MATH
NATION
The data from a survey of ages of people taking an exercise class was skewed to the left.
Part C: The box plot represents the data. Calculate the appropriate measure of spread.
Answer choices:
A. IQR= 45
B. IQR= 13
C. Standard deviation = 8
D. Standard deviation=55

Answer:

A)94.5 cm

Step-by-step explanation:

height = 9cm

Base 1 = 5cm

Area of a Trapezoid = 1/2 × (b1 + b2)h

h = 9cm

b1 = 5cm

b2 = (9 cm + 5cm + 2cm) = 16cm.

Area of Trapezoid

= 1/2 (5 + 16) × 9

= 1/2 × 21 × 9

= 94.5 cm

Option A is the correct answer

It takes approximately 14 minutes for the thermometer to reach a temperature of 58°F in the cold storage room. This calculation is based on Newton's Law of Cooling and the initial and final temperature readings.

To determine how long it takes for the thermometer to reach 58°F, we can use Newton's Law of Cooling. Let's plug in the given values into the equation and solve for the time (t):

88 = 37 + (96 - 37)e^(k * 5)

Simplifying the equation, we have:

51 = 59e^(5k)

Taking the natural logarithm of both sides:

ln(51/59) = 5k

Solving for k, we find:

k ≈ -0.0436

Now, we can use this value of k to find the time (t) when the thermometer reaches 58°F:

58 = 37 + (96 - 37)e^(-0.0436 * t)

Simplifying further, we have:

21 = 59e^(-0.0436 * t)

Taking the natural logarithm again:

ln(21/59) = -0.0436 * t

Solving for t, we find:

t ≈ 13.58

Rounding to the nearest whole minute, it takes approximately 14 minutes for the thermometer to reach 58°F.

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The annual growth rate under the exponential model is approximately 0.17 or 17%.

To calculate the annual growth rate under the exponential model, we can use the formula:

Annual Growth Rate = (Final Value / Initial Value) ^ (1 / Number of Years) - 1

In this case, the initial value is 2,535,225 complaints of domestic violence as of December 31, 2017, and the final value is 2,956,300 complaints as of December 31, 2019. The number of years is 2.

Plugging in the values:

Annual Growth Rate = (2,956,300 / 2,535,225) ^ (1 / 2) - 1

= 1.1654 - 1

= 0.1654

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Answer:

taco bell

Step-by-step explanation:

per one taco at taco bell $0.53

per one taco at los comales $0.62

The expression for dL/dA, which represents the rate of change of ladybugs (L) with respect to aphids (A), is 0.5L + 0.0001AL - 2A + 0.01AL.

To find the expression for dL/dA, we need to differentiate the equation dL/dt with respect to A. The given equations are:

dA/dt = 2A - 0.01AL

dL/dt = -0.5L + 0.0001AL

To find dL/dA, we differentiate dL/dt with respect to A:

dL/dA = (dL/dt) / (dA/dt)

Substituting the given equations into this expression, we have:

dL/dA = (-0.5L + 0.0001AL) / (2A - 0.01AL)

Simplifying further, we can rearrange the terms:

dL/dA = -0.5L / (2A - 0.01AL) + 0.0001AL / (2A - 0.01AL)

Combining the terms with a common denominator, we get:

dL/dA = (0.0001AL - 0.5L) / (2A - 0.01AL)

So, the expression for dL/dA is (0.0001AL - 0.5L) / (2A - 0.01AL), which represents the rate of change of ladybugs with respect to aphids in the given model.

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Answer:

1) x = 36

2) x = 127

3) x = 36

Step-by-step explanation:

1)

x + 144 = 180

x = 36

2)

15 + x + 38 = 180

x + 53 = 180

x = 127

3)

2x + 16 + 92 = 180

2x + 108 = 180

2x = 72

x = 36

Answer: what do you need help with??

Step-by-step explanation:

Answer: $770

Step-by-step explanation:

Number of units to be purchased by Alicia:

= 200,000 / 1,000

= 200 units

Alicia is purchasing a 5-year term life insurance policy. At age 30, the cost per $1,000 unit of insurance is $3.85 for a female.

