What are the missing segment lengths shown in the image?

Applying law of sine and law of cosine, the unknown values x and y are 16.2 units and 37.1 degrees respectively.

To determine the value of x and y in the given triangle, we can use law of sine or law of cosine depending on the variables available and what we need to determine.

Applying law of cosine;

x² = 15² + 10² - 2(15)(10)cos78

x² = 225 + 100 - 300cos78

x² = 225 + 100 - 62.4

x² = 262.6

x = √262.6

x = 16.2 units

From this, we can apply law of sine to determine y;

x / sin X = y / sin Y

Substituting the values into the formula above;

16.2 / sin78 = 10 / sin y

Cross multiply both sides and solve for y;

16.2siny = 10sin78

sin y = 10sin78 / 16.2

sin y = 0.6038

y = sin⁻¹ (0.6038)

y = 37.14°

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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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In a randomized controlled experiment, there is a control group and a treatment group.

This statement is i.e. option d is correct.

Randomized controlled experiments are commonly used in scientific research, particularly in medicine and psychology.

They are used to determine whether a treatment or intervention is effective or not.

In a randomized controlled experiment, the participants are randomly assigned to either the control group or the treatment group.

The control group is used as a comparison group and does not receive the treatment or intervention.

The treatment group, on the other hand, receives the treatment or intervention being studied.

There are several ways that a randomized controlled experiment can be designed to minimize the potential for bias. For example, in a randomized controlled experiment, random assignment of participants to groups helps to ensure that the two groups are similar at the outset of the study.

This reduces the likelihood that differences between the groups will be due to factors other than the treatment or intervention being studied.

Other ways that a randomized controlled experiment can be designed to minimize bias include blinding and use of placebos.

Blinding refers to the practice of keeping certain participants, such as those administering the treatment, unaware of which group a participant is in.

This helps to ensure that any differences between the two groups are not due to the expectations of the researchers or participants.

Use of placebos is another way to reduce bias in a randomized controlled experiment.

Placebos are inactive substances that are given to the control group to mimic the treatment group, ensuring that any differences between the groups are due to the treatment being studied and not other factors.

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The points where the direction of the fastest change of the function is in i j is (1, 1) and (-1, -1).

In order to find the direction of the fastest change, we need to find the gradient of the given function. The gradient is a vector that points in the direction of the steepest ascent, which is also the direction of the fastest change. Let's take the partial derivative of f(x, y) with respect to x and y.

f(x, y) = x²y² − 4x − 6y∂f/∂x = 2xy² − 4∂f/∂y = 2x²y − 6

The gradient of f(x, y) is given by:

∇f(x, y) = <2xy² − 4, 2x²y − 6>

Now we need to find the values of x and y such that the direction of the gradient vector is i j. We know that the direction of the gradient vector is given by: ∇f/|∇f|

Therefore, we need to solve the following equations for x and y.

<2xy² − 4, 2x²y − 6> = k

where k is a constant and is the unit vector in the i j direction. Now we have to solve the following system of equations.

2xy² − 4 = ki2x²y − 6 = kj

By solving the above two equations, we get, x=±1 and y=±1

Substitute these values in the first equation, we get, k=√(8/9)

Hence, the answer is (x, y) = (1, 1), (-1, -1).

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Answer:

-2

Step-by-step explanation:

Answer:

Your answer is: Undefined

Use the slope formula to find the slope  m .

Step-by-step explanation:

Hope this helped : )

The slope of the line that passes through the points (-4, -2) and (-4, -22) is an infinite slope.

The slope of a line can be found using the formula below.

Therefore,

x₁  = -4

x₂ =  - 4

y₁ = -2

y₂ = -22

Therefore,

m = -22 - (-2) / - 4 - (-4)

m = -22 + 2 / - 4 + 4

m = 20 / 0

m = infinity

The slope is an infinite slope.

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Answer:

3.(-2/0) this is your answer

The interest practice described in the question is known as "bundling." Bundling refers to the act of combining individual campaign contributions from multiple sources into a single larger contribution from a group or organization.

Bundling allows interest groups or individuals to pool their resources and present a more substantial contribution to a candidate. By consolidating smaller contributions into a larger sum, bundlers can demonstrate greater financial support and influence.

This practice is often employed by special interest groups, lobbyists, or individuals with shared political objectives who want to maximize their influence on the political process. Bundlers can leverage their collective financial power to gain access to candidates, shape policy agendas, and potentially gain favorable treatment or influence over decision-making.

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Answer:

Fraction form: 1/8

Decimal form: 0.125

Step-by-step explanation:

Slope of line = [-6 - (-8)]/[8 - ( -8)]

= [-6 + 8]/[8 + 8]

= 2/16

= 1/8

= 0.125

The percent of slope if there is a rise of 72 metres in 600 metres is given as follows:

12%.

The percent of slope is obtained applying the proportions in the context of this problem.

