Triangle 1 and triangle 2 are similar right triangles formed from a ladder leaning against a building.




Determine the distance from the bottom of the building to the point where the ladder is touching the building for triangle 2.
4 feet
7 feet
9 feet
14 feet

The probability that the mean of a random sample of 52 pregnancies is less than or equal to 222 days is approximately 0.0005 (rounded to four decimal places).

Let's discuss it further below.

To solve the problem, we use the z-score formula, which is as follows:

z=(X−μ)/σX = sample mean = 222 days

μ = population mean = 226 days

σ = standard deviation of the population = 15 days

n = sample size = 52

To find the probability, we need to convert the sample mean to a z-score, which is calculated as follows:

z=(X−μ)/σ=(222−226)/(15/√52)=−4/2.096=−1.91

Now we need to find the probability that a random sample of 52 pregnancies has a mean gestation period of 222 days or less, which is equivalent to finding the probability that a z-score is less than or equal to −1.91.

Using a z-table or calculator, we find that the probability of a z-score being less than or equal to −1.91 is approximately 0.0005 (rounded to four decimal places).

Therefore, the answer is 0.0005.

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Answer:

Step-by-step explanation:

Option 3

The amount of water that the pitcher contained before Mai added more water was 7.8 liters.

Let x be the amount of water the pitcher contained before Mai added more water.

When Mai poured 2.6 liters of water, the total amount of water in the pitcher became x + 2.6 liters.

According to the problem, the pitcher then contained 10.4 liters of water. Therefore, we can write:

x + 2.6 = 10.4

Subtracting 2.6 from both sides, we get:

x = 7.8

Therefore, the pitcher contained 7.8 liters of water before Mai added more water.

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Answer:

x=5 or x=-5

Step-by-step explanation:

[tex]x^{2} -25=0[/tex]

[tex](x-5)(x+5) =0[/tex]

[tex]x=-5 \\x=5[/tex]

Number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

To find the percent of wolves that are neither female nor hunt in medium-sized packs, follow these steps:
1. Determine the total number of wolves.
2. Identify the number of female wolves and those that hunt in medium-sized packs.
3. Subtract the number of wolves that fit into either category from the total number of wolves.
4. Divide the remaining number of wolves by the total number and multiply by 100 to get the percentage.
Please provide the necessary data (total number of wolves, number of female wolves, and number of wolves hunting in medium-sized packs) to perform these calculations and obtain the percentage.

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The answer would be  a) With Replacement 16,807 points will be in the sample space if batteries are selected.

The sample space with replacement would be 7^5 = 16,807 points. This means that when selecting five batteries from a bag of seven with replacement, the total number of points would be 16,807. This is because each of the five batteries could potentially be from the same brand, so the sample space would include all 16,807 possibilities of the combination of 5 batteries from the 7 available.

B) Without Replacement: The sample space without replacement would be 7P5 = 21,053 points. This means that when selecting five batteries from a bag of seven without replacement, the total number of points would be 21,053. This is because each of the five batteries must be from a different brand, so the sample space would include all 21,053 possibilities of the combination of 5 batteries from the 7 available.

In conclusion, the sample space would have more points if the batteries are selected without replacement compared to when the batteries are selected with replacement. This is because when batteries are selected without replacement, each of the five batteries must be from a different brand, whereas when batteries are selected with replacement, the same brand could be chosen multiple times.

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Answer:

first box: 4

second box: 1

Step-by-step explanation:

f(x) is a pretty standard curve, its a parabola, opens up, vertex at (0,0)

Its the most basic version of a parabola (a kind of U-ish, V-ish smooth curve shape)

But if you mess around with the x...that "- 4" that's in close to the x, it will slide the whole graph over to the right 4 units. Left and right shifts (shifts, slide, translate...all the same thing--it means what you think it should mean) anyway, left and right shifts are a little backwards from what you think it should be:

- anumber shifts right

+ anumber shifts left

There are math reasons why this happens, but just memorize it!

Up and down shifts go the way you think they should. If you tack a number on the end of an equation:

- anumber slides down

+ anumber slides up

So the graph of h is a translation (shift or slide) 4 units right and 1 unit down of f.

The transformation performed on f(x) = x² to create h(x) = 1/5f(x) is the graph is compressed horizontally by the factor 1/5

Transformations are mathematical operations performed on a graph or function to change the shape, size or orientation of the graph or function.

Given that we have the function f(x) = x² and it is transformed into the graph h(x) = 1/5f(x).

So, the graph is  compressed horizontally by the factor 1/5

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According to a national survey of youth, only about 30% of adolescents got eight or more hours of sleep on an average school night.

What is sleep?

Sleep is a process of the human body that occurs naturally, which restores the body and mind's strength. It helps one's mind and body to remain healthy by allowing the body to rest, regenerate, and re-energize.Sleep is essential for one's well-being, particularly for adolescents.

According to a national survey, only about 30% of adolescents got eight or more hours of sleep on an average school night.

Lack of sleep is a common issue among young people, and it can lead to a variety of health issues.

Sleep plays an essential role in our daily lives, particularly for young people.

Adolescents need at least eight hours of sleep per night to maintain good health and well-being.

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Answer: 12

Step-by-step explanation: if you take the number 64 and devide it by 8 you get 8. then add 4 to eight and you get twelve

The largest three-digit number satisfying the given criteria is 964.

Given that all the digits of a three-digit integer are distinct and non-zero.

Further more, the three-digit integer is divisible by each of its digits.

We are to find the largest three-digit integer that has these properties.

What we know: We know that a number is divisible by its digit if and only if the number is divisible by the least common multiple of the digits of the number.

Since all the digits are distinct and non-zero, the least common multiple of the digits of the number is simply the product of the digits.

Let's assume the number to be a b c,

where a, b, and c represent digits of the three-digit integer.

We are required to find the largest such number satisfying the given criteria.

Since the number must be divisible by each of its digits, it follows that each digit must be a factor of the number.

Hence, we can write,

a b c = a x b x c

The number must be greater than 100.

Hence, a must be at least 1. b and c must be distinct from a and from each other.

Hence, the smallest possible value for b is 2, and for c is 3.

This gives us the following equations: 123 = 1 x 2 x 3124

= 1 x 2 x 4125

= 1 x 2 x 5126

= 1 x 2 x 6128

= 1 x 2 x 8129

= 1 x 2 x 9

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Answer:

Step-by-step explanation:

yes

The probability of winning is 1/42 expressed as a fraction.

Given that the odds on a bet are 41:1 against, we are to find the probability of winning.

We know that odds against = (Number of unfavorable outcomes) : (Number of favorable outcomes).

Thus, odds against = 41:1. This implies that the number of unfavorable outcomes is 41 and the number of favorable outcomes is 1.Probability of winning is given by the formula P(winning) = Number of favorable outcomes / Total number of possible outcomes. In this case, the total number of possible outcomes is the sum of the number of favorable and unfavorable outcomes.

Number of favorable outcomes = 1 and Number of unfavorable outcomes = 41

Therefore, the total number of possible outcomes = 1 + 41 = 42

Thus, P(winning) = Number of favorable outcomes / Total number of possible outcomes

P(winning) = 1 / 42

Therefore, the probability of winning is 1/42 expressed as a fraction.

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the missing dimension of the triangle is the base, which has a length of 21 feet. To find the missing dimension of the triangle, we will use the formula for the area of a triangle, which is:

Area = 1/2 x base x height

We know that the area of the triangle is 14 ft squared and the height is 6 ft. We can substitute these values into the formula and solve for the base:

14 = 1/2 x base x 6

Multiplying both sides by 2/6 (or simplifying to 1/3) gives:

14 x 3/2 = base

21 = base

Therefore, the missing dimension of the triangle is the base, which has a length of 21 feet.

This means that the triangle has a height of 6 feet and a base of 21 feet, and its area is 14 square feet. The height of a triangle is the perpendicular distance from the base to the opposite vertex, and in this case, it is given as 6 feet. The base of a triangle is the side opposite the height, and we have found that it has a length of 21 feet.

In summary, we can find the missing dimension of a triangle by using the formula for the area of a triangle and the given dimensions. In this case, we found that the missing dimension is the base, which has a length of 21 feet, and we know that the height is 6 feet.

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The expression for r in terms of R is: r = (1-R²) / R²

In mathematics, the square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because 3 multiplied by itself gives 9:

3 x 3 = 9

The square root symbol is √, and the number under the symbol is called the radicand. So, √9 is read as "the square root of 9."

Starting with the given equation:

R = √(r-1) / √(r+1)

Let's first clear the square roots by squaring both sides:

R² = (r-1) / (r+1)

Now, let's multiply both sides by (r+1) to eliminate the denominator on the right-hand side:

R²(r+1) = r-1

Expanding the left-hand side:

R²r + R² = r-1

Subtracting R²r from both sides:

R² - R²r = -1

Factoring out R² on the left-hand side:

R²(1-r) = -1

Dividing both sides by (1-r):

R² = -1 / (1-r)

Finally, we can take the square root of both sides and multiply by -1 to isolate r:

r = -1 / R² + 1

Therefore, the expression for r in terms of R is:

r = (1-R²) / R²

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Make r the subject of the following:

R= √(r-1) / √(r+1)

Answer:

A

Step-by-step explanation:

Since both the x and y coordinates changed signs, this is a reflection over the origin. A reflection over the origin is a reflection across both axes.

Answer: A

a) The linear function that gives the sales in x years after 2011 is of: S(x) = 18x + 191.

b) The slope of the graph of S(x) is of 18, meaning that the sales increase by 18 million a year.

c) The online sales were of 227 billion in the year of 2013.

The slope-intercept representation of a linear function is given by the equation presented as follows:

y = mx + b

The coefficients of the function and their meaning are described as follows:

We take 2011 as the reference year, when the sales were of 191 billion, hence the parameter b is given as follows:

b = 191.

In 3 years, the sales increased by 54 billion, hence the slope m is given as follows:

m = 54/3

m = 18.

Hence the function modeling the sales in x years after 2011 is given as follows:

y = 18x + 191.

The sales were of 227 billion x years after 2011, for which y = 227, hence:

227 = 18x + 191

18x = 36

x = 2.

2 + 2011 = 2013.

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Answer:

B. y = (x+1)(x-3)

Step-by-step explanation:

Bbecause when y intersect the x axis, y = 0

so (x+1)(x-3) = 0, which we get x = -1 and x = 3

As shown in the graph this is true, because the function does indeed also intersect with the x axis at x = -1 and x = 3 as well.

The graph showing one cycle of the trigonometric function y = 8 cos 8x is plotted and attached

Trigonometric graphs are graphical representations of trigonometric functions, which are functions that relate the angles of a right triangle to the ratios of its sides. The three most commonly used trigonometric functions are

The graphs of these functions are periodic, meaning they repeat themselves over a regular interval.

In the problem, the graph plotted is that of cosine function and the amplitude of is 8

The 5 points marked are

(-π/16, 0) - the first point

(0, 8) - showing the amplitude and 1/4 cycle

(π/16, 0) - 1/2 cycle

(-π/16, -8) - 3/4 cycle

(3π/16, 0) - one complete cycle

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Answer:

false, 216° turns 3/5 in a 360° rotation

The value of x that makes the given image to be a rectangle is: x = 2.5

The length of the diagonals of a rectangle are equal and congruent to each other. It is also pertinent to note that the diagonals of a rectangle bisect each other at the center. Thus:

From the given parameters, we see that half of the diagonals have been labelled and as such we have:

8x - 3 = 4x + 7

Rearrange to have like terms on same side and so we have:

8x - 4x = 7 + 3

4x = 10

x = 10/4

x = 2.5

Thus, the value of x from the calculation above of the rectangle is 2.5

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lets use the two given points to form a system of equations and solve for the values of a and b.

Starting with the given equation:

y = ab

At point (2, 60):

60 = ab^(2)

At point (4, 960):

960 = ab^(4)

Now we can solve for a and b using algebraic manipulation.

First, we can divide the second equation by the first equation:

960/60 = (ab^(4))/(ab^(2))

16 = b^(2)

Taking the square root of both sides, we get:

b = 4

Substituting b = 4 into either of the two equations, we can solve for a:

60 = a(4^(2))

60 = 16a

a = 60/16

a = 15/4

Therefore, the values of a and b are:

a = 15/4

b = 4

So the exponential function is:

y = (15/4) * 4^x

"another way, same answer "

Answer: A

Step-by-step explanation:

Experiment Random Variable (x)Possible values of the random variable Discrete or Continuous.

a) Take a 20-question examination Number of questions answered correctly Discrete (0, 1, 2, 3, ..., 20)

b. Observe cars arriving at a tollbooth Number of cars arriving at tollbooth for 1 hour Discrete (0, 1, 2, 3, ...)

c. Audit 50 tax returns Number of returns containing errors Discrete (0, 1, 2, 3, ...)

d. Observe an employee’s work Number of nonproductive hours in an eight-hour workday Continuous

e.Weigh a shipment of goods Number of pounds Continuous Random variables are numerical values that are a result of a random experiment. Random variables are generally classified into two categories

Solution:

discrete random variables and continuous random variables

.Discrete random variables

 When a random variable can assume only a countable number of values, it is called a discrete random variable.

Examples: the number of cars passing by a particular point of a highway in a day or the number of customers served by a shop in a day.

Continuous random variables: 

When a random variable can assume any value within a given range or interval, it is called a continuous random variable.

Examples: temperature, the weight of a person, or the height of a person.Tax returns: The random variable is discrete, as it can only take certain values (0, 1, 2, 3, and so on) since the number of tax returns containing errors is an integer.The shipment of goods: The random variable is continuous because it can assume any value between the minimum and maximum weight of the shipment, and the weight of the shipment can be any value.

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The volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant is π units cubed. The curve is not provided here. Therefore, it is impossible to solve this question. We are unable to determine the function whose graph is being revolved around the y-axis based solely on the information given.If the curve had been given, we would have used the disk method, which states that the volume of a solid of revolution generated by rotating a plane figure about a line is equal to the sum of the volumes of an infinite number of infinitesimally thin disks perpendicular to that line. If f(x) is a non-negative function defined on [a, b], then the volume V of the solid generated by revolving the region between the curve y = f(x), the x-axis, x = a, and x = b about the y-axis is given by:V = π∫ab[f(x)]2 dxWhere π is the constant π = 3.14159..., a and b are the limits of integration, and f(x) is the function whose graph is being revolved.

It is also important to avoid ignoring any typos or irrelevant parts of the question and to not repeat the question in the answer unless necessary. Finally, when using math terminology or solving math problems, it is important to show all work and use proper notation.

For example, when solving a problem such as "find the volume of the solid generated by revolving about the y-axis the region under the curve in the first quadrant. if the answer does not exist, enter dne. otherwise, round to four decimal places," one might use the formula for finding the volume of a solid of revolution:V=π∫abf(x)2dxwhere f(x) is the function defining the curve, and a and b are the limits of integration. The limits a and b can be found by setting the equation defining the curve equal to zero and solving for x.

Once the limits are found, the function can be integrated and the result can be multiplied by π to find the volume of the solid. The answer should then be rounded to four decimal places and, if the answer does not exist, the answer should be entered as dne.

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Regional identities have led to independence movements in the United Kingdom but not in Mexico because of the history of the regions' existence as separate states in the United Kingdom.

Reason of regional identities:

In the United Kingdom, there are four countries with distinct regional identities: England, Scotland, Wales, and Northern Ireland. Each of these countries has a unique culture, language, and history, which has led to a sense of national pride and identity.Regional identities in the United Kingdom have played a significant role in independence movements.

        For example, Scotland has a long history of wanting independence from the United Kingdom. The country was an independent state until it joined the United Kingdom in 1707.

              However, many Scottish people feel that their cultural and political identity is different from the rest of the United Kingdom and have called for a referendum on Scottish independence.Mexico, on the other hand, is a unitary state with a strong central government. The country has a long history of political and cultural unity, which has led to a sense of national identity.

      Therefore, the history of the regions' existence as separate states in the United Kingdom best explains why regional identities have led to independence movements in the United Kingdom but not in Mexico.

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The first four terms of the sequence are 3, -15, 75, and -375.

In a arithmetic sequence, the common difference is the fixed value that is added to (or subtracted from) each term to get the next term in the sequence.  

To find the first four terms of the sequence given by aₙ= 3(-5)ⁿ⁻¹, we simply substitute n = 1, 2, 3, and 4, respectively, into the formula for an and evaluate:

a₁= 3(-5)¹⁻¹ = 3(-5)⁰= 3(1) = 3

a₂ = 3(-5)²⁻¹ = 3(-5)¹= -15

a₃ = 3(-5)³⁻¹ = 3(-5)²= 75

a₄= 3(-5)⁴⁻¹ = 3(-5)³= -375

Therefore, the first four terms of the sequence are 3, -15, 75, and -375.

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Answer:

Option D.

Step-by-step explanation:

To find hypotenuse [tex]c[/tex] use formula:

                                    [tex]\text{Cos(B)}=\frac{a}{c}[/tex]

       After substituting [tex]B=62^0[/tex]  and a = 7 we have:

                                 [tex]\text{cos}(62^o)=\frac{7}{c}[/tex]

                                     [tex]0.4695=\frac{7}{c}[/tex]

                                         [tex]c=\frac{7}{0.4695}[/tex]

                                          [tex]c=14.9104[/tex]

The first thing the surveyor did when he surveyed the new neighborhood was to reference the legal description of the property.

A legal description is a precise way of identifying and describing real estate in a manner that is legally sufficient to enable it to be transferred, sold, or mortgaged. Legal descriptions can take various forms, including metes and bounds, government rectangular survey, and lot and block descriptions.

In the case of Happy Acres, the surveyor created a lot and block survey for the new residential development. In this type of survey, the lots are identified by a number or letter, and the blocks are identified by a number.

This type of description is based on a recorded plat, which is a map or plan of a subdivision that has been legally recorded with the appropriate government agency.

Before creating the lot and block survey, the surveyor would have first referenced the legal description of the property, which would have provided the necessary information to accurately locate and describe the boundaries of the new development.

This legal description could have been obtained from various sources, including deeds, recorded plats, and other legal documents.

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The value of x for the angle 100 + x under the top parallel line is equal to -10.

When a transversal line intersects a pair of parallel lines, several angles are formed which includes: Corresponding angles, vertical angles, and alternate angles.

The angle 100 + x formed by the top parallel line and the transversal line perpendicular to to it is equal to 90° so we can solve for the value of x as follows:

100 + x = 90

subtract 100 from both sides

x = 90 - 100

x = -10.

Therefore, the value of x for the angle 100 + x under the top parallel line is equal to -10.

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