The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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A school had 1 200 students last year and only 1 080 students this year. What was the percent decrease in the number of students?
The percentage decrease in the number of students in the school was 10%.
What is the percentage?The percentage refers to the ratio or proportion of students that reduced the number of the school population for the present year in comparison to last year's.
We can compute the percentage by finding the decrease in population and taking the result as a numerator of the total number in the last year and multiplying the result by 100.
Percentages represent fractional values and are usually depicted by the percentage sign (%).
The total number of students in the school last year = 1,200
The total number of students in the school this year = 1,080
The decrease in the number of students = 120 (1,200 - 1,080)
The percentage decrease = 10% (120/1,200 x 100)
Thus, we can conclude that the school population decreased by 10%.
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A car is moving north at 60km/h. The driver sees a sign beside the road ahead of him. What is the velocity of the sign relative to:
a) The car
b) The ground
*Please leave an explanation*
The velocity of the sign are given as follows:
a) Relative to the car: 60 kilometers an hour.
b) Relative to the ground: 0 kilometers an hour.
What is relative speed?The relative speed of one object towards another is given by the rate of change in the position of each these objects relative to each other in regard to time.
Relative to the car, the sign gets 60 kilometers closer every hour, hence the relative speed of the sign will be of 60 kilometers. an hour.
Now, for the ground, the distance between the sign and the ground will always be the same, that is, there is no change in the distance. Hence, the velocity of the sign relative to the ground is of 0 kilometers and hour.
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Cual es el número que sigue en la sucesión 1,3,4,7,11,18
Answer:
29
Step-by-step explanation:
1+3= 4
3+4=7
4+7=11
7+11=18
11+18=29
The Venn diagam represents the
information from the following sets.
= {Prime numbers less than 38}
R = {2, 3, 5, 17, 19, 37}
S = {3, 5, 7, 11, 13, 37}
R
17 5
2
19 37
3/13
S
11
231 23
Find P(RUS)
P(RUS) =
=======================================================
Explanation:
The U refers to set union. We combine the elements of set R and set S together in one big set. Toss out any duplicates. Sorting the items is optional, but I recommend it.
R U S = {2, 3, 5, 17, 19, 37} U {3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 17, 19, 37, 3, 5, 7, 11, 13, 37}
R U S = {2, 3, 5, 7, 11, 13, 17, 19, 37}
This list of values consist of items in set R, set S, or both.
There are 9 items in set R U S.
This is out of 12 items total in the universal set rectangle.
The probability of randomly selecting something from set R U S is 9/12 = 3/4
true or false? the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
What is Discrete uniform distribution?The Discrete uniform distribution is a symmetric probability distribution used in probability theory and statistics. It contains a finite number of values that are equally likely to be observed; each value has an equal chance of 1/n. "A known, finite number of outcomes equally likely to occur" is another approach to describe the discrete uniform distribution.
The perfect example of Discrete uniform distribution is throwing a die. Tossing a fair dice is an easy illustration of the discrete uniform distribution. The possible results are 1, 2, 3, 4, 5, and 6, and the likelihood of a certain result is 1/6 each time the die is thrown. Because not all sums have an equal chance, the distribution that results when two dice are thrown and their values are summed is no longer uniform.
From the above observation, we can say that the sum of the number of dots that show up when we roll three dice simultaneously will follow a discrete uniform distribution.
It is false, that the sum of the numbers of dots that show up when we roll three dice simultaneously does not follow a discrete uniform distribution.
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Starting at the beginning of the year, Kianna was able to save $215 each month. However
for the last 3 months, she increases her saving to $305 each month, and she plans to
continue saving the same amount of money for 2 more months (until end of the year).
What will be the amount of money Kianna save this year?
By using addition and multiplication, the result obtained is
Kianna saves $3020 this year
What is addition and multiplication?
Suppose there are many numbers. To get the sum total of all the numbers, addition is used
Repeated addition is called multiplication
Addition and multiplication will be used here
Amount of money Kianna saves each month for the first 7 months = $215
Total amount of money Kianna saved in the first 7 months = $215 [tex]\times[/tex] 7
= $1505
Amount of money she saves each month for the last 5 months = $305
Amount of money she saves in the last 5 months = $305 [tex]\times[/tex] 5 = $1515
Total amount of money Kianna saves this year = $(1505 + 1515)
= $3020
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In a paragraph, explain the difference between an opinion piece of writing and an informational/informative piece of writing. What are the fundamental differences between the two? What do you write about in each? What do they have in common? I ONLY HAVE THIRTY MINUTES
The main difference between opinion based and informational essay is that in opinion based you have to share your own opinion reading any topic or something but in case of informative essay to have to provide particular information about the subject.
What is essay?Generally speaking, an essay is a bit of writing in which the author presents their own arguments; nevertheless, this definition seems ambiguous and includes elements of letters, papers, articles, pamphlets, and short story collections. Essays are divided into two categories: formally and informally. Formal writings are distinguished by their "serious aim, dignity, logical arrangement, and length," whilst informal papers are distinguished by their "personal element."
To express your opinions on a subject and persuade the reader of your point of view, you must write an opinions essay. To accomplish it, you must first present the subject and express your viewpoint. Following that, you should provide three arguments in favor of your viewpoint. Finally, create a closing in which you summarize your case and restate your viewpoint in a new way.
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n is an integer greater than 1
Prove algebraically that 10 + [tex]n^{2}[/tex] - (n-2)[tex]^{2}[/tex] is always an even number.
Your final line must have, "always even" as part of the line.
The algebraic proof that 10+n²-(n - 2)² is always an even number is 2(5+(2n-2))
How to prove algebraically that 10+ n² - (n - 2)² is always an even number?To show that this will always give an even number, we need to express in a form that it is 2 multiplied by some positive integer
Given: n is an integer greater than 1, prove 10+ n² - (n - 2)² algebraically
10+ n² - (n - 2)² = 10+ ( n² - (n - 2)² ) (factorize difference of two squares)
= 10+(n-(n-2))(n+(n-2))
= 10+(n-n+2)(n+n-2) (simplify)
= 10+(2)(2n-2) (factorize)
= 2(5+(2n-2))
Therefore, due to the factor of 2, the given expression is always even for integer n
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Please help me with this.
Step-by-step explanation:
they are parabolas.
their line of symmetry is exactly in the middle between their x-intercepts (when y = 0).
these x-intercepts we get from the factors : y can only be 0, when at least one of the factors is 0.
y = (x + 14)(x + 16)
means y = 0, when x = -14 or x = -16.
so, the line of symmetry is
x = -15
y = (x - 12)(x - 18)
y = 0, when x = 12 or x = 18
line of symmetry is
x = 15
y = (x + 13)(x - 17)
x = -13 or x = 17
line of symmetry
x = 2 (again, the middle between -13 and +17)
y = (x - 10)(x + 20)
x = 10 or x = -20
line of symmetry
x = -5
HELP
At a Junk Yard a study was conducted using 48 cars and found that the average mileage on a car before it was junked was 164,000 and the population standard deviation is known to be approximately 28,000. Construct a 99% confidence interval of what the actual average mileage is for a car before it is junked.
A 99% confidence interval of what the actual average mileage is for a car before it is junked is; (153589, 174411)
How to find the confidence Interval?The formula for confidence interval is;
CI = x' ± z(s/√n)
where;
x' is sample mean
s is standard deviation
n is sample size
z is critical value at confidence level
We are given;
x' = 164000
n = 48
s = 28000
CL = 99%
z-score at confidence level of 99% is 2.576
Thus;
CI = 164000 ± 2.576(28000/√48)
CI = 164000 ± 10410.78
CI = (164000 - 10410.78), (164000 + 10410.78)
CI = (153589, 174411)
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Three people each have a tendency to lie 1/3 of the time. There is a coin flip that they all see. They all say it's Heads. What's the probability it is actually Heads
The probability is 8/9.
From the question, we have
probability = (1/3)*(1/3)*(1/3) = 1/27 chance (all of them lie)
probability = (2/3)*(2/3)*(2/3) = 8/27 chance (all of them true).
Since, they all say it's heads.
Thus, the probability of it being heads = (8/27)/ ((8/27)+(1/27)) = 8/9.
Probability:
Chance is referred to as probability. This branch of mathematics studies the probability of a random event. The value is between 0 and 1. Probability is a concept that mathematics has adopted to predict the likelihood of particular events. Probability is just the measure of how likely something is to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will be able to comprehend the possible results for a random experiment. How likely something is to occur can be determined using probability. It might be challenging to predict many things with complete certainty. We can only predict whether an event will occur or how likely it is using it, not if it will actually occur.
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can you help me in graph
i came back home now....
you are flying a kite and the angle of elevation from the horizon is 36 if your kite string is 15 feet long, how high are you flying the kite ?
By using a trigonometric relation we will see that the height of the kite is 8.82 feet above the point where you hold the line.
how high are you flying the kite?We can view this as a right triangle, where the hypotenuse has a measure of 15 feet, we know one angle that measures 36°, and the opposite cathetus to that angle is x, the height we want to find.
We want to get the value of x, which is the opposite cathetus to the given angle, then we can use the trigonometric relation:
sin(a) = (opposite cathetus)/(hypotenuse)
Replacing what we know we will get:
sin(36°) = x/15ft
Solving this for x we get:
x = sin(36°)*15ft = 8.82ft
The height of the kite is 8.82 feet.
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Your friend Alex has won a scholarship to
study abroad. (Congratulations!) Alex has
only 8 weeks to earn enough money to buy a
plane ticket, and he wants to work at an
amusement park over the summer to achieve
this goal.
Tech intership
Schedule- Part Time (20hours/week)
Wage-11.50/hour
Amusement park attendant
Schedule- full time (40hours/week)
Wage - 9/hour+ 100 bonus
8 weeks to buy airplane ticket $2200
Please help with the table
In tech internship
Slope of the line m is $11.50, y intercept is 0 and the point slope form is y = 11.50x + 0
In Amusement park attendant
The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100
In tech internship
Schedule = part time (20 hours/week)
The wage = $11.50/hour
The slope intercept form
y = 11.50x
Slope of the line m = $11.50
y intercept = 0
y = 11.50x + 0
In Amusement park attendant
Schedule- full time (40hours/week)
Wage - 9/hour+ 100 bonus
The slope of the line = $9
y intercept = 100
The equation is
y = 9x + 100
Hence,
In tech internship
Slope of the line m is $11.50, y intercept is 0 and the point slope form is y = 11.50x + 0
In Amusement park attendant
The slope of the line = $9, y intercept is 100 and Point slope form y = 9x + 100
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Zion Sun Chairs manufactures 3,575 beach chairs each month. Determine the minimum sales price Zion Sun Chairs must sell each chair for to earn a monthly profit of $55,000, if the total monthly fixed costs are $17,363.50 and the variable cost per chair is $52.17. $72.41 $70.80 $25.38 $20.24
Answer:
A) $72.41------------------------------
Find the total cost to produce 3575 chairs. It includes the fixed costs as well as the variable cost per chair.
17363.50 + 3575*52.17 = 203871.25Add the profit we want to have
203871.25 + 55000 = 258871.25This is the minimum amount to be made from sale.
Find minimum sales price per chair:
258871.25 / 3575 = 72.41 (rounded)This is matching the first answer choice.
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeeeeeeeeee pleaseeee rn rnnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
From the graph:
vertex:
The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.
here vertex = (-2,2)
Axis of symmetry:
The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.
x = -2.
Parabola:
It is clearly visible that the parabola is facing downward so it is a downward parabola.
Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.
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A rectangular garden must have a perimeter of 540 feet and and area of at least
12,000 square feet. Describe the possible lengths of the garden. round to the nearest
whole number
I need help please!
The length of the garden is: l ≥ 6225ft.
Area = L multiplied by W. Since you measure the area in square feet, your final number should reflect that.
What is a Rectangle?The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. At each corner or vertex, the two sides come together at a straight angle. The rectangle differs from a square because its two opposite sides are of equal length.
Let l serve as a symbol for the garden's length.
Let w be the symbol for the garden's width.
The perimeter is 540 feet.
The rectangle's circumference is equal to
2(l + w)2(l + w) = 540 l + w = 270. (1)
The rectangle's area is equal to its length times its width, which equals 12000. (2)
Make the variable w the subject of the following equation:
w = 270 - l. (3)
Substitute equation (3) into equation (2)
(270 - l)(l) ≤ 12000
270l - l² ≤ 12000
0 ≤ l² - 270l + 12000
l² - 270l + 1200 ≥ 0
Solving the quadratic inequality above:
l ≥ 6225
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Write a function rule for the table. x ƒ(x) –3 –6 –2 –4 –1 –2 0 0 ƒ(x) = x + 2 ƒ(x) = –2x ƒ(x) = x – 2 ƒ(x) = 2x
A function rule for the table: f(x) = 2x
In this question, we have been given a table.
We need to write a function rule for the table.
x ƒ(x)
-3 -6
-2 -4
-1 -2
0 0
We can observe that f(x) = 2x
Therefore, a function rule for the table: f(x) = 2x
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Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
Answer:
$210 in bank
Step-by-step explanation:
Kelly earned 300 dollars and put 70% of it into the bank. How much did she put into the bank?
70% = 0.7
300 * 0.7 = $210 in bank
Use remainder theorem for x^3+8x^2+11x-20 by x-5
The remainder is 360.
What is the remainder theorem?When a polynomial p(x) is divided by a linear polynomial (x - a), then the remainder is equal to p(a).
Given a cubic polynomial, x³+8x²+11x-20
The zero of the linear polynomial.
Substitute it in the given polynomial.
As a result, we get the remainder.
x - 5 = 0
x = 5
Substitute 5 to x³ + 8x² + 11x - 20:
5³ + 8×5² + 11×5 - 20 = 125 + 8×25 + 55 - 20 = 160 + 200 = 360
Hence, The remainder is 360.
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Betsie is going to buy 250 envelopes.
Here is some information about the cost of envelopes in two shops.
Letters2go
Pack of 25 envelopes for £3.19
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Betsie wants to buy the envelopes for the best possible price.
Which shop should Betsie buy the 250 envelopes from?
You must show how you get your answer.
Using mathematical operations, Betsie should buy the 250 envelopes from Letters2go Shop at a total cost of £319.
How is the total cost determined?To determine the total cost, we first determine the unit cost of an envelope at each shop.
The unit cost is multiplied by the number of envelopes required less the cost of free envelopes at Value World.
The mathematical operations used include division and multiplication.
Deals:
Letters2go
Pack of 25 envelopes for £3.19
Value World
Pack of 10 envelopes for £1.99
Buy 2 packs get 1 pack free
Letters2go Value World
Cost per pack £3.19 £1.99
Cost per envelope £0.1276 £0.199
The number of envelopes 250 250
The number of packs 10 (250/25) 25 (250/10)
Cost of free envelopes £24.875 (25/2 x £1.99)
Total cost of envelopes £319 (£3.19 x 10) £472.63 (£1.99 x 250 - $24.875)
Thus, using mathematical operations, the total cost of 250 envelopes at Letter2go is less than the total cost at Value World.
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lin rode he skateboard 3 miles in 9 minutes. she rode at a constant speed. how far did she go if she only went for 1 minute?
First, break down the problem.
Someone can skate 3 miles in 9 minutes.
What is their speed? How far would they go if they did that speed for 1 minute?
To find speed given time and distance, divide distance by time.
3/9 = 1/3
Speed is 1/3 mile per minute
if they travel one minute, they will travel 1/3 of a mile
hope this helps :)
Find the least common multiple of the given algebraic terms. x², 2xy, 3y
Step-by-step explanation:
common factor= x and y
remaining factor = x , 2 , 3
L.C.M = 6 x sq. y
sin(2x)cos(7x) - cos(2x)sin(7x) = 0.1
Answer:
x≈-0.0200335+2kπ/5
x≈-0.648352+2kπ/5
Step-by-step explanation:
sin(-5x)=0.1
-sin(5x)=0.1
sin(5x)=-0.1
sin(5x)=1/10
5x=arcsin(- 1/10)
5x=π-arcsin(- 1/10)
5x=π-arcsin(- 1/10)
5x=π-arcsin(- 1/10)+2kπ
5x=π-arcsin(- 1/10)+2kπ
x=arcsin (1/10)/5 + 2kπ/5
x=arcsin (1/10)/5 + 2kπ/5
x≈-0.0200335+2kπ/5
x≈-0.648352+2kπ/5
A group of 4 people go to a restaurant and the bill without tax comes to $105.73. Tax is 6%. Remember to round to the nearest hundredth because this is money. After tax is added, you want to leave a 20% tip on the new total. The group of 4 people decides to split the total cost equally. How much will each person pay?
The amount of money paid by each of the 4 persons will be $33.6.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a group of 4 people go to a restaurant and the bill without tax comes to $105.73. The tax is 6%. Remember to round to the nearest hundredth because this is money. After-tax is added, you want to leave a 20% tip on the new total.
Total cost = $105.73 x 1.06 x 120
Total cost = $134.48
Amount for each person,
A = $134.48 / 4
Amount = $33.62
Therefore, the amount of money paid by each of the 4 persons will be $33.6.
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Use the "Insert Line" Tool to construct the line
showing the given distance. If you need to extend
the line outside the shape, use a dotted line.
The distance from B to AC can be constructed as
The distance from G to EF can be constructed as
The distance from Q to SR can be constructed as
What is the distance of a line from a point?
A point-to-line distance is the shortest distance from a point to any point on an infinite line. This is the perpendicular distance from the point to the line and the length of the line segment connecting the point to the nearest point on the line.
For the first figure,
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Convert Decimal to Percent
1.56 =
0.31 =
Convert Percent to Decimal
62%=
94% =
Convert Decimal to Fraction
1.12 =
12
100
0.223 =
223
1000
0.728=
1.67 =
91.8% =
36.2 % =
0.57 =
0.67=
0.7 =
0.783=
148 % =
32.6% =
0.393 =
0.28=
100-
25
Answer: Your question is too long for me to answer
Step-by-step explanation:
Let's find
11
6
- Im
First, write the addition so the fractions have denominator 6.
Then add.
1 1
6
1
3 6
0 0
6
The required addition of the given fraction is given as 7/6.
Given that, a mixed fraction is given 1 1 /6 we have to determine the simplified fraction.
Fraction is defined as the number of compositions that constitutes the Whole.
Here,
Given fraction = 1 1 /6
This fraction is written as 1 + 1/6
Simplifying the fraction by multiplying the one with 6 and adding the product to the 1 in the numerator,
= [1×6 + 1]/6
= 7/6
Thus, the required addition of the given fraction is given as 7/6.
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Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Quetion
The elevation of a unken hip i −120 feet. Your elevation i 58 of the hip’ elevation. What i your elevation?
Our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
Given, The elevation of a sunken ship is 120 feet.
Your elevation is 58 of the ship elevation.
as it is given that the elevation of a sunken ship is 120 feet and our elevation is 58 of the ship elevation.
So, on using the concept of application of trigonometry we can conclude that our elevation is 58.
As, it is given that our elevation is 58 of the ship elevation.
So, our elevation is 120 + 58 = 178 feet.
Hence, our elevation is 178 feet when the elevation of a sunken ship is 120 feet.
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2) Find the slope of the line passing through the points (5, 5) and (2, -3).
the answer is 1 but it could be a I took the test
