Out of the 301 seniors, 117 are boys. What is the ratio of boys to the total number of seniors?

Question 9: No, 10n + 20 is not in O(n^2) .Question 10: No, 2n^2 + 10 is not in o(n). Question 11: Yes, 5n^2 + 2 is in ω(n). Question 12: Yes, 2n + 10 is in ω(n^2). In the context of asymptotic notation, the notation "O" represents an upper bound, while "o" represents a strict upper bound.

On the other hand, the notation "ω" represents a lower bound.

In Question 9, the function 10n + 20 grows linearly with respect to n, and it does not exhibit quadratic growth. Therefore, it is not in O(n^2).

In Question 10, the function 2n^2 + 10 grows quadratically with respect to n, and it does not grow at a slower rate compared to n. Therefore, it is not in o(n).

In Question 11, the function 5n^2 + 2 grows quadratically with respect to n, and it grows at a faster rate compared to n. Therefore, it is in ω(n).

In Question 12, the function 2n + 10 grows linearly with respect to n, and it grows at a faster rate compared to n^2. Therefore, it is in ω(n^2).

These answers provide insights into the growth rates and comparisons between different functions, allowing us to understand how they scale and compare as the input size increases.

Learn more about quadratic functions here: brainly.com/question/18958913

#SPJ11

The volume of the region in the first octant bounded by the coordinate planes, the plane y z=12, and the cylinder x=144−y2 is 432 cubic units. To find the volume of the region in the first octant bounded by the coordinate planes, the plane y z=12, and the cylinder x=144−y2, we need to set up a triple integral.

Since the region is in the first octant, we have the following limits of integration:
0 ≤ x ≤ 144 - y^2
0 ≤ y ≤ √(12/z)
0 ≤ z ≤ 12
So the volume V of the region is given by the triple integral:
V = ∫∫∫ R dV
Where R is the region defined by the above limits of integration, and dV = dxdydz is the differential volume element. Substituting in the limits of integration, we have:
V = ∫0^12 ∫0^√(12/z) ∫0^(144-y^2) dxdydz
Evaluating the integral using the order dzdydx, we get:
V = ∫0^12 ∫0^√(12/z) (144-y^2)dydz
   = ∫0^12 [144y - (1/3)y^3]0^√(12/z) dz
   = ∫0^12 [144√(12/z) - (1/3)(12/z)^(3/2)]dz
   = 576∫0^1 (1 - u^3)du          (where u = √(12/z))
Evaluating the final integral, we get:
V = 576(1 - 1/4)
 = 432 cubic units.

Learn more about integral here:

brainly.com/question/14502499

#SPJ11

Answer:

m∠B = 100°

a = 4.6

b = 7.36

Step-by-step explanation:

By applying sine rule in the given triangle,

\(\frac{\text{sin(A)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(C)}}{c}\)

Now substitute the values in the expression,

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(B)}}{b}= \frac{\text{sin(42)}}{5}\)

\(\frac{\text{sin(38)}}{a}= \frac{\text{sin(42)}}{5}\)

\(a=\frac{5\text{sin(38)}}{\text{sin(42)}}\)

a = 4.6

By applying triangle sum theorem in ΔABC,

m∠A + m∠B + m∠C = 180°

38° + m∠B + 42° = 180°

m∠B = 180° - 80°

m∠B = 100°

\(\frac{\text{sin(100)}}{b}= \frac{\text{sin(42)}}{5}\)

\(b=\frac{5\text{sin(100)}}{\text{sin(42)}}\)

b = 7.36

Answer:

The answer is in the picture

Answer:

Domain= time

Range= temperature

Step-by-step explanation:

Initially hot water cools down over time.

This can be expressed as a function of a temperature by a time. It takes 25 minutes for water to cooled down from 100°F to body temperature.

For any value of the time (from zero to 25 minutes), the temperature has certain value (from 100°F to body temperature). As time value increases, temperature value decreases accordingly.

In this example, time is the domain and temperature is the range.

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

To know more about third quartile click the link:

brainly.com/question/24329548

#SPJ1

The employee's hourly wage is 10.6 dollars.

The graph below describes the relationship between hour worked and the money earned.

The hour worked is on the x axis. This makes the hour worked an independent variable.

The money earn is on the y axis. The money earn is the dependent variable.

Therefore, the hourly wages can be calculated from the graph as follows:

Let's pick two points (5, 53)(10, 106) and find the slope

m = 106 - 53 / 10 - 5

m = 53 / 5

m = 10.6

The equation of the line is as follows;

let's find b using (5, 53)

y = 10.6x + b

53  = 10.6(5) + b

b = 53 - 53

b = 0

Hence, the equation is  y = 10.6x

Hourly wages is 1 hour wage.

Therefore,

y = 10.6(1)

y = 10.6

Hence, the hourly wage is 10.6 dollars.

learn more on hourly wages here: https://brainly.com/question/14659672

#SPJ1

The recommended food plan - MyPlate guidelines were established to enable individuals to follow a balanced diet, ensuring they get all the nutrients their bodies require. The Grains category is one of the five food groups, which is part of the MyPlate guidelines. It is advised to consume approximately six ounces of grains each day. Brown rice, whole-wheat bread, oatmeal, pasta, and cereals are all healthy grains that provide the nutrients our bodies need. To the roasted chicken, adding brown rice from the Grains category and consuming a balanced diet can provide several nutrients.

The USDA recommends that adults consume about 46-56 grams of protein per day, but this can vary depending on age, sex, weight, and activity level. To calculate the amount of protein in the meal, we can use the following formula:

Amount of protein in brown rice: 1 cup of cooked brown rice contains 5 grams of protein.

Amount of protein in roasted chicken: 3 ounces of roasted chicken contains 27 grams of protein.To calculate the total amount of protein in the meal, add the protein amounts in both the chicken and brown rice:

5 grams of protein in brown rice + 27 grams of protein in roasted chicken = 32 grams of protein in the meal

Therefore, the meal contains 32 grams of protein.

The amount of fiber in brown rice and roasted chicken, respectively, is as follows:

Amount of fiber in 1 cup of cooked brown rice: 3.5 grams

Amount of fiber in 3 ounces of roasted chicken: 0 grams

To calculate the total amount of fiber in the meal, add the fiber amounts in both the chicken and brown rice:

3.5 grams of fiber in brown rice + 0 grams of fiber in roasted chicken = 3.5 grams of fiber in the meal

Therefore, the meal contains 3.5 grams of fiber in total.

The MyPlate guidelines advise individuals to consume a balanced diet that contains all the nutrients their bodies need. The Grains category is an essential component of a balanced diet that includes healthy grains such as brown rice, whole-wheat bread, oatmeal, pasta, and cereals. Brown rice is a great source of fiber, vitamins B and E, minerals like iron and zinc, and antioxidants that can help protect the body against various diseases.Adding brown rice from the Grains category to roasted chicken provides the meal with an excellent source of protein. Protein is essential for building and repairing tissues, making enzymes and hormones, and preserving lean muscle mass. A balanced diet should contain approximately six ounces of grains, and brown rice is a great way to achieve this recommendation.

Brown rice is also high in fiber, making it a filling food that can help reduce appetite and aid in weight loss. Additionally, fiber can help regulate bowel movements and prevent digestive disorders. Consuming fiber-rich foods such as brown rice can also help reduce the risk of heart disease, diabetes, and certain types of cancer.Thus adding brown rice from the Grains category to roasted chicken provides the meal with 32 grams of protein and 3.5 grams of fiber, making it a nutritious meal that can provide several health benefits. Consuming a balanced diet that contains all the nutrients our bodies need can help reduce the risk of various diseases and ensure optimal health.

To know more about USDA visit:

brainly.com/question/29787478

#SPJ11

The height of the lean-to on its vertical side is 8 feet.

To find the height of the lean-to on its vertical side, we need to use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the vertical side is the hypotenuse, and the length and width are the other two sides.

So, we have:

\(height^2 = hypotenuse^2 - width^2\)

We know the length of the roof (the hypotenuse) is 17 feet, and the width is 15 feet. So we can plug these values into the equation and solve for the height:

\(height^2 = 17^2 - 15^2\\height^2 = 289 - 225\\height^2 = 64\\height = 8\)

Therefore, the height of the lean-to on its vertical side is 8 feet.

Learn more about Height

brainly.com/question/30106412

#SPJ11

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.

Answer:

Step-by-step explanation:

Let say a and b the 2 natural integers with 0 < a< b.

Since a*b=GCF(a,b)*LCM(a,b)

a*b < 3*20=60

\(\begin{array}{c|c|c|c|c|c}a&b&a*b&GCF&LCM&GCF*LCM\\---&---&---&---&---&---\\3&6&18&3&6&18\\3&9&27&3&9&27\\3&12&36&3&12&36\\3&15&45&3&15&45\\3&18&54&3&18&54\\6&9&54&3&18&54\\---&---&---&---&---&---\\\end {array}\)

Answer:

\(x = 9\)

Step-by-step explanation:

Question:

\(x-3=6\\\)

Take (-3) to the right side

\(x-3=6\\x=6+3\\x=9\)

Hope this helps you.

Let me know if you have any other questions:-)

Answer:

\(x=9\)

Step-by-step explanation:

\(x-3=6\)

\(x-3+3=6+3\) ( Add 3 to both sides)

\(x=9\)

Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Researchers are careful about drawing conclusions regarding statistical significance because statistical significance is a measure of the likelihood that the observed results are not due to random chance. When conducting research, researchers aim to make inferences and draw conclusions based on evidence that is reliable and valid.

Here are a few reasons why researchers exercise caution when interpreting statistical significance: Avoiding Type I and Type II errors, Generalizability, Replicability, Methodological limitations.

Avoiding Type I and Type II errors: When testing hypotheses, there is always a possibility of making errors. Type I error occurs when a researcher mistakenly rejects a true null hypothesis (false positive), and Type II error occurs when a researcher fails to reject a false null hypothesis (false negative). By being cautious, researchers strive to minimize these errors and ensure that their conclusions are accurate.

Generalizability: Researchers often want to generalize their findings from a sample to a larger population. Statistical significance provides an indication of how likely the findings can be applied to the broader population. Drawing conclusions without considering statistical significance may lead to misleading or unreliable generalizations.

Replicability: Scientific research should be replicable, meaning that other researchers should be able to obtain similar results when conducting the same study. Statistical significance helps assess whether the observed effects are consistent and reproducible across different studies. Without proper consideration of statistical significance, it becomes difficult to determine if the results can be replicated reliably.

Methodological limitations: Research studies can have various limitations such as small sample sizes, confounding factors, measurement errors, or biases. By carefully assessing statistical significance, researchers can better understand the limitations of their study and make more informed conclusions.

In summary, researchers are cautious about drawing conclusions regarding statistical significance to ensure the validity, reliability, generalizability, and replicability of their findings. By exercising care in interpreting statistical significance, researchers aim to make robust and trustworthy conclusions based on the available evidence.

Learn more about exercise from

https://brainly.com/question/30131075

#SPJ11

The correct option regarding the scale factor and the statement in this problem is given as follows:

D. The statement is false. Because there are 3 feet in one​ yard, there are 9 square feet in one square yard.

The scale factor between the length dimensions of the yard are given as follows:

3 feet = 1 yard.

(as these length dimensions are given in yards).

Then for the square units, the correct scale factor is found applying the proportion as follows:

(3 feet)² = (1 yard)².

9 feet squared = 1 square yard.

Hence the statement given in this problem, that because there are 3 feet in one​ yard, there are also 3 square feet in one square yard, is false, and the correct option is given by option D.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

the sWe have the next quadratic formula:

Use the form x²+bx+c

Where:

a=1

b=-12

c=85

Then,

Hence, the correct answer is option A.

(4,5) i'm pretty sure I can't explain why but just go with it

The value of p(10) we get as  123.

What is Quadratic polynomial ?

A quadratic polynomial is a polynomial of degree 2, which means that it is a polynomial expression in one variable (usually written as x) that contains only terms of the form ax² + bx + c, where a, b, and c are constants. The highest exponent of the variable x in a quadratic polynomial is 2.

We are given a table of values for the quadratic polynomial p. Since p is a quadratic polynomial, it can be written in the form:

p(x) = ax² + bx + c

where a, b, and c are constants.

To find the value of p(10), we need to substitute x = 10 in the above equation and simplify:

p(10) = a(10)² + b(10) + c

p(10) = 100a + 10b + c

We don't know the values of a, b, and c, but we can use the values in the table to set up a system of equations.

From the table, we can see that:

p(0) = c = 3

p(1) = a + b + c = 6

p(2) = 4a + 2b + c = 11

Solving this system of equations, we get:

a = 1

b = 2

c = 3

Therefore, the quadratic polynomial p is:

p(x) = x² + 2x + 3

To find p(10), we substitute x = 10 in the above equation:

p(10) = (10)² + 2(10) + 3

p(10) = 100 + 20 + 3

p(10) = 123

Therefore, the value of p(10) is 123.

To learn more about Quadratic polynomial from given link.

https://brainly.com/question/30288154

#SPJ1

Answer:

$22,263

Step-by-step explanation:

15% of $74,210 is $11,131.50 so $11,131.50 X 2= $22,263

so after 2 years the total amount of money along with interest will be a total of = $96,473

Answer:2490-2312=w; w=178 so 178 pounds

Step-by-step explanation:

Answer:

hey!

Your answer is 178 pounds!!

Step-by-step explanation:

by doing 2490lb-2312lb gives us the value of w

soo w=178 pounds!!

HOPE THIS HELPS!!

Answer:

Step-by-step explanation:

Given

Angle =57°

So by linear property of the angles 57°+c=180°

c=180°-57°

c=123°

Angle c is 123°

Angle b=angle c (opposite angle)

angle b 123°

Answer:

Area

Step-by-step explanation:

Answer:

4.125 inches.

Step-by-step explanation:

Based on the information provided we see that she took 90 minutes before shovelling which is 1 hour and 30 minutes or 1 1/2 hours (1.5 hours). Since we also know that the snow has been accumulating at a rate of 3/4 (0.75) inch per hour then we simply multiply these two values together to find out how much snow has accumulated.

0.75 * 1.5 = 1.125 inches

Now we can add this amount to the initial amount at 6:00 in the morning to find how many inches of snow were on the driveway when she started shovelling

3 + 1.125 = 4.125 inches.

Answer:

8n² - 5

Step-by-step explanation:

n = 'a number'

The expression is  8x² - 5.

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Let's examine the writing of expressions. The other number is x, and a number is 6 greater than half of it. In a mathematical expression, this proposition is denoted by the expression x/2 + 6.

Given:

The product of eight and a number squared decreased by 5

let the number be x.

product of eight and a number squared

= 8x²

and decreased by 5

= 8x² - 5

hence, the expression is  8x² - 5.

Learn more about expression here:

https://brainly.com/question/14083225

#SPJ2

Answer:

The girl is 2.5 meters below sea level

Step-by-step explanation:

We are told in the question that:

A girl is snorkeling 1 meter below sea level

Hence, her elevation in meters below the sea level = -1m

We are told in the question that:

She then dives down another 1.5 meters

Once again: Her elevation in meters below the sea level = -1.5m

How far below sea level is the girl?

This is calculated as:

-1 m + -1.5m

= -1m - 1.5m

= -2.5m

Therefore, the girl is 2.5 meters below sea level

Using the stated transformation, the graph of g(2x) is given at the end of the answer.

An horizontal stretch or an horizontal compression happens when a constant is multiplied at the domain of the function, as follows:

g(x) = f(ax).

The definition of stretch or compression depends on the value of the constant a, as follows:

In this problem, the rule is:

f(x) = g(2x).

Meaning that f(x) is an horizontal compression by a factor of 1/2 of g(x), and then the vertices are given as follows:

That is, in each vertex, the x-coordinate was divided by 2, and thus the graph with these vertices is given at the end of the answer.

More can be learned about transformations at https://brainly.com/question/28725644
#SPJ1

Answer:

9,945,936,000.

Step-by-step explanation:

This is the number of permutations of 6 letters from 26 multiplied by number of permutations of 3 odd digits between 0 and 9.

The total number of odd digits between 0 and 9 are 1,3,5,7,9 = 5.

So the number of choices are

26P6 * 5P3.

=  26!/(26-6)! * 5!/ 2!

= 26!/20! * 5!/2!

= 165765600 * 60

= 9945936000.

\( \: \)

\( \: \)

\( \: \)

\( \: \)

\( \: \)

where,

\( \star \sf{ \pink{x_1 = -2 , x_2 = 4}}\)

\( \star \sf{ \color{hotpink}y_1 = 6 , y_2 = -2}\)

\( \: \)

\( \: \)

\( \: \)

[ divide by 2 ]

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

hope it helps ⸙