The explicit formula of the sequence is aₙ = -10 + 8n
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
The first term and the common difference
These values of the first term and the common difference are given as
First term = -2
Common difference = 8
The interpretation of the above sequence is that the 8 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 8
When represented explicitly, we have
aₙ = a + (n - 1) * d
Where
a = -2 and d = 8
Substitute the known values in the above equation, so, we have the following representation
aₙ = -2 + (n - 1) * 8
Evaluate the products
aₙ = -2 + 8n - 8
Evaluate the like terms
aₙ = -10 + 8n
Hence, the explicit formula is aₙ = -10 + 8n
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a stadium is filled to 80% capacity. If 2,560 people are in the stadium, how many people would fill the stadium to its full capacity?
2048 people would fill the stadium to its full capacity
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that a stadium is filled to 80% capacity
There are 2,560 people are in the stadium
We need to find how many people would fill the stadium to its full capacity.
We have to convert 80% to decimal by dividing 2560 with 100
80/100
0.8
Now multiply 0.8 with 2560
0.8×2560
2048
Hence, 2048 people would fill the stadium to its full capacity
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Classify each variable as qualitative or quantitative.
1. Marital status of nurses in a hospital.
2. Time it takes to run a marathon.
3. Weights of lobsters in a tank in a restaurant.
4. Colors of automobiles in a shopping center parking lot.
5. Ounces of ice cream in a large milkshake.
6. Capacity of the NFL football stadiums.
7. Ages of people living in a personal care home.
Quantitative variable are - 2,3,5,7 and Qualitative are 1, 4 ,6
1. Marital status of nurses in a hospital-qualitative
2. Time it takes to run a marathon-quantitative
3. Weights of lobsters in a tank in a restaurant- quantitative
4. Colors of automobiles in a shopping center parking lot- qualitative
5. Ounces of ice cream in a large milkshake- quantitative
6. Capacity of the NFL football stadiums -qualitative
7. Ages of people living in a personal care home- quantitative
Qualitative variables are categorized or labelled to belong to a certain category or group.
There are two types of qualitative variables, Categorical and ordinal.
Categorical variable are those variables that are labelled in non-numeric or numeric form, where the numbers have no value. The order also does not matters. For example, the number on the jerseys of football players. It is not necessary that the player number 1 is actually the best player.
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A "Pick 2" lottery game involves drawing 2 numbered balls from separate bins each containing balls labeled from 0 to 9. So there are 100 possible selections in total: 00, 01, 02, ..., 98, 99. Players can choose to play a "straight" bet, where the player wins if they choose both digits in the correct order. Since there are 100 possible selections, the probability a player wins a straight bet is 1/100. The lottery pays $50 on a successful $1 straight bet, so a player's net gain if they win this bet is $49. Let X represent a player's net gain on a $1 straight bet. Calculate the expected net gain E(X). Hint: The expected net gain can be negative. E(X) = dollars
The expected net gain E(X) in the context of this problem is given as follows:
E(X) = -$0.5.
How to obtain the expected net gain?The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:
Winning $49.Losing $1.The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:
P(X = -1) = 0.99.P(X = 49) = 0.01.The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.
Hence the expected net gain for this game is calculated as follows:
E(X) = -1 x 0.99 + 49 x 0.01.
E(X) = -$0.5.
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Condition A a recangle with four right angles condition B: a square with one side measuring 5 inches conddion C: a rhombus with one angle measuring 43 condition D: a parallelogram with one angle measuring 32 condition E a parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches condition F: a rectangle with adjacent sides measuring 4 inches and 3 inches One Quadrilateral Many Quadrilaterals
The conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.
What is a quadrilateral?
A quadrilateral has four sides, four vertices, and four angles. It is a form of polygon. Quadrilaterals always have a total internal angle of 360 degrees.
Given,
condition A : a rectangle with four right angles
condition B : a square with one side measuring 5 inches
condition C : a rhombus with one angle measuring 43°
condition D : a parallelogram with one angle measuring 32°
condition E : a parallelogram with one angle measuring 48° and adjacent sides measuring 6 inches and 8 inches
condition F : a rectangle with adjacent sides measuring 4 inches and 3 inches.
Now we are asked to match the above conditions to one quadrilateral and many quadrilaterals groups according to the number of quadrilaterals that can be constructed using the given condition.
Condition A : Many Quadrilaterals
All the rectangles have four right angles in them. So many rectangles of different lengths can be formed.
Condition B : One Quadrilateral
The defining factor that make a square unique is the length of its side. All the sides of the square also has equal length. So only one square of 5 inches side can be made.
Condition C: Many Quadrilaterals
For a rhombus the opposite angles are equal and the sum of angles should be 360°. Even though the angles are fixed, this rhombus can have any side length.
Condition D: Many Quadrilaterals
As discussed for rhombus, even though the angles of the parallelogram is fixed, there can be many sides lengths.
Condition E: One Quadrilateral
In this case, side length as well as the angle of the parallelogram is given. So there can be only one parallelogram.
Condition F:One Quadrilateral
The side lengths are what make a rectangle one of its kind. So one one rectangle can be formed with lengths 4 inches and 3 inches.
Therefore conditions (b),(e) and (f) comes under one quadrilateral and conditions (a),(c) and (d) comes under many quadrilaterals.
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What does − [infinity] [infinity] mean?
This expression has no defined meaning. It is not a valid mathematical expression.
− [infinity] [infinity] is not a valid mathematical expression so it has no defined meaning.
The expression − [infinity] [infinity] is not a valid mathematical expression, and thus it has no defined meaning. It is not a valid mathematical expression because it contains two symbols, infinity and negative infinity, which do not interact with each other in any meaningful way. Infinity is a concept that is used to represent an unbounded or infinitely large value, while negative infinity is a concept used to represent a value that is infinitely small. When combined, these two symbols do not represent any meaningful mathematical quantity. Therefore, the expression − [infinity] [infinity] has no defined meaning.
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Question Progress
Here are some temperatures.
Ottawa
New York
Oslo
Moscow
-9.5 °C
-11.6 °C
-4.3 °C
-7.9 °C
a) Which place has the highest temperature?
b) What is the difference in temperature between Ottawa and Oslo?
The temperature in Moscow falls by 3.1°C.
c) What is the new temperature in Moscow?
The place with the highest temperature is Oslo.
The difference between the temperature in Ottawa and Oslo is 5.2 degrees Celsius .
The new temperature in Moscow is 11 degrees Celsius .
How to find the temperature ?When temperatures are in the negatives, the higher temperature would be the smaller number. Oslo therefore has the highest temperature at - 4.3 °C.
The difference between the temperature in Ottawa and Oslo can be found by subtracting the temperatures:
= - 4 . 3 - ( - 9 . 5 )
= - 4.3 + 9 .5
= 5. 2 degrees Celsius
The new temperature in Moscow is:
= - 7.9 - 3.1
= 11 degrees Celsius
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Explain a few ways that placing figures in a coordinate plane can be helpful for solving different problems.
Use the coordinate plane to graph points, lines, and geometric forms in the different quadrants, and then use the absolute value to determine the distances between them.
What does ordinate math entail?
An exact position of a point in the coordinate plane can be demonstrated using a collection of values called coordinates. Meaning of a Coordinate Plane. The intersection of the x-axis and y-axis, two perpendicular lines that form a 2D plane known as a coordinate plane.
Which three coordinate systems are there?
Cartesian, cylindrical, and spherical are the three most often used coordinate systems. We'll discuss a cylinder-based coordinate system as well as a cartesian-based one in this chapter.
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The joint and marginal pdf's of x = amount of almonds and Y = amount of cashews are
F(x,y) = fx(x) =
with fy(y) obtained by replacing x by y in fx(x). It is easily verified that Mu x = Mu y = A, and E(XY) = 2/ 5 Compute the correlation coefficient p for X and Y. P=
The correlation coefficient ρ for X and Y is ρ = -0.6675 in the given function.
What is correlation coefficient?The correlation coefficient is a statistical concept that aids in establishing a relationship between expected and actual values obtained through statistical experimentation. The calculated correlation coefficient's value explains why the difference between the predicted and actual values is so exact.
Correlation Coefficient value is always in the range of -1 to +1. A similar and identical relationship exists between the two variables if the correlation coefficient value is positive. Otherwise, it reveals how differently the two variables behave.
Pearson's correlation coefficient is calculated by taking the covariance of two variables and dividing it by the sum of their standard deviations. is typically used to represent it (rho).
The correlation coefficient is computed as,
[tex]$ \rho & =\frac{{Cov}(X, Y)}{\sqrt{V(X)} \times \sqrt{V(Y)}}[/tex]
[tex]$=\frac{-0.0267}{\sqrt{0.04} \times \sqrt{0.04}}[/tex]
= -0.6675
Thus, the correlation coefficient ρ for X and Y is ρ = -0.6675.
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What is an example of ordered pair function?
An ordered pair function is a type of mathematical function that associates certain pairs of elements (called ordered pairs) with a single output. For example, the function f(x,y) = x+y associates the ordered pair (2,3) with the output 5.
What is function?A function is a block of organized, reusable code that is used to perform a single, related action. Functions provide better modularity for your application and a high degree of code reusing. As you already know, Python gives you many built-in functions such as print(), etc. but you can also create your own functions. These functions are called user-defined functions.
This is because 2+3 = 5. Another example is the function f(x,y) = x×y,
which associates the ordered pair (3,4) with the output 12, since 3×4 = 12.
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77:9 =
nt :
is there anyone named christina mansell?
Christian Mansell (born 9 February 2005) is an Australian racing driver set to compete in the 2023 FIA Formula 3 Championship with Campos Racing. He previously competed in the 2022 Neuroforamina Open Championship for Crypto Tower Racing, finishing in third overall in the standings.
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NEED HELP ASAPP 100 POINTSSS
Answer:
Statement 1) Corresponding angles
Statement 2) Congruent
Statement 3) 150 degrees
Statement 4) Vertical Angles
Statement 5) Congruent
Statement 6) 150 degrees
Statement 7) Alternate exterior angles
Statement 8) Congruent
Statement 9) Alternate Interior angles are congruent
Step-by-step explanation:
Explanation:
1) I've learned this before
2) Not all Corresponding angles are obtuse
3) Corresponding angles have the same measure
4) I've learned this before
5) Vertical Angles are congruent
6) Same reason as before
7) I've learned this before
8) Alternate Interior angles are congruent
9) I've learned this before
Please mark me the brainliest! Thank you!
Margo borrows $700, agreeing to pay it back with 8% annual interest after 16 months. How
much interest will she pay?
After 16 months, Margo will pay $74.67 interest
We know that the simple Interest Formula
I = P × r × t
Where: P = Principal Amount
I = Interest Amount
R = Rate of Interest as a percent
r = Rate of Interest in decimal
r = R/100
t = Time Periods involved
Here we have been given P = $700, t = 16 months and R = 8%
First we convert interest rate R percent to r a decimal
r = R/100
= 0.08 per year,
Now we convert time from months to years .
16 months ÷ 12 months/year
= 1.333333 years,
Using above formula of simple interest,
I = P × r × t
I = 700 × 0.08 × 1.333333
I = $ 74.67
Hence, the simple interest accumulated on a principal of $ 700.00 at a rate of 8% per year for 16 months is $ 74.67.
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PLEASE HELP: Given AC and BD bisect each other, prove that ΔABX≅ΔCDX using the SAS congruence theorem. ??
The ∆ABX and ∆CDX formed after the mutual bisection of AC and BD each other at point X are congruent i.e ΔABX ≅ ΔCDX, by SAS congruance theorem.
SAS congruence theorem: "SAS " stands for "Side-Angle-Side". If there is two sides and the angle between these two sides are congruent to the corresponding sides and angle of another triangle, then the two triangles are said to be congruent. We have , A Quadrilateral ABCD, such that AC and BD bisect each other at point X. After bisection there is formed 4 triangles. We have to show ΔABX ≅ ΔCDX by SAS Congruance Rule. Now, as we know that bisect point divides the sides into two equal parts, i.e, AX = CX and DX = BX. So, in ΔABX and ΔCDX
AX = CX ( since X is bisecter point )BX = DX ( from bisection )m∠AXB = m∠CXD ( corresponding angles)As we see ∠AXB is angle in between to two sied AX and BX . Similarly, ∠CXD is in between CX and DX . So, by using SAS congruance theorem ∆ABX is congruent to ∆CDX i.e., ΔABX ≅ ΔCDX.
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How do you calculate the number of seeds per acre?
1. Convert lb./acre to grams/acre
2. Use the TKW to calculate seeds per acre.
What is acre?The imperial system and US customary systems both use acres as a measure of land area.
According to traditional definitions, it is the area of one chain by one furlong (66 by 660 feet), which is exactly equal to 10 square chains, 1640 of a square mile, 4,840 square yards, or 43,560 square feet, and roughly 4,047 m2, or roughly 40% of an acre.
A declared acre is equal to 4,046.8564224 square metres according to the 1959 international yard and pound agreement. Although the word "acre" is typically spelled out, the abbreviation "ac" is sometimes used instead.
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If triangle NPZ ~ triangle HBZ find the measure of angle B.
Please show the steps
The measure of angle B is 107°.
What do similar triangles mean?
If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.
Given a triangle, NPZ is similar to triangle HBZ.
Which can also be written as ΔNPZ ≈ ΔHBZ
So, by equating the corresponding angles that are angle P = angle B:
8x-37°=180-(2x-5+42)°
10x=180
x=18°
So, H=36-5=31°
Since the sum of all angles in a triangle is 180°, angle B can be calculated as
B= 180°-(42+31)°
B=107°
Therefore the measure of angle B is 107 degrees
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Why is there only 180 degrees in a triangle?
A triangle is a three-sided polygon and each of its interior angles must add up to 180°; so each angle can have at most 180°.
A triangle is a three-sided polygon with three interior angles. According to the mathematical rule known as the “sum of interior angles”, the sum of the three interior angles of any triangle must always equal 180 degrees. Therefore, if the three angles of a triangle are A, B, and C, then A + B + C = 180. Since the sum of the three angles must equal 180 degrees, it means that each angle can have at most 180 degrees; none of the angles can be greater than 180 degrees. In other words, the maximum possible value of the angles in a triangle is 180 degrees, so the triangle can have only 180 degrees in total.
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help! determine the equation of the circle graphed below:
The equation of a circle is (x+3)² + (y+5)² = 4² with a center at (-3,-5).
What is the equation of a circle?The equation of a circle with center (h,k) and radius r is :
r² = (x−h)² + (y−k)²
The center is approximated to lie at the position (-3,-5) in the graph below with the axes of symmetry. The points of intersection of the circle with any of the two axes (broken lines) provide a diameter of around 8 units, and so the radius is half the diameter, which is 4 units.
The equation of the circle whose graph is given below is:
(x+3)² + (y+5)² = 4²
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The price of a video game was orginally $60. There was a $15 discount. By what percentage was the price of the video game reduced?
Answer$84:
Step-by-step explanation:
Answer: 25%
Step-by-step explanation:
find the value of X.
L,M∈KN
Select the correct image.
Barry wants to host an event at a hotel that has four conference rooms. Each conference room has a maximum capacity of 150 people, but the
hotel limits the capacity to 1 person for every 4 square feet.
Sketches of the four conference rooms are shown below. Which room will stop Barry from hosting the event at the hotel?
25 ft
24 ft
28 ft
28 ft
The room that would stop Barry from hosting the event is the semicircular room.
Which room has a capacity that is less than 1 person per 4 square feet?Would the first rectangular room allow Barry have the meeting?
The first step is to determine the area of the room
Area of a rectangle = length x width
25 x 30 = 750 feet²
Number of people per square foot - 750 / 150 = 1 person for every 5 feet
Would the trapezoidal room allow Barry have the meeting?
The first step is to determine the area of the room
Area of a trapezoid = 1/2 x (sum of parallel sides) x height
1/2 x (24 + 36) x 28 = 840 feet²
Number of people per square foot = 840 / 150 = 1 person for every 5.6 feet
Would the square room allow Barry have the meeting?
The first step is to determine the area of the room
Area of a square = length x width
28 x 28 = 784 feet²
Number of people per square foot - 784 / 150 = 1 person for every 5.2 feet
Would the semi circular room allow Barry have the meeting?
The first step is to determine the area of the room
Area of a semicircle = 1/2πr²
Where:
r = 3.14
r = radius = diameter / 2 = 28 / 2 = 14 feet
1/2 x 3.14 x 14² = 307.72 feet²
Number of people per square foot - 307.72/ 150 = 1 person for every 2.05 feet
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Answer:
The semicircle
Step-by-step explanation:
ewomazinoade's answer is correct, not sure why at time of writing the rating is so low for their answer (3.7).
See pic!
I need help with this, please
Bob made 15,000 in taxable income lat year. Suppoe the income tax rate i 15% for the firt 8000 plu 19% for the amount over 8000. How much mut Bob pay in income tax for lat year?
Therefore, Bob must pay $2530 in income tax for last year if Bob made 15,000 in taxable income last year.
What is taxable income?The basis of an income tax system is referred to as taxable income. In other words, the amount of revenue that was subject to taxation.
Define revenue.Revenue is the entire amount of money made through the sale of products and services that are essential to the business's core activities.
The first $8000 of Bob's taxable income is taxed at 15%:
Tax on first $8000 = $8000 * 0.15 = $1200
The remaining $7000 of Bob's taxable income is taxed at 19%:
Tax on remaining income = $7000 * 0.19 = $1330
Total tax = $1200 + $1330 = $2530
So Bob must pay $2530 in income tax for last year.
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please help!!!!
Solving Systems of Linear Equations by Elimination
C.
0.6x = 1.2 +0.3y
2.2x-1.8y-1.6=0
By using systems of linear equations by elimination, it can be determined that x = 0.5 y +2 and 2.2x-1.8y-1.6=0 are equivalent to x=0.818182 and y+0.727273.
What do you meant by Systems of Linear Equations by Elimination ?Using elimination, let's fix your system. 0.6 x=1.2+0.3 y, 2.2 x-1.8 y-1.6=0 in the graph, and y=2 x-4, y=1.222222 x-0.88888
Step 1: Divide both sides by 0.6 to find the solution for x = 0.6 x=1.2 + 0.3 y.
[tex]$$\begin{aligned}& \frac{0.6 x}{0.6}=\frac{0.3 y+1.2}{0.6} \\& x=0.5 y+2\end{aligned}$$[/tex]
Let's figure out what x is, 2.2 x-1.8 y-1.6=0.
First, multiply both sides by 1.8 y.
[tex]$$\begin{aligned}& 2.2 x-1.8 y-1.6+1.8 y=0+1.8 y \\& 2.2 x-1.6=1.8 y\end{aligned}$$[/tex]
Add 1.6 to both sides in step two.
[tex]$$\begin{aligned}& 2.2 x-1.6+1.6=1.8 y+1.6 \\& 2.2 x=1.8 y+1.6\end{aligned}$$[/tex]
3. Multiply both sides by 2.2.
[tex]$\frac{2.2 x}{2.2}=\frac{1.8 y+1.6}{2.2}$[/tex]
x=0.818182 y+0.727273
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23. We are laying new carpet in the classroom which is 84 square feet. If the width is 5 feet
more than the length, what are the dimensions of the floor?/
Let l be the length of the classroom in feet, and w be the width of the classroom in feet. We know that l + 5 = w and l * w = 84.
We can use these two equations to solve for the length and width of the classroom.
First, we can solve the second equation for l:
l = 84 / w
Substituting this expression for l into the first equation gives us:
84 / w + 5 = w
Expanding the left side of the equation gives us:
84 / w + 5 = w
84 / w = w - 5
84 = w^2 - 5w
w^2 - 5w - 84 = 0
This is a quadratic equation that we can solve using the quadratic formula:
w = (5 + sqrt(5^2 - 4 * 1 * -84)) / 2 * 1
= (5 + sqrt(25 + 336)) / 2
= (5 + sqrt(361)) / 2
= (5 + 19) / 2
= 24 / 2
= 12
Now that we know the value of w, we can substitute it back into the equation l = 84 / w to find the value of l:
l = 84 / 12
= 7
Therefore, the dimensions of the classroom are 7 feet by 12 feet.
How do you draw an acute angled isosceles triangle?
Answer:
To draw an isosceles acute triangle, the first step is to draw a line segment horizontally which will be the base of the triangle.
Step-by-step explanation:
Now, draw two angles of equal measurements (each should be less than 90 degrees) on both the ends of the line segment. Join the arms of the angles. In this way, we will get an acute isosceles triangle.
4 12. DISCUSS MATHEMATICAL THINKING Recall that a perfect square is a number with integers as its
square roots. Is the product of two perfect squares always a perfect square? Is the quotient of two
perfect squares always a perfect square? Explain your reasoning.
Please help will give Brain liest
Yes the product of two perfect squares is always a perfect square, But the quotient of two perfect squares is not always a perfect square.
What is perfect square?A perfect square is a number that can be expressed as the product of an integer multiplied by itself.
Examples of perfect squares include 4 (2*2), 9 (3*3), and 25 (5*5).
What is quotient of a number?The quotient is the result obtained after performing division of one number by another. It is the number of times that the divisor can be subtracted from the dividend until the remainder is smaller than the divisor.
The product of two perfect squares is always a perfect square because the root of the products is equal to the product of roots as shown below,
let us take the two perfect squares 4 and 9, so the square root of 4*9 is,
[tex]\sqrt{4*9} =\sqrt{4} *\sqrt{9} \ =2*3=6[/tex]
But , the quotient of two perfect squares is a perfect square,
When we divide two perfect squares we are not always going to get a quotient that can be represented as the square of an integer. For example, (36/16) = 9/4 which is not a perfect square.
However, if the numerator and denominator in the quotient are the same perfect square then the quotient will be 1 which is a perfect square.
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What is the smallest multiple of 6 greater than 115?
Answer:
120
Step-by-step explanation:
First, divide 115 by 6:
115/6 =
(114 + 1)/6 = ==> 114 is a multiple of 6
114/6 + 1/6 = ==> distribution property
19 + 1/6 = ==> simplify
19 1/6 ==> the smallest integer greater than 19 1/6 is 20
Hence, multiply 20 by 6 to get 120.
Bruce has been offered a position selling bungee seat belts to sports car manufacturers. He was given a choice of receiving a monthly salary of $500 plus a bonus of 25% of his monthly sales or a $2,000 monthly salary with a 5% bonus on sales. How much would Bruce have to sell to make the same amount of money from each?
Answer:
$7500
Step-by-step explanation:
Let x = amount of monthly sales.
Choice A:
"monthly salary of $500 plus a bonus of 25% of his monthly sales"
monthly salary = 0.25x + 500
Choice B:
"$2,000 monthly salary with a 5% bonus on sales"
monthly salary = 0.05x + 2000
We set the total monthly salaries equal and solve for x.
0.25x + 500 = 0.05x + 2000
0.2x = 1500
x = 1500/0.2
x = 7500
Answer: $7500
In the diagram below, \overline{MN}
MN
is parallel to \overline{JK}
JK
. If MNMN is 1212 more than LNLN, LK=33LK=33, and JK=55JK=55, find the length of \overline{LN}
LN
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
The value of the missing length LN of the similar triangles is; LN = 18
How to solve Similar Triangles?Similar triangles are defined as triangles that have the same shape, but their sizes may vary. This means therefore that, if two triangles are similar, then we can say that their corresponding angles are congruent and also their corresponding sides are in equal proportion.
In the given triangle attached, we can say that if we apply the concept of similar triangles, we will get;
LN/LK = MN/JK
We are told that;
MN is 12 more than LN. Thus; MN = 12 + LN
LK = 33
JK = 55
Thus;
LN/33 = (12 + LN)/55
55LN = 33(12 + LN)
55LN = 396 + 33LN
22LN = 396
LN = 396/22
LN = 18
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solve 2x+4y=4 -2x+y=-4 using substitution 
According to the solving by using substitution method the x and y are x = 6/5 and y = -8/5 respectively.
What is a method of substitution?The algebraic approach to solving simultaneous linear equations is known as substitution method. The value of one variable through one equation is substituted in the second equation in this procedure, as the name implies.
According to the given information:given equations are 2x+4y = 4 and -2x+ y = -4
Now, simplifying -2x+y = -4
-2x+y = -4
∴ y = -4 + 2x
i.e. y = 2x - 4
By substitution method,
y = 2x - 4 in other given equation 2x+4y = 4,
2x+4y = 4
2x+4(2x - 4) = 4
∴ 2x + 8x - 8 = 4
∴ 10x = 4 + 8
∴10x = 12
∴ x = 12/10
∴ x = 6/5
Now ,
substituting x = 6/5 in y = 2x - 4,
y = 2(6/5) - 4
∴ y = - 8/5
∴ x = 6/5 & y = - 8/5.
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