Which function has a greater output value for x = 10? Explain your reasoning.

If [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio of the series, then the sum of the first [tex]n[/tex] terms is

[tex]S_n = a + ar + ar^2 + \cdots + ar^n[/tex]

Multiply by [tex]r[/tex] on both sides, then subtract that from and solve for [tex]S_n[/tex].

[tex]rS_n = ar + ar^2 + ar^3 + \cdots + ar^{n+1}[/tex]

[tex](1-r)S_n = a - ar^{n+1}[/tex]

[tex]S_n = \dfrac{a(1-r^{n+1})}{1-r}[/tex]

Use the given first and second terms of the sequence to find [tex]a[/tex] and [tex]r[/tex].

[tex]a = \dfrac1{64}[/tex]

[tex]ar = \dfrac1{32} \implies \dfrac r{64} = \dfrac1{32} \implies r = \dfrac{64}{32}=2[/tex]

Solve for [tex]n[/tex].

[tex]S_n = \dfrac{1-2^{n+1}}{64(1-2)} = 2^{36} - 2^{-6}[/tex]

[tex]\dfrac{2^{n+1} - 1}{2^6} = 2^{36} - 2^{-6}[/tex]

[tex]2^{n-5} - 2^{-6} = 2^{36} - 2^{-6}[/tex]

[tex]\implies n-5 = 36 \implies \boxed{n = 41}[/tex]

The probability that a person chosen at random is younger than 65 is 0.967.

Probability calculates the odds that a random event would happen. The odds that the random event happens lie between 0 and 1.

The probability that a person chosen at random is younger than 65 = (total number of people younger than 65 / total number of respondents)

(350 + 412 + 318 + 200 + 107 + 51 ) / (350 + 412 + 318 + 200 + 107 + 51 + 49)

1438 / 1487 = 0.967

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5000\\ P=\textit{original amount deposited}\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases}[/tex]

[tex]5000=P\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies 5000=P(1.05)^3 \\\\\\ \cfrac{5000}{1.05^3}=P\implies 4319\approx P[/tex]

The amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

The annual payments represent the periodic cash outflows invested in accumulating a future value using an interest rate compounded for a period.

This can be achieved using the future value and present value formulas or factors.

We can also use an online finance calculator, as follows:

Future value = $5,000

Investment period = 3 years

Annual compound interest = 5%

N (# of periods) = 3 years

I/Y (Interest per year) = 5%

PV (Present Value) = $0

FV (Future Value) = $5,000 ($4,531.56 + $468.44)

Results:

PMT = $1,510.52

Sum of all periodic payments = $4,531.56 ($1,510.52 x 3_)

Total Interest = $468.44

Thus, the amount to be invested annually to save $5,000 in 3 years, if the investment earns 5% annual interest, is $1,510.52.

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The rule that describes the transformation is (x, y) - (-y, -x).

The fourth option among the available choices depicts a 180° clockwise or counterclockwise rotation, in which is The vertices' x- and y-coordinates change to their opposites, i.e., x becomes -x and y becomes -y.

The rule that describes the transformation is (x, y) - (-y, -x).

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Based on the required rate of return, the real risk free rate, and the inflation premium, the default risk premium on the corporate bonds is 1.2%

The default risk premium can be found as:

=real risk free rate + Inflation premium + default risk premium + liquidity premium + maturity risk premium

Solving gives:

= 0.07 - 0.0275 - 0.0205 - (0.1 x (t - 1)%)

=  0.07 - 0.0275 - 0.0205 - (0.1 x (5 years - 1)%)

= 1.2%

The default risk premium refers to the return that the bond is offering over what a risk-free bond would offer.

This means that the corporate bond described is offering 1.2% more than what a risk-free government bond would offer.

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Based on the number of goals scored in the football matches, the mode is 4 goals. The median is 3 goals and the mean goals scored is 2.6 goals.

The mode is the number of goals that was scored in the most matches. This number is 4 goals as this was scored in 6 matches.

To find the median, order the numbers:

0, 0, 0, 0, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 6

The median is:

= (3 + 3) / 2

= 3

The mean is:

= (0 + 0 + 0 + 0 + 1 + 1 + 2 +2 +2 + 3 + 3 + 3 + 4 + 4+ 4 + 4 +4 + 4 + 5 + 6) / 20

= 2.6 goals

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Answer:

1/8

Step-by-step explanation:

Look at the screen shots

Answer:

Median is 83

Range: 61

Step-by-step explanation:

The median is the number in the middle.  The range is the max. number subtracted from the min number.

Answer:

-6

Step-by-step explanation:

[tex]7(6+x)-x > 0[/tex]

[tex]42 + 7x-x > 0[/tex]

[tex]42+6x > 0[/tex]

[tex]6x > -42[/tex]

[tex]x > -7[/tex]

The smallest integer that satisfies the condition, [tex]x > -7[/tex], is -6.

The domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

The function is given as:

[tex]y=4\log_5(x-3)[/tex]

Set the expression in bracket greater than 0

x -3 > 0

Add 3 to both sides

x > 3

Hence, the domain of [tex]y=4\log_5(x-3)[/tex] is (d) all real numbers greater than 3.

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Answer:

12

Step-by-step explanation:

3x^2

because the information provided states that x = -2, that is what we are going to replace x with.

3(-2)^2

the next step is to evaluate the power because that is next in PEMDAS.

(-2)^2 = 4

that leaves us with:

3 * 4 = 12      ( the " * " represents the multiplication sign)

hope this helps!

The regression equation is y = -0.42647x + 29.11471 and the correlation coefficient is -0.9607

The table of values is given as:

Completion Percentage 57 59 62 63 64

Interception Percentage 5 3.5 3 2.5 1.5

Next, we enter the above values in a graphing calculator.

From the graphing calculator, we have the following summary:

Regression Equation = ŷ = bX + a

b = SP/SSX = -14.5/34 = -0.42647

a = MY - bMX = 3.1 - (-0.43*61) = 29.11471

So, the regression equation is

y = -0.42647x + 29.11471

And the correlation coefficient is -0.9607

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Answer: I think its A

Step-by-step explanation: maybe

The number of each kind of office supply oscar bought is = markers= (43.2 - 4.2y)/3 notebooks = (43.2-3x)/4.2, sticky notes = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3.

The number of markers he bought = X

The number of notebooks he bought= y

The number of sticky notes he bought= z= 3 + X+y

The amount he paid for markers = $1.05*X

The amount he paid for notebooks = $2.25*y

The amount he paid for sticky notes= $1.95 (3 + X+y)

The total amount he paid is = $49.05

That is;

$49.05 = $1.05x + $2.25y + $1.95 (3 + X+y)

$49.05 = $1.05x + $2.25y + $5.85 + $1.95x + $1.95y

$49.05 - $5.85 = 3x + 4.2y

$43.2 = 3x + 4.2y

Make X the subject of formula,

3x = 43.2 - 4.2y

X = (43.2 - 4.2y)/3

y= (43.2-3x)/4.2

z = [43.2 - 4.2y)/3 + (43.2-3x)/4.2] + 3

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Answer: [tex](a-b)(y-1)[/tex]

Step-by-step explanation:

Factoring out (a-b) gives [tex](a-b)(y-1)[/tex].

The height of the ramp above the ground is 1.55 meters.

The difference between the height of the tree is 33.20 meters

The situation forms a right angle triangle.

Therefore, the height the ramp above the ground can be calculated as follows:

Using Pythagoras theorem,

sin 15  = opposite / hypotenuse

sin 15 = x / 6

cross multiply

x = 6 sin 15

x = 6 × 0.2588190451

x = 1.55291427062

x = 1.55

Therefore, the height of the ramp above the ground is 1.55 meters

tan 36  = opposite / adjacent

tan 36 = x / 60

x = 60 tan 36

x = 43.5925516803

x = 43.60 meters

tan 52 = y / 60

60 tan 52 = y

y = 76.7964979316

y = 76.79 meters

The difference between the height of the tree = 76.79 - 43.60 = 33.20 meters

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The information given illustrates that the graph of the function decreasing.

We say that a function is increasing on an interval if the function values increase as the input values increase within that interval.

Similarly, a function is decreasing on an interval if the function values decrease as the input values increase over that interval.

So according to the given graph on the interval (-3, 1) the graph is decreasing.

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Using the elimination method, the value of x in the system of equations is calculated as: 8.

To solve a system of equations given using the elimination method, do the following:

Multiply 2x - 5y = 1 by 2 and multiply -3x + 2y = -18 by 5 to get the following:

4x - 10y = 2 --> eqn. 1

-15x + 10y = -90 --> eqn. 2

Add

-11x = -88

Divide both sides by -11

x = 8

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Answer:

y = 3x + 1

Step-by-step explanation:

The formula for equation of a line in slope intercept form is;

y = mx + c

Where;

m is slope

c is y-intercept

Now, since we have coordinates, we will get the equation as;

(y - y1)/(x - x1) = m

(y - 1)/(x - 0) = 3

y - 1 = 3x

y = 3x + 1

The number of steps they climbed can be represented by positive

From the question, we understand that they climbed up

Upward movements are usually represented by the positive sign

This means that:

Steps = 125 or +125

Hence, the number of steps they climbed can be represented by positive

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Here, 12 is the mode.

Step-by-step explanation:

Find the mode of the set of numbers (6,12,9,9,6,12,3,3,12,12) ?

The mode of a data set is the number that occurs most frequently in the set. To easily find the mode, put the numbers in order from least to greatest and count how many times each number occurs. The number that occurs the most is the mode.

So let's talk in brief:-

First, we arrange it in ascending order.

3,3,6,6,9,9,12,12,12,12

and now as we see that we get 12 as the most repeated ones.

reference link-

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Step-by-step explanation:

s = number of standard downloads

2s = number of high-quality downloads

2.8s + 4.6(2s) = 2760

2.8s + 9.2s = 2760

12s = 2760

s = 230

The standard version was downloaded 230 times and the high-quality version was downloaded 460 times.

Answer:

$6.45/hour

110.26%

Step-by-step explanation:

The absolute change is the difference between salaries now ands then.

12.30 - 5.85 = 6.45

The relative change in the percent increase.

percent increase = (new number - old number)/(old number) × 100%

percent increase = (12.3 - 5.85)/(5.85) × 100%

percent increase = 110.26%

1. The sequence that will minimize the total completion time is sequence 4. B-A-C-D-E.

2. The determination of the amount of idle time for Workstation B is 37 minutes.

According to Johnson's sequencing rule, start listing jobs with minimum completion time first.

If the job occurs at Workstation A, list it on the left side.  If the job occurs at Workstation B, list it on the right side, as below:

JOB TIMES (minutes)     A     B    C     D     E

Workstation A                27   18   70   26   15

Workstation B                45  33   30   24   10

The first job with a minimum completion time is Job E at Workstation B.

The second job with a minimum completion time after Job E is Job B at Workstation A.

The third job with a minimum completion time after Job B is Job D at Workstation B.

The fourth job with a minimum completion time after Job D is Job A at Workstation A.

The last job is Job C at Workstation B.

The sequence that minimizes total completion time is as follows:

        B         A            C              D          E

A                                                                    B

Job       Workstation A               Workstation B                  Idle Time

              In           Out                  In           Out               Workstation B

B            0            0+18 =  18       18        18+33 = 51                   18

A          18           18+27 = 45       51        51+45 = 96                  19

C         45          45+70 = 115      115      115+30 = 145                 0

D        115          115+26 = 141     145     145+24 = 169                 0

E        141           141+15 = 156    169     169+10 =  179                 0

Total Idle Time at Workstation B =                                         37 (18 + 19)

Thus, the sequence that minimizes the total completion time is sequence 4, while the idle time at Workstation B is 37 minutes.

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1. A-B-C-D-E

2. E-D-B-C-A

3. D-C-B-A-E

4. B-A-C-D-E

5. C-A-B-D-E

Answer:

=57198.98

Step-by-step explanation:

Volume of Cylinder = pi x radius^2 x height

= pi x 17^2 x 63

=57198.9774439

=57198.98

Answer: A. ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]

Step-by-step explanation:

± [tex]\frac{1, 3, 5, 15}{1, 3}[/tex]

= ± [tex]1, 3, 5, 15, 1/3, 5/3, 5[/tex]

Rearranging, we get:

= ± [tex]\frac{1}{3} ,\frac{5}{3} ,1,3,5,15[/tex]

Answer:

1/4

Step-by-step explanation:

Given [tex]\displaystyle{s=\dfrac{1}{4}}[/tex] and we have to evaluate [tex]\displaystyle{4s^2}[/tex]. We can do by substituting the given value s = 1/4 in 4s² term:

[tex]\displaystyle{4\cdot \left(\dfrac{1}{4}\right)^2}\\\\\displaystyle{4\cdot \dfrac{1}{16}}\\\\\displaystyle{\dfrac{1}{4}}[/tex]

Therefore the value is 1/4

The equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

[tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex]

Evaluate the product

[tex]7 * 6x^2 \sqrt{2x^4*2x^{12 }[/tex]

This gives

[tex]42x^2 \sqrt{4x^{16}[/tex]

Take the square root of 4

[tex]2*42x^2 \sqrt{x^{16}[/tex]

Take the square root of x^16

[tex]2*42x^2 *x^8[/tex]

So, we have:

[tex]84x^{10[/tex]

Hence, the equivalent expression of [tex]7x^2 \sqrt{2x^4} \times 6 \sqrt {2x^{12 }[/tex] is [tex]84x^{10[/tex]

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Answer:

Step-by-step explanation:

The equivalent expression of  is

How to determine the equivalent expression?

The expression is given as:

7x^2 sqrt 2x^4 times 6 sqrt 2x^12

Rewrite properly as:

Evaluate the product

This gives

Take the square root of 4

Take the square root of x^16

So, we have:

Hence, the equivalent expression of is

You can just replace [tex]u[/tex] with 2:

[tex]2^2 - 4\times2 + 2 = 4 - 8 + 2 = \boxed{-2}[/tex]

Alternatively, you can complete the square.

[tex]u^2 - 4u + 2 = u^2 - 4u + 4 - 2 = (u-2)^2 - 2[/tex]

When [tex]u=2[/tex], the quadratic term vanishes and we again get -2.

Answer: b and e

Step-by-step explanation:

b - the slope is positive

the slope is 8 not negative 8 because, 4+4/2-1 = 8/1 = 8 since subtracting 4 and -4 makes it 4+4

e - it is possible for x to be positive and for y to be negative