Applying the laws of cosine, in the second section of her ride, Andariel traveled about 3.012 km, as rounded to 2 decimal places.
What is the law of cosines?The law of cosines is a mathematical formula used to determine the unknown length or angle of a triangle when two sides and an angle or all three sides are known.
Hence, we can think of it as trying to know Andariel's travel distance around a big triangle.
Thus to calculate, using the law of cosines, we have:
[tex]c^2 = a^2 + b^2 - 2ab*cos(C)[/tex]
Where in our case:
a = 6 km (distance traveled east)b = x km (distance traveled in the second section)C = 180 - 125 = 55 degrees (angle between a and b)c = 5.5 km (distance traveled straight back to the starting position)If we substitute the values above into the cosine formula, we get:
[tex](5.5)^2 = (6)^2 + (x)^2 - 2(6)(x)*cos(55)[/tex]
[tex]30.25 = 36 + x^2 - 12.0627x[/tex]
Simplifying and rearranging the equation further:
[tex]x^2 - 12.0627x + 5.75 = 0[/tex]
Applying the quadratic formula to simply:
[tex]x = (12.0627 ± sqrt(12.0627^2 - 415.75))/2[/tex]
x = 9.05 or x =3.012.
Remember, we are told Andariel turned left twice and ended up at her starting position, we know that she traveled in a closed loop.
Therefore, the distance she traveled in the second section of her ride must be less than 6 km (the distance she traveled east in the first section). Thus, the distance she traveled last or second section of her ride was 3.012 km.
You can learn more about the law of cosines here https://brainly.com/question/4372174
#SPJ1
a company received a shipment of 30 laser printers, including 6 that are defective. 3 of these printers are selected to be used in the copy room. (a) how many selections can be made?
We have to calculate the number of combinations of 3 laser printers that can be selected from the 30 shipped. In this case, the number of possible combinations is 4060.
The combination can be calculated using the formula
ⁿCr = n! / r! (n-r)!
Where n is the total number of items and r is the number of items chosen. In this case, n is 30 and r is 3.
³⁰C₃= 30! / (3! * (30-3)!) ⇒ 30! / (6 * 24)
⇒ 30 * 29 * 28 / 6
⇒ 4,060
Therefore, the answer is 4060 possible combinations of 3 laser printers that can be selected from the 30 shipped.
To know more about the "combinations": https://brainly.com/question/4658834
#SPJ11
find the area of the image below
Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. How much interest will he have earned after 3 years?
Answer:
$45
Step-by-step explanation:
Interest earned in a year
5/100x300= $15
Interest earned in 3 years
=$15x3
=$45
What is the answer in the photo
The sale price of the reusable water bottle is $18.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating these symbols. It is a broad area that includes various subfields such as elementary algebra, abstract algebra, and linear algebra, among others.
In elementary algebra, the focus is on the basic rules and operations involving variables, numbers, and equations. These concepts are used to solve problems in a wide range of fields, such as science, engineering, and finance. Abstract algebra, on the other hand, deals with the study of algebraic structures such as groups, rings, and fields. Linear algebra is the study of vector spaces and linear transformations, and is used extensively in fields such as computer science, physics, and engineering.
The discount on the reusable water bottles is 10%, which means that the customer pays only 90% of the regular price. To find the sale price, we can multiply the regular price by 90% or 0.9.
Sale price = Regular price x (1 - Discount rate)
Sale price = $20 x (1 - 0.1)
Sale price = $20 x 0.9
Sale price = $18
Therefore, the sale price of the reusable water bottle is $18.
To know more about rate visit:
https://brainly.com/question/199664
#SPJ1
2.8 is what percent of 2.24
Two or more terms having the same variables are called?
Answer:
Like terms
Step-by-step explanation:
Are the terms that contain same variables, same exponents of variables and same coefficients.
HOPE THIS HELPS
HELP PLEASE MATH IS HARD
The box plot displays the number of flowers planted in a town last summer. A box plot uses a number line from 6 to 21 with tick marks every one-half unit. The box extends from 10 to 15 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 20. The graph is titled Flowers Planted In Town, and the line is labeled Number of Flowers. Which of the following is the best measure of center for the data shown, and what is that value? The mean is the best measure of center and equals 11. The mean is the best measure of center and equals 12. The median is the best measure of center and equals 11. The median is the best measure of center and equals 12.
