Use the Triangle Angle Sum Theorem to find the measure of the angle on point C.

Two of the solutions of the equation cos(x/2) = -(sqrt2/2) are 135 degrees and 225 degrees (or 3π/4 radians and 5π/4 radians).

Two of the solutions of the equation cos(x/2) = -(sqrt2/2) can be found by considering the unit circle and the properties of cosine.

Since the cosine function represents the x-coordinate of a point on the unit circle, we can look for the angles where the x-coordinate is -(sqrt2/2).

One such angle is 135 degrees (or 3π/4 radians), where the cosine is equal to -(sqrt2/2). At this angle, the x-coordinate of the corresponding point on the unit circle is -(sqrt2/2).

Another angle with the same x-coordinate is 225 degrees (or 5π/4 radians). At this angle, the cosine is also equal to -(sqrt2/2).

Two of the solutions of the equation cos(x/2) = -(sqrt2/2) are 135 degrees and 225 degrees (or 3π/4 radians and 5π/4 radians). These angles satisfy the given equation and have the desired x-coordinate on the unit circle.

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Answer:

∠O = 95°

Step-by-step explanation:

since ∠Q = 85°, arc NOP = 2(85°) = 170°

arc PQN = 360° - arc NOP

arc PQN = 360° - 170° = 190°

∠O = 1/2(arc PQN) = 1/2(190°) = 95°

To determine whether there is enough evidence to reject the null hypothesis, we need to compare the computed test statistic to the critical value.

In this case, the computed test statistic is 2.50 and the critical value is 2.33. If the computed test statistic falls in the rejection region beyond the critical value, we can reject the null hypothesis. Conversely, if the computed test statistic falls within the non-rejection region, we fail to reject the null hypothesis.In this scenario, since the computed test statistic (2.50) is greater than the critical value (2.33), it falls in the rejection region. This means that the observed data is unlikely to occur if the null hypothesis were true.

Therefore, based on the given information, there is enough evidence for the emergency room nurse to reject the null hypothesis. This suggests that there is sufficient evidence to support the claim that the average number of cases of upper respiratory infections per day at the hospital is over 21 cases.

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There is enough evidence to reject the null hypothesis in this case because the computed test statistic (2.50) is higher than the critical value (2.33). This suggests the average number of daily respiratory infections exceeds 21, providing substantial evidence against the null hypothesis.

Yes, there is enough evidence for the emergency room nurse to reject the null hypothesis. The null hypothesis is typically a claim of no difference or no effect. In this case, the null hypothesis would be an average of 21 upper respiratory infections per day. The test statistic computed (2.50) exceeds the critical value (2.33). This suggests that the average daily cases indeed exceed 21, hence providing enough evidence to reject the null hypothesis.

It's crucial to understand that when the test statistic is larger than the critical value, we reject the null hypothesis because the observed sample is inconsistent with the null hypothesis. The statistical test indicated a significant difference, upheld by the test statistic value of 2.50. The significance level (alpha) of 0.05 is a commonly used threshold for significance in scientific studies. In this context, the finding suggests that the increase in respiratory infection cases is statistically significant, and the null hypothesis can be rejected.

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In this question, the gradual, long-term movement in time series data is referred to as temporal variation.

The correct answer is a. temporal variation. Temporal variation describes the systematic and long-term changes that occur in time series data over an extended period. It is characterized by a gradual shift or trend in the data points, indicating an underlying pattern or direction.

Temporal variation can be observed in various contexts, such as economic indicators, population growth, weather patterns, and stock market trends. It reflects the impact of factors that change over time, such as demographic shifts, technological advancements, economic cycles, or environmental conditions.

It is important to differentiate temporal variation from other types of movements in time series data. Cyclical movement refers to regular fluctuations that occur within a specific time frame, while exponential smoothing and linear regression are statistical techniques used to analyze and forecast time series data. Therefore, the correct term to describe the gradual, long-term movement in time series data is temporal variation.

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To find the value of x, we multiply the given values for molar and seconds by the distance cubed in meters. This results in an answer of 0.039 m²

To solve for x, we simply need to multiply (3.5×10³ m⁻²s⁻¹) and (0.33m)³ together. This gives us:

x = (3.5×10³ m⁻²s⁻¹) * (0.33m)³

x = 0.039 m²

Therefore, the answer is 0.039 m², with units of square meters.


