9 ft
4.7 ft
6.5 ft
6.5 ft
Find the area of the triangle.

The average slope of the climb is approximately 0.404.

To find the average slope of the climb, we need to calculate the change in elevation divided by the horizontal distance covered.

Change in elevation = Final elevation - Initial elevation = 1943 ft - 875 ft = 1068 ft

Horizontal distance covered = 2645 ft

Average slope = Change in elevation / Horizontal distance covered = 1068 ft / 2645 ft

Using a calculator or dividing these values, we find that the average slope is approximately 0.404 to the nearest hundredth.

The average slope of the climb is approximately 0.404. This means that for every 1 foot of horizontal distance covered, the hiker ascends approximately 0.404 feet in elevation.

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Answer:

m = 3

Step-by-step explanation:

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

Pick 2 points (-1,-1) (0,2)

We see the y increase by 3 and the x increase by 1, so the slope is

m = 3

Answer:

slope = 3

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, - 1) and (x₂, y₂ ) = (0, 2) ← 2 points on the line

m = [tex]\frac{2-(-1)}{0-(-1)}[/tex] = [tex]\frac{2+1}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

The angle C in the triangle is 34.05 degrees.

The sum of angles in a triangle is 180 degrees. The angle in a triangle can be found using cosine law as follows:

Therefore, let's find the unknown angle in the triangle as follows;

c² = a² + b² - 2ab cos C

Hence,

4² = 5² + 7² - 2 × 7 × 5 cos X

16 = 25 + 49 - 70 cos X

16 = 74 - 70 cos X

16  - 74 = -70 cos X

-58 = -70 cos X

cos X = 58 / 70

X = cos⁻¹ 0.82857142857

X = 34.0478785629

X = 34.05 degrees

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a.  The investment to double in value take about 14 years for the funding to double in value.

b.  The genuine time it will take for the funding to double in fee is about 13.86 years.

(a) To estimate the time it takes for an funding to double in cost the use of the rule of 70, we want to decide the increase rate. In this case, the increase price is given as 5% per 12 months compounded continuously.

Using the rule of 70, we can calculate the estimated doubling time:

Time to double ≈ 70 / boom rate

Time to double ≈ 70 / 5

Simplifying, we have:

Time to double ≈ 14 years

Therefore, it would take about 14 years for the funding to double in value.

(b) To decide the genuine time it will take for the funding to double in value, we can use the formulation for non-stop compounding:

Doubling time (exact) = ln(2) / (ln(1 + r))

where r is the increase fee as a decimal.

In this case, the increase charge is 5% per year, or 0.05 as a decimal.

Doubling time (exact) = ln(2) / (ln(1 + 0.05))

Doubling time (exact) ≈ 13.86 years (rounded to two decimal places)

Therefore, the genuine time it will take for the funding to double in fee is about 13.86 years.

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The x-coordinate of the vertex is given by h = -2 and the equation of the axis of symmetry is x = -2.

Given function is H(x) = -(x + 2)² + 8.

The axis of symmetry of a quadratic function y = ax² + bx + c is defined by x = -b/2a.

So, let's solve the problem as follows:

To find the axis of symmetry, we need to convert the given function into standard form y = a(x - h)² + k.

We can do this by completing the square.

For that, we have

H(x) = -(x + 2)² + 8H(x)

= -1(x² + 4x + 4) + 8H(x)

= -1(x + 2)² + 8

The standard form is y = a(x - h)² + k, so the given function is y = -1(x + 2)² + 8.

The vertex form of a quadratic equation is y = a(x - h)² + k

Where(h, k) is the vertex.

The vertex form of the given function H(x) = -(x + 2)² + 8 can be calculated as follows:  

y = a(x - h)² + k

The vertex form is y = a(x - h)² + k.

Where the vertex form of the given function is:

y = -1(x + 2)² + 8.

Since the vertex form is y = a(x - h)² + k the vertex form of the given function is y = a(x + 2)² + 8 and (h, k) = (-2, 8).

Vertex is given by h = -2.

Axis of symmetry is x = -2.

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Answer:

a=55°

b=123°

c=55°

d=123°

The area of the figure WXYZ which can be calculated as the sum of the area of the composite triangles ΔXYZ and ΔXWZ is 12 square units

Composite figures are figures comprising of two or more regular figures.

The slope of the side WZ = 2/5

The slope of YZ = -2/1 = -2

The slope of WZ is not the negative inverse of the slope of YZ, therefore, the figure WZ is not perpendicular to YZ and the figure is not a rectangle.

Considering the two triangles formed by the diagonal XZ, we get;

The figure XYZW is a quadrilateral, which is a composite figure comprising of two triangles, triangle ΔXYZ and ΔXWZ

Area of triangle ΔXYZ = (1/2) × 6 × 2 = 6 square units

Area of triangle ΔXWZ = (1/2) × 6 × 2 = 6 square units

The area of the figure = Area of triangle ΔXYZ + Area of triangle ΔXWZ

Area of triangle ΔXYZ + Area of triangle ΔXWZ = 6 + 6 = 12 square units

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Answer:

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

Step-by-step explanation:

Para calcular el capital final, utilizaremos la fórmula del interés compuesto:

Capital Final = Capital Inicial * (1 + Tasa de Interés)^Tiempo

Donde:

Capital Inicial = $1200

Tasa de Interés = 8% = 0.08 (expresada como decimal)

Tiempo = 8 años

Sustituyendo los valores en la fórmula:

Capital Final = $1200 * (1 + 0.08)^8

Calculando el resultado:

Capital Final = $1200 * (1.08)^8 ≈ $2061.68

Por lo tanto, el capital final después de 8 años sería de aproximadamente $2061.68.

The range of the inverse of the function is [2, ∝)

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

f(x) = √x - 2

Set the radicand greater tahn or equal to 0

So, we have

x - 2 ≥ 0

When evaluated, we have

x ≥ 2

This means that

[2, ∝)

Hence, the range of the inverse of the function is [2, ∝)

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Inferences about the interaction between Anna and Mrs. Morgan are supported by the information in paragraphs 7 and 8 are as follows: Mrs. Morgan is not very patient with Anna and is trying to get rid of her.Mrs. Morgan thinks Anna is lying and is not telling the truth.

Mrs. Morgan appears to be strict and unkind towards Anna, as well as being skeptical about her intentions. She is not really interested in Anna's concerns and is rather impatient and dismissive, trying to get rid of her as soon as possible. Additionally, Mrs. Morgan doesn't believe Anna, thinking she is lying and hiding something from her.

This suggests that Mrs. Morgan might not be a trustworthy person and has a negative impression of Anna without even knowing her well.

The textual evidence used to support these inferences is the description of Mrs. Morgan's tone and behavior towards Anna as well as her verbal responses, such as the abruptness of her question about the purse and her insistence on Anna leaving.

These actions suggest that Mrs. Morgan is not open to listening to Anna's story and is only interested in getting her out of the way, as well as indicating that she doesn't believe Anna's story.

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Yes, there is a difference in the shapes of the displacement-time graphs for uniform acceleration towards the positive direction, uniform acceleration towards the negative direction, uniform deceleration towards the positive direction, and uniform deceleration towards the negative direction.

Uniform acceleration towards the positive direction:

In this case, the object's velocity increases in the positive direction over time. The displacement-time graph will have a concave-upward shape, forming a curve that starts with a small slope and gradually becomes steeper as time progresses.

Uniform acceleration towards the negative direction:

Here, the object's velocity increases in the negative direction, meaning it accelerates in the opposite direction to its positive direction.

The displacement-time graph will have a concave-downward shape, forming a curve that starts with a steep slope and gradually becomes less steep as time progresses.

Uniform deceleration towards the positive direction:

In this scenario, the object's velocity decreases in the positive direction, but it still moves towards the positive direction.

The displacement-time graph will show a curve with a decreasing slope, forming a concave-downward shape, indicating that the object is slowing down.

Uniform deceleration towards the negative direction:

Here, the object's velocity decreases in the negative direction, opposing its initial direction.

The displacement-time graph will have a curve with a decreasing slope, forming a concave-upward shape, indicating that the object is slowing down but still moving in the negative direction.

In summary, the shapes of the displacement-time graphs differ based on the direction and type of acceleration (positive or negative) and whether the object is undergoing uniform acceleration or uniform deceleration. These differences can be observed through the concavity and slope of the graphs.

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The domain for the time in this context is (0, 7.4)

An equation is an expression that shows how numbers and variables are related to each other using mathematical operators.

Let h represent the height of the ball after spending t seconds. A ball is thrown straight up from the top of a building that is 168 ft high with an initial velocity of 96 ft/s.

Given the equation:

h(t) = -16t² + 96t + 168

The reasonable domain restriction for t, is when  the height of the rocket is above the ground. Hence the domain for the time in this context is (0, 7.4)

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The histogram in the school newspaper report provides a visual summary of the commute distances for a sample of 24 students at the major university in Southern California, supporting the students' claims of a housing crunch and long commutes.

According to the study reported in the school newspaper, a histogram was used to summarize the commute distances for a sample of 24 students at the major university in Southern California.

A histogram is a graphical representation that displays the distribution of a dataset by organizing it into intervals or bins along the horizontal axis and showing the frequency or count of observations in each bin on the vertical axis.

The histogram provides valuable insights into the commute distances of the university's students and helps assess the housing crunch issue.

By analyzing the histogram, university officials can gain a better understanding of the distribution of commute distances and identify any patterns or concentrations that may indicate the severity of the problem.

The histogram should provide information about the range of commute distances and the frequency of students within each interval.

It allows university officials to visualize the distribution and assess whether there is a significant portion of students facing long commutes due to the lack of housing near campus.

The officials can use the histogram to determine the central tendency measures such as the mean or median commute distance, which can provide a representative value of the typical commute for the student population.

Additionally, they can examine the spread or variability of the data to understand if there are extreme cases or if most students face similar distances.

By studying the histogram, university officials can gather quantitative evidence to support the students' claims of a housing crunch.

This information can guide their decision-making process in addressing the issue, such as implementing policies to increase affordable on-campus housing options or exploring partnerships with nearby housing providers.

In summary, the histogram in the school newspaper report provides a visual representation of the commute distances of a sample of 24 students at the university.

It serves as a valuable tool for university officials to analyze the housing crunch problem and make informed decisions to alleviate the commuting burden on the students.

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The coefficient of [tex]x^2y^3[/tex] in the expression [tex](2x+y)^5[/tex] is 10

To find the coefficient of the term containing [tex]x^2y^3\\[/tex] in the expansion of [tex](2x+y)^5[/tex], we can use the binomial theorem. The binomial theorem states that the expansion of [tex](a + b)^n[/tex] can be written as the sum of the binomial coefficients multiplied by the respective powers of a and b, where n is a positive integer.

In this case, we have [tex](2x + y)^5[/tex]. The term [tex]x^2y^3[/tex] can be obtained by selecting two x's from [tex](2x)^2[/tex] and three y's from [tex]y^3[/tex]. The coefficient of [tex]x^2y^3[/tex] will be the product of the corresponding binomial coefficients.

The binomial coefficients for this term can be calculated as follows:

Coefficient = C(5, 2) * C(3, 3)

C(n, k) represents the binomial coefficient, which is calculated as n! / (k! * (n - k)!), where "!" denotes the factorial operation.

Plugging in the values, we have:

Coefficient = C(5, 2) * C(3, 3)

[tex]= (5! / (2! * (5 - 2)!)) * (3! / (3! * (3 - 3)!))\\= (5! / (2! * 3!)) * (3! / (3! * 0!))\\= (5 * 4 * 3! / (2 * 1 * 3!)) * 1\\= (5 * 4) / (2 * 1)\\= 10.[/tex]

Therefore, the coefficient of [tex]x^2y^3[/tex] in the expression [tex](2x+y)^5[/tex] is 10.

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the answer is D

The figure can be divided into a rectangle and 2 triangles

The probability that a cell phone will fail within 2 years is 0.4866.

The average lifetime of the cell phone is 6 years, so the decay rate is 1 / 6 = 0.1667.

The probability that a phone will fail within 2 years is given by:

[tex]P(x < 2) = 1 - e^{-0.1667 * 2} = 1 - 0.5134 = 0.4866[/tex]

Rounded to four decimal places, the probability is 0.4866.

Therefore, the probability that a cell phone will fail within 2 years is 0.4866.

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Answer:

Step-by-step explanation:

144*33/

a) Heather contributed $135,000 and Lesley contributed $150,000 to their accounts.

b) Heather's investment is approximately $273,714.17, while Lesley's investment is approximately $191,048.18 when they are 65 years old.

c) Heather has more money by approximately $82,665.99 at age 65.

a) To find out how much money Heather and Lesley contributed to their accounts, we need to calculate the total contributions made by each of them.

Heather:

Heather started investing at age 20 and stopped at age 65, contributing $3000 annually. The number of years she contributed is (65 - 20) = 45 years.

Total contributions by Heather = $3000 × 45 = $135,000.

Lesley:

Lesley started investing at age 40 and stopped at age 65, contributing $6000 annually. The number of years she contributed is (65 - 40) = 25 years.

Total contributions by Lesley = $6000 × 25 = $150,000.

Therefore, Heather contributed $135,000 and Lesley contributed $150,000 to their respective accounts.

b) To calculate the value of their investments at age 65, we can use the formula for compound interest:

Future Value = Principal × (1 + interest rate)^number of years

Heather:

Principal (initial investment) = $3000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 20 = 45

Future Value of Heather's investment = $3000 × (1 + 0.075)^45

Lesley:

Principal (initial investment) = $6000

Interest rate = 7.5% = 0.075 (converted to decimal)

Number of years = 65 - 40 = 25

Future Value of Lesley's investment = $6000 × (1 + 0.075)^25

Calculating these values:

Future Value of Heather's investment = $3000 × (1.075)^45 ≈ $273,714.17

Future Value of Lesley's investment = $6000 × (1.075)^25 ≈ $191,048.18

c) To determine who has more money at age 65 and by how much, we compare the future values of their investments.

Heather's investment value at age 65 = $273,714.17

Lesley's investment value at age 65 = $191,048.18

Therefore, Heather has more money at age 65, and the difference in their investments is approximately $273,714.17 - $191,048.18 = $82,665.99.

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Answer:

The formula for calculating the future value (VF) of a periodic sum of money is:

VF = P * [(1 + r) n - 1] / r

where:

   VF is the future value (the total amount in the savings account)

   P is the periodic amount (monthly deposit)

   r is the periodic interest rate (annual interest rate divided by the number of periods in the year)

   n is the total number of periods (months)

In this case, P = $110, r = 3% / 12 = 0.03/ 12 = 0.0025 (monthly interest rate) and n = 3 * 12 = 36 (three years equivalent to 36 months).

Using these values in the formula, we can calculate the future value (VF):

VF = 110 * [(1 + 0.0025) 36 - 1] / 0.0025

Now let’s calculate this:

VF = 110 * [(1.0025) 36 - 1] / 0.0025

110 * (1.0965726572 - 1) / 0.0025

110 * 0.0965726572 / 0.0025

So Jackson will have about $4,239.52 in his savings account after three years, assuming he doesn’t make any withdrawals during that period.

Step-by-step explanation:

The area of the parallelogram ABCD is (a) 13 square units.

Area of a parallelogram = Length × Width

Length = distance AB

Where

A = (3, 6) and B = (6, 5)

So, we have

[tex]Length = \sqrt{ {(3 - 6)}^{2} + (6 - 5) ^{2} }[/tex]

[tex] = \sqrt{ {( - 3)}^{2} + (1) ^{2} }[/tex]

[tex] = \sqrt{ 9 + 1 }[/tex]

[tex]= \sqrt{10}[/tex]

Next, we have

Width = distance AD

Where

A = (3, 6) and D = (2, 2)

So, we have

[tex]width = \sqrt{ {(3 - 2)}^{2} + (6 - 2) ^{2} }[/tex]

[tex] = \sqrt{ {( 1)}^{2} + (4) ^{2} }[/tex]

[tex]= \sqrt{ 1 + 16 }[/tex]

[tex]= \sqrt{17}[/tex]

Recall that

Area of a parallelogram = Length × Width

So, we have

= √10 × √17

Evaluate the products

√170

Take the square rppt

= 13.03840481040529

Approximately, 13 square units

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Complete question:

What is the area of parallelogram ABCD?

O 13 square units

O 14 square units

O 15 square units

O 16 square units

See attachment

Answer:

x = 4 , ∠ AXC = 150°

Step-by-step explanation:

∠ 1 and ∠ 2 form the angle AXC , that is

∠ AXC = ∠ 1 + ∠ 2 , then

6(6x + 1) = 102 + 10x + 8

36x + 6 = 10x + 110 ( subtract 10x from both sides )

26x + 6 = 110 ( subtract 6 from both sides )

26x = 104 ( divide both sides by 26 )

x = 4

Then by substituting x = 4

∠ AXC = 6(6x + 1) = 36x + 6 = 36(4) + 6 = 144 + 6 = 150°

Answer:

4710

Step-by-step explanation:

6580 minus

1870

4710

The solution to the piecewise-defined function is shown in the attached graph.

The function g(x) is defined as follows:

g(x) = -4     if x ≠ 0

g(x) = 5       if x = 0

On the graph, when x is any value other than 0, the function takes the value of -4. This means that there will be a horizontal line at y = -4 for all x ≠ 0. The point (0, 5) will be represented by a solid dot since it's the only point where g(x) equals 5.

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The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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The equation for true airspeed T in terms of altitude and differential pressure p - T = k * (1 + A/50,000) * p

To write the equation for true airspeed T in terms of altitude A and differential pressure p, we need to consider the relationship between indicated airspeed S and differential pressure.The indicated airspeed S is typically measured using a pitot tube, which measures the dynamic pressure of the air flowing around the aircraft. The differential pressure p represents the difference between the dynamic pressure measured by the pitot tube and the static pressure of the surrounding air. In other words, p = dynamic pressure - static pressure.

The equation T = (1 + A/50,000) * S, we can express S in terms of the differential pressure p. Let's assume that S is directly proportional to p:

S = k * p

where k is a constant of proportionality. By substituting this expression for S into the equation for true airspeed, we have:

T = (1 + A/50,000) * (k * p)

Simplifying, we can write the equation for true airspeed T in terms of altitude A and differential pressure p as:

T = k * (1 + A/50,000) * p

where k is the constant of proportionality relating differential pressure to indicated airspeed.

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Mr. Marshal spent 1/4 of his salary on miscellaneous expenses and $1,680 on rental; therefore, he spent 1/36 of his entire salary on the trip.

To find the fraction of money spent on miscellaneous, we need to calculate the sum of the fractions spent on rental, food, and bank and subtract it from 1.

Rental: 1/5

Food: 1/10

Bank: 1/4

To find the fraction spent on miscellaneous:

Fraction spent on miscellaneous = 1 - (Rental + Food + Bank)

Rental + Food + Bank = 1/5 + 1/10 + 1/4 = (8 + 4 + 5)/40 = 17/40

Fraction spent on miscellaneous = 1 - 17/40 = 23/40

So, Mr. Marshal spent 23/40 of his salary on miscellaneous.

To find the amount spent on rental, we multiply the fraction spent on rental by his salary:

Amount spent on rental = (1/5) [tex]\times[/tex] $8,400 = $1,680

Therefore, Mr. Marshal spent $1,680 on rental.

If Mr. Marshal spent 4/9 of the miscellaneous amount on a trip, we need to calculate the fraction of his entire salary spent on the trip.

Fraction spent on the trip = (4/9) [tex]\times[/tex] (23/40) = 92/360 = 23/90

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Answer:

the two numbers are 20 and 1.