After answering the presented question, we can conclude that thus, the equation correct answer is: The median, which equals 11, is the best measure of center.
What box plot represent?The box plot depicts the distribution of the quantity of flowers planted in a town last summer based on the information provided. The box spans the number line from 10 to 15, with a line at 11 inside the box and lines outside the box ending at 7 and 20.
The median is depicted by the line in the box, which is positioned at 11 in the box plot. As a result, the median is the best measure of center for the data provided, and its value is 11.
Thus, the correct answer is: The median, which equals 11, is the best measure of center.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
119. What is the linear equation for the pricing formula for Logan's Paint? One gallon cost $11 (1,11) and 5 gallons cost $35 (5, 35).
The linear equation is y = 6x + 5
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
To find the equation for the pricing formula, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the cost, x is the number of gallons, m is the slope (i.e., the rate of change of the cost per gallon), and b is the y-intercept (i.e., the cost when x = 0).
Using the given information, we can calculate the slope:
m = (35 - 11) / (5 - 1) = 24 / 4 = 6
The y-intercept can be found by plugging in one of the points:
11 = 6(1) + b
b = 5
Therefore, the linear equation for the pricing formula for Logan's Paint is:
y = 6x + 5
where y is the cost in dollars and x is the number of gallons.
To know more about linear equation, visit:
https://brainly.com/question/12788590
#SPJ1
2,188,180 rounded to nearest tenth
Answer:
2,188,180
Step-by-step explanation:
since 0 can't give anything to 8 the number would stay the same
What fraction of 1/2 square centimeter 1/2 centimeter square?
1/4 square centimeter is therefore equal to 1/2 square centimeter.
In math, what is a fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears inside the numerator and denominator of a complex fraction. The numerator of a proper fraction has a smaller denominator.
While "1/2-centimeter square" refers to a square having the side length of half a centimeter, the marking "1/2 square centimeter" typically refers to an area equal half a square centimeter. Even though these aren't the same object, we can still calculate the ratio of one to the other.
The area of such a square of side length 1/2 centimeter is:
(1/2 cm) x (1/2 cm) = 1/4 square centimeter
We may divide 1/4 by 1/2 to determine the percentage of 1/2 square centimeter that corresponds to 1/4 square centimeter:
(1/4 square cm) ÷ (1/2 square cm) = (1/4) x (2/1) = 1/2
Hence, 1/4 square centimeter is equal to 1/2 square centimeter in size.
To know more about fraction visit:
https://brainly.com/question/28372533
#SPJ1
The number of air conditioner units that 10 sales representatives sold last year are:
{6, 8, 10, 11, 12, 16, 17, 21, 32, 36}
How is the mean effected if the representative who sold the lowest number of units left the department, causing his sales to cancel out?
Responses:
The mean would increase.
The mean would remain the same.
The mean would decrease.
The correct option is (a), i.e. The mean would increase.
What is mean?
Mean is a measure of central tendency that is commonly used in statistics and mathematics. The mean of a set of numbers is calculated by adding up all the numbers in the set and dividing the sum by the total number of values in the set.
The mean of the number of air conditioner units sold by the 10 sales representatives last year can be calculated by adding up all the sales and then dividing by the total number of representatives, which is 10:
Mean = (6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36) / 10
= 169 / 10
= 16.9
So the mean number of air conditioner units sold per representative is 15.9.
If the representative who sold the lowest number of units left the department and his sales are cancelled out, the new sum of sales will be:
6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36 - 6 = 163
This is because we subtract the sales of the representative who left (which is 6 units in this case). The new mean can then be calculated by dividing this sum by the new total number of representatives, which is 9:
New mean = 163 / 9
= 18.11
So the new mean number of air conditioner units sold per representative is 18.11, which is higher than the original mean of 16.9. This is because removing the lowest value (which is smaller than the mean) increases the overall average.
To learn more about mean, visit the link:
https://brainly.com/question/1136789
#SPJ1
f(x) = x + 6 g(x) = 5x Work out the value of gf(3)
Answer:
45
Step-by-step explanation:
[tex]g(f(x))=5(x+6)[/tex]
[tex]g(f(3))=5(3+6)\\[/tex]
[tex]g(f(3))=5(9)\\[/tex]
[tex]g(f(3))=45[/tex]
Answer:
f(x) =x + 6g(x) =5x =
Calculate the formula weights:
mass of mole of
F(x) = x + 6g (x) = 5x = 19g
in a sample of 500 customers, 140 say that service is poor. you select two customers without replacement to get more information on their satisfaction. what is the probability that both say service is poor?
The probability that both customers say that the service is poor is 0.0588 or 5.88%.
To determine the probability that both customers say the service is poor, use the binomial distribution and the following formula:P(X = k) = (nCk) * p^k * (1 - p)^(n - k)Where:P(X = k) represents the probability that k successes occurn is the sample sizep is the probability of successk is the number of successes requested(1 - p) represents the probability of failure.Substitute the given values and calculate:P(X = 2) = (2C2) * (140/500)^2 * (1 - 140/500)^(2 - 2) = 0.0588 or 5.88%
Learn more about Probability
brainly.com/question/30034780
#SPJ11
Question
Julio buys a salad and a container of yogurt. These bills and coins represent the cost of each item.
How much did Julio spend in all?
The total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
To determine how much Julio spent while buying a salad and a container of yogurt, we have to multiply the value of each notes into their quantity then add all of them.
Number of 25 cents coins = 4
⇒ 4×0.25 = 1.00
Number of 5 dollar note = 1
⇒ 1×5 = 5.00
Number of 10 cents coins = 3
⇒ 3×0.10=0.30
Number of 1 cents = 3
⇒ 3×0.01=0.03
Number of 5 cents = 1
⇒ 1×0.05=0.05
Julio spent = 1.00 + 5.00 + 0.30 + 0.03 + 0.05
= $6.38
Therefore, the total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
Learn more about multiply :
https://brainly.com/question/30875464
#SPJ1
The complete question is :
Julio buys a salad and a container of yogurt. These bills and coins shown in attached image represent the cost of each item. How much did Julio spend in all?
Every year, Martha and her sister attend 'The Nutcracker' at the Greenpoint Ballet. Last year, orchestra seating cost $60 per ticket. This year, each ticket was 15% cheaper. What was the cost of each ticket this year?
Answer:
$51
Step-by-step explanation:
You convery the percentage into a decimal, by dividing it by a hundred.
15÷100= 0.15
then you multiply the decimal and the price.
60×0.15= 9.
The question said it got cheaper so we have to subtract 9 from the original price.
60-9=51.
I NEed HELP ON THIS ASAP!
Answer:
length times with equals to base times height
Step-by-step explanation:
length times with times height equals to 3400
Explain how to use what you know about whole number division to check your work when you divide with fractions, use at least three terms from the world word list in your explanation
using what we know about whole number division can be helpful when dividing with fractions. We can use the inverse operation of multiplication, simplify fractions, and use estimation to check our work and ensure that our division is accurate.
When dividing with fractions, one can use what they know about whole number division to check their work. This is because the rules of division remain the same for both whole numbers and fractions. One important rule is that division is the inverse operation of multiplication. In other words, when we divide, we are essentially finding how many times one number (the divisor) fits into another number (the dividend).
To check our work when dividing with fractions, we can use the same approach. We can multiply the quotient (the result of our division) by the divisor to see if we get back the dividend. If we do, then we know that our division was correct. For example, if we divide 3/4 by 1/2 and get a quotient of 3/2, we can check our work by multiplying 3/2 by 1/2.
Another important rule is that we can simplify fractions before dividing them to make the process easier. This means that we can divide both the numerator and the denominator by a common factor to get an equivalent fraction with smaller numbers. For example, if we want to divide 6/8 by 2/3, we can simplify 6/8 to 3/4 and 2/3 to 8/12. Then we can divide 3/4 by 8/12, which is much easier.
Finally, we can also use estimation to check our work when dividing with fractions. Estimation involves rounding the fractions to the nearest whole number or using benchmarks, such as 1/2 or 1, to get an approximate answer. This can help us quickly check if our quotient is reasonable or if we made an error in our division.
Learn more about fraction here
https://brainly.com/question/10354322
#SPJ4
Find the exact side length of a square with an area of 9/49 square meters.
Answer:
3/7 meters
Step-by-step explanation:
[tex] \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]
Normalmente, el concepto griego "logos" se entiende como la máxima expresión de la cultura racionalista occidental, fundada por las primeras escuelas de filosofía clásica. De hecho, el nombre de las disciplinas científicas provienen de él: biología, filología, psicología, tecnología, etc. No obstante, el concepto "logos" no tiene un significado tan abstracto, puesto que involucra tanto el pensamiento como la acción, tanto lo interno como lo externo, tanto la idea mental como el decir la palabra. Tema:_________________________________________________________ Idea Principal: ___________________________________________________
Concept: "Logos" has greatly affected Western philosophy and a variety of scientific disciplines. Acknowledgement: the interaction between logical reasoning and empirical observation as well as the influence of language and discourse worldview.
For the concept:
Topic: The significance of the Greek philosophical idea of "Logos" in contemporary scientific disciplines.
Greek philosophy's basic idea of "Logos" has had numerous interpretations throughout history. The word "logos" is most commonly used to refer to reasoned discourse and language. It is frequently linked to human conversation and reasoning as well as the cosmic or divine principle that creates and sustains the universe.
The significance of "Logos" can be observed in its impact on contemporary scientific disciplines, including, but not limited to, biology, psychology, and technology. For instance, the word "biology" is derived from the Greek terms "bios" (life) and "logos" (word or reason), illustrating the notion that the study of life necessitates both practical observation and logical analysis.
Parallel to this, the scientific discipline of psychology, which examines how the human mind and behaviour function, gets its name from the Greek words "psyche," which means "soul," and "logos," which means "reason." This illustrates the notion that both empirical research and theoretical analysis are necessary for the study of the mind and behaviour.
Learn more about concept here:
https://brainly.com/question/31038302
#SPJ4
Translation: The first schools of classical philosophy founded by the Greek word "logos" are widely understood as the apex of Western rationalist culture. In actuality, he is the one who gave the titles of numerous branches of science, including philology, psychology, technology, and biology. The idea of "logos" does not have such an abstract meaning because it involves both internal and exterior mental and physical actions, as well as the mental idea and word pronunciation. Topic: Main Idea:
in how many ways can we list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions?
There are 144 ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions.
We have to list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions. We can use the knowledge of permutations and combinations to solve this problem. We can start by selecting the positions for the distinct digits, i.e., (3, 4, 5). There are 3 distinct digits, so there are 3! = 6 ways to arrange them.
Once we have placed the distinct digits, we can place the two 1's and two 2's in the remaining positions such that no two identical digits are in consecutive positions. To do this, we can use the following approach:
We can start by placing one of the 1's. There are 4 positions available for the first 1.
We can then place one of the 2's. There are 3 positions available for the first 2.
We can then place the second 1. There are 2 positions available for the second 1.
We can then place the second 2. There are 1 positions available for the second 2.
Therefore, the total number of ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions is:
6 (arrangements of distinct digits) x 4 x 3 x 2 x 1 = 144.
To learn more about permutations and combinations visit : https://brainly.com/question/28065038
#SPJ11
a company plans to manufacture a rectangular box with a square base, an open top, and a volume of 246 in.3. the cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch. determine the dimensions of the box that will minimize the cost of manufacturing it. what is the minimum cost?
The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in
And the minimum cost is 32.65 cents
Let us assume that x represents the base side of the box, and y represents the height of the box.
The volume of the box would be:
V = x²y
246 = x²y ........(1)
The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.
Since this box has 4 sides and 1 base, the total cost would be,
C = (0.2 × x² × 1) + (0.3 × 4 × xy)
C = 0.2x² + 1.2x(246x⁻²) (from (1) y = 246x⁻²)
C = 0.2x² + 295.2 x⁻¹
Consider derivative with respect to x,
dC/dx = 0.4x - 295.2 x⁻²
Consider dC/dx = 0
So, 0.4x - 295.2 x⁻² = 0
0.4x³ = 295.2
x³ = 738
So, x = 9.04
So, the value of y would be:
y = 246 x⁻²
y = 246 × (9.04)⁻²
y = 3.01
So, the minimum cost would be:
C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)
C = 32.65
Therefore, the minimum cost is: 32.65 cents
Learn more about the cost here:
https://brainly.com/question/19075809
#SPJ4
Bob's dog, Buster, is a finicky eater. Bob is trying to determine which of two brands of
canned cat food Buster prefers, Busted Nuggets or Busted Tenders. For two months, he
flips a coin each day to decide which of the two foods to feed Buster, and weighs how
much Buster eats (in grams). Here are the data:
Dog Food
n X
S
Busted Nuggets 31 152.6 4.45
Busted Tenders 31 163.7 5.75
Construct and interpret a 98% confidence interval for the difference in mean amount of
food Buster eats when he is offered Busted Nuggets and when he is offered Busted
Tenders.
We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams
Hοw tο cοnstruct cοnfidence interval?Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.
The sample mean difference is:
X1 - X2 = 152.6 - 163.7 = -11.1 grams.
The standard errοr οf the difference can be calculated as fοllοws:
SE = √(S1²/n1 + S2²/n2)
where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.
Substituting the values, we get:
SE = √(4.45²/31 + 5.75²/31) = 1.463
ME = t x (SE) = 2.365 x 1.463 = 3.466
Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:
-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466
-14.566 < µ1 - µ2 < -7.634
Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.
To know more about percentage visit :-
brainly.com/question/24877689
#SPJ1
alana is making a ball out of rubber bands. when the ball has 54 rubber bands, it has a diameter of 3 cm. how many rubber bands should alana add to the ball to increase its diameter by 1 cm? assume that all of alana's rubber bands have the same volume.
The number of rubber bands that Alana has to add to the ball to increase its diameter by 1 cm is 74.
Given that:
Alana is making a ball out of rubber bands.
The volume of the ball with 54 rubber bands is found as below:
Diameter of the ball = 3 cm
The radius of the ball is half of the diameter.
So, radius, r = 1.5 cm
So, the volume of the ball formed by 54 rubberbands is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Substitute r = 1.5.
[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]
[tex]V=4.5\pi[/tex]
Now, the volume of the ball formed by 1 rubber band or the volume of the rubber band is:
[tex]V(r)=\frac{4.5\pi }{54}[/tex]
[tex]V(r)=\frac{\pi }{12}[/tex]
When the diameter increased by 1 cm, the new diameter is 4 cm and thus the radius is 2 cm.
So, the increase in volume is:
[tex]\frac{4}{3} \pi (2)^3-\frac{4}{3} \pi (\frac{3}{2} )^3=\frac{37\pi }{6}[/tex]
Now, divide this by the volume of one rubber band to get the number of rubber bands to be added.
[tex]\frac{\frac{37\pi }{6}}{\frac{\pi }{12} } =74[/tex]
Hence, the number of bands added is 74.
Learn more about Volume here :
https://brainly.com/question/28058531
#SPJ12
[Questions in image]
Answer:
tesla electric company:
hours :cost
0:$50
1:$ 75
2: $100
3: $125
4: $150
Ac-Ad electric
hours: cost
0: $0
1: $50
2: $100
3: $150
4: $200
find the equation of the straight line passinh throigh (3,5) and making x-intercept 3 times the y-intercept.
After answering the presented question, we can conclude that As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is: 5x - 9y = -42
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
To find a straight line's equation, we must first establish its slope and y-intercept.
[tex](y - 5) = m(x - 3) (x - 3)\\b - 5 = -3m\\[/tex]
When we solve for b, we get:
[tex]b = -3m + 5\\5 - 5 = m(3 - 3) (3 - 3)\\0 - 5 = m(3b - 3) (3b - 3)\\-5 = 3bm - 3m\\[/tex]
When we simplify, we get:
[tex]m = 5/(9b) (9b)\\[/tex]
Substituting this expression for m in the equation for the y-intercept b results in:
[tex]b = -15/(9b) + 5\\9b^2 = -15b + 45b\\9b^2 - 30b = 0\\3b(3b - 10) = 0\\b = 10/3\\(y - 5) = m(x - 3) (x - 3)\\(y - 5) = 5x/(9*10) - 1/3\\9y - 45 = 5x - 3\\5x - 9y = -42\\[/tex]
As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is:
5x - 9y = -42
To know more about equation visit:
https://brainly.com/question/649785
#SPJ9
Maria needs to wraps the box shown below with no overlap of the wrapping paper. How much wrapping paper does she need?
As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².
What is surface area?Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.
To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:
SA = 6 x (side)²
In this case, the side of the cube is 2in,
so the SA = 6 x (2in)² = 24in²
To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².
Therefore, the total amount of wrapping paper needed is
24in² x 4 = 96in²
To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.
Therefore, the total amount of wrapping paper needed is
96in² / 4
= 24in x 4
= 64in².
For more questions related to cube
https://brainly.com/question/13329957
#SPJ1
You made $25,000 last year and spend 20% of your money on food. How much money did you spend on food?
Answer:
$5,000 was spent on food.Step-by-step explanation:
To find:-
Money spent on food .Answer:-
We are here given that, out of the total money made 20% was spent on food .
To calculate the money spent on food we need to find out 20% of $25,00 .
So that,
==> 20% of $25,000
==> 20/100 * $25,000
==> 0.2 * $25,000
==> $5,000
Hence the total money spent on food was $5,000 .
25 POINTS
The sound wave of two music notes can be represented by the function y = 2sin2x and y = sin x, where x represents the time since the note is played. At what times will the frequencies of the sound waves be the same in the interval [0°, 360°)?
x = 0°, 30°, 150°, 180°
x = 0°, 180°, 210°, 330°
x = 30°, 90°, 150°, 270°
x = 90°, 210°, 270°, 330°
Answer:
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
Step-by-step explanation:
The frequency of a sound wave is the number of cycles it completes in a given amount of time. In this case, we can find the frequency of each sound wave by looking at the period of the functions.
The function y = 2sin2x has a period of π (since 2sin(2x) has a period of π/2, which is then compressed horizontally by a factor of 2). The function y = sinx has a period of 2π.
If the frequencies are the same, then the two functions must complete an equal number of cycles in the interval [0°, 360°), which is the same as the interval [0, 2π) in radians.
Let's first look at the function y = sin x. It completes one cycle in the interval [0, 2π), so we can say that it completes n cycles in the same interval, where n is an integer.
Now let's look at the function y = 2sin2x. It completes two cycles in the interval [0, π), so it completes four cycles in the interval [0, 2π). Therefore, we can say that it completes m cycles in the interval [0, 2π), where m is an integer.
For the frequencies to be the same, we need to find values of n and m such that:
n = m
Solving for n and m, we get:
n = m = 2
So both functions complete two cycles in the interval [0, 2π). We can find the times when this occurs by setting the angles in radians equal to multiples of 2π/2, or π:
2sin2x = sin x
2sin2x - sin x = 0
sin x (2sin x - 1) = 0
sin x = 0 or 2sin x - 1 = 0
sin x = 0 when x is an integer multiple of π.
2sin x - 1 = 0 when sin x = 1/2, which occurs when x = π/6 or x = 5π/6.
Therefore, the frequencies of the sound waves are the same at x = π/6, x = π/2, x = 5π/6, and x = 3π/2.
The correct answer is:
x = 0°, 30°, 150°, 180°
This is because the sine function equals 0 at 0° and 180° and equals 1/2 at 30° and 150°.
If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A'(0,5)
A'(2,5)
A'(5,2)
A'(-5, -2)
The coordinate A when the triangle is reflected over the y-axis is (2, 5)
Reflecting the triangle over the y-axisFrom the triangle, we have
A = (-2, 5)
Reflecting a point over the x-axis is a type of transformation that involves flipping the point across the x-axis.
The reflection involves keeping the y-coordinate of the point the same, but changing the sign of the x-coordinate.
In this case, the original point is (-2, 5). To reflect this point over the y-axis, we keep the y-coordinate (5) the same, but change the sign of the x-coordinate to positive,
Resulting in the reflected point (2, 5).
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
Solve the system of inequalities 2x +y >3 and x- 2y 5- 1
The system of inequalities "2x – y > 1 and x – 2y < –1." are graphically shown below in the image section.
Inequalities in mathematics describe the connection between two non-equal values. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, a number of inequality comparisons are made to determine whether one value is greater than or less than another. The various inequality symbols, their meanings, and methods for solving them will all be covered in this article using examples of both one- and two-variable linear inequalities. We'll also discuss the algebraic inequalities that are commonly used.
Visit here to learn more about the inequalities: https://brainly.com/question/30228778
#SPJ4
—------ CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - -
(Q). Solve the following system of inequalities graphically: 2x – y > 1 and x – 2y < –1.