Using the measurements given below, find the hypotenuse of the triangle.
Leg = 20 units
Leg = 21 units
400 units
841 units
29 units pleaseee hurry up its in a test im taking rn

Answer: 4 seconds

Step-by-step explanation:

After solving the expression ∛ (27 • 250), we get that option (C) 15 ∛2 is the correct option.

We are given the expression:

(27 • 250)^1/3

We need to evaluate the expression.

We can also write this expression as:

∛ (27 • 250)

First we will make factors of 27 and 250:

27 = 3 × 3 × 3

250 = 2 × 5 × 5 × 5

Now, we can write the expression as:

∛2 × 3 × 3 × 3 × 5 × 5 × 5

Now solving the cube root we get that:

= 3 × 5 × ∛2

= 15 ∛2

Therefore, after solving the expression ∛ (27 • 250), we get that option (C) 15 ∛2 is the correct option.

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The best big-o bound that any algorithm that multiplies two n-bit numbers can achieve is O(n²). This is because each of the n bits of a number x must be multiplied by each of the n bits of a number y, resulting in a total of n² multiplications.

Even with the most efficient algorithms, there is no way to avoid performing each of these multiplications, leading to a complexity of O(n²). While some algorithms may have lower constant factors or improved optimizations, they cannot fundamentally change the nature of the problem at hand. Therefore, any algorithm that performs the multiplication of two n-bit numbers must have a complexity of at least O(n²).

However, there are certain techniques and optimizations that can be used to improve the efficiency of the algorithm and reduce the constant factors involved. These include techniques like Karatsuba multiplication and Fast Fourier Transform, which can reduce the number of multiplications needed to perform the operation, thereby improving the overall performance of the algorithm.

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If you wanted to determine if your PSYC210 class performed significantly better than another section on a stats knowledge test, you would use a hypothesis test, specifically a two-sample t-test.

A hypothesis test is a statistical method used to determine whether there is a significant difference between two groups or populations based on their observed data. In this case, you would compare the mean score of your PSYC210 class on the stats knowledge test with the mean score of the other section using a two-sample t-test. The null hypothesis would be that there is no significant difference between the means of the two sections, and the alternative hypothesis would be that there is a significant difference.

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The output of each function include the following:

u'(1) = 0.

v'(5) = -2/3

By critically observing the graph of the functions f and g, we can logically deduce the following parameters;

f(1) = 2         f(5) = 3

g(1) = 1         g(5) = 2

f'(1) = 2         f'(5) = -1/3

g'(1) = -1        g'(5) = 2/3

Next, we would take the first derivative of u with respect to x and then, substitute the x-value into the composite function, and then evaluate as follows;

u(x) = f(x)g(x)

u'(x) = f'(x)g(x) + g'(x)f(x)

u'(1) = f'(1)g(1) + g'(1)f(1)

u'(1) = 2(1) + (-1)2

u'(1) = 2 - 2

u'(1) = 0.

For v'(5), we have the following function by applying quotient rule:

\(v'(x) = \frac{f'(x)g(x)\;-\;f(x)g'(x)}{g^2(x)} \\\\v'(5) = \frac{f'(5)g(5)\;-\;f(5)g'(5)}{g^2(5)} \\\\v'(5) = \frac{\frac{-1}{3} \times 2 - (3 \times \frac{2}{3}) }{2^2}\)

v'(5) = -8/3 × 1/4

v'(5) = -2/3

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The disc jockey could use a Monte Carlo simulation to estimate the probability that the next three songs are all rock songs.

In this simulation, she would randomly select a rock or pop song for each of the three slots, and then repeat this process many times (e.g. 10,000 times). She could then count the number of times that all three songs were rock songs, and divide this by the total number of simulations to get an estimate of the probability.

To estimate the probability that the next three songs are all rock songs, the disc jockey could use the following simulation design:
1. Assign a number to each rock and pop song, ensuring that both genres have equal numbers.
2. Use a random number generator to select three numbers corresponding to the songs.
3. Record the genres of the chosen songs and note if all three are rock songs.
4. Repeat the simulation process multiple times (e.g., 1000 times) to obtain a larger sample.
5. Calculate the probability by dividing the number of times all three selected songs were rock songs by the total number of simulations performed.
This simulation design will help estimate the probability of the next three songs being rock songs by accounting for the equal number of rock and pop songs in the selection pool.

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Answer

root 354

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(√19 -√7)(√19 +√7)

( a +b)( a -b) = a²-b²

(√19)² -(√7)² = 19 -7 = 12

The radius of the path taken by the particle is 4.5 meters if the time difference between t2 and t1 is less than one period.

To find the radius, we can use the centripetal acceleration formula, which relates the acceleration and the radius of circular motion. In this case, the particle's acceleration at t1 is given as 1 m/s² in the i-direction and 6 m/s² in the j-direction. At t2, the acceleration is given as 6 m/s² in the i-direction and -1 m/s² in the j-direction.

Since the particle is moving at a constant speed, the magnitude of the acceleration is equal to the centripetal acceleration. Using the formula for centripetal acceleration, we can equate the magnitudes of the two accelerations and solve for the radius. Considering the given accelerations at t1 and t2, we can determine that the radius is 4.5 meters.

Therefore, the radius of the path taken by the particle, when the time difference between t2 and t1 is less than one period, is 4.5 meters.

(a) To calculate the y-coordinate when the particle's x-coordinate is 30 meters, we can use the equation of motion. Given the particle's initial velocity, constant acceleration, and displacement in the x-direction, we can determine the time it takes to reach x = 30 m. Using this time, we can then calculate the corresponding y-coordinate using the equations of motion.

(b) To find the speed when the particle's x-coordinate is 30 meters, we can use the equation for velocity. By differentiating the equation of motion with respect to time, we can determine the velocity of the particle at any given time. Substituting x = 30 m into the equation will give us the particle's velocity. The speed is simply the magnitude of this velocity vector.

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Answer:

42 cm

Step-by-step explanation:

7+4+2+4+2+4+7+12

The estimated population for an area can be Red is 2611.2 and Green is 1894.4 respectively.

Given the population for a 1 cm2 area, the population of a 20 cm by 40 cm area is;

Green = 1894.4 Red = 2611.2

How can you determine the population using the population density?

The following are some probable details for a population density of 1 cm2:

The number of people per 6.25 cm2 is;

Red = 20.4

Green ≈ 14.8

Therefore, the density per 1 cm2 is;

Red = 20.4/6.25 = 3.264

Green ≈ 14.8 = 2.368

Consequently, the inhabitants of a 20 by 40 cm region are;

Red = 3.264 × 20 × 40 = 2611.2

Green ≈ 14.8 = 2.368 = 1894.4

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Answer:

10 shelves

Step-by-step explanation:

In order to calculate how many whole shelves we can fill we simply need to divide the total number of cereal boxes that John has in the back by the number of boxes that each shelf can hold like so...

85 / 8 = 10.625

Based on these numbers we can see that with the number of cereal boxes available we can fill a total of 10 shelves by using

10 * 8 = 80 cereal boxes

80 cereal boxes. That would leave 5 cereal boxes left which is not enough to fill another shelve.

Answer:

2282 divided by 3over7

Answer:

1304

Step-by-step explanation:

2282:7 =326

326 . 3 = 978

2282 - 978 = 1304

Answer:

26 is your answer. I hope this helps!

Step-by-step explanation:

The diameter of the circle is approximately 60 inches.

To explain further, we can use the formula relating the central angle of a sector to the length of its intercepted arc. The formula states that the length of the intercepted arc (A) is equal to the radius (r) multiplied by the central angle (θ) in radians.

In this case, we are given the central angle (225 degrees) and the length of the intercepted arc (30π inches).

To find the diameter (d) of the circle, we need to find the radius (r) first. Since the length of the intercepted arc is equal to the radius multiplied by the central angle, we can set up the equation 30π = r * (225π/180). Simplifying this equation gives us r = 20 inches.

The diameter of the circle is twice the radius, so the diameter is equal to 2 * 20 inches, which is 40 inches. Therefore, the diameter of the circle is approximately 60 inches.

In summary, by using the formula for the relationship between central angle and intercepted arc length, we can determine the radius of the circle. Doubling the radius gives us the diameter, which is approximately 60 inches.

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In an isosceles triangle, two of the angles are congruent, which means they have the same measure. Let x be the measure of each of the congruent angles. Then, we can use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation:

x + x + 26 = 180

Simplifying and solving for x, we get:

2x + 26 = 180

2x = 154

x = 77

So each of the congruent angles in the triangle measures 77 degrees. Therefore, the other two possible angle measures are 77 degrees and 26 degrees.

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To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. Substitute the coordinates of the vertex and the other point into the vertex form to find the value of a. Then, substitute the value of a back into the vertex form to get the quadratic function.

To write a quadratic function from its vertex and another point, we can use the vertex form of a quadratic function, which is f(x) = a(x-h)^2 + k. In this form, (h, k) represents the coordinates of the vertex of the parabola.

Let's say the vertex of the quadratic function is (h, k) and the other point is (x1, y1). We can substitute these values into the vertex form to find the value of a.

Substituting the vertex coordinates, we get:

f(h) = a(h-h)^2 + k

f(h) = k

Substituting the coordinates of the other point, we get:

f(x1) = a(x1-h)^2 + k

Now, we have two equations:

k = a(0)^2 + k

y1 = a(x1-h)^2 + k

From the first equation, we can see that k = k, which is always true. Therefore, we can ignore this equation.

From the second equation, we can solve for a:

y1 - k = a(x1-h)^2

a = (y1 - k) / (x1-h)^2

Now that we have the value of a, we can substitute it back into the vertex form to get the quadratic function:

f(x) = a(x-h)^2 + k

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Answer: 31.5

Step-by-step explanation:

6.3 x 5

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Amber earns more than Svetlana.

The wages of Amber and Svetlana must be contrasted in order to discover who makes more money.

Let's determine each person's earnings:

Amber:

13 necklaces are created per hour.

Each necklace costs £0.58.

Earnings per hour = Number of necklaces made per hour × Cost of each necklace

= 13 × £0.58

= £7.54 (rounded to two decimal places)

Svetlana:

Worked 38 hours; earned £285 for 38 hours.

Let's compare their salaries now:

While Svetlana receives a set payment of £285 for 38 hours of labour, Amber is paid £7.54 per hour.

We must compare their hourly rates to ascertain who makes more money. We'll split each person's profits by the number of hours they each put in:

£7.54 is Amber's hourly wage.

The hourly wage for Svetlana is £285 / 38 = £7.50.

We can tell that Amber makes more money per hour (£7.54) than Svetlana does (£7.50) by comparing the hourly rates.

Hence, Amber makes more money than Svetlana.

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The complete question is =

Amber makes pearls necklaces. She makes at least 13 necklaces per hour. She is paid 58p for each necklace she makes.

Svetlana is a personal assistant. She works 38 hours and is paid £285

Which of Amber or Svetlana has the highest hourly rate of pay?

The total utility of 4 units is 50 and the marginal utility is 5

Total utility is the sum of satisfaction that is derived from the consumption of units of a good or service.

Total utility can be determined by adding the marginal utility of each unit that is consumed.

Total utility of consuming 4 units = marginal utility of the first unit + marginal utility of the second unit + marginal utility of the third unit + marginal utility of the fourth unit  

20 + 15 + 10 + 5 = 50

Marginal utility is the change in total utility when consumption increases by unit. Marginal utility is 5

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Answer:

(a) Explained below.

(b) The 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Step-by-step explanation:

The information provided is:

n (Men who finished the marathon) = 25,221

n (Women who finished the marathon) = 12,883

Compute the proportion of men and women who finished the marathon as follows:

\(\hat p_{1}=\frac{25221}{25221 +253}=0.99\\\\\hat p_{2}=\frac{12883 }{12883+163}=0.988\)

The combined proportion is:

\(\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}\\\\=\frac{25221+12883}{38520}\\\\=0.989\)

(a)

The hypothesis is:

H₀: The rate of those who finish the marathon is the same for men and women, i.e. p₁ - p₂ = 0.

Hₐ: The rate of those who finish the marathon is not same for men and women, i.e. p₁ - p₂ ≠ 0.

Compute the test statistic as follows:

\(Z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)\cdot [\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}\)

   \(=\frac{0.99-0.988}{\sqrt{0.989(1-0.989)\times[\frac{1}{25474}+\frac{1}{13046}]}}\\\\=1.78\)

Compute the p-value as follows:

\(p-value=2\times P(Z>1.78)\\\\=2\times 0.03754\\\\=0.07508\\\\\approx 0.075\)

The p-value of the test is more than the significance level. The null hypothesis was failed to be rejected.

Thus, concluding that the rate of those who finish is the same for men and women.

(b)

Compute the 99% confidence interval for the difference between proportions as follows:

The critical value of z for 99% confidence level is 2.58.

\(CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p_{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p_{2})}{n_{2}}}\)

     \(=(0.99-0.988)\pm 2.58\times\sqrt{\frac{0.99(1-0.99)}{25474}+\frac{0.988(1-0.988)}{13046}}\\\\=0.002\pm 0.00294\\\\=(-0.00094, 0.00494)\\\\\)

Thu, the 99% confidence interval for the difference between proportions is (-0.00094, 0.00494).

Answer:

2 is the correct answer yes

The value of n is 22.

In this question, we have been given the parallel lines HE and AD are

cut by transversal BF at points G and C, respectively.

Consider the following diagram.

If m∠HGF = 5n and m∠BCD = 2n +66, we need to find n.

∠HGF and ∠BCD are alternate exterior angles.

We know that  alternate exterior angles are congruent.

So, m∠HGF = m∠BCD

5n = 2n +66

5n - 2n = 66

3n = 66

n = 66/3

n = 22

Therefore, the value of n is 22.

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The exact value of cscθ is (35 * √(1190)) / 1190.

To find the value of cscθ (cosecant θ) given that cosθ = 1/√35 and sinθ < 0, we can use the reciprocal relationship between sine and cosecant.

Recall that cscθ is the reciprocal of sinθ. Since sinθ is negative, we can determine its value based on the quadrant in which θ lies.

In the unit circle, the cosine is positive in the first and fourth quadrants, while the sine is negative in the third and fourth quadrants.

Given that cosθ = 1/√35 and sinθ < 0, we can conclude that θ lies in the fourth quadrant.

Using the Pythagorean identity, sinθ = √(1 - cos^2θ), we can calculate the value of sinθ:

sinθ = √(1 - (1/√35)^2)

     = √(1 - 1/35)

     = √(34/35)

     = √34 / √35

     = (√34 / √35) * (√35 / √35)     [Multiplying numerator and denominator by √35 to rationalize the denominator]

     = √(34 * 35) / 35

     = √(1190) / 35

Now, since cscθ is the reciprocal of sinθ, we have:

cscθ = 1 / sinθ

     = 1 / (√(1190) / 35)

     = 35 / √(1190)

     = (35 * √(1190)) / 1190.

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Answer:

The answer is 81 yards

Step-by-step explanation:

First: you divide 40.5 by 5 s to see how far is goes in the air in 1 second

second: you should get 8.1 as the answer it rises 8.1 yards in one second

third: multiply 8.1 by 10 s to get 81 yards

Answer:

C. 58 degrees

To find the measure of angle R in triangle QRS, we can use the fact that the sum of the angles in a triangle is 180 degrees.

Given:

Q = 8x

m/R = 14x + 2 degrees

m/S = 10x + 50 degrees

The sum of angles Q, R, and S is 180 degrees:

Q + R + S = 180

Substituting the given values:

8x + (14x + 2) + (10x + 50) = 180

Simplifying the equation:

8x + 14x + 2 + 10x + 50 = 180

32x + 52 = 180

32x = 180 - 52

32x = 128

x = 128/32

x = 4

Now that we have the value of x, we can substitute it back into the given expressions to find the measures of angles Q, R, and S.

Q = 8x = 8 * 4 = 32 degrees

m/R = 14x + 2 = 14 * 4 + 2 = 58 degrees

m/S = 10x + 50 = 10 * 4 + 50 = 90 degrees

Therefore, the measure of angle R is 58 degrees. So, the correct answer is C. 58°.

I hope you do great and pass this Unit test!!

The statement "If x = -10, then x² = 100" is false. When we square -10, we get 100, so the correct statement would be "If x = -10, then x² = 100."

The statement that is NOT true is:

If x = -10, then x² = 100.

The other three statements are all true:

If x² = 100, then x = 10.This is true because the square root of 100 is ±10, and when we take the square root, we consider the positive square root, which is 10.

If x = 10, then x² = 100. This is also true because when we square 10, we get 100.The statement x² = 100 if and only if x = 10 or x = -10 is true.

This statement is based on the fact that the square root of 100 is ±10, so when we square either 10 or -10, we get 100.

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\(\qquad\qquad\huge\underline{{\sf Answer}}☂\)

Let's solve, using Trigonometry ~

\(\qquad \sf  \dashrightarrow \: \tan(x) = \frac{54}{72} \)

\(\qquad \sf  \dashrightarrow \: \tan(x) = \frac{3}{4} \)

\(\qquad \sf  \dashrightarrow \:x = \tan { }^{ - 1} ( \frac{3}{4} ) \)

\(\qquad \sf  \dashrightarrow \:x = 37 \degree\)

Answer:

\(\displaystyle 36,9\)

Step-by-step explanation:

\(\displaystyle 1\frac{1}{3} = cot\:x \hookrightarrow cot^{-1}\:1\frac{1}{3} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x\)

OR

\(\displaystyle \frac{3}{4} = tan\:x \hookrightarrow tan^{-1}\:\frac{3}{4} = x \hookrightarrow 36,869897646...° = x \\ \\ 36,9° ≈ x\)

Information on trigonometric ratios

\(\displaystyle \frac{OPPOCITE}{HYPOTENUSE} = sin\:θ \\ \frac{ADJACENT}{HYPOTENUSE} = cos\:θ \\ \frac{OPPOCITE}{ADJACENT} = tan\:θ \\ \frac{HYPOTENUSE}{ADJACENT} = sec\:θ \\ \frac{HYPOTENUSE}{OPPOCITE} = csc\:θ \\ \frac{ADJACENT}{OPPOCITE} = cot\:θ\)

I am joyous to assist you at any time.

Answer:

5.7 metres

Step-by-step explanation:

2.5+3.2=5.7

Answer:

If you're trying to evaluate 6x + 9 + (-6), then the answer would be ↓

Step-by-step explanation:

6x + 3

Answer:

If you're trying to evaluate 6x + 9 + (-6), then the answer would be ↓

Step-by-step explanation:

6x + 3

True. Hexadecimal numbers are written using the base 16 number system, where digits range from 0 to 9 and A to F. They are commonly used in computer systems for concise representation and easy conversion to binary.

In the hexadecimal number system, there are 16 symbols used to represent values, namely 0-9 and A-F. Each digit in a hexadecimal number represents a multiple of a power of 16.

The symbols 0-9 represent the values 0-9, respectively. The symbols A-F represent the values 10-15, respectively, where A represents 10, B represents 11, C represents 12, D represents 13, E represents 14, and F represents 15.

For example, the hexadecimal number "3F" represents the value (3 * 16^1) + (15 * 16^0) = 48 + 15 = 63 in decimal.

Similarly, the hexadecimal number "AB8" represents the value (10 * 16^2) + (11 * 16^1) + (8 * 16^0) = 2560 + 176 + 8 = 2744 in decimal.

Hexadecimal numbers are commonly used in computer systems, as they provide a convenient way to represent large binary numbers concisely. Each hexadecimal digit corresponds to a four-bit binary number, allowing for easy conversion between binary and hexadecimal representations.

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