max observes the zoo and the library from a helicopter flying at a height of 300 times square root of 3 feet above the ground, as shown below: a helicopter is flying at a height of 300 multiplied by square root of 3 feet above the ground. a zoo and a library are on the ground on the same side of the helicopter. the angle made by the line joining the helicopter and the zoo with the ground is 60 degrees. the angle made by the line joining the helicopter and the library with the ground is 30 degrees. what is the distance between the zoo and the library? 300 feet 600 feet 900 feet 1,200 feet

Answer: Quarters

Step-by-step explanation:

y = 9(sin(a - 2) - 5)

Explanation:

The original equation of a sine wave is given by `y = sin a`.

The new equation can be obtained by making the following transformations to the original equation:

y = sin(a)

Right 2 units => y = sin(a - 2)

Downward 5 units => y = sin(a - 2) - 5

Vertically stretched by a factor of 9 => y = 9(sin(a - 2) - 5)

Comparing with y = sin(2), we see that the frequency of the new wave is the same as that of the original wave. The only difference is the phase shift, vertical translation, and amplitude change.

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The 95% confidence interval for the mean tip percentage at the restaurant, using the Restaurant Tips dataset, is (x).  The 95% confidence interval for the mean tip percentage at the restaurant using the RestaurantTips dataset cannot be determined without access to the dataset.

To determine the 95% confidence interval for the mean tip percentage at the restaurant, we can use statistical analysis techniques. However, since the RestaurantTips dataset is not available for reference, we cannot provide an exact confidence interval.

Typically, to calculate a confidence interval, we need the sample mean, standard deviation, sample size, and the level of confidence. The sample mean represents the average tip percentage, the standard deviation indicates the variability of the data, and the sample size determines the precision of the estimate. The level of confidence, in this case, is 95%.

Using the available data, one could calculate the mean and standard deviation of tip percentages and then apply the appropriate statistical formula to compute the confidence interval. However, without access to the dataset, we cannot provide the specific values or calculate the interval.

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Answer:

360

Step-by-step explanation:

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Answer:

What do you mean?

Step-by-step explanation:

Answer:

Step-by-step explanation:

 x - 3y = 5

2x +  y = 10  multiply by 3 to eliminate y and solve for x

 x - 3y = 5

6x + 3y = 30  then add

7x          = 35

simplify:

x = 35 / 7

x = 5  

substitute x = 5 back into the eq.2

 2x +  y = 10

2(5) +  y = 10

           y = 10 - 10

           y = 0

therefore the answer is ( 5, 0 )

There are 144 possible sequences of chip colors.

We can solve this problem by counting the number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7.

Let's consider all the possible sequences of chips that can be drawn from the bag. The first chip can be any of the 6 chips in the bag. For each chip color, there are different scenarios that can happen after drawing the first chip:

Therefore, the total number of possible sequences of chip colors that can be drawn from the bag until the total value of the chips is at least $7 is: 2 x 32 + 1 x 32 + 3 x 16 = 144

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The coordinates of the particle are (0, 6) at t = 0, (-4, 16) at t = 1, and (-100, 630) at t = 5.

the coordinates of the particle at different times. Let's start by identifying the correct path equations for the particle:

x = -4t^2
y = 6 + 10t^3

Now, we'll find the coordinates at t = 0, 1, and 5:

1. For t = 0:
x = -4(0)^2 = 0
y = 6 + 10(0)^3 = 6
Coordinates at t = 0: (0, 6)

2. For t = 1:
x = -4(1)^2 = -4
y = 6 + 10(1)^3 = 16
Coordinates at t = 1: (-4, 16)

3. For t = 5:
x = -4(5)^2 = -100
y = 6 + 10(5)^3 = 630
Coordinates at t = 5: (-100, 630)

So, the coordinates of the particle are (0, 6) at t = 0, (-4, 16) at t = 1, and (-100, 630) at t = 5.

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Answer:

The expression log3 2x + 3 log3 4x can be condensed to log3 8x + 3. This is because log3 4x = 2 log3 2x, so when we add the two logarithms together, the result is log3 8x + 3

Step-by-step explanation:

Answer:

The answer Is A 1 1/5 < -2 2/5

Step-by-step explanation:

It says that this statement is true because 1 1/5 is to the left of -2 2/5 on the number line but it is actually to the right because -2 2/5 is negative while 1 1/5 is positive therefore making it larger and the correct statement would be that    1 1/5 > -2 2/5

a) d/dt [√(289 - 8²)] = d/dt [√(255)] = d/dt [√(5²*17)] = 5/2√17 m/s.

b) The required value is the rate of change of x when the top of the ladder is 8 feet from the ground, then y = 15 feet.

a) Determine how fast the bottom of the ladder is sliding away when the top of the ladder is 8 feet from the ground. As the ladder leans against the side of the house, it makes a right angle with the ground. Using Pythagorean Theorem, the length of the ladder is given by.

Ladder length = √(hypotenuse)² - (height)²= √(17² - height²) meters. Taking the derivative of both sides of this equation, we get: dL/dt = [d/dt √(289 - h²)] meters/sec. Let h = 8 feet, dL/dt = -5 feet/sec.

Thus, the rate of change of the bottom of the ladder is d/dt [√(289 - h²)] meters/sec when the top of the ladder is 8 feet from the ground, and the bottom of the ladder is sliding away at a rate of 5 feet/sec.

b) At what rate is the angle o between the ladder and the ground changing then. Let y be the height of the ladder and the angle it makes with the ground be x. From the given values, y = 17 cos x.

Taking the derivative of both sides with respect to time: dy/dt = -17 sin x (dx/dt)In the given problem, dx/dt = -5/17sin x. Then, dy/dt = 5 sin x cos x= (5/2) sin 2x.

Solving this value of sin x by Pythagorean Theorem, sin x = 8/17. Substituting the value in the equation for the derivative, we get: dy/dt = (5/2) * sin 2x= (5/2) * sin 2(arc sin(8/17))= (5/2) * (2*8/17 * 15/17)= (600/289) ft/sec.

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V≈37.7ft³

The angle between the two vectors (4,1) and (-8,3) will be 145.4°.

It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.

It is possible to calculate the angle () between two vectors using the formula

\(\rm \theta = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

Calculate dot product:

=a · b

= ax · bx + ay · by

= 4 · (-8) + 1 · 3

= - 32 + 3

= -29

=|a|

= √ax² + ay²

= √4² + 1²

= √16 + 1

= √17

=|b|

=√ bx² + by²

= √(-8)² + 3²

= √64 + 9

= √73

\(\rm \alpha = cos ^{-1} \frac{ (a.b)}{|a||b|}\)

α = 145.40771131249005°

Thus, the angle between the two vectors (4,1) and (-8,3) will be 145.4°.

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Based on the data collected in the 2000 United States Census and the expanded number of households, we can fill in the values for the random variable X and the probability distribution P(X=x) consistent with the histogram above.

The values of X represent the number of people per household, and the values of P(X=x) represent the probability of a household having that number of people.

The values for X are already given in the table, so we just need to fill in the values for P(X=x). To do this, we can use the frequencies from the histogram and divide them by the total number of households.

For example, the frequency for 1 person per household is 27, so the probability of a household having 1 person is 27/100 = 0.27. We can do the same for the other values of X to find the probabilities:
x P(X=x)
1 0.27
2 0.33
3 0.17
4 0.13
5 0.10
So the completed probability distribution table is:
x P(X=x)
1 0.27
2 0.33
3 0.17
4 0.13
5 0.10

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The percent of the variance in the dependent variable unexplained by the independent variable is 81%

A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively correlated, the value either rises or falls together.

9 percent of the variance is explained by the independent variable if the correlation coefficient is 0.3.

The correlation coefficient is therefore represented as follows:

\(r = 0.3\)

The explained variance is found using the following formula:

\(R^{2} = r^{2} \\R^{2} = (0.3)^{2} \\R^{2} = (0.3)*(0.3)\\R^{2} = 0.9\)

Thus, 81% of the variance remains unexplained by variations in the independent variable.

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The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

59 is a prime number.

This means that it cannot be divided evenly by any other number except for 1 and itself. A composite number, on the other hand, can be divided evenly by at least one other number besides 1 and itself.

To determine if a number is prime or composite, you can use a simple test. Start by dividing the number by 2. If the result is a whole number, then the number is composite.

If the result is not a whole number, try dividing by 3, 4, 5, and so on until you find a whole number result or until you reach the square root of the original number. If you reach the square root without finding a whole number result, then the number is prime.

For example, with the number 59:

59 / 2 = 29.5 (not a whole number)
59 / 3 = 19.67 (not a whole number)
59 / 4 = 14.75 (not a whole number)
59 / 5 = 11.8 (not a whole number)
59 / 6 = 9.83 (not a whole number)
59 / 7 = 8.43 (not a whole number)
59 / 8 = 7.38 (not a whole number)

Since we have reached the square root of 59 without finding a whole number result, we can conclude that 59 is a prime number.

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Work Shown:

36 inches = 3 feet

Divide by 12 to go from inches to feet

The block has the dimensions

Use the formula below to calculate the surface area

SA = 2*(LW+LH+WH)

SA = 2*(5*8+5*3+8*3)

SA = 2*(40+15+24)

SA = 2*(79)

SA = 158 square feet

So if you had 158 square feet of wrapping paper, then you can cover this entire 3D box without any gaps or overlaps. The paper can be folded over the box, or you can cut/glue the pieces on, but make sure there isn't any leftover scraps of paper.

we have:

$15.50 -----> 100%

x --------------> 15%

then

so,

answer: $ 17.83 is the final bill

Answer:

7/10 is the answer as a fractions

Answer: 2. 6 X 2 -4

Step-by-step explanation:

Only 2 fits the descriptions, where 6 is multiply 2, 6 x 2. And we subtract 4 from it, 6 x 2 -4.

Answer:

\(d=4\sqrt{5}\)

Step-by-step explanation:

Midpoint Formula: \((\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\)

Distance Formula: \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Step 1: Find midpoint m

\(m=(\frac{2+4}{2} ,\frac{4+6}{2} )\)

\(m=(\frac{6}{2} ,\frac{10}{2} )\)

\(m=(3 ,5 )\)

Step 2: Find distance d

\(d=\sqrt{(3-(-1))^2+(5-(-3))^2}\)

\(d=\sqrt{(3+1)^2+(5+3)^2}\)

\(d=\sqrt{(4)^2+(8)^2}\)

\(d=\sqrt{16+64}\)

\(d=\sqrt{80}\)

\(d=4\sqrt{5}\)

Answer:

36° and 54°

Step-by-step explanation:

Complementary angles are angles whose sum equals to 90°

Hence C +D = 90°

The ratio of C &D = 2:3 respectively

Sum of the ratio = 2+3 = 5

Hence we divide each of the ratio by the sum of the entire ratio and then multiply by 90°

For angle C :

2/5 × 90

2×18 = 36°

For angle D :

3/5× 90

3×18 = 54°

Hence the angles are 36° and 54° respectively

To proof that we are actually right

C+D = 90°

36+54 = 90°

Hence the answer is right.

Answer:

w = -8

Step-by-step explanation:

19 = -9w - 5 + 6w

19 = -3w - 5

19 + 5 = -3w

24 = - 3w

w = -8

Answer:

the answer is -7.7  

Step-by-step explanation:

−2.2−5.5

−2.2+ −5.5

= --7.7

hope it helps :)

Answer:

The answer is -8

Step-by-step explanation:

-(2.5+5.5)

-8

Answer: A

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

An isosceles triangle is one with two equal-length sides. The value of x is 58°.

An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.

Since the given triangle is an isosceles triangle, therefore, the angle opposite to side 6.25 units will be equal, therefore, the sum of all the angles of the triangle will be,

61° + 61° + x = 180°

x = 58°

Hence, the value of x is 58°.

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Given the expression:

You need to expand it in order to find an equivalent expression.

It is important to remember the Sign Rules for Multiplication:

Now you have to apply the Distributive Property in order to expand the expression. You get:

Hence, the answer is: Last option.

Answer:

The coordinates would be (3,7)