Suppose that a report by a leading medical organization claims that the healthy human heart beats an average of 7272 times per minute. Advances in science have led some researchers to question if the healthy human heart beats an entirely different amount of time, on average, per minute. They obtain pulse rate data from a sample of 8585 healthy adults and find the average number of heart beats per minute to be 76,76, with a standard deviation of 13.13. Before conducting a statistical test of significance, this outcome needs to be converted to a standard score, or a test statistic. What would that test statistic be

Looking at the image, the radius (r) of the circle appears to cover half of the length of a side of the square. Hence, the side of the square has a length of 2r.

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\(Ratio=\frac{\pi r^{2} }{4r^2} =\frac{\pi}{4}\).

Notice that the value "r²" disappears from the expression because is being multiplied and divided by it at the same time.

\(Ratio=\frac{4\pi }{16} =0.7854.\)

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c. Complete the table.

To complete each cell of the table, simply take the equation of the asked parameter and substitute the value of r by the number indicated in the title of the column. For example, column 3 should be filled out like this:

Area of Circle (units²): π(3)²or 9π.

Length of 1 Side of the Square: 2r= 2(3)= 6.

Area of Square (units²)= 4r²= 4(3)²= 36.

Ratio: \(\frac{\pi}{4}\).

Do the same for all the other columns.

The answers to the table are presented on the attached image.

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d. What can you conclude about the relationship between the area of the circle and the square?

They will always have the same value, π/4, regardless of the size of the square and circle. As long as the circle borders meet the square's at the middle of each side of the square, the relationship will be the same.

k is the y-coordinate of the vertex. Changing k moves the parabola up/down.

Answer:

Step 3 because they didn't add correctly

Answer:

non - collinear points

Step-by-step explanation:

points that dont lie on the same line

Answer:

the answer is option c.

Step-by-step explanation:

please mark me brainliest.

The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%

The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

x' = 51

μ = 47

σ = 4

Thus;

z = (51 - 47)/4

z = 1

From empirical formula at 1 standard deviation above the means, the probability is 68%.

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Answer:

y + 1 = -1/4 (x - 1) Answer choice C is correct.

Step-by-step explanation:

Point Slope Formula: y - y1 = m (x-x1)

Your points:

(1,-1) and (5,-2)

You need to find the slope first:

Use the formula: y2 - y1 / x2 - x1

Your y2 is -2

y1 is -1

x2 is 5

x1 is 1

-2 - (-1)/5-1

-2 + 1 /4

-1/4 is your slope and the "m" in the formula.

Now we know our y1 is -1 and x1 is 1 you just need to plug them in

y + 1 = -1/4 (x - 1)

Notice that I didn't write y - (-1) this is because the negatives cancel into positives.

Answer choice C is correct.

Answer:

c. \(y+1=-\frac{1}{4} (x-1)\)

Step-by-step explanation:

Hi there!

We are given the points (1, -1) and (5, -2)

We want to find the equation of that line using those points, in point-slope form

Point-slope form is written as \(y-y_1=m(x-x_1)\), where m is the slope and \((x_1, y_1)\) is a point

First, let's find the slope of the line

The formula for the slope (m) calculated from 2 points is \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We already have everything we need to find the slope, but let's label the values of the points to avoid any confusion when calculating.

\(x_1=1\\y_1=-1\\x_2=5\\y_2=-2\)

Now substitute:

m=\(\frac{y_2-y_1}{x_2-x_1}\)

m=\(\frac{-2--1}{5-1}\)

Subtract

m=\(\frac{-2+1}{5-1}\)

m=\(\frac{-1}{4}\)

The slope of the line is -1/4

Now substitute this into the formula to find point-slope form (remember that this is \(y-y_1=m(x-x_1)\), and that m is the slope value)

Therefore:

\(y-y_1=-\frac{1}{4} (x-x_1)\)

Now, let's substitute the values of \(x_1\) and \(y_1\), which we found earlier (which are 1 and -1 respectively) into the equation

\(y--1=-\frac{1}{4} (x-1)\)

Simplify

\(y+1=-\frac{1}{4} (x-1)\)

This equation matches option c, which is the answer.
Hope this helps!

