Diagonals of a parallelogram bisect each other true or false

A) The exponential function that models the mass show many grams remain from a 480-gram sample after t minutes is G(t) = 22(1/2)^(t/5.5)

B) The grams that remain after 2 hours is 51.42 grams.

A substance's half-life is the amount of time needed for half of a radioactive substance to decay. It is a word that is used in nuclear chemistry to describe how quickly unstable atoms undergo radioactive decay into other nuclear species by emitting particles or the amount of time needed for the rate of disintegrations per second of radioactive material in order to reduce by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) A formula for the amount remaining could be ...

G(t) = 22(1/2)^(t/5.5)

c) After 2 hours, the amount remaining is ...

G(120) = 135(1/2)^(47/33.75) ≈ 51.42 . . . grams

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A). After t minutes, the exponential function used to describe the mass remaining from a 480-gram sample is [tex]G(t) = 22(\frac{1}{2} )^{(t/5.5)}[/tex]

B). 51.42 grammes are still there after two hours.

The amount of time required for a radioactive substance to decay by half is known as its half-life. It is a term used in nuclear chemistry to describe how quickly unstable atoms transform into different nuclear species by emitting particles or how long it takes for the rate of radioactive material's disintegrations per second to fall by half of its initial value.

Given:

The half-life of goo is 22 minutes/4 = 33.75 minutes

b) The amount left could be calculated using the method...

[tex]G(t) = 22(\frac{1}{2} )^{(t/5.5)}[/tex]

c) The amount left after two hours is...

[tex]G(120)=135(\frac{1}{2} )^{(\frac{47}{33.5} )}[/tex] ≈ 51.42 . . . grams

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Answer:

Step-by-step explanation:

it would be shaped like a but because you cut it into 6cm

The dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

Let's assume that the package has a height 'h' and a radius 'r'. The perimeter of the cross-section of a cylinder is the circumference of the circle plus the height multiplied by two, which can be written as:

Perimeter = 2πr + 2h

Given that the maximum combined length and circumference is 114 inches, we can write:

2πr + 2h + 2r = 114

Simplifying this equation, we get:

πr + h = 57 - r ----(1)

The volume of the cylinder is given by:

[tex]V = πr^2h[/tex]

Now, we can use equation (1) to eliminate 'h' from the volume equation:

[tex]V = πr^2(57 - r - πr)[/tex]

Expanding and simplifying this equation, we get:

[tex]V = πr^3 - π^2r^3/3 + 57πr^2 - 57π^2r[/tex]

To find the dimensions of the package that maximize the volume, we need to find the value of 'r' that maximizes the volume. We can do this by taking the derivative of the volume equation with respect to 'r' and setting it equal to zero:

[tex]dV/dr = 3πr^2 - π^2r^2 + 114πr - 57π^2 = 0[/tex]

Solving for 'r', we get:

r ≈ 7.8 inches

Substituting this value of 'r' back into equation (1), we can find the value of 'h':

h ≈ 21.3 inches

Therefore, the dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

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The arithmetic series can be written in summation notation as:

∑_{i=1}⁶ 5i = 5 + 10 + 15 + 20 + 25 + 30 = 105.

What is arithmetic series?

The sum of a series in which each term is computed from the preceding one by adding and subtracting constants is known as an arithmetic series. Alternately, we could say that an arithmetic progression is a set of numbers where, for every pair of successive terms, the second number is obtained by adding a fixed amount to the first.

The common difference in this arithmetic series is 10 - 5 = 5. Therefore, the nth term of the series is given by a_n = 5n.

The first term of the series is 5, which corresponds to n = 1. The last term is 30, which corresponds to n = 6.

The sum of an arithmetic series can be calculated using the formula: S_n = (n/2)(a_1 + a_n), where S_n is the sum of the first n terms, a_1 is the first term, and a_n is the nth term.

Substituting the values of a_1, a_n, and n, we get:

S_6 = (6/2)(5 + 30) = 3(35) = 105

Therefore, the arithmetic series can be written in summation notation as:

∑_{i=1}⁶ 5i = 5 + 10 + 15 + 20 + 25 + 30 = 105.

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y = 3x + 6 is the equation of the line with gradient 3 and passing through the point (-1,3).

