Factor the following expression. 36y - 12

The HDD for the month of January in State College, PA is 930.

To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.

HDD = 65°F - 35°F
HDD = 30°F

Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:

1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.

So, the HDD for the month of January in State College, PA is 930.

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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.

To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:

HDD = (65 - 35) x 31
HDD = 930

So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.

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When examining the problem and purpose portions of a research study, the important question to ask is (option d) Is the objective of the study clearly stated?

Given,

What should I look for while  reviewing the problem and purpose sections of a research article?

To do this, we suggest reading the content numerous times before criticizing it, making notes, and adding annotations. Be sure to take notes while you read on crucial elements such as the thesis, purpose, research questions, hypotheses, methods, evidence, significant findings, tone, and publishing information.

Here,

The pertinent question when reviewing the problem and purpose sections of a research article is (option d) Is the objective of the study clearly stated?

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\( {c}^{2} - {b}^{2} = {a}^{2} \)

\( {15}^{2} - {13}^{2} = {56}^{2} \)

\( \sqrt{56} = 7.5\: yd\)

//

\(sin = \frac{opp}{hyp} \)

\( {sin}^{ - 1} = \frac{13}{15} \)

\( = 60 \: degrees\)

//

\(180 - 90 - 60 = 30 \: degrees\)

He have 48 different possible outfits to wear at work with three one-piece jump suits, five pairs of work pants, and eight work shirts.

The basic counting principle is a method for keeping track of all the potential outcomes in a situation. According to this statement, there are n m n times m n ways to carry out both of these actions if there are n ways to perform one action and m ways to perform another action after that.

Here,

5 pants with each of 8 shirts,

=5 x 8

=40 combinations of shirts and pants.

40 shirt/pants outfits + 8 jumpsuits = 48 total outfits.

With three one-piece jumpsuits, five pairs of work pants, and eight work shirts, he has 48 different work-appropriate outfit options.

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Yes, the table contains the solution of the system of equations, and the solution is (7, 6).

Here we have a table that defines a system of equations of the form:

ya = f(x)

yb = f(x)

And a solution of that system is a point of the form:

yb = f(x) = ya

So we wan to find a pair such that for the same value of x, the values of ya and yb are the same ones.

We can see that when x = 6 that happens, then yes, the table has the solution to the system of equations, and the solutions is (6, 7)

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Answer:

£68

Step-by-step explanation:

Width of one tile = 20cm

Calculate how many tiles you need to fit the width of the wall:

width of wall ÷ width of tile = 300 ÷ 20 = 15 tiles wide

Height of one tile = 25cm

Calculate how many tiles you need to fit the height of the wall:

height of wall ÷ height of tile = 250 ÷ 25 = 10 tiles high

Therefore, total tiles needed = 15 x 10 = 150 tiles

If there are 20 tiles in each box,  

total tiles ÷ 20 = 150 ÷ 20 = 7.5 boxes

So we need to round this UP to 8 boxes (else we won't have enough tiles)

Therefore, 8 boxes of tiles at £8.50 per box:

Total cost = 8 x 8.50 = £68

To make a water balloon explode on the ground near the opposing team, you need to launch the balloon with enough speed and at the right angle to clear the flat-topped building.

To successfully splash the other team, you must consider the height and distance of the building. Since a direct shot is not possible, you need to launch the water balloon at an angle that allows it to clear the building and explode on the ground near the opposing team. The height of the building, which is 30.0 ft, and the distance between the building and the opposing team, which is 100 ft, will affect the trajectory of the water balloon.

By calibrating the balloon launcher to launch speeds that can reach up to 115 mph at angles between 0 and 85 degrees from the horizontal, you have a range of options to choose from. The optimal angle will depend on the distance between your launch position and the target area. By adjusting the angle, you can control the trajectory of the water balloon and ensure it clears the building before reaching the ground near the opposing team.

It is crucial to find the right balance between launch speed and launch angle to achieve the desired outcome. A higher launch speed will increase the range but may also result in the balloon overshooting the target area. On the other hand, a lower launch speed may not allow the balloon to clear the building. Therefore, careful experimentation and adjustment of the launch speed and angle will be necessary to hit the desired spot.

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The mean score is a measure of central tendency that represents the average value of a set of numerical data. It is calculated by adding up all the values in the data set and then dividing the sum by the number of values.

To find the mean score for the class in terms of n and h, follow these steps:

1. Calculate the total score for students who scored 100: h * 100
2. Calculate the total score for students who scored 50: (n - h) * 50
3. Add the total scores from steps 1 and 2: 100h + 50(n - h)
4. Divide the sum from step 3 by the total number of students (n) to find the mean: (100h + 50(n - h))/n

So, the algebraic expression for the mean score of the class in terms of n and h is:

(100h + 50(n - h))/n

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Answer:

0.38095238095238

Step-by-step explanation:

Therefore, this equation is true: 24/63 = 8/21 If the numerator is greater than or equal to the denominator of a fraction, then it is called an improper fraction.

Step-by-step explanation:

sin if -7.2 = -0.79 approximately -0.8

Hope you understand and hope this helps.

Good luck ✅.

The area of the triangle with side lengths 9, 8, and 8 is approximately 20.630 square units. To find the area of a triangle with side lengths a = 9, b = 8, and c = 8, we can use Heron's formula.

Heron's formula states that the area of a triangle with side lengths a, b, and c is given by the square root of s(s - a)(s - b)(s - c), where s is the semiperimeter of the triangle.

The semiperimeter, s, is calculated by adding the lengths of all three sides and dividing by 2. In this case, s = (a + b + c)/2 = (9 + 8 + 8)/2 = 25/2 = 12.5.

Using Heron's formula, the area of the triangle is given by:

A = √(s(s - a)(s - b)(s - c))

Substituting the given values, we have:

A = √(12.5(12.5 - 9)(12.5 - 8)(12.5 - 8))

Simplifying the expression inside the square root:

A = √(12.5 * 3.5 * 4.5 * 4.5)

Calculating the product:

A = √(425.625)

Rounding the result to three decimal places, we have:

A ≈ 20.630

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Answer:

its "A"

Step-by-step explanation:

A run-on sentence results from two or more complete sentences being connected without any punctuation

Hello!

It's Option A.

Run-on sentences are sentences that aren't properly connected.

Eat your vegetables then you can go to bed.

This is a run-on sentence, as two short sentences are put together, but they aren't connected properly.

Hope this helps!

Do ask me if you have any query.

~A gloomy teen

\(MagicalNature\)

Answer:

B. 3x + 4

Step-by-step explanation:

Perimeter garden = 8x + 8

Perimeter = 2 * length + 2 * width

Width = x

8x + 8 = 2 * length + 2x

8x - 2x + 8 = 2* length

6x + 8 = 2 * length

3x + 4 = length

So the order from left to right would be: Mode, Median, Mean.

In a positively skewed distribution, the mean is typically larger than the median, and the median is larger than the mode.

This can be illustrated in the following way:

Mean: The mean is affected by extreme values in the tail of the distribution, and will be pulled in the direction of the skew. Therefore, in a positively skewed distribution, the mean will be to the right of the median.

Median: The median is the value that separates the lower 50% of the data from the upper 50% of the data. In a positively skewed distribution, the tail of the distribution is on the right-hand side, which means that the median will be closer to the left-hand side than the mean.

Mode: The mode is the most frequent value in the distribution. In a positively skewed distribution, the mode will be the smallest value, located at the left-hand side of the distribution, while the mean and median will be to the right of it.

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Answer:

x=2

Step-by-step explanation:

-x+5=-11x+25

add +x on both sides -11x+x =-10x

-10x+25=5

subtract 25 on both sides

you get -10x=-20

x=2

Answer:

100cm^2

Step-by-step explanation:

5×2=10 which is one side

base×height=area

10×10=100

Formula to calculate combinations is given by -

nCr=[n !]/[r ! * (n-r) !]

where,

nCr = number of combinations

n = total number of objects in the set

r = number of choosing objects from the set

Now, according to given -

n = 10 people

r = 5 callers

Hence,

Number of possible combinations = nCr

= 10C5

= (10!)/[5! * (10-5)!]

= 252

Thus, 252 different people could have made successful calls to the radio station.

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Answer:

10

Step-by-step explanation:

\( \frac{5}{12} = \frac{1}{a} + \frac{1}{b} \\ \\ \frac{5}{12} = \frac{b + a}{ab}..(by \: taking \: lcm) \\ \\ \frac{5}{12} = \frac{a + b}{ab} \\ \\ \frac{5}{12} = \frac{a + b}{24} ...( \because \: ab = 24) \\ \\ a + b = \frac{5 \times 24}{12} \\ \\ a + b = 5 \times 2 \\ \\ \huge \red{ \boxed{ a + b = 10}}\)

Answer: A. 33

Step-by-step explanation:

Answer:

x+46

Step-by-step explanation:

Distribute

Combine like terms

To find the relationship between the volume of a prism and a pyramid with congruent bases and equal heights, we need to consider their formulas.  
The volume of a pyramid is given by the formula V = (1/3)Bh,

where B represents the area of the base and h represents the height. Since the bases of the prism and pyramid are congruent and their heights are equal, we can write the equation:

Volume of Prism = 2 × Volume of Pyramid Using the formulas mentioned earlier, we can substitute the expressions for the volumes:

Bh = 2 × (1/3)Bh
Simplifying this equation, we can cancel out the B's:

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The statement "a prism and a pyramid have congruent bases and equal heights, and the volume of the prism is twice the volume of the pyramid" is FALSE.

To understand why, let's consider a simple example. Imagine we have a triangular prism and a triangular pyramid with congruent bases and equal heights. The base of both shapes is a triangle, and their heights are the same.

The volume of a prism can be calculated by multiplying the area of its base by its height. Similarly, the volume of a pyramid can be calculated by multiplying the area of its base by one-third of its height.

Since the prism and the pyramid have congruent bases and equal heights, the only difference in the volume calculation is the factor of 1/3 for the pyramid.

This means that the volume of the pyramid is one-third the volume of the prism, not half. Therefore, the statement that the volume of the prism is twice the volume of the pyramid is false.

Therefore, the statement is incorrect, and the volume of the prism is not twice the volume of the pyramid, but rather three times as much.

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The value of k for which P(X > k) = 0.75 is approximately 4.696. Option D

To find the value of k for which P(X > k) = 0.75, we need to use the properties of the standard normal distribution.

Given that X has a normal distribution with a mean of 2 and a standard deviation of 4, we can standardize the variable X using the z-score formula:

z = (X - μ) / σ

where μ is the mean and σ is the standard deviation.

Substituting the given values, we have:

z = (X - 2) / 4

To find the value of k, we need to determine the z-score that corresponds to a cumulative probability of 0.75.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to a cumulative probability of 0.75 is approximately 0.674.

Setting the standardized value equal to 0.674, we have:

0.674 = (k - 2) / 4

Solving for k, we find:

k - 2 = 0.674 * 4

k - 2 = 2.696

k ≈ 4.696

Therefore, the value of k for which P(X > k) = 0.75 is approximately 4.696.

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The best description of the geometric construction of the quotient z/w on the complex plane is; Option A; z is scaled by a factor of One-fifth and rotated 90 degrees clockwise

We are given;

z = 3(cos(15°) + i sin(15°))

w = 5(cos(90°) + i sin(90°))

Now, if we want to find the quotient z/w, it is clear that in geometric construction, the procedure will be to scale z by a factor of 1/5 and thereafter we will rotate by 90° clockwise.

Thus, option A is the correct answer.

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Answer:

A linear function can be represented by a graph that is a straight line. The equation for a linear function is of the form y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis). The slope of the line tells us how steep the line is, and whether it has a positive or negative slope. A positive slope means that the line is sloping upwards from left to right, while a negative slope means that the line is sloping downwards from left to right.

Answer: $23.92

Step-by-step explanation:

First, we know that 6 bagels is $2.99.

48/6=8

This means that 6 is a multiple of 48, which makes it easier to solve.

$2.99 x 8 = 23.92

= $23.92

The correct statement is Option B: I and III are true, II is false. Amy and Bob will continue to specialize and trade to mutual advantage, and Bob is better off than before.

I. Amy and Bob will continue to specialize and trade to mutual advantage: This statement is true. Since Amy can pick three baskets of either apples or grapes in an hour, she has a comparative advantage in picking both fruits compared to Bob. Bob, on the other hand, can only pick two baskets of either fruit in an hour. By specializing in their respective areas of comparative advantage and trading with each other, both Amy and Bob can benefit from increased productivity and efficiency.

II. Amy is better off than she was before: This statement is false. Although Amy has become more efficient in picking both apples and grapes, she is not better off compared to before because her productivity remains the same. She can still pick three baskets in an hour, whether it's apples or grapes.

III. Bob is better off than he was before: This statement is true. Bob has improved his productivity in both apple and grape picking. Previously, he could only pick one basket of either fruit, but now he can pick two baskets in an hour. This increase in productivity makes Bob better off than he was before.

Therefore, the correct statement is Option B: I and III are true, II is false.

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Trevor and Kim will be situated 21 kilometers apart from each other at 1:30 PM. They will be separated by a distance of 21 km when the clock strikes 1:30 in the afternoon.

To determine at what time Trevor and Kim will be 21 km apart, we can set up a distance-time equation based on their relative speeds and distances.

Let's assume that t represents the time elapsed in hours since noon. At time t, Trevor would have traveled a distance of 8t km, while Kim would have traveled a distance of 6t km in the opposite direction.

Since they are running in opposite directions, the total distance between them is the sum of the distances they have traveled:

Total distance = 8t + 6t

We want to find the time when this total distance equals 21 km:

8t + 6t = 21

Combining like terms, we have:

14t = 21

To solve for t, we divide both sides of the equation by 14:

t = 21 / 14

Simplifying, we find:

t = 3 / 2

So, they will be 21 km apart after 3/2 hours, which is equivalent to 1 hour and 30 minutes.

Therefore, Trevor and Kim will be 21 km apart at 1:30 PM.

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The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

Standard deviation is defined as the square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

The table shows the number of goals made by two hockey players.

Player A:

2, 3, 1, 3, 2, 2, 1, 3, 6

Using  a statistics calculator, we have:

Mean = 2.56

S.D. = 1.51

Player B:

1, 4, 5, 1, 2, 4, 5, 5, 11

S.D. = 3.03

The best measure of variability is the standard deviation.

Player A is the most consistent, with an IQR of 1.5.

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