zoe is 1.55 meters tall. at 2 pm she measure the lenght of a tree's shadow to be 17.35 meters . she stands 12.7 meters away from the tree so that the tip of her shadow meets the tip of tye tree's shadow. find the height of yhe tree to the nearest hundredth of a meter.

The two ships are 1933.32 ft apart

Given:

The height of the lighthouse = 350 ft

The angles of depression to the ships are 4 degree and 6.5 degree

To find:

the distance between the two ships

To determine the distance, we will use an illustration of the situation

First we will find the value of y as we need to know this value to get x

To get y, we will apply tan ratio (TOA)

Next is to find x using tan ratio (TOA):

Given data:

The diameter of cylinder is d=12 cm.

The height of the cylinder is h= 27 cm.

The dimension of the aquarium is V=(35 cm)(40 cm)( 42 cm).

The volume of the cylinder is,

The volume of the aquarium is,

The number of cylinders that can be pour into aquarium is,

Thus, the number of cylinders that can be pour into aquarium is 19.25.

Sara spent 15 minutes longer than (the difference is 15 min) Mia in her homework.

According to the question,

We have the following information:

Sara spent 35 minutes on math homework and 20 minutes on reading homework. Mia spent a total of 40 minutes on reading and math homework.

So, it means that the total time spent by Sara in her homework is:

35+20 minutes

55 minutes

So, the differences between their time spent in her homework (will give us the more time taken by Sara) is:

Time spent by Sara in her homework-time spent by Mia in her homework

(55-40) minutes

15 minutes

Hence, Sara spent 15 more minutes than Mia.

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Evaluate the product of the expression.

So answer is 9.1X10^3.

To solve this equation, we need to subtract both, 9c - 3c:

Dividing by 6 at both sides of the equation

Then

Then the answer C = 8. (Option D)

Find 2 given that =

−4/5 and < < 3/2

we know that

sin(2x) = 2 sin(x) cos(x)

so

step 1

Find the value of cos(x)

Remember that

we have

sin(x)=-4/5

The angle x lies on III quadrant

that means

cos(x) is negative

substitute the value of sin(x)

step 2

Find the value of sin(2x)

sin(2x) = 2 sin(x) cos(x)

we have

sin(x)=-4/5

cos(x)=-3/5

substitute

sin(2x)=2(-4/5)(-3/5)

Explanation:

We have the expression:

where i represents the complex number i defined as follows:

To find if i^3 is real or complex, we represent it as follows:

And we find the value of i^2 using the definition of i:

Since the square root and the power of 2 cancel each other

And therefore, using this value for i^2, we can now write i^3 as follows:

This simplifies to -i

Because -i is still a complex number, that means that i^3 is a complex number.

Answer: Complex

The formula to find the volume of a triangular prism is the following:

where:

h - height

b - base length

w - width

for this problem:

h = 8 cm

b = 5 cm

w = 7 cm

then

solving this, we obtain that the volume of the triangular prism is 140 cm^3 or cubic centimeters

We have the next functions

Function notation

Describe the transformation in words

we have 2 transformations, the 2 that multiplies the function f(x) means that we will have an expansion in the y axis by 2, the one means that we will have a shift up by one unit

Answer:

The two lines are parallel.

Explanation:

We have the equations:

Let's solve the first one for y, so we get the same formatting on both euqations:

SInce the two lines have the same slope, 2/5, the two lines are parallel.

The change of base formula states that:

this means that we can caculate any logarithm using the natural logarithm if we make the quotient of the natural logarithm of the original value and the natural logarithm of the original base.

In this case we have:

Then, using the change of base formula, we have:

Once we have the expression we just evaluate the expression on the right to get the appoximation we need:

Given that:

Where:

Where:

Therefore, applying this formula, you can find the measure of angles A and B:

(a) By definition:

Knowing that:

You can substitute the known values into the equation in order to find the opposite side for angle A:

Now you know that:

Using the same reasoning for angle B, you get:

Now you know that:

Substitute values into the Trigonometric Identity:

Simplifying, you get:

(b) By definition:

Knowing all the values, you get:

(c) By definition:

By definition:

Therefore, in this case:

- For angle A:

- And for angle B:

Therefore, you can substitute values into the formula and simplify:

(d) By definition:

Knowing all the values, you can substitute and simplify:

(e) Knowing that:

Remember the Quadrants:

By definition, in Quadrant II the Sine is positive and the Tangent is negative.

Since in this case, you found that the Sine is positive and the Tangent negative, you can determine that this angle is in the Quadrant II:

We need to identify the team that has the smallest sample standard deviation.

In order to do so, we need to find the stand deviation of each experiment based on the confidence level and confidence interval of each of them.

A. A confidence level of 99.7% corresponds to a confidence interval of 3 standard deviations above and 3 standard deviations below the mean.

Thus, for the confidence interval 42 to 48, the mean is 45. And the standard deviation is given by:

B. A confidence level of 95% corresponds to a confident interval of 2 standard deviations above and 2 standard deviations below the mean.

Thus, for the confidence interval 43 to 47, the mean is 45. And the standard deviation is given by:

C. A confidence level of 68% corresponds to a confident interval of 1 standard deviation above and 1 standard deviation below the mean.

Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:

D. Again, we have a confidence level of 95%, which corresponds to 2 standard deviations.

Thus, for the confidence interval 44 to 46, the mean is 45. And the standard deviation is given by:

Therefore, the team that has the smallest sample standard deviation is:

Answer

Part b.

In this case, we have the following function:

First, we need to solve for x. Then, by applying natural logarithm to both sides, we have

By the properties of the logarithm, it yields

By moving log5 to the left hand side, we have

By moving log2.4 to the left hand side, we obtain

Therfore, the answer is

Part C.

In this case, the given function is

and we need to solve x. Then, by raising both side to the power 10, we have

By moving 17 to the left hand side, we get

Therefore, the answer is

Given the number

We can express it in scientific notation below;

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8.

Therefore, in the given question, we will have;

Answer: Option C

Since the critical value of the test is greater than the absolute value of the test statistic, there is not enough evidence to conclude that the proportion is different of 20%.

At the null hypothesis, it is tested if the proportion is of 20%, that is:

[tex]H_0: p = 0.2[/tex]

At the alternative hypothesis, it is tested if the proportion is different of 20%, hence:

[tex]H_1: p \neq 0.2[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

The test statistic is given by the rule presented as follows:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

In the context of this problem, the parameters are given as follows:

[tex]p = 0.2, n = 200, \overline{p} = \frac{38}{200} = 0.19[/tex]

Hence the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.19 - 0.2}{\sqrt{\frac{0.2(0.8)}{200}}}[/tex]

z = -0.35.

|z| < 1.96, hence there is not enough evidence to conclude that the proportion is different of 20%.

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Given:

Population in 2000 = 572 thousand

Rate of growth per year = 1.15%

Let's solve for the following:

(a) Explicit formula for the population years after 2000.

Where:

In year 2000, t = 0

To write the explicit formula, apply the exponantial growth function formula:

Where:

a is the initial amount

r is the growth rate.

Thus, we have:

Therefore, the explicit formula for the population years after 2000 is:

(b) What will be the district's population in 2025.

Where:

In the year 2000, t = 0

In the year 2025, t will be = 25

To find the population in 2025, substitute 25 for t in the explicit formula for evalaute:

The population in 2025 if the trend continues will be approximately 761 thousand.

(c) When does the model predict the population to exceeed 800 thousand.

Substitute 800 for Pt and solve for t.

We have:

Divide both sides by 572:

Take the natural logarithm of both sides:

Divide both sides by 0.01143:

When t = 29, the year is 2000 + 29 = 2029

Therefore, using this model, DC's population will exceed 800 thousand in the year 2029.

ANSWERS:

Solution

a)

200 km/h on a bearing of 020°

Scale 1 cm = 50 km/h.

b)

B. 75 km/h S 10° W

C. 350 km/h NE

Okay, here we have this:

We need to identify the x-value at which the-following function touches but does not cross the x-axis in the following function: 3x^3- 18^2 + 27x. So, considering that if is a zero with even multiplicity, the graph touches the x-axis and bounces off of the axis. And if it is a zero with odd multiplicity, the graph crosses the x-axis at a zero.

According with this let's

Let's convert the given equation first into a vertex form.

where (h, k) is the vertex.

The vertex form of the equatio that we have is:

Hence, the vertex of the equation is at the origin (0, 0).

Since "a" is negative, our parabola is opening downward.

Let's identify two points to the left of the vertex. Let's say at x = -1. Replace "x" with -1 in the equation.

Hence, we have a point to the left of the parabola at (-1, -2).

Let's say x = -2. Replace "x" with -2 in the equation.

Hence, we also have another point to the left of the parabola at (-2, -8).

If our x is to the right of the vertex, say, x = 1. Replace "x" with 1 in the equation.

We have a point to the right of the parabola at (1, -2).

If x = 2, let's replace "x" with 2 in the equation.

Hence, we also have another point to the right of the parabola at (2, -8).

The graph of this equation is:

x-intercepts

1) In a quadratic equation, the Real solutions correspond to the points in which the parabola intercepts the x-axis.

2) Note that when the roots are not real solutions, then we'd have complex numbers and the parabola wouldn't intercept the x-axis.

3) Therefore, the answer is: x-intercepts

we have

m=4

point (0,3)

y-y1=m(x-x1)

substitute given values

Convert to slope-intercept form

y=mx+b

y-3=4x

adds 3 both sides

Volume of sandbox (to be built) = 50,445 cubic inches

A sandbox is the shape of a cuboid and is calculated by the formula

Volume = Length * Width * Height

Volume = 50,445 cubic inches, Length = 59 in. Width = 57 in, Height = ?

50,445 = 59 * 57 * h

Make h the subject of the formula, we have:

h = 50445 / (59 * 57) = 15 in

Answer: 77 = 46 + r, r = 31

Step-by-step explanation:

      We will write an equation to represent this situation. Then, we will solve for r by isolating the variable.

  Seventy-seven is forty-six more than r.

77 is forty-six more than r.

77 = forty-six more than r.

77 = 46 more than r.

  77 = 46 + r

  77 = 46 + r

(77) - 46 = (46 + r) - 46

31 = r

  r = 31

Given the folllowing equation:

You need to solve for "x" in order to find its value. To do this, you can follow the steps shown below:

1. You can apply the Addition property of equality by adding 0.04 to both sides of the equation:

2. Now you need to add the like terms on the left side of the equation:

3. Finally, you can apply the Division property of equality by dividing both sides of the equation by 0.41:

The answer is:

Answer:

0.10389610389

Step-by-step explanation:

Hi!

I plugged it into a calculator:

0.024 ÷ 0.231​ = 0.10389610389

Have a great day! :)

The polar coordinates for each point are given as follows:

a. [tex](r, \theta) = \left(2\sqrt{5}, \frac{7\pi}{4}\right)[/tex]

b. [tex](r, \theta) = \left(6, \frac{\pi}{3}\right)[/tex]

Suppose we have a point with Cartesian coordinates given as follows:

(x,y).

The polar coordinates will be found as follows:

For item a), the Cartesian coordinates are as follows:

(-4, 4).

Hence the polar coordinates will be given as follows:

For item a), the Cartesian coordinates are as follows:

(3, 3sqrt(3)).

Hence the polar coordinates will be given as follows:

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