To solve for x, we use the formula x = (3.5×10³ m⁻²s⁻¹) * (0.33m)³. This involves multiplying the values for molar and seconds by the distance cubed in meters. The calculation is straightforward and yields an answer of 0.039 m². This means that the area is 0.039 square meters. It's important to use the correct units when working with equations that involve different measurements, as this can affect the final result. Overall, it's a simple problem to solve using basic mathematical operations.


To find the value of x, we multiply the given values for molar and seconds by the distance cubed in meters. This results in an answer of 0.039 m², with units of square meters. It's important to use the correct units when working with equations that involve different measurements to get an accurate result. The calculation is straightforward and can be easily solved using basic mathematical operations.

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Answer:

C. Reflection across the y-axis

Step-by-step explanation:

Reflection across y axis= (x,y) to (-x,y) so B (1,2) is now B'(-1,2). Hope this helped!

Answer:

$ 3820

Step-by-step explanation:

When the car is new, it is 0 year old. It means, t = 0

Initial value = 26,000 (0.84)^0 = 26,000(1)

Initial value = $ 26000

Similarly, when car is 11 year old, t = 11

=> 26000(0.84)¹¹ = 26000(0.14691)

≈ $ 3819.842

≈ $ 3820 (round to near ten)

Answer:

13.33333333

Step-by-step explanation:

Answer:

13.33333

Step-by-step explanation:

The length L of the curve is approximately 185.35 units.

To find the length of the curve, we first need to find the derivative of the given function:

f'(y) = 1 - (25/32) y^(-2/3)

Next, we need to find the integrand by squaring the derivative and adding 1:

g(y) = √(1 + [1 - (25/32) y^(-2/3)]^2)

Then, we can use this integrand to set up the integral:

L = ∫[0,243] g(y) dy

L= 185.35 units

Using a calculator or software, we can evaluate this integral to find the length L of the curve, which is approximately 185.35 units. Hence the length of curve is  185.35 units

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Answer:

Boys equal 189 and girls equal 108

Step-by-step explanation:

Let b = the number of boys

Let g = the number of girls

b + g = 297

Rewrite as g = 297 - b

\(\frac{4}{9}\)b = \(\frac{7}{9}\)g Multiply both sides by 9

4b = 7g  Substitute 297 - b for g

4b = 7(297 -b)  Distribute the 7

4b = 2079 - 7b   Add 7 b to both sides

11b = 2097  Divide both sides by 11

b = 189

There are 189 boys.

g = 297 - b  Substitute 189 for b to solve for g

g = 297 - 189

g = 180

The number of girls is 108.

Helping in  the name of Jesus.

Answer:

x = 14 cm

Step-by-step explanation:

Start by drawing the triangles separately and labeling the points properly. After doing so, we can see that the RT is 6 cm larger than RP. Similarly, ST which is given a value of x is on the same side as QP which has a value of 8 cm. When you scale QP by 6 cm you will get ST. 8 + 6 = 14, so 14 cm is the value for x.

Answer:

Decimal--x= -1.39

Fraction--x= -139/100

Step-by-step explanation:

You want to get x by itself in this problem

You have to distribute the 3 into the parenthesis first

1.2/8=15x+21

Now you can do 2 of either things....you can either divide 1.2/8 and then subtract 21 from both sides or you can just subtract 21 from both sides without dividing. I will use option 2.

1.2/8-21=15x+21-21

So now you cancel out the 21 on the right side and get...

-20.85=15x

Now divide by 15

-1.39=x in fraction form -139/100=x

Hope this helped!

Answer:

18ft

Step-by-step explanation:

just add all the sides. since it’s a rectangle, you there is 2 sides that’s 3ft long and that are 6ft long. so you would do 3+3+6+6

If Rene started with the below equation;

The addition and subtraction properties of equality states in order to keep both sides of the equation balanced, you have to subtract or add the same value to both sides.

But Rene added 12 to the left side and subtracted 3 from the right side instead of adding or subtracting the same value to both sides.

So all we need to do balance the equation again is add 15 to the right side of the equation;

Answer:

A = 36√3 - 12π

Step-by-step explanation:

Make 2 identical 30-60-90 triangles out of the "wedge"

For each 30-60-90 triangle:

Since the short leg is 6 the long leg is 6√3

short leg is the base and long leg is the height

a = (1/2)bh

a = (1/2)(6)(6√3)

a = 3(6√3)

a = 18√3

Since there are 2 triangles

a = 36√3

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

Then subtract off the area of the 120º sector

a = (120/360)πr^2

a = (1/3)π(6^2)

a  = (1/3)π(36)

a = 12π

Shaded area

a = 36√3 - 12π

Step-by-step explanation:

we have the areas of 2 right-angled triangles minus 1/3 the area of the circle (because the 120 degree segment of the circle is 1/3 of the whole 360 degree circle).

since the answer is asking for a square root, we need to aim for the result of a Pythagoras calculation.

basically, the area of a triangle is

1/2 × b×c × sin(A)

A being the angle between the 2 sides b and c. for any 2 sides of the triangle.

one triangle is from the outmost left point to the center of the circle and up to the 90 degree angle. the other triangle is then down to the second right angle.

we know all angles in such a triangle : 90, 120/2 = 60, 180-90-60 = 30.

remember, the sum of all angles in a triangle is 180 degrees.

so, via the law of sines we can then calculate all sides :

a/sin(A) = b/sin(B) = c/sin(C)

with the angles being opposite of the sides.

6/sin(30) = baseline/sin(90)

6/0.5 = baseline/1

12 = baseline

top side² + 6² = 12²

top side² = 12² - 6² = 144 - 36 = 108

top side = sqrt(108) = sqrt(36×3) = 6×sqrt(3)

we pick then top side and 6 as the 2 sides, so that we can use sin(90)=1 in the formula.

the area of the 2 triangles is then

6×sqrt(3)×6×sin(90) = 36×sqrt(3)

and the circle segment to be deducted is

pi×r²/3 = pi×6²/3 = pi×36/3 = pi×12

so, the complete answer is

A = 36×sqrt(3) - 12×pi

Answer:

(–5, 12) is the correct answer.

Step-by-step explanation:

We are given the following values:

\(cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}\)

Now, we know the following identities:

\(sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}\)

Now, the values are:

\(sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}\)

Sine value is positive and cos, tan values are negative.

It can be clearly observed that \(\theta\) is in 2nd quadrant.

2nd quadrant means, the value of \(x\) will be negative and \(y\) will be positive.

Let us have a look at the value of \(tan\theta\):

\(tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5\)

Please refer to the attached image for clear understanding and detailed explanation.

Hence, the correct answer is coordinate (x,y) is (–5, 12)

Answer:

A (–5, 12) on E2020

Step-by-step explanation:

Answer:

12 units²

Step-by-step explanation:

AB = \(\sqrt{(x_{2} -x_{1})^2 +(y_{2} -y_{1})^2 }\) = \(\sqrt{(0-3)^2 +(0-3)^2}\) = 3√2

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

\(A_{ABCD}\) = AB × BC = 3√2 × 2√2 = 12 units²

Answer:

So I did the assignment, and the answer that you're looking for in this problem would be 12.

Using proportional relationships, the unit rates are given as follows:

A direct proportional relationship is a function in which the output variable is given by the multiplication of the input variable and the constant of proportionality, also called the unit rate k, as follows:

y = kx

For this problem, the functions are given as follows:

The unit rates are the constants of proportionality, respectively, given by:

k = 62, k = 65 and k = 63.

The functions for Fosbert's Contracting and Durable B Construction are missing, and are given as follows:

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Answer: 1/6

Step-by-step explanation: Have a blessed day

The solutions for the system of equations given by Substitution method is (27, 114), (-0.25, -5.625), (0, -3) and (0, -2).

Linear equations involve one or more expressions including variables and constants and the highest exponent of the variable is 1.

System of linear equations involve two or more linear equations.

1) -4x + y = 6

5x - y = 21

We are using Substitution Method.

From, -4x + y = 6, we get, y = 4x + 6

Substituting y = 4x + 6 in the equation 5x - y = 21, we get,

5x - (4x + 6) = 21

5x - 4x - 6 = 21

x = 27

So, y = 4x + 6 = 114

2) -7x - 2y = 13

x - 2y = 11 ⇒ x = 2y + 11

Substituting x = 2y + 11 in the first equation -7x - 2y = 13,

-7(2y + 11) - 2y = 13

-14y - 77 - 2y = 13

-16y = 90

y = -5.625

So, x = 2y + 11 = -0.25

3) -5x + y = -3 ⇒ y = 5x - 3

3x - 8y = 24

Substituting y = 5x - 3 in the second equation 3x - 8y = 24,

3x - 8(5x - 3) = 24

3x - 40x + 24 = 24

x = 0

y = 5x - 3 = -3

4) -5x + y = -2 ⇒ y = 5x - 2

-3x + 6y = -12

Substituting y = 5x - 2 in the second equation -3x + 6y = -12,

-3x + 6 (5x - 2) = -12

-3x + 30x - 12 = -12

x = 0

So, y = 5x - 2 = -2

Hence the system of equations are solved.

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The correct answer is "Employees." All employees pay 7.65% of their taxable income to Social Security.

The correct answer is "Employees." This is because Social Security taxes are typically deducted from employees' wages or salaries. The 7.65% deduction represents the combined rate for Social Security and Medicare taxes, commonly known as FICA taxes (Federal Insurance Contributions Act). Employers also contribute an additional 7.65% on behalf of their employees. However, in this context, the focus is on the portion paid by the employees themselves, hence the answer "Employees."

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If in a survey, 200 college students were asked whether they live on campus and if they own a car, 55% of college students in the survey don't own a car.

To find the percent of college students who don't own a car, we need to add up the number of students who don't own a car and divide it by the total number of students in the survey. In this case, the total number of students in the survey is 200.

From the table, we can see that there are 88 students who live on campus and don't own a car, and 22 students who don't live on campus and don't own a car. So the total number of students who don't own a car is 88 + 22 = 110.

To find the percentage, we divide the number of students who don't own a car by the total number of students in the survey and then multiply by 100 to get the percentage:

Percentage of students who don't own a car = (110/200) x 100% = 55%

When working with percentages, we need to divide the number we are interested in by the total and then multiply by 100 to get the percentage.

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Answer:

C

Step-by-step explanation:

A difference of squares can be factored in general as

a² - b² = (a - b)(a + b)

We are looking for 2 terms separated by a - and perfect squares on either side. The only one meeting this criteria is

25x² - 64y²

= (5x)² - (8y)²

= (5x - 8y)(5x + 8y) ← in factored form

Answer:

since the toy is marked down 15%,

you do p*.85  

to find the remaining cost

If the fuselage of the Boeing 777 were made of steel instead of aluminum, the number of passengers it could carry would decrease.

Given that the fuselage of the Boeing 777 is a hollow aluminum cylinder, we can calculate its volume using the dimensions provided: length = 64.0 m, width = 6.2 m, and thickness = 2.5 mm. Using the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height, we can determine the volume of the aluminum fuselage. Since the cylinder has no ends, the height is the same as the length of the fuselage. The radius can be calculated by dividing the width by 2. By substituting these values into the formula, we can find the volume of the aluminum fuselage. Once we have the volume, we can multiply it by the density of aluminum to find the mass of the aluminum fuselage. Dividing the mass by the average passenger mass of 79 kg will give us the approximate number of passengers the Boeing 777 could carry if its fuselage were made of steel. However, we need the specific maximum total mass or engine's lifting capacity to provide an exact answer.

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The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed, For runner J, it would take 12 minutes to go one mile.

For runner J, it would take 12 minutes to go one mile.

Athlete J needs eight minutes to complete a half-mile.

Running one mile in an hour equals one minute for athlete H.

Athlete J's time needed to complete a mile of running.

12 minutes are needed to complete one mile.

Running one mile would take J 12 minutes.

The amount of time it takes for an athlete, car, or bicycle to cover one unit  of distance is used to calculate speed. For runner J, it would take 12 minutes to go one mile.

The complete question is,

Athlete J completes a 1/3 mile run in 8 minutes. Athlete H completes 2 3/4 miles in a half-hour.

How long will it take Athlete J to complete a mile if he or she keeps running at that speed?

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Answer: This statement represents  →A Division prolem

The correct equation is →8=n÷5                                                                

                  I Hop This Helped :)

Step-by-step explanation:

Answer:

Write an equation to model the problem containing an unknown number.

                                             Eight is the quotient of a number and five.

This statement represents:

✔ a division problem

.

The correct equation is:

✔ 8 = n ÷ 5

Correct on Edge nuity 2021

Answer: -3

Step-by-step explanation: