Austin purchased a new laptop in 2018 for $1875. The laptop decreases in 7pm
value by 30% each year. What is the value of the laptop in 2022? Round to
the nearest whole dollar.

Answer:

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

where a, b, and c are the side lengths of the triangle, and A, B, and C are the opposite angles, respectively.

We are given A, C, and c, so we can use the Law of Sines to find B, a, and b.

a/sin(A) = c/sin(C)

a/sin(22) = 2.69/sin(51.4)

a = sin(22) * (2.69/sin(51.4))

a = 1.00

b/sin(B) = c/sin(C)

b/sin(B) = 2.69/sin(51.4)

b = sin(B) * (2.69/sin(51.4))

We can use the fact that the sum of the angles in a triangle is 180 degrees to find B:

B = 180 - A - C

B = 180 - 22 - 51.4

B = 106.6

Now we can substitute the values we have found into the Law of Sines to find b:

a/sin(A) = b/sin(B)

1/sin(22) = b/sin(106.6)

b = sin(106.6) * (1/sin(22))

b = 2.69

Therefore, B is approximately 106.6 degrees, a is approximately 1.00, and b is approximately 2.69.

The equation that represents the proportional relationship between the initial height and the rebound height of the bouncy ball is D . r = 0.6 h

The proportional relationship can be found by the formula :

= Change in y / Change in x

= Change in rebound height / Change in initial height

= ( 0. 50 - 0. 30 ) / ( 0. 3 / 0 . 18 )

= 0.6 meters

The proportional relationship is :

= 0. 6 x initial height

= 0. 6 h

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The polynomial equation in the complete 30x^(4)+83x^(3)-52x^(2)+4x+1=0. The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.

The question asks you to solve the polynomial equation: 30x4 + 83x3 - 52x2 + 4x + 1 = 0.

To solve this equation, you will need to factor it into the form (ax + b)(cx + d) = 0. The solutions of this equation will be when either ax + b or cx + d are equal to 0.

First, factor out the Greatest Common Factor (GCF) of the polynomial, which is 4x. This will leave us with:

4x(7x3 + 20x2 - 13x + 1) = 0.

Now, factor this expression into two binomials. One of the binomials is already in the form ax + b, and the other will need to be factored further.

4x(7x2 + 5x - 1)(x + 1) = 0.

Therefore, the solutions of this equation are when

or

.

The solutions are: x = -1 and x = -1/7, 1/7, -5/7, 5/7.

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This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

It may contain one or more variables, which are symbols that represent unknown quantities or values that can vary. Algebraic expressions can be written using letters, symbols, or a combination of both, and they can be used to model real-world situations, solve problems, and express mathematical relationships.

For example, "3x + 5" is an algebraic expression that represents a linear equation with one variable "x".

2.077×10⁻⁴ means "2.077 times 10 to the power of -4", which can be rewritten as 0.0002077. This is a very small number, as indicated by the negative exponent. Specifically, it is 207.7 divided by 1,000,000.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$113\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, thus 52} \end{array}\dotfill &52\\ t=years\dotfill &4 \end{cases}[/tex]

[tex]A = 113\left(1+\frac{0.06}{52}\right)^{52\cdot 4} \implies \boxed{A \approx 143.63}\hspace{5em}\underset{ earned~interest }{\stackrel{ 143.63~~ - ~~113 }{\boxed{\approx 30.63}}}[/tex]

The corner point (8, 4) and is equal to 550

The minimum value of P = 50x + 75y exists at the corner point (3, 0) and is equal to 150. The maximum value of P = 50x + 75y exists at the corner point (8, 4) and is equal to 550.

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The correct option is C, the area of the triangle is 9 square units.

For a triangle of base B and height H the area is:

A = B*H/2

Here we can see that:

B = x

H = 2x

And we know that x = 6 - 3 = 3

Then we can use the value of x to find the values of H and B.

B = 3

H = 2*3 = 6

Now we can replace these two values in the formula for the area, then we will get the area of the triangle:

A = 3*6/2 = 3*3 = 9 square units.

When x = 3, the area is 9 square units.

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The total surface area of the tires making contact with the ground at any one time for the truck with 18 wheels, tire radius of 21 in, tire width of 12 in, and 20% contact area is approximately 5700.24 square inches.

The surface area of one tire making contact with the ground can be calculated as follows:

The diameter of the tire is 2 * radius = 2 * 21 in = 42 in

The length of the portion of the tire making contact with the ground is 20% of the circumference of the tire = 0.2 * π * 42 in ≈ 26.39 in

The width of the tire making contact with the ground is given as 12 in

Therefore, the surface area of one tire making contact with the ground is approximately 26.39 in * 12 in = 316.68 square inches

Since the truck has 18 wheels, the total surface area of all the tires making contact with the ground at any one time is 18 * 316.68 square inches = 5700.24 square inches.

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x1 = 5 and x2 = 0

The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.

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Answer:

33361

Step-by-step explanation:

The equation appears to be
75 ( 1 + 0.84 )^x

Since it increases by 84% every 2 days, you'd devide 20 by 2, making 10

So to do the equation you'd shove that into a calculator since no one wants to hand do that sort of equation.

75 ( 1 + 0.84 )^10 = 33361.0332844 = 33361

Answer:

[tex]\frac{y + x}{y\y - x}[/tex]

Step-by-step explanation:

Helping in Jesus' name.

Answer:

277 milliliters

Step-by-step explanation:

do 945-668

this gives you 277

Answer:

The answer to your problem is, 277 milliliters.

Step-by-step explanation:

The reason I say that is because our problem that you are is a subtraction problem, so.. :

945 - 668 = 277.

Then we just add milliliters.

Thus the answer to your problem is, 277 milliliters.

The 7th term of the geometric sequence is 5,103.

To find the 7th term of a geometric sequence with a first term of 7 and a common ratio of -3, we can use the formula:

an = a1 × [tex]r^(n-1)[/tex]

where an is the nth term of the sequence, a1 is the first term of the sequence, r is the common ratio, and n is the number of the term we want to find.

Substituting the given values, we get:

a7 = 7 × [tex](-3)^(7-1)[/tex]

Simplifying the exponent, we get:

a7 = 7 × [tex](-3)^6[/tex]

Evaluating the exponent, we get:

a7 = 7 × 729

Multiplying, we get:

a7 = 5,103

Therefore, the 7th term of the geometric sequence is 5,103.

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Answer:

False

Step-by-step explanation:

False, you need at least one angle and three sides to use the law of sines    or two angles  and two different sides.

sin A    sin B   sin C

------  = ------- = -------

 a           b           c

True, the law of sines can be used when you are given 3 sides of a triangle, and you are solving for an angle.

The law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in a given triangle. Therefore, if you know the lengths of all three sides of a triangle, you can use the law of sines to solve for one of the angles.

An angle is the measure that determines two straight lines, which when joined together create a point of origin, which is called the vertex of the angle.

The unit of measurement associated with angles is degrees.

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The set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

The set of vectors {v1, v2, v3} is linearly dependent if there exists a set of real numbers a, b, and c such that a*v1 + b*v2 + c*v3 = 0 and at least one of a, b, or c is not equal to zero. In this case, we can write the equation as:

a*1 + b*2 + c*(-1) = 0

We can rearrange this equation to solve for h:

h = -a - 2*b + c

Now we can plug in the values for v1, v2, and v3:

h = -1 - 2*2 + (-1)*(-1)

h = -4

Therefore, the set of vectors {v1, v2, v3} is linearly dependent when h = -4.

Alternatively, we can also use the determinant of the matrix formed by the vectors to determine when the set is linearly dependent. The determinant of the matrix is given by:

| 1 2 -1 |
| -1 1 3 | = (1)(1)(h) + (2)(3)(-1) + (-1)(-1)(2) - (-1)(1)(-1) - (2)(-1)(1) - (1)(3)(2)
| 2 1 h |

Simplifying this equation gives:

h - 6 - 2 + 1 + 2 - 6 = 0

h - 11 = 0

h = 11

Therefore, the set of vectors {v1, v2, v3} is also linearly dependent when h = 11.

So the set of vectors {v1, v2, v3} is linearly dependent for all real number h ≠ 4 and all real number h ≠ -4.

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There will be 22 blue signs at the end of the event.

The probability of an event can be determined by dividing the number of favorable outcomes by the total number of possible outcomes. For example, the probability of rolling a six on a standard six-sided die is 1/6, as there is only one favorable outcome (rolling a six) out of six possible outcomes (rolling a one, two, three, four, five, or six).

To solve this problem, we need to consider the factors that determine whether a house's sign will be flipped or not. A sign will only be flipped if the number of residents can divide the house number. For example, the sign on house number 12 will be flipped by the residents of that house because 12 is divisible by 2, 3, 4, and 6 (the factors of 12).

At the beginning, all signs are red, which means that none of the houses have had their sign flipped yet. Let's start with house number 1 and consider which houses will flip its sign.

For house number 1, its sign will not be flipped because 1 is only divisible by 1.

For house number 2, its sign will be flipped because 2 is divisible by 2.

For house number 3, its sign will not be flipped because 3 is only divisible by 1 and 3.

For house number 4, its sign will be flipped because 4 is divisible by 2 and 4.

For house number 5, its sign will not be flipped because 5 is only divisible by 1 and 5.

And so on, continuing this process for all 500 houses.

We can see that the signs on the houses with numbers that have an odd number of factors will end up blue, and the signs on the houses with numbers that have an even number of factors will end up red. This is because a factor always comes in pairs, except when the number is a perfect square, in which case the factor pair is identical (e.g. 4 has factors 1, 2, and 4, which is an odd number of factors).

So we need to count the number of integers from 1 to 500 that have an odd number of factors. These are the perfect squares, which are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484.

Therefore, there will be 22 blue signs at the end of the event.

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The average amount of trash collected is found to be 3 pounds.

Let the average amount of trash collected be 'x'.

As per the given conditions, equation form:

80*(1.5 + x ) = 360

Applying the Distributive Property:

120 + 80x = 360

Simplifying:

80x = 240

x = 240/80

x = 3

Thus, the average amount of trash collected is found to be 3 pounds.

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The complete question is attached.

Lee's gross pay is $472.

First, we need to calculate the commission Lee earned. To do this, we take her total sales and multiply it by her commission rate.

Commission = Total Sales x Commission Rate

Commission = $4,000 x 0.04

Commission = $160

So, Lee earned $160 in commission.

Next, we need to calculate her base pay. To do this, we multiply her hourly rate by the number of hours she worked.

Base Pay = Hourly Rate x Hours Worked

Base Pay = $8.00 x 39

Base Pay = $312

Now that we have calculated her commission and base pay, we can add them together to find her gross pay.

Gross Pay = Base Pay + Commission

Gross Pay = $312 + $160

Gross Pay = $472

This means that before any deductions (such as taxes), Lee would earn $472 for working 39 hours and making $4,000 in sales.

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The results of the matrix operations are:

To compute each matrix sum or product, we first need to determine if the operation is defined. Then, we can use the rules of matrix arithmetic to find the result.

-2A is defined, since we can multiply a matrix by a scalar. To find the result, we simply multiply each element of A by -2:

-2A = [-2(2) -2(0) -2(-1); -2(4) -2(-3) -2(2)] = [-4 0 2; -8 6 -4]

B - 2A is defined, since both matrices have the same dimensions. To find the result, we first compute -2A as shown above, then subtract each corresponding element of B and -2A:

B - 2A = [7 -5 1; 1 -4 -3] - [-4 0 2; -8 6 -4] = [7-(-4) -5-0 1-2; 1-(-8) -4-6 -3-(-4)] = [11 -5 -1; 9 -10 1]

AC is undefined, since the number of columns in A (3) does not match the number of rows in C (2).

CD is defined, since the number of columns in C (2) matches the number of rows in D (2). To find the result, we multiply each row of C by each column of D and sum the products:

CD = [(1)(3)+(2)(-1) (1)(5)+(2)(4); (-2)(3)+(1)(-1) (-2)(5)+(1)(4)] = [1 13; -7 -6]

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Answer:

I believe the answer you are looking for is [tex]6b^{4}[/tex] -  [tex]8b^{2}[/tex]

Step-by-step explanation:

Hope it helps

Sorry if I'm wrong

Gail should pick a Beautiful bank if she plans to have her money in the account for 15 years.

To determine which bank would be better for Gail, we need to calculate the future value of her investment after 15 years for each bank and compare the results.

For Neighborhood Bank, we can use the formula:

FV = P(1 + r/n)^(n*t)

where FV is the future value,

P is the principal (the initial amount invested),

r is the annual interest rate (as a decimal),

n is the number of times the interest is compounded per year,

and t is the number of years.

Plugging in the values, we get:

FV = 5,500(1 + 0.012/1)^(1*15)

FV = 5,500(1.012)^15

FV = 7,130.34

For Beautiful Day Bank, we can use the formula:

FV = P(1 + r/n)^(n*t)

Plugging in the values, we get:

FV = 5,500(1 + 0.012/365)^(365*15)

FV = 5,500(1.000032876)^5475

FV = 7,145.25

Therefore, Beautiful Day Bank would be the better choice for Gail, as she would earn a higher amount of interest and end up with a higher future value for her investment after 15 years.

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The Ratio fractions decimal percent is as follows:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

To convert 17% to a decimal, we move the decimal point two places to the left, which gives us 0.17.

To convert 3/4 to a decimal, we divide 3 by 4, which gives us 0.75.

To convert 0.17 to a fraction, we write it as 17/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 17 in this case. Therefore, 0.17 as a simplified fraction is 17/100.

To convert 0.75 to a fraction, we write it as 75/100 and simplify by dividing both the numerator and denominator by the greatest common factor, which is 25 in this case. Therefore, 0.75 as a simplified fraction is 3/4.

To convert 17% to a ratio, we write it as 17:100.

Therefore:

17% as a decimal = 0.17

17% as a fraction = 17/100

17% as a ratio = 17:100

3/4 as a decimal = 0.75

3/4 as a fraction = 3/4

3/4 as a ratio = 3:4

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The solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

In the elimination method, the two equations are solved by eliminating one variable and by substituting the value of one variable in the equation to get the value of another variable.

The two equations can be solved as below,

2a-b=-1

a-2b=4

Multiply the second equation by two and subtract from the first equation,

2a-b=-1

2a - 4b = -8

________

       3b = - 9

         b = -3

2a + 3 = -1

2a = -4

a = -2

For the other two equations,

3m-n=8

m+n= 4

_______

4m = 12

m = 3

m + n = 4

n = 4 - 3

n = 1

Therefore, the solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

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If A varies directly as B and inversely as C then The value of A when B is 12 and C is 3 is 16.

To find the value of A, we can use the formula for direct and inverse variation of the given :
A = k*B/C

We are given that A is 12 when B is 6 and C is 2. We can plug these values into the formula to find the value of k:
12 = k*6/2
12 = 3k
k = 4

Now that we know the value of k, we can plug in the new values for B and C to find the value of A:
A = 4*12/3
A = 48/3
A = 16

Therefore, the value of A when B is 12 and C is 3 is 16. The correct answer is O 16.

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The functions that are odd or even can be determined by replacing x with -x and seeing if the function remains the same or changes sign.

(a) f(x) = -tan(x) is an odd function because f(-x) = -tan(-x) = tan(x) = -f(x)

(b) f(x) = tan(x+T/2) is an odd function because f(-x) = tan(-x+T/2) = -tan(x+T/2) = -f(x)

(c) f(x) = tan(x)+cot(x) is neither an odd nor an even function because f(-x) = tan(-x)+cot(-x) = -tan(x)-cot(x) ≠ f(x) or -f(x)

(d) f(x) = 5cot(x) is an even function because f(-x) = 5cot(-x) = 5cot(x) = f(x)

(e) f(x) = (tan(x))2 is an even function because f(-x) = (tan(-x))2 = (tan(x))2 = f(x)

(f) f(x) = tan(4x) is an odd function because f(-x) = tan(4(-x)) = -tan(4x) = -f(x)

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The height of the flagpole is approximately 23,047.11 feet.

To resolve this issue, we can make use of the similar triangles property. The teacher, the flagpole, and each of their corresponding triangles are similar because they have the same angles.

Let h be the height of the flagpole. Then, we can set up the following proportion:

h / 3112 = 612 / 9

When we simplify this ratio, we obtain:

h = (3112 x 612) / 9

h = 207424 / 9

h ≈ 23,047.11 feet

Hence, the flagpole is roughly 23,047.11 feet tall.

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The number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D. Option B

Since there are more than 72 demos

Each executive will receive at least 72/6 = 12 demos.

The number of demos that each executive will receive is 12 demos

Therefore, the number in the sentence that represents the number of demos, D, that each executive will receive is 72 ÷ 6 < D.

Hence, the correct inequality is 72 ÷ 6 < D.

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The height of the helium tank is 49 inches.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

The volume V of a cylinder is given by the formula:

V = πr²h

where r is the radius of the base and h is the height of the cylinder.

Since the diameter of the helium tank is given as 14 inches, the radius r is half of the diameter, which is 7 inches.

We also know that the volume inside the tank is 2,401π cubic inches. Therefore, we can write:

2,401π = π(7)²h

Simplifying the right-hand side, we get:

2,401π = 49πh

Dividing both sides by 49π, we get:

h = 2,401π / 49π

Simplifying, we get:

h = 49

Therefore, the height of the helium tank is 49 inches.

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Answer:

49

Step-by-step explanation:

I took the test and got it right :)

For (a): 52 + 35/10m, rationalizing the denominator gives the result (25√2 + 6√5)/10.
For (b): 33x + 3y/3xy, rationalizing the denominator gives the result √3(x+y)/xy.

To rationalize the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of a binomial expression is the same expression with the sign between the terms changed. For example, the conjugate of (a+b) is (a-b) and the conjugate of (a-b) is (a+b). By multiplying by the conjugate, we eliminate any radicals in the denominator.

(a) 5/√2 + 3/√5

  = (5/√2)(√2/√2) + (3/√5)(√5/√5)

  = (5√2)/2 + (3√5)/5

  = (25√2 + 6√5)/10

(b) (3√3x + 3√y)/(3√xy)

  = (3√3x + 3√y)(3√xy)/(3√xy)(3√xy)

  = (9x√3xy + 9y√3xy)/(9xy)

  = (9√3xy(x+y))/(9xy)

   = √3(x+y)/xy

Therefore, the rationalized denominators are (a) (25√2 + 6√5)/10 and (b) √3(x+y)/xy.

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