Please see the attached photo. I do not know how to calculate any of this using my TI 84+ CE calculator and the answers I am getting when trying to calculate by hand are not correct.

Answer:

  279/1640

Step-by-step explanation:

The relations between the various trig functions can be used to find the necessary function values.

Solving for cos(θ), we have ...

  41 cos(θ) = 9

  cos(θ) = 9/41 . . . . . divide by 41

The Pythagorean relation tells you ...

  sin²(θ) +cos²(θ) = 1   ⇒   sin(θ) = √(1 -cos²(θ))

  sin(θ) = √(1 -(9/41)²) = (√(41² -9²))/41 = 40/41

The tangent relation is ...

  tan(θ) = sin(θ)/cos(θ) = (40/41)/(9/41) = 40/9

The value of the given expression is ...

  (sin(θ) -cos(θ))/tan(θ) = (40/41 -9/41)/(40/9) = (31/41)(9/40) = 279/1640

__

Additional comment

This can also be figured by a suitable calculator or spreadsheet. Output formatted as a fraction is often an option. Here, the result is rational.

Answer:

x³+3x²-28x

Step-by-step explanation:

(x-4)(x-0)(x+7)

(x-4)(x)(x+7)

(x-4)(x+7)=(x²+3x-28)

(x²+3x-28)(x)=x³+3x²-28x

Answer:

SR = 5

Step-by-step explanation:

We know that the two lines are equal to each other and thus TS + SR = 13

So, we can simply set the two equations of the first line equal to 13:

x + 2 + 2x - 7 = 13

3x - 5 = 13

3x = 18

x = 6

Now we plug in 6 for x in the SR equation:

2 * 6 = 12 - 7 = 5

El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

En esta pregunta debemos encontrar el volumen remanente entre el espacio de una caja cúbica y una esfera introducida en el elemento anterior. El volumen remanente es igual a sustraer el volumen de la pelota del volumen de la caja.

Primero, se calcula los volúmenes del cubo y la esfera mediante las ecuaciones geométricas correspondientes:

Cubo

V = l³

V = (4 cm)³

V = 64 cm³

Esfera

V' = (4π / 3) · R³

V' = (4π / 3) · (2 cm)³

V' ≈ 33.5103 cm³

Segundo, determinamos la diferencia de volumen entre los dos elementos:

V'' = V - V'

V'' = 64 cm³ - 33.5103 cm³

V'' = 30.4897 cm³

El volumen remanente entre la esfera y el cubo es igual a 30.4897 centímetros cúbicos.

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The length of the semi-major axis of the ellipse is 7.

What is the semi-major axis of an ellipse?

The semi-major axis of an ellipse is the half of the longest diameter passing through its vertex and focus.

The general equation of an ellipse is :

⇒ x²/a²+y²/b²=1, where a is the semi-major axis and b, is the semi-minor axis

x²/49+y²/36=1

x²/(7²)+y²/(6²)=1

x²/a²+y²/b²=1

a=7

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Answer:

54°

Step-by-step explanation:

Opposite angles of a parallelogram are congruent, so;

[tex]9x+9=8x+14 \\ \\ x=5 \\ \\ m\angle S=9(5)+9=54^{\circ}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

In a Parallelogram, opposite angles are equal, so we infer that :

[tex] \qquad❖ \: \sf \:9x + 9 = 8x + 14 [/tex]

[tex] \qquad❖ \: \sf \:9x - 8x = 14 - 9[/tex]

[tex] \qquad❖ \: \sf \:x = 5 \degree[/tex]

Next,

Measure of Angle S is :

[tex] \qquad❖ \: \sf \:9x + 9[/tex]

[tex] \qquad❖ \: \sf \:9(5) + 9[/tex]

[tex] \qquad❖ \: \sf \:45 + 9[/tex]

[tex] \qquad❖ \: \sf \:54 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

Answer:

Step-by-step explanation:

1479

Area equals Length times Width.

since the width of this equation is 5 units Longer then its Length

W = L + 5

To put this area in a equation we could say

L(L+5)=A
Simplify the equation, L^2 + 5L = A.

Answer:

It is a rational number.

Step-by-step explanation:

A number is only irrational if it has a decimal that never ends and doesn't have a pattern. So a number like Pi (3.141592653589...) is irrational while a number like 1/3 (0.33333333...) is rational.

Hi :)

Below is the difference between rational & irrational numbers

Evidently,

Let's test the given number, [tex]\boldsymbol{3\dfrac{1}{4}}[/tex]

Well isn't it already in [tex]\sf{\dfrac{p}{q}}[/tex] form? It is.

Thus

[tex]\longrightarrow\darkblue\boldsymbol{3\dfrac{1}{4}\:is\:rational}[/tex]

[tex]\tt{Learn\:More;Work\:Harder}[/tex]

:)

Answer:

[tex] \pmb{ \pink{QUESTION�}}[/tex]

Find the midsegment of the triangle which is parallel to CA.

[tex] \pmb{ \pink{ANSWER:-}}[/tex]

Tip

[tex] \frak{Explanation:-} [/tex]

We have to find the segment which is parallel to CA.

From the given data,

The segment EG is the midsegment of the triangle[tex]\triangle[/tex] ABC.

So we have,

A midsegment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment has two special properties. It is always parallel to the third side.

[tex]\implies\rm{midsegment \: EG \: parallel \: to \: CA}[/tex]

[tex]\frak{RainbowSalt}[/tex]~

Answer:

[tex]\fbox {EG}[/tex]

Step-by-step explanation:

Based on the given diagram, we can clearly see the midsegment (lies in the middle of the figure) that is parallel to AC is EG

I hope it helped you solve the problem.

Good luck on your studies!

y=2

-5(2)²-3(2)-2

-5(4)-3(2)-2

-20-6-2

=12

The spread of the disease will take a time 100 days to reach 2,500 infected people.

In this problem we have a radical equation that represents the number of infected people as a function of time, we are suppose to find the time when that number will be 2,500 by algebra properties: (N = 2,500)

2,500 = 250 · √t

√t = 2,500 / 250

√t = 10

t = 10²

t = 100

The spread of the disease will take a time 100 days to reach 2,500 infected people.

The statement is poorly formatted and presents typing mistakes, correct form is shown below:

The spread of a disease can be modeled as N(t) = 250 · √t, where N is the number of infected people, and t is time (in days). How long will it take until the number of infected people reaches 2,500?

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Answer:

■ Sales tax: $52.75

■ Cost/Price before ST: $540.99

■ Total Cost/Price including ST: $593.74

Step-by-step explanation:

540.99 x 0.0975

= 52.75

Total

= 540.99+52.75

=593.74

A line segment can be defined as the part of a line in a geometric figure such as a parallelogram, that is bounded by two (2) distinct points and it typically has a fixed length.

In Geometry, a line segment can be measured by using the following measuring instruments:

A parallelogram refers to a geometrical figure (shape) and it can be defined as a type of quadrilateral and two-dimensional geometrical figure that has two (2) equal and parallel opposite sides.

Based on the previous experiment conducted in question 5, 6 and 7, we can logically conclude that the opposite sides of quadrilateral ABCD have the same (equal) slopes, which implies that the opposite sides are parallel. Hence, quadrilateral ABCD is simply a parallelogram by definition.

In this context, yes I would you reach the same conclusion that I reached in question 7 because the line segments that I drew represent the diagonals of a parallelogram.

Therefore, if the point of intersection of the diagonals divide each diagonal in half, then, the quadrilateral belonging to these diagonals forms a parallelogram.

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The dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height if the storage shed is to be built in the shape of a box with a square base.

It is defined as a three-dimensional space enclosed by an object or thing.

It is given that:

A storage shed is to be built in the shape of a box with a square base.

It is to have a volume of 729 cubic feet.

Let x be the length of the base

Let y be the height of the box.

V = 729 cubic feet

The base is square:

l = w = x

V = x²y

y =  729/x²

Cost of the base = $8x²

Cost of the roof = 3x²

Cost of the sides = 4(5.50)xy

= 22xy

Total cost

C= 8x² + 3x² + 22xy

C = 11x² + 22x(729/x²)

C = 11x² + 16038/x

Find the first derivative:

dC/dx = 22x - 16038/x²

Equate; dC/dx = 0

22x - 16038/x² = 0

22x = 16038/x²

22x³ =16038

x³ = 729

x = 9

y = 729/(9)² = 9

Length of base = 9 ft

Width of base  = 9 ft

Height of box = 9 ft

Thus, the dimensions of the most economical shed are 9 ft in length, 9 ft in width, and 9 ft in height.

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Step-by-step explanation:

1. Lower the confidence level.

2. Use a one-sided confidence interval. ...

3. Increase the sample size. Often, the most practical way to decrease the margin of error is to increase the sample size. ...

4. Reduce variability. The less that your data varies, the more precisely you can estimate a population parameter. ...

PLEASE MARK ME AS BRAINLIST

Answer:

Increase the sample size.

Usually, the more observations that you have, the narrower the interval around the sample statistic is.

Put the equation in standard linear form.

[tex]x'(t) + \dfrac{x(t)}{t + 5} = 5e^{5t}[/tex]

Find the integrating factor.

[tex]\mu = \exp\left(\displaystyle \int \frac{dt}{t+5}\right) = e^{\ln|t+5|} = t+5[/tex]

Multiply both sides by [tex]\mu[/tex].

[tex](t+5) x'(t) + x(t) = 5(t+5)e^{5t}[/tex]

Now the left side the derivative of a product,

[tex]\bigg((t+5) x(t)\bigg)' = 5(t+5)e^{5t}[/tex]

Integrate both sides.

[tex](t+5) x(t) = \displaystyle 5 \int (t+5) e^{5t} \, dt[/tex]

On the right side, integrate by parts.

[tex](t+5) x(t) = \dfrac15 (5t+24) e^{5t} + C[/tex]

Solve for [tex]x(t)[/tex].

[tex]\boxed{x(t) = \dfrac{5t+24}{5t+25} e^{5t} + \dfrac C{t+5}}[/tex]

[tex]f(x) = 2 {}^{x} \\ g(x) = f(x + 2) = 2 {}^{x + 2} \\ g(x) = 2 {}^{x + 2} =2 {}^{x} .2 {}^{2} = 4.2 {}^{x} [/tex]

[tex]a.b {}^{x} = > horizontal \: asymp \: y = 0[/tex]

[tex]4.2 {}^{0} = 4 = > vertical \: int \: (0,4)[/tex]

[tex]a.b {}^{x} = > x ∈ \: ] -∞ , ∞ [[/tex]

The horizontal asymptote of the function f ( x ) = 2ˣ is y = 0 and the y-intercept is ( 0 , 4 )

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

Given data ,

Let the function be denoted as f ( x )

Now , the value of f ( x ) is

f ( x ) = 2ˣ   be equation (1)

The y-intercept of the function is when x = 0

So , when x = 0

f ( 0 ) = 2⁰

f ( 0 ) = 1

So , the y-intercept of the function is at ( 0 , 4 )

And , when the function f ( x ) is tending to zero , the horizontal asymptote is y = 0

Therefore , the horizontal asymptote is y = 0

The domain of the exponential function is { -∞ < x < ∞ }

Hence , the horizontal asymptote of the function f ( x ) = 2ˣ is y = 0

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5√2 · 9√6

Simplify.

5 × 9 √ 2 x 6 ⇒ Multiply 2 × 6.

5 × 9 √12

Simplify √12 to 2√3.

5 × 9 × 2√3 ⇔ Multiply

90√3

Therefore, the correct alternative is option "B".

The simplified form of the given expression is 90√3. Therefore, the correct answer is option B.

The given expression is 5√2·9√6.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here, 5×9×√2×√6

= 45√12

= 45√4×3

= 90√3

Therefore, the correct answer is option B.

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Answer:

See below

Step-by-step explanation:

Assuming the interest is compounded annually

x * (1 + .10)^5 = 1.61051  x

  your final amount will be  1.61051 times bigger than the initial deposit

The base of the exponential function model in order to get 15% decay should be 0.85

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.

The first step would be figuring out the function's base.

The function's form should be, [tex]y=a*b^{t}[/tex]

Here,

'a' denotes the starting value.

'b' denotes the decrease rate.

't' denotes time.

According to the question, the exponential function model is,

[tex]y=b^{\frac{t}{12} }[/tex]

In order to get a 15% decay,

The base of the function should be (100-15)/100 = 0.85

Thus, Base of function(b) = 0.85

The exponential function model is written as:

[tex]y=0.85^{t/12}[/tex]

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Katrina would pay less amount of interest on the nonsubsidized student loan

The total interest paid on the nonsubsidized loan is $3,860.80

What is monthly compounding?

Monthly compounding means that the interest is computed and added to existing outstanding loan balance at the end of each month.

In this case, the loan would be repaid monthly but the first monthly payment would occur after 2 years of taking out the loans.

In other words, for the first 2 years, the interest would increase the balances with no corresponding reductions by a way of loan repayment, note that interest to be added monthly, as a result, we can compute outstanding balance 2 years for both loans using the future value formula of a single cash flow shown below:

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

FV=balance after 2 years=unknown

PV=loan amount

r=annual interest rate

n=number of times interest is compounded annually=12

t=number of years before repayments commence=2

Non-subsidized loan:

FV=$29,000*(1+2.5%/12)^(12*2)

FV=$30,485.28

Subsidized loan:

FV=$29,000*(1+4.5%/12)^(12*2)

FV=$31,725.71

Having determined the loan balances after 2 years, we can now compute the monthly payments that would be made in the remaining 6 years using the present value formula of an ordinary annuity because monthly  payments would occur at the end of each month:

PV=PMT*(1-(1+r)^-N/r

PV=balance of loan after 2 years

PMT=monthly payment=unknown

r=monthly interest rate=annual interest rate/12

N=number of monthly payments in 6 years=12*6=72

Non-subsidized loan:

$30,485.28=PMT*(1-(1+2.5%/12)^-72/(2.5%/12)

PMT=$456.40

total monthly payments=$456.40*72

total monthly payments=$32,860.80

Interest= total monthly payments-loan

interest=$32,860.80-$29,000

interest=$3,860.80

Subsidized loan:

$31,725.71 =PMT*(1-(1+4.5%/12)^-72/(4.5%/12)

PMT=$503.61

total monthly payments=$503.61 *72

total monthly payments=$36,259.92

Interest= total monthly payments-loan

interest=$36,259.92 -$29,000

interest=$7,259.92

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Answer:

18

Step-by-step explanation:

For this problem, you have to look at the ratios of the corresponding sides.

Side DC and ZY correspond. It has a length of 10 and 15, respectively. So The ratio is 2:3. Same with BC and XY. If 12 is 2, than 3 must be 18 since 12x(2/3)=18

The total company fund before any bonuses were paid is $995 and there were 20 staffs.

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

Let y represent the total company fund and x represent the number of staffs.

From the first statement:

y - 50x = -5  (1)

Also:

y - 45x = 95    (2)

From equation 1 and 2:

x = 20, y = 995

The total company fund before any bonuses were paid is $995 and there were 20 staffs.

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Answer:

  2800

Step-by-step explanation:

The choice at any node (except the edges) is to go right or go down.

To get from A to B requires a total of 4 choices to go down, and 4 choices to go right. Those can occur in any order. Locating the "right" choices in the list of "all" choices is effectively choosing 4 of 8. The number of ways those choices can be made is ...

  C(8, 4) = 8!/(4!(8-4)!) = 8·7·6·5/(4·3·2) = 70

Similarly a total of 2 choices must be made, 1 of which is a "right" choice. The number of ways those can be ordered is ...

  C(2, 1) = 2 . . . . . . . that is: (right, down) or (down, right)

A total of 6 choices must be made, of which 3 are "right." The number of possible orderings is ...

  C(6, 3) = 6·5·4/(3·2·1) = 20

Each set of choices is independent of the others, so the total possible number is the product of the numbers of choices on the subpaths:

  total paths = (70)(2)(20) = 2800

There are 2800 possible paths from A to D.

Answer:

5/16

Step-by-step explanation:

assuming you mean 5(1/2) = 8x

5(1/2) is the same as 5/2

so, 5/2 = 8x

5 = 16x

x= 5/16

The given focal points and the lengths of the minor and major axis of 16 and 20 gives the equation of the ellipse as the option;

[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

The equation of an ellipse is presented as follows;

[tex] \mathbf{ \frac{(x - h)^{2}}{ {a}^{2} } + \frac{(y - k)^{2}}{ {b}^{2} } } = 1 [/tex]

Where;

(x, y) = Coordinates of the center of the ellipse

a = Semi major axis

b = Semi minor axis

Length of minor axis = 16 units

Length of major axis = 20 units

By observation of the coordinates of the focal point, we have;

y-value of the center of the ellipse, k = 2

x-value of the center, h = (-9 + (3 - (-9))/2 = -3

The equation of the ellipse is therefore;

[tex] \frac{(x - ( - 3))^{2}}{ {10}^{2} } + \frac{(y - 2)^{2}}{ {8}^{2} } = 1 [/tex]

[tex] \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

The equation that represents the ellipse is the option;

[tex] B. \: \frac{(x + 3)^{2}}{ 100} + \frac{(y - 2)^{2}}{ 64} = 1 [/tex]

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Answer: -1

Step-by-step explanation:

Evaluate 4x if x = -1/4

4(-1/4) = -1

Answer: -1

Step-by-step explanation:

4x and x = -1/4

plug x into the expression

[tex]4(-\frac{1}{4} )[/tex]

simplifies to:

[tex]-\frac{4}{4}[/tex]

4 divided by 4 is just 1, but it is negative so your final answer is

-1