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Using Fermat's Little Theorem  83^98 mod 13 is 2.

Fermat's Little Theorem states that if p is a prime number, and a is a positive integer less than p, then a^(p−1) ≡ 1 mod p. Now we can use this theorem to compute 83^98 mod 13.

a = 83 and p = 13

Since 83 is not divisible by 13, we can use Fermat's Little Theorem. Here, we have to find the exponent (p-1), which is 12 because 13-1=12.Therefore, we can use a^(p-1) ≡ 1 mod p to simplify the expression:

83^(12) ≡ 1 mod 13

Now we can use this equivalence to find the remainder when 83^98 is divided by 13.83^(12) = 1 mod 1383^96 = (83^12)^8 = 1^8 = 1 mod 1383^98 = 83^96 * 83^2 = 1 * 83^2 mod 13

Now, we need to calculate the remainder when 83^2 is divided by 13.83^2 = 6889 = 13 * 529 + 2

Hence, 83^98 ≡ 83^2 ≡ 2 mod 13.

Therefore, 83^98 mod 13 is 2.

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The commission earned by the salesman last month is $160.

For the given question,

The commission earned by the salesman is 20% on his sells.

Last month total sell = $800.

Let x be the total commission earned.

Then,

20% of 800 = x

x = 20× 800 / 100

x = 160

Thus, the commission earned by the salesman last month is $160.

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Answer:

C: ratio of the horizontal change to the vertical change of a line

Step-by-step explanation:

A and B are correct.

C is incorrect.

Answer:

:)......................

Bao's age is 12 years old.

Integers are defined as the collection of Whole Numbers and the negative values of Natural Numbers make up an integer. Fractional numbers are not included in integers. Integers are represented by the symbol Z.

Let's call Bao's age "x".

Since their ages are consecutive even integers, the next sibling's age would be x + 2, the next one x + 4, and the last one x + 6.

The sum of all their ages is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12 = 60.

Solving for x, we get 4x + 12 = 60, and subtracting 12 from both sides gives 4x = 48.

Dividing both sides by 4 gives x = 12.

Therefore, Bao's age is 12 years old.

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Answer:

??????????????

Step-by-step explanation:

Ummm is that a equation??? If so ill try.....

(-6,3)-(1,9)= (-8,2)

(-6,3)+(1,9)= (-4,4)

Answer:

4x24

Step-by-step explanation:

Answer:

4x24= 96, Amanda spends 96 dollars on tickets

Step-by-step explanation:

4x24=96

4 tickets x 24 dollars each

4x24

96

The error message displayed in Excel Solver when attempting to solve an unbounded problem is "Solver could not find a bounded solution."

This error message indicates that the Solver was unable to find a solution that satisfies all the constraints while still remaining within the defined bounds. An unbounded problem is one in which the objective function can be improved without limit, meaning that there is no upper limit on the optimal solution.

This can occur when there are no constraints on the variables, or when the constraints are too loose to define a unique optimal solution. In such cases, the Solver may continue to search for a solution without ever converging to a final answer. It is important to review the constraints and variables in the problem to ensure that they are properly defined and that the Solver is set up correctly.

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Answer:

(0,7)

Step-by-step explanation:

there is no problem work shown.

We have shown that the determinant of the 3x3 matrix M, divided by 2, gives us the area of the triangle formed by the three given vertices on a coordinate plane.

To prove that the determinant of a 3x3 matrix representing three vertices of a triangle on a coordinate plane can solve the area of a triangle, we can use the following steps:

Let's consider a triangle with vertices A(x1, y1), B(x2, y2), and C(x3, y3).

