Answers
Using an exponential function, it is found that:
For Country A, the doubling time is of 43 years.For Country B, the growth rate is of 1.9% per year.What is the exponential function for population growth?The exponential function for population growth is given as follows:
[tex]P(t) = P(0)e^{kt}[/tex]
In which:
P(t) is the population after t years.P(0) is the initial population.k is the exponential growth rate, as a decimal.t is the time in years.For Country A, we have that k = 0.016. The doubling time is t for which P(t) = 2P(0), hence:
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{0.016t}[/tex]
[tex]e^{0.016t} = 2[/tex]
[tex]\ln{e^{0.016t}} = \ln{2}[/tex]
[tex]0.016t = \ln{2}[/tex]
[tex]t = \frac{\ln{2}}{0.016}[/tex]
t = 43 years.
For Country B, P(36) = 2P(0), hence we have to solve for k to find the growth rate.
[tex]P(t) = P(0)e^{kt}[/tex]
[tex]2P(0) = P(0)e^{36k}[/tex]
[tex]e^{36k} = 2[/tex]
[tex]\ln{e^{36k}} = \ln{2}[/tex]
[tex]36k = \ln{2}[/tex]
[tex]k = \frac{\ln{2}}{36}[/tex]
k = 0.019.
For Country B, the growth rate is of 1.9% per year.
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Related Questions
Suppose that 37% of college students own cats. If you were to ask random college students if they own a cat what would the probability that:
a) a single student doesn’t own a cat?
b) 3 students own cats?
c) 2 students own cats while 2 students don't own cats?
Answers
Using the binomial distribution, the probabilities are given as follows:
a) 0.37 = 37%.
b) 0.5065 = 50.65%.
c) 0.3260 = 32.60%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the fixed parameter is:
p = 0.37.
Item a:
The probability is P(X = 1) when n = 1, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{1,1}.(0.37)^{1}.(0.63)^{0} = 0.37[/tex]
Item b:
The probability is P(X = 3) when n = 3, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.37)^{3}.(0.63)^{0} = 0.5065[/tex]
Item c:
The probability is P(X = 2) when n = 4, hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.37)^{2}.(0.63)^{2} = 0.3260[/tex]
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The table shows preferences of dancing or playing sports for male and female students:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason mistakenly calculated the conditional relative frequency for female students who prefer playing sports to be 21%. What statistic did Mason actually calculate, and what should he have done differently?
Answers
The conditional relative frequency for female students who prefer playing sports is 34%.
How to determine the statistic calculated?The table of values is given as:
Sports Dancing Row totals
Male students 18 16 34
Female students 18 35 53
Column totals 36 51 87
Mason's calculation is given as:
P = 21%
This is gotten by
18/87 = 21%
The above represents the joint relative frequency of female students who prefer playing sports.
To calculate the conditional relative frequency, he should divide 18 by the row total.
So, we have
18/53 = 34%
Hence, the conditional relative frequency for female students who prefer playing sports is 34%.
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Factor the greatest common binomial factor from each polynomial
Answers
(5x-1)(6x^2+1)
Solution:
6x^2(5x-1)+5x-1
=30x^3-6x^2+5x-1
=(30x^3-6x^2) + (5x-1)
=6x^2(5x-1)+(5x-1)
=(5x-1)(6x^2+1)
HOPE THIS HELPS!
Find the mode for the scores 3,760, 5,200, 8,750, 4,400, 5,250
Answers
This is because mode is when two numbers show up the same like 4 and 4.
Find the limit
lim x->0 (4x/tan2x)
Answers
Answer:
Step-by-step explanation:
hello : here is a solution
answer me please as soon as possible plot the graph same as shown in the question using green orange and black colors
Answers
Due to length restrictions, we kindly invite to read the explanation of this question for further details about the table and graph of the function.
How to plot the graph of a function
In this problem we must plot the graph of a function on a Cartesian plane. The procedure is summarized below:
Create a table for a series of equally spaced x-values.Calculate the y-values for corresponding values and fill the table.Mark the points on the Cartesian plane.Match the points with line segments.After following the procedure, we have the following result:
Input, x x + 4 Output, y (x, y)
- 2 - 2 + 4 2 (- 2, 2)
0 0 + 4 4 (0, 4)
2 2 + 4 6 (2, 6)
4 4 + 4 8 (4, 8)
6 6 + 4 10 (6, 10)
8 8 + 4 12 (8, 12)
Lastly, we plot the graph of the linear function.
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A box contains 5 red marbles and 2 yellow marbles. Consider the two–stage experiment of randomly selecting a marble from a box, NOT replacing it, and then selecting a second marble. Determine the probabilities of the following events:
a. Selecting 2 red marbles.
P (red) =
b. Selecting a red marble on the first draw and a yellow marble on the second.
P (red then yellow) =
c. Selecting at least 1 yellow marble.
P (at least 1 yellow) =
Answers
Answer:
a) 10/21 b) 5/21 c)1/21
Step-by-step explanation:
a) your have 7 choice and 5 or them or red, 5/7. You do not replace the red marble, so for your second draw, you now only have 6 choices and of those 6 choices only 4 of them are now red or 4/6 or 2/3. We multiple these two numbers together:
5/7(2/3) = 10/21
b) For the first draw, you have 5 red marbles available out of a total 7 marbles or 5/7. The second draw now only has 6 marbles and 2 of them or yellow to make 2/6 or 1/3 (simplified). We multiply these together.
5/7(1/3) =5/21
c) I am assuming that you are still selecting 2 marbles. The first draw would be 2/7. This time I am selecting yellow and there are only 2 choices for yellow. My next draw will only have 6 marbles and only 1 of them will be yellow, so 1/6. We multiply these together
2/7(1/6) = 2/42 or 1/21
How to find the missing side?
Answers
Answer:
refer to the attachment
Dave leaves his office in Padelford Hall on his way to teach in Gould Hall. Below are several different scenarios. Take distance units to be “feet” and time units to be “minutes.” Assume Dave’s path to Gould Hall is along a straight line which is 2400 feet long.
I. Dave leaves Padelford Hall and walks at a constant spend until he reaches Gould Hall 10 minutes later.
II. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the halfway point. Then he gets confused and stops for 1 minute. He then continues on to Gould Hall at the same constant speed he had when he originally left Padelford Hall.
III. Dave leaves Padelford Hall and walks at a constant speed. It takes him 6 minutes to reach the half-way point. Then he gets confused and stops for 1 minute to figure out where he is. Dave then continues on to Gould Hall at twice the constant speed he had when he originally left Padelford Hall.
g. Using all three scenarios, represent each scenario as an algebraic function.
Answers
See below for the algebraic expressions of the scenarios.
How to represent the scenarios?The given parameters are:
Distance = 2400 feetUnit of time = MinutesScenario 1
Represent the speed with x.
So, we have:
Speed = Distance/Time
The time is given as:
Time = 10 minutes
Since he did not stop at all;
The speed is
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 1.
Scenario 2
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at the same initial speed
So, the total time it 13 minutes
The speed is represented as:
x = 2400/13
Multiply both sides by 13
13x = 2400
The above expression represents the scenario 2.
Scenario 3
Represent the speed with x, and time with t
So, we have:
Speed = Distance/Time
The time to reach halfway is given as:
Time = 6 minutes
He stopped for 1 minute, before continuing at twice the initial speed
So, the total time is
t = 6 + 1 + 1/2 * 6 minutes
t = 10 minutes
The speed is represented as:
x = 2400/10
Multiply both sides by 10
10x = 2400
The above expression represents the scenario 3.
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Given square ERTN, what is the length of NT ?
Answers
Answer:
|NT| = 25
Step-by-step explanation:
The four sides of this square all have the same length. Thus, 5x = 10x - 25, which, in turn, becomes 25 = 5x, giving us x = 5. The length of NT is 5(x), or |NT| = 25.
Identify the vertices of the feasible region and use them to find the maximum and/or minimum value for the given linear programming constraints.
System of Linear Programming:
z=−3x+5y
x+y≥−2
3x−y≤2
x−y≥−4
Maximum value of z:
Minimum value of z
Answers
The maximum value of the objective function is 26 and the minimum is -10
How to determine the maximum and the minimum values?The objective function is given as:
z=−3x+5y
The constraints are
x+y≥−2
3x−y≤2
x−y≥−4
Start by plotting the constraints on a graph (see attachment)
From the attached graph, the vertices of the feasible region are
(3, 7), (0, -2), (-3, 1)
Substitute these values in the objective function
So, we have
z= −3 * 3 + 5 * 7 = 26
z= −3 * 0 + 5 * -2 = -10
z= −3 * -3 + 5 * 1 =14
Using the above values, we have:
The maximum value of the objective function is 26 and the minimum is -10
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Instructions: Find the missing side of the triangle 27,36,x
Answers
Answer:
x = 117
Step-by-step explanation:
Foremost, we know that the three angles of the triangle always add up to 180 degrees.
So, there are two sides which are 27 degrees and 36 degrees, we need to find the third one's degree.
Add 27 and 36 (27 + 36 = 63)
Two sides equal 63.
Then, subtract 180 - 63 = 117
So the third angle's measurement is 117 degrees. The answer is 117.
To check, add 117 + 27 + 36 = 180
Hope it helps.
Following a group of truck drivers and noting the number of miles traveled for one year refers to which type of statistical study?
Answers
Considering that the data is only noted and not changed, this is an example of an observational study.
What are observational and experimental studies?Experimental study: In an experimental study, there is an intervention in a sample, and it's effect is studied.Observational study: In an observational study, the sample is just analyzed, without any intervention.In this problem, the data, which is the number of miles traveled, is only analyzed, no interventions are made, hence this is an example of an observational study.
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Set B and the universal set U are defined as follows.
U={f,g,h,p,q,r}
B={g,q,r}
Find the following sets.
Write your answer in roster form or as Ø.
(a) B' U U =
(b) B ∩ Ø =
Answers
Answer:
(a) B' U U = { f,g,h,p,q,r}
(b) B ∩ U = {g,q,r}
Step-by-step explanation:
Greetings !
(a) B/c B'= {X: X∈U and X∉B}
thus,B'= {f,h,p}
B' U U= {f,h,p} U {f,g,h,p,q,r}
= {f,g,h,p,q,r}
(b) B ∩ U= {g,q,r}
Factor completely 81x2 − 100. (1 point) (10x − 9)(10x − 9) (10x − 9)(10x + 9) (9x − 10)(9x + 10) (9x − 10)(9x − 10)
Answers
The complete factorization of the equation 81x² - 100 is; (9x - 10)(9x + 10)
How to factorize quadratic equations?We are given the quadratic equation;
81x² - 100
Now, according to quadratic identities, we know that;
(a + b) * (a - b) = a² - b²
Now, our equation can also be expressed as;
81x² - 100 = 9²x² - 10²
Thus, applying the quadratic identity gives us;
(9x + 10)(9x - 10)
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Suppose that $6500 is placed in an account that pays 12% interest compounded each year.
Assume that no withdrawals are made from the account.
Follow the instructions below. Do not do any rounding.
Answers
The amount after 1 year is $7280 and the amount after two year is $8153.
Given that $6500 is placed in an account that pays 12% interest compounded each year.
Compounding is the addition of interest to the principal of a loan or deposit, or in other words, interest on principal plus interest.
Compounded interest=12%
Principal amount=$6500
Time period = 1 year
[tex]A=P\left(1+\frac{r}{n}\right)^{nt}[/tex]
where P is Principle amount, r is annual interest, n is number of times the interest compounded monthly, t is number of years
Here P=6500, r=12%, n=1, t=1
Substitute these values in the formula, we get
A=6500(1+(0.12/1))¹⁽¹⁾
A=6500(1+0.12)¹
A=6500×1.12
A=7280
Now we have to calculate for two years.
That is if n=2 , then
A=6500(1+(0.12/1))¹⁽²⁾
A=6500(1+0.12)
A=6500×1.2544
A=8153.6
Hence, the amount for one year and two year when $6500 is placed in an account that pays 12% interest compounded is $7280 and $8153.60.
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if A and B are events with P(A) = 0.2, P(B) = 0.8, P(A and B) = 0.07, find P(A or B)
Answers
Work Shown:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.2 + 0.8 - 0.07
P(A or B) = 0.93
Jermy deposited money into a savings account that pays a simple annual interest rate of 1.6%. He earned 55.04 in interest after 4 years. How much did he deposit?.
860
1376
2976
3440
Answers
Simple interest rate is 1.6 percent.
$55.04 after simple interest.
t = 4 years
We must ascertain the principal sum.
Simple interest
The formula for simple interest is:
pxrxI
100
Substitute the given values.
D x 1.6x 4
55.04
100
5504 = 6.4p
5504
6.4
860 = 0
The principal value is $860. So, option A is
correct.
Answer: THE ANSWER IS A) $860
Step-by-step explanation: I GOT A 100 ON THE TEST
Suppose the mean of a normally distributed population is 300,and 200 simple random samples are drawn from the population.At a 68% confidence level(one standard divination from the mean) about how many of the samples confidence intervals would you expect to contain population mean?
A)64
B)96
C)136
D)204
Answers
samples confidence intervals needed is Option C 136.
How to estimate the number of sample confidence intervals?According to the Empirical rule, if data exists normally distributed then about 68% of the population lies within one standard deviation from the mean.
We assume that the mean of a normally distributed population exists at 300, and 200 simple random samples exist drawn from the population.
Number of simple random samples, n= 200
By Empirical rule, approximately 68% of 200 samples’ confidence intervals we would expect to have the population mean.
