2
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The corresponding sides of the triangles are congruent.
B. The corresponding angles of the triangles are congruent.
C. The triangles have the same shape and size.
D. The triangles have the same shape, but not the same size.
SUBMIT

The speed of sound at the coldest place on Earth. Temperatures on the East Antarctic Plateau can reach -100° C is B. 231 m/s

In this equation, v signifies the pace of sound measured in meters per second, while T represents the temperature expressed in Celsius degrees; and 273.15 denotes the standardized temperature in Kelvin.

When substituting T value as -100°C into our function implies that:

v = 331.3 * ✓(-100)/273.15)

v = 231 m/s

Thus, select option indicating 231 m/s.

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The volume using the dimensions 13m 5m and 9m​ is 585 cubic meters

Volume is calculated using the three dimensions, hence to talk about volume we have a 3 dimensional perspective.

The formula for volume is given as the product of length, width, and depth or thickness.

this is represented mathematically as

length x width x depth

Information from the problem have it that

length = 13 m

width = 5m

depth = 9m

plugging in the values results to

= 13 * 9 * 5

= 585 cubic meters

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The area of the polygon to the nearest tenth is 471.7 units²

A polygon is any closed curve consisting of a set of line segments (sides) connected such that no two segments cross. Examples of polygon include triangle, quadrilateral, pentagon e.t.c.

The area of a polygon is expressed as;

A = 1/2( asn)

where a is the apothem and s is the side length and n is the number of side.

To calculate the area, we have to know the side length.

side length = apothem × 2tan(180/n)

= 12 × 2 tan(180/9)

= 12 × 2 × 0.364

= 8.736

Therefore area of the polygon

= 1/2 × 12 × 8.736 × 9

= 943.49/2

= 471.7 units² (nearest tenth)

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The maximum total number of observations with a deviation of at least 5 is 1.

If the sum of deviations of 100 observations from 20 is 5, then the maximum total number of them, such that each of which is at least 5, can be found by considering the minimum deviation for the other observations.

Since we want the maximum total number of observations with a deviation of at least 5, let's assume all other observations have a deviation of 0 (meaning they are equal to 20). Let x be the number of observations with a deviation of at least 5. Then, the sum of deviations can be represented as:

5x + 0(100-x) = 5

Solving for x, we get:

5x = 5
x = 1

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If we know the 4 numbers used but do not know the order, there are 24 possible combinations to use to find the password.

When you have 4 distinct numbers and need to find the order, you are looking to determine the number of possible combinations.
A combination is an arrangement of items in a specific order. In your case, you are trying to find the possible arrangements for the 4 numbers you know, which can be used to unlock the password.
To calculate the number of combinations, you can use the formula for permutations, which is n!/(n-r)!, where n is the total number of items (numbers) and r is the number of items you want to arrange.
In this situation, n = 4 (the 4 numbers you know), and r = 4 (since you want to arrange all of the numbers). Applying the formula, you'll have:
4!/(4-4)!
4! (which is 4 x 3 x 2 x 1) divided by 0! (0! is equal to 1)
4! = 24
So, you have 24 different possible combinations for the order of the 4 numbers. To find the correct password, you would need to try each of these 24 combinations.

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The value of x is 3 in a right triangle for the u side angle having equation u = 9x+6.

Angle v = 57

Angle u =9x+6

The right angle triangle follows a rule that the sum of the two acute angles is 90 degrees. That means the angles u + v must be equal to 90 degrees.

v + u = 90

From the given angle equations, we can write

57 + 9x + 6 = 90

9x + 63 = 90

9x = 90-63

9x = 27

x = 27 ÷ 3

x = 3

Therefore we can conclude that the value of x is 3.

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A graph of the piecewise function is shown on the coordinate plane in the image attached below.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is decreasing over the interval x < -1 and increasing over the interval x ≥ −1.

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Answer:

y = 3x + 15

Step-by-step explanation:

The slope-intercept form is y = mx + b

m = the slope

b = y-intercept

Slope = rise/run or (y2 - y1) / (x2 - x1)

Points (-3,6) (-2,9)

We see the y increase by 3 and the x increase by 1, so the slope is

m = 3

Y-intercept is located at (0,15)

So, the equation is y = 3x + 15

The rectangular coordinates of each point (4, 60°) are (2, 2 * sqrt(3)). To find the rectangular coordinates of a point given in polar coordinates, we use the following formulas:

[tex]x = r cos(theta)[/tex]
[tex]y = r sin(theta)[/tex]

where r is the distance from the origin (also known as the radial coordinate) and theta is the angle between the positive x-axis and the line connecting the point to the origin (also known as the angular coordinate).

For example, let's say we have a point given in polar coordinates as (4, 60°). To find its rectangular coordinates, we plug in the values into the formulas:

x = 4 cos(60°) = 4 * 0.5 = 2
y = 4 sin(60°) = 4 * sqrt(3)/2 = 2 * sqrt(3)

Therefore, the rectangular coordinates of the point (4, 60°) are (2, 2 * sqrt(3)).

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Yes, it is possible to have a nonzero q-module (q-vector space) with finitely many elements. A nonzero q-module has at least two elements, which distinguishes it from the trivial module containing only the zero element. When the module has finitely many elements, it is referred to as a finite q-module.

In a q-module, the elements are combined through operations that follow the module's underlying ring or field structure. For instance, in a q-vector space, the operations are defined over a field, like the rational numbers (Q) or real numbers (R). These operations adhere to certain rules such as associativity, commutativity, and distributivity.

An example of a finite q-module is the integers modulo n (Z/nZ) as a Z-module, where n is a positive integer. In this case, there are n elements (0, 1, 2, ..., n-1), which form a finite set. The operations of addition and scalar multiplication are performed modulo n, making this a finite module.

In summary, it is possible to have a nonzero q-module with finitely many elements, known as a finite q-module. The operations within the module follow the rules set by its underlying ring or field, allowing for a structured combination of its elements.

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AnswerAnswer:1/11

Step-by-step explanation:

The given triangle with side lengths 3, 4, and 5 is a right triangle which can be proved by applying the Pythagoras theorem.

To prove that the given measures of a triangle are typically the measures of a right triangle, we will use the support from Pythagorean theorem. It states that in a right triangle, the sum of the squares of the base and perpendicular is equal to the square of the hypotenuse of the triangle. Hypotenuse is the side opposite to the perpendicular which is diagonally inclined.

In this case, we will put the values as follows:

3² + 4² = 5²

= 9 + 16 = 25

= 25 = 25

This triangle is a right triangle because the squares of the two shorter sides added together equal the square of the longest side.

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Correct question:

Decide if the triangle is a right triangle. Use pencil and paper. How can you use your results to decide if a triangle with side lengths 3​, 4​, and 5 is a right​ triangle?

Answer:

  5/8 apple

Step-by-step explanation:

You want to know each person's share if 5 apples are shared equally among 8 people.

A 1/8 share of the 5 apples is ...

  (1/8) × (5 apples) = 5/8 apple

Each person gets 5/8 apple.

__

Additional comment

This can be nicely accommodated by dividing 4 apples in half, and one apple into 8 equal slices. Then each person gets 1/2 + 1/8 = 5/8 of the total number of apples.

Compound statements that are made up of the same simple statements and have the same corresponding truth values for all true-false combinations of these simple statements are said to be logically equivalent.

In other words, if two compound statements are logically equivalent, they have the same truth value for every possible combination of truth values of the simple statements that they are composed of. This means that the logic of the two statements is exactly the same, and they can be used interchangeably in any logical argument or deduction.

For example, the compound statement "not (A or B)" is logically equivalent to "not A and not B". This can be shown using a truth table, which lists the truth values of the compound statement for all possible combinations of truth values of A and B. In this case, the truth table shows that the two compound statements have the same truth values for all possible combinations of A and B, and therefore they are logically equivalent.

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In the year 2003, which is one year after 2002, 500 hamburgers were consumed per person in Michigan.

y = ( 5,000 175,000 x)(1/2)   where y represents the average number of hamburgers consumed by people in Michigan and x is the number of times since 2002.   To find the time when 500 hamburgers were consumed per person, we need to  break for x in the equation  

500 = ( 5,000 175,000 x)(1/2)  

Squaring both sides of the equation,

we get   =  5,000 175,000 x  

Simplifying, we have   x =  245,000

 Dividing both sides by 175,000, we get   x = 1.4  

thus, 500 hamburgers were consumed per person in Michigan1.4 times after 2002. To find the time, we add1.4 to 2002  

20021.4 = 2003.4

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The unit circle), and the curve does not oscillate rapidly or change direction abruptly, so we would expect the arc length to be less than 2.

To find the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1, we can use the following formula for arc length:

L = ∫√(dx/dt)^2 + (dy/dt)^2 dt, where the integral is taken over the range of t.

Taking the derivatives of x and y with respect to t, we have:

dx/dt = -sin(4t)sin(cos(4t))

dy/dt = cos(4t)sin(cos(4t))

Substituting these into the formula for arc length, we get:

L = ∫√((-sin(4t)sin(cos(4t)))^2 + (cos(4t)sin(cos(4t)))^2) dt

L = ∫√(sin^2(4t)sin^2(cos(4t)) + cos^2(4t)sin^2(cos(4t))) dt

L = ∫√(sin^2(cos(4t))) dt

L = ∫|sin(cos(4t))| dt

Since we know that the sine function oscillates between -1 and 1, we can see that the absolute value of sin(cos(4t)) is always between 0 and 1. Therefore, the integral of |sin(cos(4t))| over the range 0 to 1 gives us the total distance traced out by the curve, which is the arc length.

Evaluating the integral, we get:L = ∫|sin(cos(4t))| dt = ∫sin(cos(4t)) dt

Let u = cos(4t), then du/dt = -4sin(4t), and dt = -du/(4sin(4t))

Substituting for dt and u, we have:

L = ∫sin(u) * (-du/(4sin(4t))) = (-1/4) ∫sin(u) du = (-1/4)cos(u) + C

Substituting back for u and simplifying, we get:

L = (-1/4)cos(cos(4t)) + C

To find the constant C, we use the fact that L = 0 when t = 0:

0 = (-1/4)cos(cos(0)) + C = (-1/4)cos(1) + C

C = (1/4)cos(1)

Therefore, the arc length traced out by the parametric curve x = cos(cos(4t)), y = sin(cos(4t)) as t goes through the range 0 to 1 is:

L = (-1/4)cos(cos(4t)) + (1/4)cos(1)

L = (-1/4)cos(cos(4)) + (1/4)cos(1)

L ≈ 0.615

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I understand you're asking about the volume percentage removed from a solid box when a cube is removed from each corner. Let's consider the dimensions of the original box as L cm x W cm x H cm. When a cube of side length x cm is removed from each corner, there are a total of 8 corners (since a box has 8 corners).

The volume of each removed cube is x^3 cubic cm. Since there are 8 cubes removed, the total volume removed is 8 * x^3 cubic cm. The volume of the original box is L * W * H cubic cm.

Now, to calculate the percentage of the original volume removed, we use the formula:

[tex]Percentage removed = (Total volume removed / Original volume) * 100[/tex]

In this case, it would be:

Percentage removed = (8 * x^3) / (L * W * H) * 100

Keep in mind that the specific values of L, W, H, and x would be needed to calculate the exact percentage of the original volume removed. However, the general formula above can be used to determine the percentage removed for any solid box with given dimensions and removed cubes.

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Answer:

mean is the answer

Step-by-step explanation:

because mean or average is when the numbers of different value is added over the number you added

for example

the average of 5+4+5+6+4 is

5+4+5+6+4/5

24/5=4.8

THANK YOU

MAY I GET BRAINLIEST

The expected number of patients experiencing flulike symptoms is 17.33.

Based on the information given, researchers selected 825 patients at random who take a certain widely-used prescription drug daily. In a clinical trial, 22 out of the 825 patients complained of flulike symptoms. The researchers' hypothesis is that more than 2.1% of this drug's users experience flulike symptoms as a side effect.

