A skier is trying to decide whether or not to buy a season ski pass. A daily pass costs ​$78. A season ski pass costs ​$450. The skier would have to rent skis with either pass for ​$25 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes? The skier would have to go skiing ______
days. ​(Type a whole​ number.)

Answer: 272/3 OR 90.67

Step-by-step explanation:

First, turn the mixed fraction into an improper fraction. Using the times-addition method, you take the whole number (2) and multiply it by the denomitor (3). You get 6, and then add the numerator (2) to 6, getting 8, so th improper fraction of the first term is 8/3.

Then, you multiply 8/3 by 34. To do this, you do 8 times 34 divided by 3. 34 times 8 is 272, and then you divide it by 3. You don't get a whole number, so the answer could be written as 272/3 or 90.67

Answer:

$84 was the original bill.

Step-by-step explanation:

12 x 7 = 84

(Hard) A composite number n is called a Carmichael number bn−1 ≡ 1 (mod n) for every number b such ... Base case: When n = 2 the formula a + c ≡ b + d (mod m) was already given. ... The sequence goes 1, 3, 7, 15, 31,... guess that it is equal to 2n+1 − 1. ... Prove (now using induction on n) that fm|fmn for all n ≥ 1.

Answer:

That would be n\(\geq 1\\\)

Step-by-step explanation:

Answer:

In a pair of similar triangles, the corresponding sides are proportional. Corresponding sides touch the same two angle pairs. When the sides are corresponding it means to go from one triangle to another you can multiply each side by the same number

As per the question, in context of mathematics the relation between 2 and 2 is equality relationship.

n mathematics, an equality relationship is a relationship between two quantities or expressions that are equal to each other. This relationship is represented using the equals sign (=).

Relations are important in mathematics because they allow us to describe and analyze the relationships between different quantities or values. Relations can be used to describe how two quantities are related to each other, such as whether they are equal, greater than, or less than each other.

The relationship between 2 and 2 is that they are both equal to each other. In mathematics, two is a number that is equal to the sum of one plus one. It is a cardinal number, which means it is used to count the number of objects in a set. Two is also an even number, which means it is divisible by 2 without a remainder.

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The required equation is 3 + 2.50m = 25.50. The total number of miles in Miriam's trip is 9 miles.

Given:

Cost of the initial flat rate = 3.00 dollar

Cost per mile = $2.5 per mile

Miriam paid = $25. 50

Let the charge or cost of the hare-ride service be represented by the variable C1. We can write the equations given below.

C1 = 3 + 2.5m

m is the number of miles.

The value of C1 given is 25.50. So, putting we get,

25.50 = 3 + 2.50 m

=> 2.50m = 22.50

=> m = 22.50/2.5

=> m = 9 miles.

So, the number of miles m is 9 miles.

The required equation is 3 + 2.50m = 25.50.

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Answer:

\(f(x)=\sqrt{x+5}-3\)

Step-by-step explanation:

Given function for graph: \(f(x)=\sqrt{x-h}+k\)

Therefore, the parent function is \(f(x)=\sqrt{x}\)

\(f(x)=\sqrt{x-h}+k\) can be obtained by translating \(f(x)=\sqrt{x}\) to \(h\) units to the right and \(k\) units up

The x and y intercept of \(f(x)=\sqrt{x}\) is the origin

Therefore, this graph has been translated 5 units to the left and 3 units down.

Therefore, \(h=-5\) and \(k=-3\)

Substituting these values into the given function:

\(\implies f(x)=\sqrt{x-(-5)}+(-3)\)

\(\implies f(x)=\sqrt{x+5}-3\)

The probability that the family will have three children of the same gender is 1/4 or 25%.

To calculate the probability of having three children of the same gender, we can consider the possible outcomes for each child's gender.

Since the probability of having a boy or a girl is equal (assuming a 50% chance for each), we have two possible outcomes for each child: boy (B) or girl (G).

The total number of possible outcomes for the three children is 2 * 2 * 2 = 8, as each child has two possible genders.

Now, let's calculate the number of favorable outcomes where all three children have the same gender.

If they have all boys (BBB), there is only one favorable outcome.

If they have all girls (GGG), there is also only one favorable outcome.

Therefore, the total number of favorable outcomes is 1 + 1 = 2.

