Are these triangles similar, congruent or neither? What theorem supports your answer?
options:

Similar: AA


Similar: SAS


Similar: SSS


Congruent: HL


Congruent: ASA


Congruent: AAS


Neither

In order to be correct, a line graph of the number of marriages per year in the United States must have years on the

horizontal scale.

It is defined as the process of adding more instances of the same type to the existing pool of resources and not

increasing the capacity of existing resources like in vertical scaling. This kind of scaling also helps in decreasing the

load on the server. This is called Horizontal Scaling

This allows for a clear representation of the number of marriages over time. To create such a graph, follow these steps:

1. Label the horizontal axis with years, making sure to use equal intervals between each year.

2. Label the vertical axis with the number of marriages.

3. Plot the data points for each year, representing the number of marriages.

4. Connect the data points with a line to show the trend over time.

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The volume of the oblique prism is 75 cm³, which is option D.

An oblique prism is a three-dimensional geometric shape that has two parallel and congruent bases that are connected by parallelogram-shaped lateral faces. Unlike a right prism, the lateral faces of an oblique prism are not perpendicular to the base faces.

The formula for the volume of an oblique prism is given by:

Volume = Base Area × Height

Since the base of the prism is a square, its area is given by:

Base Area = Side × Side = 5 × 5 = 25 square centimeters

Substituting this and the height given as 3 cm in the formula for the volume, we get:

Volume = Base Area × Height

= 25 × 3

= 75 cubic centimeters

Therefore, the volume of the oblique prism is 75 cm³, which is option D.

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Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

An structured of integers or objects that adhere to a particular pattern or rule is referred to as a sequence in mathematics. The name for each number or item in the sequence is. A series can be explicitly created or defined recursively, and it can be infinite or finite. A method or rule that directly expresses the n - th term of the series in terms of n defines an explicit sequence. For instance, the explicit sequence 2, 4, 6, 8, 10,... has the formula a = 2n, where n is the term's position inside the sequence. A starting value and recursive formula that determines the nth word of the series in terms of the preceding terms describe a recursive sequence.

given

The number sequence is as follows: 64, -128, 256, -512.

We must determine the common ratio between the following terms in order to get the rule for this sequence.

Any term can be divided by its previous term to obtain the common ratio (r). For instance, the result of subtracting the second term (-128) from the first term (64) is

r = (-128) / 64 = -2

The third term (256) divided by the second term (-128) results in:

r = 256 / (-128) = -2

And when the fourth term (-512) is divided by the third term (256), the result is

r = (-512) / 256 = -2

We can observe that for all pairings of following terms, the common ratio is -2.

Now we can apply the following formula to a geometric sequence's general term:

a = a1 * r^(n-1) (n-1)

where r is the common ratio and a1 is the first term.

In place of the values we hold:

[tex]a = 64 * (-2)^(n-1) (n-1)[/tex]

Thus, the following is the rule for the given geometric sequence: [tex]a = 64 * (-2)^(n-1) (n-1)[/tex]. Thus, the solution is (C) a = 64(-2)n-1.

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The probability of choosing water and Black & White Sundae is 1/6.

Probability is a measure of the likelihood or chance of an event occurring. It is represented as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event.

a. Image is attached below.

b. The probability of choosing water and Black & White Sundae is the product of the probabilities of choosing water and Black & White Sundae given that water was chosen. This can be calculated as:

P(Water and B&W Sundae) = P(Water) * P(B&W Sundae | Water)

= 1/2× 1/3

= 1/6

Therefore, the probability of choosing water and Black & White Sundae is 1/6.

c. To calculate the total number of different combinations, we need to multiply the number of drink options by the number of dessert options. Since there are 2 drink options (water and soda) and 3 dessert options (Black & White Sundae, milkshake, and banana split) with 3 different sizes for the milkshake and banana split, we can calculate the total number of different combinations as:

Total combinations = 2×(1 + 3 + 3×3)

= 2 × 13

= 26

Therefore, there are 26 total different combinations.

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The 69.15% of the corks produced by the machine are acceptable. 80% of all corks produced by the machine have diameters less than 3.0772cm.

a) To find the percentage of acceptable corks, we have to calculate the area under the normal distribution curve corks have diameters between the limits of 2.95 cm and 3.05 cm.

Let X be the diameter of the corks produced by the machine. Then X follows a

The corks with diameters that have a normal distribution with mean μ = 3.01 cm

Standard deviation σ = 0.08cm.

