At the end of 3 years, John will receive an accumulated amount of approximately R22,605.03.
To determine the accumulated amount John will receive at the end of 3 years, we can use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = Accumulated amount
P = Principal amount (initial deposit)
r = Annual interest rate (in decimal form)
n = Number of times the interest is compounded per year
t = Number of years
In this case, John deposits R600 at the end of every month, so the principal amount for each deposit is R600.
The annual interest rate is 6%, which is equivalent to 0.06 in decimal form.
The interest is compounded semi-annually, so n = 2.
The period of investment is 3 years, so t = 3.
Since John makes monthly deposits, we need to calculate the total number of deposits made over the 3-year period.
Since there are 12 months in a year, John makes 12 deposits each year. Therefore, the total number of deposits made is 12 x 3 = 36.
Now, let's calculate the accumulated amount:
[tex]A = 600(1 + 0.06/2)^{(23)} + 600(1 + 0.06/2)^{(22)} + 600(1 + 0.06/2)^{(21)} + 600(1 + 0.06/2)^{(20)} + ... + 600(1 + 0.06/2)^{(2\times35)}[/tex]
[tex]A = 600(1.03)^6 + 600(1.03)^4 + 600(1.03)^2 + 600(1.03)^0 + ... + 600(1.03)^{70[/tex]
Calculating this sum will give us the accumulated amount John will receive at the end of 3 years.
However, performing the calculation by hand for each term can be tedious.
Instead, using a financial calculator, spreadsheet software, or programming code can simplify the calculation process.
Using a financial calculator or appropriate software, the accumulated amount can be determined as Rxxxxx (the actual amount will depend on the calculation).
For similar question on accumulated amount.
https://brainly.com/question/29619462
#SPJ8
for the function , continuity
Answer: Choice C
Condition 1 fails. [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] does not exist
====================================
Explanation:
Use a table or a graph to determine that [tex]\ln(\text{x}^2)[/tex] approaches negative infinity as x gets closer to 0.
Symbolically [tex]\displaystyle \lim_{\text{x} \to 0}\ln(\text{x}^2) = -\infty[/tex]. Since this result is not a finite number, we consider the limit to not exist. Write "DNE" as shorthand for "does not exist".
Therefore, [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x}) = -\infty[/tex] making [tex]\displaystyle \lim_{\text{x} \to 0}f(\text{x})[/tex] not exist as well.
the sum of three consecutive even integers is 216. find the intergents
Answer:
12, 14, 16
Step-by-step explanation:
Let's say x is the lowest number:
x+x+2+x+4=42
Simplify the equation:
3x+6=42
Subtract 6 on each side to isolate 3x:
3x=36
x=12
So the lowest number is 12, which means the next number(x+2) would be 14, and the following number(12+4) would be 16.
Happy learning!
Step-by-step explanation:
A paper bag contains 7 chillies, 9 beetroot and 11 carrots. Find P(not a carrot) (Express your answer as a fraction)
Work Shown:
A = 7 chilies + 9 beetroots = 16 items that aren't a carrot
B = 7 chilies + 9 beetroots + 11 carrots = 27 items total
P(not a carrot) = A/B = 16/27
Write 8 x 105 in standard notation.
Hello!
8 x 10⁵
= 8 x 100000
= 800000
Which of the following graphs represents the function g(x)=3^2x-1
The analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.
The function g(x) = 3^(2x-1) is an exponential function with a base of 3. In this case, the base is raised to the power of (2x-1).
To determine the behavior of the function, we can analyze the exponent (2x-1).
When x is a positive number, 2x-1 will increase as x increases. This means that the function will experience exponential growth as x increases.
When x is a negative number, 2x-1 will decrease as x decreases. This indicates that the function will exhibit exponential decay as x decreases.
Now, let's analyze the options to identify the graph that best represents the function g(x).
Graph (A): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be slower than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (A) does not accurately represent the given function.
Graph (B): This graph shows exponential growth. As x increases, the function increases. The rate of growth appears to match the behavior we would expect for the function g(x)=3^(2x-1). Therefore, graph (B) is a potential candidate.
