HELP ASAP! I’m very confused and need help. Thank you!

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

Given that:

Endpoints of diameter, (13, -1) and (15, 9)

The equation of the circle when endpoints of diameter are given is written as,

(x - x₁)(x - x₂) + (y - y₁)(y - y₂) = 0

The equation of the circle is calculated as,

(x - 13)(x - 15) + (y + 1)(y - 9) = 0

x² - 28x + 195 + y² - 8y - 9 = 0

x² + y² - 28x - 8y + 186 = 0

The equation of a circle with diameter endpoints of (13, -1) and (15, 9) will be x² + y² - 28x - 8y + 186 = 0.

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Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Answer:

a), y=62       b.) c=1 3/5 or 8/5

Step-by-step explanation:

Okay so these are fairly simple lets start with A

4y=248, all we have to do is divide 4 on both sides

4y/4=y

248/4=62

Pretty Simple

For b just subtract 2/5 from both sides

(c+2/5)-2/5=c

2-2/5=1 3/5 or 8/5

Answer:

nope

Step-by-step explanation:

Apply dot product which must = 0 for orthogonality.

In this case,

-(3)(2) + (-2)(-2) + (-3)(1) + (1)(4) = -1.

Given a certain rate of return, present value (PV) is the current value of a future sum of money or stream of cash flows.

$ 3,682.21 is the present value.

A future sum of money or stream of cash flows' present value (PV), assuming a given rate of return, is their current value.

Future value is converted to present value by using either a discount rate or the interest rate that would be earned if an investment were made.

Present Value = FV/(1+r/n)^nt

Solution:

Present Value = FV/(1+r/n)^nt

Present Value = 7400/(1+7/12)^10*12

Present Value = 7400/(19/12)^120

Present Value = 7400/(1.58)^120

Present Value = 7400/2^120

Present Value = $ 3,682.21

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A is either 45° or 135°.

To prove the given statement, let's assume that the points B and C lie on a coordinate plane, with the origin (0, 0) as the common vertex of the right angles at points B, C, and A. Let the coordinates of points B and C be (x₁, y₁) and (x₂, y₂) respectively.

Using the distance formula, we have:

AB² = x₁² + y₁²

AC² = x₂² + y₂²

According to the given equation, +b4+c4 = 20² (b²+c²), we can rewrite it as:

(x₁² + y₁²) + (x₂² + y₂²) = 20² [(x₁² + y₁²) + (x₂² + y₂²)]

Expanding and simplifying the equation, we get:

x₁² + y₁² + x₂² + y₂² = 20² (x₁² + y₁² + x₂² + y₂²)

This equation can be further simplified to:

(x₁² + y₁²) + (x₂² + y₂²) = (20² - 1) (x₁² + y₁² + x₂² + y₂²)

Since the left side represents the sum of the squares of the distances from the origin to points B and C, and the right side is a constant multiplied by the same sum, we can conclude that the points B and C must lie on a circle centered at the origin.

In a circle, the sum of angles subtended by two perpendicular chords at the center is either 180° or 360°. Since the given problem involves right angles, we consider the sum of angles to be 180°.

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Hello!

surface area

= 2(4 x 2) + 2(12 x 4) + 2(12 x 2)

= 160cm²

(A)

\(\dfrac{\partial f}{\partial x}=-16x+2y\)

\(\implies f(x,y)=-8x^2+2xy+g(y)\)

\(\implies\dfrac{\partial f}{\partial y}=2x+\dfrac{\mathrm dg}{\mathrm dy}=2x+10y\)

\(\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\)

\(\implies g(y)=5y^2+C\)

\(\implies f(x,y)=\boxed{-8x^2+2xy+5y^2+C}\)

(B)

\(\dfrac{\partial f}{\partial x}=-8y\)

\(\implies f(x,y)=-8xy+g(y)\)

\(\implies\dfrac{\partial f}{\partial y}=-8x+\dfrac{\mathrm dg}{\mathrm dy}=-7x\)

\(\implies \dfrac{\mathrm dg}{\mathrm dy}=x\)

But we assume \(g(y)\) is a function of \(y\) alone, so there is not potential function here.

(C)

\(\dfrac{\partial f}{\partial x}=-8\sin y\)

\(\implies f(x,y)=-8x\sin y+g(x,y)\)

\(\implies\dfrac{\partial f}{\partial y}=-8x\cos y+\dfrac{\mathrm dg}{\mathrm dy}=4y-8x\cos y\)

\(\implies\dfrac{\mathrm dg}{\mathrm dy}=4y\)

\(\implies g(y)=2y^2+C\)

\(\implies f(x,y)=\boxed{-8x\sin y+2y^2+C}\)

For (A) and (C), we have \(f(0,0)=0\), which makes \(C=0\) for both.

The solution of the equation for t is t = i/pr

The equation is given as

i = prt

Divide both sides of the equation by p

So, we have the following equation

i/p = prt/p

Divide both sides of the equation by r

So, we have the following equation

i/pr = prt/pr

Evaluate the quotients

i/pr = t

Rewrite as

t = i/pr

By the above computation, we changed the subject of the formula in i = prt from i to t.

This implies that solving for t is a concept of subject of formula

Hence, the solution is t = i/pr

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Answer:

x/5 = 5280/1

Step-by-step explanation:

this is a proportion set up and then cross multiple. You will get your answer for x. Which is 26, 400 feet.

Hey there!

Basically the word “distance” means subtract, so that either means you’re taking away or going downward (like to the (LEFT side of your number line since you’re counting DOWN)

So, question reads….

Find the DISTANCE BETWEEN 23 & -16

That means your equation should look like:

23 - (-16)

Simplify it:

23 - (-16)
= 23 - -16

= 23 + 16

= 39

Therefore, your answer should be:

39

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Evaluating the function in the values of the domain we will get some coordinate pairs. The graph of these is in the image at the end.

Here we have the function:

3x - y = 1

And we want to graph this in the domain (-3, -1, 0, 4)

To do so, we need to evaluate the function (the values of x) in the values of the domain.

Solving the equation for y we get:

y = 3x - 1

Now, when x = -3

y = 3*-3 - 1 = -10

when x = -1

y = 3*-1 - 1 = -4

when x = 0

y = 3*0 - 1 = -1

When x = 4

y = 3*4 - 1 = 11

So we have the points (-3, -10), (-1, -4),  (0, -1), (4, 11)

The graph of these points is on the image below.

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Answer: angle BEC = 43 degrees

Step-by-step explanation:

Straight angle = 180 degrees

75 + 62 = 137

180 - 137 = 43

The sprinter will complete the race in approximately 17.07 seconds.

To calculate the time for the race, we need to consider two parts: the acceleration phase and the constant velocity phase.

Acceleration Phase:

The acceleration of the sprinter is 1.64 m/s², and the distance covered during this phase is 25 m. We can use the equation of motion to calculate the time taken during acceleration:

v = u + at

Here:

v = final velocity (which is the velocity at the end of the acceleration phase)

u = initial velocity (which is 0 since the sprinter starts from rest)

a = acceleration

t = time

Rearranging the equation, we have:

t = (v - u) / a

Since the sprinter starts from rest, the initial velocity (u) is 0. Therefore:

t = v / a

Plugging in the values, we get:

t = 25 m / 1.64 m/s²

Constant Velocity Phase:

Once the sprinter reaches the end of the acceleration phase, the velocity remains constant. The remaining distance to be covered is 100 m - 25 m = 75 m. We can calculate the time taken during this phase using the formula:

t = d / v

Here:

d = distance

v = velocity

Plugging in the values, we get:

t = 75 m / (v)

Since the velocity remains constant, we can use the final velocity from the acceleration phase.

Now, let's calculate the time for each phase and sum them up to get the total race time:

Acceleration Phase:

t1 = 25 m / 1.64 m/s²

Constant Velocity Phase:

t2 = 75 m / v

Total race time:

Total time = t1 + t2

Let's calculate the values:

t1 = 25 m / 1.64 m/s² = 15.24 s (rounded to two decimal places)

Now, we need to calculate the final velocity (v) at the end of the acceleration phase. We can use the formula:

v = u + at

Here:

u = initial velocity (0 m/s)

a = acceleration (1.64 m/s²)

t = time (25 m)

Plugging in the values, we get:

v = 0 m/s + (1.64 m/s²)(25 m) = 41 m/s

Now, let's calculate the time for the constant velocity phase:

t2 = 75 m / 41 m/s ≈ 1.83 s (rounded to two decimal places)

Finally, let's calculate the total race time:

Total time = t1 + t2 = 15.24 s + 1.83 s ≈ 17.07 s (rounded to two decimal places)

Therefore, the sprinter will complete the race in approximately 17.07 seconds.

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Answer:

C

Step-by-step explanation:

trust me c is the correct answer

6 tables are required. Each prime number attender should serve 3 customers each.

The prime numbers between 1 and 100 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97.

All the numbers other than prime numbers are composite numbers.

The composite numbers from 1 to 100 are: 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100.

Now, as there are 25 primes and 75 composites in the group that visited the restaurant, we can calculate the number of tables required by dividing the number of people by the seating capacity of each table.

Each table has a seating capacity of 15, so the number of tables required will be: Number of tables = (Number of customers)/(Seating capacity of each table)Number of customers = 25 (the number of primes) + 75 (the number of composites) = 100Number of tables = 100/15 = 6 tables

Therefore, 6 tables are required.

Now, as each prime number attender has to serve an equal number of customers, we need to calculate how many customers each one should serve.

Each prime attender has to serve 75/25 = 3 customers each, as there are 75 composites and 25 primes.

Thus, each prime number attender should serve 3 customers each.

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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The rate of decrease of the weather in degrees per hour is 2 degrees.

The time elapsed is from 5:00 PM to 9:00 PM, which is 4 hours.

The temperature dropped from 20 degrees to 12 degrees, which is a change of -8 degrees.

Therefore, the rate of decrease of the weather in degrees per hour is:

-8 degrees / 4 hours = -2 degrees per hour

A measurement of how quickly the temperature changes over time is the rate of change. Depending on the time frame being considered, it is typically represented in units of degrees per hour, degrees per minute, or degrees per second. Depending on whether the temperature is rising or falling, the rate of temperature change can be either positive or negative. The temperature rises when the rate of change is positive; it falls when the rate of change is negative.

Many variables, including the amount of sunlight, wind speed, humidity, and the time of day, have an impact on the pace of temperature change. Generally speaking, temperature varies more quickly during the day than it does at night, and it varies more quickly in places with less foliage and more exposed ground. Human activity, such as the emission of greenhouse gases into the atmosphere, which can eventually lead to an increase in global temperatures, can also have an impact on the pace of change of temperature.

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The grade 9 and 10 students are 975.

The total students in school are 1500.

Grade 9 and 10 students are 65% of 1500.

1500*65/100 = 975

Therfore the grade 9 and 10 students are 975.

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The distance between the points (-6, 4) and (5, 4) is 11 units.

To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:

Distance = √[(5 - (-6))² + (4 - 4)²]

        = √[(5 + 6)² + 0²]

        = √[11² + 0]

        = √[121]

        = 11

Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.

In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.

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The probability that the company will have to refund money to a customer is approximately 0.5276

A subfield of statistics known as probability studies random events and their likelihood of happening. It is used to anticipate the future and calculate the likelihood of events by dividing the number of positive outcomes by the total number of possible outcomes.

The probability that the dishwasher will last at least 6 years is the probability that it will not fail in the first 6 years, which can be calculated as:

\(P(X \geq 6) = e^{(-\frac{6}{8} )}\) = 0.4724

Therefore, the probability that the company will have to refund money to a customer is the complement of this probability, which can be calculated as:

P(refund) = 1 - P(X ≥ 6) = (1 - 0.4724) = 0.5276

So, the probability that the company will have to refund money to a customer is approximately 0.5276, assuming that the expected lifetime of the dishwasher is 8 years and the probability of failure in any given year is constant and independent of other years.

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The probability that the company will have to refund money to a customer, you would need information about the failure rate of the dishwasher over a six-year period.

If that information is available, you can calculate the probability. If it's not provided, then it's impossible to determine the probability accurately.

Without more information about the reliability of the dishwasher and the likelihood of it breaking down within the warranty period, it is difficult to determine the exact probability of the company having to refund money to a customer. However, assuming the company has reliable and durable products, the probability of them having to refund money may be low.

It is important to note that warranties typically have terms and conditions that must be met in order to qualify for a refund, so it is always best to read and understand the warranty before making a purchase.

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The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

I'm sorry i cant help you rn, download symbolab or math solver, I'm sure you will find your answer g

Your question is incomplete. The complete question is: Consider the following algebraic statements and determine the values of x for which each statement is true. On a number line, show the set of all points corresponding to the values of x.

|x| = 7

4=|-2x|

The values of x for which each statement is true are:

|x| = 7: x = -7 or x = 7

4 = |-2x|: x = -2    or x = 2

a) |x| = 7

-x = 7 or x = 7

x = -7 or x = 7

This statement is true for two values of x:

x = -7 and x = 7.

b) 4 = |-2x|

4 = -2x or 4 = 2x

x = -2    or x = 2

This statement is true for two values of x:

x = -2 and x = 2.

The number line is shown in the image attached.

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Answer:

15 shirts

Step-by-step explanation:

Store A charges 12.50 for a custom shirt with 0.40 per each custom character. Store B charges 14.75 for the same shirt but charges 0.25 per each custom character would make the cost from both stores the same

A: 12.5 + 0.40x

B: 14.75 + 0.25x

12.5 + 0.40x = 14.75 + 0.25x

subtract 12.5 from both sides:

12.5 + 0.40x - 12.5 = 14.75 + 0.25x - 12.5

0.40x = 2.25 + 0.25x

subtract 0.25x from both sides:

0.40x - 0.25x = 2.25 + 0.25x - 0.25x

0.15x = 2.25

divide both sides by 0.15:

0.15x/0.15 = 2.25/0.15

x = 15

The equation of remaining chocolate C  in terms of t is C = 30 - 3t.

A mathematical statement called an equation demonstrates the balance or equality of two expressions. It contains of variables, integers, and mathematical operations and is denoted by the equal symbol (=). Equations may be solved to determine unknown values and are used to express relationships between various quantities. To solve for x in the equation 2x + 3 = 7, for instance, remove 3 from both sides, which gives 2x = 4, then divide both sides by 2, which gives x = 2.

Given that,

Initial number of chocolates in box = 30

Also given that after 8 nights, number of remaining chocolates = 6

Implies that,

In 8 nights, 24 chocolates were treated.

In 1 night, 3 chocolates were treated.

The equation of remaining chocolate C  in terms of t can be written as

C = 30 - 3t.

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1 package is needed for the tablecloth.

Binding required = Perimeter

\(\sf Perimeter = 2(67 +47)\)

\(\sf = 2(114) = 228\)

228 inches are required

Each package contains 16 ft = 16 × 12 = 192 inches

No. of packages = 228 ÷ 192

= 1.188

So only 1 package is needed.

Problem-solving is the act of defining a problem; figuring out the purpose of the trouble; identifying, prioritizing, and selecting alternatives for an answer; and imposing an answer.

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Answer:

2 packages are needed.

Step-by-step explanation:

The bias tape is supposed to go all the way around the tablecloth.

That is:

67 + 47 + 67 +47

= 228 inches

Since there are 12 inches in a foot, we divide:

228 ÷ 12

= 19

The distance all the way around the tablecloth is 19 feet. The package of bias tape is only 16 feet. So you will need two packages. You'll only use 3 feet from the second package, you'll have a lot left over from the second package. But literally, you cannot finish the job if you only have one package.

You need 2 packages of bias tape.