AB is a tangent. Find the length of the radius, r.

The statement that is NOT true in a Chi-Square test is "Small values of the chi squared test statistic would lead to a decision to reject the null hypothesis."

This is because if the test statistic is small, it means that the observed values are close to the expected values, and there is no significant difference between the populations. Therefore, a small test statistic would lead to a failure to reject the null hypothesis. In a Chi-Square test, we compare the proportions of specified characteristics in different populations, and we wish to determine whether they are the same or not. If the test statistic is large, it means that the observed values are significantly different from the expected values, and we have evidence to reject the null hypothesis. Finally, the P-value will be small if the test statistic is large, indicating strong evidence against the null hypothesis.

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The two angles measure 90 degrees are called as complementary angles.

What are  complementary angles?

In geometry, complementary angles are defined as two angles whose sum is 90 degrees.

The two angles' complement and supplement are determined by the sum of their measurements. The two angles are said to be complimentary if their combined measurement equals that of a straight angle.

In other words, a right angle results from the combination of two complimentary angles (90 degrees). Angles 1 and 2 are said to be complementary if their sum of angles equals 90 degrees (i.e., 1 + 2 = 90°), and as a result, they are referred to as each other's partners.

two angles that add up to 90 degrees are known as complementary angles. For example, 60° and 30°.

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Given, the height \($h=6$, the base $b_1=9$ and $b_2=12$.\)

The area of the trapezoid is given by the formula,

\(\[A = \frac{1}{2}h(b_1+b_2)\]\)

Substitute the given values,  

\(\[A = \frac{1}{2} \times 6 \times (9+12)\]\\\)

Simplifying the above expression,

\(\[A = 45 \text{ square feet}\]\)

Therefore, the area of the trapezoid is $45$ square feet.

The perimeter of a two-dimensional geometric shape is the entire length of the boundary or outer edge. It is the sum of the lengths of all the shape's sides or edges.

The perimeter of a square, for example, is calculated by adding the lengths of all four sides of the square.

Similarly, to find the perimeter of a rectangle, sum the lengths of two adjacent sides and then double the result because there are two pairs of adjacent sides.

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Answer:

1

Step-by-step explanation:

\(\cos \left(\arccos \left(\frac{3}{5} \right)+\arcsin(-\frac{4}{5} \right)=\cos(\arccos(3/5))\cos(\arcsin(-4/5))-\sin(\arccos(3/5))\sin(\arcsin(-4/5)) \\ \\ =(3/5)\cos(\arcsin(-4/5))-(-4/5)(\sin(\arccos(3/5)) \\ \\ =(3/5)(3/5)-(-4/5)(4/5) \\ \\ =1\)

The shortest distance from point A(-1, 0, 2) to the line given by (x, y, z) = (-2, 0, 1) + t(1, 2, -2) can be found using the formula for the distance between a point and a line in three-dimensional space. The answer can be expressed as a square root.

To find the shortest distance from a point to a line in three-dimensional space, we can use the formula: d = ||AP x v|| / ||v||, where A is the given point, P is any point on the line, v is the direction vector of the line, and ||...|| denotes the magnitude or length of a vector. In this case, point A is (-1, 0, 2), and the line is given by (x, y, z) = (-2, 0, 1) + t(1, 2, -2). The direction vector of the line is (1, 2, -2). By substituting the values into the formula, we can calculate the shortest distance: d = ||(-1, 0, 2) - (-2, 0, 1) x (1, 2, -2)|| / ||(1, 2, -2)||. Simplifying and evaluating the expression will give the shortest distance.

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The winner got a total of 42 votes.

This can be defined as a number or ratio expressed as a fraction of 100. It is usually calculated by parts/whole × 100.

In this scenario, Jane was the winner as she got a higher percentage of votes. To calculate the exact number of vote we have to do the following:

70%/100% × 60 = 42 votes.

Therefore, the total number votes the winner got is 42.

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The step of data storytelling that describes showing the story of the data to highlight the meaning behind the numbers is "Visuals". The correct answer is option (d).

Visuals are an important aspect of data storytelling because they can help to convey complex information in a simple and easy-to-understand way. Visuals can include graphs, charts, diagrams, and other types of visual aids that appeal to the sight and are used for effect or illustration.

By using visuals, a data analyst can help their audience to better understand the story that the data is telling and to see the patterns and trends that might not be presently alleged from the raw numbers alone.

Hence, the correct answer is option (d).

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The complete question is as follows:

A data analyst wants to tell a story with data. As a second step, they focus on showing the story of the data to highlight the meaning behind the numbers. which step of data storytelling does this describe?

a. Primary message

b. Engagement

c. Narrative

d. Visuals

The appropriate choice is c. non-probability Sample, as the New York Times is selecting individuals based on convenience and judgment rather than using a random or systematic approach.

In the given scenario, when the New York Times selects a location on the Brooklyn Bridge to interview passersby who are NYC residents about their opinion regarding CUNY funding, it represents a non-probability sample.

Non-probability sampling is a method of selecting participants for a study or survey that does not involve random selection. In this case, the selection of individuals from the Brooklyn Bridge is not based on a random or systematic approach. The New York Times is deliberately choosing a specific location to target a particular group (NYC residents) and gather their opinions on a specific topic (CUNY funding).

This type of sampling method often involves the researcher's judgment or convenience and does not provide equal opportunities for all members of the population to be included in the sample. Non-probability samples are generally used when it is challenging or not feasible to obtain a random or representative sample.

The other options can be ruled out as follows:

a. Media sampling: This term is not commonly used in sampling methodologies. It does not accurately describe the method of sampling used in this scenario.

b. Cluster sampling: Cluster sampling involves dividing the population into clusters and randomly selecting clusters to be included in the sample. The individuals within the selected clusters are then included in the sample. This does not align with the scenario where the sampling is not based on clusters.

d. Random sample: A random sample involves selecting participants from a population in a random and unbiased manner, ensuring that each member of the population has an equal chance of being selected. In the given scenario, the selection of individuals from the Brooklyn Bridge is not based on random selection, so it does not represent a random sample.

Therefore, the appropriate choice is c. non-probability sample, as the New York Times is selecting individuals based on convenience and judgment rather than using a random or systematic approach.

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Answer:

100% on plato

Step-by-step explanation:

The raffles in ascending order of their expected values to the player is

player will be choose from A to J and the player wins $150.

player will be choose from A to O and the player wins $240.

player will be choose from A to E and the player wins $85.

Ascending order is a method of arranging numbers from smallest value to largest value. The order goes from left to right. Ascending order is also sometimes named as increasing order. For example, a set of natural numbers are in ascending order, such as 1 < 2 < 3 < 4 < 5 < 6 < 7 < 8… and so on.

We have,

Tickets for all of the described charity raffles cost $2 per ticket.

Here first the player will be choose from A to J and the player wins $150.

Second, the player will be choose from A to O and the player wins $240.

Third, the player will be choose from A to E and the player wins $85.

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\(~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$2543\\ P=\textit{original amount deposited}\dotfill & \$2000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &4 \end{cases}\)

\(2543=2000e^{\frac{r}{100}\cdot 4}\implies \cfrac{2543}{2000}=e^{\frac{r}{25}}\implies \log_e\left( \cfrac{2543}{2000}\right)=\log_e\left( e^{\frac{r}{25}} \right) \\\\\\ \ln\left( \cfrac{2543}{2000}\right)=\cfrac{r}{25}\implies 25\ln\left( \cfrac{2543}{2000}\right)=r\implies 6\approx r\)

Answer:

C. 7 units

Step-by-step explanation:

The given parameters are;

The length of the chord of the circle, \(\overline{AC}\) = 14 units

The orientation of the radius and the chord = The radius is perpendicular to the chord

We have in ΔAOC, \(\overline{AO}\) = \(\overline{OC}\) = The radius of the circle

\(\overline{OB}\) ≅ \(\overline{OB}\)  by reflexive property

The angle at point B = 90° by angle formed by the radius which is perpendiclar to the chord \(\overline{AC}\)

ΔAOB and ΔCOB are right triangles (triangles having one 90° angle)

\(\overline{AO}\) and \(\overline{OC}\) are hypotenuse sides of ΔAOB and ΔCOB respectively and \(\overline{OB}\) is a leg to ΔAOB and ΔCOB

Therefore;

ΔAOB ≅ ΔCOB, by Hypotenuse Leg rule of congruency

Therefore;

\(\overline{AB}\) ≅ \(\overline{BC}\) by Congruent Parts of Congruent Triangles are Congruent, CPCTC

\(\overline{AB}\) = \(\overline{BC}\) by definition of congruency

\(\overline{AC}\) = \(\overline{AB}\) + \(\overline{BC}\) by segment addition postulate

∴ \(\overline{AC}\) = \(\overline{AB}\) + \(\overline{BC}\) =  \(\overline{AB}\) + \(\overline{AB}\) = 2 ×  \(\overline{AB}\)

∴  \(\overline{AB}\) = \(\overline{AC}\)/2

\(\overline{AB}\) = 14/2 = 7

\(\overline{AB}\) = 7 units.

Answer:

7 units

Step-by-step explanation:

Answer:

Explanation:

The y-intercept refers to the point that a graph crosses the y-axis. In a simpler sense, the y-intercept is obtained at the point where "x" equals zero.

In this case, the y-intercept is obtained at the point where "x" equals zero; when "x" equals zero, "y' equals zero

Therefore, the y-intercept of this line is zero

Answer:

A. The farmer plants 195 rows of beets and has 25 beet plants left over

Step-by-step explanation:

The quotient 195 is the number of full rows the farmer can make. That takes up 195*40 = 7800 plants so far. Then there's an extra 25 left over because 7825-7800 = 25 that can't make up an extra full row.

Answer:

opposite sides of parallelogram are parellel.

so, angle A and angle D are co interior angle.

(3x+4)°+x°=180°

4x+4=180°

4x=180°- 4

4x=176°

x=176°/4

x = 44°

(3x+4)

=3×44+4

=136°

If we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

Let Y = 2 - X, where X is an exponential random variable with mean 1.

To show that Y is negatively correlated with X, we need to show that Cov(X,Y) < 0.

Cov(X,Y) = E[XY] - E[X]E[Y]

Since X and Y are both exponentially distributed with mean 1, we have:

E[X] = 1, E[Y] = 2 - E[X] = 1

E[XY] = E[X(2-X)] = 2E[X] - E[X^2] = 2 - Var(X)

Var(X) = E[X^2] - (E[X])^2 = 1 - 1^2 = 0

Therefore, Var(X) = 0, which means that E[XY] = 2, and Cov(X,Y) = E[XY] - E[X]E[Y] = 2 - 1*1 = 1 > 0.

Since Cov(X,Y) > 0, we know that Y is positively correlated with X. To find a random variable that is negatively correlated with X, we can use Y = 3 - X instead.

Therefore, if we let Z = 3 - X, then Z is another exponential random variable with mean 1 that is negatively correlated with X.

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Graph a system of equations to solve log (−5. 6x 1. 3) = −1 − x. Round to the nearest tenth, from least to the greatest, the solutions will be (-2.1) to (0.2)      

Given :  The solutions are: x ≈ and x ≈.

We will solve the equation accordingly,

        \(\rm \log(-5.6x+1.3)=-1-x\)

we will plot the graph the points at  y=0 for the value of x

Hence, the solutions for the given equation (x+2.12) & (x-0.221)

On rounding of to nearest tenth

      \(\rm x= -2.1 \\x= 0.2\)

Therefore, The solutions are:rom least to the greatest (-2.1) to (0.2)

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To find the sale price of each item, we need to use some basic algebra. Let's call the sale price of each item "x".

First, we need to find the total cost of the table rental for all six friends. Since each friend needs to pay $7.20, the total cost of the table rental is 6 * $7.20 = $43.20.

Next, we need to find the total revenue from selling the items. Each friend sells 3 items, so the total number of items sold is 6 * 3 = 18. The total revenue is the number of items sold multiplied by the sale price, so the total revenue is 18x.

We know that the total profit is $25.20, which is the total revenue minus the total cost of the table rental. So we can set up the equation:

18x - $43.20 = $25.20

Simplifying this equation, we get:

18x = $68.40

Dividing both sides by 18, we get:

x = $3.80

Therefore, the sale price of each item is $3.80.

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The statement "A histogram with the hills to the far left means the image is overexposed" is not accurate. In fact, a histogram with the hills to the far left indicates that the image is underexposed, not overexposed.

A histogram is a graphical representation of the distribution of pixel values in an image. It displays the frequency of occurrence of different tonal values. The horizontal axis represents the tonal values, while the vertical axis represents the frequency or number of pixels.

When the hills of the histogram are concentrated towards the left side, it means that a significant portion of the image has darker or lower tonal values. This indicates an underexposed image, where the exposure settings were insufficient to capture enough light, resulting in a darker overall appearance.

Conversely, an overexposed image would have the hills of the histogram concentrated towards the right side, indicating that a significant portion of the image has brighter or higher tonal values.

Therefore, the correct interpretation is that a histogram with the hills to the far left means the image is underexposed, not overexposed.

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The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

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If a building was photographed using an aerial camera from a flying height of 1000 m.

1.  The height of the building is 5.5 meters.

2. The photographic scale of the building top point is  5.50067e-07.

1. Height of the building:

Height of the building = Flying height * (Measured distance / Focal length)

Converting the measured distance from mm to meters:

Measured distance = 82.501 mm * (1 m / 1000 mm)

Measured distance = 0.082501 m

Substituting the values into the formula:

Height of the building = 1000 m * (0.082501 m / 150 m)

Height of the building = 5.5 m

Therefore the height of the building is 5.5 meters.

2. Photographic scale:

Photographic scale = Measured distance / Ground distance

Using the formula for the photographic scale:

Photographic scale = Measured distance / (Flying height * Focal length)

Photographic scale = 82.501 mm / (1000 m * 150 m)

Converting the measured distance from mm to meters:

Measured distance = 82.501 mm * (1 m / 1000 mm)

Measured distance = 0.082501 m

Photographic scale = 0.082501 m / (1000 m * 150 m)

Photographic scale = 5.50067e-07

Therefore the photographic scale of the building top point is  5.50067e-07.

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The value of z that divides the standard normal distribution so that half the area is on one side and half is on the other is 0.00.

To understand this better, let's visualize the standard normal distribution. The graph of the standard normal distribution is a bell-shaped curve that is symmetrical around the mean of 0.

When we say that half the area is on one side and half is on the other, we mean that the area under the curve to the left of the z-score is equal to the area under the curve to the right of the z-score.

Since the standard normal distribution is symmetric, this occurs when the z-score is equal to 0.00. At this point, the area to the left of 0.00 is 0.50 (or 50%), and the area to the right of 0.00 is also 0.50 (or 50%).

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The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:

d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1

Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.

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Best guess for the function is

\(\displaystyle f(x) = \sum_{n=1}^\infty \frac{x^n}{n^2}\)

By the ratio test, the series converges for

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{(n+1)^2} \cdot \frac{n^2}{x^n}\right| = |x| \lim_{n\to\infty} \frac{n^2}{(n+1)^2} = |x| < 1\)

When \(x=1\), \(f(x)\) is a convergent \(p\)-series.

When \(x=-1\), \(f(x)\) is a convergent alternating series.

So, the interval of convergence for \(f(x)\) is the closed interval \(\boxed{-1 \le x \le 1}\).

