What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent and the compound interest earned when you invest the same sum for 2 years at 5 percent ?
The simple interest earned when you invest $1,000 for 3 years at 10 % is $
. The interest compounded when you invest the same sum for 2 years at 5 % is $
.






There are 7 trout fish in a pond,
and the population doubles every year.
Find the population after t years.
arrowBoth

A company buys a machine for $3,000.
The value of the machine depreciates
by 7% every year. Find the value of
the machine after t years.
arrowBoth

The initial population of a colony of ants
is 300. The number of ants increases
at a rate of 1.5% every month. Find the
population of ants after t months.
arrowBoth

A research laboratory is testing a new
vaccine on 300 infected cells. The decay
rate is 1.5% per minute. Find the
number of infected cells after t minutes.
arrowBoth

For this case we must simplify the following expression:

[tex](\frac {n ^ {\frac {3} {2}}} {n ^ {- \frac {1} {6}}}) ^ {- 3}[/tex]

By definition of power properties we have:

[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]

Then, rewriting the expression:

[tex](n ^ {\frac {3} {2}} * n ^ {\frac {1} {6}}) ^ {- 3} =[/tex]

To multiply powers of the same base, we put the same base and add the exponents:

[tex](n ^ {\frac {3} {2} + \frac {1} {6}}) ^ {- 3} =\\(n ^ {\frac {18 + 2} {12}}) ^ {- 3} =\\(n ^ {\frac {20} {12}}) ^ {- 3} =\\(n ^ {\frac {5} {3}}) ^ {- 3} =[/tex]

We multiply the exponents:

[tex]n ^ {\frac {-15} {3}} =\\n^{-5}[/tex]

ANswer:

Option D

Answer:

D)  [tex]S_{14} = 875[/tex].

Step-by-step explanation:

Given  : If the first term of the series is 30 and the 14th term is 95,

To find : what is the sum of all the terms of the series.

Solution : We have given

First term = 30 .

14 th term = 95.

Sum of all term = [tex]S_{n} =\frac{n(first\ term +\ last\ term)}{2}[/tex].

Here, n = 14.

 [tex]S_{14} =\frac{14(30 +95)}{2}[/tex].

 [tex]S_{14} =\frac{14(125)}{2}[/tex].

 [tex]S_{14} =\frac{1750}{2}[/tex].

 [tex]S_{14} = 875[/tex].

Therefore, D)  [tex]S_{14} = 875[/tex].

Answer:

The sum of all the terms in series is 875.

Step-by-step explanation:

Given : If the first term of the series is 30 and the 14th term is 95,

To find : What is the sum of all the terms of the series?            

Solution :

The first term of the  series is 30 i.e. a=30

The 14th term of series is 95 i.e. [tex]a_{14}=95[/tex]

We know that in arithmetic series the 14th term is defined as

[tex]a_{14}=a+13d[/tex]

Substitute the value of a,

[tex]95=30+13d[/tex]

[tex]95-30=13d[/tex]

[tex]65=13d[/tex]

[tex]d=\frac{65}{13}[/tex]

[tex]d=5[/tex]

The common difference is 5.

The sum of the series is given by,

[tex]S_{n}=\frac{n}{2}[2a+(n-1)d][/tex]

[tex]S_{14}=\frac{14}{2}[2(30)+(14-1)5][/tex]

[tex]S_{14}=7[60+(13)5][/tex]

[tex]S_{14}=7[60+65][/tex]

[tex]S_{14}=7[125][/tex]

[tex]S_{14}=875[/tex]

Therefore, The sum of all the terms in series is 875.

Answer:

D

Step-by-step explanation:

It's easiest to divide everything by 3.

The best variable to solve for is x in the first equation.

Let 3x+6y=9 be equation (1)

and 2x-10y=13 be equation (2)

2x-10y=13

10y = 2x - 13

y =[tex]\frac{2x - 13}{10}[/tex]  

substitute the value of y in equation (1)

3x+6y=9

3x + [tex]6(\frac{2x - 13}{10})[/tex] = 9

3x + [tex]3(\frac{2x - 13}{5})[/tex] = 9

[tex]\frac{15x + 6x - 39}{5}[/tex] = 9

21x - 39 = 45

21x = 84

x = [tex]\frac{84}{21}[/tex]

x = 4

Therefore, option D) x in the first equation is the correct answer

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Answer:

29/40

Step-by-step explanation:

A basket contains 14 white eggs, 15 brown eggs, and 11 lemons. The exact probability that Taylor picks an egg from the basket is;

(14+15)/(14+15+11) = 29/40

Answer:

The exact probability that Taylor picks an egg from the basket is 0.725

Step-by-step explanation:

A basket contains 14 white eggs, 15 brown eggs and 11 lemons.

Total number of items in the basket [tex]=14+15+11= 40[/tex]

Total number of eggs in the basket [tex]=14+15= 29[/tex]

Taylor picks one item at random from the basket.

So, the probability that Taylor picks an egg [tex]=\frac{total\ number\ of\ eggs}{total\ number\ of\ items}=\frac{29}{40}=0.725[/tex]

Answer:

∠7 = 34°

Step-by-step explanation:

Since a and b are parallel lines then

∠3 and ∠7 are corresponding angles and congruent, so

∠7 = ∠3 = 34°

Answer:

34 degrees

Step-by-step explanation:

Answer:

b=10

Step-by-step explanation:

A=1/2bh

The A and h are already given

100=1/2b(20)

So what times 20 equals 2 times as much as 100? Its 10

100=1/2(10)(20)

100=1/2(200)

100=100

So the answer is b=10

Answer:

A. (0,0)

Step-by-step explanation:

both lines run through (4,-4)

they meet at 0 on the Y axis

so the answer is (0,0)

Answer:

The larger model’s volume is 3 times greater than the volume of the smaller model

Step-by-step explanation:

we know that

The volume of a pyramid is equal to

[tex]V=\frac{1}{3}Bh[/tex]

where

B is the area of the base of pyramid

h is the height of the pyramid

Find the volume of the smaller model

we have

[tex]h=10\ cm[/tex]

substitute

[tex]V=\frac{1}{3}B(10)[/tex]

[tex]V=\frac{10}{3}B\ cm^{3}[/tex]

Find the volume of the larger model

we have

[tex]h=30\ cm[/tex]

substitute

[tex]V=\frac{1}{3}B(30)[/tex]

[tex]V=\frac{30}{3}B=10B\ cm^{3}[/tex]

To find how many times greater than the smaller model is the larger model’s volume, divide the volume of the larger model by the volume of the smaller model

so

[tex]10B/(\frac{10}{3}B)=3[/tex]

The larger model’s volume is 3 times greater than the volume of the smaller model

Bill is the one who wrote this statistical question so there will be there will be variability in the responses collected.

Bill, because there will be variability in the responses collected

Answer:

The answer is C, the graph has the y intercept of 2

Step-by-step explanation:

You can see from the graph that the line intercepts the y axis at 2

It wouldn't be the slope of 1/2 because that choice isn't negative and this is a decreasing/negative graph

Jay spent 19 hours painting both parts of his house, which is obtained by adding the time he spent painting each side: 7 hours and 12 hours.

The question is asking about the total time Jay spent painting two sides of his house. We know that he spent 7 hours painting one side and 12 hours painting another side. To find the total time spent, we simply need to add the two times together. So, 7 hours + 12 hours equals 19 hours. Therefore, Jay spent 19 hours in total painting both parts of his house.

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Answer:

a. 38.3

b. 41.0

Step-by-step explanation:

We have been given the linear model;

a = 0.25t + 29

where a represents the median age of females in the United States and t the number of years since 1970

a.

We are required to predict the median age of females in 2007. The first step is to determine the number of years from 1970 to 2007 by finding the difference;

2007 - 1970 = 37

2007 is  thus 37 years after 1970.

The next step is to substitute t = 37 in the given linear model;

a = 0.25( 37) + 29 = 38.25

b.

We are required to predict the median age of females in 2018. The first step is to determine the number of years from 1970 to 2018 by finding the difference;

2018 - 1970 = 48

2018 is thus 48 years after 1970

The next step is to substitute t = 48 in the given linear model;

a = 0.25( 48) + 29 = 41

Answer:

y=50x+100

Step-by-step explanation:

y=mx+b

100 is b because its a flat fee

The slope is 50 because it is dependent on x, the amount of people.

The correct answer is y=150x.For example, if I were to equal 300. Then that would mean two people would have bought the membership. So, X equals two.

Answer:

Option D is correct.

Step-by-step explanation:

2x^2 -4x +9

We need to find root of the equation.

We will use quadratic equation to solve.

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

here a =2, b=-4 and c=9

Putting values and finding the value of x

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\x=\frac{-(-4)\pm\sqrt{(-4)^2-4(2)(9)}}{2(2)}\\x=\frac{4\pm\sqrt{16-72}}{4}\\x=\frac{4\pm\sqrt{-56}}{4}\\x=\frac{4\pm\sqrt{-(2*2*2*7)}}{4}\\x=\frac{4\pm\sqrt{-(2^2*2*7)}}{4}\\x=\frac{4\pm\sqrt{2^2}\sqrt{-14}}{4}\\We\,\,know\,\,\sqrt{-1}=i\,\,\\x=\frac{4\pm2\sqrt{14}i}{4}\\Dividing\,\,by\,\,4\,\,\\x= 1\pm\frac{\sqrt{14}i}{2} \\So,\\x=1+\frac{\sqrt{14}i}{2} \,\,and\,\, x=1-\frac{\sqrt{14}i}{2}[/tex]

So, one of the root is [tex]x=1+\frac{\sqrt{14}i}{2}[/tex]

So, Option D is correct.

Answer:

[tex]\large\boxed{A=(223.3+49\pi)m^2}[/tex]

Step-by-step explanation:

(look at the picture)

We have:

two halves of circle (whole circle) with radius r = 7m;

the suqare wih length side a = 14m;

the triangle with base b = 14m and hight h = 3.9m.

The formula of an area of a circle:

[tex]A_1=\pi r^2[/tex]

Substitute:

[tex]A_1=\pi(7^2)=49\pi\ m^2[/tex]

The formula of an area of a square:

[tex]A_2=a^2[/tex]

Substitute:

[tex]A_2=14^2=196\ m^2[/tex]

The formula of an area of a triangle:

[tex]A_3=\dfrac{bh}{2}[/tex]

Substitute:

[tex]A_3=\dfrac{(14)(3.9)}{2}=(7)(3.9)=27.3\ m^2[/tex]

The area of a figure:

[tex]A=A_1+A_2+A_3\\\\A=49\pi+196+27.3=223.3+49\pi[/tex]

Answer:

113.0 inches per square

Step-by-step explanation:

Given

r=6 inches

The formula for finding the area of a circle is:

A= πr^2

Here, A denotes the area and r denotes the radius whereas the value of π is 22/7 or 3.14.

As in the question it is directed to use 3.14 for the value of π  

So,

A=3.14*(6)^2

=3.14*36

=113.04 inches^2

Rounding off to the nearest 10

A=113.0 inches^2

So the area of given circle is 113.0 inches per square ..  

Answer:

Plane: C) A flat surface that extends infinitively and has no depth; it has length and width

Perpendicular Lines: B) Two lines that intersect at 90° angles

Parallel Lines: E) Two lines that lie within the same plane and never intersect

Circle: D) A set of all points in a plane that are given distance from a plane

Angle: A) A figure consisting of two rays with a common endpoint

I hope this helps

this is 100% correct

plz mark me brainliest

Answer:

32

Step-by-step explanation:

Answer:

Tn = -4^n/2

Step-by-step explanation:

The formula for nth tern of a geometric sequence is given as:

Tn = ar^n-1 where;

a is the first term

r is the common ratio

n is the number of terms

Since we are looking for the nth term if the geometric sequence, we will write our answer as a function if 'n'.

Given the second and fifth terms to be -8 and 512, respectively, this can be interpreted as;

T2 = ar^2-1 = -8

T5 = ar^5-1 = 512

From the equations above, we have;

ar = -8... (1)

ar⁴ = 512

Dividing both equation, we have;

ar⁴/ar = -512/8

r³ = -64

r = -4

Substituting r = -4 into equation 1, we have;

a(-4) = -8

-4a = -8

a = 2

Since nth term Tn = ar^n-1

Substituting the value of a and r into the equation will give;

Tn = 2(-4)^n-1

2(-4^n × -4^-1)

2(-4^n × -1/4)

= -4^n/2

Answer:

[tex]y=\frac{-3}{2}x +\frac{5}{2} \\or \\y=\frac{5}{2} -\frac{3}{2} x[/tex]

Step-by-step explanation:

slope-intercept form is: [tex]y= mx+b[/tex]

3x + 2y = 5.

rearrange

[tex]2y=5-3x\\y=\frac{5}{2} -\frac{3x}{2}[/tex]

Answer:

b on ed2020

IG: user_6232003

Step-by-step explanation:

Step-by-step explanation:

1. 4x - 7 = -2x + 12, Given

2. 4x - 7 + 2x = -2x + 12 + 2x, Addition property of equality

3. 6x - 7 = 12, Simplification

4. 6x - 7 + 7 = 12 + 7, Addition property of equality

5. 6x = 19, Simplification

6. 6x/6 = 19/6, Division property of equality

7. x = 19/6, Simplification

Answer:

The steps are :

1. [tex]4x-7=-2x+12[/tex] - This is Given

2. [tex]4x-7+2x=-2x+12+2x[/tex] - Here, addition property of equality is used.

3. [tex]6x-7=12[/tex] - This step is simplification as both the LHS and RHS are being calculated and simplified.

4. [tex]6x-7+ 7=12+7[/tex] - Here, again addition property of equality is applied.

5. [tex]6x =19[/tex] - This is simplification again.

6. [tex]\frac{6x}{6}=\frac{19}{6}[/tex] - Here the division property of equality is applied.

7. [tex]x=\frac{19}{6}[/tex] - This step is simplification.

The correct answer is 44.1 [tex]cm^{2}[/tex]. I took the test.

To determine the numerator of a fraction that simplifies to 36 with a denominator of 6x^5, you solve the equation Numerator/6x^5 = 36 by multiplying both sides by 6x^5, resulting in a numerator of 216x^5.

To find the numerator of a fraction that reduces to 36 with a denominator of 6x^5, we set up an equation to represent the fraction in its simplest form.

We know that when we divide the numerator by the denominator, the result is 36. Therefore, the equation to solve is Numerator/6x^5 = 36.

Multiplying both sides of the equation by 6x^5 will isolate the numerator on one side.

The calculation becomes:

Numerator = 36 × 6x^5

Next, we carry out the multiplication to find:

Numerator = 216x^5

This means that the numerator of the original fraction is 216x^5.

Answer:

# x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

# 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

# 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

# x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Step-by-step explanation:

* Lets study the problem to solve it

- Use the terms of x and y in the general form to find the standard form

∵ x² + y² - 4x + 12y - 20 = 0

- Use the term x term

∵ -4x ÷ 2 = -2x ⇒ x × -2

∴ (x - 2)²

- Use the term y term

∵ 12y ÷ 2 = 6y ⇒ y × 6

∴ (y + 6)²

∵ (-2)² + (6)² + 20 = 4 + 36 + 20 = 60

∴ x² + y² - 4x + 12y - 20 = 0 ⇒ (x - 2)² + (y + 6)² = 60

∵ x² + y² + 6x - 8y + 10 = 0

- Use the term x term

∵ 6x ÷ 2 = 3x ⇒ x × 3

∴ (x + 3)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (3)² + (-4)² - 10 = 9 + 16 - 10 = 5

∴ x² + y² + 6x - 8y + 10 = 0 ⇒ (x + 3)² + (y - 4)² = 5 ⇒ not in answer

∵ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ divide all terms by 3

∴ x² + y² + 4x + 6y - 5 = 0

- Use the term x term

∵ 4x ÷ 2 = 2x ⇒ x × 2

∴ (x + 2)²

- Use the term y term

∵ 6y ÷ 2 = 3y ⇒ y × 3

∴ (y + 3)²

∵ (2)² + (3)² + 5 = 4 + 9 + 5 = 18

∴ 3x² + 3y² + 12x + 18y - 15 = 0 ⇒ (x + 2)² + (y + 3)² = 18

∵ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ divide both sides by 5

∴ x² + y² - 2x + 4y - 6 = 0

- Use the term x term

∵ -2x ÷ 2 = -x ⇒ x × -1

∴ (x - 1)²

- Use the term y term

∵ 4y ÷ 2 = 2y ⇒ y × 2

∴ (y + 2)²

∵ (-1)² + (2)² + 6 = 1 + 4 + 6 = 11

∴ 5x² + 5y² - 10x + 20y - 30 = 0 ⇒ (x - 1)² + (y + 2)² = 11 ⇒ not in answer

∵ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ divide both sides by 2

∴ x² + y² - 12x - 8y - 4 = 0

- Use the term x term

∵ -12x ÷ 2 = -6x ⇒ x × -6

∴ (x - 6)²

- Use the term y term

∵ -8y ÷ 2 = -4y ⇒ y × -4

∴ (y - 4)²

∵ (-6)² + (-4)² + 4 = 36 + 16 + 4 = 56

∴ 2x² + 2y² - 24x - 16y - 8 = 0 ⇒ (x - 6)² + (y - 4)² = 56

∵ x² + y² + 2x - 12y - 9 = 0

- Use the term x term

∵ 2x ÷ 2 = x ⇒ x × 1

∴ (x + 1)²

- Use the term y term

∵ -12y ÷ 2 = -6y ⇒ y × -6

∴ (y - 6)²

∵ (1)² + (-6)² + 9 = 1 + 36 + 9 = 46

∴ x² + y² + 2x - 12y - 9 = 0 ⇒ (x + 1)² + (y - 6)² = 46

Answer:

-6 -4 -2 4

Step-by-step explanation:

A B C F

Answer:

A. B. C. F.

Step-by-step explanation:

My answers are in the picture above.

To perform a horizontal translation on a function, replace x with x - h in the function

To perform a horizontal translation on a function, we need to replace x with x - h in the function where h is the amount of translation. In the given case, the correct equation for a horizontal translation would be g(x) = f(x - h) = (x - h)² - 12, where h represents the amount of horizontal translation.

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Step-by-step explanation:

it is solved directly by using the formula

To calculate the length of CE, use the properties of similar triangles. Use the same proportion to calculate the length of DE. To find the area of the quadrilateral BDEC, calculate the area of the triangle CDE and subtract it from the area of ABCD.

To calculate the length of CE, we need to use the properties of similar triangles. Since ABC and AED are similar, we can set up the proportion AB/AC = AD/AE. We know that AB = 5cm and AC = 10cm, and we need to solve for AE. Rearranging the proportion, we get AE = AD * AC / AB. Plugging in the values, AE = 6cm.

To calculate the length of DE, we can use the same proportion from above, but this time solving for DE. Rearranging the proportion, we get DE = AD * AC / AB. Plugging in the values, DE = 3cm.

The area of triangle ABD is given as 36cm. To calculate the area of the quadrilateral BDEC, we need to find the area of the triangle CDE and subtract it from the area of the quadrilateral ABCD. Since triangles CDE and ABC share the same height, we can use the ratios of their bases to calculate the area of CDE. The ratio of CE to CB is 6/10, so the ratio of the areas of CDE to ABC is (6/10)^2 = 0.36. Therefore, the area of CDE is 0.36 times the area of ABC, or 0.36 * 36cm = 12.96cm.

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Answer:

J

Step-by-step explanation:

Find the common ratio r of the geometric sequence then multiply a term by r to obtain the next term

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{-36}[/tex] = - [tex]\frac{1}{6}[/tex]

The next 3 terms are

[tex]\frac{1}{6}[/tex] × - [tex]\frac{1}{6}[/tex] = - [tex]\frac{1}{36}[/tex]

- [tex]\frac{1}{36}[/tex] × - [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{216}[/tex]

[tex]\frac{1}{216}[/tex] × - [tex]\frac{1}{6}[/tex] = - [tex]\frac{1}{1296}[/tex]

Answer:

J. [tex]-\frac{1}{36}[/tex], [tex]\frac{1}{216}[/tex], [tex]-\frac{1}{1296}[/tex]

Step-by-step explanation:

We are given the following geometric sequence and we are to find its 8th term:

[tex]-36, 6, -1, \frac{1}{6},...[/tex]

Here [tex]a_1=-36[/tex] and common ratio [tex](r) = \frac{-1}{6}=\frac{-1}{6}[/tex].

The formula we will use to find the next three terms is:

nth term = [tex]a_1 \times r^{(n-1)}[/tex]

5th term = [tex]-36 \times \frac{-1}{6}^{(5-1)}[/tex]  = [tex]-\frac{1}{36}[/tex]

6th term = [tex]-36 \times \frac{-1}{6}^{(6-1)}[/tex]  = [tex]\frac{1}{216}[/tex]

7th term = [tex]-36 \times \frac{-1}{6}^{(7-1)}[/tex]  = [tex]-\frac{1}{1296}[/tex]

Hello! :)

The answer is probably from changing first to decimals by dividing by 100: 90 and 30 become .9 and .3.

Then, multiply the two: .9 x .3 = .27

Finally, you multiply .27 by 100 = 27

Add the percentage sign: 27%

So there is a 27% chance that it will rain and the baseball game is postponed.

Very unlikely, I know. ;D

Hope this helped and I hope I answered in time!

Good luck!

~ Destiny ^_^

The probability it will rain tomorrow and the baseball game is postponed is 0.93 .

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

According to classical definition of probability, a random experiment consists of a set of possible outcomes and each set of possible outcomes is equally likely to occur in the course of the event.

It is given that there is a 90% chance of rain tomorrow and a 30% chance that the baseball game is postpone.

Let A be the probability that there is a chance of rain tomorrow and B be the probability that the baseball game is postpone.

P(A) = 90% = 0.9 and P(B) = 30% = 0.3 and P(A∩B) = (0.9*0.3) = 0.27 .

The probability it will rain tomorrow and the baseball game is postponed is given by P(A∪B) .

By formula,

⇒ P(A∪B) = P(A) + P(B) - P(A∩B)

⇒ P(A∪B) = 0.9 + 0.3 - 0.27

∴  P(A∪B) = 0.93 .

Therefore, the probability it will rain tomorrow and the baseball game is postponed is 0.93 .

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