In the triangle below, what is the sine of 60°?
site
60°
2
1
30°
13
ОА.
NI
O B. 2
O c. 1
D. VE

Answer:

    3631.681108 ft^2

Step-by-step explanation:

The surface area of a cylinder is

SA = 2pi r^2 + 2pi r h  where r is the radius and h is the height

    = 2pi (17)^2  + 2 pi (17)(17)

    = 578pi +578pi

    = 1156pi

Approximate pi with the pi button

    3631.681108 ft^2

The correct statement is: double d = 123456789

In the given statements:

1. int i = 3.0; - This is incorrect because a decimal value (3.0) cannot be assigned directly to an integer variable. It should be assigned to a floating-point type variable instead.

2. float f = 4.5; - This is correct as a floating-point value (4.5) can be assigned to a float variable.

3. byte b = 123456789; - This is incorrect because the value 123456789 is outside the range of a byte (-128 to 127). It should be assigned to a data type with a larger range, such as into or long.

4. double d = 123456789; - This is correct as the value 123456789 can be assigned to a double variable.

5. boolean b = 1; - This is incorrect because the value 1 cannot be directly assigned to a boolean variable. It should be assigned with either true or false.

Among the given statements, the correct one is "double d = 123456789;", as it assigns the value 123456789 to a double variable.

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The ratio of 3:4 for 363 days is equivalent to the ratio of 1.05:1.40.

To find the equivalent ratio for 363 days in the ratio of 3:4, we can use the following steps:

Step 1: Add the ratio terms (3 + 4 = 7) to get the total number of parts.

Step 2: Divide the total number of parts by the denominator of the ratio (7 ÷ 4 = 1.75).

Step 3: Multiply the numerator and denominator of the ratio by the result from Step 2 to get the equivalent ratio.

Therefore, the equivalent ratio of 3:4 for 363 days is:

3 : 4 = 3/7 x 1.75 : 4/7 x 1.75

= 1.05 : 1.40

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Answer:

B. No, Hannah should have used the ratio \( \frac{adjacent}{opposite} \)

Step-by-step explanation:

✍️The formula for calculating cotangent of an angle is given as:

\( cot = \frac{adjacent}{opposite} \).

The ratio, \( \frac{opposite}{adjacent} \), used by Hannah is the formula for calculating tangent of an angle.

Therefore, Hannah did not calculate the cotangent of the angle correctly.

She should have used, the ratio, \( \frac{adjacent}{opposite} \) instead.

The value of  Pw(w) and Fw(w) are (0, 0.4, 0.8, 1) for different random variable X. And E[W] = -E[X] = -0 = 0.

(a) To find Pw(w), we need to determine the probability that the transformed random variable W takes on a specific value w. In this case, W = -X.

Since W is the negative of X, the probability that W equals w is equal to the probability that X equals -w.

Pw(w) = P(X = -w)

Considering the CDF of X, we have the following intervals:

For -∞ < x < -3: Fx(x) = 0

For -3 < x < 5: Fx(x) = 0.4

For 5 < x < 7: Fx(x) = 0.8

For 7 < x < ∞: Fx(x) = 1

Since W = -X, we can rewrite the intervals as:

For ∞ < w < 3: Fw(w) = 0 (since X = -w is not within the range of X)

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(b) To find Fw(w), we need to determine the cumulative distribution function (CDF) of W. From the previous calculations:

For ∞ < w < 3: Fw(w) = 0

For -3 < w < -5: Fw(w) = 0.4

For -5 < w < -7: Fw(w) = 0.8

For -∞ < w < -7: Fw(w) = 1

(c) To find E[W], we need to calculate the expected value of W. Since W = -X, we can express E[W] as:

E[W] = E[-X] = -E[X]

We can use the CDF Fx(x) to find the expected value of X:

E[X] = ∫ x * f(x) dx

Using the intervals and probabilities from the CDF:

E[X] = (-3 * 0.4) + (0 * (0.8 - 0.4)) + (6 * (1 - 0.8))

E[X] = -1.2 + 0 + 1.2

E[X] = 0

Therefore, E[W] = -E[X] = -0 = 0.

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Answer:

x = 25

Step-by-step explanation:

by alternate exterior angles theorem

\(127 = 5x + 2 \\ 127 - 2 = 5x \\ 125 = 5x \\ \frac{125}{5} = \frac{5x}{5} \\ x = 25\)

check

\(5(25) + 2 = 127 \\ 125 + 2 = 127 \\ 127 = 127\)

The magnitude of the projection of f1 onto the line of action of f2 is 5.55.

The magnitude of the projection of f1 onto the line of action of f2 can be calculated using the dot product of the two vectors. The dot product is given by the formula:

f1 • f2 = |f1| |f2| cos θ

Where f1 • f2 is the dot product of f1 and f2, |f1| and |f2| are the magnitudes of f1 and f2 respectively, and θ is the angle between the two vectors.

To find the magnitude of the projection, we need to find the dot product of f1 and f2 and divide it by the magnitude of f2. The magnitude of the projection is given by:

Magnitude of the projection = (f1 • f2) / |f2|

Let's calculate it step by step:

Step 1: Calculate the dot product of f1 and f2:
f1 • f2 = (3.8 * 9.3) + (6.3 * 3.0) = 35.34 + 18.9 = 54.24

Step 2: Calculate the magnitude of f2:
|f2| = √(9.3^2 + 3.0^2) = √(86.49 + 9) = √95.49 = 9.772

Step 3: Calculate the magnitude of the projection:
Magnitude of the projection = (f1 • f2) / |f2| = 54.24 / 9.772 = 5.55

Therefore, the magnitude of the projection of f1 onto the line of action of f2 is 5.55.

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Answer:

225

Step-by-step explanation:

Take 675/3 to find one third of its current depth. That gives you your answer. Does that make sense?

Given:

The equation is:

\(x^2-12x+32=4\)

To find:

The result of completing the square for the given equation.

Solution:

We have,

\(x^2-12x+32=4\)

It can be written as:

\(x^2-12x=4-32\)

\(x^2-12x=-28\)

Now, we need to add half of square of coefficient of x, to complete the square.

Adding \((\dfrac{-12}{2})^2\) on both sides, we get

\(x^2-12x+(\dfrac{-12}{2})^2=-28+(\dfrac{-12}{2})^2\)

\(x^2-2(x)(6)+(-6)^2=-28+(-6)^2\)

\(x^2-2(x)(6)+(6)^2=-28+36\)                 \([\because (-a)^2=(a)^2]\)

Using the formula \((a-b)^2=a^2-2ab+b^2\), we get

\((x-6)^2=8\)

Therefore, the required equation after completing the square is \((x-6)^2=8\).

Answer:

8.64

Explanation: I just did the math

Answer:

The number of times a variable appears in a date set is called a constant.

Answer:

\(x\leq 120\)

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

Hope this helps!

Have a great day and God bless! :)

The instructor should use an independent samples t-test to determine if there is a difference in the average test scores between the two groups.

To determine if there is a difference in the average test scores between two groups, the instructor should use a statistical test called the t-test.

The t-test is commonly used to compare the means of two groups and determine if there is a statistically significant difference between them.

There are different types of t-tests depending on the characteristics of the data and the research question. The most commonly used t-test is the independent samples t-test, which is used when the two groups being compared are independent of each other (i.e., the individuals in one group are different from the individuals in the other group).

The independent samples t-test compares the means of the two groups and calculates a t-value, which represents the difference between the group means relative to the variability within each group.

This t-value is then compared to a critical value from the t-distribution based on the sample size and desired level of significance (usually 0.05 or 0.01).

If the calculated t-value exceeds the critical value, it indicates that there is a statistically significant difference in the average test scores between the two groups.

On the other hand, if the calculated t-value does not exceed the critical value, it suggests that there is no significant difference in the average test scores.

In summary, the instructor should use an independent samples t-test to determine if there is a difference in the average test scores between the two groups.

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The answer is 360

Explanation:

5 x 2 = 10

10x3=30

30x2=60

60x3=180

180x2 = 360

Answer:

The answer is 360

Step-by-step explanation:

Because the pattern is x2, x3

so the next would be 360 and the next would be 1080

Answer:

86

Step-by-step explanation:

58+ (4x7=28)

58+28= 86

The validity of measurement or data refers to the accuracy of the measurement instrument or data-acquisition tool. The answer is option(e).

The constructive nature of perception is best described as the influence of expectations on sense-perception. The answer is option(a).

1) The validity of measurement or data refers to the accuracy of the measurement instrument or data-acquisition tool. It is a basic assessment of the instrument's accuracy, including whether it can properly and appropriately evaluate what it was intended to evaluate.

2) Our experiences can affect how we interpret sensory data, causing us to see things that aren't there or failing to see things that are. As a result, perception is a two-way street in which sensory input is combined with prior experiences to create our understanding of the world around us.

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When the fractions of gasoline in the tanks are divided equally among all drivers, each tank will be 1/2 filled.

From the information, the station attendant asks drivers how full their gas tanks are when they refuel and the line plot displays the drivers' responses.

A line plot is a graph that shows data as dots or checkmarks above a number line to indicate how frequently each value occurs.

The fraction can be calculated as:

= (2 × 1/8) + (2 × 1/4) + (4 × 1/8) + (6 × 1/2) + (1 × 5/8) + (2 × 3/4) + (3 × 7/8) / 20

= 10 / 20

= 1/2

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Answer:

x = 12 in ; Type in 12 in the box

Step-by-step explanation:

If we were to apply triangle formula ; 1/2 * base * height, we would see that length of height ⇒ 10 inches, and length of base ⇒ x inches,

Given an Area of 60 square inches let us substitute into the formula 1/2 * base * height and solve for x;

Area of Triangle = 1/2 * base * height,

60 in^2 = 1/2 * x in * 10 in ⇒ take 1/2 * 10,

60 in^2 = 5 in * x in ⇒ divide either side by 5 in,

12 in = x in ⇒ divide either side by inches,

x = 12 inches,

Solution; x = 12 in

We need to identify the true statement for every polynomial P with degree n.

The degree n of a polynomial is the exponent of the highest power of x in that polynomial. For example, the polynomial

has degree 3, since the highest power of x has exponent 3.

Thus, if the degree is n, then the highest power is n (not n-1). Therefore, (a) is False.

About the number of solutions to P(x) = 0, it can equal the number of the polynomial degree. For some polynomials, the solutions can repeat, so the number of solutions will be less than n. For some of them, the solutions may not belong to the real numbers.

As an example, for P(x) = x²+4, we have:

The above polynomial has degree 2 and 2 solutions. Therefore, (b) is False.

Each turning point is where the graph of the polynomial P(x) changes from decreasing to increasing or vice versa. The graph of any polynomial of degree n has at most n-1 turning points.

Therefore, (c) is True.

We can see that (d) is False from the following example:

the line P(x) = x+1 has degree n = 1 and n = 1 x-intercept, which is its zero x = -1.

Answer:

c) The graph of P has at most n-1 turning points

Hope this helps

x > -17

The sample size for the given data is 17

The sample size is a term used in market research for defining the number of subjects included in a sample size.

Given that, a sample size has an 80% confidence interval, the population standard deviation is s = 120, the margin of error to be approximately 10, We need to find the sample size,

Sample size = (z-score)²×SD×(1-SD) / (confidence interval)²

z-score of 80% confidence interval = 1.28

Sample size = (1.28)²×0.12(1-0.12)/0.10²

= 1.6384×0.12×0.88/0.01

= 17.30

Hence, the sample size for the given data is 17

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Angle constructed by bisecting a 45° angle: By bisecting a 45° angle, we can construct an angle with a measure of 22.5 degrees.

To bisect an angle means to divide it into two equal parts. When we bisect a 45° angle, we are essentially dividing it in half to create two angles of equal measure.

To construct the bisector of a 45° angle, we can follow these steps:

Begin by drawing a ray (a straight line extending indefinitely in one direction) to serve as one side of the angle.

Using a protractor, measure and mark a 45° angle on the ray. This will be our original angle.

Place the point of the compass on the vertex (the point where the two sides of the original angle meet) and draw an arc that intersects both sides of the angle.

Without changing the compass width, place the compass point on one of the intersection points of the arc with the angle.

Draw another arc that cuts across the first arc, creating two points of intersection.

Finally, draw a ray connecting the vertex of the angle to one of the points of intersection on the second arc. This ray will be the bisector of the 45° angle.

Upon completing these steps, we will have constructed an angle bisector that divides the 45° angle into two equal angles, each measuring 22.5 degrees.

It's important to note that bisecting an angle is a fundamental geometric construction technique and can be used to divide any given angle into two equal parts. The process described above is specifically for bisecting a 45° angle, but the same principles can be applied to bisect angles of different measures.

In summary, by bisecting a 45° angle, we can construct an angle with a measure of 22.5 degrees. This construction involves drawing an arc from the vertex, creating two intersection points, and connecting the vertex to one of those points to form the angle bisector.

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Answer:

r² = (4 - 2)² + (5 - (-2))² = 2² + 7² = 53

So the equation of this circle is

(x - 2)² + (y + 2)² = 53

Answer:

-9/4 or -2.25

Step-by-step explanation:

−2(x+1/4)+1=5 ​ ​

-2x - 0.5 + 1 = 5

-2x + 0.5 = 5

-2x = 4.5

x = -2.25

Fraction form: -9/4

Answer:19/3

Step-by-step explanation:

Answer:19/3

Step-by-step explanation:

Answer:

the answer is D :)

Step-by-step explanation:

Answer:

a and b connect to d in the slope

Step-by-step explanation:

Answer:

Aight mate

Step-by-step explanation:

So every triangles angles will add up to 180 degrees no matter the triangle. Now a circle is 360 and a line is 180. Look at the line that A and C are on this line equals 180. So angle c and d added together make 180 and angles a b and c added together make 180. so if a+b+c = c+d then a+b=c. I hope thaqtmakes sense.

For Pearson correlation the most common purpose to examine is given by option a. The relationship between 2 variables.

The Pearson correlation is a statistical measure that indicates the extent to which two continuous variables are linearly related.

It measures the strength and direction of the relationship between two variables.

Ranging from -1 perfect negative correlation to 1 perfect positive correlation.

And with 0 indicating no correlation.

It is commonly used in research to examine the association between two variables.

Such as the relationship between height and weight, or between income and education level.

Therefore, the most common purpose of a Pearson correlation is to examine the relationship between 2 variables.

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The above question is incomplete, the complete question is:

The most common purpose for a Pearson correlation is to examine,

a. The relationship between 2 variables

b. Relationships among groups

c. Differences between variables

d. Differences between two or more groups

Answer:

x = 3 cm

Step-by-step explanation:

The chords that are equal distance from the center are equal.

       CD = AB

  4x + 8 = 20

Subtract 8 from both sides,

          4x = 20 - 8

          4x = 12

Divide both sides by 4,

            x = 12 ÷4

            \(\sf \boxed{x = 3 \ cm}\)

The equivalent square root for \(\sqrt[\sf 2]{\sf 81\text{x}}\) is \(\sf 9\sqrt{\text{x}}\).

In mathematics, a square root of a number x is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is x.

Given the the square root, we need to find the equivalent square root for \(\sqrt[\sf 2]{\sf81\text{x}}\).

So,

Rewrite \(\sqrt[\sf 2]{\sf81\text{x}}\) as \(\sqrt{\sf9(\text{x})}\).

Then, pull terms out from under the radical, assuming positive real numbers.

\(\sqrt{\sf9(\text{x})}=\bold{9\sqrt{x}}\)

Therefore, The equivalent square root for \(\sqrt[\sf 2]{\sf 81\text{x}}\) is \(\sf 9\sqrt{\text{x}}\).

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