A random sample of 35 used car lots found that the average price of a used car is $11.750. Assume the population standard deviation is $1.225. Using a 98% confidence level, calculate the following: Critical Value 2.33 O 1.645 1.96 1.28 D Question

Midpoint = (x1 + x2)/2 , (y1+ y2)/2

Midpoint = (9 +-6)/2 , (-8 + -3)/2

Midpoint = (3/2, -11/2)

Answer:

51

Step-by-step explanation:

x + y + z  = 0   →-  -(x + y)  = z  →   z^3 =  - (x^3 + 3x^2y + 3xy^2 + y^3)

xyz  = 17

xy [ -(x + y) ]  = 17

xy (x + y)  = -17  →  x^2y + xy^2  = -17  →  3x^2y + 3xy^2  = -51

So......

x^3  + y^3  +  [ z^3 ]

x^3  + y^3  +  [ -  ( x^3 + 3x^2y + 3xy^2 + y^3) ]  =

-3x^2y - 3xy^2  =

-[ 3x^2y + 3xy^2]  =

- [-51]  =

51

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The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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The number of reindeer in St. Elsewhere in 1920 will be approximately 475.

The growth rate of .12 indicates an annual increase of 12%, meaning that each year the number of reindeer will be multiplied by 1.12. To find the number of reindeer in 1920, we need to use this growth rate over the 20-year period from 1900 to 1920.
Starting with the initial 52 reindeer, we can multiply by 1.12 for each year. This gives us:
Year 1: 52 * 1.12 = 58.24
Year 2: 58.24 * 1.12 = 65.10
Year 3: 65.10 * 1.12 = 72.90
Year 4: 72.90 * 1.12 = 81.60
Year 5: 81.60 * 1.12 = 91.15
Year 6: 91.15 * 1.12 = 101.66
Year 7: 101.66 * 1.12 = 113.27
Year 8: 113.27 * 1.12 = 126.13
Year 9: 126.13 * 1.12 = 140.43
Year 10: 140.43 * 1.12 = 156.36
Year 11: 156.36 * 1.12 = 174.16
Year 12: 174.16 * 1.12 = 194.10
Year 13: 194.10 * 1.12 = 216.45
Year 14: 216.45 * 1.12 = 241.58
Year 15: 241.58 * 1.12 = 269.87
Year 16: 269.87 * 1.12 = 301.72
Year 17: 301.72 * 1.12 = 337.62
Year 18: 337.62 * 1.12 = 378.10
Year 19: 378.10 * 1.12 = 423.77
Year 20: 423.77 * 1.12 = 475.30
Therefore, the number of reindeer in St. Elsewhere in 1920 will be approximately 475.

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\(~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 30000\\ P=\textit{original amount deposited}\dotfill & \$20000\\ r=rate\to 9\%\to \frac{9}{100}\dotfill &0.09\\ t=years \end{cases} \\\\\\ 30000 = 20000[1+(0.09)(t)] \implies \cfrac{30000}{20000}=1+0.09t\implies \cfrac{3}{2}=1+0.09t \\\\\\ \cfrac{3}{2}-1=0.09t\implies \cfrac{1}{2}=0.09t\implies \cfrac{1}{2(0.09)}=t\implies 5.6\approx t\)

Answer:

22 hours

Step-by-step explanation:

So, 143 equals eleven hours. 143 plus 143 would equal 243. So, you have two 143s which means you should multiply the 11 hours by two. 11x2 equals 22.

A number ratio specifies the number of times a given number or value is present in another number

The ratio of Amy's score to Bill's score to Cara's score is 10 : 1 : 5

The reason the above values are correct are given as follows:

The known parameters are;

Amy's score = 10 × Bill's score

Cara's score = \(\dfrac{1}{2}\) × Amy's score

Required;

To write down the ratio of Amy's score to Bill's score to Cara's score

Solution:

Let A represent Amy's score, let B represent Bill's score, and let C represent Cara's score

A = 10·B

C = \(\dfrac{1}{2}\) × A

Therefore, 2·C = A, which gives;

2·C = 10·B

C = 5·B

A:B:C = 10·B : B : 5·B

Taking B as unit gives;

10·B : B : 5·B = 10:1:5

The ratio of Amy's score to Bill's score to Cara's score, A:B:C = 10: 1 : 5

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The Polynesian Triangle is a vast region of the Pacific Ocean that encompasses Hawaii, New Zealand, and Easter Island. The Polynesians were skilled navigators who traveled across this vast expanse of water using only the stars, winds, and currents to guide them. They developed a sophisticated system of navigation that allowed them to travel thousands of miles across the open ocean with remarkable accuracy.

