A fair coin and a spinner with an
equal chance of landing on the
numbers 1, 2, 3, 4, 5, and 6 are used
in a game. What is the probability of
getting an even number on the
spinner and heads on the coin?
A 1/12
B 1/6
C 1/4
D 1/2

Answer:

\(\displaystyle \frac{7}{3-15i}=\frac{7}{78}+\frac{35}{78}i\)

Step-by-step explanation:

\(\displaystyle \frac{7}{3-15i}\\\\\frac{7}{3-15i}*\frac{3+15i}{3+15i}\\\\\frac{21+105i}{9-225i^2}\\\\\frac{21+105i}{9+225}\\\\\frac{21+105i}{234}\\\\\frac{21}{234}+\frac{105}{234}i\\ \\\frac{7}{78}+\frac{35}{78}i\)

Hannah drove 450 miles to her brother's house at an average speed of 60 miles per hour. How long did she take? (Time)

\(t=\dfrac{Distance}{Speed}\)

\(t=\dfrac{450}{60}\)

\(t=7.5hours\)

Remember, time must be converted to seconds as it is the unit for time.

7.5 hours to seconds

1 hour = 3600 seconds

3600 seconds * 7.5 hours

\(=\fbox{27000 seconds}\)

Answer: i think c

Step-by-step explanation:

the probability of the complement of (A ∪ B) is 0.3.

How to find and what is Morgan's law?

Since A and B are mutually exclusive, we have:

P(A ∩ B) = 0

The complement of (A ∪ B) is the set of outcomes that are not in A or B. So:

(A ∪ B)′ = A′ ∩ B′

Using De Morgan's law, we have:

A′ ∩ B′ = (A ∪ B)′

We can now use the formula for the probability of the complement:

P((A ∪ B)′) = 1 - P(A ∪ B)

Since A and B are mutually exclusive, we have:

P(A ∪ B) = P(A) + P(B)

So:

P((A ∪ B)′) = 1 - (P(A) + P(B))

Substituting the given probabilities, we get:

P((A ∪ B)′) = 1 - (0.2 + 0.5)

P((A ∪ B)′) = 1 - 0.7

P((A ∪ B)′) = 0.3

Therefore, the probability of the complement of (A ∪ B) is 0.3.

De Morgan's laws are a pair of fundamental laws in Boolean algebra and set theory that describe the relationship between the intersection and union of sets and their complements. The two laws are:

The complement of the union of two sets is equal to the intersection of their complements.

Symbolically: (A ∪ B)′ = A′ ∩ B′

The complement of the intersection of two sets is equal to the union of their complements.

Symbolically: (A ∩ B)′ = A′ ∪ B′

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First, calculate how much is the discount equal to. Then, substract the discount from the original price to find the selling price.

Since the discount is 10%, find how much is 10% of $15 by multiplying 15 times 10/100:

Then, 10% of 15 is equal to 1.5. Now, substract 1.5 from 15 to find the final price:

Therefore, the girl will pay $13.5. The answer is:

The area of the rectangle = 91 square units, while the perimeter is: 40 units.

Area = length × width

Perimeter = 2(length + width).

The length of rectangle ABCD is AD or CB = 13 units

The width of rectangle ABCD is DC or AB = 7 units

The area of the rectangle = 13 × 7 = 91 square units

The perimeter of the rectangle = 2(13 + 7)

= 2(20)

= 40 units.

Therefore, the perimeter is 40 units, while the area if 91 square units.

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The complete table for the time it takes to empty the barrel for the given rates is attached below. The value of constant k is 60.

To solve the problem, we can use the formula for inverse variation

time = k/leaking rate

where k is a constant of proportionality. We can find k by using the information given in the problem

30 = k/2

Solving for k, we get:

k = 60

Now we can use this value of k to fill in the table

Leaking rate (gallons per minute)                Time to empty (minutes)

      2                                                                           30

      1                                                                            60

      0.5                                                                        120

      0.25                                                                     240

      0.1                                                                        600

As the leaking rate decreases, the time to empty the barrel increases, because the liquid is leaking out more slowly.

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Answer: it is a $16,000 increase

Step-by-step explanation:

21x²-2x +1/2 = 0

x² - 2x ×21 + 1/2× 21 = 0

Answer:

x= 3

    2

Step-by-step explanation:

Answer:

Now that you have x² - 8x + 16 = 9 + 16, apply the square root property to the equation.

