The data represents the heights of eruptions by a geyser. Use the heights to construct a stemplot. Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest.

Height of eruption
62 33 50 90
80 50 40 70
50 63 74 53
55 64 60 60
78 70 43 82

Required:
Identify the two values that are closest to the middle when the data are sorted in order from lowest to highest. The values closest to the middle are_________inches and_______inches.

To match the graphs of cylinders a and b to cylinders P and Q, we need to analyze the relationship between the height of the water and the volume of water in each cylinder.

Cylinder P would correspond to graph b, while Cylinder Q would correspond to graph a.

The reasoning behind this is as follows:

Cylinder P, corresponding to graph b, shows a steeper increase in height with increasing volume. This indicates that the water level rises quickly as more volume is added, suggesting that the cylinder has a smaller cross-sectional area. Since height is directly proportional to volume for a cylinder, a smaller cross-sectional area would result in a higher rise in height for the same volume of water.

Cylinder Q, corresponding to graph a, shows a slower increase in height with increasing volume. This implies that the water level rises more gradually as more volume is added, indicating a larger cross-sectional area. A larger cross-sectional area would result in a smaller increase in height for the same volume of water.

In summary, the steeper graph b matches Cylinder P with a smaller cross-sectional area, while the gentler graph a matches Cylinder Q with a larger cross-sectional area.

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Answer:

Number of courses would best be considered a discrete variable and drive time would be considered a continuous variable.

Step-by-step explanation:

Discrete variable:

Countable amounts(0, 1, 2, 3,...)

Continuous variables:

Can be decimal values.

In this question:

The number of courses is a countable amount(0,1,2,3,...), you cant take half a course, for example, so it is discrete. Otherwise, drive time accepts half minutes, for example, 10.5 minutes, so is continuous.

Number of courses would best be considered a discrete variable and drive time would be considered a continuous variable.

The number 3.01 is a statistic, the symbol for the number 3.01 is μ_hat; and To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours).

The number 3.01 is a statistic.

The symbol for the mean number of hours per day spent watching TV for the sample of 100 Cal Poly students is μ_hat.

To conduct a simulation-based test of significance, we need to compare the observed mean (3.01 hours) with the hypothesized mean (2.75 hours). The null hypothesis is that the population mean (μ) is equal to 2.75 hours, and the alternative hypothesis is that the population mean is not equal to 2.75 hours.

Steps to find p-value:

1. Calculate the difference between the observed mean and the hypothesized mean: d = μ_hat - 2.75 hours

2. Generate a large number of random samples with the same sample size as the original sample, and calculate the mean of each sample.

3. Calculate the difference between the mean of each sample and the hypothesized mean and store the values in a list.

4. Count the number of differences that are equal to or greater than the difference between the observed mean and the hypothesized mean (d).

5. Divide the count by the total number of simulations to get the p-value. This gives us the probability of getting a sample mean equal to or greater than the observed mean if the null hypothesis is true.

6. Compare the p-value with the significance level (α) to determine whether to reject or fail to reject the null hypothesis. If the p-value is less than α, we reject the null hypothesis and conclude that the data provide evidence that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.

If the p-value is greater than α, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the average number of hours per day Cal Poly students spending the time watching TV is different from 2.75 hours.

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--The given question is incomplete; the complete question is

"Reconsider Dr Sameer's research question about how much time Cal Poly students spend watching television. Suppose that Dr Sameer surveys a random sample of 100 Cal Poly students, and for this sample, the mean number of hours per day spent watching TV turns out to be 3.01 hours.

1. Is the number 3.01 a parameter or a statistic?

2. Assign an appropriate symbol to the number 3.01.

3. Describe how you can conduct a simulation‐based test of significance to investigate whether the data provide evidence that the average number of hours per day Cal Poly students spend watching TV is different from 2.75 hours. Be sure to provide details on how one would find a p‐value."--

The course of the airplane relative to true north is 094°, and the ground speed is 344.2 km/h.

The horizontal and vertical component of the airspeed is calculated as follows;

Vx = 300 cos(30) = 259.8 km/h

Vy = 300 x sin(30) = 150 km/h

The horizontal and vertical component of the wind velocity is calculated as follows;

Vx = 50 cos(60) = 25 km/h

Vy = 50 sin(60) = 43.3 km/h

To find the resultant velocity, we can add the x and y components separately:

Vx = 259.8 km/h  +  25 km/h = 284.8 km/h

Vy = 150 km/h  +  43.3 km/h  = 193.3 km/h

The magnitude of the resultant velocity is calculated as;

V = √(284.8² + 193.3²)

V = 344.2 km/h

The direction of the resultant velocity is calculated as;

θ = arc tan (193.3/284.8)

θ = 34.2⁰

The resultant direction to true north is calculated as;

track = 34.2 + 60 = 94.2°

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From the given formulas, formula A is a tautology or always true. Formula B is a contradiction or never true. And, formula C is contingency or sometimes true.

Using the truth table, a given expression is said to be in tautology when all the values are true. The given expression is said to be a contradiction when all the values are false or never true. And the given expression is said to be contingency when the values are either true or false.

In the given formulas, formula A (p→q)∨(q→r) is a tautology. This is because the values in all rows are true (T).

In the given formulas, formula B (¬(¬(p∧q)→(p→¬q))) is a contradiction. This is because the values in all rows are false (F).

In the given formulas, formula C ((¬p∨q)→q) is a contingency. This is because some values are true and some are false.

The complete question is -

Determine whether each of the following formulas is a tautology, contingency, or contradiction (this means always true, sometimes true, never true). Show how you arrived at each answer. Use equivalence-style proofs.

A. (p→q)∨(q→r)

B. ¬(¬(p∧q)→(p→¬q))

C. ((¬p∨q)→q)

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An equation has terms, variables, constants and coefficients.

A term is the part of the equation that is separated by addition or subtraction signs.

A variable is usually symbolized by a letter in place of an unknown value.

The coefficient is the number before the variable, the ones that multiply it.

The constans are the known values or numbers that appear in the equation.

For example:

3X+16

This equation has two terms "3X" and "16"

One variable "X"

One coefficient "3"

One constant "16"

Answer:

y = -3x + 2

Step-by-step explanation:

Use rise over run to find the slope of the line:

change in y / change in x:

-6 / 2

= -3

Plug in the slope and a given point into y = mx + b, and solve for b:

y = mx + b

5 = -3(-1) + b

5 = 3 + b

2 = b

Plug in the slope and b into y = mx + b:

y = mx + b

y = -3x + 2

So, the equation of the line is y = -3x + 2

Answer:

3(x + 5y) - 2(x + y)

3x + 15y - 2x - 2y

x + 13y

(3x + 15y) + (-2x + -2y)

x + 13y

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

Answer

1/3

Step-by-step explanation:

This is because the number of spaces in between all the dots is 3 and so each of those spaces is 1/3, therefore a-b is one line which is 1/3. :3

Answer: plant → grasshopper → spider → frog → lizard → fox → hawk.

This is just one food chain that shows the sider and the lizard in the same foodchain. The frog eats the spider, and the lizard eats the frog.

Step-by-step explanation:

Answer:

$10.40

Step-by-step explanation:

Just like any other percent problem, subtract 20%.

$13 - 30% = $10.40

Your answer is $10.40. Hope this helps!

The x and y-intercepts of the rational function are; (-3, 0) and (0, -3/25).

The vertical asymptotes of the function are; x = ± 5.

The horizontal asymptotes of the function is f(x) = 0.

For x-intercept; let f (x) = 0;

0 = (x + 3) / (x² - 25)

x + 3 = 0; x = -3 or (-3, 0).

For the y-intercept; let x = 0.

f (0) = (0 + 3) / (0² - 25)

= -3/25 or (0, -3/25).

For the vertical asymptotes;

x² - 25 = 0

x² = 25

x = ±5.

For the horizontal asymptote;

Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is; f (x) = 0.

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The expressions are simplified to;

1. 72n² + 63n

2. 18t - 18t²

3. -18b² - 18b

4. -56r - 21r²

5. -6m + 9m²

Algebraic expressions are simply described as expressions that are known to consist of coefficients of variables, variables, constants, terms, and factors.

These algebraic expressions are also made up of mathematical or arithmetic operations.

These operations are;

From the information given, we have;

1. -9n (-8n -7)

expand the bracket

72n² + 63n

2. -2t(-9 + 9t)

expand the bracket

18t - 18t²

3. -3b(6b + 6)

expand the bracket

-18b² - 18b

4. -7r(8 + 3r)

expand the bracket

-56r - 21r²

5. 3m(-2 + 3m)

expand the bracket

-6m + 9m²

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Answer:

605

Step-by-step explanation:

11x55=605

Answer:

\( - \frac{1}{10} \times (25z + 52)\)

Step-by-step explanation:

-1/2 (7z + 4) + 1/5 (5z - 16)

-1/10 × (5(7z + 4) - 2 (5z - 16))

-1/10 × (35z + 20 - 10z + 32)

= -1/10 × (25z + 52)

Answer:

23

Step-by-step explanation:

plug in

2(7)+3(3)

14+9

23

Answer:

23 is the answer

Step-by-step explanation:

2*7+3*3

14+9

23

Ok, in the first one we have the following posible side lenghts:

3,12,13

We are going to check if S+M>L, so let's do it: 3+12>13 --->15>13, that is true so the answer is Yes.

Now let's check if is a right triangle:

¿3²+12²=13²?

9+144=169

153 is diferent of 169, so isn't a right triangle.

Considering that isn't a right triangle neither is it "triple pythagorean" because don't satisfy that a²+b²=c.

So, the answer in the first row are: Yes, No, No.

Answer:

Its J

Step-by-step explanation:

Answer:

The slope of the line.

Step-by-step explanation:

In other words, SLOPE is the VERTICAL change between any two points divided by the HORIZONTAL change in any two points.

Answer

The constant rate of change of a line is also called what

...SLOPE...

Answer:

4/7

Step-by-step explanation:

(8-4)/(10-3) = 4/7

parallel = same slope

Answer:

The slope of line n is 4/7

Step-by-step explanation:

First find the slope of line m

m = ( y2-y1)/(x2-x1)

m = (8 - 4)/(10 -3)

m = 4/7

Parallel lines have the same slope

The slope of line n is the same as slope of line m

The slope of line n is 4/7

The lengths of the segments x and y in the right triangles are x = 6√2 and y = 12√2

The given shape is the right-angled triangle

Such that

We have angles = 30 degrees and 45 degrees

The measure of y can be calculated using the following sine ratio

sin(45) = y/24

Make y the subject

So, we have

y = 24 * sin(45)

When evaluated, we have

y = 12√2

The length x is calculated as

sin(30) = x/y

So, we have

x = y * sin(30)

This gives

x = 12√2 * 1/2

Evaluate

x = 6√2

Hence, the value of x in the triangle is 6√2

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Step-by-step explanation:

The bisection method is a root-finding algorithm that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. To apply the bisection method to the equation x^3 - x - 9 = 0, you need to find two initial values a and b such that f(a) and f(b) have opposite signs. This means that there is at least one root of the equation in the interval [a, b].

Let’s take a = 2 and b = 3 as our initial interval. We can see that f(2) = 2^3 - 2 - 9 = -1 and f(3) = 3^3 - 3 - 9 = 18, so f(a) and f(b) have opposite signs.

Now we can apply the bisection method as follows:

Calculate the midpoint c = (a + b)/2 = (2 + 3)/2 = 2.5.

Evaluate f© = 2.5^3 - 2.5 - 9 ≈ 5.625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

Calculate the new midpoint c = (a + b)/2 = (2 + 2.5)/2 = 2.25.

Evaluate f© ≈ 1.765625.

Since f© > 0 and f(a) < 0, there must be a root in the interval [a, c]. So we set b = c and repeat the process.

We can continue this process until we reach the desired level of accuracy.

Answer:

Step-by-step explanation:

(2⁶)ˣ = 1

2⁶ˣ = 1

6x = 0

x = 0

Answer:

The answer is $700

Step-by-step explanation:

Brainliest plzz

Answer:

9 minutes is the half life of the radioisotope.

Step-by-step explanation:

Given;

initial count rate = 7,600 counts per minute

final count rate = 1,900 counts per minute

elapsed time, t = 18 minutes

The half life of the radioisotope is calculated as;

       Time (half life) --------------------------remaining count rate

                     0  ------------------------------7,600 counts per minute

                      x ------------------------------3,800 counts per minute

                     2x----------------------------- 1,900 counts per minute

thus, 2x = 18 minutes

x = 18 / 2

x = 9 minutes

Therefore, 9 minutes is the half life of the radioisotope.

Answer:

The indicated angle is approximately 31 degrees

Step-by-step explanation:

Since this is a right angle, we can use trig functions

cos theta = adj/ hyp

cos theta = 12/14

Take the inverse cos of each side

cos ^-1 cos theta = cos ^-1 ( 12/14)

theta =31.00271913

The indicated angle is approximately 31 degrees