Use the recursive formula to find the first five terms in the arithmetic sequence.

Answer: [tex]\Large\boxed{2}[/tex]

Concept:

Here, we need to know the idea of the PEMDAS method.

PEMDAS is an acronym for the order of operations.

Solve:

Given expression

[tex]\dfrac{3^3~-~13}{11~-~2^2}[/tex]

Simplify the exponents

[tex]=\dfrac{27~-~13}{11~-~4}[/tex]

Simplify by subtraction

[tex]=\dfrac{14}{7}[/tex]

Simplify the fraction

[tex]\Large\boxed{=2}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

When we make inferences about the difference of two independent population proportions, we assume that it is a random sample, and the number of successes and failures are at least 15 in each group.

Two independent proportions tests involve comparing the proportions of two unrelated datasets.

For these two datasets to be regarded as an independent population, the following must be true or assumed to be true

Hence, the above highlights are the assumptions of two independent population proportions.

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Answer:

4/5 of the students would have protractors.

Step-by-step explanation:

Answer:

[tex]x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\[/tex]

A quadratic can generally be expressed as: [tex]y=ax^2+bx+c[/tex]

So using the equation you gave: [tex]0=x^2-5x-1[/tex]

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

[tex]x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}[/tex]

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

Answer:

15?

Step-by-step explanation:

2×15=30 i am not fully sure but this should be it

I'll go for the third option. It seems sensible to having a balance in estimating provided data, even though that may not always be the case.

Hope this helps!

The best information that describes your routes is the second route was steeper than your first, and the second route was higher up the mountain.

The slope of a linear equation is the change in the rise over the run. So, the slope of a linear equation shows that the larger the slope, the steeper the line becomes.

From the given information:

y = 2x + 4  --- (1)

y = 4x + 1  --- (2)

Using the slope-intercept formula:

y = mx + b

From the first equation, the slope is 2 and in the second equation, the slope is 4.

Therefore, we can conclude that the second route was steeper than your first, and the second route was higher up the mountain.

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Using compound interest, the rates per compounding period are given as follows:

a) 0.1273 = 12.73%.

b) 0.0833 = 8.33%

c) 0.0617 = 6.17%

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

The interest rate per compounding period is given as follows:

[tex]\left(1 + \frac{r}{n}\right)^n - 1[/tex]

For item a, the parameters are:

r = 0.12, n = 52.

Hence:

[tex]\left(1 + \frac{0.12}{52}\right)^{52} - 1 = 0.1273[/tex]

For item b, the parameters are:

r = 0.08, n = 104.

Hence:

[tex]\left(1 + \frac{0.08}{104}\right)^{104} - 1 = 0.0833[/tex]

For item c, the parameters are:

r = 0.06, n = 12.

Hence:

[tex]\left(1 + \frac{0.06}{12}\right)^{12} - 1 = 0.0617[/tex]

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Answer:

See below

Step-by-step explanation:

An area of  2km  x  2km = 4 km^2    

1 km = .62137 miles

2 (.62137)      x      2  (.62137)    =   1.5444 mi^2

Answer:

(-4,0) , (0,9)

Step-by-step explanation:

x-intercept is the point where the line touches the x-axis, which means, y = 0.

So when y = 0,

-9x + 4(0) = 36

-9x = 36

x = [tex]\frac{36}{-9}[/tex]

x = -4

Therefore, the coordinates of the x - intercept is (-4,0)

y-intercept is the point where the line touches the y-axis, which means , x = 0.

so when x = 0,

-9(0) + 4y = 36

4y = 36

y = [tex]\frac{36}{4}[/tex]

y = 9

Therefore, the coordinates of the y - intercept is (0,9)

Answer:

x - intercept (-4,0)

y -intercept (0,9)

Step-by-step explanation:

Put in 0 for x.

-9(0) + 4y = 36

4y = 36  Divide both sides by 4

y = 9

(0,9) This is where the line will cross the y axis.

Put in 0 for y

-9y + 4(0) = 36

-9y = 36 Divide both sides by -9

Y = -4

Answer:

4/10

Step-by-step explanation:

Let the numerator be 2x and the denominator is 5x. The denominator is 6 more than the numerator so if we add 6 to the numerator both numbers should be equal.

Solve:

2x+6 = 5x

6 = 3x

x = 2

2x = 4

5x = 10

Step-by-step explanation:

Let the numerator be 2x and denominator be 5x,

A.T.Q,

2x+6 = 5x

2x-5x = -6

-3x = -6

3x = 6

x = 2

So, the fraction is 4/10 = 2/5

Answer:

1

Step-by-step explanation:

f(x) = x² + 3x

g(x) = 5x + 2

f(3) = 3² + 3 x 3

f(3) = 9 + 9

f(3) = 18

g(3) = 5(3) + 2

g(3) = 15 + 2

g(3) = 17

(f - g)(3) = 18 - 17

(f - g)(3) = 1.

Answer:

The average price of a ticket is $25.

Step-by-step explanation:

Lets us say 100% = 1

0.75 x 30 + 0.25 x 10 = 25

Answer:

$4.58

Step-by-step explanation:

Lets convert 10 feet to meters.

