What do we call the underlined part of the following sentence? the lecture lasted for two hours. phrasal preposition prepositional verb phrasal verb prepositional phrase

We have defined the criteria for SAS congruency of triangles.

What is SAS?

The SAS theorem states that "Triangles are congruent if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle."

According to the SAS criteria for triangle similarity, two sides of one triangle are similar to two sides of another triangle if their included angles are congruent.

Hence, we have defined the criteria for SAS congruency of triangles.

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Step-by-step explanation:

you can just put in some values to check.

I actually used p =2 and q=3

the It will be

2^3-1 + 3^2-1 = 1 (mod 2×3)

2^2 +3^1 = 1 (mod 6)

4+3= 1 (mod6)

7= 1 (mod6)

which is true.

therefore p^(q-1) + q^( p-1) = 1 ( mod pq) is true

To show that p^(q-1) + q^(p-1) = 1 (mod pq), we can use Fermat's Little Theorem, which states that if p is a prime number and a is an integer not divisible by p, then a^(p-1) = 1 (mod p). Using this theorem, we can first show that p^(q-1) = 1 (mod q), since q is a prime number and p is not divisible by q. Similarly, we can show that q^(p-1) = 1 (mod p), since p is a prime number and q is not divisible by p.

Therefore, we can write:

p^(q-1) + q^(p-1) = 1 (mod q)
p^(q-1) + q^(p-1) = 1 (mod p)

By the Chinese Remainder Theorem, we can combine these two equations to obtain:

p^(q-1) + q^(p-1) = 1 (mod pq)

Thus, we have shown that p^(q-1) + q^(p-1) = 1 (mod pq).
We'll use Fermat's Little Theorem to show that p^(q-1) + q^(p-1) = 1 (mod pq).

Fermat's Little Theorem states that if p is a prime number and a is an integer not divisible by p, then:
a^(p-1) ≡ 1 (mod p)

Step 1: Apply Fermat's Little Theorem for p and q:
Since p and q are prime numbers, we have:
p^(q-1) ≡ 1 (mod q) and q^(p-1) ≡ 1 (mod p)

Step 2: Add the two congruences:
p^(q-1) + q^(p-1) ≡ 1 + 1 (mod lcm(p, q))

Step 3: Simplify the congruence:
Since p and q are prime, lcm(p, q) = pq, so we get:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

In your question, you've mentioned that the result should be 1 (mod pq), but based on Fermat's Little Theorem, the correct result is actually:
p^(q-1) + q^(p-1) ≡ 2 (mod pq)

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Answer:

Step-by-step explanation:cc

Answer:

Hello, I am also working on graphs at the moment!

Step-by-step explanation:

it is -8 units. If you place the points on a graph, you can see that it is going from point (4,5) and (4,-3) (the points given) now all you do is count the units between them.

Thus, the distance between the two points is, -8 units. Hope this helps! let me know if its right pls :) thx <3 (can also be written as- (0,-8) because its decreasing)

The product of a, b and c would be 6.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions do not contain an equal sign and they can't be solved for a single value. They are used to represent a value or a set of values.

The given expression is     \(\frac{\sqrt[4]{16xy^4}}{x^{\frac{1}{2}}y^{\frac{1}{2}}}\)

In order to write the expression in the form of \(ax^by^c\), we need to simplify it.

First, we simplify the fourth root of \(16xy^4\) by taking the fourth root of 16, which is 2. So, the expression becomes

\(2\frac{xy^4}{x^{\frac{1}{2}}y^{\frac{1}{2}}}\)

Next, we simplify the fraction by canceling out the\(x^{\frac{1}{2}} $$ and $ y^{\frac{1}{2}}\) from the numerator and denominator. This gives us \(2xy^3\)

So the expression in the form of \(ax^by^c\) is \(2xy^3\), where a = 2, b=1, and c=3.

the product of a, b, and c is 2 * 1 * 3 = 6.

Hence, the product of a, b and c would be 6.

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The required value of the upper limit for both the integral are,
4. a = -1 or a = 1/2
5. b = 1

The limit of a sum can be used to express the definite integral of any function, or if the interval [a, b] has an antiderivative F, the definite integral of the function is the difference of the values at points a and b.

Here,

4.
Given expression,
\(= \int _{-2}^{a}x^2dx = 7/3\\= [x^3]_{-2}^a = 7 / 3\\= a^3 + 8 / 3 = 7/3\\a=-1,\:a=\frac{1}{2}-\frac{\sqrt{3}}{2}i,\:a=\frac{1}{2}+\frac{\sqrt{3}}{2}i\)

Since as mentioned that a must be greater than -2 so the considered value of a is, a = -1 and a = 1/2, and a graph of the area of the expression is shown,

Similarly,
5.
b = 1
A graph of the area under the given integration has been shown.

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The measure of dispersion is a statistical term that refers to the degree of variability in a set of data. The extent to which the data in the set deviate from the mean or the central value is referred to as the measure of dispersion. There are several measures of dispersion, and some of them are more suitable for certain types of data than others. The following is not a measure of dispersion:

Mode. Mode is not a measure of dispersion, but rather a measure of central tendency. It represents the most frequent value in a data set. In statistics, the mode is the most common value in a data set, which is usually the highest peak of a frequency distribution graph. In summary, mode is not a measure of dispersion, but rather a measure of central tendency. Standard deviation, range, and interquartile range are all measures of dispersion. Standard deviation is a measure of how spread out the data is from the mean, while range and interquartile range are measures of how much the data is spread out from the minimum and maximum values or the median, respectively.

Therefore, if you want to find the amount of variability in a data set, you should use one of these three measures of dispersion. To summarize, the mode is not a measure of dispersion, while standard deviation, range, and interquartile range are measures of dispersion.

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Our conjecture is that the second differences of quadratic functions are constant and equal to 2a.

Given:

y = 7x² + 3x + 1

To make a table of second differences for the given polynomial function y = 7x² + 3x + 1, we will follow the below steps:

Step 1:

Compute the first differences of the polynomial function.

First Difference = y₂ - y₁ = {7(x + 1)² + 3(x + 1) + 1} - {7x² + 3x + 1} = 14x + 10

Step 2: Compute the second difference of the polynomial function.

Second Difference = First Difference₂ - First Difference₁ = {14(x + 1) + 10} - {14x + 10} = 14

Step 3: Make a table of first and second differences.

X  y = 7x² + 3x + 1 1 11 2 29 3 61 4 107 5 167

First Difference = 14x + 10 24 38 54 72

Second Difference = 14 14 14 14

Using the above table, we can make a conjecture about the second difference of quadratic functions.

The second differences between quadratic functions are constant (same) and always equal to 2a where "a" is the coefficient of the x² term in the quadratic function.

In the given quadratic function, "a" = 7, so the second difference is constant and equal to 2a=14.

Hence, our conjecture is that the second differences of quadratic functions are constant and equal to 2a.

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The 14th term of the geometric sequence 10, 20, 40, ... is 81920.

"A geometric sequence is a special type of sequence. It is a sequence in which every term (except the first term) is multiplied by a constant number to get its next term."

The geometric sequence formulas include the formulas for finding its nth term and the sum of its n terms. We will see the geometric sequence formulas related to a geometric sequence with its first term 'a' and common ratio 'r' (i.e., the geometric sequence is of form \(a, ar, ar^{2},ar^{3} ,.............\)). Here are the geometric sequence formulas.

\(a_{n}=ar^{n-1}\)

Given geometric sequence

10, 20, 40, .........

From the given sequence

\(a_{1} = 10\), \(a_{2} = 20\), \(a_{3} = 40\)

Using the formula \(a_{n}=ar^{n-1}\)

⇒ \(a_{4} = 10(2)^{3} =80\)

⇒ \(a_{5} = 10(2)^{4} =160\)

⇒ \(a_{6} = 10(2)^{5} =320\)

⇒ \(a_{7} = 10(2)^{6} =640\)

⇒ \(a_{8} = 10(2)^{7} =1280\)

⇒ \(a_{9} = 10(2)^{8} =2560\)

.

.

.

⇒ \(a_{14} = 10(2)^{13} =81920\)

Hence, the 14th term of the geometric sequence 10, 20, 40, ... is 81920.

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I believe that may be false

Answer:

Step-by-step explanation:

True.

Aldosterone is a hormone produced by the adrenal gland that plays an important role in regulating electrolyte and water balance in the body. It acts on the cells of the distal tubules and collecting ducts of the kidneys to increase the reabsorption of sodium ions and the secretion of potassium ions.

This helps to increase blood volume and blood pressure by retaining more sodium and water in the body while getting rid of excess potassium. Aldosterone release is regulated by the renin-angiotensin-aldosterone system, which is activated in response to low blood pressure or low sodium levels in the blood.

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Answer:

331776

Step-by-step explanation:

The formula for geometric

sequence is given below

ar^n-1

Where a= first term, r= common ratio

From the question, a1 = - 4, r = 6 , n= 5

Then if we substitute, we have

ar^n-1

5th term= ar^n-1

= (-4×6)^(5-1)

=-24 ^ 4

=331776

Hence, the first five terms is =331776

The formula is 5th term= ar^(5-1)

If the length of the confidence interval for the mean of a normal population is reduced by 1/3, the sample size needs to be increased.

When the population standard deviation is known, the formula for calculating the confidence interval for the mean is given by:

Confidence interval = mean ± (z * (σ/√n))

Where:

mean represents the sample mean

z is the z-score corresponding to the desired level of confidence

σ is the population standard deviation

n is the sample size

To reduce the length of the confidence interval, we need to decrease the value of (z * (σ/√n)).

Since the population standard deviation (σ) is known, the only way to decrease this value is by increasing the sample size (n).

By increasing the sample size, the standard error (σ/√n) decreases, resulting in a narrower confidence interval.

Therefore, the sample size needs to be increased to achieve a reduction in the length of the confidence interval.

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The minimum sterilization time required to achieve a 99.9% confidence level in successfully sterilizing 50 L of medium containing 10^6 contaminating organisms is approximately 1.95 minutes.

To calculate the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms, we need to use the concept of decimal reduction time (D-value) and the number of organisms.

The D-value represents the time required to reduce the population of microorganisms by one log or 90%. In this case, the given D-value is 0.65 minutes.

To achieve a 99.9% confidence level, we need to reduce the population of microorganisms by three logs or 99.9%, which corresponds to a 10^-3 reduction.

To calculate the minimum sterilization time, we can use the following formula:

Minimum Sterilization Time = D-value × log10(N0/Nf)

Where:

D-value is the decimal reduction time (0.65 minutes).

N0 is the initial number of organisms (10^6).

Nf is the final number of organisms (10^6 × 10^-3).

Let's calculate it step by step:

Nf = N0 × 10^-3

= 10^6 × 10^-3

= 10^3

Minimum Sterilization Time = D-value × log10(N0/Nf)

= 0.65 minutes × log10(10^6/10^3)

= 0.65 minutes × log10(10^3)

= 0.65 minutes × 3

= 1.95 minutes

Therefore, the minimum sterilization time required to yield 99.9% confidence of successfully sterilizing 50 L of medium containing 10^6 contaminating organisms using this procedure is approximately 1.95 minutes

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Answer:

(

−

4

)

2

+

(

−

1

)

2

=

h

2

16

+

1

=

h

2

h

=

±

√

17

Step-by-step explanation:

The equation of the line in slope-intercept form is: y = -2x + 12.

To write the equation of a line in slope-intercept form, rewrite any equation given of a line as y = mx + b, where the slope is m and the y-intercept is b.

Given the equation of a line in standard form as, 4x + 2y = 24, rewrite in slope-intercept form as:

2y = -4x + 24

Divide both sides by 2:

2y/2 = -4x/2 + 24/2

y = -2x + 12

In slope-intercept form, the equation is: y = -2x + 12.

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The form of the partial fraction decomposition of the given functions are: Partial fraction decomposition

x² + x + 12(ax + b) / (x² + x + 12)x⁴ + 1 / ((25 + 623³)) [Ax + B]/ (x² + 1) + [Cx + D] / (x² - 1)(x² – 9)² [A / (x - 9)] + [B / (x - 9)²] + [C / (x + 9)] + [D / (x + 9)²]

Given function is x² + x + 12, we are to write out the form of the partial fraction decomposition of the function and not to determine the numerical values of the coefficients.

Partial fraction decomposition of the given function x² + x + 12 is:  

x² + x + 12 = (ax + b) / (x² + x + 12)

Where a and b are constants.

We are also given another function which is:

(a) X⁴ +1 25 + 623 3

To write out the form of the partial fraction decomposition of the function, it is important to factorize the denominator of the function in order to determine the form of the partial fraction decomposition.

The factors of x⁴ + 1 can be obtained as: (x² + 1)(x² - 1) = (x² + 1)(x + 1)(x - 1)

Therefore, the partial fraction decomposition of x⁴ + 1 / ((25 + 623³) is given as:

(x⁴ + 1) / ((25 + 623³)) = [Ax + B]/ (x² + 1) + [Cx + D] / (x² - 1)(b) (x² – 9)²

To write out the form of the partial fraction decomposition of the function, we will consider the factors of the denominator.

The factors of (x² - 9)² can be obtained as:

(x - 9)² (x + 9)²

Therefore, the partial fraction decomposition of (x² – 9)² is given as:

(x² – 9)² = [A / (x - 9)] + [B / (x - 9)²] + [C / (x + 9)] + [D / (x + 9)²]

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The  answer is:

\((x² – 9)² = (A / x + 3) + (B / (x + 3)²) + (C / x – 3) + (D / (x – 3)²)\)

(a) x² + x + 12

Partial fraction decomposition is the process of expressing a fraction that contains a polynomial of the numerator and a polynomial of the denominator as the sum of two or more fractions with simpler denominators. By using partial fraction decomposition, it is possible to integrate many rational functions.To write out the form of the partial fraction decomposition of the function x² + x + 12, first, we need to factorize the denominator. In this case, we cannot factorize x² + x + 12 into linear factors with real coefficients. Therefore, the partial fraction decomposition does not exist, and the answer is DNE.(b) (x² – 9)²We can factorize the denominator of (x² – 9)² to obtain\((x² – 9)² = (x + 3)²(x – 3)²\)Now, we can express the function as(x² – 9)² = (A / x + 3) + (B / (x + 3)²) + (C / x – 3) + (D / (x – 3)²)By solving for the constants A, B, C, and D, we can obtain the numerical values of the coefficients.

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Answer:

4. (d) option is correct because -7-(-5) = -7+5 ( Because - and - makes a plus .

Hope it does aid you .

Pls mark brilliant .

12 + 14x - 10x^2

.............................

For a random day with the standard deviation, the probability that there are less than 300 shoppers on a random day, is 0.00585.

Probability is a measure of the likelihood that an event will occur.

The average total number of shoppers on a grocery store in 1 day is 505; the standard deviation is 115.

Let, X be the random variable denoting the number of shoppers on a random day.

Then, X follows normal with mean 505 and standard deviation of 115.

Then, we can say that,

Z=(X-505)/115 follows standard normal with mean 0 and standard deviation of 1.

We have to find

P (250 <X< 450)

= P {(250-505)/155} < Z < {(450-505)/155}

= P (-1.64 <Z< -0.03)

Where, Z is the standard normal variate.

ρ = -1.64 <ρ< -0.03

Where, ρ is the distribution function of the standard normal variate.

From the standard normal table, this becomes

=0.00585

For a random day, the probability that there are less than 300 shoppers on a random day, is 0.00585.