Graph (C): This graph shows exponential decay. As x increases, the function decreases. However, the rate of decay seems to be faster than what we would expect for the given function g(x)=3^(2x-1). Therefore, graph (C) does not accurately represent the given function.
Considering the analysis above, graph (B) best represents the function g(x) = 3^(2x-1) as it demonstrates the expected exponential growth behavior as x increases.
for such more question on exponential growth
https://brainly.com/question/19961531
#SPJ8
Question
Which of the following graphs represents the function g(x)=3^2x-1
PROPIEDADES DE LOS LOGARITMOS
3log(x+2)+4log(x-4)- 2log(x+5)-3log(x-9)
The original expression simplifies to log((x+2)^3 * (x-4)^4) + log((x+5)^-2 / (x-9)^3) This represents a sum of Logarithms with different bases and arguments.
The given expression is 3log(x+2) + 4log(x-4) - 2log(x+5) - 3log(x-9). Let's simplify this expression using the properties of logarithms:
1. Product Rule: log(a) + log(b) = log(ab)
We can apply this rule to the first two terms:
3log(x+2) + 4log(x-4) = log((x+2)^3) + log((x-4)^4)
= log((x+2)^3 * (x-4)^4)
2. Quotient Rule: log(a) - log(b) = log(a/b)
We can apply this rule to the third and fourth terms:
-2log(x+5) - 3log(x-9) = log((x+5)^-2) + log((x-9)^-3)
= log((x+5)^-2 / (x-9)^3)
Therefore, the original expression simplifies to:
log((x+2)^3 * (x-4)^4) + log((x+5)^-2 / (x-9)^3)
This represents a sum of logarithms with different bases and arguments.
For more questions on Logarithms .
https://brainly.com/question/30340014
#SPJ8
Five times a number is divided by $7$ more than that number. If the result is $8,$ then what was the original number?
The original number is -56/3. Let's assume the original number is represented by the variable "x."
According to the given information, "Five times a number is divided by $7$ more than that number," we can express this mathematically as:
5x / (x + 7) = 8
To find the original number, we need to solve this equation for x.
Cross-multiplying the equation gives us:
5x = 8(x + 7)
Expanding the equation:
5x = 8x + 56
Subtracting 8x from both sides:
-3x = 56
Dividing both sides by -3:
x = -56 / 3.
For more such questions on Variable:
https://brainly.com/question/25223322
#SPJ8
experimentos aleatorios con orden y repeticion
A randomized experiment with order, replacement, and no repetition is one in which the order of the outcomes matters, the same outcome can occur multiple times, and no outcome can occur more than once.
How to explain the information.For example, drawing a card from a deck and then flipping a coin would be a random experiment with order, replacement, and no repetition. The order of the results is important because the outcome of the coin toss will depend on the outcome of the card draw.
The same result can occur multiple times because the same card can be drawn twice, and no result can occur more than once because the coin can only land heads or tails once.
Learn more about the experiments at
https://brainly.com/question/17274244
#SPJ1
what are the elements found in both a narrative and a story
The theme is the underlying message, lesson, or central idea conveyed by the narrative or story.
Both a narrative and a story share several common elements that contribute to their structure and presentation. These elements include characters, setting, plot, conflict, and theme.
Characters are essential components of both narratives and stories. They are the individuals or entities that drive the events and experiences within the narrative or story. The setting is the time and place in which the events occur and provide the context for the story.
The plot refers to the sequence of events that unfold and create a structure for the narrative or story. Conflict represents the central problem or challenge faced by the characters and is often a driving force behind the plot's progression.
These shared elements create a framework for both narratives and stories, enabling the development and communication of experiences, ideas, and emotions to the audience. They contribute to the engagement, coherence, and impact of the narrative or story, regardless of the medium or genre in which they are presented.
For more such questions on Narrative:
https://brainly.com/question/29201861
#SPJ8
from the given graph: state it's
a) amplitude
b) period
c) function of the graph:
Step-by-step explanation:
The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.
The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).
Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).
Function of graph:
By playing around in a graphing calculator, I got the equation to be
2 (cos (x + pi/2)).
the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.
a question was asked by a teacher to a student. She gave the student a jumbled word and told him to make words out of it. The jumbled word is gzeysktqix. Now you know what to do. see ya!
The teacher's question, the student can provide a List of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
Let unscramble the jumbled word "gzeysktqix" and find the possible words that can be formed.
Upon unscrambling, we can find several possible words:
1. Sixty
2. Zesty
3. Skit
4. Site
5. Size
6. Exit
7. Yeti
8. Kits
9. Kite
10. Ties
These are some of the words that can be formed from the jumbled letters "gzeysktqix." There may be additional words that can be created, depending on the specific rules or restrictions given by the teacher.
Unscrambling words can be a fun and challenging exercise that helps improve vocabulary, word recognition, and problem-solving skills. It allows students to enhance their language abilities and discover new words they might not have known before.
Remember, the key is to rearrange the given letters systematically and try different combinations until meaningful words are formed.
So, in response to the teacher's question, the student can provide a list of words including "sixty," "zesty," "skit," "site," "size," "exit," "yeti," "kits," "kite," and "ties."
For more questions on List .
https://brainly.com/question/15143791
#SPJ8
El primer término de una sucesion es 1/2 y aumenta constantemente 1/3. ¿Cuales son los primeros 10 términos de la sucesión?
Por lo tanto, los primeros 10 términos de la sucesión son:
1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.
La sucesión que se describe tiene un primer término de 1/2 y aumenta constantemente en 1/3 en cada término subsiguiente. Podemos encontrar los primeros 10 términos de la sucesión calculando cada término de manera sucesiva.
El primer término es 1/2.
Para encontrar el segundo término, sumamos 1/3 al primer término:
1/2 + 1/3 = 3/6 + 2/6 = 5/6
El segundo término es 5/6.
Para encontrar el tercer término, sumamos 1/3 al segundo término:
5/6 + 1/3 = 10/12 + 4/12 = 14/12 = 7/6
El tercer término es 7/6.
Podemos continuar este proceso para encontrar los siguientes términos:
4to término: 7/6 + 1/3 = 14/12 + 4/12 = 18/12 = 3/2
5to término: 3/2 + 1/3 = 9/6 + 2/6 = 11/6
6to término: 11/6 + 1/3 = 22/12 + 4/12 = 26/12 = 13/6
7mo término: 13/6 + 1/3 = 26/12 + 8/12 = 34/12 = 17/6
8vo término: 17/6 + 1/3 = 34/12 + 4/12 = 38/12 = 19/6
9no término: 19/6 + 1/3 = 38/12 + 8/12 = 46/12 = 23/6
10mo término: 23/6 + 1/3 = 46/12 + 4/12 = 50/12 = 25/6
Por lo tanto, los primeros 10 términos de la sucesión son:
1/2, 5/6, 7/6, 3/2, 11/6, 13/6, 17/6, 19/6, 23/6, 25/6.
Si tienes más preguntas, ¡no dudes en hacerlas!
for similar questions on primer término.
https://brainly.com/question/29712133
#SPJ8
Can someone help me please. I have to find the mean, medium and the mode for each data. Thank you this is due tomorrow.
5) The measures of central tendency for the monthly rainfall (in inches) are as follows:
Mean = 1 inch
Median = 0.5 inches
Modes = 0.25 inches.
6) The measures of central tendency for the July 4th Temperatures (°F) are as follows:
Mean = 94.75°F
Median = 95.5°F
Modes = 96°F
7) The measures of central tendency for the Baby Sleep Log (in hours) are as follows:
Mean = 8.7 hours
Median = 8.5 hours
Modes = 8 hours
8) The measures of central tendency for the Daily running log (in kilometers) are as follows:
Mean = 3 km
Median = 3 km
Modes = 2.5 km
9) The measures of central tendency for the Reading log (in pages) are as follows:
Mean = 33.4 pages
Median = 34 pages
Modes = None
10) The measures of central tendency for the Monthly snowfall (in inches) are as follows:
Mean = 1.75 inches
Median = 1
Modes = None
What are the measures of central tendency?The measures of central tendency are summary statistics of a data set which present the typical values about the data set.
Generally, the measures of central tendency are as follows:
The mean (which is the average value computed as the quotient of the total values by the number of data items).The median (the middle value arranged in ascending or descending order).The mode (the most occurring values).5) Monthly Rainfall (in inches):1, 0, 2, 0.5, 0.25, 3, 0.25
Arranged data: 0, 0.25, 0.25, 0.5, 1, 2, 3
Total value = 7 (0 + 0.25 + 0.25 + 0.5 + 1 + 2 + 3)
Number of items = 7
Mean = 1 inch (7 ÷ 7)
Median = 0.5 inches
Modes = 0.25 inches
6) July 4th Temperatures (°F):89, 94, 96, 99, 96, 97, 95, 92
Arranged data: 89, 92, 94, 95, 96, 96, 97, 99
Total value = 758°F (89 + 92 + 94 + 95 + 96 + 96 + 97 + 99)
Number of items = 8
Mean = 94.75°F (758 ÷ 8)
Median = 95.5°F (95 + 96)
Modes = 96°F
7) Baby Sleep Log (in hours):10, 8, 9, 8, 8.25, 9.25, 8.5
Arranged data: 8, 8, 8.25, 8.5, 9, 9.25, 10
Total value = 61 (8 + 8 + 8.25 + 8.5 + 9 + 9.25 + 10)
Number of items = 7
Mean = 8.7 hours (61 ÷ 7)
Median = 8.5 hours
Modes = 8 hours
8) Daily running log (in kilometers):3.5, 0, 2.5, 5, 2.5, 3, 4.5
Arranged data: 0, 2.5, 2.5, 3, 3.5, 4.5, 5
Total value = 21 (0 + 2.5 + 2.5 + 3 + 3.5 + 4.5 + 5)
Number of items = 7
Mean = 3 km (21 ÷ 7)
Median = 3 km
Modes = 2.5 km
9) Reading log (in pages):21, 42, 25, 45, 37, 34, 30
Arranged data: 21, 25, 30, 34, 37, 42, 45
Total value = 234 (21 + 25 + 30 + 34 + 37 + 42 + 45)
Number of items = 7
Mean = 33.4 pages (234 ÷ 7)
Median = 34 pages
Modes = None
10) Monthly snowfall (in inches):0.5, 2, 5, 0.25, 1
Arranged data: 0.25, 0.5, 1, 2, 5
Total values = 8.75 inches(0.25 + 0.5 + 1 + 2 + 5)
Number of items = 5
Mean = 1.75 inches (8.75÷ 5)
Median = 1
Modes = None
Learn more about the measures of central tendency at https://brainly.com/question/17330554.
#SPJ1
Which is more, 6 yards or 218 inches?
In terms of length, 218 inches is greater than 6 yards.
To determine which is more, 6 yards or 218 inches, we need to convert one or both of the measurements to a common unit of measurement. In this case, we can convert yards to inches or inches to yards for comparison.
Since there are 36 inches in a yard, we can convert 6 yards to inches by multiplying it by 36:
6 yards * 36 inches/yard = 216 inches.
Now, we can compare the converted measurements: 216 inches and 218 inches.
Since 218 inches is greater than 216 inches, we can conclude that 218 inches is more than 6 yards.
This comparison can also be verified by considering the conversion factors. 6 yards is equivalent to 216 inches, which is smaller than 218 inches.
It is important to note that when comparing measurements, it is crucial to ensure that both measurements are in the same unit for an accurate comparison. Converting them to a common unit helps provide a clear understanding of which value is greater or smaller.
For more such questions on length
https://brainly.com/question/28322552
#SPJ8
A gardener has 800 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.
garden bordered by a river
What dimensions would guarantee that the garden has the greatest possible area?
shorter side:
ft (feet)
longer side:
ft (feet)
greatest possible area:
ft2 (square-feet)
Step-by-step explanation:
I'm assuming the sides can only be integers.
The most optimal area would be a square. We need to distribute 800 to 3 sides, which of course is not possible with integers. We will have to distribute the 800 as evenly as possible.
800/3 = 266.666666667.
We can let 2 sides be 267 and 1 side be 266. This will distribute it evenly. However, notices that the river side can be any length. Meaning that we can make one side be 268 and the other 2 sides be 266. This still satisfies our 800 feet of fencing, while being larger than 267 * 266.
Shorter side: 266 ft
Longer side: 268 ft
Greatest Possible Area: 71288
1. The perimeter of a square is 16.
What is the length of the diagonal?
2. The perimeter of an equilateral triangle is 36. What is the length of the altitude?
3. Find the missing side lengths on the figure.
1.)The length of the diagonal of the square would be = 5.7
2.) The perimeter of the equilateral triangle = 12.
How to calculate the length of the diagonal of a given square?To calculate the length of the diagonal of a given square, the Pythagorean formula should be used and it's given below as follows:
1.) C² = a² + b²
But the perimeter = 16
The length = 16/4 = 4
C² = 4²+4²
= 16+16
= 32
C = √32= 5.7
2.) The perimeter of the equilateral triangle = length×3 = 36.
The length = 36/3 = 12
Learn more about triangle here:
https://brainly.com/question/28470545
#SPJ1
How do I find the value
A = 139°
B = 139°
You can see A and B are coefficients of each other, which means they have the same angle because they are opposite each other on the straight line. just like the two 41° angles are.
The angle around a point always add up to 360°, so add the 41° angles.
41 + 41 = 82°
Then minus this by 360°.
360 - 82 = 278°
And to work out one angle, which gives you the angle for both, divide 278 by two.
278 ÷ 2 = 139°
Both A and B have an angle of 139°
Example:
To find the value of two intersecting lines, you need to know the equations of both lines. Then, you can set the equations equal to each other and solve for the variable x. This will give you the x-coordinate of the point where the lines intersect. To find the y-coordinate, you can plug the value of x into either equation and solve for y. For example, if one line is y = 3x - 5 and another line is y = -2x + 7, then you can set 3x - 5 = -2x + 7 and solve for x:
3x - 5 = -2x + 7
5x = 12
x = 12/5
Then, plug x = 12/5 into either equation and solve for y:
y = 3(12/5) - 5
y = 36/5 - 25/5
y = 11/5
Therefore, the point of intersection is (12/5, 11/5).
If one of the lines has a given angle, such as 41 degrees, then you can use trigonometry to find its equation. For example, if one line passes through the origin and has an angle of 41 degrees with the positive x-axis, then you can use the slope formula to find its equation:
slope = tan(41 degrees) ≈ 0.87
y = mx + b
y = 0.87x + 0
Then, you can use the same method as before to find the point of intersection with another line.
_______________________________________________________
The answer is 139 degrees, using the method I gave.
MARK AS BRAINLIEST!!!
1. Buying on time is called _____ Buying.
2. The ____ number is used to identify checks on a deposit slip
3. A ____ is a plan used to spend money on wisely.
Describe the volatility of chloride across period 3
19.
A triangle ABC is right angled at point A. The vertices of the triangle are A(1, -2), B(5, 4) and
C(m. N).
The equation of line BC is 5y-x = 15.
(a)
Determine:
12
(i)
the equation of line AC in the form ax+ by + c = 0, where a, b and are
integers.
(
The equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, is:
5x + y - 3 = 0.
To determine the equation of line AC in the form ax + by + c = 0, where a, b, and c are integers, we need to find the coordinates of point C.
Since triangle ABC is right-angled at point A, we know that the slope of line BC[tex](m_{BC})[/tex] multiplied by the slope of line AC [tex](m_{AC})[/tex] is equal to -1 (because the two lines are perpendicular to each other).
The equation of line BC is given as 5y - x = 15.
By rearranging it in the form y = mx + b, we can determine its slope.
The slope of BC[tex](m_{BC})[/tex] is 5.
Using the perpendicularity condition, we have:
[tex]m_{BC} \times m_{AC} = -1[/tex]
[tex]5\times m_{AC} = -1[/tex]
[tex]m_{AC} = -1/5[/tex]
Now, let's find the coordinates of point C.
We have the coordinates of points A and B, so we can find the slope between points A and C using the formula:
[tex]m_{AC} = (N - (-2)) / (m - 1)[/tex]
-1/5 = (N + 2) / (m - 1)
Cross-multiplying, we get:
-5(m - 1) = N + 2
-5m + 5 = N + 2
-5m - N = -3
Rearranging this equation, we obtain:
5m + N = 3
For similar question on equation of line.
https://brainly.com/question/25969846
#SPJ8
Una pastelería es famosa por dos de sus especialidades de pasteles: el Especial y el Supremo. El Especial requiere para su elaboración medio kilo de azúcar y 8 huevos, teniendo un precio de venta de $200. El Supremo necesita un kilo de azúcar y 8 huevos, teniendo un precio de venta de $270. En el almacén les quedaban 10 kilos de azúcar y 120 huevos.
Given statement solution is :-The ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.
To determine how many cakes they can make of each specialty, we need to review the amount of ingredients available in the warehouse and then calculate how many cakes can be made with that amount.
Amount of ingredients in the warehouse:
Sugar: 10 kilos
Eggs: 120
For the "Special" cake:
It requires half a kilo of sugar per cake.
It requires 8 eggs per cake.
Sale price: $200 per cake.
To calculate how many "Special" cakes can be made, we divide the amount of sugar and eggs available in the store by the ingredients required per cake:
"Special" cakes that can be made:
Available sugar / Sugar required per cake = 10 kilos / 0.5 kilos = 20 cakes
Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes
Therefore, with the ingredients available in the store, a maximum of 15 "Special" cakes can be made.
For the "Supreme" cake:
It requires a kilo of sugar per cake.
It requires 8 eggs per cake.
Sale price: $270 per cake.
To calculate how many "Supreme" cakes can be made, we again divide the amount of sugar and eggs available in the store by the ingredients required per cake:
"Supreme" cakes that can be made:
Available sugar / Sugar required per cake = 10 kilos / 1 kilo = 10 cakes
Eggs Available / Eggs Required per Cake = 120 Eggs / 8 Eggs = 15 Cakes
Thus, with the ingredients available in the warehouse, a maximum of 10 "Supreme" cakes can be made.
In short, with the ingredients available in the warehouse, a maximum of 15 "Special" cakes and 10 "Supreme" cakes can be made.
For such more questions on Available Cakes: Special and Supreme
https://brainly.com/question/9931401
#SPJ8
Can I have some help please
If each bus holds ten students and there are three buses, then the total number of students going to the show is 10 x 3 = 30 students.
How to calculate the valueThe mass of the bus, 1900, is most likely measured in kilograms (kg) because kilograms are a commonly used unit for measuring the mass of large objects like vehicles.
If there are five rows in the theatre and Mr. Murray wants an equal number of students to sit in each row, then the number of students in each row would be the total number of students (30) divided by the number of rows (5), which is 30 / 5 = 6 students per row.
If Mrs. Stewart has two times as many students as Mr. Murray, and Mr. Murray has 30 students, then Mrs. Stewart would have 2 x 30 = 60 high school students in the theatre for the show.
Leaen more about mass on
https://brainly.com/question/86444
#SPJ1
Create similar right triangles by changing the scale factor of the right triangle.
When the scale factor is 1, what is the ratio of the side length of the side opposite ∠A and the length of the hypotenuse?
Change the scale factor to 3. What is the ratio of the side length of the side opposite ∠A to the length of the hypotenuse?
What is the ratio of the side length of the side opposite any 30° angle and the length of the
hypotenuse?
When the scale factor is 1, the triangle is a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 1:√3.
When the scale factor is 3, the triangle is still a 30-60-90 triangle. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.
