What is the length of Line segment B C? Round to the nearest tenth. Triangle A B C is shown. Angle B C A is a right angle and angle C A B is 65 degrees. The length of hypotenuse B A is 16 centimeters and the length of B C is x. 6.8 cm 7.5 cm 14.5 cm 17.7 cm

Answer:x=5,x=-8

Step-by-step explanation:

First, you will need to simplify, rearrange the terms, move your terms to the left , distribute, and lastly combine like terms.

x^2 - 6x =40 -9x

x^2 +3x -40 =0 this is what you will get once you do all of the steps.

then use the quadratic formula, and simplify.

Step-by-step explanation:

first let's bring the equation into "normal" form :

x - 2y = 2

-2y = 2 - x

2y = x - 2

y = x/2 - 1

so, the slope of this line is 1/2 (the factor of x - that is always the case in all lines).

a parallel line must have the same slope, of course.

so, its equation is

y = x/2 + b

now, b will be different to the -1 of the original equation, or the lines are identical.

it is the point of interception of the line through the y-axis (x = 0).

we get this by using the coordinates of the given point (4, -3).

so,

-3 = 4/2 + b = 2 + b

b = -5

therefore, the formula for the parallel line is

y = x/2 - 5

Answer:

I believe the answer is y = -7/3x

Step-by-step explanation:

When you rearrange the equation, y = -3x - 8y, you will get -7y = -3x.

We want the equation to be equal to y by itself. So we divide -7 from both sides, giving us the equation y = 3/7x.

The graph that is perpendicular to y = 3/7x is it's reciprocal: y = -7/3x

Answer:

3

Step-by-step explanation:

Find the Slope of a Perpendicular Line

y = −3x − 8y

Rewrite in slope-intercept form.

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

y = mx + b

Move all terms containing y to the left side of the equation.

9y = −3x

Divide each term by 9 and simplify.

y = −(x/3)

Write in y = mx + b form.

y = -(1/3)x

Using the slope-intercept form, the slope is − (1/3)

m = -(1/3)

The equation of a perpendicular line to y = − (1/3)x must have a slope that is the negative  reciprocal of the original slope.

\(m\)perpendicular = \(-\frac{1}{-\frac{1}{3} }\)

Simplify the result.

\(m\)perpendicular = 3

The proportion of baby boys in the United States that are born with low birth weight is 0.0495

In a set with mean  u and standard deviation σ , the z score of a measure X is given by:

Z= X - u / σ

Z = 2.5- 3.41/ 0.55

Z= -1.6545

Z= -1.65 has a p value of 0.0495

The proportion of baby boys in the United States that are born with low birth weight is 0.0495.

the complete question is

In the United States, the mean birth weight for boys is 3.41 kg with a standard deviation of 0.55 kg. Assume that the distribution of birth weight is approximately normal. A baby is considered of low birth weight if it weighs less than 2.5 kg. What proportion of baby boys in the United States are born with low birth weight

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The volume of the sphere is 4 π × 3 × h. Option C

To determine the expression, we need to know the formula for volume of a sphere.

The formula that is used for calculating the volume of a sphere is expressed as;

V = 1/3 πr²h

Given that the parameters of the formula are;

Now, substitute the values, we have;

Volume, V= 4/3 × π × 3² × h

Multiply the values, we get;

Volume =4 π × 3² × h/3

Divide the values

Volume =4 π × 3 × h

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The probability that at least two of the balls have the same number is 27.40%

Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.

Probability requested is equivalent to:

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(no 2 have same number) = No. of ways to succeed / No. of possible outcomes

No. of ways to succeed = 90P8

No. of possible outcomes = 90^8

No. of ways to succeed =

nPr = n! / (n-r)!

90P8 = 90! / (90-8)!

90P8 = 90! / (82)!

90P8 = 90*89*88*87*86*85*84*83*82! / [(82)!

90P8 = 90*89*88*87*86*85*84*83

90P8 = 3.13x10^15

P(no 2 have same number) = 3.13x10^15 / 90^8

P(no 2 have same number) = 0.73

P(at least 2 have same number) = 1 - P(no 2 have the same number)

P(at least 2 have same number) = 1 - 0.73

P(at least 2 have same number) = 0.2740 = 27.40%

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We will investigate how to your direct proportions to evaluate the number of pages Henry can write given a set of time frame.

There is a relationship established between the number of pages that Henry writes in a certain amount off time. We will go ahead and define the variables:

We see that there is a direct relationship between the two variables ( x and y ). We can express a direct relation with the following equation:

Where,

To determine the constant of proportionality ( k ) we need a set of data. I.e the number of pages written in an amount of time. We are given that Henry can write 5 pages of his novel in 3 hours. So:

We will use the direct proportion relation expressed above and evaluate the constant of proportionality ( k ) as follows:

Therefore, the direct relationship between the two variables becomes:

Now we can use the above relation to determine either off the two variables given the other one. We are asked to find the number of pages that Henry can write if he takes 8 hours. Hence,

Using the defined relationship we can calculate as follows:

Therefore, the answer is:

The code first creates a data frame df with two columns: CustomerId and Product. The Product column contains the values "Toaster" and "Radio".

Here is the code to get a sub data frame where the product is "Toaster" from the data frame df:

df = pd.DataFrame({

 "CustomerId": range(1, 8),

 "Product": ["Toaster", "Toaster", "Toaster", "Radio", "Radio", "Radio", "Radio"]

})

sub_df = df[df["Product"] == "Toaster"]

print(sub_df)

This code will print the following sub data frame:

  CustomerId Product

0       1            Toaster

1       2            Toaster

2       3            Toaster

Sure, here is the code to get a sub data frame where the product is "Toaster" from the data frame df:

Python

df = pd.DataFrame({

 "CustomerId": range(1, 8),

 "Product": ["Toaster", "Toaster", "Toaster", "Radio", "Radio", "Radio", "Radio"]

})

sub_df = df[df["Product"] == "Toaster"]

print(sub_df)

Use code with caution. Learn more

This code will print the following sub data frame:

Code snippet

 CustomerId Product

0       1       Toaster

1       2       Toaster

2       3       Toaster

The code first creates a data frame df with two columns: CustomerId and Product. The Product column contains the values "Toaster" and "Radio".

The next line of code uses logical slicing to create a sub data frame sub_df where the Product column is equal to "Toaster". The print() statement then prints the sub data frame.

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Answer:

h(x) = 5x²-6

Step-by-step explanation:

f(x) = 5x²-1, translated vertically downward by 5 units, it becomes

h(x) = 5x² -1-5 = 5x²-6

Answer:

Slope is X

Y-intercept is B

Answer:

0.3656

Step-by-step explanation:

0.3656

I hope it's helped

the probability of rolling a seven on or before the eighth roll when rolling two dice is approximately 0.665 or 66.5%.

To determine the probability of rolling a seven on or before the eighth roll when rolling two dice, we need to consider the possible combinations that result in a sum of seven.

There are six possible outcomes when rolling two dice: (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), and (1, 6). Similarly, there are (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), and (2, 6), and so on, up to (6, 6).

Out of these possible outcomes, there are six combinations that result in a sum of seven: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1).

The probability of rolling a seven on a single roll is 6/36 or 1/6 since there are six favorable outcomes out of a total of 36 possible outcomes (6 sides on each die).

To find the probability of rolling a seven on or before the eighth roll, we need to consider the complementary probability. The complementary probability is the probability of not rolling a seven on the first seven rolls.

The probability of not rolling a seven on a single roll is 5/6 since there are five outcomes (not including the combinations that result in a seven) out of six possible outcomes.

Therefore, the probability of not rolling a seven on the first seven rolls is (5/6)^7.

The probability of rolling a seven on or before the eighth roll is then 1 - (5/6)^7, which is approximately 0.665 or 66.5%.

So, the probability of rolling a seven on or before the eighth roll when rolling two dice is approximately 0.665 or 66.5%.

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Answer:

The car would be going 305mph as the average, because it took an hour to go 305 miles.

(a) Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

(b) Where both players are indifferent between their available strategies.

(c)  The normal form representation of the game is above.

(d) No player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

(a) To derive the best response functions, we need to find the strategies that maximize the payoffs for each player given the mixed strategy of the other player.

Player Row's best response function:

If Player Column chooses L with probability q, Player Row's expected payoff for choosing U is 0q + 2(1-q) = 2 - 2q.

If Player Column chooses R with probability 1-q, Player Row's expected payoff for choosing U is 0*(1-q) + 1*q = q.

Therefore, Player Row's best response is given by:

BR_Row(q) = { U if q < 1/3, D if q > 1/3 (indifferent if q = 1/3)

Player Column's best response function:

If Player Row chooses U with probability p, Player Column's expected payoff for choosing L is 0p + 2(1-p) = 2 - 2p.

If Player Row chooses D with probability 1-p, Player Column's expected payoff for choosing L is 0*(1-p) + (-1)*p = -p.

Therefore, Player Column's best response is given by:

BR_Column(p) = { L if p < 1/2, R if p > 1/2 (indifferent if p = 1/2)

Plotting the best response functions on a graph with p on the horizontal axis and q on the vertical axis will result in two line segments: BR_Row(q) is horizontal at U for q < 1/3 and horizontal at D for q > 1/3, while BR_Column(p) is vertical at L for p < 1/2 and vertical at R for p > 1/2.

The two segments intersect at the point (p, q) = (1/2, 1/3).

(b) To find the Nash equilibria, we look for the points where the best response functions intersect. In this case, the only Nash equilibrium is at (p, q) = (1/2, 1/3), where both players are indifferent between their available strategies.

Now let's move on to the rock-paper-scissors-lizard game:

(c) The normal form representation of the game can be written as follows:

    R    P    S    L

------------------------

R | 0,0 -1,1 1,-1 1,-1

P | 1,-1 0,0 -1,1 1,-1

S | -1,1 1,-1 0,0 -1,1

L | -1,1 -1,1 1,-1 0,0

(d) To find the Nash equilibria, we look for any strategy profiles where no player can unilaterally deviate to improve their payoff.

In this game, there are no pure strategy Nash equilibria since each strategy can be countered by another strategy with a higher payoff.

However, there is a mixed strategy Nash equilibrium where each player chooses their actions with equal probabilities: r = p = s = l = 1/4.

In this case, no player can gain an advantage by deviating from this strategy.

This equilibrium results in an expected payoff of 0 for each player.

In summary, the rock-paper-scissors-lizard game has a unique mixed strategy Nash equilibrium where each player randomly chooses their actions with equal probabilities.

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Overall, building a theory is a complex process that requires careful planning, attention to detail, and a willingness to remain open to alternative explanations and interpretations.

An important first step when building a theory is to formulate a clear and testable research question or hypothesis. A research question or hypothesis is a statement that suggests a relationship between two or more variables, and it guides the development of the theory. The research question or hypothesis should be specific, measurable, and falsifiable, meaning that it can be tested and potentially proven false through empirical research. Once a clear research question or hypothesis has been formulated, the researcher can then begin to gather and analyze data to support or refute the theory.

Another important first step when building a theory is to conduct a comprehensive review of existing literature and research in the field. This review helps the researcher to identify gaps or inconsistencies in current knowledge and to develop a clear understanding of the state of the field. This step can also help the researcher to refine their research question or hypothesis, as well as to identify potential variables and relationships that may be relevant to the theory.

Another important step when building a theory is to select an appropriate research design and methodology that will allow for the systematic collection and analysis of data. The research design should be aligned with the research question or hypothesis, and should enable the researcher to collect high-quality data that can be analyzed using appropriate statistical or qualitative methods.

In addition, it is important to be mindful of potential biases that can impact the development of a theory, such as confirmation bias or researcher bias. It is important for the researcher to be objective and to consider all possible explanations for their data, rather than solely seeking out evidence that supports their hypothesis or preconceived ideas.

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Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

\(d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ \)

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(2, 3) and (-3, -2)

The distance between them is

\(d = \sqrt{( {2 + 3})^{2} + ({3 + 2})^{2} } \\ = \sqrt{ {5}^{2} + {5}^{2} } \\ = \sqrt{25 + 25} \\ = \sqrt{50} \\ = 5 \sqrt{2} \)

We have the final answer as

\(5 \sqrt{2} \: \: \: \: units\)

Hope this helps you

Answer:

I think 1 hour and 6 mins.

Step-by-step explanation:

Answer:

2nd Column: \(\frac{39-78}{25-59}\)

3rd Column:\(1.56\)

Step-by-step explanation:

2) For this, just follow the formula given underneath the chart.

3) Here, simplify the equation used in the 2nd Column.  \(\frac{39-78}{25-50} = \frac{-39}{-25} = -1.56\)

The missing side a is √10 yd.

To find the missing side of each right triangle, we can use the Pythagorean theorem.

Given a = 11 m and c = 15 m.

Using the Pythagorean theorem, we have:

a² + b² = c²

Substituting the given values, we get:

(11)² + b² = (15)²

121 + b² = 225

b² = 225 - 121

b² = 104

Taking the square root of both sides, we get:

b = √104

Simplifying √104, we can rewrite it as √(4 * 26) = 2√26.

Therefore, the missing side b is 2√26 m.

Given b = √6 yd and c = 4 yd.

Using the Pythagorean theorem, we have:

a² + (√6)² = (4)²

a² + 6 = 16

a² = 16 - 6

a² = 10

Taking the square root of both sides, we get:

a = √10

Therefore, the missing side a is √10 yd.

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Answer:

x = 7  x = -6

Step-by-step explanation:

x^2−x−42=0

Factor

What two numbers multiply to -42 and add to -1

-7*6 = -42

-7+6 = -1

(x-7) (x+6) =0

Using the zero product property

x-7 =0   x+6 =0

x = 7  x = -6

To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

Given:

Eliminating negative exponents:

Example:

1)  \(x^{-5}\)

on reciprocal:

= 1/x^5

eliminated negative

2) \(x^{-7}y^{-4}\)

= x^-7*1/y^4

= 1/x^7y^4

Therefore To eliminate negative exponents the base is inverted by taking its reciprocal, and the exponent then becomes positive.

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Answer:

See below

Step-by-step explanation:

Plot these points and that will be the reflection:

S is going to equal (3,1)

R is going to equal (-3,3)

T is going to equal (-1,-5)

Q is going to equal (-4,-2)

Let me know if you need help plotting points too.

Answer:

≈   4 ,  86

Step-by-step explanation:

Explanation:

If you want to find the average of a set of numbers, you have to add up all the numbers and divide by how many numbers there are in your set.

For example if you want to find the average between  

4

,

5

,

6

,

you will have to add up  

4

,

5

,

6

=

15

and divide by  

3

, since you have 3 numbers.

You have 7 numbers, that are  

8

,

7

,

7

,

5

,

3

,

2

,

2

The sum of them are 34

34

7

≈

4.86

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions