The distance between the tent pole to the rope along the ground is 15 feet.
What is a cone?
A cone is a three-dimensional geometric form with a flat base and a smooth tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that connect the apex—the common point—to every point on a base that is in a plane other than the apex.
Given that length of the tent pole is 8 feet.
The angle between the tent pole and the ground is 90°.
Thus the tent pole, the rope and the ground form a right angle triangle.
According too Pythagorean theorem, the square of the hypotenuse is equal to the sum of the square of the legs.
Here the legs of the right angle triangle is the tent pole and the the distance the tent pole to the rope along the ground.
Assume that the distance the tent pole to the rope along the ground be x.
The length of the rope is 17 feet which is hypotenuse of the right angle triangle.
Therefore,
x² + 8² = 17²
x² + 64 = 289
x² = 225
x = 15
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Answer: 15 feet
Step-by-step explanation:
first we grab 17 feet a square it
17^2 = 289
then we square 8 feet
8^2 = 64
subtract
289-64= 225
what squared equals 225?
15 does
A certain volcano has an elevation of 13,410 feet. A nearby oceanic trench has an elevation of 21,795 feet below sea
level. Find the difference in elevation between those two points.
For the piecewise function below, which of the following statements are true?
Please help will give brainlist if correct!
The correct option is (b) i.e. f(0) > f(2).
What is Domain?
The entire range of independent variable values is the domain of a function. In straightforward terms, this definition means The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.
We have,
f(x) = (x+2)^2 - 1 , -4 ≤ x ≤ 0
-x + 1 , 0 ≤ x ≤ 2
5/2 log ( -x +5) - 1 , 2 < x < 5
Now, f(0) = (x+2)^2 - 1
= (0+2)^2 - 1
= 4 - 1 = 3
Similarly, f(2) = - x +1
= - 2 + 1
= - 1.
Hence, f(0) > f(2) because 3 > -1.
∴ The correct option is (b).
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Which of the following is equivalent to 5/13³?
Answer:
D 13 [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
I’m ur math man
9. Passive solar heating systems use solar collectors.
true or false
Passive solar heating systems use solar collectors. This is false.
What is a solar collector?An apparatus that gathers and/or concentrates solar radiation from the Sun is called a solar collector. These gadgets enable the heating of water for personal use and are primarily used for active solar heating.
Through the absorption of sunlight, a solar thermal collector gathers heat. Commonly, a solar hot water heater is referred to as a "solar collector," but the term can also refer to large power generation facilities like solar parabolic troughs and solar towers or non-water heating equipment like solar air heaters.
In conclusion, it's false.
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A small heater has a rectangular filter that has a width of 16.0 in. and a length of 20.0 in. Another larger heater requires a similar filter that has a 56 in. width. What is the length (in inches) of this larger filter? (Round your answer using the rules for working with measurements.)
The length of the larger filter is 6 inches.
What is area of rectangle ?
The area of a rectangle is the product of its length and width. That is, A = l x w where l is the length and w is the width
Given:
Small heater : Length = 20 inches , width = 16 inches
larger heater : Length = ?, width = 56 inches
Since, larger heater requires a similar filter
∴Area of small heater = Area of larger heater
(length * width) of smaller heater = (length * width) of larger heater
20 * 16 = length * 56
length = 20*16/56 = 320/56
length = 5.714
0r , length = 6 inches
Hence , the length of the larger filter is 6 inches.
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(3 pts total) Suppose local sales tax is 8.75% and the price of a car is $36,500.
a) How much tax would be paid when purchasing this car?
b) What is the total amount of money needed to buy the car (list price and tax)?
Answer:
a) 3193.75
b)39,693.75
In July, Lily's family used 12,568 gallons of water. In August, they used 11,562 gallons of water.
What is the percent decrease in their water usage? Round your answer to the nearest
whole-number percent.
Answer:
Step-by-step explanation:
Look at the original value of the gallons of water =12568 this is in July
Look at the value of the gallons of water in August =11,562
Find the difference between the two values=12568-11562=1006
Place the larger value of gallons of water first, as you are going from a large number to a small number you are decreasing by 1006
We put this value of the difference over the original gallons of water and then multiply by 100%
1006/12568 x100%=
This can be done on your calculator
1006÷12568 x100=8.004455761
Rounding to the nearest whole percent gives 8% decrease
Six people start a new town. Every 20 years , the population doubles. After years will the town have more than people? Make the pattern: ____________________Answer the question: ____________________
The complete statement is "After 80 years, the town will have more than 96 people."
What is the population?Generally, A population is the whole set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from whom a statistical sample is taken in statistics.
Here is the pattern:
20 years: 6*2=12 people 40 years: 12*2=24 people 60 years: 24*2=48 people 80 years: 48*2=96 peopleAfter 80 years, the town will have more than 96 people.
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How much would you need to deposit in an account now in order to have $5,000.00 in the account in 697 days?
Assume the account earns 5% simple interest.
You would need to deposit _____ in your account now.
Step-by-step explanation:
To find out how much you need to deposit in an account now to have a certain amount after a certain number of days, you can use the formula:
P = F / (1 + r * t)
where:
P is the present value or the amount you need to deposit now.
F is the future value or the amount you want to have in the account after a certain number of days.
r is the annual interest rate, expressed as a decimal.
t is the number of years for which the money will be invested.
In this case, you want to have $5,000 in the account in 697 days, which is equivalent to 697 / 365 = 1.91 years. The annual interest rate is 0.0375. Plugging these values into the formula, we get:
P = 5000 / (1 + 0.0375 * 1.91)
Solving this equation, we find that you would need to deposit $4,921.15 in your account now to have $5,000 in the account in 697 days.
explain how you would compare "-2/3" and "-1/4." use words and numbers to explain your answer
0.4166667 is the difference between 2/ 3 and 1 /4.
Explain about the fractions?A fraction is a symbol used in mathematics to represent a part or element of the whole. It represents the proportional components of the whole. A fraction is made up of the denominator and the numerator. The top number is the numerator, and the lower number is the denominator.
More manageable pieces of a whole are represented by fractions. The components could be combined to make one thing or several things. In any instance, they come together to create the concept of a whole. As parts of wholes or sets, as the result of dividing two numbers, as the ratio of two quantities, as operators, and as measures are only a few examples of how to use fractions, they are all examples of fractions.
= 2/3 - 1/4
= 512
= 0.4166667
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Albert got a regular salary of $312 every two weeks. He also made 9% commission on all of his
sales. If he sold $98 worth of merchandise, how much was his total earnings for the last two
weeks?
Albert's total earnings for the last two weeks is $320.82.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, Albert got a regular salary of $312 every two weeks.
Also given, he makes 9% of the commission on sales and he sold worth $98.
So, His total earnings of Albert is the sum of his fixed earnings and the percentage of commission he made which is,
= $[312 + (9/100)×98].
= $[312 + 8.82].
= $320.82.
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In the diagram below, TU is parallel to QR. If TU is 6 more than Q T, T S=12, and Q R=18, find the length of QT. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing side QT using the similar triangles concept is;
QT = 6
How to solve similar triangles?We are given;
TU is parallel to QR.
TS = 12
QR = 18
Now, TU is 6 more than QT, Thus;
TU = QT + 6
From the concept of similar triangles, we can say that;
QS/TS = QR/TU
Plugging in the relevant values gives us;
(12 + QT)/12 = 18/(QT + 6)
(12 + QT)(QT + 6) = 18*12
QT² + 18QT + 72 - 216 = 0
QT² + 18QT - 144 = 0
Solving this using online quadratic equation calculator gives;
QT = 6
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What is the probability of NOT selecting a 5 out of a deck of cards
The probability of not drawing a 5 from the deck is 48/52.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
There are 4 number 5's in the deck of 52 cards.
They are as follows:
The 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds.
Using the formula,
Probability = (Number of possible outcomes)/(Total number of outcomes)
The probability of drawing a 5 from the deck is 4/52.
The probability of not drawing a 5 from the deck is 48/52.
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It takes a turtle 3 1/4 hours to walk 1/2 miles how many hours does it take to walk one mile?
Using the principle of proportional relationship, the time taken by the turtle to walk one mile is 2.1667 hours
What is proportional relationship?
