The two-way table shows the number of houses on the market in the castillos’ price range. a 6-column table has 4 rows. the first column has entries 1 bathroom, 2 bathrooms, 3 bathrooms, total. the second column is labeled 1 bedroom with entries 67, 0, 0, 67. the third column is labeled 2 bedrooms with entries 21, 6, 18, 45. the fourth column is labeled 3 bedrooms with entries 0, 24, 16, 40. the fifth column is labeled 4 bedrooms with entries 0, 0, 56, 56. the sixth column is labeled total with entries 88, 30, 90, 208. what is the probability that a randomly selected house with 2 bathrooms has 3 bedrooms? 0.2 0.4 0.6 0.8

Answer:

Step-by-step explanation:

The given probability, the collection of all possible outcomes is sample space.

Probability is the statistics term that defines a number that reflects the chance or likelihood that a particular event will occur.

Here we have given that i roll a four-sided die. the possible outcomes are 1, 2, 3, or 4, depending on the number of spots on the side of the die that is face down.

And we need to find collection of all possible outcomes is called.

While we looking into the given question, we know that,

In order to solve this one, we must know the definition of sample space.

The term sample space means a collection or a set of possible outcomes of a random experiment.

According to the definition, here the sample space is the set composed by all the possible outcomes of your random variable.

According this case, the random variable is 4 sided dice,

Therefore the sample space is

S = {1, 2, 3, 4}

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The difference in the elevation between the canyon and the bird's nest is 737. 3 feet

From the information given, we have that;

Let's convert the mixed fractions to improper fraction;

= - 263/ 5 = - 52. 6 feet

789 3/ 10 = 7893/ 10 = 789. 3 feet

The difference in the elevation between the canyon and the bird's nest ;

= -52. 6 + 789. 9

= 737. 3 feet

Thus, the difference in the elevation between the canyon and the bird's nest is 737. 3 feet

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The confidence interval estimate of the change in occupancy for the one-year period is approximately 53.90 to 54.10.

The confidence interval estimate of the change in occupancy for the one-year period can be calculated using the formula:

Change in occupancy = Current year occupancy - Previous year occupancy

First, let's calculate the change in occupancy:
Change in occupancy = 1,512 - 1,458 = 54

Next, we need to calculate the standard error of the change in occupancy. The formula for the standard error is:
Standard error = Square root of [(Current year occupancy rate * (1 - Current year occupancy rate))/Current year total rooms + (Previous year occupancy rate * (1 - Previous year occupancy rate))/Previous year total rooms]

To calculate the occupancy rates:
Current year occupancy rate = Current year occupancy / Current year total rooms
Previous year occupancy rate = Previous year occupancy / Previous year total rooms

Plugging in the values:
Current year occupancy rate = 1,512 / 1,800 ≈ 0.84
Previous year occupancy rate = 1,458 / 1,800 ≈ 0.81

Now we can calculate the standard error:
Standard error = Square root of [(0.84 * (1 - 0.84))/1,800 + (0.81 * (1 - 0.81))/1,800]

Simplifying the equation:
Standard error = Square root of [(0.84 * 0.16)/1,800 + (0.81 * 0.19)/1,800]
Standard error ≈ Square root of (0.001344 + 0.001449)
Standard error ≈ Square root of 0.002793

Standard error ≈ 0.0529

Finally, we can calculate the confidence interval using the formula:

Confidence interval = Change in occupancy ± (Critical value * Standard error)
The critical value depends on the desired confidence level. Let's assume a 95% confidence level, which corresponds to a critical value of 1.96 (for a large sample size).

Confidence interval = 54 ± (1.96 * 0.0529)
Confidence interval = 54 ± 0.1039
Confidence interval ≈ 53.90 to 54.10

Therefore, the confidence interval estimate of the change in occupancy for the one-year period is approximately 53.90 to 54.10.