One of the primary methods used by the Polynesians to navigate the Polynesian Triangle was celestial navigation. They used the stars, moon, and planets to determine their position and direction. They had an intimate knowledge of the night sky and could identify hundreds of stars and constellations. They used these celestial bodies to create mental maps of the sky that they could use to navigate by. They also used the position of the sun during the day to determine their direction.

Another method used by the Polynesians was wayfinding. Wayfinding is a complex system of navigation that involves observing the natural environment, such as waves, clouds, and birds, to determine one's position and direction. The Polynesians had an intimate knowledge of the ocean currents and wind patterns in their region. They could read the waves and clouds to determine their direction and could even detect land from great distances by observing the behavior of birds.

The Polynesians also used navigational instruments such as the kamalae and the kapele. The kamalae was a wooden board with a small hole in it that was used to measure the angle between two stars. The kapele was a cord with knots tied in it that was used to measure distance traveled.

It is important to note that Indigenous knowledge is often passed down through oral traditions and cultural practices. When interpreting this knowledge, it is essential to do so with respect for its origins and context. Adding interpretations or misrepresenting Indigenous knowledge can dilute its meaning and significance.

In conclusion, the Polynesians used a variety of methods to navigate the Polynesian Triangle, including celestial navigation, wayfinding, and navigational instruments. Their knowledge of the natural environment and their ability to read the stars and currents allowed them to travel vast distances across the open ocean with remarkable accuracy. When interpreting Indigenous knowledge, it is essential to do so with respect for its origins and context.

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Overall, a line plot or line graph provides a clear and concise way to visualize the time trends in sales data, enabling Jade to make informed decisions and observations about her business performance over the years.

Time-based Representation: A line plot uses the x-axis to represent time, allowing Jade to easily track changes in sales over the years. The chronological order of the data points helps in observing patterns and trends over time.

Continuous Data Connection: A line plot connects the data points with a line, indicating the continuity of the variable being plotted. This is particularly useful for sales data, as it emphasizes the flow and progression of sales over time.

Visualizing Trends: By examining the slope and direction of the line in the graph, Jade can identify whether her sales are increasing, decreasing, or remaining relatively stable over the years. This visual representation helps in understanding the overall trend in sales performance.

Comparative Analysis: Jade can compare sales data from different years by observing the relative position of the lines or data points on the graph. This allows her to identify specific years or periods that experienced significant changes in sales.

Seasonal Patterns: If there are recurring patterns or seasonality in the sales data, a line plot can reveal these fluctuations. Jade can identify regular peaks and valleys in sales and analyze how they align with specific times of the year.

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Answer:

15

Step-by-step explanation:

5x3 = 15 It's Simple Hope it helps

Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

The percentage of people surveyed that were satisfied with the car is 55%.

Step-by-step explanation:

1,100/2,000=0.55*100= 55%

Answer:

Only the second one(B)

Step-by-step explanation:

Only the second one had a right angle of 90 degrees.

Below are the attachments of the triangle drawings.

Hope this helps!

Answer:

2, 6, and 7.

Step-by-step explanation:

In a right triangle, the hypotenuse (longest side of the triangle) squared is equal to the sum of the other sides squared.

So for the second triangle, add 36 squared to 15 squared. The result is 1521. Compare that to the hypotenuse (39) squared. The second triangle is a right triangle because the hypotenuse squared is also 1521. I did this with each triangle and the 2nd, 6th, and 7th were right triangles.

Midsegment is half the parallel side:

ORT is isosceles, the angles O and R are equal and measure:

IRN is isosceles, the angles N and I are equal and measure:

ABC is isosceles, the angles A and B are equal and measure:

The linear function rule for an input of x + 1 is given as follows:

f(x + 1) = 2x + 5.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

For this problem, the slope and the intercept of the function are given as follows:

Hence the function rule is:

y = 2x + 3.

The numeric value at x = x + 1 is given as follows:

f(x + 1) = 2(x + 1) + 3

f(x + 1) = 2x + 2 + 3

f(x + 1) = 2x + 5.

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They sold 150 copies for 500 rupees and 50 copies for 450 rupees

Total number of copies = 200

Consider the number of books that sells for 500 naira = x

The number of books that sells for 450 naira = y

Then the first equation will be,

x + y = 200

x = 200 - y

The total amount he made by selling the books = 97500 naira

Then the next equation will be

500x + 450y = 97500

Here we have to use the substitution method here

500(200-y) + 450y = 97500

100000 - 500y +450y = 97500

-50y = 97500-100000

-50y = -2500

y = 50

Then the value of x is

x = 200-y

x = 200 - 50

x = 150

Hence, they sold 150 copies for 500 rupees and 50 copies for 450 rupees

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Answers:

a) 140, 57

b) Positive

c) 150 cm

Answer:

19.95 + .71 × x = 125.74

x = 141.053

x is the answer

The value of an investment of $10,000 for 11 years at an annual interest rate of 4.55% compounded continuously is approximately $15,177.96.

When an investment is compounded continuously, we use the formula for continuous compound interest, which is given by the equation A = P*e^(rt), where A is the final amount, P is the principal amount (initial investment), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (expressed as a decimal), and t is the time in years.

In this case, the principal amount P is $10,000, the annual interest rate r is 4.55% (or 0.0455 as a decimal), and the time period t is 11 years. Plugging these values into the formula, we get A = $10,000e^(0.045511) ≈ $15,177.96. Therefore, the value of the investment after 11 years is approximately $15,177.96.

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Answer:

a) \(p \geq 60\,ft^{2}\), b) \(w \geq 36\,ft\), c) \(1\,qt \leq q \leq 2\,qt\), d) \(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\)

Step-by-step explanation:

In this question we proceed to translate each sentence into mathematical language and, more specifically, inequations:

a) At least 60 square feet of plywood for the surface

Let \(p\) the surface area of plywood, measured in square feet, and the inequation is:

\(p \geq 60\,ft^{2}\) (Eq. 1)

b) At least 36 feet of wood planks for the frame of the dog house

Let \(w\) the total length of wood planks, measured in feet, and the inequation is:

\(w \geq 36\,ft\) (Eq. 2)

c) Between 1 and 2 quarts of paint

Let \(q\) the total capacity of paint, measured in quarts, and the inequation is:

\(1\,qt \leq q \leq 2\,qt\) (Eq. 3)

d) Han's budget is $ 65. Plywood costs $ 0.70 per square foot, planks of wood cost $ 0.10 per foot and paint costs $ 8 per quart.

Dimensionally speaking, we understand that cost equals unit cost multiplied by physical variable (i.e. Area, length or capacity). Let \(p\), \(w\) and \(q\) the surface area of plywood, the total length of wood planks and the total capacity of paint, respectively. The sentence is represented by the following inequation:

\(0.70\cdot p + 0.10\cdot w + 8\cdot q \leq 65\) (Eq. 4)

Write an inequality to represent each constraint(material and cost)

Plywood:

plywood ≥ 60 square feet

Planks:

planks ≥ 36 feet

Paints

1 quarts ≤ paints ≤ 2 quarts

Inequality to represent cost constraint

Plywood = $0.70

planks of wood = $0.10

paint costs $8

Total cost = $65

0.70 × p + 0.10 × pw + 8 × Pa ≤ 65

0.70p + 0.10pw + 8pa ≤ 65

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Answer: 3/5

Step-by-step explanation:

\(\frac{-6-15}{-18-17}=\frac{3}{5}\)

The radius of the track is 0.5 m

In this question, we have been given a 700 kg race car makes one lap around a track.

It has a velocity of 20 m/s with a centripetal force of 5,600 N.

We need to find the radius of the track.

The centripetal force is given by,

F = mv²/r

where m = mass

v = velocity

r = radius

In this question, m = 700 kg, v = 20 m/s, F = 5600 N

Using the formula of the centripetal force,

F = mv²/r

5600 = (700 × 20²) / r

r = (700 × 400)/ 5600

r = 2800 / 5600

r = 1/2 m

r = 0.5 m

Therefore, the radius of the track is 0.5 m

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Answer:

B

Step-by-step explanation:

Answer:

The wingspan of the model will be 11 feet long

Step-by-step explanation:

Here, we want to find the length of the wingspan of the model.

From the question, the scale we have is; 2 inches to 40 inches

So let’s say the ratio of the model length to the actual length is 2:40 = 1:20

Now , we have an actual length but we do not know the model length. Let the model length we are looking for be x;

Thus;

1/20 = x/220

Cross multiply;

20 * x = 220 * 1

20x = 220

x = 220/20

x = 11 feet

Kindly note that since we are working with ratio here, we do not need any unit conversion from feet to inches or vice versa

a) To determine the vector equation of the plane containing the points A(-3, 2, 8), B(4, 3, 9), and C(-2, -1, 3), we can use the cross product of two vectors in the plane to find the normal vector.

Let's find two vectors lying in the plane:

Vector AB = B - A = (4, 3, 9) - (-3, 2, 8) = (7, 1, 1)

Vector AC = C - A = (-2, -1, 3) - (-3, 2, 8) = (1, -3, -5)

Next, we calculate the cross product of AB and AC to find the normal vector:

Normal vector N = AB × AC = (7, 1, 1) × (1, -3, -5)

Using the determinant method, we can calculate the components of the cross product:

N = (i, j, k)

  = | 1   -3  -5 |

    | 7    1   1 |

    | 0    7   1 |

  = (1 * 1 - (-3) * 7)i - (1 * 1 - 7 * 0)j + (7 * (-5) - 1 * 0)k

  = (-20)i - 1j - 35k

So, the normal vector N is (-20, -1, -35).

Now, using the normal vector N and one of the points (let's choose point A), we can write the vector equation of the plane:

N · (P - A) = 0, where P = (x, y, z) is any point on the plane.

Substituting the values, we have:

(-20, -1, -35) · (x + 3, y - 2, z - 8) = 0

Expanding this equation, we get:

-20(x + 3) - (y - 2) - 35(z - 8) = 0

-20x - 60 - y + 2 - 35z + 280 = 0

-20x - y - 35z + 222 = 0

Therefore, the vector equation of the plane is:

-20x - y - 35z + 222 = 0.

To find the parametric equations of the plane, we can solve the vector equation for one of the variables (let's choose z) and express the other variables (x and y) in terms of a parameter.

-20x - y - 35z + 222 = 0

-35z = 20x + y - 222

z = (-20/35)x - (1/35)y + (222/35)

So, the parametric equations of the plane are:

x = t

y = -35t - 222

z = (-20/35)t - (1/35)(-35t - 222) + (222/35)

z = (-20/35)t + (1/35)(35t + 222) + (222/35)

z = (-20/35)t + t + (222/35) + (222/35)

z = (15/35)t + (444/35)

z = (3/7)t + (12/7)

b) To determine the vector, parametric, and symmetric equations of the line passing through points A(-3, 2, 8) and B(4, 3, 9), we can find the direction vector of the line and use it to form the equations.

Vector AB = B - A = (4, 3, 9) - (-3, 2, 8) = (7, 1, 1).

The direction vector of the line is AB = (7, 1, 1).

Vector equation:

R = A + t(AB)

R = (-3, 2, 8) + t(7, 1, 1)

R = (-3 + 7t, 2 + t, 8 + t)

Parametric equations:

x = -3 + 7t

y = 2 + t

z = 8 + t

Symmetric equations:

(x + 3) / 7 = (y - 2) / 1 = (z - 8) / 1

c) A symmetric equation cannot exist for a plane because symmetric equations are used to represent lines. Symmetric equations involve comparing the ratios of differences between the coordinates of a point on the line to the components of the direction vector. However, planes are two-dimensional surfaces and cannot be represented using a single equation with ratios like symmetric equations. Instead, planes are typically represented using vector or Cartesian equations.

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The required expression can express h in terms of A and b as \($ h = \frac{2A - a}{b} $$\)

Mathematical expressions consist of at least two numbers or variables, at least one math procedure, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical procedure. An expression's form is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

First, we can start by isolating the term that contains h on one side of the equation. To do this, we will first distribute the 0.5 term to get:

A = 0.5a + 0.5bh

Then, we can subtract 0.5a from both sides to get:

A - 0.5a = 0.5bh

Next, we can divide both sides by 0.5b to isolate h:

\($ \frac{A - 0.5a}{0.5b} = h $$\)

Simplifying the expression further, we can see that:

\($$ \boxed{h = \frac{2A - a}{b}} $$\)

Therefore, we can express h in terms of A and b as:

\($ h = \frac{2A - a}{b} $$\)

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