The equation of a straight line with gradient m and passing through the point (x₁, y₁) is given by:

y - y₁ = m(x - x₁)

In this case, we have a gradient of m = 3 and a point (x₁, y₁) = (-1, 3). Plugging in these values, we get:

y - 3 = 3(x - (-1))

Simplifying this equation, we get:

y - 3 = 3x + 3

Adding 3 to both sides, we get:

y = 3x + 6

Therefore, the equation of the line with gradient 3 and passing through the point (-1,3) is y = 3x + 6.

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The point estimate for least-squares regression line x=1 is approximately 3.85, and the point estimate for x=7 is approximately 24.02.

In a linear regression, the coefficient of determination (R-squared) is a statistical indicator that shows how much of the variance in the dependent variable is explained by the independent variable (s). Higher values suggest a better fit of the regression line to the data, and it has a value between 0 and 1. R-squared is derived by dividing the regression's sum of squares (SSR) by the sum of all squares (SST).

The least-squares regression line is given by the formula:

b1 = Σ[(xi - x)(yi - y)] / Σ[(xi - x)²]

The means of x and y:

x = (−2 + 2 + 5 + 7 + 10) / 5 = 4.4

y = (2 + 9 + 13 + 19 + 24) / 5 = 13.4

Substituting the value we have:

Σ[(xi - x)(yi - y)] = (-2-4.4)(2-13.4) + (2-4.4)(9-13.4) + (5-4.4)(13-13.4) + (7-4.4)(19-13.4) + (10-4.4)(24-13.4) = 400.8

Σ[(xi - x)²] = (-2-4.4)²+ (2-4.4)² + (5-4.4)² + (7-4.4)² + (10-4.4)² = 86.8

Thus, the value of:

b1 = Σ[(xi - x)(yi - y)] / Σ[(xi - x)²] = 400.8 / 86.8 ≈ 4.617

Now, for y-intercept we have:

b0 = y - b1x = 13.4 - 4.617(4.4) ≈ -0.767

y = -0.767 + 4.617x

Now, the point estimate is:

For x=1, y = -0.767 + 4.617(1) ≈ 3.85

For x=7, y = -0.767 + 4.617(7) ≈ 24.02

Therefore, the point estimate for x=1 is approximately 3.85, and the point estimate for x=7 is approximately 24.02.

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Step-by-step explanation:

If a polynomial function has roots at x=-5 and x=√3, it means that it can be factored as follows:

h(x) = a(x+5)(x-√3)

where 'a' is a constant coefficient that represents the leading term of the polynomial function.

To find the value of 'a' and express the polynomial function in standard form, we can multiply the factors and simplify as follows:

h(x) = a(x+5)(x-√3)

h(x) = a(x^2 - √3x + 5x - 5√3)

h(x) = a(x^2 + 2x√3 - 5√3)

To find the value of 'a', we can substitute one of the given roots into the equation and solve for 'a'. Let's choose x = -5:

h(-5) = a((-5)^2 + 2(-5)√3 - 5√3)

h(-5) = a(25 - 10√3 - 5√3)

Since x=-5 is a root, h(-5) = 0. Therefore:

0 = a(25 - 15√3)

a = 0 or a = (15√3)/25 = (3√3)/5

Since the coefficient 'a' cannot be zero, the polynomial function h(x) of lowest degree in standard form is:

h(x) = (3√3/5)(x^2 + 2x√3 - 5√3)

h(x) = (3√3/5)x^2 + (6/5)√3x - 3√3

There are 8 coins.

In my bag, one coin is worth $50. The rest are worth $10. The average value of all the coins in my bag is $15. How many coins are in my bag?

Let's say that there are x $10 coins in the bag. Then, the total value of these coins would be 10x.

We also know that there is one $50 coin in the bag, so the total value of all the coins in the bag is 10x + 50.

The average value of all the coins in the bag is $15, so we can set up the following equation:

(10x + 50)/(x + 1) = 15

Multiplying both sides by x+1, we get:

10x + 50 = 15(x + 1)

Expanding the right side, we get:

10x + 50 = 15x + 15

Subtracting 10x and 15 from both sides, we get:

35 = 5x

Solving for x, we get:

x = 7

So there are 7 $10 coins in the bag and 1 $50 coin, for a total of 8 coins in the bag.

