The length of the fencing that the city needs to surround the park will be 380.50 yards.
What is the area and perimeter of the rectangle?Assume L is the length and W is the width. Then the area is given as,
A = L × W
And the perimeter is given as,
P = 2(L + W)
The city of vine View is building a new rectangular park for the townspeople. The park will have an area of 8,925 square yards if the width of the park is to be 84 yards. Then the length of the rectangular park is calculated as,
8925 = L × 84
L = 106.25 years
Then the length of the fencing that the city needs to surround the park will be given as,
P = 2(106.25 + 84)
P = 2 × 190.25
P = 380.5 yards
The length of the fencing that the city needs to surround the park will be 380.50 yards.
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A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales. How much does he need to sell this week to earn the same amount with the two options?
The total amount of sales he must make should be of $20800.
What is expression?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that a salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $26. Option B is a commission rate of 5% on weekly sales
Assume that the amount of sales he needs to make is of ${x}. So, for same amount, we can write -
(26 x 40) = 5% of {x}
(26 x 40) = (5/100) x {x}
{x} = (26 x 40 x 100)/5
{x} = (26 x 40 x 20)
{x} = 26 x 800
{x} = 20800
Therefore, the total amount of sales he must make should be of $20800.
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Number of study sessions Total Enrollment
Morning class 25 16
Night class 20 22
If the total study sessions for the night class were proportional to the morning class, how many would you expect the night class to have? How does this compare to the actual amount of study session the night class has?
If the night class were proportional to the morning class, we would expect them to have
[ Select ]
[ Select ]
than the number of study sessions they have currently
If the total study sessions for the night class were proportional to the morning class that is 25: 20 then night class have the actual amount 80% students
we can calculate 20/25 *100
and we obtain the actual amount 80%
If the total study sessions for the night class were proportional to the morning class is 25: 20 and 16: 22
What is a proportion simple definition?
the size, number, or amount of one thing or group as compared to the size, number, or amount of another. the proportion of boys to girls in our class is three to one. : a balanced or pleasing arrangement
Initially, the number of lectures is 3 while the number of fieldwork is 12. Furthermore, the class sessions increased to 18 and the number of fieldwork remains the same (i.e. 12). Therefore, the number of lectures will be 18 - 12 = 6. The percentage of the sessions that were lectures will be:
(6/18)*100% = 33.3%
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help i really don’t understand this
Answer:
45 degree
Step-by-step explanation:
45+45 90 +90 180
All triangles will have 180 degrees angle
What is 5 in the expression 5x called?
The term 5 in 5x is known as the coefficient of the expression.
A coefficient is defined as a term or a number which is multiplied by a variable. This constant terms generally precedes the variable term.
A coefficient is a generally a multiplicative factor in a polynomial series, or in an equation.
Expressions are mathematical statements which are composed of two terms in which at least one contain variables, numbers, or both. These terms are either numbers or variables or numbers and variables multiplying each other. These expressions are a combination of numbers with mathematical ,operators are used to separate them.
Eg, 2x - 90 =45
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What are the 4 steps to solve by elimination?
Elimination is a very easy method when it comes to solving simultaneous equations.
First, the best thing to do is bring the equations down to their lowest form. Try to remove the fractions in the co-efficient and have the equation in the standard form where every variable is expressed as individually as possible.
The next thing to do is to select a variable and manipulate the equations in such a way that the coefficients of that variable across all of the equations are the same. Here select any 2 equations to work on first if more than 2 are given
Now take one of the equations and multiply it by -1.
