Running continues to be a very popular sport in America. At a major race, like the Peachtree Road Race in Atlanta, there may be over 10,000 people entered to run. The race promoters for a road race in the Pacific Northwest took a random sample of 924 runners out of the 5000 runners entered to estimate the number of runners who will need hotel accommodations. There were 441 runners that indicated they would need hotel accommodations. Construct a 98% confidence interval for the true proportion of runners who will need hotel accommodations. Round your answer to four decimal places. Additionally, report your percentage as a decimal (i.e, a value between 0 and 1). (Round to 4 decimal places) Answer Tables Incorrect Answer o out of 10 Points Lower Limit.4536 (Round to 4 decimal places) Upper Limit.4864 Round to 4 decimal places)

The correct answer is h(t) = 14.25 + 0.25 * sin((π/26) * t)

To model the hours of daylight in a year using a sinusoidal equation, we can consider the average length of daylight, the amplitude of the variation, and the period of the function.

Given:

Summer solstice (longest day) is 14.5 hours

Winter solstice (longest night) is 14 hours

Let's analyze the information:

Average daylight: The average daylight throughout the year would be the average of the summer and winter solstices. It can be calculated as:

Average daylight = (14.5 + 14) / 2 = 14.25 hours

Amplitude: The difference between the average daylight and the longest day or night is the amplitude. In this case, the amplitude is half the difference between the summer and winter solstices. It can be calculated as:

Amplitude = (14.5 - 14) / 2 = 0.25 hours

Period: We are modeling the function over a year, which we'll consider as 52 weeks. Since we want to measure time in weeks (t), the period of the function is 52 weeks.

Putting all the information together, we can write the sinusoidal equation:

h(t) = Average daylight + Amplitude * sin((2π / Period) * t)

Substituting the values we calculated:

h(t) = 14.25 + 0.25 * sin((2π / 52) * t)

Simplifying further, the sinusoidal equation modeling the hours of daylight in a year is:

h(t) = 14.25 + 0.25 * sin(π/26 * t)

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Answer:

23

Step-by-step explanation:

Answer:

x=37

Step-by-step explanation:

Complementary angles are a set of 2 angles that when added together, add up to 90. In order to solve for x, both angles have to be added and set to be equal to 90... but Jackie only used one of the angles, not both. The correct equation is: x+16+x=90

Answer:

Jackie forgot to add variable X

Step-by-step explanation:

Jackie Did

X +16= 90

equation :

x+x+16= 90

Answer:

1.0

Step-by-step explanation:

If you have any questions feel free to ask in the comments

Answer: 1.0

Step-by-step explanation:

Given:  "0.995 inches" ; round to the nearest TENTH of an inch.

(which means; round to the nearest "first decimal point" ; and to include the actual first decimal point (and that decimal point only, the "tenths place").

We are given the number:  "0.955" .  This is given to the nearest THOUSANDS.  

We examine the "tenths place":  "0.9" .  So we know our choices are:

"0.9" (round down to the nearest tenths place); or, "1.0" (round up to the nearest tenths place).  

           →  We examine the number: "0.955" ; and look to the next value, the "hundredths place".  

           → If that digit is 5 or greater (i.e. 5 to 9), we "round up" ; and the correct answer is:  "1.0" .  If that number is "4" or less (i.e. 0 to 4), we round down; and the correct answer is:  "0.9".

________________________________________

In the case of our give value:  "0.955" .  The digit to the right of "9" is "5" ; so, as previously mentioned, we "round up" ;  to:  "1.0".

Do not forget to include the units.

______________________________________________________

The answer is:  1.0 inches.

_________________________________________________

Answer:

y= -3

Step-by-step explanation:

adding both the equation we get x= 7

and then put value of x in any one equation u will get y as -3

On solving the given set of equations, we get the value of y = 3.

A set of equations having two or more variables whose values ​​can satisfy all the equations in the set at the same time, with the number of variables equal to or fewer than the number of equations in the set is called simultaneous equations.

We are given a set of simultaneous equations in x and y,

x + 2y = 1

x - 2y = 13.

We are asked to find the value of y.

Let the equations

x + 2y = 1... (i)

x 2y = 13 ... (ii).

To solve for y, we subtract (i) from (ii) to get,

\(x - 2y = 13\\x+2y=1\\(-)(-)(-)\\------\\-4y = 12\)

∴ We get -4y = 12.

Dividing both sides of this equation by -4, we get,

(-4y)/(-4) = 12/(-4)

or, y = -3.

∴ On solving the given set of the equation we get the value of y = 3.

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Answer:

Common denominator is the smallest number the two can be divided by both numbers like the common denominator of 3 and 4 is 12. You can multiply two numbers together to get it too

Step-by-step explanation:

Step-by-step explanation:

In the first part, he was travelling with twice the speed, or Vs, for distance

48 - d, for 2 hours.

speed = distance/time

distance = speed * time

First part :

48 - d = 2V * 2

⇒d + 4V = 48  

Second part:

d = V * 2

⇒d = 2V  

Substitute 2s for d in equation 1.

2s + 4s = 48

6s = 48

s = 8

The speed in the second part is 8 mph.

The speed in the first part is 2s = 2(8) = 16

I hope this helps

Answer:

x=27 degrees

Step-by-step explanation:

This triangle is a right angle, meaning that all the angle measures combined will equal to 180 degrees.

The square in the right handed corner is equal to 90 degrees.

We know that there is also a measure that is equal to 63 degrees.

Therefore, knowing that all the angles combined will equal 180 degrees.

We add 90 + 63.

90+63=153

The we take the sum and subtract it from 180 to get our answer.

180-153=27.

Step-by-step explanation:

1- The probability of obtaining at most 2 red balls is equal to the probability of obtaining 0 red balls plus the probability of obtaining 1 red ball plus the probability of obtaining 2 red balls. Since there are a total of 12 balls in the urn and each ball has an equal chance of being drawn, the probability of drawing a red ball is

4/12 = 1/3.

Using the binomial formula, we can calculate that

P(J) = (3C0)(1/3)^0(2/3)^3 + (3C1)(1/3)^1(2/3)^2 + (3C2)(1/3)^2(2/3)^1

= 26/27.

2- The probability of getting a red ball followed by a white ball then a black ball is equal to the product of the probabilities of each event happening. Since there are 4 red balls out of 12 total balls, the probability of drawing a red ball is

4/12 = 1/3.

Similarly, the probability of drawing a white ball is 5/12 and the probability of drawing a black ball is 3/12.

Therefore, P(K) = (1/3)(5/12)(3/12)

= 5/108.

3- The probability that the first ball drawn is the only black ball can be calculated as follows: There are three possible sequences in which this can happen: BBW, BWB and WBB. The probability for each sequence happening is

(3/12)(2/9)(5/9) =

10/108.

Therefore P(L) = 3(10/108)

= 5/18.

4- The easiest way to calculate P(M) would be to calculate the complement event: neither red nor white balls are drawn or only one color (either red or white) is drawn. The probability that no red or white balls are drawn is

(3C0)(3C0)(6C3)/(12C3)

=1/220.

The probability that only red balls are drawn is

(4C1)(8C2)/(12C3)

=56/220 and similarly for only white balls being drawn.

Therefore P(M)=1-(1+56+56)/220

=107/220.

I hope this helps!

PLS MRK ME BRAINLIEST

Answer:

Step-by-step explanation:

A,because it goes diagonally which (with the fraction) means that the fraction should be equal to the problem

Answer:

A

Step-by-step explanation:

I believe this is the right answer becasue all the other lines and curved (not constant) and the other goes in different directions.

The slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

What is the slope?

The slope of a line represents the change in the dependent variable (y) for a unit change in the independent variable (x). In this case, the slope of the line of best fit represents the average change in the test grade for a one hour increase in studying. To find the slope, you can use the formula:

m = (Σxy - (Σx)(Σy)/n) / (Σx² - (Σx)²/n)

To find the slope-intercept equation of the trend line using the first and last data points, we'll first find the slope (m) of the line. The slope can be found using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

where x₁ and y₁ are the values for the first data point, and x₂ and y₂ are the values for the last data point. In this case, the first data point is (1, 15) and the last data point is (7, 47):

m = (47 - 15) / (7 - 1) = 32 / 6 = 5.3333

Next, we'll use the slope and the first data point to find the y-intercept (b) using the formula:

b = y₁ - m * x₁

b = 15 - 5.3333 * 1 = 15 - 5.3333 = 9.6666

Finally, we'll use the slope and y-intercept to write the slope-intercept equation of the line:

y = mx + b

y = 5.3333x + 9.6666

Hence, the slope-intercept equation of the line that best fits the data, with a slope of 5.3333 and a y-intercept of 9.6666.

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Answer:

\(y=\dfrac{16}{3}x+\dfrac{29}{3}\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}\)

The first and last data points of the given table are:

Substitute the data points into the slope formula to find the slope of the trend line:

\(\text{Slope}\;(m)=\dfrac{47-15}{7-1}=\dfrac{32}{6}=\dfrac{16}{3}\)

\(\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}\)

Substitute the found slope and the first data point into the slope-intercept formula and solve for b:

\(\implies 15=\dfrac{16}{3}(1)+b\)

\(\implies 15=\dfrac{16}{3}+b\)

\(\implies b=15-\dfrac{16}{3}\)

\(\implies b=\dfrac{45}{3}-\dfrac{16}{3}\)

\(\implies b=\dfrac{45-16}{3}\)

\(\implies b=\dfrac{29}{3}\)

Therefore, the equation of the trend line in slope-intercept form is:

\(y=\dfrac{16}{3}x+\dfrac{29}{3}\)

Using Excel, the probability that 2 or fewer students are left-handed in a random sample of 70 students from a school where 10% of the students are left-handed can be calculated as approximately 0.9999.

To calculate the probability using Excel, we can utilize the binomial distribution function. The binomial distribution is appropriate for situations with a fixed number of independent trials (sampling 70 students) and two possible outcomes (left-handed or not left-handed).

In Excel, the formula to calculate the probability of 2 or fewer left-handed students can be written as "=BINOM.DIST(2, 70, 0.1, TRUE)". Here, "2" represents the number of left-handed students (or fewer) we want to calculate the probability for, "70" is the total number of students in the sample, and "0.1" is the probability of a student being left-handed (10% or 0.10).

Evaluating this formula in Excel yields a probability of approximately 0.9999 when rounded to four decimal places. This implies that there is an extremely high probability (close to 100%) of having 2 or fewer left-handed students in a random sample of 70 students from the school, given that the overall proportion of left-handed students in the school is 10%.

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Answer:

p > 31

Step-by-step explanation:

If their record is 31, and they need to beat it, then it would mean his score needs to be greater than 31, which is written as:

p > 31

Hope this helps

Answer: x= -3t/26

if it’s for x = -3t/26

If it’s for t= 26x/3

Step-by-step explanation:

Hope it helps

Answer:

I love algebra anyways

The ans is in the picture with the  steps how i got it

(hope this helps can i plz have brainlist :D hehe)

Step-by-step explanation:

The value of K is given by the expression 4a - 1.

To solve for K in the equation K - 4a = -1, we want to isolate the variable K on one side of the equation. Here's the step-by-step process:

Start with the equation: K - 4a = -1.

To isolate K, we need to move the -4a term to the other side of the equation. We can do this by adding 4a to both sides of the equation:

K - 4a + 4a = -1 + 4a.

This simplifies to:

K = 4a - 1.

Therefore, the value of K is given by the expression 4a - 1.

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Answer:

No, Yes, No, No

Step-by-step explanation:

Input the x and y values in the coordinates into the equation

(-3,-11):

-11 =  -5(-3) - 4

-11 =  15 - 4

-11 ≠ 11

The equation is not correct, so it is not a solution

(-7,31):

31 = -5(-7) - 4

31 = 35 - 4

31 = 31

The equation is correct, so it is a solution

(4,17):

17 = -5(4) - 4

17 = -20 - 4

17 ≠ -24

The equation is not correct, so it is not a solution

(6,-25):

-25 = -5(6) - 4

-25 = -30 - 4

-25 ≠ -34

The equation is not correct, so it is not a solution

-Chetan K

Answer:

The longest side of room is 24m

Answer:

At 50 miles, the rental costs are the same from either company.

Company A:

0.3 x 50 = 15

15+50= 65

Company B:

0.7 x 50 = 35

35 + 30 = 65

Answer:

Step-by-step explanation:

The answer is 3

The reasonable domain is all real numbers greater than or equal to 0.

The collection of all conceivable independent values that a function or relation may take is known as its domain.

Given:

In a research experiment,

the population of a colony of bacteria doubles every hour.

Here, we can use exponential growth function.

The population, f(x), of the colony after x hours can be modeled by the function f(x)=25 ⋅ 2ˣ.

The value of x can not be negative because it represents time.

The domain of the function is all achievable values.

So, the domain is  all real numbers greater than or equal to 0

Therefore, the domain is all real numbers greater than or equal to 0.

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Answer:

x²-9=x²-3²=(x+3)(x-3)

Step-by-step explanation:

use formula

a²-b²=(a+b)(a-b)

The answer is option A. No, there is a good chance that 12 randomly selected adult male passengers will exceed the elevator capacity.

Probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is 0.0229.Round to four decimal places as needed.Based on the calculations the elevator does not appear to be safe.The solution for the given problem is as follows:

Given that, the maximum capacity of the elevator is 1884 lb - 12 passengers.

We can write as below:

Maximum capacity per person=1884/12=157lb.

And, weights of males are normally distributed with a mean of 165 lb and a standard deviation of 32 lb.Thus, Z = (157-165) / (32 / √12) = -1.7321Then, P(Z > -1.7321) = 0.9586

Hence, the probability that it is overloaded if 12 adult male passengers have a mean weight greater than 157 lb is:P(Z > -1.7321) = 1 - P(Z < -1.7321) = 1 - 0.0229 = 0.9771 (rounded off to 4 decimal places).This probability is greater than 5% and therefore, the elevator does not appear to be safe.

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The value of the expression is the same as the second option: !a || (b & !c).

Boolean variables are variables that can have only one of two possible values: true or false. They are named after the 19th-century mathematician George Boole, who developed a system of logic based on binary values. In computer programming, boolean variables are commonly used to represent conditions or states that can be either true or false, such as whether a certain condition is met or whether a certain task has been completed.

The expression !(a & !(b & !c)) can be simplified using De Morgan's laws and distributive property to obtain:

!(a & !(b & !c)) = !a || (b & !c)

Therefore, the value of the expression is the same as the second option: !a || (b & !c).

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The sale price of a bottle of perfume, if its original price was $60.83 with a 12.4% discount, is $53.30.

The given:Original price of the bottle of perfume = $60.83Discount = 12.4%

We have to calculate the sale price of the bottle of perfume. Formula: Sale Price = Original Price − DiscountWe can use the above formula to solve the problem.

Therefore, the sale price of the bottle of perfume, if its original price was $60.83 with a 12.4% discount, is $53.30.

Summary:We need to calculate the sale price of the bottle of perfume given with original price of $60.83 and 12.4% discount. We used the formula, Sale Price = Original Price − Discount to calculate the sale price. Finally, the sale price of the bottle of perfume is $53.30.

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Answer:

44

Step-by-step explanation:

\(\frac{9}{11} x=36\)

\(x=36/\frac{11}{9}\\x=\frac{36*11}{9} \\x=4*11=44\)

Answer:

Step-by-step explanation:

9/11x = 36

9x = 396

x = 44

Answer:

One of the answers could be linear

Step-by-step explanation:A linear graph is always a straight line, and this looks to demonstrate that. Sorry if this is incorrect, just my understanding.

Answer:

Scale factor = 4

If you multiply by 4 the two sides of ABCD, you will get the corresponding sides of A’B’C’D’

Answer:

I= PRT ÷100

Step-by-step explanation:

I = 340000×30×3 ÷100