Required number of samples = 68% of 200
= 0.68 x 200 = 136
The required number of samples = 136
Therefore, the correct answer is option C) 136.
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Sets A, B, and C are subsets of the universal set U. These sets are defined as follows.
U= {f,g,h,p,q,r,x,y,z}
A={f,g,p,q}
B={g,h,q,x,y}
C={p.q.x.y.z}
Find (C ∪ B) ∩ A'.
Write your answer in roster form or as Ø.
Answers
Answer:
(C U B )=(q,x,y)
(C U B )n A=q
guys can you help me with this i just dont understand how to plot it so u just have to tell me how
Answers
Answer:
no
Step-by-step explanation:
Answer:
Step-by-step explanation:
6(3x-5)≤2(9x+7)+10
divide by 2
3(3x-5)≤9x+7+5
3(3x-5)≤9x+12
divide by 3
3x-5≤3x+4
-5≤4
which is true.
How do you find the value of 5,016 with as few steps as possible?
Answers
The estimated value of 5,016 exists 1 / 264 ≈ 0.00379.
What is a fraction?Fractions describe the regions of a complete or group of objects. A fraction contains two regions. The number on the top of the line exists named the numerator. It describes how many equivalent regions of the real or group stand accepted. The number below the line exists named the denominator. It exhibits the total number of equivalent regions the whole exists divided into or the total number of the exact objects in a group.
How to estimate the value of 5,016 with as few steps?The value of 5,016 can be simplified by using a fraction
Consider a denominator 19, then
19 divided by 5,016, then we get
19 and 5016 have a common divisor of 19.
then, we get
19 / 5016 = 1 / 264
Now, you need to divide.
1 / 264 ≈ 0.00379
Therefore, the estimated value of 5,016 exists 1 / 264 ≈ 0.00379.
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How do you classify the following polynomial?
-4x³ + 2x² - 5x+3x²
(I need de classification, no the result)
Answers
Simplify the following fractions.
Answer =
[tex] \frac{9}{16 \\ \\ } [/tex]
Show me step by step
Answers
Answer:
Expressions with numerous operators must be simplified in "BODMAS" order only, from left to right. The brackets are solved first, followed by powers or roots,division, or multiplication (whatever comes first from the left side of the formula), and finally subtraction or addition. The BODMAS simplification of fractions is a solution for addressing fractions that include many operations such as addition (+), subtraction (-), multiplication (×),division(÷), and brackets ().[tex] \pink{\maltese{ \text{BODMAS \:Full \: Form \: }}}[/tex]
To make numerical equations easier to understand, operations must be performed according to the BODMAS rule, which involves division, multiplication, addition, and subtraction to be performed in the order brackets.For example,The expression (48-24)÷3×4 as per BODMAS rule.
(48-24)÷3×4
=24÷3×4
=8×4
=32
Now,
The given question is,
Simplify:
[tex] \displaystyle{ \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{7}{8} \div \frac{16}{3} \times \frac{24}{7} }[/tex]
[tex] \displaystyle{ = \frac{ \cancel{7} \times 3 \times \cancel{24} \: {}^{3} }{ \cancel{8 } \times 16 \times \cancel{7}} }[/tex]
[tex] \displaystyle{ = \frac{3 \times 3}{16} }[/tex]
[tex] \displaystyle{} = \frac{9}{16} [/tex]
Thus,the final answer is 9/16.
Solution -:
[tex] \frac{7}{8} \div 5 \frac{1}{3} \times \frac{24}{7} [/tex]
Let's begin-
solve,,,
Now,,According to BODMAS rule fist we divide ,
[tex] \frac{7}{8} \times \frac{3}{16} \times \frac{24}{7} \\[/tex]
Now , we multiple
[tex] \frac{3 \times 3}{16} \\ \\ = \frac{9}{16} [/tex]
and this is our final answers
▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃▃
Division → Multiplication → Addition → Subtraction
B stand bracket O stand of D stand divisionM stand MultiplicationA stand for additionS stand for subtractionSimplify: Simplify: StartRoot StartFraction 27 x Superscript 12 Baseline Over 300 x Superscript 8 Baseline EndFraction EndRoot
Answers
The solution of the given expression is 9*[tex]x^{4}[/tex]/100.
GIven an expression equal to 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
We have to simplify the expression in which variable comes only once.
Expression is combination of numbers ,symbols, fraction, coefficients, indeterminants,determinants, etc. It is mostly not found in equal to form. It expresses a relationship between variables.
The given fraction is 27[tex]x^{12}[/tex]/300[tex]x^{8}[/tex].
When we observe we find that in numerator x has large power and denominator x has small power as compared to power in numerator. So we will deduct the powers so that they will give only one power to us.
=27[tex]x^{4}[/tex]/300
Now divide numerator an denominator by 3.
=9[tex]x^{4}[/tex]/300
Hence the expression 27[tex]x^{12} /300x^{8}[/tex] will look like [tex]9x^{4} /100[/tex] after simplifying.
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Answer:
[tex]Simplify:\sqrt\frac{27x^{12} }{300x^{8} }[/tex]
[tex]O \frac{9}{100}x^{4}[/tex]
✔ [tex]\frac{3}{10} x^{2}[/tex]
[tex]O \frac{27}{300} x^{4}[/tex]
[tex]O\frac{9}{10} x^{2}[/tex]
A study showed that low-intensity shock therapy reduces pain levels in patients with lupus. During each session, electrodes were placed on the pain site indicated by the patient. Pain reduction was measured through self-reporting after each session.
Another study is being designed to examine whether low-intensity shock therapy also reduces pain in patients suffering from bulging disks in the thoracic region of the back. Two hundred female patients are subjects in the new study.
Part A: What is an appropriate design for the new study? Include treatments used, method of treatment assignment, and variables that should be measured. (4 points)
Part B: If the study consisted of 100 male and 100 female patients instead of 200 female patients, would you change the study design? If so, how would you modify your design? If not, why not? (4 points)
Part C: Could your design be double-blind? Explain. (2 points)
Answers
The experiment is illustrated below.
How to explain the experiment?A. The type of experimental design is a completely randomized design experiment where experimental units of 200 female subjects which are allocated randomly to say 4 treatment groups with each treatment group consist of 50 female patients.
Here the treatment used is low-intensity shock therapy which is also factor or explanatory variable. After administrating above treatment for a period of say 2-3 weeks, the response in pain reduction can be measured among all patients in 4 treatment groups by comparing their earlier pain level for reduction in pain.
If the study consist of 100 male and female patients, the experimental design can be changed into randomized block design by blocking subjects by gender.
The above design can be double blinded by not letting either the patients or lab technicians aware about which treatment groups, each of these subjects are experimented against to keep the data confidential.
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The base of a triangle is twelve more than twice its height. If the area of the triangle is 43 square centimeters, find its base and height.
Answers
Answer:
B=37
H=66
Step-by-step explanation:
Use algebra and find the answer.
Solve for x.
x-2.13 = 5.3
Answers
+2.13
Process:
Start by isolating the variable by itself, in this case we add 2.13 to the -2.13 as whatever we do to one side of the equation we do to the other hence we add 2.13 to 5.3 which will become x = 7.43 and we can verify our answer by substituting our answer for x
7.43 - 2.13 = 5.3
Answer:
x = 7.43
Step-by-step explanation:
X - 2.13 = 5.3
add -2.13 to both sides
x -2.13+2.13 = 5.3 + 2.13
-2.13 + 2.13 cancel out and 5.3 +2.13 equals 7.43
therefore x =7.43
check your work by substituting 7.43 for x
7.43 - 2.13 = 5.3
A ladder 8 m long is leaning against a building. How high on the building will the ladder reach when the bottom of the ladder is x = 1m from the building?
Answers
Answer:
7.9
Step-by-step explanation:
this would just be sqrt (8^2 - 1^2) or sqrt 63 or about 7.9
The ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
What is the Pythagoras theorem?The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
It is given that:
A ladder 8 m long is leaning against a building.
From the data given, a right angle triangle is formed:
Applying the Pythagoras theorem:
Building high² = 8² - 1²
Building high² = 63
Building high = 7.9 meters
Thus, the ladder reaches 7.9 meters when the bottom of the ladder is x = 1m from the building.
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SOLVE AND EXPLAIN HOW TO SOLVE
Answers
Answer:
4.13
Step-by-step explanation:
Using sine ratio where it states that sine of a measurement is equal to ratio of opposite of measurement to hypotenuse (slant side/side with slope)
From the question, our opposite is x, hypotenuse is given as 15 units and the measurement is 16°. Apply the formula:
[tex]\displaystyle{\sin 16^{\circ} = \dfrac{x}{15}}[/tex]
Move 15 to multiply sin(16°):
[tex]\displaystyle{15\sin 16^{\circ} = x}[/tex]
Go ahead and input the value in a calculator since it's not a special triangle - a measurement that can be found using hand method - after you find the value, round it to 2 decimal places:
[tex]\displaystyle{x = 4.13456033...}[/tex]
Therefore, after rounding to 2 decimal places, the answer is:
[tex]\displaystyle{x=4.13}[/tex]
Therefore, the value of x is 4.13 units.