A proportion is applied because the percent of slope is given by the division of the vertical rise by the horizontal movement, multiplied by 100%.

The parameters for this problem are given as follows:

Hence the percent of slope is obtained as follows:

72/600 x 100 = 12%.

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Answer:

the answer is 'a' and 'e'

Adelaide's monthly payment for financing the refrigerator over 36 months at an APR of 12.5% is approximately $55.33

This calculation is based on the formula for calculating the monthly payment on a loan, taking into account the principal amount, the monthly interest rate, and the number of months.

In the first paragraph, we determine the principal amount as $1750, which represents the cost of the refrigerator. The annual percentage rate (APR) of 12.5% is converted to a monthly interest rate (r) by dividing it by 12 and then by 100. The number of months (n) is given as 36.

In the second paragraph, we substitute the values into the monthly payment formula and perform the necessary calculations. The formula incorporates the principal, the monthly interest rate, and the number of months to determine the monthly payment amount. After evaluating the expression, we find that Adelaide's monthly payment is approximately $55.33.

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a) a minimum of 3 doctors required so that at least 70% of the arriving patients.

b) a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes

a) Minimum number of doctors required so that at least 70% of the arriving patients can receive treatment immediately

Formula used:

The number of patients arriving in an hour: λ = 9

Treatment time: μ = 6 minutes

Per the Little’s law, the waiting time is proportional to the average number of patients present at any given time.

λ/μ is the average number of patients present at any given time.

If there are k servers present in the ER, the number of patients they can serve is given by kμ.

Hence, the percentage of patients who have to wait is given by:

Percentage of patients waiting = λ / (kμ + λ)

Percentage of patients receiving treatment immediately = kμ / (kμ + λ)

Thus, we can now form an equation as:

kμ / (kμ + λ) ≥ 0.7

=> kμ / (kμ + 9) ≥ 0.7

=> k ≥ 3 doctors (Approximately)

Therefore, a minimum of 3 doctors required so that at least 70% of the arriving patients can receive treatment immediately.

b) Minimum number of doctors required so that the average time a patient waits for treatment is no more than 30 minutes as advertised

The percentage of patients who have to wait = λ / (kμ + λ)

Again, let us use the Little's law to find the average time patients spend waiting in the queue, which is equal to

λ / (k(μ - λ/k)).

We are given that the waiting time should not be more than 30 minutes, which can be converted to 0.5 hours.

Thus:

λ / (k(μ - λ/k)) ≤ 0.5

=> 9 / (k(0.1 - 1/k)) ≤ 0.5

=> 18 ≤ k(0.1 - 1/k)

=> 0.1k - 1 ≤ 18/k

=> 0.1k² - k - 18 ≥ 0

Using the quadratic formula, the solution is k = 6.66, which is rounded up to 7, and k = 2.5, which is rounded up to 3.

Therefore, a minimum of 7 doctors are required so that the average time a patient waits for treatment is no more than 30 minutes as advertised and a minimum of 3 doctors are required so that the average time a patient waits for treatment is no more than 15 minutes.

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Answer:

The Answers are down below

Step-by-step explanation:

1) y=MX+B

y=-1/2X+B

(-6,-8)

-8=-1/2(-6)+b

-8=6/2+b

-8=3+b

b=-8-3

b=-11

\(y = - \frac{1}{2} x - 11\)

2)y=mx+b

y=-4/3x+b

(30,24)

24=-4/3(30)+b

24=-40+b

b=24+40

b=64

\(y = - \frac{4}{3} x + 64\)

Answer:

24

Step-by-step explanation:

75 x .32 = 24

Answer:

32 percent of 75 is 24

Answer:

12+ 6 = 18

Step-by-step explanation:

parenthesis means distribute

Answer:

They will meet in 1 hour

Step-by-step explanation:

(1)  d = 10t

(2)  d - 8t = 2   rearrange this equation to:  d = 8t + 2

Set equation (1) equal to equation (2):

10t = 8t + 2

Solve for t:

10t - 8t = 2

2t = 2

t = 2/2 = 1 hr

Answer:

b)42, x=-2

Step-by-step explanation:

Answer:

The option 'b' is correct.

Step-by-step explanation:

Given the function

\(f\left(x\right)\:=\:10x^2\:+\:40x\:+\:42\)

Determining the y-intercept

The y-intercept can be obtained by setting the value x = 0

\(y\:=\:10x^2\:+\:40x\:+\:42\)

\(y\:=\:10\left(0\right)^2\:+\:40\left(0\right)\:+\:42\)

    \(= 0+0+42\)

    \(=42\)

Therefore, the y-intercept is:

Determining the axis of symmetry

Given the equation

\(y=\:10x^2\:+\:40x\:+\:42\)

For a parabola in standard form \(y=ax^2\:+\:bx\:+c\)

the axis of symmetry is the vertical line that goes through the vertex

\(x=\frac{-b}{2a}\)

so

The  axis of symmetry for \(y=ax^2\:+\:bx\:+c\)  is \(x=\frac{-b}{2a}\)

\(a=10,\:b=40\)

\(x=\frac{-b}{2a}\)

\(x=\frac{-40}{2\cdot \:10}\)

\(x=-2\)

Therefore, the option 'b' is correct.

The equation is b1 = 2Ah - b2

Note that the subject of formula is described as the variable that is made to stand alone on one of the equality sign.

From the information given, we have the equation as;

A = 1/2h(b1+ b2)

Such that the parameters are;

Now, make B1, the subject of formula;

cross multiply the values

2Ah = (b1+ b2)

collect the like terms

b1 = 2Ah - b2

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The calculated value of the surface area of the cylinder is 652.94 square cm

From the question, we have the following parameters that can be used in our computation:

Height, h = 12 cm

Radius, r = 6 cm

Using the above as a guide, we have the following:

SA = 2πr(r + h) * 3/4 + 2 * area of rectanglt

Substitute the known values in the above equation, so, we have the following representation

SA = 2π * 6(6 + 12) * 3/4 + 2 * 6 * 12

Evaluate

SA = 652.94

Hence, the surface area of the cylinder is 652.94 square cm

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The percent of the field goals did Samuel make will be 77.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:

= 31 / 40 × 100

= 77.5%

The percentage is 77.5%.

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The correct answer is A. line. A line is a straight path that extends infinitely in both directions. It has no endpoints and continues indefinitely.

A line is a basic geometric object that is defined by two points or can be represented by a single equation. It is characterized by its straightness and infinite length, extending in both directions without any boundaries or endpoints. A line can be represented by a straight line segment with two distinct points or by an equation such as y = mx + b in a coordinate system.

On the other hand, a plane refers to a two-dimensional flat surface that extends infinitely in all directions. It is not a straight path but rather a flat, continuous surface. A ray, is a part of a line that has one endpoint and extends infinitely in one direction. It is not a straight path that continues indefinitely in both directions like a line.

A triangle is a closed geometric shape with three sides and three angles. It is not a straight path but rather a closed figure formed by connecting three non-collinear points.Therefore ,the correct answer is A.

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The eye color of people on commercial aircraft flights is not a random variable.

What is random variable?

Random variables are variables that can take on different values based on the outcome of a random event or experiment.

However, eye color is a characteristic of individuals and does not vary randomly within a specific context, such as being on a commercial aircraft flight. Eye color is determined by genetic factors and does not change during a flight or as a result of being on a flight.

Eye color is a categorical variable that represents the color of an individual's eyes, such as blue, green, brown, or hazel. While it is not a random variable in the context of commercial aircraft flights, it can still be observed and recorded as a characteristic of the passengers on the flight.

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Answer:

4

Step-by-step explanation:

D (-1, -3) and F( 2, 3)

G (-4, -4)

Which point on the y-axis lies on the line that passes through point G and is parallel to line DF?

If the line is parallel to DF then they have the same slope.

slope of line DF is m= difference in y/ difference in x = (-3-3)/( -1-2) = -6/-3 = 2

so slope of line that passes trough G and is ║ with DF is also m= 2

From point G (-4, -4) we go with a slope of 2 until we get to the y-axis

So we go up 2 and 1 left, 2up and 1 left, ... until we get to the point (0, 4), because the slope = rise/run = rise 2/run 1

Answer:

1. 0.27 (with bar notation)

2. -7.6

Step-by-step explanation:

Answer:

8 and 4 is the answer!

Yes, it is possible to graph the tangent line on an Excel graph. You can do this by following the steps below:

Step 1: Create a scatter plot using the given data

Step 2: Add a trendline by selecting the scatter plot and right-clicking on it. Select the “Add Trendline” option.

Step 3: In the “Trendline Options” tab, choose “Linear” as the trendline type.

Step 4: Check the “Display equation on chart” and “Display R-squared value on chart” boxes.

Step 5: Click on the “Close” button.

Step 6: Click on the trendline to select it. Right-click on it and select “Format Trendline” from the drop-down menu.

Step 7: In the “Format Trendline” window, select the “Options” tab and check the “Display equation on chart” and “Display R-squared value on chart” boxes.

Step8: Close the “Format Trendline” window. Step 9: You can use the equation of the line to calculate the slope of the tangent line at any point on the graph.

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Answer:

6

Step-by-step explanation:

\( {(3 \sqrt{13}) }^{2} - {9}^{2} = {x}^{2} \\ 9(13) - 81 = {x}^{2} \\ 117 - 81 = {x}^{2} \\ 36 = {x}^{2} \\ x = 6

Use Pythagorean theorem

\(\\ \sf\longmapsto P^2=H^2-B^2\)

\(\\ \sf\longmapsto P^2=(3√13)^2-9^2\)

\(\\ \sf\longmapsto P^2=117-81\)

\(\\ \sf\longmapsto P^2=36\)

\(\\ \sf\longmapsto P=6\)