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Answer:

3.7

Step-by-step explanation:

Answer:

The Unit Rate would be 0.27:1

Step-by-step explanation:

Divide 4.86 by 18 to get 0.27

Hope this helps! Pls make brainliest

Answer:

99/104

Step-by-step explanation:

1 3/8 divided by 1 4/9

1 3/8 = 11/8

1 4/9 = 13/9

11/8 divided by 13/9

= 11/8 times 9/13

= 99/104

Answer:

31-12=-2m -m

19=m

or

m=19

Step-by-step explanation:

Given the following equation:

You know, based on the information given in the exercise, that it is a true equation. You can notice that the sum (the result of the Addition) of the terms on the left side of the equation, is:

Then, knowing the above and having the following expression:

You can substitute the sum of the equation into the expression:

Finally, adding the numbers, you get that the value of the expression is:

Answer:

(e^3 / e^2n)

Step-by-step explanation:

The values for representing probabilty must be greater or equal to zero and less or equal to one.

So, the values which cannot be probabilities would be:

-0.05 ( It is less than zero)

1.48 (It is greater than one)

7/2 (It is greater than one)

-1/4 ( It is less than zero)

Yes, the 5x5 matrix is diagonalizable because it has two eigenvalues with eigenspaces of dimensions 3 and 2.

A matrix is diagonalizable if and only if the sum of the dimensions of its eigenspaces equals its size (the number of rows or columns).

a matrix is a rectangular array of numbers or symbols arranged in rows and columns. Each element in the matrix is

identified by its row and column index. Matrices are commonly used in linear algebra, where they are used to

represent linear transformations and systems of linear equations.

In this case, the three-dimensional eigenspace and the two-dimensional eigenspace have a combined dimension of 5, which is the size of the matrix.

Therefore, the 5x5 matrix is diagonalizable.

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Question

A is a 5 x 5 matrix with two eigenvalues. One eigenspace is three-dimensional, and the other eigenspace is two-dimensional. Is A diagonalizable?

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The distance from the point (-4, 5, 5) to the plane 3x - 5y + 2z = 2 is 29 / √38 units.

To find the distance from a point to a plane, we can use the formula:

Distance = |Ax + By + Cz + D| / √(A^2 + B^2 + C^2)

Given the point P(-4, 5, 5) and the plane 3x - 5y + 2z = 2, we can rewrite the plane equation in the form Ax + By + Cz + D = 0 by subtracting 2 from both sides:

3x - 5y + 2z - 2 = 0

Comparing the coefficients, we have A = 3, B = -5, C = 2, and D = -2.

Now, we can substitute these values into the distance formula:

Distance = |(3 * -4) + (-5 * 5) + (2 * 5) + (-2)| / √(3^2 + (-5)^2 + 2^2)

Simplifying:

Distance = |-12 - 25 + 10 - 2| / √(9 + 25 + 4)

Distance = |-29| / √38

Distance = 29 / √38

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Answer:

233 dollars will be left in your account.

Step-by-step explanation:

First you need to add how much money you are going to spend.

EX: 62 + 78 + 54 = 194

Now you take that number and subtract it from the amount of money you already have.

EX: 427 - 194 = 233.

hope this helped!

To determine if a function crosses the horizontal asymptote, analyse the behavior of the function as it approaches the asymptote and on either side of it.

1. Identify the horizontal asymptote of the function. The horizontal asymptote is a horizontal line that the function approaches as the independent variable (usually denoted as x) goes to positive or negative infinity. It is often denoted by a horizontal line y = a, where "a" is a constant.

2. Examine the behavior of the function as x approaches positive infinity. Evaluate the limit of the function as x goes to positive infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. However, if the limit does not equal the asymptote, move to the next step.

3. Examine the behavior of the function as x approaches negative infinity. Evaluate the limit of the function as x goes to negative infinity. If the limit is equal to the value of the horizontal asymptote, then the function does not cross the asymptote. If the limit does not equal the asymptote, proceed to the next step.

4. Investigate the behavior of the function around critical points or points where the function changes its behavior. These points may include the x-intercepts or vertical asymptotes. Determine if the function crosses the asymptote around these points by analyzing the behavior of the function in their vicinity.

If, at any point in this process, the function crosses the horizontal asymptote, then it does not have a true horizontal asymptote. However, if the function approaches the asymptote and does not cross it at any point, then it has a horizontal asymptote.

It's important to note that some functions may have multiple horizontal asymptotes or no horizontal asymptote at all. The steps outlined above are a general guideline, but the specific behavior of the function needs to be analyzed to make a conclusive determination.

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