Consider the first six terms of this sequence: 3,6,12,24,48,96,.......... What would be the sum of the first 19 terms of this sequence? *
393,216
786,429
1,572,861
1,162,261,467​

Answer:

Step-by-step explanation:Let's first substitute the values of A, P, and T in the formula A = P(1 + r)^T.

Given: A = 1,000,000; P = 10,000; T = 2

1,000,000 = 10,000(1 + r)^2

Now let's express it as a quadratic equation. First, divide both sides by 10,000:

100 = (1 + r)^2

Next, expand the square:

100 = 1 + 2r + r^2

Finally, rearrange to form the quadratic equation:

r^2 + 2r - 99 = 0

To represent the formula A = P(1 + r) as a quadratic equation with the given values, we substitute A = 1,000,000, P = 10,000, and T = 2. The resulting equation is 10,000r - 9,000,000 = 0.

To express the formula A = P(1 + r) as a quadratic equation, we substitute the given values for A, P, and T.

Given:

Substituting these values into the formula:

1,000,000 = 10,000(1 + r)

To express this equation as a quadratic form, we can expand the parentheses:

1,000,000 = 10,000 + 10,000r

Now, let's move all the terms to one side to form a quadratic equation:

10,000r - 9,000,000 = 0

Therefore, the quadratic equation that represents A = P(1 + r) with the given values is 10,000r - 9,000,000 = 0.

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A good practice to remember when adding transitions to a presentation is to ensure that they are purposeful, consistent, and enhance the overall flow of the presentation.

Purposeful: Use transitions to guide the audience through your key points and ideas, making sure they complement the content and contribute to the overall message.
Consistent: Maintain a consistent style of transitions throughout your presentation to maintain a cohesive look and feel. Avoid using too many different types of transitions, as this may be distracting.
Enhance flow: Transitions should help create a smooth flow between slides and ideas, making it easy for the audience to follow your presentation. Avoid using abrupt or overly flashy transitions that may interrupt the natural progression of your content.

finally, Test your presentation with the transitions to make sure they enhance the overall flow and comprehension of your message.

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the surface area of the cylinder is approximately 471 dm².

Now, For the surface area of the cylinder, we need to find the lateral area  and the area of the two circular bases.

Since, The formula for the lateral area of a cylinder is

L = 2πrh,

where r is the radius of the cylinder and h is the height.

In this case, the diameter is 10 dm,

So the radius is 5 dm.

And the height is also 10 dm.

Therefore, the lateral area is:

L = 2πrh

L = 2π(5 dm)(10 dm)

L = 100π dm²

The formula for the area of a circle is

A = πr²,

where r is the radius.

In this case, the radius is 5 dm,

So the area of each base is:

A = πr²

A = π(5 dm)²

A = 25π dm²

To find the total surface area, we add the lateral area and the area of the two bases:

SA = 2(Area of Base) + Lateral Area

SA = 2(25π dm²) + 100π dm²

SA = 50π dm² + 100π dm²

SA = 150π dm²

Substitute pi as 3.14, we can calculate:

SA ≈ 150(3.14) dm²

SA ≈ 471 dm²

Therefore, the surface area of the cylinder is approximately 471 dm².

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Answer:

did u get the answers to this exam?

Step-by-step explanation:

The rate at which the volume of the cube is changing is 1200 in³/seconds.

Volume is the space occupied by a solid object.

To calculate the rate at which the volume of the cube is changing, we use the formula below.

Formula:

Where:

From the question,

Given:

If, the volume of a cube is V = L³,

Then,

Substitute these values into equation 1

Hence, the rate at which the volume is changing is 1200 in³/seconds.
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Answer:

Answer: I don't know ...

An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

plus a square and minus a square gets cancel

b^2 + b^2

since they are like terms they can be added

2b^2

Answer:

2b^2

Step-by-step explanation:

according to the question equation is

(a^2 + b^2 ) - (a^2 - b^2)

a^2 + b^2 - a^2 + b^2

= b^2 + b^2

like terms can be added

+2b^2

Answer:

C

Step-by-step explanation:

if your suitcase already weighs 8 lbs and the limit is 45:

assume x is how much additional weight you can have

x+8 has to be ≤ 45.

subtract 8 for both sides

x≤37

Answer:The amount of a 80% acid solution that must be mixed with a 55% solution to produce 600 mL of a 60% solution can be calculated using a simple algebraic equation. Let x represent the amount of the 80% acid solution in mL that needs to be mixed with the 55% solution.

The equation can be set up as follows:

0.80x + 0.55(600 - x) = 0.60(600)

Step-by-step explanation: The left-hand side of the equation represents the total amount of acid in the mixture. The first term, 0.80x, represents the amount of acid from the 80% solution, and the second term, 0.55(600 - x), represents the amount of acid from the 55% solution. The right-hand side of the equation represents the total amount of acid in the final 60% solution, which is 60% of 600 mL.

By solving this equation for x, we can determine the amount of the 80% acid solution that needs to be mixed with the 55% solution. Once we have the value of x, we can then calculate the amount of the 55% solution by subtracting x from 600 mL.

Internal Link: For a verified answer on a similar topic, check out this link: https://brainly.com/question/1234567 intext:Answer Expert Verified.

Let x=amount of 80% solution needed

Then 600-x=amount of 30% solution needed

Now we know that the pure acid in the 80% solution (0.80x) plus the amount of pure acid in the 30% solution ((0.30)(600-x)) has to equal the amount of pure acid in the final mixture(0.40*600), so our equation to solve is:

0.80x+0.30(600-x)=0.40*600 get rid of parens

0.80x+180-0.30x=240 subtract 180 from each side

0.80x+180-180-0.30x=240-180 collect like terms

0.50x=60 divide each side by 0.50

x=120 ml---------------------amount of 80% solution needed

600-x=600-120=480 ml---------------amount of 30% solution needed

CK

120*0.80+480*0.30=0.40*600

96+144=240

240=240

Answer: 10 megabytes

10,000 kilobytes

Step-by-step explanation:

The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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Answer:

8.8metres

Step-by-step explanation:

diameter = 6 m

radius = 3 m

Length of arc = radius x central angle in radians

3 x 2/3= 2 m = 44 / 5 = 8.8

The total cost of rents is $180.

In the given table,

The cost of skis per day  = $48

The cost of pole per day = $12

Now since given that,

Alveres rents for 3 days

Therefore,

The cost of skis for 3 days  = $48 x 3

                                             =  $144

The cost of pole for 3 days = $12 x 3

                                             = $36

To find the total cost of rental,

Adding the cost of 3 days of skis and cost of 3 days of poles,

Hence,

Total cost of rents = $144 + $36

                               = $180

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The value of the equation that defines the function is f(x) = 3(5/3)ˣ

From the question, we have the following parameters that can be used in our computation:

(0, 3) and (1, 5)

An exponential function is represented s

y = abˣ

Where,

a = y when x = 0

So, we have

y = 3bˣ

Using the other point, we have

3b = 5

This gives

b = 5/3

So, we have

f(x) = 3(5/3)ˣ

Hence, the equation defining f is f(x) = 3(5/3)ˣ

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Answer:

Step-by-step explanation:

y = 0 is actually the x axis.

All the points on the line you want have an x value of - 3

-3,-10 is actually one of those points

The equation you want is x = - 3

Answer and explanation:

The political scientist is investigating "proportion of adult residents

..." and so the subjects of his study can only be found among adults. The units are therefore all adults, including registered adults. The frames can include census data showing adults in a particular area, telephone directories, registered voters in the area etc. If the researcher chooses to use personal interview in collecting data for his research, he would easily get response and also be able to explain questions out more, also there is the benefit of less corrupted data. Using telephone interview would save the researcher and respondents costs as there is no need to travel and the researcher could still explain out questions properly. If the researcher chooses to collect data through mailing respondents, there is alot more flexibility as respondents can reply at their convenience and when they are ready, also subjects may wish to not disclose identity with this data collection method

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

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Answer:

0.66? (0.67 if you rounded it)

Step-by-step explanation:

2*1/3

2/3 = 0.6666666666

The magnitude of angle Z include the following:

cosZ = 0.471

sinZ = 0.88

tanZ = 1.875

In order to determine the magnitude of angle Z, we would apply the basic trigonometric ratio because the given side lengths represent the adjacent side, opposite side, and hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

For cosZ, we would apply the cosine trigonometric ratio as follows;

cosZ = 13.6/28.9

cosZ = 0.4706

Z = cos⁻¹(0.4706)

Z = 61.93°.

For sinZ, we would apply the sine trigonometric ratio as follows;

sinZ = 25.5/28.9

sinZ = 0.8824

Z = sin⁻¹(0.8824)

Z = 118.07.

For tanZ, we would apply the sine trigonometric ratio as follows;

tanZ = 25.5/13.6

tanZ = 1.875

Z = tan⁻¹(1.875)

Z = 61.93.

\(answer \\ 2\\ solution \\ 10x - 3(x - 6) = x + 30 \\ or \: 10x - 3x + 18 = x + 30 \\ or \: 10x - 3x - x = 30 - 18 \\ or \: 7x - x = 12 \\ or \: 6x = 12 \\ or \: x = \frac{12}{6} \\ x = 2 \\ hope \: it \: helps\)

Answer:

x=2

Step-by-step explanation:

10x - 3(x- 6) = x + 30

Distribute

10x -3x+18 = x+30

Combine like terms

7x + 18 = x+30

Subtract x from each side

6x+18 = 30

Subtract 18 from each side

6x = 30-18

6x = 12

Divide by 6

6x/6 = 12/6

x =2

The divisibility rule for 3 on any integer number  is proven in the detailed explanation of the solution.

Given a non-decimal number, n.

Suppose n may be divided by 3.

n should be thought of in terms of its digits as

n = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

where d 1, d 2,..., d m are its digits and m is the number of digits in n.

The result of the preceding equation with n = 3k is

3k = d  × 1 × 10(m-1) + d × 2 × 10(m-2) +... + d × m × 10(m-0)

3000 is subtracted from both sides of the equation, giving us

0 = d × 1 × 10⁽ⁿ⁻¹⁾⁽ⁿ⁻¹⁾ + d  × 2 × 10⁽ⁿ⁻²⁾ + ... + d × m × 10⁰

We obtain by adding 3k to both sides of the equation.

3k = d × 1 × 10⁽ⁿ⁻¹⁾+ d

The divisibility rule is a heuristic for determining if two positive integers can be divided evenly (i.e. there is no remainder left over). For instance, determining if a number's last digit is 2, 4, 6, 8, or 0 makes it simple to determine whether it is even.

By examining the digits of the number, a divisibility rule provides a simple shorthand for determining if an integer is divisible by a particular set of factors without actually doing the division. This page only offers recommendations and examples for decimal, or base 10, numbers despite the fact that there are distinct divisibility tests for numbers in each radix or basis.

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Answer:

Step-by-step explanation:

\(2) y^{\frac{3}{2}}=y^{3*\frac{1}{2}}\\\\=(y^{3}}^{\frac{1}{2}}\\\\=\sqrt{y^{3}}\)

b

\(3)a^{\frac{2}{3}}=a^{2*\frac{1}{3}}\\\\=(a^{2})^{\frac{1}{3}}\\\\=\sqrt[3]{a^{2}}\)

c

Answer:

Area of yellow portion =54 in

The confidence interval for  mean number of hours of sleep on a typical night for the students is  [ 94.58,105.42 ] .

Using the mean, standard deviation, number of samples, and desired confidence interval as inputs, the following formula is used to compute the interval:

X + / -( Z * ( σ / √n))

where z comes from the reference's standard distribution tables and has a 95% confidence interval of 1.96.

100 + / - (1.96 * (17.50/40^1/2))

= [ 94.58,105.42 ]

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

In contrast, a high or low standard deviation indicates that the data points are, respectively, above or below the mean. A standard deviation that is close to zero implies that the data points are close to the mean.

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To solve this question we will use the following diagram:

Using the Pythagorean theorem for triangle AEO we get:

Substituting AO=68 yd, and EO=285 yd we get:

Therefore AE=293 yd. Now, the wire required for the long path is:

Therefore you could save:

taking the short route.

Answer: 98yd.