A student designed a flag for the school's Gaming Club. The design is rectangular with vertices at (3, 7), (11, −9), and (3, −9). Find the missing vertex and the area of the flag in square inches?

The missing vertex is (−9, 7) with an area of 16 in2.
The missing vertex is (7, 11) with an area of 16 in2.
The missing vertex is (−9, 11) with an area of 128 in2.
The missing vertex is (11, 7) with an area of 128 in2

Answer:

5y+11

Step-by-step explanation:

y+3+4(y+2)

Use the distributive property to multiply 4 by y+2.

y+3+4y+8

Combine y and 4y to get 5y.

5y+3+8

Add 3 and 8 to get 11.

Answer:

x=10

Step-by-step explanation:

If we subtract 2 from 52 we get 50 and ten mutiplys into 50.

Answer: Sorry, I cannot provide visual aids or diagrams. However, I can help with the mathematical calculations and solutions to the given problems.

(a) To construct a trapezium WXYZ, follow the steps below:

Draw a straight line segment WX of length 10.2 cm and draw a line segment YZ of length 5.8 cm parallel to WX, such that the distance between them is 8.3 cm.

Draw a line segment XY of length 5.6 cm perpendicular to both WX and YZ, joining their endpoints.

From the endpoint Z, draw a perpendicular line segment ZN to WX.

Angle LWXY is given as 60°, so mark a point L on WX, such that angle WLY is 60°.

Therefore, the trapezium WXYZ is constructed.

(b) From the diagram, we can see that ZN is perpendicular to WX, so triangles ZWX and ZYN are similar.

Using the similar triangles ZWX and ZYN, we can write:

WX/WY = ZN/XY

10.2/5.6 = ZN/5.8

ZN = (10.2/5.6) * 5.8

ZN ≈ 10.57 cm

(c) Using Pythagoras' theorem, we can find the length of WZ:

WZ² = WX² - XZ²

WZ² = 10.2² - 8.3²

WZ ≈ 4.3 cm

Therefore, |WZ| ≈ 4.3 cm and |ZN| ≈ 10.57 cm.

(a) Let the width of the frame be w and the length be l. Then, according to the problem,

cost ∝ w * √l

cost = k * w * √l, where k is the constant of proportionality.

Using the given information, we can find the value of k as follows:

N115 = k * 10 * √25

k = N115 / 50

k = N2.3

Therefore, the law of variation is cost = N2.3 * w * √l.

(b) For a frame of width 12 cm and length 49 cm,

cost = N2.3 * 12 * √49

cost = N2.3 * 12 * 7

cost = N193.2

(a) Since the range R = {2, 5, 10}, we know that f(x) can take only these three values. Therefore,

x² + 1 = 2 or x² + 1 = 5 or x² + 1 = 10

Solving each of these equations for x, we get:

x = ±√1 or x = ±√4 or x = ±√9

x = ±1 or x = ±2 or x = ±3

Therefore, the domain D = {-3, -2, -1, 1, 2, 3}.

To find f-¹(5), we need to find the values of x for which f(x) = 5. From the equation x² + 1 = 5, we get:

x² = 4

x = ±2

Therefore, f-¹(5) = {-2, 2}.

Step-by-step explanation:

Answer:

x  =  5.12938423

Step-by-step explanation:

Solve for  x   by simplifying both sides of the equation, then isolating the variable.

Answer:

5

Step-by-step explanation:

Based on the given conditions, formulate:: 8-3

Calculate the sum or difference: 5

There are 7 months in the year that have thirty-one days.

These months are January, March, May, July, August, October, and December.

There are seven months in the Gregorian calendar that have thirty-one days: January, March, May, July, August, October, and December.

This pattern of months with 31 days followed by months with fewer days repeats throughout the year.

This pattern was established by the Roman calendar, which had ten months totaling 304 days in a year.

The months of January and February were later added by King Numa Pompilius to align the calendar with the lunar year.

The months of January and February initially had 29 and 28 days respectively, but in 45 BC, Julius Caesar added one day to January and one day to August, which was originally a 30-day month, to make them both 31-day months.

In the Gregorian calendar, which is the most widely used calendar in the world, January, March, May, July, August, October, and December all have 31 days.

The remaining five months have fewer days, with February having 28 days most of the time, and 29 days in a leap year.

Knowing the number of days in each month is important for various reasons, such as planning events, scheduling appointments, and calculating pay periods.

There are several mnemonics used to remember the number of days in each month, such as "30 days hath September, April, June, and November, all the rest have 31, except February, with 28 days clear, and 29 in each leap year."

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Answer:

100

Step-by-step explanation:

If you need 20 for every 2 pizzas, that means you would need 10 for 1 pizza. (tomato's) 10 x (pizzas)10 = 100

Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.

What is factor ?

A factor is a quantity or element that contributes to a particular result or outcome.

There are several factors that may have contributed to the different results of the two surveys:

Response Bias: The online survey may have attracted participants who are more tech-savvy and have a different perspective than those who are less comfortable with technology. On the other hand, the telephone survey may have attracted participants who are older or less mobile, and have a different perspective than those who prefer online communication.

Sampling Bias: The online survey may not have been representative of the entire population, as it was conducted on a specific website and only attracted those who use that website. Similarly, the telephone survey may have only reached those who answered the phone and were willing to participate.

Question Bias: The questions asked in the online survey may have been different from those asked in the telephone survey, leading to different results. The questions may have been worded in a way that biased the responses, either consciously or unconsciously.

Mode of Administration: The mode of administration, or the method of conducting the survey, may have influenced the responses. Online surveys allow participants to respond at their own pace and in their own environment, while telephone surveys may put pressure on participants to respond quickly and may not allow them to think through their responses.

Data Collection Method: The data collection method, such as self-reported data, may have influenced the results. Self-reported data may not always be accurate, as participants may not remember details accurately or may be unwilling to report certain information.

Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.

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Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.

A factor is a quantity or element that contributes to a particular result or outcome.

There are several factors that may have contributed to the different results of the two surveys:

Response Bias: The online survey may have attracted participants who are more tech-savvy and have a different perspective than those who are less comfortable with technology. On the other hand, the telephone survey may have attracted participants who are older or less mobile, and have a different perspective than those who prefer online communication.

Sampling Bias: The online survey may not have been representative of the entire population, as it was conducted on a specific website and only attracted those who use that website. Similarly, the telephone survey may have only reached those who answered the phone and were willing to participate.

Question Bias: The questions asked in the online survey may have been different from those asked in the telephone survey, leading to different results. The questions may have been worded in a way that biased the responses, either consciously or unconsciously.

Mode of Administration: The mode of administration, or the method of conducting the survey, may have influenced the responses. Online surveys allow participants to respond at their own pace and in their own environment, while telephone surveys may put pressure on participants to respond quickly and may not allow them to think through their responses.

Data Collection Method: The data collection method, such as self-reported data, may have influenced the results. Self-reported data may not always be accurate, as participants may not remember details accurately or may be unwilling to report certain information.

Survey results may be impacted by response bias, sampling bias, question bias, mode of administration, and data collection method.

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The corresponding growth factor of +70% is 1.7

The formula for the annual rate of change is

                    1 ± r             (1)

where r = rate of change

and ± sign depends upon whether it is a growth or decay factor. If it is growth factor then it is plus sign otherwise negative sign.

According to the question we have been given the growth that is +70%. Since there is plus sign therefore it is a growth factor.

Thus, r = + 0.7

Putting this value in equation (1) we get

= 1 + 0.7

= 1.7

Hence the corresponding growth factor of +70% is 1.7

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The weigh of Quarters is approximately 5.67 g.

It's a common misconception that some of the coins in our pockets are made of precious metals. There was a time in U.S. history when the coins in circulation were actually made of gold and silver. As the prices of these metals rose, it became impractical to mint coins from them. It was made of silver and 10% copper. Today, quarters are made from a much cheaper combination of copper and nickel.

The US dollar and established official weights for various coins, including the new quarter coin. The new coin weighed 0.211 ounces (6.01 grams) of pure silver, or 0.237 standard ounces (6.74 grams). These weights continued until the Money Act of 1873, when a quarter of the United States was 90% silver and 10% copper and weighed only 0.022 ounces (6.25 grams). Since 1965, the US quarter has weighed 0.2 ounces (5.76 grams). They are 24.66mm in diameter and 1.75mm thick and consist primarily of a "cladding sandwich" of inner copper (91.67%) and outer nickel plating (8.33%).

Therefore, the weigh of quarter is 0.2 ounces i.e 5.76 g.

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Answer:

\( 2.58 \times {10}^{8} \)

Step-by-step explanation:

\(9.3. {10}^{7} - 3.4. {10}^{6} \\ = (27 \times 10 - 12) \times {10}^{6}\\ = (270 - 12) \times {10}^{6} \\ = 258 \times {10}^{6} \\ = 2.58 \times {10}^{6 + 2} \\ = 2.58 \times {10}^{8} \)

Answer: i don't know

Step-by-step explanation:

what is this

also i need points! sry

The margin of error for a 95% confidence interval can be calculated using the following formula:

Margin of error = z* (o/√n)

where z* is the z-score corresponding to the level of confidence (95% in this case), o is the population standard deviation, and n is the sample size.

So, plugging in the given values, we get:

Margin of error = 1.96 * (13.5/√45)

The z-score for a 95% confidence level is 1.96. This is a standard value that is obtained from the standard normal distribution table.

The margin of error represents the maximum amount by which the sample mean is expected to differ from the true population mean. In other words, if we were to repeat this process many times, and each time draw a sample of size 45 and compute a confidence interval, we would expect 95% of these intervals to contain the true population mean, and 5% of these intervals to not contain it. The margin of error gives us an idea of how much uncertainty there is in our estimate of the population mean.
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Answer:

the cake that was left is 1 by 15

Step-by-step explanation:

The computation is shown below:

= sale - gave away

\(= \frac{2}{5} - \frac{1}{3}\\\\= \frac{6 - 5}{15} \\\\= \frac{1}{15}\)

Hence, the cake that was left is 1 by 15

So the same is relevant and considered too

Answer:

It increased by 150%

Step-by-step explanation:

Use the rules of exponents to simplify the expression.

\(\large\displaystyle\text{$\begin{gathered}\sf (C^{4})^{3} \end{gathered}$}\)

To raise a power to another power, multiply the exponents.

\(\large\displaystyle\text{$\begin{gathered}\sf C^{4\times3} \ \to \ Multiply \end{gathered}$}\)

\(\boxed{\large\displaystyle\text{$\begin{gathered}\sf C^{12} \end{gathered}$}}\)

Therefore, the correct option is "C".

Answer: $195 in debt

Step-by-step explanation:

$225+$120= $345

$345-$150= $195

Answer:

C

Step-by-step explanation:

So we know that:

\(f(3)=-2\text{ and } f(4)=-4\)

This is the same as saying we have two coordinates: (3,-2) and (4,-4).

Let's find the equation of the linear function.

First, let's find the slope:

\(m=\frac{y_2-y_1}{x_2-x_1}\)

Substitute (3,-2) for x₁ and y₁ and let (4,-4) be x₂ and y₂:

\(m=\frac{-4--2}{4-3}\)

Simplify:

\(m=-2/1=-2\)

So our slope is -2.

Now, use the point-slope form:

\(y-y_1=m(x-x_1)\)

Let's use (3,-2) for x₁ and y₁ and use -2 for m:

\(y+2=-2(x-3)\)

Now, we can figure out the x-intercept.

Recall that the x-intercept is when the graph touches the x-axis.

In other words, the y-value would be 0. It will be (x,0).

So, to solve for the x-intercept, substitute 0 for y and solve for x:

\(0+2=-2(x-3)\)

Simplify and distribute the right:

\(2=-2x+6\)

Subtract 6:

\(-4=-2x\)

Divide both sides by -2:

\(x=2\)

So, our x-intercept is (2,0)

Answer:

10.) Proportional

11.) Not Proportional

Step-by-step explanation:

The graph in number 10 is steady so it is proportional and crosses the origin. Number 11 is not proportional because it does not cross the origin.

Evaluating a sample.

Answer:

A=791.68 m

1. Plug in the numbers into the formula for the surface area of a sphere: A=2πrh+2πr2

2. Solve for A (Area)

Answer:

about 10 dollers

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

triangles are pyramids and it has 6 sides

Answer:

Hexagonal prism

Step-by-step explanation:

We can rule out B and D because if it was a pyramid, there would be a triangle in the net (The net of a 3D shape is what it looks like if it is opened out flat). We can also rule on C because it it was a cylinder, there would be a circle in the net. Therefore, our remaining answer is A.

The cost of Comcast's 560 obsolete cable boxes in ending inventory is $12,796.

Hi, I understand that you need help calculating the cost of Comcast's obsolete cable boxes using the provided inventory and purchase information. To do this, we'll follow these steps:

1. Identify the number of obsolete boxes: 560.
2. Calculate the total number of boxes in inventory.
3. Determine the weighted average cost per box.
4. Multiply the number of obsolete boxes by the weighted average cost per box.

Step 1: We already know that there are 560 obsolete boxes in ending inventory.

Step 2: Calculate the total number of boxes in inventory.
Beginning inventory: 16,100 boxes
March 1: 7,100 boxes
June 1: 3,100 boxes
September 1: 1,800 boxes
December 1: 1,000 boxes
Total inventory: 29,100 boxes

Step 3: Determine the weighted average cost per box.
Total cost of inventory: $665,100
Total number of boxes: 29,100
Weighted average cost per box: $665,100 / 29,100 = $22.85 (rounded to two decimal places)

Step 4: Multiply the number of obsolete boxes by the weighted average cost per box.
Number of obsolete boxes: 560
Weighted average cost per box: $22.85
Cost of obsolete boxes: 560 * $22.85 = $12,796

So, the cost of Comcast's 560 obsolete cable boxes in ending inventory is $12,796.

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The statements that accurately compare the domain and range of the functions are: The domain of all three functions is all real numbers, The range of f(x) and h(x) is all real numbers, but the range of g(x) is all real numbers except 0.

The domain of a function refers to all the possible input values that make the function defined. For the quadratic function f(x) = 3x², there are no values of x that make the function undefined, so the domain of f(x) is all real numbers. To find the range of f(x), we can calculate the vertex of the parabola, which is (0,0). The range of f(x) is all real numbers greater than or equal to zero.

For the quadratic function f(x) = 3x², we can determine the vertex using the formula:

h = -b/2a

In this case, a = 3 and b = 0, so:

h = -0/2(3) = 0/6 = 0

The x-coordinate of the vertex is 0.

To find the y-coordinate, we evaluate the function at the vertex:

f(0) = 3(0)² = 0

So the vertex of the parabola is (0,0).

Since the coefficient of x² is positive, the parabola opens upwards, and the minimum value of the function occurs at the vertex. Therefore, the range of f(x) is all real numbers greater than or equal to zero.

For the rational function g(x) = 1/3x, the function is undefined when the denominator is equal to zero. Thus, we solve for the value(s) of x that make the denominator zero:

3x = 0

Dividing both sides by 3, we get:

x = 0

Therefore, the domain of g(x) is all real numbers except zero. The range of g(x) is all real numbers except zero, since the function cannot equal zero.

For the linear function h(x) = 3x, there are no values of x that make the function undefined. Thus, the domain of h(x) is all real numbers. The range of h(x) is also all real numbers, since the function is a straight line that passes through the origin and extend infinitely in both directions.

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Answer:

Intersecting

Step-by-step explanation:

10x - 5y = 3 Subtract 10x from both sides

-10x         -10x

-5y = -10x + 3 Divide both sides by -5

y = 2x - 3/5

5x - 10y = 3 Subtract both sides by 5x

-5x         -5x

-10y = -5x + 3 Divide both sides by -10

y = 1/2x - 0.3

Their slopes are different, so they will probably intercept.

Answer:

\(\boxed {\tt 11.6 \ feet}\)

Step-by-step explanation:

The area of a square can be found using the following formula.

\(A=s^2\)

We know the area of the patio is 135 square feet. Substitute 135 ft² in for A.

\(135 \ ft^2=s^2\)

We want to find the side length. We must isolate the variable, \(s\). on one side of the equation.

s is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

\(\sqrt{135 \ ft^2} =\sqrt{s^2}\)

\(\sqrt{135 \ ft^2} =s\)

\(11.61895 \ ft =s\)

Round to the nearest tenth. The 1 in the hundredth place tells us to leave the 6 in the tenth place.

\(11.6 \ ft \approx s\)

Each side of the patio is about 11.6 feet.

Answer:

Win $1,423.59

Step-by-step explanation:

There are 52 cards in a deck, 13 of which are spades.

The probability if drawing two consecutive spades without replacement is:

\(P(W) = \frac{13}{52}*\frac{12}{51}\\ P(W) = \frac{3}{51}\)

Therefore, there is a 3 in 51 chance of you winning $225 and a 48 in 51 chance of you losing $12.

The expected value for 738 games is:

\(E= 738(\frac{3}{51}*225-\frac{48}{51}*12)\\ E=\$1,423.59\)

You are expected to win $1,423.59.

0.0472 (approx.)

Anwer:
a) P(A) = P(X is even) = P(X = 2) + P(X = 4) + P(X = 6) + ...Let us take  p = 1/3, thus P(X = k) = (1 - p)^(k - 1)p, for k = 1, 2, 3, .... Therefore, P(X = 2) = (2 - 1)p(1-p), P(X = 4) = (4 - 1)p(1 - p)^3, P(X = 6) = (6 - 1)p(1 - p)^5, ...So, we haveP(A) = [(2-1)p(1-p)] + [(4-1)p(1-p)^3] + [(6-1)p(1-p)^5] + ...= p(1-p)[1 + 3(1-p)^2 + 5(1-p)^4 + ...]= p(1-p)/(1-(1-p)^2)= 2p(1-p) = 2/9.b) For a geometric random variable, we have E(X) = 1/p and Var(X) = (1 - p)/p^2.The expected value of e^X is:E(e^X) = Σ e^k (1-p)^(k-1) p= p Σ [e^(ln(1-p))]^(k-1) = p Σ (1-p)^(k-1)= p/(1-(1-p)) = 1/pAnd the variance of e^X is:Var(e^X) = E((e^X)^2) - [E(e^X)]^2= E(e^(2X)) - (1/p)^2= Σ e^(2k) (1-p)^(k-1) p - 1/p^2= p Σ [e^(2ln(1-p))]^(k-1) - 1/p^2= p Σ (1-p)^(2(k-1)) - 1/p^2= p/[1-(1-p)^2] - 1/p^2= (2-p)/(p(1-p)^2).c) P(e^X > 10) = P(X > ln(10)) = (1-p)^[ln(10)] = 0.0472 (approx.)

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