b) in a distribution of scores, is it possible for more than half of the scores to have values that are below the mean? why or why not?

Answer:

93

Step-by-step explanation:

triangle = 1/2*5*6=15

B = 9*6=54

C = 4*6=24

total =54+24+15 = 93

The equation solved for the variable y is:

y = 4 - x

To do this, we need to isolate the variable y in the given equation.

We have the equation:

3y -2 = 10 - 3x

Adding 2 in both sides we will get:

3y -2 +2 = 10 - 3x + 2

3y = 12 - 3x

Now we can divide both sides by 3 to get:

3y/3 = (12 - 3x)/3

y = 4 - x

That is the equation solved for y.

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60 engineering students are divided into 24 who take math and 29 who take physics. 10 students take statistics and physics together, 13 students take math and physics together. a) There are 26 students take statistics. b) P(A/B)=4/13.

The science of statistics is concerned with the research and advancement of methods for collecting, analyzing, interpreting, and presenting empirical data. The science of learning from data is called statistics, which is also possibly an art. The discipline's focus is on the gathering, analyzing, and interpretation of data as well as the efficient dissemination and presentation of findings that rely on data.

We can assume the following:

1). There are 13-8=5 pupils who study physics and math together but not statistics (green colour)

2). There are 10-8=2 pupils who study physics and statistics together but not math (grey colour)

3). Students who take algebra and statistics but not physics total 11-8=3. (yellow colour)

4). There are 14 pupils (29-5-8-2) who only take physics (pink colour)

We can now determine how many students solely take statistics by doing the following: The number of students enrolled in at least one course (60–7) less the number taking only math or just physics or just statistics but not math.

53-24-14-2=13 students take only statistics

There are 26 students who take statistics, or 13 + 2 + 3 + 8

b) Let's say A takes all three, and B takes statistics. Finding conditional probability is the goal.

P(A/B)= P(A⋂B)/P(B)

P(A⋂B)= 8/60, P(B)=26/60

So,

P(A/B)=P(A⋂B)/P(B)=8/26=4/13

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Answer:

Below

Step-by-step explanation:

The ENTIRE perimeter of a circle is  pi * d

 a semi circle circumference is 1/2 of this  1/2 pi * d   PLUS the diameter line

               1/2 pi * ( 2 mm)  + 2mm = 5.14 mm

Answer:

2a+4+b+d

Step-by-step explanation:

a+a= 2a

4+0=4

b+0=b

c+0=c

d+0=c

Above 700: 5%, Above 550: 34%, Between 400 and 550: 26%, Below 400: 16%, Below 550: 55%.

To calculate the fraction of students who scored above 700, we can use the z-score formula, which is (x - μ) / σ, where x is the score, μ is the mean, and σ is the standard deviation. In this case, μ = 500 and σ = 100. Plugging in 700 for x, we get (700 - 500) / 100 = 2. This corresponds to a z-score of 2, which is .9772, meaning that 97.72% of the scores are below 700. This means that 5% are above 700. To calculate the fraction of students who scored above 550, we can use the same formula, but with 550 for x. This gives us (550 - 500) / 100 = .5, which corresponds to a z-score of .5, meaning that 84% of the scores are below 550. This means that 34% are above 550. To calculate the fraction of students who scored between 400 and 550, we can subtract the z-score of 400 from that of 550. This gives us .84 - .2 = .64, meaning that 64% of the scores are below 550. This means that 26% are between 400 and 550.

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Answer: The Y intercept is 50 and it represents where the temperature starts.

Step-by-step explanation: The Y intercept is basically where the line is touching on the y line.

Let's call the number of hours spent on a job as "h". Then, the fee charged to the client can be represented as a function of "h" as follows:

f(h) = 30h + 40

This means that for any value of "h" (representing the number of hours spent on a job), the function f(h) gives the corresponding fee charged to the client.

Function notation is a mathematical notation used to express a mathematical function, which assigns a unique output to each input of a set. The function is represented by a symbol, usually a letter (such as f or g), followed by a variable in parentheses.

For example, the function f(x) = x^2 assigns the value x^2 to the input x. The input is usually referred to as the argument of the function. The function notation is commonly used in calculus, algebra, and other branches of mathematics.

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{1}{3^2} \right)^{-1}\implies \left( \cfrac{3^2}{1} \right)^{+1}\implies 3^2\implies 9[/tex]

There are 45 possible choices for the five members.

There are ten people on the debate team, but only two of them can be in position 5. Positions 1 through 4 can be filled by any 10 members. Using the combination formula nCr, where n is the total number of items and r is the number of items chosen from that set, we can determine the number of ways to select these five members.

In this instance, we have 10C2, which simplifies to 10!/(2!(10-2)!)) or 10 items chosen from a set of 10. This can be reduced to 45, or 109/2. As a result, there are 45 ways to select the five debate team members.

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Step-by-step explanation:

So it's...

[tex] \frac{5\pi}{4} - \frac{\pi}{4} [/tex]

Since the denominators are the same (both of the fractions have 4 on the bottom), you can do simple subtraction to the top while keeping the bottom 4

[tex]5\pi - \pi = 4\pi[/tex]

Which means the answer is

[tex] \frac{4\pi}{4} [/tex]

Answer:

[tex]\frac{1}{9}[/tex] or 11.11%

Step-by-step explanation:

P(A) = probability of an event

f = favored outcomes

N = number of total outcomes

[tex]P(A)=\frac{f}{N}[/tex]

In this equation there is one favored income, when the first counter is blue and the second one is green. There are also nine total outcomes. This means that the equation necessary is:

[tex]P(A)=\frac{1}{9}[/tex]

The probability that Mike takes a blue counter and then Ellie takes a green counter is [tex]\frac{1}{9}[/tex] or around 11.11%

The two numbers are 7/6 and 5 when the sum of two numbers is 3 more than four times the first number.

Let's call the two numbers x and y, where x is the first number and y is the second number.

The problem gives us two equations that relate the two numbers:

[tex]x + y = 3 + 4x\\y - x = 2y - 10[/tex]

We can substitute the expression for y from equation 1 into equation 2:

[tex]y - x = 2(3 + 4x) - 10[/tex]

Expanding the right side and simplifying, we get:

[tex]y - x = 6 + 8x - 10\\y - x = 8x - 4[/tex]

Adding x to both sides:

[tex]y = 9x - 4[/tex]

Substituting this expression for y into equation 1:

[tex]x + (9x - 4) = 3 + 4x[/tex]

Expanding and simplifying the right side:

[tex]10x - 4 = 3 + 4x[/tex]

Subtracting 4x from both sides:

[tex]6x - 4 = 3[/tex]

Adding 4 to both sides:

[tex]6x = 7[/tex]

Dividing both sides by 6:

[tex]x = 7/6[/tex]

Substituting this value of x back into the expression for y:

[tex]y = 9x - 4 = 9 * (7/6) - 4 = 63/6 - 4 = 9 - 4 = 5[/tex]

So the two numbers are 7/6 and 5.

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The length of the stone walkway would be 536.64 inches.

To find the length of the stone walkway, the landscaper needs to determine the length of the diagonal of the rectangular lawn.

The length of the diagonal can be calculated using the Pythagorean theorem:

[tex]d^2 = l^2 + w^2[/tex]

Where d is the length of the diagonal, l is the length of the rectangle, and w is the width of the rectangle.

So to find the length of the walkway, the landscaper would need to know the length and width of the rectangular lawn.

Suppose a landscaper wants to place a stone walkway from one corner of a rectangular lawn that is 40 feet long and 20 feet wide to the opposite corner.

Using the Pythagorean theorem, we can calculate the length of the diagonal:

[tex]d^2 = 40^2 + 20^2[/tex]

[tex]d^2 = 1600 + 400[/tex]

[tex]d^2 = 2000[/tex]

[tex]d =\sqrt{2000}[/tex]

[tex]d = 44.72 feet[/tex]

Rounding to the nearest inch, the length of the stone walkway would be 44.72 * 12 = 536.64 inches, which can be rounded to 536 inches.

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The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

We have to given that;

The given relation is,

⇒ y = 62.5x

Where, y represent distance in mile and x represent the time in hour.

We know that;

The proportional relation is defined as;

⇒ y = kx

Where, k is constant of variation.

Hence, By comparing,

The constant of variation is 62.5 and this means that the bus travel 62.5 miles per hour.

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Answer:

-12

Step-by-step explanation:

Answer: -12

Step-by-step Explanation: 2 times -3= -6, -6 times 2= -12

The value of 'x' in the expression (1/2)(4x - 5) + 5/2 = 10 is, x = 5.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression  (1/2)(4x - 5) + 5/2 = 10.

(1/2)(4x - 5) = 10 - 5/2.

(1/2)(4x - 5) = (20 - 5)/2.

(1/2)(4x - 5) = 15/2. ('2' on both sides of the denominator cancels)

4x - 5 = 15.

4x = 20.

x = 5.

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[tex]10~~ : ~~45\implies \cfrac{10}{45}\implies \cfrac{5\cdot 2}{5\cdot 9}\implies \cfrac{5}{5}\cdot \cfrac{2}{9}\implies \cfrac{2}{9}\implies 2~~ : ~~9[/tex]

Answer:

Step-by-step explanation:

the rise is 100

Tthe population of the colony after 2 hours is 64a

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

Rate = doubles every 20 minutes

Represent the initial population with a

So, we have the following representation

f(t) = a(2)^t

Where t is the number of 20 minutes in the time

The time is given as 2 hours

So, we have

t = 2 hours/20 minutes

Evaluate

t = 6

The function becomes

f(t) = a(2)^6

Evaluate

f(t) = 64a

hence, the population is 64a

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The equation for the Bowler world is c = $1.1g + $5,

The equation for the Lucky spares is c = $1.5g + $3.

and the cost is the same for 5 games and the cost is $10.5.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given the Bowler, World charges $5.00 to rent shoes and $1.10 per game. Lucky Spares charges $3.00 for shoes and $1.50 per game.

Part A

using g for the number of games and c for the cost

for Bowler World

charges for shoes = $5

cost for per game = $1.1

cost for g games = $1.1g

total cost c =  $1.1g + $5 ..........(1)

for Lucky spares

charges for shoes = $3

cost for per game = $1.5

cost for g games = $1.5g

total cost c =  $1.5g + $3 ..........(2)

B. if the cost used in both places is equal then equation 1 equals equation 2

so $1.1g + $5 = $1.5g + $3

1.5g - 1.1g = 5 - 3

0.4g = 2

g = 2/0.4

g = 5

and cost is c =  $1.1g + $5

c = 1.1*5  + 5

c = 5.5 + 5

c = $10.5

Hence equations are  c =  $1.1g + $5 and  c =  $1.5g + $3,

and the cost is same for 5 games and the cost is $10.5.

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If x and y are complementary angles, then x and y are supplementary vertical.

Complementary angles are two angles whose sum is equal to 90 degrees. Supplementary vertical angles are two angles that are vertically opposite each other and add up to 180 degrees.

Therefore, the correct answer is as given above. It could then be concluded that the correct answer in the case of x and y being complementary angles, then x and y are supplementary vertical.

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Answer:

x= 10.2 when rounded to nearest tenth

The coordinates of another point with the same y-value are (10, 10).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

f(x) = |x|

For (-10, 10)

i.e,

x = -10

f(-10) = |-10| = 10

So,

(-10, 10) is on the graph.

Now,

For x = 10,

f(10) = |10| = 10

This means,

(10, 10) is also on the graph.

We see that,

(-10, 10) and (10, 10) has the same y-value.

Thus,

The coordinates of another point are (10, 10).

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Answer:

The total average decrease in the stock after 8 weeks is -10 - 8 = -2 dollars.

Step-by-step explanation:

There are a total of 10 different combinations for each of the four-letter words.

If reiteration is permitted

There are 10 possible combinations for each of the four letters, making a total of 104 four-letter words.

If reiteration is prohibited

The first letter has 10 potential outcomes, followed by 9 for the second, 8 for the third, and 8 for the fourth, for a total of 10 * 9 * 8 * 7 outcomes.

If the first letter must be A, there is only one alternative for that letter and ten possibilities for each of the following three letters, for a total of 103.

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Answer:

you count from the top to the bottem

Answer:

(5 , -6) I believe this is the answer because I tried it