Richard lends to Martin P154,600. 00 under the condition that simple interest will be charged at 8. 5% per annum and the debt is payable after months. How much will Martin have to pay Richard after 36 months ?
Answers
We know that after 36 months, Martin will have to pay Richard P193,969.
Hi! Based on your question, Richard lends P154,600 to Martin at an 8.5% simple interest rate per annum, and the debt is payable after 36 months. To find out how much Martin will have to pay Richard after 36 months, we'll first calculate the interest.
Simple Interest = Principal × Rate × Time
Interest = P154,600 × 8.5% × (36 months / 12 months per year)
Interest = P154,600 × 0.085 × 3
Interest = P39,369
Now, add the interest to the principal to find the total amount Martin needs to pay Richard:
Total Amount = Principal + Interest
Total Amount = P154,600 + P39,369
Total Amount = P193,969
After 36 months, Martin will have to pay Richard P193,969.
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Related Questions
Please see the image. Assist quickly please, thanks!
Answers
Answer:
Point A' should be 2 units left and 8 units above of Point C.
Point B' should be 10 units right and above Point C.
Point C stays the same.
at a carnival game, the chance of winning a prize is 0.45. kylee plays the game 3 times. using the table, what is the probability that she wins at most 2 prizes?
Answers
The probability that Kylee wins at most 2 prizes in 3 attempts is 0.95625.
To answer this question, we can use the binomial distribution formula:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
where X is the number of times Kylee wins a prize, and P(X = k) is the probability of winning k prizes in 3 attempts.
Using the binomial distribution formula, we can calculate these probabilities using the following formula:
\(P(X = k) = (n choose k) × p^k × (1-p)^(n-k)\)
where n is the number of trials (in this case, 3), p is the probability of winning a prize (0.45), and k is the number of
successes we want to calculate the probability for.
Now, let's plug in the values for k = 0, 1, and 2:
\(P(X = 0) = (3 choose 0) × 0.45^0 × (1-0.45)^3 = 0.342
P(X = 1) = (3 choose 1) × 0.45^1 × (1-0.45)^2 = 0.4095
P(X = 2) = (3 choose 2) × 0.45^2 × (1-0.45)^1 = 0.20475\)
Now, we can add up these probabilities to find the probability that Kylee wins at most 2 prizes:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.342 + 0.4095 + 0.20475 = 0.95625
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An observation deck extends 311 feet out above a valley. The deck sits 261 feet above the valley floor. If an object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-16t²+261. How long will it take for the object to be 5 feet above the valley floor?
Answers
Answer:
4 secondsStep-by-step explanation:
Find the value of t in the following equation:
-16t² + 261 = 5-16t² = - 255t² = 255/16t = √255/4 ≈ 4 secondsThe makers of Aspaway brand aspirin want to be sure that their tablets contain the right amount of active ingredient (acetylsalicylic acid). So they inspect a random sample of 30 tablets from a batch in production. When the production process is working properly, Aspaway tablets have an average of μ = 320 milligrams (mg) of active ingredient. The amount of active ingredient in the 30 selected tablets has a mean of 319 mg and a standard deviation of 3 mg. We want to perform a test at the a= 0.05 significance level of H₂:μ = 320 H₂: 320 where μ = the mean amount of active ingredient (in mg) in all Aspaway brand aspirin tablets.
Answers
Based on the information, there is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.
How to explain the hypothesisH0: µ = 320 versus Ha: µ ≠ 320
This is a two tailed test.
The test statistic formula is given as below:
t = (x - µ)/[S/✓(n)]
n = Sample size = 36 n = Population mean = 320 x = Sample mean = 319 S = Sample Standard deviation = 3
We have = Level of significance = 0.09 from the given data.
df = n - 1 = 35
1.7436 is the critical value.
[Using a t-table, we can determine this value.]
The P-value is 0.0533.
P-value = 0.09.
So, we reject the null hypothesis. There is not sufficient evidence to conclude that tablets contain the right amount of active ingredients.
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What are the 7 laws of exponents?
Answers
Answer:
1- Product of powers rule.
2- Quotient of powers rule.
3- Power of a power rule.
4- Power of a product rule.
5- Power of a quotient rule.
6- Zero power rule.
7- Negative exponent rule.
Step-by-step explanation:
Hope I helped! ^v^
Product of powers rule.
Quotient of powers rule.
Power of a power rule.
Power of a product rule.
Power of a quotient rule.
Zero power rule.
Negative exponent rule.
1. This Question Is Compulsory (a) Find the following Laplace transform and verse Laplace transform (1) Llet+')} (1) L- [8 marks) (b) 18 = 1+k8-2+ 3+ 3k and 7 - 1 - 2k, obtain the following (1) ä. ax, (1) 6x5)-(ä xk), (iv) 2:a)3 +34 (12 marks) () Find the point at which the plane 22 - 5y + z = 5 and the line Ft) - (+1) + (24+ 1)3+ (t+1)! (where t is a real number) intersect. [3 marks) (d) Compute the curvature and principal unit normal vector for the curve rt) 2 sin(t)+ 2 con(e) { for t > 0. [6 marks] 2t? (e) For the two matrices A= 12 0 0-7 5 3 B= B=(- :) 0 Find (1) AT, (1) BT, (ii) B(AT) and (iv) (AB)". [8 marks) (t) Find the determinant and trace of the matrix 5-13 10 0 - 2 1 0 3 [6 marks) Solve the following system of simultaneous equations using Gauss-Jordan elimination: 2.11 + 12 = -2, -92+372 = 4. [7 marks] Page 2 of 4
Answers
Part a. Find the Laplace transform and inverse Laplace transform of Let+')} and L- [8 marks]Laplace transform of Let+')} is given as: L(et+')} = 1/s-(1/ s+2)Let's try to this.1/s-(1/ s+2) = (s+2-s)/s(s+2) = 2/s(s+2)L-1{2/s(s+2)}= L-1{(1/s)-(1/s+2)} = e^(-2t) - 1
Part b. 18 = 1+k8-2+ 3+ 3k and 7 - 1 - 2k, obtain the following: i) ä. ax, ii) (ä xk), iii) 2:a)3 +34 i) 18 = 1+k8-2+ 3+ 3k
Let's simplify this as follows.18 = 12 + k + 3k - 2k + 3k-1 - 4k+1/218 = 12 - k + 2k + 2k + 3(1/k) - 4k+1/2a=12, b=-1, c=2 and d=2Therefore,ä. ax = ad-bc = 24 + 2 = 26ii) (ä xk) = (cd - bc)i + (ab - ad)j + (ad - bc)k = 1i - 2j + 24kiii) 2:a)3 +34 = 2(ad-bc) + 3(ab-ad) + 4(cd-bc) + 3(bd - ac) = 52
Part c. Find the point at which the plane 22 - 5y + z = 5 and the line Ft) - (+1) + (24+ 1)3+ (t+1)! (where t is a real number) intersect. [3 marks]. Let's substitute the given line in the plane equation. 2(1+4t) - 5(3+1t) + z = 5 solving for z, we get
z = 12t - 13
Substitute this z in line equation to get the point of intersection.(1+t, 4+2t, 12t-13)
Part d. Compute the curvature and principal unit normal vector for the curve rt) 2 sin(t)+ 2 con(e) { for t > 0. [6 marks]. Given curve r(t) = 2 sin(t) + 2 cos(t).
We need to find the first and second derivatives. r'(t) = 2 cos(t) - 2 sin(t)r''(t) = -2cos(t) - 2sin(t)
From these values, we get |r'(t)| = sqrt(8)K(t) = |r'(t)|/|r"(t)|^3/2K(t) = 2^(3/2)/8^(3/2)K(t) = 1/4^(1/2)K(t) = 1/2
Therefore the curvature is 1/2Now, let's find the principal unit normal vector. N(t) = r''(t)/|r"(t)|N(t) = <-1/sqrt(2),1/sqrt(2)>
Part e. For the two matrices A= 12 0 0-7 5 3 B= B=(- :) 0
Find i) AT, ii) BT, iii) B(AT) and iv) (AB)" [8 marks]
i) AT =Transpose of A = 1 -7 0 2 5 3
ii) BT =Transpose of B = 1 0 -3 0 2 1
iii) B(AT) =B(Transpose of A) = 1 -7 0 2 5 3(-1) 0 0 7 -5 -3= -1 7 0 -2 -5 -3
iv) (AB)" =(AB)^-1=Inverse of AB Let's calculate AB first. AB =12 0 0-7 5 3(-1) 0 0-5 2 -1= -1 0 0 1
Therefore, the inverse of AB is1 0 0-1
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Consider these preferences defined overstudent submitted image, transcription available below2+ by (x1' , x2 ')student submitted image, transcription available below(x1'' , x2 '') if x1'+x2' < x1''+x2 '' , in which x1 is the total number of hours worked and x2 is the quantity of particle pollution inhaled.
(a) Are those preferences monotonic? Explain.
(b) Suppose the consumer has exogenous income m > 0 and has strictly positive prices p1 and p2. Which of these bundles would be taken by the consumer? Is the budget constraint binding? Explain why it cannot be that prices are strictly positive if all consumers similar preferences.
(c) Assume that prices are strictly negative. To simplify the interpretation we will denote p1 = −ω and p2 = −e, where ω > 0, e > 0. Furthermore, assume that the consumer has no exogenous income but an initial endowment of good 2, P > 0. Represent graphically the budget set of the consumer and give an economic interpretation: particularly, provide an interpretation of the initial endowment P. (Hint: when interpreting the budget constraint, try to isolate what corresponds to expenditures by the consumer and what corresponds to money earned by the consumer)
(d) Characterize the optimal selection of the consumer depending on whether ω > e or e > ω. You can solve the problem with a graph by drawing indifference curves alongside the budget set. Provide an interpretation of these choices.
Answers
a) Given preferences are not monotonic.
b) The budget constraint is binding and the consumer cannot afford that bundle.
c) The interpretation of these choices is that the consumer maximizes their utility.
(a) These preferences are not monotonic. Monotonicity means that if one bundle is preferred to another, any bundle with more of both goods should also be preferred. In this case, if x1'+x2' < x1''+x2'', it does not necessarily mean that x1'+x2' < x1''+x2'' for all bundles with more of both goods.
(b) To determine which bundle would be chosen by the consumer, we need to compare the total expenditure on each bundle to the consumer's income. If the total expenditure on a bundle is less than or equal to the consumer's income, then that bundle would be chosen.
If the total expenditure exceeds the consumer's income, then the budget constraint is binding and the consumer cannot afford that bundle.
(c) When prices are strictly negative (p1 = -ω, p2 = -e), the budget set can be represented graphically as a set of bundles that the consumer can afford.
The initial endowment P represents the amount of good 2 that the consumer already possesses without having to spend any money. It is a starting point for the consumer's choices.
(d) To characterize the optimal selection of the consumer, we need to consider whether ω > e or e > ω.
If ω > e, the consumer's optimal choice would lie on the highest attainable indifference curve that is tangent to the budget set.
If e > ω, the optimal choice would lie on the indifference curve that is tangent to the budget set at a point where the consumer exhausts their initial endowment P.
The interpretation of these choices is that the consumer maximizes their utility by selecting the bundle that provides the most satisfaction given their budget constraints and initial endowment.
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A golf ball is hit from the ground with an initial speed of 192 feet per second. assume the starting height of the ball is 0 feet. how long will it take the golf ball to hit the ground?
Answers
It will take the golf ball 12 seconds to hit the ground using the kinematic equation for vertical motion.
To determine the time it takes for the golf ball to hit the ground, we can use the kinematic equation for vertical motion:
\(h = ut + (1/2)gt^2\)
Where:
h is the height (0 feet, as the ball is on the ground)
u is the initial velocity (192 feet per second)
g is the acceleration due to gravity (-32 feet per second squared, considering downward direction)
t is the time we want to find
Plugging in the given values, we get:
\(0 = (192)t + (1/2)(-32)t^2\)
Simplifying the equation, we have:
\(-16t^2 + 192t = 0\)
Factoring out t, we get:
t(-16t + 192) = 0
Setting each factor equal to zero, we have:
t = 0 (not applicable in this case)
-16t + 192 = 0
Solving for t, we get:
-16t = -192
t = 12
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The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
The time it takes for the golf ball to hit the ground can be determined using the equation of motion. We can use the formula:
h0 = 0
v0 = 192
g = 32.2
a = 16.1
b = 192
t1 = 0
t2 = -b / a
t(-16t + 192) = 0
Setting each factor equal to zero, we have:
t = 0 (not applicable in this case)
-16t + 192 = 0
Solving for t, we get:
-16t = -192
t = 12
t2 >= 0:
time_to_hit_ground = t2
time_to_hit_ground = t1
The time it takes for the golf ball to hit the ground is approximately", round(time_to_hit_ground, 2 seconds.
The time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
Since time cannot be negative in this context, we discard the negative solution. Therefore, the time it takes for the golf ball to hit the ground is approximately 11.92 seconds.
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Jada is comparing membership costs for two gyms. What is the difference in membership costs after m months if she joins Be Strong instead of Zippy Health Club?
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or a new cookbook is becoming popular. the local bookstore ordered 86 copies in may, 172 copies in june, 344 copies in july, and 688 copies in august. what kind of sequence is this?
Answers
This is a geometric sequence with a common ratio of 2. So the predicted order quantity for September is 1376 copies.
In a geometric sequence, each term is found by multiplying the previous term by a fixed number called the common ratio. In this case, we can see that each month's order quantity is double the previous month's order quantity. This makes it a geometric sequence with a common ratio of 2.
To verify, we can divide any term by its preceding term and see that we always get the same ratio of 2. For example:
June order / May order = 172 / 86 = 2
July order / June order = 344 / 172 = 2
August order / July order = 688 / 344 = 2
Knowing that this is a geometric sequence with a common ratio of 2, we can use the formula for the nth term of a geometric sequence to find the order quantity for any given month:
an = a1 * r^(n-1)
where:
an = the nth term
a1 = the first term
r = the common ratio
n = the number of terms
For example, to find the order quantity for September (the 5th month), we can plug in the values:
a5 = 86 * 2^(5-1) = 86 * 16 = 1376
So the predicted order quantity for September is 1376 copies.
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Solve the equation using the square root method
X^2 – 100 = 0
Answers
-5 1/4-(-7 1/2) I need this simplified please help!!
Answers
Answer:
-51/4 or -12.75
Step-by-step explanation:
In a line-weaver burke plot what does the 1/Y-intercept and 1/X-intercept equal?
Answers
In a Lineweaver-Burk plot, the 1/Y-intercept represents the reciprocal of the maximum velocity (1/Vmax) of the enzyme-catalyzed reaction. The 1/X-intercept represents the negative reciprocal of the Michaelis constant (1/Km) for the substrate.
In a Lineweaver-Burk plot, the 1/Y-intercept represents the reciprocal of the maximum velocity (1/Vmax) of the enzyme-catalyzed reaction being studied, while the 1/X-intercept represents the negative reciprocal of the Michaelis constant (1/Km) for the substrate.
The Lineweaver-Burk plot is a linear transformation of the Michaelis-Menten equation, which relates the initial reaction rate (v0) of an enzyme-catalyzed reaction to the substrate concentration ([S]):
v0 = (Vmax [S]) / (Km + [S])
Taking the reciprocal of both sides of the equation, we get:
1/v0 = (Km/Vmax) (1/[S]) + 1/Vmax
This equation has the same form as the equation of a straight line y = mx + b, where y = 1/v0, x = 1/[S], m = Km/Vmax, and b = 1/Vmax. Therefore, plotting 1/v0 against 1/[S] on a Lineweaver-Burk plot produces a straight line with a slope of Km/Vmax and a y-intercept of 1/Vmax.
Taking the reciprocal of the slope, we get:
1/(Km/Vmax) = Vmax/Km
which is equal to the 1/X-intercept of the Lineweaver-Burk plot. Similarly, taking the reciprocal of the y-intercept, we get:
1/(1/Vmax) = Vmax
which is equal to the 1/Y-intercept of the Lineweaver-Burk plot.
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20 ÷ ____ = 5 need your help
Answers
Answer:
4
Step-by-step explanation:
Who know this please I need help asap !!
Answers
Answer:
Step-by-step explanation:
\(tan\theta =\frac{12}{5}\\ \\ \theta =tan{-1}\frac{12}{5}\\ \\ \theta =67.38^o\\ \\ \theta \approx 67^o\)
what was the speed of a 10 gg bullet if the block's mass is 2.0 kgkg and if the spring, with kkk = 55 n/mn/m , was compressed by 45 cmcm ?
Answers
The speed of the 10 g bullet was approximately 1.732 m/s. This can be answered by the concept of conservation of momentum.
To find the speed of the 10 g bullet, we can use the conservation of momentum and the potential energy stored in the spring. The initial momentum of the bullet-block system is equal to the final momentum after the bullet embeds itself in the block, and the potential energy in the spring equals the initial kinetic energy of the bullet-block system.
1. Convert the bullet mass to kg: 10 g = 0.01 kg
2. Convert the compression of the spring to meters: 45 cm = 0.45 m
First, find the potential energy stored in the spring when it is compressed by 0.45 m:
PE_spring = 0.5 × k × x²
PE_spring = 0.5 × 55 N/m × (0.45 m)²
PE_spring = 6.06875 J
Now, equate the potential energy to the initial kinetic energy of the bullet-block system:
KE_initial = PE_spring
Since KE = 0.5 × m × v², we can write:
0.5 × (0.01 kg + 2.0 kg) × v² = 6.06875 J
Solve for v (bullet's speed):
v^2 = (6.06875 J) / (0.5 × (0.01 kg + 2.0 kg))
v^2 = 2.9971
v = 1.732 m/s
So, the speed of the 10 g bullet was approximately 1.732 m/s.
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Joe would like to paint a rectangular shaped wall. The measures of dimensions of the wall are 8 inches by 4 inches. Every 1 inch represents 3 feet of the actual wall. If the cost of the painting is $2.50 per square feet, find the total cost of paint needed for the entire wall.
Answers
Answer:
$90
Step-by-step explanation:
8 + 4 = 12
12 x 3 (3 feet for each inch) = 36
36 x 2.50 (cost per square foot) = $90
Answer:
$240
Step-by-step explanation:
8 x 4 is 32
32 x 3 is 96
96 x 2.5 is 240
The measure of an angle is 68.8 degrees. What is the measure of its complementary angle
Answers
Answer:
complementary angles are sum up to 180°
68.8+x=180°
68.8 complementary angle is 111.2
the complement of an angle is 57 degrees, what is the size of the angle?
Answers
Answer:
43 degreesStep-by-step explanation:
So I think I know how to do this but tell me if I’m wrong so, 2x+45 and then it’s verticals angle is the same thing so it’s the same, then it’s same side with x so it’s whatever 2x+45 is solved? If I’m wrong then please explain how to do this
Answers
Since the two lines in the figure are parallel, due to interior angles theorem, it follows:
\(\begin{gathered} x+2x+45=180 \\ 3x=180-45 \\ 3x=135 \\ x=\frac{135}{3} \\ x=45 \end{gathered}\)So the value of x is 45.
Answer choices: | Please help!
50 cm; 42 cm2
50 cm; 54 cm2
34 cm; 54 cm2
34 cm; 42 cm2
Answers
The perimeter and area of the given composite figure are:
Area = 50 cm²
Perimeter = 42 cm
How to find the area of the composite figure?To find the total surface area of the composite figure, we will find the area of each individual surfaces and then add them together.
Formula for area of a triangle is:
Area = ¹/₂ * base * height
Formula for area of a rectangle is:
Area = Length * Width
Thus:
T.S.A = 2(¹/₂ * 4 * 5) + (10 * 3)
T.S.A = 20 + 30
T.S.A = 50 cm²
The perimeter will be the sum of the entire boundary length. Thus:
Perimeter = 3 + 10 + 10 + 3 + 3 + 3 + 5 + 5
Perimeter = 42 cm
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Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below.
Alexandra
Chi
Swim
5 km/hr
6 km/hr
Transition 1
4 minutes
5 minutes
Cycle
15 km/hr
15 km/hr
Transition 2
3 minutes
5 minutes
Run
6 km/hr
7.5 km/hr
Answers
Complete question :
Alexandra and Chi compete in an Olympic-type triathlon consisting of a 1.5 km swim, a 40 km bicycle ride, and a 10 km run. There are two transitions in the race where the participants take time to change from one mode of the race to another. Their times from the race are shown. Complete questions 1dash4 below.
How long does it take Alexandra to complete the triathlon. Write a linear equation to model total time t in hours.
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following :
SWIM:
Alexandra __5km/hr
Chi _______ 6km/hr
Transition 1:
Alexandra __ 4 minutes
Chi _______ 5 minutes
CYCLE:
Alexandra __15km/hr
Chi _______ 15km/hr
Transition 2:
Alexandra __ 3 minutes
Chi _______ 5 minutes
RUN:
Alexandra __6km/hr
Chi _______ 7.5km/hr
Distances:
swim distance = 1.5km
bicycle ride distance = 40km
run distance = 10km
Time taken by Alexandra :
time = distance / speed
Swim time = 1.5km / 5km/hr = 0.3 hr
Transition 1 = 4/60 = 0.067 hr
Cycle time = 40km / 15km/hr = 2.67 hours
Transition 2 = 3/60 = 0.05 hr
Run time = 10 / 6km/hr = 1.67 hrs
Total time(t) in hours taken by Alexandra :
(0.3 + 0.067 + 2.67 + 0.05 + 1.67) hrs = 4.757 hours
Time taken by Chi :
time = distance / speed
Swim time = 1.5km / 6km/hr = 0.25 hr
Transition 1 = 5/60 = 0.083 hr
Cycle time = 40km / 15km/hr = 2.67 hours
Transition 2 = 5/60 = 0.083 hr
Run time = 10 / 7.5km/hr = 1.33 hrs
Total time(t) in hours taken by Chi
(0.25 + 0.083 + 2.67 + 0.083 + 1.33) hrs = 4.757 hours = 4.416 hours
4,12,20 find the 41st term
Answers
Answer:
The 41st term of the given series is 324
Step-by-step explanation:
a= 4
a2= 12
d= a2-a
d= 12-4 = 8
now, we have to find 41 term that is a41
a41 = a+ 40d
a41= 4+ 40× 8
a41= 4+ 320
= 324
therefore the 41st term is 324
Answer:
324
Step-by-step explanation:
The sequence observed appears to be an arithmetic sequence. The formula for an arithmetic sequence is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term position, and d is the common difference. Let's write down what we know.
n = 41
a1 = 4
d = 8
So, let's plug our values into the equation and solve.
an = 4 + (41 - 1)8
an = 4 + (40)8
an = 4 + 320
an = 324
The ratio of the quantities of salt to baking soda needed to complete a science experiment is 3:7. What is the quantity of salt in grams needed for this experiment, if 420 grams of baking soda is used to complete the experiment?
Answers
The quantity of salt in grams needed to complete the experiment is 180 grams.
What are ratios?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
What is the quantity of sat needed?Quantity of salt needed = (grams of baking soda x ratio of salt) / ratio of baking soda
(3 x 420) / 7 = 180 grams
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Chen is bringing fruit and veggies to serve at an afternoon meeting. He spends a total of $28.70 on 5 pints of cut veggies and 7 pints of cut fruit. The food cost is modeled by the equation 5 v plus 7 f equals 28.70, where v represents the cost of one pint of cut veggies and f represents the cost of one pint of cut fruit. If the cost of each pint of fruit is $2.85, what is the approximate price of a pint of veggies? (Round to the nearest cent, as needed.)
PLEASE ANSWER ASAP!!!!
Answers
Answer:
Step-by-step explanation:
you suck
you measure the angle of elevation from the goround to the top of a building as 32. when you move 50 meters closer to the building, the angle of elecation is 53. what is the height of the building?
Answers
The height of the building from which the angle of elevation is 32 degrees is 127.87m.
The angle of elevation is found to be 32 degrees and when moving 50 closer to the building, the angle of elevation is 53.
Let us say that the height of the building is X.
Now, let us say the distance between the building and the person is Y.
So, we write,
tan(32°) = X/Y
Also, tan(53°) = X/(Y-50)
0.62 = X/Y and 1.32 = X/(Y-50)
0.62Y = 1.32Y - 66
66 = 0.32Y
Y = 206.25 m
Now, we know, X = 206.25m x 0.62
X = 127.87m
So, the height of the building is 127.87m.
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Warm-Up
Identifying Shaded Regions
Analyze the linear inequalities and determine if the solution set is the shaded region above or below the boundary
line.
y> -1.4x+7
y> 3x-2
y<19-5x
y>-x-42
y<3x
y<-3.5x+2.8
(Solution Set Shaded Above)
(Solution Set Shaded Below)
Answers
The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).
what is inequality ?In mathematics, an inequality is a connection that does not have an equal sign between two expressions or values. Inequality follows imbalance, therefore. When two numerical values are not equal, an inequality establishes a connection between them. Difference between equality and inequality Use the not equal symbol, which is most often used, when two values are not equal (). No matter how little or huge the values, various inequalities are employed to contrast them. The two sides can be changed until the variables are all that is left in order to solve several basic inequalities. Unevenness is caused by a number of factors, including: The sum or division of negative values on both sides. The left and right are exchanged.
given
inequality for y
5x – 2y ≤ 10
– 2y ≤ – 5x + 10
y ≥ 5/2x - 5
When dividing by a negative number, remember to switch the inequality sign.
In a linear inequality, you will shade below the boundary line if the sign is (less than) or (less than or equal to). The borderline if the linear inequality's symbol is > (greater than) or (greater than or equal to).
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Complete the description of the piecewise function graphed below. Use interval notation to indicate intervals.
Answers
Answer:
{ -2 if x ∈ -4 < x < -3
{ -5 if x ∈ -3 ≤ x < 2
[ 5 if x ∈ 2 ≤ x < 5
Step-by-step explanation:
From the graph, we have;
{ -2 if x ∈ -4 < x < -3
For the next inequality line at y = -5, we have;
1) The inequality line, starts with an open circle on the left at x = -3, which is equivalent to less than or equal to symbol, ≤ as -3 ≤ x because the point x =-3 is the left boundary. The inequality line extends to the point x = 2, where we have a closed circle (on the right), which is equivalent to a x ≤ 2 with the 2 on the right hand side because, the 2 is the right boundary of the inequality
2) The inequality can be summarized as starting from x = -3 extends to x = 2
3) As stated in point 1) the point x = 3, we have -3 ≤ x and at point x = 2, we have x ≤ 3 which can be combined as -3 ≤ x < 2, to give;
{ -5 if x ∈ -3 ≤ x < 2
For the next inequality line at y = 5, we have;
1) The inequality line, starts with an open circle on the left at x = 2, which is equivalent to less than or equal to symbol, ≤ as 2 ≤ x because the point x =2 is the left boundary. The inequality line extends to the right to reach point x = 5, where we have a closed circle (on the right), which is equivalent to a x ≤ 5 inequality, with the 5 on the right hand side because, the 5 is the right boundary of the inequality
2) The inequality can be summarized as starting from x = 2 extends to x = 5
3) As stated in point 1) the point x = 2, we have 2 ≤ x and at point x = 5, we have x ≤ 5 which can be combined as 2 ≤ x < 5, to give;
[ 5 if x ∈ 2 ≤ x < 5.
Answer:
1st box = [-4, -3]
2nd box = (-3, 2]
3rd box = (2, 5]
For f(x) = -2 we see that x is between -4 to -3 with closed endpoints.
So the interval will be [-4, -3].
For f(x) = -5 we see that x is between -3 to 2 with closed endpoint at 2 and open endpoints at -3.
So the interval will be (-3, 2].
For f(x) = 5 we see that x is between 2 to 5 with open endpoint at 2 and closed endpoint at 5.
So the interval will be (2, 5].
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One class contain 5 girls and 10 boys and a second class contain 13 boys and 12 girls. If a student is randomly picked from the second class and transferred to the first one. After that a student is randomly chosen from the first class. What is the probability that this student is a boy?
Answers
To solve this question, we need to consider the two steps: transferring a student from the second class to the first class, and then randomly choosing a student from the first class.
Let's calculate the probabilities step by step:
Step 1: Transferring a student from the second class to the first class
The probability of transferring a boy from the second class is the ratio of the number of boys in the second class (13 boys) to the total number of students in the second class (13 boys + 12 girls).
P(boy transferred) = 13 / (13 + 12) = 13 / 25
Step 2: Randomly choosing a student from the first class
After the transfer, the first class will have 10 boys and 11 girls. The probability of randomly choosing a boy from the first class is the ratio of the number of boys in the first class (10 boys) to the total number of students in the first class (10 boys + 11 girls).
P(boy chosen from first class) = 10 / (10 + 11) = 10 / 21
Now, to find the overall probability, we multiply the probabilities of the two steps:
P(boy chosen) = P(boy transferred) * P(boy chosen from first class) = (13/25) * (10/21)
Therefore, the probability that the student chosen from the first class is a boy is (13/25) * (10/21), which can be simplified or approximated as needed.
LaTeX code snippet for the answer:
The probability that the student chosen from the first class is a boy is
\($\left(\frac{13}{25}\right) \times \left(\frac{10}{21}\right)$.\)
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Build a deterministic FA M
3
for the following language L
3
=L(M
3
)={x over {a,b,c}∣x has strictly more than 3c symbols and does not end in c} For example, abcca ∈
/
L
3
and bacccc ∈
/
L
3
, but cccca ∈L
3
and acbcaaabcccb ∈L
3
.
Answers
The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.
To build a deterministic finite automaton (DFA) for the language L3 = {x ∈ {a, b, c}* | x has strictly more than 3 'c' symbols and does not end in 'c'}, we can design the following DFA M3:1. Start with an initial state q0.
2. Create a loop on q0 for 'a', 'b', and 'c' inputs, leading back to q0.
3. From q0, transition to a state q1 on input 'c'. This represents the first 'c' encountered.
4. From q1, create a loop for 'a' and 'b' inputs, leading back to q1.
5. Transition from q1 to q2 on input 'c'. This represents the second 'c' encountered.
6. Similarly, create a loop on q2 for 'a' and 'b' inputs, leading back to q2.
7. Transition from q2 to q3 on input 'c'. This represents the third 'c' encountered.
8. From q3, create a loop for 'a', 'b', and 'c' inputs, leading back to q3.
9. Create a final accepting state q4 and transition from q3 to q4 on 'a' or 'b' inputs.
In this DFA, any string that ends with 'c' or has less than three 'c' symbols will not reach the accepting state q4, hence not belonging to L3.
Therefore, The deterministic finite automaton (DFA) M3 for the language L3, where strings have more than 3 'c' symbols and do not end in 'c', is designed with states q0, q1, q2, q3, and q4. Transitions and loops are created to determine acceptance.
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