A 30-point questionnaire used to assess the severity of dementia, and is useful for tracking the progression of dementia in patients. A random sample of 10 dementia patients from a care home was taken and their MMSE scores are as follow:
9 12 17 18 13 14 11 15 12 10
Use this data as a pilot study to determine the sample size needed to estimate p, the true mean MMSE score for dementia patients in the care home, to within a score of 0.5 with 98% confidence.

Answer: I am not sure but you can do research on what you are looking for like I always do and get it right

Step-by-step explanation:

The equation of the line of best fit of the scatter plot is y = 1/2x + 3

The scatter plot passes through the points

(0,3) and (6,6)

The slope is calculated using:

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

This gives

m = (6 - 3)/(6 - 0)

Evaluate

m = 1/2

The graph cross the y-axis at y = 3

So, the equation of the line of best fit is:

y = 1/2x + 3

This means that:

x = 2 1/3

So, we have:

y = 1/2 * 2 1/3 + 3

Evaluate

y = 1 1/6 + 3

Add the expressions

y = 4 1/6

Hence, the temperature if the thickness is 2 1/3 inches is 4 1/6°F

This means that:

y = 12

So, we have:

12 = 1/2 * x + 3

Subtract 3  from both sides

9 = 1/2 x

Multiply through by 2

x = 18

Hence, the thickness if the temperature is 12°F is 18 inches

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Answer:

x + 7

Step-by-step explanation:

1+7=8

2+7+9

so on

Answer:

Step-by-step explanation:

is this in college?

As currently written, solving for \(x\), we have

\(\sqrt{15} - x + \sqrt3 - x = 6\)

\(2x = \sqrt{15} + \sqrt3 - 6\)

\(x = \dfrac{\sqrt{15} +\sqrt3 - 6}2\)

I suspect you meant to write

\(\sqrt{15 - x} + \sqrt{3 - x} = 6\)

Move one of the roots to the other side, then take squares on both sides.

\(\sqrt{15 - x} = 6 - \sqrt{3 - x}\)

\(\left(\sqrt{15 - x}\right)^2 = \left(6 - \sqrt{3 - x}\right)^2\)

\(15 - x = 36 - 12 \sqrt{3 - x} + (3 - x)\)

\(12 \sqrt{3 - x} = 24\)

Take squares again

\(\left(12\sqrt{3-x}\right)^2 = 24^2\)

\(144 (3 - x) = 576\)

\(432 - 144x = 576\)

\(144x = -144\)

\(\boxed{x = -1}\)

9514 1404 393

Answer:

Step-by-step explanation:

Opposite sides of a parallelogram have the same length, so ...

  5b +5c = 60

  5b +4c = 55

Subtracting the second equation from the first, we get ...

  c = 5

Substituting that into the first equation, we have ...

  5b +5·5 = 60

  5b = 35 . . . . . . . subtract 25

  b = 7 . . . . . . . . . . divide by 5

The values b = 7 and c = 5 will make this a parallelogram.

Answer:

See attached worksheet.

Step-by-step explanation:

The worksheet summarizes the steps for analyzing the data on the graph.  Note that a "line of best fit" was drawn to help illustrate the linear behavior of the data, and to better the question concerning hours of sunshine in another British town.  There are techniques for ensuring a line such as this fits the actual data as closely as possible.  These techniques draw a line that has the least overall deviation from the actual data.  For our purposes, a hand-drawn line appears to match the data reasonably well, so we are able to concule that the relationship is liner:  There is a proportional change in y for every set change in x.  That change is known as the slope.  The slope of this liner would represent the direct relationship between hours of sun and maximum temperature.

Answer:

e

Step-by-step explanation:

Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

Step-by-step explanation:

Jeremiah solved equation by multiplicative inverse.

Therefore,

Option D is correct ✔

And

Kelly solved equation by Additive inverse.

Therefore,

Option B is correct ✔

Answer:

itanong mo kay kapatid na arlene

It is D. If you multiply D by 3.14 and it matches the C, it is the right one. So it is D

Answer:

equation: 30+(x×6)

x= amount of shirts

Step-by-step explanation:

Number of shirts: Total Cost

0. 0

5. 60

10. 90

15. 120

18. 138

30. 210

Answer:

6.1

Step-by-step explanation:

hope this helps :D pls mark brainliest :D

the distance between the two number is 6.1

The items with the shortest lifespan will last less than approximately 4.3 years.

In a normally distributed lifespan, the mean represents the average lifespan of the items, and the standard deviation indicates how spread out the data points are from the mean. In this case, the manufacturer's items have a mean lifespan of 6.5 years and a standard deviation of 1.7 years.

