Dan cut ribbon into different leghts To wrap gifts. He made a line plot to display his data

The given equation is a recursive formula where a subscript i equals the product of a subscript i-1 and 2, with the initial value of a subscript 1 being -4a.

The equation represents a recursive relationship between the terms of the sequence. Starting with the initial term, a subscript 1, the subsequent terms are determined by multiplying the previous term, a subscript i-1, by 2. This recursive formula can be written as a subscript i = a subscript i-1 * 2.

Given that a subscript 1 = -4a, we can use this initial value to find the subsequent terms of the sequence. To calculate a subscript 2, we substitute i = 2 into the formula:

a subscript 2 = a subscript 2-1 * 2 = a subscript 1 * 2 = -4a * 2 = -8a.

Similarly, for a subscript 3:

a subscript 3 = a subscript 3-1 * 2 = a subscript 2 * 2 = -8a * 2 = -16a.

By applying the recursive formula repeatedly, we can generate the terms of the sequence. Each term is obtained by multiplying the previous term by 2.

Learn more about recursive formula here:

https://brainly.com/question/1470853

#SPJ11

Given

The formula of the volume of a cylinder

Substitute the given to the volume

The volume of a cylinder with a radius of 5 and a height of 3 is

\(\Large\underline{\rm Solution :- }\)

According to the Question ,

\(\implies Volume = \pi r^2 h \)

And ,

Therefore ,

\(\implies Volume = \pi r^2h \\\\\implies Volume = \pi \times (2x + 4)^2 \times (-3x ) \\\\\implies Volume = \pi ( 4x^2 + 16x + 16 ) (-3x) \\\\\implies \underline{\boxed{Volume = \pi ( -12x^3 - 48x - 48 ) }}\)

Answer:

The most common form of explicit proof in high school geometry is two column proof consists of various five parts they are; the given, the proposition, the statement column, the reason column, and the diagram ( if its given).

Answer:

Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

Step-by-step explanation:

The probability of getting a head and a number greater than 5 i.e, independent events is 0.0833.

A coin is tossed and a die is rolled. These are two independent events. Two events are defined as independent if the outcome of one event has no effect on the outcome of another event. The probability is calculated by multiplying two independent probabilities together, i.e, P(A and B) = P(A) x P(B)

We have, Let us assume two independent events be ,

A : A coin is tossed and the head is thrown.

B : A die is rolled, and a number greater than 5 occurs.

Total possible outcomes when a coin tossed = 2 ={ H ,T }

Total possible outcomes when a die rolled = 6 = { 1,2,3,4,5,6} .

We have to determine probability of getting a head and a number greater

than 5.

Probability of getting the head on toss a coin, P(A) = 1/2

Probability of occuring a number greater than 5 on rolling a die = P(B) = 1/6

So, the probability of getting a head on coin and a number greater than 5 on die =P(A)×P(B)

=(1/2)× 1/6 = 1/12=0.0833

Hence, required probability is 0.0833.

To learn more about probability, visit:

https://brainly.com/question/13604758

#SPJ4

Answer:

y=2x is similar to y=2x-7 in such way that they share the same slope of 2/1. y=2x is different from y=2x-7 in such a way that they have different y-intercepts, as y=2x automatically has a y-intercept of 0 (0,0), while y=2x-7 has a y-intercept of -7 (0,-7).

Step-by-step explanation:

y=mx+b

y and x are variables, dependent and independent

m is the slope (coefficient)

b is the y-intercept (constant)

Step-by-step explanation:

\((1) \: \: \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } \)

Note that the 1st two factors can be combined:

\( \sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } = \sqrt[3]{5 \times \frac{2}{5} } = \sqrt[3]{2} \)

We also know that the numerator in the 3rd factor can be rewritten as

\( \sqrt[3]{64} = 4\)

And the numerator in the 4th term can be rewritten as

\( \sqrt[6]{9} =({( {3})^{2} })^{ \frac{1}{6} } = \sqrt[3]{3} \)

So let's rewrite expression #1

\( \sqrt[3]{2} \times \frac{4}{ \sqrt[3]{3} } \times \frac{ \sqrt[3]{3} }{ \sqrt[3]{2} } \)

Notice that all the radical terms cancel out except for 4 therefore,

\(\sqrt[3]{5} \times \sqrt[3]{ \frac{2}{5} } \times \frac{ \sqrt[3]{64} }{ \sqrt[3]{3} } \times \frac{ \sqrt[6]{9} }{ \sqrt[3]{2} } = 4\)

Answer:

3/8 or 0.375mph.

Step-by-step explanation:

All you have to do for this is divide one fourth by two thirds. This way, you get the units to work out as well.

\(\frac{1}{4}/\frac{2}{3}=\frac{1}{4}*\frac{3}{2}=\frac{3}8=0.375mph\)

The probability that exactly 10 of the 20 women have dark eyes is 0.2051.

The theory used in this question is the binomial probability formula, which is used to calculate the probability of a certain number of successes in a given number of trials.

The steps for this process are as follows

Step 1: Calculate the binomial formula: (n!)/(x!(n-x)!) * p^x * (1-p)^(n-x),

where n is the number of trials (in this case, 20), x is the number of successes (10), p is the probability of a success (0.40 in this case), and n-x is the number of failures (10).

Step 2: Plug the values into the formula: (20!)/(10!(20-10)!) * 0.40^10 * (1-0.40)^(20-10)

Step 3: Simplify the formula: (20*19*18*17*16*15*14*13*12*11) / (10*9*8*7*6*5*4*3*2*1) * 0.40^10 * 0.60^10

Step 4: Calculate the result: 0.2051

To learn more about binomial probability refer :

https://brainly.com/question/29350029

#SPJ4

Answer : \(22.000\) x \(10x^{3}\)

Step-by-step explanation:

Answer:22 x 10^3

Step-by-step explanation:

Answer:

Step-by-step explanation:

If the variables x and y vary inversely, this is expressed as;

x ∝ 1/y

x = k/y

k is the constant of proportionality

Given;

x = 7/2 and y = 3/5

Substitute;

7/2 =k/(3/5)

Cross multiply

k = 7/2 * 3/5

k = 21/10

Substitute the value of k into the formula;

x = k/y

x = (21/10)/y

x = 21/10 * 1/y

x = 21/10y

Hence the equation relating x and y is x = 21/10y

The probability of rolling one of these five numbers is 5/37.

Suppose you roll a special 37-sided die. The probability that one of the following numbers is rolled is as follows:

35 | 25 | 33 | 9 | 19.

The total number of sides of a die is 37. As a result, there are 37 numbers in the die.

Rolling one of the 5 given numbers implies that you can select either 35 or 25 or 33 or 9 or 19.

Therefore, the probability of rolling any of these numbers is:

1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 + 1 / 37 = 5 / 37

So, the probability of rolling one of these five numbers is 5/37.

To know more about probability of rolling dies: https://brainly.com/question/30369361

#SPJ11

The length of the rectangle is approximately 41.34 inches.

Let's assume the width of the rectangle is represented by the variable w. According to the given information, the length of the rectangle is four less than twice the width, which can be expressed as 2w - 4.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 128 inches. Since a rectangle has two pairs of equal sides, we can set up the equation:

2w + 2(2w - 4) = 128.

Simplifying the equation, we get:

2w + 4w - 8 = 128,

6w - 8 = 128,

6w = 136,

w = 22.67.

So, the width of the rectangle is approximately 22.67 inches. To find the length, we can substitute this value back into the expression 2w - 4:

2(22.67) - 4 = 41.34.

Therefore, the length of the rectangle is approximately 41.34 inches.

In summary, the length of the rectangle is approximately 41.34 inches. This is determined by setting up a system of equations based on the given information: the perimeter of the rectangle being 128 inches and the length being four less than twice the width.

By solving the system of equations, we find that the width is approximately 22.67 inches, and substituting this value back, we obtain the length of approximately 41.34 inches.

To know more about length refer here:

https://brainly.com/question/2497593

#SPJ11

1) x = 5y - 30  

2) x = - 1.6y + 3.3

im assuming these are 2 different questions

Start with the equation:

x - 5y= -30

add 5y to both sides:

x = 5y - 30

Your answer is x = 5y - 30  

Start with the equation:

3x+5y=10

subtract 5y from both sides:

3x = -5y + 10

divide by 3 to get x singular

x = - 1.6y + 3.3

Your answer is x = - 1.6y + 3.3

Hope this helps :)

The number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To determine this:

Each cow has 4 legs, so the cows have 3 cows * 4 legs/cow = 12 legs.

Each chicken has 2 legs, so the chickens have 8 chickens * 2 legs/chicken = 16 legs.

We know the total number of farm animal legs is 40 legs.

So the number of duck legs can be calculated by subtracting the number of cow legs and chicken legs from the total number of farm animal legs: 40 legs - 12 legs - 16 legs = 12 legs.

Since each duck has 2 legs, the number of ducks on the farm is 12 legs / 2 legs/duck = 6 ducks.

To learn more about subtracting, visit:

brainly.com/question/2346316

#SPJ4

She used 29.8 feet of fencing for the fence -> The circumference of the circular garden is 29.8ft

Formula for circumference : 2πr

So, the radius is equal to : 29.8 : 2 : π = 4.74281730414... (round to 4.7)

Recheck : 4.7 x 2π = 29.5309709437... (close to 29.8)

Answer: I believe it is a. Sorry if I am incorrect

Step-by-step explanation:

Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

For more such questions on diameter visit:

https://brainly.com/question/28162977

#SPJ8

Answer:

c

Step-by-step explanation:

i took a test on it

Dan Hostetler purchases 2,000 shares of Ballon Synergy stock at $4.10 per share. Thus, The total cost of stock including the commission is $15917.

Stocks are types of security to shareholders that represent fractional ownership of equity in any organization.

Dan Hostetler purchases 2,000 shares of Ballon Synergy stock at $4.10 per share. He also purchased 500 shares of Matell Scientific at $26.76 per share.

We have a number of shares at $44.41 per share = 100

Number of shares at $19.08 per share = 600

Total number of shares = 700

Broker's charges per share = $0.04

Hence, The total cost of the stock including the commission

= Cost of stock + commission

= (100 × 44.41) + (600 × 19.08) + (700 × 0.04)

= 15,917

Thus, the total cost of stock including the commission is $15917.

Learn more about stocks here;

https://brainly.com/question/14649952

#SPJ1

The force of the block on the rope is 35 N and it's downward. This force is acting downwards because the block is being lowered with a downward acceleration of `2.8 m/s²` by means of a rope.Thus, the correct option is 35 N. down.

The force of the block on the rope is the force due to gravity acting on it. This force is given by

`F=mg`,

where m is the mass of the block, g is the acceleration due to gravity and F is the force due to gravity acting on the block.In this case, the block is being lowered with a downward acceleration of

`2.8 m/s²`.

The acceleration of the block is given as

`a=2.8 m/s²`.

We need to find the force of the block on the rope. The force of the block on the rope is the force due to gravity acting on the block. The mass of the block is

`5-kg`.

Therefore, we can find the force due to gravity acting on the block as follows:

F = mg = 5 kg × 9.8 m/s² = 49 N

The force of the block on the rope is `49 N`.

This force is acting downwards because the block is being lowered with a downward acceleration of `2.8 m/s²` by means of a rope.Thus, the correct option is 35 N. down.

To know more about acceleration visit:

https://brainly.com/question/2303856

#SPJ11

Each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

1. Horizontal Shift (c):
If there is a horizontal shift, the equation becomes y = (x - c)^3.
For example, if there is a shift of 2 units to the right, the equation would be y = (x - 2)^3.

2. Vertical Shift (d):
If there is a vertical shift, the equation becomes y = x^3 + d.
For example, if there is a shift of 3 units upwards, the equation would be y = x^3 + 3.

3. Vertical Stretch (a):
If there is a vertical stretch or compression, the equation becomes y = a * x^3.
For example, if there is a vertical stretch by a factor of 2, the equation would be y = 2 * x^3.

4. Reflection (along the x-axis):
If there is a reflection along the x-axis, the equation becomes y = -x^3.
This flips the graph of the original function upside down.

5. Reflection (along the y-axis):
If there is a reflection along the y-axis, the equation becomes y = (-x)^3.
This mirrors the graph of the original function.

6. Combined Transformations:
If there are multiple transformations, we can apply them in the order they are given. For example, if there is a vertical stretch by a factor of 2 and a horizontal shift of 3 units to the right, the equation would be y = 2 * (x - 3)^3.

Remember, each transformation affects the shape and position of the graph. It is important to carefully consider the order of the transformations and their impact on the equation.

To know more about equation here:

brainly.com/question/29292690

#SPJ11

Answer:

20

Step-by-step explanation:

2 in 529 is in the tens place - 10

So if 2 is in the tens place, we have 20 as the value of 2.

Answer:

the answer to ur question would be 20 B)

The solution to the inequality is the interval notation:

(-∞, 3] ∪ [4, +∞)

To solve the rational inequality:

x^2 - 4x - 7x + 12 ≤ 0

We can start by factoring the quadratic expression:

(x - 4)(x - 3) ≤ 0

Now, we can determine the critical points by setting each factor equal to zero:

x - 4 = 0 => x = 4

x - 3 = 0 => x = 3

These critical points divide the number line into three intervals: (-∞, 3), (3, 4), and (4, +∞).

To determine the sign of the inequality within each interval, we can choose test points. For example, we can choose x = 0 for the interval (-∞, 3):

(0 - 4)(0 - 3) ≤ 0

(-4)(-3) ≤ 0

12 ≤ 0

Since 12 is not less than or equal to 0, the inequality is not satisfied for x = 0 within this interval.

Next, we can choose x = 3 for the interval (3, 4):

(3 - 4)(3 - 3) ≤ 0

(-1)(0) ≤ 0

0 ≤ 0

Since 0 is equal to 0, the inequality is satisfied for x = 3 within this interval.

Finally, we can choose x = 5 for the interval (4, +∞):

(5 - 4)(5 - 3) ≤ 0

(1)(2) ≤ 0

2 ≤ 0

Since 2 is not less than or equal to 0, the inequality is not satisfied for x = 5 within this interval.

Therefore, the solution to the inequality is the interval notation:

(-∞, 3] ∪ [4, +∞)

for such more question on inequality

https://brainly.com/question/17448505

#SPJ8