To give a recursive definition of the functions max and min, we can start by defining the base case and then building upon it.
For the function max, the base case would be when we have only two numbers, a1 and a2. In this case, we would simply compare the two numbers and return the maximum.
max(a1, a2) =
- a1 if a1 > a2
- a2 if a2 > a1
To extend this definition to n numbers, we can use recursion. We first find the maximum of the first n-1 numbers using the same recursive definition. We then compare this maximum with the nth number and return the greater of the two.
max(a1, a2, ..., an) =
- max(a1, a2, ..., an-1) if max(a1, a2, ..., an-1) > an
- an if an > max(a1, a2, ..., an-1)
Similarly, for the function min, the base case would be when we have only two numbers, a1 and a2. In this case, we would simply compare the two numbers and return the minimum.
min(a1, a2) =
- a1 if a1 < a2
- a2 if a2 < a1
To extend this definition to n numbers, we can use recursion. We first find the minimum of the first n-1 numbers using the same recursive definition. We then compare this minimum with the nth number and return the smaller of the two.
min(a1, a2, ..., an) =
- min(a1, a2, ..., an-1) if min(a1, a2, ..., an-1) < an
- an if an < min(a1, a2, ..., an-1)
Therefore, we have provided recursive definitions of the functions max and min, where max(a1, a2,.. an) and min(a1, a2,. an) are the maximum and minimum of the n numbers a1, a2,.... an respectively.
Let's start with the base cases:
1. max(a1): In this case, the maximum value is a1 itself, as there's only one number.
2. min(a1): Similarly, the minimum value is a1 when there's only one number.
Now, let's define the recursive steps for both max and min functions:
1. max(a1, a2, ..., an):
- Compare a1 with the maximum value of the remaining n-1 numbers, i.e., max(a2, a3, ..., an).
- If a1 is greater than max(a2, a3, ..., an), then max(a1, a2, ..., an) = a1.
- Otherwise, max(a1, a2, ..., an) = max(a2, a3, ..., an).
2. min(a1, a2, ..., an):
- Compare a1 with the minimum value of the remaining n-1 numbers, i.e., min(a2, a3, ..., an).
- If a1 is smaller than min(a2, a3, ..., an), then min(a1, a2, ..., an) = a1.
- Otherwise, min(a1, a2, ..., an) = min(a2, a3, ..., an).
By using these recursive definitions, you can find the maximum and minimum of n numbers a1, a2, ..., an respectively.
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WILL MARK AS BRAINLEIST!!
Question in picture!!
I HAVE MORE QUESTIONS ON MY ACCOUNT IF YOU CAN HELP ME OUT!!
The area of the enclosed region between y = 10x² and y = x² + 2 is given as follows:
A = 1.257 units².
How to obtain the area of the enclosed region?We are given two curves, hence the area of the enclosed region between the two curves is given by the define integral of the upper curve subtracted by the lower curve.
For the image given at the end of the answer, the parameters of the integral are given as follows:
Upper curve of x² + 2.Lower curve of 10x².Lower bound of -0.471.Upper bound of 0.471.Hence the integral used to calculate the area is given as follows:
[tex]A = \int_{-0.471}^{0.471} (x^2 + 2 - 10x^2) dx[/tex]
[tex]A = \int_{-0.471}^{0.471} (9x^2 + 2) dx[/tex]
Using a calculator, the area is given as follows:
A = 1.257 units².
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What is the total annual dividend received from
owning 100 shares of stock A, if Company A
issues a $0.20 quarterly dividend to its
shareholders?
total annual dividend = [?]
Round to the nearest hundredth.
Step-by-step explanation:
100 shares * .20 / share * 4 times / year = $80.00 annual
The annual dividend received from owning 100 shares of stock of company A that pays 20 cents per quarter will be $80.
Dividend is a regular payment made by the company to its equity shareholders on pro-rata basis as a percentage of the profit earned by the company. The company pays its subscribers a dividend 20 cents per quarter. So annually, the company will pay four times the amount, i.e., 80 cents (20 x 4).
80 cents will be the dividend paid by the company per share per year. so for a hundred shares of stock, the company will pay the:
Annual Dividend = 0.20 x 4 x 100
Annual Dividend = 0.80 x 100
Annual Dividend = 80
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a client is receiving an iv solution of 2 grams of medication diluted in 100 ml of normal saline over a one hour time period. how many mg of medication is the client receiving per minute? (enter numeric value only. if rounding is required, round to the nearest whole number.)
The client will be receiving 1.67 ml of medication in one minute and it will have 0.334 g of medication per minute.
Here 2g of medication is diluted with 100 ml of normal saline. So concentration of 1ml of normal saline would be,
Concentration of 1 ml = 2/100 = 0.02 g/ml
It is delivered over a period of 1 hour. So, the amount delivered per minute will be,
Amount per minute = Volume/ time = 100/60 = 1.67 ml
Amount of medication in 1.67 ml = Volume × Amount per ml
= 1.67 × 0.02 = 0.334 g
So 0.334 g of medication will be received per minute. So the rate will be 1.67 ml per minute.
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a box contains many tickets, with an average value of 30 and an sd of 10. if we draw 200 times with replacement from the box and keep track of the sum of draws, what is the approximate chance that the sum of draws is smaller than 6100? choose the answer that is closest.
The approximate chance that the sum of draws is smaller than 6100 is 58.9%.
We can use the central limit theorem to approximate the distribution of the sum of draws from the box. According to the central limit theorem, the sum of draws will be approximately normally distributed with a mean of 200*30 = 6000 and a standard deviation of sqrt(200)*10 = 447.21.
To find the probability that the sum of draws is smaller than 6100, we can standardize the value using the formula for z-score:
z = (x - mu) / sigma
where x is the value of interest (6100), mu is the mean (6000), and sigma is the standard deviation (447.21).
z = (6100 - 6000) / 447.21 = 0.2238
Using a standard normal distribution table or calculator, we can find the probability that a standard normal variable is less than 0.2238. This is approximately 0.589, or 58.9%.
Therefore, the approximate chance that the sum of draws is smaller than 6100 is 58.9%.
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4. A bag of candy has 22 twix, 14 reeces, and 16 hersheys. Give a reduced ratio of non-twix to ALL candy.
Answer: 30/52 or 58%
Step-by-step explanation:
The non-Twix candies to all candies is 30 pieces of non-Twix to 52 total candies. This is a ratio of 30:52 or 58%. I hope this helps you. <3
Answer: 15 non-twix to 26 total candy
Step-by-step explanation:
non twix: 14+16=30
all candy: 22+14+16=52
30:52
simplify
15:26
brainliest+100 points
2x + 2y = 4xy is wrong
2x + 2y = 2(x+y) is correct
b.3x+4= 7x wrong
c4x²+5x = 9x² wrong
23x²+3x²+4x = 6x² + 4x = 2x(3x + 2)
3sorry I don't understand this one.....
4-4(3x-5) = -12x + 20
5 120 12 10 4 3 5 26Answer:
120
12 10
4 2 5 2
2 2
If you’re are doing a gift exchange, and everyone has to spend at least 10 dollars but less than 20 dollars, what inequality represents the situation?
A. 10 > x > 20
B. 10 ≤ x < 20
C. 10 ≥ x ≥ 20
D. 10 < x < 20
The correct inequality to represent the situation where everyone has to spend at least 10 dollars but less than 20 dollars in a gift exchange is 10 ≤ x < 20. (option b).
The correct inequality to represent the situation is B. 10 ≤ x < 20. This inequality reads "x is greater than or equal to 10, but less than 20". In other words, the amount of money each person spends (represented by x) must be at least 10 dollars, but cannot exceed 20 dollars.
To understand why this is the correct inequality, let's break it down. The symbol ≤ means "less than or equal to", and the symbol < means "less than". So, 10 ≤ x means "x is greater than or equal to 10", and x < 20 means "x is less than 20". Combining these two expressions gives us the inequality 10 ≤ x < 20, which represents the range of values that x can take on in this gift exchange.
Hence the correct option is (b).
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please help!
If r=0.5 m, A = ???
(Use the r key.)
The area of a circle of radius of 0.5 meters is 0.785 square meters.
How to find the area of the circle?Remember that for a circle of radius r, the area is:
A = pi*r²
Where pi = 3.14
Here we know that r = 0.5m, then we can input that in the formula for the area that is above, we will get.
A = 3.14*(0.5m)²
A = 3.14*0.25 m²
A = 0.785 m²
That is the area of the circle.
Complete question: Let's say that r is the radius of a circle and A is its area, then: If r=0.5 m, A = ?
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A European derivative instrument on IBM has the following payoff structure at the maturity date in 3 years:
a) ST if ST < 120
b) 120 + 2 * (ST – 120) if 120 < = ST <= 160
c) 200 if 160 <= ST <= 200
d) ST if 200 <= ST where ST is the price at the maturity date.
The spot price is 154 and the volatility is 25%. The risk-free interest rate is 4% and we consider a 6-step binomial tree.
(a) Use Excel to draw this payoff pattern for the following price interval [0 , 300] with a step of 10. (2 marks)
(b) Based on the graph in (a), explain briefly how the premium of this derivative security should compare to IBM spot price. (2 marks)
(c) Price this contract using a 6-step binomial tree and confirm your findings in (b). Show all details and only state if arbitrage opportunity is available or not. (3 marks)
The price of the European derivative instrument on IBM is approximately $212.80.
Based on the graph, we can see that the payoff of the derivative instrument is capped at 200, regardless of the price of IBM at the maturity date.
Therefore, the premium of this derivative security should be lower than the spot price of IBM, as the potential upside is limited.
To price the derivative instrument using a binomial tree, we first need to calculate the up and down factors:
u = e(σ * √Δt) = e(0.25 * √(3/6)) = 1.35914
d = 1/u = 0.73516
where σ is the volatility, Δt is the time step, and u and d are the up and down factors, respectively.
Next, we calculate the risk-neutral probability of an up move:
p = (e(r * Δt) - d) / (u - d) = (e(0.04 * 3/6) - 0.73516) / (1.35914 - 0.73516)
= 0.57348
Expected payoff at node (2, 1) = 200
Expected payoff at node (2, 2) = 44.16
Expected payoff at node (2, 3) = 44.16
Expected payoff at node (3, 1) = 57.76
Expected payoff at node (3, 2) = 57.76
Expected payoff at node (3, 3) = 32.04
Expected payoff at node (4, 1) = 75.68
Expected payoff at node (4, 2) = 44.16
Expected payoff at node (4, 3) = 32.04
Expected payoff at node (5, 1) = 108.36
Expected payoff at node (5, 2) = 57.76
Expected payoff at node (6, 1) = 158.28
Where r is the risk-free interest rate and p is the risk-neutral probability of an up move.
The expected payoff at each node can be calculated using the risk-neutral probabilities and the corresponding payoffs:
At node 5, the expected payoff is:
0.4575 * 0 + 0.5425 * (120 + 2 * (1.25 * 154 – 120)) = 212.80
At node 4, the expected payoff is:
0.4278 * 0 + 0.5722 * (120 + 2 * (1.25 * 136 – 120)) = 199.13
At node 3, the expected payoff is:
0.4008 * 0 + 0.5992 * (120 + 2 * (1.25 * 120 – 120)) = 185.58
At node 2, the expected payoff is:
0.3766 * 0 + 0.6234 * (120 + 2 * (1.25 * 105 – 120)) = 172.98
At node 1, the expected payoff is:
0.3549 * 0 + 0.6451 * (120 + 2 * (1.25 * 92 – 120)) = 161.27
At node 0, the expected payoff is:
0.3354 * 0 + 0.6646 * (1.25 * 80) = 83.07
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Bus stops A,B,C, and D are on a straight road. The distance from A to D is exactly 1 km. The distance from B to C is 2 km. The distance from B to D is 3 km, the distance from A to B is 4 km, and the distance from C to D is 5 km. What is the distance between stops A and C?
Answer:
The answer is: 1+4+2+3+4+5=19 km
The distance between stops A and C is 11 km.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To find the distance between stops A and C, we can use the fact that the distance from A to D is 1 km and the distance from B to C is 2 km.
We can also use the fact that the distance from A to B is 4 km, the distance from B to D is 3 km, and the distance from C to D is 5 km.
We can start by finding the distance from A to B to C to D as follows:
Distance from A to B: 4 km
Distance from B to D: 3 km
Distance from D to C: 5 km
Total distance from A to C:
distance from A to B + distance from B to C + distance from C to D
So, the total distance from A to C is:
4 km + 2 km + 5 km = 11 km
Therefore,
The distance between stops A and C is 11 km.
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What is the product (6√5 - 6i) (√3 + √3i) in polar form example : (e - fi) and what quadrant of the complex plane does the product lie?
Answer: Plain: the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.
Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:
6√5 - 6i = 6(√5 - i) = 12 ∠ -30°
(√3 + √3i) = √3(1 + i) = 2 ∠ 45°
where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.
Now, we can multiply the two complex numbers in polar form:
(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°
= 24 ∠ 15°
Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.
To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.
some airlines have restrictions on the size of items of luggage that passengers are allowed to take with them. suppose that one has a rule that the sum of the length, width and height of any piece of luggage must be less than or equal to 180 cm. a passenger wants to take a box of the maximum allowable volume. if the length and width are to be equal, what should the dimensions be?length
the maximum dimensions of the box would be 60 cm x 60 cm x 60 cm in order to have the maximum allowable volume while still meeting the airline's luggage restrictions.
If the length and width of the box are equal, we can call the length and width x. Then, the height of the box would also be x in order to maximize the volume.
The sum of the length, width, and height of the box would be:
x + x + x = 3x
We know that the sum of the length, width, and height must be less than or equal to 180 cm. So:
3x ≤ 180
Simplifying, we get:
x ≤ 60
Therefore, the maximum dimensions of the box would be 60 cm x 60 cm x 60 cm in order to have the maximum allowable volume while still meeting the airline's luggage restrictions.
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Dimensions, the sum of the length, width, and height is 360 cm.
Let's assume that the length, width, and height of the box are all equal to
x cm. Since the length and width are equal, we can write:
Length = Width = x
The volume of the box can be expressed as:
Volume = Length x Width x Height
Volume = x × x × (180 - 2x) (since the height is equal to 180 - length - width)
To find the dimensions of the box that would give us the maximum volume, we need to differentiate the volume function with respect to x and set it equal to zero:
[tex]dV/dx = 3x^2 - 360x = 0[/tex]
Solving this equation, we get:
x = 0 or x = 120
Since x cannot be zero, the only possible value for x is 120 cm. Therefore, the dimensions of the box should be:
Length = Width = Height = 120 cm
With these dimensions, the sum of the length, width, and height is:
Length + Width + Height = 120 + 120 + 120 = 360 cm
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Can someone help me asap? It’s due tomorrow. I will give brainliest if it’s correct.
The simulation that represents the context is given as follows:
2,5, 8 of diamonds: gold plastic ring.3, 6, 9 of diamonds: silver plastic ring.4, 7, 10 of diamonds: black plastic ring.How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
In the context of this problem, we have an equal number of gold rings, silver rings and black rins, thus each outcome should have the same probability, which is represented by the last option.
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Which of the following ratios is in proportion to the ratio 3:4? (choose any that work)
5:6
12:14
12:16
6:7
4:5
6:8
Answer: 12:16
Step-by-step explanation: If you simply the ratio by dividing each side by 4 you are left with 3:4
Answer: 12:16,6:8
Step-by-step explanation:
simplify
12:16=3:4
6:8=3:4
What value of a will make the equation true?
(x+a)^2=x^2+16x+64
A. a=16
B. a=8
C. a=64
D. a=4
Answer:
To solve for the value of a that will make the equation true, we can expand the left side of the equation using the square of a binomial formula:
(x + a)^2 = x^2 + 2ax + a^2
Substituting this expression back into the original equation, we get:
x^2 + 2ax + a^2 = x^2 + 16x + 64
We can then simplify this equation by canceling out the x^2 terms on both sides, which gives:
2ax + a^2 = 16x + 64
Next, we can isolate the variable a on one side of the equation by subtracting 2ax and 64 from both sides:
a^2 - 2ax = 64 - 16x
Finally, we can factor out the variable a from the left side of the equation:
a(a - 2x) = 64 - 16x
To solve for a, we can divide both sides by (a - 2x):
a = (64 - 16x)/(a - 2x)
However, we must also note that the denominator (a - 2x) cannot be zero, as this would result in a division by zero error. Thus, we must ensure that a ≠ 2x.
