Number graph ranging from negative two to ten on the x and y axes. A line labeled y equals begin fraction three over two end fraction times x is drawn on the graph. A second line, labeled y equals begin fraction negative one over two end fraction x plus four, is drawn on the graph. What is the solution to the system of equations represented by these two lines? Responses (2, 0) (2, 0) (0, 4) (0, 4) (4, 2) (4, 2) (2, 3)

T = 29 minutes.

The rate of hits per minute is 12, and the time interval of interest is from 8:14 P.M. to 8:43 P.M., which is 29 minutes. However, we need to adjust for the fact that the Poisson process is occurring within a larger time frame (7:00 P.M. to 9:00 P.M.).

To do this, we can find the proportion of time between 8:14 P.M. and 8:43 P.M. relative to the entire 2-hour period between 7:00 P.M. and 9:00 P.M.:

(29 minutes) / (2 hours × 60 minutes per hour) = 0.2417

So, the expected number of hits within the interval from 8:14 P.M. to 8:43 P.M. is:

lambda = (0.2417)(12 hits per minute) = 2.901

Thus, lambda = 2.901 hits per 29-minute period.

The value of t for this Poisson process is the length of the time interval we are interested in, which is:

t = 29 minutes.

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The lengths of the diagonals in the isosceles trapezoid are 11.045 units and 7.2 units.

From the given figure, the vertices of the quadrilateral are (1, 6), (3, 0), (-5, 0) and (-1, 6).

From lower left to upper right: (-5, 0) and (1, 6)

Here, length = √(6+5)²+(1-0)²

= √122

= 11.045 units

From lower right to upper left: (3, 0) and (-1, 6)

Here, length = √(-1-3)²+(6-0)²

= √52

= 7.2 units

Therefore, the lengths of the diagonals in the isosceles trapezoid are 11.045 units and 7.2 units.

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The probability of getting heads or tails when flipping a coin is 0.5 or 50%. The final probability will give you the chance of getting between 4900 and 5100 heads when flipping a fair coin 10,000 times.

However, the probability of getting a certain number of heads when flipping a coin, a certain number of times can be calculated using probability theory. In this case, the probability of getting between 4900 and 5100 heads when flipping a fair coin 10000 times can be calculated using the binomial distribution formula.

The binomial distribution formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where P(X=k) is the probability of getting k heads, n is the number of coin flips, p is the probability of getting a head (0.5 in this case), and (n choose k) is the binomial coefficient.

Using this formula, the probability of getting between 4900 and 5100 heads when flipping a fair coin 10000 times is approximately 0.023 or 2.3%. This means that out of 1000 trials, you can expect to get between 4900 and 5100 heads around 23 times.

In summary, the probability of getting between 4900 and 5100 heads when flipping a fair coin 10000 times is around 2.3%. This probability can be calculated using the binomial distribution formula, which takes into account the number of coin flips and the probability of getting a head.

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Answer: 8 2/5 feet (positive)

Step-by-step explanation:

Answer: The correct answer is A

i have no clue if this is correct if it is goodluck lol

The basic eigenvector corresponding to λ₁ = 4 is v₁ = [3.75, 4], and the basic eigenvector corresponding to λ₂ = -3 is v₂ = [5, 6].

To find the eigenvalues of matrix A, we need to solve the characteristic equation:

|A - λI| = 0

where I is the identity matrix of the same size as A, and λ is the eigenvalue we are trying to find.

For matrix A given as:

a=[8 -15]

[6 -10]

we have:

|A - λI| =

|8 - λ -15 |

|6 -10- λ |

Expanding the determinant, we get:

(8 - λ)(-10 - λ) - (-15)(6) = 0

Simplifying the expression, we get:

λ² - 2λ - 12 = 0

Using the quadratic formula, we get:

λ₁ = 4

λ₂ = -3

Therefore, the distinct eigenvalues of A are λ₁ = 4 and λ₂ = -3.

Next, we find the eigenvectors corresponding to each eigenvalue. We do this by solving the system of equations:

(A - λI)x = 0

For λ₁ = 4:

A - λ₁I =

|8 - 4 -15 |

|6 -10 - 4 |

=

|4 -15 |

|6 -14|

RREF:

|1 -3.75|

|0 0 |

Thus, we have a free variable x₂. Setting x₂ = 4, we get the basic eigenvector:

v₁ = [3.75, 4]

Therefore, there is one basic eigenvector corresponding to eigenvalue λ₁ = 4.

For λ₂ = -3:

A - λ₂I =

|8 15 |

|6 7 |

RREF:

|1 -5/6|

|0 0 |

Thus, we have a free variable x₂. Setting x₂ = 6, we get the basic eigenvector:

v₂ = [5, 6]

Therefore, there is one basic eigenvector corresponding to eigenvalue λ₂ = -3.

In summary, the distinct eigenvalues of matrix A are λ₁ = 4 and λ₂ = -3. There is one basic eigenvector corresponding to each eigenvalue. The basic eigenvector corresponding to λ₁ = 4 is v₁ = [3.75, 4], and the basic eigenvector corresponding to λ₂ = -3 is v₂ = [5, 6].

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The team that has best overall record for the season is the falcons because they have a larger mean value of 20.9 points

The mean of the dataset is defined the sum of all values divided by the total number of values. Therefore mean can be expressed as;

mean = sum of items/number of items

The mean value of Eagles = (3 + 24 + 14 + 27 + 10 + 13 + 10 + 21 + 24 + 17 + 27 + 7 + 40 + 37 + 55)/15

= 310/15 = 20.67

The mean value of falcons = (24 + 24  + 10 + 7 + 30 + 28 + 21 + 6 + 17 + 16 + 35 + 30 + 28 + 24 + 14)/15

= 314/15 = 20.93

Therefore since the mean value of falcons is higher than eagles, falcons has the best overall performance.

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An element of the sample space is a sample point. Your answer: a. sample point. In this context, an "element" refers to an individual outcome within the "sample space," which is the set of all possible outcomes. A "sample point" is a single outcome in the sample space. Therefore, an element of the sample space is a sample point.

An element of the sample space is a sample point. A sample point represents the most basic outcome of an experiment or observation. For example, if we roll a dice, the sample space would be {1, 2, 3, 4, 5, 6}, and each number in the sample space would be a sample point.

Similarly, in a coin toss experiment, the sample space would be {heads, tails}, and each outcome would be a sample point. The sample space is the set of all possible outcomes of an experiment or observation, and each element in the sample space represents a unique sample point. Understanding the sample space is essential in probability theory as it forms the basis for defining events and calculating probabilities.

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Answer:

4 muffins to each friend

Step-by-step explanation:

72-60=3x

12=3x

4=x

We apply the Gram-Schmidt process to these vectors to find an orthonormal basis:

v1 = x1 = [3, -4, 1

To find a basis of the null space N(A), we need to find all vectors x such that Ax = 0, where 0 is the zero vector.

To do this, we set up the augmented matrix [A | 0] and row reduce:

[ 1 2 1 3 2 | 0 ]

[ 4 1 0 6 1 | 0 ]

[ 1 1 2 4 5 | 0 ]

R2 - 4R1 -> R2:

[ 1 2 1 3 2 | 0 ]

[ 0 -7 -4 6 -7 | 0 ]

[ 1 1 2 4 5 | 0 ]

R3 - R1 -> R3:

[ 1 2 1 3 2 | 0 ]

[ 0 -7 -4 6 -7 | 0 ]

[ 0 -1 1 1 3 | 0 ]

R2 / -7 -> R2:

[ 1 2 1 3 2 | 0 ]

[ 0 1 4/7 -6/7 1 | 0 ]

[ 0 -1 1 1 3 | 0 ]

R1 - 2R2 - R3 -> R1:

[ 0 0 0 0 0 | 0 ]

[ 0 1 4/7 -6/7 1 | 0 ]

[ 0 0 11/7 -1/7 1 | 0 ]

We can write the system of equations corresponding to this row echelon form as:

x2 + (4/7)x3 - (6/7)x4 + x5 = 0

(11/7)x3 - (1/7)x4 + x5 = 0

Solving for the variables in terms of the free variables x3, x4, and x5, we get:

x1 = -[(4/7)x3 - (6/7)x4 - x5]/2

x2 = -(4/7)x3 + (6/7)x4 - x5

x3 = x3 (free variable)

x4 = x4 (free variable)

x5 = x5 (free variable)

So the null space N(A) is the set of all vectors of the form:

x = [ -[(4/7)x3 - (6/7)x4 - x5]/2, -(4/7)x3 + (6/7)x4 - x5, x3, x4, x5 ]

To find an orthogonal basis for N(A), we can use the Gram-Schmidt process. Let's call the columns of A a1, a2, a3, a4, and a5.

First, we need to find a basis for N(A) by setting the free variables to 1 and the others to 0:

x1 = [3, -4, 1, 0, 0]

x2 = [-2, 3, 0, 1, 0]

x3 = [-2, 1, 0, 0, 1]

Next, we apply the Gram-Schmidt process to these vectors to find an orthonormal basis:

v1 = x1 = [3, -4, 1

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After 10 rolls, we won 3 times and lost 7 times, and we have $11 left.

The probability distribution for this game is:

Outcome Probability

Lose 2/3

Win $2 1/6

Win $5 1/6

It should be noted that to calculate the anticipated value, multiply the likelihood of each scenario by its payment and add them together:

E(X) = (2/3) * (-1) + (1/6) * 2 + (1/6) * 5 = -2/3 + 1/3 + 5/6 = 1/2

As a result, the expected value of this game is $0.50. This indicates that if you play it frequently, you can expect to win $0.50 each game on average. However, you could win or lose money in any particular game.

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Answer:

The answer to your problem is, 2.04 inches

Step-by-step explanation:

We can assume that the width of the new phone is ‘ x ‘ inches

We know that [tex]\frac{x}{0.84} = \frac{3.4}{1.4}[/tex]

x = [tex]\frac{3.4}{1.4}[/tex] × 0.84

x = 2.04

Thus the answer to your problem is, 2.04 inches

The width of each locker is 1 1/4 foot.

We have,

Length = 1 foot

Volume = 7 1/2 cubic feet

Height = 6 foot

So, Volume of Prism = l w h

7 1/2 = (1) w (6)

15/2 = 6w

w= 15/(2 x 6)

w = 5/4

w= 1 1/4 foot

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The evidence supports the claim that the average life of electric light bulbs is greater than 2000 hours.

a. Null Hypothesis: The average life of electric light bulbs is not greater than 2000 hours. Alternative Hypothesis: The average life of electric light bulbs is greater than 2000 hours.

b. The critical value for a one-tailed test at the 2% level of significance with 63 degrees of freedom is 2.33.

c. The relevant test statistic is:
t = (x - μ) / (s / √n)=[tex]= \frac{(2008 - 2000)}{\frac{12.31}{\sqrt{64}}}= 13.03[/tex]
Since the test statistic is greater than the critical value of 2.33, we can reject the null hypothesis and conclude that there is sufficient evidence to support the claim.

d. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. Using a t-distribution table with 63 degrees of freedom, the p-value is less than 0.01. Since the p-value is less than the significance level of 0.02, we can reject the null hypothesis.

e. Yes, we reject the null hypothesis.

f. No, we do not reject the claim. The evidence supports the claim that the average life of electric light bulbs is greater than 2000 hours.

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X(t) = Xo/[1 + (1 - Xo)/Xo exp(-[r - o^2/2]t - oW(t))]

E[X(t)] = Xo/(1 + (1 - Xo)/Xo exp(-r t)),

V[X(t)] = Xo^2 exp(rt)/(1 + (1 - Xo)/Xo exp(rt))^2 - Xo^2/(1 + (1 - Xo)/Xo exp(-r t))^2.

The given equation is a stochastic differential equation (SDE) of the form dX(t) = a(X(t))dt + b(X(t))dW(t), where W(t) is a Wiener process (Brownian motion), a(X(t)) = rX(t)(1 - X(t)), b(X(t)) = oX(t), and Xo is the initial condition.

To solve this SDE, we use Itô's lemma, which states that for a function f(X(t)) of a stochastic process X(t), the SDE for f(X(t)) is given by df(X(t)) = (∂f/∂t)dt + (∂f/∂X)dX(t) + 1/2(∂^2f/∂X^2)(dX(t))^2.

Applying Itô's lemma to the function f(X(t)) = ln(X(t)/(1 - X(t))), we get df(X(t)) = [1/X(t) + 1/(1 - X(t))]dX(t) - 1/2[X(t)^(-2) + (1 - X(t))^(-2)](dX(t))^2.

Substituting a(X(t)) and b(X(t)) in the above expression, we get d[f(X(t))] = [r(1 - 2X(t))dt + o(1 - 2X(t))dW(t)] - 1/2[r^2X(t)(1 - X(t))^2 + o^2X(t)^2]dt.

Integrating both sides of the above expression from time 0 to t and using the initial condition X(0) = Xo, we get ln[X(t)/(1 - X(t))] = ln[Xo/(1 - Xo)] + [r - o^2/2]t + oW(t).

Solving for X(t), we get X(t) = Xo/[1 + (1 - Xo)/Xo exp(-[r - o^2/2]t - oW(t))].

Taking the expectation and variance of X(t), we get:

E[X(t)] = Xo/(1 + (1 - Xo)/Xo exp(-r t)),

V[X(t)] = Xo^2 exp(rt)/(1 + (1 - Xo)/Xo exp(rt))^2 - Xo^2/(1 + (1 - Xo)/Xo exp(-r t))^2.

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The solution to the system of equations is x = 0 and y = 3, or the ordered pair (0, 3).

To solve this system of equations, we can use the method of elimination. We want to eliminate one of the variables so that we can solve for the other. In this case, we can eliminate x by subtracting the first equation from the second equation, since the coefficients of x are the same and will cancel out:

(2x + 4y) - (2x + 2y) = 12 - 6

Simplifying the left side and right side of the equation, we get:

2y = 6

y = 3

Now that we have solved for y, we can substitute this value back into either equation to solve for x. Using the first equation, we get:

2x + 2(3) = 6

x = 0

Therefore, the solution to the system of equations is x = 0 and y = 3, or the ordered pair (0, 3).

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Using the expression 24÷4=6 to calculate the equation, the solution is 60

From the question, we have the following parameters that can be used in our computation:

24÷4=6

To find 240÷4, we simply multiply both sides of 24÷4=6 by 10

Using the above as a guide, we have the following:

10 * 24 ÷ 4 = 6 * 10

Evaluate the products

240 ÷ 4 = 60

Hence, the solution is 60

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Answer:

To find the inverse of the function y = π/2 + sin(x), we need to first swap the positions of x and y:

x = π/2 + sin(y)

Now, we can solve for y:

sin(y) = x - π/2

y = sin⁻¹(x - π/2)

Therefore, the equation for the inverse of the function y = π/2 + sin(x) is y = sin⁻¹(x - π/2).

Answer:

Step-by-step explanation:

To find the optimal ticket price that will maximize revenue, we need to determine the price point where the increase in revenue from selling each ticket at a higher price is greater than the decrease in revenue from selling fewer tickets due to the higher price.

Let's start by calculating the current revenue generated at the current ticket price of $6.00:

Current revenue = 1800 x $6.00 = $10,800

Now, we need to determine the effect of increasing ticket prices by $0.50 on the number of tickets sold:

For each $0.50 increase in ticket price, 100 fewer people will attend. So, for a $0.50 increase, the new ticket price will be $6.50, and the number of attendees will be:

1800 - 100 = 1700

For a $1.00 increase, the new ticket price will be $7.00, and the number of attendees will be:

1700 - 100 = 1600

And so on.

We can create a table to calculate the revenue at different price points:

Ticket Price Number of Tickets Sold Revenue

$6.00                 1800                                $10,800

$6.50                 1700                                $11,050

$7.00                 1600                          $11,200

$7.50                 1500                                $11,250

$8.00                  1400                          $11,200

$8.50                  1300                          $11,050

$9.00                  1200                          $10,800

As we can see from the table, the optimal ticket price that will maximize revenue is $7.50, where the revenue is $11,250. Beyond this point, the decrease in attendance outweighs the increase in ticket price, resulting in a decrease in revenue.

Therefore, the owner should increase the ticket price to $7.50 to maximize revenue.

The particular solution for the given differential equation when y(1) = 1 is:
arctan(y) = x + π/4 - 1

The given equation is:
dy/dx = y² + 1

To solve this first-order, nonlinear, ordinary differential equation, we can use the separation of variables method. Here are the steps:

1. Rewrite the equation to separate variables:
dy/(y² + 1) = dx

2. Integrate both sides:
∫(1/(y² + 1)) dy = ∫(1) dx

On the left side, the integral is arctan(y), and on the right side, it's x + C:
arctan(y) = x + C

Now, we'll find the particular solution using the initial condition y(1) = 1:
arctan(1) = 1 + C

Since arctan(1) = π/4, we can solve for C:

π/4 = 1 + C
C = π/4 - 1

So, the particular solution for the given differential equation when y(1) = 1 is:

arctan(y) = x + π/4 - 1

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The rule for the table is y = -8x + 88.

The price of the shoes after 8 month is 24 dollars.

The table shows the discount prices for a pair of shoes over several months.

Therefore, the rule for the tables can be represented as follows:

y = mx + b

where

Therefore, using (1,80)(2, 72)

m = 72 - 80 / 2 - 1

m = -8

Hence,

y = -8x + b

using (1, 80)

80 = -8 + b

b = 88

Therefore,

y = -8x + 88

Therefore, let's find the price after 8 months

y = -8(8) + 88

y = -64 + 88

y = 24

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The gradient of the path from the trailhead to the mountain peak can be calculated by dividing the change in elevation (in feet) by the length of the trail (in miles). i.e., Gradient = (Change in Elevation) / (Trail Length)

To calculate the elevation change, we can subtract the elevation at the trailhead from the elevation at the mountain peak:

Change in Elevation = Peak Elevation - Trailhead Elevation
Change in Elevation = 9,262 ft - 3,874 ft
Change in Elevation = 5,388 ft

To calculate the length of the trail in miles, we simply divide the length in feet by the number of feet in a mile:

Trail Length = 3 miles

Now we can calculate the gradient:

Gradient = (Change in Elevation) / (Trail Length)
Gradient = 5,388 ft / 3 miles
Gradient = 1,796 ft/mi

Therefore, the gradient of the path from the trailhead to the mountain peak is 1,796 ft/mi. This means that for every mile traveled along the path, there is an increase in elevation of 1,796 feet. The steepness of this path may pose a challenge to hikers, especially those who are not accustomed to hiking at high elevations. Hikers need to be prepared and take appropriate safety precautions when hiking in mountainous terrain.

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The value of x in the equation 2x² + 10x + 12 = 0 is -2 and -3.

An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.

The standard form of a quadratic equation is:

ax² + bx + c = 0

The quadratic formula is given by:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\\\Given\ the\ equation\ 2x^2+10x+12=0:\\\\a=2;b=10;c=12\\\\x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} \\\\substituting:\\\\x=\frac{-10\pm\sqrt{10^2-4(2)(12)} }{2(2)} \\\\x=-3; and\ x=-2\\[/tex]

The value of x is -2 and -3.

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We have successfully drawn the given planes when working on a body centered cubic structure.

When working with a body centered cubic structure, it's important to understand that the unit cell consists of a cube with one additional atom at the center of the cube. This gives rise to unique properties and symmetry within the crystal structure.

To draw the planes (100), (010), and (101) within this structure, we can use the Miller indices notation. In this notation, each plane is represented by three integers that correspond to the intercepts of the plane with the three axes of the unit cell.

For example, the (100) plane intersects the x-axis at a point where x=1, and intersects the y- and z-axes at points where y=0 and z=0, respectively. Using the Miller indices notation, we can write this plane as (100).

Similarly, the (010) plane intersects the y-axis at a point where y=1, and intersects the x- and z-axes at points where x=0 and z=0. Therefore, this plane can be written as (010).

Finally, the (101) plane intersects the x-axis at a point where x=1, the y-axis at a point where y=0, and the z-axis at a point where z=1. Using Miller indices notation, we can represent this plane as (101).

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The probability of the arrow landing on an odd number is the number of odd numbers divided by the total number of possible outcomes. Therefore, the probability of the arrow landing on an odd number is  0.5 or 50%.


To find the probability that the arrow will point at an odd number on a circular board with 8 equal parts, we'll first determine the total number of odd numbers present and then divide that by the total number of possible outcomes.

Step 1: Identify the odd numbers on the board. They are 1, 3, 5, and 7. The game consists of spinning the arrow on a circular board with 8 equal parts, which means there are 8 possible outcomes or numbers. Since we want to know the probability of landing on an odd number, we need to count how many odd numbers are on the board. In this case, there are four odd numbers: 1, 3, 5, and 7.

Step 2: Count the total number of odd numbers. There are 4 odd numbers.

Step 3: Count the total number of possible outcomes. Since the board is divided into 8 equal parts, there are 8 possible outcomes.

Step 4: Calculate the probability. The probability of the arrow pointing at an odd number is the number of odd numbers divided by the total number of possible outcomes.

Probability = (Number of odd numbers) / (Total number of possible outcomes)
Probability of landing on an odd number = Number of odd numbers / Total number of possible outcomes
Probability of landing on an odd number = 4 / 8

Step 5: Simplify the fraction. The probability of the arrow pointing at an odd number is 1/2 or 50%.

