The real root of the equation can be written in the form , where , , and are positive integers. Find .

A because 2 is half of 4 and 18 is half of 36.

Step-by-step explanation: because 2 is half of 4 and 18 is half of 36.

Answer:

The total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Step-by-step explanation:

Circumference of ellipse = \(\pi(a+b)\)

Circumference of semi-ellipse = \(\frac{\pi(a+b)}{2}\)

we are given that The opening is to have a height of 2 feet at the center and a width of 6 feet along the base.

So, \(a = \frac{6}{2}=3 , b = 2\)

Circumference of semi-ellipse =\(\frac{3.14(3+2)}{2}=7.85 feet\)

Distance from center =\(\sqrt{a^2-b^2}=\sqrt{3^2-2^2}=2.236 feet\)

Hence the total length of the string is 7.85 feet and  the center should be 2.236 feet far the string be nailed into the base

Answer:

(a) 2.22

(b) 1.3986

(c) 1.183

Step-by-step explanation:

Let X denote the number of women who consider themselves fans of professional baseball.

The proportion of women who consider themselves fans of professional baseball is, p = 0.37.

A random sample of n = 6 women are selected and each was asked if she considers herself a fan of professional baseball.

Each woman's reply is independent of the others.

The random variable X thus follows a binomial distribution with parameters n = 6 and p = 0.37.

(a)

Compute the mean of the binomial distribution as follows:

\(\text{Mean}=np=6\times 0.37=2.22\)

(b)

Compute the variance of the binomial distribution as follows:

\(\text{Variance}=np(1-p)=6\times 0.37\times (1-0.37)=1.3986\)

(c)

Compute the standard deviation of the binomial distribution as follows:

\(\text{Standard Deviation}=\sqrt{np(1-p)}=\sqrt{6\times 0.37\times (1-0.37)}=1.183\)

Answer:

ok only gid know the answer

(a) the expected value of the amount you win 2/9 , (b) the variance of the amount you win 5/18 , c) The expected value of the amount you win is -$0.0667 and d)The variance of the amount you win is 1.2898.

Let's calculate the expected value and variance of the amount you win step by step:

a) Calculate the probability of drawing two marbles of the same color.

First, calculate the probability of drawing two red marbles:

P(RR) = (5/10) * (4/9) = 20/90 = 2/9

Similarly, calculate the probability of drawing two blue marbles:

P(BB) = (5/10) * (4/9) = 20/90 = 2/9

b) Calculate the probability of drawing two marbles of different colors.

P(RB) = (5/10) * (5/9) = 25/90 = 5/18

P(BR) = (5/10) * (5/9) = 25/90 = 5/18

c) Calculate the expected value.

The expected value (EV) is calculated by multiplying each outcome by its probability and summing them up.

EV = (P(RR) * $1.10) + (P(RB) * -$1.00) + (P(BR) * -$1.00) + (P(BB) * $1.10)

= (2/9 * $1.10) + (5/18 * -$1.00) + (5/18 * -$1.00) + (2/9 * $1.10)

= $0.2444 - $0.2778 - $0.2778 + $0.2444

= -$0.0667

Therefore, the expected value of the amount you win is -$0.0667.

d) Calculate the variance.

The variance is a measure of the dispersion of the outcomes around the expected value. It is calculated as the sum of the squared differences between each outcome and the expected value, weighted by their probabilities.

Variance = (P(RR) * ($1.10 - EV)²) + (P(RB) * (-$1.00 - EV)²) + (P(BR) * (-$1.00 - EV)²) + (P(BB) * ($1.10 - EV)²)

Variance = (2/9 * ($1.10 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (5/18 * (-$1.00 - (-$0.0667))²) + (2/9 * ($1.10 - (-$0.0667))²)

= (2/9 * $1.1667²) + (5/18 * -$0.9333²) + (5/18 * -$0.9333²) + (2/9 * $1.1667²)

= 1.2898

Therefore, the variance of the amount you win is 1.2898.

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The answer is 200000∠-50°.

The multiplication of complex numbers can be done by using the distributive property of multiplication.

Let's find the solution to this problem using the given formula which is:

(a + bi)(c + di) = (ac - bd) + (ad + bc)i

where a, b, c, and d are real numbers.(1000∠-30°) × (200∠-20°)

To multiply these complex numbers, we need to multiply their magnitudes and add their angles to get the angle of the resultant complex number.

So, the solution can be calculated as:1000 × 200 = 200000∠(-30°-20°)200000∠-50°

Thus, the answer is 200000∠-50°.

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To determine the height of the hole in the tree, we can use trigonometry and the given angle of elevation. The correct answer is -6.43 ft.

Let's consider a right triangle formed by the squirrel, the base of the tree, and the height of the hole. The angle of elevation is the angle between the line of sight from the squirrel to the hole and the horizontal ground.

In this case, we have the opposite side (height of the hole) and the adjacent side (distance from the squirrel to the base of the tree). We need to find the length of the opposite side.

Using trigonometric functions, we can determine that the tangent of the angle of elevation is equal to the opposite side divided by the adjacent side. In this case, we have:

tan(40°) = opposite/10 ft

To isolate the opposite side, we can multiply both sides of the equation by 10 ft:

10 ft * tan(40°) = opposite

Using a calculator, we can evaluate tan(40°) ≈ 0.8391:

opposite ≈ 10 ft * 0.8391 ≈ 8.391 ft

Rounding this value to the nearest hundredth foot gives us approximately -6.43 ft.

Therefore, the height of the hole in the tree is approximately -6.43 ft. The negative sign indicates that the hole is below the squirrel's position.

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Using technology to estimate the absolute maximum and minimum values: The given function is f(x) = x⁵ - x³ + 3 for -1 ≤ x ≤ 1.

Here are the steps to find the absolute maximum and minimum values of f(x):

Step 1: Plot the graph of the given function by using the graphing calculator or software.

Step 2: Observe the points where the graph attains its maximum or minimum value. From the graph, it is clear that the absolute maximum value of f(x) is approximately equal to 3.00 at x = 1 and the absolute minimum value is approximately equal to 2.00 at x = -1. Using calculus to find the exact maximum and minimum values: The given function is f(x) = x⁵ - x³ + 3 for -1 ≤ x ≤ 1. Here are the steps to find the absolute maximum and minimum values of f(x):

Step 1: Find the first derivative of f(x) and equate it to zero to find the critical points of f(x)

f'(x) = 5x⁴ - 3x² = x²(5x² - 3) Critical points are x = 0 and x = ± √(3/5)

Step 2: Evaluate the value of the function f(x) at each critical point and the endpoints of the given interval

f(-1) = (-1)⁵ - (-1)³ + 3 = 2

f(0) = 0⁵ - 0³ + 3 = 3

f(1) = 1⁵ - 1³ + 3 = 3

f(√(3/5)) = (√(3/5))⁵ - (√(3/5))³ + 3 ≈ 2.69

f(-√(3/5)) = (-√(3/5))⁵ - (-√(3/5))³ + 3 ≈ 2.69

Step 3: Compare the values of f(x) at all critical points and endpoints to find the absolute maximum and minimum values. Absolute maximum value of f(x) is 3, which occurs at x = 0 and x = 1. Absolute minimum value of f(x) is 2, which occurs at x = -1.

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Answer: 5.872

Step-by-step explanation:

Two thirds of twelve is eight and three sevenths of five is around 2.14 so subtract 2.14 from eight and you get the answer above

The slope of the line is -3/4.

What is a line?

A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.

The points on the line are (-4, 5), (0,2), (4, -1).

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ -  y₁)/(x₂ -  x₁).

The slope of the line is

(2 - 5)/(0 - (-4)) = -3/4

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Answer:

y = -4

Step-by-step explanation:

-3 - 4y = 9 - y

Add 3 to both sides

-4y = 9 - y + 3

-4y = 12 - y

Add y to both sides

-4y + y = 12

-3y = 12

Divide both sides by -3

y = -4

Among the statements provided, the only true statement is that 235 is congruent to 23 modulo 13.

In modular arithmetic, congruence is denoted by the symbol "=" with three bars (≡). It indicates that two numbers have the same remainder when divided by a given modulus.

Let's evaluate each statement:

1. 57 ≡ -13 (mod 7): This statement is false. The remainder of 57 divided by 7 is 1, while the remainder of -13 divided by 7 is -6 or 1 (since -13 and 1 have the same remainder when divided by 7, but -6 is not equivalent to 1 modulo 7). Therefore, 57 is not congruent to -13 modulo 7.

2. 235 ≡ 23 (mod 13): This statement is true. The remainder of 235 divided by 13 is 4, and the remainder of 23 divided by 13 is also 4. Hence, 235 is congruent to 23 modulo 13.

3. 57 ≡ 13 (mod 7): This statement is false. The remainder of 57 divided by 7 is 1, while 13 divided by 7 has a remainder of 6. Thus, 57 is not congruent to 13 modulo 7.

4. 2 - 14 ≡ -28 (mod 7): This statement is false. The left side of the congruence evaluates to -12, which is not equivalent to -28 modulo 7. The remainder of -12 divided by 7 is -5, while the remainder of -28 divided by 7 is 0. Hence, -12 is not congruent to -28 modulo 7.

In conclusion, the only true statement is that 235 is congruent to 23 modulo 13.

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Answer: Mean- 89.1, Median- 89, Mode- No mode

Step-by-step explanation:

Mean: 82+85+88+89+92+94+94= 624

624/7= 89.1

Median: 82, 85, 88, 89, 92, 94, 94

89 is the median because it has 3 numbers on the right and 3 on the left.

Mode: No mode because a number doesn't show up more than 2 times.

Answer:x − x^{2} − 1.

Step-by-step explanation:

.

Answer:

B

Step-by-step explanation:

X is the number of hours, which for this question is 11.

So you do X × 8.9 --> 11 × 8.9 = 97.9

Y = 100 - 97.9

Y = 2.1

Therefore the answer is B

The outbound flight is 2.5 hours, and the return flight is 2 hours and 18 minutes.

To solve this problem, let's break it down step by step.

Step 1: Convert the flying time to a single unit

The total flying time is given as 4 hours and 48 minutes. We need to convert this to a single unit, preferably hours. Since there are 60 minutes in an hour, we can calculate the total flying time as follows:

Total flying time = 4 hours + (48 minutes / 60 minutes per hour)

Total flying time = 4 hours + (0.8 hours)

Total flying time = 4.8 hours

Step 2: Define variables

Let's define the variables for the time taken for the outbound flight and the return flight. Let's call the time for the outbound flight "x" hours.

Outbound flight time = x hours

Step 3: Calculate the time for the return flight

We are given that the return flight averages 500 miles per hour due to a tailwind. Therefore, the time for the return flight can be calculated using the formula:

Return flight time = Total flying time - Outbound flight time

Substituting the values, we get:

Return flight time = 4.8 hours - x hours

Step 4: Calculate the distances for each flight

The distance for the outbound flight can be calculated using the formula:

Outbound distance = Outbound flight time * Average speed

Substituting the values, we get:

Outbound distance = x hours * 460 miles per hour

Similarly, the distance for the return flight can be calculated as:

Return distance = Return flight time * Average speed

Substituting the values, we get:

Return distance = (4.8 hours - x hours) * 500 miles per hour

Step 5: Set up the distance equation

Since the outbound and return flights cover the same distance (round trip), we can set up the equation:

Outbound distance = Return distance

Substituting the previously calculated values, we get:

x * 460 = (4.8 - x) * 500

Step 6: Solve the equation

Now, we solve the equation for x to find the time for the outbound flight:

460x = 2400 - 500x

Add 500x to both sides:

460x + 500x = 2400

Combine like terms:

960x = 2400

Divide both sides by 960:

x = 2400 / 960

Simplifying:

x = 2.5

Step 7: Calculate the time for the return flight

We can calculate the time for the return flight using the equation:

Return flight time = Total flying time - Outbound flight time

Substituting the values, we get:

Return flight time = 4.8 - 2.5

Return flight time = 2.3 hours

Step 8: Convert the return flight time to hours and minutes

Since the return flight time is given in hours, we can convert it to hours and minutes. Multiply the decimal part (0.3) by 60 to get the minutes:

Minutes = 0.3 * 60

Minutes = 18

Therefore, the return flight time is 2 hours and 18 minutes.

Step 9: Summarize the results

The time for the outbound flight is 2.5 hours, and the time for the return flight is 2 hours and 18 minutes.

In summary:

Outbound flight time: 2.5 hours

Return flight time: 2 hours and 18 minutes

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Answer:

I think it might be the last answer

Step-by-step explanation:

sorry just tryna help ok dokie

Answer:

yaaa last one

Step-by-step explanation:

The solution to the initial value problem for the vector function r(t) is:

r(t) = -9kt² + 30k, where k is a constant.

This solution satisfies the given differential equation and initial conditions.

To solve the initial value problem for the vector function r(t), we are given the following differential equation and initial conditions:

Differential equation: d²r/dt² = -18k

Initial conditions: r(0) = 30k and dr/dt(0) = 6i + 6j + Di + k

To solve this, we will integrate the given differential equation twice and apply the initial conditions.

First integration:

Integrating -18k with respect to t gives us: dr/dt = -18kt + C1, where C1 is the constant of integration.

Second integration:

Integrating dr/dt with respect to t gives us: r(t) = -9kt² + C1t + C2, where C2 is the constant of integration.

Now, applying the initial conditions:

Given r(0) = 30k, we substitute t = 0 into the equation: r(0) = -9(0)² + C1(0) + C2 = C2 = 30k.

Therefore, C2 = 30k.

Next, given dr/dt(0) = 6i + 6j + Di + k, we substitute t = 0 into the equation: dr/dt(0) = -18(0) + C1 = C1 = 0.

Therefore, C1 = 0.

Substituting these values of C1 and C2 into the second integration equation, we have:

r(t) = -9kt² + 30k.

So, the solution to the initial value problem is:

r(t) = -9kt² + 30k, where k is a constant.

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To evaluate the triple integral ∭exydv over the solid tetrahedron, we need to determine the limits of integration for each variable.

The solid tetrahedron is defined by its vertices, which are not provided in the question. Without the specific vertices, it is not possible to determine the limits of integration or calculate the volume of the tetrahedron.

In general, when evaluating a triple integral over a solid tetrahedron, we first determine the limits of integration for each variable based on the boundaries of the tetrahedron. This involves finding the equations of the planes that define the tetrahedron's faces and determining the corresponding limits for each variable within those boundaries. Once the limits of integration are established, the integral can be evaluated.

However, since the specific vertices of the tetrahedron are not provided in the question, it is not possible to proceed with evaluating the triple integral ∭exydv.

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Answer:

is 3, because ‘six’ has three letters

The normal price of each chair is

The percentage off the normal price is

The percentage of the present price of each chair will be

To calculate the present value of one chair, we will use the formula below

By substituting the values, we will have

Since Mr .Krabs bought 4 chairs, the amount he spent will be

By substituting the values, we will have

Therefore,

The amount Mr.Krabs spent is = $6.30

The radical form of each of the given expressions are respectively;

1)  √7

2) √4⁷

3) ⁷√4

4)  ∜7

A radical expression of a number is simply defined as an expression containing a radical symbol which is also a square root.

1) The expression given to us as 7^(¹/₂) expressed in radical form is; √7

2) The expression given to us as 4^(7/2) expressed in radical form is; √4⁷

3) The expression given to us as 4^(1/7) expressed in radical form is; ⁷√4

4) The expression given to us as 7^(¹/₄) expressed in radical form is; ∜7

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a) Any value outside of Q1 - 1.5(IQR) and Q3 + 1.5(IQR) can be considered a potential outlier.

b) This will give us a visual representation of the distribution of income among the full-time students.

c) It is important to analyze outliers carefully to ensure that they are not artificially skewing the results of our analysis.

(a) To check for outliers in the data set, we can use the box-and-whisker plot or the z-score method. However, since we do not have the exact data, we cannot use these methods. One way to identify potential outliers is to calculate the quartiles (Q1, Q2, and Q3) and the interquartile range (IQR).

(b) To draw a histogram of the data, we can use the frequency distribution table given in the question. The x-axis should represent the income ranges (e.g. $0-$100, $100-$200, etc.) and the y-axis should represent the frequency (i.e. the number of students who earned income within each range).

(c) If there are any outliers in the data set, we need to investigate them further to determine the reason for their unusual values. Possible reasons for outliers could be data entry errors, extreme values due to high- or low-income jobs, or unique situations such as unexpected windfalls or emergencies.

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Answer:

it is 6...................

The missing points are listed below:

The picture attached aside shows us a right-angled parallelepiped and the Euclidean geometry indicates that a plane is generated by three non-colinear points, that is, three points that cannot be contained by a line.

Therefore, coplanar points are points that can be contained by one and same plane. Parallelepipeds are solids with eight vertices and twelve sides, each of them corresponding to a plane.

In this problem we must determine what fourth point is contained by the same plane that comprises the other three. Now we show the corresponding answers:

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Answer:

58.5

Step-by-step explanation:

1.The machine will have no value after 48 months. 2.The graph of the machine's value over time will be a straight line. 3.The slope of the graph represents the rate of depreciation per month. 4.The intercepts of the graph indicate the initial value and zero value. 5.The expression V = -750x + 28,000 represents the value of the machine. 6.The machine has no value when x = 37 according to the expression. 7.The answer obtained using the expression differs from the answer in 8.question 1 due to possible rounding errors or calculation variations.

To determine when the machine has no value, we observe the pattern of depreciation. Based on the given data, the machine depreciates by $3,500 every 6 months. Therefore, it will take 48 months (8 cycles of 6 months) for the machine to have no value.

The table shows a consistent decrease in value over time with equal intervals of 6 months. This indicates a linear relationship between the number of months and the value. A linear relationship is represented by a straight line on a graph.

The slope of the graph can be determined by calculating the change in value divided by the change in time. In this case, the slope is (-750), meaning the value decreases by $750 per month. It represents the rate of depreciation per month.

The intercepts of the graph are obtained by determining the value of the machine at the start (initial value intercept) and when it reaches zero (zero value intercept). The initial value intercept is $28,000, which represents the starting value of the machine. The zero value intercept occurs when the machine has no value.

The expression V = -750x + 28,000 represents the value of the machine. The coefficient of x (-750) represents the rate of depreciation per month, while the constant term (28,000) represents the initial value.

Using the expression, when x = 37, the machine has no value. This differs from the answer in question 1 (48 months). The discrepancy could be due to rounding errors or variations in the method used to calculate the exact point at which the value reaches zero.

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we can estimate that about 12% of the students surveyed spend 6 or more hours playing a sport or game outdoors.

To estimate the probability of a student answering 6 or more hours, we need to count the number of students who spend 6 or more hours and divide by the total number of students surveyed.

Looking at the table, we can see that there are 3 students who spend 6 or more hours playing a sport or game outdoors. Therefore, the estimated probability of a student answering 6 or more hours is:

3/25 = 0.12 or 12%

what is probability?

In mathematics, probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

The probability of an event A happening is denoted by P(A) and is defined as the ratio of the number of favorable outcomes for event A to the total number of possible outcomes in the sample space.

For example, if you toss a fair coin, the probability of getting heads is 0.5 because there is one favorable outcome (getting heads) out of two possible outcomes (getting heads or tails).

Probability is used in many fields, including statistics, finance, science, and engineering, to model and analyze uncertain events and make predictions about future outcomes.

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