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T is time, so replace t with 2 seconds and solve:

-16(2)^2 + 48(2)

-16(4) + 96

-64 + 96 = 32

The ball is 32 feet high in 2 seconds

Answer:

The ball is 32 feet high in 2 seconds

Step-by-step explanation:

T is time, so replace t with 2 seconds and solve:

-16(2)^2 + 48(2)

-16(4) + 96

-64 + 96 = 32

The ball is 32 feet high in 2 seconds

Answer:

The coordinates of  D(5,2)

Step-by-step explanation:

Step(i):-

Given point C(1,-4) and mid point M( 3,-1)

we have to use mid-point formula

          \((\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )\)

Step(ii):-

Given mid point M( 3,-1) and (x₂ , y₂ ) be the 'D' co-ordinates

                \((\frac{1+x_{2} }{2} ,\frac{-4+y_{2} }{2} ) = (3,-1)\)

          ⇒  \(\frac{1+x_{2} }{2} = 3\)        and  \(\frac{-4+y_{2} }{2} = -1\)

           1 + x₂ = 3 ˣ 2      and  -4 +y₂ = -2

   ⇒     x₂ = 6-1 =5         and    y₂ = -2 +4

  ⇒     x₂  = 5   and y₂ = 2

Final answer:-

The coordinates of 'D' = (5,2)

The integral ∫-Bxdx is divergent.

To determine the convergence or divergence of the integral ∫-Bxdx, we need to evaluate the integral. Since the integrand is a linear function of x, we can integrate it using the power rule for integration. Applying the power rule, we get ∫-Bxdx = -B(x^2)/2 + C, where C is the constant of integration.

Now, to determine the convergence or divergence, we need to consider the limits of the integral. As there is no specific limit given, we assume the limits of integration to be from negative infinity to positive infinity.

When we evaluate the definite integral of -Bxdx from negative infinity to positive infinity, we get the result as [-B(x^2)/2] evaluated from negative infinity to positive infinity. However, the value of x^2 approaches infinity as x approaches infinity or negative infinity. Hence, the value of the integral also approaches infinity in both directions.

Since the integral diverges and does not have a finite value, we conclude that the integral ∫-Bxdx is divergent.

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Answer:

√2 and √3

Step-by-step explanation:

Answer:

Step-by-step explanation:

√2 and 5√2 are two irrational numbers

√2 * 5√2 = \(5*\sqrt{2*2} = 5 * 2 = 10\)

and here 10 is an integer

The set that represents the intersection of sets B and C is option d. {1, d, e}.

The intersection of two sets, B and C, consists of the elements that are common to both sets. Looking at the given sets, B = {1, {2, 3}, d, e} and C = {1, 3, d, e}, we can identify the elements that are present in both sets.

Set B contains the elements 1, {2, 3}, d, and e. Set C contains the elements 1, 3, d, and e. To find the intersection of B and C, we need to identify the elements that are present in both sets.

From the given sets, we can see that the elements {2, 3} and 3 are only present in set B and not in set C. Therefore, they are not part of the intersection.

The elements that are common to both sets B and C are 1, d, and e. These elements are present in both sets B and C. Hence, the intersection of B and C is {1, d, e}.

Therefore, option d. {1, d, e} represents the set B ∩ C.

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A qualitative research paradigm is a research approach that focuses on understanding and interpreting subjective experiences, meanings, and social phenomena.

It involves collecting and analyzing non-numerical data to gain insights into individuals' perspectives and the social context in which they exist. Focus group techniques are one of the methods used within the qualitative research paradigm to gather data through group discussions.

The qualitative research paradigm aims to explore and understand the complexity and nuances of human experiences, behaviors, and social phenomena. It recognizes the importance of context and seeks to generate rich and in-depth understandings rather than generalizable conclusions. Qualitative research methods involve collecting data through methods such as interviews, observations, and document analysis. The data collected is typically in the form of words, images, or other non-numerical formats. Researchers then analyze the data using various techniques, such as thematic analysis or grounded theory, to identify patterns, themes, and meanings.