A game that uses exponent rules and scientific notation on paper are given below as exponent explorer.

We have,

A game that incorporates exponent rules and scientific notation:

Title: Exponent Explorer

Objective: The goal of the game is to become an "Exponent Explorer" by solving a series of challenges related to real-world phenomena that involve exponent rules and scientific notation.

Materials: Pencils, paper, and a list of challenges.

Instructions:

The game is played in rounds, with each round consisting of a challenge.

Before starting the game, explain the exponent rules and scientific notation to the players, and provide examples of how they are used in real-world phenomena.

Start the first round by presenting a challenge to the players. Each challenge should involve a real-world phenomenon, such as the size of the universe, the speed of light, or the population of a city. The challenge should require players to use exponent rules and/or scientific notation to solve a problem related to the phenomenon.

Players work individually or in teams to solve the challenge. They must show their work and write their answer in scientific notation.

After a set amount of time, reveal the correct answer and award points to the players or teams that solved the challenge correctly.

The number of points awarded can vary based on the difficulty of the challenge.

Play additional rounds with new challenges, and continue awarding points.

The player or team with the most points at the end of the game is the winner and becomes an "Exponent Explorer."

Example Challenge:

Challenge:

The population of New York City is approximately 8,336,817.

Write this number in scientific notation, and then determine how many times larger it is than the population of San Francisco, which is approximately 883,305.

Solution:

8,336,817 = 8.336817 x 10^6

To find how many times larger New York City's population is than San Francisco's, divide the two numbers:

8,336,817 / 883,305

= 9.44

New York City's population is approximately 9.44 times larger than San Francisco's population.

Thus,

A game that uses exponent rules and scientific notation on paper is given above.

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Answer:

Step-by-step explanation:

Answer:

1 3/5

Step-by-step explanation:

[tex](2\frac{2}{3} )(\frac{3}{5})= (2\frac{10}{15})( \frac{9}{15} )= (\frac{40}{15} )( \frac{9}{15} )= \frac{360}{225}[/tex]

Divide by 45 to simplify

[tex]\frac{8}{5} = 1\frac{3}{5}[/tex]

The angles with a common reference angle of 340° are:

To find an angle in each quadrant with a common reference angle of 340°, we need to determine the reference angle of 340° and then find angles in each quadrant with that same reference angle.

The reference angle of 340° is found by subtracting the nearest multiple of 360°, which is 0°, from 340°. Therefore, the reference angle of 340° is 20°.

Quadrant I:

To find an angle in quadrant I with a reference angle of 20°, we simply take the reference angle itself, which is 20°.

Quadrant II:

To find an angle in quadrant II with a reference angle of 20°, we need to add the reference angle to 180°, which gives us 200°.

Quadrant III:

To find an angle in quadrant III with a reference angle of 20°, we need to subtract the reference angle from 180°, which gives us 160°.

Quadrant IV:

To find an angle in quadrant IV with a reference angle of 20°, we need to subtract the reference angle from 360°, which gives us 340° (which is the original angle we started with).

Therefore, the angles in each quadrant with a common reference angle of 20° are:

The complete question is:-

Find an angle in each quadrant with a common reference angle with 340°, from 0°≤θ<360°

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The calculated t-statistic (3.24) is greater than the critical value (1.699), reject the null hypothesis

Since the calculated t-statistic (3.24) is greater than the critical value (1.699), we reject the null hypothesis.
In conclusion, the dentist's claim is supported.

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The biased statistical measure among the given options is mean.

Statistical bias is anything that leads to a systematic difference between the true parameters of a population and the statistics used to estimate those parameters.

The mean of a sampling distribution is biased when the sample is drawn from a non-normal population or when the sample size is small. In such cases, the mean tends to be pulled towards the extremes of the distribution, resulting in a biased estimate of the population mean.

In contrast, the median is a robust measure that is less affected by extreme values, and is therefore less likely to be biased. The variance and proportion are also unbiased measures of the sampling distribution.

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The area of the shaded portion as shown in the diagram is 118.74 ft².

Area is the region bounded by a plane shape.

To calculate the area of the shaded portion, we use the formula below

Formula:

Where:

From the diagram,

Given:

Substitute these values into equation 1

Hence, the area of the shaded portion is 118.74 ft².

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Answer:

To find 4% of 975, we can use the percent equation:

x = (4/100) * 975

Simplifying this expression, we get:

x = 0.04 * 975

Multiplying 0.04 and 975, we get:

x = 39

Therefore, 4% of 975 is 39.

The penny will fall from distance of 232 feet during the 8th second only, as it falls 960 feet in the first 8 seconds, but 728 feet in the first 8 seconds.

The distance the penny falls each second is increasing by 32 feet (16 feet + 32 feet = 48 feet, 48 feet + 32 feet = 80 feet, and so on). Therefore, during the 8th second, the distance it will fall is:

16 + 48 + 80 + ... + (8 - 1) * 32 feet

Using the formula for the sum of an arithmetic sequence, we get:

(8 / 2) * (16 + (8 - 1) * 32) feet

= 4 * (16 + 7 * 32) feet

= 4 * 240 feet

= 960 feet

So the penny will fall 960 feet during the first 8 seconds. However, we need to subtract the distance it fell during the first 7 seconds to find the distance it fell during the 8th second only. The total distance it fell during the first 7 seconds is:

16 + 48 + 80 + ... + (7 - 1) * 32 feet

= (7 / 2) * (16 + (7 - 1) * 32) feet

= 3.5 * (16 + 6 * 32) feet

= 3.5 * 208 feet

= 728 feet

Therefore, the penny will fall 960 - 728 = 232 feet during the 8th second only.

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Step-by-step explanation:

i dony know the answer of this question

a) The probability of 6 is 1/3.

b) Probability of sum of an even numbers = 1/2.

c) Probability of getting a 2 on at least one dice = 11/36.

a) The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

Experiment: A trial or procedure carried out to generate a result is referred to as an experiment.

Sample Space: A sample space is the collection of all potential results of an experiment. Tossing a coin, for instance, has two possible outcomes: head or tail.

Favorable Consequence: An occurrence is deemed to have generated the desired outcome or an anticipated event if it did so.

Trial: To conduct a trial is to conduct a random experiment.

It is given to us that a die is rolled

Then, the sample space = {1,2,3,4,5,6}

We are given that it is an even number.

The, we have left with reduced sample space is {2,4,6}

Thus, the probability of 6 is 1/3.

b) So, the number of possibilities of the sum of even numbers is 18.

The probability of an event = number of favorable outcomes/ total number of outcomes.

Probability of sum of an even numbers = 18 / 36 = 1 / 2.

c) Probability of getting a 2 on at least one dice = Favorable outcomes / Total outcomes = 11 / 36 So, P (getting 2 at least on 1 dice) = 11/36.

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So the angle measure for ∠L is 22.5° when two parallel lines cut by a transversal.

In geometry, a transversal is a line that intersects two or more other lines in a plane. When a transversal intersects two parallel lines, it creates a series of corresponding angles, alternate angles, and interior angles, which have specific relationships and properties.

Here,

Since lines a and b are parallel, we know that alternate interior angles are congruent. Therefore, we have:

∠F = ∠L + 180° - 135°

Simplifying this expression, we get:

∠F = ∠L + 45°

Substituting the value of ∠F as 67.5°, we can solve for ∠L:

67.5° = ∠L + 45°

22.5° = ∠L

The relationship between ∠F and ∠L is that they are supplementary angles, meaning they add up to 180°. This is because they are on opposite sides of the transversal and both intersect with the same parallel lines a and b.

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Complete question:

Two parallel lines cut by a transversal. For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines a and b are parallel. a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠L? Describe the relationship between ∠F and ∠L. (1 point)

let us consider x as the number of stools and y be the number of recliners

therefore, total seats [tex]\leq[/tex] 50

= x + y [tex]\leq[/tex] 50

then, owner wants a least 20 of the seats to  be stools

x [tex]\geq[/tex] 20

the rest are the number of recliners.

the equation of inequality is x + y [tex]\leq[/tex] 50

x + y =50

if x = 0 and y = 50

if y = 0 and x = 50

therefore the joining points are (0, 50) and ( 50, 0) in the coordinate plan

0+0 [tex]\leq[/tex] 50

then the shaded region will contain the origin

Graphing of x [tex]\geq[/tex] 20

shading the region left side x = 20

Hence, number of materials can never be negative.

therefore,

x [tex]\geq[/tex] 0 and y [tex]\geq[/tex] 0

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Answer: u = -15/32 ( check if you can simplify, I didn't)

- subtraction/negative

x multiplication

/ division/fraction bar

Step-by-step explanation:

-8/3u -1/2 = 3/4

         +1/2   +1/2

-8/3u = 3/4 + 1/2

                     x2

            3/4 + 2/4

-8/3u = 5/4

x-3/8     x-3/8

u = -15/32

Answer:

Step-by-step explanation:

(-3,4)

Answer:

La probabilidad de sacar dos cartas rojas sin reemplazo de una baraja con 10 cartas rojas, 4 cartas azules y 2 cartas amarillas es 3/8 o 0.375.

Step-by-step explanation:

1. Determina la probabilidad de sacar una carta roja del mazo:

P(Rojo) = Número de Tarjetas Rojas / Número Total de Tarjetas

P(Rojo) = 10 / (10 + 4 + 2)

P(Rojo) = 10 / 16

P(Rojo) = 5 / 8

2. Determine la probabilidad de sacar una segunda tarjeta roja después de sacar la primera carta. Como ya se sacó una carta roja, solo quedan 9 cartas rojas en el mazo, y el número total de cartas restantes es 15:

P(Roja en el segundo sorteo) = Número de tarjetas rojas restantes / Total de tarjetas restantes

P (Rojo en el segundo sorteo) = 9 / 15

3. Multiplique la probabilidad de sacar una tarjeta roja por la probabilidad de sacar una segunda tarjeta roja después de sacar la primera para obtener la probabilidad de sacar dos tarjetas rojas sin reemplazo:

P(Dos tarjetas rojas) = ​​P(Roja) * P(Roja en el segundo sorteo | Roja en el primer sorteo)

P(Dos tarjetas rojas) = ​​(5/8) * (9/15)

P(Dos tarjetas rojas) = ​​3/8 o 0,375

Por lo tanto, la probabilidad de sacar dos cartas rojas sin reemplazo del mazo es 3/8 o 0.375.

Answer:

False

Step-by-step explanation:

The answer is False

The given statement is false, as the letters are used as keys in the dictionary.

The dictionary used in counting letters examples to keep track of letter frequencies uses the letters as the key and the count as the value. This means that for each letter encountered in a string, the value corresponding to the key (letter) in the dictionary is incremented by 1.

For example, if the string is "hello", the dictionary would initially be empty, and for each letter encountered in the string, the value for the corresponding key in the dictionary would be incremented by 1, resulting in a dictionary like {"h": 1, "e": 1, "l": 2, "o": 1}.

Therefore, the correct answer is false, as the letters are used as keys in the dictionary.

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The function representing the car's value after t years is V(t) = [tex]$10,000 \times (1 - 0.4231)^4t[/tex]. The percentage rate of change per quarter is approximately 57.69%.

[tex]V(t) = $10,000 \times 0.2835^t[/tex]

To represent the value of the car after t years, we can use the following formula:

V(t) = V(0)  x (1 - r)⁴t

where V(0) is the car's initial value ($10,000), r is the quarterly rate of change, and t is the number of years.

To find the quarterly rate of change, we can use the annual rate of change of 18%:

r = (1 - 0.18)^(1/4)

r ≈ 0.4231

Therefore, the function to represent the value of the car after t years is:

[tex]V(t) = $10,000 \times (1 - 0.4231)^4t\\V(t) = $10,000 \times 0.2835^t[/tex]

To determine the percentage rate of change per quarter, we can use the formula:

q = (1 - r) x 100%

q = 57.69%

Therefore, the percentage rate of change per quarter is approximately 57.69%.

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t-value (-4.38) is greater than the absolute value of

the critical t-value (1.990), we can reject the null hypothesis and conclude

that there is convincing evidence that the mean reading level for health-

related pages differs for Wikipedia and WebMD.

To test if there is convincing evidence that the mean reading level for

health-related pages differs for Wikipedia and WebMD, we can use a

two-sample t-test.

Let's set up the null and alternative hypotheses:

Null hypothesis: The mean reading level for health-related pages is the

same for Wikipedia and WebMD (μ1 = μ2)

Alternative hypothesis: The mean reading level for health-related pages

differs for Wikipedia and WebMD (μ1 ≠ μ2)

We will use a significance level of 0.05, which means that we are willing

to accept a 5% chance of making a Type I error (rejecting the null

hypothesis when it is actually true).

We can use the following formula to calculate the test statistic:

t = (x_1 - x_2) / (s_pool × √(2/n))

Where:

x_1 and x_2 are the sample means

s_pool is the pooled standard deviation, calculated as:

[tex]\sqrt{ (((n1-1)\timess1^2 + (n2-1)\timess2^2) / (n1+n2-2))}[/tex]

n is the sample size for each group

Plugging in the values, we get:

x1 = 26.2

x2 = 43.6

s1 = 14.2

s2 = 19.9

n1 = n2 = 40

s_pool = [tex]\sqrt{(((40-1)\times14.2^2 + (40-1)\times19.9^2) / (40+40-2))} = 17.0[/tex]

t = (26.2 - 43.6) / (17.0 × √(2/40)) = -4.38 (rounded to two decimal places)

Looking up the critical t-value with degrees of freedom = 78 (df = n1 + n2 - 2), and a significance level of 0.05, we get:

t_critical = ±1.990

Since our calculated t-value (-4.38) is greater than the absolute value of

the critical t-value (1.990), we can reject the null hypothesis and conclude

that there is convincing evidence that the mean reading level for health-

related pages differs for Wikipedia and WebMD.

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a. ln 7 = y in exponential equation is e^y = 7

b. e² = x in logarithm function is log x base e = 2

What is exponential and logarithmic function?

An exponential function is a mathematical function used to calculate the exponential growth or decay of a given set of data.

The logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as. For x > 0 , a > 0, and a ≠1, y= loga x if and only if x = a^y

Therefore,

ln 7 = y

using inverse of ln

7 = e^y

and;

e² = x

using logarithm function as inverse

log x base e = 2.

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Answer:

Yes, the students' reasoning is correct. The percent of a part compared to the whole is calculated by dividing the part by the whole and multiplying the result by 100. Since the part is much less than the whole, the result of the division will be a very small number, and when multiplied by 100, it will be an even smaller number, which is the percentage.

Step-by-step explanation:

1. Divide the part by the whole to calculate the fraction that the part is of the whole.

2. Multiply the result by 100 to convert the fraction to a percentage.

3. Since the part is much less than the whole, the result of the division will be a very small number, and when multiplied by 100, it will be an even smaller number, which is the percentage.

The appropriate null hypothesis for this study is that there is no significant difference between the mean weight of U.S. adults before and after the Thanksgiving holiday period.

The null hypothesis is a statement that there is no significant difference between two groups being compared. In this case, the two groups are the weight of U.S. adults before and after the Thanksgiving holiday period. The null hypothesis assumes that there is no significant difference between these two groups.

To test this hypothesis, the researchers will collect data on the weight of U.S. adults before and after Thanksgiving and compare the mean weight of the two groups. If the mean weight after Thanksgiving is significantly different from the mean weight before Thanksgiving, the null hypothesis will be rejected, and the researchers can conclude that there is strong evidence that the weight of U.S. adults changes between Thanksgiving and January.

Therefore, the appropriate null hypothesis for this study is that there is no significant difference between the mean weight of U.S. adults before and after the Thanksgiving holiday period.

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H1 is a treatment that affects the patient's memory. Alternative hypothesis H1 indicates that the treatment affected the patient's memory.

To test this hypothesis, the researcher should compare the test result to the population mean of 50. Researchers will use a one-tailed t-test with a significance level of 0.01.

If the calculated t-value is greater than the critical value, the null hypothesis is rejected and the alternative hypothesis is accepted.

To perform a t-test, the researcher must calculate the mean, standard deviation, and t-value of the patient's test scores. The average is calculated by dividing the sum of the test scores by the number of test scores. The standard deviation is calculated as the square root of the sum of the squared deviations from the mean divided by the number of test scores minus one.

The t-value is calculated by dividing the difference between the mean of the patient's test scores and the population mean by the standard deviation of the patient's test scores, multiplied by the square root of the number of test scores.

If the calculated t-value is greater than the critical value, you can reject the null hypothesis and accept the alternative hypothesis that the treatment did indeed affect the patient's memory.

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