5.9 = x/9 round to nearest 100th

Let \(a\) be the first term in the sequence, and \(r\) the common ratio between consecutive terms. Let \(a_n\) denote the \(n\)-th term in the sequence. The first several terms are

\(\{a, ar, ar^2, ar^3, \ldots\}\)

and so the \(n\)-th term is given by \(a_n = ar^{n-1}\).

Let \(S_N\) denote the \(N\)-th partial sum of the series,

\(\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}\)

Multiply both sides by \(r\).

\(r S_N = ar + ar^2 + ar^3 + \cdots + ar^N\)

Subtract this from, then solve for, \(S_N\).

\(S_N - r S_N = a - ar^N \implies S_N = \dfrac{a(1 - r^N)}{1 - r}\)

We know the infinite series converges, so \(|r|<1\), which means the \(S_N \to \frac a{1-r}\) as \(N\to\infty\). And since we know the infinite sum is 25, we have

\(\dfrac a{1-r} = 25 \implies a + 25r = 25\)

Meanwhile, the sum of the first 2 terms is

\(a + ar = 16\)

Solve for \(r\).

\(a + ar = 16 \implies ar = 16 - a \\\\ \implies r = \dfrac{16}a - 1\)

Substitute this into the other equation and solve for \(a\), then again for \(r\).

\(a + 25\left(\dfrac{16}a - 1\right) = 25 \implies a + \dfrac{400}a - 25 = 25 \\\\ \implies a - 50 + \dfrac{400}a = 0 \\\\ \implies a^2 - 50a + 400 = 0 \\\\ \implies (a-10) (a-40) = 0 \\\\ \implies a = 10 \text{ or } a = 40\)

\(\implies r = \dfrac{16}{10} - 1 = \dfrac35 \text{ or } r = \dfrac{16}{40} - 1 = -\dfrac35\)

We're given that the ration is positive, so \(r=\frac35\) and \(a=10\).

i) The fifth term in the sequence is

\(ar^{5-1} = 10 \left(\dfrac35\right)^4 = \dfrac{162}{125} = 1.296\)

ii) The sum of the first 4 terms is

\(\displaystyle S_4 = \sum_{n=1}^4 ar^{n-1} = \frac{a(1 - r^4)}{1 - r} = \dfrac{10\left(1 - \left(\frac35\right)^4\right)}{1 - \frac35} = \dfrac{544}{25} = 21.76\)

Answer:

\(\displaystyle y=\frac{1}{2}x+5\)

Step-by-step explanation:

We want to find the slope in slope-intercept form of a line that is parallel to:

\(\displaystyle y=\frac{1}{2}x-2\)

And passes through the point (-8, 1).

Recall that parallel lines have equivalent slopes.

Since the slope of our given line is 1/2, the slope of our new line must also be 1/2.

We are also given that it passes through the point (-8, 1). Since we are given a slope and a point, we can use the point-slope form:

\(y-y_1=m(x-x_1)\)

Substitute 1/2 for m and (-8, 1) for (x₁, y₁). Hence:

\(\displaystyle y-(1)=\frac{1}{2}(x-(-8))\)

Since we want the equation in slope-intercept form, we can isolate y. Distribute:

\(\displaystyle y-1=\frac{1}{2}x+4\)

Therefore, our equation is:

\(\displaystyle y=\frac{1}{2}x+5\)

Answer:

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = - 120\)

Step-by-step explanation:

By the rule of Integer multiplications,

\((-1) \times (-2) \times (-3) \times (-4) \times (-5) = [ (-1) \times (-2) ] \times [(-3) \times (-4)] \times (-5)\)

                                                      \(= [2] \times [12] \times (-5)\)

                                                      \(= -120\)

Learn more about Integer here,

brainly.in/question/54087058

Answer:

12 and 18

Step-by-step explanation:

Lets say the two numbers are A and B, with A the smaller.

We are told that A/B = 2/3     [in the ratio of 2 to 3]

We also find that A + B = 30  [Their sum is 30]

Rearrange the first equation to isolate A:

A/B = 2/3

A = 2B/3        [multiply both sides by B]

Now use this value of A in the second equation:

A + B = 30

2B/3 + B = 30

(2/3)B + (3/3)B = 30

(5/3)B = 30

B = (30)(3/5)

B = 6*3

B = 18

Since A + B = 30:

A + B = 30

A + 18 = 30

A = 12

A is 12 and B is 18

===================

Check:

Does A/B = 2/3??

(12/18) = (6/9)

(6/9) = (2/3)   YES

Does A + B = 30  ???

12 + 18 = 30   YES

Answer:

renee is correct

Step-by-step explanation:

because when linda multipled -2 by 4 she forgot to change the positive sign to a negative sign

A snowmobile can be rented for $14 per day with a $50 initial fix cost.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Let the initial fee be x and daily fee be y,

92=x+3y

120=x+5y

x+5y=120

x+3y=92

Subtract both,

2y=28

y=$14

x+5y=120

x+70=120

x=$50

The daily fee to rent a snowmobile is $14 per day with a initial fix fee of $50.

To know more about equation,

https://brainly.com/question/649785

#SPJ4

Answer:

A = BH x 1/2

Like they said, use the formula to find the base.

We plug in our given values, to find the base out.

A = BH x 1/2

14 = B(7) x 1/2

14= b7 x 1/2

Divide by 1/2 from both sides(basically multiplying by 2/1)

*2/1    *2/1

28 = b7(let's reverse this to be);

28 = 7b

/7     /7

4 = b

Answer:

2x + 9y + 5

Step-by-step explanation:

Combine like terms:

(6x - 4x) + (4y + 5y) + 5

2x + 9y + 5

Answer:

2, 9, 5

Step-by-step explanation:

These are the numbers to plug into this equation.

The 4 properties of the rhombus are:

A quadrilateral in Euclidean geometry is a rhombus. It's a parallelogram with all sides equal and diagonals intersecting at 90 degrees. In addition, opposing sides are parallel, and opposing angles are equal. This is a fundamental property of the rhombus. A rhombus is shaped like a diamond. As a result, it's also known as a diamond.

To know more about Rhombus visit the link

https://brainly.com/question/27870968

#SPJ4

Answer:

Range: {5, 3, 1, -1}  or in numerical order: {-1, 1, 3, 5}

Step-by-step explanation:

The range is the set of output or y-values for every input (or x-values). Given the following domain: {-2, 0, 2, 4} and the given linear function, y = -x + 3:

Domain (x)            Range (y)

   -2                 y = -(-2) + 3 = 2 + 3  = 5

    0                 y = - (0) + 3 = 0 + 3  = 3

    2                 y = -(2) + 3  = -2 + 3  = 1

    4                 y = -(4) + 3  = - 4 + 3 = -1

The probability that a randomly selected adult does not own shares of stock is 66.84%.

To calculate the probability that a randomly selected adult does not own shares of stock, we need to subtract the probability that the person is a shareholder from the probability that the person has some college education. We can use the formula:

P(A') = 1 - P(A)

where P(A) is the probability that the person is a shareholder, and P(A') is the probability that the person is not a shareholder.

P(A) = 52%

P(A') = 100% - P(A') = 100% - 52% = 48%

Next, we need to calculate the probability that the person has some college education.

We can use the formula:

P(B) = 47%

Now we can use the formula for conditional probability to calculate the probability that the person has some college education given that they are not a shareholder:

P(B|A') = P(A' and B) / P(A')

To calculate P(A' and B), we can use the formula:

P(A' and B) = P(B) - P(A and B)

P(A and B) = P(A) x P(B|A) = 52% x P(B|A)

To calculate P(B|A), we can use Bayes' theorem:

P(B|A) = P(A|B) x P(B) / P(A)P(A|B) = P(A and B) / P(B) = (52% x P(B|A)) / P(B)

Now we can substitute this expression into the formula for P(A' and B):

P(A' and B) = P(B) - P(A) x P(A|B) x P(B) / P(A) = 47% - (52% x P(B|A)) x 47% / P(B)

Now we can substitute these expressions into the formula for P(B|A') and simplify:

P(B|A') = (47% - (52% x P(B|A)) x 47% / P(B)) / 48%

We are given that 16% of all shareholders have some college education, so we can substitute this value for P(B|A):

P(B|A') = (47% - (52% x 16%)) x 47% / P(B) / 48% = 33.16%

Finally, we can substitute this value into the formula for P(A'):

P(A') = 100% - P(A') = 100% - 33.16% = 66.84%

Learn more about Probability:

https://brainly.com/question/24756209

#SPJ11

Answer:

\(|{\sf XY}| = 10\; {\rm cm}\).

Step-by-step explanation:

Refer to the diagram attached. The dashed segment attached to \(\!{\sf Z}\) points to the north. Rotating this segment clockwise with point \({\sf Z}\!\!\) as the fixed center of rotation would eventually align this segment with the one between point \(\!\!{\sf Z}\) and point \(\!\!{\sf X}\). The bearing of point \({\sf X}\) from point \({\sf Z}\) is the size of the angle between these two line segments when measured in the clockwise direction.

Subtract the bearing of \({\sf Y}\) from \({\sf Z}\) from the bearing of \({\sf X}\) from \({\sf Z}\) to find the measure of the angle \(\angle {\sf YZX}\):

\(\begin{aligned}\angle {\sf YZX} &= 135^{\circ} - 45^{\circ} \\ &= 90^{\circ}\end{aligned}\).

Thus, triangle \(\triangle {\sf YZX}\) is a right triangle (\(90^{\circ}\)) with segment \({\sf YX}\) as the hypotenuse. It is given that \(|{\sf XZ}| = 6\; {\rm cm}\) whereas \(|{\sf ZY}| = 6\; {\rm cm}\). Thus, by Pythagorean's Theorem:

\(\begin{aligned}|{\sf ZY}| &= \sqrt{|{\sf ZX}|^{2} + |{\sf ZY}|^{2}} \\ &= \sqrt{(8\; {\rm cm})^{2} + (6\; {\rm cm})^{2}} \\ &= 10\; {\rm cm}\end{aligned}\).

Answer:

36

2×18

2×9×2

2×2×3×3

6²

=> square root of 36 =6

Answer:

2 and 6, 1 and 5, 3 and 7, 4 and 8

Step-by-step explanation:

Any one of those would work

Answer: <1 and <5

Step-by-step explanation:

Answer:

121

Step-by-step explanation:

Convert 550% into a decimal by moving the decimal point 2 times to the left. 5.5. Then multiply 5.5 x 22 to get 550% of 22.

Therefore, the volume of the solid E is 0.25 cubic units.

Given the solid E is bounded by the planes y = 0, z = 0, z = 1 - x - y, and the parabolic cylinder y = 1 - x².

Here we are to calculate the volume of the solid E.

The parabolic cylinder y = 1 - x² can be rewritten as x² + y = 1, which represents a parabola opening along the y-axis.

Let us set up the limits of integration and choose a suitable order of integration.

Since the parabolic cylinder is parallel to the yz-plane, we choose to integrate with respect to x first.

The limits of integration for x, y, and z are given as follows;

y = 0 to y = 1 - x², z = 0 to z = 1 - x - y, and x = -1 to x = 1.

Hence the required volume can be obtained as follows;

∫∫∫ dV=∫−1^1∫0^(1−x²)∫0^(1−x−y)dzdydx

≈0.25 cubic units

To know more about parabolic visit:

https://brainly.com/question/14003217

#SPJ11

:))))))

Step-by-step explanation:

videochamp, picsart

Picsart , Inshot , Gandr , Photo lab and Viva video.

Answer:

\(g\circ f=\{(1,3),(3,6),(5,8)\}\).

\(f\circ g\) does not exist.  

Step-by-step explanation:

It is given that,

\(f=\{(1,2),(3,4),(5,6)\}\)

\(g=\{(2,3),(4,6),(6,8)\}\)

We need to find the composition gof.

\((g\circ f)(x)=g(f(x))\)

Now,

\((g\circ f)(1)=g(f(1))=g(2)=3\)

\((g\circ f)(3)=g(f(3))=g(4)=6\)

\((g\circ f)(5)=g(f(5))=g(6)=8\)

So, \(g\circ f=\{(1,3),(3,6),(5,8)\}\).

We need to check whether \(f\circ g\) exist of not.

If range of g(x) is subset of domain of f(x), then we can say composition function \(f\circ g\) exists.  

Now,

Range of g(x) = {3,6,8}

Domain of f(x) = {1,3,5}

Since range of g(x) is not a subset of domain of f(x), then we can say composition function \(f\circ g\) does not exist.  

Answer:

-7 is the second number

Step-by-step explanation:

The range of exponential functions is y > 0. An exponential function's graph may be found to be strictly increasing or strictly decreasing graph.

The graph of an exponential function is found to be asymptotic to the x-axis in nature as x approaches negative infinity or as it approaches positive infinity.

An exponential function is a mathematical function which has the formula f (x) = axe, where "x" is a variable and "a" is a constant also known as the base of the function and it should be greater than zero.

The number e, which is approximately equal to 2.71828, is the most often used exponential function base.

To learn more about exponential

brainly.com/question/24427773

#SPJ4

The he statement d(k) + (k + 1) = d(k+1) is true for all natural numbers, n, by mathematical induction.

To prove that the statement is true for all natural numbers, n, we can use mathematical induction.

The statement we want to prove is that d(k) + (k + 1) = d(k + 1), where d(n) represents the total number of dots in a pattern of n squares.

Base Case (n = 1):

First, let's prove the statement for the base case, n = 1.

For n = 1:

d(1) + (1 + 1) = d(1) + 2

Now, consider a single square with 1 dot.

In this case, d(1) = 1.

So, we have:

1 + 2 = 3

Now, let's consider a pattern of 2 squares (n = 2).

The first square has 1 dot, and the second square has 2 dots. So, d(2) = 1 + 2 = 3.

So, the statement is true for n = 1.

Inductive Hypothesis (Assume true for n = k):

Now, assume that the statement is true for some arbitrary natural number k.

That is, assume that: d(k) + (k + 1) = d(k + 1)

Inductive Step (Prove true for n = k + 1):

To prove that the statement is true for n = k + 1.

d(k + 1) + (k + 2) = d(k + 2)

Now, consider a pattern of (k + 1) squares.

By the inductive hypothesis, assume that the statement is true for k squares:

d(k) + (k + 1) = d(k + 1)

Now, let's add one more square to the pattern.

This square will have (k + 2) dots.

So, the total number of dots in the pattern of (k + 1) squares plus the (k + 2) dots in the additional square is:

d(k + 1) + (k + 2)

And by the inductive hypothesis, d(k) + (k + 1) = d(k + 1).

Therefore:

d(k + 1) + (k + 2) = (d(k) + (k + 1)) + (k + 2) = d(k) + (k + 1) + (k + 2)

Now, simplify:

d(k + 1) + (k + 2) = d(k + 1) + (k + 1 + 1)

So, it is shown that for n = k + 1, d(k + 1) + (k + 2) = d(k + 1) + (k + 1) + 1.

Since it is assumed the statement to be true for k and proved it for k + 1, it is shown that the statement is true for all natural numbers, n, by mathematical induction.

Learn more about Principal of Mathematical induction here:

https://brainly.com/question/29503103

#SPJ12

Answer:

B

Step-by-step explanation:

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.

Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.

The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .

To learn more about Experimental Study refer to :

https://brainly.com/question/30363686

#SPJ4

Answer: A

Step-by-step explanation:

I hope this still helps my guy :D let me know if it does!

Answer: the height is 18 cm.

Step-by-step explanation:

The equation for the volume of a cone is the following: V = 1/3 × B × h, where B (base) = πr². Because we are given the radius of the base, but not the base’s area itself, we will use V = 1/3πr²h.

Here, we are trying to solve for h, the height, so first we can first rearrange the equation to solve for h:

1) V = 1/3πr²h

2) h = V ÷ 1/3πr² (divide both sides by 1/3πr²h)

Now, we just need to input the given values: V = 471, π = 3.14, r = 5

h = 471 ÷ 1/3(3.14)(5²)

= 471 ÷ 1/3(3.14)(25)

= 471 ÷ 1/3(78.5)

= 471 ÷ (78.5/3)

= 18 cm

The probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

In order to determine the probability of exactly two flaws in a 50-yard piece of material, we will use the Poisson distribution formula.

The Poisson distribution is used to calculate the probability of a given number of events occurring in a fixed interval of time or space when these events happen independently of each other and at an average rate.

To find the probability of exactly two flaws in a 50-yard piece of material, we will use the following formula:

P(X = k) = (e^(-λ) * λ^k) / k!

Where: P(X = k) is the probability of k flaws occurring in a 50-yard piece of material

λ = the average rate of flaws per unit of material (in this case, 50 yards)

k = the number of flaws we want to calculate is the mathematical constant ≈ 2.71828...

k! is the factorial of k, which is the product of all positive integers up to k

Let's plug in the values we have for this problem:

P(X = 2) = (e^(-λ) * λ^2) / 2!

λ = 2 flaws per 50 yards of material produced = 2/50 = 0.04 flaws per yard.

Therefore, the average number of flaws in a 50-yard piece of material is:

λ = 0.04 * 50 = 2e is a mathematical constant that equals ≈ 2.71828...

Then, let's plug in these values into the formula:

P(X = 2) = (e^(-2) * 2^2) / 2!P(X = 2) = (0.1353 * 4) / 2P(X = 2) = 0.2706

The probability of exactly two flaws occurring in a 50-yard piece of material is 0.2706 or approximately 27.06%.

Therefore, the probability of exactly two flaws in a 50-yard piece of material is approximately 0.2706 or 27.06%.

Learn more about Poisson distribution here:

https://brainly.com/question/30388228

#SPJ11

Answer:

7/50 = x/75

x = 10.5

therefore he would run 10.5 miles in 75 minutes

Answer:

In 75 minutes, she runs (7/50) x 75 = 10.5.

She runs 10.5 miles in 75 minutes.

Step-by-step explanation:

Answer:

Chandler will need 82.2  cm of fabric.

Step-by-step explanation:

Given that,

Chandler has 822 millimeters of fabric.

We know that,

1 mm = 0.1 cm

To convert 822 mm to cm, use the unitary method.

822 mm = (0.1×822) cm

= 82.2  cm

So, Chandler will need 82.2  cm of fabric.