Focus group techniques are one of the commonly used methods within the qualitative research paradigm. Focus groups involve bringing together a small group of participants who share common characteristics or experiences to engage in a facilitated discussion on a specific topic of interest. The group interaction allows participants to share their perspectives, experiences, and opinions while also influencing and being influenced by others in the group. This method provides rich qualitative data and allows researchers to explore group dynamics, collective meanings, and shared understandings.

Overall, the qualitative research paradigm and focus group techniques emphasize the importance of understanding subjective experiences, social interactions, and contextual factors to gain insights into human phenomena.

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The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.

The polynomials are given below.

10x⁶ + 20x⁴ - 15x² and 5x²

The factor of the polynomial 10x⁶ + 20x⁴ - 15x² will be given as,

10x⁶ + 20x⁴ - 15x² = (5x²) · (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be given as,

⇒ (10x⁶ + 20x⁴ - 15x²) ÷ (5x²)

⇒ [(5x²) · (2x⁴ + 4x² - 3)] ÷ (5x²)

⇒ (2x⁴ + 4x² - 3)

The quotient of the polynomial 10x⁶ + 20x⁴ - 15x² by 5x² will be (2x⁴ + 4x² - 3).

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The growth constant for this exponential decay problem is -1/3, differential equation describing exponential decay is dy/dt = -k * y, when 15 grams of the material remain, rate of decay is 5 grams per unit of time.

(i) The growth constant k can be determined based on the value of the decay constant λ. In this case, the decay constant λ is given as 1/3. The relationship between the decay constant and the growth constant for exponential decay is given by the equation λ = -k.

Since we know that λ = 1/3, we can determine the value of the growth constant k by substituting this into the equation: -k = 1/3. Multiplying both sides by -1, we get k = -1/3.

Therefore, the growth constant for this exponential decay problem is -1/3.

(ii) The simple differential equation that describes exponential decay is given by dy/dt = -k * y, where y represents the quantity of the decaying material, t represents time, and k is the growth constant. The negative sign indicates that the quantity is decreasing over time due to decay.

(iii) Based on the information from parts (i) and (ii), we can now calculate the specific numeric value for the rate at which the material is decaying when we have 15 grams remaining.

Given that y = 15 grams, and the growth constant k = -1/3, we substitute these values into the differential equation:

dy/dt = -(-1/3) * 15 = 5 grams per unit of time.

Therefore, the rate at which the material is currently decaying, when we have 15 grams of the material remaining, is 5 grams per unit of time.

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The probability that a student who had a dog also had a cat would be = 7/25.

To calculate the possible outcome of the given event, the formula for probability should be used and it's given below as follows. That is;

Probability = possible outcome/sample space

possible outcome = 7

sample space = 7+2+3+13 = 25

Probability = 7/25

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Answer:

-21

you "forget" the negative symbol and add like normal, then put the negative symbol in front of your answer

The height of the tree is approximately 156.7 feet.

What is Trigonometry?

Trigonometry is the study of angles and the angular relationships of planar and three-dimensional shapes. Trigonometry is made up of trigonometric functions (also known as circle functions) such as cosecant, cosine, cotangent, secant, sine, and tangent.

The height of the tree can be calculated using trigonometry.

Let's call the height of the tree "h".

Then, using the right triangle formed by the height of the tree, the distance from the base of the tree to where Jerome is standing, and the angle between the ground and the top of the tree, we can set up the following equation:

tan(33°) = h / 90

Solving for h, we get:

h = 90 * tan(33°)

Using a calculator to find the value of tan(33°), we get:

h = 90 * 1.730

h ≈ 156.7 feet

So, The height of the tree is approximately 156.7 feet.

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Answer:

D) 10x - 24

Step-by-step explanation:

Bc I know maths a lot

Answer:

20%

Step-by-step explanation:

1.2*1.2=1.44

We are asked to determine the p-values for a proportion that is greater than 0.51. Since we are asked about the hypothesis being greater then the p-value is given by:

This is a right-tailed test. To determine this probability we need to use the fact that:

replacing we get:

Now, from the tables for z-scores in the normal distribution we get:

Therefore, the p-value is 0.0011

Answer:

Step-by-step explanation:

Distance between two points \((x_1,y_1)\) and \((x_2,y_2)\) is given by the formula,

Distance = \(\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

a). A(-6, -4), B(-3, -1)

Distance between A and B = \(\sqrt{(-6+3)^2+(-4+1)^2}\)

                                             = \(\sqrt{9+9}\)

                                             = 3√2

                                             = 4.2 units

b). C(3.5, 1), D(-4, 2.5)

Distance between C and D = \(\sqrt{(3.5+4)^2+(1-2.5)^2}\)

                                              = \(\sqrt{58.5}\)

                                              = 7.65

                                              ≈ 7.7 units

c). Distance between X(5, -5) and Y(-5, 5)

    Distance = \(\sqrt{(5+5)^2+(-5-5)^2}\)

                    = \(\sqrt{200}\)

                    = 10√2

                    = 14.14

                    ≈ 14.1 units

Answer:

61 gallons

Step-by-step explanation:

16 cups per gallon: 976 cups/16 cups= 61 gallons

Answer:

61 gallons

Step-by-step explanation:

if you converted 976 cups to gallons, you would have 61 gallons.

P.S. your calculator should have volume calculations on it.

Answer:

-6

cuz I'm smart. big brain time

Point (2, 10) is lie on the graph of the line.

What is Equation of line?

The equation of line with slope m is defined as;

y - y₁ = m (x - x₁)

Given that;

A student graphs a line that passes through the points (3, 15) and (0, 0).

Now, We find slope of line as,

m = 0 - 15 / 0 - 3

m = 5

So, The equation of line that passes through the points (3, 15) and (0, 0) is,

y - 15 = 5 (x - 3)

y - 15 = 5x - 15

y = 5x

Now, We can draw the graph of line y = 5x.

Clearly, the point (2, 10) is lie on the graph of line.

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The complete question is this;

A student graphs a line that passes through the point (3, 15) and the origin.

Which points could also be on the graph of the line?

Select all that apply.

A (1.3)

B (2.10)

С (2.14)

D (6, 30)

E (7.21)

F (8.20)

The length of the curve ⟨2t, ln(t), t²⟩ over the interval 1 ≤ t ≤ 5 is 32.54 units

Here, the parametric form of he curve is ⟨2t, ln(t), t²⟩

We know that the arc length of a curve r(t) = ⟨x(t), y(t), z(t)⟩ can be found by the formula S =\(\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dx\) over the interval a ≤ t ≤ b

Here, x(t) = 2t

x'(t) = 2

y(t) = ln(t)

y'(t) = 1/t

z(t) = t²

z'(t) = 2t

Using above formula the length of the curve would be,

\(S=\int\limits^8_1 {\sqrt{(2)^2+(\frac{1}{t} )^2+(2t)^2} } \, dt\\\\ S=\int\limits^8_1 {\sqrt{4+\frac{1}{t^2}+4t^2} } \, dt\\\\S=2\int\limits^8_1 {\sqrt{1+\frac{1}{4t^2}+t^2} } \, dt\\\\S=\frac{ln(8)+63}{2}\)

S = 32.54 units

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The complete question is:

Compute the length of the curve ⟨2t, ln(t), t²⟩ over the interval 1 ≤ t ≤ 5.

Answer:

There were 15 small boxes shipped and 5 large boxes shipped.

Step-by-step explanation:

Let s = the number of small boxes shipped

Let l = the number of large boxes shipped

Each small box weigh 35 pounds, so (s) small boxes weigh 35s pounds. Each large box weigh 65 pounds, so (l) large boxes weigh 65l pounds. Therefore, the total weight 35s + 65l equals 850:

                                                 35s + 65l = 850

Since there were 3 times as many small boxes shipped as large boxes, there were MORE small boxes, so if we multiply 3 by the number of large boxes, we will get the number of small boxes, meaning s equals 3l

                                                  s = 3l

Write System of Equations:

                                                 35s + 65l = 850

                                                     s = 3l

Substitute value of s into the first equation:

35(3l) + 65l = 850

105l + 65l = 850

170l    850

__   =   __  

170      170

  l = 5

Since l = 5, we know 5 large boxes were shipped.

Use l = 5 to solve for s:

s = 3l

s = 3(5)

s = 15

Since s = 15, we know 15 small boxes were shipped.

The value of the expression is r'(t) = (4, 6t, 12t²), T(1) = (2/7, 3/7, 6/7), r''(t) = (0, 6, 24t), r'(t) ร r''(t) = 144t³.

We are given the vector-valued function r(t) = (4t, 3t², 4t³).

To find r'(t), we need to take the derivative of each component of r(t) with respect to t:

r'(t) = (d/dt)(4t), (d/dt)(3t²), (d/dt)(4t³)

r'(t) = (4, 6t, 12t²)

To find T(1), we need to evaluate r'(t) at t = 1 and then divide by the magnitude of r'(1):

r'(1) = (4, 6(1), 12(1)²) = (4, 6, 12)

| r'(1) | = sqrt(4² + 6² + 12²) = sqrt(196) = 14

T(1) = r'(1) / | r'(1) | = (4/14, 6/14, 12/14) = (2/7, 3/7, 6/7)

To find r''(t), we need to take the derivative of each component of r'(t) with respect to t:

r''(t) = (d/dt)(4), (d/dt)(6t), (d/dt)(12t²)

r''(t) = (0, 6, 24t)

Finally, to find r'(t) ร r''(t), we need to take the dot product of r'(t) and r''(t):

r'(t) ร r''(t) = (4, 6t, 12t²) ร (0, 6, 24t)

r'(t) ร r''(t) = 0 + 6t(6t) + 12t²(24t)

r'(t) ร r''(t) = 144t³

Therefore, we have:

r'(t) = (4, 6t, 12t²)

T(1) = (2/7, 3/7, 6/7)

r''(t) = (0, 6, 24t)

r'(t) ร r''(t) = 144t³

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The edge length of the unit cell of Chromium (Cr) in a BCC structure with a density of 7.19 g/cm3 is approximately 2.88 Å, and the radius of the Chromium atom is approximately 1.15 Å.

To calculate the edge length of the unit cell, we can use the formula: edge length = (4 * atomic radius) / √3.

Given that the density is 7.19 g/cm3 and the atomic mass of Chromium is 51.996 g/mol, we can calculate the volume of the unit cell using the formula: volume = (mass / density) * (1 mole / atomic mass).

Next, we can calculate the number of atoms per unit cell using the formula: number of atoms = (6.022 × 10^23) / (volume * Avogadro's number).

Since Chromium has a BCC structure, there is one atom at each corner of the cube and an additional atom at the center of the cube. Therefore, the number of atoms per unit cell is 2.

Using the number of atoms per unit cell, we can find the radius of the Chromium atom using the formula: radius = (edge length * √3) / 4.

Substituting the values into the formulas, we find that the edge length is approximately 2.88 Å and the radius is approximately 1.15 Å.

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In order for the chi-square statistic to be valid, one of the assumptions that must be met is that the frequency for each cell must be at least 5.

In the given scenario, the observed frequencies are 3 and 5, while the expected frequencies are also 3 and 5. As per the assumption, both observed and expected frequencies need to be at least 5 for each cell.

This assumption is crucial because when the frequency in a cell is too low, it may lead to unreliable results and an inaccurate assessment of the association between variables. When the frequencies are small, the chi-square test becomes less reliable and can produce misleading outcomes. This is because the chi-square distribution, which underlies the test, assumes that the sample size is large enough for the approximation to hold. By setting a minimum frequency of 5, it helps ensure that the sample size is sufficient for the chi-square test to be appropriate and valid.

In the given scenario, the observed frequencies do not meet the assumption since one of the cells has an observed frequency of 3, which is below the required minimum of 5. Therefore, this violates the assumption necessary for the chi-square statistic to be applied reliably. It would be advisable to either increase the sample size or combine categories to meet the minimum frequency requirement and ensure the validity of the chi-square test results.

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Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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