An initial deposit of $1200 is put into an account that earns 5% interest compounded annually. Each year year an additional of $1200 is added to the account. Whats the value of the account after the 10th deposit if no withdraws or additional deposits are made.

Answer:

1) To calculate length of fringe, we need to find the perimeter

The question does not clearly say how much is length and width

Assuming length = 245 and width = 234 inches

P = 2(length + width)

P = 2 ( 245 + 234)

P = 2 (479)

P = 958 inches

2) To calculate length of fringe, when length is increased by 33 inches

P = 2 ( l + w)

P = 2 (278 + 234)

P = 2 x 512

P = 1024 inches

Hello there! :)

Answer:

y = -4x.

Step-by-step explanation:

Begin by finding the slope of the line using the slope formula:

[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Plug in two points on the graph. We can use the points (-1, 4) and (0, 0):

[tex]m = \frac{0 - 4}{0 - (-1)}[/tex]

Simplify:

m = -4.

Therefore, the equation of this line in slope-intercept form (y = mx + b) is:

y = -4x.

Step-by-step explanation:

a) $410 × £0.72 = £295.20

Answer:

A. -259

B. inverse function is 1/2 √(-x-3)

Step-by-step explanation:

Here, we want to find f(8)

Simply substitute x = 8 in the equation.

The equation is

f(x) = -4x^2 -3

So f(8) = -4(8)^2-3

f(8) = -256-3

f(8) = -259

Inverse of f(x) = -4x^2 -3

Simply equate this to m

m = -4x^2-3

-4x^2 = m + 3

x^2 = (m + 3)/-4

x^2 = -m/4 -3/4

x = √(-m-3)/4

x = 1/2√(-m-3)

Put back the value of x for m

x = 1/2 √(-x-3)

Answer:

50

Step-by-step explanation:

d-nr of ducks

g- nr of goats

2*d+4*g=260

d+g=80            /*(-2)

2d+4g=260

-2d-2g=-160

------------------

      2g=100

      g=100/2

     g=50

Answer:

Option D is the correct option

Solution,

Let no.of ducks be X

Let no.of goats be y.

Total heads= X+y=80 ➡️ equation (i)

Total legs= 2x+4y=260➡️ equation (ii)

X= 80-y

[tex]2(80 - y) + 4y = 260 \\ or \: 160 - 2y + 4y = 260 \\ or \: 160 + 2y = 260 \\ or \: 2y = 260 - 160 \\ or \: 2y = 100 \\ or \: y = \frac{100}{2} \\ y = 50[/tex]

Number of goats= 50

Hope this helps...

Good luck on your assignment...

Answer: OA) (4, -2), (-2, 2), (2, -2), (4, 2)

Step-by-step explanation:

Answer:  

Step-by-step explanation:

Concentration            Amount of             Amount

of Solution                   Solution (L)             of Acid

    15%                                x                         0.15x

    33%                               y                         0.33y

    21%                              40                      0.21•40      

x + y = 40    ⇒  x = 40 - y

0.15x + 0.33y = 0.21•40

0.15(40 - y) + 0.33y = 0.21•40

6 - 0.15y + 0.33y = 8.4

  0.18y = 2.4

        y = 13¹/₃

x = 40 -  13¹/₃ = 26²/₃

Answer:

see below

Step-by-step explanation:

3 ^ ( 6/5)

The base a is 3

The power is 6 which is b

the root is 5 which is c

[tex]\sqrt[5]{3^6}[/tex]

Answer:

x≤7.8  ⇒(-∞;7.8]

x<7.8  ⇒ (-∞;7.8)

x>7.8  ⇒ (7.8; ∞)

x≥7.8  ⇒ [7.8; ∞)

Step-by-step explanation:

Hi, to answer this question we have to analyze each expression:

• x≤7.8

The solution is all the numbers less or equal to 7.8, since it can be equal to 7.8, it includes 7.8 , we have to use closed brackets

(-∞;7.8]

• x<7.8

All the numbers less than 7.8 , it excludes the endpoint , it's an open interval (parenthesis)

(-∞;7.8)

• x>7.8

All the numbers higher than 7.8, open interval (parenthesis)

(7.8; ∞)

• x≥7.8

All the numbers higher or equal to 7.8, closed interval (closed brackets for the endpoint)

[7.8; ∞)

Answer:

Step-by-step explanation:

Choice A: [tex]2,2, \sqrt{4}[/tex]

Choice B: 9, 40, 41

Choice C: [tex]\sqrt{5}, 10$ and \sqrt{125}[/tex]

Answer:

(B)9, 40, 41

Step-by-step explanation:

To check if the sides form a right triangle, you check to see if they satisfy the Pythagorean theorem.

[tex]Hypotenuse^2=Opposite^2+Adjacent^2[/tex]

Note that the longest side length is always the hypotenuse.

Choice A: [tex]2,2, \sqrt{4}[/tex]

Now, [tex]\sqrt{4}=2[/tex]

Therefore:

[tex]2^2\neq 2^2+2^2\\4 \neq 8[/tex]

These side lengths form an equilateral triangle. They do not satisfy the theorem.

Choice B: 9, 40, 41

The longest side length is 41.

[tex]41^2=1681[/tex]

[tex]40^2+9^2=1681[/tex]

Therefore:

[tex]41^2=40^2+9^2[/tex]

These side lengths form a right triangle.

Choice C: [tex]\sqrt{5}, 10$ and \sqrt{125}[/tex]

[tex]\sqrt{5} \approx 2.24 \\ \sqrt{125}\approx11.18[/tex]

Therefore, the longest side length is [tex]\sqrt{125}[/tex]

[tex](\sqrt{125})^2=125\\(\sqrt{5})^2+10^2=5+100=105\\\\(\sqrt{125})^2 \neq (\sqrt{5})^2+10^2[/tex]

These side lengths do not form a right triangle.

[tex]\text{In this question, we're trying to find the quotient}\\\\\text{The quotient is basically the result or answer when you divide a number}\\\\\text{To find the quotient, divide 36 by 6}\\\\36\div6=6\\\\\boxed{\text{Answer: 6}}[/tex]

Answer:

6

Step-by-step explanation:

6x6=36 so, 36÷6=6

Answer:

a. No, because she will need money a year from now. Generally, stocks are long term investments. It is very unlikely that she will get a return on her investment in a year.

Step-by-step explanation:

Stocks are a riskier investment in comparison to bonds, and may pay higher interest rates, but still require the investment to "sit" for a long period of time. Like a 3 month (APY of about .50%), 6 month (APY of about .30%), 8 month (APY of about .10%), etc. bond, stocks will not grow considerably in a short amount of time.

Answer:

10 to the left I believe

Step-by-step explanation:

Answer: 7 square units

Step-by-step explanation:

<!> Brainliest is appreciated! <!>

Answer:

you need 2 cups of sugar

Step-by-step explanation:

1/2 cups of sugar = 3/4 cup of flour

x = 3 cups of flour

1/2*3 = 3/4x

3/2 = 3/4x

x =3/2 ÷ 3/4

x =2

Answer:

$342

Step-by-step explanation:

Let the total cost of the dinner = C

If it was shared equally by k employees who attended the dinner and each of the k employees who shared the cost of the dinner paid $19.

We have:

[tex]\dfrac{C}{k}=19 \\\\C=19k[/tex]

If the total cost(C) had been shared equally by k + 1 employees who attended the dinner, each of the k + 1 employees would have paid $18.

This written mathematically is:

[tex]\dfrac{C}{k+1}=18 \\\\C=18(k+1)[/tex]

Equating the cost, C from both equations

19k=18(k+1)

19k=18k+18

19k-18k=18

k=18

Therefore, the total cost of the dinner,

C=19k

=19 X 18

=$342

Answer:

6(4f - 5g)

Step-by-step explanation:

4f × 6 - 6g × 5 = 24f - 6g × 5

24f - 30g → 6 (4f - 5g)

Hope this helped! :)

Answer:

f(6)−6*g(5)= 6f - 30g

Step-by-step explanation:

Hope this helped you!

Answer:

Both of these examples are wrong. You cannot add/subtract integers and square roots together, however, you could add square roots together if they have the same number under the square root. For example, 2 - 2√6 will stay as 2 - 2√6 because they aren't like terms. 25 + 5√5 + 5√5 + 5 = 30 + 10√5 because 25 + 5 = 30 and 5√5 + 5√5 = 10√5. We can add 5√5 and 5√5 together because they have the same number under the square root. If we were to compute √2 + √3, we would just leave it as is because they don't have the same number under the square root.

Answer:

Erica has 51 action figures and Ricardo has 17 action figures.

Step-by-step explanation:

First, label your variables.

x=the number of action figures Erica has

y=the number of action figures Ricardo has

You know that they have 68 total action figures so x+y=68.

Erica has 3 times as many as Ricardo so 3y=x. Then solve for x and y.

x+y=68    3y=x   (Substitue 3y for x)

3y+y=68   (Then combine like terms)

4y=68  (Divide each side by 4)

y= 17

Now that you know that Ricardo has 17 action figures, you can plug 17 in for y in either equation to find x.

3(17)=x

x=51

To check your answers, you can plug them back into the original equations.

Answer:

Erica:51 action figures; Ricardo: 17 action figures

Reason:

68/4=17

17*3=51<- this is the amount of action figures that Erica has.

17 <-this is the amount of action figures that Ricardo has.

17 (Ricardo) + 51 (Erica) = 68 (total amount)

Answer:

The growth rate is 7.2%

Step-by-step explanation:

First thing we need to do here is to set up an exponential equation;

This can be written as follows;

F = I(1 + r)^t

where F is the future value = 20,000

I is the initial value = 10,000

r is the rate in percent which we want to calculate

t is time in years = 10 years

Substituting the values in the question into the exponential equation, we have;

20,000 = 10,000(1 + r)^10

divide both side by 10,000

2 = (1+r)^10

Find the 10th root of both sides

1+ r = 2^(1/10)

1 + r = 1.07177346254

r = 1.07177346254-1 = 0.07177346253

Let’s approximate r as 0.072

Now this to percentage?

That would be 72/1000 * 100% = 7.2%

Answer:

Periodic phenomena means that the phenomena has a (almost) constant time period or space period.

As you know, the trigonometric functions cos(x) and sin(x) also have a constant period of 2*pi, so these functions are really useful to model periodic phenomena.

Now, the problem may be that the trigonometric functions may be useful to describe the "periodic" part, but not to describe the actual phenomena.

An example of this can be a square alternating current.

While it has a constant period like a trigonometric function, the trigonometric functions can not really model the "square" part of this current (you know that the sinusoidal functions actually are curves and continuous)

Here comes something called the Fourier Series, that are series of the form:

F(x) = a₀ + ∑(aₙ*cos(nx) + bₙ*sin(nx))

That can be used to model almost any periodic phenomena, but the actual Fourier Series may be hard to construct.

Answer:

Option D.

Step-by-step explanation:

The given expression is

[tex]\dfrac{(5ab)^3}{30a^{-6}b^{-7}}[/tex]

We need to find the expression, which is equivalent to the given expression.

The given expression can be rewritten as

[tex]\dfrac{5^3a^3b^3}{30a^{-6}b^{-7}}[/tex]     [tex][\because (ab)^m=a^mb^m][/tex]

[tex]\dfrac{125}{30}\times \dfrac{a^3}{a^{-6}}\times \dfrac{b^3}{b^{-7}}[/tex]

[tex]\dfrac{25}{6}\times a^{3-(-6)}\times b^{3-(-7)}[/tex]    [tex][\because \dfrac{a^m}{a^n}=a^{m-n}][/tex]

[tex]\dfrac{25}{6}\times a^{3+6}\times b^{3+7}[/tex]

[tex]\dfrac{25a^9b^{10}}{6}[/tex]

Therefore, the correct option is D.

Answer:

The correct option is D

Step-by-step explanation:

Step-by-step explanation:

The expression:

[tex]\frac{1}{1+a} + b^{-1} + \frac{1}{1+b} + c^{-1} + \frac{1}{1+c} + a^{-1}[/tex]

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

[tex]a^{-1}+b^{-1}+c^{-1} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

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

Therefore, the whole expression gives:

[tex]\frac{1}{a} + \frac{1}{b} + \frac{1}{c} + \frac{1}{1+a} + \frac{1}{1+b} + \frac{1}{1+c}[/tex]

Taking the common denominator in the first three expressions, we have

[tex]\frac{a+b+c}{abc} + \frac{1}{1+a} +\frac{1}{1+b} + \frac{1}{1+c} \\[/tex]

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

The expression:

It is possible that there are values for a, b, and c, but are omitted. If this is not the case, then the expression can be rewritten in another form. These are about all that can be done.

The second case is more plausible, given there are no values given for a, b, and c.

The expression can be rewritten as:

When a number has an index of -1, it is the same as taking the reciprocal of the number.

That is;

Therefore, the whole expression gives:

Taking the common denominator in the first three expressions, we have

It is also possible to take the common denominator of the whole whole expression, this will however, make the expression look more tedious, rather than simple.

Answer:

a) P(X=x) = p× (1-p)^(x-1)

b) P(X=3) = 0.081

c) P(X≤5) = 0.40951

d) Mean of X= 10

e) Var(X)= 90

Step-by-step explanation:

This is a question on geometric distribution.

In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.

This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)

For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}

We stop the trials when we get a success.

From the question, there are 10 numbers

The probability of success = p = 1/10

For the solutions of the question from (a-e), See attachment below.

f(x) = P(X= x)

Where P(X= x) is the probability of X taking on a value x

Answer:

13.6

Step-by-step explanation:

Since it is asking for 1 decimal place, we assume that it is the tenths decimal place. Since the hundredths decimal place is ≥5, we round up to 6.

There is no such thing as ones in decimals, so I am assuming you mean tenths. If you were to round this to the tenths place, the answer would be 13.6.

13.555 → 13.6 (4 and below, leave it alone. 5 and up, round it up)\

Hope this helps!

Answer:

answer D

Step-by-step explanation:

hello,

[tex]f(x)=-5^x-4 \ and \ g(x)=-3x-2\\(f-g)(x)=f(x)-g(x)=-5^x-4+3x+2=-5^x+3x-2[/tex]

hope this helps

The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Functions are,

⇒ f (x) = - 5ˣ - 4

⇒ g (x) = - 3x - 2

Hence, We get;

The value of function (f - g) (x) is,

⇒ (f - g) (x)

⇒ f (x) - g(x)

⇒ (5ˣ - 4) - (- 3x - 2)

⇒ 5ˣ - 4 + 3x + 2

⇒ 5ˣ + 3x - 2

Thus, The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

Learn more about the function visit:

https://brainly.com/question/11624077

#SPJ7

Answer:

-4 points

Step-by-step explanation:

Since each incorrect answer is worth the same amount of negative points, use the equation below.

3x = -12      DIvide both sides by 3

x = -4 points  

Answer:

Step-by-step explanation:

Volume of a sphere is

[tex]V = \frac{4}{3} \pi {r}^{3} [/tex]

Where r is the radius

diameter = radius × 2

To find the diameter we must first find the radius

Volume = 34cm³

That's

[tex]34 = \frac{4}{3} \pi {r}^{3} \\ \\ 34 \times 3 = 4\pi {r}^{3} \\ \\ 102 = 4\pi {r}^{3} \\ {r}^{3} = \frac{102}{4} \pi \\ \\ r = \sqrt[3]{ \frac{51}{2\pi}} \\ \\ r = 2.01 \\ \\ r = 2.0 cm[/tex]

Diameter = 2 × 2cm

Hope this helps you

Answer:

The answer is 4

Step-by-step explanation:

Answer:

The fourth one

Step-by-step explanation:

Only the first one x and y interval 1, 2. The rest aren't linear.

Answer:

Step-by-step explanation:

it is the fourth one

Answer:

The dimensions of the rectangular room is 48 ft by 20 ft

Step-by-step explanation:

Drawing a Diagonal line in a rectangle forms two right angle triangles

The diagonal line will represent the hypotenuse

In a right angle triangle:

Hypotenuse^2= adjacent^2+opposite^3

One wall measures 28 ft longer than the adjacent wall.

Let the adjacent=x ft

Opposite=28+x ft

Hypotenuse=52 ft

Hypotenuse^2= adjacent^2+opposite^3

52^2 = x^2 + (28+x)^2

2704 =x^2 + 784 + 56x + x^2

2704=2x^2+784+56x

2x^2+56x+784-2704=0

2x^2+56x-1920=0

Solve the quadratic equation using the quadratic formula

x= -b +or- √b^2-4ac / 2a

a=2

b=56

c=-1920

x= -b +or- √b^2-4ac / 2a

= -56 +or- √56^2 - (4)(2)(-1920) / (2)(2)

= -56 +or- √3136 - (-15,360) / 4

= -56 +or- √3136+15,360) / 4

= -56 +or - √ 18496/ 4

= -56 +or- 136 / 4

x= -56 + 136 / 4

=- 56/4 + 136/4

= -14+34

=20

OR

x= -56 - 136/4

= -56/4 - 136/4

= -14 - 34

= -48

The value of x can't be negative, so will use the positive value of x which is 20

Recall,

Adjacent=x

=20 ft

Opposite=28+x ft

=28+20

=48 ft

The dimensions of the rectangular room is 48 ft by 20 ft