The art club is designing a rectangular mural for the school hallway. Three
corners are located at (21,21),(21, 1), and (4.1) on a coordinate plane. Find the
fourth vertex and graph the rectangle on the coordinate plane below.
Fourth vertex:

Answer:

Give me a heart and 5 stars

Step-by-step explanation:

Answer:

This is straightforward. To find how long each garden plot would be, we only need to divide. So to obtain 10 equal-sized garden plots from a 3694.7 feet land we have 3694.7/ 10 = 369.47 ft.

THERE MARK ME BRINILYLIST

Answer:

-5, -4

Step-by-step explanation:

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The domain and range of the graphed function

Domain; -5 ≤ x < 1

Range; -4 ≤ y < 7

Simply expressed, the domain is the collection of all potential input values. This means the values on the graph's x-axis. Meanwhile, the range is the collection of all output values, which in this case are the y-axis values.

Now, from the graph, we see that the line stopped at 2 points.

The bottom one is darkened, indicating that it contains the numbers at that point.

So, the domain as x ≥ -5

While the range will be as follows;  y ≥ -5

The location where it is not coloured on the graph for the second point above indicates that the coordinates at that point are not included in the range or domain.

Hence, the domain here is; x < 1

and, y < 7 is the range.

Now, combining the Domain and Range as

Domain = -5 ≤ x < 1

Range; -4 ≤ y < 7

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Answer:

The 95% confidence interval for the difference in population proportions is (0.001, 0.079).

Step-by-step explanation:

The (1 - α)% confidence interval for the difference in population proportions is:

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

The information provided is as follows:

\(\hat p_{1}=0.95\\\hat p_{2}=0.91\\n_{1}=300\\n_{2}=350\\\)

The critical value of z for 95% confidence level is 1.96.

Compute the 95% confidence interval for the difference in population proportions as follows:

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha /2}\times\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.95-0.91)\pm 1.96\times\sqrt{\frac{0.95(1-0.95)}{300}+\frac{0.91(1-0.91)}{350}}\\\\=0.04\pm 0.0388\\\\=(0.0012, 0.0788)\\\\\approx (0.001, 0.079)\)

Thus, the 95% confidence interval for the difference in population proportions is (0.001, 0.079).

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

\(y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\\)

Apply substitution to get

\(y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\\)

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a  -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

The probabilities, we need to understand the context. Assuming we are working with a fair six-sided die, where each face has an equal chance of landing, here are the probabilities:

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The cost of students ticket is $37.5and the cost of general admission is $187.5.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, also known as a system of equations or an equation system.

Assume s be the students tickets cost and g be the general admission cost.

From the given information,

⇒  s + g = 225             ..(1)

 5s + 7g = 1500         ..(2)

From equation (1),

s = 225 - g

Plug the value of s in equation (2)

5(225 - g) + 7g = 1500

1125 - 5g + 7g = 1500

                  2g = 1500 - 1125

                  2g = 375

                    g = 187.5

Plug g = 125 in equation (1),

s + 187.5= 225

        s = 225 - 187.5

        s = 37.5

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So Isabelle is 18 times old.

Ben is one time youngish than Amara, so Ben's age is 18- 1 = 17.

Maria is 5 times old, and Tony is 2 times old.

Let's use" i" to represent Isabelle's age. also, we can set up the equation

5 2 i = total family age

We can simplify this equation to

24 i = total family age

To find Isabelle's age, we need to know the total family age. We can calculate this by adding up the periods of all the family members

18 17 5 2 i = 42 i

Now we can substitute this expression for the total family age back into our equation

24 i = 42 i

Simplifying this equation, we get

i = 18

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The number of triangles that can be drawn from the given side lengths is; 1 perfect right angle triangle

We are given the sides of the triangle to be;

3 units, 4 units and 5 units

Now, let us test if it is a right angled triangle by using the Pythagoras theorem as follows where;

a² + b² = c²

let a and b be 3 and 4 respectively. Thus;

3² + 4² = 16 + 9 = 25

c is 5. Thus; 5² = 25

Thus, we see that the 3 given sides fulfill the conditions of a right angle triangle.

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Answer:I’m guessing the second one

Step-by-step explanation:

I thinking that because if u add it all up also this is just a thought

The solution to the inequality equation \(x^{2}\) – 9x < –18 is 3 < X < 6

Inequality equation means a mathematical expression in which the sides are not equal to each other

\(x^{2}\) – 9x < –18

Rewrite in standard form

x^2 -9x +18 < 0

Factorise the equation

\(x^{2}\)  - 3x -6x +18 < 0

x (x - 3) - 6 (x - 3) < 0

(x - 3) ( x- 6) < 0

(x - 3) < 0

x < 3

( x- 6) < 0

x < 6

3 < X < 6

Therefore, the solution to the inequality is 3 < X < 6

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Answer: 20/3 square inches

Step-by-step explanation:

Area = length*width

length = 5 in.

width = 4/3 in.

A = 5 * (4/3) = 20/3 in^2

The doctor recommends rest if the patient has the flu. Then the correct option is A.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

Read the following two statements.

Then, if possible, use the Law of Detachment to draw a conclusion.

Then the correct option is A.

The doctor recommends rest if the patient has the flu.

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Answer:

A) 310 cm²

Step-by-step explanation:

The surface area is the area of the two-dimensional surfaces of this three-dimensional figure.

Start by multiplying each 5x4 rectangle. There are four of them that are visible from the front.

Now, find the surface area of the large rectangle in the back and the left side of the figure.

Find the surface area of the top of this figure.

Find the surface area of the bottom of this figure (it's the same as the area of the top).

Add all of the surface areas together to find the total surface area of the figure.

Answer:

C > –½

Step-by-step explanation:

10C + 4 > 2C

The above inequality can be solved as follow:

10C + 4 > 2C

Collect like terms

4 > 2C – 10C

4 > – 8C

Divide both side by –8

Note: the inequality sign will change since we are dividing by a negative value.

4/ –8 < –8C/ –8

– ½ < C

Thus,

C > –½

Answer:

the answer is A

I followed the point slope formula and added in the x and y values

Answer:

\(a = \frac{20}{3}\)

Step-by-step explanation:

Answer: 3.971

Step-by-step explanation: first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

3.85

0.004

0.117

+————-

Then you add vertically and you get your answer of 3.971

Your welcome :)

The value of the given expression ( 3.85+0.004+0.117 ) is 3.971.

The process of increment of any number of quantities or the process of integrating small parts to make a big part is called summation.

first, you need to set up your addition problem. When adding decimals, you need to line up the decimal points. So you get something like this:

 3.850

 0.004

 0.117

+————-

3.971.

Then you add vertically and you get your answer of 3.971.

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Answer:\(\color{yellow}{}\)

∆ABC

∆DEF

∆ABC

<C

<D

<X

BE>

CF>

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A=3.7

Supplementary angles mean two angles that add up to 180.

180 = 139.2 (angle 1) + x (angle 2)

180 - 139.2 = x (angle 2)

40.8 = x

angle 2 = 40.8

Answer:

40.8°

Step-by-step explanation:

The sum of two supplementary angles is 180°.

180 -  139.2 = 40.8

The measure of it's supplement should be 40.8°.

Hope this helps.

Answer:

Ann traveled 165 miles on 5 gallons of gas

Step-by-step explanation:

First we must know how many miles are in a gallon (in this situation). Last weekend Ann drove 132 miles with 4 gallons of gas, we can divide to find out how many miles she drove on 1 gallon. 132/4 = 33. This means Ann drove 33 miles on 1 gallon of gas. To get your answer, simply multiply 5 and 33. 5 times 33 = 165.

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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Step-by-step explanation:

problem 10 is function

but problem 9 is not

Answer:

Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!

(a) The probability that the instrument does not fail in an 8-hour shift is 0.7183 or 71.83%.

(b) The probability of at least one failure in a 24-hour day is 0.999 or 99.9%.

The number of failures of a testing instrument in a given time period is modeled by a Poisson distribution with a rate parameter equal to the mean number of failures per unit time.

(a) To find the probability that the instrument does not fail in an 8-hour shift, we can use the cumulative distribution function (CDF) of the Poisson distribution. The CDF gives the probability that the number of failures is less than or equal to a given value. In this case, we want to find the probability that there are 0 failures in an 8-hour shift, so the CDF can be expressed as:

P(X ≤ 0) = e^(-0.025 * 8) = 0.7183

So, the probability that the instrument does not fail in an 8-hour shift is 0.7183 or 71.83%.

(b) To find the probability of at least one failure in a 24-hour day, we can subtract the probability of 0 failures from 1. That is,

P(X ≥ 1) = 1 - P(X ≤ 0) = 1 - e^(-0.025 * 24) = 0.999

So, the probability of at least one failure in a 24-hour day is 0.999 or 99.9%.

Note: In these calculations, we use the formula for the cumulative distribution function of the Poisson distribution, which is:

P(X ≤ k) = e^(-lambda) * (lambda^k / k!)

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The equation which describes the relationship between the side length and shaded area of the quilt is y=0.5x²

Side length, x = 1,3,4,5,8

Shaded Area, y = 0.5, 4.5, 8, 12.5, 32

The relationship can be modeled as a quadratic function. Using a graphing calculator for the quadratic function written in the form y = ax² + bx + c

a = 0.5 ; b = 0 ; c = 0

Therefore, the quadratic function can be written as y = 0.5x²

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Answer:

relationship

the exterior angle of triangle is equal to the sum of its opposite angle

<A+<B=<BÇD

Answer: C. 3/4 of a cup of corn syrup

Step-by-step explanation:

    We will set up a proportion to help us solve.

\(\displaystyle \frac{1/4\text{ cup corn syrup}}{6\text{ cups of soap and water}} =\frac{x\text{ cups corn syrup}}{18\text{ cups of soap and water}}\)

    Next, we will cross-multiply.

1/4 * 18 = 6 * x

9/2 = 6x

    Lastly, we will divide both sides of the equation by 6.

x = 3/4 of a cup of corn syrup

                       C. 3/4 of a cup of corn syrup