The side lengths for each triangle are as follows. Triangle L ≈ 4.0337, 7.9663, and 12Triangle R ≈ 7.9556, 12.0444, and 20Triangle Z ≈ 6.0452, 9.9548, and 16. We have given that all three triangles are similar, so all three have the same angle measures. Let us first consider triangle L.
Given: Three right triangles are similar with acute angles LL, LR, and ZZ, all approximately measured to be 66.9°. We have to find the side lengths for each triangle.
Solution: We have given that all three triangles are similar, so all three have the same angle measures. Let us first consider triangle L.
Triangle L: In right triangle L, the hypotenuse is given as 12 and one acute angle is given as 66.9°. Let the length of the leg opposite 66.9° angle in triangle L be x. Thus, the length of the other leg is 12-x, since the length of the hypotenuse is 12. Using trigonometric ratios in right triangle L, we get:
tan 66.9° = opposite/hypotenuse=> tan 66.9° = x/(12-x)=> x = (12)(tan 66.9°) / (1 + tan 66.9°)≈ 4.0337
Hence, the lengths of the sides in triangle L are approximately 4.0337, 7.9663 (12-4.0337), and 12.
Triangle R: In right triangle R, the hypotenuse is given as 20 and one acute angle is given as 66.9°. Let the length of the leg opposite 66.9° angle in triangle R be y. Thus, the length of the other leg is 20-y, since the length of the hypotenuse is 20. Using trigonometric ratios in right triangle R, we get:
tan 66.9° = opposite/hypotenuse=> tan 66.9° = y/(20-y)=> y = (20)(tan 66.9°) / (1 + tan 66.9°)≈ 7.9556
Hence, the lengths of the sides in triangle R are approximately 7.9556, 12.0444 (20-7.9556), and 20.
Triangle Z: In right triangle Z, the hypotenuse is given as 16 and one acute angle is given as 66.9°. Let the length of the leg opposite 66.9° angle in triangle Z be z. Thus, the length of the other leg is 16-z, since the length of the hypotenuse is 16.Using trigonometric ratios in right triangle Z, we get:
tan 66.9° = opposite/hypotenuse=> tan 66.9° = z/(16-z)=> z = (16)(tan 66.9°) / (1 + tan 66.9°)≈ 6.0452
Hence, the lengths of the sides in triangle Z are approximately 6.0452, 9.9548 (16-6.0452), and 16.
Answer: So, the side lengths for each triangle are as follows. Triangle L ≈ 4.0337, 7.9663, and 12Triangle R ≈ 7.9556, 12.0444, and 20Triangle Z ≈ 6.0452, 9.9548, and 16.
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the north equity fund has a beta of 1.67 and a standard deviation of 22.6%. it has returned 13.8% during the past year when the return on one-year treasury bills has been 3.6%. the sharpe ratio of the north equity fund is closest to: 0.45. 0.61. 6.11. 8.26.
It has returned 13.8% during the past year when the return on one-year treasury bills has been 3.6%. The Sharpe ratio of the North Equity Fund is closest to 0.45.
The Sharpe ratio is a measure of risk-adjusted return and helps investors assess the return they receive for each unit of risk taken. In this case, the North Equity Fund has a beta of 1.67, indicating that it is more volatile than the overall market. The standard deviation of 22.6% also highlights the fund's volatility.
Despite this, the fund has delivered a return of 13.8% over the past year, outperforming the return on one-year Treasury bills, which was 3.6%. The Sharpe ratio, calculated by subtracting the risk-free rate (T-bills return) from the fund's return and dividing it by the fund's standard deviation, yields a value closest to 0.45.
The Sharpe ratio is calculated by subtracting the risk-free rate (in this case, the return on one-year Treasury bills) from the fund's return and dividing it by the fund's standard deviation. In this scenario, the North Equity Fund's return is 13.8% minus the risk-free rate of 3.6%, resulting in a risk premium of 10.2%.
Dividing this risk premium by the fund's standard deviation of 22.6% gives us a Sharpe ratio of approximately 0.45. The Sharpe ratio measures the excess return per unit of risk, with a higher ratio indicating better risk-adjusted performance.
Therefore, the closest answer is 0.45, suggesting that the North Equity Fund provides a relatively modest risk-adjusted return.
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Susan has two coupons for a bicycle. Coupon A: 20% off of a $81 bicycle Coupon B: $19 rebate on a $81 bicycle Choose the coupon that gives the lower price. Then fill in the blank with the correct value.
The coupon that gives the lower price, based on the percentage discounts is Coupon B.
How to find the better coupon?To find the coupon that gives the lower price, apply the coupons to the price of the bicycle to see which value would be less after the coupon is applied.
Coupon A value after discount is:
= 81 x ( 1 - discount)
= 81 x ( 1 - 20%)
= $64.80
Coupon B value after discount is:
= 81 - 19
= $62
The coupon that gives the lower price is Coupon B.
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Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1. 5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0. 5, 6), crosses the x-axis at (negative 1. 5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1. 75, negative 3. 9) and a maximum value of (0, 2), crosses the x-axis at (negative 2. 2, 0), (negative 0. 75, 0), and (0. 75, 0), and crosses the y-axis at (0, 2)
The function that is positive for the entire interval [-3, -2] is:
The function has a minimum value of (0, -3) and crosses the x-axis at (-3, 0) and (3, 0). This means that the function is positive for the entire interval [-3, -2] because it is above the x-axis for this interval.
To further explain, a function is positive when its value is above the x-axis on a coordinate plane. In this case, the first function has a minimum value of (0, -3) which means that it is below the x-axis at this point. However, it crosses the x-axis at (-3, 0) and (3, 0), meaning that it is above the x-axis for the entire interval between these two points, including the interval [-3, -2].
The other functions are not positive for the entire interval [-3, -2] because they either have minimum values that are below the x-axis within this interval, or they cross the x-axis within this interval, meaning that they are not positive for the entire interval.
In conclusion, the function that is positive for the entire interval [-3, -2] is the first one because it is above the x-axis for this entire interval.
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Rosie bought a car for £4000. 3 years later, she sells it for £1400. What is the percentage loss that Rosie has made?
Answer:
65%
Step-by-step explanation:
Given data
Cost price= £4000
Selling price= £1400
% loss= cost price-selling price/cost*100
% loss= 4000-1400/4000*100
% loss= 2600/4000*100
% loss= 0.65*100
% loss= 65%
Hence the %loss is 65%
Consider a hash table using separate chaining with an array of size 10 and a hash function of key % 10. What would linked list at index 9 be after the following operations? For simplicity, we ignore the value. 1/SeparateChainingHashST SeparateChainingHashST st = new SeparateChainingHashST(); st.put(19,-); st.put(20,-); st.put(10,-); st.put(32,-); st.put(9,-); st.put(43, -); st.put(39, -); O 39,9,19 O 10.20 O null O 19,20,10,32,9,43,39
The linked list at index 9 would be: 39,9,19. This is because the hash function key % 10 would place the keys 19, 20, 10, 32, 9, 43, and 39 into the array indices 9, 0, 0, 2, 9, 3, and 9 respectively. Since all the keys at index 9 collide, they are placed in a linked list using separate chaining.
The order in which they were inserted is 19, 20, 10, 32, 9, 43, and 39. Therefore, the resulting linked list at index 9 would be 39,9,19.
Based on the given operations and the hash function key % 10, I'll explain the contents of the linked list at index 9 in the separate chaining hash table.
1. Create a new SeparateChainingHashST named st.
2. Perform the following put operations:
- st.put(19, -): 19 % 10 = 9, so 19 is added to the linked list at index 9.
- st.put(20, -): 20 % 10 = 0, so 20 is added to the linked list at index 0.
- st.put(10, -): 10 % 10 = 0, so 10 is added to the linked list at index 0.
- st.put(32, -): 32 % 10 = 2, so 32 is added to the linked list at index 2.
- st.put(9, -): 9 % 10 = 9, so 9 is added to the linked list at index 9.
- st.put(43, -): 43 % 10 = 3, so 43 is added to the linked list at index 3.