The probability of having three children of the same gender is then 2 favorable outcomes out of 8 possible outcomes, which can be expressed as 2/8 or simplified to 1/4.

So, the probability that the family will have three children of the same gender is 1/4 or 25%.

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Answer:

me neither (TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)(TT)

Answer:

16x^2 - 8x + 1

Step-by-step explanation:

1. The area of a square can be represented as s^2 or (s)(s), where s = side.

2. (Solving)

Step 1: Set up expression

Step 2: Apply the FOIL method (first, outside, inside, last)

Step 3: Simplify.

Therefore, the area of the square in terms of x is 16x^2 - 8x + 1.

The solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

According to the given question.

We have a linear equation in one variable.

4y - 6 = 2y + 8

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is given by

4y - 6 = 2y + 8

⇒ 4y - 2y - 6 = 8     ( subtracting 2y from both the sides)

⇒ 2y -6 -8 = 0           (subtracting 8 from both the sides)

⇒ 2y - 14 = 0

⇒ 2y = 14

⇒ y = 14/2

⇒ y = 7

Hence, the solution of the linear equation in one variable 4y - 6 = 2y + 8 is at y = 7.

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Answer:

x = -22

Step-by-step explanation:

Subtract 5 from both sides

3x + 5 (-5) = 2x - 17 (-5)  

3x = 2x - 17

Subtract 2x from both sides

3x (-2x) = 2x (-2) -22  

x = -22

Answer:

  176 +80√5

Step-by-step explanation:

You want the exact value of (1 +√5)^5.

The coefficient of the expansion are found in Pascal's triangle (attached). Row 5 is used for the 5th power:

  (a +b)^5 = a^5 +5·a^4·b + 10·a^3·b^2 +10·a^2·b^3 +5·a·b^4 +b^5

When a = 1 and b = √5, this becomes ...

  (1 +√5)^5 = 1 + 5·√5 +10·5 + 10·5√5 +5·25 +25√5

  = (1 +50 +125) +(5 +50 +25)√5

  (1 +√5)^5 = 176 +80√5

just a quick addition to "sqdancefan" superb reply above

\(\qquad \qquad \textit{binomial theorem expansion} \\\\ \qquad \qquad (1+\sqrt{5})^{5}~\hspace{4em} \begin{array}{clcl} term&coefficient&value\\ \cline{1-3}&\\ 1&+1&(1)^{5 }(\sqrt{5})^0\\ 2&+5&(1)^{4}(\sqrt{5})^1\\ 3&+10&(1)^{3}(\sqrt{5})^2\\ 4&+10&(1)^{2}(\sqrt{5})^3\\ 5&+5&(1)^{1}(\sqrt{5})^4\\ 6&+1&(1)^{0}(\sqrt{5})^5 \end{array} \\\\[-0.35em] ~\dotfill\)

\(1(1)+5(1)(\sqrt{5})^1+10(\sqrt{5})^2+10(1)(\sqrt{5})^3+5(\sqrt{5})^4+(\sqrt{5})^5 \\\\\\ 1+5\sqrt{5}+50+50\sqrt{5}+125+25\sqrt{5}\implies {\Large \begin{array}{llll} 176+80\sqrt{5} \end{array}}\)

a. The probability that the system will operate as shown is approximately 0.6141.

b. Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

a. To find the probability that the system will operate as shown, we multiply the probabilities of each component. Since the system is shown to have three components with a probability of 0.85 each, we can calculate:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141

The probability that the system will operate as shown is approximately 0.6141.

b. In this case, each system component has a backup with a probability of 0.85 and a switch that is 100% reliable. Since the backup has a probability of 0.85, and the switch is 100% reliable (probability = 1), we can calculate the probability as:

Probability = 0.85 × 0.85 × 0.85

Probability ≈ 0.6141The probability remains the same as in the previous case, which is approximately 0.6141.

c. In this scenario, each system component has a backup with a probability of 0.85, but the switch is 90% reliable (probability = 0.90). We can calculate the probability as:

Probability = 0.85 × 0.90 × 0.85

Probability ≈ 0.6485

The probability that the system will operate with each component having a backup with a probability of 0.85 and a switch that is 90% reliable is approximately 0.6485.

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Answer:

(f+g)x= 2x²+5x-3

The domain x∈ Real number.

Step-by-step explanation:

Given that f(x) = 5x - 3 and g(x) = 2x²

(f+g)x = f(x) + g(x)

So, by using the given function

(f+g)x= (5x-3) + (2x²)= 2x²+5x-3

As the result, 2x²+5x-3, is a polynomial, so domain of the result is all the real numbers.

The orthogonal trajectories of the family of curves x² + 2y² = k² are given by the equation x² = K²y⁴.

To find the orthogonal trajectories of the family of curves x² + 2y² = k², follow these steps:

1. Write the given equation as a function: x² + 2y² = k².
2. Differentiate the equation implicitly with respect to x: 2x + 4y(dy/dx) = 0.
3. Solve for dy/dx: dy/dx = -2x / (4y) = -x / (2y).
4. Replace dy/dx with -dx/dy to obtain the orthogonal trajectory: -dx/dy = -x / (2y).
5. Simplify the equation: dx/dy = x / (2y).
6. Separate the variables: dx/x = 2dy/y.
7. Integrate both sides: ∫(1/x)dx = 2∫(1/y)dy.
8. Obtain the integrals: ln|x| = 2ln|y| + C.
9. Remove the natural logarithm by raising e to the power of both sides: |x| = \(|y|^2 * e^C\).
10. Introduce a new constant K, where K = \(e^C: |x| = K|y|^2\).
11. Eliminate the absolute values by squaring both sides: x² = K²y⁴.

The orthogonal trajectories of the family of curves x² + 2y² = k² are given by the equation x² = K²y⁴.

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There are 455 ways to choose a dozen donuts from the 15 available varieties with no restrictions. To determine the number of ways to choose a dozen donuts from 15 varieties with no restrictions, we can use the concept of combinations.

The number of ways to choose a dozen donuts from 15 varieties with no restrictions can be calculated using the combination formula. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.

In this case, we have 15 varieties of donuts, and we want to choose 12 donuts. Applying the combination formula, we have C(15, 12) = 15! / (12!(15-12)!).

Evaluating this expression:

C(15, 12) = 15! / (12! * 3!) = (15 * 14 * 13 * 12!) / (12! * 3 * 2 * 1).

The factor of 12! cancels out in the numerator and denominator, leaving us with:

C(15, 12) = (15 * 14 * 13) / (3 * 2 * 1) = 455.

Therefore, there are 455 ways to choose a dozen donuts from the 15 available varieties with no restrictions.

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The second term in the sequence is 0.

To solve the problem, we can use the fact that each term after the second is the sum of the two preceding terms. Let's call the first term a and the second term b. Then, according to the problem, we have:

a = 3 (the first term is 3)

b = ?

c = a + b = 3 + b

d = b + c = b + (3 + b) = 2b + 3

e = c + d = (3 + b) + (2b + 3) = 3b + 6

We also know that the fifth term is 3, so we can set e equal to 3 and solve for b:

3b + 6 = 3

3b = -3

b = -1

Therefore, the second term in the sequence is 0, since each term after the second is the sum of the two preceding terms and the first term is 3.

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Answer:

11z+ 13

Step-by-step explanation:

22z - 11z = 11z

11z+ 13

Answer:

I know the correct ones!

Step-by-step explanation:

28 to 12, 63 to 27, 56 to 24

Answer:

its B C and D

Step-by-step explanation:

Answer:

6 degrees.

Step-by-step explanation:

Answer:

6°

Step-by-step explanation:

A full rotation of the minutes hand is 360° and 60 minutes.

360° / 60 minutes = 6°/minute

Answer: 6°

Answer:

b/a

Step-by-step explanation:

Perpendicular lines have slopes that are opposite sign and reciprocals (flipped over).

In the equation

ax + by = c,

the slope of the line is

-a/b

If you haven't memorized this pattern yet, you can calculate it by solving ax+by=c for y.

by = -ax +c

y = -a/b x + c/b

The slope is -a/b

So a perpendicular line would be opposite sign and flipped, b/a

Answer:

1328.88 cm^2

Step-by-step explanation:

Area = 6 * 1/2 * 22.6 * 19.6

= 1328.88 cm^2

Answer:

6,048

Step-by-step explanation:

l=3w

3w + 3w + w +w =96

8w =96

w=12

l= 36

12×36×14 = 6,048