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The true statements about the Pythagorean theorem are :

a) Only used on Right Triangles

b) The legs are sides a and b of the triangles

c) The last step is to take the square root of both sides

Given data ,

The Pythagorean Theorem is a mathematical theorem that applies only to right triangles, and it states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the two other sides, called the legs.

a² + b² = c²

where a and b are the lengths of the legs, and c is the length of the hypotenuse

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Answer:

[tex]C.\quad \dfrac{\sqrt{17}}{6}[/tex]  

Step-by-step explanation:

We are given
[tex]\tan\theta = - \dfrac{\sqrt{19}}{\sqrt{17}} \\\\[/tex]

Square both sides
[tex]\tan^2\theta = \left(- \dfrac{\sqrt{19}}{\sqrt{17}} \right)^2 = \dfrac{19}{17}[/tex]

[tex]\tan \theta = \dfrac{\sin\theta}{\cos\theta}\\\\\tan^2 \theta = \dfrac{\sin^2\theta}{\cos^2\theta}\\[/tex]

Substituting for [tex]tan^2 \theta[/tex] and switching sides we get

[tex]\dfrac{\sin^2\theta}{\cos^2\theta} = \dfrac{19}{17}\\\\\text{Add 1 to both sides:}\\\\ \\ \dfrac{\sin^2\theta}{\cos^2\theta} + 1 = \dfrac{19}{17} + 1 \\\[/tex]

[tex]\dfrac{\sin^2\theta + cos^2\theta}{\cos^2\theta} = \dfrac{19 + 17}{17} = \dfrac{36}{17}[/tex]

[tex]\sin^2\theta + cos^2\theta = 1[/tex]

giving

[tex]\dfrac{1}{\cos^2\theta} = \dfrac{36}{17}[/tex]

[tex]\dfrac{17}{36} = \cos^2\theta\\\\ \cos^2\theta = \dfrac{17}{36}\\\\ \cos\theta = \sqrt{\dfrac{17}{36}}\\\\ \cos\theta = \dfrac{\sqrt{17}}{6} \\\\[/tex]

This is choice C. You had it right

Answer:

  0.13

Step-by-step explanation:

You want the probability that a point in the figure lies in the red shaded area.

The desired probability is the ratio of the red area to the entire area.

The red area is half a 4×4 square, so is (4×4)/2 = 8 square units.

The area of the whole figure is that of an 8×8 square, so is (8×8) = 64 square units.

The ratio of the areas is ...

  red/whole = 8/64 = 1/8 = 0.125 ≈ 0.13

The probability that a randomly selected point falls in the red area is about 0.13.

<95141404393>

The calculated amount paid by Leroy is 4.75

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

Ticket = 5

Reduction = A quarter

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

Amount paid = 5 - A quarter

Evaluate

Amount paid = 4.75

Hence, the amount paid = 4.75

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To find the equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3), follow these steps: 1. Find the derivative of the function: dy/dx r,

Represents the slope of the tangent line at any point (x, y) on the curve.
y = 9x - (6/x)
dy/dx = d(9x)/dx - d(6/x)/dx

Using the power rule for the first term and the quotient rule for the second term:
dy/dx = 9 - (-6/x^2)
dy/dx = 9 + 6/x^2

2. Find the slope of the tangent line at the given point (1, 3) by plugging x = 1 into the derivative:
m = 9 + 6/1^2
m = 9 + 6
m = 15

3. Use the point-slope form of a linear equation to find the equation of the tangent line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (1, 3) and m is the slope:
y - 3 = 15(x - 1)

4. Solve for y to get the equation of the tangent line:
y = 15(x - 1) + 3
y = 15x - 15 + 3
y = 15x - 12

The equation of the tangent line to the curve y = 9x - (6/x) at the given point (1, 3) is y = 15x - 12.

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25. If point A is the incenter then point A is the point of concurrence of the  angle bisectors of a triangle

26. ST = 15

27. x = 8

28. ∠ QRT = 24 degrees

29. ∠ RPT = 31 degrees

This is a point where the angle bisectors of the triangle intersect. The incenter is also the center of the circle

since incenter is the center of the triangle therefore

ST = WT = UT = 16

The incenter is meeting point of angle bisectors too hence we have that

∠ QRT = ∠ PRT = 24 degrees.

Also, ∠ RPT = ∠ RPQ / 2 = 62 / 2 = 31 degrees

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If the probability that a tire has an expected life of at least 30000 miles is 0.85, then the probability that a tire will have a life of less than 30000 miles is 0.15.

Using this information, we can find the probability that among 20 tires, a certain number will have a life of less than 30000 miles. This can be done using a binomial distribution, where the probability of success (a tire having a life of at least 30000 miles) is p = 0.85 and the number of trials is n = 20.

The probability of having k tires with a life of less than 30000 miles is given by the formula:

[tex]P(k) = (n choose k) * p^k * (1-p)^(n-k)[/tex]

where (n choose k) represents the number of ways to choose k items out of n, and is calculated by the formula:

(n choose k) = n! / (k! * (n-k)!)

Using this formula, we can find the probabilities of having 0, 1, 2, ..., 20 tires with a life of less than 30000 miles.

For example, the probability of having exactly 3 tires with a life of less than 30000 miles is:

P(3) = (20 choose 3) * 0.85^17 * 0.15^3

= 1140 * 0.085 * 0.003375

= 0.02736

Similarly, we can find the probabilities of having any other number of tires with a life of less than 30000 miles.

Note that the sum of all these probabilities is equal to 1, since one of these outcomes must occur.

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Answer:

  2π yards

Step-by-step explanation:

You want the circumference of a circle with a radius of 1 yard.

When the radius is given, the formula for circumference is ...

  C = 2πr . . . . . circumference for radius r

When the diameter is given, the formula for circumference is ...

  C = πd . . . . . circumference for diameter d

For a radius of 1 yard, the circumference is ...

  C = 2π(1 yard) = 2π yards

The circle's circumference is 2π yards.

__

Additional comment

The diameter is twice the radius, so ...

  d = 2r

That is, the diameter of the given circle is 2 yards. Using the second formula, we get ...

  C = π(2 yards) = 2π yards

Rearranging the second formula, we can get the equation ...

  π = C/d

That is, π (pi) is the ratio of the circumference to the diameter.

2x - 8 = 2(2x - 15) and 11 are the correct equation and answer respectively.

The given diagram is a triangle. From the figure, the triangles QLK is similar to triangle QRP.

Hence, the correct expression to solve for x will be:
RP = 2LK

Substitute the expression given

RP = 2x - 8

LK = 2x - 15

Substitute to have:

2x - 8 = 2(2x - 15)

Simplify to have:

2x - 8 = 4x - 30

2x - 4x = -30 + 8

-2x = -22

x = 11

Hence the correct equation and answer to solve for x using the triangle are 2x - 8 = 2(2x - 15) and 11 respectively.

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Therefore, the probability of observing 8 occurrences of the event in a 10-minute interval is about 10.49%.

The Poisson distribution with a mean of 5.1 occurrences over a 10-minute interval can be used to model the number of occurrences of an event in that interval. The probability of observing k occurrences in this interval is given by the following formula:

[tex]P(X=k) = (e^(-λ) * λ^k) / k![/tex]

where λ is the mean number of occurrences over the interval.

In this case, we want to find the probability of observing 8 occurrences in 10 minutes, so we can plug in λ=5.1 and k=8 into the formula above:

[tex]P(X=8) = (e^{(-5.1)} * 5.1^8) / 8![/tex]

Using a calculator or software, we can evaluate this probability to be approximately 0.1049, or about 10.49%.

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"A researcher is curious about the average IQ of all currently registered voters in the state of Iowa. If the average could be attained, it would be an example of a population parameter."

In statistical terms, a population parameter refers to a characteristic of a whole population. In this case, the researcher is interested in the average IQ of all registered voters in Iowa, which would be a population parameter. The researcher would need to gather IQ data from every registered voter in the state and calculate the mean IQ to obtain the population parameter.

However, it's important to note that obtaining the true population parameter is often impractical or impossible due to logistical constraints, so researchers typically rely on samples to estimate population parameters with a certain level of confidence.

This question should be provided as:

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Answer:

  7.2 hours

Step-by-step explanation:

You want the number of rental hours that will result in the same charge if one store rents for $22.25 per hour, and the other store rents for $21.00 per hour with an added $9 charge.

The cost for h hours at the first store is ...

  cost = 22.25h

The cost for h hours at the second store is ...

  cost = 21.00h +9.00

The costs are the same when ...

  22.25h = 21.00h +9.00

  1.25h = 9.00 . . . . . . . . . . . . . subtract 21h

  h = 9.00/1.25 = 7.20 . . . . . . . divide by 1.25

Annalisa will spend the same at each store for a rental of 7.2 hours.

__

Additional comment

The cost at either place for a 7.2 hour rental is $160.20.

<95141404393>

Answer: )Step-by-step explanation:

When you say that the matrices form a basis for the linear space, I assume you mean that they form a basis for the vector space of matrices with the same dimensions.

To write the matrix of the linear transformation relative to the given basis, follow these steps:

1. Identify the basis matrices for the linear space.
2. Apply the linear transformation to each basis matrix.
3. Express the transformed matrices as linear combinations of the basis matrices.
4. Write the coefficients of these linear combinations as columns in the matrix of the linear transformation.

By following these steps, you will have the matrix of the linear transformation relative to the given basis. Note that I cannot provide specific numbers or examples since no specific matrices or transformations were provided in your question.

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Answer:

21.7 in^2

Step-by-step explanation:

A = 6a^2 =6 · 1.9^2 = 21.66in²

Round: 21.7 in^2

The amount of glass needed to cover the entire pyramid is given as follows:

144.53 ft².

The amount of glass needed to cover the entire pyramid is given by the surface area of the pyramid.

The surface area of any prism is given by the sum of the areas of all the parts of the prism.

The pyramid in this problem is composed as follows:

The areas are calculated as follows:

Hence the surface area of the pyramid is given as follows:

S = 7 x 6 + 2 x 0.5 x (7 x 7.79 + 6 x 8)

S = 144.53 ft².

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The trigonometric identity cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x

A trigonometric identity is a mathematical expression that contains trigonometric ratios.

To prove that : cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = sin²x + 1 ​, we proceed as follows

We need to show that Left hand side L.H.S = right hand side R.H.S

Now

So, substituting the values of the variables into the equation, we have that

L.H.S = Cos²(180 - x) + 2CosxCos(90 + x)tan(360 - x) = (-Cosx)² + 2Cosx(-sinx)(-tanx)

= (Cosx)² + 2Cosxsinxtanx

Now tanx = sinx/cosx,

So, substituting the values of the variables into the equation, we have that

(Cosx)² + 2Cosxsinxtanx = (cosx)² + 2cosxsinxsinx/cosx

= cos²x + 2sin²x

= cos²x + sin²x + sin²x

Now the trigonometric identity cos²x + sin²x = 1.

So, we have that

cos²x + sin²x + sin²x = 1 + sin²x = R.H.S

So, cos²(180 - x) + 2cosxcos(90 + x)tan(360 - x) = 1 + sin²x

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The constant of proportionality is expressed as a fraction in reduced terms as: k = 1/9.

The constant of proportionality is a constant which represents the rate at which one variable vary directly with another variable, proportionately.

For example, if x and y are the two variables, and y is dependent on x, therefore:

Constant of proportionality (k) = y/x.

The table given as shown in the attachment shows a relationship between v and w. Therefore, we have:

Constant of proportionality (k) = 16/144 = 7/63 = 4/36

Constant of proportionality (k) = 1/9

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To prove that DE is parallel to FB, we can use the property that the line joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

We can see triangles AED and CFB with DE and FB as their respective midsegments. Then, we can show that these triangles are similar and that their corresponding sides are proportional. This will imply that DE and FB are parallel.

Proof:

ABCD is a parallelogram, E is the midpoint of AB and F is the midpoint of DC.

Given

Construct triangles AED and CFB with DE and FB as their midsegments, respectively.

Definition of midsegment

AE = ED and CF = FB

Given that E and F are midpoints

AD = BC

Opposite sides of a parallelogram are congruent

∠AED = ∠DCF

Opposite angles of a parallelogram are congruent

∠ADE = ∠CDB

Alternate interior angles formed by parallel lines and a transversal

Triangles ADE and CFB are similar

By angle-angle similarity (AA)

AD/CF = DE/FB

Corresponding sides of similar triangles are proportional

Substituting AD = BC and simplifying, we get:

BC/CF = DE/FB

Since CF = FB (given), we have:

BC/FB = DE/FB

Therefore, BC = DE

Since the corresponding sides of similar triangles are proportional, we can equate BC/CF and DE/FB to get this result.

Hence, DE is parallel to FB

If a line segment joining the midpoints of two sides of a triangle is parallel to the third side, then it is half its length.

Therefore, DE is parallel to FB, as required.

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Answer:

If this is the full question, 60x

Step-by-step explanation:

Let x = # of liters leaked per minute.  There are 60 minutes in an hour.

If this isn't the full question and you forgot to write the # of liters leaked per minute, just multiply that number by 60.

The main difference between sequential and combinational circuits is that sequential circuit have internal memory and state, while combinational circuits do not.

Sequential circuit and combinational circuits are both types of digital circuits that are used in electronics and computer engineering. The main difference between the two is that sequential circuits use feedback and memory elements to store and propagate information, while combinational circuits do not.

Combinational circuits are made up of logic gates that are connected together to perform a specific function, such as addition or subtraction. The output of a combinational circuit depends only on the current inputs, and there is no internal memory or state.

In contrast, sequential circuits use feedback to store and propagate information, and the output of a sequential circuit depends not only on the current inputs but also on the past inputs and the internal state of the circuit. Sequential circuits include flip-flops, registers, and counters, which are used to store and manipulate data over time.

In summary, the main difference between sequential and combinational circuits is that sequential circuits have internal memory and state, while combinational circuits do not.

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The measure of <1 is 80 and <2 is 100 degree.

we have,

m<1 (4 x + 12)° and m <2 = (6x - 2)°

As, <1 and <2 are in linear pair then

m<1 + m<2 = 180

4x+ 12 + 6x -2= 180

10x + 10 = 180

10x= 170

x= 170/10

x= 17

Thus, the measure of each angle is

m <1 = 4x+ 12 = 68 + 12=  80

m<2= 6x-2 = 102-2= 100

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The linear pattern between Shops and Crimes is established through the visible increasing trend formed by data points within the scatterplot.

This is further reinforced by the noteworthy clustering of evidence along the least squares line, implying an undeniable relationship exists between the number of coffee shops and cases of reported property crime in these counties.

Moreover, the correlation coefficient, at 0.94, strongly accentuates the strong positive link that has been deduced between both external and internal variables. .

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The amount of fabric needed to make the tent is given as follows:

C. 18,350 sq. in.

The amount of fabric needed is given by the surface area of the figure presented in this problem.

The surface area is given by the sum of all areas that compose the figure in the context of the problem.

The figure is composed as follows:

Hence the surface area is given as follows:

S = 198 x 75 + 2 x 0.5 x 50 x 70

S = 18,350 sq. in.

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Given bakery can offer 27 distinct types of breakfasts.

The number of pastries available must be multiplied by the number of beverages available in order to determine how many distinct breakfast options are available at the bakery.

The overall amount of varied breakfast options is nine pastries and three beverage selections.

3 drinks plus 9 pastries equal 27 distinct breakfast options.

As a result, the bakery offers 27 distinct breakfast options.

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Answer:

504

Step-by-step explanation:

use pemdas

multiply 8 and 7 first then u have 56 so multiply it by 9

The expression 9x (8x7) can be rewritten as (9x8) x7 or 72x7 by using the associative law of multiplication. This law states that the way numbers are grouped doesn't affect the result of multiplication.

The question asks to rewrite 9x (8x7) using the associative law of multiplication. The associative law of multiplication, in basic terms, states that the way in which numbers are grouped in multiplication does not change the result.

To apply this law to the given expression, we just need to change the grouping of the numbers. Instead of grouping (8x7) together, we could group (9x8) together. So, the content loaded rewrite of 9x (8x7) using the associative law of multiplication would be: (9x8) x7 or we can write it as 72x7.

This does not change the result of the multiplication, thus demonstrating the associative property. This is a helpful principle to understand, as it is commonly applied in a variety of mathematical operations and can simplify complex equations.

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The angle that has a cosine of 3/5 is: ∠A

The three main trigonometric ratios are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

The given fraction is actually 3/5. This can also be written as 6/10. Thus:

From the given triangle, we can say that:

cos A = 6/10

Thus, it represents angle A.

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Answer:

Step-by-step explanation:

dior dior

The statement is false.

In fact, the correct statement is the opposite: if the linear transformation T(x) = Ax is one-to-one, then the columns of A form a linearly independent set.

To see why, suppose that T(x) = Ax is one-to-one, which means that for any two distinct vectors x1 and x2, we have T(x1) = Ax1 and T(x2) = Ax2, and Ax1 ≠ Ax2. This implies that x1 ≠ x2, since if x1 = x2, then we would have Ax1 = Ax2, which contradicts the assumption that Ax1 ≠ Ax2.

Now suppose that the columns of A are linearly dependent, which means that there exist scalars c1, c2, ..., cn, not all zero, such that c1a1 + c2a2 + ... + cnan = 0, where a1, a2, ..., an are the columns of A. Then we can rewrite this equation as A(c1e1 + c2e2 + ... + cnen) = 0, where e1, e2, ..., en are the standard basis vectors. Since not all of the ci's are zero, there exists a non-zero vector c = (c1, c2, ..., cn) such that Ac = 0. But this means that T(c) = Ac = 0, which contradicts the assumption that T(x) is one-to-one, since c ≠ 0 but T(c) = 0. Therefore, the columns of A must be linearly independent if T(x) = Ax is one-to-one.

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In this context, a type I error would occur if the null hypothesis was rejected when it is actually true, meaning that the patient does not have the disease but is diagnosed with it.

This would be a false positive result. It is important to note that a type I error is related to the level of significance chosen for the hypothesis test, and it represents the probability of rejecting the null hypothesis when it is true.

In this case, if the level of significance was set at 0.05, for example, there would be a 5% chance of making a type I error. It is also important to consider the consequences of making a type I error in a medical context, as it could lead to unnecessary treatments or interventions that could harm the patient.

Therefore, it is crucial to carefully design hypothesis tests and choose appropriate levels of significance to minimize the risk of making such errors.

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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! :)