Read following problem. Identify what you need to know. Then use the information in the problem to solve. Show your work.
R S is the midsegment of trapezoid M N O P . What is the length of RS ?
A 14 units B 19 units C 23 units D 26 units

Answer:

The range is -7 ≤ y ≤ 8

Step-by-step explanation:

The range is the full measurement of a graph on the y-axis.

I know this can be confusing at times as I had struggles with this in the past

Hopefully, this helps!

The interquartile range (IQR) is a measure of the spread or variability of the middle 50 percent of the data.

The interquartile range (IQR) is a statistical measure that describes the spread or dispersion of the middle 50 percent of the data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1) of a dataset.

The quartiles divide a dataset into four equal parts, each representing 25 percent of the data. The first quartile (Q1) represents the lower boundary of the middle 50 percent, while the third quartile (Q3) represents the upper boundary of the middle 50 percent. The IQR captures the range of values within this middle range.

By focusing on the middle 50 percent of the data and excluding the extreme values, the interquartile range provides a measure of variability that is less affected by outliers or extreme values. It is commonly used in descriptive statistics and data analysis to understand the spread and distribution of a dataset, particularly when the data is not symmetrically distributed or contains outliers.

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Answer: 1) x> -21

2) x is less than or equal to -21

3) x is less than or equal to 16

4) x less than or equal to 3/4

(a)The solution to \(y[n]\) with the given initial condition and input sequence is: \[y[n] = \{1, 1.5, 1.75, 1.875, \ldots\}\]

(b) The solution to \(y[n]\) with the given initial conditions and input sequence is: \[y[n] = \left\{\frac{1}{3}, -\frac{1}{18}, \frac{5}{54}, \ldots\right\}\]

(a) To find the solution to \(y[n]\) when \(y[-1]=1\) and \(x[n]=u[n]\), we can recursively apply the given system equation.

Given:

\[y[n] = 0.5y[n-1] + x[n]\]

\(y[-1] = 1\) (initial condition)

\(x[n] = u[n]\) (unit step input)

To solve for \(y[n]\), we can substitute the values and iterate through the equation:

For \(n = 0\):

\[y[0] = 0.5y[-1] + x[0] = 0.5 \cdot 1 + 1 = 1.5\]

For \(n = 1\):

\[y[1] = 0.5y[0] + x[1] = 0.5 \cdot 1.5 + 1 = 1.75\]

For \(n = 2\):

\[y[2] = 0.5y[1] + x[2] = 0.5 \cdot 1.75 + 1 = 1.875\]

And so on...

The solution to \(y[n]\) with the given initial condition and input sequence is:

\[y[n] = \{1, 1.5, 1.75, 1.875, \ldots\}\]

(b) To solve the difference equation \[y[n] = \frac{1}{3}x_1[n] - 0.5y[n-1] + 0.25y[n-2]\] with the given initial conditions \(y[-1]=0\) and \(y[-2]=1\) and the input sequence \(x_1[n]=\left(\frac{1}{3}\right)^n\), we can use a similar iterative approach.

For \(n = 0\):

\[y[0] = \frac{1}{3}x_1[0] - 0.5y[-1] + 0.25y[-2] = \frac{1}{3} - 0.5 \cdot 0 + 0.25 \cdot 1 = \frac{4}{12} = \frac{1}{3}\]

For \(n = 1\):

\[y[1] = \frac{1}{3}x_1[1] - 0.5y[0] + 0.25y[-1] = \frac{1}{3} \cdot \left(\frac{1}{3}\right)^1 - 0.5 \cdot \frac{1}{3} + 0.25 \cdot 0 = \frac{1}{9} - \frac{1}{6} = -\frac{1}{18}\]

For \(n = 2\):

\[y[2] = \frac{1}{3}x_1[2] - 0.5y[1] + 0.25y[0] = \frac{1}{3} \cdot \left(\frac{1}{3}\right)^2 - 0.5 \cdot \left(-\frac{1}{18}\right) + 0.25 \cdot \frac{1}{3} = \frac{1}{27} + \frac{1}{36} + \frac{1}{12} = \frac{5}{54}\]

And so on...

The solution to \(y[n]\) with the given initial conditions and input sequence is:

\[y[n] = \left\{\frac{1}{3}, -\frac{1}{18}, \frac{5}{54}, \ldots\right\}\]

The iteration process can be continued to find the values of \(y[n]\) for subsequent values of \(n\).

It's important to note that in part (b), the input sequence \(x_1[n] = \left(\frac{1}{3}\right)^n\) was used instead of \(x[n]\) to solve the difference equation.

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Answer:

The answer would be 2,240

Step-by-step explanation:

Answer:

2240

Step-by-step explanation:

1. 5x4=20x7 and keep on going

Answer:

A. 100

Step-by-step explanation:

84

Step-by-step explanation:

c + 100 =180

c=180-100

c=80

100+96+d+c=360

100+96+d+80=360

276+d=360

d=360-276

d=84

Answer:

area of shaded portion=56 - 1/2 ×3×4=56-6= 50 yd^2

Answer:

3*4=12

Step-by-step explanation:

the answer is 12

Answer:

A

Step-by-step explanation:

I would say A if the c is equal to 65. If you follow the Pythagorean's Theorem, it states a^2+b^2=c^2

The average rate of change of the account value from t = 0 to t = 5 is the change in the account value divided by the change in time, or (A(5) - A(0))/(5 - 0).

We can substitute the given function into the equation:

A(t) = 50,000(1.02)^t

So,

A(5) = 50,000(1.02)^5

and

A(0) = 50,000(1.02)^0

Now we can substitute these values in the equation of average rate of change:

(A(5) - A(0))/(5 - 0) = (50000(1.02)^5 - 50000(1.02)^0) / (5-0)

This simplifies to

(50000(1.02)^5 - 50000) / 5

Which is approximately equal to 67,622.05

So the average rate of change of the account value from t = 0 to t = 5 is approximately 67,622.05.

The transformations that took for mapping ΔA onto ΔB are:

a) Translated the triangle A 2 units to the right,

b) Reflected the ΔA' (translated A) over the y-axis,

c) Reflected the ΔA'' (reflected A) over the x-axis, resulting in ΔB.

The transformation rules are:

a) Translation: (x, y) ⇒ (x + 2, y) (In the right side direction)

b) Reflection over the y-axis: (x, y) ⇒ (-x, y)

c) Reflection over the x-axis: (x, y) ⇒ (x, -y)

The given vertices of triangle A are: (-2, 3), (-5, 3), and (-5, 5).

a) Applying translation by 2 units to the right to triangle A:

(-2, 3) → (-2 + 2, 3) → (0, 3)

(-5, 3) → (-5 + 2, 3) → (-3, 3)

(-5, 5) → (-5 + 2, 5) → (-3, 5)

So, triangle A is translated to triangle A'.

b) Applying reflection over the y-axis to the triangle A':

(0, 3) → (0, 3)

(-3, 3) → (3, 3)

(-3, 5) → (3, 5)

So, triangle A' is reflected as triangle A''.

c) Applying reflection over the x-axis to triangle A'':

(0, 3) → (0, -3)

(3, 3) → (3, -3)

(3, 5) → (3, -5)

Thus, the formed triangle is B at the vertices (0, -3), (3, -3), and (3, -5).

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Answer:

400+100c<550+70c

Step-by-step explanation:

Second salesperson makes more money weekly

The number of cars will be 5.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

One car salesperson makes a weekly salary of $400, plus $100 commission for each car sold.

And, The other car salesperson makes a weekly salary of $550, plus $70 commission for each car sold.

Now,

Let the number of cars = c

So, We can formulate;

⇒ 400 + 100c = 550 + 70c

Solve for c as;

⇒ 100c - 70c = 550 - 400

⇒ 30c = 150

⇒ c = 5

Thus, The number of cars will be 5.

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Answer:

-13y

Step-by-step explanation:

Since this expression has the same coefficient, all you have to do is solve -6-7. Just follow the keep change change rule when subtracting negative numbers so -6 + -7 = -13. Therefore, your answer will be -13y.

Let me know if you do not understand or need more explanation.

9514 1404 393

Answer:

  3x -4y = -9

Step-by-step explanation:

Multiply by 4 to clear the fraction.

  4(y -6) = 3(x -5)

Subtract the left-side term to get variables on the same side, with a positive x-coefficient.

  0 = 3(x -5) -4(y -6)

Eliminate parentheses and collect terms.

  0 = 3x -15 -4y +24

  0 = 3x -4y +9

Subtract 9 and swap sides to get standard form.

  3x -4y = -9

_____

Standard form is ...

  ax +by = c

where a ≥ 0, and a, b, c are mutually prime integers. If a=0, then b > 0.

__

The attached graph shows the equations give the same line. The original line is shown dotted so that you can see they overlap.

Answer:

The answer is (1,0) and (5,2)

Step-by-step explanation:

Since they are asking for parallel lines that means the slopes of the lines has to be the same line AB slope is 1/2 if you find the slope of (1,0) and (5,2) it will be the same as 1/2

From the 12 listed amount, the amount which are within 1.5 standard deviation of the mean are (E) Eleven.

The term "Standard-deviation" is defined as a statistical measure of amount of variation of a set of data points from mean value.

The amounts which are within 1.5 standard deviation means can eb calculated by the formula :

⇒ {mean - 1.5×(S.D.), mean + 1.5×(S.D.)}

Substituting the values,

We get,

⇒ {8.1 - 1.5×0.3,  8.1 + 1.5×0.3}

⇒ {7.65 , 8.55}.

The 12 listed amount are : {8.22, 7.51, 7.86, 8.36, 7.83, 8.30, 8.09, 8.01, 7.73, 8.53, 8.25, 7.96},

We can see that, from the 12 listed amounts, only 7.51 is out of this rage and the remaining 11 amounts are within this rage.

Therefore, the correct option is (E) Eleven.

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The given question is incomplete, the complete question is

A vending machine is designed to dispense 8 ounces of coffee into a cup. after a test that recorded the number of ounces of coffee in each of 1,000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data. if the 1,000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.3 ounce, how many of the 12 listed amounts are within 1.5 standard deviations of the mean?

7.51, 8.22, 7.86, 8.36, 8.09, 7.83, 8.30, 8.01, 7.73, 8.25, 7.96, 8.53.

(A) Four

(B) Six

(C) Nine

(D) Ten

(E) Eleven

We have -4(x - 6) + 3(a - 7) = -4x + 24 + 3a - 21 = -4a + 3a + 3

so the answer is B

ok done. Thank to me :>

The statement " The random device method involves using an apparatus or a procedure to ensure that every member of the population has the same chance of being selected into the sample" is true

The random device method is defined as the method used to choose one member from the population. The random device method is also called the random sampling method. It is also allows the the randomization of sample selection from the population

The selection of member is fully random. So the chances of the being selected will be same for all the members in the population

Therefore, the given statement is true

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Answer:

A.) 1/6

Step-by-step explanation:

3/8 x 4/9 = 12/72 ---> 1/6

D its aswer

Step-by-step explanation:

Answer: No solution (please give me the brainiest this took so long)

Step-by-step explanation:

step 1: distribute

7+5(+3)=8+4(+2)

7+5+15=8+4(+2)

step 2: combine like terms

7+5+15=8+4(+2)

12+15=8+4(+2)

step 3: distribute again

12+15=8+4(+2)

12+15=8+4+8

step 4: combine like terms

12+15=8+4+8

12+15=12+8

step 5: subtract 15 from both sides of the equation

12+15=12+8

12+15−15=12+8−15

step 6: simplify

subtract the numbers

12+15−15=12+8−15

12=12+8−15

subtract the numbers

12=12+8−15

12=12−7

step 7: subtract 12a from both sides of the equation

12=12−7

12−12=12−7−12

step 8: simplify

combine like terms

12−12=12−7−12

0=12−7−12

combine like terms

0=12−7−12

0=−7

The input is a contradiction: it has no solutions

The median of the random variable x-bar is 300.The distribution of the sample mean (x-bar) from a normally distributed population follows a normal distribution as well.

For large sample sizes (n ≥ 30), the sample mean will be approximately normally distributed, regardless of the shape of the original population.

Given that x follows a normal distribution with a mean of 300 and a standard deviation of 15, the sample mean x-bar (when sampling 20 observations at a time) will also follow a normal distribution with a mean equal to the population mean (300) and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

The standard deviation of x-bar is given by σ_x-bar = σ_x / √n, where σ_x is the population standard deviation and n is the sample size.

In this case, the standard deviation of x-bar is σ_x-bar = 15 / √20 ≈ 3.3541.

Since the sample mean x-bar follows a normal distribution, its median will be equal to its mean, which is the same as the population mean of 300.

Therefore, the median of the random variable x-bar is 300.

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In the given figure,

Thus the given statement is TRUE.

The statement "using higher order functions, complete the mul by num function. this function should take an argument and return a one argument function that multiplies any value passed to it by the original number" is True. It is possible to complete the `mul_by_num` function using higher order functions. A higher order function is a function that either takes one or more functions as arguments, or returns a function as its result.

In this case, the `mul_by_num` function should take an argument and return a one argument function that multiplies any value passed to it by the original number. Here's how you can do it:

```python
def mul_by_num(num):
   def num_function(val):
       return val * num
   return num_function
```

The `mul_by_num` function takes an argument `num` and returns a one argument function `num_function` that multiplies any value passed to it by the original number `num`. The `num_function` is a higher order function because it is returned by the `mul_by_num` function.

You can use the `mul_by_num` function like this:
```python
mul_by_5 = mul_by_num(5)
print(mul_by_5(10)) # 50
```

The `mul_by_num` function is called with the argument `5` and returns a one argument function `mul_by_5` that multiplies any value passed to it by 5. When the `mul_by_5` function is called with the argument `10`, it returns the result `50`.

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Answer:

Open the image. (Hope you don't mind about bad writing)

Answer:

501,000 adults 976,000 people total

Step-by-step explanation:

First step is adding 26,000 to 475,000 to find the number of adults, you get 501,000

Then you add 501,000 to 475,000 to get the total number of people, you get 976,000

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

If 501,000 grownups total then 976,000 people.

An expression, also known as a mathematical expression, is a finite combination of symbols that are well-formed in accordance with context-dependent rules.

Mathematical expressions consist of at least two numbers or variables, at least one math operation, and a sentence. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in some terms have a number in front of them. A coefficient is the number placed before a term.

Given:

There were 475,000 children at a state fair.

There were 26,000 more adults than children at the state fair.

Number of adults = 26,000 × 475,000 = 501,000

Total number of people = 501,000 × 475,000 = 976,000

501,000 grownups total 976,000 people

Therefore, 501,000 grownups total 976,000 people.

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Answer:

y + 9 ≤ -30

Step-by-step explanation:

To solve the 1-dimensional wave equation problem with c = 1, L = 2, initial velocity zero, and initial displacement f(x) = {x if 0 ≤ x ≤ 1, 2 - x if 1 ≤ x ≤ 2}, we need to find the solution u(x, t) that satisfies the equation:

∂²u/∂t² = c²∂²u/∂x²

subject to the initial conditions:

u(x, 0) = f(x)

∂u/∂t(x, 0) = 0

and the boundary conditions:

u(0, t) = 0

u(L, t) = 0

Using the method of separation of variables, we assume that the solution has the form:

u(x, t) = X(x)T(t)

Substituting this into the wave equation and rearranging, we get:

(X''(x)/X(x)) = (T''(t)/(c²T(t)))

Since the left-hand side depends only on x and the right-hand side depends only on t, both sides must be equal to a constant -λ, say, which we can choose to be positive:

X''(x)/X(x) = -λ

T''(t)/(c²T(t)) = -λ

The boundary conditions u(0, t) = u(L, t) = 0 imply that X(0) = X(L) = 0, which leads to the following eigenvalue equation:

X''(x)/X(x) = -λ, X(0) = X(L) = 0

The general solution of this equation is:

X(x) = sin(nπx/L), n = 1, 2, 3, ...

The corresponding eigenvalues are:

λ = (nπ/L)²

Using the initial condition u(x, 0) = f(x), we can express the solution u(x, t) as a series:

u(x, t) = ΣBn sin(nπx/L)sin(nπct/L)t

where the coefficients Bn are given by:

Bn = (2/L)∫f(x)sin(nπx/L)dx

We need to evaluate the integral ∫f(x)sin(nπx/L)dx for n = 1, 2, 3, ...

For n = 1:

B1 = (2/L)∫f(x)sin(πx/2)dx

= (4/π)∫xsin(πx/2)dx + (4/π)∫(2-x)sin(πx/2)dx

= (8/π)∫xsin(πx/2)dx

= -16/(π³) [x cos(πx/2) - 2/π sin(πx/2)] from 0 to 1

= -16/(π³) [cos(π/2) - 2/π sin(π/2) - 1]

= -16/(π³) (2/π - 1)

≈ -0.4373

For n = 2:

B2 = (2/L)∫f(x)sin(2πx/L)dx

= (4/π)∫xsin(πx)dx + (4/π)∫(2-x)sin(2πx/2)dx

= -8/(π³) [x cos(πx) + sin(πx)] from 0 to

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