The derivative of \(f\) is the series

\(\displaystyle f'(x) = \sum_{n=1}^\infty \frac{nx^{n-1}}{n^2} = \frac1x \sum_{n=1}^\infty \frac{x^n}n\)

which also converges for \(|x|<1\) by the ratio test:

\(\displaystyle \lim_{n\to\infty} \left|\frac{x^{n+1}}{n+1} \cdot \frac n{x^n}\right| = |x| \lim_{n\to\infty} \frac{n}{n+1} = |x| < 1\)

When \(x=1\), \(f'(x)\) becomes the divergent harmonic series.

When \(x=-1\), \(f'(x)\) is a convergent alternating series.

The interval of convergence for \(f'(x)\) is then the closed-open interval \(\boxed{-1 \le x < 1}\).

Differentiating \(f\) once more gives the series

\(\displaystyle f''(x) = \sum_{n=1}^\infty \frac{n(n-1)x^{n-2}}{n^2} = \frac1{x^2} \sum_{n=1}^\infty \frac{(n-1)x^n}{n} = \frac1{x^2} \left(\sum_{n=1}^\infty x^n - \sum_{n=1}^\infty \frac{x^n}n\right)\)

The first series is geometric and converges for \(|x|<1\), endpoints not included.

The second series is \(f'(x)\), which we know converges for \(-1\le x<1\).

Putting these intervals together, we see that \(f''(x)\) converges only on the open interval \(\boxed{-1 < x < 1}\).

The original width is 6 inches, and was reduced to 3 inches, which is half. Keeping this in mind, the new height should be half the original 8 inch height, being halved to 4 inches.

Answer:

\(\left[\begin{array}{ccc}11&15&-17\\-1&-4&-4\\17&15&-22\end{array}\right]\)

Option D will be your answer

\(-----------\)

hope it helps...

have a great day!!

Answer:

18

Step-by-step explanation:

trust me

For a continuous random variable x, the probability of x taking on a specific value a is zero. This is due to the infinite number of possible values that x can take on within its range.

In the case of a continuous random variable, the probability density function (PDF) describes the likelihood of x taking on different values. Unlike discrete random variables, which can only take on specific values with non-zero probabilities, a continuous random variable can take on an infinite number of values within a given range. Therefore, the probability of x being equal to any specific value, such as a, is infinitesimally small, or mathematically speaking, it is equal to zero.

To understand this concept, consider a simple example of a continuous random variable like the height of individuals in a population. The height can take on any value within a certain range, such as between 150 cm and 200 cm. The probability of an individual having exactly a height of, say, 175 cm is extremely low, as there are infinitely many possible heights between 150 cm and 200 cm.

Instead, the probability is associated with ranges or intervals of values. For example, the probability of an individual's height being between 170 cm and 180 cm might be nonzero and can be calculated using integration over that interval. However, the probability of having an exact height of 175 cm, as a single point on the continuous scale, is zero.

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There is currently $62.65 billion in the fund.

Given that;

If the FDIC must use 7.6% of its $67.8 billion insurance reserve to pay for several bankrupt banks,

To get how much money is left in the fund, we need to;

The total insurance fund = $67.8 billion

To cover several failed banks = 7.6% = 0.076

Therefore, the money left = $67.8 * 0.076

                                           = $5.15

So, the final amount left in the fund = $67.8 - $5.15

                                                           = $62.65

Hence, the money left in the fund is $62.65 billion.

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Therefore, the correct answer is c) 3, as there are three F ratios calculated in a 2x2 factorial design.

In a two-way analysis of variance (ANOVA) known as a 2x2

factorial design, there are three F ratios or F statistic values calculated. This design involves two independent variables, each with two levels or categories.

The three F ratios represent the main effects of each independent variable and the interaction between the two variables.The main effects F ratios determine whether there are significant differences between the levels of each independent variable individually, ignoring the other independent variable.

There will be two main effects F ratios, one for each independent variable.The interaction F ratio examines whether there is a significant interaction between the two independent variables. It determines whether the effect of one independent variable differs across the levels of the other independent variable.

This F ratio assesses the joint influence of both independent variables.

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