Use a calculator to find the trigonometric ratio. Round your answer to four decimal places
sin 98°~

Aurelia should order about 150 hamburgers for the school picnic.

Now, Based on the survey results, out of the 80 students surveyed, 30 students preferred hamburgers.

Hence, we assume that this proportion of students who prefer hamburgers remains consistent throughout the entire school, we can estimate that about;

⇒ 30/80

⇒ 0.375

⇒ 37.5% of the 400 students would prefer hamburgers.

Hence, For number of hamburgers Aurelia should order, we can multiply the estimated proportion of students who prefer hamburgers (0.375) by the total number of students (400):

0.375 x 400 = 150

Therefore, Aurelia should order about 150 hamburgers for the school picnic.

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Answer:

2nd choice. -a^3 - 8ab^2

Step-by-step explanation:

(3a^3b - 4ab^2 + 5ab) - (4a^3b + 4ab^2 + 5ab)

Distribute the minus sign and take out the parenthesis.

3a^3b - 4ab^2 + 5ab - 4a^3b - 4ab^2 - 5ab

Combine like terms.

3a^3b - 4ab^2 -4ab^2 - 4ab^2 + 5ab - 5ab

-1a^3b - 8ab^2

Answer:

C. 62.8 mi

Step-by-step explanation:

Formulas to know:

[tex]c = \pi d[/tex]

[tex]c=2\pi r[/tex]

For this problem use c = [tex]\pi[/tex]d

[tex]c =\pi d[/tex]

[tex]c = 3.14*20[/tex]

[tex]c = 62.8[/tex]

The smallest number of students who go to one of these clubs is 21.

A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).

Based on the given stem and leaf diagram, the smallest number of students who go to one of these clubs is represented by the leaf value "1" in the stem "2."

Therefore, the smallest number of students who go to one of these clubs is 21.

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The larger the sample size, the smaller the SEM, and the more precise our estimates of the population mean become. However, it is important to note that the SEM only reflects the amount of error due to chance factors, and does not account for any bias or systematic error in the sampling process.

The standard deviation of the distribution of the sample means (sampling distribution) for all possible samples of size 81 that could be drawn from the parent population is known as the standard error of the mean (SEM). The SEM is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if the population standard deviation is known, we can calculate the SEM by dividing it by the square root of 81. If the population standard deviation is unknown, we can estimate it using the sample standard deviation.
The SEM represents the amount of variability in the sample means that we would expect to see if we repeatedly drew samples of size 81 from the same population. In other words, the SEM tells us how much error we would expect to see in our sample means due to chance factors alone.
The SEM is an important measure in inferential statistics because it helps us to calculate confidence intervals and to perform hypothesis tests. In general, the larger the sample size, the smaller the SEM, and the more precise our estimates of the population mean become. However, it is important to note that the SEM only reflects the amount of error due to chance factors, and does not account for any bias or systematic error in the sampling process.

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b) The critical value is 11.34.

c) By Using a chi-squared distribution table with 100 degrees of freedom and a significance level of 0.005, the critical value is 137.18.

Now, WE can simplify as;

a) For conduct a chi-squared test for the fairness of a 6-sided die with a significance level of 0.05,

we have 5 degrees of freedom

Hence, By Using a chi-squared distribution table with 5 degrees of freedom and a significance level of 0.05, the critical value is 11.07.

And, When calculated chi-squared value exceeds 11.07, then the results are statistically significant at the given level.

b) Now, When examining the results of an experiment with 4 treatments and a significance level of 0.01, we have 3 degrees of freedom

Hence, By Using a chi-squared distribution table with 3 degrees of freedom and a significance level of 0.01, the critical value is 11.34.

And, When calculated chi-squared value exceeds 11.34, then the results are statistically significant at the given level.

c) Hence, For comparing outcomes in 101 different categories with a significance level of 0.005, we have 100 degrees of freedom.

So, By Using a chi-squared distribution table with 100 degrees of freedom and a significance level of 0.005, the critical value is 137.18.

And, When calculated chi-squared value exceeds 137.18, then the results are statistically significant at the given level.

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Answer:  From the calculations, the pair of points with a slope of 4 is option c. (0, -3), (1, 1).

Step-by-step explanation:  

To determine the slope between two points, we can use the formula:

slope = (change in y) / (change in x)

Let's calculate the slope for each pair of points:

a. (1, 4), (–1, 4)

The change in y is 4 - 4 = 0

The change in x is -1 - 1 = -2

slope = 0 / -2 = 0

b. (0, 4), (4, 0)

The change in y is 0 - 4 = -4

The change in x is 4 - 0 = 4

slope = -4 / 4 = -1

c. (0, –3), (1, 1)

The change in y is 1 - (-3) = 4

The change in x is 1 - 0 = 1

slope = 4 / 1 = 4

d. (3, 0), (–1, –1)

The change in y is -1 - 0 = -1

The change in x is -1 - 3 = -4

slope = -1 / -4 = 1/4

Answer:

c. (0, –3), (1, 1)

Step-by-step explanation:

To find the slope, we use the slope formula

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

a. (1, 4), (–1, 4)

m = (4-4)/(-1-1) = 0/-2 = 0

b. (0, 4), (4, 0)

m = ( 4-0)/(0-4) = 4/-4 = -1

c. (0, –3), (1, 1)

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

d. (3, 0), (–1, –1)

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

Answer:

Therefore, the estimated actual number of storks in the bird reserve is 259. So, the answer is A. 260.

Step-by-step explanation:

This problem can be solved using a proportion.

Let x be the actual number of storks in the bird reserve.

According to the problem, Tara tagged 41 birds on the first day. Let's assume that these birds are representative of the total population. Therefore, the proportion of tagged birds to the total population should be equal to the proportion of tagged birds that Tara captured on the first day:

41/x = tagged birds from 57 captured two weeks later

We are also given that 48 of the 57 birds captured two weeks later were not tagged. Using this information, we can find the proportion of untagged birds in the total population:

48/x = untagged birds from 57 captured two weeks later

Now we can set up an equation to solve for x:

41/x = (57-48)/57

Multiplying both sides by x and simplifying, we get:

x = 41 * 57 / 9 = 259

Answer:

  [tex]f_{ave}=\dfrac{9\pi}{4}[/tex]

Step-by-step explanation:

You want the average value of f(x) = √(81 -x²) on the interval [0, 9].

The function f(x) defines a quarter circle of radius 9 in the first quadrant on the given interval. Its area is given by the formula in the problem statement:

  A = (1/4)πr² = (π/4)·81

The average value of the function is the area divided by the width of the interval:

  [tex]f_{ave}=\dfrac{\dfrac{81\pi}{4}}{9}\\\\\\\boxed{f_{ave}=\dfrac{9\pi}{4}}[/tex]

__

Additional comment

You will notice that the average value is π/4 times the radius. This is also true for a semicircle. The attachment shows the rectangle with area equal to that of the quarter circle.

<95141404393>

Answer:

Michael is 33 yrs old. John is 16 yrs old.

Step-by-step explanation:

Let M = Michael's age

Let J = John's age

M + J = 49

M-17 = J

Substitute the 2nd equation for J in the 1st equation and solve for M.

M + J = 49

M + (M-17) = 49

2M - 17 = 49

2M = 49+17

2M = 66

M = 33

So Michael is 33.

M + J = 49

33 + J = 49

J = 49-33

J = 16 John is 16.

Check that the answers work

33-16 = 17

33+16+49

Answer:

John is 16 and Michael is 33

Step-by-step explanation:

(Let John’s age be x)

Michael is 17 years older than John.

The sum of their ages is 49. So:

Simplifying the equation:

Subtracting 17 from both sides gives:

Dividing both sides by 2 gives:

So, John is 16 years old. If Michael is 17 years older, we can add 17 to 16:

Therefore, John’s age is 16 and Michael’s age is 33.

Answer:

-4

Step-by-step explanation:

5x=-13-7

5x=-20

x=-20/5

x=-4

Answer:

5x+7=-13

5x=-13-7

5x=-20

x=-20 divide by 5

x=-4

Answer:

Part A:

Let x be the amount the artist receives for her products this week. Then, the absolute value equation that represents the scenario is:

|250 - x| ≤ 25

Part B:

To solve the equation, we need to consider two cases:

Case 1: 250 - x ≤ 25

In this case, we have:

250 - x ≤ 25

x ≤ -225

x ≥ 225

Case 2: 250 - x ≥ -25

In this case, we have:

250 - x ≥ -25

x ≥ -275

x ≤ 275

Therefore, the solution to the absolute value equation is:

225 ≤ x ≤ 275

Part C:

The minimum amount the artist received for her products is $225, and the maximum amount is $275.

Step-by-step explanation:

The area of the image of the rectangle under the transformation is 10 square units

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

Matrix transformation: [tex]\left[\begin{array}{cc}-7&-2\\6&12\end{array}\right][/tex]

And, we have rectangle plotted on the graph

The transformation is a rigid transformation

This means that the area of the rectangle would be the same before and after the transformation

From the graph, the side lengths of the rectangle are

Length = 2

Width = 5

So, we have

Area = 2 * 5

Evaluate

Area = 10

Hence, the area of the image of the rectangle under the transformation is 10 square units

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Answer: AE=10, AD=14, x=5, BC=36, DE=52

Step-by-step explanation: finding x

4x-32=2(3x-21) || 4x-32=6x-42 || 10=2x || 5=x

The product of (-3/4) and (3/4) can be found by multiplying the numerators and the denominators separately.  The fraction -9/16 represents the product of (-3/4) and (3/4) in its simplest form

The step-by-step solution for finding the product of (-3/4) and (3/4).

To multiply fractions, you multiply the numerators (the numbers on top) and the denominators (the numbers on the bottom) separately. In this case, you have:

Numerators: -3 * 3 = -9

Denominators: 4 * 4 = 16

The numerator of the product is -9, and the denominator is 16.

The resulting numerator, -9, indicates that the product will have a negative value. This happens because one of the original fractions, (-3/4), is negative.

The resulting denominator, 16, is obtained by multiplying the original denominators, 4 and 4.

Putting it all together, the product of (-3/4) and (3/4) is -9/16. This means that when you multiply (-3/4) by (3/4), the result is a fraction with a numerator of -9 and a denominator of 16.

The fraction -9/16 represents the product of (-3/4) and (3/4) in its simplest form.

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Answer:

Triangular Pyramid

Step-by-step explanation:

It is triangular and looks like a pyramid. It also has a square base and four triangular faces, which is usual for a triangular pyramid.

The height of the building is approximately 45.44 ft when it casts a 68-ft shadow under an angle of elevation of 34 degrees.It's important to note that this calculation assumes the ground is flat and the sun's rays are parallel. Real-world conditions may introduce slight variations.

To determine the height of the building, we can use the           trigonometric relationship involving the angle of elevation, the height of the building, and the length of its shadow.

Let's denote the height of the building as h. The length of the shadow cast by the building is given as 68 ft, and the angle of elevation of the sun is 34 degrees.

Using the tangent function, we have the equation:

tan(34°) = h / 68To

solve for h, we can rearrange the equation:

h = 68 * tan(34°)

Calculating this expression, we find:

h ≈ 68 * 0.668178 = 45.439344 ft.

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The volume of the prism is 1368 cubic feet.

We have,

The three steps that should be taken to calculate the volume of the prism are:

- Use the formula A = b h to find the area of the base, where b is the length of the base and h is the width of the base.

For a rectangular prism, the base is a rectangle, so the formula is:

A = length x width.

- Use the formula V = B h to find the volume of the prism, where B is the area of the base and h is the height of the prism.

For a rectangular prism, the formula.

V = length x width x height.

- Substitute the given values into the formulas and solve for the volume. For the given rectangular prism with a length of 9 and one-half feet, a width of 24 feet, and a height of 6 feet, we can find the volume by using the formula V = B h.

First, we find the area of the base by using the formula:

A = length x width:

A = (9.5 ft) x (24 ft)

= 228 sq ft

Next, we use the formula V = B h to find the volume:

V = (228 sq ft) x (6 ft)

= 1368 cubic feet

Therefore,

The volume of the prism is 1368 cubic feet.

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The scale factor from triangle BAC to triangle GHF is 3/4.

We have,

The two triangles are:

ΔBAC and ΔGHF

Now,

The scale factor can be used as:

Taking the corresponding sides.

BA x M = GH

36 x M = 27

M = 27/36

M = 3/4

We can also see that,

EC x 3/4 = CF

28 x 3/4 = 21

7 x 3 = 21

21 = 21

Thus,

The scale factor from triangle BAC to triangle GHF is 3/4.

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The possible values of x in the circle using the theorem of intersecting secants are x = 7.38 and x = -11.38

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

The intersecting secants

Using the theorem of intersecting secants, we have the following equation

(5 + 7) * 7 = (x + 4) * x

When the sum is evaluated, we have

12 * 7 = (x + 4) * x

When the product is evaluated, we have

84 = x² + 4x

So, we have

x² + 4x - 84 = 0

When solved for x, we get

x = 7.38 and x = -11.38

The value of x = -11.38 cannot be used

This is because x cannot be negative

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After considering all the given options we conclude that the value of the given formula is y₁ = y₂ - m(x₂ - x₁) which is Option C.

To evaluate for y₁ in the equation m = (y₂ - y₁) / (x₂ - x₁), we can apply algebraic manipulation to isolate y₁.
In the first step, we  multiply both sides of the equation by (x₂ - x₁) to eliminate the denominator. Therefore,
m(x₂ - x₁) = y₂ - y₁
In the second step, we can subtract y₂ from both sides of the equation to isolate y₁.
Therefore,
y₁ = y₂ - m(x₂ - x₁)
So, the solution for y₁ is given by the formula:
y₁ = y₂ - m(x₂ - x₁)
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Answer:

  276.460 mi²

Step-by-step explanation:

You want the surface area of a cylinder with radius 4 mi and height 7 mi.

The area of a cylinder is given by the formula ...

  A = 2πr(r +h)

  A = 2π(4 mi)(4 mi +7 mi) = 88π mi² ≈ 276.460 mi²

The area of the cylinder is about 276.460 square miles.

__

Additional comment

The surface area is the sum of the areas of the two circular bases and the lateral area. The lateral area is the product of the cylinder height and circumference. These are combined in the formula given.

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the volume of the cone to be filled up if it has the same radius and height with is  376. 6 cm³

To determine the volume, we need to know the formula for the volume of a cone.

The formula for the volume of a cone is expressed as;

V = πr²h/3

Such that the parameters are expressed as;

Substitute the values, we have;

Volume = 3.14 × 6² × 10/3

Find the square value

Multiply the value, we have;

Volume = 1130. 4/3

Divide the values

Volume = 376. 6 cm³

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Carly has $2342.67 in her account in 2047.

Growth rate of the account is 3.75% per year.

To get amount of money Carly has in her account in 2047, we need to substitute t = 2047 into equation [tex]P = 600(1.0375)^t.[/tex]

Years = 2047 - 2010

Years = 37

[tex]P = 600*(1.0375)^{37}\\P = 600*(3.90445030158)\\P = 2342.67018095\\P = $2342.67[/tex]

The growth rate is calculated by finding the exponent coefficient in the equation [tex]P = 600(1.0375)^t[/tex]

Growth rate = (1.0375 - 1) × 100

Growth rate = 0.0375 × 100

Growth rate = 3.75%

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Answer:

  x = 106

Step-by-step explanation:

You want the measure of the unknown angle (x°) in the quadrilateral with angles 47°, 138°, and 69° given.

The sum of angles in a quadrilateral is 360°, so the measure of x is ...

  x = 360 -47 -138 -69 = 106

Angle x° is 106°.

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Answer: 8.3

Step-by-step explanation: Add all the numbers together, 11.7+5.4+17.3+3.3+3.8+9.4+6.9 equals 57.8 BUT WAIT! We aren't done, we have to divide the answer by the sum of all answers, so since there are 7 numbers we are adding together, we divide by 7, so 57.8 divided by 7 equals 8.3 (which is rounded to the nearest tenth) and theres your asnwer. Hope this helps!

The equation of line L2 in the form y = mx + c is y = (2/3)x + 23/3.  the x-intercept of L3 is -14/3. the y-intercept of L3 is -7. The point of intersection between L2 and L3 is (-88/13, 41/13).  The x-intercept of L3 is -14/3.

(a) To find the equation of line L2 perpendicular to line L1, we need to determine the slope of L1 and then use the negative reciprocal of that slope for L2.

Given the equation of line L1: 3x + 2y = 12

Rearrange the equation to isolate y:

2y = -3x + 12

y = (-3/2)x + 6

The slope of L1 is -3/2.

Since L2 is perpendicular to L1, the slope of L2 is the negative reciprocal of -3/2, which is 2/3.

Using the slope-intercept form y = mx + c, where m is the slope and c is the y-intercept, we can write the equation of L2:

y = (2/3)x + c

To find c, we substitute the coordinates of the point (2,9) into the equation:

9 = (2/3)(2) + c

9 = 4/3 + c

c = 9 - 4/3

c = 27/3 - 4/3

c = 23/3

Therefore, the equation of line L2 in the form y = mx + c is:

y = (2/3)x + 23/3

(b)(i) To find the equation of line L3 parallel to line L1, we can use the same slope as L1, which is -3/2, and substitute the given point (-4,-1) into the point-slope form y - y1 = m(x - x1):

y - (-1) = (-3/2)(x - (-4))

y + 1 = (-3/2)(x + 4)

y + 1 = (-3/2)x - 6

y = (-3/2)x - 7

Therefore, the equation of line L3 in the form ax + by = c is:

(3/2)x + y = -7

(ii) To find the x-intercept of L3, we set y = 0 and solve for x:

0 = (-3/2)x - 7

(3/2)x = -7

x = (-7)(2/3)

x = -14/3

Therefore, the x-intercept of L3 is -14/3.

To find the y-intercept of L3, we set x = 0 and solve for y:

y = (-3/2)(0) - 7

y = -7

Therefore, the y-intercept of L3 is -7.

(iii) To find the point of intersection between L2 and L3, we can set the equations of L2 and L3 equal to each other and solve for x and y:

(2/3)x + 23/3 = (-3/2)x - 7

To solve for x:

Multiply both sides by 6 to eliminate the fractions:

4x + 46 = -9x - 42

4x + 9x = -42 - 46

13x = -88

x = -88/13

Substitute the value of x back into either equation to solve for y:

y = (2/3)(-88/13) + 23/3

y = -176/39 + 299/39

y = 123/39

y = 41/13

Therefore, the point of intersection between L2 and L3 is (-88/13, 41/13).

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