I need the answer I do not understand this problem

I Need The Answer I Do Not Understand This Problem

Answers

Answer 1

The possible estimation of the acute angle will be 14.5⁰, 14.6⁰, 14.7⁰, 14.8⁰, 14.9⁰ or 15⁰.

What is the measure of the acute angle?

An acute angle is an angle that measures less than 90 degrees. In other words, it is an angle that is smaller than a right angle. A right angle measures exactly 90 degrees, while an acute angle measures less than that.

The measure of the given angle is less than 90 degrees, and the measure can range from 0⁰ to 90 degrees.

If we are to estimate within 15⁰, then the possible measure will be 14.5⁰, 14.6⁰, 14.7⁰, 14.8⁰, 14.9⁰ or 15⁰

All the estimation of the angle given above is less than 90 degrees and can be considered an acute angle.

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Related Questions

3. Technology required. Here are the data for the population f, in thousands, of a city d decades after 1960 along with the graph of the function given by f(d) = 25 - (1.19)ª. Elena thinks that shifting the graph off up by 50 will match the data. Han thinks that shifting the graph of f up by 60 and then right by 1 will match the data. a. What functions define Elena's and Han's graphs? b. Use graphing technology to graph Elena's and Han's proposed functions along with f. population (thousands) c. Which graph do you think fits the data better? Explain your reasoning.​

Answers

The relationship between the functions are indicated in the attached graph. see further explanation below.


What is the explanation for the above response?

a. Elena's graph is obtained by shifting the original function f up by 50 units, so her function is g(d) = f(d) + 50 = 75 - (1.19)ª.

Han's graph is obtained by shifting the original function f up by 60 units and then to the right by 1 unit, so his function is h(d) = f(d - 1) + 60 = 85 - (1.19)^(a-1).

b. Using graphing technology, we can graph the three functions f, g, and h to compare how well they fit the given data. Here's an example graph:

graph of f, g, and h

c. From the graph, it appears that Han's function h fits the data better than Elena's function g. The graph of h seems to align more closely with the plotted data points than the other two functions. Moreover, the shift to the right and up of the graph of f seems to better capture the overall trend of the data, as it appears that the population increased and shifted slightly to the right over time.

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What is the loan factor is Magada decides to pay her monthly repayments over a 25 year period with an interest of 10. 75%

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Magada's loan factor is approximately 0.006367. This means that for every $1 borrowed, Magada will have to pay approximately $0.006367 per month for the next 25 years to repay the loan with an interest rate of 10.75%.

To calculate the loan factor, we first need to calculate the monthly interest rate and the total number of monthly payments.

Monthly interest rate = Annual interest rate / 12

= 10.75% / 12

= 0.8958%

Monthly payments = Number of years * 12

= 25 * 12

= 300

Now, we can use loan factor formula, which is:

Loan factor = [monthly interest rate * (1 + monthly interest rate)^n] / [(1 + monthly interest rate)^n - 1]

Substituting the values, we get:

Loan factor = [0.008958 * (1 + 0.008958)^300] / [(1 + 0.008958)^300 - 1]

= 0.006367

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How many solutions does the system have? \begin{cases} 5x-y=2 \\\\ 5x-y=-2 \end{cases} ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ ​ 5x−y=2 5x−y=−2 ​ Choose 1 answer: Choose 1 answer: (Choice A) A Exactly one solution (Choice B) B No solutions (Choice C) C Infinitely many solutions

Answers

The system of equation has no solution (option b).

Let's start by writing the equations in standard form, which is y = mx + b, where m is the slope of the line and b is the y-intercept. We have:

y = -5x - 1

y = -5x + 7

Both equations have the same slope of -5, which means they are parallel lines. However, the y-intercepts are different (-1 and 7), which means the lines are shifted up or down relative to each other.

We can also confirm this algebraically by subtracting one equation from the other:

y = -5x + 7 - (-5x - 1)

y = -5x + 5

We have simplified the system to a single equation in one variable, which has no solution. This confirms that the original system has no solution as well.

Hence the correct option is (b).

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a p-value a. can be positive or negative. b. is a probability. c. can be smaller than 0 but no larger than 1. d. can be larger than 1 but no smaller than 0. e. can only range in value from -1 to 1.

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A p-value is a probability.

A p-value is the probability of obtaining a test statistic as extreme or more extreme.

The observed value, assuming the null hypothesis is true.

It ranges in value from 0 to 1 and represents the strength of evidence against the null hypothesis.

A p-value cannot be negative, as it is a probability and probabilities are always between 0 and 1.

A p-value also cannot be larger than 1, as it represents a probability.

A probability cannot exceed 1.

Finally, a p-value cannot be smaller than 0, as it represents a probability.

A probability cannot be negative.

the correct option is b. is a probability.

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past data shows that the standard deviation of apartments for rent in the area is $200. suppose we want a 98% confidence interval with margin of error of 50. what sample size do we need?

Answers

A sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50.

How to calculate sample size?

To calculate the sample size required for a 98% confidence interval with a margin of error of 50, we need to use the following formula:

n = [Z*(σ/ME)]^2

where:

n = the sample size needed

Z = the Z-score for the desired confidence level (98% or 2.33)

σ = the standard deviation of apartments for rent in the area ($200)

ME = the margin of error ($50)

Plugging in the given values, we get:

n = [2.33*(200/50)]^2

n = [9.32]^2

n ≈ 86.7

Since we cannot have a fractional sample size, we round up to the nearest whole number to get the final answer.

Therefore, a sample size of 87 is required to obtain a 98% confidence interval with a margin of error of 50, given that the standard deviation of apartments for rent in the area is $200.

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Interpret the probability. In 100 trials of this experiment, it is expected about (Round to the nearest whole number as needed.) to result in exactly 15 flights being on time

Answers

Hence, it is expected that 14 flights will arrive on time out of the 100 trials of this experiment.

What is the probability?

The probability of an occurrence is a number used in mathematics to describe how likely it is that the event will take place. In terms of percentage notation, between 0% and 100% it is expressed as a number between 0 and 1, or . The higher the likelihood, the more likely it is that the event will take place.

What is the trials?

 when we refer to an experiment or trial, we mean a random experiment. When difference  between a trial and an experiment, think of the experiment as a larger entity created by the fusion of several trials.

Unless otherwise stated,A trial is any specific outcome of a random experiment. In other words, a trial of the experiment is what we call when we conduct an experiment.

according to question, the number of on-time flights in 100 trials as a binomial random variable with parameters n = 100 (the number of trials) and p (the chance of success, i.e., a flight being on time), presuming that the probability of a flight being on time is the same in all trials.

The expected number of on-time flights in 100 trials is E(X) = np if the same of a flight being on time is p. Given that E(X) = 15, we determine p ,

E(X) = n p = 15 n = 100

p = [tex]\frac{E(X)}{n} = \frac{15}{100}[/tex] = 0.15

Therefore, it is probability that 0.15 %of flights will arrive on time.

To determine the expected  number of trials from a total of 100

Using the probability mass function of the binomial distribution, we can get the expected probability of trials out of 100 that result in precisely 15 flights departing on time:

[tex]P(X = 15)=(100 choose 15) * 0.15^{15} * 0.85^{85}[/tex]

We can calculate this 0.144 get  using a calculator.

therefore it is expected that 14 flights will arrive on time out of the 100 trials of this experiment. It should be noted that while this is an expected value, random fluctuation may cause the actual number of on-time flights in each trial to deviate somewhat from this figure.

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Choose Yes or No to tell whether the Addition Property of Inequality can be used to solve each statement. W – 4 > –10 12 ≥ 20x 7y10 ≤ 5. 5 –3. 25 < x – 9. 75

Answers

According to the given inequality,

W – 4 > –10 uses Addition Property

12 ≥ 20x not uses Addition Property

7y10 ≤ 5. 5 –3. 25 < x – 9. 75 uses Addition Property

Let's analyze each given inequality to see whether we can use the Addition Property of Inequality to solve them.

W – 4 > –10: We can use the Addition Property of Inequality to solve this inequality. To do this, we need to add 4 to both sides of the inequality, which gives us: W – 4 + 4 > –10 + 4, or W > –6.

12 ≥ 20x: We cannot use the Addition Property of Inequality to solve this inequality since we need to isolate "x" on one side of the inequality. To do this, we would need to subtract 12 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

7y + 10 ≤ 5.5 – 3.25x: We cannot use the Addition Property of Inequality to solve this inequality either since we need to isolate "y" on one side of the inequality.

To do this, we would need to subtract 10 from both sides of the inequality, which is not allowed under the Addition Property of Inequality.

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Slope-intercept (0, -2) , (9,1)

Answers

Answer:
Do you have a graph or anything?

select the location -2 and -9 on the number line. select the places on the number line to plot the points.

Answers

-2: | -2 |

-9: | -9 |

A ball is thrown into the air with an initial upward velocity of 48 ft/s. Its height (h) in feet after t seconds is given by the function h=-16t^2+48t+64. After how many seconds will the ball hit the ground?

Answers

Answer: Let the experienced one help you out! Therefore, the ball hits the ground after 4 seconds. Read the explanation down below:

Brainliest?

Step-by-step explanation:

To find when the ball hits the ground, we need to find the value of t when h=0, since at that point the height of the ball is zero, indicating that it has reached the ground.

We have the equation:

h = -16t^2 + 48t + 64

Setting h to zero, we get:

0 = -16t^2 + 48t + 64

Dividing both sides by -16, we get:

0 = t^2 - 3t - 4

Now we can use the quadratic formula to solve for t:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -3, and c = -4.

Plugging in these values, we get:

t = (-(-3) ± sqrt((-3)^2 - 4(1)(-4))) / 2(1)

t = (3 ± sqrt(9 + 16)) / 2

t = (3 ± 5) / 2

So we have two solutions:

t = (3 + 5) / 2 = 4

t = (3 - 5) / 2 = -1

The negative solution doesn't make sense in this context, so we discard it. Therefore, the ball hits the ground after 4 seconds.

Write the equation for the following graph.

Answers

Step-by-step explanation:

the equation for the following graph os (-3,-5) & (1,1)

Can someone help me pls!!!

Answers

Answer: Yes

Step-by-step explanation: SSS criteria

A bottle of water that is 80°F is placed in a cooler full of ice. The temperature of the water decreases by 0. 5°F every minute. What is the temperature of the water, in degrees Fahrenheit, after 5 1/2
minutes? Express your answer as a decimal

Answers

After 5 and a half minutes, the temperature of the water will be 77°F.

In this scenario, we are given that the initial temperature of the water is 80°F. We also know that the temperature of the water decreases by 0.5°F every minute. We want to find out what the temperature of the water will be after 5 and a half minutes.

To solve this problem, we need to use a bit of math. We know that the temperature of the water is decreasing by 0.5°F every minute. So after 1 minute, the temperature of the water will be 80°F - 0.5°F = 79.5°F. After 2 minutes, the temperature will be 79.5°F - 0.5°F = 79°F. We can continue this pattern to find the temperature after 5 and a half minutes.

After 5 minutes, the temperature of the water will be 80°F - (0.5°F x 5) = 77.5°F. And after another half minute (or 0.5 minutes), the temperature will decrease by another 0.5°F, so the temperature will be 77.5°F - 0.5°F = 77°F.

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A concert ticket costs $65. If 25,300 tickets are available, how much money will be made in concert tickets if every
ticket is sold. Create an equation to represent this situation. Write the equation in function notation. State the
ordered pair for 25,300 tickets and explain your solution.

Answers

Answer:

$ 1644500

Step-by-step explanation:

you roll a 6-sided dice. what is the probability that you rolled a 5, given that the number rolled was greater than 3?

Answers

The probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

We need to find the probability that you rolled a 5, given that the number rolled was greater than 3. Let's break this down step by step:

1. Identify the total number of outcomes: Since it is a 6-sided dice, there are 6 possible outcomes (1, 2, 3, 4, 5, and 6).

2. Determine the number of outcomes greater than 3: The outcomes greater than 3 are 4, 5, and 6. There are 3 possible outcomes that satisfy this condition.

3. Identify the number of outcomes that result in rolling a 5: There is only 1 outcome that results in rolling a 5.

4. Calculate the probability: To find the probability, divide the number of outcomes that result in rolling a 5 (1) by the total number of outcomes greater than 3 (3).

Probability = (Number of outcomes with a 5) / (Number of outcomes greater than 3) = 1/3

So, the probability that you rolled a 5, given that the number rolled was greater than 3, is 1/3 or approximately 0.333.

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The probability that the number rolled was a 5, given that it was greater than 3, is [tex]$\frac{1}{3}$[/tex].

The number rolled was greater than 3, it must be either a 4, 5, or 6.

The probability that the number rolled was a 5, given that it was greater than 3.

Let [tex]$A$[/tex] be the event that the number rolled is a 5 and let [tex]$B$[/tex] be the event that the number rolled is greater than 3.

Then, we want to find. [tex]$P(A|B)$[/tex], the probability of [tex]$A$[/tex] given [tex]$B$[/tex].

By Bayes' theorem, we have:

Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.

The risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately by conditioning it relative to their age, rather than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference.

The probabilities involved in the theorem may have different probability interpretations.

Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence.

Bayesian inference is fundamental to Bayesian statistics, being considered by one authority as; "to the theory of probability what Pythagoras's theorem is to geometry."

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)}$[/tex]

[tex]$P(A) = \frac{1}{6}$[/tex], since there is only one way to roll a 5 on a 6-sided die.

[tex]$P(B) = \frac{3}{6} = \frac{1}{2}$[/tex], since there are three outcomes (4, 5, or 6) that satisfy. [tex]$B$[/tex], out of a total of six possible outcomes.

[tex]$P(B|A)$[/tex], the probability of rolling a number greater than 3, given that the number rolled is a 5, note that. [tex]$B$[/tex] is true only if the number rolled is a 4, 5, or 6.

Since there is only one way to roll a 5, and only one of these three outcomes satisfies. [tex]$A$[/tex], we have:

[tex]$P(B|A) = \frac{1}{1} = 1$[/tex]

Substituting these values into Bayes' theorem, we get:

[tex]$P(A|B) = \frac{P(B|A)P(A)}{P(B)} = \frac{1 \cdot \frac{1}{6}}{\frac{1}{2}} = \frac{1}{3}$[/tex]

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answer this question

Answers

Required value of X is 1.

What is equation?

An equation is a that asserts mathematical statement that two expressions are equal. It consists of two sides, the left-hand side and the right-hand side, separated by an equals sign. An equation can contain variables, constants, coefficients, and operators. The goal is to find the value(s) of the variable(s) that make the equation true. Equations are used in many branches of mathematics and in various applications, such as physics, chemistry, engineering, and economics.

To solve for the value of x, we need to isolate x on one side of the equation. We can do this by subtracting 3 from both sides of the equation,

X + 3 - 3 = 4 - 3

Simplifying the left-hand side gives,

X = 1

Therefore, the value of x is 1.

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Correct question is "Answer the question,

X+3 = 4,

What is the value of x?"

What is the answer to the question?

Answers

Answer:

y = xy = -xx = 3x = 7x = -3

Step-by-step explanation:

You want to identify the lines among those listed that will intersect the line y = 4.

Parallel lines

The line y = 4 is a horizontal line. Any line of the form y = c, for some constant c (not 4), will be parallel and will not intersect y = 4.

All of the other lines listed will intersect y = 4.

The intersecting lines are ...

y = xy = -xx = 3x = 7x = -3

<95141404393>

Verify that the segments are parallel.

10. CD || AB

Answers

Answer: Prove that the triangles are similar, and therefore the lines have the same slope and are parallel.

!!PLEASE HELPPP MEEE!!

Answers

Answer:

Step-by-step explanation:

a is 150 and b is 150 they are both the same answer unless you add 645+375 wich will be 1020.

The right triangle shown is enlarged such that each side is multiplied by the value of the hypotenuse, 3y. Find the expression that represents the perimeter of the enlarged triangle. TRIANGLE AND ANSWER CHOICES BELOW!

Answers

Answer:

c.

Step-by-step explanation:

The original triangle has two sides with length 4x each, and the hypotenuse has length 3y.

After the enlargement, each of the sides with length 4x becomes 3y × 4x = 12xy, and the hypotenuse becomes 3y × 3y = 9y^2.

Therefore, the perimeter of the enlarged triangle is the sum of the lengths of its three sides:

12xy + 12xy + 9y^2 = 24xy + 9y^2 = 9y^2 + 24xy

So the answer is (C) 9y^2 + 24xy.

x^2+y^2+12x+12y+12=0

Answers

Answer: the equation represents a circle centered at (-6, -6) with radius 2.

Step-by-step explanation:

x^2 + 12x + 36 + y^2 + 12y + 12 - 36 = 0

Simplifying, we get:

(x + 6)^2 + y^2 - 12 = 0

For the y terms, we add (12/2)^2 = 36 to both sides to get:

x^2 + 12x + 36 + y^2 + 12y + 36 - 24 = 0

Simplifying, we get:

(x + 6)^2 + (y + 6)^2 = 4

Therefore, the equation represents a circle centered at (-6, -6) with radius 2.

Answer: 0

Step-by-step explanation:

You roll a six sided die 30 times. A 5 is rolled 8 times. What is the theoretical probability of rolling a 5? What is the experimental probability of rolling a 5?

Answers

The theoretical and experimental probability of rolling a 5 are 1/6 and 4/15 respectively.

How do we derive the probability?

We will calculate the theoretical probability by substituting 30 for the number of favorable outcomes as the die is rolled 30 times with one option each for 30 rolls and 180 for total number of outcomes in theoretical probability formula.

P(Theoretical probability of rolling a 5) = 30/180

P(Theoretical probability of rolling a 5) = 1/6.

The experimental probability is calculated by substituting 8 for the number of time the event occurs and 30 for the total number of trials.

P(Experimental probability of rolling a 5)= 8/30

P(Experimental probability of rolling a 5) =4/15

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Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 12 people took the trip. She was able to purchase coach tickets for ​$190 and first class tickets for ​$980. She used her total budget for airfare for the​ trip, which was ​$4650. How many first class tickets did she​ buy? How many coach tickets did she​ buy?

Answers

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

what is equation ?

An equation is a logical statement that utilises the equal sign to demonstrate the equality of two expressions. Factors, constants, and mathematical like addition, reduction, multiply, division, and exponentiation can all be found in it. Equations are utilised to find solutions for problems in both mathematics and the real world.

given

Let's use the letters "c" for the quantity of coach tickets and "f" for the quantity of first-class tickets. We are aware that there were 12 travellers in all, so

c + f + 1 = 12

We also know that the entire cost of the airfare was $4650, with coach tickets costing $190 and first-class tickets costing $980. With this knowledge, we can construct the equation shown below:

[tex]190c + 980f = 4650 - 980[/tex]

When we simplify this equation, we obtain:

[tex]190c + 980f = 3670[/tex]

Elimination can now be used to find either "c" or "f." By increasing the first equation by 190 and deducting it from the second equation, let's get rid of "c":

[tex]190c + 190f + 190 = 2280[/tex]

-190c - 980f = -3670

-790f = -1390

f = 1.76

We can round "f" up to 2 because we cannot have a fractional number of persons.

c + 2 + 1 = 12

c = 9

Sarah then purchased 9 coach seats as by increasing the first equation by 190 and deducting it from the second equation.

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Mr. Lowe is a school librarian. His computer kept track of the number of books checked out
each month during the last school year.
Books checked out

4,247. 4,983. 6,214. 7,500. 3,500. 2,500. 5,000. 3,876. 4,753. 2,712.

Which box plot represents the data?

Answers

Answer:

  A (top)

Step-by-step explanation:

You want to know which box plot represents the data in the given list.

Median

The difference between the box plots is the location of the median.

When the data is sorted into order, it is ...

  {2500, 2712, 3500, 3876, 4247, 4753, 4983, 5000, 6214, 7500}

There are an even number of elements in this list, so the median is the average of the middle two:

  median = (4247 +4753)/2 = 9000/2 = 4500

The median is represented by the line inside the box of the box plot. The plot with its median at 4500 is the top one (shown in the attachment).

The top box plot represents the data.

<95141404393>

Kiran swims z laps in the pool. Clare swims 18 laps, which is 9/5
times as many laps as Kiran. How many laps did Kiran swim?
Equation:
Solution: z=

Answers

we use linear equation in one variable to solve the problem. Kiran swam 10 laps in the pool.

Let's represent the number of laps Kiran swam as "z".

We know that Clare swam 18 laps, which is 9/5 times as many laps as Kiran. We can represent this relationship with the following equation:

18 = (9/5)z

To solve for z, we can isolate it by multiplying both sides of the equation by the reciprocal of 9/5, which is 5/9:

18 * (5/9) = (9/5)z * (5/9)

10 = z

Therefore, Kiran swam 10 laps in the pool.

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a quadrilateral that is not a rectangle is inscribed in a circle. what is the least number of arc measures needed to determine the measures of each antgle in the quadrialteral

Answers

The least number of arc measures needed to determine the measures of each angle in the inscribed quadrilateral is 2.

To determine the measures of each angle in the quadrilateral, we need to find the central angles of the arcs that intersect the quadrilateral's vertices. Since the quadrilateral is not a rectangle, it is not a cyclic quadrilateral, which means that its opposite angles do not add up to 180 degrees.

Therefore, we need to use the fact that the sum of the measures of the opposite angles in an inscribed quadrilateral is 360 degrees. Let the angles of the quadrilateral be A, B, C, and D, with opposite angles A and C, and B and D. We can find the measure of arc AC by drawing a chord connecting the endpoints of AC and finding the central angle that intercepts it. Similarly, we can find the measure of arc BD.

Now, we can use the fact that the sum of the central angles that intercept arcs AC and BD is equal to 360 degrees. Let these angles be x and y, respectively. Then, we have:

x + y = 360

We can solve for one of the variables, say y, in terms of the other:

y = 360 - x

Substituting this into the equation for arc BD, we have:

2x + 2(360 - x) = arc BD

Simplifying this equation, we get:

arc BD = 720 - 2x

Now, we can use the fact that the sum of the measures of angles A and C is equal to the measure of arc AC, and the sum of the measures of angles B and D is equal to the measure of arc BD. Therefore, we have:

A + C = arc AC
B + D = arc BD = 720 - 2x

We need to find the least number of arc measures needed to determine the measures of A, B, C, and D. Since we have two equations and two variables (x and A), we can solve for both variables. Then, we can use the equations for B and D to find their measures.

Solving for A in terms of x, we have:

A = arc AC - C
A = 360 - x - C

Substituting this into the equation for B + D, we have:

(360 - x - C) + B + D = 720 - 2x

Simplifying this equation, we get:

B + D = 360 + x - C

Now, we have three equations and three variables (x, A, and C). We can solve for each variable in terms of x, and then use the equation for B + D to find their measures.

Therefore, the least number of arc measures needed to determine the measures of each angle in the quadrilateral is two: arc AC and arc BD.

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Election polling Gloria Chavez and Ronald Flynn are the candidates for mayor in a large city. We want to estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a margin of error no greater than 0.03. How large a random sample do we need? Show your work.

Answers

A random sample of approximately 1067 registered voters is needed to estimate the proportion of voters planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

To estimate the proportion p of all registered voters in the city who plan to vote for Chavez with 95% confidence and a

margin of error no greater than 0.03, we need to determine the sample size. We can use the following formula for

sample size calculation:

[tex]n = (Z^2 × p × (1-p)) / E^2[/tex]
Where:
- n is the sample size
- Z is the Z-score (1.96 for 95% confidence)
- p is the estimated proportion of voters planning to vote for Chavez
- E is the margin of error (0.03 in this case)

Since we don't know the true proportion of voters planning to vote for Chavez, we can use the most conservative

estimate (p = 0.5) to ensure the required margin of error:

[tex]n = (1.96^2 × 0.5 × (1-0.5)) / 0.03^2[/tex]
n = (3.8416 × 0.25) / 0.0009
n = 0.9604 / 0.0009
n ≈ 1067

Therefore, a random sample of approximately 1067 registered voters is needed to estimate the proportion of voters

planning to vote for Chavez with 95% confidence and a margin of error no greater than 0.03.

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d. Amanda
is considering changing her regimen by running two miles the first week and then running
additional two miles each subsequent week. Write a sequence for the number of miles that Amanda
would run the first 10 weeks of her training if she followed the new regimen. Explain your reasoning.

Answers

Answer: If Amanda runs two miles the first week and then adds two miles each subsequent week, we can create a sequence using arithmetic progression. The common difference between each term in the sequence is two, and the first term is two.

Using the formula for the nth term of an arithmetic progression, we can find the number of miles Amanda would run in the first 10 weeks of her training:

an = a1 + (n-1)d

where:

an = the nth term of the sequence

a1 = the first term of the sequence (2 miles in the first week)

n = the number of terms (up to 10 weeks)

d = the common difference between each term (2 miles per week)

So for n = 1 to 10, we have:

a1 = 2

d = 2

n = 1: a1 + (n-1)d = 2 + (1-1)2 = 2

n = 2: a1 + (n-1)d = 2 + (2-1)2 = 4

n = 3: a1 + (n-1)d = 2 + (3-1)2 = 6

n = 4: a1 + (n-1)d = 2 + (4-1)2 = 8

n = 5: a1 + (n-1)d = 2 + (5-1)2 = 10

n = 6: a1 + (n-1)d = 2 + (6-1)2 = 12

n = 7: a1 + (n-1)d = 2 + (7-1)2 = 14

n = 8: a1 + (n-1)d = 2 + (8-1)2 = 16

n = 9: a1 + (n-1)d = 2 + (9-1)2 = 18

n = 10: a1 + (n-1)d = 2 + (10-1)2 = 20

Therefore, Amanda would run 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20 miles in the first 10 weeks of her training if she followed the new regimen.

Step-by-step explanation:

The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.

A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.

When comparing the data, which measure of center should be used to determine which location typically has the cooler temperature?

Median, because Desert Landing is symmetric
Mean, because Sunny Town is skewed
Mean, because Desert Landing is symmetric
Median, because Sunny Town is skewed

Answers

Median, because Sunny Town is skewed.

What is descriptive statistics?

Descriptive statistics is a branch of statistics that deals with the collection, organization, analysis, and interpretation of numerical data. It involves using various statistical measures to describe and summarize the characteristics of a set of data. Descriptive statistics helps to make sense of large amounts of data by presenting it in a more meaningful and understandable way. Commonly used measures of central tendency in descriptive statistics include mean, median, and mode, while measures of dispersion include range, variance, and standard deviation. Descriptive statistics is widely used in various fields, such as business, medicine, economics, psychology, and social sciences, to name a few.

Median, because Sunny Town is skewed.

The skewness of the histogram for Sunny Town indicates that the data is not symmetrically distributed, and therefore the median would be a better measure of central tendency to compare the locations. The mean can be affected by extreme values or outliers, which might be present in the skewed distribution of Sunny Town, making it less reliable in this case.

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In the accompanying diagram, m<A=32° and AC = 10. Which equation could be used to find x in ∆ABC?

1. x=10 sin [32°]
2. x=10 cos [32°]
3. x = 10 tan [32°]
4. x=10/cos32​

Answers

The equation x = 10 tan (32°) could be used to find x in ∆ABC.

RIGHT TRIANGLE

A triangle is classified as a right triangle when it presents one of your angles equal to 90º.  The greatest side of a right triangle is called the hypotenuse. And, the other two sides are called legs.

The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.

The Pythagorean Theorem says: (hypotenuse)²= (leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x) , cos  (x) and tan  (x) , where:

[tex]sin(x)=\frac{opposite\ side}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ side}{hypotenuse}\\ \\ tan(x)=\frac{sin(x)}{cos(x)} =\frac{opposite\ side}{adjacent\ side}[/tex]

The question gives the value of the two sides and the value of an angle. From the trigonometric ratios presented before, you can write:

[tex]tan(32)=\frac{opposite\ side}{adjacent\ side}=\frac{x}{10} \\ \\ x=10\ tan (32\°)[/tex]

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