QUADRATIC EQUATION – WORD PROBLEMS
The length of a playground is 15 meters more than the width and the area is 2700 . If the width is x m, find an equation in x and hence, find the dimensions of the classroom.

The answer width =45 m , length = 60 m
I just need the steps

The probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

To find the probability that a single randomly selected value is between 189.7 and 213, we can use the standard normal distribution.

Step 1: Calculate the z-scores for the given values using the formula:

  z = (x - μ) / σ

  For 189.7:

  z1 = (189.7 - 189.7) / 96.7 = 0

  For 213:

  z2 = (213 - 189.7) / 96.7 ≈ 0.2417

Step 2: Utilize a standard typical conveyance table or number cruncher to find the probabilities comparing to the z-scores.

  P(189.7 < X < 213) = P(0 < Z < 0.2417) ≈ 0.0939

Therefore, the probability that a single randomly selected value is between 189.7 and 213 is approximately 0.0939.

To find the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213, we use the central limit theorem. Under specific circumstances, the testing dispersion of the example mean methodologies a typical conveyance

Step 1: Calculate the standard error of the mean (σ_m) using the formula:

  σ_m = σ / sqrt(n)

  σ_m = 96.7 / sqrt(62) ≈ 12.2878

Step 2: Convert the given qualities to z-scores utilizing the equation:

  z = (x - μ) / σ_m

  For 189.7:

  z1 = (189.7 - 189.7) / 12.2878 = 0

  For 213:

  z2 = (213 - 189.7) / 12.2878 ≈ 1.8967

Step 3: Utilize a standard typical conveyance table or mini-computer to find the probabilities relating to the z-scores.

  P(189.7 < M < 213) = P(0 < Z < 1.8967) ≈ 0.9702

Therefore, the probability that a sample of size n = 62 is randomly selected with a mean between 189.7 and 213 is approximately 0.9702.

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Answer:

area = 2.3 x 2.8

area is 6.44 meters

Step-by-step explanation:

area is length multiplied by width

The distance traveled by airplane is 180 miles.

The speed of the airplane is 3 miles per minute and the angle of direction from the origin is 51.34°

The airplane landed 100 miles north and 80 miles east from its origin and it flew for one hour.

Then, the total distance traveled by airplane will be:

= 100 miles + 80 miles = 180 miles.

The speed can be defined as the distance traveled by the total time taken.

Speed = distance/time

Speed = 180 miles/ 1 hour

Speed = 180 miles/60 minutes

Speed = 3 miles per minute

The angle of direction from its origin will be:

tan (x) = 100 miles/80 miles

x = tan⁻¹ ( 100/80)

x = tan⁻¹ ( 10/8) =  tan⁻¹ ( 5/4)

x = 51.34°

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Answer:

19/12 or 1 \(\frac{7}{12}\) kg

Step-by-step explanation:

5/6 + 3/4

10/12 + 9/12 = 19/12 or 1 \(\frac{7}{12}\) kg

The probability that all three number cubes will land on an odd number is 1/8

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

Number of cubes = 3

Sections on each cube = 6

Odd sections on each cube = 3

This means that

P(Odd) = Odd sections/Total sections

So, we have the following representation

P(Odd) = 3/6

Simplify

P(Odd) = 1/2

For the three cubes, we have

P(All odd) = P(Odd)^Number of cubes

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

P(All odd) = (1/2)³

Evaluate

P(All odd) = 1/8

Hence, the probability is 1/8

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Answer: 1/8

    ;

 ; l       .

                        .

      /.         ;      

      .

B) no real solution

Explanation

Step 1

make

then

Hence

Step 2

find x, using the quadratic formula

Let

a=-1

b=-18

c=-145

replace,

Now

is not a real number, so the answer is

B) no real solution

Solve for x.

2x + 9 = 33

2x = 24

x = 12

A. x = 7.5

B. x = 12

C. x = 21

D. x = 84

Answer:

\(2x + 9 = 33 \\ 2x = 33 - 9 \\ 2x = 24 \\ x = \frac{24}{2} \\ x = 12\)

Answer

Exponential function, in mathematics, a relation of the form

Option A is correct

Option B is correct , yes 200 represent the initial saving

Option C is incorrect 2 % is not the rate of decay

Option D is incorrect

Option E is correct

It is less than $220

The final answer

Answer:

Yes

Step-by-step explanation:

2 times 19=38

1 times 19=19

Answer:

yep it is equivalent by decreased orchard Harvick hdiwbxgcysnabudnd

Answer:

132 students

Step-by-step explanation:

Let S(t) model the number of students who have not heard the story after t days.

We are told that the rate of change of S is proportional to S:

\(\frac{dS}{dt} = kS\)

​

This sort of differential equation describes an exponential model, and its solution is

\(S(t) = C\) * \(e^{kt}\)

Let's find the values for C and k.

We are told that there were 900 students who had not heard the story initially. From this we can tell that C=900

We are also told that the number of students is divided by 3 every4 days. From this we can tell that \(k= \frac{ln(0.3)}{4}\)

We found that \(S(t) = 900e^{\frac{ln(0.3)}{4}t }\),  The number of students who have not heard the story after 7 days is S(7):

\(S(7) = 900e^{\frac{ln(0.3)}{4}(7) }\) ≈ 132

Answer:

ubeovgtnwjggswgtepibvqyytkhfhduygvtqyaccjvgvdbbetedgtdgyegghjgdbecdkbfbgdhebhjegeckgbkhbeiubuvvsakvhfe

Step-by-step explanation:

hrtrrrrrrrrrrrrrrrrhhhhhhrhhhhhhhhhhhhhhhhhhhhhhhhhhhhrhhrhhrrhhhrhhhhh

The pattern is formed by adding 4 tiles to the previous cross.

In the first cross, there is 1 tile on each arm. In the second cross, there are 5 tiles on each arm, which is 4 more than the first cross. In the third cross, there are 9 tiles on each arm, which is 4 more than the second cross. And so on.

The following formula can be used to calculate the number of tiles in the nth cross:

tiles = 4 × (n - 1) + 1

where n = number of the cross.

For example, to calculate the number of tiles in the 4th cross, use the following formula:

tiles = 4 × (4 - 1) + 1 = 17

Therefore, there are 17 tiles in the 4th cross.

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Answer:

7.58 miles on average per week

Step-by-step explanation:

\( \qquad \qquad\huge \sf༆ Answer ༄\)

let's solve ~

\(\qquad \sf \dashrightarrow \: {x}^{2} - 7x + 12 = 0 \)

\(\qquad \sf \dashrightarrow \: x {}^{2} - 4x - 3x + 12 = 0 \)

\(\qquad \sf \dashrightarrow \: x(x - 4) - 3(x - 4) = 0\)

\(\qquad \sf \dashrightarrow \: (x - 4)(x - 3) = 0\)

Therefore, the required values of x are ~

\(\overbrace{  \underbrace{\underline{ \boxed{ \sf 3 \: and \: 4}}}}\)

Answer:

x = 3,4

Step-by-step explanation:

\(\displaystyle \large{(x-a)(x-b)=x^2-bx-ax+ab \longrightarrow x^2-(b+a)x+ab}\)

Above is formula for factoring of two brackets for a = 1 from ax^2 + bx + c.

First, find the factors of 12:

If we multiply the factors together, we get same ab-value which is 12. Next, we find the middle term. A middle term can’t be found by adding factors together.

Our middle term is -7x and the only factors that satisfy -7x would be 3 and r using (x-a)(x-b) standard.

Hence, our a is 3 and b is 4. Substitute in:

\(x^2-7x+12 = x^2-(3+4)x + 3(4) = (x-3)(x-4)\)

Set (x-3)(x-4) = 0 then we obtain:

x-3 = 0 or x-4 = 0 —> solve like linear by transporting the constant and change the sign.

Hence, “x = 3 or x = 4”

You can also write x = 3,4 instead or x = 4,3.

Complete the square in the denominator to get

tan²(t ) + 14 tan(t ) + 48 = tan²(t ) + 14 tan(t ) + 49 - 1

… = (tan(t ) + 7)² - 1

Substitute u = tan(t ) + 7 and du = sec²(t ) dt. Then the integral becomes

\(\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt = 2 \int \frac{\mathrm du}{u^2-1}\)

Separate the integrand into partial fractions:

\(\dfrac1{u^2-1} = \dfrac12 \left(\dfrac1{u-1}-\dfrac1{u+1}\right)\)

Then we get

\(\displaystyle \int \frac{2\sec^2(t)}{\tan^2(t)+14\tan(t)+48} \,\mathrm dt =  \int \left(\frac1{u-1}-\frac1{u+1}\right)\,\mathrm du \\\\ =\ln|u-1|-\ln|u+1| + C \\\\ = \ln\left|\frac{u-1}{u+1}\right|+C \\\\ = \boxed{\ln\left|\frac{\tan(t)+6}{\tan(t)+8}\right|+C}\)

Answer:

See Explanation

Step-by-step explanation:

For ASA

\( \angle R \cong \angle E\)

\( RQ \cong EF\)

\( \angle Q \cong \angle F\)

\( \triangle PRQ \cong \triangle GEF\)

For AAS

\( \angle P \cong \angle G\)

\( \angle R \cong \angle E\)

\( RQ \cong EF\)

\( \triangle PRQ \cong \triangle GEF\)

Answer:

Step-by-step explanation:

Plotting a point A and tracing a point B at 4 units from A results in a circle.

▪The locus of a point at equal distance from a fixed point is a circle.

▪Point A is (5,5) and length of AB is 4 units

This implies that the radius of circle is 4 units.

▪The point B can be swirled around A keeping the distance AB constant.

▪The resulting figure is a circle.

▪This circle is plotted and attached below.

I hope this helped. I am sorry if you get it wrong

Answer:

This is the right answer for Edementum and Plato users

Like and Rate!

Answer:

Yes, they make sense outside the context of temperature.

Step-by-step explanation:

If you are standing in a line, and mark your current position as 0 then if you take two steps ahead it can be counted as positive and if you take two steps back from your current position it can be counted as negative. The positive and negative can denote your forward and backward movement respectively.

If we denote the growth in companies revenue as positive and dip as negative then it would also make sense. A positive number would mean profit for the company while a negative sign would show loss.

Answer:

$ 17.35

Step-by-step explanation:

Answer:

Ok ill get back to you when I figure it out so see you in 5 minutes!

Answer:

Step-by-step explanation:

Each decision variable must be non-negative in the optimal solution.

According to this restriction or constraint, x11, x12, x21, and x22 must all be bigger than zero. They cannot, therefore, be negative numbers. All the variables would have to be positive values if the limitation had been > (greater than). However, since it is (more than or equal to), the choice of 0 is acceptable.

The function \(f(x_{1} ,x_{2} ,....)=x_{1} ^{2},x_{2} ^{2} ......\) is always positive except at the origin where it is equal to zero. This means that the absolute minimum of this function must be a = 0 . Absolute maximum is when all of the variables are equal to zero except \(x_{1}\) which is equal to 1 (f evaluated at this point is equal to 1 do b=1). The function itself is then equal to 1. This is because when \(f(.....) = x_{1} ^{2} +x_{2} ^{2} .....\leq x_{1} ^{2} +2x_{2} ^{2}+3x_{3} ^{2} ....\leq 1\)

so it is at most equal to 1 and this happens exactly at the point

\((x_{1} ,x_{2} ,x_{3} .....) = (1,0,0...)\)

Therefore,

Each decision variable must be non-negative in the optimal solution.

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a. To create an exponential model for new cases in terms of days, we can use the formula: y = a * b ^ x, where y is the number of new cases, x is the number of days since the first observation, and a and b are constants that we need to determine. Using the two data points given, we can set up a system of equations:

235 = a * b ^ 0

395 = a * b ^ 10

Solving for a and b, we get:

a = 235

b = (395/235)^(1/10) = 1.067

Therefore, the exponential model for new cases in Milwaukee is:

y = 235 * 1.067 ^ x

b. To find the number of new cases on Oct. 31, 2020, we need to plug in x = 19 (since Oct. 31 is 19 days after Oct. 12) into the model:

y = 235 * 1.067 ^ 19 = 1018.5

Therefore, based on the exponential model, we would expect around 1019 new cases on Oct. 31, 2020.

c. The actual number of new cases on Oct. 31, 2020, was 1043. This is higher than the predicted value of 1019, but not by a huge margin. Overall, the model seems to fit the data reasonably well, especially considering that there are many factors that can affect the number of new cases in a given area, and that the model is based on only two data points. However, it is worth noting that the exponential model assumes that the growth rate of new cases remains constant over time, which may not be a realistic assumption in the long run.

Answer:

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Substituting the points (0,2) and (1,0) into the slope formula, \(m=\frac{2-0}{0-1}=-2\).

Answer:

C

Step-by-step explanation: A would not make sense because 19 x 10 is 190 and 19 x 20 is 380. B would not make sense because 19 x 22 is 418 and 19 x 40 is 760. D would not make sense because 19 x 220 is 4180 which is above what you are looking for. Therefore, the only option left is C.

The system of equations that shows the situation is option 1.  L+J=29  L=2J-10

The question tells us that the summation of the age of Latifa and Jameel is 29

Let J = Jameel

L = Latifa

L + J = 29

The question says that Latifa's age is 2 time of Jameels age = 2J with 10 years subracted

L = 2J - 10

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Answer:

Step-by-step explanation:

\(3)\frac{5x}{2}+125 = 180\\\\\frac{5x}{2}=180-125\\\\\frac{5x}{2}=55\\\\ 5x = 55*2\\\\ x =\frac{55*2}{5}\\\\ x = 11*2 = 22\)

4) 3x+ 42 + 90= 180

3x + 132 = 180

        3x = 180 -132

        3x = 48

          x = 48/3

         x = 16

Answer:

12

Step-by-step explanation:

area =1/2 base×height

=1/2 ×4×6

=12