What way can you simplify this equation?

first off, let's check the equation for each year.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$736.80\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ 736.80=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 4}\implies 736.80=P\left(1+\frac{r}{100} \right)^4 \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$788.82\\ P=\textit{original amount deposited}\\ r=rate\to r\%\to \frac{r}{100}\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &7 \end{cases} \\\\\\ 788.82=P\left(1+\frac{\frac{r}{100}}{1}\right)^{1\cdot 7}\implies 788.82=P\left(1+\frac{r}{100} \right)^7 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{using the 1st equation}}{736.80=P\left(1+\frac{r}{100} \right)^4}\implies \cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}=P \\\\\\ \stackrel{\textit{using the 2nd equation}}{788.82=P\left(1+\frac{r}{100} \right)^7}\implies \stackrel{\textit{substituting on the 2nd equation}}{788.82=\cfrac{736.80}{\left(1+\frac{r}{100} \right)^4}\left(1+\frac{r}{100} \right)^7}[/tex]

[tex]788.82=736.80\cfrac{ ~~ \left(1+\frac{r}{100} \right)^7 ~~ }{\left(1+\frac{r}{100} \right)^4}\implies 788.82=736.80\left(1+\frac{r}{100} \right)^3 \\\\\\ \cfrac{788.82}{736.80}=\left(1+\frac{r}{100} \right)^3\implies \sqrt[3]{\cfrac{788.82}{736.80}}=1+\cfrac{r}{100}\implies \sqrt[3]{\cfrac{788.82}{736.80}}=\cfrac{100+r}{100} \\\\\\ 100\sqrt[3]{\cfrac{788.82}{736.80}}=100+r\implies 100\sqrt[3]{\cfrac{788.82}{736.80}}-100=r\implies {\Large \begin{array}{llll} \stackrel{\%}{2.3}\approx r \end{array}}[/tex]

Answer:

No solution

Step-by-step explanation:

The absolute value function outputs non-negative values.

Answer:  No solutions

This is because absolute value is never negative. It represents distance, and negative distance does not make sense.

The smallest possible output of |x+5| is zero.

Answer:

5 i think

Step-by-step explanation:

The equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

What is the equivalent measure?

In mathematics, and more specifically in measure theory, equivalence refers to the idea that two measures are qualitatively similar. The two measures specifically agree on which events have measure zero.

The unit "qt" stands for quart, which is a unit of volume.

It is equal to 32 fluid ounces or 0.946 liters.

Therefore, 19 quarts is equal to 19 * 32 = 1932= 608  fluid ounces,

or 19 * 0.946 = 190.946 =18.094 liters.

Hence, the equivalent measure of 19 quarts is either 608 fluid ounces or 18.094 liters.

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Answer:

y = [tex]\frac{1}{8}[/tex]x

Step-by-step explanation:

You need to find the unit rate.  In a proportional relationship,  you can find this by taking any point on the line and putting it the form y/x

Look at point (16,2)  y/x = 2/16 = 1/8

Answer:

31 [tex]\frac{3}{5}[/tex] miles per gallon.

Step-by-step explanation:

[tex]\frac{39\frac{1}{2} }{1\frac{1}{4} }[/tex]

39 [tex]\frac{1}{2}[/tex] ÷  1 [tex]\frac{1}{4}[/tex]

[tex]\frac{79}{2}[/tex] ÷ [tex]\frac{5}{4}[/tex]

[tex]\frac{79}{2}[/tex] x [tex]\frac{4}{5}[/tex] = [tex]\frac{158}{5}[/tex] = 31 [tex]\frac{3}{5}[/tex] miles per gallon or 31.6 miles per gallon

Answer: 17 packs

Step-by-step explanation: 16 packs of 10 equals 160 beads, and one pack of 5 will give you 164 beads with 1 left over.

The positive numbers are 36 and 47.

What is a positive number?

Any positive number is one that is higher than zero.

A number can be zero, negative, or positive. Zero has no positive or bad aspects. The most frequent positive numbers in daily life include 34, 9.22, and other examples such as these. They are typically depicted on a number line to the right of zero, increasing bigger as you move to the right.

Assume that the positive numbers be x and y.

Given that the difference x and y is 11.

Therefore x - y = 11

x = y + 11 ....(i)

The product of the numbers is 1692.

xy = 1692 .....(ii)

Putting x = y - 11 in equation (ii):

(y + 11)y = 1692

y² +11y = 1692

y² +11y - 1692 = 0

y² +47y - 36y - 1692 = 0

y(y + 47) - 36(y+47) = 0

(y + 47) (y-36)=0

y = -47 and 36

Since the numbers are positive, thus y = 36.

The value of x is 36 + 11 = 47

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Answer:

25

Step-by-step explanation:

The probability of having fewer than three television sets in the apartment is 0.7

Probability is solved by finding the ratio of required outcome to the total sample

In the given problem the total sample space is the sum of the frequencies which

sum of the frequencies

= 1 + 6 + 14 + 7 + 2

= 30

The required outcome is the number of people that have less than three tv sets in their apartment, In this case 3 is not inclusive from 2 to o is added

= 1 + 6 + 14

= 21

The probability P(X < 3) = 0.7

= 21 / 30

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Answer:

B

Step-by-step explanation:

Assuming these 4 are the only possibilities:

A: This cannot be correct because if 181 were divisible by 9, it would not be prime, as the problem suggests.

C: This cannot be correct because 181/9 is 21.11, which is not a whole number

D: This cannot be correct because 181/3 is 60.333, which is not a whole number

Thus, the answer is B.

FUN FACT:

When seeing whether a number is divisible by 3, add up its digits, and if they are divisible by 3, so is the number. Example: 36 is divisible by 3 because   3 + 6 = 9, and 9 is divisible by 3. 181 is not, however, because 1+8+1=10, and 10 is not divisible by 3.

Same with 9! 459 is divisible by 9 because 4+5+9 = 18, which is divisible by 9. 181 is not, however, because 1+8+1 = 10, which is not divisible by 9.

I hope this helps!

Answer:

B. 181 is prime because its only factors are 1 and itself.

Step-by-step explanation:

Prime number

A whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).  

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.

Composite number

A number that is divisible by a number other than 1 and itself (so it has more than 2 factors).  

An example of a composite number is 6 as its factors are 1, 2, 3 and 6.

The factors of 181 are 1 and 181.

Therefore, it is prime because its only factors are 1 and itself.

The band have to sell 76 tickets for each concert to meet the goal

From the question, we have the following parameters that can be used in our computation:

P = 850 + 5x

Also, we have

Bonus = $50

This means that

Cost = 850 + 5x + 50x

So, we have

Cost= 850 + 55x

When they earn $5000, we have

850 + 55x = 5000

Evaluate the like terms

55x = 4150

Divide

x = 76

Hence, the number of tickets is 76

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Answer:

C 76

Step-by-step explanation:

let x = 1st number

let x+ 2 = 2nd number

let x + 4 = 3rd number

let x + 6 = 4th number

Let x + 8 = 5th number

x + x + 2 + x+ 4 + x + 6 + x + 8 = 400  Combine like terms

5x + 20 = 400 Subtract 20 from each side

5x  = 380  Divide both sides by 5

x = 76

Check:

76 + 78 + 80 + 82 + 84 = 400

Using synthetic division we get, the remainder is 24
and the quotient is [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex]

What is synthetic division?

Particularly when we need to divide the polynomial by a linear factor, the Synthetic division provides a faster method of doing so. Instead of dividing factors, it is typically employed to determine the polynomial's zeroes or roots.

Here, in the question we have [tex]\frac{-x^{4} +2x^{3}+12x^{2} -16 }{x+2}[/tex]

First we find x from the divisor,

x+2=0

x=-2

Next, we arrange it in the division form with only the coefficients of the dividend terms.

[tex]-2 | -1 \space\ \space\ 2 \space\ \space\ 12 \space\ \space\ 0 \space\ \space\ -16\\[/tex]

             [tex]2 \space\ -2 \space\ -20 \space\ 40[/tex]

 ----------------------------------

     [tex]-1 \space\ \space\ 0 \space\ \space\ 10 \space\ \space\ -20 \space\ \space\ 24[/tex]

Therefore, we get the remainder as 24

And the quotient as [tex]-x^{3} +10x-20-\frac{24}{x+2}[/tex].

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Answer:

Below

Step-by-step explanation:

WOW! THIS is not 'jogging' :

4 miles / 1/5 hr = 20 m/hr

(A) Positive

When z and y are both positive, the expression{ [tex]\frac{-z}{-y}[/tex] }is equal to [tex]\frac{-z}{-y}[/tex]. Since both z and y are positive, -z is negative and -y is negative, so the expression [tex]\frac{-z}{-y}[/tex] is equal to the positive number [tex]\frac{z}{\\y}[/tex].

Therefore, the sign of {-z}/{-y} when z>0 and y>0 is positive.

So the correct answer is:

(A) Positive

What is sign?

In mathematics, a sign is a symbol that is used to represent the relative size or value of a number or expression. The most common signs used in mathematics are the plus (+) and minus (-) signs, which are used to represent positive and negative numbers, respectively.

For example, the number 5 is a positive number, and it is represented using the plus sign. On the other hand, the number -5 is a negative number, and it is represented using the minus sign.

In addition to the plus and minus signs, there are also other signs used in mathematics, such as the equal sign (=), which is used to indicate that two quantities are equal, and the inequality signs (>, <, ≥, ≤), which are used to indicate that one quantity is greater than or less than another.

Overall, signs play a vital role in mathematics as they help to indicate the size and value of numbers and expressions, and they are essential for performing various mathematical operations and solving mathematical problems.

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Answer:

Exact area = 81π ft²

Approximate area = 254 ft²

Step-by-step explanation:

A = πr²

A = π × (9 ft)²

A = 81π ft²

A = 81(3.14) ft²

A = 254 ft²

[tex] \Large{\boxed{\sf A = 81 \pi \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

The area of a circle is given by the following formula:

[tex] \Large{\sf A = \pi \times r^2 } [/tex]

Where:

[tex] \\ [/tex]

We know that the diameter of a circle is twice its radius. Therefore, we can find the value of the circle's radius by dividing its diameter by 2.

[tex] \sf Diameter =2 \times radius \Longleftrightarrow radius = \dfrac{Diameter}{2} \\ \\ \\ \star \: \sf r = \dfrac{18 \ ft}{2} = \boxed{\sf 9 \ ft} [/tex]

[tex] \\ [/tex]

Now, substitute the value of the radius into the formula:

[tex] \sf A = \pi \times (9 \ ft)^2 = \boxed{\boxed{\sf 81 \pi \ \ ft^2 \approx 254.5 \ ft^2 \ (1 \ d.p.) }} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

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Answer: -48

Step-by-step explanation:

-18-30 = -48

Answer:

O y = mx + b

Step-by-step explanation:

y = y coordinate

m = slope

x = x coordinate

b = y intercept

Answer:

[tex]f(x)=3^{x+1}-3[/tex]

Step-by-step explanation:

The curve of the graph shows it is Exponential:  [tex]f(x)=b^{x-h}+k[/tex]

To find b, h, and k, we need to "un-transform" the graph from  [tex]f(x)=b^{x}[/tex]

1. h = horizontal shift/translation;  k = vertical translation:

  (0,1) ⇒ (-1,-2), so h = -1  and  k = -3  and  [tex]f(x)=b^{x+1}-3[/tex]

2. Given the points (-1,-2), (0,0), and (1,6), use one of them to find b:

     [tex]f(x)=b^{x+1}-3\\0=b^{0+1}-3\\0=b^{1}-3\\3=b^1\\3=b[/tex]

3. Place b, h, and k in their correct places in the function.

By solving the following trigonometric function of m(x)= x cos(-x) we get m(x) = cos(x).

What is trigonometry ?

Given that;

              m(x) = x cos(-x)

              m(x) = x cos (x)    [ we know that cos(-x) = cos(x) ]

           m(x)/x = x cos(x)/x   [divide both sides by x]

                   m = cos(x)

Therefore, m(x)=x cos(-x) ⇒cos(x)

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1. 177.441177

2. 354.882354

3. 118.294118

4. 473.176472

5. 236.588236

Answer:

(I will only answer one and I think my explanation can help you understand so you do it yourself) For number 8: the slope-intercept form is: y=-1/3x-11

Step-by-step explanation:

x+3y=-33
3y=-x-33(take away x from both sides of the = sign)

y=-1/3x-11(divide 3 on both sides of the = sign)

The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

Solution:

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                          = 4.08

Area of the triangle = [tex]\sqrt{S(S-TQ)((S-TU)(S-QU)}[/tex]

                                = [tex]\sqrt{4.08(0.92)(2.08)(1.08)}[/tex]

                                = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

  sin T  = 0.61

∴  ∠T = [tex]sin^{-1}[/tex](0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

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The measure of angle TQU is 41.1°

What is angle of measure?

The measure of the angle is formed by the two lines or arms having a same vertex.

We know that,

PQ² + PT² = QT²   -------- By Pythagoras theorem

∴QT = √10

∵ PT + TU + US = 4

∴ TU = 4 - PT - US

TU = 4 - 1 - 1

∴TU = 2

Now, using Pythagoras theorem in triangle PQU

PQ² + PU² = QU²

∴ QU =√ 3² + 3²         (∵PU = PT + TU = 1 + 2)

∴ QU = 3

Now using Heron's formula in triangle TQU

Semi-perimeter = (2 + √10 + 3)/2

                         = 4.08

Area of the triangle = 2.903 unit²

Now, we know that

Area of a scalene triangle = ab/2 × sin c

∴ 2.903 = (√10×3/)2 × sin T

∴ sin T = 2.903×2/3√10

 sin T  = 0.61

∴  ∠T = (0.61)

∴∠T = 93.9°

Using sum of interior angles of a triangle = 180 i.e. (a + b + c =180°)

∠U + ∠T + ∠Q  = 180°

∴ ∠Q = 180 - 93.9 - 45

∴∠Q  = 41.1°

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The diagram that shows a valid approach to the given construction is option a for the perpendicular bisector.

A perpendicular bisector is a section of a line that divides a straight segment into two congruent or equal segments. At exactly its midpoint, they split the line section. With the line segment it divides, a perpendicular bisector produces a 90° angle. A line segment that bisects another line segment at an angle of 90 degrees is referred to as a perpendicular bisector. In other terms, a perpendicular bisector separates a line segment into two equal pieces by intersecting it at a 90° angle. The term "perpendicular bisector" refers to a precise drawing in which a line is accurately divided in half by another line that is perpendicular to the first line. To divide into two equal portions, or bisect, is a verb.

Therefore, The diagram that shows a valid approach to the f=given construction is option a.

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The quantities we need circumference for are: A and C.

The quantities we need area for are: B and D.

The circumference of a circular shape is described as the distance around the circular shape. It is calculated using the formula, 2πr.

On the other hand, the area of a circular shape is the amount of space a circular shape has. It is calculated as πr².

Therefore:

For quantity A, to know the distance around a Ferris wheel, we would need to calculate is the circumference, so also for quantity C.

For quantity B, to know the amount of paint needed, we would calculate the area, so also is it for quantity D.

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0.53.The elements left over after the given set's components have been eliminated from the universal set are the complement of the set.

Explanation:

P(event E)=0.47

Consequently, P(not E)=1P(E) [P(E)+P(not E)=1] =10.47 =0.53

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The of interest earned by Cedric's account  after 1 year and 9 months is $34.83.

The simple interest formula is expressed as;

I = P × r × t

Where I is interest, P is principal, r is interest rate and t is time.

Given the data in the question;

Plug the given values into the above formula and solve for interest.

I = P × r × t

I = $796 × 2.5% × 21/12

I = $796 × 0.025 × 1.75

I = $796 × 0.025 × 1.75

I = $34.83

Therefore, the interest earned in the account is $34.83.

Option B is the correct answer.

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1) The growth rate is 40%

2) The number of bacteria initially present is 990

3) The number after four hours is  4904

4) The function in terms of time is written as F(t) = 120e^-1.6t

We know that the number of the bacteria can be obtained on the basis of the function that we have. We know that the process of exponential increase of decrease would have to be modelled by the use of an exponential equation. In this case, we have the equation; n(t) = 990e^0.4t

We know that in this case, the time of the multiplication of the bacterial is t, the percent growth rate of the bacteria is 40% and the initial number of the bacteria is 990.

After 4 hours we have;

n(4) = 990e^0.4(4)

n(4) = 4904

b) Given that the initial temperature  if the system is 120°F and the rate of the cooling is 1.6, the formula is written as;

F(t) = 120e^-1.6t

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Answer:

Z=3

Step-by-step explanation:

1 1/2+1 1/2= 2+1=3