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The number of ways are there to arrange these people in a row if the men and women alternate is 2880.

The concepts of counting are permutation and combination, and they are used in a variety of contexts. A permutation is a list of the many configurations that may be created from the given set of items. Details are crucial in permutation because the order or sequence is crucial.

The techniques used to count the number of outcomes that can occur under different circumstances are permutation and combination. Combinations and permutations are also referred to as arrangements and choices, respectively. The sum rules and product rules may be used to conveniently apply counting according to the basic idea of counting.

5 men and 5 women sit around a table so that they all seat alternately

Formula used:

n! = n x (n - 1) x (n-2) x....... (n-n1)

According to the question,

5 Men sit alternate in 5! ways

5 women can be seated around the circle in (5 - 1)!

⇒ 5! × 4!

⇒ 5 × 4 × 3 × 2 × 1 × 4 × 3 × 2 × 1

⇒ 120 × 24

⇒ 2880

:. The number of ways is 2880.

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Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex] the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

We know that the product of two factors is equal to zero only when at least one of the factors is zero.

[tex](x + 4) \ (2x - a) = 0[/tex]

This equation has two factors:  [tex](x + 4)[/tex] and [tex](2x - a)[/tex] . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.

Setting  [tex](x + 4)[/tex] equal to zero, we get:

[tex]x + 4 = 0[/tex]

[tex]x = -4[/tex]

This means that  [tex]-4[/tex] is one of the solutions of the equation.

Setting  [tex](2x - a)[/tex] equal to zero, we get:

[tex]2x - a = 0[/tex]

[tex]2x = a[/tex]

[tex]x = a/2[/tex]

This means that [tex]a/2[/tex] is another solution of the equation.

Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex]  , we can substitute these values into the expression we found for x in terms of a to get:

[tex]a/2 = 4[/tex] or  [tex]a/2 = -4[/tex]

Solving for a in each case, we get:

[tex]a = 8[/tex] or [tex]a = -8[/tex]

Therefore, the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

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Simple random sampling is the sampling procedure that assures each element in the population of an equal chance of being included in the sample.

Simple random sampling is a type of probability sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected. Data is then collected from as large a percentage as possible of this random subset.

Random sampling ensures that results obtained from your sample should approximate what would have been obtained if the entire population had been measured . The simplest random sample allows all the units in the population to have an equal chance of being selected.

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Yes, there could be total number 50 kids in the group. If there are 50 kids in the group, then more than half of them would be boys, which means there would be at least 26 boys in the group.

Let B be the number of boys and G be the total number of kids in the group.

Given that more than 1/2 are boys, we have B > G/2. Also, given that the boys are less than 2/3 of the group, we have B < 2G/3.

If there are 50 kids in the group, then we have:B > 50/2

B > 25B < 50(2/3)

B < 33.33

B ≤ 33 (since B is an integer)

Therefore, the number of boys in the group can be any integer between 26 and 33, inclusive.

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The repeated measures studies require fewer subjects than matched subjects studies with the same number of outcomes is that repeated measures designs reduce intersubject variability.

In repeated measures studies, each participant is measured multiple times under different conditions or treatments.

Whereas, In a matched-subjects study, each participant in the treatment group is compared to participants in the control group.

Intersubject variability can be large, and differences between treatment and control groups may be attributed to differences in these individual characteristics.

However, in a repeated-measures design, each participant served as its own control, reducing inter-subject variability.

This makes it easier to recognize differences in treatment conditions and can increase effect sizes.

Therefore, a repeated measures study may require fewer subjects to achieve the same statistical power as a matched subjects study with the same number of outcomes.

However, it is important to note that repeated measures designs may have their own limitations:  Potential Order Effect or Practice Effect.

These limitations should be carefully considered when designing a study, and an appropriate design should be chosen based on the research question and the nature of the data.

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In the proportion ,  a=-3 when b=4 and c=-3.

What is proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

Here the given is a directly proportional to b and c . then,

=> a ∝ bc

Now converting into equation add constant then

=> a = kbc [ where k is constant]

Now a= 24 when b= 8 and c= 12 then,

=>24=k(8*12)

=> k = 24/(8*12) = 2/8 = 1/4

Then the equation is [tex]a=\frac{1}{4}bc[/tex]

Now b=4 and c=-3 then,

=> a= (1/4)*4*-3 = -3.

Hence a=-3 when b=4 and c=-3.

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Answer:

a = -3

Step-by-step explanation:

The temperature should be 99.471° F.  If we want only 2.0% of healthy people.

Given that:

μ = 98.20

σ = 0.62

Determine the z-score in the normal probability table in the appendix that corresponds with a probability of:

1 − 0.02 =0.98

It is calculated by subtracting the population mean from the individual raw scores and dividing the difference by the population standard deviation. The process of converting raw scores to standardized scores is called standardization or normalization (although "normalization" can refer to different types of comparisons; see Normalization for more information).

The standardized score is the value x decreased by the mean and then divided by the standard deviation:

​     Z = X - μ / σ

⇒ x = μ+ zσ

      = 98.20+ (2.05)(0.62) = 99.471

Therefore, Only 2% of the healthy people exceed 99.471° F.

Complete Question:

Assume that human body temperatures are normally distributed with a mean of 98.20 F and a standard deviation of 0.62∘F. Physicians want to select a minimum temperature for requiring further medical tests. What should that temperature be, if we want only 2.0% of healthy people to exceed it? (Such a result is a false positive, meaning that the test result is positive, but the subject is not really sick.)

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Answer:

≈ 0,9

Step-by-step explanation:

To the nearest tenth:

[tex] \frac{20}{23} ≈0.9[/tex]

Answer:

See below

Step-by-step explanation:

Helping in the name of Jesus.

Answer:

96

Step-by-step explanation:

Because it is

Putting the negative sign to the numerator, we have the value of x = -6/7.

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

The given equation is:

x³ = -216/343

To solve for x, we can take the cube root of both sides of the equation:

∛(x³) = -∛(216/343)

x = -∛(216/343)

Solving for numerator:

216 =  6 × 6 × 6

∛216 = 6

Solving for denominator:

343 = 7 × 7 × 7

∛343  = 7

Therefore,

x = -∛(216/343)

x = -(6/7)

x = -6/7

Putting the negative sign to the numerator, we have the value of x = -6/7.

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Answer:

A.

Step-by-step explanation:

IM GUEssing that thi sis it

This is used to calculate the height of the object at any time t during its flight.

The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.

The acceleration due to gravity is taken to be -9.8 m/[tex]s^2[/tex] (negative since it acts downward), and the formula for the height is derived from the equation of motion:

h(t) = -1/2 [tex]gt^2[/tex] + vt + hi

Where:

g = 9.8 m/[tex]s^2[/tex] (acceleration due to gravity)

t = time (in seconds)

v = initial velocity (in meters per second)

hi = initial height (in meters)

The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).

This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/[tex]s^2[/tex] until it reaches the maximum height and then starts to fall back down.

So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.

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Answer: TRUE

Step-by-step explanation:

Answer: 3

Step-by-step explanation:

Answer: h=3

Step-by-step explanation:

Answer:

12.2 miles

Step-by-step explanation:

We can use the Pythagorean theorem to solve this problem. Here, A represents the airport, C represents Centerville, and N represents Newberry. We want to find the distance x between N and A.

Since Centerville is 7 miles due north of the airport, the distance AC is 7 miles. Since the distance between Centerville and Newberry is 10 miles, we can use the Pythagorean theorem to find the distance AN. So the distance between Newberry and the airport is approximately 12.2 miles.

ANSWERS:

A. 6 old printers would produce the batch of magazines in less time than 2 new printers
B. Using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers

EXPLANATIONS:

a) To determine which option would produce a batch of magazines in less time, we need to compare the printing rates of each option.

The old printers can produce a batch of magazines in 30 minutes, which means their printing rate is:

5 printers / 30 minutes = 1/6 printers per minute

The new printers can produce the same batch of magazines in 16 minutes, which means their printing rate is:

4 printers / 16 minutes = 1/4 printers per minute

If we use 6 old printers, their printing rate would be:

6 printers / 30 minutes = 1/5 printers per minute

If we use 2 new printers, their printing rate would be:

2 printers / 16 minutes = 1/8 printers per minute

Therefore, 6 old printers would produce the batch of magazines in less time than 2 new printers.

b) To determine how much less time it would take to produce the batch of magazines with 6 old printers, we can set up a proportion:

1/5 printers per minute = 1/x minutes

Solving for x, we get:

x = 5 minutes

Therefore, using 6 old printers would produce the batch of magazines in 5 minutes, which is 25 minutes faster than using 5 old printers.

Answer:

Mary is 36 years old

Her son is 12 years old

Step-by-step explanation:

Let's assume, that Mary's son is x years old and Mary is 3x years old

Let's write 2 equations according to the given information:

x = 3x (Mary is 3 times older than her son)

3x + 12 = 2(x + 12) (after 12 years, she will be 2 times older than her son)

3x + 12 = 2x + 24

3x - 2x = 24 - 12

x = 12

That means, Mary's son is 12 years old

Mary is 3 × 12 = 36 years old

The medical devices company must find data for at least 543 MRI machines.

To calculate the number of MRI machines needed for a 98% confidence interval with a margin of error of 0.20 hour, we need to use the formula:

n = [(z*σ)/E]²

where:

Substituting the values:

n = [(2.33*4)/0.20]²

n = 542.89

Rounding up to the nearest whole number, the medical devices company must find data for at least 543 MRI machines to have a margin of error of at most 0.20 hour when calculating a 98% confidence interval.

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Answer: divide 1/5 by the price of the CD

Formula: A = P(1+r/n)(nt)

Step-by-step explanation: , if you have a $1,000 CD with a term of three years and an APY of 5%, you can multiply $1,000 by 5% to find the interest

Answer:

20% of his money

Step-by-step explanation:

it's 1/5 of 100% of his money

Answer:

A and B

Step-by-step explanation:

Let's factor this the "old fashioned" way. The standard form of a quadratic is

[tex]y=ax^2+bx+c[/tex]

If you're familiar with the quadratic formula I'd say throw it into that, but if not, again, let's do it the "old fashioned" way.  

We need to find the product of our a and c. Our a = 2 and our c = -3. So that gives us a -6. Now we have to find the factors of 6 (the negative right now doesn't matter so much). The factors of 6 are 1, 6  and 2, 3.  Both of those possibilities will work to give us a +5, which is the linear term. Putting in the 2, 3 first:

[tex]0=2x^2+3x+2x-3[/tex]

Now group the terms together into groups of 2:

[tex]0=(2x^2+3x)+(2x-3)[/tex]

The idea is to factor out something common in each term so that what's left over in the parenthesis in both terms is exactly the same.  In the first term we can factor out a common x, and in the second term, the only thing common is a 1.  So that looks like this:

[tex]x(2x+3)+1(2x-3)[/tex]

What's inside those parenthesis are not actually identical, so 2 and 3 won't work.  Lets try 1 and 6.  For those 2 numbers to equal a +5, the 6 is positive and the 1 is negative.  So let's try that:

[tex](2x^2+6x)+(-x-3)[/tex]

In the first term we can factor out the common 2x and in the second term we can factor out the common -1:

[tex]2x(x + 3) - 1(x + 3)[/tex]

Now what's common is [tex](x + 3)[/tex], so we can factor THAT out and what is left over is [tex]2x - 1[/tex]:

[tex](x + 3)(2x - 1) = 0[/tex]

If [tex]x + 3 = 0[/tex], then [tex]\bold{x = -3}[/tex]

and if [tex]2x - 1 = 0[/tex], then [tex]2x = 1[/tex] and [tex]\bold{x = \frac{1}{2} }[/tex]

The calculated length of AC from the right triangles is 320 units

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

The right triangle

The length of the segment AC is calculated as

sin(30) = 160/AC

Make AC the subject

So, we have

AC = 160/sin(30)

When evaluated, we get

AC = 320

Hence the length of AC is 320 units

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The point with the y-coordinate of 0 splits the directed line segment from J to K into a 5:1 ratio.

An X coordinate value denotes a location that is relative to a point of reference to the east or west. A Y coordinate value denotes a location that is relative to a point of reference to the north or south.

Considering J (1, -10) and K (7, 2)

In this case, let's suppose that point L divides the directed line segment from J to K into a 5:1 ratio.

We know that from coordinate geometry's inherent characteristics.

The point's coordinates are (x1, y1), (x2, y2) where they meet in the ratio of m:n.

[tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]

Now putting the respective values,

= ([tex](\frac{(5 .1)(1 .1) }{5 +1} , \frac{(5 . 2)(1 . (-10))}{5+1}[/tex]

= (6, 0)

Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

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The equation of the line parallel to the given line and passing through the point (-4, -6) is: y = -6

The given line goes through the points (-8, 4) and (8, 4).

Since the y-coordinates of both points are the same, the line is horizontal.

The equation of a horizontal line is given in the form y = k,

where k is the y-coordinate of any point on the line.
In this case, the equation of the given line is y = 4.
Now, we want to find the equation of a line that is parallel to the given line and passes through the point (-4, -6).

Since parallel lines have the same slope, and the slope of a horizontal line is 0, the line we're looking for will also be horizontal.

So, its equation will be in the form y = k as well.
The point (-4, -6) lies on this new line, and its y-coordinate is -6.

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The lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.

What are the lengths?

To solve this problem, we can use the Law of Sines, which states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.

Let's start by finding the measure of ∠G, using the fact that the sum of the angles in a triangle is 180 degrees:

m∠G = 180° - m∠E - m∠F = 180° - 39° - 86° = 55 °

Now we can use the Law of Sines to find the lengths of EF and FG:

EF/sin(F) = EG/sin(G)

EF/sin(86) = 7.9/sin(55)

EF = sin(86)*7.9/sin(55) ≈ 10.2

Similarly,

FG/sin(E) = EG/sin(G)

FG/sin(39) = 7.9/sin(55)

FG = sin(39)*7.9/sin(55) ≈ 5.8

Therefore, the lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.

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Complete question is: The lengths of EF and FG to the nearest tenth are approximately 10.2 and 5.8, respectively.

The function is linear because as the x-value increases, the y-values increases.

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;

y = mx + c

Where:

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (1 - 3)/(0 - 1)

Slope (m) = -2/-1

Slope (m) = 2

Based on the information provided above at point (0, 9), an equation that models the line is represented by this mathematical equation;

y = mx + c

y = 5x + 9

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Answer:

the height of the water in Container B is 22.48 feet.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Hello : let A(-1,3) B(2,4)

the slope is : (YB - YA)/(XB -XA)

(4-3)/(2+1) = 1/3

an equation is : y=ax+b a is a slope

y = 1/3x +b

the line through point B (2,4) : 4 = (1/3)(2)+b

b =10/3           the equation is : y =1/3x+10/3