Add the equations up to eliminate the variable and derive the other variable(s)
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A PE Teacher pays a total of $960 for 6 basketballs and 8 volleyballs. The price of 6 basketballs is equivalent to 8 volleyballs. How much does each basketball cost than each volleyball?
solve by assuming question
Answer: solving by forming simple algebra equation
Step-by-step explanation:
8x (x is the cost of 1 volleyball)
6y (y is the cost of 1 basketball)
We know that cost of 8 volleyballs is = cost of 6 basketballs
i.e. 8x = 6y
& total money spent to buy 8 volleyballs and 6 basketballs is $960
so we can write;
8x + 6y = 960
= (6y) + 6y = 960
= 12y = 960
= y or cost of 1 basketball is (960/12) = $80
& if we want to know the value of x (cost of 1 volleyball)
8x = 6y
= 8x = 6(80)
& x = 6(80/8)
= 6 (10) = 60
so the cost of basketball is $80 & 1 volleyball is $60
Hope it helps :)
p.s. that the equation I formed were made as if I was making an assumption & the conditions were kept uniform from the beginning, this is very applicable in day to day scenario; for e.g. when you go out with you friends to eat and have to split the bill - this assumption and division is called algebra - so value this education!
How can you identify and write equivalent expressions?
You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.
What is an Equivalent expression?These are the type of expressions that have similar value or worth but do not look the same.
This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:
3(x + 3) and 3x + 9
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What are the 3 types of polynomials and how many terms does each one have?
Monomial, binomial, and trinomial expressions are all categorized by the number of terms they include.
A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).
A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a binomial. An algebraic expression having three terms is called a trinomial.
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(iv)The ratio of 5m to 150cm is ________.
identify the initial amount a and the growth factor b in the exponential function: f(X) = 610 • 7.54
The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?
An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
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The initial amount is 610 and the growth factor is 7.54.
What is an exponential function?An exponential function has the form f(x) = a*b^x, where a is the initial amount, also called the y-intercept, and b is the growth factor.
What is growth factor?A growth factor is a naturally occurring substance that stimulates a cell to grow, divide, and differentiate. Growth factors are typically proteins or peptides that bind to specific receptors on the surface of cells, triggering signaling pathways that lead to cell proliferation and survival.
In the function f(X) = 610 • 7.54, the initial amount is a = 610, and the growth factor is b = 7.54.
Hence, the initial amount is 610 and the growth factor is 7.54.
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if crystals room measures 10.5 ft long and 7 feet wide and 9 feet tall how much paint will be needed to paint her bedroom
Answer:
She needs 18,731.6 Litres of paint to paint her bedroom.
Step-by-step explanation:
Given;Length (l) = 10.5 ftWidth (w) = 7 feetHeight (h) = 9 feetTo Find;How much paint will be needed to paint her bedroom.Formula;V = l × w × hSo,
V = l × w × h
V = 10.5 × 7 × 9 feet
V = 661.5 cubic feet
We know that,
1 cubic foot = 28.317 litresSo,
661.5 × 28.317 = 18,731.6 Litres
Thus, She needs 18,731.6 Litres of paint to paint her bedroom.
Answer to this question pls
It would change to about 9. 960 atmospheres
How to determine the valueFollowing the Boyle's law of gases which states that the product of pressure and volume is exactly a constant for an ideal gas.
This is represented as;
PV = K
then,
P₁V₁ = P₂V₂
From the information given, we have that;
P₁ = 8.9 atmospheresP₂ = unknownV₁ = 4. 7 litersV₂ = 4. 2 litersNow, substitute the values
8. 9(4. 7) = P₂(4. 2)
mulitply the values
41. 83 = P₂(4. 2)
Divide both sides by 4.2
P₂ = 9. 960 atmospheres
Hence, the value is 9. 960 atmospheres
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Find the perimeter of a rectangle with the width (w) that is 12 cm less than the length (L).
Answer:
4x-24
Step-by-step explanation:
assume x=Length
perimeter
= x+(x-12)+x+(x-12)
= x+x -12+x+x-12
=4x-24
Is 10 12 15 a Pythagorean triple?
No, 10 12 15 is not a Pythagorean triple. A Pythagorean triple is a set of three positive integers a, b, and c such that a^2 + b^2 = c^2.
To determine whether 10 12 15 is a Pythagorean triple, we need to calculate a^2 + b^2.
In this case, 10^2 + 12^2 = 100 + 144 = 244. Since 244 ≠ 15^2, 10 12 15 is not a Pythagorean triple. We can also confirm this by plugging 10, 12, and 15 into the Pythagorean Theorem, a^2 + b^2 = c^2.
10^2 + 12^2 = 100 + 144 = 244
244 ≠ 15^2
Therefore, 10 12 15 is not a Pythagorean triple.
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The table shows pairs of values for the linear function f(x) = 3x -2. Which conjencture about linear functions in general is best supported by the table?
The information in a table shows that f(x) = 3(2)x exponential function. An exponential function has the formula y = abx, wherein y and x are variables.
Describe the exponential function.An exponential function is a mathematical function with the following formula: f (x) = 1 x. where an is a fixed sum that serves as the function's basis and x is a variable. The most frequent exponential-function base is the transcendent number e, or around 2.71828. Your function must be exponential if it has the equation y = a b x, or where are constant, a Zero and b > 0 and b 1. You always used functions to the power of 2 while solving quadratic equations. An exponential function's exponent is a variable.
Here,
given:
Using the table's (0, 3):
3 = ab° , a = 3
(2) and (12):
=>12 = ab²
=>12 = 3b²
=>b² = 4
=>b = 2
=>f(x) = 3(2)ˣ
The information in a table shows that the exponential function, f(x), equals 3(2)x.
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Help!! Stuff about triangles
Answer:
3
Step-by-step explanation:
Since [tex]\angle A \cong \angle A[/tex] by the reflexive property and [tex]\angle ABC \cong \angle ADE[/tex] since they are both right angles, [tex]\triangle ABC \sim \triangle ADE[/tex] by AA.
It follows that:
[tex]\frac{x}{9}=\frac{5}{9+6} \implies x=3[/tex]
A school plans to spend twice the amount it did last year on its winter dance, less the cost of the disco ball which was $150, since they have it from last year. A total of $1,500 is being spent this year. Fill in the blanks to write an equation that will determine the amount of last year’s budget, a.(2 points)
__(a −__) = __
Equation that will determine the amount of last year’s budget
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that a school plans to spend twice the amount it did last year on its winter dance , less the cost of the disco ball which was $150 since they have it from last year
A total of $1,500 is being spent this year.
We need to find the equation which determine the amount of last year’s budget
2a-150=1500
When a is the amount of last year’s budget
Hence, 2a-150=1500 is the equation that will determine the amount of last year’s budget
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Select the correct answer
A geneticist needs to grow a stock of fruit flies for her experiments. She currently has a stock of 200 fruit flies and predicts the stock will grow by
38% each day. Which function could she use to calculate f(n), the number of days required for her stock to grow to n fruit flies?
200
A f(n) = 1081. 38
OB. F(n) = 1080. 88
OC f(n) = log1. 38(260)
OD. F(n) = logo. 38
198(260)
(200)
Reset
Next
For her research, a geneticist has to raise a stock of fruit flies. She presently has 200 fruit flies in stock;
The mathematical function she may use to calculate is given as
f(n)=log1.38(n/200)
Which function could she use to calculate, the number of days required for her stock to grow to n fruit flies?
Generally, the equation for the final value is mathematically given as
A=Ao(1+u)^t
Therefore
n=200(1+0.38)*t
log(1.38^t)=log(n/200)
t=log1.38(n/200)
In conclusion, The function she could use to calculate is
f(n)=log1.38(n/200)
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If 25% of a number is 20 and 60% of the same number is 48, find 85% of that number
Answer:
68
Step-by-step explanation:
25% of a number is 20, where the number is 80 because 25% times 4 is 100% and 20 times 4 is 80.
We can check by doing 60% of 80 to see if it is 48. Instead of 60%, we can do 10% of 80, which is 8. Since we divided by 6, we multiply 8 by 6 which is 48.
Since we know 80 is the number, we have to find 85% of 80. First, let's find 5% of 80, which is 4 since 4 x 20 is 80 and 5% x 20 is 100%. Now, 85 divided by 5 is 17, let's multiply 17 by 4 to get 85% of 80. 17 x 4 is 68 which is 85% of 80.
If Y=6 and X=10 then find the value of y when x=8
Answer:
when x=10 & y=6
10-6=4 so,
x=8
y=4
Please help with all
Find three consecutive positive integers such that the product of the median and largest integer is 8 times the sum of the smallest and largest interger.
The positive integers are 14, 15 and 16
What is an algebraic expression?
An algebraic expression can be defined as an expression that is made up of coefficients, terms, variables, factors and constants.
From the given information, we have that;
Let the consecutive integers be;
x, x+ 1, x+ 2
This can be represented as;
(x+1)(x+2) = 8(x + x+ 2)
Now, expand the bracket
x² + 2x + x + 2 = 8(2x + 2)
x² + 3x + 2 = 16x + 16
collect like terms
x² + 3x - 16x + 2 - 16 = 0
Add or subtract like terms
x² - 13x - 14 = 0
Solve the quadratic equation
x² -14x + x - 14 = 0
factor in pairs
x(x- 14) + 1(x -14) = 0
Then,
x = -1
x = 14
Take 'x' as 14
smallest integer = 14
Median = 14 + 1 = 15
Largest integer = 16
Hence, the values are 14, 15 and 16
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Reasoning Which of these is the best estimate for 225% of 50? greater than O but less than 1. 50 greater than 1-50 but less than 2. 50 greater than 2. 50 but less than 3. 50 greater than 3. 50
The best estimate for 225% of 50 is (a) greater than O but less than 1. 50
What is another term for estimate?The maximum likelihood method will be used to calculate the point estimate as follows:
T, note the total number of trials.
List the number of accomplishments, S.
MLE = S / T should be used. Your point estimate is the outcome. Prior to explaining a "formal" method of approximation by rounding each number in the calculation to one significant figure, students must first estimate the result of a computation, use a calculator to determine the precise result, then compare the two results. The most accurate estimate is a definite estimate, as it is created by estimating the individual expenses for the various aspects of the project and then combining them into one estimate. Typically, bottom-up estimates are classified under this heading.
The best estimate for 225% of 50 is
= (225*50)/100
= 11250/100
= 112.5
So that, The best estimate for 225% of 50 is (a) greater than O but less than 1. 50
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What Is 8 1/8 - 4 3/8
Answer:
3 3/4 or 3 6/8
Step-by-step explanation:
hope this helps <3
OrScruffy Pals Pet Boxes sends pet supplies in the mail each month. Irma prepaid a 4-month subscription for her cats. She used a one-time coupon and received $8 off the total cost. Irma paid $64 in all. Which equation can you use to find m, the regular cost per month?
We employ the following equation to get the normal monthly cost:
4m - 8 = 64
Regular monthly expenses amount to $18.
Irma paid for her cats' subscription in advance for a 4-month period.
She saved $8 overall when she utilized a one-time discount.
Irma totaled $64 in payment.
We must identify the equation that can be utilized to calculate m, the average monthly cost.
Let's use m to symbolize the normal monthly expenditure. She signed up for a subscription that would last for four months, thus the full price without the voucher is 4m.
When the coupon is used, the final price is (4m - $8), since she was given a $8 discount.
Irma paid a total of $64 according to the problem, thus we can create the following equation:
4m - $8 = $64
We must now solve for m in order to determine it. Isolating 4m on one side of the equation will be our first step.
4m = $64 + $8
4m = $72
Finally, divide both sides by 4 to solve for m:
m = $72 / 4
m = $18
So, the regular cost per month, m, is $18.
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you and three friends spent $35 on tickets at the movies. Write and solve an equantion to find the price p of one ticket
Answer:
35/4=8.75
Step-by-step explanation:
You and your 3 friends add up to 4 people so you do 35 divided by 4 and get 8.75
Answer:
Step-by-step explanation:
35/3 = p
p = 11.67 per person
What is the height of the triangle 12 units?
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
what is triangle ?
A triangle, which is a polygon, has three sides and three vertices. One of geometry's basic shapes is it. A triangle with the vertices A, B, and C is referred to as Triangle ABC. A unique plane and triangle are discovered in Euclidean geometry when the three points are not collinear. Having three sides and three corners, a triangle is a polygon. The triangle's corners are defined as where the three sides meet one another end to end. 180 degrees is the sum of the angles in a triangle.
given
Given, side length, a = 12 units.
the height of equilateral triangle, h = (a√3)/2.
Substituting the value of 'a',
h = (12√3)/2 = 6√3 =
10.39 units.
The triangle of 12 units has a height of 10.39 units by Divide the result by the area (A) after first multiplying the base (b) by 1/2.
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Amelie is making a recipe that uses 134 cups flour. She is making 212 times the original recipe. Amelie draws this model to represent the number of cups of flour she needs. How many cups of flour does Amelie need
Amelie needed 335 cups of flour for the recipe.
How is quantity calculated?The whole centre line length, as well as the construction's breadth and depth, must be multiplied in order to determine the required amount of quantity. Every time the main wall is attached to a cross wall, a partition, or a verandah, the centre line length will be halved at that intersection.Any number, variable, or algebraic combination of other numbers can be a quantity in a mathematical equation. Seven, ten, x, and the product of x and seven, or x + seven, are the four numbers in the equation x + 7 = 10.The unit price is the cost per unit of the product you are purchasing. The amount might be given per thing or per measurement type, such ounces, grammes, gallons, or litres.Given data :
She is making 2 1/2 or 2.5 times the original recipe.
Cups in original recipe= 134 cups
cups Amelie will need= 2.5 × 134
= 335 cups
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Donald plays with his wood cubes and decides to make pyramids.
He carries on with his pyramids and labels following the same pattern.
After making p4 donald realises that he only has 12 wood cubes left. How many more cubes will he need to make p5?
Donald would need to use 5 levels of cubes, So to make p5 he would need 25-12 = 13 more cubes.
What is pyramid?A pyramid is a structure with a square or triangular base and four triangular sides that meet at a point, called the apex. Pyramids were built by ancient civilizations, such as the Egyptians, as tombs for pharaohs and their queens.
What is pyramid levels?In the context of building pyramids with wood cubes, it seems like "pyramid levels" refers to the layers of cubes used to construct the pyramid. Each level is a layer of cubes that sits on top of the previous one, and the number of cubes in each level increases as you move up the pyramid. For example, in the case of p4, the base level would use 1 cube, the next level would use 4 cubes, the next level would use 9 cubes, and so on. The top level, which forms the apex of the pyramid, would use the most cubes. So the pyramid levels refer to the different layers of the pyramid and the number of cubes used in each layer.
To make a pyramid labeled p5, Donald would need to use 5 levels of cubes.
Donald uses 1 cube for the base of p4, 4 cubes for the next layer, 9 cubes for the next, 16 cubes for the next and 25 cubes for the top level.
So to make p5 he would need 25-12 = 13 more cubes.
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Perry learned to play a total of 18 piece over the coure of 9 week of piano leon. After 12 week of piano leon, how many total piece will Perry be able to play? Solve uing unit rate
In a course of 12 weeks, Perry will be able to play a total of 25 pieces of the piano Leon.
A total of 18 pieces of piano are learnt by Perry in a course of 9 weeks.
By using simple algebra, we can find the number of pieces that will be played by Perry in one week,
So, we can write, The learing speed,
Number of piano pieces learnt = Weeks
19 pieces = 9 weeks
Learning speed = 19/9 Pieces per week
So, the number of pieces learnt in 12 weeks is,
Number of pieces learnt = 19/9 x 12
Number of pieces learnt = 25.22
Number of pieces learnt = 25
So, Perry will be able to play 25 pieces.
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