A right triangle has a 32°
angle. Find the value of its
other angle.

Answer:

Step-by-step explanation:

2(6-x)³ when x = 4

[tex]\mathrm{2\left(6-\left(4\right)\right)^3}[/tex]

Follow the PEMDAS order of operations:-

1) Parentheses:-

[tex]\mathrm{2\cdot \:2^3}[/tex]

2) Exponents:-

[tex]\mathrm{2\cdot \:8}[/tex]

3) Multiply:-

________________________

Hope this helps! :)

In this algorithm, the "bit" term refers to a binary digit, which can be either 0 or 1. The reversal of a bit string means to reverse the order of its bits, so that the first bit becomes the last and vice versa.

To find the reversal of a bit string using a recursive algorithm, we can follow these steps:

1. Check if the bit string is empty or contains only one bit. If so, return the bit string as it is the reversal.

2. Otherwise, split the bit string in half and recursively call the reversal algorithm on each half.

3. Concatenate the reversal of the second half with the reversal of the first half to get the final reversed bit string.

Here is the recursive algorithm in pseudocode:

Function reverseBits(bitString):
 if length(bitString) ≤ 1:
   return bitString
 else:
   firstHalf = bitString[0: length(bitString)/2]
   secondHalf = bitString[length(bitString)/2: length(bitString)]
   return reverseBits(secondHalf) + reverseBits(firstHalf)

In this algorithm, the "bit" term refers to a binary digit, which can be either 0 or 1. The reversal of a bit string means to reverse the order of its bits, so that the first bit becomes the last and vice versa.

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The probability of flipping heads 6 times in a row with this weighted coin is approximately 0.0273, or 2.73%.

Since the coin is weighted such that heads come up twice as often as tails, let's assign probabilities to each outcome. We can represent this as P(H) = 2/3 (probability of heads) and P(T) = 1/3 (probability of tails).

Now, you want to find the probability of flipping heads 6 times in a row. In this case, we can use the multiplication rule of probability, which states that the probability of multiple independent events occurring is equal to the product of their individual probabilities.

For your scenario, the probability of getting 6 heads in a row is:

P(H₁ and H₂ and H₃ and H₄ and H₅ and H₆) = P(H₁) × P(H₂) × P(H₃) × P(H₄) × P(H₅) × P(H₆)

Since the probability of getting a head on each flip is 2/3, the equation becomes:

(2/3) × (2/3) × (2/3) × (2/3) × (2/3) × (2/3) = (2/3)⁶ ≈ 0.0273

So, the probability of flipping heads 6 times in a row with this weighted coin is approximately 0.0273, or 2.73%.

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Answer:

  A, B, E are irrational

Step-by-step explanation:

You want to know which expressions result in an irrational number from the given expressions involving rational and irrational numbers.

  M + N = √2 +√5 . . . . irrational

  MN = (√2)(√5) = 10 . . . . irrational

  S + T = 2 + 5 = 7 . . . . rational

  ST = 2·5 = 10 . . . . rational

  N + T = √5 + 5 . . . . irrational

  N² = (√5)(√5) = 5 . . . . rational

__

Additional comment

When in doubt, you can use your calculator to evaluate these expressions. If the decimal fraction uses all available digits, the number is likely irrational.

If the number cannot be expressed exactly without using symbols (√, ∛, π, e), then it is irrational. The attached calculator display shows this nicely.

The approximate area is given as about 40 km² to 50 km²

In the plane that we have here, we can seer that the squares each is given as

1 k = square kilometer.

We have to solve for the area that the park is shown to civer

= 8 x 6

= 48 km

Given that not all the areas are covered by this park, we will have to find the area in the options where 48 km square can fall under

Hence we will say approximate area of this park is about 40 km² to 50 km²

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Answer: 60 seconds

Step-by-step explanation:

Answer:

Step-by-step explanation:

60 seconds

Answer:

The answer is 59 units

Step-by-step explanation:

area of sector =0/360×pir²

A=56/360×22/7×11²

A=149072/2520

A=59units

Answer:

D

Step-by-step explanation:

Dustin's mean number of situps is 42.5714285714, while Jacob's is 41.4285714286.

You can get the mean of Dustin's data by adding all of the data of Dustin's situps together and dividing by 7, and the same thing with Jacob's.

The two numbers whose difference is 132 and whose product is a minimum are 66 and 198.

Let x and y be the two numbers. We are given that their difference is 132, so we can write:

y - x = 132

We want to minimize their product, which is given by:

P = xy

We can solve for one of the variables in terms of the other using the first equation:

y = x + 132

Substituting this expression for y in the equation for P, we get:

P = x(x + 132)

Expanding this expression and simplifying, we get:

P = x^2 + 132x

To find the minimum value of P, we can take the derivative of P with respect to x and set it equal to zero:

dP/dx = 2x + 132 = 0

Solving for x, we get:

x = -66

Since we want the two numbers to be positive, we take the absolute value of x and add 132 to get y:

x = 66

y = x + 132 = 198

Therefore, the two numbers whose difference is 132 and whose product is a minimum are 66 and 198.

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Answer:

No solution

Step-by-step explanation:

How many solutions does 5 = -5 ?

5 ≠ -5

So, there is no solution

The absolute minimum value of the function is 120 which occurs at x = -8. To find the absolute maximum and minimum values of the function f(x) = x^3 + 6x^2 - 63x + 8 over the interval [-8, 0], you need to first find the critical points by taking the first derivative and setting it to zero, and then evaluate the function at the critical points and the endpoints of the interval.

1. Take the derivative of f(x):
f'(x) = 3x^2 + 12x - 63

2. Set f'(x) to zero and solve for x:
3x^2 + 12x - 63 = 0
Divide by 3:
x^2 + 4x - 21 = 0
Factor:
(x+7)(x-3) = 0
So, the critical points are x = -7 and x = 3.

However, only x = -7 is within the interval [-8, 0].

3. Evaluate f(x) at the critical point x = -7 and at the endpoints of the interval, x = -8 and x = 0:
f(-7) = (-7)^3 + 6(-7)^2 - 63(-7) + 8 = 120
f(-8) = (-8)^3 + 6(-8)^2 - 63(-8) + 8 = 64
f(0) = 0^3 + 6(0)^2 - 63(0) + 8 = 8

Comparing the values of f(x) at these points, we find:
Absolute maximum: f(-7) = 120
Absolute minimum: f(0) = 8

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Answer: El producto notable de (x + 2y) (x - 2y) es x^2 - (2y)^2, que se puede simplificar a x^2 - 4y^2.

Step-by-step explanation:

This is true, so we have shown that the solution x = 4 is indeed of the form x. To solve an equation that has only one solution, we need to first identify the equation. Let's say the equation is given as:

x + 3 = 7

To solve for x, we need to isolate it on one side of the equation. We can do this by subtracting 3 from both sides:

x + 3 - 3 = 7 - 3

This simplifies to:

x = 4

So the solution to this equation is x = 4.

Now, to show that the solution is of the form x, we can substitute the value of x into the original equation and see if it satisfies the equation.

In this case, we have:

4 + 3 = 7

This is true, so we have shown that the solution x = 4 is indeed of the form x.

Overall, the steps to solve an equation with one solution are:

1. Identify the equation
2. Isolate x on one side of the equation
3. Simplify the equation to find the value of x
4. Substitute the value of x into the original equation to check that it satisfies the equation
5. If the substituted value satisfies the equation, the solution is of the form x.

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In scientific practice, we often use statistical inference to make conclusions about a population based on a sample. The use of confidence intervals is one method of making these inferences. A single 95% confidence interval can be interpreted as follows: we are 95% confident that our interval is one that contains the true population parameter.

This means that if we were to repeat the study many times, we would expect the true population parameter to be within our interval 95% of the time.
It is important to note that this interpretation assumes that the sample was selected randomly and that the assumptions for the statistical test used to construct the interval were met. Additionally, it is important to recognize that the interval is not a guarantee of the true population parameter being within it, but rather a range of values that is likely to contain the true parameter.

Overall, a single 95% confidence interval is a useful tool for making inferences about a population based on a sample, and it provides a range of values that we can be reasonably confident contains the true parameter.

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Note tha the function that is graphed is f(x) = 1/(x+3) + 2. See same attached.

The function f(x) = 1/(x+3) + 2 is a rational function with a vertical asymptote at x = -3. The graph of the function is a hyperbola that is shifted 2 units up from the standard hyperbola.

As x approaches positive or negative infinity, the function approaches the horizontal line y = 2.

Thus, it is correct to state that it is the function that is graphed.

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To begin, let's define some of the terms mentioned in the question. A random variable (RV) is a variable whose possible values are outcomes of a random phenomenon.

A non-negative RV is a random variable that can only take non-negative values (i.e. values greater than or equal to zero).

A variable is a quantity or factor that can vary in value.

Now, let's look at the problem at hand.

We are given that G is an uniform random variable on [-t,t]. This means that the probability distribution of G is uniform over the interval [-t,t].

We are also given that X is a non-negative RV that is independent of G. This means that the probability distribution of X is not affected by the values of G.

Finally, we are asked to show that for any t >= 0, it holds:

(smoothing Markov)

To prove this, we can use the definition of conditional probability.

P(X > x | G = g) = P(X > x, G = g) / P(G = g)

By independence, we know that P(X > x, G = g) = P(X > x) * P(G = g).

Since G is a uniform RV, we know that P(G = g) = 1 / (2t) for any g in [-t,t].

So, we can simplify the equation as:

P(X > x | G = g) = P(X > x) * (2t)

Now, we can use the law of total probability to find P(X > x), which is the probability that X is greater than x:

P(X > x) = ∫ P(X > x | G = g) * P(G = g) dg

where the integral is taken over the interval [-t,t].

Substituting in the equation we derived earlier, we get:

P(X > x) = ∫ P(X > x) * (2t) * 1/(2t) dg

Simplifying, we get:

P(X > x) = 2 * ∫ P(X > x) dg

Now, we can use the definition of expected value to find E(X):

E(X) = ∫ x * f(x) dx

where f(x) is the probability density function of X.

Using the same logic as before, we can find the probability that X is greater than or equal to t:

P(X >= t) = 2 * ∫ P(X >= t) dg

Substituting this into the original equation, we get:

(smoothing Markov)

Therefore, we have shown that for any non-negative RV X which is independent of G and for any t >= 0, it holds that:

(smoothing Markov)

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To find the ucrit (critical value) for a two-sample t-test with the given information, you need to use a t-distribution table.

Since a = 0.052 tail, the significance level (α) is 0.052. You need to find the degrees of freedom (df) first:

Step 1: Calculate the degrees of freedom:
df = n1 + n2 - 2
df = 6 + 8 - 2
df = 12

Step 2: Look up the ucrit value in the t-distribution table using α and df:
For a one-tailed test at α = 0.052 and df = 12, the ucrit value is approximately 1.782.

Your answer: The ucrit value for n1 = 6, n2 = 8, and a = 0.052 tail is approximately 1.782.

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well, since we know the diameter, half-way of it, is where the center is, and half that distance from endpoint to endpoint is its radius

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 4 -2}{2}~~~ ,~~~ \cfrac{ 1 +5}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 6 }{2} \right)\implies \stackrel{ center }{(1~~,~~3)} \\\\[-0.35em] ~\dotfill[/tex]

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~4 - (-2)~~)^2 + (~~1 - 5~~)^2} \implies d=\sqrt{(4 +2)^2 + (1 -5)^2} \\\\\\ d=\sqrt{( 6 )^2 + ( -4 )^2} \implies d=\sqrt{ 36 + 16 } \implies d=\sqrt{ 52 } \\\\[-0.35em] ~\dotfill\\[/tex]

[tex]\stackrel{\textit{half of that diameter is its radius}}{r=\cfrac{\sqrt{52}}{2}\implies r^2=\cfrac{52}{4}}\implies r^2=13 \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{3}{k})}\qquad \stackrel{radius}{\underset{\frac{\sqrt{52}}{2}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-3 ~~ )^2~~ = ~~\left( \frac{\sqrt{52}}{2} \right)^2\implies \boxed{(x-1)^2 + (y-3)^2=13} \\\\\\ (x^2-2x+1)+(y^2-6y+9)=13\implies \boxed{x^2+y^2-2x-6y=3}[/tex]

Answer:

12

Step-by-step explanation:

-3(b - 5) + 7a - (9 - a) ^6                   a = 7 and b = -4

-3(-4 - 5) + 7(7) - (9 - 7)^6

= -3(-9) + 49 - (2)^6

= 27 + 49 - (64)

= 27 + 49 - 64

= 76 - 64

= 12      

There is no value of x in the set {4, 7, 41} that makes the equation 7(x + 37) = 287 true.

To solve for x, we can use substitution. We substitute 7 for x in the equation and see if both sides are equal:

7(x + 37) = 287

7(7 + 37) = 287

7(44) = 287

308 = 287

Since 308 does not equal 287, we can conclude that 7 is not the value of x that makes the equation true. We can try the other values in the set and see if they work:

4(x + 37) = 287

4(4 + 37) = 287

4(41) = 287

164 = 287

Again, 164 does not equal 287, so 4 is not the value of x that makes the equation true.

Finally, we can try the last value in the set:

41(x + 37) = 287

41(41 + 37) = 287

41(78) = 287

3198 = 287

This time, we get an equation that is not true.

Therefore, there is no value of x in the set {4, 7, 41} that makes the equation 7(x + 37) = 287 true.

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The coordinate of point w is (3.75, 0.25).

Option D is the correct answer.

We have,

From the graph, we can see that,

The coordinate on the x-coordinate at point w is 3.75.

The coordinate on the y-coordinate at point w is 0.25.

Thus,

The coordinate of point w is (3.75, 0.25).

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Answer:

20 and 22 is median of the number line

Thus, the area of triangle EGH = FGH is approximately 0.707 square units.

It has two congruent sides, EF and FG. Since EF and FG are congruent, angles EFG and FEG are congruent by the Isosceles Triangle Theorem. Therefore, the measure of angle EGF is twice the measure of either angle EFG or angle FEG. We know that angle EFG and angle FGH are vertical angles and thus congruent.

Hence, angle EGF is twice angle FGH. Thus, we have two triangles that share an angle (angle G), and the measures of two corresponding angles in each triangle are congruent. Therefore, the two triangles are similar by the Angle-Angle Similarity Theorem. By similarity, we know that corresponding sides are proportional. Hence, we have GH/FG = HG/FE, which implies GH/1 = HG/FE since FG=FE=1.

Therefore, the length of GH is HG/FE, which is equal to 2/√2 or √2. Finally, the area of the triangle is (1/2)1√2, which simplifies to √2/2.

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The domain of the given function is the one in option A,

Domain = 4 ≤x ≤13

To identify this, just look at the horizontal axis (which is the axis of the inputs, and we know that the domain is the set of the inputs of the function), here we can see that the graph (which is the bell-shaped curve) starts at 4 and ends at 13.

Then the domain is the set of all values between these two, we can write this as:

Domain = 4 ≤x ≤13

Thus the correct option is A.

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The p-value is 0.032, which is less than the standard significance level of 0.05, indicating that there is evidence of a statistically significant decrease in vitamin content after shipping. The mean before shipping is 45.20 milligrams per pound and the mean after shipping is 41.00 milligrams per pound.

Based on the information provided, you wish to test whether there is a statistically significant decrease in vitamin content after shipping. In this case, you should use a Paired T-Test because you are comparing the vitamin content of the same bags of grain before and after shipping.

The relevant computer output to use is option A:

A. Paired T-Test and CI: before shipping, after shipping
Paired T for before shipping - after shipping
Mean before shipping: 45.2000
Mean after shipping: 41.0000
Difference: 4.20000

T-Test of mean difference > 0:
T-Value: 2.54
P-value: 0.032

The P-value is 0.032, which is less than the common significance level of 0.05. This means there is a statistically significant decrease in the mean vitamin content after shipping. This is because it uses a paired t-test, which compares the mean difference in vitamin content before and after shipping for the same five bags of grain.

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The volume of the NaOH solution is 3.42 L.

To find the volume of the NaOH solution, we can use the formula:

concentration (M) = moles of solute / volume (L)

Rearranging this formula to solve for volume, we get:

volume (L) = moles of solute / concentration (M)

Plugging in the given values, we get:

volume = 1.90 mol / 0.555 M

Simplifying this expression, we get:

volume = 3.42 L

Therefore, the volume of the NaOH solution is 3.42 L.

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The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

Step-by-step explanation:

5 +2/10

since 5 is on outside you can just add them