What can you say about ∠ADB and ∠BDC based on the sum of their angles? How are the angles related?

The perimeter of the rectangle is 8 1/4 feet. the correct answer is A.

Perimeter is the total length of the sides of a two-dimensional shape. In a rectangle, opposite sides are equal in length, so the perimeter can be found by adding the lengths of all four sides. To find the perimeter of a rectangle, we use the formula:

Perimeter = 2(length + width)

In this case, the length is given as 3 1/4 feet and the width is given as 7/8 feet. To find the perimeter, we substitute these values into the formula:

Perimeter = 2(3 1/4 + 7/8)

To simplify, we need to convert the mixed number to an improper fraction and find a common denominator for the fractions:

Perimeter = 2(13/4 + 7/8)

Perimeter = 2(26/8 + 7/8)

Perimeter = 2(33/8)

Now we can simplify the expression by multiplying 2 by the fraction:

Perimeter = 66/8

We can reduce this fraction by dividing both the numerator and denominator by 2:

Perimeter = 33/4

Therefore, the perimeter of the rectangle is 8 1/4 feet, which is answer choice A.

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Answer:  \(f^{-1}(\text{x}) = (\text{x}-9)^2+4\) when \(\text{x} \ge 9\)

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Work Shown:

\(f(\text{x}) = 9 + \sqrt{\text{x} - 4}\\\\\text{y} = 9 + \sqrt{\text{x} - 4}\\\\\text{x} = 9 + \sqrt{\text{y} - 4}\\\\\text{x}-9 = \sqrt{\text{y} - 4}\\\\(\text{x}-9)^2 = (\sqrt{\text{y} - 4})^2\\\\(\text{x}-9)^2 = \text{y}-4\\\\(\text{x}-9)^2+4 = \text{y}\\\\f^{-1}(x) = (\text{x} - 9)^2+4\)

Explanation:

I replaced f(x) with y. After that I swapped x and y, then solved for y to get the inverse.

The smallest that \(\sqrt{\text{x}-4}\) can get is 0, which means the smallest f(x) can get is 9+0 = 9. The range for f(x) is \(\text{y} \ge 9\)

Since x and y swap to determine the inverse, the domain and range swap roles. Therefore, the domain of the inverse \(f^{-1}(\text{x})\) is \(\text{x} \ge 9\)

So we will only consider the right half portion of the parabola.

The graph is below. The red curve mirrors over the black dashed line to get the blue curve, and vice versa.

Answer:

\(f^-^1(x)=(x-9)^2+4\)   OR \(x^2-18x+85\) if you simplify it

Step-by-step explanation:

to find the inverse function you have to switch x and y with each other and solve for y.

\(y=9+\sqrt{x-4}\\x=9+\sqrt{y-4}\)           step 1: switch x and y with each other

\(x-9=\sqrt{y-4}\)           step 2: subtract 9 from both sides

\((x-9)^2=\sqrt{y-4}^2\)     step 3: square both sides to get rid of the square root

\((x-9)^2=y-4\\(x-9)^2+4=y\\\)         step 4: add 4 to both sides

you could leave the answer like this or you can simplify to get \(x^2-18x+85\)

The value of x/y is 37/35, if a square with side length x is inscribed in a right triangle and a square with side length y is inscribed in another right triangle.

Note that triangle ABC and triangle FBE are similar,(by AAA)

As \(\angle B\) is common in both, and \(\angle F= \angle A\) as they both are 90°

so, the \(\angle C\) will also be equal to \(\angle E\)

so \(\frac{BF}{FR} = \frac{AB}{AC}\)

This can be written as \(\frac{4-x}{x} = \frac{4}{3}\)

solving: 12 - 3x = 4x

7x = 12 or x = 12/7

Similarly, triangle A'B'C' and triangle RB'Q are similar,

so RB' = \(\frac{4}{3}y\) and C'S= \(\frac{3}{4}y\)

Thus, C'B' = C'S+ SR+ RB'

or  \(\frac{4}{3}y + y + \frac{3}{4} = 5\)

solving y = 60/37

Now, x/y = \(\frac{12}{7} \times \frac{37}{60}\) = 37/35

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Answer:

It is the second one, b..

Step-by-step explanation:

If you look at the days and amount of time you can clearly see that y=5/2x is where the cost in cents for a book that is x days overdue. Hope this helped.

The value of T(1) by taking cross product r'(t) x r"(t) = \((-144(1)^2, 0, 24)\) = (-144, 0, 24).

To find the derivative of r(t), we can differentiate each term separately with respect to t:

r(t) = \((4t, 3t^2, 4t^3)\)

r'(t) = \((d/dt)(4t, 3t^2, 4t^3) = (4, 6t, 12t^2)\)

To find r"(t), we can differentiate r'(t) with respect to t:

r"(t) = \((d/dt)(4, 6t, 12t^2)\) = (0, 6, 24t)

To find r'(1), we can substitute t = 1 into r'(t):

r'(1) = \((4, 6(1), 12(1)^2)\) = (4, 6, 12)

To find r′(t) x r″(t), we can take the cross product of r'(t) and r"(t):

r'(t) x r"(t) = \((4, 6t, 12t^2) * (0, 6, 24t) = (-144t^2, 0, 24)\)

Finally, we can substitute the values we found into the last equation to find T(1):

T(1) = r'(t) x r"(t) = \((-144(1)^2, 0, 24) = (-144, 0, 24)\)

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Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.

Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.

To calculate the number of weeks Londell needs to work, we can set up an equation:

$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)

Simplifying the equation:

$40 + $15 = $400

Subtracting $40 from both sides of the equation:

$15 = $400 - $40

$15 = $360

Dividing both sides of the equation by $15:

= $360 / $15

≈ 24

Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.

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A)  The 95% confidence interval is:

     0.58 ± 0.062

B) At the 0.01 probability value, there is neither substantial evidence of a home-field  advantage in professional football (they won and over half of the games).

Now, According to the question:

A) Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × \(\frac{\sqrt{pq} }{n}\)

Where:

z = The z score corresponds to the amount of confidence.

p = sample proportion.

q = probability of failure

q = 1 - p

p = x/n

Where

n = the number of samples

x = the number of success

From the information given,

n = 240

x = 138

p = 138/240 = 0.58

q = 1 - 0.58 = 0.42

To determine the z score,  The confidence level from 100% to get α

α = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

Thus,

1 - 0.025 = 0.975

The z -score associated with the area just on z table approximately 1.96. Therefore, the z score with a 95% confidence level is 1.96.

As a result, the 95% confidence interval becomes

0.58 ± 1.96√(0.58)(0.42)/240

Confidence interval is

0.58 ± 0.062

B) Earning more than half of the games equates to winning 120 games or more.

p = 120/240 = 0.5

The hypothesis test will be

For the null hypothesis,

P ≥ 0.5

For the alternative hypothesis,

P < 0.5

Probability of success, p = 0.5

q = probability of failure = 1 - p

q = 1 - 0.5 = 0.5

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 138

n = number of samples = 240

P = 138/240 = 0.58

We need to find the values of  the test statistic which will be the z score

z = (P - p)/√pq/n

z = (0.58 - 0.5)/√(0.5 × 0.5)/240 = 2.48

Remember that this is a two-tailed test. We would use the normal distribution table to calculate the probability potential of the property to the right of both the z score.

P value will be = 1 - 0.9934 = 0.0066

Since alpha, 0.01 > the p value, 0.0066, then we would reject the null hypothesis.

The given question is incomplete, The complete question is this:

__"During the 2000 season, the home team won 138 out of 240 regular season National Football League games. (15 points) a) Construct a 95% confidence interval for the winning proportion of the home team during this season. b) At the 0.01 significance level, is there strong evidence of a home field advantage (they win more than half of the games) in professional football? State hypotheses, calculate the test statistic and p-value, and make a conclusion in context"__

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The value of the missing length √5

What Pythagoras Theorem?

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a key relationship in Euclidean geometry between a right triangle's three sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Given,

Hypotenuse = 3cm

One side = 2cm

Let the one side given be Base

Then, base = 2cm

Now, by Pythagoras Theorem we can find out the missing length or Perpendicular of the triangle

By Pythagoras Theorem:

H² = P² + B²

If we have to find perpendicular then,

P² = H² - B²

or,

P = √H² - B²

Putting the values we get,

P = √(3)² - (2)²

P = √(9 - 4)

P = √(5)

P = √5

Hence, The missing length of the triangle is √5

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The truth statements about the transformations are:

There are four types of transformation, and they are:

The representation of the types of transformation are:

Of the above transformation, only the dilation transformation do not preserve side lengths or distance

Hence, the categories of the transformations are

(a), (c) and (d) ⇒ Preserve

(b) and (e) ⇒ Do not preserve

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Answer:

33.89

Step-by-step explanation:faci regula de 3 simpla

1 euro....... 1,475 usd

X euro....... 50 USD => x = 50/1.475 = 33,89

Answer:

identify

Step-by-step explanation:

Answer:

41 units

Step-by-step explanation:

To do this, you can simply count on your fingers, or you can take the absolute value of both, add them, and that's how far apart they are.

The absolute value of -25 is 25, and the absolute value of 16 is, well, 16, and 16+25 is 41.

The distance between 16 and -25 on the number line is 41 units. To find the distance between two points on a number line, you can simply subtract their positions, regardless of whether they are positive or negative numbers.

Distance = |Position of point 1 - Position of point 2|

In this case, we want to find the distance between 16 and -25:

Distance = |16 - (-25)|

To simplify the calculation:

Distance = |16 + 25|

Distance = |41|

The distance between 16 and -25 on the number line is 41 units.

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Answer:

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In the context of the problem, - 0.12 inches per year represents the slope (negative to show a decrease) of the line and 54.3 inches represent the y-intercept as the starting point.

Considering m = - 0.12 and b = 54.3 in the slope-intercept equation:

Find the value of y when x = 101:

The solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

y≤x−3​.........(1)

y≥x+1​.............(2)

If we solve the inequality using the graphical method we can see that the inequalities gives the parallel line.

Also, the solution for the inequalities, y≥x+1​ is (0, 1) and (-1, 0).

and, the solution for the inequalities, y≤x−3​ is (0, -3) and (3, 0).

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This means the Probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

To make the game fair, we need to ensure that the probability of drawing a card with a star is the same as the probability of drawing a card without a star.

Currently, there are 4 cards with stars and 6 cards without stars, which means the probability of drawing a star is 4/10 or 2/5, while the probability of drawing a card without a star is 6/10 or 3/5.

To make the game fair, we need to adjust the number of cards with stars and without stars so that the probabilities are equal.

Option A is not correct because the game is not currently fair.

Option B is not correct because adding 2 cards with stars will increase the probability of drawing a star to 6/12 or 1/2, which is not equal to the probability of drawing a card without a star.

Option C is also not correct because adding a star to 1 of the blank cards will still result in a probability of drawing a star that is not equal to the probability of drawing a card without a star.

Therefore, the correct answer is option D: take away 2 blank cards. If we remove 2 blank cards, we are left with 4 cards with stars and 4 cards without stars. This means the probability of drawing a star is now 4/8 or 1/2, which is equal to the probability of drawing a card without a star. Thus, the game is now fair.

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Mary needs to score 96 on the fifth test to raise her average test score from 92.25 to 93.

Let's use the formula for the mean

mean = (sum of all scores) / (number of scores)

We can rearrange this formula to solve for the sum of all scores

sum of all scores = mean x number of scores

We know that Mary's mean test score is currently 92.25 and she has taken four tests, so

sum of all scores = 92.25 x 4 = 369

To raise her mean test score to 93, Mary needs the sum of all five test scores to be

sum of all scores = 93 x 5 = 465

To find out what score Mary needs to earn on the fifth test, we can subtract the sum of her first four test scores from the required sum of all five test scores

score on fifth test = sum of all five tests - sum of first four tests

score on fifth test = 465 - 369

score on fifth test = 96

Therefore, Mary needs to earn a score of 96 on the fifth test in order to raise her mean test score to 93.

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Since 1/2 is distributed over 1/3 and 1/4 hence the law applied is the distribution law of addition.

Given the following integers A, B and C. According to the distribution law;

A(B + C) = AB + AC

This shows that the  value A is distributed over B and C

Given the expression

1/2 + (1/3*1/4) = (1/2*1/3) + (1/2*1/4)

From the result, you can see that 1/2 is distributed over 1/3 and 1/4 showing that the law applied is the distribution law of addition

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The length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In this case, the fence, building, and ladder form a right triangle, where the fence and building are the legs, and the ladder is the hypotenuse.

We know that the fence is 8 feet tall and the building is 4 feet away from the fence, so the height of the right triangle (the distance from the ground to the top of the building) is also 8 feet.

To find the length of the ladder, we need to use the Pythagorean theorem:

ladder^2 = fence^2 + height^2
ladder^2 = 8^2 + 4^2
ladder^2 = 64 + 16
ladder^2 = 80
ladder ≈ 8.94 feet

Therefore, the length of the shortest ladder that will reach from the ground over the fence to the wall of the building is approximately 8.94 feet.

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Answer: This situation involves choosing a group of 5 players out of a total of 12 players, where the order in which the players are chosen does not matter. Therefore, this is an example of a combination problem.

The number of ways to choose a group of 5 players out of 12 is given by the formula for combinations:

n C r = n! / (r! * (n-r)!)

where n is the total number of players, r is the number of players being chosen, and "!" represents the factorial operation.

In this case, we have n = 12 and r = 5, so the number of different choices of starters is:

12 C 5 = 12! / (5! * (12-5)!)

= 792

Therefore, there are 792 different choices of starters that the coach can make from the team of 12 players.

Step-by-step explanation:

Answer: 4(2x-5)

Simplified: 8x-20

Answer:

8x-20

Step-by-step explanation:

Just simplify if this is the answer you're looking for next time be specific with the question

Answer: b is the answer

Step-by-step explanation:

Answer:

Step One: We need to find a way to equate either the x terms of the y terms in each equation. ...

Step Two: Take equation b) from equation a) to eliminate the x component. ...

Step Three: substitute the value of y into either equation to find the value of x.

Step-by-step explanation:

The rule that best represents the dilation that was applied to quadrilateral FGHJ to create quadrilateral F'G'H'J' is option B, which is (x, y) à (1.4x, 1.4y).

A dilation is a transformation that changes the size of an object without changing its shape. It is performed by multiplying the coordinates of each point by a scale factor.

In this case, the center of dilation is the origin, which means that the coordinates of each point are multiplied by the same scale factor in both the x and y directions.

The scale factor can be found by comparing the corresponding side lengths of the two quadrilaterals. In this case, the scale factor is 1.4, which means that the lengths of the sides of F'G'H'J' are 1.4 times the lengths of the corresponding sides of FGHJ.

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The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.

The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.

For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.

Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.

The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.

So, the probability of rolling a 1 is:

P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6

Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\

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The average payment will be $611.64.

It should be noted that average means mean. This implies that we will add the numbers and then divide.

This will be:

= ($23.42 + $14.95 + $276.50 + $219.93 + $76.84) / 5.

= $611.64

Therefore, the average payment will be $611.64.

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Answer:

All these added amount to $611.64, yes.

However, to find average, you then divide by 6.

Which equals; $101.94.

That is the average payment.

Step-by-step explanation:

Hope it helps.

Answer:

The given rectangle is not fully defined, as it is missing some measurements such as the length and width. Without this information, it is not possible to accurately calculate the perimeter of the rectangle.

However, assuming that the missing measurement is the width of the rectangle, then the expressions given by the five students would be:

2(3x + 4x + 3) = 14x + 6

2(6x + 6) + 2(4x + 6) = 20x + 24

2(3x + 3) + 2(4x + 3) = 14x + 12

2(6x + 3) + 2(4x + 3) = 20x + 12

2(6x + 3x) + 2(3 + 4x) = 18x + 10

Note that all expressions follow the formula for the perimeter of a rectangle, which is P = 2l + 2w, where l is the length and w is the width of the rectangle.

a. Domain of f(x) = (-∞, ∞)

b. Domain of g(x) = (-∞, ∞)

c. (fog)(x) simplifies to -6.

Given:

f(x) = -6

g(x) = 4x - 10

h(x) = x^2 + 3

a) The domain of f(x) is all real numbers, since there are no restrictions on the input that would make the function undefined. Therefore, we can write the domain as:

Domain of f(x) = (-∞, ∞)

b) To find the domain of g(x), we need to look for any input values that would make the function undefined. In this case, there are no restrictions on the input, so the domain of g(x) is also all real numbers:

Domain of g(x) = (-∞, ∞)

c) (fog)(x) means to plug g(x) into f(x), or f(g(x)). We have:

(fog)(x) = f(g(x))

      = f(4x - 10)  (we substitute g(x) = 4x - 10)

      = -6   (since f(x) = -6 for all x)

Therefore, (fog)(x) simplifies to -6.

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Answer: it gets smaller, 13 times smaller

Step-by-step explanation:

Size of the figure/13