A flashlight is projecting a triangle onto a wall, as shown below.

The original triangle and its projection are similar. What is the missing length n on the projection?

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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Part A:

the cost of the fabric is 29.07

Part B:

Rounding to the nearest cent, the cost of the fabric is $29.07.

we need to calculate the area of the front of the bulletin board and then multiply it by the cost per square foot in order to find the cost of the fabric.

The area of a circle with radius 2.5 feet is:

A = πr^2

A = 3.14 x 2.5^2

A = 19.625 square feet

So, the cost of the fabric is:

Cost = area x cost per square foot

Cost = 19.625 x 1.48

Cost = 29.07

Rounding to the nearest cent, the cost of the fabric is $29.07.

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Answer:

Come on man you are in high school and you can't answer this?

Step-by-step explanation:

To write 0.45 as a common fraction, we can use the fact that the decimal point separates the whole number part from the fractional part. So we have:

0.45 = 45/100

To simplify this fraction, we can divide both the numerator and the denominator by the greatest common factor, which is 5:

45/100 = (45 ÷ 5) / (100 ÷ 5) = 9/20

Therefore, 0.45 written as a common fraction, in its simplest form, is 9/20.

Step-by-step explanation:

30 is 5   below the mean of 25

      this is  ONE standard deviation BELOW the mean    ( the standard deviation is given as 5)

  this represents  a     Z -score of -1    

From Z-score table this represents .1587 of the sample or 15.87 %

The percentage of all scores that occur at 30 or below in a distribution with a mean of 25 and a standard deviation of 5 is 84.13%.

To find the percentage of all scores that occur at 30 or below, we need to calculate the z-score first. The z-score formula is (x - μ) / σ, where x is the score of interest, μ is the mean, and σ is the standard deviation.

So, for x = 30, μ = 25, and σ = 5, the z-score is calculated as (30 - 25) / 5 = 1.

We can then use a standard normal distribution table or a calculator to find the proportion of the area under the curve to the left of z = 1. This gives us the percentage of all scores that occur at 30 or below.

Using a standard normal distribution table, we find that the proportion of the area under the curve to the left of z = 1 is 0.8413.

Therefore, the percentage of all scores that occur at 30 or below in this distribution is 84.13%.

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Answer: 3

Step-by-step explanation:

Answer: h=3

Step-by-step explanation:

0.98

When you see this kind of problem, try to see how cos 2x and sin x relate--don't go straight to finding x because it is unnecessary. In this case, there is a formula that shows the relationship between cos 2x and sin x as shown:

cos 2x = 1 - 2(sin x)^2

All we have to do is plug in the value of sin x to find the value of cos 2x.

cos 2x = 1 - 2(-0.1)^2 = 1 - 2(0.01) = 1 - 0.02 = 0.98

Answer:

A.

Step-by-step explanation:

IM GUEssing that thi sis it

The inequality that is true for all values of x is:

√(4x²) ≤ 4x²

Let's try to find which inequality is true for all real values of x.

For example, let's look at option C, here we have the inequality:

4(x² - 3) ≤ 3(x² - 4)

Let's expand both sides to get:

4x² - 12 ≤ 3x² - 12

4x² ≤ 3x²

4 ≤3

We removed the x-variable, but 4 is not smaller or equal to 3, so this is false.

Now option D, we have:

√(4x²) ≤ 4x²

Notice that bout outcomes are always positive, but in the left side we have a square root.

We can simplify this to get:

2x ≤ 4x²

x ≤ 2x²

This is trivially true, the only region where we can have problems is the region between 0 and 1, but the factor corrects that.

So this one is the correct option.

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the average rate of change of the function h(x) over the interval 2 ≤ x ≤ 5 is -23. The answer is B) -23.

[tex]\frac{6}{8} + \frac{1}{12} = \frac{5}{6}[/tex] when added and simplified.

What is a fraction?

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).

To add fractions with different denominators, we need to first find a common denominator.

The common denominator of 8 and 12 is 24.

So we can rewrite the problem as:

6/8 + 1/12 =6×3/8×3 + 1×2/12×2 = 18/24 + 2/24 = 8/6 + 12/1

Now we can add the fractions:

18/24 + 2/24 = 20/24

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:

20/24 = 5/6

​

Therefore, [tex]\frac{6}{8} + \frac{1}{12} = \frac{5}{6}[/tex] when added and simplified.

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Answer:

The exponential function that represents the membership after t years is given by:

y(t) = 100,000(1 + r)^t

where r is the annual growth rate as a decimal, which is equal to 0.12 in this case.

So the correct answer is:

A. y(t) = 100,000(1 + 0.12)^t

Note that the other options have incorrect expressions for the growth rate and/or the exponent.

Answer: 4 x (7+5) = 48

              8 . (5-3) . 4 = 64

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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The distance between the points (4, 5) and (2, 2) is approximately 3.61 units.

What is the distance?

To find the distance between two points, we can use the distance formula:

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Using the given points (4, 5) and (2, 2), we have:

distance = √[(2 - 4)² + (2 - 5)²]

= √[(-2)² + (-3)²]

= √[4 + 9]

= √13

So the distance between the points (4, 5) and (2, 2) is approximately 3.61 units.

To graph these points, we would plot them on a coordinate plane. The point (4, 5) would be two units to the right of the y-axis and five units up from the x-axis.

The point (2, 2) would be two units to the right of the y-axis and two units up from the x-axis. We could then use a ruler to measure the distance between the two points on the graph to verify that it is approximately 3.61 units.

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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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the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

The Θ-intercepts of a graph of a function f are the values of Θ where the graph intersects the Θ-axis, i.e., where f(Θ) = 0.

In the case of f(Θ) = tan(Θ), we know that the function has vertical asymptotes at Θ = π/2, 3π/2, etc., where the function is undefined. Therefore, the graph of f will intersect the Θ-axis at these values of Θ, since the function is negative for Θ between π/2 and 3π/2 and positive for Θ outside of that interval.

Thus, the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

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Answer: TRUE

Step-by-step explanation:

Answer:

Step-by-step explanation:

its 45 cm due too

The bell tolls 6 times between 11:45 AM and 3:10 PM.

Determine how many times the bell tolls between 11:45 AM and 3:10 PM, follow these steps:

1. Calculate the time interval between 11:45 AM and 3:10 PM:
3:10 PM - 11:45 AM = 3 hours and 25 minutes
2. Find the next bell toll after 11:45 AM:
Since the bell tolls at half past the hour, the next bell toll is at 12:30 PM.
3. Calculate the time interval between 12:30 PM and 3:10 PM:
3:10 PM - 12:30 PM = 2 hours and 40 minutes
4. Divide the time interval by the bell's tolling interval:
2 hours and 40 minutes = 160 minutes
160 minutes / 30 minutes (bell's tolling interval) = 5.33
5. Since the bell can't toll a fraction of a time, round down the result:
5.33 rounds down to 5
6. Add 1 to the rounded result to include the bell toll at 12:30 PM:
5 + 1 = 6.

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Answer:$0.53

9 pack  =   $4.77

1 pack   =   $?

9÷1=9, $4.77÷9=$0.53

Answer: $0.53

Step-by-step explanation: 9 divided by 1 is 9 and 4.77 divided by 9 is 0.53. ;)

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 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 box requires a minimum of 4032 square inches of material.

Let's assume that the square base of the box has side length 'x', and the height of the box is 'h'. Then the volume of the box is

V = x^2 × h = 6912

We need to find the dimensions of the box that require the least amount of material. This means we need to minimize the surface area of the box. The surface area of the box is given by

S = x^2 + 4xh

We can solve for 'h' in terms of 'x' using the volume equation

h = 6912 / x^2

Substituting this expression for 'h' into the surface area equation, we get

S = x^2 + 4x(6912/x^2)

Simplifying and taking the derivative of 'S' with respect to 'x', we get

dS/dx = 2x - 27744/x^3

Setting this derivative equal to zero to find the critical points

2x - 27744/x^3 = 0

Multiplying both sides by x^3 and solving for 'x', we get

x = (27744/2)^(1/4) = 18

To confirm that this is a minimum, we need to check the second derivative of 'S' with respect to 'x'

d^2S/dx^2 = 2 + 83208/x^4

At x = 18, we have

d^2S/dx^2 = 2 + 83208/18^4 > 0

Therefore, the critical point at x = 18 corresponds to a minimum surface area.

So the dimensions of the box with the least amount of material are

The side length of the base is 18 inches, and

The height of the box is h = 6912 / 18^2 = 32 inches.

The minimum amount of material required is the surface area of the box, which is

S = 18^2 + 4(18)(32) = 1728 + 2304 = 4032 in^2.

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Step-by-step explanation:

54÷9+12-4

=6+12-4

=14//

The weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. whereas there is a net change in the x coordinate, the y coordinate changes just little.

Given the modeled equation for puppy's growth is 2x - y = -2.

The standard equation of line is y = mx + c.

Converting the given model in standard form we have:

2x - y = -2

-y = - 2x - 2

y = 2x + 2

From the equation we see that the y-intercept is 2 and slope is 2.

The graph that has the y-intercept at 2 and slope of 2 is graph H.

Hence, the weight of a puppy modeled by the equation 2x - y = 2 is represented by graph H.

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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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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

Answer:

approximately 48 agate marbles in the tin.

Step-by-step explanation:

Out of the 10 marbles Naomi picked, 3 are agate. We can use this ratio to estimate the number of agate marbles in the tin.

If we assume that the distribution of marbles in the tin is similar to the distribution in the sample of 10 marbles, we can set up a proportion to estimate the number of agate marbles:

3/10 = x/160

Where x is the estimated number of agate marbles in the tin.

Solving for x, we can cross-multiply and get:

3 * 160 = 10 * x

x = 48

we estimate that there are approximately 48 agate marbles in the tin.

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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