The fish's total distance traveled is 17 meters in 5 minutes based on multiplication and addition operations.

The total distance the fish traveled can be determined using mathematical operations, especially multiplication and addition.

We know that distance is the product of speed and time, i.e. d = st, where s is speed, t is time, and d is distance.

In this situation, we separately find the distance the fish traveled during its descent and ascent by multiplying time and speed.

The results are added to obtain the total distance the fish traveled for both activities.

The fish's descent speed = 4 meters per minute (MPM)

The total time for the descent = 2

The total distance for the descent = 8 miles (4 x 2)

The fish's ascent speed = 3 meters per minute (MPM)

The total time during ascent = 3 minutes

The total distance for the ascent = 9 miles (3 x 3)

The total distance the fish traveled for descent and ascent = 17 meters (8 + 9)

Thus, we can mathematically conclude that the fish traveled 17 meters.

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Answer:

Grogg's dad is 22

Step-by-step explanation:

Let D = dad's current age

Let g = Grogg's current age

6(d - 7) = g - 7 → 6d - 42 = g - 7 → 6d -35 = g

4(d - 3) = g - 3 → 4d -12 = g - 3 → 4d -9 = g

Set the two equations equal to each other and solve for d

6d - 35 = 4d - 9  Subtract 4d from both sides

2d -35 = -9  Add 35 to both sides

2d = 44  Divide both sides by 2

d = 22

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

d = current dad age

g = current grogg age

d-7 = 6(g-7)

d-3 = 4(g-3)

Let's solve the first equation first:

Add 7 to both sides: d - 7 +7 = 6g - 42 + 7 so d = 6g - 35

Substitude d = 6g - 35 for d in d - 3 = 4g - 12

(6g-35)-3 = 4g-12 = 6g-38 = 4g-12

Subtract 4g from both sides: 2g - 38 = -12

Add 38 to both sides: 2g = 26

Easy: g = 13

And now substitude g in for any equations.

d-3 = 52-12

d = 43

Answer:

C. 48 squares

Step-by-step explanation:

Brainliest pls

150 times

90 times tails

a)

Probability = 90/150 = 0.6

b)

From 50 tosses, 60 are tails = then 50 x 0.6 = 30, there will be 30 more tails.

The expected value of X or E(X) is 2.45.

To find the expected value of a random variable X, denoted by E(X), we use the formula:

E(X) = ∑[x*P(X=x)]

where x is the value of X and P(X=x) is the probability of X taking the value x.

Using this formula, we can calculate the expected value of X based on the probability distribution table given to us.

X    1    2    3    4

P(X)   0.25 0.30 0.20 0.25

E(X) = (1 * 0.25) + (2 * 0.30) + (3 * 0.20) + (4 * 0.25)

= 0.25 + 0.60 + 0.60 + 1.00

= 2.45

Therefore, the expected value of X is 2.45.

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The probability distribution of the random variable X is given in the following table. Find the expected value of X . (Round your answer to 4 decimal places.) x -2 -1 0 1 2 P(X =x)  

a. 3

b. 2.45

c.6.9

d.1.2

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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The shaded area represents the solution of the inequalities. Hence, points A, C, D and K are the solution of the system.

Get y first when graphing a linear inequality with two variables, such as x and y alone on one side. Then, take into account the associated equation that was created by switching the inequality sign for an equality sign. This equation has a line as its graph.

The last step is to choose a point that is not on either line (usually (0, 0) is the simplest) and determine whether or not these coordinates satisfy the inequality. If so, shade the portion of the half-plane that contains that point. If not, shade the opposite half-plane.

Create a comparable graph for each of the system's inequalities. The place where all of the system's solutions overlap is known as the system's solution.

Given that, the inequality is:

y ≤ −2x + 10 & y > 1/(2x − 2)

The given points: A(-5,4), B(4,7), C(-2,7), D(-7,1), E(4,-2), F(1,-6), G(-3,-10), H(-4,-4), I(9,3), J(7,-4) and K(2,3).

The shaded area represents the solution of the inequalities.

Hence, points A, C, D and K are the solution of the system.

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The complete question is:

The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

From the question, we have the following parameters that can be used in our computation:

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

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the task is to ensure that the PDSB can effectively manage its personnel requirements and maintain its policy of promoting from within.

As an HR analyst for the Peel District School Board (PDSB), the task is to determine the number of positions that will require replacement over the next year and the impact these openings will have on current employees' movements throughout the Secondary School Division. The PDSB has a policy of promoting from within for all vacancies above the entry-level, and the Secondary School Division does not have any personnel in authority levels 1 or 2.

Based on historical annual loss rates, retirements and attrition rates have been determined for each level. The number of positions at the start of the 2006-07 school year has also been provided.

To calculate the number of positions to be filled in the next year, we can use the information provided and apply the relevant rates for retirements and attrition. The number of positions at the start of the year is subtracted from the total number of positions to arrive at the number of positions to be filled. This calculation is done for each level, and the results are tabulated in the first table.

Once the number of positions to be filled has been determined, the next step is to calculate the impact on current employees' movements. This is done by determining the number of promotions required to fill the vacancies and the resulting vacancies at the lower level. These calculations are tabulated in the second table, and the numbers are organized in columns.

Overall, the task is to ensure that the PDSB can effectively manage its personnel requirements and maintain its policy of promoting from within. By analyzing the historical loss rates and current personnel numbers, the organization can plan for the future and ensure that it has the right staff in the right positions to meet its goals.

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The value which is equivalent to the 1 in 8 chance of the player winning a game is Choice J: 0.125.

The question statement implies that the probability of a player winning a game is 1 in 8.

We must know that the probability of an event occuring can be expressed as any choice of real numbers. However, the probability must ultimately not be more than 1 upon evaluation.

For choice F:

For choice G:

For choice H:

For Choice J:

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Answer:

0.3

Step-by-step explanation:

Answer:

0.3

Step-by-step explanation:

I hope this is what you where asking for?

Considering the given tables in the quetion

the table below

from the table, notice that

when

x = 2, y = 4

when

x = 4, y = 8

when

x = 9, y = 18

From these values we can deduce that

for every value of x

This gives a proportional relationship between x and y

y = 2x

Answer:

The answer is mode, median, mean.

Step-by-step explanation:

From the smallest to the largest we have the mode, median, mean. If a distribution is positively skewed it means that it is right skewed. It tells us that the right tail of this distribution has longer length compared to the left tail. The average, mean would be moved slightly to the left, the mode occurs at the top while the median is in the middle.

Answer:

500,000 can be written in expanded form in two different ways:

500,000 = 500,000

500,000 = 5 x 100,000 + 0 x 10,000 + 0 x 1,000 + 0 x 100 + 0 x 10 + 0 x 1

In both cases, the expanded form shows the value of each digit in the number. The first way simply lists the number itself, while the second way breaks down the number into its component parts and shows the value of each digit in relation to the place value it holds in the number.

Answer:

Variance = 5

Standard deviation = 2.236

0.2650257

Step-by-step explanation:

For a Poisson distribution is σ² = μ.

Given that:

Mean , μ of bankruptcies files per hour = 5

μ = 5

For a Poisson distribution :

P(x = x) = (μ^x * e^-μ) / x!

The Variance and standard deviation :

Variance : σ² = μ = 5

Standard deviation = sqrt(variance) = sqrt(5) = 2.236

B.) Find the probability that at most three businesses will file bankruptcy in any given hour.

P( x ≤ 3) = P(0) + P(1) + P(2) + P(3)

P(x = 0) = (5^0 * e^-5) / 0! = 0.0067379

P(x = 1) = (5^1 * e^-5) / 1! = 0.0336897

P(x = 2) = (5^2 * e^-5) / 2! = 0.0842243

P(x = 3) = (5^3 * e^-5) / 3! = 0.1403738

0.0067379 + 0.0336897 + 0.0842243 + 0.1403738

= 0.2650257

Using the Poisson distribution, it is found that:

a) The variance is of 5 while the standard deviation is of 2.24. It means that over many hours, the number of bankruptcies should be within 2.24 of 5.

b) 0.265 = 26.5% probability that at most three businesses will file bankruptcy in any given hour.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are:

In this problem, the mean is of \(\mu = 5\).

Item a:

The variance is of 5 while the standard deviation is of 2.24. It means that over many hours, the number of bankruptcies should be within 2.24 of 5.

Item b:

This probability is:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)\)

In which

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-5}(5)^{0}}{(0)!} = 0.0067\)

\(P(X = 1) = \frac{e^{-5}(5)^{1}}{(1)!} = 0.0337\)

\(P(X = 2) = \frac{e^{-5}(5)^{2}}{(2)!} = 0.0842\)

\(P(X = 3) = \frac{e^{-5}(5)^{3}}{(3)!} = 0.1404\)

Then:

\(P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0067 + 0.0337 + 0.0842 + 0.1404 = 0.265\)

0.265 = 26.5% probability that at most three businesses will file bankruptcy in any given hour.

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Using the addition and subtraction operators and tweaking the position of the given values, we can write three different expressions using the same values and obtaining different output, such as :

Step-by-step explanation:

Using the numbers : 5 ; 6 and 7

First expression :

5 + 6 - 7 = 4

Second expression :

5 - 6 + 7 = 6

Third expression :

7 + 6 - 5 = 8

Therefore, the expressions given above results in different output due to the positions of the digits and the operatiors.

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Answer:

30x

Step-by-step explanation:

Answer:

30x

Step-by-step explanation:

a negative multiplied by a negative is positive.

-5x x -6 =30x

Hope I helped!

Answer:

You can add graph by using the edit button and uploading a picture of the screen. if you then cut the picture before uploading so it just shows the graphand not the question. We cna then try answer for you.

Step-by-step explanation:

Generally graphs starting at point x=0 would show a different value for y by looking and counting up to its temperature.

if this shows positive it would be above the x axis line if it shows negative it would be a minus value below the x axis line under zero on y.

Therefore when we get to hr 2 and see this change you can count across and count up and see the rate of change is either 1,2,3,4,56,7,8 etc difference or 1x 2x 3x 4 x 5x 6 x as multiples.This then indicates a scale change at certain points.

Answer:

supplementary

Step-by-step explanation:

Not really sure what you are asking, but supplementary is when the sum of two angle measures to 180 degrees

Answer:

Supplementary angles

Step-by-step explanation:

Supplementary angles are two angles whose sum is 180 degrees while complementary angles are two angles whose sum is 90 degrees.

Answer:

The answer is 14.76 to 2d.p

Step-by-step explanation:

Hyp²=opp²+adj²

let Hyp be x

x²=13²+7²

x²=169+49

x²=218

Square root of both sides

√x²=√218

x=14.76 to 2d.p

Answer:

14.76

Step-by-step explanation:

A square + b square = c square

13 square=169

b square=49

169+49=218

the root of 218 is 14.76

Answer:

Simplifying the expression `n + n - 0.18n`, we get:

n + n - 0.18n = 2n - 0.18n

Therefore, the expression `n + n - 0.18n` is equivalent to `2n - 0.18n`.

Looking at the answer choices:

a. 1.18n

b. 1.82n

c. n- 0.18

d. 2n - 0.82

We can see that choice d is equivalent to the simplified expression `2n - 0.18n`.

Therefore, the answer is d. 2n - 0.82.

Step-by-step explanation: