a 60 foot tree casts a shadow 85ft long. the sine of the angle between the ground and the line that connects the tip of the shadow to the top of the tree is approximately?

The observer and the balloon form a right triangle (see attachment).

The balloon is rising at 1.2 rad per min

Using tangent rule, we have:

[tex]\mathbf{tan(\theta) = \frac{y}{x}}[/tex]

Substitute 3 for x

[tex]\mathbf{tan(\theta) = \frac{y}{3}}[/tex]

Differentiate both sides with respect to time (t)

[tex]\mathbf{sec^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{3} \cdot \frac{dy}{dt}}[/tex]

Make dy/dt, the subject

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\theta) \cdot \frac{d\theta}{dt} }[/tex]

Substitute [tex]\mathbf{\theta = \frac{\pi}{3}\ and\ \frac{d\theta}{dt} = 0.1}[/tex]

So, we have:

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot sec^2(\pi/3) \cdot 0.1 }[/tex]

Using a calculator, we have:

[tex]\mathbf{\frac{dy}{dt} = 3 \cdot 2^2 \cdot 0.1 }[/tex]

Multiply

[tex]\mathbf{\frac{dy}{dt} = 1.2}[/tex]

Hence, the balloon is rising at 1.2 rad per min

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Final answer:

The effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.

Explanation:

The effective rate on a treasury bill is the annualized interest rate that takes into account the compounding of interest over the term of the bill. To calculate the effective rate, you can use the formula:

[tex]Effective Rate = (1 + (Nominal Rate / M))^M - 1[/tex]

Where:

Plugging in the values:

Effective Rate =  [tex](1 + (0.04 / 4))^4[/tex]- 1

= [tex](1 + 0.01)^4 - 1[/tex]

= [tex]1.01^4 - 1[/tex]

= 1.04060401 - 1

= 0.04060401 (or 4.06% rounded to two decimal places)

Therefore, the effective rate on a $10,000 treasury bill with a nominal rate of 4% for 13 weeks is 4.06%.

Answer:

16%; 2.5%; 34%; 81.5%

Step-by-step explanation:

Using the empirical rule, we know that 68% of data falls within one standard deviation of the mean; 95% of data falls within two standard deviations of the mean; and 99.7% of data falls within 3 standard deviations of the mean.

This means from the mean to 1 standard deviation (σ) above is 34% of data; from the mean to 1 σ below is 34% of data; from 1 σ to 2σ above is 13.5% of data; from 1σ to 2σ below is 13.5% of data; from 2σ to 3σ above is 2.35% of data; from 2σ to 3σ below is 2.35% of data; more than 3σ above is 0.15% of data; and more than 3σ below is 0.15% of data.

647 is 1 σ above the mean.  This means that we go from here above;

13.5+2.35+0.15 = 16%

747 is 2σ above the mean.  This means that we go from here above:

2.35+0.15 = 2.5%

447 is 1σ below the mean and 547 is the mean.  This means that we have 34%.

347 is 2σ below the mean and 647 is 1 above the mean.  This means we go from:

13.5+34+34 = 81.5%

To find the percentage of GMAT scores between 347 and 647, find the z-scores and use a z-table to calculate the cumulative area.

To find the percentage of GMAT scores between 347 and 647, we need to find the area under the bell curve between these two scores. First, we need to find the z-scores for both scores using the formula z = (x - μ) / σ. For 347, the z-score is (-200) / 100 = -2, and for 647, the z-score is 100 / 100 = 1.

Next, we need to find the percentage of data between these z-scores. We can use a z-table to find the cumulative area. The cumulative area for -2 is 0.0228 and for 1 is 0.8413.

To find the percentage between these two z-scores, we subtract the cumulative area for -2 from the cumulative area for 1: 0.8413 - 0.0228 = 0.8185.

Therefore, the percentage of GMAT scores between 347 and 647 is 81.85%.

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Sarah made total 13 sandwiches.

What is an algebraic expression?

An algebraic expression is consists of variables, numbers with various mathematical operations.

Given that,

The number of sandwiches chad have = 7

Also, Chad has 6 fewer sandwiches than Sarah,

Let the number of sandwiches Sarah have = x,

According to condition,

Sarah has 6 more sandwiches than Chad,

⇒x = 7 + 6

⇒x = 13

The number of sandwiches that Sarah made is 13.

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To predict the number of cruise passengers in 2002, multiply the growth rate by the previous year's number of passengers and add that to the previous year's total.

To predict the number of cruise passengers in the year 2002, we need to apply the growth rate of 9% to the number of passengers in the previous year (2001).

Therefore, the predicted number of cruise passengers in the year 2002 is

7.848 million

.

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2000 / 100 = 20

20 * 6 = 120 liters total gas

 120 * 1.20 = $144 total for gas

144 / 3 = $48 each

Answer:

A

Step-by-step explanation:

The denominator in the original question is 5.

Therefore the answer must have 5 in the numerator. The answer can only be A.

6 4/5 = (30 + 4) / 5 = 34/5 This is the original fraction. The upside down of the original fraction is the reciprocal. Upside down of 34/5 is 5/34. You can come to this conclusion by doing this.

The formal definition of a reciprocal is 1/a where a is a fraction.

In this case a = 34/5. The reciprocal is 1/a = 1 // 34/5. You don't change anything by making it 1/1 // 34/5

1/1 // (34/5) Invert and multiply the bottom.

1/1 * 5/34 = 5/34

the 2600 is the constant so you initially invested $2600

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

The unequal side is the base of the triangle.

The length of the base of the isosceles triangle is

10 cm or 4 cm.

An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

The unequal side is the base of the triangle.

We have,

Two sides of an isosceles triangle have lengths:

= 10 cm and 4 cm

The unequal side of the isosceles triangle is the base and the other two sides have to be equal.

We can have two cases-

Case 1.

If the equal two sides are 10 cm.

Base = 4 cm

Case 2.

If the equal two sides are 4 cm.

Base = 10 cm.

Thus the length of the base of the isosceles triangle is

10 cm or 4 cm.

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To write equations for four lines forming a parallelogram, we use the slope-intercept form ensuring two sets of parallel lines. Opposite lines have equal slopes and by manipulating the y-intercepts, we ensure they intersect appropriately to form a parallelogram.

Writing an equation for four lines that intersect to form the sides of a parallelogram involves ensuring that opposite sides are parallel and equal in length. One straightforward approach is to use the slope-intercept form of a line, y = mx + b, to define the lines.

Let's start by defining two lines with slopes 'm' and 'm' (since opposite sides of a parallelogram are parallel) and two lines with slopes '-1/m' to ensure they are also parallel to each other but perpendicular to the first set of lines. If we assume lines have y-intercepts at 'b' and '-b' respectively (to ensure symmetry and simplify calculations), our equations would be:

Here, m represents the slope of the first set of parallel lines, b represents the y-intercept of line 1, -b represents the y-intercept of line 2, and k and l are the y-intercepts of lines 3 and 4. By adjusting 'b', 'k', and 'l' we ensure the lines intersect to form a parallelogram.

These lines will form a parallelogram as long as 'k' and 'l' are chosen such that the distances between the y-intercepts of lines 1 and 2, and lines 3 and 4, are equal, satisfying the condition for parallel lines in a parallelogram. This way, we can visually imagine or draw a parallelogram with these four lines as its sides.

Final answer:

To find the length of the rectangle, set up a proportion using the given information. Solve the equation to find the length of the rectangle is 10 feet.

Explanation:

To find the length of the rectangle, we can set up a proportion using the given information. Let the length of the rectangle be L and the width be W. From the problem, we know that the width is 2 feet shorter than the length, so we can write the equation W = L - 2. We also know that the area of the rectangle is 80 square feet, so we can write the equation L * W = 80.

Substituting W = L - 2 into the equation L * W = 80, we get L * (L - 2) = 80. Expanding and rearranging the equation gives us L2 - 2L - 80 = 0. Factoring the quadratic equation, we find (L - 10)(L + 8) = 0.

Since we are looking for the length of the rectangle, we discard the negative solution and find that L = 10. Therefore, the length of the rectangle is 10 feet.

draw a graph with number of bottles on the x axis ( and number  it 1 through 10 )

 put price on the y axis and label it in increments of $1.50 ( 1.50,  3.00 , 4.50,  6.00, etc.

 Then put dots on the intersection of price with the number of bottles and then draw a straight line through the dots.

for every 1 bottle of water sold the price increases by 1.50

so at x 1 y = 1.50

 at x 2 y = 3.00

 at x 3 y = 4.50

 and so on

Answer:

70 kilometers per hour.

Step-by-step explanation:

Remember that unit rate is the direct correlation between two different units, but the numerator should be 1, this means that for example if you can cook 20 muffins in 4 ovens, you have to calculate how many muffins can you cook in one oven, to calculate this problem you have to divide the kilometers by the hours you have:

350 kilometers/ 5 hours= 70 km/hr.

So that would be the answer.

1 year = 52 weeks

52 * 5 = 260 loads