the iron bank offers a range of financial services and investment opportunities. of its customers, 36% invest in stocks, 22% invest in futures, and 15% invest in both stocks and futures. use this information and the rules of probability to answer the following:Part A: What proportion of Iron Bank customers invest in neither Stocks nor Futures? Part B: Of the Iron Bank customers who invest in Futures, what percentage invest in Stocks? Part C: What is the probability that a randomly selected Iron Bank customer invests in Stocks aud does not invest in Futures?

Therefore , the solution of the given problem of triangle comes out to be EG  = 23.14.

A triangle is a hexagon because it has two or more extra polygon sections. Its form is a simple rectangular one. A and B are the only 2 different edges of a form that can set it apart from a regular triangular. When bounds are still not precisely collinear, Euclidean geometry produces a single section rather than a full cube. Three edges and three angles make up a triangle.

Here,

The length of EG can be determined as follows if EF = 24:

First, we calculate the length of FG using the Pythagorean theorem:

=> FG² = EF² - EG²

=> 10² = 24² - EG²

=> EG² = 24² - 10²

=> EG² = 536

=> EG = √536 ≈ 23.14

Consequently, EG 23.14 when FG = 10 and GH = 7 if E is the right angle apex of a right triangle EFG and EF = 24.

To know more about triangle visit:

https://brainly.com/question/2773823

#SPJ1

The probability of randomly selecting a girl is 0.606. the correct option is (C).

Given that, Total newborn babies = 850

No. of boys = 335

We need to find the probability of randomly selecting a girl baby from this population of 850 babies.

Let G be the no. of girls in the population. Then, G + 335 = 850=> G = 850 - 335=> G = 515

Therefore, the number of girls in the population is 515. Hence, the probability of randomly selecting a girl from the population is:

P (girl) = No. of girls / Total newborn babies= 515 / 850= 0.606

Thus, the correct option is (c) 0.606.

To know more about the population: https://brainly.com/question/25630111

#SPJ11

modeling function the population of carp with respect to time is: P(t) = 100 * [tex]e^{0.707t}[/tex]

To model the population of carp with respect to time, we can use the following exponential growth formula:

P(t) = P(0) * [tex]e^{rt}[/tex]

where P(0) is the initial population, r is the annual growth rate, and t is the number of years from now.

We know that initially there are 100 carp in the lake, so P(0) = 100.

We also know that the population varies by 20 fish seasonally, so the annual growth rate is:

r = ln(625/100) / 5 = 0.707

Thus, the function modeling the population of carp with respect to time is:

P(t) = 100 * [tex]e^{0.707t}[/tex]

where t is the number of years from now.

To know more about modeling function click here:

brainly.com/question/4515364

#SPJ4

Answer:

1

Step-by-step explanation:

we just find the middle of the 2 places

The parts of the algebraic expression 3x - 2 are:

3 is the coefficient of x.

x is the variable

2 is the constant term

The algebraic Expression is given as:

3x - 2

Now, some parts of algebraic expressions are coefficients, variables and constant.

Coefficient is defined as the figure or number that is attached to the variable in an algebraic expression.

The variable is the letter that can change because different numbers are used for it.

The constant is the number that stands alone and doesn't change.

Thus, in 3x - 2:

3 is the coefficient of x.

x is the variable

2 is the constant term

Read more about Algebraic Expression at: https://brainly.com/question/4344214

#SPJ1

Based on according to the ratio given for PQ:QR, The length of side PS on the line is 34 inches.

We can use the ratios given to find the lengths of the other segments and then add them up to get the length of PS.

Let x be the length of QR. Then, according to the ratio given for PQ:QR, we have:

PQ:QR = 3:4

6:x = 3:4

Multiplying both sides by 4x, we get:

24 = 3x

x = 8

So, QR is 8 inches long. Now, using the ratio given for QR:RS, we have:

QR:RS = 2:5

8:y = 2:5

Multiplying both sides by 5y, we get:

40 = 2y

y = 20

So, RS is 20 inches long. Finally, we can add up the lengths of PQ, QR, and RS to get the length of PS:

PS = PQ + QR + RS

PS = 6 + 8 + 20

PS = 34

Therefore, the length of PS is 34 inches.

Find out more on equation at:

https://brainly.com/question/2972832

#SPJ1

The side length x is given as follows:

[tex]x = \frac{7}{\sqrt{3}}[/tex]

The number that belongs in the green box is of 7.

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the side x, we have that:

Hence the tangent can be applied, as follows:

tan(30º) = x/7

x = 7 x tangent of 30 degrees

[tex]x = 7 \times \frac{1}{\sqrt{3}}[/tex]

[tex]x = \frac{7}{\sqrt{3}}[/tex]

More can be learned about trigonometric ratios at brainly.com/question/24349828

#SPJ1

The measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.

The trigonometric ratios involves the relationship of an angle of a right-angled triangle to ratios of two side lengths. Basic trigonometric ratios includes; sine cosine and tangent.

recall that tan 60° = √2

tan 60° = 7/x {opposite/adjacent}

√2 = 7/x

by cross multiplication

x = 7/√2.

Therefore, the measure of the length of x is equal to 7/√2 using the trigonometric ratio of tangent for angle 60°.

Know more about trigonometric ratio here:https://brainly.com/question/23130410

#SPJ1

Answer:

To find out how many windows Kendall can wash in one hour, we can divide the number of windows washed by the time taken:

Number of windows washed per hour = (Number of windows washed) / (Time taken)

We can first convert the mixed number 10 1/2 to an improper fraction:

10 1/2 = (10 x 2 + 1) / 2 = 21/2

Substituting the given values:

Number of windows washed per hour = (21/2) / (3/4) hours

To divide by a fraction, we can multiply by its reciprocal:

Number of windows washed per hour = (21/2) x (4/3) = 28 windows/hour

Therefore, Kendall can wash 28 windows in one hour at this rate.

Answer:

14 windows

Step-by-step explanation:

All you have to do is a simple equation 10 1/2÷3 which equals 14

The number of products of each type that they can assemble each week to maintain maximum production are 3 Type A and 2 Type B.

In order to write a system of linear equations that could be used to model the situation, we would assign variables to the cost of component and the labour man-hours respectively as follows:

Next, we would translate the word problem into system of linear equations as follows. Since the business has $156.00 available to buy components each week, a linear equation that models the situation is given by;

36x + 24y = 156      .....equation 1.

Additionally, the total labour man-hours available each week is 96 man-hours;

16x + 24y = 96      .....equation 2.

Subtracting equation 2 from equation 1, we have:

20x = 60

x = 3.

y = (96 - 16x)/2

y = (96 - 16(3))/24

y = 48/24

y = 2.

Read more on equation here: brainly.com/question/18912929

#SPJ1

The length of the other  parallel side of the parallelogram (b2) is 8.3m with the area of the parallelogram 100m².

It is a four-sided shape that has two pairs of parallel lines with all sides equal in length.

The area of the parallelogram is 100m² and the height is 10m, so the base of the parallelogram is 13m. This forms a right triangle with one side of the parallelogram. To calculate the length of the other non-parallel side (b²), we can use the squaring method.

This can be expressed as:

a² + b² = c²

Where a and b are the two shorter sides of the triangle, and c is the longest side.

Substituting in the values given, we get:

x² + 10² = 13²

x²=13²-10²

x= √169-100

x = √69

x = 8.3m

Therefore, the length of the other non-parallel side of the parallelogram (b2) is 8.3m.

For more questions related to area

https://brainly.com/question/25292087

#SPJ1

After solving the equation using the elimination method, the value of x is 1 and y is 3.

The given system of equations are:

y = x + 2...............(1)

y = 5x - 2...............(2)

We solving equation by the elimination method.

The elimination method is a method of solving systems of linear equations. It involves performing operations on the equations, such as addition and multiplication, to transform the equations into simpler forms.

Subtract equation 1 and equation 2

x+2 - 5x + 2 = 0

-4x + 4 = 0

Subtract 4 on both side, we get

-4x = -4

Divide by -4 on both side, we get

x = 1

Now put the value of x in equation 1.

y = 1 + 2

y = 3

The solution set is {1, 3}.

To learn more about elimination method link is here

brainly.com/question/12090959

#SPJ4

The complete question is:

Find the value of x and y.

y = x+2

y=5x-2

Answer:

[tex]\boxed{f(x)=(3)(2)^x}[/tex]

Step-by-step explanation:

First, we need to substitute the coordinates of the two given points in the ecuation [tex]f(x)=ab^x[/tex]:

[tex]3=ab^{0} \qquad \textbf{ec.1}\\6=ab^{1} \qquad \textbf{ec.2}[/tex]

Remember that any number raised to the power 0 is equal to 1.  So:

[tex]3=a \qquad \textbf{ec.3}[/tex]

now, we can substitute in ec.2 and solve for b:

[tex]6=3b\\ b=2[/tex]

Finally:

[tex]f(x)=(3)(2)^x[/tex]

Therefore, we have found the solution to the exercise

[tex]\text{-B$\mathfrak{randon}$VN}[/tex]

Step-by-step explanation:

Slope is y2 - y1 / x2 - x1

X1 =2 y1 =4 x2 =-4 y2= 0

0 - 4/ - 4 - 2 = - 4/-6

Sslope =2/3 or 0.67

Round it up if you are asked to.

Answer:

Uhm i think its ABD weeweee

Step-by-step explanation:

Because monkeys wooowooo not weewee so the commentary would be weeeweee

Zack wheeler had a war of 7. 8 in the 2021  season this means that He scored an average of 7.8 runs per game.

This means that Zack scored an average 7.8 runs per game.

An average is a single number represented as a list of numbers, usually the sum of the numbers divided by the number of numbers in the list (arithmetic mean). For example, the numbers 2, 3, 4, 7, and 9 (for a total of 25) have an average of 5. Depending on the context, the average can be another statistic, such as the median or the mode. Average personal income, for example, is often given as the median – a figure below 50% of personal income and above 50% of personal income – because the average would be higher if some personal income of billionaires were included. Therefore, it is recommended to avoid using the word "average" when referring to measures of central tendency.

Complete Question:

Zack Wheeler had a WAR of 7.8 in the 2021 season. What does this mean?

A. He scored an average of 7.8 runs per game.

B. His team won an average of 7.8 more games than other teams in MLB.

C. His team won around 7.8 more games than it would have with a replacement player.

 D. He scored around 7.8 more runs than a replacement player would have.

Learn more about Average:

https://brainly.com/question/24057012

#SPJ4

After answering the presented question, we can conclude that As a result, the equation that reflects the stock's value after two years in terms of x is: 0.7161x

An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).

Because the stock's value fell by 7% after the first year, it is now worth:

x - 0.07x = 0.93x

The stock's value dropped by 23% after the second year, therefore it would be worth:

0.93x - 0.23(0.93x) = 0.93x - 0.2139x = 0.7161x

As a result, the expression that reflects the stock's value after two years in terms of x is:

0.7161x

To know more about equation visit:

https://brainly.com/question/649785

#SPJ1

Answer:

c) The vertical asymptotes are x = (-5 + √(13))/4 and x = (-5 - √(13))/4. To find them, set the denominator equal to zero and solve for x.

d) There are no holes in the function.

e) The zeros are x = 0, x = 2, and x = -3. To find them, set the numerator equal to zero and solve for x.

f) The slant asymptote is y = x + 2 - (3.5x + 1.5)/(2x^2 + 5x + 3). To find it, use long division to divide the numerator by the denominator. To find the slant asymptote of the given rational function, we use long division to divide the numerator by the denominator. The quotient of the division gives the equation of the slant asymptote.

g) The domain is (-∞, (-5 - √(13))/4) U ((-5 + √(13))/4, ∞). To find it, set the denominator not equal to zero and solve for x. To find the domain of the given rational function, we set the denominator not equal to zero and solve for x. The domain is all real numbers except the values of x that make the denominator equal to zero.

I hope this helps you! I'm sorry if it's wrong! If you need more help, ask me! :]

The correct answer to the given question is a)29, (b) 91cm is median waist measurement and (c)13cm is interquartile range

(a)From the graph, 11 men have a waist measurement of 85cm and below. Since the cumulative frequency is 40

Number of men who have a waist measurement of more than 85 cm

= 40 − 11

= 29

(b)Median

Given a dataset of size N = 40, the median can be calculated as:

Median = (N + 1) / 2

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Median = (40 + 1) / 2

Median = 20.5

Since the median has to be a whole number, we take the 20th item as the median. Tracing 20 from the y-axis to the x-axis, the median waist measurement is 91cm.

(c)Interquartile Range = Q3 - Q1

To find the first quartile, denoted as Q1, you need to determine the value that separates the lowest 25% of the dataset from the rest of the dataset.

The formula for the first quartile is: Q1 = (N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q1 = (40 + 1) / 4

Q1 = 10.25

Since we need to find the 10th item, which corresponds to the 25th percentile of the dataset, we take the integer part of Q1, which is 10. Therefore, the first quartile, Q1, is the 10th item.

​From the graph, at y= 10, x= 84 cm

To find the third quartile, denoted as Q3, you need to determine the value that separates the highest 25% of the dataset from the rest of the dataset.

The formula for the third quartile is: Q3 = 3(N + 1) / 4

where N is the total number of items in the dataset.

Substituting the given value of N, we get:

Q3 = 3(40 + 1) / 4

Q3 = 30.75

Since we need to find the 30th item, which corresponds to the 75th percentile of the dataset, we take the integer part of Q3, which is 30. Therefore, the third quartile, Q3, is the 30th item.

From the graph, at y= 30, x =97 cm

Therefore: Interquartile Range = 97 - 84 = 13cm

To learn more about interquartile range click here

brainly.com/question/29204101

#SPJ4

Complete Question

a) how many men have a waist measurement of more than 85 cm

b) what is the median waist measurement

c) what is the interquartile range of the waist measurements

Answer:

(1.5)x + 1.5 = 30

Step-by-step explanation:

Result in (d) refutes the claim in (a), since it is less than the 5% level of significance. Actual proportion is lower than 0.4.

A recent article in a national newspaper claimed that 40% of all students in US colleges drink some alcoholic beverages at least once a week. A students association argued that actually fewer students drink alcohol. In support of its claim the student association has sampled at random 500 students and found that only 180 of them stated that they do drink at least once a week.

Calculate the Claimed Population Proportion

The claimed population proportion is p=0.4

Calculate the Parameters for the Normal Distribution of Sample Proportion

By the Central Limit Theorem, the distribution of the sample proportion p is the normal distribution with mean μj=p=0.4 and standard deviation σj=npq= √[(0.4)(0.6)/500]=0.047.

Calculate the Observed Sample Proportion

The observed sample proportion of those who said "Yes" (that they do drink at least once a week) is pˆ0=500/180=0.36.

Calculate the Probability to Observe Such, or Smaller, Sample Proportion if the Claim in (a) Were to be Correct

Using the CLT and the parameters in (b), the probability to observe such, or smaller, sample proportion if the claim in (a) were to be correct is Pr(p≤pˆ0)=0.056.

Conclusion

The result in (d) refutes the claim in (a), since it is less than the 5% level of significance. This means that we reject the null hypothesis that the proportion of students drinking at least once a week is 0.4, and instead conclude that the actual proportion is lower than 0.4.

Learn more about Proportion

brainly.com/question/30657439

#SPJ4

Answer:

[tex]x=\frac{7}{30}[/tex]

Step-by-step explanation:

Solve for x:

[tex]x+\frac{2}{3}=\frac{9}{10}[/tex]

Subtract [tex]\frac{2}{3}[/tex] on both sides

[tex]x=\frac{7}{30}[/tex]

Answer:

X= 7/30

Step-by-step explanation:

subtract 2/3 from both sides.

X+ 2/3 = 9/10

X +2/3 -2/3 =9/10 -2/3

simplify the expression

X + 2/3 -2/3 =9/10 -2/3

X=7/30

The value of the angle X is 99 degrees. Option E

To determine the value of the angle, we need to note that the sum of the interior angles of a given regular polygon is determined with the formula;

(n -2)180

Such that 'n' is the number of sides of the polygon

From the information given, we have that;

The value of n = 6

Then, the sum of interior angles = (6-2)180 = 4(180)

Multiply the values

= 720

Equate the angles

x + 108 + 146 + 101 + 113 + 153 = 720

Add the values

x = 720 - 621

subtract the values

x = 99 degrees

Learn about polygons at: https://brainly.com/question/1592456

#SPJ1

The linear relation is (a) A the population of a town in increasing by ten people each year

From the question, we have the following parameters that can be used in our computation:

The list of options that represent the situations

Situation A is linear because the increase in population is constant and can be represented by a linear equation (y = mx + b),

The equation would be y = 10x + b, where b is the population at year 0.

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

Each squad has to have an equal amount of men and women. The maximum number of teams that can participate is 8.

A location in mathematics where a function has its maximum value. The value is an absolute maximum if it exceeds or is equal to all other function values. It is a relative or local maximum if it is simply greater than any neighboring point.

Number of girls = 16.

Number of boys = 20.

In order to calculate the maximum number of teams that can enter, we must determine the most prevalent criteria for both boys and girls based on the information provided. As follows:

Factors of 18 [tex]= 1, 2, 4, 8[/tex]  and 16.

Factors of 24 = [tex]1, 2, 3, 4, 6, 8, 12[/tex] and 24.

Highest common factor = 8

Therefore, the greatest number will be 8.

Learn more about maximum number here

https://brainly.com/question/29795588

#SPJ1

the atmosphere has the smallest mass, followed by the oceans, inner core, crust, outer core, and mantle having the largest mass.

Based on the given masses, the order from least to greatest for the parts of the Earth would be:

Atmosphere (5.1 × 10¹⁸ kg)

Oceans (1.4 × 10²¹ kg)

Inner core (9.675 × 10²² kg)

Crust (2.6 × 10²² kg)

Outer core (1.835 × 10²⁴ kg)

Mantle (4.043 × 10²⁴ kg)

Therefore, the atmosphere has the smallest mass, and the list goes according oceans, inner core, crust, outer core, and mantle having the largest mass. The Earth is composed of several layers, including the crust, mantle, outer core, and inner core. The mass of the Earth is distributed unevenly among these layers, with the mantle being the most massive layer, accounting for about 84% (percentage) of the Earth's total mass. The core of the Earth is made up of the outer core and the inner core, which are predominantly composed of iron and nickel. The crust is the thin, outermost layer of the Earth, while the atmosphere is the layer of gases that surround the planet. Despite the atmosphere being the layer with the smallest mass, it plays a critical role in regulating the Earth's climate and sustaining life on the planet.

To learn more about order click here

brainly.com/question/1623384

#SPJ4

Complete question

The mass of Earth is made up of these parts.

oceans     1.4 × 1021kg

crust      2.6 × 1022kg

atmosphere   5.1 × 1018kg

mantle     4.043 × 1024kg

outer core   1.835 × 1024kg

inner core   9.675 × 1022kg

What is the order, from least to greatest, of the masses of each part of Earth? Order the parts from least to greatest, with 1 being the smallest mass and 5 the greatest mass.

The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. Probability is used to assess the outcome of any random event, such as the roll of a die or the flip of a coin. It can also be used to measure the likelihood of future events, such as the stock market rising or falling.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

This phenomenon is occurring because the normal distribution is symmetrical. The area to the left and to the right of the mean are equal, and thus the probability of P(z < 1.645) is the same as the probability of P(z > 1.645). The normal distribution is also unimodal, meaning that there is a single peak and all other data points have lower probability than the peak. Since the peak of the normal distribution is at the mean (0 in this case), any value to the right of the mean will have a higher probability than any value to the left of the mean. Thus, the probability of P(z > 1.645) is greater than the probability of P(z < 1.645).

To know more about probability click-
https://brainly.com/question/24756209
#SPJ1

The probability P(z < 1.645) is the area under the standard normal curve to the left of 1.645.

What is Probability?

Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain.

This probability is calculated by using Table 3 in Appendix I. The probability is 0.9500, which means that 95% of the area under the normal curve is to the right of 1.645.

The symmetric nature of the normal distribution is what is causing this phenomena. Because the area to the left and right of the mean are equal, the likelihood that z will be less than or more than 1.645 is equally likely. Furthermore, the normal distribution is unimodal, which means that there is only one peak and that all other data points have a probability that is smaller than the peak. Since the mean (0 in this case) is where the normal distribution's peak occurs, any value to the right of the mean will be more likely to occur than any value to the left of the mean. As P(z > 1.645) is more likely than P(z 1.645), the former is true.

To know more about probability click-

brainly.com/question/24756209

#SPJ1

Answer:

See attached image

Step-by-step explanation:

This is how I did it

I made point A as (0,0)

Point B is 12 units right and 4 units up from A. So B is(12,4)

Point C is 8 units right and 8 units down from A so it is at (8, -8)

When dilated by 1/4 with point A as center of dilation, B coordinates are reduced by 1/4 so the image B' coordinates are (12/4, 4/4) = (3,1)

C coordinates are reduced by 1/4 so C' coordinates of image are (8/4, -8/4) = (2, -2)

The A' coordinates are unchanged at A'(0,0)

So the image is A'B'C' as shown in the blue triangle

I do not know what that other triangle is for, it plays no role in the dilation

I also realize you may have been given some other strategy for solving but this is the way I did it

I hope that works for you.

The probability that during a 10-hour flight an airplane will fail to reach its intended destination or crash is

To solve this problem, we can use the binomial distribution, which gives the probability of k successes in n independent trials, each with the same probability of success p. In this case, a "success" is defined as the engine not failing, and a "failure" is defined as the engine failing.

Let X be the number of engines that fail during the flight. Since each engine can fail independently of the other engine, X follows a binomial distribution with n = 2 (the number of engines) and p = 0.21 (the probability of a single engine failing). The probability of X failures is:

P(X = 0) + P(X = 1) + P(X = 2)

where P(X = k) = (n choose k) * p^k * (1 - p)^(n - k), and (n choose k) is the binomial coefficient.

Using this formula, we can calculate the probability of each possible value of X and add them up:

P(X = 0) = (2 choose 0) * 0.21⁰* 0.79²= 0.6241

P(X = 1) = (2 choose 1) * 0.21¹* 0.79¹= 0.32994

P(X = 2) = (2 choose 2) * 0.21² * 0.79⁰ = 0.04689

Therefore, the probability of the plane failing to reach its intended destination or crashing is:

P(X >= 1) = P(X = 1) + P(X = 2) = 0.32994 + 0.04689 = 0.37683

So the probability of the plane not making it to its destination is about 37.7%.

Learn more about probability

brainly.com/question/30034780

#SPJ11

By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x). Thus, Left by 4 units is the answer.

A quadratic function is a function of the form f(x) = ax² + bx + c, where a, b, and c are real numbers and a ≠ 0.

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are real numbers and a ≠ 0. The solutions of the equation are the points at which the graph of the function intersects the x-axis.

The functions, that are quadratic, f(x) and g(x) are described in the table. From the table, it can be seen that f(x) and g(x) are not equal to each other, as the values for each x are different. To match f(x) and g(x), one of the functions must be shifted.

By inspecting the table, it can be seen that f(x) must be shifted left by 4 units in order to match g(x).

This can be calculated by subtracting the g(x) values from the f(x) values for each x.

For example, at x = -2, the difference between f(x) and g(x) is -32.

This difference is the same for all x values, meaning that f(x) must be shifted left by 4 units to match g(x). Thus, the correct answer is Left by 4 units.

For more questions related to x-axis

https://brainly.com/question/29125848

#SPJ1

[tex]cos \beta = \frac{adjuscent}{hypotenuse} \\ cos15 = \frac{47}{x} \\ x = \frac{47}{cos15} \\ x = 48.7[/tex]