11 You deposit $1200 in an account. The annual interest rate is 3%. How long will it take you to earn S108 in simple interest?

Answer:

Option b.

Step-by-step explanation:

If the starting value a, the growth factor b, and the growth rate r, then

[tex]Q=ab^t=a(1+r)^t[/tex]        ...(1)

It is given that

[tex]Q=1750(1.593)^t[/tex]        ...(2)

On comparing (1) and (2), we get

[tex]a=1750, b=1.593[/tex]

Now, equation (2) can be rewritten as

[tex]Q=1750(1+0.593)^t[/tex]        ...(3)

On comparing (1) and (2), we get

[tex]r=0.593[/tex]

[tex]r=(0.593\times 100)\%[/tex]

[tex]r=59.3\%[/tex]

Therefore, the correct option is b.

Step-by-step explanation:

1.32:24

32/8:24/8

4:3

2.20:32

20/4:32/4

5:8

3.24:76

24/4:76/4

6:19

4.24:32:20

24/4:32/4:20/4

6:8:5

Answer:27.5

Step-by-step explanation:

Answer:

B. 27.5

Step-by-step explanation:

37 is the Q2, which is the median,

Q1 is 27 + 28 / 2 = 27.5

Answer:

Step-by-step explanation:

find the slope

[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]

take a coordinate to fill in

[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]

this means that the equation is y=2x-13

and if you add m and b

you get :-11

I HOPE THIS HELPS

Answer:

7/2

Step-by-step explanation:

Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.

The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by

\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find

\[y = -\frac{1}{2} x + 4.\]

Answer:

14.4 cm

Step-by-step explanation:

Answer:

4√13

Step-by-step explanation:

Let's call the missing side length x

The given is a right triangle and in right triangle the square

length of hypotenuse is equal to square sum of other two side lengths

17^2 = 9^2 + x^2

289 = 81 + x^2 subtract 81 from both sides

208 = x^2

4√13 = x

Answer:

The answer is option B.

y = 1/8x² + 5

Hope this helps you

Answer:

f(x - n) - shift the graph n units right

f(x + n) - shift the graph n units left

f(x) - n - shift the graph n units down

f(x) + n - shift the graph n units up ----------------------------------------------------------------------------

Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.

Answer:

Vertex: (0, 12)

Direction: Upwards

Step-by-step explanation:

Easiest way to do this is to graph it. When you do so you should be able to see that your vertex is at (0, 12) and that the graph opens upwards (a is not negative, so no reflection over the x-axis).

Answer:

(1) N or n = 20

(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4

(3) σ = 9.78 and s = 10.04.

Step-by-step explanation:

We are given with the following data set below;

{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}

(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.

(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;

        Mean  =  [tex]\frac{\sum X}{n}[/tex]

              =  [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]

              =  [tex]\frac{868}{20}[/tex]  = 43.4

So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.

(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;

        Standard deviation, [tex]\sigma[/tex] =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]

             =  9.78

Similarly, the formula for calculating sample standard deviation (s) is given by;

        Sample Standard deviation, s =  [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]

             =  [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]

             =  10.04

Answer:

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Step-by-step explanation:

least of 3 consecutive integers is a, and the greatest is z

if a is the least one

we know that integers differ by value of 1.

example -2, -1, 0, 1,2

they all differ by

then next consecutive integer will be a+1

third integer will be  second integer +1 = a+1 + 1 = a+2

Thus, 3 consecutive integer

a , a+1, a+2

but given that greatest is z

thus, a+2 is greatest and hence

a+2 = z

we have to find   value of a + 2z/ 2 in terms of a

a + 2z/ 2 = a + 2(a+2)/2 = (a+ 2a +4)/2 = (3a+4)/2.

The value of a + 2z/ 2 in terms of a is (3a+4)/2

Answer:

B

Step-by-step explanation:

The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.

Answer:

[tex]5\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{2\sqrt{8^2+15^2}+\sqrt{9^2+40^2}}=?\\\\1)\sqrt{8^2+15^2}=\sqrt{289}=17\\2)\sqrt{9^2+40^2}=\sqrt{1681}=41\\3)2\times17=34\\4)\sqrt{34+41}=5\sqrt{3}[/tex]

All Done!

Answer:

Your correct answer is 8.660254

Step-by-step explanation:

√2√82 + 152 + √92 + 402 = 8.660254

ffefefertjuylijhq DS3NUFHUFH4UFUFHUFUEFNUEFNUEFN

Answer:

≈ 5.8

Step-by-step explanation:

Step 1: Round the fractions

29 1/5 = 146/5 = 29.2 ≈ 29

4 6/7 = 34/7 = 4.85714 ≈ 5

Step 2: Divide

29/5 = 5.8

The answer is under

Answer:

11,8,5

Step-by-step explanation:

an=11-3(n-1)

Let n=1

a1 = 11 - 3(1-1)

    = 11 -0

    =11

Let n=2

a2 = 11-3(2-1)

     = 11 -3(1)

     = 8

Let n=3

a3 = 11-3(3-1)

    = 11 -3(2)

    = 11 -6

    =5

Answer:

The answer is 11,8,5

Step-by-step explanation:

that's the correct answer

Answer:

Find GCF of all values in the given ratio

GCF(100, 199, 47) = 1

When GCF value is equal to 1, the given ratio can not be simplified.

Step-by-step explanation:

It cant be simplified

Answer:

100:199:47

Step-by-step explanation:

The ratio cannot be simplified.

The numbers 199 and 47 are prime numbers, and only have the factors of 1 and themselves.

Answer: a = 0.3

Step-by-step explanation:

First, distribute(-1)

5.3a-0.8-1.6+4.7a=2a-(a-0.3)

Then, distribute(-1)

5.3a-0.8-1.6+4.7a=2a-a+0.3

Then, combine like terms

10a-2.4=a+0.3

Then, add(2.4)

10a=a+2.7

Then, subtract(a)

9a=2.7

Then, divide(9)

a = 0.3

Hope it helps <3

Answer:

a = 0.3.

Step-by-step explanation:

(5.3a−0.8)−(1.6−4.7a)=2a−(a−0.3)

5.3a − 0.8 − 1.6 + 4.7a = 2a − a + 0.3

5.3a + 4.7a - 2a + a =  0.3 + 0.8 + 1.6

9a = 2.7

a = 0.3.

Step-by-step explanation:To find the interest accumulated over a period of time you use:

A = P [1 + (r/n)]^(nt)

with A = new amount in the account, P = principal, r = percent rate as a decimal, n = how many times you compound during one year, t = time in years.

A = 2000

P = 1500

r = 0.035

n=1

Thus you get:

2000 = 1500 (1+0.035)^t

Divide by 1500:

(4/3) = (1.035)^t

Apply "ln" on both sides:

ln(4/3) = t*ln(1.035)

Calculate the logarithms:

0.28768 = t*0.03440

Divide by 0.03440 on both sides:

t = 8.36 years

So after approximately 8 years and 5 month you will have $2000 or more in the account.

Answer:

361.25

Step-by-step explanation:

first subtract her sales

900 - 500 equals 400

next subtract her earnings

489-405= 85

next divide the remainder of her earnings by the remainder of her sales

85/400=.2125

finally multiply this by 1700

0.21 to 5 * 1700 equals 361.25

Answer:

[tex]\frac{r^{15}}{512}[/tex]

Step-by-step explanation:

Given

[tex](8r^{-5})^{-3}[/tex]

Required

Simplify

This can be simplified using the following law of indices;

[tex](ab)^n = a^{n}b^{n}[/tex]

The equation becomes

[tex](8^{-3})(r^{-5})^{-3}[/tex]

Express [tex]8^{-3}[/tex] as a fraction

[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]

Simplify [tex]8^3[/tex]

[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]

The expression can further be simplified using the following law of indices;

[tex](a^m)^n = a^{mn}[/tex]

[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes

[tex](\frac{1}{512})(r^{-5*-3})[/tex]

[tex](\frac{1}{512})(r^{15})[/tex]

[tex]\frac{r^{15}}{512}[/tex]

Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

The car dealership has 252 sedans.

Step-by-step explanation:

Number of SUVs = 140

Ratio of SUVs to sedans = 5:9

Sum of ratios = 5+9 = 14

Total number of cars = 14/5 × 140 = 392

Number of sedans = 9/14 × 392 = 252

Answer:

Park Q has greatest percentage of pink butterflies.

Step-by-step explanation:

Butterfly Park Survey Park           P     Q      R       S

No, of Pink Butterflies                  25    35   37      23

Total Number of Butterflies          53    64   75     55

Now we are supposed to find which park had the greatest percentage of pink butterflies

So, Percentage of pink butterflies in park P =[tex]\frac{25}{53} \times 100=47.169\%[/tex]

Percentage of pink butterflies in park Q =[tex]\frac{35}{64} \times 100=54.68\%[/tex]

Percentage of pink butterflies in park R= [tex]\frac{37}{75} \times 100=49.33\%[/tex]

Percentage of pink butterflies in park S= [tex]\frac{23}{55} \times 100=41.81\%[/tex]

So, Park Q has greatest percentage of pink butterflies.

So, Option B is true

Hence Park Q has greatest percentage of pink butterflies.

Answer:

I think it's A but I could be wrong

Answer: B

Step-by-step explanation:

A graph or table is a function if it passes the vertical line test. That means, each x and only 1 y. One x cannot have more than 1 y because, that means it does not pass the veritcal line test. In the vertical line test, the vertival line only passes through 1 point, not 2. Since we know that this graph does not pass the vertical in test, we can eliminate C and D. We can eliminate A because 2 y-values can be the same as lone as there have different x. B fits the description of what we see on the table. Therefore, the answer is B.

Answer:

A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers

I hope that is what your asking...

Answer:

On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

The third and fourth options.

Step-by-step explanation:

You simplify the inequality first...

-6x + 15 < 10 - 5x

-x < -5

x > 5

The first option is incorrect since it is less than.

The second option is basically -5x < 15; x > -3; that's incorrect.

The third option is basically -x < -5; x > 5; that is correct!

The fourth option is correct since it shows more than 5.

The fifth option is incorrect because it shows less than -5.

Hope this helps!

Answer: The answer is C and E

Step-by-step explanation:

Hope this helps;)

Answer:

[tex]mGH=80^\circ[/tex]

Step-by-step explanation:

Circle F and J are congruent.

[tex]\angle DFE \cong \angle GJH[/tex]

Given that: m∠DFE = 80°

DFE is the central angle of the circle F.

The measure of arc GH is equal to the central angle of Circle J.

Since both circles are congruent

[tex]mGH=\angle DFE = 80^\circ[/tex]

The measure of arc GH is 80 degrees.

Answer:

Arc GH=80°

Step-by-step explanation:

Edge 2020

Answer:

You can verify if lines are parallel if they have the same slope and different y-intercepts and if they don't intersect each other. You can also graph the 2 equations to see if they ever intersect.

Step-by-step explanation:

Answer:

C. Check the intersecting lines with the corner of a piece of paper to ensure the lines create 90° angles. Took the test just now and got it right

Step-by-step explanation:

Answer:

price paid of speakers= £40.5

price paid of headphones=£ 5.6

price paid of book=£6.65

price paid of mobile phone=£42

price paid of mouse=£ 15.75

price paid of DVD=£11.05

solution,

1. Cost of speakers:

Discount percent=10 %

Marked price=£45

discount amount= discount % of MP

=10% of 45

=£4.5

Selling price= MP - discount amount

=£45-£4.5

=£ 40.5

2. cost of headphones:

discount amount= discount% of MP

=20% of 7

=£1.4

Selling price= MP- Discount amount

=£7-£1.4

=£ 5.6

3. cost of books:

discount amount= discount percent of MP

= 30% Of 9.50

=£ 2.85

selling price= MP- Discount amount

= £ 9.50-£2.85

=£ 6.65

4. cost of mobile phone:

discount amount= discount% of MP

=40% of 70

=£ 28

selling price= MP- Discount amount

=£70-£28

=£ 42

5. cost of mouse:

discount amount= discount% of MP

= 25% of 21

=£ 5.25

selling price= MP- Discount amount

=£21-£5.25

=£ 15.75

6. cost of DVD:

discount amount= discount % of MP

= 15% of 13

= £ 1.95

selling price= MP- discount amount

=£ 13 -£ 1.95

=£ 11.05

Hope this helps...

Good luck on your assignment..