A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 32 centimeters, and the
length of the other leg is 26 centimeters. The student incorrectly says that the length of the hypotenuse is 7.6 centimeters
a. Find the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter

Answer:

The proportion of the pooled samples is 0.54.

Step-by-step explanation:

We have that:

70% of men own cats.

The proportion of men in the sample is:

\(\frac{170}{170+190} = 0.4722\)

40% of women own cats.

The proportion of women in the sample is: 1 - 0.4722 = 0.5278

Proportion of the pooled samples

\(p = 0.7*0.4722 + 0.4*0.5278 = 0.54\)

The proportion of the pooled samples is 0.54.

Two of them have the same remaining. The proof using the pigeonhole principle is now complete.

When an integer is divided by 4, there are four potential remainders: 0, 1, 2, or 3. Take any set of five numbers as an example.

If at least three of them have the same remainder when divided by 4, then we are done, since two of them will have the same remainder. This is because if three integers have the same remainder, then we can subtract that remainder from all of them, and the resulting three integers will all be divisible by 4, which means that two of them will have the same remainder when divided by 4.

So suppose that at most two of the integers have the same remainder when divided by 4. Then there are at most two integers with remainder 0, at most two integers with remainder 1, at most two integers with remainder 2, and at most two integers with remainder 3. This means that there are at most 8 integers in total, which is a contradiction since we started with 5 integers. Therefore, there must be at least three integers with the same remainder when divided by 4, and hence there are two with the same remainder. This completes the proof by the pigeonhole principle.

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Answer:

x = 2

Explanation:

Given:

BG = 27

AG = 13 + 7x

Note that when three perpendicular bisectors of the sides of a triangle meet at a point, the point is called a Circumcenter.

Also, note that the Circumcenter is equidistant from the vertices of the triangle.

So for the given triangle, G is the circumcenter, and AG = BG = CG.

Let's go ahead and solve for x as seen below;

Let's subtract 13 from both sides of the equation, we'll have;

Let's divide both sides by 7;

So the value of x is 2

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

\(f(x)=\frac{x^2+9}{x-3}\)

We have to find true statement about given function.

\(\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}\)

=\(\infty\)

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

Answer:

126°

Step-by-step explanation:

Given that the yellow portion covers 35% of the circle, the degree formed by its edges can be calculated as follows:

The degree of a full circle = 360°

To find the degree formed by the edges of the yellow region, we would calculate 35% of 360°:

\( \frac{35}{100}*360 \)

\( \frac{35*360}{100} \)

\( \frac{12600}{100} \)

\( \frac{126}{1} \)

\( 126 \)

126° is formed by the edges of the yellow region.

16 units, is the length of a side of the hexagon or square

The perimeter of the square = the Sum of the lengths of 4 sides. = side + side + side + side. = 4 × side.

Therefore, the perimeter of Square = 4s

Consider x to be the perimeter of the square=4x

The perimeter of a regular hexagon is just the sum of all 6 sides. Because in a regular hexagon, the perimeter is just six times one side (6 cm) or 36 cm.

Consider x to be the perimeter of the hexagon=6x

Now, to find the length:

4x + 32 = 6x

6x-4x=32

2x=32

X=16

So, the length of the side = 16 units.

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Answer:

Hope this helps!

Answer:

48

Step-by-step explanation:

If the area of each square is 16, then each side length has side length of 4 because the area of a square is:

\(s^2=A\)

\(s^2=16\\s=4\)

Each of the outer edges has 4+4+4 and there are four of them so:

\((4+4+4)*4=48\)

Answer:

got n=13

Step-by-step explanation:

I set it up 4n+7=59 because 4 dollars you can get a dvd and when you solve you

Answer:

6

Step-by-step explanation:

Answer:

12x + 50 =210

Step-by-step explanation:

Given the data on the world problem, we know that one of our terms will be 12x because it says "each month" in the problem. If his mom is going to give him 50 dollars, and the Jordans cost 210, then we can write  a simple equation.

x = number of months it will take him

\(12x+50=210\)

Answer: 5.8=x

Step-by-step explanation:

$210=Price

$12=Each Month

$50=From Mom

120-50=70

70/12=5.8 Months

Answer:

4.02%

Step-by-step explanation:

0.0402×100=4.02%

Answer:

4.02%

Step-by-step explanation:

The transition matrix for Markovian is,

[ 0.7     0.3 ]

[ 0.3     0.7 ]

Probability is an area of mathematics that deals with numerical descriptions of the likelihood of an event happening or a proposition being true. An event's probability is a number between 0 and 1, where 0 indicates impossibility and 1 represents certainty.

Probability is simply the possibility of something happening. When we are confused about the outcome of an event, we might discuss the probabilities of certain outcomes—how likely they are. Statistics is the study of occurrences based on probability.

Let \(S_{i}\), i = 1, 2, is denoted for state i.

If \(T_{ij}\) is denoted for the transition from \(S_{j}\)  to \(S_{i}\),

The transition probabilities are given by:

Probability(T₁₁) = 0.7

Probability(T₂₁) = 1- Probability(T₁₁) = 1 - 0.7 = 0.3

Probability(T₁₂) = 0.3

Probability(T₂₂) = 1- Prob(T₁₂) = 1 - 0.3 = 0.7

So, the transition matrix for Markovian is,

[ 0.7     0.3 ]

[ 0.3     0.7 ]

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The maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

To analyze the bias of the maximum likelihood estimator (MLE) for the variance, we need to consider the assumptions and properties of the regression model.

In the given regression model:

\(Y_i\) = β₁ + β₂\(X_{2i}\) + β₃\(X_{3i}\) + β₄\(X_{4i}\) + U\(_{i}\)

Here, \(Y_i\) represents the dependent variable, \(X_{2i}, X_{3i},\) and \(X_{4i}\) are the independent variables, β₁, β₂, β₃, and β₄ are the coefficients, U\(_{i}\) is the error term, and i represents the observation index.

The assumption of the classical linear regression model states that the error term, U\(_{i}\), follows a normal distribution with zero mean and constant variance (σ²).

Let's denote the variance as Var(U\(_{i}\)) = σ².

The maximum likelihood estimator (MLE) for the variance, σ², in a simple linear regression model is given by:

σ² = (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

To determine the bias of this estimator, we need to compare its expected value (E[σ²]) to the true value of the variance (σ²). If E[σ²] ≠ σ², then the estimator is biased.

Taking the expectation (E) of the MLE for the variance:

E[σ²] = E[ (1 / n) × Σ[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

Now, let's break down the expression inside the expectation:

[( \(Y_i\) - β₁ - β₂\(X_{2i}\) - β₃\(X_{3i}\) - β₄\(X_{4i}\))²]

= [ (β₁ - β₁) + (β₂\(X_{2i}\) - β₂\(X_{2i}\)) + (β₃\(X_{3i}\) - β₃\(X_{3i}\)) + (β₄\(X_{4i}\) - β₄\(X_{4i}\)) + \(U_{i}\)]²

= \(U_{i}\)²

Since the error term, \(U_{i}\), follows a normal distribution with zero mean and constant variance (σ²), the squared error term \(U_{i}\)² follows a chi-squared distribution with one degree of freedom (χ²(1)).

Therefore, we can rewrite the expectation as:

E[σ²] = E[ (1 / n) × Σ[\(U_{i}\)²] ]

= (1 / n) × Σ[ E[\(U_{i}\)²] ]

= (1 / n) × Σ[ Var( \(U_{i}\)) + E[\(U_{i}\)²] ]

= (1 / n) × Σ[ σ² + 0 ] (since E[ \(U_{i}\)] = 0)

Simplifying further:

E[σ²] = (1 / n) × n × σ²

= σ²

From the above derivation, we see that the expected value of the MLE for the variance, E[σ²], is equal to the true value of the variance, σ². Hence, the MLE for the variance in this regression model is unbiased.

Therefore, the maximum likelihood estimator for the variance, (ui|\(X_{2i}\), \(X_{3i}\), β₄\(X_{4i}\)), is unbiased.

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Answer:

4m-20

Step-by-step explanation:

\((m - 5)4 \\ = m \times 4 + - 5 \times 4 \\ = 4m - 20\)

Answer: the correct graph is the one that shows a horizontal segment, followed by a positive slope segment, followed by a flat segment, and then a negative slope segment that is option c.

What is graph?

In mathematics, a graph is a visual representation of a set of objects and the connections between them. The objects, which are often called vertices or nodes, are typically represented by points or circles on the graph. The connections between the objects, which are often called edges or arcs, are typically represented by lines or curves connecting the points or circles.

Here,

To represent Marie's situation in a graph, we need to plot her golf cart's distance from the first hole over time. Let's analyze the given information to determine what the graph should look like.

For the first 30 minutes, Marie stayed at the first hole, so her distance from the first hole would be 0 during that time.

For the next 2 hours, Marie drove away from the first hole. Her distance from the first hole would increase during this time.

After 2 hours of driving, Marie stopped for lunch. Her distance from the first hole would remain constant during this time.

After lunch, Marie took 2 more hours to drive back to the first hole. Her distance from the first hole would decrease during this time.

The x-axis represents time in hours, and the y-axis represents distance from the first hole in miles. The graph starts at the origin, where the golf cart stays for the first 30 minutes, and then goes up with a positive slope for 2 hours as the golf cart moves away from the first hole. Then, the graph remains flat for 1 hour during lunch, before going down with a negative slope for 2 hours as the golf cart returns to the first hole.

As a result, the right graph is option c, which displays a horizontal section followed by a positive slope segment, a flat segment, and then a negative slope segment.

Step-by-step explanation:

Answer: Good morning, to answer your question

The midpoint  is (2 7/2)

Step-by-step explanation:

Midpoint is calculated using formula x1/2 plus x2/2 plus y1/2 plus y2/2

0 plus 4 over 2 = 4/2

4 plus 3 over 2 is 7/2

Add 7/2 plus 4/2

4/2 plus 7/2 is = 2 7/2

You can turn it into a mixed number if you want! :)

Answer:

\(-6\leq x < 5\)

Step-by-step explanation:

Given compound inequality:

\(31 \geq-4x+7\;\;\;\textsf{and}\;\;\;-4x+7 > -13\)

Solve the first inequality:

\(\begin{aligned}31 & \geq -4x+7\\\\31 +4x& \geq -4x+7+4x\\\\4x+31& \geq 7\\\\4x+31-31 & \geq 7-31\\\\4x & \geq -24\\\\\dfrac{4x}{4} & \geq \dfrac{-24}{4}\\\\x & \geq -6\end{aligned}\)

Solve the second inequality:

\(\begin{aligned}-4x+7& > -13\\\\-4x+7-7& > -13-7\\\\-4x& > -20\\\\\dfrac{-4x}{-4}& > \dfrac{-20}{-4}\\\\x& < 5\end{aligned}\)

Therefore, combining the solutions, the solution to the compound inequality is:

\(\large\boxed{-6\leq x < 5}\)

When graphing inequalities:

To graph the solution:

Answer:

I do believe it is B

Step-by-step explanation:

Volume of a cone

1/4π ft³

To find the volume of the cone, we use the formula

volume = (1/3) × π × r² × h

From the question, we are given its height and radius

we substitute for these in the equation above. these will give us the answer. (note in terms of pi)

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Answer:

15

Step-by-step explanation:

y/x=constant

20/4=y/3

y=5*3

y=15

Pumped 8 gallons of water out of her pool. this was done over a period of 4 minutes at a constant rate. so the change in the amount of water in the pool each minute is 2 gallons.

To find the change in the amount of water in the pool each minute, we need to divide the total change in gallons by the total time in minutes. In this case, Charmaine pumped 8 gallons of water out of her pool over a period of 4 minutes.
To find the change in the amount of water in the pool each minute, we divide the total change in gallons (8 gallons) by the total time in minutes (4 minutes):
Change in amount of water per minute = Total change in gallons / Total time in minutes
Change in amount of water per minute = 8 gallons / 4 minutes
Change in amount of water per minute = 2 gallons per minute
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Given that \(\(T(n)\) = \(10n^2-3n\)\) if (\(\(n=1\)\)), you have to prove it by induction. So, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if ( n= 1). The given statement is true for all positive integers n

Let's do it below: The base case (n=1) is given as follows: \(T(1)\) =\(10\cdot 1^2-3\cdot 1\\&\)=\(7\end{aligned}$$\). This implies that \(\(T(1)\)\) holds true for the base case.

Now, let's assume that \(\(T(k)=10k^2-3k\)\) holds true for some arbitrary \(\(k\geq 1\).\)

Thus, for n=k+1, T(k+1) = \(10(k+1)^2-3(k+1)\\&\) = \(10(k^2+2k+1)-3k-3\\&\)=\(10k^2+20k+7k+7\\&\) = \(10k^2-3k+20k+7k+7\\&\) = \(T(k)+23k+7\\&\) = \((10k^2-3k)+23k+7\\&\) =  \(10(k+1)^2-3(k+1)\).

Therefore, we have proved that the statement holds true for n=k+1 as well. Hence, we have proved it by induction that  \($$\(T(n)=10n^2-3n\)$$\)  if (n=1). Therefore, the given statement is true for all positive integers n.

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Answer:

196 miles

Step-by-step explanation:

distance (D) is calculated as

D = S × T ( S is average speed and T is time in hours )

here T = 3 and a half hours = 3.5 hours and S = 56 , then

D = 56 × 3.5 = 196 miles