when x = -2, y = []
when x = 0, y = []
when x = 2, y = []
when x = 4, y = []​

The probability that exactly three out of two hundred randomly chosen individuals will have the disease is approximately 0.1668 or 16.68%.

To solve this problem, we need to use the binomial distribution formula. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes (success or failure) and the probability of success is constant.

In this case, the probability of success is 1.2%, which is equivalent to 0.012. The number of trials is 200, and we want to know the probability of exactly three successes.

The formula for the probability of exactly k successes in n trials is:

P(k) = (n choose k) * p^k * (1-p)^(n-k)

where "n choose k" represents the number of ways to choose k items from a set of n items, and p is the probability of success.

Using this formula and plugging in the values we have, we get:

P(3) = (200 choose 3) * 0.012^3 * (1-0.012)^(200-3)

P(3) = (200! / (3! * 197!)) * 0.012^3 * 0.988^197

P(3) = 0.1668

Therefore, the probability that exactly three out of two hundred randomly chosen individuals will have the disease is approximately 0.1668 or 16.68%. This means that if we were to repeat this experiment many times, we would expect to see about 16.68% of the time that exactly three people out of two hundred have the disease.

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Answer:

Whats the question?

Step-by-step explanation:

The symbol used to represent the y-intercept in a regression line in statistics is usually denoted as "b0" or "β0".

In linear regression analysis, a regression line is used to model the relationship between an independent variable (x) and a dependent variable (y). The regression line is expressed as y = b0 + b1x, where "y" is the predicted value of the dependent variable, "x" is the independent variable, "b0" represents the y-intercept, and "b1" represents the slope of the line.

The y-intercept, denoted as "b0" or "β0" (beta-zero), represents the value of the dependent variable (y) when the independent variable (x) is equal to zero. It is the point where the regression line intersects the y-axis. The y-intercept is an important parameter in regression analysis as it provides information about the initial value of the dependent variable before any changes in the independent variable occur.

The estimation of the y-intercept in regression analysis involves finding the value of "b0" or "β0" that minimizes the sum of squared differences between the observed values of the dependent variable and the predicted values on the regression line. This estimation is typically done using statistical software or through mathematical calculations based on the data points and the least squares method.

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Therefore, the area of the quarter circle of radius 8 cm is 16π square centimeters (or approximately 50.2655 square centimeters if we use a decimal approximation for π).

A circle is a two-dimensional shape that is defined as the set of all points that are a fixed distance (called the radius) from a central point (called the center) in a plane. It is one of the most basic geometric shapes and is often used in a variety of mathematical and scientific contexts. One important thing to note about circles is that they are symmetrical: any line passing through the center of a circle divides the circle into two halves that are mirror images of each other. Circles are commonly used in a variety of contexts, including geometry, trigonometry, physics, engineering, and many other fields. They are also used in everyday life, such as in the design of wheels and other circular objects, the calculation of the areas of circular fields or gardens, and the measurement of circular objects like plates and bowls.

Here,

The formula for the area of a quarter circle is given by:

A = (1/4)πr²

where A is the area of the quarter circle, r is the radius of the circle, and π is the mathematical constant pi (approximately 3.14159).

In this case, the radius of the quarter circle is 8 cm, so we can substitute this value into the formula and simplify as follows:

A = (1/4)π(8 cm)²

A = (1/4)π(64 cm²)

A = 16π cm²

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Answer:

89

Step-by-step explanation:

First multiply 94*2 = 188

Subtract 99 from 188

188 - 99 = 89

Check:

89 + 99 = 188

188/2 = 94

Answer:

5.71

Step-by-step explanation:

you divide 2 by 1.34 and then divide 4 by that

For each given sample result, the p-value and conclusion are as follows:

a. p-value = 0.0067, Conclusion: Reject H0,  b. p-value = 0.0830, Conclusion: Fail to reject H0, c. p-value = 0.0322, Conclusion: Reject H0

d. p-value = 0.6221, Conclusion: Fail to reject H0

The p-value is a measure of the evidence against the null hypothesis (H0). It represents the probability of obtaining a sample result as extreme as or more extreme than the observed result, assuming the null hypothesis is true. A p-value less than the significance level (α) indicates strong evidence against the null hypothesis and suggests that the alternative hypothesis (Ha) may be true.

a. For p = .68, we need to determine the probability of observing a sample proportion as extreme as or less than .68, assuming the null hypothesis is true. By conducting the appropriate statistical test (e.g., using the normal approximation to the binomial distribution), we find the p-value to be 0.0067. Since the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to support the claim that the proportion is less than .75.

b. For p = .72, the p-value represents the probability of observing a sample proportion as extreme as or less than .72. Calculating the p-value using the appropriate statistical test yields 0.0830. Since the p-value is greater than α = .05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion is less than .75.

c. With p = .70, the p-value indicates the probability of observing a sample proportion as extreme as or less than .70. The calculated p-value is 0.0322. As the p-value is less than α = .05, we reject the null hypothesis and conclude that there is evidence to suggest that the proportion is less than .75.

d. For p = .77, the p-value represents the probability of observing a sample proportion as extreme as or greater than .77. After performing the necessary calculations, we find the p-value to be 0.6221. Since the p-value is much greater than α = .05, we fail to reject the null hypothesis. Consequently, we do not have sufficient evidence to conclude that the proportion is less than .75.

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Answer:

A: the equation is y=2x+5, and the height is 40 inches

It will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

Let's use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/k)

Where:

N0 = initial population (8 rabbits)

N = final population (5,800 rabbits)

k = doubling time (1 month)

t = time in months (what we're trying to find)

Substituting the values we have:

5,800 = 8 * 2^(t/1)

Dividing both sides by 8:

725 = 2^(t/1)

Taking the logarithm of both sides (base 2):

log2(725) = t/1

t = log2(725) ≈ 9.515

So it will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

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Answer:

i. square

ii. triangle

iii. trapezoid

Step-by-step explanation:

A cross section of a figure or shape can be produced by cutting a slice through the figure.

From the given question, since the angle of intersection of the planes could either be parallel or perpendicular to the base, the cross section could either be a square, a triangle or a trapezoid.

A square is generated when the angle is parallel to the base, a triangle could also be produced when the angle is perpendicular to the base, and a  trapezoid is formed when the angle is perpendicular to the base.

Answer:

A, B, C

Step-by-step explanation:

EDGE 2020

The time necessary for p dollars to double when it is invested at interest rate r compounded annually is given by the formula:

t = (ln 2) / (r ln (1 + r))

When compounded monthly, the formula becomes:

t = (ln 2) / (12 r ln (1 + r/12))

When compounded daily, the formula becomes:

t = (ln 2) / (365 r ln (1 + r/365))

When compounded continuously, the formula becomes:

t = ln 2 / (r)

Note that ln is the natural logarithm function.

To use these formulas, you need to know the value of the interest rate r. For example, if r is 5%, then:

When compounded annually, t = (ln 2) / (0.05 ln 1.05) = 13.86 years
When compounded monthly, t = (ln 2) / (12 x 0.05 ln 1.0041) = 14.21 years
When compounded daily, t = (ln 2) / (365 x 0.05 ln 1.000137) = 14.27 years
When compounded continuously, t = ln 2 / (0.05) = 13.86 years

Therefore, the time necessary for p dollars to double depends on the interest rate and the frequency of compounding. Generally, the more frequently the interest is compounded, the shorter the time necessary for p dollars to double.

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Using substitution method, the cost of hotel per night is $ 85

Let hotel cost per night = x

Let car rental per day = y

4x + 2y = 500 ____(1)

4x + 5y = 740 ____(2)

Solving for x in the equation

Equation (1) - (2)

-3y = - 240

y = 80

Substitute the value of y in (1)

4x + 2(80) = 500

4x + 160 = 500

4x = 500-160

4x = 340

x = $85

Therefore, hotel cost per night is $85

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Answer:

ok check the attachment.

Step-by-step explanation:

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A pharmacist puts 32 pills into a prescription order that calls for 30 pills: The absolute error, in this case, would be 2 pills.

To find the absolute error in this situation, we'll follow these steps:

1. Determine the actual number of pills the pharmacist put in the prescription order: 32 pills
2. Determine the number of pills the order calls for 30 pills
3. Calculate the absolute error by subtracting the expected number of pills from the actual number: |32 - 30|

The absolute error, in this case, is |32 - 30| = 2 pills.

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The data being skewed and indicating higher wait times above 7 minutes due to a busy park is the most suitable description based on the given line plot.

The best description of the shape of the data is that it is skewed and might mean that the wait times were higher than 7 minutes because the park was busy.

Here's the explanation:

From the line plot, we can observe that there are 6 dots above 6, 5 dots above 7, 3 dots above 5, and 2 dots above 8.

The distribution is not symmetric, as the data points are not evenly spread around a central value.

The fact that there are more dots above 7 and 8 suggests that the wait times were higher than these values for a significant number of rides. This skewness in the data indicates that there were instances of longer wait times.

Additionally, the presence of dots above 5 and 6 suggests that there were some rides with shorter wait times as well.

However, the higher concentration of dots above 7 and 8 indicates that the park was likely busy, leading to longer wait times.

The option stating that the data is skewed and might mean that the wait times were higher than 7 minutes because the park was busy best aligns with the information provided by the line plot.

It acknowledges the skewness of the data towards higher wait times, suggesting that the park experienced increased demand and longer queues during the fair.

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Answer:

She needs to order 12 cars

Step-by-step explanation:

To find the total number of models, we just need to multiply the number of options for each choice:

body style: 2 options

interior package: 3 options

drive train: 2 options

So the number of different models is:

2 * 3 * 2 = 12 different models

So in order to have all the possible models, she needs to order 12 cars.

Answer:

53361

Step-by-step explanation:

All you need to do is sub in 225 for x.

So: 225^2+12(225)+36

= 53361

Answer:

It will be 40

Step-by-step explanation:

Hope this helped have an amazing day!

The given statement is,

→ if u have 10 and add 20 and add 10.

In mathematical expression,

→ (10 + 20) + 10

→ 30 + 10

→ 40 is the answer.

The statement "Quadrilaterals A and B are both squares" does not provide enough information to determine whether A and B are scale copies of one another.

To determine if two quadrilaterals are scale copies of each other, we need to compare their corresponding sides and angles. If the corresponding sides of two quadrilaterals are proportional and their corresponding angles are congruent, then they are scale copies of each other.

In this case, since both A and B are squares, we know that all of their angles are right angles (90 degrees). However, we do not have any information about the lengths of their sides. Without knowing the lengths of the sides of A and B, we cannot determine if they are scale copies of each other.

Therefore, the statement cannot be determined as true or false based on the given information.

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Answer:

hope you have understood

Alessia spent $5,408 on entertainment in 2021.

To determine how much Alessia spent on entertainment in 2021, we need to work backward from the given information about her salary in 2022.

Let's assume Alessia's salary in 2021 was the same as in 2022, which is $26,000 after tax.

Since Alessia spends 35% of her after-tax salary on rent, we can calculate her rent expenditure:

Rent = 35% × $26,000

= $9,100

The remaining amount is split between food, petrol, and entertainment in the ratio 6:11:8.

To determine the ratio's total parts, we sum the individual parts:

Total parts = 6 + 11 + 8 = 25

Next, we calculate the value of one part of the ratio:

One part = ($26,000 - $9,100) / 25

= $16,900 / 25

= $676

Now, we can calculate how much Alessia spent on entertainment in 2021, which is 8 parts of the ratio:

Entertainment expenditure = 8 × $676

= $5,408

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The requirement f(x1) * f(x2) < 0 for choosing initial guesses x1 and x2 with opposite signs ensures the validity and convergence of certain numerical root-finding methods such as the bisection method or the regula falsi method.

The statement you provided is true for certain numerical methods used to find roots of equations, such as the bisection method or the regula falsi method. These methods are iterative and require an initial interval or range where the root is expected to be found. To ensure convergence and a valid solution, it is necessary to choose initial guesses x1 and x2 such that the function f(x) evaluated at those points have opposite signs, i.e., f(x1) * f(x2) < 0.

The rationale behind this requirement is based on the Intermediate Value Theorem, which states that if a continuous function f(x) changes sign over an interval [x1, x2], then there exists at least one root within that interval. By ensuring that f(x1) and f(x2) have opposite signs, we guarantee the existence of a root within the interval [x1, x2].

The bisection method works by repeatedly bisecting the interval and selecting a new subinterval that contains the root. At each iteration, the method narrows down the interval by halving it, based on the sign change observed in the function evaluations.

Similarly, the regula falsi (or false position) method also operates by iteratively refining the interval based on the linear interpolation between the function values at the endpoints. The method adjusts the interval based on the sign change of the function, converging to the root.

Both methods rely on the property of opposite signs to guarantee convergence and avoid getting stuck in a non-converging or incorrect solution. If the initial guesses do not satisfy the condition f(x1) * f(x2) < 0, it is possible that the method fails to converge or converges to a different root or solution.

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Answer:

transformed function, g (x) = (1/5)(-x)+7

Step-by-step explanation:

Assuming

f (x) = -x           (and not f(x)-=x)

To compress/expand, we apply

g (x) = a*f(bx-k)+h

where

a=vertical stretch factor, a= 1/5 for compression (to stretch 5 times, a=5)

b=horizontal compression factor (=1 i this case)

h=vertical translation (=7)

k=horizontal translation (=0)

So the transformed function,

g (x) = (1/5)(-x)+7

Answer:

the second one?

Step-by-step explanation:

Answer:

a. Jack's rate of change is 0.7 miles per hour

b. Jack is hiking upwards

Step-by-step explanation:

a. 0.7 is his slope (a.k.a change) 0.7 miles because that is how distance is being measured and t is the time in hours

b. since his slope is positive I am assuming that he is going upwards like (/) the line is raising

False. In cubic closest packing (CCP) or face-centered cubic (FCC) structure, the unit cell is not body-centered cubic (BCC). The unit cell in CCP/FCC is composed of a cube with lattice points at the corners and an additional lattice point at the center of each face.

The term "cubic closest packing" refers to the arrangement of atoms or spheres in a cubic lattice where the spheres touch each other along their faces.

This arrangement is achieved by stacking layers of spheres in an ABCABC... pattern. Each sphere is in contact with 12 surrounding spheres, resulting in a coordination number of 12.

On the other hand, the body-centered cubic (BCC) structure has a different arrangement. In BCC, the unit cell consists of a cube with lattice points at the corners and an additional lattice point at the center of the cube. Each atom or sphere in BCC is in contact with eight neighboring atoms.

Therefore, the statement that the unit cell in cubic closest packing is body-centered cubic is false. The correct unit cell for cubic closest packing or face-centered cubic packing is the face-centered cubic (FCC) structure.

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The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

We have,

To prove the equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 using mathematical induction,

We will follow the three steps of mathematical induction:

The base case, the induction hypothesis, and the inductive step.

Step 1: Base case

Let's start by checking if the equation holds true for the base case, which is n = 1.

When n = 1, the left-hand side (LHS) is 1² = 1, and the right-hand side (RHS) is 1(1 + 1)(2(1) + 1) / 6 = 1.

Since LHS = RHS for the base case, the equation holds true.

Step 2: Induction hypothesis

Assume the equation holds true for some positive integer k, where k ≥ 1. This is our induction hypothesis:

1 + 4 + 9 + ... + k² = k(k + 1)(2k + 1) / 6

Step 3: Inductive step

We need to prove that if the equation holds true for k, it also holds true for k + 1.

Starting with the left-hand side of the equation, we add (k + 1)² to both sides:

1 + 4 + 9 + ... + k² + (k + 1)² = k(k + 1)(2k + 1) / 6 + (k + 1)²

Simplifying the right-hand side:

= [k(k + 1)(2k + 1) + 6(k + 1)²] / 6

= [(2k³ + 3k² + k) + (6k² + 12k + 6)] / 6

= (2k³ + 9k² + 13k + 6) / 6

= [(k + 1)(k + 2)(2k + 3)] / 6

We can see that the right-hand side is now in the form

(k + 1)((k + 1) + 1)(2(k + 1) + 1) / 6, which matches the equation for k + 1.

Since the equation holds true for k implies it holds true for k + 1, and the base case is true, we have proven the equation using mathematical induction.

Therefore,

The equation 1 + 4 + 9 + ... + n² = n(n + 1)(2n + 1) / 6 is proven by mathematical induction.

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[2×3]^5 = ( 2^5 ) * (3^5) = 32 * 243 =7,776

we have used the rule

Answer: \(m=\frac{1}{9}\)

Step-by-step explanation:

\(\frac{9}{7}m=\frac{1}{7}\)

Multiply by the reciprocal to isolate m.

\((\frac{7}{9} )\frac{9}{7}m=\frac{1}{7}(\frac{7}{9} )\)

\(m=\frac{1}{9}\)