Step 1: Construct the matrix M:

M = | x1 y1 1 |

| x2 y2 1 |

| x3 y3 1 |

Step 2: Calculate the determinant of matrix M:

det(M) = (x1 * y2 * 1 + y1 * 1 * x3 + 1 * x2 * y3) - (1 * y2 * x3 + x1 * 1 * y3 + y1 * x2 * 1)

= (x1 * y2 + y1 * x3 + x2 * y3) - (y2 * x3 + x1 * y3 + y1 * x2)

= x1 * y2 + y1 * x3 + x2 * y3 - y2 * x3 - x1 * y3 - y1 * x2

Step 3: Simplify the determinant:

det(M) = x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)

Step 4: Divide the determinant by 2 to get the area of the triangle:

Area = 1/2 * det(M)

= 1/2 * [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)]

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Answer:

$805

Step-by-step explanation:

(3500)(0.2) = 700    and 700 x 0.15 = 105

add 700 + 105 = 805 <- Answer

On solving the provided question, we can say that by probability the value of P(x > 1.05) is 0.16

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.

The value of P(x > 1.05) is 0.16

н = 0.05 standard deviation

α = 1.0000 mean

Ψ = sample reading

z-score

z = x - u/p

z   =  1.05 - 1 / 0.05

soz

P(x>1.05) = 0.1587

P(x>1.05) =  0.16

Hence, the value of P(x > 1.05) is 0.16

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a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

x = 5

Step-by-step explanation:

21 - 3x = 6

21 - 6 = 3x

15 = 3x

5 = x

therefore x=5

Answer:

-284

Step-by-step explanation:

If it's not im truly sorry

The parameter often associated with enzyme affinity for substrates is Km.

Km, also known as the Michaelis constant, is a parameter commonly used to quantify the affinity of an enzyme for its substrate. It is an important parameter in enzyme kinetics and plays a crucial role in determining the efficiency of an enzyme-substrate interaction.

Km represents the substrate concentration at which the rate of the enzymatic reaction is half of its maximum velocity (Vmax). In other words, enzymes with lower Km values have higher affinity for their substrates, as they can achieve half of their maximum velocity at lower substrate concentrations. Therefore, Km serves as an indicator of the enzyme's ability to bind and convert substrates into products efficiently.

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The length of any side of given cube with subjected to pressure 2.0 x 105 pa is equal to 5.702 cm.

Let us consider bulk modulus represented by B

And the pressure is represented by  P applied to a material

Relation between pressure, bulk modulus and change in volume ΔV/V is equal to

P = B (ΔV/V)

For a cube, each side has the same initial volume V₀.

⇒Relative change in volume is the same for all sides

⇒P = B (ΔV/V₀)

The initial volume of the cube is V₀ = (4 cm)³ = 64 cm³.

Pressure applied is P = 2.0 x 10⁵ Pa

Bulk modulus is B = 4.7 x 10⁵ N/m²

ΔV/V₀ = P/B

          =(2.0 x 10⁵ Pa) / (4.7 x 10⁵ N/m²)

          = 0.4255

Relative change in volume is the same as the relative change in length of any side.

Each side has the same initial volume.

⇒ length of any side of the cube after it is subjected to the pressure is,

⇒L = L₀ (1 + ΔV/V₀)

     = (4 cm) (1 + 0.4255)

     = 5.702 cm

Therefore, the length of any side of the cube is approximately 5.702 cm for the given condition of pressure.

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Answer:

The answer is A.

Step-by-step explanation:

All of earths bodies of water including groundwater. the hydrosphere also includes the cryosphere, which is made up of the worlds ice sheets and sea ice.

Answer:

a. the hydrosphere

Step-by-step explanation:

hydro means water

Answer:

12 is the largest one number of gift bags he can make. Each will have 4 gingerbread cookies and 5 candy canes

Step-by-step explanation:

Answer:

26 meters

Step-by-step explanation:

Answer:

the answer is 20.

add up the length, and the hight,

then times it by 2.

BOOM

you get the answer :)

Step-by-step explanation:

Answer:

Substitute point (4, 8)

y = y1 + m(x - x1)

y = 8 + m(x - 4)

y = 8 + mx - 4m

let m = 3 (It can be anything) Substitute m into equation:

y = 8 + (3)x - 4(3)

y = 2x - 4

Answer:

B

Step-by-step explanation:

the diagonals of a parallelogram bisect each other , then

GX = XE , that is

3x - 5 = 2x ( subtract 2x from both sides )

x - 5 = 0 ( add 5 to both sides )

x = 5

Then

DF = 5x + 1 = 5(5) + 1 = 25 + 1 = 26 , so

XF = \(\frac{1}{2}\) DF = \(\frac{1}{2}\) × 26 = 13

The probability that the average of all 30 rolls is less than 3 can be calculated using the Central Limit Theorem.

The Central Limit Theorem states that the distribution of sample means from a large sample size will approach a normal distribution, regardless of the shape of the population distribution.

In this case, the mean of the sample means will be equal to the population mean (3.5) and the standard deviation of the sample means (also known as the standard error) will be equal to the population standard deviation divided by the square root of the sample size (1.71 / √ √(30)).

To find the probability that the average of all 30 rolls is less than 3, we can convert it to a standard normal distribution by using the Z-score formula: Z = (X - μ) / σ, where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, we have Z = (3 - 3.5) / (1.71 / √(30)). By looking up the Z-score in a standard normal distribution table or using statistical software, we can determine the probability associated with that Z-score, which represents the probability that the average of all 30 rolls is less than 3.

It's important to note that we assume the rolls of the die are independent and identically distributed, and that the die is fair.

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The integer would be -250, since it is a decrease.

There is not strong evidence against the claimed value of 43%.

N = 400
P = 0.43

Check Conditions:
10% Condition: We assume 400 hectares is less than 10% of all hectares, so this condition is met.
Large Counts Condition: 400(0.43) = 172 and 400(1-0.43) = 228 are both greater than 10, so this condition is met.

Is this approximately normal? Yes, because both the 10% condition and the Large Counts condition are met.

Find the Important Values:
Mean of p-hat: 0.43
Standard Deviation of p-hat: sqrt((0.43)(1-0.43)/400) = 0.0248

Assuming that the Forestry Commission's report is accurate, what is the approximate probability that more than 47% of the sample would have had the certification in 2016?
We need to find the z-score for 0.47: z = (0.47-0.43)/0.0248 = 1.61
Using a z-table, we find that the probability of getting a z-score greater than 1.61 is 0.0537.

Since our probability of 0.0537 is greater than 5%, there is not strong evidence against the claimed value of 43%.

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ᴇʏᴏᴀᴘᴜᴀ8ᴡ8ᴇɪᴇᴜᴇᴜɪᴇ8ᴡ8ᴡ8ǫ

Answer: i think it's 75

Step-by-step explanation: because 5 is half of 10 and 10 is half it makes 75

Answer:

Step-by-step explanation:

75

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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Sample is biased. Based on her findings, Arianna revealed the percentage in her state after polling 600 residents of her city. Thus, the sample fails to accurately reflect the population. Option (4) is correct.

When some members of a population are systematically more likely to be chosen in a sample than others, this is known as sampling bias. What makes sampling bias significant? Sampling bias poses a risk to external validity since it restricts the applicability of your findings to a larger population. When some population members have a higher or lower sampling probability than others, the sample is biased.

This includes choosing or sampling people according to their hobbies, gender, or age. Therefore, a fair or impartial sample must be representative of the entire population under investigation. When a research study design fails to gather a representative sample of a target population, the phenomenon known as sampling bias takes place. This usually happens as a result of the respondents' selection criteria not capturing a broad enough sampling frame to include all points of view.

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Correct Question:

Arianna collected data from a random sample of 600 people in her city asking whether or not they bike to work. Based on the results, she reports that 44% of the people in her state bike to work. Why is this statistic misleading?

Select the correct answer below:

1. The statistic contains a calculation error.

2. The sample is self-selected.

3. The data contains an outlier.

4. The sample is biased.