Sandy borrowed a book from Liabrary and read notice about fines. Each day fine doubles.if snook is 1day overdue ,the fine is $0.02 .if it is 2days overdue,the fine is$0.04,if it is 3 days overdue,it is $0.08 and so on. If sandy book is one week overdue how much will he fine be

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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The total cost needed to tile the training room with an area of 100 m² is R110.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let assume that the area of the trainig room is 100 m² and one box can complete 50 m², hence:

number of box needed = 100 m² / 50 m² = 2

Total  cost = R55 per box * 2 box = R110

The total cost needed to tile the training room with an area of 100 m² is R110.

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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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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

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]

[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 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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Answer:

The monthly cost = $9 + $0.39x

Step-by-step explanation:

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

Step-by-step explanation:

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

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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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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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:

$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%

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 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:

3/8 or 0.375 or 37.5%

Step-by-step explanation:

So since the coin is tossed three times, it's not to hard to write out every scenario since there will only be 2^3  combinations or 8 combinations. But we can also use Binomial Distribution Formula.

Binomial Distribution Formula:

   [tex]P(x)=(^n_x)p^xq^{n-x}[/tex]

   Where p = probability of success and q=probability of failure, x=how many successes, and n=total number of trials

   Combination Formula:

       [tex](^n_x) = \frac{n!}{x!(n-x)!}[/tex]

So let's define the variable values, since it's a coin, the probability of heads/tails should be 50/50 so p=0.50 and q=0.50. Since we want 2 heads then x=2, and since the total number of trials is 3, n=3.

So let's plug the values into the equation:

[tex]P(x)=\frac{3!}{2!}*(0.50)^2*(0.50)^1[/tex]

Rewrite 0.50 as a fraction

[tex]P(x)=\frac{3*2*1}{2*1}*(\frac{1}{2})^2*(\frac{1}{2})^1[/tex]

Cancel out values in fraction, and also square the fraction

[tex]P(x)=3*\frac{1}{4}*\frac{1}{2}[/tex]

Multiply fractions

[tex]P(x)=3*\frac{1}{8}[/tex]

Multiply the two values

[tex]P(x)=\frac{3}{8}[/tex]

This means the probability is 3/8 or 0.375 or 37.5%

I also provided a diagram on how to just draw out each scenario/combination

Using the normal distribution, the probabilities are given as follows:

a) 0.6826 = 68.26%.

b) 0.9759 = 97.59%.

c) 0.0004 = 0.04%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Item a:

The probability is the p-value of Z = 1(0.8413) subtracted by the p-value of Z = -1(0.1587), hence:

0.8413 - 0.1587 = 0.6826

Item b:

The probability is the p-value of Z = 2(0.9772) subtracted by the p-value of Z = -3(0.0013), hence:

0.9772 - 0.0013 = 0.9759.

Item c:

This probability is P(|Z| > 3.5), which is 2 multiplied by the p-value of Z = -3.5, which is of 0.0002.

Hence:

2 x 0.0002 = 0.0004 = 0.04%.

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Answer: I think its A

Step-by-step explanation: maybe

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

Answer:

1/8

Step-by-step explanation:

Look at the screen shots

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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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

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 other sides measure:

All the measures must be multiplied by the same scale factor to get a similar pentagon.

If in the original pentagon the shortest side measures 2", and in the similar pentagon the shortest side measures 5", then we have:

5" = k*2"

5"/2" = k = 2.5

Then the scale factor is 2.5

To get the other sides of the pentagon, we just need to multiply the other sides of the original pentagon by 2.5

The other sides measure:

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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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It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.

Given that the field is 160 yards long and the diameter is 12 yards and charge of 1 square yard of fertilizing is $0.25.

We are required to find the total cost of fertilizing the field.

The total cost of fertilizing the field will be the product of the cost of 1 square yards and the area of the field.

When we will observe the field carefully then we will say that the diameter of the semi circle is equal to the breadth of the rectangle. There are two semicircles so we have to just find the area of 1 circle and the area of 1 rectangle.

Area of the field=Area of rectangle+Area of circle

=length* breadth+π[tex]r^{2}[/tex]

=160*12+3.14*[tex]6^{2}[/tex]

=1920+3.14*36

=1920+113.04

=2033.04 [tex]yards^{2}[/tex]

Cost of fertilzing the field=2033.04*0.25

=$508.26

Hence It will cost $508.26 to fertilize the field having the length 160 yards and the diameter of the semicircles is 12 yards.

Question is incomplete as the figure which is attached should be included.

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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.

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.

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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