. In 1940 the average size of a U.S. farm was 174 acres. The standard deviation was 45 acres. Define the random variable x in words. X = _________.

We can see the following given data table:

And from this table, we have to find the five-number summary.

The five-number summary gives us:

• The minimum value for the data set

• The first quartile (Q1): this is a value for which 25% of the observations are below it, and 75% of the observations are above it.

• The median (50% of the observations are above (and below) this value.

• The third quartile (Q3): this is a value for which 75% of the observations are below it, and 25% of the observations are above it

• The maximum value for the data set

Then to find those numbers, we can proceed as follows:

1. We have to rewrite the information from the data as a list, and we have to take into account the frequencies for each observation:

And we already have the observations ordered in ascending order. The total of observations is 19 cases.

2. Now we can find the minimum and the maximum values as follows:

• Minimum value = 5

• Maximum value = 14

3. We have to find the median as follows:

Since we have that the total number of observations is 19, and this is an odd number, then the median is the middle value. In this case, below the median, we have 9 values, and above it, 9 values too.

Therefore, the median is equal to 7.

4. Find the first quartile (Q1) and the third quartile (Q3)

The first quartile, roughly speaking, is the median for the first half of the values, and we can say that the third quartile is the median for the second half of the values. Then we have:

We use here the Method of Moore and McCabe in which we do not include the median in finding both values.

Therefore, Q1 = 6, and Q3 = 9.

Therefore, in summary, the five-number summary can be written as follows:

Min = 5

Q1 =

Answer:

12

Step-by-step explanation:

You simply add the coefficients together.
3 + 4 + 5 = 12

For the function  f(x) = 2x + 3 the third iterate x₃  is 37

To find the third iterate, x3, of the function f(x) = 2x + 3, given an initial value of x₀ = 2,

we can apply the function repeatedly.

Starting with x₀ = 2:

x₁ = f(x₀)

= 2(2) + 3

= 7

x₂ = f(x₁)

= 2(7) + 3 = 17

x₃ = f(x₂)

= 2(17) + 3

= 37

Therefore, the third iterate x₃  is 37.

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Answer:

y = 3. last option is correct answer for 2nd question.

Step-by-step explanation:

f(x) just means y.

horizontal asymptote is y = 'something.'

the graph crosses y = 4, so y = 4 cannot be asymptote.

y = 3 is since the graph never quite touches it.

as for ∞, we see that as x approaches -∞, y almost reaches 3. but not quite. also, as x approaches +∞, y approaches +∞.

so the last option is the correct answer.

Answer: There is 1 compounding period for this investment.

Step-by-step explanation: To determine the number of compounding periods, we can use the following formula:

n = (t / p) * m

where:

n = number of compounding periods

t = time period in years

p = payment frequency per year

m = compounding frequency per payment period

In this case, we have:

Principal = $1832

Future value = $2193

Interest rate = 8.1%

Payment frequency = 12 (monthly)

First, let's calculate the time period in years:

t = 1 year / 12 months = 0.0833 years

Next, let's determine the compounding frequency per payment period:

m = 12 (since interest is compounded monthly)

Now we can calculate the number of compounding periods:

n = (t / p) * m = (0.0833 / 1) * 12 = 1

Therefore, there is 1 compounding period for this investment.

To find the number of compounding periods, we can use the formula:

n = (t x f)

where:

n = number of compounding periods

t = time in years

f = frequency of conversion

We are given that the principal is $1832, the future value is $2193, the interest rate is 8.1%, and the frequency of conversion is monthly. We need to find the time in years.

To find the time in years, we can use the formula:

FV = PV x (1 + r/n)^(nt)

where:

FV = future value

PV = present value

r = interest rate

n = number of compounding periods per year

t = time in years

Substituting the given values, we get:

$2193 = $1832 x (1 + 0.081/12)^(12t)

Simplifying this equation, we get:

1.1971^(12t) = 1.1971

Taking the natural logarithm of both sides, we get:

12t x ln(1.1971) = ln(1.1971)

Solving for t, we get:

t = ln(1.1971) / (12 x ln(1.1971))

t = 3 years

Now that we know the time in years, we can find the number of compounding periods:

n = (t x f)

n = (3 x 12)

n = 36

Therefore, the number of compounding periods is 36.

Answer:

No, the two sides are not congruent.

I flipped my whole laptop around to check loll

Answer:

w(3-3+3)

Step-by-step explanation:

distibutitve property

Answer:

9,-17,0

Step-by-step explanation:

An integer is a whole number

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

It must be number 2.

1 and 3 number is wrong as parallelogram don't need have right angle

Answer:

Step-by-step explanation:

a) Let's denote the number of coffees sold as 'x' and the number of cappuccinos sold as 'y'.

The equation that represents the given information is:

2.50x + 3.75y = 222.50

b) To solve the equation, we need to find the values of 'x' and 'y' that satisfy the equation.

Since we have two variables and only one equation, we cannot determine the exact values of 'x' and 'y' independently. However, we can find possible combinations that satisfy the equation.

Let's proceed by assuming values for one of the variables and solving for the other. For example, let's assume 'x' is 40 (number of coffees):

2.50(40) + 3.75y = 222.50

100 + 3.75y = 222.50

3.75y = 222.50 - 100

3.75y = 122.50

y = 122.50 / 3.75

y ≈ 32.67

In this case, assuming 40 coffees were sold, we get approximately 32.67 cappuccinos.

We can also assume different values for 'x' and solve for 'y' to find other possible combinations. However, keep in mind that the number of drinks sold should be a whole number since it cannot be fractional.

Therefore, one possible combination could be around 40 coffees and 33 cappuccinos sold.

The possible formula for the polynomial in discuss whose roots are described as; having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is; P(x) = x^5 -5x⁴-6x³+18x².

The polynomial which is as described in the task content whose roots are as given can be written in its factorised form as follows;

P(x) = (x-3) (x-3) (x) (x) (x+1)

The expanded form is therefore;

P(x) = x^5 - 5x⁴- 6x³+ 18x².

Therefore, the polynomial having roots of multiplicity 2 at x = 3 and x = 0 , and a root of multiplicity 1 at x = − 1 is P(x) = x^5 - 5x⁴- 6x³+ 18x².

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Answer:

S = 2π(3^2) + 2π(3)(8.2) = 67.2π = 211 cm^3

c = 8

d = -5

3 (c + d) [Substitute the values of c & d]

= 3 (8 - 5)

= 3 - 3

= 0

Hope it helps!

꧁✿ ᴿᴬᴵᴺᴮᴼᵂˢᴬᴸᵀ2222 ✬꧂

Answer:

9

Step-by-step explanation:

3(8+(-5))=3 X (8-5)

=3x3

=9

The three successive positive numbers are 3, 4, and 5.

The largest of these 5.

Integers are made up of zeros, natural numbers, and their additive inverses. Except for the fractional part, it can be represented on a number line.

Let's call the smallest of three successive positive numbers x. The following two consecutive integers would then be x + 1 and x + 2.

The product of the two smaller integers (x and x + 1) is eight times that of the largest integer (x + 2). This can be written as an equation:

x(x + 1) = 8 + (x + 2)

By enlarging and simplifying the left side, we get:

\(x^2 + x = x + 10\)

When we subtract x and 10 from both sides, we get:

\(x^2 - 9 = 0\)

After factoring in, we get:

(x - 3)(x + 3) = 0

As a result, x = 3 or x = -3. We can disregard the negative solution because we're seeking positive integers and infer that x = 3.

As a result, the three successive positive numbers are 3, 4, and 5.

The largest of these 5.

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Supplementary angles are those that when summed, add up 180°. Two angles are complementary when they add up 90°.

Vertical angles are opposed by the vertex when two lines intersect each other. Vertical angles have always the same measure.

Now, following that logic, we can evaluate the two options.

1. m(∠A) = 45:

A supplementary angle will sum 180° when added to 45. Let's call that supplementary angle S1:

The measure of a supplementary angle will be 135°.

Similarly, let's call that complementary angle C1:

The measure of a complementary angle will be also 45°.

For the vertical angle, we stated that vertical angles are equal; then it will also be 45°.

For the second option we follow exactly the same process:

1. m(∠A) = 45:

A supplementary angle S2:

180° - w° will be a supplementary angle.

A complementary angle C2:

90° - w° will be a complementary angle.

And for the vertical angle, just like before, it will have exactly the same measure: w°.

Answer:

Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32

Step-by-step explanation:Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32vSamantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32Samantha has 8 quarts of milk.  The ratio of quarts to gallons is 4:1. How many gallons of milk does Samantha have?   x  a. 1 over 32   x  b. begin mathsize 16px style 1 half end style   x  c. 2   x  d. 32

Answer:

$44

Step-by-step explanation:

Hello!

It said that 7 cameras cost $308, right?

If each camera costs the same, it means that 7 cameras with the same value equal $308.
If we use this in an equation, and if x is a variable we want to solve, it would be:

7x = 308.

If 7x = 308, it would be

308/7 =

44.

So, $44 is the answer.

The value of the Integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

The length of the curve described by the function f(x) = 1 + 3x^2 + 2x^3 is to be found. The formula used to find the length of a curve is:

L = ∫(sqrt(1 + [f'(x)]^2))dx where f'(x) is the derivative of f(x)We have to first find f'(x):f(x) = 1 + 3x^2 + 2x^3f'(x) = 6x + 6x^2

The integral becomes:L = ∫(sqrt(1 + [6x + 6x^2]^2))dx = ∫(sqrt(1 + 36x^2 + 72x^3 + 36x^4))dx The integral appears to be difficult to evaluate by hand.

Therefore, we use software like Mathematica or Wolfram Alpha to solve the problem. Integrating the expression using Wolfram Alpha gives:

L = 1/54(9sqrt(10)arcsinh(3xsqrt(2/5)) + 2sqrt(5)(2x^2 + 3x)sqrt(9x^2 + 4))The limits of integration are not given. Therefore, the definite integral  be solved.

We can, however, find a general solution. We use the above formula and substitute the limits of integration.

Then, we subtract the value of the integral at the lower limit from the value of the integral at the upper limit to get the length of the curve.

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The  areas of rectangles D, E and F are 24p units², 14m units² and (15x + 40) units² respectively

Given: rectangles D, E and F as labeled

For rectangle D, the length will be the addition of the four p's

length(L) = p + p + p + p = 4p

width (W) = 6

Area = L × W

Area = 4p × 6 = 24p units²

For rectangle E:

It should be noted that the length will be the addition of 6 and 8. The width is also represented by m.

length(L) = 6 + 8 = 14

width (W) = m

Area = L × W

Area = 14 × m = 14m units²

For rectangle F:

length(L) = 3x + 8

width (W) = 5

Area = L × W

Area = (3x + 8) × 5 = (15x + 40) units²

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Answer:

4 AU

Step-by-step explanation:

20.8 ÷ 5.2 = 4

5.2 increased by 4.

Scale means to get bigger or smaller evenly.

-kiniwih426

Let's denote the amount Jolene invested at 3 percent interest as 'x' dollars. Since she put twice as much in the lower-yielding account, the amount she invested at 9 percent interest would be '2x' dollars.

To calculate the interest earned from each account, we'll use the formula: Interest = Principal × Rate × Time.

For the 3 percent interest account:

Interest_3_percent = x × 0.03

For the 9 percent interest account:

Interest_9_percent = 2x × 0.09

We know that the total annual interest is $3120, so we can set up the equation:

Interest_3_percent + Interest_9_percent = 3120

Substituting the above equations, we have:

x × 0.03 + 2x × 0.09 = 3120

Simplifying the equation:

0.03x + 0.18x = 3120

0.21x = 3120

Dividing both sides of the equation by 0.21:

x = 3120 / 0.21

x = 14857.14

Therefore, Jolene invested approximately $14,857.14 at 3 percent interest and twice that amount, $29,714.29, at 9 percent interest.

Answer:

Step-by-step explanation:

X is the amount invested at 6%

Y is the amount invested at 9%

0.06X + 0.09Y = 4998

X = 2Y

0.06(2Y) + 0.09Y  = 4998

.12Y + 0.09Y = 4998

0.21Y = 4998

21Y = 499800

Y = 499800/21 = 23800

So X = 2*23800 = 47600

$47,600 is invested at 6% and $23800 is invested at 9%

Answer:

3

Step-by-step explanation:

14.50 + 13.00 = 27.50

27.50 x 3 = 82.50

Answer:

6

Step-by-step explanation:

\color{red}{14.5}x+\color{blue}{13}=

14.5x+13=

\,\,\color{purple}{100}

100

-\color{blue}{13}\phantom{=}

−13=

\,\,-\color{blue}{13}

−13

Subtract 13 from both sides

\color{red}{14.5}x=

14.5x=

\,\,87

87

\frac{\color{red}{14.5}x}{\color{red}{14.5}}=

14.5

14.5x

​

=

\,\,\frac{87}{\color{red}{14.5}}

14.5

87

​

Divide both sides by 14.5

x=

x=

\,\,\boxed{6}

6

​

\text{6 people can go to the amusement park.}

6 people can go to the amusement park.

Answer:

x = 58.03°

Step-by-step explanation:

Given:

Solve for x:

1. \(x=cos^{-1}(\frac{9}{17})=58.03\)

Answer:

So, the measure of angle x is equal to 58.03.

Answer:

4.8*10^7

Step-by-step explanation: You chose the right answer. Hint plug it exactly like it is in the calculator and change your mode to scientific notation. That’s what I did

The end behavior of the polynomials are as follows;

(a) y = x³ - 9·x² + 8·x - 14

End behavior; y → ∞ as x → ∞

\({}\)                        y → -∞ as x → -∞

(b) y = -8·x⁴ + 13·x + 800

End behavior; y → -∞ as x → -∞

\({}\)                        y → -∞ as x → ∞

The end behavior of a polynomial is the characteristics of the graph of the polynomial as the input (x-values), tends to plus and minus infinity.

The factors that effect the end behavior of a polynomial are;

The degree of the polynomial, (even or odd)

The sign of the leading coefficient of the polynomial (positive or negative)

The leading coefficient is the coefficient of the term with the highest degree.

(a) The polynomial, function, y = x³ - 9·x² + 8·x  - 14

The specified polynomial is a third degree polynomial, with a positive leading coefficient of 1, the end behavior is therefore;

y tends to positive infinity as x tends to positive infinity

y tends to negative infinity as x tends to negative infinity

End behavior;

y → ∞ as x → ∞

y → -∞ as x → -∞

(b) The polynomial function can be expressed as follows;

y = -8·x⁴ + 13·x + 800

The above polynomial of degree 4 is an even degree polynomial

The leading coefficient of the polynomial is -8, therefore, the leading coefficient is negative

The shape of the graph of the polynomial is therefore ∩ shaped, such that the end behavior is as follows;

y-values approaches negative infinity as x approaches negative infinity

y-values approaches negative infinity as x approaches positive infinity

End behavior;

y → -∞ as x → -∞

y → -∞ as x → ∞

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The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.

The vertical line test supports the definition of a function. That is, every x-value of a function must be paired to a single yy-value. If we think of a vertical line as an infinite set of x-values, then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x-value is only paired to a unique value of y.

If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

If a vertical line intersects the graph in some places at more than one point, then the relation is NOT a function.

With the above illustration,

Graph 3 is not a function using vertical test because it has infinitely many solutions

Graph 4 is not a function because the vertical cuts the graph and intersect at a points

Graph 5 is a constant function because it has a repeated value of x and a constant y value

Graph 6 is not a function because the x-values which is the domain is repeated for different values of y

Graph 7 is not a function because the vertical line cuts the graph at two-point

Graph 8 is a function because it has one point intersection and each value of x have a corresponding value of y

Answer:

0

Step-by-step explanation:

Step 1:

- 4k + 1 = 1 + k + 3k     Equation

Step 2:

- 4k + 1 = 1 + 4k     Add

Step 3:

1 = 1 + 8k       Add 4k on both sides

Step 4:

0 = 8k     Subtract 1 on both sides

Answer:

k = 0

Hope This Helps :)

The values of f(x) for the given x - values rounded to 4 decimal places are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013 respectively

Given the function :

Substitute the given value of x to obtain the corresponding f(x) values :

x = -0.6

f(x) = (tanπ(-0.6))/7(-0.6) = 0.0078358

x = -0.51

f(x) = (tanπ(-0.51))/7(-0.51) = 0.0078350

x = -0.501

f(x) = (tanπ(-0.501))/7(-0.501) = 0.001967

x = -0.5

f(x) = (tanπ(-0.5))/7(-0.5) = 0.001959

x = -0.4999

f(x) = (tanπ(-0.4999))/7(-0.4999) = 0.001958

x = 0.499

f(x) = (tanπ(-0.499))/7(-0.499) = 0.001951

x = -0.49

f(x) = (tanπ(-0.49))/7(-0.49) = 0.00188

x = -0.4

f(x) = (tanπ(-0.4))/7(-0.4) = 0.00125

Therefore, values which complete the table are 0.0078, 0.0078, 0.0020, 0.0020, 0.0019 and 0.0013

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