8.
Find the value of the missing side.
64°
X
Write the trig equation to solve for x.
11

Supply and demand are two factors that affect how much a country's currency is worth.

The supply and demand of a country's currency determine the value of that currency in a free-floating currency exchange market. A currency improves in value or appreciates when demand for it rises. A currency loses value or depreciates when there is less demand for it.

Money's demand determines how much it is worth. When there is still a strong demand for treasuries, the US dollar increases. The value of a currency determines both its supply and demand. For instance, if a nation prints a lot of currency, the value relative to other currencies will drop because supply exceeds demand. Inflation will happen if the cost of products rises or the value of money declines in comparison to other assets.

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In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a  minimum amount of 0.4 g of.

Given that:

A hospital needs 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex]

and it takes 10 days for the shipment to arrive:

the half life [tex]t_{\frac{1}{2}[/tex]  = 5 days.

So, since the half life = 5 days ;

decay constant [tex]\lambda = \frac{In_{2} }{t_{\frac{1}{2} } } }[/tex]

where:

        [tex]No=?[/tex]

       [tex]N=0.100\\\\t=10days\\\\N(t)=N_{o} e^{-\lambda\ t} \\\\0.1=N_{o}e^{-In\ 4} \\\\0.1=N_{o}e^{In\ \frac{1}{4} }\\\\0.1=\frac{N_{o}}{4} \\\\N_{o}=01*4\\\\N_{o}=0.4\ g[/tex]

Therefore, In order to get 0.100 g of [tex]^{133 }_\ {54} \ Xe[/tex] , the hospital needs to order for a  minimum amount of 0.4 g of.

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There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

A percentage is a fraction of a whole in mathematics, which is denoted by the symbol per 100. A single unit out of a hundred, or one hundredth of something, is represented as a single percent, such as 1%. The Latin phrase per centum, which means by the hundred, is where the word percent originates. Percentage does really refer to a hundredth or 1/100 of something.

Given,

Total number of guests = 425

Guest who ordered food = 170

For percentage,

Value/ Total × 100%

170/425 × 100%

0.4 × 100%

40%

There were 425 guests at a hotel. 170 guests ordered food. 40 percentage of the guests ordered food.

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Answer:6,155.55

Step-by-step explanation: 6.255*1010=6,317.55

1.5*108=162

6,317.55-162=6,155.55

The y is the variable that used in the different situations like to find the unknown variable, graphing, and function

y in the math is usually used as the variable in function, graphing etc.

y variables can be used in the equation to find the unknown values in the equation

Example = 5y + 10 = 15

Similarly in the graphing the y is used in the slope intercept form

The slope intercept form is

y = mx + b

Y can be used in the function as well

Example: y = 2x + 4

Therefore, the y can be used as the variable in the different situation

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a) Cost of debt, I = 4.25%(annual)

b) After tax cost of debt = 3.315%

c) After tax cost of debt of 3.135% is more relevant.

Given:

FV = 100

Semiannual bond issued 3 years ago

Maturity = 27

Price, PV = 104

coupon rate = 4.5%

Tax rate = 22%

a) Semiannual bond issued 3 years ago

Maturity, n = 27 years × 2 = 54

Coupon C = 4.5%/2×100 = 2.25

Now,

Pretax cost of debt,

Cost of debt, I = [C+(FV-PV)/n] / (FV+PV)/2

= [2.25 +(100 - 104)/54] / [ 100+1040/2

= 2.12%

= 2.12×2

Cost of debt, I = 4.25%(annual)

b) After tax cost of debt = cost of debt × (1-T)

= 4.25% × (1-22%)

After tax cost of debt = 3.315%

c) After tax cost of debt is more relevant.

Hence we get the required answer.

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the jensen measure of performance evaluation for sooner stock fund will be 2.6%.

What is the percentage?

A percentage that represents a tenth of a quantity. One percent, denoted by the symbol 1%, is equal to one-hundredth of something; hence, 100 percent denotes the full thing, and 200 percent designates twice the amount specified. A portion per hundred is what the percentage denotes. The percentage refers to one in a hundred. The % sign is used to denote it.

the risk-free return during the sample period was 3%.

performance evaluation for sooner stock fund.

Expected return of Sooner Stock Fund = E(Rp) = 20%

Beta of stock = 1.8

risk free rate Rf = 3%

Market Return Rm = 11%

So, Jensen measure alpha = E(Rp) - Rf - beta*(Rm - Rf) = 20 - 3 - 1.8*(11-8) = 2.6%

Hence the Jensen measure of performance evaluation for the sooner stock fund will be 2.6%.

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The minimum cost for the area can be fenced is $1920

It is given that the area of the rectangular field is 900 m²

Let the length of one side of the field be x m

Therefore, the length of the other side will be

900/x

The perimeter of the rectangular field

= 2(length + breadth)

= 2(x + 900/x)

= 2x + 1800/x  m

Therefore, the cost of fencing will be

$(32x + 28800/x )

Let f(x) = 32x + 28800/x

We need to minimize f(x)

Differentiating with respect to x and equating it to 0 gives us

32 - 28800/x² = 0

or, x² = 28800/32

or, x² = 900

or, x = 30

This is because the length cannot be negative hence -30 cannot be a value

Now

f''(x) = 57600/x³

f''(30) = 2/1333

Since f"(x) is positive, x = 30 is the minimum value of x for which the cost is minimum.

Hence, the minimum cost will be

f(30)

= 960 + 960

= $1920

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Complete Question

A rectangular field is to have an area of 900 m² and is to be surrounded by a fence. The cost of the fence is 16 dollars per meter of length. What is the minimum cost this can be done for?

Answer:

To determine which region represents the solution to a system of linear inequalities, you need to graph each inequality on the same coordinate plane and then find the intersection of the regions that satisfy each inequality. This intersection is the solution to the system of linear inequalities, as every point in this region satisfies all of the inequalities in the system.

To graph the solution, you can use a number line for each variable and plot the inequalities as points or lines on the coordinate plane. For example, if the system of linear inequalities is given by the equations y > 2x + 3 and y < -x + 5, you can plot the lines y = 2x + 3 and y = -x + 5 on the coordinate plane and find the intersection of the two lines. This intersection represents the solution to the system of linear inequalities, as every point in this region satisfies both inequalities.

Another way to find the solution to a system of linear inequalities is by using algebra to solve the system. This involves writing the equations in standard form, eliminating variables, and solving for the remaining variable. The solution can then be written as a set of ordered pairs that represent the points on the coordinate plane that satisfy the system of linear inequalities.

In either case, the solution to a system of linear inequalities is the region of the coordinate plane that satisfies all of the inequalities in the system.

Step-by-step explanation:

Answer:6.47 ft^2

Step-by-step explanation:

The p -value for the hypothesis test is; 0.4195

Let us first define the hypotheses.

We are told that the mean of u.s. college students in general, is estimated to be 4.73. Thus;

Null Hypothesis; H₀: μ = 4.73

Alternative Hypothesis; Hₐ: μ ≠ 4.73

Since we have the standard deviation for the sample, we will use the t-distribution with the formula;

t = (x' - μ)/(s/√n)

Where;

x' is the sample mean.

μ is the value tested at the null hypothesis.

s is the standard deviation of the sample.

n is the sample size.

We are given;

x' = 5.11

μ = 4.73

s = 3.98

n = 52

Thus;

t = (5.11 - 4.73)/(3.98/√52)

t = 0.688

Using a t-distribution calculator, this p-value is 0.4195

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The linear function can be represented by slope intercept form, point slope form and standard form.

Given,

Linear function;

A straight line on the coordinate plane is represented by a linear function. As an illustration, the equation y = 3x – 2 depicts a linear function because it is a straight line in the coordinate plane. This function can be expressed as f(x) = 3x - 2 since y can be replaced with f(x).

We can represent linear function by;

The slope intercept form, point slope form, and standard form can all be used to express a linear function.

Slope intercept form;

The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.

Point slope form;

The equation of a straight line that passes through a particular point and is inclined at a specific angle to the x-axis can be found using the point slope form.

Standard form;

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

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Answer:

To find the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18), we can use the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to find the slope of the line. The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Substituting the coordinates of the points given in the problem, we have:

m = (18 - 6) / (−1 - (−2)) = 12 / 3 = 4

Next, we need to find the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, which has an x-coordinate of 0. Substituting the slope and the coordinates of one of the points given in the problem, we can solve for b:

y = mx + b

6 = 4 * (−2) + b

6 = −8 + b

b = 6 + 8 = 14

Therefore, the slope-intercept form of the line that passes through the points (−2, 6) and (−1, 18) is y = 4x + 14.

Step-by-step explanation:

From the given the option moved left 1 unit; reflected across the x axis is the correct.

what is function?

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, and the set Y is known as the function's codomain.

We have to describe the position of the function [tex]f(x) = -2^x^+^1[/tex] relative to the basic function [tex]2^x[/tex].

Let the parent function is [tex]2^x[/tex].

After shifting one unit right it becomes, [tex]2^x^+^1[/tex].

After reflection in x axis it  becomes, [tex]-2^x^+^1[/tex].

Hence, from the given the option moved left 1 unit; reflected across the x axis is the correct.

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Answer:

Step-by-step explanation:  -73.73 D, If its not and its like A,B, or C and one of them is -73.73 its still going to be correct

Answer:

$442.75

Step-by-step explanation:

40.25 x 11.00= 442.75

If Point M lies on AB, AB = 24 , and BM = 13, then the length of AM is; 11 units

We are given the following parameters;

Length of line segment AB = 24

Length of line segment BM = 13

Now, we are told that M lies on the line segment AB and as such;

If BM = 13, then it means that;

AM + BM = AB

AM + 13 = 24

AM = 24 - 13

AM = 11 Units

We conclude that the length of AM is 11 units.

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Considering the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis, the signs for the slope are as follows;

In Mathematics, a slope is also referred to as gradient and it is typically used to describe both the ratio, direction, and steepness of the function of a straight line.

Mathematically, the rate of change is also referred to as slope or gradient and it can be calculated by using this formula;

Rate of change, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Rate of change, m = (y₂ - y₁)/(x₂ - x₁)

In this scenario, the sign of the slope of the graph of this plane's equation, with time being represented on the horizontal axis and elevation on the vertical axis are as follows;

In conclusion, the slope of a graph would be positive because there is an increase in the variables on the cartesian coordinate.

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Complete Question:

Suppose that during its flight, the elevation e (in feet) of a certain airplane and its time t in minutes since takeoff, are related by a linear equation. Consider the graph of this equation, with time represented on the horizontal axis and elevation on the vertical axis. For each situation, decide if the slope is positive, zero, or negative.

a. The plane is cruising at an altitude of 37,000 feet above sea level.

b. The plane is descending at rate of 1000 feet per minute.

c. The plane is ascending at a rate of 2000 feet per minute.

When you have a distribution without extreme values, the range typically provides you with a decent indication of variability.

In the given question, we have explain why we find the range.

When you have a distribution without extreme values, the range typically provides you with a decent indication of variability. The range can provide information about the breadth of the distribution when combined with metrics of central tendency. But if your data collection contains outliers, the range may be deceptive.

The difference between both the highest and lowest numbers in a collection or set is known as the range. Put together all statistics in order before considering a range. The lowest number should then be subtracted from the highest. The range of the list is provided in the response.

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Answer:

480 minutes

Step-by-step explanation:

One hour is 60 minutes, so 8*60 will give you your answer.

Answer:

Step-by-step explanation:

Theres 60 minutes in 1 hour, and you are trying to find how many in 8 hours, so you would multiply 60 by 8. The answer would be 480 minutes

We can determine that we need 216 mL of 100% alcohol and 384 mL of 50% alcohol using the percentage by volume of the solutions that have been provided.

Volume/volume percentage, often known as v/v percent or %v/v, is a unit used to express how much of a substance is present in a solution.

It is defined as the volume of the solute divided by the sum of the volumes of the solution, multiplied by one hundred.

So, we know that:

A + B = 600 mL

We also understand that the final solution's total alcohol content must equal:

0.68 * 600 mL = 408 mL

So, it follows that:

0.50 * A + B = 408 mL

We can infer the following from the first equation:

A = 600 mL - B

In the second equation, using that A, we obtain:

0.50 * (600 mL - B) + B = 408 mL

300 mL - 0.50 B + B = 408 mL

The result of rearranging this equation is:

B - 0.50 * B = 408 mL - 300 mL

0.50 * B = 108 mL

B = 108 mL / 0.50

B = 216 mL

A = 600 mL - 216 mL = 384 mL

Therefore, we can determine that we need 216 mL of 100% alcohol and 384 mL of 50% alcohol using the percentage by volume of the solutions that have been provided.

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Answer:

V= Base X Height X Length

Step-by-step explanation:

Base = 5

Length = 7

Height = 3

Volume = 105

Answer:

x=4

Step-by-step explanation:

If we were to perform a reduction, the scale factor would be ½. This means we have to divide by 2. 14÷2=7 and 12÷2=6.

Line segment AB is equal to 7.

Line segment BC is equal to 6.

AB: If you want to double check, 4+3=7

BC: 2×4=8 and 8-2=6

Answer: 26

Explanation: Well, by using the formula to find volume of frustum. (this can be shown in a easier way or harder i choose my own way)

Step 1: The hight is: h=15h=15

Step 2: The top radius of the frustum is: r=19r=19

Step 3: The lower base radius of the frustum is: R=26R=26

Message: If you found this helpful let me know by giving a small thanks! :)

Answer:

Below

Step-by-step explanation:

Question 1:

The quadratic equation is of the form ax^2 + bx + c = 0, where a, b, and c are constants. If one solution of the equation is 7-13i, the other solution must be the complex conjugate of 7-13i, which is 7+13i. To find the complex conjugate of a complex number, you simply need to change the sign of the imaginary part of the number. In this case, the complex conjugate of 7-13i is 7+13i.

Question 2:

1. (4-3i) (-7+21)

To add two complex numbers, we need to add their real parts and imaginary parts separately. In this case, we have:

(4-3i) (-7+21)

= (4 - 7) + (-3i + 21)

= -3 + 18i

2. (-7+6i)+(2-3i)+(4+5i)

To add multiple complex numbers, we can add them one at a time using the same procedure as before. In this case, we have:

(-7+6i)+(2-3i)+(4+5i)

= (-7+2) + (6i - 3i) + (4 + 5i)

= -5 + 3i + 4 + 5i

= -1 + 8i

3. (-6-i)/4-2i

To divide two complex numbers, we need to multiply the numerator and denominator by the complex conjugate of the denominator. In this case, we have:

4. (-6-i)/4-2i

= (-6-i)(4+2i)/(4-2i)(4+2i)

= (-24 - 2i + 6i - i^2)/20

= (-24 + 4 -1)/20

= (-21)/20

= -1.05 - 0.05i

5. (-2-7i)(-2+7i)

To multiply two complex numbers, we use the FOIL method, which involves multiplying the First, Outer, Inner, and Last terms separately and then adding the results. In this case, we have:

(-2-7i)(-2+7i)

= (-2 * -2) + (-2 * 7i) + (-7i * -2) + (-7i * 7i)

= 4 + (-14i) + 14i + 49

= 4 + 49

= 53

6. (5-3i)-(-2-6i)

To subtract two complex numbers, we need to add the first number to the opposite of the second number. In this case, we have:

(5-3i)-(-2-6i)

= (5-3i) + (2 + 6i)

= 7 + 3i

This is the final answer for each of the problems.

Answer:

x=11

Step-by-step explanation:

2x+1=5x-32   ==>   since the two triangles are congruent, their angle measures are congruent as well.

2x-2x+1=5x-2x-32

1=3x-32

1+32=3x-32+32

33=3x

x=11

The equation of the line that passes through the point (−11,−14) is y = x - 3.

What is the slope of the line?

A line's steepness can be determined by looking at its slope. The slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the point (−11,−14)

With Slope (m) = 1,

The general equation of a straight line is

y = mx + c,

where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.

so here,

y = mx + c,

(-14) = 1(-11) + c

c = -14 + 11

c = -3

The equation becomes:

y = x - 3.

Hence, the equation of the line that passes through the point (−11,−14) is

y = x - 3.

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The half-life of the substance is of 10.31 years.

What is exponential?

The exponential is an example of a mathematical function that is useful in determining if something is increasing or decreasing exponentially is the exponential function. As implied by its name, an exponential function uses exponents. But take note that an exponential function does not have a variable as its exponent and a constant as its base (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function).

a sample of a radioactive substance decayed to 93% of its original amount after a year.

The half-life is t for which:

exp(-0.067 t) = (0.5)

ln(0.5) = -0.067 t

t = 10.31 years.

Hence the half-life of the substance is of 10.31 years.

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The value of x from the given isosceles triangle GHJ is 5.

Isosceles triangles are those triangles that have at least two sides of equal measure and two base angles are equal.

In the given isosceles triangle GHJ, GJ=GH, ∠G=38° and ∠J=(14x+1)°.

Since, sides GJ=GH

∠J=∠H

Now, ∠G+∠J+∠H=180° (Angle sum property of a triangle)

⇒ 38°+(14x+1)°+(14x+1)°=180°

⇒ 28x+40°=180°

⇒ 28x=140°

⇒ x=140/28

⇒ x=5

Therefore, the value of x is 5.

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"Your question is incomplete, probably the complete question/missing part is:"

If triangle GHJ is isosceles find the value of x.