condition.

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The matrix operation add -4(row 1) to row 3 is\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right]\)

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

Using the above as a guide, we have the following:

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

Hence, the result of the matrix expression is \(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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The correct statement is that "Line p must be drawn in plane B."

If a new line, p, is drawn parallel to line /, the statement that is true is "Line p must be drawn in plane B."

To understand this, let's analyze the given information:

Planes A and B are shown.

Line m is shown in plane A.

Line n is shown in plane B.

Line / is the line that connects planes A and B.

When a new line, p, is drawn parallel to line /, it means that line p will also connect planes A and B. However, since line / itself is connecting planes A and B, line p must also lie in plane B to maintain its parallel relationship with line /. This is because parallel lines lie in the same plane.

This ensures that line p remains parallel to line / and maintains its connection between planes A and B.

It is important to note that line p being drawn in plane B does not necessarily imply that it intersects with line n. It simply means that line p lies within plane B and remains parallel to line /.

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Answer:

andrew

Step-by-step explanation:

The contribution to geometry is attributed to the work of René Descartes B. the use of functions to describe lines and curves.

Rene Descartes is a famous person known for his great contribution to Mathematics and Philosophy.

He is also called the "Father of Modern Philosophy".

One of the major ways in which the French philosopher René Descartes contributed to geometry was through his mathematical skills and progress, which allowed scientists to better quantify and analyze data.

The contribution to geometry is attributed to the work of René Descartes B. the use of functions to describe lines and curves.

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Step-by-step explanation:

Answer:

Reflection across \(x=4\)

Step-by-step explanation:

You must measure the distance between the rightmost point on the blue figure and the leftmost point on the orange figure. Then divide it in half and these dots will be the answer, how are they asking for a line you need to specify if it is horizontal or vertical, because the interchanged points are \(B\) with \(C\) and \(D\) with \(A\) we know that is a vertical line, so the answer is:

Reflection across \(x=4\)

y = mx + b

for b

the equation is

y = 1 x + 80 or y = x + 80

Answer:

4,000

600

160

12

Step-by-step explanation:

When using partial products, you basically break up the number into ones, tens, hundreds, thousands, etc.

So the partial products of 1,643 x 4 will be,

1,000 x 4

600 x 4

40 x 4

3 x 4

The partial products of the multiplication problems are,

4000

600

160

12

The answer will be 4,772.

The partial products of the multiplication problems are,

4000, 2400, 160 and 12

Multiplication is a method of finding the product of two or more numbers

When using partial products, you basically break the number into ones, tens, hundreds, thousands, etc.

So the partial products of 1,643 x 4 will be,

1,643 can be written as 1000+600×40+3.

Now multiply with 4.

(1000+600×40+3)×4

1,000 x 4+600 x 4+40 x 4+3 x 4

4000+2400+160+12

Hence the partial products of the multiplication problems are,

4000, 2400, 160 and 12 and The answer will be 4,772.

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The Solution:

We are asked to determine the percentage of 20 out of 225.

That is,

Therefore, the correct answer is approximately 8.889%

Further explanation:

20 out of 225 gives the fraction: 20/225

To write this as a percentage, you have to multiply by 100.

Answer:

B

Step-by-step explanation:

From the graph, we know when x -> -∞, y -> 3

Note x -> -∞, 2^x -> 0

so only A and B may be right.

Note y-intercept is 7 when x = 0, so only B is right

Answer:

(- 3, - 4 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ) , then

(3, - 4 ) → (- 3, - 4 )

Answer:

$48.66

Step-by-step explanation:

$45.99 x 1.058 = 48.65742

Answer:

19. 7

20. 11

21. -12

22. 15

23. 77

24. −6

Step-by-step explanation:

Simply plug the values of a, b and c into each equation and evaluate using a calculator or manually

Answer:

Step-by-step explanation:

This doesn't factor. Not only that, but it does not give real results. The discriminate is negative.

a = 2

b = 4

c = 10

You could divide this equation by 2

a = 1

b = 2

c = 5  

These three are smaller and easier to calculate. The answer will be the same.

x = (- b +/- sqrt(b^2 - 4*a*c ) / (2 a)

x = (-2 +/- sqrt(^2 - 4(1)*(5) ) / 2*1

x = (-2 +/- sqrt(4 - 20) ) / 2

X = (-2 +/- sqrt(-16) ) /2

x = (-2 +/- 4i ) / 2

x = ( - 1) +/- 2i

1) The total number of possible outcomes is; 20 outcomes

2) The probability that someone  will adopt an adult cat that has grey fur is;  5%

In probability theory, conditional probability is defined as a measure of the probability of an event occurring, given the fact that another event has already occurred.

From the question;

Types of animals = 2 types

1) Dogs

2) Cats

Classification of Animals into age groups;

1) Babies

2) Adults

Colors of the fur of the animals;

1) Black

2) Brown

3) Tan

4) Grey

5) Mixed

1) The total number of possible outcomes = 2 * 2 * 5 = 20 outcomes

2) The probability that someone  will adopt an adult cat that has grey fur is; P(Adult cat and grey fur) = 0.5 * 0.5 * (1/5) = 0.05 = 5%

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Answer:

36 red roses

Step-by-step explanation:

54-18=36

Therefore, **x < 7** is the inequality that may be utilized to find x

A mathematical statement known as an inequality compares two expressions using an inequality sign, such as (less than), > (greater than), or (less than or equal to).

For instance, the inequality x + 2 5 signifies that "x + 2 is less than 5".

Let x represent how many days the client paid for pet sitting.

$15 per day plus a $20 fixed service fee equals the total cost of pet sitting.

We are aware that the customer's purchase was under $125. Consequently, we can write:

20 + 15x < 125

Putting this disparity simply:

15x < 105

x < 7

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Answer:

85 square inches.

Step-by-step explanation:

The area of a triangle can be found by the formula \(1/2bh\), assuming b is the base and h is the height.

If b is 17 inches and h is 10 inches:

\(1/2(17)(10)\)

\(1/2(170)\)

\(A = 85\)

Therefore, the area is 85 square inches.

The length of side CB to one decimal place is 89.3.

To find the length of side CB in the given triangle, we can use the sine rule. The sine rule states that in a triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

In this case, we have the angle C as 53° and the side opposite to it, side CB, as the unknown. Let's denote the length of side CB as x.

According to the sine rule:

sin(C) / x = sin(A) / AB

We know that angle A is 37° and AB is 120 units. Plugging in the values:

sin(53°) / x = sin(37°) / 120

To find x, we can rearrange the equation:

x = (120 * sin(53°)) / sin(37°)

Calculating this expression gives us:

x ≈ 89.32

Rounding this value to one decimal place, the length of side CB is approximately 89.3.

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8/21 of the lawn still needs to be mowed.

To compare fractions, we need a common denominator. The least common multiple of 7 and 3 is 21.

Miss Lianto's fraction: (2/7) x (3/3) = 6/21

Son's fraction: (1/3) x (7/7) = 7/21

To calculate how much of the lawn still needs to be mowed, we can subtract the combined fractions mowed from the total:

Combined fractions mowed: 6/21 + 7/21 = 13/21

So, Remaining fraction: 1 - 13/21 = 8/21

Therefore, 8/21 of the lawn still needs to be mowed.

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Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

Let's denote the original scholarship amount as "P."

According to the given information, Margaret receives $72,000, which means the remaining scholarship amount for the other three individuals is P - $72,000.

Ron receives 1/3 of the scholarship, which can be represented as (1/3)(P - $72,000). Nick receives 1/4 of the scholarship, which can be represented as (1/4)(P - $72,000). Mary receives the same as Nick, so Mary's share is also (1/4)(P - $72,000).

Now, we can sum up all the shares to equal the original scholarship amount:

Ron's share + Nick's share + Mary's share + Margaret's share = P

(1/3)(P - $72,000) + (1/4)(P - $72,000) + (1/4)(P - $72,000) + $72,000 = P

To simplify the equation, we can combine like terms:

(P/3 - $24,000) + (P/4 - $18,000) + (P/4 - $18,000) + $72,000 = P

Combining the fractions and constants:

(4P + 3P - 3P + 12P)/12 - $24,000 - $18,000 - $18,000 + $72,000 = P

16P/12 - $48,000 = P

Multiplying both sides of the equation by 12 to eliminate the denominator:

16P - $576,000 = 12P

Subtracting 12P from both sides of the equation:

4P = $576,000

Dividing both sides of the equation by 4:

P = $144,000

Therefore, the original scholarship amount is $144,000.

Ron's share: (1/3)($144,000 - $72,000) = $24,000

Nick's share: (1/4)($144,000 - $72,000) = $18,000

Mary's share: (1/4)($144,000 - $72,000) = $18,000

Margaret's share: $72,000

Thus, Ron's share is $24,000, Nick's share is $18,000, Mary's share is $18,000, and Margaret's share is $72,000.

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Answer:

The monthly payment for this loan is $127.80

Step-by-step explanation:

The formula of the monthly payment is

\(M.P=\frac{P(\frac{r}{n})}{1-(1+\frac{r}{n})^{-nt}}\)

∵ Mario is taking a $2,900, 2-year loan with an APR of 5.44%

∴ P = 2,900

∴ t = 2

∵ ART means annual percent rate

∴ r = 5.44% = 5.44 ÷ 100 = 0.0544

∴ n = 12

→ Substitute all these values in the formula above

∵ M.P = \(\frac{2,900(\frac{0.0544}{12})}{1-(1+\frac{0.0544}{12})^{-(12)(2)}}\)

→ use your calculator to find the answer

∴ M.P = 127.7992528

→ Round it to the nearest cent ⇒ 2d.p

∴ M.P = 127.80

∴ The monthly payment for this loan is $127.80

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The mean of the data is 4, the median is also 4. The range is 9, with an interquartile range of 2. The standard deviation is 2.14 and the skewness measure is 0.38, indicating a slight positive skew. No outliers are present.

(a) \(Mean = (7 + 2 + 6 + 4 + 9 + 4 + 1 + 4 + 2 + 4 + 5 + 2 + 3 + 5 + 2 + 0 + 6 + 7 + 4 + 2) / 20 = 4.\)

\(Median = 4\) (after sorting the data)

(b) First quartile (Q1) = 2 (after sorting the data and finding the median of  the lower half)

Third quartile (Q3) = 6 (after sorting the data and finding the median of the upper half)

(c) Range = 9 - 0 = 9

Interquartile Range (IQR) = Q3 - Q1 = 6 - 2 = 4

(d)\(Variance = ((7-4)^2 + (2-4)^2 + (6-4)^2 + (4-4)^2 + (9-4)^2 + (4-4)^2 + (1-4)^2 + (4-4)^2 + (2-4)^2 + (4-4)^2 + (5-4)^2 + (2-4)^2 + (3-4)^2 + (5-4)^2 + (2-4)^2 + (0-4)^2 + (6-4)^2 + (7-4)^2 + (4-4)^2 + (2-4)^2) / 20 = 9.05\)

Standard deviation = √Variance = √9.05 = 3.01

(e) Skewness measure = 0. The data are symmetrically distributed (i.e., not skewed to the left or to the right)

(f) Lower limit = 4 - 3.01 x 1.5 = -1.51

Upper limit = 4 + 3.01 x 1.5 = 8.51

Data does not contain outliers as all values are within the lower and upper limits.

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A total of 7 Cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

A line plot is drawn with the cyclists' names plotted on the x-axis and their corresponding distances covered plotted on the y-axis.

The dots are then joined to form a line, revealing the relationship between the cyclist's names and their corresponding distance traveled. The cyclist names and their corresponding distances are given in the table below.

Name Distance (in miles) Gina 40 1/2 Rey 50 Faye 35 3/4 Mark 60 John 45 1/2 James 40 1/2 Albert 40 1/4 William 54 1/4 Nathan 40 Kate 40 1/4 Mary 60 Risa 40 Abi 35 3/4 Joan 50 1/2 1. The number of cyclists is 14. 2. The longest distance covered by a cyclist is 60 miles.

Mary and Mark both covered this distance.3. A total of 7 cyclists traveled less than 50 miles. 4. The most common distance traveled by cyclists is 40 1/2 miles. Gina, James, and Albert covered this distance. 5. 2 more cyclists traveled 45 miles than 55 1/4 miles. Only William traveled 55 1/4 miles, while John and James both traveled 45 1/2 miles.6.

A total of 7 cyclists traveled more than 45 miles. 4 cyclists traveled 50 miles or more, and 3 cyclists traveled more than 54 1/4 miles.

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