when examining the relationship between two numerical variables, a scatter plot is a simple, yet useful, graphical tool. what does each point in a scatter plot represent?

Answer:

52 units.

Step-by-step explanation:

Use the Triple 5-12-13

20 / 4 = 5

48/ 4 = 12

So  the hypotenuse = 4 * 13 = 52.

The lengths of Hypotenuse 52 units.

The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

According to the Pythagoras theorem, the square of the hypotenuse of a triangle, which has a straight angle of 90 degrees, equals the sum of the squares of the other two sides.

Given:

The measurement of two sides are 20 units and 48 units.

Now, Using Pythagoras theorem

H² = P² + B²

H² = 20² + 48²

H² = 400 + 2304

H² = 2704

H = 52 units.

Hence, lengths of Hypotenuse 52 units.

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Answer:

What can I answer ehh that's just an help ‍♀️‍♀️

Answer:

(0, 15)

Step-by-step explanation:

Answer:

x = -3

Step-by-step explanation:

In this situation, x is always -3.

So, the equation is x = -3

At point P (2, π/4, 2), vector A in Cartesian coordinates is A = <1, 2.5, 2>.

To express vector A in Cartesian coordinates, we can use the following conversions between cylindrical and Cartesian coordinates:

x = ρ * cos(θ)

y = ρ * sin(θ)

z = z

Given vector A = cos(θ) - ρ * sin(θ) + 2 * cos(θ) * sin(θ), we can substitute the corresponding expressions for ρ, θ, and z:

x = cos(θ) * cos(θ) - ρ * sin(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Simplifying these expressions, we get:

x = cos^2(θ) + 2 * cos(θ) * sin(θ) - ρ * sin^2(θ)

y = cos(θ) * sin(θ) + ρ * cos(θ) * sin(θ) + 2 * cos(θ) * sin(θ)

z = 2

Now, we can evaluate vector A at point P (2, π/4, 2):

x = cos^2(π/4) + 2 * cos(π/4) * sin(π/4) - 2 * sin^2(π/4)

y = cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4) + 2 * cos(π/4) * sin(π/4)

z = 2

Simplifying further, we have:

x = (1/2) + 1 - (1/2) = 1

y = (1/2) + 1 + 1 = 2.5

z = 2

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Answer:

container A

Step-by-step explanation:

In Container A, we can plot the points (0,60) adn (2, 35)

The slope is :

\(m_A = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{35-60}{2-0} \\\\= \frac{-25}{2}\\ \\m_A = -12.5\\\)

For container B, the slope is:

\(m_B = \frac{y_2-y_1}{x_2-x_1} \\\\= \frac{32-54}{3-1} \\\\= \frac{-22}{2}\\ \\m_B = -11\\\)

The negative sign of the slope indicates the direction of the slope

\(|m_A| = 12.5\\\\|m_B| = 11\)

12.5 > 11

The slope of container A is steeper than container B

Therefore, the water is draining out of container A at a faster rate than container B

Answer:

  an = 6 +8(n -1)

Step-by-step explanation:

Usually, you're asked for a general term when you're studying arithmetic and/or geometric sequences. One way to tell which kind of sequence you have is to look at the differences between adjacent terms. If they are all the same, the sequence is arithmetic, and the general term is ...

  an = a1 +d(n -1)

where a1 is the first term, and d is the common difference.

Here, the differences are ...

  14 -6 = 8

  22 -14 = 8

  30 -22 = 8

These are all the same, hence a "common" difference. The first term is 6, so the general term is ...

  an = 6 +8(n -1)

The value of the surface integral or flux is \(\(2\pi\)\) for the given vector field \(\(\mathbf{f}\)\) across the surface defined by the unit sphere centered at the origin.

To properly solve the problem, let's consider a specific example. Suppose we have the vector field \(\(\mathbf{f}(x, y, z) = x^2\mathbf{i} + y^2\mathbf{j} + z^2\mathbf{k}\)\), and we want to calculate the surface integral or flux of \(\(\mathbf{f}\)\) across the surface \(\(S\)\) defined by the unit sphere centered at the origin.

Using the divergence theorem, the surface integral can be calculated as follows:

\(\[\iint_S \mathbf{f} \cdot d\mathbf{S} = \iiint_V \nabla \cdot \mathbf{f} \, dV\]\)

Since \(\(\nabla \cdot \mathbf{f} = \frac{\partial}{\partial x}(x^2) + \frac{\partial}{\partial y}(y^2) + \frac{\partial}{\partial z}(z^2) = 2x + 2y + 2z\)\), the triple integral becomes:

\(\[\iiint_V (2x + 2y + 2z) \, dV\]\)

Considering the unit sphere as the volume \(\(V\)\), we can switch to spherical coordinates with \(\(x = \rho\sin\phi\cos\theta\), \(y = \rho\sin\phi\sin\theta\), and \(z = \rho\cos\phi\), and \(\rho\) ranging from 0 to 1, \(\phi\) ranging from 0 to \(\pi\), and \(\theta\) ranging from 0 to \(2\pi\).\)

To further solve the problem, let's evaluate the triple integral using the given limits and spherical coordinates:

\(\[\iiint_V (2x + 2y + 2z) \, dV\]\)

In spherical coordinates, the volume element \(\(dV\) becomes \(\rho^2 \sin \phi \, d\rho \, d\phi \, d\theta\)\).

Substituting the coordinates and limits into the triple integral, we have:

\(\iiint_V (2x + 2y + 2z) \, dV &= \int_0^{2\pi} \int_0^{\pi} \int_0^1 (2\rho\sin\phi\cos\theta + 2\rho\sin\phi\sin\theta + 2\rho\cos\phi) \rho^2 \sin \phi \, d\rho \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \int_0^1 (2\rho^3\sin^2\phi\cos\theta + 2\rho^3\sin^2\phi\sin\theta + 2\rho^2\sin\phi\cos\phi) \, d\rho \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \left[\frac{1}{2}\rho^4\sin^2\phi\cos\theta + \frac{1}{2}\rho^4\sin^2\phi\sin\theta + \frac{2}{3}\rho^3\sin\phi\cos\phi\right]_0^1 \, d\phi \, d\theta \\\)

\(&= \int_0^{2\pi} \int_0^{\pi} \left(\frac{1}{2}\sin^2\phi\cos\theta + \frac{1}{2}\sin^2\phi\sin\theta + \frac{2}{3}\sin\phi\cos\phi\right) \, d\phi \, d\theta\end{aligned}\]\)

Evaluating the inner integral with respect to \(\(\phi\)\), we get:

\(\[\int_0^{\pi} \left(\frac{1}{2}\sin^2\phi\cos\theta + \frac{1}{2}\sin^2\phi\sin\theta + \frac{2}{3}\sin\phi\cos\phi\right) \, d\phi = \frac{\pi}{2}\]\)

Substituting this result into the outer integral with respect to \(\(\theta\)\), we have:

\(\[\int_0^{2\pi} \frac{\pi}{2} \, d\theta = \pi \cdot 2 = 2\pi\]\)

Therefore, the value of the surface integral or flux is \(\(2\pi\)\) for the given vector field \(\(\mathbf{f}\)\) across the surface defined by the unit sphere centered at the origin.

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Answer:

i typed in • and actually got the answer have a good Friday

a) a 99% confidence interval calculated from the same sample data would be longer than the 95% confidence interval, b) the statement that there is a 95% chance that µ is between 0.49 and 0.82 is incorrect

c) to compute a 90% confidence interval with a width of 2.3 and given a population standard deviation of 5.6, a sample size of approximately 71 is needed.

a) A 99% confidence interval provides a higher level of confidence compared to a 95% confidence interval. As the level of confidence increases, the width of the confidence interval also increases. This is because a higher confidence level requires a wider interval to capture a larger proportion of possible population values. Therefore, the 99% confidence interval calculated from the same sample data would be longer than the 95% confidence interval.

b) The statement that there is a 95% chance that µ (the population mean) is between 0.49 and 0.82 is incorrect. Confidence intervals are not a measure of the probability of a parameter falling within the interval. Instead, they provide a range of values within which the true parameter is likely to lie. The interpretation of a 95% confidence interval is that if we were to repeat the sampling process many times and construct 95% confidence intervals, approximately 95% of those intervals would contain the true population parameter. However, for any specific confidence interval, we cannot make probabilistic statements about the parameter's presence within that interval.

c) To compute a confidence interval with a specific width, we can use the formula:

Sample Size (n) = (Z * σ / E)^2,

where Z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the desired margin of error (half the width of the confidence interval). In this case, the desired confidence level is 90%, the desired width is 2.3, and the population standard deviation is 5.6. Plugging these values into the formula, we can solve for the sample size (n).

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Answer:

1 minute = 1/6

2 minutes = 1/3

3 minutes =1/2

Step-by-step explanation:

one can eat a bag in 15 minutes so in 1 minute this cat can eat 1/15 of a bag

the other cat can eat a bag in 10 minutes so in 1 minute the cat can eat 1/10 of the bag

to find how much they can eat in 1 minute, add 1/10 and 1/15 which gives you 1/6. to find 2 and 3 minutes just multiply by 1/6 by 2 or 3

Answer:

it would be 0 cause 142 and 308 already equal 450

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

450 - (142 + 308) = 0. ) is the answer.

Hope it helps!

The function of the given graph is y=3sec(1/2)x. So, option A is correct.

A mathematical function from a set X to a set Y assigns exactly one element of Y to each element of X. The terms "domain" and "codomain" are used to describe the sets X and Y, respectively.

Two Persian mathematicians named Al-Biruni and Sharaf al-Din al-Tusi are credited with creating the earliest known notion of function. The link between varying amounts and other variables was the foundational idea behind functions. The concept was first introduced with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration up to the 19th century were differentiable.

We must examine each alternative.

A) y=3sec(1/2)x

y-intercept=3

So, Trigonometric function is 4π

B) y=sec(1/2)x+3

y-intercept=4

So, Trigonometric function is 4π

C) y=(1/3)sec(2x)

y-intercept=1/3

So, Trigonometric function is π

D) y=3sec(1/2)x

y-intercept= does not exist.

T=4π

So, choose the option A. y=3sec(1/2)x

This is the property of trigonometry function.

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Answer:

it's D. y = 3sec(1/2x)

Step-by-step explanation:

aplex

psd check your written answers as they are wrong, so there will be no confusion, have a nice day :)

The number of biology textbooks sold =  156

The number of psychology textbooks sold = 95

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Let x be the number of biology textbooks sold. Then, the number of psychology textbooks sold was x - 61.

The combined total of the two types of textbooks sold was 251, so we can write an equation:

x + (x - 61) = 251

Expanding the right side:

2x - 61 = 251

Adding 61 to both sides:

2x = 312

Dividing both sides by 2:

x = 156

the number of psychology textbooks sold =  x - 61

                                                                      =  156 - 61

                                                                      =  95

So, 156 biology textbooks were sold and 95 psychology textbooks were sold.

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580 miles.

On the first day of the tour, she went = east

On the second day she went = north

On the third day = west

On the fourth day she went = south

On the fifth day she went = east

Miles was she from her starting point at the end of the 40th day =?

She was 580 miles from her starting point at the end of the 40th day.

Solution is given in the attached picture.

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Answer: y=(x-9)(x-1)

Step-by-step explanation:

The first step to conducting a statistical study is to clearly define the research question or problem.

This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.

It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.

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Answer:

Step-by-step explanation:

Calculate the side length (s) of this equilateral triangle with perimeter 43,8cm​

An equilateral triangle is a triangle with all three sides of equal length,

so:

43.8 : 3 = 14.6 cm

------------------------

check

find perimeter

14.6 * 3 = 43.8

the answer is good

Step-by-step explanation:

2527 is the first line so 5 in the box

then 47 so a 4 in that box

top answer row

315 E7 so a 5 in that box.

Answer: B.)

Step-by-step explanation:

No solution.

Answer:

22

Step-by-step explanation:

Let us interpret this problem;

        ---------------34-------------------

       P         Q       S      R            T

                    ----- 8 --------

        --------  --------- --------

             x        x         x

Let PQ = SQ = SR

Find RT;

    QS + SR = 8

    Also;

          x + x = 8

            2x = 8

              x = 4

To find RT;

    RT = PT - (PQ + QR)

   RT = 34 - (4 + 8) = 34 - 12 = 22

Answer:

22

Step-by-step explanation:

Answer:

2/3

Step-by-step explanation:

18/27 simplified is 2/3

The Number system from least to greatest of the given number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 is 8.03 ,  8.1,  8.116, 8.119, 8.14, 8.11.

We were given the number 8.116, 8.119, 8.18, 8.03, 8.14, 8.1 so that we can arrange them from the smallest number to the highest number.

The first number will be 8.03 , then follow by 8.1, the after that we can see that the next number will be 8.116, which will be followed by the number 8.14, then this will be followed by 8.119 then followed by the number 8.18.

Therefore, the arrangement will be  8.03 ,  8.1,  8.116, 8.119, 8.14, 8.11.

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Answer:

x/5 - 4

Step-by-step explanation:

Based on the comparison of standard deviations, one would feel more confident using the least squares line to predict the useful life for a given cutting speed with Brand B.

To determine which brand would be more reliable for predicting the useful life of a cutting tool based on cutting speed, the standard deviations for Brand A and Brand B are compared. The standard deviation for Brand B is lower (s=2.828) compared to Brand A (s=1.882), indicating that Brand B would be a more accurate predictor for the useful life of a cutting tool at a given cutting speed.

The standard deviation is a measure of the dispersion or variability of a dataset. In this case, it represents the spread of the useful life values for each brand of cutting tool at different cutting speeds. A lower standard deviation indicates less variability and more consistency in the data.

By comparing the standard deviations, we can assess the level of precision in the data and the reliability of using the least squares line for prediction. A smaller standard deviation implies that the data points are closer to the fitted regression line, indicating a stronger linear relationship between cutting speed and useful life.

In this scenario, Brand B has a lower standard deviation (s=2.828) compared to Brand A (s=1.882). This suggests that the useful life values for Brand B are more tightly clustered around the regression line, indicating a stronger linear relationship and making Brand B a more reliable predictor for the useful life of a cutting tool at a given cutting speed.

Therefore, based on the comparison of standard deviations, one would feel more confident using the least squares line to predict the useful life for a given cutting speed with Brand B.

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There are 15 different combinations of shows can gabe choose to watch.

Given,

Number of shows to be telecasted = 6

Number of allowed shows to watch =4

Gabe is allowed to watch 4 shows from total 6 shows.

To calculate combinations of shows that can gabe choose to watch, use formula

\(nCr=\frac{n!}{r!(n-r)!}\)

Where, n=Total number of shows i.e. 6

r= Number of choosing shows i.e.

\(nCr=\frac{6!}{4!(6-2)!}\\\\nCr=\frac{6*5*4*3*2*1}{4*3*2*1(2)!}\\\\nCr=\frac{6*5*4*3*2*1}{4*3*2*1*2}\\\\nCr=15\)

Thus, there are 15 different combinations of shows can gabe choose to watch.

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(8 + k³ - 6k⁴) + (4 - 3k⁴ + 8k²)

8 + k³ - 6k⁴ + 4 - 3k⁴ + 8k²

(8 + 4) + (8k²) + (k³) + (-6k⁴ -3k⁴)

(12) + (8k²) + (k³) + (-9k⁴)

12 + 8k² + k³ - 9k⁴

The probability that at least 5 of them started smoking before 21 years of age is 0.9997.2. The probability that at most 11 of them started smoking before 21 years of age is 0.9982.3. The probability that exactly 13 of them started smoking before 21 years of age is 0.000006.

(1) The probability that at least 5 of them started smoking before 21 years of age isThe probability of at least 5 smokers out of 14 to start smoking before 21 is the probability of 5 or more smokers out of 14 smokers who started smoking before 21.  Using the complement rule to find this probability: 1-P(X≤4) =1-0.0003

=0.9997Therefore, the probability that at least 5 of them started smoking before 21 years of age is 0.9997.

(2) The probability that at most 11 of them started smoking before 21 years of age isThe probability of at most 11 smokers out of 14 to start smoking before 21 is the probability of 11 or fewer smokers out of 14 smokers who started smoking before 21. Using the cumulative distribution function of the binomial distribution, we have:P(X ≤ 11) = binomcdf(14,0.9,11)

=0.9982

Therefore, the probability that at most 11 of them started smoking before 21 years of age is 0.9982.(3) The probability that exactly 13 of them started smoking before 21 years of age isThe probability of exactly 13 smokers out of 14 to start smoking before 21 is:P(X = 13)

= binompdf(14,0.9,13)

=0.000006Therefore, the probability that exactly 13 of them started smoking before 21 years of age is 0.000006.

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