- st.put(39, -): 39 % 10 = 9, so 39 is added to the linked list at index 9.
After these operations, the linked list at index 9 contains the following elements (in the order they were added): 19, 9, 39.
Your answer: 19, 9, 39
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PLEASE HELP HURRY!!!!
Answer:
1) y=-2/3x+5
Step-by-step explanation:
Now I know that I didn't actually do the math for this one. I did see though that it needs to have the point (3,3) on the graph. So then I went to desmos graphing calculator, and I put all of them on the graph. The only one with a (3,3) point was number 1. I put it in the image below so you could see. I know that the rest aren't on there, that's because I removed them because they were in the way.
I hope this helps!!!
On an Idaho map, 1" represents 20 miles. If the distance on the map between two towns on the river measures 2 5/8" how many miles apart are the towns?
ANSWERS:
A. 42 1/2 miles
B. 45 miles
C. 47 5/8 miles
D. 52 1/2 miles
E. 40 miles
Answer: D
Step-by-step explanation:
20 x 2= 40
5/8 of 20 is 12.5
40+12.5= 52.5 or 52 1/2
Sorry I’m terrible at explaining
Write the decimal 5.666… as a mixed number in simplest form.
Answer:
5 2/3
Step-by-step explanation:
The decimal of .6 repeating is a common fraction that represents 2/3.
To write that in a mixed number is to put the whole number out front and the fraction afterward.
Answer:
The answer is 5 2/3
The graph of a quadratic function is shown.
What is the minimum value of the function?
4
-2
-8
-9
Answer:
- 9
Step-by-step explanation:
the minimum value is the y- coordinate of the vertex ( turning point )
coordinates of vertex = (1, - 9 )
then the minimum value is - 9
The function f(x) = -4.9x² + 17x + 0.6 describes the height in meters of a basketball x seconds after it has been thrown vertically into the air. Solve the following problem. If your answer is correct you will see an image appear on your screen. WHEN will the basketball reach its maximum height? Round your answer to 3 decimal places if necessary. Use your graph from screen 5 to help. Do not include units.
The basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
Define the term function?A function is a relationship between a set of inputs and a set of possible outputs with the property that each input is related to exactly one output. A function can be represented as an equation, a graph, a table of values, or a verbal description. For example, the function f(x) = 2x + 1 represents a relationship between the input x and the output 2x + 1.
To find the maximum height of the basketball, we need to find the vertex of the parabola represented by the function f(x). The vertex of x-coordinate is:
x = -b/2a
The coefficients of the quadratic equation a\(x^2\) + b\(x\) + c are a, b, and c. In this case, a = -4.9 and b = 17, so:
x = -17/(2*(-4.9)) = 1.735 (rounded to 3 decimal places)
Therefore, the basketball will reach its maximum height 1.735 seconds after it has been thrown vertically into the air.
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PLEASE HELP
I DONT UNDERSTAND
In the diagram below, DE AE, BA | CE, CB || D A and mZE = 54°. Find mZC.
Answer:
angle D should be equal to angle C
Step-by-step explanation:
i think this is the answer you need but i'm not sure
A gigameter is 1.0×10^6 kilometers. How many square kilometers are in 5 square gigameters?
Write your answer in scientific notation.
The number of kilometers in 5 square gigameters is 5. 0 × 10^18
What is proportion?Proportion can be described as an expression or equation in which two ratios are made equal to each other.
It is also known as the mathematical comparison between two numbers or elements.
From the information given, we have;
1 gigameter = 1.0×10^6 kilometers
But,
5 square gigameters = 5. 1.0×10^6 . 1.0×10^6
Add the powers
5 square gigameters = 5..0×10^12
If 1 gigameter = 1.0×10^6 kilometers
Then 5. 1.0×10^12 gigameter = x
cross multiply
x = 5.0×10^12 × 1.0×10^6
x = 5. 0 × 10^18 kilometers
Hence, the value is 5. 0 × 10^18 kilometers
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how to calculate 27 divided by 3
Answer:
Use a calculator it is 9
Step-by-step explanation:
*WILL GIVE BRAINLIEST FOR BEST ANSWER*
Find the missing angle in the triangle.
Question 1 options:
A. 90°
B. 25°
C. 108°
D. 130°
Answer:
90 degrees
Step-by-step explanation:
A triangle's degrees add up to 180. You are already given 2 of the. Let x be the 3rd angle. Here is the equation: 29+61+x=18. x=90.
Hope this helped!
Answer:
A.90°
Step-by-step explanation:
A triangle's interior angles are equal to 180°.
So since two angles are given all you need to do is add the given angles and subtract the sum from 180°.
61°+29°=90°
180°-90°=90°
The missing angle m<R is equal to 90°
Your answer is: A.90°
Hope this helps! :)
Directions - Convert each equation to slope intercept form.
A) 2x + 2y = 10
B) 12 + 4y = -44
Answer: y=-x+5 and y=-14 \(2x+2y=10 subtract 2x from both sides\\2x+2y-2x=10-2x \\2y=10-2x divide both sides by 2\\y=5-x rewriting using the commutative property\\y=-x+5\)
Step-by-step explanation:
Slope Intercept form is y=mx+b
Equation A:
Help me with this problem
Answer:
The slope is 8
Step-by-step explanation:
because the line is intercepting is the 8
Answer:
Slope is -6/6.5
Step-by-step explanation:
the points are (0,6) and (6.5,0)
m=(0-6)/(6.5-0)=-6/6.5
What does the number 58 represent in the following: t(58) = 2.001, p < .05?
a. Test statistic
b. t value
c. Degrees of freedom
d. Significance level
(a) 6+ (+2) (b) –4 + (-3) (e) -8 + (-2) (f) 6 - (+3) (c) 3 - (+2) (g) 9+ (+4) (d) -2-(-4) (h) -5-(-3)
how to solve these?
Answer:
a 8
b -7
c 1
d 2
e -10
f 3
g 13
h -2
Define convenience purchases, shopping purchases, and specialty purchases. Describe three specific brand name products in the consumer marketplace today that would correspond to these three types of purchases.
Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.
Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.
Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.
Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.
Three specific brand name products in the consumer marketplace that correspond to these types of purchases are
Convenience Purchase: Coca-Cola (Soft Drink)
Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.
With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.
Shopping Purchase: Apple iPhone (Smartphone)
The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.
The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.
Specialty Purchase: Rolex (Luxury Watches)
Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.
Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.
These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.
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Which of the following is a solution to the equation x^2 = -144?
A.) x=12
B.) x= -12
C.) x= -72
D.) this equation has no real solution
Answer: No real solutions
Step-by-step explanation: to solve for x and find a solution you need to take the square root of -144
This is not possible as this a negative number . There is a solution if we use complex numbers, but this not included in the question
convert 2 Bigha into kattha
Answer:
To convert 2 Bigha into Kattha:
If 1 Bigha = 20 Kattha:
2 Bigha = 2 * 20 Kattha = 40 Kattha
If 1 Bigha = 16 Kattha:
2 Bigha = 2 * 16 Kattha = 32 Kattha
a women has 5 keys, of which one will open her door. (i) if she tries the keys at random, discarding those that do not work, what is the probability that she will open the door on her 3rd try? (ii) if she does not discard previously tried keys, what is the probability that she will open the door on her 3rd try?
If she discard previously tried keys the probability is 1/n
If she doesn't discard previously tried keys the probability is: \(\frac{(n-1)^k}{n^k}\)
If she discard previously tried keys, the probability of open the door in the 1st, 2nd and 3rd try are:
1st try: \(\frac{1}{n}\)
2nd try: \((\frac{n-1}{n}) * (\frac{n}{n-1} ) = \frac{1}{n}\)
3rd try: \((\frac{n-1}{n}) * (\frac{n-2}{n-1} ) * (\frac{1}{n}) = \frac{1}{n}\)
Where, for example, the probability of open the door in the 2nd try is the multiplication of the probability that the woman didn't open the door in the 1st try with the probability that she open the door in the 2nd try.
So, the probability that she open the door in the kth try is: 1/n
On the other hand, if she doesn't discard previously tried keys, the probability to open the door in the 1st, 2nd and 3rd try are:
1st try: \(\frac{1}{n}\)
2nd try: \((\frac{n-1}{n}) *( \frac{1}{n}) = \frac{n-1}{n^2}\)
3rd try: \((\frac{n-1}{n}) * (\frac{n}{n-1} ) * (\frac{1}{n}) = \frac{(n-1)^2}{n^3}\)
So, the probability that she open the door in the kth try is:
\(\frac{(n-1)^k^-^1}{n^k}\)
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(7/8 - 5/2) + 10/2 x 1/4
Answer:
-3/8
Step-by-step explanation:
Answer:
-\(\frac{3}{8}\)
____________
Also, I see that this is your first question on here. Welcome to Brainly, midiostepague347!
Step-by-step explanation:
Consider this expression. - 4 x 2 + 2 x − 5 ( 1 + x ) What expression is equivalent to the given expression? x 2 + x +
The expression equivalent to\(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)
This expression matches the form \(x^2 + x + c,\) where c = 5.
To simplify the given expression \(-4x^2 + 2x - 5(1 + x)\) and make it equivalent to the expression \(x^2 + x + c,\) where c is a constant term, we need to perform some algebraic operations.
First, let's distribute the -5 to the terms inside the parentheses:
\(-4x^2 + 2x - 5 - 5x\)
Next, we can combine like terms:
\(-4x^2 + (2x - 5x) - 5 - 5x\)
Simplifying further:
\(-4x^2 - 3x - 5 - 5x\)
Now, let's rearrange the terms to match the form \(x^2 + x + c:\)
\(-4x^2 - 3x - 5x - 5\)
To make the leading coefficient positive, we can multiply the entire expression by -1:
\(4x^2 + 3x + 5x + 5\)
Now, we can combine the x-terms:
\(4x^2 + 8x + 5\)
So, the expression equivalent to \(-4x^2 + 2x - 5(1 + x)\) is \(4x^2 + 8x + 5.\)This expression matches the form \(x^2 + x + c,\) where c = 5.
It's important to note that the original expression and the equivalent expression have different coefficients and constants, but they represent the same mathematical relationship.
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Can anyone help me with this question?
Given that X = [3, 5) and Y = (4, 9). Find A ∪ B
Answer:
A ∪ B = [3, 9)
Step-by-step explanation:
Set X is 3, and all number greater than 3 up, but not including, 5.
Set Y is all numbers from 4 to 9, but not including 4 or 9.
The union of the sets is all numbers from 3 up to 9, including 3 but not including 9.
A ∪ B = [3, 9)
HI GUYS! Could you help me out? 30 points
Answer:
I think 2 but I'm not positive
Answer:
0 there is no solution
My spanish teacher just embarrassed me in front of everyone. How is everyone else doing?
Answer:
Don't wanna do math :(
Step-by-step explanation:
can anyone help me please anyone
Answer:
x=104
Step-by-step explanation:
In case you didn't know, "m || n" means that line "m" is parallel to line "n".
Line "t" crosses over lines "m" and "n". Since "m" and "n" are parallel, the angles of Line "t" are the same on either line. The angle measuring 104° is what's known as an exterior angle. In the image shown, B and G have the same measurement and so does A and H. Therefore, Angle "x" measure 104°.
I need help with 12 and 13 please.
Answer:
12. 3a + 5= 2a -6 = 3a + 5 2a - 6-5
Step-by-step explanation:
13. is just 9 and 55
What is the slope-intercept form of 3x 4y 5?
The slope of equation 3x-4y = 5 is 3/4.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Given equation:
3x-4y = 5
To find the slope:
First, we simplify the equation.
-4y = 5 -3x
Divide by -4.
(-4/-4)y = 5/-4 + (-3/-4)x
y = (3/4)x -5/4
Now, we know the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Comparing, both the equation,
we get,
m =3/4.
So, the slope is 3/4.
Therefore, the slope is 5/3.
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