1 ft = 0.305m

10ft = 0.305 * 10

10ft = 3.05m

Now we will work out the cost of the fabric.

Given 1m = $1.50

3.05m = 3.05 * $1.50 = $4.58 (nearest cent)

Answer:

The slope between these two points is m=-4.

Step-by-step explanation:

Greetings !

[tex]the \: equation \: for \: slope \: m \: is \\ m = \frac{Y₂-Y}{X₂-X₁}..substitute \: known \: values \\ m = \frac{ (-11 - 9) }{(3 - ( - 2)} \\ m = \frac{ - 20}{5} \\ m = - 4[/tex]

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-5})\hspace{10em} \stackrel{slope}{m} ~=~ 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{6}(x-\stackrel{x_1}{(-2)})\implies y+5=6(x+2)[/tex]

The number of terms in the geometric series is 9

The geometric series given as:

96 - 48 + 24 -....,-3/8 .

Calculate the common ratio (r) as follows

r = T2/T1

Substitute the known values in the above equation

r = -48/96

Evaluate

r = -0.5

The number of terms is then calculated as:

Tn = a * r^n-1

Let n = 9

So, we have:

T9 = a * r^9

Substitute the known values in the above equation

T9 = 96 * (-0.5)^8

Evaluate the product

T9 = -3/8

Hence, the number of terms in the geometric series is 9

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The true statements are:

The independent variable is the variable that determines the value of the dependent variable. There is a positive relationship between the number of people at the picnic and the total cost. This is because it can be seen as the number of people at the picnic increases, the total cost changes.

Rate of change = total cost / number of people

$52 / 6 = $8.67

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Answer:

A, B, D

Step-by-step explanation:

right on edge

Answer:

Graph B

Step-by-step explanation:

Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = -12

2y = 3x + 12

y = 3/2x + 6

Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.

Using the binomial distribution, there exists a 0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

The formula exists:

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

The parameters exists:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

The values of the parameters are: p = 0.5 and n = 13

The probability that at most eleven of the thirteen babies are girls is:

[tex]$P(X \leq 11)=1-P(X > 11)$$[/tex] then

[tex]$P(X > 11)=P(X=12)+P(X=13)$$[/tex]

By using the binomial distribution formula

[tex]$&P(X=x)=C_{n, x} \cdot p^{x} \cdot(1-p)^{n-x} \\[/tex]

substitute the values in the above equation, we get

[tex]$&P(X=12)=C_{13,12} \cdot(0.5)^{12} \cdot(0.5)^{1}=0.0016 \\[/tex]

[tex]$&P(X=13)=C_{13,13} \cdot(0.5)^{13} \cdot(0.5)^{0}=0.0001[/tex]

So, [tex]$&P(X > 11)=P(X=12)+P(X=13)[/tex]

[tex]=0.0016+0.0001=0.0017 \\[/tex]

[tex]$&P(X \leq 11)=1-P(X > 11)[/tex]

[tex]=1-0.0017=0.9983[/tex]

0.9983 = 99.83% probability that at most eleven of the thirteen babies exists girls.

Therefore, the correct answer is option c. 4089/4096

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Answer:

Sean's rocket lands 3 seconds after Kiara's rocket.

Step-by-step explanation:

Kiara:  f(t)= -16t² + 80t

Sean:  h(t) = -16t² + 120t + 64

Assume that both rockets launch at the same time.  We need to be suspicious of Sean's rocket launch.  His equation for height has "+64" at the end, whereas Kiara's has no such term.  The +64 is the starting height iof Sean's rocket.  So Kiara has a 64 foot disadvantage from the start.  But if it is a race to the ground, then the 64 feet may be a disadvantage.  [Turn the rocket upside down, in that case.  :) ]

We want the time, t, at which f(t) and h(t) are both equal to 0 (ground).  So we can set both equation to 0 and calculate t:

Kiara:  f(t)= -16t² + 80t

0 = -16t² + 80t

Use the quadratic equation or solve by factoring.  I'll factor:

0 = -16t(t - 5)

T can either be 0 or 5

We'll choose 5.  Kiara's rocket lands in 5 seconds.

Sean:  h(t) = -16t² + 120t + 64

0= -16t² + 120t + 64

We can also factor this equation (or solve with the quadratic equation):

0 = -8(t-8)(2t+1)

T can be 8 or -(1/2) seconds. We'll use 8 seconds.  Sean's rocket lands in 8 seconds.

Sean's rocket lands 3 seconds after Kiara's rocket.

Answer:

D) 4 8/12

Step-by-step explanation:

To first start this, let's make 2 5/6 an in-proper fraction by adding 12 and removing the whole 2. =17/6. Then let's get a common denominator by multiplying both the denominators by each other...6x4 and 4x6, but we also multiply the numerators by the same thing that the denominators are getting multiplied by... 17x4 and 7x6. We will then get 68/24 and 42/24. And then we can add both numerators with eachother and keep the denominator to get, 110/24... and making this into a propor fraction would equal 4 16/24... and dividing by 2 would equal 4 8/12

The behavior sees the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

The behavior of the graph of the polynomial function f(x) as the variable x approaches either positive or negative infinity represents the end behavior of the function. The final behavior of a polynomial function's graph is determined by the degree of the function as well as the leading coefficient.

Generally, the equation for is zeros  mathematically given as

y=x^4−2x^3−11x^2+12x+36

Therefore

(x+2)^2(x-3)^2=0

x=-2

x=3

since the graph attached has a positive leading coefficient and a positive degree

In conclusion, If the leading coefficient is already positive, then increasing the size of the inputs will simply result in the leading term being even more positively skewed. The line on the graph will start to slope to the right.

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Answer:

Nope.  It would take 32 and 4/13 minutes, which is longer than 30 min.

Step-by-step explanation:

The distance is 35 miles and the speed 65 miles/hour

Dividie the distance by the speed to obtian the time required,

(35 miles)/(65 miles/hour) = 0.538 hours

No, 35 miles at the speed limit of 65 mph would require 0.538 hours, 0.038 hours more than 1/2 hour.  2 and 4/13 minutes more than 30 minutes.

To conduct a test of hypothesis with a small sample, we make an assumption that the population is normally distributed .

What is normal distribution?

A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.

The normal distribution appears as a "bell curve" on a graph.

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Answer:

First:

5x + 9 < 2

x= 9/5= 1,8 < 2

Second:

x + 6 < 12

x= 12/6= 2 < 12

I'll focus on part (b) only.

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

Explanation:

Replace the variable b with the commonly used variable x and c with some other constant, let's say the letter m. These replacements will become apparent when we use the quadratic formula shortly later on.

After the replacements are made, we have -3c²-4cb+4b²​ turn into -3m²-4mx+4x²​

This is the same as 4x²​-4mx-3m²

Compare this to the format of ax²​+bx+c

We can see that

Once again, m is constant.

Let's compute the discriminant.

[tex]d = b^2 - 4ac\\\\d = (-4m)^2-4(4)(-3m^2)\\\\d = 16m^2+48m^2\\\\d = 64m^2\\\\[/tex]

This discriminant is under the square root as part of the quadratic formula.

So 4x²​-4mx-3m² would have roots of...

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-b\pm\sqrt{d}}{2a}\\\\x = \frac{-(-4m)\pm\sqrt{64m^2}}{2(4)}\\\\x = \frac{4m\pm\sqrt{(8m)^2}}{8}\\\\x = \frac{4m\pm 8m}{8}\\\\x = \frac{4(m\pm 2m)}{4*2}\\\\x = \frac{m\pm 2m}{2}\\\\x = \frac{m+ 2m}{2} \ \text{ or } \ x = \frac{m-2m}{2}\\\\x = \frac{3m}{2} \ \text{ or } \ x = \frac{-m}{2}\\\\[/tex]

The whole time, the term "m" is treated as a constant. It is fixed to some unchanging number.

So why did we go through all that trouble to use the quadratic formula in the first place? It turns out that this formula is helpful to factoring quadratics. Recall that the roots of a polynomial tie very closely to its factorization.

For example, x²-4 factors to (x-2)(x+2) to have roots of x = 2 or x = -2. You could use the quadratic formula to solve x²-4 = 0 or x²+0x-4 = 0 and you should get x = 2 or x = -2 as the two solutions.

Anyways, back to the problem at hand.

Let's use the first root we found to form one of the factors needed.

The idea is to do a bit of algebra to get everything to one side. If fractions are present, then multiply both sides by the LCD to clear them out. We need to have 0 isolated on its own side.

[tex]x = \frac{3m}{2} \\\\ 2x = 3m\\\\ 2x-3m = 0[/tex]

So (2x-3m) is one factor

Through similar steps, you would find that the root [tex]x = \frac{-m}{2}[/tex] yields the factor of (2x+m)

Therefore, the factors are (2x-3m) and (2x+m)

------------------------------------

In summary so far, 4x²​-4mx-3m² factors to (2x-3m)(2x+m)

From here we replace x with b and replace m with c, so that we return back to the original variables used.

(2x-3m)(2x+m) becomes (2b-3c)(2b+c)

This can be confirmed using WolframAlpha. You could use the FOIL rule to expand out (2b-3c)(2b+c) and you should get 4b²​-4bc-3c²​ aka -3c²-4cb+4b²​

-------------------------------------

Those previous sections talked about part (i)

Part (ii) is where we plug in b = 4 and c = 3. In other words, we replace every copy of b with 4, and every copy of c with 3.

If you use the original expression, then,

-3c²-4cb+4b²​ = -3(3)²-4(3)(4)+4(4)²​ = -3(9)-4(12)+4(16) = -11

Or you could use the factored expression.

(2b-3c)(2b+c) = (2*4-3*3)(2*4+3) = (8-9)(8+3) = (-1)*(11) = -11

This very partially confirms that -3c²-4cb+4b² = (2b-3c)(2b+c) is indeed the case. Unfortunately you'd have to use infinitely many numeric examples to confirm the answer to part (i); however, something like the FOIL rule is far more efficient.

Answer:

1.09575e+11

Step-by-step explanation: