Discrete Math1) True or false? [1,5] = { 1, 2, 3, 4, 5 }.2) True or false? The interval (2,5) is the same as the interval [3,4].3) True or false? The interval [1,2] contains exactly two numbers - the numbers 1 and 2.

Answer:

1. Room size (length * width) for carpet

2. From window top to floor for curtains

Step-by-step explanation:

The mode (A) is the measure of variability used for nominal variables such as gender and political party.

When dealing with nominal variables, which represent categories or labels rather than numerical values, the mode is the most appropriate measure of variability. The mode identifies the category that appears most frequently in the dataset, representing the most common or prevalent attribute among the respondents.

In the case of gender, for example, the mode would indicate whether the majority of the sample identifies as male or female. Similarly, for political party affiliation, the mode would identify the party that has the highest number of members within the dataset.

Unlike other measures such as the standard deviation (C) or stratified variance (D), which are more suitable for numerical variables, the mode is specifically designed to capture the distribution and central tendency of nominal variables. It provides valuable insight into the dominant category within the dataset, highlighting the most frequent attribute among the observations.

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Answer:

2) 1) 25

   2) 30

Step-by-step explanation:

2) 1) 650 - 400 = 250

       250 / 10 = 25

    2) 850 - 400 = 450

         450 / 15 = 30

Answer:

The correct option is c.

Step-by-step explanation:

Given that,

u = 7i+4j and v = 2i-3j

We need to find the product of u and v. The dot product of two vectors is given by :

\(u{\cdot}v=(7i+4j){\cdot} (2i-3j)\\\\=(7i)(2i)+(4j)(-3j)\\\\=14-12\\\\=2\)

So, the dot product of u and v is equal to 2.

Answer:

75%

Step-by-step explanation:

24/6=4

1/4=6

4*6=24

24-6=18

3/4 of 24=18

3/4=75%

The percentage decrease in length of the board is 25%

From the given statement we can deduce the following:

The change in the length of the board is calculated as:

The percentage decrease in the length is calculated as;

\(Percentage \ decrease = \frac{change \ in \ length }{original \ length} \times 100\%\\\\Percentage \ decrease = \frac{6}{24} \times 100\%\\\\Percentage \ decrease = 25\%\)

Thus, the percentage decrease in length of the board is 25%

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Given the data from the question, reaction 2 is 2.83 times faster compared to reaction 1

We can determine how many times faster is reaction 2 to reaction by doing the following:

R₂ / R₁ = 0.510 / 0.180

R₂ / R₁ = 2.83

Cross multiply

R₂ = 2.83 × R₁

From the above illustration, we can see that reaction 2 is 2.83 times faster than reaction 1

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Answer:

(1,4)

Step-by-step explanation:

this is the new answer after some reviewing of the problem

The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the sampling distribution of the mean.

The sampling distribution of the mean refers to the distribution of sample means obtained from repeated sampling from the same population.

In this case, we have 15,504 different samples of size 5 drawn from a population of 20 hospitals.

Each sample has its own sample mean. The relative frequency distribution of these sample means would specify the sampling distribution of the mean.

The sampling distribution of the mean is important in statistics because it allows us to make inferences about the population mean based on the distribution of sample means.

It helps us understand the variability of sample means and provides a basis for constructing confidence intervals and conducting hypothesis tests.

Therefore, the relative frequency distribution of the mean values from the different samples would describe the characteristics of the sampling distribution of the mean..

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Answer:

27/50

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

54/100 simplified is 27/50

Mean of the sampling distribution:  μ = 63.79.

Standard deviation of the sampling distribution: σ = 0.355.

(a) Mean of the sampling distribution:

Mean of the sampling distribution = average volume.

μ = 63.79.

(b) Standard deviation of the sampling distribution:

Find σ / √n.

σ  =  2.49 ounces; n = 49 bottles

2.49 / √49 = 0.355

Thus, the mean and the standard deviation of this sampling distribution is found.

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Answer:

Step-by-step explanation:the answer is : Name the relationship between the angles below. What is the sum of the angles? Explain how you would find the missing angle. Explain each step. (replace with 120 & x)

Answer:

Base area is 36 square meters

Step-by-step explanation:

The volume of a rectangular prism is V = (height)(length)(width).  We know all of these dimensions except for the area of the base, which is (length)(width).

Solving this equation for (length)(width), we get:

                                                       volume        72 m^3

(length)(width) = (area of base) = -------------- = -------------  = 36 m^2

                                                         height          2 m

Answer:

6:9,2:3

Step-by-step explanation:

sorry I Only knew this much

Answer:

well to make life easier

You can always just simplify the given ratio

12:18 is basically 2:3 and we can use that as a base line

so we got

2:3

6:9

12:18

24:36

48: 72

It goes on you can just multiply by 2

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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The least whole number possibility for the third side is 8 cm. The greatest whole number possibility for the third side is 22 cm.

A triangle is a three-sided polygon. It is a geometric shape that has three edges and three vertices. Triangles can be classified based on their side lengths (such as equilateral, isosceles, or scalene) or based on the angles between their sides (such as acute, right, or obtuse). Triangles are a fundamental shape in geometry and are used in many branches of mathematics and physics. To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Using this rule, we can find the possible range of values for the third side of the triangle.