✔ (x – 4)² = 25

Step-by-step explanation:

You have the next:

- Sides JK and LK are congruent:

-Angles MKJ and MKL are congruent:

-Side MK is part of both triangles.

Then, as angle MKJ is between sides JL and MK, angle MKL is between sides LK and MK:

Answer:

\(h(f(4))=20\)

Step-by-step explanation:

We are given the functions:

\(f(x)=x^2,\, g(x)=5x\text{, and } h(x)=x+4\)

And we want to find

\(h(f(4))\)

Find f(4) first:

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

Thus:

\(h(f(4))=h(16)\)

Now, evaluate h(16):

\(h(16)=(16)+4=20\)

Hence:

\(h(f(4))=20\)

In conclusion MN is approximately 8.73.

How to solve?

In triangle MNK, we know that MN = NK and the angle between them is 110 degrees. Let's call the third angle in this triangle A.

We also know that MK = 5.

Since the sum of the angles in a triangle is always 180 degrees, we can find angle A:

A + 110 + A = 180

2A = 70

A = 35

Now we can use the Law of Sines to find MN:

MN/sin(110) = MK/sin(A)

MN/sin(110) = 5/sin(35)

MN = 5×sin(110)/sin(35)

MN ≈ 8.73

Therefore, MN is approximately 8.73.

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Complete Quedtion:

In triangle AMNK, we have MN = NK, angle M/N = 110 degrees, and MK = 5. What is the length of MN?

Answer:

i belive it should add up to 180

Step-by-step explanation:

Answer:

The third angle is 128 degrees

Step-by-step explanation:

The interior angles of a triangle add up to 180 degrees, therefore we can set up the equation x+34+18=180 to find the missing angle. Solving the equation gets us x=128

Answer:

Angles of a triangle add up to 180 degrees. The third angle would be 128 degrees.

Step-by-step explanation:

34 + 18 = 52

180 - 52 = 128

Answer:

6

Step-by-step explanation:

3x12 = 36

(4+2)    6

simplify

36/6=6

The value is indeed 6 and there shouldn't be a variable because if there is, then there should be a variable in the question.

The simplified form of the expression (3 × 12)/(4 + 2) is 6.

PEMDAS rule states the correct order of simplifying an expression is as follows -: Parenthesis, exponents, multiplications, divisions, additions, and, subtractions.

Given, An expression (3 × 12)/(4 + 2).

Now, 12×3 is 36, and (4 + 2) is 6.

Therefore the simplified form of the expression is,

= 36/6.

Now, we know that 6 times 6 is 36 so, 36 divided by 6 the quotient should be 6.

Therefore,

36/6.

= 6.

So, The value of the expression  (3 × 12)/(4 + 2) is 6.

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Answer:

1)-26

2)-5

3)-2

4)1

5)22

Step-by-step explanation:

1)3*(-4+2)^3-2=3*(-2)^3-2=-26

2)3*(-1)^3-2=-5

Answer:

distributive property

Step-by-step explanation:

2(a+5)

2 is being distributed

Answer:

49

Step-by-step explanation:

3x3x5+4

Answer:

The answer is 49

Step-by-step explanation:

1. First you have to evaluate 3 to the power of 2 which would change it to 9

2. Then you would multiply 9 and 5 and you would get 45

3. Then you take 45 and add +4 to 45 making it 49

Answer:

? = 152-x

Step-by-step explanation:

The sum of the angles of a triangle equal 180

A+B+C = 180

28 + ? +x = 180

? = 180 - 28 - x

? = 152-x

Answer:

? = ( 152 - x )°

Step-by-step explanation:

28° + x° + ? = 180°

subtract 28° from each side

28° - 28° + x + ? = 180° - 28°

x + ? = 152

Now, subtract x from each side

x - x + ? = 152 - x

? = 152 - x

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

The value of N that satisfies the following equation, 5!9!= 12N!, is 10.

Factorial notation (n!) means to multiply a series of descending natural numbers. Also stated in the problem that for positive integer n, the factorial notation n! represents the product of the integers from n to 1.

Take for example 6! which can be written as 6 x 5 x 4 x 3 x 2 x 1 = 720.

Given the equation 5!9!= 12N!, expand the factorial notation.

(5 x 4 x 3 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) = (4 x 3) N!

N! = (5 x 2 x 1)(9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

N! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

N = 10

Therefore, the value of N that satisfies the following equation, 5!9!= 12N!, is 10.

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I think its r=13 hope this helps :)

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

Answer:

1 days= 24 hrs

3 days = 3×1 days

= 3×24 hrs

= 72 hrs