A researcher is trying to find the average pulse rate of a group of patients with diabetes, and the distribution of pulse rates appears normally distributed. Which procedure should he use?
Median
Independent samples t-test
Mean
Mode

To show that the given equation is exact, we need to check if its partial derivatives satisfy the condition ∂M/∂y = ∂N/∂x. In this case, M = 2xy^3 + cos(x) and N = 3x^2y^2 - sin(y).

Taking the partial derivative of M with respect to y, we get:

∂M/∂y = 6xy^2

And taking the partial derivative of N with respect to x, we get:

∂N/∂x = 6xy^2

Since ∂M/∂y = ∂N/∂x, the equation is exact.

To find the general solutions, we can use the fact that an exact equation can be written as the derivative of a function, known as the potential function or the integrating factor. Let Φ(x, y) be the potential function.

We have:

∂Φ/∂x = M   ⇒   Φ = ∫(2xy^3 + cos(x))dx = x^2y^3 + sin(x) + C(y)

Taking the partial derivative of Φ with respect to y, we get:

∂Φ/∂y = N   ⇒   C'(y) = 3x^2y^2 - sin(y)

To find C(y), we integrate C'(y) with respect to y:

C(y) = ∫(3x^2y^2 - sin(y))dy = x^2y^3 + cos(y) + K

Combining the two equations for Φ, we have the general solution:

Φ(x, y) = x^2y^3 + sin(x) + x^2y^3 + cos(y) + K

To find the particular solution when y(0) = π, substitute x = 0 and y = π into the general solution:

Φ(0, π) = 0 + sin(0) + 0 + cos(π) + K = -1 + K

Therefore, the particular solution is:

x^2y^3 + sin(x) + x^2y^3 + cos(y) = -1 + K

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Answer: 0.04 inches²

Step-by-step explanation:A of Triangle = 1/2*B*H where B is base and H is height. Find the area of the bigger triangle and then subtract the area of the smaller triangle

1/2*(0.4)*(0.3) = 0.06

1/2*(0.4)*(0.1) = 0.02

0.06 - 0.02 = 0.04

The equations given are x - 5y = 3 and 3x - 2y = -4. To find the solution to this system of equations, we need to find the values of x and y that satisfy both equations simultaneously.

One way to solve this system of equations is by substitution. We can solve one equation for x or y, and then substitute that expression into the other equation to eliminate one variable. Let's solve the first equation for x:

x - 5y = 3

x = 5y + 3

Now we can substitute this expression for x into the second equation:

3x - 2y = -4

3(5y + 3) - 2y = -4

15y + 9 - 2y = -4

13y = -13

y = -1

We can now substitute this value for y back into either equation to find the value of x:

x - 5y = 3

x - 5(-1) = 3

x + 5 = 3

x = -2

Therefore, the solution to the system of equations x - 5y = 3 and 3x - 2y = -4 is (-2, -1). This is the point where the solid line and dotted line intersect, as shown in the image.

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Answer:

$150

Step-by-step explanation:

5+10+30+100+5=150

10

Step-by-step explanation:

The way I look at it I think 10.00 cause it says I had in the beginning k and it says what people gave me and at the end it says what I had as well so I had 5.00 in the beginning and then I had another 5.00 so that makes it 10.00 in all realatly really let me know if I'm right as it's the only thing that makes since with it all..... lol so the answer is 10.00.... so if it would of said how much do I have all together then it would be what my granddaughter said but it didn't. It's a tricky question here and a good one to get people thinking on it haaa haaa

The exact values of the remaining trigonometric functions are listed below:

Case 3: cos θ = 3 / 5, tan θ = 4 / 3, cot θ = 3 / 4, sec θ = 5 / 3, csc θ = 5 / 4

Case 4: sin θ = √11 / 6, tan θ = √11 / 5, cot θ = 5√11 / 5, sec θ = 6 / 5, csc θ = 6√11 / 11

Case 5: cos θ = 8√73 / 73, sin θ = 3√73 / 73, tan θ = 3 / 8, cot θ = 8 / 3, csc θ = √73 / 3

Case 6: sin θ = 1 / 2, cos θ = √3 / 2, tan θ = √3 / 3, sec θ = 2√3 / 3, csc θ = 2

In this problem we find four cases of trigonometric functions, whose exact values of remaining trigonometric functions must be found. The trigonometric functions are defined below:

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = √(x² + y²) / y

Now we proceed to determine the exact values of the trigonometric functions:

Case 3: y = 4, √(x² + y²) = 5

x = √(5² - 4²)

x = 3

cos θ = 3 / 5

tan θ = 4 / 3

cot θ = 3 / 4

sec θ = 5 / 3

csc θ = 5 / 4

Case 4: x = 5, √(x² + y²) = 6

y = √(6² - 5²)

y = √11

sin θ = √11 / 6

tan θ = √11 / 5

cot θ = 5√11 / 5

sec θ = 6 / 5

csc θ = 6√11 / 11

Case 5: x = 8, √(x² + y²) = √73

y = √(73 - 8²)

y = 3

cos θ = 8√73 / 73

sin θ = 3√73 / 73

tan θ = 3 / 8

cot θ = 8 / 3

csc θ = √73 / 3

Case 6: x = √3, y = 1

sin θ = 1 / 2

cos θ = √3 / 2

tan θ = √3 / 3

sec θ = 2√3 / 3

csc θ = 2

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Step 1. There are 5 red marbles and 3 blue marbles, 8 marbles in total:

Step 2. Two marbles are drawn simultaneously, which means that there is no replacing of the marbles.

To make the tree diagram with the probabilities for each marble, remember the probability formula:

The three will look as follows:

For the first marble, the probability of getting a red one is 5/8 because there are 5 red marbles out of a total of 8, and similar to the first one is blue.

For the second marble, we consider that the total number of marbles is now 7.

Step 3. To find the probability of each combination, we multiply the values of each branch:

The results of the multiplications is:

The ones that have at least one red marble are the first three branches: red-red, red-blue, and blue-red.

To find the probability of at least one red marble, we add the results of the first three branches:

The result is:

The probability is 50/56.

The fraction can be simplified to:

The probability simplified is 25/28.

Answer:

Answer:

31.25

Step-by-step explanation:

Answer:

31.25%

Step-by-step explanation:

We can write this as a fraction:

10/32

Now you divide it to get a decimal:

10 ÷ 32 = 0.3125

0.3125 = 31.25%

Hope this helps!

Using the exponential growth formula, the population in 2005 was 161 million.

The equation f(x) = a(1 + r)^x can also be used to compute exponential growth, where: The function is represented by the word f(x). The initial value of your data is represented by the a variable. The growth rate is represented by the r variable. To calculate growth rates, divide the difference between the starting and ending values for the period under study by the starting value.

Growth factor = (159/154) for the eleven-year period between 1990 and 2001.

The population growth might thus be described by the exponential equation

p(t) = 154(159/154)^(t/11), where t is the number of years since 1990.

The model forecasts a population of... p(15) = 154(159/154)^(15/11)

= 160.86 = 161 million

In 2005, there were about 161 million people living there.

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Correct Question:

A country's population in 1990 was 154 million. In 2001 it was 159 million. Estimate the population in 2005 using the exponential growth formula. Round your answer to the nearest million.

Answer:

Step-by-step explanation:

Answer:

X = 56 degrees

Step-by-step explanation:

Angles D and F are equivalent. Because the three angles must add up to 180 degrees, you must add 112 to 68 in order to reach 180. Then you must divide this in half, getting 56 degrees as your answer.

180 - 68 = 112

112/2 = 56

X=56

Answer:

12 cups

Step-by-step explanation

If the size of the bag decreased by 20%, so will the number of cups held.

Number of cups held before the change = 15 cups

If the number of cups held after the 20% reduction in the size of the bag

= (100 - 20)% × 15

=80% × 15

= 12 cups

The new bags will hold 12 cups.

Answer:

T is equal to I divided by pr. \(t=\frac{I}{pr}\)

Step-by-step explanation:

This is the equation for interest.

I is interest.

P is the principal

r is the interest rate

t is the time in years

you have to isolate for t.

Because multiply p times r times t, divide both sides by pr due to the fact that division is the inverse operation of multiplication

Then you are left with t= i divided by pr.

hope this helps

Pedro eats 14.4 ounce of bread.

Given that, Pedro makes a loaf of bread that weighs 24 ounces.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Pedro gives 1/3 of the loaf to his sister,

So, 1/3 × 24 = 8 ounce

Pedro gives 20% of the loaf to his friend. That is,

20% of 8

= 0.2 × 8

= 1.6 ounce

Remaining = 24 - (8+1.6)

= 24 - 9.6

= 14.4 ounce

Therefore, Pedro eats 14.4 ounce of bread.

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Answer:

5/6 chance of getting something greater than 4

Step-by-step explanation:

Step-by-step explanation:

that means 2 blue or 2 red or 2 green.

12 marbles in total.

when the first marble is picked, there are only 11 left.

a probability is always the ratio of

desired cases / totally possible cases

the probabilty to pull first a blue marble is

5/12 = 0.416666666...

if that is the case, then the probabilty for the second marble to be blue too is

4/11 = 0.363636363...

(there are only 4 blue marbles in a total of 11 marbles).

and the probabilty for getting 2 blue marbles is

5/12 × 4/11 = 20/132 = 5/33 = 0.151515151...

the probabilty to pull first a red marble is

4/12 = 1/3 = 0.333333333...

if that is the case, then the probabilty for the second marble to be red too is

3/11 = 0.272727272...

(there are only 3 red marbles in a total of 11 marbles).

and the probabilty for getting 2 red marbles is

1/3 × 3/11 = 3/33 = 1/11 = 0.0909090909...

the probabilty to pull first a green marble is

3/12 = 1/4 = 0.25

if that is the case, then the probabilty for the second marble to be green too is

2/11 = 0.181818181...

(there are only 2 green marbles in a total of 11 marbles).

and the probabilty for getting 2 green marbles is

1/4 × 2/11 = 2/44 = 1/22 = 0.045454545...

the probabilty to have any of these 3 mutually exclusive cases (to get a pair of the same color) is the sum of the probabilities :

0.151515151... + 0.09090909... + 0.045454545... =

5/33 + 1/11 + 1/22 = 10/66 + 6/66 + 3/66 = 19/66 =

= 0.287878787...

Answer:

Answer is d=9t.

Step-by-Step:

4.5/.5=9

6.75/.75=9

13.5/1.5=9

Continuous variables must lie between a clearly defined interval that is true.

Continuous variables could take any value that is limited within a specified range. These variables are not limited to certain values only as can have both positive and negative values. They can usually cover a continuous set of values.

Unlike discrete variables, continuous variables are often associated with measurements and observations that can be further subdivided. For example; temperature, length, and weight. This concept of continuity states that there exists an infinite number of intermediate values. This property makes continuous variables best suitable for statistical analysis.

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Answer:

Step-by-step explanation:

Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.

Area of a circle A = πr²

r is the radius of the circle

The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;

dr/dt is the rate at which the area is increasing.

If dA/dr = 2πr (by mere differentiation)

dA/dt = 2πr * dr/dt

Given dr/dt = 3ft/sec and r = 30feet

dA/dt = 2π(30) * 3

dA/dt = 180π ft/sec

Hence, the area is increasing at the rate of 180π ft/sec

False, r2adj is the adjusted coefficient of determination that can exceed r2 if there are several weak predictors.

R2adj is the adjusted coefficient of determination and takes into account the number of predictors in the model. It penalizes the addition of insignificant predictors that do not improve the model fit.

R2, on the other hand, is the coefficient of determination and measures the proportion of variability in the dependent variable that is explained by the independent variables in the model.

It is possible for R2 to increase when weak predictors are added, but this increase is not necessarily mean that the predictors do not have a significant impact on the outcome.

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The question is -

R2adj can exceed R2 if there are several weak predictors. true or false?

To find the lengths of the sides of the triangle with vertices at a(0, -4), b(0, -9), and c(-2, -5), we can use the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Let's label the sides of the triangle as AB, BC, and CA, where A = (0, -4), B = (0, -9), and C = (-2, -5).

Length of AB:

AB = √((y2 - y1)² + (x2 - x1)²) (Note: We switched the order of x and y for this calculation to match the order of the points given)

= √((-9 - (-4))² + (0 - 0)²)

= √(5²)

= 5

Length of BC:

BC = √((y2 - y1)² + (x2 - x1)²)

= √((-5 - (-9))² + (-2 - 0)²)

= √(4² + 4²)

= √32

= 4√2

= 5.66

Length of CA:

CA = √((y2 - y1)² + (x2 - x1)²)

= √((-4 - (-5))² + (0 - (-2))²)

= √(1² + 2²)

= √5

= 2.24

Therefore, the lengths of the sides of the triangle areAB = 5

BC = 4√2 ≈ 5.66

CA = √5 ≈ 2.24

Since they are unequal, the triangle is a scalene triangle.

2)
To determine if AABC is a right-angled triangle, we need to check if any of its angles measure 90 degrees. We can use the slopes of the sides to determine this.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the three sides of AABC:

Slope of AB:

AB passes through the points A(0, -4) and B(0, -9).

slope_AB = (-9 - (-4)) / (0 - 0) = -5/0 (undefined)

Note that the slope of AB is undefined, since the line is vertical and has no defined slope.

Slope of BC:

BC passes through the points B(0, -9) and C(-2, -5).

slope_BC = (-5 - (-9)) / (-2 - 0) = 2

Slope of CA:

CA passes through the points C(-2, -5) and A(0, -4).

slope_CA = (-4 - (-5)) / (0 - (-2)) = 1/2

Since AB is vertical and has undefined slope, we cannot use its slope to determine the angle at A. However, we can use the slopes of BC and CA to check the other angles.

The angle at B is opposite the side BC, so we need to check if the slope of BC is the negative reciprocal of the slope of AB. Since AB has undefined slope, we cannot determine its reciprocal or negative reciprocal. Therefore, we cannot use this method to check if the angle at B is 90 degrees.

The angle at C is opposite the side CA, so we need to check if the slope of CA is the negative reciprocal of the slope of BC. If it is, then the angle at C is 90 degrees. Let's check:

slope_BC * slope_CA = 2 * 1/2 = 1

The negative reciprocal of slope_BC is -1/2.

Since slope_CA is not equal to the negative reciprocal of slope_BC, we can conclude that the angle at C is not 90 degrees.

Therefore, we CANNOT conclude that AABC is a right-angled triangle based on the slopes of its sides.

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Answer:

  x = 1 or 5

Step-by-step explanation:

You want the value(s) of x that make 3x^2-x+1 and 2x^2+5x-4 have the same value.

Equating their values, we have ...

  3x² -x +1 = 2x² +5x -4

  x² -6x +5 = 0 . . . . . . . . . subtract (2x²+5x-4)

  (x -5)(x -1) = 0 . . . . . . . factor

  x = 1 or x = 5 . . . . . . values of x that make the factors zero

The two trinomials will have the same value for x=1 and for x=5.

__

Additional comment

The attached graph shows the points where the trinomials have the same value.

Answer: a

Step-by-step explanation:

The value of n from the given parallel lines is 6. Therefore, the option A is the correct answer.

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.

Given that, the angles from the parallel lines are (3n+16)° and (5n+4)°.

Here, (3n+16)°=(5n+4)° (Interior alternate angles are equal)

5n-3n=16-4

2n=12

n=6

Therefore, the option A is the correct answer.

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Answers: -0.5 m

here you go

Answer:

D

Step-by-step explanation:

the number of days for 80 - 82 is 7 and the number of days for 82-84 is 9. Those are the only temperatures below 84 degrees, so you add them and get 16 :)

Shin splints are a common cause of lower leg pain and can be caused by a variety of factors, such as poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot.

Shin splints is a term used to describe pain that occurs along the shin bone (tibia), which runs down the front of the lower leg. Common causes of shin splints include poorly fitting shoes, weak calf muscles, running on uneven terrain, and overpronation of the foot. Poorly fitting shoes can put excessive pressure on the back of the heel and the front of the foot, leading to inflammation and pain in the shin area. Weak calf muscles can cause the foot to overpronate or roll inward, which can put extra strain on the shin bone and its muscles. Running on uneven terrain can also cause the shin bone to suffer from too much pressure, leading to shin splints. Finally, overpronation of the foot is when the foot rolls inward excessively and puts extra strain on the shin bone and its muscles. Shin splints can cause pain and discomfort and should be treated as soon as possible by rest, stretching, icing, and wearing properly fitting shoes.

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Answer:

2. The difference between the flat fees of the two companies is $20

Step-by-step explanation:

3. 15 units

the equation for the table is y= 8x-17 and if you plug zero in for x, then the answer is -17. -17 is the y-intercept of the equation and the distance between negative 17 and 2 is 15.

To find the domain of the function f(x, y) = ln(16 − x^2 − 16y^2), we need to determine the values of x and y for which the function is defined.

The natural logarithm function ln(x) is defined only for positive values of x. Therefore, for the given function to be defined, the expression inside the logarithm (16 − x^2 − 16y^2) must be greater than zero.

Setting 16 − x^2 − 16y^2 > 0, we can solve for the values of x and y that satisfy this inequality:

16 − x^2 − 16y^2 > 0

-x^2 − 16y^2 > -16

x^2 + 16y^2 < 16

This is the inequality of an ellipse centered at the origin with semi-major axis length 2 and semi-minor axis length 1. Therefore, the domain of the function f(x, y) is the interior of this ellipse.

To sketch the domain, draw the ellipse centered at the origin and shade the interior of the ellipse. The shaded region represents the domain of the function.

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The control limits help to separate common and special causes from each other.

Control lines are the horizontal lines drawn on the control chart. A control chart has several components. It has two control limits. They are represented by dashed lines. The lower one is called the lower control limit (LCL) and the upper one is called the upper control limit (UCL).

The control limits help us mark the highest (by UCL) and lowest (by LCL) error that is bearable. All those errors that occur between UCL and LCL are common errors/variations while the errors that occur above UCL or below LCL are the products with assignable causes variations.

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Answer: yes these lines are

Answer:

yes

Step-by-step explanation:

Perpendicular lines intersect eachother