What is the value of x ?

Answer: To find the explicit formula for the geometric sequence with the recursive formula an = 2an-1 and a1 = 1/8, we can use the following steps:

First, we can write out the first few terms of the sequence using the recursive formula:

a1 = 1/8

a2 = 2a1 = 2/8 = 1/4

a3 = 2a2 = 2/4 = 1/2

a4 = 2a3 = 2/2 = 1

a5 = 2a4 = 2

We can see that the common ratio between any two consecutive terms is 2, so we can write:

a2/a1 = 2

a3/a2 = 2

a4/a3 = 2

a5/a4 = 2

In general, we can write the ratio of any two consecutive terms as:

an/an-1 = 2

We can use this to find an expression for an in terms of a1:

a2/a1 = 2

a2 = 2a1

a3/a2 = 2

a3 = 2a2 = 2(2a1) = 4a1

a4/a3 = 2

a4 = 2a3 = 2(4a1) = 8a1

a5/a4 = 2

a5 = 2a4 = 2(8a1) = 16a1

In general, we can write:

an = 2^(n-1) * a1

Substituting a1 = 1/8, we get:

an = 2^(n-1) * (1/8) = 1/(2^(8-n))

Therefore, the explicit formula for the geometric sequence is:

an = 1/(2^(8-n))

Step-by-step explanation:

3. If triangle ABC was reflected over the x-axis, what would be the coordinate of B'?

When you reflect over the x-axis, you will flip the sign for the y-coordinate. If you reflect over the y-axis, you will flip the sign for the x-coordinate.

In this case, you are reflecting point B (4 , 3) over the x-axis, which will flip the x-coordinate sign to B' (-4 , 3)

D) (-4 , 3)

2. Rotate this figure 270 degrees clockwise

Clock-wise mean you are rotating turning right. 180° is half way, and so it will be D), as 180° is the 3rd option, and then a extra 90° will become D).

Answer:

(4, -3)

last option

Step-by-step explanation:

If a point is reflected over the x-axis then (x, y) → (x, -y)

B = (4, 3)

Therefore, B' = (4, -3)

The original arrowhead is pointing south (down).

If the arrowhead is rotated 270° clockwise, then it will point to the east (right).  So the solution is the last option.

Answer: The percent was 12.5%

Answer:

Right.

Step-by-step explanation:

The answer is right on edge2020 I just took the test.

The direction in which the parabola will open is; To the right

We are given;

The vertex of the parabola is at (0, 0)

Directrix of the parabola is x = -4

We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;

y² = 4ax

Thus, we can conclude that the parabola opens towards the right.

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\(f(x)=x^2+4x-21\\f(x)=(x+7)(x-3)\)

These are x-intercepts form. So the answer is (x+7)(x-3).

Answer:

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Answer:

Slope = \(\frac{3}{2}\)

Step-by-step explanation:

Slope = \(\frac{6}{4} =\frac{3}{2}\)

The rate at which calories are burned was gotten by finding the slope of the graph which gives; 4 calories per minute

To get the slope of a linear graph, we will take two coordinates and make use of the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

The two coordinates we will pick for this slope are;

(10, 40) and (20, 80)

Thus;

Slope = (80 - 40)/(20 - 10)

Slope = 40/10

Slope = 4

Since the y-axis represents calories burned and the x-axis represents minutes of exercise, then we can say that;

Rate at which  calories get burned by bike riding = 4 calories per minute

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Answer:

17

Step-by-step explanation:

Answer:

When the imposter is sus da da da da da da dada ding

Step-by-step explanation:

Answer:

13) x=n-11

15) x=3*10

Step-by-step explanation:

I used x as the variable. The questions are pretty straightforward. They are asking you to put the terms in the description on the right side of the equation. The questions = x. That was probably confusing, but it is correct. I hope this helped!

Product of 3 and 10 and12

The steps involved in deriving the answers for the given questions are as follows: 1. Apply the covariance rules to prove the variance rules. 2. Substitute the linear relationship between X and Y into the formula for correlation coefficient (rhoxy) to prove that rhoxy equals 1. 3. Calculate the expected values (E(X), E(Y)), variances (Var(X), Var(Y)), covariance (Cov(X, Y)), conditional expected value (E(X | Y < 3)), and conditional variance (Var(X | Y < 3)) using the provided probability distribution.

1. Variance Rules:

To prove each of the variance rules using the covariance rules, start with the fact that variance equals the covariance of a variable with itself: \(Var(X) = Cov(X, X).\)

a) \(Var(X+Y) = Var(X) + Var(Y) + 2Cov(X,Y)\)

Using the covariance rules, expand \(Cov(X+Y, X+Y)\) and simplify to derive the variance rule.

b)\(Var(bX) = b^2 * Var(X)\)

Applying the covariance rules and simplifying \(Cov(bX, bX)\) yields the variance rule.

c) \(Var(X+b) = Var(X)\)

Using the covariance rules, show that \(Cov(X, b) = 0\), which leads to \(Var(X+b) = Var(X).\)

d) \(Var(b) = 0\)

Apply the covariance rules to demonstrate that Cov(b, b) = 0, resulting in \(Var(b) = 0.\)

2. Linear Relationship:

Substitute Y = α + βX into the formula for correlation coefficient (rhoxy) and use the covariance rules to prove that rhoxy equals 1. The covariance term will simplify to the product of the variances of X and Y, and the denominator will simplify to the square root of the product of the variances of X and Y.

3. Probability Distribution:

Given the probability distribution of X and Y, calculate the expected values (E(X), E(Y)), variances (Var(X), Var(Y)), covariance (Cov(X, Y)), conditional expected value (E(X | Y < 3)), and conditional variance (Var(X | Y < 3)) using the formulas for discrete random variables. Compute the sums and weighted averages as necessary based on the provided probabilities for each outcome.

By following these steps, you will be able to derive the answers for the given questions regarding expected values, variances, covariance, correlation coefficient, and conditional expectations and variances.

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Answer:

21

Step-by-step explanation:

We require to calculate

\(\frac{3}{25}\) of 175

= \(\frac{3}{25}\) × 175 ( cancel 25 and 175 by 25 )

= 3 × 7

= 21

That is 21 dogs had red collars

The curve is y = In(sec(x)) and we have to find its length. We are given the range as 0 ≤ x ≤ π/4. So, the formula for the length of the curve is given as:

To solve for the length of the curve of y = In(sec(x)), we use the formula,

`L = ∫[a,b] √[1+(f′(x))^2] dx`.Where, `a = 0` and `b = π/4`. And `f′(x)` is the derivative of `In(sec(x))`.

We know that:`f′(x) = d/dx[In(sec(x))]`

Using the formula of logarithm differentiation, we can write the above equation as:

`f′(x) = d/dx[In(1/cos(x))]`

So,`f′(x) = -d/dx[In(cos(x))]`

Therefore,`f′(x) = -sin(x)/cos(x)`

Substituting the values, we get:

`L = ∫[a,b] √[1+(f′(x))^2] dx`

`L = ∫[0,π/4] √[1+(-sin(x)/cos(x))^2] dx`

`L = ∫[0,π/4] √[(cos^2(x)+sin^2(x))/(cos^2(x))] dx`

`L = ∫[0,π/4] sec(x) dx`

Now, `L = ln(sec(x) + tan(x)) + C` where `C` is a constant.

We calculate the constant by substituting the values of `a = 0` and `b = π/4`:

`L = ln(sec(π/4) + tan(π/4)) - ln(sec(0) + tan(0))`

`L = ln(√2 + 1) - ln(1 + 0)`

`L = ln(√2 + 1)`

Thus, the exact length of the curve is `ln(√2 + 1)` units.

Thus, the exact length of the curve of y = In(sec(x)), 0≤x≤π/4 is `ln(√2 + 1)` units.

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The values of d that make the inequality 9d > 9 true are given as follows:

2, 4, 11.

Hence the equivalent inequality is given as follows:

d > 1.

The inequality in the context of this problem is defined as follows:

9d > 9.

To solve the inequality, we solve it similarly to an equality, isolating the desired variable d, hence the solution is given as follows:

d > 9/9

d > 1.

The > symbol means that the solution is composed by values that are greater than 1, hence the options are 2, 4, 6 and 11.

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Answer:

Step-by-step explanation:

Correct choice is B

Answer:

Can not be determined

Step-by-step explanation:

regularly, you would +20 to both sides, but without a full =, you cant solve. If the equation is 6x-20=0, x would equal 3 2/6.

Hope this helps!

Answer:

Nominal decisions can be broken into two distinct categories: dichotomous decisions and polychotomous decisions.

The error of posting $50 as $500 can be detected by comparing the recorded amount to the expected amount. Here are the steps to detect this error:

1. Calculate the expected amount: Determine the correct amount that should have been posted. In this case, the expected amount is $50.

2. Compare the recorded amount with the expected amount: Check the posted amount and compare it to the expected amount. If the recorded amount shows $500 instead of $50, then an error has occurred.

3. Identify the discrepancy: Recognize that the recorded amount of $500 is significantly higher than the expected amount of $50.

4. Investigate the source of the error: Look for the cause of the error. It could be a data entry mistake, a typo, or a misunderstanding.

5. Take corrective actions: Once the error is detected, rectify it by posting the correct amount of $50. Additionally, ensure that the source of the error is addressed to prevent similar mistakes in the future.

By following these steps, the error of posting $50 as $500 can be detected, corrected, and prevented from happening again.

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Using Normal Distribution, the safety stock for a 95% service level is 209 units, and the reorder point is 2588 units.

To calculate the safety stock and reorder point, we need to use the following formulas:

Safety stock = z × σ × √(L)

Reorder point = d × L + SS

Where:

z = Z-score corresponding to the desired service level (95%)

σ = Standard deviation of daily demand

L = Lead time in days

d = Average daily demand

SS = Safety stock

We are given that the average daily demand is 250 units and the standard deviation of daily demand is 40 units. The lead time has an average of 10 days and a standard deviation of 3 days.

First, we need to find the Z-score for a 95% service level, which corresponds to 1.65.

Next, we can calculate the safety stock using the formula:

Safety stock = 1.65 × 40 × √(10) = 208.8 units (rounded to the nearest tenth)

Finally, we can calculate the reorder point using the formula:

Reorder point = 250 × 10 + 208.8 = 2588 units (rounded to the nearest whole number)

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The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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The geometric series which represent the provided number in the fraction form is,

\(\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}\)

Geometric sequence is the sequence in which the next term is obtained by multiplying the previous term with the same number for the whole series.

The fraction number given in the problem is,

\(n=0.4444.....\)

Let's break the given number into the parts as,

\(n=0.4+0.04+0.004+0.0004+.....\)

The decimal number 0.4 is written as 4/10. Similarly, 0.04 can be written as 4/100. Thus, the above number can also be written as,

\(n=\dfrac{4}{10}+\dfrac{4}{100}+\dfrac{4}{1000}+\dfrac{4}{10,000}+\cdots\)

Hence, the geometric series which represent the provided number in the fraction form is,

\(\dfrac{4}{10}, \dfrac{4}{100},\dfrac{4}{1000},\dfrac{4}{10,000}\)

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Answer:

it b

Step-by-step explanation:just did the quiz

The number of adult tickets that were sold would be = 435 tickets.

A ticket is an official document that gives an individual access to an event.

The cost of adult tickets = $8

The cost for student tickets = $4

The number of students tickets sold = X

The number of adults tickets sold = X +30

The told number of tickets sold = 840

To find X;

X + X + 30 = 840

2x + 30 = 840

2x = 840-30

2x = 810

X = 810/2

X = 405

Therefore, the number of tickets sold for adults = 405 +30 = 435 tickets.

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Answer:

27 Units

I just took the test and got 100 percent

The area of triangle DFG is 27 square units.

The area of a triangle with 3 sides can be calculated with the help of the Heron's formula according to which, the area of a triangle is √[s(s-a)(s-b)(s-c)], where a, b, and c, are the three different sides and 's' is the semi perimeter of the triangle that can be calculated as follows: semi perimeter = (a + b + c)/2

If a triangle has 3 equal sides, it is called an equilateral triangle. The area of an equilateral triangle can be calculated using the formula, Area = a2(√3/4), where 'a' is the side of the triangle.

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Answer:

\(<A=106\)

Step-by-step explanation:

The given figure is an isosceles trapezoid, this means that the two non-parallel sides in the trapezoid are congruent. One of the properties of an isosceles triangle is that opposite angles are supplementary. This means that the sum of angles opposite each other in an isosceles trapezoid is (180) degrees. One can apply this here by stating the following,

\(<A+<C=180\)

Substitute,

\(<A+74=180\)

Inverse operations.

\(<A=106\)

Answer:

(6.25\(\pi\) + 25)cm is the exact answer

44.625 cm is an approximation

Step-by-step explanation:

c = circumference (perimeter)

d = diameter

C = \(\frac{\pi d}{4}\)

C = \(\frac{25\pi }{4}\) = 6.25\(\pi\) This is the exact answer

That would be the curved part of the pi.  Then we need to add the 2 sides which would be \(\frac{25}{2}\) + \(\frac{25}{2}\) = \(\frac{50}{2}\) = 25  The sides are the length of the radius which is half of the diameter.

(6.25\(\pi\) + 25)cm is the exact answer

If we use 3.14 for \(\pi\) The approximate answer would be:

6.25(3.14) + 25

19.625 + 25

44.625 cm is an approximation

Answer: 9

Step-by-step explanation:

Answer:

The volume is 25cm

Step-by-step explanation: