Find the amount of money accumulated after investing a principle P for years t at interest rate r, compounded continuously. P = $10,000 r = 11% r = 11% t = 20 Round your answer to the nearest cent (hundredth). Enter

Answer:

Step-by-step explanation:

from the sign it's a right angle, so 90°

90 = x - 8 + 6x

90 + 8 = 7x

98 = 7x

x = 98 : 7

x = 14

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

check

90 = 14 - 8 + 6 * 14       (remember pemdas)

90 = 14 - 8 + 84

90 = 90

the answer is good

Find angle 1

x - 8

14 - 8 =

6°

Find angle 2

6x

6 * 14 = 84°

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

check

84 + 6 = 90°

the answer is good

Answer:

[tex]\textsf{a)} \quad \textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]

[tex]\begin{aligned}\textsf{b)} \quad m \angle 1 & =\boxed{6^{\circ}}\\ m \angle 2 & =\boxed{84^{\circ}}\end{aligned}[/tex]

Step-by-step explanation:

From inspection of the given diagram, the sum of the two angles is 90° (indicated by the right angle sign):

[tex]\implies m \angle 1+m \angle 2=90^{\circ}[/tex]

[tex]\implies (x - 8)^{\circ} + (6x)^{\circ} = 90^{\circ}[/tex]

[tex]\implies x-8+6x=90[/tex]

[tex]\textsf{Equation}: \quad \boxed{x-8+6x=90}[/tex]

To find the measure of each angle, solve the equation for x:

[tex]\implies x-8+6x=90[/tex]

[tex]\implies x+6x-8=90[/tex]

[tex]\implies 7x-8=90[/tex]

[tex]\implies 7x-8+8=90+8[/tex]

[tex]\implies 7x=98[/tex]

[tex]\implies \dfrac{7x}{7}=\dfrac{98}{7}[/tex]

[tex]\implies x=14[/tex]

Substitute the found value of x into the expression for each angle:

[tex]\implies m \angle 1=(x-8)^{\circ}[/tex]

[tex]\implies m \angle 1=(14-8)^{\circ}[/tex]

[tex]\implies m \angle 1=\boxed{6^{\circ}}[/tex]

[tex]\implies m \angle 2=(6x)^{\circ}[/tex]

[tex]\implies m \angle 2=(6 \cdot 14)^{\circ}[/tex]

[tex]\implies m \angle 2=\boxed{84^{\circ}}[/tex]

The volume of water in the sink after x minutes can be represented by a function V(x) = 0.25 x and its domain is 0 ≤ x ≤ 10

After x minutes, the volume of water in the sink will be:

   V = filling rate ⨉ time interval

Information from the problem:

filling rate = 0.25 gallons per minute

time interval = x

Substitute these parameters into the formula:

   V = 0.25 x

The domain of a function is the set of all possible inputs, of which the function is defined.

In this problem, the function is the volume, which is a function of x.

V(x) = 0.25 x

To determine its domain, check the minimum and maximum values of V(x).

When the sink is empty, V = 0.

Then,

V(x) = 0.25 x

  0   = 0.25 x

  x   = 0

When the sink is full, V = 2.5.

Then,

V(x) = 0.25 x

 2.5 = 0.25 x

  x   = 10

Since V(x) has value 0 ≤ V(x) ≤ 2.5, its corresponding input should be  0 ≤ x ≤ 10. This is the domain.

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The following are the linear relationships between two variables measured in statistics:

So,

The following are the linear relationships between two variables measured in statistics:

Therefore, the following are the linear relationships between two variables measured in statistics:

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The dimension of the smallest flowering plant is 59/2500 in. long and 129/10,000 in. wide.

To convert Decimal into Fraction form:

Do the following Steps:

Step 1: Make a fraction with the decimal number as the numerator and a 1 as the denominator.

Step 2: Remove the decimal places by multiplication.

Step 3: Reduce the fraction.

