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

Answer:

x = -2.5
x = 2

Step-by-step explanation:

Hello!

We can remove the denominators by multiplying everything by it.

Solve:

Let's make one side equal to 0.

Solve by factoring, and then the zero product property.

Multiply 2 and -10. You get -20. Think of two number that multiply to -20, and add to 1. If we think about the standard form of a quadratic, [tex]ax^2 + bx + c[/tex], think two numbers that equal "ac" and add up to "b".

Using the zero product property, set each factor to 0 and solve for x.

The two answers are x = -2.5, and x = 2.

Answer:

x = -5/2, 2

Step-by-step explanation:

Given:

[tex]\displaystyle \large{\dfrac{5}{x+3}+\dfrac{4}{x+2} = 2}[/tex]

With restriction that x-values cannot be -3 and -2 else it will turn the expression as in undefined.

First, multiply both sides by (x+3)(x+2) to get rid of the denominator.

[tex]\displaystyle \large{\dfrac{5}{x+3}\cdot (x+2)(x+3)+\dfrac{4}{x+2} \cdot (x+2)(x+3) = 2 \cdot (x+2)(x+3)}\\\\\displaystyle \large{5(x+2)+4(x+3) = 2(x+2)(x+3)}[/tex]

Simplify/Expand in:

[tex]\displaystyle \large{5x+10+4x+12 = 2(x^2+5x+6)}\\\\\displaystyle \large{9x+22=2x^2+10x+12}[/tex]

Arrange the terms or expression in quadratic equation:

[tex]\displaystyle \large{0=2x^2+10x+12-9x-22}\\\\\displaystyle \large{2x^2+x-10=0}[/tex]

Factor the expression:

[tex]\displaystyle \large{(2x+5)(x-2)=0}[/tex]

Solve like linear equation as we get:

[tex]\displaystyle \large{x=-\dfrac{5}{2}, 2}[/tex]

Since both x-values are not exact -2 or -3 - therefore, these values are valid. Hence, x = -5/2, 2

Answer:

  73 cm²

Step-by-step explanation:

Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.

__

This shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)

The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:

  4 cm + 5 cm + 3 cm = 12 cm

The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.

The area of each rectangle is the product of its width and height.

  A = WH

__

  top rectangle area = WH = (12 cm)(4 cm) = 48 cm²

  bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²

  Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)

  Area = 73 cm²

The area of this composite shape is 73 cm².

_____

Additional comment

The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...

  figure area = bounding rectangle area - removed areas

  = (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²

  = 73 cm²

Answer:

b = -8

Step-by-step explanation:

-2b + 9 =25

-9 = -9

-2b = 16

/-2 /-2

b = -8

Answer: C i think.

Step-by-step explanation:

8 different trees multipled by s equal to 6 meters tall in total.

Answer:

1.42 cm

Step-by-step explanation:

2.5 m = 98.4251 inches

98.4251 in / 11.5 in =8.5587

  .5587 inches left over =1.42 cm

There will be 18.87 centimeters of rope left over.

It is the conversion of one unit to another unit with its standard conversion.

Examples:

1 hour = 60 minutes

1 minute = 60 seconds

1 km = 1000 m

We have,

Let's convert the length of the rope to inches.

1 meter = 39.37 inches

2.50m = 98.43 inches

Now,

The number of 1.5-inch pieces.

=  98.43 / 11.5

= 8.55 pieces

Now,

11.5 inches pieces are cut.

This means,

= 98.43 - (8x11.5)

= 7.43 inches

Now,

1 inch = 2.54 cm

7.43 inch = 18.87 cm

Thus,

There will be 18.87 centimeters of rope left over.

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Answer: See attached

Step-by-step explanation:

   [] Since the inequality uses greater than (>) and not greater than or equal to (≥), the line will be dashed.

   [] The inequality is greater than (>) so we will shade above the line as values "above" are greater.

Answer:

here is what i got

Step-by-step explanation:

Answer:

d = 3

Step-by-step explanation:

6*3=18
2d*6=12d
54-18 = 12d
36/12 = 12d/12
d = 3

Answer:

d = 3

Step-by-step explanation:

6 ( 3 + 2d ) = 54

First, solve the brackets.

18 + 12d = 54

Take 18 to the right side.

12d = 54 - 18

12d = 36

Divide both sides by 12.

d = 3

Answer:

C) [tex]3x^2-14x-5[/tex]

Step-by-step explanation:

[tex](5x^2-5x+1)-(2x^2+9x-6)\\\\5x^2-5x+1-2x^2-9x-6\\\\3x^2-14x-5[/tex]

The subtraction of the given expressions gives D. 3x² - 14x + 7.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given are two expressions.

5x² - 5x + 1 and 2x² + 9x - 6

We have to find the difference of the given expression.

(5x² - 5x + 1) - (2x² + 9x - 6)

= 5x² - 5x + 1 - 2x² - 9x + 6

Operating the like terms together,

= (5x² - 2x²) + (-5x - 9x) + (1 + 6)

= 3x² - 14x + 7

Hence the correct option is D.

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Answer:

The answer to this is 9.

Step-by-step explanation:

First of all, you wrote the expression wrong, but that's okay. It's supposed to be written as (-3)².

Second of all, since multiplying two negatives makes a positive and squaring is just multiplying the integer to itself, then -3×-3=9. I hope this helps! :)

Answer:

cost of a doughnut is $0.75

cost of a cookie is $0.60

Step-by-step explanation:

As you wrote:
Let x = doughnuts

Let y = cookies

The first sentence of the problem (alexandra) can be written as:

[tex]2x + 3y = 3.30[/tex]

The second sentence of the equation (briana) can be written as:

[tex]5x + 2y = 4.95[/tex]

We must now solve for either [tex]x[/tex] or [tex]y[/tex] in this system of equations.

I will solve for [tex]x[/tex] in this example.

First we need to multiply the first equation by [tex]2[/tex] and the second equation by [tex]3[/tex]. This is so both equations have [tex]6y[/tex] as a term.

Equation 1:

[tex]2(2x + 3y) = (3.30)2\\4x + 6y = 6.60[/tex]

Equation 2:

[tex]3(5x + 2y) = (4.95)3\\15x+6y=14.85[/tex]

Now that both equations have [tex]6y[/tex] as a term, we can subtract Equation 1 from Equation 2. This will remove y from the equation and allow us to solve for x.

[tex](15x+6y) - (4x+6y) = (14.85) - (6.60)\\11x = 8.25\\\boxed{x = 0.75}[/tex]

We now know the cost of a doughnut is $0.75. Now we can solve for the cost of a cookie through substitution.

[tex]2x + 3y = 3.30\\2(0.75) + 3y = 3.30\\1.50 + 3y = 3.30\\3y = 1.80\\\boxed{y = 0.6}[/tex]

Now we know the cost of a cookie is $0.60.

These are the answers,

- Kan Academy Advance

The equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

The equation of a line in pint slope form is expressed as:

y - y1 = m(x-x1)

where

m is the slope = -7

(x1, y1) = (7, -54 ) is the point on the line

Substitute

y + 54 = -7(x -7)

Write in slope intercept form

y + 54 = -7(x -7)

y + 54 = -7x + 49
y = -7x - 5

Hence the equation of the line with Slope = −7 and passing through (7,−54) is y = -7x - 5

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Answer:18

Step-by-step explanation:

Answer:

C. 16

Explanation:

[tex]\rightarrow \sf \dfrac{9}{4} = \dfrac{x+2}{8}[/tex]

cross multiply

[tex]\rightarrow \sf \dfrac{9(8)}{4} = x + 2[/tex]

simplify integers

[tex]\rightarrow \sf 18 = x + 2[/tex]

exchange sides

[tex]\rightarrow \sf x =18-2[/tex]

subtract integers

[tex]\rightarrow \sf x =16[/tex]

The estimate for the number of people in the town who have not been to their doctor in the last year is 7062.

It is described as a collection of data with the same entity that is linked to a problem. The sample is a subset of the population, yet it is still a part of it.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

Total population = 1819 + 6150 + 2003 + 5918 = 15890

Emily takes a random sample of 90 people from the town.

40 of these people have not been to their doctor in the last year.

The estimate for the number of people in the town who have not been to their doctor in the last year:

= (40/90)×15890

= 7062.22 ≈ 7062

Thus, the estimate for the number of people in the town who have not been to their doctor in the last year is 7062.

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The number of 1/3 cm-cubes that would fill the rectangular prism is approximately 20 cubes.

Volume = a³, where a is the side length.

Volume = lwh

Given the following:

Volume of the rectangular prism = (1/2)(1)(3/2)

Volume of the rectangular prism = (1/2)(1)(3/2) = 0.75 cm³

Volume of the cube = (⅓)³ = 0.037 cm³

Number of cubes that would fill the prism = 0.75/0.037 ≈ 20 cubes.

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After 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

During exponential decay, a quantity falls slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decline and can also be used to calculate half-life.

We have:

If a doctor prescribes 75 milligrams of a specific drug to her patient how many milligrams of the drug will remain in the patients' bloodstream.

We know the exponential decay can be given as:

D = a(1 - r)ⁿ

a is the starting value and n is the number of hours.

D = 75(1 - 0.20)⁶

D = 19.66 milligrams

Thus, the after 6 hours the drug remains is 19.66 mg if the drug decays at a rate of 20 percent per hour.

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Answer: C

Step-by-step explanation:

Complementary angles have measures that add to 180 degrees, so since angle EAD measures 20 degrees, we need an angle that measures 70 degrees. This is angle DAB.

Answer:

the image should help.

Step-by-step explanation:

image explains everything.

Step-by-step explanation:

a general line equation is

y = ax + b

"a" being the slope is the line, "b" being the y-intercept (the y value when x = 0).

we see from the 2 marked points (by we could choose any points on the line) that

y changes by 2 units, when x changes by 3 units.

so the slope is 2/3.

we use one point (1, 2) to solve for b

2 = 2/3 × 1 + b = 2/3 + b

6/3 = 2/3 + b

4/3 = b

and the full equation is

y = 2/3 x + 4/3

Circumference = 2 x radius x PI

Circumference = 2 x 3.8 x 3.14

Circumference = 23.86

answer: the closest one is A. 23.8 FT.

Answer:

[tex] \large {\boxed{ \sf{y = 2x + 5}}}[/tex]

Step-by-step explanation:

Suppose the slope of the line is k.

So,

[tex] \large {\bold {k = \frac{7 - ( - 1)}{1 - (3)} = \frac{7 + 1}{1 + 3} = \frac{8}{4} = 2 }}\\ [/tex]

So the line:

[tex] \large \bold{ \frac{y - 7}{x - 1} = k = 2 } \\ [/tex]

[tex] \: [/tex]

So,

[tex] \large \bold{y - 7 = 2(x - 1)}[/tex]

[tex]\large \bold{y - 7 = 2x - 2}[/tex]

[tex]\large \bold{y = 2x - 2 + 7}[/tex]

[tex]\large \bold{y = 2x + 5}[/tex]

[tex]{\rule{200pt}{4pt}}[/tex]

[tex] \large \bold{-N} \frak{unx-}[/tex]

The probability that he would have done at least this well if he had no ESP is 0.99979

To determine the probability, we need to first find the probability of doing well with ESP.

The probability of having 20 correct answers out of 23 coin flips is:

[tex]\mathbf{=(\dfrac{1}{2})^{20}}[/tex]

Since we have 20 correct answers, we also need to find the probability of getting 3 answers wrong, which is:

[tex]\mathbf{=(\dfrac{1}{2})^{3}}[/tex]

There are [tex](^{23}_{20})[/tex] = 1771 ways to get 20 correct answers out of 23.

Therefore, the probability of doing well with ESP is:

[tex]\mathbf{= 1771 \times (\dfrac{1}{2})^{20}} \times (\dfrac{1}{2})^{3}}[/tex]

= 0.00021

The probability that he would have at least done well if he had no ESP is:

= 1 - 0.00021

= 0.99979

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Answer:

23.292°

Step-by-step explanation:

see the attachment photo.

The value of x to the nearest tenth is 23.3°.

Law of sines is defined as that ratio of the length of the sides of a triangle to the sine of the angle opposite to the these sides are equal.

That is, if a, b and c are sides opposite to the angles A, B and C respectively, then,

a / sin A = b / sin B = c / sin C

Given is a triangle ABC.

Using the law of sines,

AB / Sin C = BC / Sin A

We have to find the angle A.

Substituting,

18 / sin 22 = 19 / sin x

18 × sin(x) = 19 × sin (22°)

sin(x) = (19 × sin (22°)) / 18

sin x = 0.3954

x = 23.29° ≈ 23.3°

Hence the value of x is 23.3°.

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The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation. See the attached image for details.

Rotation in math refers to the change in the angle of a geometric shape around a central axis on a point on the geometric plane such that it's original coordinates are modified but it's size or shape.

Hence, it is correct to state that The rotation that that translates AWXY to AW'X'Y' is a 45° anticlockwise rotation.

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Answer:

The quadratic equation 3x² - 12x + 9 = 0 has two real roots when solved:

x₁ = 1 and x₂ = 3

Step-by-step explanation:

✍ An equation of type ax² + bx + c = 0, can be solved, for example, using the quadratic formula:

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

either

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta} }{2a} }[/tex]

where

[tex]\bf{\Delta=b^{2}-4ac }[/tex]

Identify the coefficients

a = 3, b = -12 and c = 9

Calculate the discriminant value

Δ = b² - 4ac

Δ = (-12)² - 4.3.9 = 144 - 12.9

Δ = 144 - 108 = 36

Enter the values of a, b and the discriminant value in the quadratic formula

[tex]\boldsymbol{x=\dfrac{-b\pm\sqrt{\Delta } }{2a} }[/tex]

[tex]\boldsymbol{x=\dfrac{-(-12\pm\sqrt{36} }{2\cdot3 } }[/tex]

[tex]\boldsymbol{x=\dfrac{(12\pm\sqrt{36} }{6 } \ ==== > \ (Solution \ general) }[/tex]

As we can see above, the discriminant (Δ) of this equation is positive (Δ> 0) which means that there are two real roots (two solutions), x₁ and x₂.

[tex]\boldsymbol{x_{1}=\dfrac{-12-\sqrt{36} }{6}=\dfrac{12-6}{6}=\dfrac{6}{6}=1 \ === > (First \ solution) }[/tex]

To find x₁, just choose the positive sign before the square root. Later,

[tex]\boldsymbol{x_{1}=\dfrac{12+\sqrt{36} }{6}=\dfrac{12+6}{6}=\dfrac{18}{6}=3 \ === > (Second \ solution) }[/tex]

A straight line is represented by a linear equation given below.

The points are given as (1, 2) and (4, 4).

Start by calculating the slope (m)

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

So, we have

[tex]m=\frac{4-2}{4-1} \\m=\frac{2}{3}[/tex]

The equation in slope-intercept form is then calculated as:

[tex]y=m(x-x_1)+y_1[/tex]

So, we have:

[tex]y=\frac{2}{3}(x-1)+2\\ \\y=\frac{2}{3}(x-4)+4\\[/tex]

Expand

[tex]y=\frac{2}{3}(x-1)+2\\ y=\frac{2}{3} x-\frac{2}{3}+2[/tex]

Take LCM

[tex]y=2/3x+4/3[/tex]

Multiply through by 3

3y=2x+4

So, the possible equations are:

.[tex]3y=2x+4\\y=\frac{2}{3}x+\frac{4}{3} \\y=\frac{2}{3}(x-1)+2\\y=\frac{2}{3}(x-4)+{4}[/tex]

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Answer:

B

C

E

Step-by-step explanation:

other dudes are  wrong

By taking a common factor, we will see that the equivalent expression is:

[tex]12*\sqrt[3]{6c}[/tex]

Here we start with the expression:

[tex]5*\sqrt[3]{6c} + 7*\sqrt[3]{6c}[/tex]

Notice that if we define:

[tex]\sqrt[3]{6c} = u[/tex]

We can rewrite our expression as:

[tex]5u + 7u[/tex]

Now we can take the common factor u to write:

[tex](5 + 7)u = 12u[/tex]

Now if we replace u y the cubic root, we will get:

[tex]12*\sqrt[3]{6c}[/tex]

So the correct option is the third one.

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Answer:

D

Step-by-step explanation:

-1.5(-6m+8n) = 9m-12n

3(3m -4n) = 9m - 12n

9m -12n = 9m -12n

-6(-1.5m +2n) = 9m - 12n

-2(-4.5m+ 4n) = 9m - 8n

Answer: D. -2(-4.5m + 4n)

Step-by-step explanation:

   First, let us simplify -1.5(-6m+8n).

Given:

-1.5(-6m + 8n)

Distribute:

9m - 12n

[A] ✗

   9 /3 = 3 and 12 / 3 = 4

   This means that 3(3m - 4n) = 9m - 12n = -1.5(-6m+8n)

Option A is not our answer.

[B] ✗

   Using this simplified version we did above, option B is not our answer as 9m - 12n = 9m - 12n and 9m - 12n = -1.5(-6m+8n).

[C] ✗

   We will distribute option C to see if we reach the same expression. Seeing below, we do, so option C is not our answer.

-6(-1.5m + 2n)

9m - 12n

[D] ✓

   Since none of the other options are correct, the answer to your question D because it is not equivalent.

                Answer:

          D. -2(-4.5m + 4n)

Answer:

multiply the probability of the first event by the second.

Step-by-step explanation:

Use the specific multiplication rule formula. Just multiply the probability of the first event by the second. For example, if the probability of event A is 2/9 and the probability of event B is 3/9 then the probability of both events happening at the same time is (2/9)*(3/9) = 6/81 = 2/27.

Answer:

[tex]\frac{1}{26} * \frac{1}{26} = \frac{1}{676} = .00148.[/tex]

Step-by-step explanation:

Multiply the probability of P by the probability of Q.

In which the probability of P is equal to [tex]\frac{R}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

In which the probability of Q is equal to [tex]\frac{P}{Total NumberOf LettersInAlphabet} = \frac{1}{26}[/tex]

There's a 1 in 676 chance that you'd randomly pick R, put the tile back in, and then pick P in a sack of 26 letters of the latin alphabet.

Answer:

The value of m in the figure is 28.

Step-by-step explanation:

When we look at the figure, we see that 6 and 21, are connected with parallel lines to 8 and m. We can also see that 21 is dilated from 6. When dilating, we multiply or divide by a number, to get the extended or shortened length. (Just keep multiplication and division in mind)                

To get m, we can do the same that we did to get 21, from 6.

To get 21 from 6, you must divide 21 by 6. So when we do the same thing to 8, we should get m.

21 / 6 = 3.5

Now that we have the dilation of 3.5, we simply multiply that by 8.

3.5 * 8 = 28

The value of x in the figure is 28.

[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{21}{6}[/tex]

[tex]\\ \rm\dashrightarrow \dfrac{m}{8}=\dfrac{7}{2}[/tex]

[tex]\\ \rm\dashrightarrow 2m=56[/tex]

[tex]\\ \rm\dashrightarrow m=28[/tex]