So, the probability that the arrow will point at an odd number is 1/2 or 50%.

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The linear function for the given statement is y = (-1/2)x + 6.

To write a linear function for the statement "A candle is 6 inches tall and burns at a rate of 1/2 inch per hour," we will need to use the slope-intercept form of a linear function, which is y = mx + b. In this case, y represents the remaining height of the candle, m represents the rate of burning, x represents time in hours, and b represents the initial height of the candle.

Step 1: Identify the initial height (b). The candle is 6 inches tall, so b = 6.

Step 2: Identify the rate of burning (m). The candle burns at a rate of 1/2 inch per hour, so m = -1/2 (negative because the height decreases as time passes).

Step 3: Write the linear function using the slope-intercept form y = mx + b. Substitute the values of m and b:
y = (-1/2)x + 6

Thus, we can state that the linear function for the given statement is:

y = (-1/2)x + 6.

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The surface area of the composite figure is 1474 square feet.

In the composite figure, there are two shapes rectangular prism and triangular prism.

Surface area of rectangular prism = 2(lb+bh+hl)

= 2(19×9+9×11+11×19)

= 958 square feet

Surface area of triangular prism = (Perimeter of the base × Length of the prism) + (2 × Base Area)

= (S1 +S2 + S3)L + bh

= (13+13+10)×11+10×12

= 516 square feet

Total surface area = 958+516

= 1474 square feet

Therefore, the surface area of the composite figure is 1474 square feet.

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G and H in terms of x and y is given by H = [tex]B^d[/tex](a, 1) and G = [tex]B^{d_2}(0, 1)[/tex] , the  set S of all possible values of y is x+y≥0 the Cartesian coordinates systems is S = [-7/5, -3/5].

Choosing a point O of the line (the origin), a unit of length, and an orientation for the line are all steps in choosing a Cartesian coordinate system for a one-dimensional space, or for a straight line. The line "is oriented" (or "points") from the negative half towards the positive half when an orientation determines which of the two half-lines given by O is the positive half and which is the negative half. Then, depending on which half-line contains P, the distance between each point P on the line and O can be specified.

a) O = (0, 0) a = (2, -1)∈R²

G = [tex]B^{d_2}(0, 1)[/tex]

D = [tex]\sqrt{x^2+y^2}[/tex] < 1

So this is a circle until center at (0, 0) and no point on

[tex]x^2+y^2[/tex] and every point inside it

H = [tex]B^d[/tex](a, 1) = {v=(x,y)∈R²: d(a, v)≤1}

b) x-2 + y=1 ≤ 1

x-y ≤4

For, x-2≤0, y+1≥0  we get,

2-x+y+1≤1 y-x ≤-2

For, x-2≤0,   y+1≤0,   2-x-y-1≤1

x+y≥0

c) Therefore,

d(a, (13/5, y) ≤ 1

(13/5 -2) + (y +1) ≤ 1

S = [-7/5, -3/5].

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The 90% confidence interval for the true mean weight of the textbooks is approximately (70.062 ounces, 73.938 ounces).

Given that you measured 21 textbooks and found a mean weight of 72 ounces with a population standard deviation of 5.4 ounces, we can follow these steps:

1. Identify the sample size (n), sample mean (X), population standard deviation (σ), and confidence level (90%).

  n = 21
  X = 72 ounces
  σ = 5.4 ounces
  Confidence level = 90%

2. Determine the critical value (z) for a 90% confidence interval. For a 90% confidence interval, the critical value (z) is 1.645.

3. Calculate the standard error (SE) using the formula [tex]SE = \frac {σ }{\sqrt{n} }[/tex].

 [tex]SE = \frac{5.4}{\sqrt{21} } = 1.177[/tex]

4. Calculate the margin of error (ME) using the formula ME = z * SE.

  ME = 1.645 * 1.177 = 1.938

5. Construct the confidence interval using the formula: X ± ME.

  Lower limit = 72 - 1.938 = 70.062
  Upper limit = 72 + 1.938 = 73.938

Based on your measurements, the 90% confidence interval for the true mean weight of the textbooks is approximately (70.062 ounces, 73.938 ounces).

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Answer:

C

Step-by-step explanation:

y=-2x+4

2x+y=4

2x-2x+4=4

4=4