What is the radius of the unit circle? 2) Where is zero degrees (0∘) on the unit circle? 3) What direction around the circle is defined as positive? 4) How do we represent one time around the circle (in the positive direction) in degrees? 5) How many times around the circle is represented by 720∘ ? 6) What positive degree measure arrives at the same place on the unit circle as negative 90 degrees? 7) In what quadrant (on the xy-axis) is 300∘ on the unit circle? 8) An angle of 240 degrees arrives at the same place on the unit circle as what negative degree measure? Video #2: Vectors https://mediaplayer.pearsoncmg.com/assets/20n29t971LPTTTCXZcnF_AY TOHKoVJRf 9) How is a vector described? 10) What do we use vectors to describe in physics?

Answer:

e

Step-by-step explanation:

e

Answer:

Step-by-step explanation:

Let Dina's age = 1/2 x

Let Michel's age = x

Let Juliette's age = 1/2 x + 3

1/2 + x + 1/2x + 3 = 39

2x + 3 = 39

2x = 39 - 3

2x = 36

x = 18

Dina's age = 1/2 18 = 9

Michelle =                18

Juliet = 1/2 18 + 3  = 12

Total                        39

Answer:

e i hope that is correct answer

Answer:

a. x=21/8

b.x=5/6

c.x=5/8

d.x=4

e.x=112.5

Step-by-step explanation:

The figure is composed of 1 rectangle and 2 triangles.

Area 1: rectangle

Area of a rectangle:Length x width

Length : 6

width : 4

A1 = 6 x 4 = 24 ft2

Area 2: triangle

Area of a triangle: 1/2 x base x height

Base = (9-6)/2 = 1.5

heigth = 4

A2 = A3 = 1/2 x 1.5 x 4 = 3 ft2

Finally, add all the areas:

Area of the figure: A1 + A2 + A3 = 24 + 3 + 3 = 30ft2

The order of the numbers from least to greatest (pi, -3, sqrt 49 , sqrt 9) is -3.00 <  sqrt 9 < pi  < sqrt 9

The concept that will be used here is ordering. When you put a list of numbers in order, you rank them from least to greatest or greatest to least. An effective tool for comparing and sorting numbers is a number line. From left to right, we read a number line, with the numbers nearer to the left having lower values.

The given numbers can be converted to decimals so as to be able to arange them in the required order which can be done as :

pi= 3.147= 3.15

-3= -3.00

sqrt 49=7.00

sqrt 9 =3.00

Therefore,-3.00 <  sqrt 9 < pi  < sqrt 9

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Answer:

C. the mean is greater

Step-by-step explanation:

took the test

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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Square tile with measure of each side is 16inches have area equals to 1652 centimeters( round off to nearest square centimeters).

As given in the question,

Measure of each side length of a square tile = 16 inches

Conversion

1 inch = 2.54 centimeters

16 inches = ( 16 × 2.54 )centimeters

                = 40.64centimeters

Area of a square tile is :

= ( Side length ) × ( Side length)

= (40.64) × (40.64)

= 1651.6096 centimeters

= 1652 centimeters ( round off to nearest square centimeters)

Therefore, the area of a square tile with given measure of each side is equal to 1652 centimeters ( round off to nearest square centimeters).

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Answer:

1.04

step by step solution:

1.0416 rounded is 1.04

Answer:

the greatest common factor of 12 and 32 is 4

The expression for the amount earned in one week per hour is 18 x $10

The expression for the amount earned in four weeks is 18 x $10 x 4

An expression is when numbers or letters are connected together by a mathematical operation without an equal to sign. An example of an expression is a + 3b.

The amount earned in one week = total number of hours worked in a week x amount earned per hour

18 x $10

The amount earned in four weeks = total number of hours worked in a week x amount earned per hour x 4

18 x $10 x 4

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We can fill in the boxes to make each equation complete as follows:

1. x³x⁹ = x¹²

2. x⁷/x³ = x⁴

3. 1/x⁻⁵ = x⁵

4. (7b³c⁵)³ = 343b⁹c¹⁵

To solve the exponents as provided above, the rules have to be factored in. One of the rules is that when multiplying exponents of the same base, we simply add their powers together. So, we have the powers of 3 and 9 for the first expression and they add up to 12.

1. x³x⁹ = x³ ⁺ ⁹ = x¹²

For the second expression, the rule of exponents says that when dividing, we will subtract the powers. This gives us x⁴ for the second expression.

2. x⁷/x³ = x⁷ ⁻ ³ = x⁴

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Answer:

50

Step-by-step explanation:

Given

there is 1 water station at every 0.3 KM

If there are n water stations at every 0.3 KM

then KM covered by them = n*0.3 = 0.3n

given that total KM covered is 15 km

Thus,

0.3n = 15

=> n = 15/0.3 = 50

Thus, there are 50 water stations.

Using the Root Test, the series Σn=1 to infinity (-1)^n (1 - (9/n)n² is found to converge absolutely.

The Root Test is a criterion used to determine the convergence or divergence of a series. For the given series Σn=1 to infinity (-1)^n (1 - (9/n)n², we apply the Root Test to analyze its behavior.

We consider the nth root of the absolute value of each term of the series: [(1 - (9/n)n²)]^(1/n). Taking the limit as n approaches infinity, we have:

lim(n→∞) [(1 - (9/n)n²)]^(1/n)

To simplify this expression, we can rewrite it as:

lim(n→∞) [(1 - (9/n)n²)^(1/(n²))]^(n²/n)

The inner exponent simplifies to 1/n² as n approaches infinity. Thus, we have:

lim(n→∞) [(1 - (9/n)n²)^(1/(n²))]^(n²)

Applying the limit properties, we find:

lim(n→∞) [(1 - (9/n)n²)^(1/(n²))]^(n²) = e^0 = 1

Since the limit is less than 1, the Root Test concludes that the series converges absolutely. Therefore, the given series Σn=1 to infinity (-1)^n (1 - (9/n)n² converges absolutely.

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Answer:

  \(\textbf{A. }4\sqrt{6}\)

Step-by-step explanation:

The hypotenuse of the isosceles right triangle is √2 times the length of one leg, so is 6√2.

The hypotenuse of the 30°-60°-90° right triangle is 2/√3 times the length of the longer leg.

  \(x=\dfrac{2}{\sqrt{3}}\cdot 6\sqrt{2}\\\\=\dfrac{(2\sqrt{3})(6\sqrt{2})}{3}\quad\text{rationalize the denominator}\\\\\boxed{x=4\sqrt{6}}\)

Answer:

Lateral Area: 120                                                                                    

Surface Area: 163.3

Answer:-15

Step-by-step explanation:

multiplying both sides by -5 gives -30x-25y=-15

The collection gadget with the given transfer function and an enter of x(t) = cos(t) has a frequency response given through Y(s) = cos(t) * \([8(s+1)/(s+2)(s^2 + 4)]\). The gadget is solid due to the poor real part of the pole at s = -2. The absence of zeros in addition contributes to system stability.

To set up the frequency reaction of the collection system, we want to calculate the output Y(s) inside the Laplace domain given the input X(s) = cos(t) and the transfer function of the device.

The switch function of the series machine, as proven in Figure 1, is given as H(s) = \(8(s+1)/(s+2)(s^2 + 4).\)

To locate the output Y(s), we multiply the enter X(s) with the aid of the transfer feature H(s) and take the inverse Laplace remodel:

Y(s) = X(s) * H(s)

Y(s) = cos(t) * \([8(s+1)/(s+2)(s^2 + 4)]\)

Next, we want to determine the stability of the overall gadget. The stability is determined with the aid of analyzing the poles of the switch characteristic.

The poles of the transfer feature H(s) are the values of s that make the denominator of H(s) equal to 0. By putting the denominator same to zero and solving for s, we are able to find the poles of the machine.

S+2 = 0

s = -2

\(s^2 + 4\)= 0

\(s^2\) = -4

s = ±2i

The machine has one actual pole at s = -2 and complicated poles at s = 2i and s = -2i. To investigate balance, we observe the actual parts of the poles.

Since the real part of the pole at s = -2 is poor, the system is stable. The complicated poles at s = 2i and s = -2i have 0 real elements, which additionally contribute to stability.

Sketching the poles and zeros at the complex plane, we see that the machine has an unmarried real pole at s = -2 and no 0. The pole at s = -2 indicates balance because it has a bad real component.

In conclusion, the collection gadget with the given transfer function and an enter of x(t) = cos(t) has a frequency response given through Y(s) = cos(t) *\([8(s+1)/(s+2)(s^2 + 4)]\). The gadget is solid due to the poor real part of the pole at s = -2. The absence of zeros in addition contributes to system stability.

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The correct question is:

" Establish the frequency response of the series system with transfer function as specified in Figure 1, with an input of x(t) = cos(t). Determine the stability of the connected overall system shown in Figure 1. Also, sketch values of system poles and zeros and explain your answer in terms of the contribution made by the poles and zeros to overall system stability. x(t) 8 5 s+1 s+2 Figure 1 Block diagram of series system s+2 S² +4"

Answer:

Try 11.25 miles

Step-by-step explanation:

Answer:

This doesn´t make sense please clarify.

Step-by-step explanation:

Answer:

The volume of a sphere of radius r is:

S = (4/3)*pi*r^3

The volume of a cylinder of radius r and height h is:

C = pi*r^2*h

For this problem the height of the cylinders will be equal to the diameter of the spheres, which is equal to two times the radius.

First, let's use the radius: r = 2.

The volume of the sphere will be:

S = (4/3)*3.14*(2)^3 = 33.49

The volume of the cylinder, where h = 2*2 = 4, is:

C = 3.14*(2^2)*4 = 50.24

Now, let's choose the radius r = 3.

The volume of the sphere will be:

S = (4/3)*3.14*3^3 = 113.04

The volume of a cylinder with this radius and h = 3*2 = 6, is:

C = 3.14*(3^2)*6 = 169.56

Answer:

a)22

b)7

c)8

Step-by-step explanation: its really complicated so ill try my best.

so the say 11 like both coffee and tea so that means that they also added 11 to

the other two sections. so if we take 11 away from 18 we get 7, and that's how many people like coffee and not tea. to get answer c) we need to also subtract 11 from 15, which gets us 4. so we have 11 plus 4 plus 7. and that gets us 22.  so 30 subtract 22 gets us 8 so 8 people don't like tea or coffee. 22 is also the answer to a). did you get that? i hope so

The Project Triangle is also known as the triple constraints model and consists of three elements: cost, time and scope.

The Project Triangle is also known as the Iron Triangle or Triple Constraints and is a graphical representation of the connection between project costs, schedule, and scope. It is one of the key principles of project management, and it is utilized to help organizations and project managers understand and handle trade-offs between different objectives of a project.

The three elements of the Project Triangle are:

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There is not strong evidence against the claimed value of 43%.

N = 400
P = 0.43

Check Conditions:
10% Condition: We assume 400 hectares is less than 10% of all hectares, so this condition is met.
Large Counts Condition: 400(0.43) = 172 and 400(1-0.43) = 228 are both greater than 10, so this condition is met.

Is this approximately normal? Yes, because both the 10% condition and the Large Counts condition are met.

Find the Important Values:
Mean of p-hat: 0.43
Standard Deviation of p-hat: sqrt((0.43)(1-0.43)/400) = 0.0248

Assuming that the Forestry Commission's report is accurate, what is the approximate probability that more than 47% of the sample would have had the certification in 2016?
We need to find the z-score for 0.47: z = (0.47-0.43)/0.0248 = 1.61
Using a z-table, we find that the probability of getting a z-score greater than 1.61 is 0.0537.

Since our probability of 0.0537 is greater than 5%, there is not strong evidence against the claimed value of 43%.

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The surface whose equation is given by 6r² + z² = 1 is an ellipsoid. The surface whose equation is given by 6r^2 + z^2 = 1 is a three-dimensional shape known as an ellipsoid. An ellipsoid is a type of quadric surface that is defined by three principal axes, with the lengths of these axes determined by the coefficients of the equation.

In this case, the ellipsoid has a major axis in the z-direction with a length of 1, and minor axes in the x and y directions with lengths of √(1/6). The equation can also be rewritten as (r/√(1/6))^2 + (z/1)^2 = 1, which shows that the ellipsoid is centered at the origin and has a radius of √(1/6) in the x and y directions, and a radius of 1 in the z direction.

An ellipsoid is a 3D surface that resembles an elongated sphere, with its general equation given as (x²/a²) + (y²/b²) + (z²/c²) = 1. In this case, the given equation can be rewritten in the standard form as (x²/ (1/6)) + (y²/ (1/6)) + (z²/1) = 1, which shows it's an ellipsoid.This particular ellipsoid has its major axis along the z-axis and two equal minor axes along the x and y-axes, with semi-major axis length of 1 and semi-minor axis lengths of √(1/6).

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Answer:

Angle 1 is 35°, angle 2 is 60°, and angle 3 is 85°

Step-by-step explanation:

In seeing the measures of the angles from the problem, we see that angle 1 can be represented as x, and all the other angles rely on the value of x, so then an equasion can be built.

Angle 1 is represented as x,

Since angle 2 is 10 less than 2 times angle 1's value, it is represented as 2x-10.

Since angle 3 is 25 more than the second, you add 25 to angle 2's value, which leaves us with 2x+15.

In adding all these values together, we get \(5x+5=180\). We then subtract 5 from both sides, leaving us with \(5x=175\), and then we divide both sides by 5 to get \(x=35\).

We then plug in x's value to find the measures of the angles.

For angle 1:35=35,

For angle 2: 2(35)-10=60

For angle 3: 2(35)+15=85.

Finally, to double check, add the values of 35, 60, and 85 together, which equals 180

Based on the 95% confidence interval calculated from the random sample of 30 workouts, the conclusion is that we fail to reject the null hypothesis (H0).

The null hypothesis (H0) states that the mean heart rate during workouts is equal to 150 beats per minute. The alternative hypothesis (H1) would be that the mean heart rate differs from 150. In this case, the 95% confidence interval calculated from the sample data is between 158 and 167 beats per minute. Since this interval does not include the hypothesized mean of 150, it might initially suggest that the null hypothesis should be rejected in favor of the alternative hypothesis. However, in hypothesis testing, we consider the confidence interval as a range of plausible values for the population mean. Since the interval contains values above and below 150, it does not provide convincing evidence to reject the null hypothesis. Therefore, the correct conclusion is to fail to reject H0, indicating that there is not sufficient evidence to conclude that the individual's true mean heart rate while working out differs from 150 beats per minute.

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Answer: The two middle ones I think. This is hard to read sorry.

its easy but let me explain

Step-by-step explanation:

If she earns $8.15 an hour and she works for 4 1/2 hours.

You multiply

$8.15 x 4.5 = n

n= $36.675    But your not done yet, ROUND TO HUNDREDTHS PLACE!!!

if there is a number 5 or higher next to the hundredths place then you bump the number up by 1

she would of earned $36.68 in 4.5 hours  Glad to help