The formula for the annual premium is:

= Number of units purchased * Premium per $1,000

= 200 * 3.85

= $770

Answer:

C. 37

Step-by-step explanation:

winindoutpickc

There exists a connected undirected graph with a degree sequence of 2, 2, 3, 3, 4. This graph does not have an Euler circuit or an Euler path, but it does have a Hamiltonian circuit.

To construct a graph with the given degree sequence, we can start by connecting the vertices with the highest degree (degree 4) to each other. This ensures that each of these vertices has a degree of at least 4. Then, we can connect the vertices with degree 3 to the remaining vertices. Finally, we connect the remaining vertices with degree 2 to complete the graph.

(a) Yes, a connected undirected graph having degree sequence 2, 2, 3, 3, 4 does exist. Here is an example of such a graph:

   1

  / \

 2 - 3

  \ /

   4

    \

     5

In this graph, vertex 1 has degree 2, vertex 2 has degree 3, vertex 3 has degree 4, vertex 4 has degree 3, and vertex 5 has degree 2.

(b) (i) No, this graph does not have an Euler circuit. An undirected, connected graph has an Eulerian circuit if and only if it has 0 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit.

(ii) Yes, this graph does have an Euler path. An undirected, connected graph has an Eulerian path if and only if it has either 0 or 2 vertices of odd degree1. In this case, the graph has 4 vertices of odd degree (1, 2, 4, and 5), so it does not have an Euler circuit but it does have an Euler path.

(iii) No, this graph does not have a Hamiltonian circuit. A Hamiltonian circuit is a cycle that visits each vertex exactly once. This graph does not have a Hamiltonian circuit because there is no way to visit all the vertices exactly once and return to the starting vertex without repeating any edges or vertices.

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1. The costs the firm spends on financing should be included in its capital budget cash flow analysis. This includes expenses related to obtaining funds for the project, such as interest payments on loans or fees for issuing stocks.

2. The source of a firm's financial leverage is the use of debt and preferred stock. By utilizing debt and preferred stock, a company can increase its financial leverage, which refers to the use of borrowed funds to finance its operations or investments.

3. Operating risk derives from the risk that comes from a firm's mix of fixed and variable costs. This refers to the uncertainty and potential negative impact on profitability due to the combination of fixed costs (such as rent, salaries) and variable costs (such as raw materials, utilities) in a company's cost structure.

4. The firm's liabilities exceeding its assets is not a legal constraint on the payment of dividends. This constraint is related to solvency and insolvency issues and not directly linked to the payment of dividends.

5. According to the information effect, investors view changes in a firm's dividend policy as a signal about the firm's financial condition.

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Answer:

Sam made a mistake. The answer should have been 30.

This is what Sam should have done:

2n^2 - 20

2n^2 - 20 = 2(5)^2 - 20

= 2(25) - 20

= 50 - 20

= 30

Sam multiplied 2 and 5 when he should have done the power first.

Step-by-step explanation:

so let's say that the width is x then the length is x+15

and the area of a square is length times width

x(x+15)=100

x^2+15x-100=0

(x+20)(x-5)=0

x=5 or x=-20 but a side length can't be negative so x would equal 5

Length=x+15 with 5 as x

Length=20

Width=5

Hope that helps :)

Step-by-step explanation:

all you have to do is number the line from -5 to 5 and just plot the points next to it

The probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or less is approximately 0.0048, or 0.48%.

To calculate this probability, we need to standardize the sample mean using the z-score formula and then find the corresponding probability from the standard normal distribution.

The formula for the z-score is:

z = (x - μ) / (σ / √n)

where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, x = 6, μ = 7.5, σ = 5, and n = 64. Substituting these values into the formula, we get:

z = (6 - 7.5) / (5 / √64)

Simplifying the expression:

z = -1.5 / (5 / 8)

z = -1.5 * 8 / 5

z = -2.4

From Table A (standard normal distribution table), the area to the left of z = -2.4 is approximately 0.0082.

