Classify LMN by its side lengths and by its angles

The average rate of change over the interval x = 3 and x = 7 is 30

The average rate of change of a function, graph, table or ordered pair is simply the slope of the relation

The equation is given as

g(x) = 2ˣ - 1

The interval is given as:

x = 3 and x = 7

Start by calculating g(3) and g(7)

So, we have

g(3) = 2³ - 1 = 7

g(7) = 2⁷ - 1 = 127

So, the average rate over these intervals is calculated as:

Average rate = [g(b) - g(a)]/[b - a]

This gives

Average rate = [g(7) - g(3)]/[7 - 3]

Substitute known values

Average rate = [127 - 7]/[7 - 3]

Simplify

Average rate = 120/4

Average rate = 30

Hence, the average rate of change is 30

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Answer:

its C $12.40

Step-by-step explanation:

So regular price is $7.90 a pair

and now they are on sale THREE PAIR for $17.50, Now esteban bought SIX PAIR os sock

17.50+17.50 = 35

Lastly if you put it regular price $7.90x6 pairs = 47.4

Now for the final result

47.4 - 35 = 12.40 esteban save up

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the formula for probability

STEP 2: Wit the required data

STEP 3: Find the probability that she rolls a three

The probability that she rolls a three is 16.7%

STEP 4: Find the probability that she rolls a six

The probability that she rolls a six is 16.7%

STEP 5: Find the probability that she rolls three or a six

The probability that she rolls a three or six is 33.3%

STEP 6: Find the probability that she rolls an even number

The probability that she rolls an even number is 50.0%

Answer:

Jackie cut the cake into ten equal pieces, so each piece is 1/10 of the original cake.

If she had four-tenths of the cake left after dinner, then she had 6/10 of the cake left.

She wrapped a piece that was one-fifth of the original cake for her sister. One-fifth of the original cake is 1/5 x 1 = 1/5.

So, Jackie gave away 1/5 of the cake and had 6/10 - 1/5 = 3/10 of the cake left.

Therefore, the fraction of the cake that was left is 3/10.

Answer:

3/10

Step-by-step explanation:

Using proportions, it is found that $15.00 in quarters weigh 29.4 grams less today than before 1965.

A proportion is a fraction of a total amount.

In this problem, a quarter is worth $0.25, hence $15.00 in quarters is composed by 60 quarters, as:

\(\frac{15}{0.25} = 15 \times 4 = 60\)

Before 1965, the total weight was of:

60 x 6.25 = 375 grams.

After that, the total weight is of:

60 x 5.76 = 345.6 grams.

Hence the difference is:

375 - 345.6 = 29.4.

$15.00 in quarters weigh 29.4 grams less today than before 1965.

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Answer:

41.5

23.5

Step-by-step explanation:

Let's start by calling the two numbers we are looking for x and y.

The sum of x and y is 65. In other words, x plus y equals 65 and can be written as equation A:

x + y = 65

The difference between x and y is -18. In other words, x minus y equals -18 and can be written as equation B:

x - y = -18

Now solve equation B for x to get the revised equation B:

x = -18 + y

Then substitute x in equation A from the revised equation B and then solve for y:

x + y = 65

-18+y+y=65

-18 + 2y = 65

2y = 83

y = 41.5

Now we know y is 41.5. Which means that we can substitute y for 41.5 in equation A and solve for x:

x + y = 65

x + 41.5= 65

X = 23.5

DIfference : 23.5 - 41.5 = 18

Sum: 41.5 +23.5 = 65

Hence, The two number are 23.5 and 41.5

[RevyBreeze]

Answer:

2n ÷ (n-8)

Step-by-step explanation:

2n ÷ (n-8)

Answer:

The correct answer is (A).

Step-by-step explanation:

Because the data came from 3 groups in a randomized experiment, the appropriate test is a chi-square test for homogeneity.

Answer:

I'm gonna say false

GDP or Gross Domestic Profit is the money that is being spent/made inside the country. So it stands to reason that if people are spending more, the GDP would go up.

Hope this helps!

Answer:

the square root of 7396 by long division method is 86

Answer:

If you want to find out how many print copies the book is selling, just click the Paperback or Hardcover edition of the book on Amazon, scroll down to Product Details on that page, and find the Amazon Best Sellers Rank for the print edition.

Step-by-step explanation:

There are 8,519,680 hexadecimal numbers. The result is obtained by using the multiplication principle.

Hexadecimal number system is a numbering system with the base of 16. The 16-digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. They are usually denoted by the subscript 16. For example, 429AD₍₁₆₎.

How many combination of hexadecimal numbers that can be made if:

Let's broke the problem into 3 cases.

Using the multiplication principle, we can multiply them all.

The combination of hexadecimal numbers is

= 10 × 13 × 16³

= 8,519,680

Hence, the combination that can be made is 8,519,680 hexadecimal numbers.

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Answer:

0.00014

Have a great day!

Answer:

That would be 0.00014km.

Hope this helps!

Answer:

Step-by-step explanation:

y=180'-(59.3'+78.5')

y=180'-(137.8')

y=42.2'

degree='

Answer: y = 42.2°

Step-by-step explanation:

   We know that a straight line is equal to 180 degrees. We will set up an equation with the given values and solve.

59.3° + y + 78.5° = 180°

137.8° + y = 180°

(137.8° + y) -137.8° = (180°) - 137.8°

y = 42.2°

Answer: No solution

Steps: 8x + 3 = 8x + 27

Subtract 8x from both sides: 8x + 3 - 8x = 8x + 27 - 8x

Simplify: 3 ≠ 27

The sides are not equal so therefore there is no solution.

Plz mark brainliest:)

Answer:

No Solutions

Step-by-step explanation:

Step 1:

8x + 3 = 8x + 27        Equation

Step 2:

3 = 27            Subtract 8x on both sides

Step 3:

3 ≠ 27          No Solutions

Answer:

No Solutions

Hope This Helps :)

The solution is u(x,t) = (π − x)sin(t) + cos(x)cos(t).

The wave equation can be solved using separation of variables. Let u(x,t) = X(x)T(t). Then utt = XT'' and uxx = X''T. Substituting these into the wave equation gives XT'' = X''T, which simplifies to X''T = 0. This means that X'' = 0 or T = 0. The boundary conditions u(0,t) = 0 and u(π,t) = 0 require that X(0) = 0 and X(π) = 0. This means that X(x) = sin(x). The initial conditions u(x,0) = π − x and ut(x,0) = 1 require that T(0) = 1 and T'(0) = π. This can be solved to get T(t) = sin(t) + πcos(t). The solution is then u(x,t) = (π − x)sin(t) + cos(x)cos(t).

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The indefinite integral of\(\int\limits^a_b {(x+5)}\sqrt{2-2} \, dx\)  is \((2/5)(2-x)^{5/2} - (14/3)(2-x)^{3/2} +C\) 

To find the indefinite integral of ∫(x + 5)√(2 – x) dx by making a change of variables, follow these steps:

1. Choose a substitution for one of the variables. Let's substitute u for (2-x):
  u = 2 - x

2. Differentiate both sides of the equation with respect to x to find du/dx:
  du/dx = -1

3. Rearrange the equation to isolate dx:
  dx = -du

4. Substitute the expressions for u and dx back into the integral:
  ∫(x + 5)√(2 – x) dx = ∫(2 - u + 5)√u (-du)
 

Simplify the expression:
  ∫(7 - u)√u (-du)

5. Now, evaluate the integral:
  -∫(7 - u)√u du

6. Distribute the -1 into the integrand and split the integral into two separate integrals:
  ∫(u√u - 7√u) du

7. Rewrite the integrals using exponents instead of radicals:
  ∫(u^(3/2) - 7u^(1/2)) du

8. Integrate each term separately:
  (2/5)u^(5/2) - (14/3)u^(3/2) + C

9. Substitute back the original variable, x, for u:
  (2/5)(2-x)^(5/2) - (14/3)(2-x)^(3/2) + C

Therefore, the indefinite integral of ∫(x + 5)√(2 – x) dx is  (2/5)(2-x)^(5/2) - (14/3)(2-x)^(3/2) + C.

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Answer:

The angle between the diagonal of the rectangle is \(\frac{\pi }{2}\).

Given:

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4), and d = (4, 1)

To find:

The objective is to find the angle between the diagonals.

Step 1 of 3

Consider the diagram attached.

Step 2 of3

The position vector of diagonal AC is-

=(3-1)î+(4-0)j=2î+4j

And the position vector of diagonal BD is-

=(4-0)î+(1-3)j=4î-2j

Step 3 of 3

cosθ=\(\frac{AC.BD}{|AC|.|BD|}\)

cosθ=\(\frac{(2i-4j)(4i-2j)}{\sqrt{2^2+4^2} \sqrt{4^2+(-2)^2\\} }\)

=\(\frac{8-8}{\sqrt{20}.\sqrt{20} }\)

=0

θ=\(cos^{-1}\)(0)

θ=\(\frac{\pi }{2}\)

Therefore the angle between the diagonal of the rectangle is \(\frac{\pi }{2}\)

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The angle between the diagonals of a rectangle is π/2

The vertices of the rectangle are

a = (1, 0), b = (0, 3), c = (3, 4),  d = (4, 1)

The diagonal position vector AC  

=(3-1)î+(4-0)j=2î+4j

And the diagonal position vector BD  

=(4-0)î+(1-3)j=4î-2j

cos Ф = (AC.BD) / (|AC| . |BD|)

cos Ф = (8-8) / (root20 -roo20)

= 0

Ф = π/2

Therefore the angle between the diagonals of the rectangle is π/2

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Answer:

x = 27

Step-by-step explanation:

hope this helps :)

a) The center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

b) We have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

(a) Deriving the class equation of a finite group G involves partitioning the group into conjugacy classes. Conjugacy classes are sets of elements in the group that are related by conjugation, where two elements a and b are conjugate if there exists an element g in G such that b = gag^(-1).

To derive the class equation, we start by considering the group G and its conjugacy classes. Let [a] denote the conjugacy class containing the element a. The class equation is given by:

|G| = |Z(G)| + ∑ |[a]|

where |G| is the order of the group G, |Z(G)| is the order of the center of G (the set of elements that commute with all other elements in G), and the summation is taken over all distinct conjugacy classes [a].

The center of a group, Z(G), is the set of elements that commute with all other elements in G. It can be written as:

Z(G) = {z in G | gz = zg for all g in G}

The order of Z(G), denoted |Z(G)|, is the number of elements in the center of G.

The conjugacy classes [a] can be determined by finding representatives from each class. A representative of a conjugacy class is an element that cannot be written as a conjugate of any other element in the class. The number of distinct conjugacy classes is equal to the number of distinct representatives.

By finding the center of G and determining the distinct conjugacy classes, we can calculate the class equation of the finite group G.

(b) To prove that a Sylow p-subgroup of a finite group G is normal if and only if it is unique, we need to show two implications: if it is normal, then it is unique, and if it is unique, then it is normal.

If a Sylow p-subgroup is normal, then it is unique:

Assume that P is a normal Sylow p-subgroup of G. Let Q be another Sylow p-subgroup of G. Since P is normal, P is a subgroup of the normalizer of P in G, denoted N_G(P). Since Q is also a Sylow p-subgroup, Q is a subgroup of the normalizer of Q in G, denoted N_G(Q). Since the normalizer is a subgroup of G, we have P ⊆ N_G(P) ⊆ G and Q ⊆ N_G(Q) ⊆ G. Since P and Q are both Sylow p-subgroups, they have the same order, which implies |P| = |Q|. However, since P and Q are subgroups of G with the same order and P is normal, P = N_G(P) = Q. Hence, if a Sylow p-subgroup is normal, it is unique.

If a Sylow p-subgroup is unique, then it is normal:

Assume that P is a unique Sylow p-subgroup of G. Let Q be any Sylow p-subgroup of G. Since P is unique, P = Q. Therefore, P is equal to any Sylow p-subgroup of G, including Q. Hence, P is normal.

Therefore, we have shown both implications: if a Sylow p-subgroup is normal, then it is unique, and if it is unique, then it is normal.

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To determine whether the boxplot represents the information given in the histogram, we need to examine the characteristics of both the boxplot and the histogram.

The boxplot provides a visual representation of the distribution of a dataset, showing the minimum, first quartile, median, third quartile, and maximum values. It also displays any outliers that may be present. On the other hand, a histogram provides a graphical representation of the frequency or count of data values within specified intervals or bins.

Without specific information or visuals of the boxplot and histogram in question, it is not possible to directly compare them and determine their compatibility. Therefore, it is not possible to answer the question based on the information provided.

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Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

(2x - 5) (x + 4)

Step-by-step explanation:

3.31 it will take her to complete the triathlon.

To find this, we can apply the equation distance = rate x time.

We are aware of the length and pace of each triathlon leg. Let's name them, respectively, d and r. We must locate the time, which we shall designate as t.

d = r x t    or

t = d/r

The distance is 0.93, or 93/100, and the rate is 1.2, or 12/10 when swimming. As a result of our formula, we have:

12/10 divided by 93/100 yields the same result as

93/100 * 10/12

time to swim = 93/120 = 31/40

We have a distance of 24.8 miles, or 248/10, and a speed of 18.8 miles, or 188/10, for biking. Using the same formula, we obtain:

248/10 divided by 188/10 or

248/10 * 10/188 = 248/188 = 62/47 = time to bike

Finally, for the run, the distance is 6.2 = 62/10 and the rate is 5.1 or 51/10. Plugging this into the formula gives:

62/10 divided by 51/10 or

62/10 * 10/51 = 62/51 = time to run

= 31/40 + 62/47 + 62/51

=3.31

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Answer:

Based on the graphs shown, what would you conclude about the conditions under which enzymes function in cells?

A

Enzymes are most effective at a particular pH and temperature but can function over a range of pH and temperature.

B

С

Enzymes do not have a specific pH or temperature at which they are most effective but function optimally over a range of pH and temperature.

Enzymes work equally well at the low and high ends of their temperature range but reaction rate drops quickly at the high end of their pH range

Enzymes only function at a specific pH and temperature and cannot function over a range of pH or temperature.

D

Answer:

The answer is D

Step-by-step explanation:

Answer: C

Step-by-step explanation:

−3x + 6 > 12

Move all terms not containing x to the right side of the inequality.

Subtract 6 from both sides of the inequality.

−3x > 12 − 6

Subtract 6 from 12.

−3x > 6

Divide each term by −3 and simplify.

Divide each term in −3x > 6 by −3. When multiplying or dividing both sides of an i nequality by a negative value, flip the direction of the inequality sign.

(-3x/-3)<(6 /-3)

Cancel the common factor of −3.

Divide 6 by −3.

x < −2

( − ∞ , − 2 )

A function is even if the graphic is symmetric with respect to the y-axis.

You can symbolize an even function as -f(x)=f(x) for all values of x on the domain of the function f.

A)

The expression |y| indicates that its the absolute value of y. This means that y can be positive or negative.

This function is even.

B)

In this example x is expressed as an absolute value and can be either positive or negative:

This function is symetrical with respect to the y-axis, so it an even function.

C)

This function is not symetrical with respect to the y-axis

D)

This function is not symmetrial with respect to the y-axis

X=18

Step-by-step explanation:

In the Clausius-Clapeyron equation, the variables related to the measured values that would typically be graphed on the x and y axes depend on the specific application.

Generally, the natural logarithm of the vapor pressure (ln P) is plotted on the y-axis, while the reciprocal of the absolute temperature (1/T) is plotted on the x-axis. The slope (m) and y-intercept (b) of the resulting linear graph have specific interpretations in the context of the equation.

The Clausius-Clapeyron equation relates the vapor pressure of a substance to its temperature. It is expressed as ln(P) = -ΔHvap/R * (1/T) + C, where P is the vapor pressure, ΔHvap is the enthalpy of vaporization, R is the gas constant, T is the temperature, and C is a constant. When graphing this equation, we often plot ln(P) on the y-axis and 1/T on the x-axis.

The graph obtained from plotting these variables follows a linear relationship. The slope of the resulting line, denoted as m, is equal to -ΔHvap/R. This slope provides valuable information about the enthalpy of vaporization, which is a measure of the energy required to convert a substance from its liquid phase to its gas phase. The y-intercept, denoted as b, represents the constant C in the equation, which accounts for any initial conditions or deviations from the ideal gas behavior.

By plotting ln(P) against 1/T, we can determine the slope and y-intercept of the linear graph. These parameters have specific physical interpretations and can provide insights into the thermodynamic properties of the substance under investigation. Analyzing the slope and y-intercept values can help in quantifying the enthalpy of vaporization and understanding the behavior of the substance as its temperature changes.

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