Question: solve ABC below using either the law of sines or law of cosines. Round to the nearest tenth.

The time required to the nearest day to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days.

In the question ,

it is given that

the deposit ( principle amount P) = $1000

the final amount (A) = 1 million = $1000000

the rate of interest (r) = 3% = 0.03

let the time taken to make $1000 to 1 million be " t ".

The continuous compounding interest is given by  the formula

[tex]A = P\times e^{r t}[/tex]

where A is the final amount

P is the principle amount

r is the rate of interest

t is the time taken

Substituting the values of A , P , r and t from above , we get

1000000 = 1000×[tex]e^{0.03*t}[/tex]

10000000/1000 = [tex]e^{0.03t}[/tex]

1000 = [tex]e^{0.03t}[/tex]

taking ln on both the sides

㏑(1000) = ㏑([tex]e^{0.03t}[/tex])

㏑(1000) = (0.03t)*㏑(e)

6.9077 = (0.03t)*1           .... as ln(e) = 1 and ln(1000)=6.9077

6.9077 = 0.03*t

t = 6.907755/0.03

t = 230.2585

So , time required is 230.2585 years .

to convert into days , we multiply by 365.

time ( in days) = 230.2585×365

= 84044.3525

≈ 84044 days

Therefore , the time required to make the deposit of $1000 to grow to $1 million at 3% compounded continuously is 84044 days .

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If we plot the values of x representing the given interval on the number line, the least value would be - 12. It would be on the left and also non inclusive. The greatest value of x would be 8 on the right and inclusive. By writing it in set builder notation, it is expressed as shown in the attached photo

We need to complete the perfect square. A perfect square has the following form:

In our case we have:

We can immediately deterine the value of "a", which is the root of number multiplying x², since this number is 1, then:

This also means we can find "b", because the second term is equal to the product of 2, a, and b. So we have:

With this we can determine the blank, because it is b². So we have:

The first missing space is 16 and the second is 4.

Answer: 7 months

Step-by-step explanation: by 7 months you would have paid both memberships $300

F = cost of the songs.

C = number of songs

F ∝ C

F = KC

K = constant of proportionality.

The constant of proportionality is 0.0048.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example: 2x = 6 is an equation.

We have,

Number of songs      Total cost

1515                              $7.20

1717                               $8.16

2020                            $9.60

Let F = cost of the songs.

C = number of songs

F ∝ C

F = KC

K = constant of proportionality.

We see that,

The total cost of the songs = 0.0048 x the Number of songs.

7.20 = 0.0048 x 1515

8.16 = 0.0048 x 1717

9.60 = 0.0048 x 2020

Thus,

F ∝ C

F = KC

F = cost of the songs.

C = number of songs

K = constant of proportionality.

The constant of proportionality is 0.0048.

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We can form an equation to solve this

What is an equation?

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. The definitions of the word equation and its cognates in various languages might vary slightly. For instance, in French, an equation is defined as having one or more variables, but in English, an equation is any well-formed formula that consists of two expressions linked by the equals sign. An equation can be compared to a scale on which objects are weighed. More broadly, if the identical operation is carried out on both sides of an equation, the equation remains in balance. Algebra focuses on two primary families of equations: the specific case of linear equations and polynomial equations.

We form an equation as 0.6x=330

The equation can be solved as

0.6x = 330

or, x = 330/0.6 = 550 grams

Hence Mr. Butcher used = 550 - 330 = 220grams of sugar

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when we rotate a point 180°, we have to change the sign in every coordinate. Therefore we get that the new point is (3,5)

After performing some mathematical operations, the length of RA is 15 feet.

So, the length of RA is:

As both the pentagons are similar, then:

Similarly,

Therefore, after performing some mathematical operations, the length of RA is 15 feet.

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The mode of a data set is the number that repeats the most.

In this case, we can see that teh value $14,950 is twice.

Then the correct answer is option A. The mode is $14,950

The equation of the line in point-slope form passing through ( - 1, - 4 ) and slope 3 is y + 4 = 1( x + 1 ).

The set of points that make up a line in a coordinate system is represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y.

The point-slope form of an equation of the line is given as:

y - y₁ = m( x - x₁ ) where m is the slope and ( x₁, y₁ ) is the point on the line.

Now, the equation of line passes through ( - 1, - 4 ) and m = 1

Then,

y - y₁ = m( x - x₁ )

y - ( - 4 ) = 1( x -  ( - 1 ) )

y + 4 = x + 1

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The domain of the relation is [1,6]. The domain can be written in the roster form method like {x I x ∈ {1,....,6}} The range of the function is  [1,2].

As we can see that the range of values in x-axis is from  [1,6]. Hence, it is the domain of the relation.

Also, he range of values in y-axis is from  [1,2]. Hence, it is the range of the relation.

Domain of a relation

The domain or set of departure of a function is the set into which all of the input of the function is constrained to fall.

Range of a relation

The set of the second elements of all the ordered pairs of a relation is the range of a relation.

Set roster form

The elements (or members) of a set are listed in a row inside the curly brackets.

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The equation that is false based on the solution set is D. −32 = 2(3p − 6)

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

6 = 2y − 4

This will be:

2y - 4

2(5) - 4

10 - 4 = 6

4(b + 5) = 40

4(5 + 5)

4(10) = 40

one fifth times x plus 16 equals 17

1/5x + 16

1/5(5) + 16

1 + 16 = 17

Therefore, the last option doesn't fit in.

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Answer:D. −32 = 2(3p − 6)

Step-by-step explanation:

The value fo the expression - [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 as a mixed number is 4 1/6.

Consider the expression,

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6

By using the BODMAS rule, we will first solve the inner parenthesis.

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 9/5 ÷ 0.36 ] - 5/6

Now dividing the terms in the inner parenthesis {}.

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 1.8  ÷ 0.36 ] - 5/6

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = - [ - 5 ] - 5/6

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 5 - 5/6

By the BODMAS rule subtracting the remaining terms.

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 5/1 - 5/6

The LCM of 1 and 6 is 6.

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = ( 30 - 5 )/6

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 25/6

- [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 = 4 1/6

The value of the expression - [ - 1 4/5 ÷ 0.3( 1.2 ) ] - 5/6 is 4 1/6.

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The product of the polynomials (3x+2) and (-x^3-3) is:

(3x+2)*(-x^3-3) = (3x)*(-x^3) + (3x)*(-3) + 2*(-x^3) + 2*(-3) = -3x^4 - 2x^3 -9x - 6

Multiplying it by (3 + x), we got:

(3 + x)*(-3x^4 - 2x^3 -9x - 6) = 3*(-3x^4) + 3(-2x^3) + 3*(-9x) +3*(-6) + x*(-3x^4) + x*(-2x^3) + x*(-9x) + x*(-6) = -3x^5 -11x^4 -6x^3 -9x^2 - 33x - 18

Therefore, the coefficient of x^4 is -11.

Answer:

√39

Step-by-step explanation:

x/13 = 3/x

x^2 = 39

x = √39

The inequality that corresponds to the following expression, "A is less than 9" is:

An expression for the combined total dollar Josh earned this month is X = 15t + 13(95 - t).

A mathematical expression is a statement using a combination of numbers, variables, and mathematical operands.

Mathematical expressions may also use the equal symbol (=) to show that the two expressions are equal.  Sometimes, the inequality signs are used when two expressions are not equivalent.

The pay rate per hour as a tutor = $15

The pay rate per hour as a waiter = $13

The combined total hours worked for the month = 95 hours

Let t = the number of hours worked as a tutor

Let X = Josh's total dollars earned for the month.

Josh's total earnings as a tutor for the month, A = 15t

Josh's total earnings as a waiter for the month, B = 13(95 - t)

The combined total dollar Josh earned this month, X = A + B

X = 15t+ 13(95 - t).

Thus, the total earnings by Josh for this month can be expressed as X = 15t+ 13(95 - t).

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Solution:

Given the functions:

The graph of f(x) is as shown below:

The graph of g(x) is as shown below:

Description:

In the above graph, we observe that in the transformation, the f(x) plot is reflected across the x-axis and shifted downwards by 2 units to obtain the g(x) plot.

Explanation:

To determine the numbers, we need to find factors of -50:

We only have one of the numbers with negative because we are finding factor of a negative number.

Multiplication of opposite signs give negative number.

From the factors listed above, we find the two numbers sum up to give -50:

You have the following information:

m∠FCD = x + 41

m∠BCF = x + 78

m∠BCD = 95°

In order to find the value of x, you consider that the sum of the measure of angles ∠FCD and ∠BCF is equal to the measure of angle ∠BCD.

Thus, you have:

m∠FCD + m∠BCF = m∠BCD you replace by the given expressions

(x + 41) + (x + 78) = 95 you eliminate parenthesis

x + 41 + x + 78 = 95 simplify similar terms

x + x + 41 + 78 = 95

2x + 119 = 95 subtract 119 both sides

2x = 95 - 119

2x = -24 divide by 2 both sides

x = -24/2

x = -12

Hence, the value of x is - 12

To find the scale factor, we have to divide two corresponding sides

Using the given information, we have

40% of $280

40/100 x280

= 112

The discounted price = 280 -112

= $168

The formula for the variance of the binomial distribution is o = √npq

Equating the value is the equation

o = √npq,

[tex]o = \sqrt{80\times1\times\0.4}[/tex]

o = 5.6568

The binomial distribution is defined as the number of trials or observations when each trial has the same probability of reaching a certain value. The binomial distribution determines the probability of observing a certain number of successful outcomes for a given number of trials.

The binomial distribution model allows us  to calculate the probability of observing a certain number of "successes" if a process is repeated a certain number of times (eg, in a patient population) and the result for a given patient is either successful. or failure.

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Answer:

1.no, because 840 divide by 70 equals 12 and 12 does not equal 14

2.yes, because 480 divided by 30 does equal 16 and 16=16

3.yes, because 640 divided by 40 does equal 16 and 16=16

4.no, because 910 divide by 30 equals 30.333 and 30.333 does not equal 31

Step-by-step explanation: Hope this helps

Answer:yes no yes no

Step-by-step explanation:

im to lazy to add step my step but i 100% correct

Graph A shows  a function and its inverse A. B. C. D.

An output is produced by a function after it accepts inputs, applies specific operations to the values, and produces an output. The inverse function works, agrees with the resultant, and returns to the original function An inverse relationship is created when an independent variable is switched out for a variable that depends on a given equation; an inverse relationship may or may not be a function.

Inverse functions, indicated by f-1(x).on, are those in which the inverse of a function is that function itself.

It is common practice to swap the coordinates x and y when calculating an inverse. This new inverse is not necessarily a function, but it is a relation.

To guarantee that the inverse function is also a function, the initial function must be a one-to-one function.

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The value of the amount after the second year is $10163.817.

In order to compute compound interest, we multiply the principle of the original loan by the annual interest rate multiplied by the number of compound periods minus one. Then we are left with the principal amount of the loan plus compound interest.

Amount after Compound Interest [tex]A = P(1+\frac{r}{nt} )^{nt}[/tex] where A is the amount, P is the Principle value, r is the rate of interest, n is the number of times it is compounded daily, and t is the time.

Given Information :

For 1st year, Principal Amount (P) = $5000

Interest (r) = 1.5 %

Time = 1 year

The amount is calculated compounded daily,

So, Calculating the amount after 1 year,

[tex]A = P( 1+\frac{r}{nt}) ^{nt} \\A = 5000(1+\frac{1.5}{365*100}) ^{365*1} \\A = 5000(1+0.00004109)^{365} \\A = 5000*1.015\\A =5075.55[/tex]

For 2nd Year, Principal Amount= (P) $5000

Rate of Interest (r) = 1.75%

Time (t) = 1 year

The amount is calculated compounded daily,

So, Calculating the amount after 1 year,

[tex]A =P(1+\frac{r}{nt}) ^{nt\\}\\A= 5000(1+\frac{1.75}{365*100}) ^{365*1} \\ A = 5000(1.00004795)^{365} \\A =5000*1.077\\A =5088.26[/tex]

Now, the value of the amount after the second year = $5075.55 +$5088.26 =$10163.817.

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Jake

There is no flat fee = $0

To buy a movie = 50 cents = $0.50

Joshua

Flat fee = $5

To buy a movie = 50 cents = $0.50

Jonathan

Flat fee = $8

To buy a movie = 20 cents = $0.20

Then, we have the following expressions:

Next, to pay the same amount of money from each website. This is:

Let y = number of movies

So, solve the system:

We are told that Dontax bought the stereo on a sale of 20% off, meaning he will only have to pay 100% -20% = 80% of the price.

Now, 80% of $199 is

Hence the amount of money Dontay saved is

Which is our answer!