Therefore, the value of a that will make the equation true is:
a = (64 - 16x)/(a - 2x), where a ≠ 2x.
Step-by-step explanation:
Answer:
B. a=8
Step-by-step explanation:
First, let's look at the expression that is on the right side of the equal sign:
[tex]x^2+16x+64[/tex]
This expression is equal to:
[tex](x+a)^2[/tex]
So, it must mean that the expression on the right is merely the expanded form of the expression on the left.
Recall the expanded form for the square of a sum:
[tex](a+b)^2=a^2+b^2+2ab[/tex]
Notice that 64 is equal to 8 squared, and 16x is equal to 2 times 8 times x.
This must mean that [tex]a=8[/tex].
Thus, our answer is:
B. a=8
14. An airplane flew 2,800 miles from Los Angeles to New York. The airplane flies at approximately 500
mi/hr. How many hours did it take the plane to reach New York?
Answer:
Speed= 500ml/hr
total distance= 2800 m
total time = d/t
2800/500= 5.6hrs
Step-by-step explanation:
Mrs. Greenthumb is planning to build a rectangular planter for her garden. She wants the length to be twice as long as the width plus one foot and the total area is 300ft^2
a- What quadratic equation will represent this situation?
b- What are the dimensions of Mrs. Greenthumb's garden?
Using quadratic formula, the dimensions for the rectangular garden is 12 feet by 25 feet
What quadratic equation will represent this situation?a- To represent this situation with a quadratic equation, we can start by letting "x" represent the width of the planter in feet. According to the problem, the length of the planter is twice as long as the width plus one foot. Therefore, the length can be represented by the expression "2x + 1".
The area of a rectangle is given by the formula A = l x w, where A is the area, l is the length, and w is the width. In this case, we know that the total area of the planter is 300ft^2. Therefore, we can write the following quadratic equation to represent the situation:
A = l x w
300 = (2x + 1) * x
300 = 2x^2 + x
2x² + x - 300 = 0
b- To find the dimensions of Mrs. Greenthumb's garden, we can solve the quadratic equation 2x² + x - 300 = 0 for "x". We can use the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 2, b = 1, and c = -300. Therefore, we can plug these values into the quadratic formula and simplify to find the solutions:
x = (-1 ± √(1^2 - 4(2)(-300))) / 2(2)
x = (-1 ± √(1 + 2400)) / 4
x = (-1 ± √(2401)) / 4
We can simplify this expression further by noting that sqrt(2401) = 49. Therefore:
x = (-1 ± 49) / 4
The two solutions are:
x = 12 or x = -25/2
Since the width of the planter cannot be negative, we can discard the solution x = -25/2. Therefore, the width of the planter is x = 12 feet.
To find the length, we can use the expression for the length we found earlier: 2x + 1. Plugging in x = 12, we get:
length = 2x + 1 = 2(12) + 1 = 25
Therefore, the dimensions of Mrs. Greenthumb's garden are 12 feet by 25 feet.
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Evaluate the indefinite integral. You must show all of your work to receive credit. ∫(xe^x)/(2(x+1)2)dx
I’m rectangle LAGF, OT and GS intersect at point L
The locations of the linear pair angles, the angle expressions, indicates that the value of x is 24, and we get;
m∠FLS = 108°
m∠SLT = 72°
m∠ALG = 18°
What are linear pair angles?Linear pair angles are angles that together form a straight line.
Linear pair angles are supplementary.
The linear pair angles, ∠FLS and ∠FLG, indicates;
(4·x + 12)° + (3·x)° = 180°
7·x + 12 = 180
7·x = 180 - 12 = 168
x = 168/7 = 24
x = 24
Therefore; m∠FLS = (4 × 24 + 12)° = 108°
m∠FLS = 108°∠SLT ≅ ∠FLG, vertical angles theorem, therefore;
m∠SLT = m∠FLG = (3·x)°
x = 24
m∠SLT = m∠FLG = (3 × 24)° = 72°
m∠SLT = 72°
∠ALF = ∠FLG + ∠ALG (Angle addition property)
∠ALF is a right angle, therefore, ∠FLG and ∠ALG are complementary, angles
∠FLG + ∠ALG = 90°
m∠FLG = 72°m∠ALG = 90° - m∠FLG
m∠ALG = 90° - 72° = 18°
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Ron must spend less than $400 on a rental car. Part A create an inequality that models the amount of money ,x, in dollars Ron can spend on the rental car
The sum or difference of two fractions is not in _______________
The sum or difference of two fractions is not in Improper form.
What is Fraction?Fraction is a part of a whole number. It is represented by two numbers separated by a line. The top number is called the numerator and the bottom number is called the denominator. The numerator represents the number of parts of the whole, and the denominator represents the total number of parts. For example, 1/2 is a fraction that represents one part of a whole that is divided into two equal parts. Fractions are used in many mathematical calculations such as addition, subtraction, multiplication and division.
When adding or subtracting fractions, it is important to first convert the fractions to improper form. Improper form is when the numerator (the top number of the fraction) is larger than the denominator (the bottom number of the fraction). For example, the improper form of 1/2 is 3/2.
To convert a fraction to its improper form, simply multiply the numerator and denominator by the same number. For example, let’s convert the fraction 1/2 to its improper form. To do this, we multiply the numerator (1) and denominator (2) by 2. This gives us 2/4, which is the same as 3/2 (the improper form).
Once all the fractions have been converted to improper form, they can be added or subtracted by simply adding or subtracting the numerators (top numbers) and keeping the denominator (bottom number) the same.
For example, let’s say we want to add 3/4 and 1/2. To do this, we convert both fractions to improper form: 3/4 becomes 6/4, and 1/2 becomes 3/2. Then, we add the numerators (6 + 3 = 9) and keep the denominator the same (4). This gives us the answer of 9/4.
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Complete questions as follows-
The sum or difference of two fractions is not in _______________ form.
the mass of the box on a table is 20kg. a man applied force as below the picture. the static frictional coefficient is 0.6 and the dynamic frictional coefficient is 0.5. (gravitational acceleration =10ms^{-2}
1)what is the minimum force that should be applied to move the box?
2)What is the force that should apply to move in uniform velocity?
Okay, let's solve this problem step-by-step:
1) To move the box initially, the applied force (F) must overcome static friction.
Static frictional force = F_static = μ_static * Weight of box
= 0.6 * 20kg * 10m/s^2
= 12N
So the minimum force to move the box is 12N.
2) Once the box is moving at a uniform velocity, the applied force only needs to overcome dynamic friction.
Dynamic frictional force = F_dynamic = μ_dynamic * Weight of box
= 0.5 * 20kg * 10m/s^2
= 10N
So to keep the box moving at a constant velocity, the applied force should be 10N.
In summary:
Minimum force to move the box (static friction) = 12N
Force to move at constant velocity (dynamic friction) = 10N
Let me know if you have any other questions!
Find side a and side c when b = 12, = 93°, = 30°
The length of the third side of the triangle is approximately 5.6 units.
To find the length of the third side of the triangle, we can use the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of the angle between them. The formula is
c² = a² + b² - 2ab×cos(C)
Where c is the length of the third side of the triangle, and C is the angle opposite to side c.
We can plug in the given values to get:
c² = 4.5² + 6^2 - 24.56×cos(35°)
We can solve for c by taking the square root of both sides
c = √(4.5^2 + 6^2 - 24.56×cos(35°))
Evaluate the right-hand side to get
c ≈ 5.6 units
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I have solved the question in general, as the given question is incomplete.
The complete question is:
You are given two sides of a triangle, a = 4.5 and b = 6, the angle between them is 35 degrees, how do you find the third side?
The legs of a right triangle measure 18 cm and 26 cm.
What is the length of the hypotenuse?
Enter your answer, in simplest radical form, in the box.
Answer: The length of the hypotenuse of the right-angled triangle is 31.62 cm.
Step-by-step explanation: Given , that the legs of the right-angled triangle are 18 cm and 26 cm
Lets assume that the two sides of the right-angled triangle :
AC = 18 cm , BC = 26 cm
According to Pythagoras Theorem - In a right- angled triangle , the square of the hypotenuse side is equal to the sum of squares of two sides .
Therefore, according to the diagram AB² = AC² + BC²
⇒ AB² = (18)² + (26)²
⇒ AB² = 324 +676
⇒ AB² = 1000
⇒ AB = √1000
⇒ AB = 31.62 cm
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6) Match the probability of falling BELOW the following z-scores.
1) 1.95
2) -2.7
3) -0.08
4) 0.63
A) .9744
B) .4681
C) .7357
D) .0035
The probability of falling below each z-score is given as follows:
1) 1.95: 0.9744.
2) -2.7: 0.0035.
3) -0.08: 0.4681.
4) 0.63: 0.7357.
How to obtain the probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.Hence the probability of falling below each z-score is given by the p-value of the z-score, found using the z-table.
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I need some help……..
Answer:
3) vertical
4) neither
Step-by-step explanation:
3) they are formed by two intersecting lines, are opposite of each other and are congruent. therefore, they are vertical angles
4) adjacent angles share a common vertex and common side. since the angles do not share a common side, they are not adjacent to each other. they are also not vertical because they are not congruent and are not formed by two intersecting lines. therefore, they are neither angle type
your friend is bringing half of a crate of popsicles to the picnic. of you put what is left in the crate evenly into 6 ice buckets, what fraction of the crate will go into each of ice bucket
The fraction of crate that will fit in each ice bucket is therefore determined to be - 1/12.
Describe the fraction in detail:A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, at which numerator and the denominator are divided.
In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator.Proper fractions are those whose numerator is less than their denominator. The fraction is deemed improper when the numerator above the denominator.data provided
proportion of the friend's crate is equal to half.There are six ice buckets in total.The number of ice buckets / proportion of crate in each bucket equals fraction of crate provided by friend.
crate fraction in each bucket equals (1/2) / 6
Each bucket's fraction of the crate is 1 / (2*6).
Each bucket's percentage of the crate is 1/12.
The amount of crate that will fit in each ice bucket is therefore determined to be - 1/12.
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A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. Which of these best describes the volume of this rectangular prism? (5 points)
1 unit cube and 15 smaller cubes of volume fraction 1/125 cubic inch each
1 unit cube and 75 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 25 smaller cubes of volume fraction 1/125 cubic inch each
7 unit cubes and 125 smaller cubes of volume fraction 1/125 cubic inch each
The volume of the rectangular prism is 1.6 cubic inches.
Let's start by finding the number of cubes that can fit in each dimension of the rectangular prism. Since each cube has an edge length of 1/5 inch, the length, width, and height of the rectangular prism must be multiples of 1/5 inch. Let's call the length of the rectangular prism "L", the width "W", and the height "H". Then we have
L = 1/5 × x
W = 1/5 × y
H = 1/5 × z
where x, y, and z are integers.
Since the rectangular prism is completely packed with 200 cubes, we have
x × y × z = 200
We want to find the volume of the rectangular prism, which is given by
V = L × W × H = 1/5 × x × 1/5 × y × 1/5 × z = 1/125 × x × y × z
Substituting x × y × z = 200, we get
V = 1/125 × 200 = 8/5 = 1.6 cubic inches
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The given question is incomplete, the complete question is:
A rectangular prism is completely packed with 200 cubes of edge length fraction 1/5 inch, without any gap or overlap. find the volume of this rectangular prism
A composite figure is shown.
A five-sided figure with two parallel sides. The shorter one is 16 feet. The height of the figure is 22 feet. The portion from the vertex to the perpendicular height is 6 feet. The portion from a point to a vertical line created by two vertices is 6 feet.
Which of the following represents the total area of the figure?
968 ft2
616 ft2
484 ft2.
352ft2
Area of figure is 484ft².
Define area of rectangle and triangleThe area of a rectangle is the amount of space that is enclosed by its sides. It is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is:
Area = length x width
where "length" refers to the longer side of the rectangle, and "width" refers to the shorter side.
The formula for the area of a triangle is:
Area = (base x height) / 2
where "base" refers to the length of the side of the triangle that is parallel to the ground, and "height" refers to the length of a line that is perpendicular to the base and connects the base to the opposite vertex.
Area of figure=Area of 1st triangular part+ Area of rectangular part+ Area of 2nd triangle
=1/2× 22× 8 + 16 ×22 + 1/2 ×4×22
=88+352+44
=484ft².
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3(x + y) = y
If (x, y) is a solution to the equation above and
y = 0, what is the ratio * ?
The answer to this question is x:0