help would be absolutely appreciated

Answer: 10

Step-by-step explanation:

10

a) x= 20, y=20√3 b) x=2, y=2/√3 c) x=9, y=√162 is the correct answer.

Right triangle is that triangle in which one angle has to be 90 degree.The side opposite the right angle is called the hypotenuse, while the other two sides are called legs. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

a)sinα= perpendicular/hypotenuse

sin30°=x/40

1/2=x/40

2x=40

x=20

tanα= perpendicular/base

tan30°=x/y=20/y

1/√3=20/y

y=20√3

b) tanβ=⊥/base

tan60°=2√3/x

x√3=2√3

x=2

tanγ=⊥/base

tan30°=y/x=y/2

1/√3=y/2

y=2/√3

c) tanω=⊥/base

tan45°=9/x

1=9/x

x=9

y²=9²+x²

y²=81+81

y=√162

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The painting will be worth approximately $11,592.74 in 5 years when it increases at a rate of 3%

A quantity increases at a steady pace proportionate to its present value in an exponential growth pattern. In other words, a quantity expands more quickly the larger it is. Y = ab raise to x, where an is the starting value, b is the growth factor (i.e., the amount by which the quantity increases each time period), and x is the number of time periods, is frequently used to represent exponential growth.

The value of the painting after 5 years can be calculated using the exponential growth formula:

A = P(1 + r/n)^(nt)

Substituting the values  P = $10,000, r = 0.03, n = 1, and t = 5 we have:

A = 10000(1 + 0.03/1)^(1*5)

A = $11,592.74

Hence, the painting will be worth approximately $11,592.74 in 5 years.

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Among these expressions, (4+1)x(12-6) has a total value of 30.

To determine which expression has a total value of 30, let's evaluate each expression one by one:

4+1x12-6

Following the order of operations (PEMDAS/BODMAS), we first do the multiplication:

4 + (1x12) - 6 = 4 + 12 - 6

Now, we do the addition and subtraction from left to right:

16 - 6 = 10

(4+1x12-6)

This expression has the same operations as the first one, so its total value is also 10.

(4+1)x(12-6)

First, we evaluate the expressions within the parentheses:

(5)x(6)

Now, we do the multiplication:

5 x 6 = 30

(4+1)x12-6

First, we evaluate the expression within the parentheses:

(5)x12 - 6

Now, we do the multiplication:

60 - 6

Finally, we do the subtraction:

54
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The 'footprint' of CO2 emissions for a person in 1830 would be 818,199 tons of CO2 emissions per person.

To find the 'footprint' of CO2 emissions for a person in 1830, we need to substitute the value of x = 1830 - 1800 = 30 into the given function C(x) = 0.0365 (1.758)^x.

Plugging in x = 30 into the function, we get:

C(30) = 0.0365 * (1.758)^30

Substituting this value back into the function, we get:

C(30) = 0.0365 * 22416413.1381

C(30) = 818199.079541

C(30) ≈ 818,199.08

Answered question "Scientists studying the 'footprint' of carbon dioxide (CO2) emissions attributed to the average person for each decade from 1800 to 1910 used the function C(x) = 0.0365 (1.758)*, where x is the number of decades since 1800 and C is the number of tons of CO2 emissions per person. What is the 'footprint' of CO2 emissions for a person in 1830??"

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Answer:

negative

y=-x

y=-2x+6

y=(-1/2)x+1

y=-5x+20

undefined

x=4

x=-3

zero slope

y=2

y=-100

One of the sample t-test significance 0.10 level, we do not reject the null hypothesis that the mean volume of liquid dispensed by the machine is equal to 180 ml.

A one-sample t-test to determine whether the mean volume of liquid dispensed by the machine is significantly different from 180 ml.

The null hypothesis is that the true mean volume of liquid dispensed by the machine is equal to 180 ml, while the alternative hypothesis is that it is not equal to 180 ml.

We can calculate the t-value as follows:

[tex]t = (179.6 - 180) / (1.3 \sqrt (40)) = -1.385[/tex]

Using a t-distribution table with degrees of freedom (df) = 39 (since we have a sample size of 40 and one parameter estimated), and a significance level of 0.10, we find the critical t-value to be ±1.684.

Since our calculated t-value (-1.385) falls within the acceptance region (-1.684 < t < 1.684), we fail to reject the null hypothesis at the 0.10 significance level.

Sufficient evidence to conclude that the mean volume of liquid dispensed by the machine is significantly different from 180 ml.

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Answer:

The Correct answer is sinA/3.2=sin110°/4.6

The reasonableness of the estimate depends on the quality and reliability of the data sources and methodology used to arrive at the estimate.

In order to determine whether 12% is a reasonable estimate of the proportion of all Americans who eat chocolate

frequently, we would need to define what is meant by "frequently."

If we define "frequently" as "at least once a week," then 12% may or may not be a reasonable estimate, depending on

the data source and methodology used to arrive at that estimate.

For example, if the estimate is based on a small sample size or a non-representative sample of the population, then it

may not be a reliable estimate of the true proportion of Americans who eat chocolate frequently. Additionally, if the

estimate is several years old, it may not accurately reflect current trends and habits.

On the other hand, if the estimate is based on a large, nationally representative sample of the population, and is

relatively recent, then 12% could be a reasonable estimate of the proportion of Americans who eat chocolate

frequently.

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If p is a prime number and a is a positive integer, then pa has (a+1) distinct positive divisors.

A prime number is a positive integer greater than 1, which is divisible only by 1 and itself. Divisors are the numbers that evenly divide a given number.

For a prime number p raised to the power of a (p^a), the number of distinct positive divisors can be found using the following formula:

Number of divisors = (a + 1)

This is because each power of p from 0 to a can divide p^a without any remainder, giving us a total of a + 1 distinct divisors. These divisors are:

1, p, p^2, p^3, ..., p^(a-1), p^a

For example, if p = 2 (a prime number) and a = 3 (a positive integer), then the number of distinct positive divisors for 2^3 (which is 8) would be:

Number of divisors = (3 + 1) = 4

The divisors for 2^3 (8) are 1, 2, 4, and 8.

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Answer: i dont know if this is right but i put a^4+b^4=c^4

Step-by-step explanation:

I have no idea tho

True, an iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because iterative algorithms use loops to repeat a set of instructions, whereas recursive algorithms call themselves repeatedly until they reach a base case.

An iterative algorithm will usually run faster than an equivalent recursive algorithm. This is because recursive algorithms often involve function calls, which have overhead costs such as saving and restoring the call stack. In contrast, iterative algorithms use loops and do not require the same overhead, making them more efficient in terms of both time and memory usage.

However, it's important to note that some problems may be more elegantly or intuitively solved using recursion, even if it's less efficient. The repeated function calls in a recursive algorithm can lead to slower performance and higher memory usage compared to the more direct approach of an iterative algorithm.

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Answer:

[tex] \sqrt{41} [/tex]

Step-by-step explanation:

for finding the hypotenuse we use the pythagoras theorem

The value of x and order the length of the sides are x = 31 and BD < EB < DE

From the question, we have the following parameters that can be used in our computation:

m∠ABC=(4x)˚

m∠BED=(5+x)˚

m∠BDF=160

As a general rule, the sum of angles in a triangle is 180

Using the above as a guide, we have the following:

4x + 5 + x + 180 - 160 = 180

Evaluate the like terms

5x = 155

Divide by 5

x = 31

The angle opposite the longest side is the greatest angle, and vice versa

So, we have the following order

Smallest = BD

Next = EB

Longest = DE

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Answer:

Step-by-step explanation:

The value of x and order the length of the sides are x = 31 and BD < EB < DE

Finding the value of x and order the length of the sides.

From the question, we have the following parameters that can be used in our computation:

m∠ABC=(4x)˚

m∠BED=(5+x)˚

m∠BDF=160

As a general rule, the sum of angles in a triangle is 180

Using the above as a guide, we have the following:

4x + 5 + x + 180 - 160 = 180

Evaluate the like terms

5x = 155

Divide by 5

x = 31

The angle opposite the longest side is the greatest angle, and vice versa

So, we have the following order

Smallest = BD

Next = EB

Longest = DE

The population of your friend's town is 300,000 if the population of your town is about 30,000.

To solve this problem, we can use the fact that if one quantity is a fraction of another quantity, we can multiply or divide the given quantity by that fraction to find the other quantity. In this case, we know that the population of your town is 1/10th of your friend's town's population, so we can multiply your town's population by 10 to get your friend's town's population.

If the population of your town is about 30,000, and it's about 1/10 the population of your friend's town, we can calculate your friend's town's population by multiplying your town's population by 10.

So, the population of your friend's town is

30,000 x 10 = 300,000

Therefore, your friend's town has a population of about 300,000.

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The graph that  represents the sum w1 + w2 is: b. A line goes from (0, 0) to point (3, negative 1). On a coordinate plane, the y-axis is labeled imaginary and the x-axis is labeled real.

To find the sum of w1 and w2, we simply add their real and imaginary parts separately:

w1 + w2 = (4 + 2i) + (-1 - 3i) = 3 - i

So the real part of the sum is 3, and the imaginary part is -1. Therefore, the sum w1 + w2 corresponds to the point (3, -1) on the coordinate plane.

The graph that represents this point is option (b), where a line goes from (0, 0) to point (3, -1) on a coordinate plane with the y-axis labeled imaginary and the x-axis labeled real. The other options do not represent the correct point or are not lines passing through the origin.

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The next three terms of the sequence.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

To determine the next three terms of each sequence, we simply apply the rule or formula given above. For example, for sequence (a), the next three terms are 0, 1, 1, since the next term is 0 (since there are an even number of 1's so far), followed by two 1's (since there are now an odd number of 1's).

For sequence (b), the next three terms are 9, 10, 10, since the next term is 9 (since the next term in the pattern is odd), followed by two 10's (since the next two terms in the pattern are even). And so on for the other sequences.

(a) The sequence alternates between a run of "1"s and a run of "0"s.

Specifically, the nth term is 1 if the number of "1"s in the first n-1 terms is

odd, and 0 if the number of "1"s in the first n-1 terms is even.

(b) The nth term is[tex]\lfloor (n+1)/2\rfloor[/tex] if n is odd, and n/2 if n is even.

(c) The nth term is[tex]2^{(n-1)/2}[/tex] times the parity (i.e., 0 or 1) of n.

(d) The nth term is [tex]3\cdot 2^{n-1}[/tex].

(e) The nth term is 15-7(n-1).

(f) The nth term is the sum of the first n positive integers minus 3, i.e.,

[tex]1+2+3+\cdots+n-3.[/tex]

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The equivalent expression that could she also use to find the total cost is  (1+0. 2)35 (option d).

To find an equivalent expression that can be used to find the total cost, we need to understand the components of the original expression. The number 1.20 represents 100% of the bill plus the 20% tip, which can also be written as 1 + 0.20. The number 35 represents the cost of the meal before the tip was added.

Using this knowledge, we can rewrite the original expression as (1 + 0.20)35, which simplifies to option D, (1+0.2)35. This expression represents the total cost of the meal plus the tip, which is equal to 120% of the original cost of the meal.

Therefore, the correct equivalent expression is D, (1+0.2)35, which represents the total cost of the meal plus tip.

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the probability of a customer choosing a sandwich on white bread with ham and either provolone or American cheese is 6/36, which simplifies to 1/6. Thus, option A is correct.

There are 3 bread options, 4 meat options, and 3 cheese options listed on the board, which gives us a total of  [tex]3 \times 4 \times 3 = 36[/tex] possible sandwich combinations.

There are two cheese options that meet this criteria, so we can create two different sandwiches: one with provolone and one with American cheese.

Each of these sandwiches can be made in [tex]3 \times 1 \times 1 = 3[/tex] ways, as there are 3 bread options but only one option each for the ham and cheese. So, the total number of sandwich combinations that meet our criteria is [tex]2 \times 3 = 6.[/tex]

Therefore, the probability of a customer choosing a sandwich on white bread with ham and either provolone or American cheese is 6/36, which simplifies to   [tex]1/6[/tex].

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Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

a.) The statement P(1) is obtained by substituting n=1 into the equation. So, P(1) would be: 1³ = (1(1 + 1) / 2)²

b.) To show that P(1) is true, we need to prove that both sides of the equation are equal:

Left side: 1³ = 1

Right side: (1(1 + 1) / 2)² = (1(2) / 2)² = (2 / 2)² = 1² = 1

Since both sides of the equation are equal, we have completed the basic step of the proof, showing that P(1) is true.

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a) The equation is not true for n = 1, so P(1) is false.

b) The positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1

a) To find P(1), we substitute n = 1 into the equation given:

13 = (1(1 + 1) / 2)²

13 = (1 / 2)²

13 = 1/4

The equation is not true for n = 1, so P(1) is false.

b) To complete the basic step of the proof, we need to show that P(1) is true.

However, we have just shown that P(1) is false.

This means that the statement "for the positive integer n, 13 + 23 + … + n3 = (n(n + 1) / 2)²" is not true for n = 1.

Therefore, the proof cannot proceed and is incomplete.

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The probability that at most 7 customers will arrive at the shop during a 5-minute interval is approximately 0.9485 or 94.85%.

To find the probability that at most 7 customers will arrive at the shop during a 5-minute interval, we need to sum the probabilities of 0, 1, 2, 3, 4, 5, 6, and 7 customers arriving.

Using the Poisson probability formula, the probability of k events occurring in a given interval is:

[tex]P(k) = (\lambda ^k \times e^(-\lambda)) / k![/tex]

where λ is the mean number of events in the interval.

In this case, λ = 4. Therefore, we have:

[tex]P(0) = (4^0 \times e^(-4)) / 0![/tex] ≈ 0.0183

[tex]P(1) = (4^1 \times e^(-4)) / 1![/tex]≈ 0.0733

[tex]P(2) = (4^2 \times e^(-4))[/tex]/ 2! ≈ 0.1465

[tex]P(3) = (4^3 \times e^(-4))[/tex] / 3! ≈ 0.1954

[tex]P(4) = (4^4 \times e^(-4))[/tex]/ 4! ≈ 0.1954

[tex]P(5) = (4^5 \times e^(-4))[/tex] / 5! ≈ 0.1563

[tex]P(6) = (4^6 \times e^(-4))[/tex] / 6! ≈ 0.1042

[tex]P(7) = (4^7 \times e^(-4))[/tex]/ 7! ≈ 0.0595

To find the probability that at most 7 customers will arrive, we add up these probabilities:

P(7) = P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)

≈ 0.9485

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Ruben House is approximately 5.32 Km far than the Bank.

From the relation of the triangle we get,

c² = a² + b² - 2ab*cos(C)

where a, b, c are the side lengths opposite to the angles A, B and C respectively.

The diagram of the route of Ruben will be -

In figure A represents the Ruben's house and B represents the Bank and C represents the Store.

So here the distance from the Ruben house to store is (AC) = 37.5 km (given)

The distance of the store to the bank is (BC) = 34.5 Km

The angle ACB will be = 7 degree

We have to find the distance between the Ruben House and the Bank that is the value of AB.  

So,

AB² = AC² + BC² - 2*AC*BC*cos(angle ACB)

AB² = (37.5)² + (34.5)² - 2*37.5*34.5*cos(7)

AB² = 28.29

AB = [tex]\sqrt{28.29}\approx[/tex] 5.32 (Rounding up to two decimal places)

Hence the distance between Ruben's House and the Bank is approximately 5.32 Km.

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The question in English will be -

"Rubén leaves his house in his car and arrives at the store that is 37.5 km away. But remember that first you have to go to the bank to withdraw money, so turn 7th. If the bank located 34.5 km. Of the store. How far in km is Rubén's house from the bank?"

Therefore, the mean weight for each group in the three randomizations are:

First Randomization:

Group A: 12.5

Group B: 11.46

Second Randomization:

Group A: 11.56

Group B: 12.4

Third Randomization:

Group A: 12.18

Group B: 12.18

The mean, also known as the average, is a measure of central tendency in statistics. It is found by adding up all the values in a data set and dividing by the number of values in the set. The mean is sensitive to extreme values, or outliers, in the data set, and can be influenced by them. It is one of the most commonly used measures of central tendency, along with the median and mode.

Here,

First Randomization:

Group A: (13.6 + 12.1 + 15.9 + 11.2 + 9.7) / 5 = 12.5

Group B: (9.2 + 8.2 + 11.5 + 13.8 + 14.6) / 5 = 11.46

Second Randomization:

Group A: (8.2 + 13.8 + 15.9 + 9.2 + 9.7) / 5 = 11.56

Group B: (12.1 + 14.6 + 13.6 + 11.2 + 11.5) / 5 = 12.4

Third Randomization:

Group A: (8.2 + 9.7 + 11.5 + 14.6 + 15.9) / 5 = 12.18

Group B: (12.1 + 13.8 + 13.6 + 11.2 + 9.2) / 5 = 12.18

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Answer:

LOOK BELOW FOR ANSWER !!

Step-by-step explanation:

After the first randomization,

A  is  12.5

B  is 11.46

and A-B  is 1.04

After the second randomization,

A is 11.36

B is 12.6

A and B is -1.24

After the third randomization,

A is 11.98

B is 11.98

A and B is 1

.

The better definition of leg include the following: D. either of the two sides that form the right angle.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Generally speaking, the longest side (hypotenuse) of a triangle is equal to the sum of the square of two shorter sides (legs):

a² + b² = c²

Where:

a, b, and c represents the legs, side lengths or length of sides of a right angled triangle.

In conclusion, the legs in Mathematics simply refers to the opposite side and adjacent side of a right angled triangle.

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The value of 2m + k is 14.

The continuity of a function at a point is a fundamental concept in calculus. A function f(x) is said to be continuous at a point x = a

In other words, a function is continuous at a point if we can draw its graph without lifting the pencil from the paper at that point. This means that there are no jumps, breaks, or holes in the graph of the function at that point.

Here we have

To determine if f(x) is continuous at x = 2, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 2 are equal, and if they are both equal to f(2).

First, let's calculate the left-hand limit of f(x) as x approaches 2:

lim x → 2- f(x) = lim x → 2- (-x² + 2m) = -(2²) + 2m = 2m - 4

Next, let's calculate the right-hand limit of f(x) as x approaches 2:

lim x → 2+ f(x) = lim x → 2+ (5x - k) = 5(2) - k = 10 - k

Now alculate f(2):

f(2) = -2² + 2m = 2m - 4

For f(x) to be continuous at x = 2, the left-hand limit, right-hand limit, and the function value at x = 2 must all be equal. So we have:

2m - 4 = 10 - k = 2m - 4

Simplifying, we get:

10 - k = 2m - 4

k + 2m = 14

Therefore,

The value of 2m + k is 14.

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If bout 1.02 X 102 times farther away from the sun than Mercury. The number of kilometers is: C. about 5.91 X 10⁹ kilometers.

If Pluto is 1.02 x 10² times farther away from the Sun than Mercury, we can use the average distance of Mercury from the Sun, which is approximately 57.91 million km (5.791 x 10⁷ km) to calculate the distance of Pluto from the Sun.

Distance of Pluto from the Sun = (1.02 x 10²) x (57.91 x 10⁶ km)

Distance of Pluto from the Sun = 5.91 x 10⁹ km

Therefore, the correct option is: about 5.91 x 10⁹ kilometers.

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Answer:

x = - 5

Step-by-step explanation:

the axis of symmetry is a vertical line passing through the vertex with equation

x = c ( c is the value of the x- coordinate of the vertex )

vertex = (- 5, 4 ) with x- coordinate - 5 , then

x = - 5 ← equation of the axis of symmetry

Answer:

Step-by-step explanation:

To find which number is closest to zero, we must find the number with the lowest absolute value. Luckily to our advantage, all of these numbers have the same denominators, so the number with the lowest numerator is closest to zero.

Out of these numbers, 1/5 is the closest to zero.

The surface area is  76 square yards

You should recall that In geometry, a prism is a polyhedron comprising an n-sided polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms,

The surface area is given as 2(lb + bh + lh)

2(5*4)+2(5*2)+2(4*2)

40+20+16

76 square yards

Therefore, the surface area of the prism is 76 square yards

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