Mathematics High School

A running track consists of two parallel lines that are connected at each end but the curved boundary of a semicircle. The parallel lines are 30 meters long and 7 meters apart. Fine the area inside the running track.

Answers

Answer 1

Answer:

The area inside the running track is 248.5 m².

Step-by-step explanation:

The area inside the running track is given by the sum of the area of a rectangle and the area of a semicircle:

[tex] A_{t} = A_{r} + 2A_{c} [/tex]

[tex] A_{t} = x*(2r) + 2*(\frac{\pi r^{2}}{2}) [/tex]

Where:

x: is one side of the rectangle = 30 m

r: is the radius = half of the other side of the rectangle = 7/2 m = 3.5 m

Hence, the total area is:

[tex] A_{t} = 30*7 + \pi (3.5)^{2} = 248.5 m^{2} [/tex]

Therefore, the area inside the running track is 248.5 m².

I hope it helps you!

Related Questions

Consider the hypothetical study described below. Based solely on the information given, do you have reason to question the results of the study? Explain your reasoning.
Researchers design five survey questions to determine whether Norwegian citizens are happier than American citizens.
Is there reason to question the results? Select all that apply.
A.
No, there is not reason. The goal of the study is clear.
B.
Yes, there is reason. It is not clear how the variable of interest is defined.
C.
Yes, there is reason. The people being surveyed will likely not be representative of the population.
D.
Yes, there is reason. It is not clear how the variable of interest is measured.
E.
No, there is not reason. There is no bias in the study.
F.
No, there is not reason. It is unlikely that there are any confounding variables in the study.

Answers

There are reasons to question the results of the survey comparing the happiness of Norwegian and American citizens due to potential issues with defining the variable of interest.

The given options present various perspectives on whether there are reasons to question the results of the survey comparing the happiness of Norwegian and American citizens. Among the provided options, options B, C, and D are the most appropriate selections.

B. Yes, there is reason. It is not clear how the variable of interest is defined:

C. Yes, there is reason. The people being surveyed will likely not be representative of the population:

D. Yes, there is reason. It is not clear how the variable of interest is measured:

By considering these factors, it becomes apparent that there are reasons to question the survey results, highlighting the importance of clear definitions, representative sampling, and transparent measurement methods to ensure the validity and reliability of the study.

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Combine the like terms to create an equivalent expression for -k+3k

Answers

Answer:

Step-by-step explanation:

-k+3k

If the conclusion of a valid argument is false, then all of the premises must be false. O True O False

Answers

False. "If the conclusion of a valid argument is false, then all of the premises must be false" is incorrect.

The statement "If the conclusion of a valid argument is false, then all of the premises must be false" is incorrect. In a valid argument, the truth of the premises guarantees the truth of the conclusion, but it does not guarantee the truth of the conclusion in reverse. This means that even if the conclusion of a valid argument is false, it does not necessarily imply that all of the premises must be false.

A valid argument is one in which the conclusion logically follows from the premises. It is possible for the premises to be true and still lead to a false conclusion due to errors in reasoning or incorrect logical connections. In such cases, the argument is considered valid but unsound.

To illustrate this, consider the following example:

Premise 1: All birds have feathers.

Premise 2: Penguins are birds.

Conclusion: Therefore, penguins can fly.

This argument is logically valid because the conclusion follows logically from the premises. However, the conclusion is false because penguins cannot fly. In this case, the premises are true, but the conclusion is false.

Therefore, the statement that all of the premises must be false if the conclusion of a valid argument is false is incorrect.

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You are to create a password using 8 letters from the alphabet (repetition allowed). What is the probability that no letter is repeated if the letters were randomly chosen to be in the password?

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The probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.

To calculate the probability that no letter is repeated in a password created using 8 letters from the alphabet (repetition allowed), we need to consider the total number of possible passwords and the number of passwords without repeated letters.

The number of possible passwords can be calculated by considering that each letter in the password can be chosen independently from the 26 letters in the alphabet. Therefore, there are 26 choices for each of the 8 positions, resulting in a total of 26^8 possible passwords.

To calculate the number of passwords without repeated letters, we can consider the choices for each position. For the first position, we have 26 options. For the second position, we have 25 options (since we cannot repeat the letter chosen for the first position). Similarly, for the third position, we have 24 options, and so on.

Using the multiplication principle, the number of passwords without repeated letters is given by 26 * 25 * 24 * 23 * 22 * 21 * 20 * 19.

Therefore, the probability that no letter is repeated in the password can be calculated as:

Probability = (Number of passwords without repeated letters) / (Total number of possible passwords)
= (26 * 25 * 24 * 23 * 22 * 21 * 20 * 19) / (26^8)

Calculating this probability:

Probability ≈ 0.0000194293

So, the probability that no letter is repeated in the password is approximately 0.0000194293, or about 0.0019%.

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what's the ratio of 0.9?

Answers

Answer:

[tex] \frac{9}{10} = 0.9[/tex]

Convert fraction (ratio)
Answer: 9/10, 0.9, 90%

Please help me TwT
Please and Thank you!

Answers

Answer:

Option C (None Of The Above)

Step-by-step explanation:

Given expression = [tex] - (\frac{ - e}{ - f} )[/tex]

Lets multiply the numerator and denominator by -1.

[tex] = > - ( \frac{ - e \times - 1}{ - f \times - 1} )[/tex]

[tex] = > - ( \frac{e}{f} )[/tex]

Now , lets open the brackets.

[tex] = > \frac{ - e}{f} [/tex]

But as this expression is not there in the given options , the correct answer will be Option C.

Answer:

C. None Of The Above

Step-by-step explanation:

Hope this helps

A recent Gallup poll asked American adults if they had COVID-19 symptoms, would they avoid seeking treatment due to the high costs of healthcare? The poll contained a sample of 1,017 American adults and 143 of them said they would avoid seeking treatment due to the high costs of healthcare. Construct the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare.

What is N in this study? _____
What is P in this study? _____

Answers

The value of N in this study = 1017The value of P in this study = 0.1407

The solution to the given problem is as follows:N in this study = 1017P in this study = 143/1017 = 0.1407 (rounded to 4 decimal places)

Given, the sample size n = 1017, and the sample proportion of people who would avoid seeking treatment due to high healthcare costs = 143/1017 = 0.1407

Since we need to calculate the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare, we need to calculate the standard error of the proportion.

The formula to calculate the standard error of the proportion is:

Standard error of the proportion = sqrt [ p * (1 - p) / n ]

Substituting the values, we get:

Standard error of the proportion = sqrt [ 0.1407 * (1 - 0.1407) / 1017 ]= 0.0141 (rounded to 4 decimal places)

To calculate the 95% confidence interval, we use the following formula:

95% confidence interval = sample proportion ± margin of error

Margin of error = Z * (standard error of the proportion)

where Z is the Z-score corresponding to the confidence level.

For 95% confidence level, Z = 1.96.

Substituting the values, we get:

Margin of error = 1.96 * 0.0141= 0.0276 (rounded to 4 decimal places)

Therefore, the 95% confidence interval for the proportion of the American adult population who would avoid seeking treatment for COVID-19 due to the high costs of healthcare is given by:

0.1407 ± 0.0276= (0.1131, 0.1683) (rounded to 4 decimal places)

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please someone help me out, please don't put the incorrect answer
What is the distance between the points (-1, 2) and (2, 6)?

Answers

Answer:

Step-by-step explanation:

Distance Equation Solution:

[tex]d=\sqrt{(2-(-1)^2+(6-2)^2}\\d=\sqrt{(3)^2+(4)^2} \\d= \sqrt{9+6}\\d= \sqrt{25}\\d=5[/tex]

Question Two

The concept of sets underlies every branch of modern mathematics for economics. Suppose the universal set is a set of positive integers, Z + , and let

X={ x € Z + :x<=20 and x^ 2 € Z +}

Y={ x € Z + :x<=24 and sqrt x € Z +}

a) Determine X U Y and X n Y in enumeration and functional form.

b) Determine sets X n Z +, X U Z + ,Y n Z +, Y U Z + .

Answers

The sets X and Y are defined based on specific conditions on positive integers. In functional form, X n Y can be represented as X n Y = {x € Z + : x ≤ 20, x ≤ 24, and x^2 € Z +, sqrt(x) € Z +}.

a) To find X U Y (the union of X and Y), we need to identify all the positive integers that satisfy either the condition for X or the condition for Y. In enumeration form, X U Y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24}. In functional form, X U Y can be represented as X U Y = {x € Z + : (x ≤ 20 and x^2 € Z +) or (x ≤ 24 and sqrt(x) € Z +)}.

To find X n Y (the intersection of X and Y), we need to identify the positive integers that satisfy both the condition for X and the condition for Y. In enumeration form, X n Y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}. In functional form, X n Y can be represented as X n Y = {x € Z + : x ≤ 20, x ≤ 24, and x^2 € Z +, sqrt(x) € Z +}.

b) To determine the sets X n Z + and Y n Z +, we need to identify the positive integers that satisfy the conditions for X and Y, respectively, and also belong to the universal set of positive integers, Z +. Since X and Y are subsets of Z +, X n Z + = X and Y n Z + = Y.

To find X U Z +, we need to identify all the positive integers that satisfy either the condition for X or belong to Z +. In this case, X U Z + = Z + since all positive integers are included in X. Similarly, Y U Z + = Z + since all positive integers are included in Y.

In summary, X U Y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24} and X n Y = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16}. The sets X n Z + and Y n Z + are equal to X and Y, respectively, while X U Z + and Y U Z + are both equal to Z +.

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Evaluate SJxz dV where E is the region in the first octant inside the ball of radius 2.

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SJxz dV where E is the region in the first octant inside the ball of radius 2.

∭E xz dV = ∫₀² ∫₀√(4-x²-z²) ∫₀√(4-x²-y²) xz dy dz dx.

Integrating with respect to y first, then z, and finally x, we can calculate the value of the integral.

To evaluate the integral ∭E xz dV, where E is the region in the first octant inside the ball of radius 2, we need to set up the limits of integration.

Since we are integrating over the region inside the ball of radius 2 in the first octant, we can set up the limits as follows:

0 ≤ x ≤ 2,

0 ≤ y ≤ √(4 - x^2 - z^2),

0 ≤ z ≤ √(4 - x^2 - y^2).

Note that we are using the equation of the sphere x^2 + y^2 + z^2 = 4 to determine the limits of integration for y and z.

Now we can evaluate the integral as follows:

∭E xz dV = ∫₀² ∫₀√(4-x²-z²) ∫₀√(4-x²-y²) xz dy dz dx.

Integrating with respect to y first, then z, and finally x, we can calculate the value of the integral.

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Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). Which of the following most accurately gives a reason for this in the mathematics we use to make the confidence interval? And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. (And other aspects remain the same.)r The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) The standard error goes down because the standard deviation of the sample will go down. And the t*-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. O The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large.

Answers

Intuitively, a larger sample should lead to a smaller confidence interval (fixing the level of confidence). The following most accurately gives a reason for this in the mathematics we use to make the confidence interval:

The standard error goes down because of the greater sample size in the denominator. (And other aspects remain the same.) And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is true.

The standard error goes down because of the greater sample size in the denominator. This is because the formula for the standard error involves taking the square root of the sample size in the denominator. Therefore, as the sample size increases, the denominator of the standard error formula increases, causing the standard error to decrease. And the t'-value associated to the t-distribution goes down because t_n have "smaller tails" as n gets large. This is because the t-distribution is symmetrical and bell-shaped, with fatter tails than the normal distribution. As the sample size n increases, the t-distribution approaches the normal distribution, with thinner tails, which means that the t-values become smaller as n increases.

Hence, the correct option is (O) The standard error goes down because the standard deviation of the sample will go down. (And other aspects remain the same.) The mean will be more accurate with a larger sample size. The standard error goes down because of the greater sample size in the denominator. And the t-value associated with the t-distribution goes down because t_n has "smaller tails" as n gets large.

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( Need help !!!!!!!!!! Pls )

Answers

That answers is everything except C. If it’s a single choice question the choose B. It’s the best answer

Suppose that 8% of the patients tested in a clinic are infected with HIV. Furthermore, suppose that when a blood test for HIV is given, 92% of the patients infected with HIV test positive and that 9% of the patients not infected with HIV test positive. What is the probability that a patient testing positive for HIV with this test is not infected with HIV?

Answers

The problem involves calculating the probability that a patient who tests positive for HIV is not actually infected with HIV. Given that 8% of the patients tested are infected and that the test has a 92% true positive rate for infected patients and a 9% false positive rate for non-infected patients, we need to determine the probability of a false positive result.

Let's denote the events as follows:

A: Patient is infected with HIV

B: Patient tests positive for HIV

We are interested in finding P(A'|B), which represents the probability that a patient is not infected (A') given that they test positive (B).

According to Bayes' theorem, we can express this probability as:

P(A'|B) = (P(B|A') * P(A')) / P(B)

First, let's calculate P(B|A'), which represents the probability of testing positive given that the patient is not infected. Since the false positive rate is given as 9%, we have P(B|A') = 0.09.

Next, we need to calculate P(A'), which is the probability of not being infected. Since 8% of the patients are infected, the complement event (not being infected) has a probability of 1 - 0.08 = 0.92.

To calculate P(B), the probability of testing positive, we need to consider the total probability of testing positive, which includes both infected and non-infected patients. Therefore, we have:

P(B) = P(B|A) * P(A) + P(B|A') * P(A') = 0.92 * 0.08 + 0.09 * 0.92.

Finally, substituting these values into Bayes' theorem, we can calculate P(A'|B), the probability that a patient testing positive is not infected with HIV.

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b) A shopping center consists of two stores and two parking lots. In the diagram, w represents the width of Store B in meters. 25 13.5 Which expression for the area of the shopping center is written as the area of the stores plus the area of the parking lots? 38.5(w + 10) 10 Store A Parking Lot A 38.5w + 385 Store B Parking Lot B 25(w + 10) + 13.5(w + 10) (25 + 13.5)(10) + (25 + 13.5)w

Answers

Answer:

Step-by-step explanation:

25(w+10) + 13.5(w +10)

Answer:

25(w+10)+13.5(w+10)

Step-by-step explanation:

hope it helps

Consider the polynomials given below.
P(x) = 14 + 3.13 + 2x2 - + 2
Q*) = (x3 + 2x2 + 3)(x2 - 2)
Determine the operation that results in the simplified expression below.
25 + 14 - 513 - 312 + I-8
A. P+Q
B. P.Q
C. PQ
D. O-P

Answers

The operation that results in the simplified expression x⁵ + x⁴ - 5x³ - 3x² + x - 8 is; P + Q

How to Simplify Polynomials?

We are given the Polynomials as;

P(x) = x⁴ + 3x³ + 2x² - x + 2

Q(x) = (x³ + 2x² + 3)(x² - 2)

We want to find the combination of P and Q that would yield;

x⁵ + x⁴ - 5x³ - 3x² + x - 8

Let us expand Q(x) to get;

Q(x) = x⁵ + 2x⁴ + 3x² - 2x³ - 4x² - 6

Q(x) = x⁵ + 2x⁴ - 2x³ - x² - 6

Now, the combined polynomial shows us that coefficient of x⁴ is 1 and coefficient of x³ is - 5.

By inspection, we can say that the combination that would produce the required result is;

Q(x) - P(x) = x⁵ + 2x⁴ - 2x³ - x² - 6 - x⁴ - 3x³ - 2x² + x - 2

Q(x) - P(x) = x⁵ + x⁴ - 5x³ - 3x² + x - 8

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Can someone explain why the answer is False. Will Mark brainliest.

Answers

Answer:

Supplementary Angles are 180 degrees. A triangle has 180 degrees. One angle is already 90 degrees, so 2 more angles with 180 degrees is impossible.

Step-by-step explanation:

Work out
5.2
% of
628.55
km
Give your answer rounded to 2 DP.

Answers

18.63 is your answer please give brainliest!

What is the area of this triangle in the coordinate plane? 5 units 6 units 7 units 12 units?

Answers

Answer:

6 units

Step-by-step explanation:

Using readings taken from the coordinate upon which the triangle is drawn :

The area of triangle is given as :

Area of triangle = 0.5 * base * height

The base of the triangle = 4 units

The height of the triangle = 3 units

The Area of the triangle is thus :

0.5 * 4 * 3

0.5 * 12

= 6 units

Answer:

The area of the given triangle is 6 units²

what's 13.564^4x3.59^-39?

Answers

Answer:

Step-by-step explanation:

hope this helps :)

Write down the formula for calculating an unbiased estimate, Sry, of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items. Define any symbols you use.

Answers

The formula for calculating an unbiased estimate

of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items is:

(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)`,

where Xi and Yi are the values of the it h observation of x and y, X bar and Y bar are the means of x and y, respectively, and n is the sample size.

If we have to get an unbiased estimate of the covariance coefficient of variables x and y of a large (but finite) population, based on a random sample of n items, then we can use the formula:

(1/n-1) * ∑(Xi - X bar) * (Yi - Y bar)

where, the unbiased estimate of the covariance coefficient of x and y

Xi = the value of the it h observation of x

Yi = the value of the it h observation of y

X bar = the mean of x

Y bar = the mean of y

n = the sample size of the population

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The atmospheric pressure on an object decreases as altitude increases. If a is the height (in km) above sea level,

then the pressure P(a) (in mmHg) is approximated by P(a) = 760e-0.13a. Determine the atmospheric pressure at

8.47 km. Round to the nearest whole unit.

Answers

Answer:

253 mmHg

Step-by-step explanation:

Since the atmospheric pressure, [tex]P(a) = 760e^{-0.13a}[/tex]

when a = height (in km) = 8.47 km, then the atmospheric pressure P(a) is

[tex]P(a) = 760e^{-0.13a}\\P(8.47) = 760e^{-0.13X8.47}\\P(8.47) = 760e^{-1.1011} \\P(8.47 )= 760 X 0.33251 \\P(8.47)= 252.7 mmHg\\[/tex]

P(8.47) ≅ 253 mmHg

Which of the graphs below represents the soltuion set for d - 4 > -3?

Answers

Answer:

The answer is d

Step-by-step explanation:

Using a 0.05 significance level, what decision and conclusion should you make regarding the null hypothesis? (1 point) LOOK AT ANALYSIS OF VARIENCE TABLE
a.Because p-value > 0.05, we fail to reject H0 and conclude that age can be used to predict disease activity score.
b.Because p-value > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity score.
c.Because p-value > 0.05, we reject H0 and conclude that age can be used to predict disease activity score.
d.Because p-value > 0.05, we reject H0 and conclude that age cannot be used to predict disease activity score.
e.Because p-value < 0.05, we reject H0 and conclude that age can be used to predict disease activity score.

Answers

The correct answer is:

[tex]\textbf{b.}[/tex] Because the p-value is > 0.05, we fail to reject H0 and conclude that age cannot be used to predict disease activity scores.

What is a null hypothesis?

The null hypothesis, denoted as H0, is a fundamental concept in statistical hypothesis testing. It is a statement or assumption that suggests there is no significant difference, effect, or relationship between variables in a population.

The decision and conclusion depend on the p-value obtained from the analysis of variance (ANOVA) table.