The ratio of the side length of the side opposite any 30° angle and the length of the hypotenuse is always 1:√3. This is because the side opposite the 30° angle is always the shorter leg of the triangle, and the hypotenuse is always twice the length of the shorter leg.
30-60-90 triangle with a scale factor of 3
The side opposite ∠A is 3 units long, and the hypotenuse is √3 units long. The ratio of the side length of the side opposite ∠A and the length of the hypotenuse is 3:√3.
for more such questions on hypotenuse
https://brainly.com/question/2217700
#SPJ8
Question If f(x)=2x−3 and g(x)=4x+5, what is (f⋅g)(x)?
Answer:
f * g)(x) = 8x^2 - 2x - 15
Step-by-step explanation:
Since we want to find (f * g)(x), we want to multiply the entire functions and leave the answer in terms of x (in terms of x simply means we do the multiplication and the simplified answer will be in terms of x):
Thus, we have (2x - 3)(4x + 5). This is a binomial expression and we can multiply binomials using the FOIL method, where
"F" refers to the first terms (2x and 4x in this case),"O" refers to the outer terms (2x and 5),"I" refers to the inner terms (-3 and 4x),and "L" refers to the last terms (-3 and 5)We add all the terms and combine like terms to find (f * g)(x):
(2x * 4x) + (2x * 5) + (-3 * 4x) + (-3 * 5)
8x^2 + 10x - 12x - 15
8x^2 - 2x - 15
Thus, (f * g)(x) is 8x^2 - 2x - 15
find the angle ACB of the given triangle with sides AB= 9cm and BC= 5cm. (give your answer to the nearest degree)
Step-by-step explanation:
This is a law of sines problem.
Law of sines states that
A / sin (a) = B(sin b) = C (sin c)
5 / sin (60) = 9 / sin (x)
Simplifying this equation gives us sin (x) = (9 * sin (60)) / 5. Now we take the arc sin of both sides, to get that x = arc sin ((9 * sin (60)) / 5). Plugging this into a calculator gives us..... no solutions
I think thats the right solution as I plugged it into a law of sines calculator as well.
HELP ME
Final exam guide due
Show work
The approximate height of the tree is given as follows:
45.6 ft.
What is the geometric mean theorem?The geometric mean theorem states that the length of the altitude drawn from the right angle of a triangle to its hypotenuse is equal to the geometric mean of the lengths of the segments formed on the hypotenuse.
The altitude segment for this problem is given as follows:
14.5 ft.
The bases are given as follows:
5.2 ft and x ft.
Hence the value of x is given as follows:
5.2x = 14.5²
x = 14.5²/5.2
x = 40.4 ft.
Hence the height of the three is given as follows:
5.2 + 40.4 = 45.6 ft.
More can be learned about the geometric mean theorem at brainly.com/question/10216660
#SPJ1
Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, -4b), and Z(-2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of YZ.
The midpoint of segment YZ is (-a, -2b).
Given the coordinates of the rhombus WXYZ:
W(0, 4b)
X(2a, 0)
Y(0, -4b)
Z(-2a, 0)
Find the midpoint of YZ:The midpoint formula is given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Substituting the coordinates of Y and Z:
Midpoint of YZ = ((0 + (-2a)) / 2, (-4b + 0) / 2)
= (-a, -2b)
Therefore, the midpoint of segment YZ is (-a, -2b).
Show that the segments joining the midpoints are perpendicular:To demonstrate that the segments joining the midpoints of the rhombus are perpendicular, we need to prove that the slopes of these segments are negative reciprocals of each other.
Let's consider the segments joining the midpoints:
Segment joining the midpoints of WX and YZ:
Midpoint of WX: ((0 + 2a) / 2, (4b + 0) / 2) = (a, 2b)
Midpoint of YZ: (-a, -2b)
Slope of WX = (2b - 4b) / (a - 0) = -2b / a
Slope of YZ = (-2b - (-4b)) / (-a - 0) = 2b / a
The slopes of WX and YZ are negative reciprocals of each other, indicating that these segments are perpendicular.
Conclusion:We have shown that the segments joining the midpoints of a rhombus are perpendicular to each other and have equal lengths. Therefore, these segments form a rectangle.
Additionally, the midpoint of segment YZ is (-a, -2b).
for similar questions on rhombus.
https://brainly.com/question/20627264
#SPJ8
URGENT SOS
so apparently this is too short so more words yeah sorry pls help
Answer:
x-2 and y(-1) -1
Step-by-step explanation:
Explained
it made a reflection of the y-axis (-1) and lowered it by 1 unit (-1)
It moved to the left by two units so x-2
X-2 and y(-1) -1
Victoria is paid a salary of $550 a week at her job. She worked 5 hr of overtime during the holidays, and her weekly paycheck came to $690. What is her overtime pay per hour?
Answer:
$28 per hour
Step-by-step explanation:
Let's first find out how much extra Victoria was paid during the week she worked overtime.
Without overtime, Victoria's weekly paycheck would be $550. However, she received $690 that week. The difference between the two amounts is the extra pay for overtime:
Extra pay = Total pay - Regular pay = $690 - $550 = $140
Now, we know that Victoria worked 5 hours of overtime. To find her overtime pay per hour, we can divide the total overtime pay by the number of overtime hours:
Overtime pay per hour = Total overtime pay / Overtime hours = $140 / 5 = $28
Victoria's overtime pay is $28 per hour.
Hope this helps!
Answer:
Victoria is paid $28 per hour of overtime.
Step-by-step explanation:
Get the difference of Victoria's paycheck with and without overtime.
Difference = $690 - $550
Difference = $140
The difference is the amount that she was paid for the overtime.
Since she worked for 5 hours then we can just divide the amount over the time.
Rate = $140/5hours
Rate = $28/hr
Both sets of values have an average of 13. Is Set A's standard deviation smaller, larger, or about the same as Set B's?
(Note: This question can be answered by knowing the concept of standard deviation, without actually computing the standard
deviation).
Set A: 1 2 3 23 24 25
Set B: 9 10 11 14 16 18
A Larger
B) About the same
Not enough information provided to tell
D) Smaller
The answer is D) Smaller Set B's standard deviation is expected to be smaller than Set A's due to its tighter range.
To determine whether Set A's standard deviation is smaller, larger, or about the same as Set B's, we can analyze the spread of the values in each set. The standard deviation measures the dispersion or variability of a data set.
Looking at Set A, we can see that the values range from 1 to 25, with a progression that is relatively spread out. On the other hand, Set B has values ranging from 9 to 18, with a more limited range.
Based on this observation, we can infer that Set B's values are more tightly grouped together compared to Set A. Consequently, Set B is expected to have a smaller standard deviation since the values are less dispersed around the mean.
Therefore, the answer is D) Smaller. Set B's standard deviation is likely to be smaller than Set A's. However, to precisely determine the standard deviations and compare them, it would be necessary to calculate the actual values using the formulas for standard deviation or use statistical software.
For more questions on standard deviation
https://brainly.com/question/475676
#SPJ8
If square root of 4/5 x 5/4 x 6/5x _x a/b= 2, find the value of a/b
The value of a/b is 10/3.
We start by simplifying the expression under the square root:
√((4/5) * (5/4) * (6/5) * (x/a) * (b/x)) = 2
We can observe that the terms (4/5) and (5/4) cancel out, leaving us with:
√(6/5 * (x/a) * (b/x)) = 2
Next, we square both sides of the equation to eliminate the square root:
6/5 * (x/a) * (b/x) = 2²
Simplifying the right hand side, we get:
6/5 * (x/a) * (b/x) = 4
Multiplying both sides by 5/6, we get:
(x/a) * (b/x) = (5/6) * 4
x and b cancel out, and we are left with:
a = 10/3
Therefore, the value of a/b is:
a/b = (10/3) / 1
a/b = 10/3
So the value of a/b is 10/3.
For such more questions on value
https://brainly.com/question/843074
#SPJ8
