Venus has switches at the top and bottom of her stairs to control the light for the stairwell. She notices that when the upstairs switch is up and the downstairs switch is down, the light is turned on.

b. If both the upstairs and downstairs switches are in the up position, will the light be on?
Explain your reasoning.

AB is not perpendicular to CD

Perpendicular lines are two separate lines that cross one other at a right angle, or a 90° angle. Example: Because AB and XY overlap at a 90° angle, AB is perpendicular to XY in this instance.

Lines that cross one other at an angle are known as perpendicular lines. Their slopes are the reciprocal opposites of one another.

Given A (-2, 4, 0),B(1, 1, 1),C(2, 3, 4),D (3, 21, -8)

(-1,3,-1) for AB

(-1,-18,12) for CD

For the lines AB and CD to be perpendicular

a 1a2+b1b2+c1c2=0

-1(-1)+3(-18)+(-1)(12)

=1-54−12=-65not equal to 0

∴ AB not perpendicular to CD

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Answer:

10(theta) = 12

theta = 1.2 radians = about 68.8°

phi = .6 radians = about 34.4°

Answer:

i'm assuming it's 2*√5(13+√2) so 2√10+26√5

Step-by-step explanation:

The product of 2 square root 5 (13 + square root 2) in simplified form is 26√5 + 2√10

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

2 square root 5 (13 + square root 2)

Express as products

So, we have

2√5 * (13 + √2)

Open the brackets

So, we have

2√5 * (13 + √2) = 2√5 * 13 + 2√5 *√2

Multiply the radicands

So, we have the following

2√5 * (13 + √2) = 2√5 * 13 + 2√10

Evaluate the products

So, we have the following

2√5 * (13 + √2) = 26√5 + 2√10

Hence, the solution is 26√5 + 2√10

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The price per T-shirt should be at least $15 to achieve a profit of $250.

To calculate the price per T-shirt that will yield a profit of at least $250, we need to consider the cost of production, the desired profit, and the number of shirts to be sold.

Given that the cost to make each T-shirt is $10, and we want to sell 50 shirts, the total cost of production would be 10 * 50 = $500.

Now, let's calculate the minimum revenue needed to achieve a profit of $250. We add the desired profit to the total cost of production: $500 + $250 = $750.

Finally, to determine the price per T-shirt, we divide the total revenue by the number of shirts: $750 ÷ 50 = $15.

Therefore, to make a profit of at least $250, the price per T-shirt should be set at $15.

By selling each T-shirt for $15, the total revenue would be $15 * 50 = $750. From this revenue, we subtract the total production cost of $500 to calculate the profit, which amounts to $750 - $500 = $250. Thus, by charging $15 per T-shirt, the desired profit of $250 is achieved.

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Step-by-step explanation:

p= (45), |p|= 45

this is the solution

Clare's claim is correct and Diego's claim is incorrect.

Clare is correct. It is not always possible to inscribe a circle in a quadrilateral, as the angle bisectors of a quadrilateral are not guaranteed to intersect at a single point. To see why, consider the following example:

Start with a square ABCD and draw a diagonal from A to C, dividing the square into two congruent triangles. Label the intersection point of the diagonal and the perpendicular bisector of AB as E, and the intersection point of the diagonal and the perpendicular bisector of BC as F. Then, connect EF to form a quadrilateral BCEF.

Now, consider the angle bisectors of the quadrilateral BCEF. The angle bisectors of angle B and angle C both pass through point E, while the angle bisectors of angle E and angle F both pass through point F. Therefore, the angle bisectors do not intersect at a single point, and it is not possible to inscribe a circle in quadrilateral BCEF.

So, Clare's claim is correct and Diego's claim is incorrect.

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Answer:

more info needed

Step-by-step explanation:

Triangle based on the side lengths 7. 15 and 21​ is Obtuse triangle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The sides of triangle are 7, 15 and 21.

Let the largest angle be θ.

cosθ=7²+15²-21²/2×7×15

=-167/210

Since arc cos(-167/210)=142.68 degrees.

θ=142.68 degrees.

Which means θ>90 degrees.

So its a obtuse triangle.

7+15=22>21

21-7=14<15

So those angles can make a obtuse triangle.

Hence, triangle based on the side lengths 7. 15 and 21​ is Obtuse triangle.

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Answer:

A maximum of 43 students and 11 teachers can go to the trip.

Step-by-step explanation:

Since a group of teachers and students will take a bus trip to a museum, and each teacher will lead a group of no more than 4 students, and the bus can hold a maximum of 54 teachers and students, to determine the possible numbers of teachers and students who can go on the trip, the following calculation must be performed:

4 + 1 = 5

54/5 = X

10.8 = X

10 x 4 = 40

10 x 1 = 10

4 - 1 = 3

Therefore, a maximum of 43 students and 11 teachers can go to the trip.

Answer:

475

Step-by-step explanation:

1021-71

950/2

1) Because \(\angle ACB\) is a central angle, \(m\angle ACB=72^{\circ}\).

Since \(\angle ACB\) and \(\angle BCD\) are supplementary, they form a linear pair, and thus \(m\angle BCD=180^{\circ}-72^{\circ}=\boxed{108^{\circ}}\)

5) Tangents drawn from an external common point are congruent, so CR=CP=8 and RB=BQ=4. This means that QA=11, and so PA=11 as well. Adding CP+PA, we get AC=19.

6) By the inscribed angle theorem, angle QPR measures 36 degrees.

The values of x when solved;

a. x≥ 3. 44

b. x≥3. 44

c. x ≤ 8. 8

Inequalities are simply described as relations that makes a non-equal comparison between two numbers, variable or other mathematical expressions.

They are used to compare numbers on the number line on the basis of size

From the information given, we have to determine the value of x in the inequality given;

a. 5 1/2≥1.6x

convert to improper fraction

11/2 ≥1.6x

divide both sides by 1. 6

x≥ 3. 44

b. x≥3 7/16

convert to improper fraction

x≥ 55/ 16

x≥3. 44

c. x≤8 4/5

convert to improper fraction

x≤ 44/ 5

x ≤ 8. 8

Hence, the value are  x≥ 3. 44, x≥3. 44 and x ≤ 8. 8

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Answer:

y= -x+8

Step-by-step explanation:

slope int. form: y=mx+b

first, we need to find the slope (m)

the two points are (2,4) and (7,-1).

to find the slope we do (y2-y1)/(x2-x1)

doing this we get -5/5=-1

now we can plug in point (2,4) and the slope into y=mx+b

doing this we get:

4=-1(2)+b

4=-2+b

b=8

now we have the equation:

y= -x+8

The sequence of transformations will be relection and dilation. Then the correct option is A.

A spatial transformation is each mapping of feature shapes to itself and it maintains some spatial correlation between figures.

The sequence of transformations would yield a trapezoid similar to the original trapezoid but not congruent.

Reflection does not change the size and shape of the geometry.

Rotation does not change the size and shape of the geometry.

Translation does not change the size and shape of the geometry.

Dilation does not change the shape but changes the size of the geometry.

Then the correct option is A.

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The approximate probability of drawing one orange marble and one green marble from a bag containing five red marbles, four orange marbles, one yellow marble, and three green marbles is approximately 0.154.

To find the approximate probability of drawing marbles, we can use the following formula

probability = (number of favorable outcomes) / (total number of outcomes)

We need to find the number of favorable outcomes where one marble is orange and the other is green. We can choose one orange marble from four orange marbles in the bag in 4 ways, and one green marble from three green marbles in 3 ways. So, the number of favorable outcomes is 4 x 3 = 12.

The total number of ways of choosing two marbles from the bag is 13C2, which is the number of combinations of 2 marbles that can be drawn from the 13 marbles in the bag. Therefore, the total number of outcomes is

13C2 = (13 x 12) / (2 x 1) = 78

Thus, the approximate probability of drawing one orange marble and one green marble is

probability = number of favorable outcomes / total number of outcomes = 12/78 ≈ 0.154

Therefore, the approximate probability of drawing one orange marble and one green marble from the bag is approximately 0.154.

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Answer:

"subset"

Step-by-step explanation:

The "set within a set" is called a "subset."

Answer:

Step-by-step explanation:

A 10= 4 plus 6

Answer: The answer I got is 15.6

a) Given preferences are not monotonic.

b) The budget constraint is binding and the consumer cannot afford that bundle.
c) The interpretation of these choices is that the consumer maximizes their utility.

(a) These preferences are not monotonic. Monotonicity means that if one bundle is preferred to another, any bundle with more of both goods should also be preferred. In this case, if x1'+x2' < x1''+x2'', it does not necessarily mean that x1'+x2' < x1''+x2'' for all bundles with more of both goods.

(b) To determine which bundle would be chosen by the consumer, we need to compare the total expenditure on each bundle to the consumer's income. If the total expenditure on a bundle is less than or equal to the consumer's income, then that bundle would be chosen.

If the total expenditure exceeds the consumer's income, then the budget constraint is binding and the consumer cannot afford that bundle.

(c) When prices are strictly negative (p1 = -ω, p2 = -e), the budget set can be represented graphically as a set of bundles that the consumer can afford.

The initial endowment P represents the amount of good 2 that the consumer already possesses without having to spend any money. It is a starting point for the consumer's choices.

(d) To characterize the optimal selection of the consumer, we need to consider whether ω > e or e > ω.

If ω > e, the consumer's optimal choice would lie on the highest attainable indifference curve that is tangent to the budget set.

If e > ω, the optimal choice would lie on the indifference curve that is tangent to the budget set at a point where the consumer exhausts their initial endowment P.

The interpretation of these choices is that the consumer maximizes their utility by selecting the bundle that provides the most satisfaction given their budget constraints and initial endowment.

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Answer: 2.99914cm Rounds up to 3

Step-by-step explanation:

We can find the mean absolute deviation by the dot plot of the number line.

The mean absolute deviation is the average of all the variations in a dataset. It can be defined as a measure of finding out spread out the values of a dataset are from the mean. The mean is calculated by adding the absolute deviations and dividing the sum by the number of values in the data set.

Absolute mean deviations can be represented graphically on a number line from a dot plot. These dot plots can be used to find out the mean absolute deviation on a number line.

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The expression which is equivalent to -10 is the option b, -3 - 7.

Explanation:

We can use subtraction and addition of integers to get the value of the given expression. We can write the given expression as;

-3 - 7 = -10 (-3 - 7)

The addition of two negative integers will always give a negative integer. When we subtract a larger negative integer from a smaller negative integer, we will get a negative integer.

If we add -3 and -7 we will get -10. This makes the option b the correct answer.

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Answer:

174 square inches

Step-by-step explanation:

5 times 3 is 15, multiply 15 by two. We get 30. Keep this in mind. Now, multiply 9 by 3. This is 27. Multiply 27 by two to get 54. Also keep this in mind. Now, multiply 5 by 9 to get 45. Multiply 45 by 2 to get 90. Now, add all of the bold numbers together to get your answer.

30+90+54

120+54

174

Answer: The area, in square feet, of the piece of wood is \(32 ft^{2}\).

Step-by-step explanation:

Give: Length = 8 feet

Width = \(\frac{1}{2} \times 8\) = 4 feet

As piece of wood is similar to that of a rectangle. Hence, formula to calculate area is as follows.

\(Area = length \times width\)

Substitute the values into above formula as follows.

\(Area = length \times width\\= 8 feet \times 4 feet\\= 32 ft^{2}\)

Thus, we can conclude that the area, in square feet, of the piece of wood is \(32 ft^{2}\).

Answer:

A_16x20=320

Step-by-step explanation:

Esto se puede hacer fácilmente de 2 formas.

1) 20 se puede dividir en un múltiplo de 10 y luego multiplicar

16 x 20 =16 x 10 x 2 = 160 x 2 = 320

2) Uso de cero.

Cualquier cosa multiplicada por cero da un cero y luego multiplicar el otro número da el resultado.

16 x 20 = (16 x 2) * 10 = (32) 10 = 320

Así que separamos el cero añadiéndole un 1, lo que lo convierte en 10 y obtenemos el mismo resultado.

This can be easily done in 2 ways .

1) 20 can be broken into a multiple of 10 and then multiplied

16 x 20 =16 x10 x 2=160x 2= 320

2) Use of zero.

Anything multiplied with zero gives a zero and then multiplying the other number gives the result.

16 x 20 = (16x 2) *10= (32)10= 320

So we separated the zero by adding a 1 to it thus making it 10 and we get the same result.

Answer:

The number 3 represents the fixed cost in the equation which is the flat charge.

Answer: x= 6

Step-by-step explanation:

Since the shape is a parallelogram, the angles will either be equal to each other or add up to 180.  

You can see they do not look the same so they add up to equal 180

12x + 3 +105 = 180

12x + 108 = 180

12x = 72

x = 6

The value of K that will make the expressions equivalent is 10.

Considering the two expressions:

7 + (1/2)x - 3 + (3/4)x and 1 whole number (1/4)x + k - 6

we shall write the expression 7 + (1/2)x - 3 + (3/4)x in the form of the expression having k and then compare to know the value of k as follows;

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

(1/2)x + (3/4)x = 5x/4

7 - 3 = 10 - 3 - 3

7 - 3 = 10 - 6

so;

7 + (1/2)x - 3 + (3/4)x = 5x/4 + 10 - 6

by comparison;

5x/4 is equal to the mixed fraction 1 whole number (1/4)x

k = 10 as obviously -6 is equal to -6.

Therefore, 10 is the value of k that will make expressions equivalent.

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Answer:

Chord

Step-by-step explanation:

Notice that the highlighted part is the line segment that joins the points J and E on the circle, which is known as a chord.