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
Creating a system of proportional expression :
Cross multiply :
1.5t = (3.25 × 1)
1.5t = 3.25
Divide both sides by 1.5
t = (3.25 ÷ 1.5)
t = 2.1667 hours
Therefore, the time taken per mile is 2.1667 hours
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The turtle needs 2.16 hours to move a mile using the proportional relationship principle.
What does the word "proportional" mean?
Proportional relationships form when the ratios of two variables are equal. The fact that one variable is consistently equal to the constant value of the other in a proportionate connection is another way to think of them. The "constant of proportionality" is the name of this constant.
For instance, the time it takes a train to travel 50 kilometers per hour is equal to the time it needs to travel 250 kilometers in 5 hours. e.g., 250km/5 hours at 50 km/h.
Establishing a proportional expression system
Cross multiply :
1.5t = (3.25 × 1)
1.5t = 3.25
t = (3.25 ÷ 1.5)
t equals 2.16 hours
Consequently, the time required for each mile is 2.16 hours.
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a) It is known that in a sports club, there are 1000 registered members.
60% of members play Tennis, 50% of members play Cricket,
70% of members play Football, 20% of members play Tennis and Cricket,
40% of members play Cricket and Football and 30% of members play Football and Tennis.
If someone claimed that 20% of members play all the three sports,
what is your opinion and why?
[Use inclusion and exclusion principle to provide your opinion]
Answer:
Using the inclusion and exclusion principle, we can calculate the percentage of members who play all three sports as follows:
60% of members play Tennis, 50% of members play Cricket, and 70% of members play Football.
Therefore, 60% + 50% + 70% = 180% of members play at least one of the sports.
However, this count includes members who play more than one sport, so we need to subtract out the members who play two sports and add back in the members who play all three sports.
20% of members play Tennis and Cricket, 40% of members play Cricket and Football, and 30% of members play Football and Tennis.
Therefore, 20% + 40% + 30% = 90% of members play at least two sports.
Subtracting this number from the total number of members who play at least one sport gives us 180% - 90% = 90% of members who play at least one sport but not all three sports.
To find the number of members who play all three sports, we need to subtract this number from the total number of members who play at least one sport:
180% - 90% = 90% of members who play at least one sport but not all three sports
180% - 90% = 90% of members who play all three sports
Therefore, according to the inclusion and exclusion principle, 90% of members play all three sports.
If someone claimed that 20% of members play all three sports, this would be incorrect based on the calculations using the inclusion and exclusion principle. The correct number of members who play all three sports is 90%, not 20%. This can be verified by using the given information about the percentage of members who play each individual sport and the percentage of members who play two sports in combination.
To clarify, the inclusion and exclusion principle states that to find the number of elements in a union of sets (in this case, the number of members who play at least one sport), we can add the number of elements in each set (the percentage of members who play each individual sport) and then subtract the number of elements that are counted multiple times (the percentage of members who play two sports in combination). We then add back in the elements that were subtracted out in the previous step (the percentage of members who play all three sports).
Using this principle, we were able to calculate that 90% of members play all three sports, rather than the 20% claimed by someone.
Step-by-step explanation:
Answer:
We can conclude that there are 300 members who play tennis only. (total of 600 but 200 for members who play all 3 and 100 for players who play tennis and football)Only X = X - ( (X∩Y - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )
Only X = 600 - ( (200-200) + 200 + ( 300-200) )
Only X = 600 - (0 + 200 + 100)
Only X = 600 - (300)
Only X = 300
There are 100 members who play cricket only. (total of 500 but 200 for members who play all 3 games and 200 for players who play cricket and football)Only Y = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (X∩Y - X∩Y∩Z) )
Only Y = 500 - ( (400-200) + 200 + ( 200-200) )
Only Y = 500 - (200 + 200 + 0)
Only Y = 500 - (400)
Only Y = 100
There are 200 members who play football only. (total of 700 but 100 for tennis and football players, 200 for 3 games players, and 200 for cricket and football players.Only Z = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )
Only Z = 500 - ( (400-200) + 200 + ( 300-200) )
Only Z = 500 - (200 + 200 + 100)
Only Z = 500 - (500)
Only Z = 200
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-the wieght of ram and sam are in the ratio 4:7 and weight of aari and ram are in the ratio 3:2 .what is the maximum wieght if the maximum difference in the wieght of any two is 15 kg
Answer:
Step-by-step explanation:
If the weight of Ram and Sam are in the ratio 4:7, and the weight of Aari and Ram are in the ratio 3:2, you can use this information to set up a system of equations to represent the weights of the three people. Let's say that Ram weighs x kilograms. Then, the weight of Sam is 7x/4 kilograms, and the weight of Aari is 3x/2 kilograms.