Step 4: Simplify the remaining fraction to a mixed number fraction if possible.

Given,

The smallest flowering plant is the flowering aquatic duckweed found in Australia.

And it is 0.0236 inch long and 0.0129 inch wide.

Here we need to write these dimensions as fractions in simplest form.

Rewrite the decimal number as a fraction with 1 in the denominator

So,

=> 0.0236/1 and 0.0129/1

Now, Multiply to remove 4 decimal places. Here, you multiply top and bottom by 10⁴ = 10000.

Then we get,

=> 236/10000 and 129/10000

Now, reduce the fraction by dividing both numerator and denominator by GCF = 4,

=> 59/2500

But the fraction 129/10000 is not reducible.

Therefore, the fraction form is,

=> 59/2500 in. long and 129/10,000 in. wide.

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Answer:

hola

Step-by-step explanation:

The segment AB is perpendicular to the segment CD because the two angles it creates are each 90 degrees .

A line is said to be perpendicular to another line if the two lines intersect at a right angle . The segment AB can be called the perpendicular from A to the segment CD . The point B is called the foot of the perpendicular from A to segment CD or simply , the foot of A on CD .If a first line is perpendicular to a second line , then the second line is also perpendicular to the first .

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Answer: X= -8

Step-by-step explanation:

Rearrange your terms:

5-X=13

-x+5+13

Subtract 5 from both sides

Simplify those = -X = 8

Dive both sides by same factor, -1

Simplify again

Solution= X= -8

Answer:

10

Step-by-step explanation:

|-2(2) + (-3)(2)|

2(2) + 3(2)

4 + 6

| | indicate absolute value, negative numbers are turned to positive numbers in absolute value, making B and C (negative values) into positive values.

The probability that a student who can drive is a college student is 0.2771 or 27.7%

It will be sooved using Baye's theorem -

P(college) = P(C) / 1/5 = 0.2

P(high school students) = P(H) = 4/5 = 0.8

P(college drives) = 0.23

P(high school drives) = 0.15

We have to find, probability that a student who drives is a college student.

That is, we have to find P(C/D).

P(C/D) = P(C ∩ S)/P(S)

Since P(C ∩ S) is an independent event.

P(C ∩ S) = P(C) × P(S)

P(C ∩ S) = 0.2 × 0.23

= 0.046

Using bayes's theorem, we will get

P(C/D) = 0.2771 or 27.7%

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a) r>0 is the domain of A. b) r = (4/2π + 16)^1/2 - 4

A(r) is a function representing the surface area of a cylinder of height = 8inches and radius = r.

A(r) = 2п[tex]r^{2}[/tex] + 16пr

r must be a positive number, as we can't have a radius of negative length, so the domain of A(r)  is r>0.

Solving for r in terms of A is an odd question, and a little challenging but possible using completing the square:

A/2п = [tex]r^{2}[/tex] + 8r

A/ 2п + 16 = [tex]r^{2}[/tex] + 8r + 16

A/2п + 16 = [tex](r + 4)^{2}[/tex]

r =( A/2п + 16) ^1/2 - 4

Therefore we get to know the range of r i.e., r>0 and radius = (A/2п + 16 )^1/2 - 4

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Answer:

185

Step-by-step explanation:

Answer:

185

Factor:

5×37

The money you will have invested at one year is $560

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are:

Initial = $200

Rate = $30

Let the number of months be n

So, we have

f(n) = Initial + Rate * n

This gives

f(n) = 200 + 30n

There are 12 months in a year

So, we have:

f(12) = 200 + 30 * 12

Evaluate

f(12) = 560

Hence, the money you will have invested at one year is $560

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Answer:

$8.95

Step-by-step explanation:

Divide 107.4 by 12 and you end up with the price of each audio book.

The same can be said for each problem you want find the individual amount of

Answer:

Each audio book costs $8.95

Step-by-step explanation:

Since 12 audio books that are at all the same prize equal $107.4, therefore in order to find the total of each book we divide $107.4 by 12

➟ 107.4 ÷ 12

➟ 8.95

∴ $8.95 is the cost of each book

Answer:

132

Step-by-step explanation:

The ratios are equivalent

Ratio shows the relationship that exists between values. It shows the proportion of one value in another value.

In other words, ratios says how much of one thing there is compared to another thing.

Therefore,

Ratio of peanuts to raisins in the first version = 3 : 2

divide both numbers by 2

1.5 : 1

Ratio of peanuts to raisins in the second version = 4.5 : 3

divide both numbers by 3

1.5 : 1

The ratios of the first and second trail mix are equivalent because they are both 1.5 : 1

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Answer:

0.7¢

Step-by-step explanation:

         [tex]8 \cdot 7 = 56\\= 56 - 56\\= 0.7\:\mathrm{R0}[/tex]

Changing the class width from 4,000 to 3,000 increases the details of the frequency distribution, thereby providing a better summary of the data.

Based on a similar question, the possible part of the question appear left out includes.

The correct response is; Yes, the value or magnitude categories of the data are increased using the smaller class width of 3,000 such that more details about the influence of the different classes on the results are seen, which provides a better summary of the information in the data than the frequency distribution that a 4,000 class width.

The overall shape of the frequency histogram remains almost the same for both class widths

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Considering the images (a),(b),(c),(d),(e),(f) the oriented path is

(a) Negative

(b) Positive

(c) Positive

(d) Zero

(e) Zero

(f) Zero

calculating each quadrant's line integral and symmetry.

In calculus, a line integral is an integral where the function being evaluated is along a curve. A line integral is also known as a route integral, curve integral, or curvilinear integral.

What does a Line integral mean?

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The coordinates of the translated points if the translation sequence is repeated n times according to the task content is; (nc, nd).

It follows from the task content that the point in discuss is at the origin. Hence, the point is; (0, 0).

Also, since the point is repeatedly translated c units horizontally and d units vertically, it follows from transformations that the resulting point is;

((0+c), (0+d))

Ultimately, when the translation sequence is repeated n times; the resulting pair of coordinates is; ((0+nc), (0+nd)).

And upon simplification, we have; (nc, nd).

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The x-intercept of the line is -3

y-intercept: None

From the question, we are to find the y-intercept and x-intercept of the given line

The x-intercept of a line is the point where the line crosses the x-axis on a cartesian plane

The y-intercept of a line is the point where the line crosses the y-axis on a cartesian plane

From the graph, we can observe that the line only crosses the x-axis at the point (-3, 0). That is, at the point where x = -3

Thus,

The x-intercept of the line is -3

The graph does not cut through the y-axis

Thus,

There is no y-intercept

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We get the translation rule as (x-4, y+5) for triangle ABC.

We are given a triangle:

ABC where

A = (3, -1)

B = (7, -5)

C = (-2, -2)

And, we are also given the translation of the triangle as A'B'C'

where

A' = (-1, 4)

B' = (3, 0)

C' = (-6, 3)

We need to tell the translation rule for it,

For the x coordinate, we can see that:

- 1 - 3 = - 4

3 - 7 = - 4

- 6 - (-2) = -4

So, the rule for x coordinate will be:

x - 4

Now for y coordinate:

4 - (-1) = 5

0 - (-5) = 5

3 - (-2) = 5

So, the rule for y coordinate will be:

y + 5

Translation rule then becomes:

(x-4, y+5)

Therefore, we get the translation rule as (x-4, y+5) for triangle ABC.

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60-100 bpm and that is the range of a 16 year old heart beat

Answer:

Step-by-step explanation:

Lower limit of range:

H = [tex]\frac{7}{10}[/tex](220-a)

a = 16 [given]

∴ H = [tex]\frac{7}{10}[/tex](220-16)

H = [tex]\frac{7}{10}[/tex](204)

H = [tex]\frac{7}{10}[/tex]×[tex]\frac{204}{1}[/tex]

H = [tex]\frac{1428}{10}[/tex]

H = 142.8

H = 143 beats per minute [as an integer]

Answer:

According to my the answer is 32

Step-by-step explanation:

cuz 4 ÷ 1/8 becomes 4×8/1

which is 32

Answer:

3800

Step-by-step explanation:

(52-2)×(8×10-4)

50(80-4)

50×76=3800

Solution in Scientific Notation:

[tex]3.8[/tex] × [tex]10^{3}[/tex]

Hope this helps!

Answer: The length of AB =4 units

               The length of BD = 2.4 units.

Step-by-step explanation:

Given data,

                  AD = 3.2 unit

                  BC  = 3 unit

                 CD  = 1.8 units

Find :         AB =? units

                  BD=? units

We can use the formula of Pythagorean theorem,

Define Pythagorean theorem :

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

Hypotenuse2 = Perpendicular2 + Base2

                  c2 = a2 + b2

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

Let be a ΔABC,

                           [tex](AB)^{2} = (BC)^{2} +(AC)^{2}[/tex]

From the above formula now  determined  the value of AB and BD,

Firstly , find the value of BD

In ΔBDC, by applying Pythagorean theorem,

                             [tex](BC)^{2} = (BD)^{2} + (DC)^{2}[/tex]             (Eq - 1)

Substitute BC and CD values in equation 1,

            BC  = 3 units and CD = 1.8 units

So,

We can write,

                            [tex]3^{2} = (BD)^{2} +(1.8)^{2}[/tex]

                            9 = [tex](BD)^{2}[/tex] + 3.24

                            [tex](BD)^{2}[/tex] = 9 - 3.24

                            [tex](BD)^{2}[/tex] = 5.76

                             [tex]BD = \sqrt{5.76}[/tex]

                             BD = 2.4 units             (Eq - 2)

Now find the value of AB,

In ΔABD, by applying Pythagorean theorem,

                               [tex](AB)^{2} = (AD)^{2} +(BD)^{2}[/tex]           (Eq - 3)

Substitute AD and BD values in equation 3,

            AD  = 3.2 units and BD = 3 units

So,

We can write,

                                [tex](AB)^{2} = (3.2)^{2} + 3^{2}[/tex]

                                 [tex](AB)^{2}[/tex] = 10.24 + 5.76

                                 [tex](AB)^{2}[/tex] = 16

                                  AB = [tex]\sqrt{16}[/tex]

                                   AB = 4 units

Therefore,

The length of AB =4 units

The length of BD = 2.4 units.

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The sum of the first 13 terms is 260

The first term(a) is 2

The common difference(d) is 3

n= 13

The formular is

n/2(2a + (n-1)d)

= 13/2 [ 2(2) + (13-1)3]

= 6.5 [4 + 12(3)]

= 6.5 [4 + 36]

= 6.5(40)

= 260

Hence the sum of the first 13 terms is 260

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42 pieces of candy because math

The weight of each bag is 23.25 pounds.

For given question,

Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags.

If all the bags were identical, we need to find the weight of each bag.

Let 'm' be the weight of each bag.

As Cecilia bought 187.6 pounds of crushed limestone in a total of eight bags and all the bags were identical, we get an expression.

8 × m = 187.6

now we solve above expression to find the value of m i.e., to find the weight of each bag.

⇒ 8 × m = 187.6

⇒ m = 187.6 / 8

⇒ m = 23.25 pounds

Therefore, the weight of each bag is 23.25 pounds.

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Answer:

q = 20

Step-by-step explanation:

Angles on a straight line add up to 180 degrees.

180 - 78 = 102

so

5q+2 = 102

subtract 2 from both sides

5q = 100

100 / 5 = 20

5q / 5 = q

q = 20

Hope this makes sense.