I need help with question 24

let me answer the last one first

compound interest is just an exponential sequence really, where the next value is some exponential amount of the previous.

hmmm that can happen in say, a bouncing ball, the 1st bounce is high, let it keep on boucing by itself and the next bounce is usually a compounded value of the previous one, since it's smaller it'd be a Decay type of equation.

hmmm it also happens in say population growth, of any organism, humans, bees, amoebas.

now let's do the others

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=3000\left(1+\frac{0.026}{4}\right)^{4\cdot t}\implies \boxed{A=3000(1.0065)^t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 15 years}}{t=15}\hspace{5em} A=3000(1.0065)^{15}\implies A\approx 3306.19 \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$3000\\ r=rate\to 2.6\%\to \frac{2.6}{100}\dotfill &0.026\\ t=years\dotfill &15 \end{cases} \\\\\\ A=3000e^{0.026\cdot 15}\implies A=3000e^{0.39}\implies A\approx 4430.94[/tex]

Answer:

No, right answer is = 1017.36

Answer:

1017.36

Step-by-step explanation:

All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:

[tex]\pi * 6^{2}*9 = 1017.88[/tex]

instead of

[tex]3.14*6^{2}*9 = 1017.36[/tex]

like you had written above. So the final is actually supposed to be 1017.36

Step-by-step explanation:

hope you have a great day

The value of x will be;

⇒ x = 13.9

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in figure.

Now,

Since, We know that;

The sine rule is;

⇒ sin A / a = sin B / b = sin C / c

By given figure, we get;

⇒ sin 83°  / x = sin 68° / 13

⇒ sin 83° × 13 / sin 68° = x

⇒ x = 0.99 × 13 / 0.92

⇒ x = 13.9

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How to solve your problem

x^{2}-21=100

Quadratic formula

Factor

1

Move terms to the left side

x^{2}-21=100

x^{2}-21-100=0

2

Subtract the numbers

x^{2}\textcolor{#C58AF9}{-21}\textcolor{#C58AF9}{-100}=0

x^{2}\textcolor{#C58AF9}{-121}=0

3

Use the quadratic formula

x=\frac{-\textcolor{#F28B82}{b}\pm \sqrt{\textcolor{#F28B82}{b}^{2}-4\textcolor{#C58AF9}{a}\textcolor{#8AB4F8}{c}}}{2\textcolor{#C58AF9}{a}}

Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.

x^{2}-121=0

a=\textcolor{#C58AF9}{1}

b=\textcolor{#F28B82}{0}

c=\textcolor{#8AB4F8}{-121}

x=\frac{-\textcolor{#F28B82}{0}\pm \sqrt{\textcolor{#F28B82}{0}^{2}-4\cdot \textcolor{#C58AF9}{1}(\textcolor{#8AB4F8}{-121})}}{2\cdot \textcolor{#C58AF9}{1}}

4

Simplify

Evaluate the exponent

Multiply the numbers

Add the numbers

Evaluate the square root

Add zero

Multiply the numbers

x=\frac{\pm 22}{2}

5

Separate the equations

To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.

x=\frac{22}{2}

x=\frac{-22}{2}

6

Solve

Rearrange and isolate the variable to find each solution

x=11

x=-11

The approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

(a) t = 10 days and a day earlier

This means that:

t = 10 and t = 9

The function is given as:

[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]

Calculate N(10)

[tex]N(10) = 100000e^{\frac{-(10 - 10)^2}{8}}[/tex]

Evaluate

N(10) = 100000

Next, calculate N(9)

[tex]N(9) = 100000e^{\frac{-(9 - 10)^2}{8}}[/tex]

Evaluate

N(9) = 88249.6902585

The slope is then calculated using"

[tex]m = \frac{N(10) - N(9)}{10 - 9}[/tex]

This gives

[tex]m = \frac{100000 - 88249.6902585}{10 - 9}[/tex]

Evaluate

m = 11750.3097415

Approximate

m = 11750

(b) t = 10 days and a day later

This means that:

t = 10 and t = 100

The function is given as:

[tex]N(t) = 100000e^{\frac{-(t - 10)^2}{8}}[/tex]

In (a), we have:

N(10) = 100000

Next, calculate N(11)

[tex]N(9) = 100000e^{\frac{-(11 - 10)^2}{8}}[/tex]

Evaluate

N(11) = 88249.6902585

The slope is then calculated using:

[tex]m = \frac{N(11) - N(10)}{11 - 10}[/tex]

This gives

[tex]m = \frac{88249.6902585 - 100000}{11 - 10}[/tex]

Evaluate

m = -11750.3097415

Approximate

m = -11750

Hence, the approximation of the slope of the graph at t = 10 days using this secant lines are 11750 and -11750, respectively.

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Answer: 10 is the range, option B/ option G

Step-by-step explanation: range is the most subtracted by the least, so organize the data set which makes it (5, 7, 10, 11, 12, 13, 15, 15, 15)

15 - 5 is 10.

Answer:

Coordinate pair for Friday (3, 55). This means the length of the eruption was 3 minutes, and the wait time between the eruptions was 55 minutes.

Paulo and Jason wear smaller shoe sizes than Carmen.

Jason and Carmen scored more runs than Paulo.

Step-by-step explanation:

Paulo wears size 5 and Jason wears size 4. Carmen wears size 10, therefore the players wear smaller shoe sizes than he does

Jason scored 10 runs, and Carmen scored 11. Since Paulo only scored 5 runs, the other players scored more than him

Answer:

16

Step-by-step explanation:

7 friends = 14 hotdogs + bobby (2 hotdogs) = 16 hotdogs

Answer:

16 hot dogs

Step-by-step explanation:

since he has 7 friends + himself, we're going to have a total of 8 persons

and since it's expected for each person to have two hot dogs,

total hotdogs Bobby need to cook= 8×2= 16 hot dogs

Answer:

120 meters

Step-by-step explanation:

1.2  x 10 000 = 12000 cm   = 120 meters  

Answer:

a) 15/8   b) 25/18

Step-by-step explanation:

a) First bring all the fractions to a common denominator (I'm going to use 8th's). 5/8 is already simplified, 1/2=4/8, and 3/4=6/8. Then, simply add the numerators and leave the denominator:  [tex]\frac{5+4+6}{8} =\frac{15}{8}[/tex]

Since this can not be simplified any further, your final answer is 15/8.

b) Start by bringing all the fractions to a common denominator (for this problem, we'll use 18th's). 2/3=12/18, 1/6=3/18, and 5/9=10/18. Then just add all the numerators and leave the denominator the same: [tex]\frac{12+3+10}{18} = \frac{25}{18}[/tex]

Since this cannot be simplified further either, your final answer is 25/18.

Hope this helps! :)

Answer:

so to add we need to find lcm

Step-by-step explanation:

a) 5/8 + 1/2+3/4                            lcm of 2,4 and 8 = 8

5/8 = 5/8

1x4
2x4  =  = 4/8

3x2
4x2    = 6/8

5/8 + 4/8 + 6/8 = 15/8


b) 2/3 + 1/6 + 5/9                       lcm of 3 , 6 and 9 = 18

2x6
3x6  = 12/18

1x3
6x3      = 3/18

5x2
9x2 = 10/18

12/18 + 3/18 + 10/18 = 25/18

Answer:

3, 2, 4, 1

Step-by-step explanation:

Answer:

3/7  /    42.8% chance

Step-by-step explanation:

There are 6 striped balls (9, 10, 11, 12, 13, 14) and 8 (1, 2, 3, 4, 5, 6, 7, 8) solid colored balls. So, 6 / 14 balls are striped.

(6 / 14  = 3 / 7)

this means that the probability of a ball being striped has the odds of 3/7

(3/7 = about 42.8% chance)

Answer:

B

Step-by-step explanation:

Answer:

Total Area = 68

Step-by-step explanation:

Comment

There is 1 square at each end.

There are 2 congruent trapezoids in the middle

Draw a 7 inch line across the widest part of the middle

Area of the squares

Area = s^2

s = 3

Area = 3^2

Area = 9

But there are 2 of them                                        18

Area of the 2 trapezoids

Area = (b1 + b2)*h / 2

b1 = 3

b2 = 7    Notice that 7 was the line you drew

h = 5

Area = (3 + 7)*5/2

Area = 50 / 2

Area = 25

But there are 2 of them                                        50

Total Area                                                              68

Answer:

w = (12p - 7) / 2

Step-by-step explanation:

p = (2w + 7) / 12

12p = 2w + 7

2w = 12p - 7

w = (12p - 7) / 2

Answer:

1.) ∞

2.) -∞

3.) 0

4.) 0

Step-by-step explanation:

As you approach x = -2 from the left, the "y" values are going to infinity. You never actually get a "y" value that equals x = -2 because of the vertical asymptote.

As you approach x = -2 from the right, the "y" values are going to -infinity. You never actually get a "y" value because there is a vertical asymptote.

As you approach x = 2, both sides converge to y = 0. At this point, there is a smooth, uninterrupted line.

The actual "y" value at x = 2 is 0 because the function goes straight through this point. So, you can just read this point as usual.

Answer:

10 cm

Step-by-step explanation:

See attached image

Answer:

length = 10 cm

Step-by-step explanation:

Fyi, breadth is a synonym to width.

Since P=30, we must find the length.
l = length
w = width
P=w+w+l+l

30 = 5+5+l+l
30 = 10+2l
-2l = -20
l = 10

Hence, the length is 10 cm.

Based on the calculations, the sequence defined by the given function are 0.75, 1.1, 1.45​, 1.80 and 2.15.

In this exercise, you're required to create the first five (5) terms of the sequence defined by the given function as follows:

For the first term, we have:

f(1) = 0.75

For the second term, we have:

f(2) = f(2-1) + 0.35

f(2) = 0.75 + 0.35

f(2) = 1.1.

For the third term, we have:

f(3) = f(3-1) + 0.35

f(3) = 1.1 + 0.35

f(3) = 1.45.

For the fourth term, we have:

f(4) = f(3-1) + 0.35

f(4) = 1.45 + 0.35

f(4) = 1.80.

For the fifth term, we have:

f(5) = f(3-1) + 0.35

f(5) = 1.80 + 0.35

f(5) = 2.15.

Therefore, the sequence defined by the given function are 0.75, 1.1, 1.45​, 1.80 and 2.15.

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Answer:

in terms of pi: A = 14,400pi

A = 14,400(3.14) is 45,216

Step-by-step explanation:

Area of a circle is pir^2

Radius = diameter / 2

Radius = 240 / 2 which is 120

A = pi(120)^2

A = 14,400pi

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the area of a circle with a diameter of 240.

[tex]\triangle~\fbox{\bf{KEY:}}[/tex]

We can find the radius by dividing the diameter by 2:

[tex]\star~\large\pmb{240\div2=120}[/tex]

The radius is 120. Now it's time to compute the area!

///\\\///\\\///\\\\////\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\\

                                    Computing The Area

The formula for the area is:

[tex]\star~\large\pmb{Area_{(circle)}=\pi r^2}}[/tex]

See, there's the radius, r; we found a minute ago, and it equals 120 cm.

Now, substitute the value of r into the formula:

[tex]\begin{gathered} \sf{\longmapsto{A=\pi (120)^2} \\ \sf{\longmapsto{A=\pi\times14,400} \\ \sf{\longmapsto{A=45,238.9\;cm^2 \end[/tex]

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

Answer:

3/10

Step-by-step explanation:

So you have 2/5 left in your cupboard. Say the amount of chips originally in your cupboard would be 30. 2/5 of 30 would be 12.

Then multiply 12 by 3/4 so it would be 3/4 of 12.

The result would be 9

9/30 = 3/10

this is complicated explanation

there are much easier explanations tho

Answer:

d.  ΔMNO

Step-by-step explanation:

In geometry, two figures are congruent if they are the same shape and size (they can also be a mirror image of each other).  If they are the same shape but a different size (e,g, one is an enlargement or reduction of the other), then they are similar.

All the given triangles have the same interior angles, so we need to find a triangle with the same side lengths as ΔABC.  

The only triangle that has the same side length as ΔABC is ΔMNO:
they both have bases of 8cm.

Therefore, ΔMNO is congruent to ΔABC.

Domain F(x) = All real numbers and the Range F(x)  [ -2 ,  + ∞ ]

A domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

The curve points are

P₁ ( -1,5 , 0 )   Q ( 0. -2 ) and P₂ ( 1,5 , 0 )

We can see that P₁  and P₂ are symmetric around the y-axis, and point Q looks like a vertex so we can conclude the curve as

ax² + bx + c = y

The curve is a parabola

when x = 0      

y = -2    

then   c  = - 2

The equations we get,

a (-1.5)²  +  b (-1.5) + c = 0      

2.25a  - 1.5b - 2 = 0

a (1.5)²   +  b ( 1.5)  + c = 0    

2.25a + 1.5b -2 = 0

Adding these two equations

4.5a - 4 = 0

a =  4/4.5

The vertex is Q ( 0 , -2 )

x = - b/2a      

0 = - b/ 9      

b  =  0

Therefore the equation of the function :

ax² + c = 0

(4/4.5) x² - 2 = 0

Therefore, Domain F(x) = All real numbers and the Range F(x)  [ -2 ,  + ∞ ]

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Answer:

In a shorter explanation of what the guy above me is saying

The domain is all real numbers or A

The range is "all real numbers greater than or equal to –2" or B

Step-by-step explanation: