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Mr. Smith is building a detention room for students who like to throw spaghetti pieces in class. So he finds 3 areas and he is wanting to put clear tile flooring so those students can learn how to clean the floor. Mr. Rice wants to know the total area of all the floors. One room is a rectangle and is 4ft wide by 3ft long. The other room is shaped like a triangle with a base of 6ft and is 4ft long. The other room is a circle with a diameter of 8ft.

Answer:

16

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Using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

To approximate the integral [sin(x²+1) dx] using the trapezoidal rule with 5 ordinates, we can use the following formula:

∫[a,b]f(x)dx ≈ [(b-a)/2n][f(a) + 2f(a+h) + 2f(a+2h) + 2f(a+3h) + 2f(a+4h) + f(b)]

where n is the number of ordinates (in this case, n = 5), h = (b-a)/n is the interval width, and f(x) = sin(x²+1).

First, we need to find the interval [a,b] over which we want to integrate. Since no interval is given in the problem statement, we'll assume that we want to integrate over the interval [0,1].

Therefore, a = 0 and b = 1.

Next, we need to find h:

h = (b-a)/n = (1-0)/5 = 0.2

Now, we can apply the trapezoidal rule formula:

∫[0,1]sin(x²+1)dx ≈ [(1-0)/(2*5)][sin(0²+1) + 2sin(0.2²+1) + 2sin(0.4²+1) +             2sin(0.6²+1) + 2sin(0.8²+1) + sin(1²+1)]

≈ (1/10)[sin(1) + 2sin(0.05²+1) + 2sin(0.15²+1) + 2sin(0.35²+1) + 2sin(0.65²+1) + sin(2)]

≈ (1/10)[0.8415 + 2sin(1.0025) + 2sin(1.0225) + 2sin(1.1225) + 2sin(1.4225) + 1.5794]

≈ 0.5047

Therefore, using the trapezoidal rule with 5 ordinates, we approximate the integral [sin(x²+1) dx] over the interval [0,1] to be 0.5047 to 4 decimal places.

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The length of AE¯¯¯¯¯ is 5√2 cm.

Since quadrilateral ABCD is a square, all four sides are congruent. Let's denote the length of one side as s. Therefore, the length of BD¯¯¯¯¯ is equal to s.

Given that the length of BD¯¯¯¯¯ is 10 cm, we can conclude that s = 10 cm.

Now, we need to find the length of AE¯¯¯¯¯. Looking at the square, AE¯¯¯¯¯ is the diagonal connecting opposite corners.

In a square, the diagonal divides the square into two congruent right triangles. We can use the Pythagorean theorem to find the length of the diagonal.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the diagonal (the hypotenuse) is the same as the side length, s.

Applying the Pythagorean theorem:

s^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

10^2 = AE¯¯¯¯¯^2 + AE¯¯¯¯¯^2

100 = 2 * AE¯¯¯¯¯^2

AE¯¯¯¯¯^2 = 50

Taking the square root of both sides:

AE¯¯¯¯¯ = √50

Simplifying the square root:

AE¯¯¯¯¯ = √(25 * 2) = 5√2 cm

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Answer: answer is in picture

Step-by-step explanation:

Answer:

Confidence Interval = (1.41, 1.59)

Step-by-step explanation:

To construct a confidence interval for the population mean, we can use the following formula:

Confidence Interval = sample mean ± (margin of error * standard error)

where the standard error is equal to the standard deviation divided by the square root of the sample size.

Given the information provided, we can calculate the standard error as:

standard error = 2.16 / sqrt(1370) = 0.058

Then, we can calculate the margin of error as 0.12.

Substituting these values into the formula, we get:

Confidence Interval = 1.5 ± (0.12 * 0.058)

Confidence Interval = (1.41, 1.59)

Therefore, we can interpret the 95% confidence interval as follows: we are 95% confident that the true population mean of the number of days that people feel lonely in the past 7 days is between 1.41 and 1.59. This means that if we were to take many samples of 1370 subjects and compute the confidence intervals for each sample using the same method, we would expect about 95% of the intervals to contain the true population mean.

Answer:

(15°, 165°)

Step-by-step explanation:

Given the equation 6 sin2(x) = 3, we are to find the value of x that satisfies the equation in the interval  [0, 2π]

Given

6 sin2(x) = 3,

Divide both sides by 6

6 sin2(x)/6 = 3/6

sin2(x) = 1/2

2x = sin^-1(0.5)

2x = 30°

x = 30°/2

x = 15°

Since sin is positive in the second quadrant, x2 = 180-15

x = 165°

Hence the values within the interval are 15 and 165.

(15°, 165°)

Answer: (x > -3).

Step-by-step explanation:

To solve the inequality 4(1 - x) < 16, we will simplify and solve for x:

4(1 - x) < 16

Distribute the 4:

4 - 4x < 16

Subtract 4 from both sides:

-4x < 12

Divide both sides by -4. Note that when dividing by a negative number, the inequality sign flips:

x > -3

The solution to the inequality is x > -3. This means that x must be greater than -3 for the inequality to hold true.

To graph the solution on a number line, we mark a shaded region to the right of -3, indicating that all values greater than -3 satisfy the inequality:

The open circle at -3 indicates that -3 is not included in the solution since the inequality is strict (x > -3).

here's the graph for 4(1-x)<16

Answer:

Step-by-step explanation:

The number of farmers who grew at least one of the three crops is 921

Let's analyze the given information step by step to determine the number of farmers who grew at least one of the three crops, the number of farmers who did not grow any of the three crops, and the number of farmers who grew exactly two of the three crops.

According to the survey results:

125 farmers grow only beans.

107 farmers grow only corn.

87 farmers grow only old.

200 farmers grow wheat and corn.

50 farmers grow wheat and old.

176 farmers grow corn.

To find the number of farmers who grew at least one of the three crops, we need to sum up the number of farmers who grew each crop individually and subtract the number of farmers who grew both combinations of crops:

Number of farmers who grew beans = 125

Number of farmers who grew corn = 107 + 200 + 176 = 483

Number of farmers who grew old = 87 + 50 + 176 = 313

Adding these numbers, we get:

125 + 483 + 313 = 921

Therefore, 921 farmers grew at least one of the three crops.

To find the number of farmers who did not grow any of the three crops, we subtract the total number of farmers in the survey from the number of farmers who grew at least one of the three crops:

500 - 921 = -421

Since we can't have a negative number of farmers, we can conclude that there is an error in the given information.

As for the number of farmers who grew exactly two of the three crops (beans, corn, or old), we don't have enough information to determine this value based on the given data.

In conclusion, the number of farmers who grew at least one of the three crops is 921 (assuming there was an error in the given information). The number of farmers who did not grow any of the three crops cannot be determined with the information provided, and the number of farmers who grew exactly two of the three crops cannot be determined.

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The values into the slope-intercept form, we have y = -5x - 6

The slope-intercept form of a linear equation is given by:

y = mx + b

where 'm' represents the slope of the line, and 'b' represents the y-intercept.

In this case, the y-intercept is (0, -6), which means that the line crosses the y-axis at the point (0, -6).

The slope is given as -5.

Therefore, substituting the values into the slope-intercept form, we have:

y = -5x - 6

This equation represents the line with a y-intercept of (0, -6) and a slope of -5.

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Answer:

An x-coordinate is the first element in an ordered pair. When an ordered pair is graphed as the coordinates of a point in the coordinate plane, the x-coordinate represents the directed distance of the point from the y-axis. Another name for the x-coordinate is the abscissa.

Step-by-step explanation:

Answer:

1st number line

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

The question is not clear but I will provide info based on given

Translation of

means sliding by a points to left/right and by b points to up/down

The graph of the linear equation, x = 6, is shown in the image attached below.

The equation of a vertical line is given as x = b, where b is the x-intercept of the line. That is, b is the point on the x-axis where the line crosses.

Given the equation, x = 6, it means the line is a vertical line. Therefore, on the graph, the line would intercept the the x-axis at 6.

Thus, the graph of the linear equation, x = 6, is shown in the image attached below.

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Answer:

2(17)+8

Step-by-step explanation:

answer: 2(17+8)

explanation: 17+8=  25

25 times 2= 50

34+16=50

:)

You need to prove that all the angles measure 90 degrees and that their sides are equal

Answer:

option D

Step-by-step explanation:

To isolate the variable on one side of the equal sign, divide both sides of the equation by the coefficient of the variable.

Answer:

first is closes to the 40 second is closer to 10th

Step-by-step explanation:

your rounding to the nearest tenth

The quadrilateral formed by vertices A(-4, 3), B(-5, 1), C(0, 1), and D(-1, 3) has 1 pair of parallel sides and is a trapezoid.The correct answer is B.it has 1 pair of parallel sides and is a trapezoid  

Step 1: Find the slopes of all four sides using the slope formula,

m = (y2 - y1) / (x2 - x1).

AB: m = (1 - 3) / (-5 - (-4)) = (-2) / (-1) = 2

BC: m = (1 - 1) / (0 - (-5)) = 0 / 5 = 0

CD: m = (3 - 1) / (-1 - 0) = 2 / (-1) = -2

DA: m = (3 - 3) / (-4 - (-1)) = 0 / (-3) = 0

Step 2: Identify parallel sides by comparing slopes.

Sides AB and CD have slopes that are negative reciprocals of each other (2 and -2), which means they are not parallel.

Sides BC and DA both have a slope of 0, which means they are parallel.

Since the quadrilateral has 1 pair of parallel sides, it is a trapezoid.

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Answer:

b. The students find a p-value less than 0.05

c. Carrie ends up losing the election.

e. The students make the conclusion that Carrie does not have more than 50% of the vote.

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis.

Type I error is one in which we reject a true null hypothesis.

In the given scenario Type I error will be the one where students incorrectly estimates the p value and reject the null hypothesis when it was true. This error will result in losing the elections.

Based on the information provided, the missing number would be number 6.

When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.

In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.

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Answer:

0.75 .......................

Las cantidades de bolitas para cada una de las tres personas son las siguientes:

Amanda: 19 bolitas

Rodrigo: 15 bolitas

Patricio: 69 bolitas

En este problema tenemos a tres personas (Amanda, Rodrigo y Patricio) que se reparten 103 bolitas, en términos algebraicos, cada persona es representada por las siguientes ecuaciones:

Amanda

x = y + 4

Rodrigo

y

Patricio

z = 2 · (x + y) + 1

Total

x + y + z = 103

A continuación, determinamos la cantidad de bolitas asociada con Rodrigo:

x + y + 2 · (x + y) + 1 = 103

3 · x + 3 · y = 102

x + y = 34

y + 4 + y = 34

2 · y = 30

y = 15

Luego, determinamos las cantidades de bolitas de Amanda y Patricio:

x = 15 + 4

x = 19

z = 2 · (19 + 15) + 1

z = 2 · 34 + 1

z = 68 + 1

z = 69

El enunciado se encuentra escrito en español y el lenguaje de la respuesta es el mismo del enunciado.

The statement is written in Spanish and the language used in the answer is the same of the statement.

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Answer:

49.39 units.

Step-by-step explanation:

In Right Triangle TUV, \(\angle U\) is a right triangle.

TU = 18.5

∠T = 68 degrees

\(\cos \theta =\dfrac{Adjacent}{Hypotenuse} \\$Using the trigonometric formula above:\\\cos T =\dfrac{TU}{TV}\\\\\cos 68^\circ =\dfrac{18.5}{TV}\\\\$Cross multiply\\TV*\cos 68^\circ=18.5\\\\TV=\dfrac{18.5}{\cos 68^\circ}\\\\TV=49.39$ units\)

The length of segment TV is 49.39 units.

Answer: y = 12.6

Step-by-step explanation:

Since x = 2 and y = 6.3 * x, y = 6.3 * 2.

6.3 * 2 is equal to 12.6, so y is 12.6.

Answer:

y = 12.6

Step-by-step explanation:

y = 6.3x                     x = 2

Solve for y.

y = 6.3(2)

y = 12.6

So, the answer is 12.6

The Quotient has two parts. The Whole part and the Fractional part. The Fractional part is also known as the Remainder.

Step 1) Divide 6432 by 8 to get the Quotient. Keep the Whole part for the next step and set the Remainder aside.

Step 2) Divide the Whole part of the Quotient from step 1 by 8. Again keep the Whole part and set the Remainder aside.

Step 3) Repeat Step 2 above until the Whole part is 0.

Step 4) Write down the Remainders in reverse order to get the answer to 6432 as octal.

For the number 6432, we have:

6432/8 = 804 with 0 remainder

804/8 = 100 with 4 remainder

100/8 = 12 with 4 remainder

12/8 = 1 with 4 remainder

1/8 = 0 with 1 remainder

Then, when we put the remainders together in reverse order, we get the answer. The decimal number 6432 converted to octal is, therefore:

Answer: 14440

Answer:

  $11,250

Step-by-step explanation:

Normally, when I work "mixture" problems, I like to choose the variable so it represents the amount of the largest contributor. Here, that would be the amount invested at 15%.

Unfortunately, the question asks for the amount invested at 7%. Using a variable to represent that amount means that there will be negative numbers involved. Care must be taken in the arithmetic.

Let x represent the amount invested at 7%. Then 16000-x is the amount invested at 15%. The total interest for one year is ...

  0.07x + 0.15(16000 -x) = 1500 . . . . sum of interest amounts at each rate

  -0.08x +2400 = 1500  . . simplify

  -0.08x = -900 . . . . . . . . subtract 2400

  x = 11250 . . . . . . . . . . . . divide by -0.08

The bank loaned $11,250 at 7%.