(1) How many equilateral triangles are there? _____

(2) What is the measure of each of the three angles in the equilateral triangle? _____

(3) If we cut an equilateral triangle down the middle (segment a), what special right triangle do you create? _____

(4) What is the vocabulary word for the segment a? _____

(5) What is the length of the short side of one of the 30-60-90 triangles? _____

(6) What is the length of the hypotenuse of one of the 30-60-90 triangles? _____

(7) Using the properties of 30-60-90 triangles, calculate the length of the long leg of one of the 30-60-90 triangles. _____

(8) What is the height of one of the the equilateral triangles? _____

(9) Apply the formula for the area of a triangle to find the area of one equilateral triangle. _____

(10) Calculate the area of the complete hexagon by multiplying the area of one equilateral triangle by the number of triangles. _____

The probability that the sample proportion of individuals with diabetes in a sample of 300 is between 0.17 and 0.20 (inclusive) is approximately 0.627.



To compute the probability, we can use the normal approximation to the binomial distribution since the sample size is large (n = 300).

First, we calculate the mean of the sample proportion, which is equal to the population proportion (π) = 0.185. Next, we calculate the standard deviation of the sample proportion, which is given by the formula sqrt((π(1-π))/n), where n is the sample size. Plugging in the values, we get sqrt((0.185*(1-0.185))/300) = 0.0164.We then standardize the values 0.17 and 0.20 using the formula (x - μ)/σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 0.17, the standardized value is (0.17 - 0.185)/0.0164 = -0.913.

For 0.20, the standardized value is (0.20 - 0.185)/0.0164 = 0.913.

Using a standard normal table or calculator, we find the probability that z lies between -0.913 and 0.913 is approximately 0.627. Therefore, the probability that the sample proportion is between 0.17 and 0.20 (inclusive) is approximately 0.627.

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a) The set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

To find the set of values of k for which the line and curve meet at two distinct points, we need to solve the equation:

x^2 - kx + 2 = 3kx - 2k

Rearranging, we get:

x^2 - (3k + k)x + 2k + 2 = 0

For the line and curve to meet at two distinct points, this equation must have two distinct real roots. This means that the discriminant of the quadratic equation must be greater than zero:

(3k + k)^2 - 4(2k + 2) > 0

Simplifying, we get:

5k^2 - 8k - 8 > 0

Using the quadratic formula, we can find the roots of this inequality:

\(k < (-(-8) - \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = -2/5\\ or\\ k > (-(-8)) + \sqrt{((-8)^2 - 4(5)(-8)))} / (2(5)) = 2\)

Therefore, the set of values of k for which the line and curve meet at two distinct points is k < -2/5 or k > 2.

b) To find the two values of k for which the line is a tangent to the curve, we need to find the values of k for which the line is parallel to the tangent to the curve at the point of intersection. For m to be the slope of the tangent at the point of intersection, we need to have:

2x - 4 = m

3k = m

Substituting the first equation into the second, we get:

3k = 2x - 4

Solving for x, we get:

x = (3/2)k + (2/3)

Substituting this value of x into the equation of the curve, we get:

y = ((3/2)k + (2/3))^2 - k((3/2)k + (2/3)) + 2

Simplifying, we get:

y = (9/4)k^2 + (8/9) - (5/3)k

For this equation to have a double root, the discriminant must be zero:

(-5/3)^2 - 4(9/4)(8/9) = 0

Simplifying, we get:

25/9 - 8/3 = 0

Therefore, the constant term is 8/3. Solving for k, we get:

(9/4)k^2 - (5/3)k + 8/3 = 0

Using the quadratic formula, we get:

\(k = (-(-5/3) ± \sqrt{((-5/3)^2 - 4(9/4)(8/3)))} / (2(9/4)) = -1/3 \\or \\k= 4/3\)

Therefore, the two values of k for which the line is a tangent to the curve are k = -1/3 and k = 4/3. To show that the two tangents meet on the x-axis, we can find the x-coordinate of the point of intersection:

For k = -1/3, the x-coordinate is x = (3/2)(-1/3) + (2/3) = 1

For k = 4/3, the x-coordinate is x = (3/2)(4/3) + (2/3) = 3

Therefore, the two tangents meet on the x-axis at x = 2.

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Answer:

-6

Step-by-step explanation:

-3 + (-4) 4 + (-3) is -6 I hope that helps because that what I got

During the current year, merchandise was sold for $662,100. Of this amount, $114,000 was cash sales and $548,100 was on account. The cost of goods sold was $423,700. Therefore, the gross profit was $238,400.

The gross profit is calculated by subtracting the cost of goods sold from the total sales. The cost of goods sold is the direct cost of producing the goods that were sold. It includes the cost of materials, labor, and overhead.

The gross profit is an important measure of a company's profitability. It shows how much money the company makes from its core business activities, before deducting other expenses.

In this case, the company's gross profit margin is 35.8%. This means that for every $100 of sales, the company makes $35.80 in gross profit. A high gross profit margin is generally considered to be a sign of a healthy business.

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Answer:

Below

Step-by-step explanation:

\(\dfrac{3}{4} , -2\)

\(1,5\)

\(-2,-7\)

\(3, -\dfrac{1}{2}\)

\(6,6\)              

Yes, because for each input there is exactly one output

Answer:

songs in the final CD 13

Step-by-step explanation:

the 100% = 16

-------------------

16/x=100/62.5

(16/x)*x=(100/62.5)*x

16=1.6*x

16/1.6=x

10=x

x=10

This is the 62.5% of 16

---------------------

now the new 100% is 10 + 16 = 26

but during the editing process 50% are removed

and the 50% of 26 (half of it) is = 13

Answer:

First term = 9.

Common ratio = 2.

Step-by-step explanation:

A geometric sequence has a common ratio r.

If the first term is a:

10th term = ar^9 and 5th term is ar^4

so 1th term / 5th term = r^5

So 4608/144 = r^5

r^5 = 32

so r = 2.

Substituting for r in the 5th term:

a(2)^4 = 144

a = 144 / 16

a = 9.

Answer:

first term:9

common ratio: 2

Step-by-step explanation:

aₙ = a₁*rⁿ⁻¹

a₅ = a₁*r⁵⁻¹ = a₁*r⁴ = 144  ... (1)

a₁₀ = a₁*r¹⁰⁻¹ = a₁*r⁹ = 4608  ... (2)

(2)÷(1)  r⁵ = 32

r = 2

a₁ = 144 / 2⁴ = 9

We are given a table of temperatures that are being maintained at different times in a greenhouse . We are to consider that the temperatures increase at a constant rate and we are asked to create a graph for this.

The cost of each printer is $568.

To find the cost of each printer, we need to use a system of equations.

Let's call the cost of each printer "p" and the cost of each camera "c".

The first equation we can create is: 6p + 3c = 4773

The second equation we can create is: 4p + 6c = 5002

Now we can use the elimination method to solve for one of the variables.

Let's eliminate the "c" variable by multiplying the first equation by -2: -12p - 6c = -9546

And then add the two equations together: -8p = -4544

Now we can solve for "p" by dividing both sides by -8: p = 568

So the cost of each printer is $568.

To find the cost of each camera, we can plug the value of "p" back into one of the original equations and solve for "c":

6(568) + 3c = 4773

3408 + 3c = 4773

3c = 1365

c = 455

So the cost of each camera is $455.

Therefore, the cost of each printer is $568 and the cost of each camera is $455.

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11 miles he run per day, Monday-Friday.

The unitary technique involves first determining the value of a single unit,  followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Total distance travelled = 60 miles.

On Saturday= 5 miles

Sunday was off

So, from Monday to Friday he travelled

=60 - 5

= 55 miles.

and, per day he run

= 55/5

= 11 miles

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Answer:

yes

Step-by-step explanation:

6/ 16 both divided by 2

Answer:

Yes

Step-by-step explanation:

3/8 and 6/16 are equivalent fractions

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Answer:

23 when b =a+r=y and x=r} OQ= 78

This is the reason why Option (B) is the correct option.

The correct interpretation of the given interval is that "We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation."Option (B) is the correct option.Explanation:Confidence intervals tell us about the range of values within which we can expect the true population parameter to lie. Confidence interval is the range within which we believe the population parameter (mean, proportion or standard deviation) lies.A 95% confidence interval implies that if a researcher were to conduct a given study 100 times, 95 of those studies would produce the same interval of estimates.A confidence interval is a range of values, derived from a data sample, within which the true population value is likely to fall with a certain level of confidence. This is the reason why Option (B) is the correct option.

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Answer:

Step-by-step explanation:

1 mile = 1609 meters

24 miles = 38624 meters

So, Adam drives 38624 meters.

Answer:

The distributive property allows you multiply a sum in parenthesis by multiplying each addend separately, then add the products.

Step-by-step explanation:

How to use the distributive law example.

2(x+4) = 16

To use the distributive law in this example multiply 3 by all terms in the parenthesis. Multiply 2 and x, then 2 and 4 to open the parenthesis.

2x+8=16

That is how you use the distributive law.

To continue solving, subtract 8 from both sides.

2x+8-8=16-8

2x=8

Divide 2 from both sides.

2x/2=8/2

x=4

Hope this helps!

If not, I am sorry.

A function that satisfies the condition of having its square plus the square of its derivative equal to 1 is given by f(x) = sin(x).

The function f(x) = sin(x) has the property that its square, sin^2(x), is equal to 1 when added to the square of its derivative, \($\frac{d}{dx}\sin(x))^2 = \cos^2(x)$\).

This can be seen by directly evaluating the expression: \(sin^{2}(x) + cos^{2}(x) = 1\), which is a fundamental identity in trigonometry.

The sine function is periodic with a period of 2π, and its derivative, cosine function, also has the same period. This means that for any x, the function sin(x) and its derivative cos(x) will satisfy the given condition.

Geometrically, the sine function represents the y-coordinate of a point on the unit circle as the corresponding angle is varied. Its derivative, the cosine function, represents the rate of change of this y-coordinate with respect to the angle. The squares of the sine and cosine functions add up to 1, which is the square of the radius of the unit circle. This property is fundamental in trigonometry.

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Answer:

Answer: Option 3 40/41

Step-by-step explanation:

Sin of angle A means the opposite over hypotenuse. The opposite of Angle A is 40 and the hypotenuse is 41 so SinA is 40/41

Answer:

option 3:  \(\frac{40}{41}\)

Step-by-step explanation:

SOH CAH TOA

sine = \(\frac{opposite}{hypotenuse}\)

sine A = \(\frac{40}{41}\)

Velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.

Given,

Jet's velocity against wind 1731 / 3 = 577  mile per hour

flying with wind it   2151 / 3 = 717 miles per hour.

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x−y and with wind is x+y and therefore

x−y=577;

x+y=717

Adding the two

2x = 1294

x = 647

y= 717 − 647

y = 70

Hence velocity of jet in still air is 647 miles per hour and velocity of wind is 70 miles per hour.

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The equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is: (x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

To find the equation of the sphere passing through the point (4, 3, -1) with a center at (3, 8, 1), we can use the general equation of a sphere:

(x - h)^2 + (y - k)^2 + (z - l)^2 = r^2

where (h, k, l) represents the center of the sphere and r represents the radius.

First, we need to find the radius. The distance between the center and the given point can be calculated using the distance formula:

√[(x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2]

Substituting the coordinates of the center (3, 8, 1) and the given point (4, 3, -1), we have:

√[(4 - 3)^2 + (3 - 8)^2 + (-1 - 1)^2]

Simplifying, we get:

√[1 + 25 + 4] = √30

Therefore, the radius of the sphere is √30.

Now we can substitute the center (3, 8, 1) and the radius √30 into the general equation:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30

So, the equation of the sphere that passes through the point (4, 3, -1) and has a center at (3, 8, 1) is:

(x - 3)^2 + (y - 8)^2 + (z - 1)^2 = 30.

This equation represents all the points on the sphere's surface.

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Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

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Answer:

-36

Step-by-step explanation:

12 * 3 = 36

When you multiply by a negative number, the number becomes a negative therefore, -12*3 = -36

Answer:

-36

Step-by-step explanation:

When multiplying a negative and a positive the answer is always going to be negative.  So 12x3=36 and the 12 is negative and the 3 is positive, so the answer is -36.

The measure of the angle between the end of the shadow and the vertical side of the building is approximately 71 degrees.

Given the building is 290 feet tall and casts a 100 foot shadow.

Let x be the angle formed between the end of the shadow and the vertical side of the building.

Therefore, we can construct the following diagram;

From the diagram;

The tangent function relates the angle and the opposite side of a right triangle.

Therefore;

Tangent = opposite/adjacent

Tangent x = opposite/adjacent

Tangent x = 290/100

We can now take the inverse tangent of both sides;

x = tan^-1 (290/100)

x = 71.57 degrees, correct to two decimal places.

Therefore, the measure of the angle between the end of the shadow and the vertical side of the building is approximately 71 degrees.

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The given equation is equivalent to y = -5x/7 - 2

Given that an equation, 5x+7y = -14, we need to find an equivalent equation for thus,

So,

5x+7y = -14

Minus 5x from both the sides

7y = -14 - 5x

Divide the equation by 7,

y = -5x/7 - 2

Hence the given equation is equivalent to y = -5x/7 - 2

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Answer:

3g+15

Step-by-step explanation:

Multiply using the distributive property.

Answer:

1

Step-by-step explanation:

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}\)

Answer:

total cost = cost/hour x hours

$18.00 = ($4.50)(X hours)

X=4 hours

Step-by-step explanation:

total cost = cost/hour x hours

$18.00 / 4.50=4 hours