To test this hypothesis, we can use a one-tailed hypothesis test with a significance level of 0.01. The null hypothesis (H0) is that the proportion of patients experiencing flulike symptoms is equal to or less than 2.1%. The alternative hypothesis (Ha) is that the proportion of patients experiencing flulike symptoms is greater than 2.1%.

To calculate the test statistic, we first need to find the expected number of patients experiencing flulike symptoms under the null hypothesis. This is equal to the sample size (825) multiplied by the proportion of patients experiencing flulike symptoms under the null hypothesis (0.021). So, the expected number of patients experiencing flulike symptoms is 17.33.

Next, we can calculate the test statistic using the formula:

z = (x - μ) / σ

where x is the observed number of patients experiencing flulike symptoms (22), μ is the expected number of patients experiencing flulike symptoms under the null hypothesis (17.33), and σ is the standard deviation of the sampling distribution, which can be approximated by:

σ = sqrt[(p * (1 - p)) / n]

where p is the proportion of patients experiencing flulike symptoms under the null hypothesis (0.021) and n is the sample size (825).

Plugging in the values, we get:

z = (22 - 17.33) / sqrt[(0.021 * (1 - 0.021)) / 825] = 2.17

Looking up the critical value for a one-tailed test with a significance level of 0.01, we find that it is 2.33. Since our test statistic (2.17) is less than the critical value (2.33), we fail to reject the null hypothesis.

Therefore, we do not have sufficient evidence to conclude that more than 2.1% of this drug's users experience flulike symptoms as a side effect at the 0.01 level of significance.

In the given scenario, researchers selected 825 patients who take a certain prescription drug daily. Out of these, 22 patients experienced flulike symptoms. The hypothesis being tested is whether more than 2.1% of this drug's users experience flulike symptoms as a side effect at the α=0.01 level of significance. Since np₀(1-p₀) = 17.0 > 10, the sample size is less than 5% of the population size, and the patients were selected randomly, all requirements for testing the hypothesis are satisfied.

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False.

If A is a 5×4 matrix and B is a 4×3 matrix, then the entry of AB in the 3rd row / 2nd column is obtained by multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

If A is a 5×4 matrix and B is a 4×3 matrix, then the entry of AB in the 3rd row / 2nd column is obtained by multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

To see why, let C = AB be the product of A and B. Then, by definition, the entry in the i-th row and j-th column of C is given by the dot product of the i-th row of A and the j-th column of B. That is, Cij = Ai1B1j + Ai2B2j + ... + Ai4B4j, where Ai1, Ai2, ..., Ai4 are the entries in the i-th row of A and B1j, B2j, ..., B4j are the entries in the j-th column of B.

So, in this case, the entry in the 3rd row / 2nd column of C is given by C32 = A31B12 + A32B22 + A33B32 + A34B42. This involves multiplying the 3rd row of A by the 2nd column of B, not the 3rd column of A by the 2nd row of B.

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Does the representation show a quadratic function f(x) = 2x² + 1: B. yes.

In Mathematics and Geometry, a quadratic function can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic function is represented by the following equation;

ax² + bx + c = 0

Where:

By comparison, we have the following:

ax² + bx + c = 2x² + 1

a = 2

b = 0

c = 1

In conclusion, we can logically deduce that f(x) = 2x² + 1 represent a quadratic function.

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Answer:

-3,825

Step-by-step explanation:

When two numbers vary directly, they have a proportional relationship. That is to say that there is a constant ratio between them. In this case, we are given the ratio of x to y as:

x : y

1/2 : 150

We can make this a unit ratio by multiplying both sides by 2.

x : y

1 : 300

What this unit ratio tells us is that to find the corresponding y-value for any value of x, we can multiply the x-value by 300:

[tex]-\dfrac{51}{4} \cdot 300 = \boxed{-3,825}[/tex]

Therefore, there are 8820 groups of 9 that contain 5 women and 4 men using combination formula.

To solve part (b)(i), we need to use the combination formula. The number of ways to choose 5 women out of 9 is given by the combination C(9,5), which is:

C(9,5) = 9! / (5! * 4!)

= 126

Similarly, the number of ways to choose 4 men out of 8 is given by the combination C(8,4), which is:

C(8,4) = 8! / (4! * 4!)

= 70

To get the total number of groups of 9 that contain 5 women and 4 men, we need to multiply these two numbers:

126 * 70 = 8820

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Answer:

-4/-12 or simplified would be 1/3

Step-by-step explanation:

It cannot be determined whether the data supports the conclusion that blocking was effective in reducing experimental error at the 95% confidence level. To assess the effectiveness of blocking, it is necessary to examine the specific data and perform appropriate statistical tests, such as Analysis of Variance (ANOVA).

Blocking is a technique used in experimental design to control for extraneous factors that may affect the results. It involves grouping experimental units with similar characteristics and then applying treatments within those groups. This method helps isolate the effect of the treatment and reduce variability in the data.

To determine if there is sufficient evidence to conclude that blocking is effective in this case, one must examine the experimental data and conduct a statistical test, such as ANOVA. This test allows researchers to compare the means of different groups and determine if there are significant differences. If the p-value obtained from the ANOVA test is less than the significance level (typically 0.05 for a 95% confidence level), it can be concluded that blocking was effective in reducing experimental error.

In summary, without access to the specific data and results from statistical tests, it is not possible to confirm whether the blocking method was effective in reducing experimental error at the 95% confidence level.

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Step-by-step explanation:

four million seven hundred thousand can be written by

4,700,000

Answer: 88

Step-by-step explanation:

First, separate into familiar shapes

The area of the triangles at each side is 10 because the formula is length times times width divided by 2, when you plug the numbers in, 5 times 4 divided by two, times 2 because there are two triangles which equals 20.

That leaves the rectangle and the formula for the area of a rectangle is length times width, 17 times 4 which equals 68.

Add them, 20 plus 68 equals 88.

There are 126 ways in which four people can be chosen to stand up out of nine people sitting in chairs.

We have,
The combination formula is:

C(n, r) = n! / (r! (n-r)!)

In this case,

n = 9 (total number of people) and r = 4 (number of people to be chosen to stand up).

Step 1: Calculate n! (9!): 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Step 2: Calculate r! (4!): 4 x 3 x 2 x 1 = 24

Step 3: Calculate (n-r)! (5!): 5 x 4 x 3 x 2 x 1 = 120

Step 4: Plug these values into the combination formula: C(9, 4) = 362,880 / (24 * 120)

Step 5: Calculate the result: C(9, 4) = 362,880 / 2,880 = 126

Thus,

There are 126 ways in which four people can be chosen to stand up out of nine people sitting in chairs.

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To write the equation of a line passing through the point (8,4) and parallel to 8x-y=6, we need to first find the slope of the given line. We can rewrite the given line in slope-intercept form y=8x-6, where the slope is 8.

Since the new line is parallel to the given line, it will have the same slope of 8. Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is the given point and m is the slope.

Substituting in the values, we get:

y - 4 = 8(x - 8)

Expanding and simplifying, we get:

y = 8x - 60

This is the equation of the line in slope-intercept form.

To convert it to standard form, we move all the variables to one side and simplify:

-8x + y = -60

This is the equation of the line in standard form.

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We can say with 90% confidence that the true mean concentration of uric acid in the population lies between 4.32 and 6.24 mg/dl.

To find the 90% confidence interval for the population mean concentration of uric acid, we can use the formula:

CI = x' ± z*(σ/√n)

where:

x' = sample mean concentration = 5.28 mg/dl

z = z-score for 90% confidence level = 1.645 (from standard normal distribution table)

σ = population standard deviation = 1.77 mg/dl

n = sample size (number of tests taken) = 13

Substituting the given values into the formula, we get:

CI = 5.28 ± 1.645 x (1.77/√13)

CI = 5.28 ± 0.96

CI = (4.32, 6.24)

Therefore, we can say with 90% confidence that the true mean concentration of uric acid in the population lies between 4.32 and 6.24 mg/dl.

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