The least possible length of the third side would be:

8.5cm + 15cm - 15cm = 8.5cm

The greatest possible length of the third side would be:

(8.5cm + 15cm) - 1cm = 22.5cm

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It will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

Given:Ashley and Rod cleaned the house in 4 hours. Rod can clean the house alone in 2 hours.To find:How long will it take for Ashley to clean the house alone?Solution:Let's suppose the time Ashley takes to clean the house alone is x hours.Then, Ashley and Rod can clean the house in 4 hours.Thus, using the concept of work, we have:\begin{aligned} \text { Work done by Ashley in 1 hour } + \text { Work done by Rod in 1 hour } &= \text { Work done by Ashley and Rod in 1 hour } \\ \Rightarrow \frac {1}{x} + \frac {1}{2} &= \frac {1}{4} \\ \Rightarrow \frac {2 + x}{2x} &= \frac {1}{4} \\ \Rightarrow 8 + 4x &= 2x \\ \Rightarrow 2x - 4x &= -8 \\ \Rightarrow x &= 4 \end{aligned}Therefore, it will take 4 hours for Ashley to clean the house alone.Answer: Ashley will take 4 hours to clean the house alone.

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First, do the prime factorization.

96 = 2 x 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

The GCF is the product of their shared factors.

They share 2, 2, 2, and 3.

2 x 2 x 2 x 3 = 24.

Their GCF is 24.

The greatest common factor of the given numbers 96 and 72 will be equal to 24.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given number for GCF in the question,

Firstly, factorize the given numbers,

96 = 2 x 2 x 2 x 2 x 2 x 3

72 = 2 x 2 x 2 x 3 x 3

The result of their shared factors is the GCF.

2 x 2 x 2 x 3 = 24.

Therefore, the GCF is 24.

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Answer:

D

Step-by-step explanation:

Answer:

\( \frac{7}{4} \pi\)

or

\( \frac{3}{4} \pi\)

Step-by-step explanation:

See attached. I know (very haphazard). But the basic method is to inverse the trig function. This gives you the position of the terminal angle. -45 degrees means that you turned 45 degrees clockwise and are in quadrant 4. This corresponds to an angle of rotation of 315 degrees counter clockwise which is what we are looking for since the specified domain is betwern 0 and 360 degrees or 0 and 2 pi.

The next thing to remember is that Tan is also negative in Quadrant 2 (using the ASTC rule). This corresponds to an angle of rotation of 180 - 45 = 135 degrees.

Hope that helps.

Answer:

−2c+22

Step-by-step explanation:

Answer:

m<1 = 40°

m<2 = 118°

m<3 = 71°

Step-by-step explanation:

✔️m<2 = 180° - 62° (angles in a straight line/supplementary angles)

m<2 = 118°

✔️m<1 = 180° - (118° + 22°) (sum of ∆)

m<1 = 40°

✔️m<3 = 180 - (47 + 62) (sum of ∆)

m<3 = 71°

Answer:

y = - 3

Step-by-step explanation:

Locate x = 3 on the x- axis. Go vertically down to meet the line. At this point the corresponding y- value is - 3 on the y- axis

Thus when x = - 3 then y = - 3

The volume of the solid obtained by rotating the region bounded by the curves about the x-axis is π/77 (243 - 9sqrt(3)).

To find the volume of the solid obtained by rotating the region bounded by the curves about the x-axis, we can use the method of cylindrical shells. This involves integrating the circumference of a cylindrical shell times its height to obtain the volume of each shell, and then adding up the volumes of all the shells to get the total volume.

First, let's find the points of intersection of the two curves:

2/7 x^2 = 9/7 - x^2

9/7 = 9/7 x^2 + 2/7 x^2

9/7 = 11/7 x^2

x^2 = 9/11

x = ±sqrt(9/11)

The solid we obtain by rotating this region about the x-axis will have cylindrical shells with height dx, radius x, and circumference 2πx. Therefore, the volume of each shell will be:

dV = 2πx × h × dx

where h is the difference between the y-values of the curves at x:

h = (9/7 - x^2) - (2/7 x^2) = 9/7 - 9/7 x^2

Therefore, the total volume of the solid will be:

V = ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) 2πx * (9/7 - 9/7 x^2) dx

V = 2π/7 ∫(from x = -sqrt(9/11) to x = sqrt(9/11)) x(9 - 9x^2) dx

We can simplify the integrand by setting u = 9x^2:

du/dx = 18x

dx = du/18x

Substituting:

V = 2π/7 ∫(from u = 9/11 to u = 81/11) (1/2)u^(1/2) (9/2) (du/18x)

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / x du

V = π/7 ∫(from u = 9/11 to u = 81/11) u^(1/2) / sqrt(9/11 - u/11) du

This integral can be evaluated using a trigonometric substitution. Let u = 9/11 sin^2 θ, then:

du/dθ = (18/11) sin θ cos θ dθ

Substituting:

V = π/7 ∫(from θ = π/6 to θ = π/2) (81/121) sin^3 θ dθ

V = π/7 [(81/121) * (3/4) - (9/121) × (sqrt(3)/2)]

V = π/77 (243 - 9sqrt(3))

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\(\longrightarrow{\blue{ 2 \: ( \: 32 \: y + 3 \: x \: )}}\) 

\(\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}\)

\(64 \: y + 6 \: x\)

\( = 2 \: ( \: 32 \: y + 3 \: x \: )\)

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

2 ( 32y + 3 x)

Step-by-step explanation:

64 y + 6x

factor out 2 from the equation

2 ( 32y + 3 x)

Answer:

1740 N

Step-by-step explanation:

To find the force, you need to multiply the mass by the acceleration.

(60.0 kg) × (29.0 m/s²) = 1740 N

The force will be 1740 N.

Step-by-step explanation:

angle e = 50 degree,,,,,,,

Check the picture below.

Answer:

1,080

Step-by-step explanation:

10 x 18 x 6