Using the standard normal distribution, we can standardize X as follows:

Z = (X - μ) / σ

= (X - 3.01) / 0.08

The probability that Z lies between (2.95 - 3.01) / 0.08 = - 0.75

The probability that Z lies between(3.05 - 3.01) / 0.08 = 0.50.

Using a standard normal table that this probability is approximately 0.6915.

Therefore, the percentage of acceptable corks produced by the machine is 69.15%.

b) To find the diameter D such that 80% of the corks produced by the machine have diameters less than D.

Using the standard normal distribution the Z-score that corresponds to the 80th percentile is:

Z = InvNorm(0.8)

= 0.84

We can then solve for D:

D = μ + Zσ

= 3.01 + 0.84(0.08)

= 3.0772

Therefore, 80% of all corks produced by the machine have diameters less than 3.0772cm.

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Answer:

a. Similar

Step-by-step explanation:

The question says the triangles are right triangles, so they can't be obtuse or equilateral.

Since they are both right triangles, they both have a 90° angle. And as stated in the question, they both have a 30° angle. By Angle-Angle (AA) they are similar. But we don't know anything about any sides in either triangle, so we don't know if they are congruent or not. Just we can only know they are similar.

Answer

sqrt 544 feet

Step-by-step explanation:

Pythagorean theorem: a^2 + b^2 = c^2

12^2 + 20^2= c^2

144+400=c^2

544=c^2

c= sqrt 544

The time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters, and other solutions are below

To do this, we find h when t = 0

From the graph, we have

h(0) = 70

So, the height of the cannot at launch is 70 meters

From the graph, we have the vertex to be

Vertex, (t, h) = (3, 114.1)

So, the time to reach the maximum height is 3 seconds

From the graph, we have the vertex to be

Vertex, (t, h) = (3, 114.1)

So, the maximum height is 114.1 meters

This is when h(t) = 0

From the graph, we have

h(7.93) = 0

So, the time spent is 7.93 seconds

The given equation is

h(t) = -4.9t^2 + 29.4t + 70

If the initial velocity changes, then the equation becomes

h(t) = -4.9t^2 + 40.5t + 70

The given equation is

h(t) = -4.9t^2 + 29.4t + 70

If the initial height changes, then the equation becomes

h(t) = -4.9t^2 + 29.4t

We have

h(t) = -4.9t^2 + 29.4t

Differentiate and set to 0

-9.8t = -29.4

So, we have

t = 3

Next, we have

h(3) = -4.9 * 3^2 + 29.4 * 3

h(3) = 44.1

So, the time to reach the maximum height is 3 seconds and the maximum height is 44.1 meters

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Pythagorean theorem, trigonometric ratios, Law of sines and  Law of cosines are  different ways to find the measure of a side of triangles.

There are different ways to find the measure of a side of a triangle;

 The theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. Therefore, if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, we have c²= a² + b².

if we know the measure of one acute angle (other than the right angle) and the length of the adjacent side to that angle, we can use the cosine function to find the length of the hypotenuse, or the sine function to find the length of the opposite side.

The law states that the ratio of the length of a side to the sine of the angle opposite that side is the same for all sides and angles of the triangle. Therefore, if a, b, and c are the lengths of the sides of a triangle and A, B, and C are the measures of the angles opposite those sides, we have a/sin(A) = b/sin(B) = c/sin(C).

The law states that the square of a side is equal to the sum of the squares of the other two sides minus twice the product of those sides and the cosine of the included angle. Therefore, if a, b, and c are the lengths of the sides of a triangle and C is the measure of the included angle between sides a and b, we have c² = a² + b² - 2abcos(C).

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The perimeter of triangle XYZ with the vertices, X(2, 5), Y(10 9), and Z(6, 1), is approximately 24.07 units.

To find the perimeter of the triangle, we need to add up the lengths of all three sides. To do this, we can use the distance formula, which is:

d = √[(x2 - x1)² + (y2 - y1)²]

Using this formula, we can find the length of each side of triangle XYZ:

Side XY:

d = √[(10 - 2)² + (9 - 5)²] = √64 + 16 = √80

Side YZ:

d = √[(6 - 10)² + (1 - 9)²] = √16 + 64 = √80

Side ZX:

d = √[(6 - 2)² + (1 - 5)²] = √16 + 16 = √32

Therefore, the perimeter of triangle XYZ = XY + YZ + ZX = √80 + √80 + √32

Perimeter ≈ 24.07 (rounded to two decimal places)

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Answer:

B 1/4

Step-by-step explanation:

Because one coin have 1/2 to land either side, but if it was two coins then is will double it so it will be 1/4.

These statements are false because (a)False because the complete solution to Ax = b is actually the sum of the particular solution Xp and any linear combination of the solutions in the nullspace Xn. (b) False because if the system Ax = b has a particular solution, it will always have exactly one particular solution. (c) False because if A is invertible, there is indeed a solution Xn in the nullspace, but it is only the trivial solution Xn = 0.

(a) The complete solution to Ax = b is any linear combination of Xp and Xn is false.

Mathematically, the complete solution is given by X = Xp + Xn, not just any linear combination of Xp and Xn.

(b) The system Ax = b has at most one particular solution.

This is due to the fact that the particular solution is the unique point where the affine subspace defined by the system intersects the null space of A.

(c) If A is invertible, there is no solution Xn in the null space.

An invertible matrix has a unique solution for each b, which implies that the null space only contains the zero vector.

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Answer: True.

Step-by-step explanation: A person only pays interest on the balance remaining at the end of the billing cycle. If you carry a balance beyond the grace period, your credit card issuer will charge interest. Each month you carry a balance over from the previous month, you’ll have a finance charge added to your balance.

Answer:

see the answer in the picture

Step-by-step explanation:

I don't know which equation you want. but I put both the standard and general form. but the equation should be the stander form. the radius is 13 in this case

We will see that this circle is centered at the point (-5, -49) and has a radius of 1.

For a circle of radius R centered at the point (a, b), the equation is:

(x - a)^2 + (y - b)^2 = R^2

In this case, we have:

given the equation of the circle is

x^2 + y^2 + 10x + 14y + 73 = 0

We can rewrite this as:

(x^2 + 10x) + (y^2 + 14y) + 73 = 0

(x^2 + 2*5*x + 25) + (y^2 + 2*7*y + 49) - 25 - 49 + 73 = 0

(x + 5)^2 + (y + 49)^2 -74 + 73 = 0

(x + 5)^2 + (y + 49)^2 = 1

So we have a circle centered at the point (-5, -49) with a radius equal to 1.

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complete question:

Determine the center and radius of the following circle equation

x^2 + y^2 + 10x + 14y + 73 = 0

From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

From the given situation of fisherman , linear relationship is given by

y= 2x +20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.

As given in the question,

Number of baits in the bucket of fisherman at the beginning of trip = 20

Amount of bait increases by 2 pieces every hour

Linear relationship is defined as :

'y' represent the total number of bait in the bucket after x hours.

y = 20 + 2x

Compare it with the general equation y =mx + c

Where 'm' is the slope.

Here slope is equal to 2.

According to the situation it means the amount of bait increases by 2 pieces in every hour.

Therefore, From the given situation of fisherman , linear relationship is given by y= 2x + 20 the slope for the linear relationship is defined by 2 as amount of bait increases by each hour by 2 pieces.

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Answer: Adrian will need 4 and 1/2 cups of raisins for 2.5 batches of muffins

Answer:

  x = 90

Step-by-step explanation:

You want to know the value of x in the given diagram showing crossed chords.

The Angle of Intersecting Chords theorem tells you the angle where the chords cross is half the sum of the intercepted arc and the opposite arc.

Here, the angle marked x° is the supplement of the angle we can find based on the given arc measures:

  180° -x° = (30° +(2x -30)°)/2

  180 -x = 2x/2 = x . . . . . . . . . . divide by °, simplify

  180 = 2x . . . . . . . . . . . . add x

  90 = x . . . . . . . . . . . divide by 2

The value of x is 90.

Answer:

Step-by-step explanation:

quit

After solving the linear equation Lillian is farther along in the book than Khadija after 4 days.

A linear equation is an algebraic equation of the form:

y = mx + b

where x and y are variables, m is the slope of the line, and b is the y-intercept. The slope represents how steep the line is, and the y-intercept is the point at which the line intersects the y-axis.

As we know, Lillian was on 40 pages and Khadija was on 10 pages. So, the equation is,

And Let L represent the page of the book that Lillian is on at the end of t days into the month, and let K represent the page of the book that Khadija is on at the end of t days into the month.

[tex]L(t) = 40 + 15t[/tex]   Lillian's progress after t days

[tex]K(t) = 10 + 20t[/tex]  Khadija's progress after t days

After solving the linear equation, we will get the rate of the reading page.

Let's say t=4,

[tex]L(4) = 40 + 15(4) = 100[/tex]

[tex]K(4) = 10 + 20(4) = 90[/tex]

Therefore, after 4 days, Lillian is farther along in the book than Khadija.

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Answer:

what the quistion?

Step-by-step explanation:

sry i cant spell

The probability that the first time a battery damage is observed is during the third trial or later is 42.74%.

To solve this problem, we can use the geometric distribution, which models the number of trials until the first success in a sequence of independent trials. In this case, the probability of success is 0.24 (the probability of a battery damage) and the probability of failure is 0.76 (the probability of a glass screen damage).

The probability of observing a battery damage for the first time on the third trial or later can be calculated as the complement of the probability of observing a battery damage on the first or second trial.

The probability of observing a battery damage on the first trial is 0.24, and the probability of observing a battery damage on the second trial is (0.76)(0.24) = 0.1824 (the probability of no battery damage on the first trial times the probability of battery damage on the second trial). Therefore, the probability of observing a battery damage for the first time on the third trial or later is 1 - 0.24 - 0.1824 = 0.5776.

However, the question asks for the probability of observing a battery damage for the first time on the third trial or later, which means we need to take into account the fact that we may have observed a battery damage before the third trial. Therefore, we need to adjust our calculation by subtracting the probability of observing a battery damage for the first time on the first or second trial from our previous result.

The probability of observing a battery damage for the first time on the first or second trial is 0.24 + 0.1824 = 0.4224. Therefore, the probability of observing a battery damage for the first time on the third trial or later is 0.5776 - 0.4224 = 0.1552 or 15.52%.

Therefore, the probability that the first time a battery damage is observed is during the third trial or later is 42.74%

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Answer:

What I myself would do is plug in the given values, and we get: x = 41 * cos(220 degrees) ≈ -22.59 y = 41 * sin(220 degrees) ≈ -33.73

Therefore, the component form of the vector is (-22.59, -33.73).

Step-by-step explanation:

On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

The skew of a dataset refers to the degree to which the distribution of values is asymmetrical. A dataset is said to be skewed if the majority of the values lie on one side of the mean.

In this case, the dataset has a right skew because there are more values on the right side of the distribution (higher values) than on the left side. We can see this by noting that the median (middle value) is 3, while the mean (average value) is slightly higher at 3.375.

If the writer writes 8 more comic strips on the next day, it will increase the maximum value in the dataset from 7 to 8. This will slightly shift the distribution to the right, but the skew will remain right because the majority of the values are still clustered on the right side of the distribution.

However, the effect on the overall skew will depend on the number of comic strips the writer produces on the next day relative to the other values in the dataset. If the writer produces a large number of comic strips relative to the other values, it could shift the distribution to a more symmetrical shape.

Therefore, On the other hand, if the number of comic strips produced is similar to the other values in the dataset, it will have little effect on the overall skew.

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The probability of flipping the unfair coin given that we observed five tails in a row is approximately 0.9048

Let's define

A: the event of picking the unfair coin

B: the event of getting five tails in a row

We want to find the conditional probability of picking the unfair coin given that we observed five tails in a row, or P(A|B).

Using Bayes' theorem, we have

P(A|B) = P(B|A) × P(A) / P(B)

P(B|A) is the probability of getting five tails in a row given that we are flipping the unfair coin. Since the unfair coin is not fair, we don't know its probability of coming up as tails, but let's assume it has a probability of 0.9 of coming up as tails. Thus, P(B|A) = 0.9^5 = 0.59049.

P(A) is the prior probability of picking the unfair coin, which is 0.5 since we picked one of two coins at random.

P(B) is the total probability of getting five tails in a row, which is the sum of the probabilities of getting five tails in a row with the fair coin and the unfair coin.

The probability of getting five tails in a row with the fair coin is 0.5^5 = 0.03125. The probability of picking the unfair coin and getting five tails in a row is P(B|A) × P(A) = 0.59049 × 0.5 = 0.295245. Thus, P(B) = 0.03125 + 0.295245 = 0.326495.

Now we can calculate P(A|B)

P(A|B) = P(B|A) × P(A) / P(B) = 0.59049 × 0.5 / 0.326495 = 0.9048

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a. The null hypothesis (H0) states that the average sales per salesperson are not increased by the new remuneration scheme.

The new remuneration scheme raises the average sales per salesperson, contrary hypothesis (H1).

b. a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.

c. a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.

a. The appropriate null and alternative hypotheses are :

Null hypothesis (H0): The new compensation plan does not increase the average sales per salesperson.
Alternative hypothesis (H1): The new compensation plan increases the average sales per salesperson.

b. In this situation, a Type I error occurs if it is concluded that the new compensation plan provides a population mean weekly sales increase when, in fact, it does not.

The consequences of making this error are that the company may adopt the new compensation plan and invest resources into it, without actually benefiting from increased sales.
c. In this situation, a Type II error occurs if it is concluded that the new compensation plan does not provide a population mean weekly sales increase when, in fact, it does.

The consequences of making this error are that the company may miss out on an opportunity to increase sales by not implementing the new compensation plan, which could lead to lower profits and reduced competitiveness in the market.

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The least amount of water required to measure exactly 2 oz is 12 oz. (13 oz + 7 oz - 8 oz = 12 oz).

First, add 13 oz of water to the 20 oz bottle. The combined amount of water will now be 33 oz.

Next, pour water from the 33 oz bottle into the 13 oz bottle until the 13 oz bottle is full to the top.

The remaining amount of water in the 33 oz bottle will be 20 oz.

Now, pour out the water in the 13 oz bottle into the 20 oz bottle.

Now, the 20 oz bottle will have 13 oz of water in it. This leaves the 33 oz bottle with 7 oz of water remaining in it.

Now, pour the remaining 7 oz of water in the 33 oz bottle into the 20 oz bottle.

The 20 oz bottle will now have 20 oz + 7 oz = 27 oz of water in it.

Pour out the water in the 20 oz bottle until the amount of water in it is exactly 2 oz.

Since you started with a combined amount of 33 oz, and the amount of water remaining in the 20 oz bottle is 2 oz, the

amount of water poured out is 33 oz - 2 oz = 31 oz.

Therefore, the least amount of water required to measure exactly 2 oz is 12 oz.

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Answer:

Yes, the triangle with sides 8, 15, and 17 is a Pythagorean triple. This is because 8^2 + 15^2 = 64 + 225 = 289 = 17^2. As for the acute angle between sides 8 and 15, we can use the inverse tangent function to find it. tan(theta) = 8/15 theta = arctan(8/15) Using a calculator, we find that theta ≈ 28.07 degrees. Since we know this is an acute angle, we can conclude that it measures between 0 and 90 degrees, and is closer to 28 degrees than to 62 degrees.

Answer:

22-ounce package is the best buy as it has the lowest price per ounce.

Step-by-step explanation:

To determine which package is the best buy, we need to calculate the price per ounce of each package:

Price per ounce of 6-ounce package = 1.98 / 6 = $0.33 per ounce

Price per ounce of 14-ounce package = 4.90 / 14 = $0.35 per ounce

Price per ounce of 22-ounce package = 7.04 / 22 = $0.32 per ounce

Therefore, the 22-ounce package is the best buy as it has the lowest price per ounce.

The fraction 7/8 of a wall Michelangelo does paint in 1 minute for the given question.

In mathematics, a fraction is a representation of a part of a whole or a ratio of two quantities. It is typically represented as one number (the numerator) over another number (the denominator), separated by a horizontal line. For example, the fraction 3/4 represents three parts out of a total of four equal parts, or a ratio of three to four.

Fractions can also be represented as decimals or percentages. For instance, the fraction 1/2 is equal to the decimal 0.5 or the percentage 50%. Fractions are used in a variety of mathematical operations, such as addition, subtraction, multiplication, and division. They are also used in everyday life, such as in cooking recipes or in measurements of time or distance.

If Michelangelo paints 7/8 of a wall in 1 hour, then he paints (7/8)/1 = 7/8 of a wall in one hour.

So, the answer is 7/8 of a wall.

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Answer:

y=6x+22

Explanation:

Parallel lines have the same slope and different y-intercepts.

So, all the lines with different slopes will be eliminated.

Now, we can check which line passes through the point (3,4) by substituting x for the x coordinate and y for the y coordinate.

y=6x+22

4=6(-3)+22

4=-18+22

4=4

So, the correct answer is y=6x+22.