At a ski resort there are three different chair lifts that will take you to the top of the mountain. There are six ski trails to the bottom of the mountain. How many different paths are there to go up and down the mountain?
What components are important in a linear function?
deena has a set of 4 coasters on her coffee table, and each coaster is shaped like a cylinder with a height of 0.5 inches and a radius of 2.5 inches. which is the total surface area of the 4 coasters?
Final answer:
The total surface area for the 4 cylindrical coasters, each with a height of 0.5 inches and a radius of 2.5 inches, is approximately 188.4956 square inches.
Explanation:
Deena has a set of 4 coasters, each shaped like a cylinder.
To calculate the surface area of one coaster, we need to find the area of the two circular bases and the area of the side that wraps around the cylinder (the lateral surface area).
The formula for the surface area of a cylinder is SA = 2πr(h+R), where r is the radius, h is the height, and R is the radius of the bases.
Given a height of 0.5 inches and a radius of 2.5 inches:
SA = 2π(2.5)(0.5+2.5)
SA = 2π(2.5)(3)
SA = 2π(7.5)
SA = 15π
The result is the surface area for one coaster. As we have 4 coasters, we multiply this result by 4:
Total surface area for 4 coasters = 4 × 15π ≈ 4 × 47.1239 ≈ 188.4956 square inches.
Ratio of dogs to cats is 9:4. If there are 54 dogs, how many cats?
how do you solve this
which expression is equivalent to the expression shown?
Answer:
5 to the power of 8
Step-by-step explanation:
The volume of a cube is 1,953.125 centimeters cubed. Find the length of the sides.
If BC -16 and BD-9 then find the length of BA. Show the work you use to find your answer. Draw the two similar triangles separately to help set up the proportion.
In right triangle the leg is geometrical mean of its projection on the hypotenuse and the hypotenuse. Thus,
[tex] AB^2=BD\cdot BC [/tex].
Substitude BC=16, BD=9, then
[tex] AB^2=9\cdot 16,\\ AB^2=144,\\ AB=12 [/tex].
Answer: AB=12
Part 2!
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How do I find the slope of the line through (–9, –10) and (–2, –5)?
Carlos is 63 inches tall. What is his height in feet?
Write a function in terms of t that represents the situation.
Your starting annual salary of $35,000 increases by
4% each year.
With instructions on how you did it please!!!
To represent the situation, the function can be written as f(t) = 35000 × (1 + 0.04)^t, where t represents the number of years into the future.
Explanation:To write a function in terms of t that represents the situation, we can start with the initial salary of $35,000 and then calculate the annual increase using the 4% growth rate.
We need to multiply the current salary by (1 + 0.04) to get the new salary for each year. The function can be written as:
f(t) = 35000 × (1 + 0.04)^t
Here, t represents the number of years into the future from the initial starting point.
For example, if you want to find the salary after 3 years, you can plug in t = 3 into the function.
A function that represents your annual salary starting at $35,000 and increasing by 4% each year,
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex], where t is the number of years.
To create a function that represents your annual salary starting at $35,000 and increasing by 4% each year,
we use the formula for exponential growth,
[tex]final amount = initial amount * (1 + growth rate)^t^i^m^e.[/tex]
Given that your initial salary is $35,000 and the growth rate is 4% (or 0.04),
let's define the function S(t) where S represents your salary and t represents the number of years:
[tex]S(t) = 35000 * (1 + 0.04)^t[/tex]
the initial salary=$35,000.
Convert the percentage increase to a decimal,
4% becomes 0.04.
Set up the function using the formula for exponential growth,
which is initial amount multiplied by [tex](1 + growth rate) ^t[/tex]
Thus, for any year t, the function [tex]S(t) = 35000 * (1 + 0.04)^t[/tex] calculates your annual salary.
How do you factor 4x^2+20x-3xy-15y?
When a=-9, and b=-6, which expression has a value of -3?
A. a+b
B. a-b
C. |a+b|
D. |a-b|
What do you call a person who makes faces all day long
A person who makes faces all day is often described as expressive or animated, and may be humorously termed a 'mugger' or 'face-puller'. Facial expressions are crucial for conveying emotion in human interaction and can be particularly striking in literature and dramatic performances.
The question 'What do you call a person who makes faces all day long?' is asking about a term or description for someone who frequently changes their facial expressions. While there is no specific term that describes this behavior in a clinical or professional sense, in a colloquial context, you might call such a person expressive, animated, or if the expressions are humorous or exaggerated, a 'mugger' or 'face-puller'. In literature and drama, characters known for their expressive faces can bring a story to life or provide comic relief.
Facial expressions are an integral part of human communication. They can underscore the emotional state of a person, such as the sense of pride on the face of a monomaniacal king, the devotion seen in a religious fanatic, or the terror described in the imagery of wallpaper patterns appearing to have expressive eyes. Whether in social interactions, literature, or public speaking, the alignment of facial expressions with spoken words is important for conveying meaning and emotion.
Rational and Irrational Numbers what is it explain
The radius of a circular hat is 3.7 inches. Find the circumference. Use 3.14 for π. (1 point)
1.85 in.
11.618 in.
23.236 in.
22.2 in.
Answer:
The circumference is [tex]23.236\ in[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=3.7\ in[/tex]
substitute
[tex]C=2(3.14)(3.7)=23.236\ in[/tex]
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In a layout of Mark’s backyard, the ratio is 1 centimeter = 10 meters. The length of the deck on the layout is 4 cm and the width is 4 cm. What is the perimeter of Mark’s deck?
The perimeter of Mark's deck in real life is calculated by converting the layout measurements to actual measurements using the scale factor and then applying the perimeter formula. The perimeter is found to be 160 meters.
To calculate the perimeter of Mark's deck, which is represented on a layout where the scale is 1 centimeter = 10 meters, we use the perimeter formula for a rectangle: Perimeter (P) = 2 * (length + width). Since both the length and width of Mark's deck are provided as 4 centimeters each, and each centimeter corresponds to 10 meters in reality, we first convert the measurements from centimeters to meters by multiplying them by the scale factor.
Length in meters = 4 cm * 10 meters/cm = 40 meters
Width in meters = 4 cm * 10 meters/cm = 40 meters
Now, calculate the perimeter:
P = 2 * (40 meters + 40 meters)
P = 2 * 80 meters
P = 160 meters
The real-life perimeter of Mark's deck is 160 meters.
Solve the following system of equations graphically.
x = -5
y = -6
What is the solution set?
{(-6, -5)}
{(-5, -6)}
∅
A field is shaped like the figure shown. What is the area of the field? Use 3.14 for pi
Answer:
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Step-by-step explanation:
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A balloon that is tied to a stake in the ground is being blown sideways by the wind. The length of the string from the stake to the balloon is 26 feet, and the distance from the stake to a point directly under the balloon is 24 feet.
what does it mean to "square a circle"?
Final answer:
In mathematics, 'squaring the circle' means to create a square with the same area as a given circle, though it is impossible to achieve precisely due to the nature of π. When fitting a circle in a square, the side of the square is twice the radius of the circle, and the circle's area is approximately three-quarters that of the square.
Explanation:
To "square a circle" in mathematical terms traditionally means to create a square with the same area as a given circle, using only a finite number of steps with compass and straightedge. This problem is known to be impossible to solve exactly due to the transcendental nature of π (pi). However, when we discuss fitting a circle within a square, we often refer to having the diameter of the circle, which is twice the radius (2r), fit exactly across the side length of the square (a).
The area of the circle is πr², and when the circle fits within a square the area of the square is a². Since a = 2r, the area of the square can be expressed as 4r². From this, we can approximate that a circle's area would be less than the area of the square but more than half, possibly around three-quarters, thus approximately 3r².
Perimeter-wise, a circle within a square would have a circumference less than the perimeter of the square but significantly longer than a straight line passing through the center of the square. This understanding allows for practical estimations without requiring exact precision, which can be particularly useful in everyday contexts where an approximation suffices.
Each small cube is 1 cm3. The length of the large cube is 12 cm. What is the volume of the large cube? A. 24 cm3 B. 144 cm3 C. 864 cm3 D. 1,728 cm3
Answer:
d
Step-by-step explanation:
A student is selling baked goods in the halls before school as a fundraiser. She sells cinnamon rolls, donuts, and croissants. Students purchase the goods according to the probability distribution:
X(Product): cinnamon roll, donut, croissant
P(x): 0.20, 0.55, 0.25
A): If a cinnamon roll yields $0.25 profit, a donut yields $0.20 profit, and a croissant yields a $0.30 profit, how much profit will be made on each customer?
B):If there are 50 customers, how much can you expect her to make?
what are the mean median mode and range of the data set given the altitude of lakes in feet -9, -36, -23, -8, -17, -52, -27, and -36 A. mean=-25; median=-26; mode=-44; range=36 B. mean=-25; median=-36; mode=-36; range=44 C. mean=-26; median=-25; mode=-36; range=44 D. mean=-26; median=-44; mode=-25; range=36
Answer:
C
Step-by-step explanation:
find the length of the base indicated for each trapezoid
To find the base of a trapezoid, you can view the trapezoid as two right triangles joined together. The base of the trapezoid is the sum of the bases of these triangles. Depending on the orientations of the sides of the trapezoid and the height, you might need to use the Pythagorean theorem.
Explanation:The question asks to find the length of the base for a given trapezoid. In order to do this, we can use concepts from geometry and trigonometry. Consider the trapezoid as two right triangles back to back. The base of the trapezoid is the sum of the bases of the two right triangles.
For example, if you have a trapezoid with sides A and B, and the height is H, you can use these sides and the trigonometric principles to calculate the lengths of the bases. If side A or B is not perpendicular to the base, you would need to use the Pythagorean theorem. That formula is A^2+B^2=C^2, where C is the hypotenuse of the right triangle formed.
In case, the sides A and B are perpendicular to the base, the lengths of the bases would simply be side A + side B. This would give you the total length of the base of the trapezoid.
Learn more about Trapezoid Base Length here:https://brainly.com/question/31380175
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Iris had $900. She spend 22% of this amount on a mobile phone. How much did she pay for the mobile phone
Answer:
198
Step-by-step explanation:
Of means multiply and 22% as a decimal is 0.22, so multiply 0.22 by 900.
900*0.22=198
How could you calculate each product? Describe the strategy you would use. Then calculate.
a) 9 x 5
b) 5 x 8
Which measure is equivalent to 48 quarts? 1 cup = 8 fluid ounces 1 quart = 4 cups