The maximum difference in weight between any two people is 15 kilograms, so we can set up the following equation to represent this constraint:
|x - (7x/4)| <= 15
|x - 3.5x| <= 15
|-2.5x| <= 15
|x| <= 6
This equation tells us that the weight of Ram (x) must be less than or equal to 6 kilograms or greater than or equal to -6 kilograms.
Since the weight of a person cannot be negative, the maximum weight for Ram is 6 kilograms. Therefore, the maximum weight for Sam is 7x/4 = 76/4 = 10.5 kilograms, and the maximum weight for Aari is 3x/2 = 36/2 = 9 kilograms.
Thus, the maximum weight of the three people is 6 + 10.5 + 9 = 25.5 kilograms.
Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+4=7
X=
Answer:
x=3
Step-by-step explanation:
7-3=4 or 4+3=7
Emily is going to use a computer at an internet cafe. The cafe charges an initial fee to use the computer and then an additional price per minute of usage. An equation representing the total cost of using a computer for t minutes at the internet cafe is given by C=9+0.50t . What is the slope of the equation and what is its interpretation in the context of the problem?
The slope of the equation is 0.50 and its interpretation in the context of the problem is that Emily will spend 0.50 dollars, or 50 cents, for each minute of use.
The slope-intercept form of a straight line is used to get the equation of a line. To utilize the slope-intercept formula, we need to know the line's slope and the point at which it crosses the y-axis, or intercept. For a straight line with slope "m" and y-intercept "b," the slope-intercept form equation is: y = mx + b.
Given equation,
C = 9 + 0.50t
Here, c = 0.50
Hence, the slope is 0.50.
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match each system of equations to its graph. y = 2x + 1 y = x + 2 y = 3x y = x + 3 y = 2x − 2 y = x − 2 y = 2x + 3 y = x + 5 y = 4x + 2 y = 3x + 2 Graph shows a system of equations plotted on a coordinate plane. A line goes through (minus 3, 0) and (0, 3). Another line goes through (minus 1, minus 3) and (1, 3). Both the lines intersect at (1.5, 4.5).
In the given equation, Y = 3x is at (0, 3) and a line passes through (-3, 0).
What do you mean by Equation?A mathematical statement known as equation is given by joining two expressions with the equal sign. For instance, 3x - 5 = 16 is an equation. This equation can be solved, and the result shows that the value of the variable x is 7.
A mathematical equation links the two phrases on either side of the sign. It typically only contains an equal sign and one variable. similar to 2x - 4 = 2.
Either identities or conditional equations can be used to classify equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").
A line goes through (- 3, 0) and (0, 3)
The equation is
y - y1 = y2 - y1/ x2- x1
y - 0 = 3 - 0 / 0 - (-3) (x - (-3)
y = x + 3
y = 3x
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Of 400 college students, 120 are enrolled in math, 220 are enrolled in English, and 55 are enrolled in both. If a student is selected at random, find the probability that the student is
(a) enrolled in mathematics.
(b) enrolled in English.
(c) enrolled in both.
(d) enrolled in mathematics or English.
(e) enrolled in English but not in mathematics.
(f) not enrolled in English or is enrolled in mathematics.
The probability that the student is
(a) enrolled in mathematics is equal to [tex]\frac{3}{10}[/tex]
(b) enrolled in English is equal to [tex]\frac{11}{20}[/tex].
(c) enrolled in both is equal to [tex]\frac{11}{80}[/tex].
(d) enrolled in mathematics or English is equal to [tex]\frac{57}{80}[/tex].
(e) enrolled in English but not in mathematics is equal to [tex]\frac{33}{10}[/tex].
(f) not enrolled in English or is enrolled in mathematics is equal to [tex]\frac{23}{80}[/tex].
What is probability?
A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
The total number of students in college is 400.
Students enrolled in Mathematics = 120.
Students enrolled in English = 220.
Students enrolled in both Mathematics and English = 55.
(a) The probability that the student is enrolled in mathematics is the Number of students enrolled in mathematics divided by the total number of students which is equal to [tex]\frac{120}{400} =\frac{3}{10}[/tex].
(b) The probability that the student is enrolled in English is the Number of students enrolled in English divided by the total number of students which is equal to [tex]\frac{220}{400} =\frac{11}{20}[/tex].
(c) The probability that the student is enrolled in Both is equal to the number of students enrolled in Both divided by the total number of students which is equal to [tex]\frac{55}{400} =\frac{11}{80}[/tex].
(d) The probability that the student is enrolled in mathematics or English is the Number of students enrolled in mathematics or English that is the Number of students in (Maths+English - Both) divided by the total number of students which is equal to [tex]\frac{120+220-55}{400} =\frac{285}{400}=\frac{57}{80}[/tex].
(e) The probability that the student is enrolled in English but not in mathematics is the Number of students enrolled in (English- enrolled in both) divided by the total number of students which is equal to [tex]\frac{220-55}{400} =\frac{165}{400}=\frac{33}{80}[/tex].
(f) The probability that the student is neither enrolled in mathematics nor English is the Total Students - (Maths+English-both) divided by the total number of students which is equal to [tex]\frac{400-(120+220-55)}{400} =\frac{115}{400}=\frac{23}{80}[/tex].
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Gloria has a study guide for her math, socialstudies, and science classes.she has 3 study guides for language art.Each study guide is 3 pages.How many pagesof study guides does Gloria have in all?
Therefore, number of pages of study guide Gloria have=9
what is Equation?
In mathematics, an equation is a formula that uses the equals symbol (=) to represent how two expressions are equivalent. the act of comparing two things or "the equation of science with objectivity."
given
no. of study guides for language art= 3
no. of pages in each study guides=3
so no. of pages of study guides= no. of study guides for language art*
no. of pages in each study guides
3*3=9
therefore, number of pages of study guide Gloria have=9
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Which composition of two rigid motions maps ️ABC to ️A'B'C'
Answer:
C. Translation [tex](x,y) \longrightarrow (x-7, y+0)[/tex], Reflection in the [tex]y[/tex]-axis
100 POINTS AND THE BRAINLIEST!!
1. A sports team has 65 men and 35 women as members. A new activity has just begun and some new members have joined. Given that the number of men is now 60% of the total members, how many of the 50 new members were women?
2. A rectangle is 50cm long and 40cm wide. Its length is extended by 12% and its width is reduced by 15%. Does the perimeter of the rectangle change? Does the area of the rectangle change? Justify your answer.
Answer:
1) 25 women joined;2) Perimeter stayed same but area became smaller.-----------------------
Question 1Initial number of sports team:
65 + 35 = 100Number after new members joined:
100 + 50 = 15060% of 150 members are men, number of men is:
150*60/100 = 90Number of women:
150 - 90 = 60Number of newly joined women:
60 - 35 = 25Question 2Perimeter of the rectangle:
2(50 + 40) = 2(90) = 180 cmArea of rectangle:
50*40 = 2000 cm²New dimensions:
50 + 12% = 50*1.12 = 56 cm,40 - 15% = 40*0.85 = 34 cm.New perimeter:
2(56 + 34) = 2(90) = 180 cmNew area:
56*34 = 1904 cm²New perimeter is same as previous one but new area is smaller.
The distance a freely falling body covers in the nth second is given by S(n)=d(n)-d(n-1). Show s(n) in terms of g, in simplified form.
Answer:
Step-by-step explanation:
[tex]s=ut+\frac{1}{2}gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_{n}=d_n=\frac{1}{2}gn^2\\S_{n-1}=\frac{1}{2}g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=\frac{1}{2}gn^2-\frac{1}{2}g(n-1)^2=\fracg[n^2-(n-1)^2]\\=\frac{1}{2}g{(n+n-1)(n-n+1)]\\=\frac{1}{2}g(2n-1)[/tex]
Determine whether the following statement is Always, Sometimes, or Never true.
The smallest angle of a right triangle is across from the hypotenuse.
answer choices
Never. The hypotenuse is the longest side of a right triangle, so it will be across from the largest angle, which is a right angle.
Sometimes. The hypotenuse is across from the right angle of a right triangle, so it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
Always. The hypotenuse is the longest side and the longest side of any triangle is across from the smallest angle of the triangle.
The hypotenuse is always the longest side of a right triangle, hence it will always be across from the biggest angle, which is a right angle.
The hypotenuse of a right triangle is occasionally across from the right angle, therefore it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
The hypotenuse is never the longest side of any triangle, and the longest side of any triangle is always across from the smallest angle of the triangle.
What is triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.
Here,
It is always true that The hypotenuse is the longest side of a right triangle, so it will be across from the largest angle, which is a right angle.
It is sometimes true that The hypotenuse is across from the right angle of a right triangle, so it will only be across from the smallest angle when the right angle is the smallest angle of the triangle.
It is never true that The hypotenuse is the longest side and the longest side of any triangle is across from the smallest angle of the triangle.
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find the exact value of the expression, if possible. (if not possible, enter impossible.) cos(arcsin(15/17))
The exact value of the expression cos(arcsin(15/17)) is 1.
The inverse sine function, denoted as arcsin, gives the angle whose sine is a given value. Since the range of the sine function is -1 to 1, the range of the arcsin function is -90 degrees to 90 degrees.
In this case, the value of the expression is given by cos(arcsin(15/17)). To find the exact value of this expression, we can first use the definition of the inverse sine function to find the value of arcsin(15/17). Since the sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle, we can set up the following equation:
sin(x) = 15/17Since the sine function has a period of 180 degrees, we can add or subtract multiples of 180 degrees to the angle x to find the value of the expression for all possible angles. For example,
if x = arcsin(15/17), then x + 180 = arcsin(15/17) + 180, and x - 180 = arcsin(15/17) - 180.Using this information, we can find the values of the expression for all possible angles:
x = arcsin(15/17) => cos(arcsin(15/17)) = cos(x)
= √(1 - sin^2(x))
= √(1 - (15/17)^2)
= √(289/289)
= 1
x + 180 = arcsin(15/17) + 180 => cos(arcsin(15/17) + 180) = cos(x + 180)
= -cos(x)
= -1
x - 180 = arcsin(15/17) - 180 => cos(arcsin(15/17) - 180) = cos(x - 180)
= -cos(x)
= -1
Since the cosine function has a period of 360 degrees, the values of the expression for all possible angles can be expressed as:
cos(arcsin(15/17) + 360k) = 1 for all integers k
cos(arcsin(15/17) + 180 + 360k) = -1 for all integers k
Therefore, the exact value of the expression cos(arcsin(15/17)) is 1.
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If you wanted to make $1071 by investing $4176 for 4 years in an account that pays simple interest, what interest rate you would need to achieve your goal?
The interest rate should be 6.4116% to achieve the required goal.
What is simple interest?
The daily interest rate, the principal, and the number of days between payments are multiplied to determine simple interest. Consumers who pay their loans off on time or ahead of schedule each month benefit from simple interest. Simple-interest loans are frequently used for auto loans and short-term personal loans.
Given data:
A = 4176 + 1071 = $5247
t = 4 years
P = $4176
r = ?
By using the formula,
A = P(1 + rt)
r = (1/4)((5247/4176) - 1)
= 0.06411638
r = 0.06411638
Converting r decimal to R a percentage
R = 0.06411638 * 100
= 6.4116% per year
Hence, the interest rate should be 6.4116% to achieve the required goal.
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The sum of two numbers is 22. Three times one number increased by five is the same as twice the other number decreased by four. What is the LARGER of the two numbers?
Answer: 15
Step-by-step explanation:
To solve this problem, we first need to translate the given information into a system of equations. Let's call the first number x and the second number y. Since the sum of the two numbers is 22, we know that x + y = 22.
The second statement says that three times one number increased by five is the same as twice the other number decreased by four. We can translate this into an equation by substituting x and y for the two numbers and using the given information:
3x + 5 = 2y - 4
Now that we have a system of equations, we can solve for x and y. First, we'll solve for x by adding four to both sides of the second equation:
3x + 9 = 2y
Then, we can divide both sides by three to get the value of $x$:
x = {2y - 9} / {3}
Next, we can substitute this expression for x into the first equation to solve for y:
y + {2y - 9} / {3} = 22
We can simplify this equation by multiplying both sides by three:
3y + 2y - 9 = 66
Combining like terms on the left side, we get:
5y - 9 = 66
Then, we can add nine to both sides to solve for y:
5y = 75
Finally, we can divide both sides by five to find the value of y:
y = 15
Now that we know the value of $y$, we can substitute it back into the expression for $x$ to find the value of $x$:
x = \frac{2 \cdot 15 - 9}{3} = \frac{27}{3} = 9
Since we want the larger of the two numbers, the answer is 15
The ages of pennies at a particular bank follow a nearly normal distribution with mean 10.44 years with standard deviation 9.2 years. Say you take random samples of 30 pennies, find the mean age in each sample, and plot the distribution of these means. Which of the following are the best estimates for the center and spread of this distribution? O mean = 10.44, standard error = 9.2 O mean = 10.44, standard error 9.2/30 = 0.31 O mean = 10.44/30 = 0.348, standard error (9.2/30)2 = 0.094 O mean = 10.44, standard error = 9.2/V30 = 1.68
The correct answer is: mean = 10.44/30 = 0.348, standard error (9.2/30)^2 = 0.094
When you take random samples of 30 pennies and find the mean age in each sample, the distribution of the sample means will have a mean that is equal to the mean of the population (10.44 years in this case) divided by the sample size (30 in this case). This is known as the sampling distribution of the mean.
The standard error is a measure of the spread or dispersion of the sampling distribution. It is calculated as the standard deviation of the population divided by the square root of the sample size. In this case, the standard error would be (9.2/30)^2 = 0.094.
The other options do not correctly describe the center and spread of the sampling distribution of the means. Option A gives the mean and standard deviation of the population, not the sampling distribution. Option B gives the correct standard error, but the mean is incorrect. Option D gives the correct mean, but the standard error is incorrect.
∴ The correct answer is: mean = 0.348, standard error = 0.094.
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Penny is planning a trip to Egypt. She has mapped out the expected costs of some different components of her trip, and
has compiled them below, including whether the cost is in US
dollars ($) or Egyptian pounds (E).
Item
Cost
Currency
Plane ticket
3,241.77
£
Passport
65.00
$
Tour guide
494.25
£
International phone card
41.38
$
Hotel reservation
398.26
f
Car rental
644.48
£
If the exchange rate of the US dollar to Egyptian pound is 1:5.3841, how much has Penny currently budgeted for her trip,
in US dollars? Round all currencies to two decimal places.
a.
$895.25
b. $993.95
C.
$1,001.63
d
$1.468.01
Penny currently budgeted for her trip, in US dollars is $993.95.
What is Penny currently?
Pennies are constructed of copper-coated zinc. Only nickels—that identical alloy of 75% copper and 25% nickel—are one solid substance.
Given: Exchange rate of the US dollar to Egyptian pound is 1:5.3841
Item Cost Currency Plane ticket =
[tex]3,241.77 £=\frac{3,241.77}{5.3841}=\$ 602.100629632 \approx \$ 602.10[/tex]
Passport = $65.00
Tour guide [tex]$=494.25 £=\$ 91.7980721012 \approx \$ 91.80$[/tex]
International phone card [tex]$=\$ 41.38$[/tex]
Hotel reservation [tex]$=398.26 £=\frac{398.26}{5.3841}=\$ 73.9696513809 \approx \$ 73.97$[/tex]
Car rental [tex]$=644.48 £=\frac{644.48}{5.3841}=\$ 119.700599915=\$ 119.70$[/tex]
Therefore, the total budgeted for her trip, in US dollars= [tex]602.10+91.80+41.38+73.97+119.70+65$ $=\$ 993.95$[/tex]
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