To find the duration at which the 4% of items with the shortest lifespan will last, we need to calculate the z-score corresponding to the desired percentile. The z-score measures the number of standard deviations a data point is from the mean.

Using a standard normal distribution table or a statistical calculator, we can find the z-score that corresponds to the 4th percentile. In this case, since we want to find the items with the shortest lifespan, we are interested in the area to the left of the z-score. The z-score corresponding to the 4th percentile is approximately -1.75.

Next, we can use the formula for z-score to find the corresponding lifespan duration:

z = (x - μ) / σ

Rearranging the formula, we can solve for x (the lifespan duration):

x = z * σ + μ

Plugging in the values, we have:

\(x = -1.75 * 1.7 + 6.5 = 4.3 years\)

Therefore, the items with the shortest lifespan, comprising approximately 4% of the total, will last less than approximately 4.3 years.

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If Sally started with 2 feet of cloth, the cloth she has remaining is \(\frac{23}{21}\) feet.

Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols to solve equations and study mathematical structures. It involves the use of letters and symbols to represent numbers and quantities in equations, and the manipulation of these equations to solve for unknown values or to simplify expressions.

Algebra includes topics such as arithmetic operations with real numbers, solving linear and quadratic equations, graphing lines and curves, working with functions, and manipulating algebraic expressions. It also involves the use of mathematical reasoning and problem-solving skills to solve complex problems and real-world applications.

Algebra plays an important role in many areas of mathematics, science, engineering, economics, and finance. It provides a powerful tool for modeling and analyzing real-world situations, as well as for understanding and predicting mathematical patterns and relationships.

\(2- \frac{1}{3}-\frac{4}{7} \\\frac{5}{3}- \frac{4}{7}\\\frac{35-12}{21} \\\frac{23}{21}\)

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The complete question is:

Answer:16

Step-by-step explanation:

Answer:

  23.6 years

Step-by-step explanation:

Given that a population is described by y = 82700e^(-0.00036t), you want to know the value of t when the population is 82000.

Substitute the given number for y and solve for t:

  82000 = 82700e^(-0.00036t)

  820/827 = e^-0.00036t . . . . . . . . . . divide by 82700, simplify

  ln(820/827) = -0.00036t . . . . . . . . take natural logs

  t = ln(820/827)/-0.00036 ≈ 23.6 . . . . . divide by the coefficient of t

It will take approximately 23.6 years.

__

Additional comment

The problem statement tells us y₀ is 82700, so we used that in the given equation.

It's a bit odd that the population is reported in thousands of thousands. It could be described as 82.7 million, declinding to 82 million.

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

\(\text{To get the total surface area, all we have to do is multiply } 18 \text{ by } 12, \text{which gets us}\)\($18\cdot12 = \boxed{216\text{ ft}^2}\).

\(\text{So, our answer is } \boxed{216\text{ ft}^2}.\)

Larry needs 216 square feet of carpeting for her rectangular living room.

To find the amount of carpeting Larry needs, we need to calculate the area of her rectangular living room. The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the living room is 18 feet and the width is 12 feet.

So, the area of the living room is:

Area = Length * Width

Area = 18 feet * 12 feet

Area = 216 square feet

Therefore, Larry needs 216 square feet of carpeting for her living room.

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Three people get into an empty elevator at the first floor of a building that has floors. Therefore the probability that the buttons for consecutive floors are pressed is 1/2 x 1 = 1/2 or 0.5.

To simplify the problem we can see that there are three persons and all of them have their desired floors. Each one of them has pressed the button for their floor.

We can construct a number line to represent the floors. Let us suppose that the number line represents the floors of a 10 story building.

Number line: ... 7 8 9 10 [first person] [second person] [third person]

Let us see the scenario where the buttons for consecutive floors are pressed. Let the first person press the button for the 3rd floor. Then the second person could press the button for either the 2nd floor or the 4th floor.

We can only have the buttons for consecutive floors pressed if the second person presses the button for the 2nd floor

The probability of this happening. There are only 2 possibilities for the second person to press the button:

Press the button for the 2nd floor.

Press the button for the 4th floor.

Both of these possibilities are equally likely.

Therefore the probability that the second person will press the button for the 2nd floor is 1/2.The third person has only one choice. They can only press the button for the 4th floor.

Therefore the probability that the buttons for consecutive floors are pressed is 1/2 x 1 = 1/2 or 0.5.

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The amount of white sand in the container is 42.39 in³.

A cylinder is a three-dimensional object. It is a prism with a circular base.

The first step is to determine the volume of the cylinder

Volume of a cylinder = πr²h

Where:

1.5² x 3.14 x 16 = 113.04 in³

Now determine total amount of blue and red sand in the container

Amount of blue and red sand = 42.39 + 28.26 = 70.65 in³

Amount of white sand in the container = 113.04 in³ -  70.65 in³ = 42.39 in³

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Answer: y = 80*

all circles have 360* so we can subtract what we have to get what we want

360 - 110 - 90 - 80 = 80*

There are 1260 different strings that can be made from 5 of the 7 letters in the word "meeting."

To determine the number of unique subsets of 5 letters from the word "meeting," we can use the combination formula:

\(n_Cr = n! / r!(n-r)!\)

Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).

So, for "meeting," n = 7 and r = 5.

Plugging these values into the formula gives:

\(7C5 = 7! / 5!(7-5)! = 21\)

Therefore, there are 21 unique subsets of 5 letters that can be formed from the letters in the word "meeting."

To determine the number of different strings that can be made from 5 of those 7 letters, we can use the permutation formula:

\(n_Pr = n! / (n-r)!\)

Where n is the total number of items (in this case, the number of letters in the word "meeting") and r is the number of items being selected (in this case, 5 letters).

So, for "meeting," n = 7 and r = 5.

Plugging these values into the formula gives:

7P5 = 7! / (7-5)!

= 7! / 2!

= 2520 / 2

= 1260

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Answer:

Step-by-step explanation:

Just divide four into sixteen. You should get x=4. To check, multiply 4 by 4 (4 x 4), and you should get 16.

Answer:

11

Step-by-step explanation:

If you input the number and then solve, you should get that #=#

2(11)+9=4(11)-13

22+9=44-13

31=31

Answer: 11

Step-by-step explanation: 2(11)+9=4(11)-13, 22+9=44-13, 31=31

Answer:

The customer bought 8 DVDs for $120.00

Step-by-step explanation:

120*15=8 DVDS or as a ratio 8:1

Answer:

Uhmm you need to know the radius too to find the area...

Answer: 100 paintings

Step-by-step explanation:

To calculate the breakeven point, use the following formula:

= Fixed cost / Contribution margin

The Fixed cost is the one that does not change which is the $100 spent on brushes.

Contribution margin = Sales price - variable cost(cost that he incurs per painting)

= 10 - 9

= $1

Breakeven point = 100/1

= 100 paintings

The minimized boolean expression for this truth table is:

The given truth table for the function defined by the boolean expression X у Z F is shown below;

x y z F

0 0 0 0

0 0 1 0

0 1 0 1

0 1 1 0

1 0 0 1

1 0 1 0

1 1 0 1

1 1 1 1

To obtain the minimized expression, we can use Karnaugh maps or Boolean algebra laws like distributivity, commutativity, and associativity to simplify the original expression. However, since the expression is relatively small, we can also obtain the minimized expression by inspection.

The minimized boolean expression for this truth table is:

The given truth table is:

w x y z F
0 0 0 0 0
0 0 0 1 1
0 0 1 0 0
0 0 1 1 0
0 1 0 0 X
0 1 0 1 0
0 1 1 0 X
0 1 1 1 1
1 0 0 0 1
1 0 0 1 1
1 0 1 0 X
1 0 1 1 1
1 1 0 0 X
1 1 0 1 1
1 1 1 0 X
1 1 1 1 X

Therefore, the minimized boolean expression for this truth table is:

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It will take `t = ln 2 / ln 3` years for the initial population to triple.

Let `t` be the time in years, and `P` be the population of the community.

Then, the rate of increase in the population is given by dP/dt = kP,

where `k` is a constant of proportionality.

Using separation of variables,dP/P = k dt

Integrating both sides we get,

∫dP/P = ∫k dt

On integrating both sides we get,ln |P| = kt + C1

where `C1` is the constant of integration.

Using the initial condition that the population doubles in `t = 1`, we get

2P0 = P0e^(k*1)

where `P0` is the initial population. Simplifying this expression we get,e^k = 2or k = ln 2

Now the population is tripled, which means P = 3P0.

Substituting these values in the equation obtained by integrating the differential equation,

ln |3P0| = ln 2 * t + C1ln 3 + ln |P0| = ln 2 * t + C1

Simplifying we get,ln(P0/3) = -ln 2 * t + ln(C2)

where `C2 = e^(C1) / 3`.

Simplifying further,ln(P0/3C2) = -ln 2 * t

We know that at time `t = 2`, the population has doubled.

So,2P0 = P0e^(ln 2 * 2) = P0 * 4

or P0/3C2 = 1/4

Solving for `C2` we get,C2 = P0/12

Substituting this value in the above equation,ln(P0/4) = -ln 2 * t

Solving for `t`,t = ln 2 / ln 3 years.

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