You deposit $4000 in an account earning 7% interest compounded continuously. How much will you have in the account in 10 years?

If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0

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

[tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }\\ \\\frac{9+6\sqrt{8}+8+9-6\sqrt{8}+8 }{(3-\sqrt{8} )(3+\sqrt{8} )} \\\\\frac{34}{9-8} =34+0\sqrt{2}[/tex]

If [tex]\frac{3+\sqrt{8} }{3-\sqrt{8} } +\frac{3-\sqrt{8} }{3+\sqrt{8} }=a+b\sqrt{2}[/tex], the value of a and b is given as a = 34 and b = 0

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Answer:

a) 15:7

b) 1950 ml

c) There were 10 people in the group

Step-by-step explanation:

a) In its basic form, the ratio would be 750:350. However, to get it to it's most basic form, we must find the greatest common factor (GCF) of 750 and 350, which is 50. Then, we divide both numbers by the GCF so that 750 is 15 and 350 is 7. Therefore, the basic form of the ratio is 15:7.

b) First, we can find the amount of chicken stock needed for 12 people, which is just double of the recipe since the recipe is for 6 people. (900 * 2 = 1800). Then, we need to figure out how much chicken stock is required for one person since there are 13 and not 12. We can do this by multiplying 900 by 1/6 (since it's for 1 person out of the 6 people recipe) to get 150. Then, add the amount of chicken stock needed for 12 people and 1 person together. 1800 + 150 = 1950.

c) First, we must figure out how many grams of leeks are required for just one person. We can do this by taking the amount needed in the recipe (for 6 people) and dividing it by 6 to get the amount needed for 1 person. 750 divide by 6 is 125, so 125 g of leeks are required to make soup for 1 person. Then, we take the total amount of leeks that Delia used (1250) and divide that by 125 to get 10.

71% subtracted from 100% is 29%

Add or subtract the given percent from 100%.

71%

The percentage (p) is given as:

p = 71%

When subtracted from 100%, we have:

100% - p

Substitute p = 71%

100% - 71%

71 subtracted from 100 is 29.

So, we have:

100% - 71% = 29%

Hence, 71% subtracted from 100% is 29%

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Answer: Heyaa! ~

Your Answer would be.. =4

Step-by-step explanation:

Hopefully this helps you ! ^^

[tex]|\Omega|=12\cdot11=132\\|A|=3\cdot4=12\\\\P(A)=\dfrac{12}{132}=\dfrac{1}{11}\approx9.1\%[/tex]

Using the binomial distribution, it is found that there is a 0.7447 = 74.47% probability that fewer than 7 of them show up.

The formula is:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

p = 0.7, n = 8.

The probability that fewer than 7 of them show up is given by:

[tec]P(X < 7) = 1 - P(X \geq 7)[/tex]

In which:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8)[/tex]

Then:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 7) = C_{8,7}.(0.7)^{7}.(0.3)^{1} = 0.1977[/tex]

[tex]P(X = 8) = C_{8,8}.(0.7)^{8}.(0.3)^{0} = 0.0576[/tex]

Then:

[tex]P(X \geq 7) = P(X = 7) + P(X = 8) = 0.1977 + 0.0576 = 0.2553[/tex]

[tec]P(X < 7) = 1 - P(X \geq 7) = 1 - 0.2553 = 0.7447[/tex]

0.7447 = 74.47% probability that fewer than 7 of them show up.

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#a

V={Vowels of English alphabets}

#b

C={cube numbers between 0 to 50}

#c

M={y:y is a multiple of 3 less than 20}

The height of the toy dinosaur will be 32 inches.

In mathematics scaling is defined as the enlarging or contracting of the size of an object by reducing or increasing the units of the measurements of the object.

Given that:-

An adult mamenchisaurus dinosaur was about 24 feet tall. if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches.

The new height of the dinosaur will be calculated as:-

We know that the size of the dinosaur is scaled as 9 inches to 1 inch the actual height of the dinosaur is 24 feet so the scaled height will be:-

Actual height = 24 ft = 24 x 12 = 288 inches

9 inches  → 1 inch

288 inches  → 288 / 9 = 32 inches.

Therefore the height of the toy dinosaur will be 32 inches.

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The area of the triangle AOB is 9√3 square units

The triangle AOB is an equilateral triangle with the following parameters:

Side length, x = 6

Angle, y = 60

The area of the triangle is then calculated using:

Area = 0.5 * x^2 * sin(y)

So, we have:

Area = 0.5 * 6^2 * sin(60)

Evaluate

Area = 18 * 0.5√3

Evaluate the product

Area = 9√3

Hence, the area of the triangle AOB is 9√3 square units

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The area of a regular polygon is one-half the product of its apothem and its perimeter. Often the formula is written like this: Area=1/2(ap), where a denotes the length of an apothem, and p denotes the perimeter.

Step-by-step explanation:

#Hopeithelps

The purpose of using slang is mostly for social purposes such as:

Slangs is often used in the Sharing and keeping  of a constantly altering vocabulary aids.

It is used to show group solidarity and it is often used to include or exclude members.

The common sports slangs are:

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Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

Given that;

First, we determine the mark price.

Since the Furniture Store marks up all furniture by 45%.

Mark up price = mark up × purchase price

Mark up price = 45% × $113.00

Mark up price = 0.45 × $113.00

Mark up price = $50.85

Now, the selling price will be;

Selling price = Purchase price + mark up price

Selling price = $113.00 + $50.85

Selling price = $163.85

Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.

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Step-by-step explanation:

the volume of a cylinder is as for any other regular 3D object :

ground area ×height

the ground area of a cylinder is a circle, so it is

pi×radius² × height

the radius is always half of the diameter (of the diameter is airways twice the radius).

radius = 6/2 = 3 ft.

the volume is then

pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³

so, the answer is 81pi ft³.

Answer: [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]

Step-by-step explanation:

= [tex](2-5\sqrt{6} )-3\sqrt{2}[/tex]

= [tex]2-5\sqrt{6}-3\sqrt{2}[/tex]

This expression is simplified already

The depth of the diver is 32 feet below sea level.

The angle of elevation is the angle between the observer's eyesight horizontal line and the object. The complete question can be seen in the image attached below.

The depth of the diver is the absolute value of -32 since it can't be negative.

= |-32|

= 32

Therefore, we can conclude that the depth of the diver is 32 feet below sea level.

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Answer:

K=-6/11

Step-by-step explanation:

3(k/3+4-2k)=3(-9k)

K+12-6k=-27k

12-5k=-27k

12=-22k

K=-6/11

Answer: 123.84

Step-by-step explanation: You can set pi as 3.14. Then, you get 123.836576. Round to the nearest hundredth to get 123.84.

Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

Trigonometry is the branch of mathematics that deals with the relationship between ratios of the sides of a right-angled triangle with its angles.

Here,

tan²θ + 1 = sec²θ

sin²θ/cos²θ + 1 = 1/cos²θ

By taking LCM, we get

(sin²θ + cos²θ)/cos²θ = 1/cos²θ

(sin²θ + cos²θ) = cos²θ/cos²θ

(sin²θ + cos²θ) = 1

Thus, Students claim is correct. We can convert tan²θ + 1 = sec²θ to (sin²θ + cos²θ) = 1.

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The given equation is equivalent to Option D .

The mission option is

A. x+10= x+10

B. x+9 =x² + 20x + 100

C. x² +81 = x² + 100

D. x² + 81 = x² +20x + 100

An equation is a mathematical statement formed when two algebraic expression is equated by an equal sign .

An equation is given in the question

[tex]\rm \sqrt{x^2 + 81} = x +10[/tex]

[tex]\rm {x^2 + 9^2} = (x +10)^2[/tex]

[tex]\rm {x^2 + 81} = x^2 +20x + 100[/tex]

Therefore the given equation is equivalent to Option D .

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This is a means of reducing the cost of a goods or an asset over time. The value of the car after 9 years is approximately $888

This is a means of reducing the cost of a goods or an asset over time.

Mathematically, the cost of goods after a particular year is expressed as:

P(t) = P0e^-rt

Given

Substitute

P(17) = 41000r^0.17(9)
P(17) = 4100(0.21653)

P(17) = 887.79

Hence the value of the car after 9 years is approximately $888

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60/4= 15

15 x 3 =45 minutes

========================================================

Reason:

Ari hasn't considered the case of "red and yellow" which is almost identical to "yellow and red".

It helps to lay out a two by two table. Along the rows and columns, you'll have "red" and "yellow". See below.

Then inside the table are the list of all outcomes in the form (x,y) where x is the horizontal component along the columns, and y is the vertical component along the rows.

Example: if x = red and y = red, then we have the outcome (x,y) = (red, red)

As the table shows, we have 4 outcomes. Therefore the probability of getting two yellows is 1/4

Technically the (red, yellow) = (yellow, red) since ultimately order doesn't matter in this case. For some probability problems, order will matter. But again, order doesn't matter here and it means that we can treat these two situations the same. So I can see why Ari thinks there are only three outcomes.

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

Here's another way to look at it:

The probability of landing on yellow is 1/2 assuming red and yellow are equally likely.

This means the probability of two yellow in a row is (1/2)*(1/2) = 1/4

Each is spin is independent of any other.

Answer: -10

Step-by-step explanation:

10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50

Answer:

x=-10

Step-by-step explanation:

-4x+10=50

10=50+4x

-50+10=4x

-40=4x

4x=-40

x=-40÷4

x=-10

[tex]g(x) =3x^2 -1\\\\g(-3)=3(-3)^2 -1 \\ \\~~~~~~~~~=3(9) -1 \\\\~~~~~~~~~=27-1\\\\~~~~~~~~~=26[/tex]

Answer:

g(26)

Step-by-step explanation:

substitute -3 for x.

g(x)=3[tex]x^{2}[/tex]-1

[tex]g(-3)=3(-3)^{2} -1\\g(-3)= 3(9)-1\\g(-3)= 27-1\\g(-3)=26[/tex]

Answer:

here we have to divide the number of words per hour to the number of minutes per hour.

Step-by-step explanation:

5400÷60

=90.

therefore in a minute she types 90 words.

Answer:

To find the mean of a given data set, add up all the values then divide by how many numbers ...

Step-by-step explanation:

[tex]\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ 2^3~~ = ~~8\implies \log_2(8)~~ = ~~3[/tex]

Answer:

160 million

Step-by-step explanation:

According to the ILO as of 2021, there's an estimated 160 million children working right now, so i don't know what answer you should put :/

Answer:

D 215 million

Step-by-step explanation: