A tourist from Britain wants to exchange her British pounds for US dollar. She has 25 British pounds. How many US dollars would she get in exchange for her British pound if 1 British pound can be exchanged for 1.53 US dollars?

Answer:  [tex]-2+\sqrt{3}[/tex]

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Work Shown:

Apply the following trig identity

[tex]\tan(A - B) = \frac{\tan(A)-\tan(B)}{1+\tan(A)*\tan(B)}\\\\\tan(225 - 60) = \frac{\tan(225)-\tan(60)}{1+\tan(225)*\tan(60)}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+1*\sqrt{3}}\\\\\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\[/tex]

Now let's rationalize the denominator

[tex]\tan(165) = \frac{1-\sqrt{3}}{1+\sqrt{3}}\\\\\tan(165) = \frac{(1-\sqrt{3})(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\\tan(165) = \frac{(1-\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{(1)^2-2*1*\sqrt{3}+(\sqrt{3})^2}{(1)^2-(\sqrt{3})^2}\\\\\tan(165) = \frac{1-2\sqrt{3}+3}{1-3}\\\\\tan(165) = \frac{4-2\sqrt{3}}{-2}\\\\\tan(165) = -2+\sqrt{3}\\\\[/tex]

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As confirmation, you can use the idea that if x = y, then x-y = 0. We'll have x = tan(165) and y = -2+sqrt(3). When computing x-y, your calculator should get fairly close to 0, if not get 0 itself.

Or you can note how

[tex]\tan(165) \approx -0.267949\\\\-2+\sqrt{3} \approx -0.267949[/tex]

which helps us see that they are the same thing.

Further confirmation comes from WolframAlpha (see attached image). They decided to write the answer as [tex]\sqrt{3}-2[/tex] but it's the same as above.

Answer:

18 guests.

Step-by-step explanation:

To find the number of guests, we can simply divide 1/6 from 3. The result gives us 18.

9514 1404 393

Answer:

Step-by-step explanation:

An odd function is symmetrical about the origin:

  f(-x) = -f(x)

So, ...

  f(-2) = -f(2) = -2

  f(-3) = -f(3) = -1

  f(-4) = -f(4) = -2

  f(-6) = -f(6) = -3

Answer:

-2  

-1  

-2

-3

I did it on edge2020 and got it right

9514 1404 393

Answer:

Step-by-step explanation:

The amortization formula is ...

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

for the monthly payment on principal P at annual rate r for t years. Here, we have P=3300, r = 0.14, and t=1, so the monthly payment is ...

  A = $3300(0.14/12)/(1 -(1 +0.14/12)^-12) ≈ $296.30

The payment of $296.30 is ...

  $295.30 -158.40 = $137.90 . . . more each month

The total amount paid is 12×$296.30 = $3555.60, so 255.60 in interest. This amount is ...

  $501.60 -255.60 = $246.00 . . . less total interest

Answer:

x = 2.536 m

y = 2 m

Step-by-step explanation:

Considering the three sides of the rectangle and the isosceles triangle

when resolving the width and height of the rectangle to achieve the smallest possible perimeter.

step 1 :

Area of window =  xy + 1/2 xz  , perimeter = x + 2y + 2c

c = [tex]\sqrt{z^2 + 1/4 x^2 }[/tex]

we are tasked with minimizing the perimeter ( p ) subject to A = 6

attached below is the detailed solution of the given problem

Answer:

$92

Step-by-step explanation:

42 + 26 + 6 + 18 = 92

Answer:

a

Step-by-step explanation:

1/3 x 3/5 x 3/4 =7/12 so therefore that's what the answer isn't

Answer:

3:7

Step-by-step explanation:

i hope this helps

Answer:

The appropriate test to determine if there is an association between being a registered nurse and passing a cultural competency exam among a group of 987 randomly selected hospital employees is a:

Chi-square Test.

Step-by-step explanation:

The Chi-Square Test uses either a diagram (like a scatter plot) or a hypothesis test to show the existence of an association between two variables or statistically demonstrate that a relationship exists between the two variables.  Using the computed t-score, the significant association between two categorical variables can be measured and established.

Answer:

no solution

Step-by-step explanation:

multiply 2 and get 2x^2+18-4=0

combine like terms

2x^2+14=0

subtract 14

2x^2=-14

there can't be a square root of a negative number so there's no solution

Answer:

x = ±i sqrt(7)

Step-by-step explanation:

2(x^2+9)-4=0

Add 4 to each side

2(x^2+9)-4+4=0+4

2(x^2+9)=4

Divide by 2

2(x^2+9)/2=4/2

(x^2+9)=2

Subtract 9 from each side

x^2 +9-9 = 2-9

x^2 = -7

Taking the square root of each side

sqrt(x^2) =sqrt(-7)

x = sqrt(-1 *7)

x = ±i sqrt(7)

Answer:

[tex]f(10) = 1147.25[/tex]

Step-by-step explanation:

Given

[tex]f(-1.5) = 26[/tex]

[tex]f(5.5) = 7[/tex]

Required

f(10)

An exponential function is represented as:

[tex]f(x) = ab^x[/tex]

[tex]f(-1.5) = 26[/tex] impleies that:

[tex]26 = ab^{-1.5}[/tex] --- (1)

[tex]f(5.5) = 7[/tex] implies that

[tex]7 = ab^{5.5}[/tex] --- (2)

Divide (2) by (1)

[tex]26/7 = ab^{-1.5}/ab^{5.5}[/tex]

[tex]3.71429 = b^{-1.5+5.5}[/tex]

[tex]3.71429 = b^{4}[/tex]

Take 4th root

[tex]b = 1.39[/tex]

Substitute [tex]b = 1.39[/tex] in [tex]26 = ab^{-1.5}[/tex]

[tex]26 = a * 1.39^{-1.5}[/tex]

[tex]26 = a * 0.6102[/tex]

Solve for (a)

[tex]a = 26/0.6102[/tex]

[tex]a = 42.61[/tex]

f(10) is calculated as:

[tex]f(10) = ab^{10}[/tex]

[tex]f(10) = 42.61 * 1.39^{10}[/tex]

[tex]f(10) = 1147.25[/tex]

Answer:

3 hours 30 minutes

Step-by-step explanation:

Jan :2 hours

her husband : 1 hour 30 minutes

2hr + 1 ½ hrs = 3 ½ hrs...that is 3 hours 30 minutes....?

Answer:

11.60

Step-by-step explanation:

To find unit rate, you need to use the formula:

(amount of money) ÷ (amount of hours)

Since we have both, we can plug in

140 ÷ 12 will give you approximately 11.6

So, you receive $11.60 every hour.

Answer:

0.47

Step-step explanation:

Add 8+7 which gives you 15. So 7/15. Then turn it into decimal form which is 0.47. Hope this helps!

Solve both equations for 2y :

2y + 5x = 13   ==>   2y = 13 - 5x

2y + 3x = 5   ==>   2y = 5 - 3x

Solve for x :

13 - 5x = 5 - 3x

8 = 2x

x = 4

Solve for y :

2y = 13 - 5×4

2y = -7

y = -7/2

As an ordered pair, the solution is then the point (x, y) = (4, -7/2).

Answer:

Quadrant 2

Step-by-step explanation:

Given

[tex]\theta = 115^o[/tex]

Required

The quadrant

We have:

[tex]0^o < \theta < 90^o[/tex] --- quadrant 1

[tex]90^o < \theta < 180^o[/tex] --- quadrant 2

[tex]180^o < \theta < 270^o[/tex] --- quadrant 3

[tex]270^o < \theta < 360^o[/tex] --- quadrant 4

So, by comparison; we have:

[tex]90^o < \theta < 180^o[/tex]

Substitute 115 for [tex]\theta[/tex]

[tex]90^o < 115 < 180^o[/tex]

The above is true for quadrant 2

plug-in

-2(4) - 2

-8 - 2

-10

-10^2 + 1

-100 + 1

Your answer: -99

Answer:

We need to assume that the relationship is linear.

a) Remember that a linear relation is written as:

y = a*x + b

then we will have:

p(x) = a*x + b

where a is the slope and b is the y-intercept.

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

y = (d - b)/(c - a)

In this case, we know that:

if the ticket has a price of $12, the average attendance is 25,000

Then we can define this with the point:

(25,000 , $12)

We also know that when the price is $9, the attendance is 29,000

This can be represented with the point:

(29,000, $9)

Then we can find the slope as:

a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075

Then the equation is something like:

y = (-$0.00075)*x + b

to find the value of b we can use one of the known points.

For example, the point (25,000 , $12) means that when x = 25,000, the price is $12

then:

$12 = (-$0.00075)*25,000 + b

$12 = -$18.75 + b

$12 + $18.75 = b

$30.75 = b

Then the equation is:

p(x) = (-$0.00075)*x + $30.75

b) We want to find the ticket price such that it maximizes the revenue.

The revenue will be equal to the price per ticket, p(x) times the total attendance, x.

Then the revenue can be written as:

r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )

r(x) =  (-$0.00075)*x^2 + $30.75*x

So we want to find the maximum revenue.

Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.

Remember that for an equation like:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/2a

Then in our case, the x-value will be:

x = -$30.75/(2*(-$0.00075)) = 20,500

Then the revenue is maximized for x = 20,500

And the price for this x-vale is given by:

p( 20,500) =  (-$0.00075)*20,500 + $30.75 = $15.375

which should be rounded to $15.38

Answer:

I. C = 266 textbooks.

II. S = 207 textbooks.

Step-by-step explanation:

Let the chemistry textbook be C.

Let the sociology textbook be S.

Translating the word problem into an algebraic expression, we have;

C + S = 473 ..... equation 1

S = C - 59 ..... equation 2

Substituting eqn 2 into eqn 1, we have;

C + C - 59 = 473

2C - 59 = 473

2C = 473 + 59

2C = 532

C = 532/2

C = 266 textbooks.

Next, we would determine the value of S;

S = C - 59

S = 266 - 59

S = 207 textbooks.

Check:

C + S = 473

266 + 207 = 473

473 = 473

Answer:

kdjdeoksndoddmsnsksndjdjd

Answer:

[tex]y=-\frac{8}{7}x+4[/tex]

Step-by-step explanation:

A line is perpendicular to another if its slope is the negative reciprocal of the other.

Your lines are in slope intercept form here, y=mx+b, where m is the slope. We can see the given line has slope [tex]\frac{7}{8}[/tex]. The negative reciprocal of that is [tex]-\frac{8}{7}[/tex], which is the slope of the third answer choice.

Answer:

Solution given;

principal [P]=$125,000

depreciated rate[R]=7.5%

time[t]=2 years

worth price of house [A]=???

we have

Worth price[A]=[tex]\large \bold P(1-\frac{R}{100})^{t}[/tex]

=[tex]125,000(1-\frac{7.5}{100})^{2}[/tex]

=125,000*0.925²

=125,000*0.855625

=106953.125

Answer: [tex]4x[/tex]

Step-by-step explanation:

[tex]f(x)=8x-4x+4\\f(x-1)=8(x-1)-4(x-1)+4\\f(x-1)=8x-8-4x+4+4\\f(x-1)=4x-8+4+4\\f(x-1)=4x[/tex]

Answer:

The answer is "T-test results must not be presented if the same variations are expected".

Step-by-step explanation:

A t-test is used by a scientist to compare the average beta-lactamase of two distinct strains of bacteria. The Levene equality test does have a p-value of 0.01. Researchers know that all this means that research should report t-test findings with a failed assumption of identical variances because the Log-rank equality test has a p-value of 0.01 of less than 0.05 that shows different twp population variance.

the required ans is 3√b+b/3b

We are testing a hypothesis. So, first we identify the null and the alternative hypothesis, then we find the test statistic, and with the test statistic, the p-value is found.

Null and alternative hypothesis:

Claim the the proportion is of 60%, thus, the null hypothesis is:

[tex]H_0: p = 0.6[/tex]

Test if the proportion is greater than 60%, thus, the alternative hypothesis is:

[tex]H_1: p > 0.6[/tex]

And the answer to the first question is given by option c.

Classification:

We are testing if the proportion is greater than a value, so it is a right-tailed test.

Test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.

0.6 is tested at the null hypothesis:

This means that [tex]\mu = 0.6, \sigma = \sqrt{0.4*0.6}[/tex]

Survey, conducted over a two week period, found that in a sample of 100 people, 69% of them said they are confident of meeting their goals.

This means that [tex]n = 100, X = 0.69[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \frac{0.69 - 0.6}{\frac{\sqrt{0.4*0.6}}{\sqrt{100}}}[/tex]

[tex]z = 1.837[/tex]

The test statistic is z = 1.837.

p-value:

The p-value of the test is the probability of finding a sample proportion above 0.69, which is 1 subtracted by the p-value of z = 1.837.

Looking at the z-table, z = 1.837 has a p-value of 0.9669.

1 - 0.9669 = 0.0331

The p-value is 0.0331.

Decision:

The p-value of the test is 0.0331 > 0.01, and thus:

a. Fail to reject the null hypothesis

For another example of a problem of a test of hypothesis, you can take a look at:

https://brainly.com/question/24166849

Answer:

does this have to do with graphs

Answer:

Step-by-step explanation:

the mean is

{(12x1)+(13x1)+(14x2)+(15x2)+(17)+(18)+(19x2)+(20)+(21x2)+(22)+(24)}/11

mean=264/11

mean=24