However, since we are interested in the probability of obtaining a mean replacement time of 6 years or less, we need to find the area to the right of z = -2.4. This is given by:

1 - 0.0082 = 0.9918

Therefore, the probability that the 64 randomly selected TV sets will have a mean replacement time of 6 years or less is approximately 0.0048, or 0.48%.

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Answer:

Thanks for letting me know I might try that later today

Step-by-step explanation:

:)

Yes, it can be concluded at α = 0.05 that the average size of the farms in the two counties is different.

Traditional Method:

To test the hypothesis that the average sizes of farms in Indiana County and Greene County are different, we can use a two-sample t-test. The traditional method involves the following steps:

1. Formulate the null hypothesis (H0) and the alternative hypothesis (Ha):

  H0: μ1 = μ2 (The average sizes of farms in both counties are equal)

  Ha: μ1 ≠ μ2 (The average sizes of farms in both counties are different)

2. Determine the significance level (α): α = 0.05 (given)

3. Calculate the test statistic:

  t = (x1 - x2) / sqrt((s1^2 / n1) + (s2^2 / n2))

  where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.

4. Determine the degrees of freedom:

  df = n1 + n2 - 2

5. Find the critical value(s) corresponding to the chosen significance level and degrees of freedom from the t-distribution table.

6. Compare the test statistic with the critical value(s) to make a decision:

  If the absolute value of the test statistic is greater than the critical value(s), reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

P-value Method:

Alternatively, we can use the p-value method to perform the hypothesis test. The p-value is the probability of obtaining a test statistic as extreme as the observed value (or more extreme), assuming the null hypothesis is true.

1. Formulate the null hypothesis (H0) and the alternative hypothesis (Ha) as mentioned earlier.

2. Determine the significance level (α): α = 0.05 (given)

3. Calculate the test statistic as described above.

4. Calculate the p-value corresponding to the test statistic using the t-distribution.

5. Compare the p-value with the significance level:

  If the p-value is less than α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

In this case, both the traditional method and the p-value method lead to the same conclusion. If the p-value is less than 0.05, we reject the null hypothesis and conclude that the average sizes of farms in Indiana County and Greene County are different.

Note: Since the sample sizes are relatively small (8 and 10), it is assumed that the populations are normally distributed.

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The center of the sphere is (-2, 1, 0).

The radius of the sphere is √65.

The given equation is x² + y² + 2 + 4x - 2y - 62 = 0.

We can rewrite the given equation as follows:

x² + 4x + y² - 2y = 60

Completing the square of x and y, we get:

(x + 2)² - 4 + (y - 1)² - 1 = 60

(x + 2)² + (y - 1)² = 65

Now, we know that the general equation of the sphere is :

(x - a)² + (y - b)² + (z - c)² = r² where (a, b, c) is the center of the sphere, and r is the radius.

To compare the given equation with the equation of the sphere, we will have to convert it into the standard form as follows:

(x + 2)² + (y - 1)² + (0 - 0)² = √65²

The center of the sphere is (-2, 1, 0), and its radius is √65.

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Answer:

The answer is A.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A is the correct answer on Edge

Japan's superconducting bullet that is being tested in Yamanashi Maglev Test Line will have an elevation of 2580 meters and actual distance of the track as 6.9 kilometers.

A. To calculate the elevation change in the steepest section of the track:

Grade = 40% (Given)

Horizontal distance = 6450 meters (Given)

Elevation change = Grade × Horizontal distance

= 40% × 6,450 meters

= 0.40 × 6,450 meters

= 2,580 meters

Therefore, the elevation change in this section of the track will be 2,580 meters.

B. To find the actual distance of the track in this section:

By using Pythagorean theorem, the horizontal distance represents the base of a right triangle, and the elevation change represents the height.

Actual distance of the track = √(Horizontal distance² + Elevation change²)

= √(6,450²  + 2,580² )

= √(41,602,500 + 6,656,400)

= √48,258,900

= 6,945 meters

= 6.9 kilometers

Therefore, the actual distance of the track in this section will be 6.9 kilometers.

C.  To determine which plane is closer to the tower:

Plane A: Altitude = 20,000 ft, Distance from tower = 5 km

Plane B: Altitude = 8,000 ft, Distance from tower = 7 km

1 ft is approximately equal to 0.0003048 km.

Altitude of Plane A in km = 20,000 ft × 0.0003048 km/ft ≈ 6.096 km

Altitude of Plane B in km = 8,000 ft × 0.0003048 km/ft ≈ 2.4384 km

On comparing the distances, we find that Plane A is closer to the tower than Plane B.

Therefore, Plane A is closer to the tower as compare to Plane B.

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Answer: 60 mph

Step-by-step explanation:

Given

The red car left at 9 am and arrives at 1 pm

time taken by the red car [tex]t_a=4\ hr[/tex]

time taken by the blue car [tex]t_b=3\ hr[/tex]

Assume the speed of the red car is v

So, the speed of the blue car is v+15

distance traveled by them is the same

[tex]\Rightarrow v\times 4=(v+15)\times 3\\\Rightarrow 4v=3v+45\\\Rightarrow v=45\ mph[/tex]

Thus, the speed of the blue car is [tex]45+15=60\ mph[/tex]

Answer:

Oh Lol i didnt even see the pic

Step-by-step explanation:

Answer:

5*2=10

10*8=80

Step-by-step explanation:

Multiply all number!!!

Answer:

6.4 because subtract 9.6 from 15

Answer:

62.5%

Step-by-step explanation:

Answer:

62.5%

Explanation:

Divide 100 by 8 to get 12.5

Multiply 12.5 by 5

Equals 62.5

Answer:

The average is 5.41666667 degrees.

Step-by-step explanation:

Answer:

Well since the question ask for what in the green box, its 193

193 goes in the green box

If you solve everything it would be 13.89 (rounded to the nearest hundredths)

Step-by-step explanation:

So missing side of a right triangle, you can use the Pythagorean Theroum which is a^2+b^2=c^2

In this case we have the two legs which are a and b, we’re trying to find hypotnuse, “c”.

7^2+12^2=c^2

49+144=c^2

193= c^2

You basically do √193

which is the answer needed for this situation

Final answer: is 193 goes into the green box

Trapezoid

---

hope it helps

sorry if i'm wrong

i used mental maths

Dude That's a square not a trapezoid

The spring constant k is approximately 35 N/m.

The spring constant (k) represents the stiffness of a spring and is defined as the force required to stretch or compress the spring by a unit distance. In this case, we are given that the spring is stretched by a force of 13.5 N, resulting in a displacement of 0.5 meters.

To find the spring constant, we can use Hooke's Law, which states that the force exerted by a spring is proportional to its displacement. Mathematically, this can be expressed as F = kx, where F is the force, k is the spring constant, and x is the displacement.

Using the given values, we have:

13.5 N = k * 0.5 m

Solving for k, we find:

k ≈ 35 N/m

Therefore, the spring constant for this system is approximately 35 N/m.

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To find the value of g(1), we need to integrate g'(x) and use the given initial condition g(4)=0.325. By integrating g'(x), we can determine the function g(x) and evaluate it at x=1 to find the desired value.

To find g(x), we integrate g'(x) with respect to x. The integral of 1/x * e^(-x) * cos(x^100) requires advanced techniques and cannot be expressed in elementary functions. Therefore, we rely on numerical methods or approximation techniques to evaluate the integral. Once we obtain the antiderivative of g'(x), denoted as G(x), we can use the initial condition g(4)=0.325 to determine the constant of integration.

Once we have the expression for g(x), we substitute x=1 to find g(1), which will provide the desired value.

Note that the process of evaluating the integral and determining g(x) can be computationally intensive and may require numerical approximation methods or specialized software tools.

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Answer: $0.3

Step-by-step explanation:

Given

The owner buys 144 pens for $28.80 i.e. each pen costs

[tex]\dfrac{28.80}{144}=\$0.2[/tex]

owner sells the pen at $0.4 i.e. price marked up by

[tex]\Rightarrow \dfrac{0.4-0.2}{0.2}\times 100=100\%[/tex]

So, the claim of the owner is incorrect

The actual increase in the price to get 50% markup

[tex]\Rightarrow 0.2\times (1+0.5)=\$0.3[/tex]