Find the value of the missing angle. Round to the nearest degree.

1. 71 degrees
2. 19 degrees
3. 43 degrees
4. 90 degrees​

The rate at which the light's projection moves along the wall when the light's angle is 20 degrees from perpendicular to the wall is approximately 1.078 feet per second.

Let's let t be the time elapsed since the light started rotating, and θ be the angle that the light makes with the perpendicular to the wall, as shown in the diagram. The rate at which the light's projection moves along the wall is given by the derivative of the horizontal distance between the projection point P and the foot of perpendicular Q, with respect to time t. Let's call this distance x.

From the diagram, we can see that:

tan(θ) = x / 12

Differentiating both sides with respect to time t, we get:

sec²(θ) dθ/dt = (dx/dt) / 12

We are given that the light completes one rotation every 2 seconds, which means that the angular velocity of the light is:

dθ/dt = 2π / (2 seconds) = π radians per second

Substituting this value and θ = 20° (converted to radians), we get:

sec²(20°) (π rad/sec) = (dx/dt) / 12

Simplifying:

(1/cos²(20°)) (π/2) = (dx/dt) / 12

Multiplying both sides by 12 and evaluating the left-hand side, we get:

dx/dt = 1.078 feet per second

As a result, when the light's angle is 20 degrees from perpendicular to the wall, the pace at which the projection advances along the wall is roughly 1.078 feet per second.

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The tape diagram for the equation can be given using rectangular boxes. The unknown value of x is a. 7, b. 7.

A tape diagram, often referred to as a strip diagram, is a visual representational tool in mathematics used to compare or illustrate numerical relationships. It consists of a rectangle or a segment of a line that has been divided into equal portions, each of which represents a specific amount. The magnitude of the quantity being measured is indicated by the length or area of the parts.

In order to help students understand the information offered and to visualise the relationships between the values involved, tape diagrams are frequently utilised in problem-solving scenarios.

Given that,

a.x+9=16

x = 16 - 9

x = 7

b.4•x=28

x = 7

Hence, the unknown value of x is a. 7, b. 7.

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The diameter of the circle is √74. Answer: C.

What is circle?

A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point.

To find the diameter of the circle, we need to find the distance between points A and B, which will give us the length of the diameter.

Using the distance formula, we have:

d = √[(x2 - x1)² + (y2 - y1)²]

where (x1, y1) = (-3, 6) and (x2, y2) = (-8, -1).

Plugging in the values, we get:

d = √[(-8 - (-3))² + (-1 - 6)²]

= √[(-5)² + (-7)²]

= √[25 + 49]

= √74

Therefore, the diameter of the circle is √74. Answer: C.

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The probability that the sample mean would differ from the population mean by greater than 3 millimetres is 0.0033 + 0.0033 = 0.0066, rounded to four decimal places.

We are given that the population mean diameter of the steel bolts manufactured by Thompson and Thompson is μ = 137 millimeters and the variance is = 49.

We need to find the probability that the sample mean would differ from the population mean by greater than 3 millimeters.

The standard deviation of the sample means is given by the formula:

[tex]\sigma_{\bar{x}} = \frac{\sigma}{{\sqrt{n}}}[/tex]

Substituting the given values, we have:

[tex]\sigma \bar{x}=\frac{\sqrt{49}}{\sqrt{48}}=1.118[/tex]

To find the probability that the sample mean would differ from the population mean by greater than 3 millimeters,

we need to calculate the z-score:

[tex]z=\frac{(\bar{x}-\mu)}{ \sigma _{\bar{x}}}[/tex]

Substituting the given values, we have:

[tex]z=\frac{\bar{x}-137}{1.118}[/tex]

We want to find the probability that |z| > 3/1.118 = 2.683.

Using a standard normal distribution table, we find that the probability of z > 2.683 is 0.0033.

Since this is a two-tailed test, the probability of z < -2.683 is also 0.0033.

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The answer through which all the value of the given relation satisfied the relation is period decreases, frequency increases and reflected in y - axis.

What about frequency?

In mathematics, frequency is a term used in statistics to describe how often a particular value or set of values appears in a dataset. Specifically, frequency refers to the number of times a particular data point or value occurs in a dataset.

For example, consider a dataset of test scores for a class of students. The frequency of a particular score (e.g., 80%) would be the number of students who received that score. The frequencies can be used to create a frequency distribution, which is a table that shows the frequency of each value or group of values in a dataset.

According to the given information:

In the given condition as the value of B increases, the periodic function decreases and the frequency of the function increases where as, when the value of B is negative, the graph of the function reflected in y-axis.

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Subway ridership data can reveal useful patterns through calculations with multiple operators, informing decisions about infrastructure and scheduling to better serve riders' needs.

The subway ridership dataset can reveal a wealth of information through calculations with multiple operators. One such calculation is the average increase or decrease in ridership during specific time intervals. By comparing ridership during peak and off-peak hours or weekdays versus weekends, it is possible to determine when the subway system is busiest and when it is underutilized.

Another useful calculation is the average percentage change in ridership between different stations or subway lines. This can help identify the most popular stations or lines and can inform decisions about where to allocate resources and infrastructure improvements.

Additionally, it is possible to explore the correlation between ridership and other factors such as weather, events, or holidays. By analyzing how ridership fluctuates in response to external factors, transportation planners can adjust schedules and routes to better serve the needs of riders.

Calculations with multiple operators can also reveal patterns in ridership based on time of year or day of the week. By analyzing the average change in ridership on different days or months, transportation planners can make informed decisions about scheduling and staffing.

Finally, regression analysis can be used to identify the overall trend in ridership over time. By examining long-term ridership trends, transportation planners can identify areas for improvement and plan for future infrastructure projects to better meet the needs of subway riders.

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The average number of visitor per concert in 2020 as compare to average number of visitors in 2019 is equal to 591 ( approximately ).

Average number of visitors per concert in 2019 was 584,

And the average number of visitors per concert in 2020 increased by 1.2%,

The average number of visitors per concert in 2020 as follows,

Average number of visitors per concert in 2020

= Average number of visitors per concert in 2019 + Increase in average number of visitors per concert

Increase in average number of visitors per concert

= 1.2% of the average number of visitors per concert in 2019

= (1.2/100) x 584

= 7.008

This implies,

The increase in the average number of visitors per concert from 2019 to 2020 is approximately 7.008.

Adding this increase to the average number of visitors per concert in 2019 gives us,

Average number of visitors per concert in 2020

= 584 + 7.008

= 591.008

Rounding this to the nearest whole number, we get,

Average number of visitors per concert in 2020 ≈ 591

Therefore, the average number of visitors per concert in 2020 is approximately 591.

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The mode is 18.5.

What is mode?

In statistics, there  are most repeated value among the given set of data. Those are called mode. Among the given set of data, mode is the value which has the maximum frequency. Sometimes, it may be possible to have more than one value which has the equal maximum frequency.

Formula for mode for grouped data is given by:

Mode = l + [(f₁-f₀)/(2f₁-f₀-f₂)]×h.-------------------(1)

Where, l = lower class limit of modal class, h = class size, f₁ = frequency of modal class, f₀ = frequency of class preceding to modal class, f₂ = frequency of class succeeding to modal class.

In the given problem l= 15.5

                                   f₀= 8

                                  f₁= 10

                                  f₂= 8

                                  h= 6

Putting all the values in equation (1) we obtain mode

                     mode= 15.5 +{(10-8)/(2×10-8-8)} ×6

                              = 15.5+(2/4)×6

                              = 15.5+ 3

                               = 18.5

Hence, the mode is 18.5.

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It is important to test for interactions in a two-way ANOVA to ensure that the main effects of each variable are not being confounded by the presence of an interaction.

In a two-way ANOVA test, if the effect of one variable depends on the value of another variable, then there is an interaction between the two variables. An interaction occurs when the effect of one independent variable on the dependent variable changes depending on the level of the other independent variable. It is important to test for interactions in a two-way ANOVA to ensure that the main effects of each variable are not being confounded by the presence of an interaction.

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In a two-way ANOVA test, if the effect of one variable depends on the value of another variable, "interaction".

In a two-way ANOVA test, interaction occurs when the effect of one independent variable on the dependent variable

depends on the level of another independent variable.

This means that the effect of one variable is not constant across all levels of the other variable, and it is important to

consider this interaction effect in interpreting the results of the ANOVA test.

Correlation and multicollinearity are not directly related to ANOVA tests, while "group of answer choices" is not a

relevant term in this context.

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The probability of rolling a sum greater than 10 is 4/36, which simplifies to 1/9, or approximately 0.1111.

There are 36 possible outcomes when rolling two 6-sided dice. Each outcome is equally likely.

To find the probability of rolling a sum greater than 10, we need to count the number of outcomes where the sum is greater than 10, and then divide by the total number of outcomes.

The outcomes where the sum is greater than 10 are:

4 + 6 = 10

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

So there are 4 possible outcomes where the sum is greater than 10.

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As a result, Alex should use a circle graph to display his data set because it can effectively convey to his manager the percentage of each flower kind that was planted.

To visualise information and data, use a circle graph or pie chart. Typically, a circle graph is used to quickly and proportionately display the findings of an investigation.

A pie chart, often known as a circle chart, is a visual representation of the various values of a given variable or a means to summarise a set of nominal data. This kind of diagram consists of a circle with numerous segments.

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A qualitative variable is a variable that cannot be measured in numerical terms, but rather, is characterized by qualities or attributes that are not numerical. Option A is the correct answer.

Qualitative variables are also called categorical variables because they represent categories or groups. Examples of qualitative variables include gender, nationality, religion, and occupation.

In contrast, quantitative variables can be measured in numerical terms, such as age, height, weight, income, and test scores. Understanding the nature and characteristics of different types of variables is important for selecting appropriate statistical methods and techniques to analyze and interpret data.

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Answer:

Using similar triangles, we can set up a proportion:

(tree height)/(tree shadow) = (building height)/(building shadow)

Plugging in the given values, we get:

8/4 = 24/x

Solving for x, we get:

x = (24 x 4)/8 = 12 feet

Therefore, the length of the building's shadow is B. 12 feet.

The surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.

To solve the problem, we can start by using the formula for the area of an equilateral triangle to find the length of one side of the base. Let s be the length of one side of the base, then we have:

Area of the base = (sqrt(3)/4) * s^2 = 13

Solving for s, we get:

s^2 = (4 * 13) / sqrt(3)

s = 8.0

Therefore, the perimeter of the base is 3 * s = 24 inches

Next, we can use the formula for the surface area of a pyramid to find the surface area of the entire pyramid. Let B be the area of the base, then we have:

Surface area = B + (1/2) * P * h

where P is the perimeter of the base and h is the height of the pyramid.

Substituting the given values, we get:

Surface area = 13 + (1/2) * 4.8 * 13

Surface area = 13 + 31.2

Surface area = 44.2 square inches

Therefore, the surface area of the pyramid is 44.2 square inches, which is closest to option (C) 44.2.

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For the maximum volume of , the value of x must be smaller that is x = 2.90 inch. Size of square = 8.41 sq. in.

The issue is an application of maxima and minima, where the unknown quantity is located using the first derivative. Keep in mind that the height of a box is equal to a side of the cut square when the sides are bent upward. Moreover, the box formula's volume is

Volume = length * width * height

Given:

Volume of new box = (32 - 2x)(12 - 2x)x

Rearranging terms:

V = 4x³ - 88x² + 384x

For maximum volume, V' = 0 (first derivative)

V' = 12x² - 167x + 384

V' = 0

12x² - 167x + 384 = 0

Solve using quadratic formula:

x = [-b ± √(b² - 4ac)] / 2a

a = 12 , b = - 167 , c = 384

x = [167 ± √(167² - 4*384*12)] / 2*12

x =  [167 ± 7√193] / 24

Now,

x =  [167 + 7√193] / 24

x = 11.01 inch

and,

x = [167 - 7√193] / 24

x = 2.90 inch

For the maximum volume of , the value of x must be smaller that is x = 2.90 inch.

Size of square = x²

Size of square = 2.90²

Size of square = 8.41 sq. in.

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If there are 90 pens in a box and 36 of them are red and the rest of them are black, the ratio of red pens to black pens in the box is 2:3.

The ratio of red pens to black pens in the box can be expressed as a fraction or as a simplified ratio. To do this, we need to determine the number of black pens in the box.

We know that there are 90 pens in total, and 36 of them are red. Therefore, the number of black pens can be found by subtracting the number of red pens from the total:

90 pens - 36 red pens = 54 black pens

Now we know that there are 54 black pens and 36 red pens in the box. To express this as a ratio, we can simplify it by dividing both numbers by their greatest common factor (GCF), which in this case is 18:

36/18 : 54/18

Simplifying further, we get:

2:3

This means that for every 2 red pens, there are 3 black pens in the box.

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Using simple interest we know the Total value of annual health coverage is $9000.

Borrowers must pay lenders simple interest as a fee in exchange for a loan.

Compound interest is excluded from the calculation and just the original principal is used.

Simple interest applies to all loans, not just specific ones.

Additionally, it refers to the kind of interest that banks give their customers on their savings accounts.

So, complete yearly health coverage calculation

Let x be the total annual healthcare budget.

Ruth contributes 18% of the entire cost of healthcare, or $67.50 for two weeks. (ie 15 days)

So, total paid for one month = 67.5 x 2 = 135

The total amount paid for the entire year is 135 x 12 = 1620.

She foots 18% of the overall annual health care costs, as was already established.

Then,

18% x = 1620

18 x / 100 = 1620

x = (1620 x 100) / 18

= $9000

Therefore, using simple interest we know the Total value of annual health coverage is $9000.

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Correct question:

Ruth contributes 18% of the total cost of her individual health care. This is a $67.50 deduction from each of her biweekly paychecks. What is the total value of her individual coverage for the year?

Answer:

a=37° to the nearest whole number

Step-by-step explanation:

cos0=adj/hyp

cosa=4/5

a=cos‐¹(4/5)

a=36.869°

a=37° to the nearest whole number

We the best reason behind why we call National halothane study is an observational study rather than an experiment is: " In order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned." So, option( b) is right one.

We have data from the National Halothane Study that correlates with important research into the safety of anesthetics used in surgery. The above shows the death rate and aesthetic. There is a relationship between the anesthetic used and the death of the patient. The data was collected after that the anesthesia was administered is started. In the observational study, interesting observer in the subjects & any treatment that the subjects recive are beyond the council of the investigators. Here the motion of anaesthesia is anesthetics used her determined by the doctors and the investigators are simply observing. So, it is an observational study due to because in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. Instead, a patient's anesthetic is selected by his or her doctor(s).

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Complete question:

The National Halothane Study was a major investigation of the safety of anesthetics used in surgery. Records of over 850,000 operations performed in 34 major hospitals showed the following death rates for four common anesthetics:27 Anesthetic A Death rate B CD 1.7% 1.7% 3.4% 1.9% There is a clear association between the anesthetic used and the death rate of patients. Anesthetic C appears dangerous.

a) in order to be an experiment, the subjects would have to be randomly selected from the population. however, these are hospital patients who all have some disease or condition and have not been randomly selected from the population, which includes both healthy and sick people.

b) in order to be an experiment, the treatments (choice of anesthetic) would have to be randomly assigned. instead, a patient's anesthetic is selected by his or her doctor(s).

c) there is not enough information to say for sure, but it is safer to assume that it is only an observational study, so that we are not overconfident about the results.

d) actually, it is an experiment and not an observational study.

Using the functions f(x) and g(x) as F(x)=x²-16; g(x)=x+4, (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4. So, the correct answer is option D.

To find (f/g)(x), we need to divide f(x) by g(x). The notation (f/g)(x) is another way of representing the function f(x)/g(x).

So, we first need to find f(x)/g(x) by dividing f(x) by g(x):

f(x)/g(x) = (x^2 - 16)/(x + 4)

Now, we can plug in the values of x in each option and see which one gives us the correct function.

Option A: (f/g)(-4) = ((-4)^2 - 16)/(-4 + 4) = undefined

Option B: (f/g)(4) = (4^2 - 16)/(4 + 4) = -1

Option C: (f/g)(4 - 4) = (0^2 - 16)/(4 - 4) = undefined

Option D: (f/g)(-4 - 4) = ((-4)^2 - 16)/(-4 - 4) = 0

Therefore, the correct answer is option D: (f/g)(x) = (x^2 - 16)/(x + 4) when x = -4.

Note that options A and C give undefined values because they have x + 4 in the denominator, which makes the function undefined at x = -4 and x = 4, respectively.

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The correct answer is D. Standard deviation is a numerical indicator of how widely dispersed possible values are distributed around the mean.

It is a common measure used to assess the variability or spread of a set of data points. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. The standard deviation is an important statistical tool in many fields, including finance, economics, and engineering.

Standard deviation is a measure of variation or dispersion between values in a set of data. It is a numerical indicator of how widely dispersed possible values are distributed around the mean (or expected value), μ. The lower the standard deviation, the closer the data points tend to be to the mean

Standard deviation is a numerical indicator of how widely dispersed possible values are distributed around the mean. It is a commonly used measure to quantify the amount of variation or dispersion in a set of data values.

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Standard deviation is a statistical measure that quantifies the amount of variability or dispersion in a set of data values.

Number indicating how widely spread out possible values are from the mean. The correct answer is D.

It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean. Standard deviation provides information about how closely the data points are clustered around the mean, and a larger standard deviation indicates a greater dispersion or variability of the data points from the mean. In other words, it is a measure of how widely the possible values are distributed around the mean.

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The train will have traveled option (C) 450 km from its starting point after 4 more hours at the same average speed.

The average speed of the train is given by the distance traveled divided by the time taken to travel that distance

average speed = distance ÷ time

Using this formula, we can find the average speed of the train:

average speed = 250 km ÷ 5 h = 50 km/h

Now that we know the average speed of the train, we can use it to calculate how far it will have traveled after another 4 hours:

distance = average speed × time

distance = 50 km/h × 4 h = 200 km

Therefore, the train will have traveled 250 km + 200 km = 450 km from its starting point after 4 more hours at the same average speed.

So, the answer is (C) 450 km.

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The inference is that,  Incorrect because of a failure to distinguish between incidence and prevalence.

What is inference drawn from statistics?

Utilising data analysis to determine characteristics of a probability distribution at play, statistical inference is the process. Through the use of estimation and hypothesis testing, inferential statistical analysis infers characteristics of a population. It is presumed that a bigger population than the observed data set was sampled for this data collection.

What distinguishes random assignment from random sampling inferences?

As a method of choosing participants for your study's sample, random selection or random sampling can be used. The sample can be divided into control and experimental groups using random assignment, however.

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The complete question is -

At the initial examination in the Framingham study, coronary heart disease was found in 5 per 1,000 men aged 30yrs to 44yrs and in 5 per 1,000 women aged 30yrs to 44yrs. The inference that in this age group men and women have an equal risk of developing coronary heart disease is Selected Answer: A. Correct Answers: A. Correct B. Incorrect because of a failure to distinguish between incidence and prevalence C. Incorrect because a proportionate ratio is used when a rate is required to support the inference D. Incorrect because of failure to recognize a possible cohort phenomenon E. Incorrect because there is no control or comparison group.

Answer:

Can i see the full answer so I can help you?

Step-by-step explanation:

Based on the dot plot, the cost for each of the 22 rides is between $1 and $12.

The summary statistics show that the minimum cost is $1, the maximum cost is $12, the median cost is $3.60, and the interquartile range (IQR) is $2.30 ($2.90 - $0.60).

Knoebels Amusement Park in Elysburg, Pennsylvania is an affordable and family-friendly entertainment venue that does not charge for general admission or parking. Instead, customers are charged for each ride they take.

From the dot-plot and summary statistics provided, we can see that the cost for each ride varies, with the cheapest ride costing $2 and the most expensive costing $12. The average cost of a ride is $6.32, and the standard deviation is $2.43, indicating that there is some variability in the cost of rides.

Overall, Knoebels Amusement Park appears to be a reasonably priced entertainment option, with a range of ride options available at varying costs to suit different budgets.

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-- The figure is missing in the given question, attached below --

Answer: 14%

Step-by-step explanation:

Our formula is i=prt but we're trying to find the rate (r) so we'll rearrange it to become r=i/pt.

i = $245

p = $7000

t = 3/12= 0.25 years

[tex]r=\frac{245}{(7000)(0.25)} \\r = 0.14[/tex]

The proof of the above parallelogram is given as follows.

Statement                                                                   Reason

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Answer:

(2,-3) is the minimum

Step-by-step explanation:

y = (x-2)²-3 is a quadratic equation written in 'vertex' form:  y = (x-h)²+k where 'h' and 'k' represent the vertex

The vertex is the highest or lowest point of the curve, in this case the 'minimum' so (2,-3) is the minimum

The problem steps should be put in the correct order as follows;

Problem ≡ [tex]\frac{2}{x+1} \cdot \frac{3}{x-2}[/tex]

Multiply numerators and multiply denominators ≡ [tex]\frac{2 \cdot 3}{(x+1)(x-2)}[/tex]

Simplify numerator and Simplify denominator ≡ [tex]\frac{6}{(x^2 - x - 2)}[/tex]

In Mathematics and Geometry, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

In Mathematics and Geometry, a rational expression simply refers to a type of expression which is expressed as a fraction. In this exercise, we would factorize the numerator and denominator for this rational expression as follows;

Multiply numerators = 2 × 3 = 6

Multiply denominators = (x + 1) × (x - 2) = x² - 2x + x - 2 = x² - x - 2

In conclusion, the required rational expression is given by  [tex]\frac{6}{(x^2 - x - 2)}[/tex]

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