Solve the following simultaneous equations:

5x + 3y = 21
2x + y = 3

2x+3y=12
5x+4y=23

To determine if the given points are part of the (200) plane, we need to check if their coordinates satisfy the equation of the plane.

The equation of a plane in three-dimensional space is typically written in the form Ax + By + Cz + D = 0, where A, B, C, and D are constants. For the (200) plane, the equation would be 2x + 0y + 0z + 0 = 0, which simplifies to 2x = 0. Let's check the given points: a) (1/2, 0, 0): When we substitute x = 1/2 into the equation 2x = 0, we get 2(1/2) = 0, which is true. Therefore, point a) lies on the (200) plane. b) (-1/3, 0, 0): Substituting x = -1/3 into the equation 2x = 0 gives us 2(-1/3) = 0, which is also true. So, point b) is part of the (200) plane. c) (0, 1, 0):When we substitute x = 0 into the equation 2x = 0, we get 2(0) = 0, which is true. Thus, point c) lies on the (200) plane. All three given points (a), b), and c)) are part of the (200) plane.

In conclusion, all three given points (a), b), and c)) are part of the (200) plane.

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Answer:

A number sentence is a mathematical sentence made up of numbers and signs. So for example 15 + 7.

They can use any of the mathematical operations so addition, subtraction, multiplication and division

Number sentences can be true or false. Example, 5 + 7 = 13

good luck, i hope this helps :)

The solution to the system of inequalities is option C: (1, 1). The system of inequalities typically consists of multiple equations with inequality signs. However, the given options are not in the form of inequalities.

In the given system of inequalities, option d) satisfies all the given conditions. Let's analyze the system of inequalities and understand why option d) is the solution.

The inequalities are not explicitly mentioned, so we'll assume a general form. Let's consider two inequalities:

x > 0

y > x + 2

In option d), we have x = 2 and y = 4.

For the first inequality, x = 2 satisfies the condition x > 0 since 2 is greater than 0.

For the second inequality, y = 4 satisfies the condition y > x + 2. When we substitute x = 2 into the inequality, we get 4 > 2 + 2, which is true.

Therefore, option d) 2,4 satisfies both inequalities and is the solution to the given system.

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Answer:

1-4/5

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

4/5 = 80

80 is the price percentage.

5/5 - 4/5 = 1/5

1/5 = 20

so, 20%

The ratio of false positives to true positives is 8 over 54.

According to the Question

Results of a strep throat test performed on a sample of 400 ill people are displayed in the table's data. People who have the flu and those who don't are separated into two categories. The patients are then separated into groups based on whether they tested positive or negative for strep throat within each of these categories.

We must first define what a true positive and a false positive are in order to calculate the ratio of false positives to true positives. A patient who tests positive for strep throat but does not actually have the illness is said to have a false positive. The 8% of patients in this instance who tested positive for strep throat but did not have the flu would fall under that category. A patient who tests positive for strep throat and truly has the illness is said to have a true positive. That would be the 54% of patients who tested positive for both the flu and strep throat in this instance.

We divide the percentage of false positives (8%) by the percentage of true positives (54%), which gives us the ratio of false positives to true positives.

As a result, the ratio becomes 8% / 54%, or 8/54.

It's critical to remember that this ratio is dependent on the sample and test performed and may not be the same for different populations or testing methodologies.

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Answer:

The Y intercept is -10

The X intercept is 3

The surface area of the box with given dimensions is equal to 11.75 square meters.

To calculate the surface area of the box,

find the area of each of its six faces and then sum them up.

The box has three pairs of opposite faces, each with the same dimensions.

So, calculate the area of one face and then multiply it by two for each pair.

The dimensions of the box are as follows,

Width = 1 meter

Length = 1.5 meters

Height = 1.75 meters

The surface area of the box can be calculated as follows,

Area of the top and bottom faces,

2 × (Width × Length)

= 2 × (1 × 1.5)

= 3 square meters

Area of the front and back faces:

2 × (Width × Height)

= 2 × (1 × 1.75)

= 3.5 square meters

Area of the left and right faces,

2 × (Length × Height)

= 2 × (1.5 × 1.75)

= 5.25 square meters

Now, sum up the areas of all six faces,

Total surface area = 2 × (Width × Length) + 2 × (Width × Height) + 2 × (Length × Height)

= 2× (1 × 1.5) + 2 × (1 × 1.75) + 2 × (1.5 ×1.75)

= 3 + 3.5 + 5.25

= 11.75 square meters

Therefore, the surface area of the box is 11.75 square meters.

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Ralph needs $11.75 more to buy 5 pencils, 3 pens, and 2 notebooks from the school store.

Ralph needs to determine how much more money he needs to buy the items from the school store. He wants to buy 5 pencils, 3 pens, and 2 notebooks. The price of each item is given as follows:

Pencils: $0.50 each
Pens: $1.25 each
Notebooks: $2.75 each

To calculate how much more money Ralph needs, we need to find the total cost of the items he wants to buy.

For pencils, since he wants to buy 5, we can multiply the price of each pencil ($0.50) by the number of pencils (5). This gives us a total cost of $2.50 for the pencils.

Similarly, for pens, since he wants to buy 3, we can multiply the price of each pen ($1.25) by the number of pens (3). This gives us a total cost of $3.75 for the pens.

Lastly, for notebooks, since he wants to buy 2, we can multiply the price of each notebook ($2.75) by the number of notebooks (2). This gives us a total cost of $5.50 for the notebooks.

To find the total cost of all the items, we add the costs of pencils, pens, and notebooks together. $2.50 (pencils) + $3.75 (pens) + $5.50 (notebooks) = $11.75.

Therefore, Ralph needs $11.75 more in order to buy all the items he wants from the school store.

In conclusion, Ralph needs $11.75 more to buy 5 pencils, 3 pens, and 2 notebooks from the school store.

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Answer:

π112 or 3.14(112)

Step-by-step explanation:

Answer:

351.86

Step-by-step explanation:

a. The probability that no boats arrive in a 2-hour period is approximately 0.0003.

b. The probability that 1 boat arrives in a 2-hour period is approximately 0.0023.

c. The probability that 2 boats arrive in a 2-hour period is approximately 0.0466.

d. The probability that 2 or more boats arrive in a 2-hour period is approximately 0.9511.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.

Given that boats arrive at the inlet drawbridge according to a Poisson distribution with a rate of 4 per hour, we can use the Poisson probability formula to calculate the probabilities.

The Poisson probability mass function is given by:

P(x; λ) = \((e^{(-\lambda)} * \lambda^x) / x!\)

where x is the number of events, λ is the average rate of events.

(a) To find the probability that no boats arrive in a 2-hour period, we can calculate P(0; λ), where λ is the average rate of events in a 2-hour period. Since the rate is 4 boats per hour, the average rate in a 2-hour period is λ = 4 * 2 = 8.

P(0; 8) = \((e^{(-8)} * 8^0) / 0! = 8e^{(-8)}\) ≈ 0.0003

The probability that no boats arrive in a 2-hour period is approximately 0.0003.

(b) To find the probability that 1 boat arrives in a 2-hour period, we can calculate P(1; λ), where λ is the average rate of events in a 2-hour period (λ = 8).

P(1; 8) = \((e^{(-8)} * 8^1) / 1! = 8e^{(-8)}\) ≈ 0.0023

The probability that 1 boat arrives in a 2-hour period is approximately 0.0023.

(c) To find the probability that 2 boats arrive in a 2-hour period, we can calculate P(2; λ), where λ is the average rate of events in a 2-hour period (λ = 8).

P(2; 8) = \((e^{(-8)} * 8^2) / 2! = (64/2) * e^{(-8)}\) ≈ 0.0466

The probability that 2 boats arrive in a 2-hour period is approximately 0.0466.

(d) To find the probability that 2 or more boats arrive in a 2-hour period, we need to calculate the complement of the probability that 0 or 1 boat arrives.

P(2 or more; 8) = 1 - (P(0; 8) + P(1; 8))

P(2 or more; 8) \(= 1 - (e^(-8) + 8e^{(-8)})\) ≈ 0.9511

The probability that 2 or more boats arrive in a 2-hour period is approximately 0.9511.

Please note that the above probabilities are calculated based on the assumption of a Poisson distribution with a rate of 4 boats per hour.

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The percent of observations fall below 0.40 is 1.00

Since we are given the points we are (0, 1),(0.4, 1),(0.4, 1), and (0.8, 2), we got the graph for the points

The region beneath the chart breaks even with 1 and we are told to discover the percent of the observation that drops underneath 0.40 what this implies is that we ought to discover the rate of the observation that drops inside 0.40 of 1 which is the entire area. So,

P(O) = 0.40 × 1 = 0.40 , where O is the observations

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Answer:

0

Step-by-step explanation:

Note that + (- 7) = - 7 , thus

- 18 + (- 7) + 25 = - 18 - 7 + 25 = - 25 + 25 = 0

Answer:

81,412,650

Step-by-step explanation:

im not sure if this is what ur asking for??

Answer:

x=14

Step-by-step explanation:

3x+1 and 43 are both vertical angles so they are equivant.

3x+1=43

3x=42

x=14

a. The chart did not maintain consistent scaling

b. The graph is not the appropriate graph type to display such data

c.  The display had inaccurate or distorted visual representations

When the actual data may not support it, changing the scales on the axes might give the appearance of big changes or differences.

The visual effect of data can be exaggerated or minimized, for instance, by adopting a non-linear scale or deleting specific sections of the axis.

So it important to Choose appropriate graph type that best represents the data and the relationship you want to convey.

It also advisable to make use of  clear and accurate labeling with descriptive titles and units of measurement.

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The number of days would be 10 and the maximum percent of the population infected would be 25.752%.

What are exponential functions?

The exponential function, denoted by \(e^x\), is a mathematical function. Unless otherwise specified, the term refers to a positive-valued function of a real variable, though it can be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

\(p(t) = 7te^{-\frac{t}{10}}\)

percentage of infected people a maximum when p '(t) = 0

                    \(p '(t) = 7(1)e^\frac{-1}{10} +7te^\frac{-t}{10}(\frac{-1}{10})\\\\p'(t)=e^{-\frac{t}{10}}(7 -\frac{7t}{10})\\\\e^{-\frac{t}{10}}(7 -\frac{7t}{10})=0\\\\7 -\frac{7t}{10}=0\\\\t = 10\)

Hence percentage of infected people reaches a maximum after 10 days

maximum percent of the population infected = p(10)

    \(p(10) = 7(10)e^{-\frac{10}{10}}\\\\p(10)=\frac{70}{e}\\\\P(10)=25.752\%\)

Hence, the number of days would be 10 and the maximum percent of the population infected would be 25.752%.

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The degree measurement of angle C' would be 123 degrees.

A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. The direction or the path of this change in position of the object can vary i.e., initially the object can move left, then turn right, and so on. While translating, all the points on the shape will shift by the same number of units. For example, if one point shifts 2 units to the right, then all the points will also move 2 units to the right.

Any object represented in the coordinate plane can be translated horizontally (left/right) or vertically (up/down). A shape before translations are applied is known as "preimage" and the shape that is obtained after the application of translations is known as "image. In simple words:

1) "Preimage" is the shape before translation.

2) "Image" is the shape after translation.

The given trapezoid is translated diagonally, and thus, there is no change made in the angles.

Thus, the degree measurement of angle C' would be 123 degrees.

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Answer:

60% was loss

Step-by-step explanation:

Company faced 60% of loss in one month for selling a share.

When the Cost Price of an item is more than the Selling Price of the same item, then this is the condition of loss for the seller.

Loss percent = \(\frac{C.P-S.P}{C.P}\)× 100

Where,

C.P is the cost price

S.P is the selling price

According to the given question

We have,

Selling price of a share one month ago is $35.

One month later the selling price of the same share is $14.

So, the loss faced by a company in one month = $35 - $14 = $21

Therefore, the loss percent of the company in one month = \(\frac{21}{35}\) × 100

⇒ loss percent = 0.6 × 100 = 60%

Hence, company faced 60% of loss in one month for selling a share.

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Answer:

4

Step-by-step explanation:

Answer:

32

Step-by-step explanation:

x          

 (— -  6) -  2  = 0

  4          

6     6 • 4

   6 =  —  =  —————

        1       4

x - (6 • 4)     x - 24

———————————  =  ——————

     4            4

 (x - 24)    

 ———————— -  2  = 0

    4        

        2     2 • 4

   2 =  —  =  —————

        1       4

(x-24) - (2 • 4)     x - 32

————————————————  =  ——————

       4               4

 x - 32

 ——————  = 0

   4  

x-32

 ———— • 4 = 0 • 4

  4  

x-32

The exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

The following equation can be used to calculate an exponential function again for number of women graduating from four-year colleges in t years after 1930:

A(t) = A₀e∧(rt)

In which A₀ is the starting point and r is the exponential growth rate expressed as a decimal.

In 1930, 48780 women received a bachelor's degree.

This implies that;

A₀ = 48780

In 2004, approximately 756000  people

The year 2003 is 73 years after 1930, that also means

Using the equation as an example:

A(t) = A₀e∧(rt)

Put the values;

756000 = 48780 e∧(73r)

e∧(73r) = 756000/ 48780

e∧(73r) = 15.49

Taking log both side;

73r = ㏑ 15.49

r = 2.7/7

r = 0.037

The function becomes;

A(t) = A₀e∧(0.037t)

Thus, the exponential function which shows the exponential growth rate of graduating women is: A(t) = A₀e∧(0.037t).

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Answer:

the answers c

Step-by-step explanation:

Answer:c

Step-by-step explanation:

Gabby's 35 boxes plus Ross's b amount of boxes equals the 69 boxes

Answer:

All the letter choices are correct.

Step-by-step explanation:

If thats not what you wanted, just comment below. Thank you!

Answer:

All letters showed are correct

Step-by-step explanation:

The equation of the graph after the translation is h(x)=f(x)+6

The process of transforming an equation or existing graph into a new graph is known as graph translation.

Since the graph for h(x) has moved to the left by 6 units as we can see in the graph. Hence the co-ordinates will also change by 6 units . hence the graph is translated to the left by 6 units.

Therefore the equation after the translation is given by h(x)=f(x)+6 .

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The angle with sides 5, 9 and 10 is an obtuse triangle

This is a type of angle in which the angles are less than 180 degrees but less than 180 degrees.

In this case, we can easily determine if it's an obtuse angle.

Assuming the longest side is 10 units, the sum of it's two other sides must be greater than it's longest side which is supposedly the hypothenuse.

5 + 9 = 14

14 > 10

This indicates that the triangle is an obtuse triangle.

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Answer:

19°

Step-by-step explanation:

180-64=116

116+45=161

180-161=19

Answer:

B) 19

Step-by-step explanation:

find the other angle of W first.

to do that, take 180 - 64

that makes angle W 116

add angle W and angle Y

116 +45 = 161

take 180 - your answer

180 - 161 = 19

B is your answer

have a wonderful day <3

Slope is change in y over change in x:

Slope = (5c - 3c) / ( 2c -c)

Slope = 2c/c = 2

The answer is D. 2

2. He did not plug the correct values into the numerical equation.

The answer should be B.

We can use the formula for the power series expansion of the function f(x) = (1 - x)^{-2}:

f(x) = ∑_{n=1}^∞ n x^{n-1}

Multiplying both sides by 243 and substituting x = 4, we have:

243(1 - 4)^{-2} = 243f(4) = 243 ∑_{n=1}^∞ n 4^{n-1}

Simplifying the left-hand side, we have:

243(1 - 4)^{-2} = 243(-3)^{-2} = -27/4

So we have:

-27/4 = 243 ∑_{n=1}^∞ n 4^{n-1}

Dividing both sides by 4, we get:

-27/16 = 243/4 ∑_{n=1}^∞ n (4/16)^{n-1}

Simplifying the right-hand side, we have:

-27/16 = 243/4 ∑_{n=1}^∞ n (1/4)^{n-1}

= 243/4 ∑_{n=0}^∞ (n+1) (1/4)^n

= 243/4 ∑_{n=0}^∞ n (1/4)^n + 243/4 ∑_{n=0}^∞ (1/4)^n

= 243/4 ∑_{n=1}^∞ n (1/4)^{n-1} + 243/4 ∑_{n=0}^∞ (1/4)^n

= 243 ∑_{n=1}^∞ n (1/4)^n + 81/4

Therefore, the power series for ()=243(1−4)2 is:

∑_{n=1}^∞ n (1/4)^n = 1/4 + 2/16 + 3/64 + ... = (1/4) ∑_{n=1}^∞ n (1/4)^{n-1} = (1/4) (1/(1-(1/4))^2) = 4/9

So we have:

-27/16 = 243(4/9) + 81/4

Simplifying, we get:

() = ∑_{n=1}^∞ n (4/9)^{n-1} = 81/16

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The group with the largest uncertainty error in a 95% confidence level among Group A, B, C, and D is Group D.

To determine the uncertainty error for each group, we'll calculate the margin of error using the formula:

Margin of Error = t (95%) × (sample deviation / sqrt(sample size))

Assuming a t (95%) value of 2.0 and a sample size of 25 for all groups, we have:

Group A:

Margin of Error = \(2.0 × (0.51 / sqrt(25)) = 2.0 × (0.51 / 5) = 0.204\)

Group B:

Margin of Error =\(2.0 × (0.06 / sqrt(25)) = 2.0 × (0.06 / 5) = 0.024\)

Group C:

Margin of Error = \(2.0 × (0.55 / sqrt(25)) = 2.0 × (0.55 / 5) = 0.22\)

Group D:

Margin of Error = \(2.0 × (2.00 / sqrt(25)) = 2.0 × (2.00 / 5) = 0.8\)

Based on the margin of error calculations, Group D has the largest uncertainty error at a 95% confidence level, with a

margin of error of 0.8 mm.

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