Kimberly loves to ski in the winter, but her least favorite part is riding the slow ski lift to the top of the mountain. Each ski-lift ride takes 5 minutes. During her most recent ski session, Kimberly spent 60 minutes in all on the ski lift. Let r represent how many ski-lift rides Kimberly took. Which equation models the problem?

Answer:

  1. A. contain a right angle

  1. B. opposite sides are parallel

  2. (c) 2 pairs of parallel sides

  3. (b) 2 sides of equal length

Step-by-step explanation:

Here you are asked to find patterns and to make use of the definitions of different geometric figures.

The figures in Circle A do not all have the same number of sides, or sides of the same length. However, they do all have at least one right angle.

The figures in Circle B are rectangles and parallelograms. The attributes listed in question 2 can be used here. They all have two pairs of parallel sides.

As we observed in question 1, rectangles and parallelograms share the feature of 2 pairs of parallel sides.

A kite may have 2 pairs of equal-length sides. While a square and a rhombus have 4 sides of equal length, that description is not true of rectangles and parallelograms in general.

Angles in a rectangle are all 90°, while those in a parallelogram may not be. The offered descriptions of angles do not apply to apply to both shapes.

An isosceles triangle has two sides equal length and two equal angles. An equilateral triangle is a special case of an isosceles triangle in which all three sides are equal, as are all three angles. The description that applies to both kinds of triangles is 2 sides of equal length.

Answer: See the explanation for which answer you need, with and without pi.

Step-by-step explanation:

Knowing that the sprinkler covers a diameter of 12, let's divide this in half and get the radius, which is 6 feet.

Next, the arc is 195 degrees, so the area of the arc is the following:

A = (θ/360°) × πr^2

A = (195/360) × π(36)

Note that 36 is radius squared, which 6 squared is 36.

195/360 simplifies to 13/24

Multiply the given function and here are two answers:

- With pi in it's symbolic form, it is 19.5π feet squared.

- With pi as a decimal, it is estimated 61.26 feet squared.

Answer:

-13

Step-by-step explanation:

Answer:

less than

\(1 \frac{1}{2} \)

I believe

The possible functions are

A. F(x)=2x^2-8x-42

B. F(x)=5x^2+20x-105

C. F(x)=x^2+4x-21

The zeros are given as:

x = -7 and x = 3

Rewrite as:

x +7 = 0 and x - 3 = 0

Multiply both zeros

(x + 7) * (x - 3) = 0 * 0

Evaluate the product

x^2 + 7x - 3x - 21 = 0

Evaluate the like terms

x^2 + 4x - 21 = 0

Express as a function

f(x) = a(x^2 + 4x - 21)

Where a is a constant

Let a = 1, 2 and  5 (according to the values in the options)

f(x) = 1 * (x^2 + 4x - 21) = x^2 + 4x - 21 --- option (c)

f(x) = 2 * (x^2 + 4x - 21) = 2x^2 + 8x - 42 --- option (a)

f(x) = 5 * (x^2 + 4x - 21) = 5x^2 + 20x - 105 --- option (b)

Hence, the possible functions are (a), (b) and (c)

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Answer:

3%

Step-by-step explanation:

Blake bought a new car. He borrowed $12,500 from the bank. After 4 years he had paid off the loan and paid $1500 in interest. What rate did he borrow at?

This is a simple interest question

The formula to find the rate is given as:

Equation:

r = (1/t)(A/P - 1)

t = time = 4 years

P = Principal = $12500

I = Simple Interest = $1500

A = Total Amount = Principal + Simple Interest = $12500 + $1500

= $14000

Calculation:

Solving our equation:

r = (1/4)((14000/12500) - 1) = 0.03

r = 0.03

Converting r decimal to R a percentage

R = 0.03 * 100 = 3%/year

Answer:

11/13

Step-by-step explanation:

Answer:

Step-by-step explanation:

The small triangle is similar to the triangular face. Its side edges are half the length of the side edges of the face, so its base is half the length of the face.

2*58 ft = 116 ft

The length of the base of the pyramid is 116 ft.

The z-score of an appliance that failed after 64 months is 2.

To find the z-score:

The given parameters are:

The z-score is then computed as follows:

We have the following for an appliance that stopped working after 64 months:

So, the equation becomes:

Compare and contrast the differences:

Calculate the quotient:

Therefore, the z-score of an appliance that failed after 64 months is 2.

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The length of the diagonal distance, x, of the smaller bookend can be found using the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two side.

In this case, the height of the smaller bookshelf is 6 inches and the diagonal height (x) is unknown. We can consider these two sides as the legs of the right triangle. The equation would be:

6^2 + x^2 = diagonal height^2

36 + x^2 = diagonal height^2

Now, we need to find the diagonal height of the smaller bookshelf. Since the diagonal height of the larger bookshelf is given as 12 inches, we can use this information to find the diagonal height of the smaller bookshelf.

Let's set up a proportion using the heights of the two bookshelves:

(diagonal height of smaller bookshelf) / (height of smaller bookshelf) = (diagonal height of larger bookshelf) / (height of larger bookshelf)

x / 6 = 12 / 10

Cross-multiplying:

10x = 6 * 12

10x = 72

x = 72 / 10

x ≈ 7.2 inches

Therefore, the length of the diagonal distance, x, of the smaller bookend is approximately 7.2 inches.

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Answer:

90

Step-by-step explanation:

Answer:

x=95 degrees

Step-by-step explanation:

All of the angles in a triangle add up to 180, so 45+50+(180-x)=180.

Open the parenthesis, and you get 45+50+180-x=180.

Then subtract 180 from both sides, so 45+50-x=0.

Simplify that to 95-x=0, and add x to both sides.

x=95

Also, you can use exterior angles theorem, which states that 45+50=x.

That's the shorter way.

The angle θ between vectors a = ⟨3, -1⟩ and b = ⟨0, 15⟩ is approximately 2.944 radians.

To find the angle (θ) between two vectors, a = ⟨3, -1⟩ and b = ⟨0, 15⟩, we can use the dot product formula and the magnitudes of the vectors.

The dot product (or scalar product) of two vectors is given by the formula:

a · b = |a| |b| cos(θ)

where |a| and |b| are the magnitudes of vectors a and b, respectively.

First, let's calculate the magnitudes of vectors a and b:

|a| = √(3² + (-1)²) = √10

|b| = √(0² + 15²) = 15

Next, let's calculate the dot product of vectors a and b:

a · b = (3)(0) + (-1)(15) = -15

Now we can solve for cos(θ) by rearranging the dot product formula:

cos(θ) = (a · b) / (|a| |b|)

cos(θ) = -15 / (√10 * 15)

Finally, we can find the angle θ by taking the inverse cosine (arccos) of cos(θ):

θ = arccos(-15 / (√10 * 15))

Evaluating this expression gives θ ≈ 2.944 radians.

Therefore, the angle θ between vectors a = ⟨3, -1⟩ and b = ⟨0, 15⟩ is approximately 2.944 radians.

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The exact length of the curve is approximately 0.7386.

We're given the equation of the curve as:

\(y = ln(1 - x²)\)

and the range of x values:

\(0 ≤ x ≤ 1/8\)

The exact length of the curve can be found by using the formula:

Length of curve

\(= ∫(a to b) √[1 + (dy/dx)²]dx\)

Here, a = 0 and b = 1/8

Also,

\(dy/dx = -2x/(1 - x²)\)

We can use this to find (dy/dx)²:

\((dy/dx)² = [(-2x)/(1 - x²)]²= 4x²/(1 - x²)²\)

Now, we can substitute these values in the formula for length:

Length of curve

= \(∫(a to b) √[1 + (dy/dx)²]dx\)

= \(∫(0 to 1/8) √[1 + 4x²/(1 - x²)²]dx\)

This integral can be simplified using trigonometric substitution:

Let\(x = (1/2)tanθ\)

Then

\(dx = (1/2)sec²θ dθ\)

Also,

\(1 - x² = 1 - (1/4)tan²θ = 3/4sec²θ\)

So, the integral becomes:

\(∫(0 to 1/8) √[1 + 4x²/(1 - x²)²]dx\)

=\(∫(0 to π/6) √[1 + 16/9 sin²θ] (1/2)sec²θ dθ\)

= \((1/2) ∫(0 to π/6) √[25 + 16 sin²θ]sec²θ dθ\)

This integral can be solved using the substitution

\(u = 5tanθ\)

Then

\(du/dθ = 5sec²θ and sin²θ = (u²/25) - 1\)

Substituting these values, we get:

Length of curve

\(= (1/2) ∫(0 to arctan(5/3)) √(u² + 16) du/5\)

\(= (1/10) ∫(0 to arctan(5/3)) √(u² + 16) du\)

Now, this integral can be simplified using the substitution

\(u = 4tanψ\)

Then

\(du/dψ = 4sec²ψ and u² + 16 = 16(sec²ψ + 1)\)

Substituting these values, we get:

Length of curve

= \((1/10) ∫(0 to arctan(5/3)) √(16(sec²ψ + 1)) (1/4)4sec²ψ dψ\)

= \((1/40) ∫(0 to arctan(5/3)) 8sec³ψ dψ= (1/5) [secψ tanψ]0toarctan(5/3)\)

= \((1/5) [5 sqrt(34) - 3]\)

≈ 0.7386

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Answer:

\(\frac{4}{15}\)

Step-by-step explanation:

Answer:

Step-by-step explanation:

for the table you just add 45 to all the numbers, so it will be 135, and 270

you will just have to graph that.

Answer:

$90 to rent and 15$ per guest. equation is y=15x+90. initial value is 90, rate of change is 15.

Step-by-step explanation:

Answer:

-2 5/8

HOPE THIS HELPS

- Todo ❤️

Step-by-step explanation:

3-5=-2

6/8-1/8=5/8

Answer:

40° or 100°.

Step-by-step explanation:

If Angle ABD = 70° and Angle CBD = 30° Angle ABC can be 70° + 30° or 70° - 30°.

angle ABC measures 100 degrees.

To find the measure of angle ABC, we can use the fact that the sum of the angles in a triangle is 180 degrees.

In triangle ABC , we have angle ABD measuring 70 degrees and angle CBD measuring 30 degrees.

Since angle ABD and angle CBD are adjacent angles, they add up to form angle ABC.

Therefore, we can calculate angle ABC as follows:

m ∠ ABC = m ∠ ABD + m ∠ CBD

m ∠ ABC = 70° + 30°

m ∠ ABC = 100 degrees

Thus, angle ABC measures 100 degrees.

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Answer:

m=(2,0)................

Answer:

\(m=\frac{1}{2}\)

Step-by-step explanation:

Points (0,0) and (2,1)

\(x_{1} =0\\x_{2} =2 \\y_{1} =0\\y_{2} =1\)

\(m=\frac{changein (y)}{change in (x)}\)

\(m=\frac{y_{2}-y_{1} }{x_{2}-y_{1} }\)

\(m=\frac{{1}-(0) }{2-(0)}\)

Simplify

\(m=\frac{1}{2}\)

Answer:

D (last one)

Step-by-step explanation:

The probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters is 0.325.

The probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters can be found using the following formula for a uniform distribution:

P(X > x) = (max - x) / (max - min)

where X is the random variable (diameter of the ball bearings), x is the specific value we are interested in (5.85 millimeters), max is the maximum value of the distribution (6.5 millimeters), and min is the minimum value of the distribution (4.5 millimeters).

Plugging in the values, we get:

P(X > 5.85) = (6.5 - 5.85) / (6.5 - 4.5)

= 0.65 / 2

= 0.325

Therefore, the probability of a randomly selected ball bearing having a diameter greater than 5.85 millimeters is 0.325.

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We can order them in increasing x-coordinate as:

(0, 0), (0.585, 6.415), and (5.748, 1.252)

To find the critical points of the predator/prey model, we need to find the values of x and y that make both x' and y' equal to zero.

From the given equations, we have:

x' = 7x - x² - xy = 0

y' = -5y + xy = 0

Factoring x out of the first equation, we get:

So, either x = 0 or 7 - x - y = 0.

If x = 0, then the second equation simplifies to y' = -5y = 0, which has a critical point at y = 0.

If 7 - x - y = 0, then we can solve for y to get:

y = 7 - x

y' = -5y + xy = -5(7 - x) + x(7 - x) = 0

Simplifying, we get:

6x² - 49x + 35 = 0

x = (49 ± sqrt(49² - 4(6)(35))) / (2(6)) ≈ 0.585 or x ≈ 5.748

Substituting these values into y = 7 - x, we get:

y ≈ 6.415 or y ≈ 1.252

(0, 0), (0.585, 6.415), and (5.748, 1.252)

We can order them in increasing x-coordinate as:

(0, 0), (0.585, 6.415), and (5.748, 1.252)

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Answer:

Answer = 61/157

Step-by-step explanation:

First add all the numbers together.

56 + 61 + 14 + 26 = 157

Then take the number of brown hair and blue eyed people (61) and make a fraction out of all.

61/157

You can not simplify it more than that

Hope this helps

Explanation:

This equation represents a line, so there are many points that are solutions to the equation. To fill in this boxes we just have to pick a x-value that's in the domain, replace it into the equation and solve for y. The domain of this function is all real numbers, so any number will work.

Using x = 1:

Answers:

A solution is (-24) = 8( 1 ) - 32

(a) The probability that the current component is Brand X is 1/2, since both brands are equally likely to fail at any given time and the replacement component is always from the opposite brand.

(b) The age of the current component has a uniform distribution on [0,1] if it is a Brand Y component (since it was just replaced) and on [0,2] if it is a Brand X component (since it has been in use for some time).

(c) The total lifetime of the current component has a mixture distribution, where the probability density function is given by:

    f(t) = (1/4) for 1 ≤ t ≤ 2

    f(t) = (1/6) for 2 ≤ t ≤ 3

(d) If the replacement component is chosen randomly with a probability 1/2 for each brand, then the probability that the current component is Brand X is still 1/2.

This is because if the current component is a Brand X component, it has been in use for a time between 0 and 2 (uniformly distributed) and then it will fail at a time between 1 and 2 (uniformly distributed), for a total lifetime between 1 and 2 (with probability 1/2) or between 2 and 3 (with probability 1/2).

If the current component is a Brand Y component, it has been in use for a time between 0 and 1 (uniformly distributed) and then it will fail at a time between 1 and 3 (uniformly distributed), for a total lifetime between 1 and 2 (with probability 1/3), between 2 and 3 (with probability 1/3), or between 3 and 4 (with probability 1/3).

However, the distribution of the age and total lifetime of the current component will be different. The age of the current component will have a mixture distribution, where the probability density function is given by:

f(t) = (1/4) for 1 ≤ t ≤ 2

f(t) = (1/6) for 2 ≤ t ≤ 3

f(t) = (1/12) for 3 ≤ t ≤ 4

This is because if the current component is a Brand X component, it has been in use for a time between 0 and 2 (uniformly distributed) and then it will fail at a time between 1 and 2 (uniformly distributed), for a total lifetime between 1 and 2 (with probability 1/2). If the current component is a Brand Y component, it has been in use for a time between 0 and 3 (uniformly distributed) and then it will fail at a time between 1 and 3 (uniformly distributed), for a total lifetime between 1 and 2 (with probability 1/6), between 2 and 3 (with probability 1/3), or between 3 and 4 (with probability 1/6). The total lifetime of the current component will also have a mixture distribution, where the probability density function is the same as in part (c).

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Answer:

C

Step-by-step explanation:

Step-by-step explanation:

Hey there!

Given;

x-y = 5

Slope intercept form: y = mx+c.

Now try to make it in y= mx+c form.

Take"-y" to right side and and 5 to left side.

x-5= y

Therefore, y = x-5

Hope it helps..

Answer:

0*i+5j

Step-by-step explanation:

The vector is given by 0*i+5j