Which of the following statements could be used in the proof?

Answer:

1.1.1. The common difference is 12

1.1.2. The first term is 30

Step-by-step explanation:

1.1.1. The given quadratic pattern is presented as follows;

The 2nd term = 1

The 3rd term = -16

The 5th term = -14

Let 'd' represent the second difference, we have;

1 + 2d + a =  -16

2·d + a = -16 - 1 = -17

2·d + a = -17...(1)

-16 + 3d + a + 4d + a = -14

7·d + 2·a = -14 + 16 = 2

7·d + 2·a = 2...(2)

Making 'a' the subject of both equation (1) and (2) gives;

a = -17 - 2·d

a = 1 - 7/2·d

∴ -17 - 2·d = 1 - 7/2·d

(7/2)·d - 2·d = 1 + 17

(3/2)·d = 18

d = (2/3) × 18 = 12

The common difference, d = 12

a = -17 - 2·d = -17 - 2 × 12 = -41

1.1.2. Let 'x' represent the first term, we have;

x + a + d = 1

x = 1 - (a + d)

x = 1 - (-41 + 12) = 30

The first term, x = 30

Answer:

It is rounded

Step-by-step explanation:

Answer:

It is already rounded up, unless you have forgotten the decimal point.

Step-by-step explanation:

Answer:

answer my question first please

Step-by-step explanation:

the answer

a) The area of the rectangle has the following inequality: 12 ≤ 6 · x ≤ 36.

b) The value of the variable x has the following inequality: 2 ≤ x ≤ 6.

The area of a rectangle (A) is described by the following formula:

A = b · h

Where:

a) If we know that b = 2 · x and h = 3, then the area of the rectangle is:

A = (2 · x) · 3

A = 6 · x

And the inequality is:

12 ≤ 6 · x ≤ 36

b) And the solutions for the values of x are represented by the following inequality:

2 ≤ x ≤ 6

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Answer:For random variable X~N(3,0.75), what is the probability that X takes on a value within two standard deviations on either side of the mean?

Step-by-step explanation:

The forecasted registrations for years 2 through 12 using exponential

smoothing, with a smoothing constant (α) of 0 and a starting forecast of 4.00 for year 1 are:

Year | Forecasted registrations

------- | --------

2 | 4.00

3 | 4.00

4 | 4.00

5 | 4.00

6 | 4.00

7 | 4.00

8 | 4.00

9 | 4.00

10 | 4.00

11 | 4.00

12 | 4.00

Exponential smoothing is a forecasting method that uses past data to predict future values. The smoothing constant (α) determines how much weight is given to the most recent data. In this case, we are using a smoothing constant of 0, which means that all of the weight is given to the most recent data. This means that the forecasted registrations for all years will be the same as the starting forecast of 4.00.

Here is the formula for exponential smoothing:

```

Forecasted registrations = α * most recent data + (1 - α) * previous forecast

```

In this case, α = 0, so the formula becomes:

```

Forecasted registrations = most recent data

```

Since the most recent data is always 4.00, the forecasted registrations will always be 4.00.

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Answer:

h x c

Step-by-step explanation:

The required solution to the given inequality is x < 7/4.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Given that,
To determine the simplified solution of the inequality 1/2x−1/4 < 5/8.
1/2x−1/4<5/8 .

Adding 1/4 on both sides of the equality,

1/2x < 5 / 8 + 1 / 4
Multiply by 2 on both sides of equality,
1 / 2x < 7 / 8
x < 7 / 4

So, the solution of inequality lies x greater than 7/4, as of the given conditions.

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Answer:

The answer is C because 40% of 1450 is 580.

Answer:

the answer would be 12/5

According to the given information for the normal distribution, we can expect that the corresponding z-score may be negative.

It is given to us that -

The normal distribution has mean 11

The normal distribution has data value of 9

We have to find out if the corresponding z-score is to be positive or negative.

The z-score calculates the number of standard deviations higher or lower the mean, the data point is present.

The formula for z-score is given by -

\(z=\frac{data point - mean}{standard deviation}\)

Although we do not have the value of standard deviation in the question, we can see that the value of

data point - mean = 9-11 = -2

So, we can see that the numerator of the z-value formula is already negative.

Thus, we can expect that the corresponding z-score may be negative according to the information provided for the normal distribution.

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The linear speed of a point on the edge of the wheel is approximately 18.857 feet/second.

To find the linear speed of a point on the edge of the spinning wheel, we need to calculate the distance traveled by that point in one second.

Given:

- Radius of the wheel (r) = 3 feet

- Number of revolutions per second (n) = 6/7 revolutions/second

To convert revolutions per second to radians per second, we need to multiply the number of revolutions by 2π (the conversion factor between revolutions and radians).

n (in radians/second) = (6/7) * 2π

Now, to calculate the linear speed (v) at the edge of the wheel, we can use the formula:

v = r * n

Substituting the values:

v = 3 feet * (6/7) * 2π radians/second

Simplifying:

v ≈ 3 * (6/7) * 2 * 3.14 feet/second

v ≈ 18.857 feet/second

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Answer:

-16

Step-by-step explanation:

A (positive * negative) is a negative. Keep that in mind ^-^

Answer:

-16. a positive multiplied by a negative will always be negative. (4)(-4)= -16. hope this helps

Step-by-step explanation:

- Zombie

Answer:

domain x   [0,4]     range y  [0,64]

Step-by-step explanation:

The equivalent of the expression -(-0.1p+4) is 0.1p-4

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value.

For example: 3(x + 2) and 3x + 6 are equivalent expressions because the value of both the expressions remains the same for any value of x. 3x + 6 = 3 × 4 + 6 = 18. and can also be written as 6(x² + 2y + 1) = 6x² + 12y + 6.

Similarly -( - 0.1p + 4) can be written in another for by multiplying the negative sign with every term in the parentheses.

therefore -1× -0.1p + -1×4 = 0.1p -4

This means -(-0.1p+4) and 0.1p -4 are equivalent

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Answer:

a + 55 =180

a=180-55=125

b = 55 alternate angles

c=a=125 alternate angles

e =125. alternate angles

f=b=55

h=f=55 alternate angles

Step-by-step explanation:

(a) < a = 180-55= 125

(b) < b = 180- 125= 55

(c) < c = 189- 55 = 135

(d) < e = 125

(e) < f = 180-125= 55

(f) < h = 55

~

< a and < c are vertical angles.

< a and < b are adjacent angles.

< b and <h are Alternate interior angles.

< f and 55° are Alternate Exterior angles.

< a and < e are corresponding angles.

~

The probability that a data value is between 56 and 64 is 62.5%. Option D is the correct answer.

The given normal distribution has the following parameters:

Mean = 62

Standard deviation = 4

To find the probability that a data value is between 56 and 64, we need to find the z-scores corresponding to these values. Using the z-score formula, $$z=\frac{x-\mu}{\sigma}$$

Where x is the data value, µ is the mean, and σ is the standard deviation. Substituting the given values, we get:

For x = 56,$$z=\frac{56-62}{4}=-1.5$$For x = 64,$$z=\frac{64-62}{4}=0.5$$

Now we need to find the probability that a data value is between these z-scores using the standard normal distribution table. The table gives the area under the curve to the left of a given z-score. To find the area between two z-scores, we need to find the difference between the areas to the left of the two z-scores.

Using the standard normal distribution table, we find:

Area to the left of z = -1.5 is 0.0668

Area to the left of z = 0.5 is 0.6915

Therefore, the area between z = -1.5 and z = 0.5 is:0.6915 - 0.0668 = 0.6247

Rounding off to the nearest tenth of a percent, we get 62.5%. Hence, the correct option is D.

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Answer:

4

Step-by-step explanation: d d x ( x 2 + 4 y 2 ) = d d x ( 4 )

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Answer:

1/6

Step-by-step explanation:

fraction of water = 1 - (1/2 + 1/3)

)\(\frac{1}{2} + \frac{1}{3}\)

\(\frac{3 + 2}{6}\)

5/6

1 - 5/6

6/6 - 5/6 = 1/6

The original price of the dishes is $80

The sale price is $72

10% was off from the original price to get the sale price

The original price can be calculated as follows

100-10

= 90%

Let y represent the original price

72 ÷ 90/100

= 72 ÷ 0.9

= 80

Hence the original price of the dishes before 10% was taken off is $80

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The value of E[X^2] is approximately 3.81228668939e-14. The correct option is E: 140,000.

Step 1: Find the value of the constant k.

To do this, we integrate the probability density function over its entire range and set it equal to 1:

∫(kx^6e^(-0.02x)) dx = 1

Using integration by parts, we can simplify the integral as follows:

Let u = x^6 and dv = k e^(-0.02x) dx.

Then, du = 6x^5 dx and v = (-50/k) e^(-0.02x).

Applying the integration by parts formula, we have:

∫(kx^6e^(-0.02x)) dx = (-50/k) x^6 e^(-0.02x) - ∫((-50/k) e^(-0.02x) * 6x^5) dx

= (-50/k) x^6 e^(-0.02x) + (300/k) ∫(x^5 e^(-0.02x)) dx

Step 2: Solve the integral for ∫(x^5 e^(-0.02x)) dx.

This integral can be evaluated using integration by parts multiple times or by using other techniques like substitution. For brevity, I'll provide the final result:

∫(x^5 e^(-0.02x)) dx = -6250 e^(-0.02x) (x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32) / (0.04^6)

Step 3: Calculate E[X^2].

Now that we have the integral expression for ∫(kx^6e^(-0.02x)) dx, we can calculate E[X^2] by evaluating the integral:

E[X^2] = ∫(x^2 * kx^6e^(-0.02x)) dx

= k ∫(x^8 e^(-0.02x)) dx

Using the same techniques as before, we integrate the expression and obtain a result that is quite lengthy. For simplicity, I'll provide the final result:

E[X^2] = 8192000000 / (k * 0.0004^9) - 400000000 / (k * 0.0004^8) + 25000000 / (k * 0.0004^7)

Step 4: Calculate the value of k.

To find the value of k, we use the fact that the probability density function must integrate to 1. Therefore:

∫(kx^6e^(-0.02x)) dx = 1

By evaluating the integral, we obtain the following equation:

(50/k) - 300 / (k * 0.0004^6) = 1

Simplifying the equation and solving for k, we find k ≈ 0.0004.

Step 5: Calculate the numerical value of E[X^2].

Substituting the value of k into the expression for E[X^2], we have:

E[X^2] = 8192000000 / (0.0004^10) - 400000000 / (0.0004^9) + 25000000 / (0.0004^8)

First, let's calculate the values of the denominators:

0.0004^10 = 1.048576e+28

0.0004^9 = 2.62144e+24

0.0004^8 = 6.5536e+20

E[X^2] = 8192000000 / 1.048576e+28 - 400000000 / 2.62144e+24 + 25000000 / 6.5536e+20

To perform the division, we can rewrite the expression using scientific notation:

E[X^2] = 7.80517578125e-20 - 1.52587890625e-16 + 3.81228668942e-14

Calculating each term separately:

E[X^2] ≈ -1.52587882837e-16 + 3.81228668942e-14

Adding the terms together:

E[X^2] ≈ 3.81228668939e-14

The correct option for E[X^2] is  E: 140,000.

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The number of possible ways to partition a set A with cardinality n into r subsets with varying cardinalities is given by n! / (n1! * n2! * ... * nr!).

Partitioning a set A into subsets of varying sizes involves calculating the number of possible ways to arrange the elements in the subsets. The formula n! / (n1! * n2! * ... * nr!) accounts for the total number of permutations while considering the specific sizes of each subset.

To understand why this formula works, let's break it down step by step.

Step 1: Counting permutations

The numerator n! represents the total number of permutations of the elements in set A. This is because when we partition a set, the order in which we choose the elements for each subset matters. So, we start with n choices for the first element, (n-1) choices for the second element, and so on, resulting in n! permutations.

Step 2: Accounting for subsets

However, in the numerator, we are overcounting because the order of elements within each subset doesn't matter. To correct for this, we divide by the factorials of the sizes of the subsets (n1!, n2!, ..., nr!). This ensures that each partition is counted only once, irrespective of the order in which the elements are chosen within each subset.

Step 3: Simplifying the formula

Dividing n! by the product of the factorials simplifies the formula, giving us the final result: n! / (n1! * n2! * ... * nr!).

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Answer:

The Y intercept is two

Step-by-step explanation:

The y intercept is the point on a graph where the graph crosses the y axis.

Basically, it is the value of y when x is 0 is (x,y)

Looking at the attached graph, our y intercept is (0,2), meaning that the y-intercept is 2.

The answer is: the Y-INTERCEPT is 2

The value of x that satisfies the equation the same value of x as two-thirds (6 x + 12) = negative 24 is x = -4.

The equation is: (6x + 12) = -24/3 To find the value of x that satisfies this equation, we need to isolate x on one side of the equation.

1. Distribute the 2/3 to the terms inside the parentheses:

2/3 * (6x + 12) = -24/3

Simplifying the left side of the equation:

(2/3 * 6x) + (2/3 * 12) = -24/3

2. Multiply:

(12/3)x + (24/3) = -24/3

Simplifying the equation further: 4x + 8 = -8

3. Now, let's isolate x by subtracting 8 from both sides of the equation:

4x + 8 - 8 = -8 - 8

Simplifying: 4x = -16 4.

To find the value of x, we need to divide both sides of the equation by 4:

(4x)/4 = -16/4

Simplifying: x = -4

Therefore, the value of x that satisfies the equation (6x + 12) = -24/3 is x = -4.

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Answer:

Step-by-step explanation:

Remark

By manipulating parts of right angle triangles, you get 15/x = x/6

Solution

x^2 = 90

x = sqrt(90)

x = sqrt(3*3 * 2 * 5)

x = 3*sqrt(10)