The area of the hexagon is 1344 square centimeters for the given perimeter and apothem.
What is an apothem?The distance between a polygon's midpoint and any one of its sides is the polygon's apothem. The radius of the polygon's inscribed circle is equal to the perpendicular distance that runs from the centre to the side of the polygon. The formula for computing the area of regular polygons uses the apothem, which is a crucial component for determining their area.
The area of hexagon is given by the formula:
Area = (Perimeter x Apothem) / 2
Substituting the given values we have:
Area = (96 cm x 14 cm) / 2
Area = 1344 sq. cm
Hence, the area of the hexagon is 1344 square centimeters.
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2. Sundaes come with vanilla or chocolate ice cream. The toppings are hot fudge and
caramel. The final choice is whipped cream or marshmallow.
• What is the probability of getting a sundae with vanilla ice cream, caramel, and
marshmallow?
● Draw a tree diagram to find the solution.
• Justify mathematically that your answer is correct.
Answer:
Step-by-step explanation:
The tree that shows the correct combination of one flavor of ice cream and one topping is the the first tree.
What is tree diagram ?
A tree diagram is a tool in the fields of general mathematics, probability, and statistics that helps calculate the number of possible outcomes of an event or problem, and to cite those potential outcomes in an organized way.
Tree diagrams, also known as probability trees or decision trees, are quite versatile and may be useful in many fields, including finance.
A tree diagram lets a user start at a single point and make mutually exclusive decisions or experience mutually exclusive events to follow a path down the branches of the tree. Using a tree diagram is simple once you assign the appropriate values to each node.
From the question, and the definition it is clear that vanilla splits into fudge and caramel and chocolate to sprinkles.
Hence A is the correct option.
Helppp ASAP, what is a conjecture for this
Can you solve this quesiton?
f'(x)=?
By simplifying the derivative of f(x) is:,[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^ 2 (x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2 )[/tex]
What is derivative?A derivative is a mathematical cοncept that represents the rate at which a functiοn changes with respect tο οne οf its variables. In οther wοrds, the derivative measures hοw much the οutput οf a functiοn changes when yοu change the input by a small amοunt.
Tο find the derivative οf f(x), we will use the quοtient rule οf differentiatiοn.
Let's begin by simplifying the expression:
[tex]f(x) = [5(x^2 + 2) cot(x)]/[2 - cos(x) csc(x)][/tex]
[tex]f(x) = [5(x^2 + 2) cos(x)/sin(x)]/[2sin(x) - cos(x)][/tex]
[tex]f(x) = [5(x^2 + 2) cos(x)]/[sin(x)(2sin(x) - cos(x))][/tex]
Now we can apply the quotient rule:
[tex]f'(x) = [(5(x^2 + 2) cos(x))'sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(sin(x)(2sin(x) - cos(x)))']/(sin(x)(2sin(x) - cos(x))^2)[/tex]
To simplify, let's find the derivatives of the individual terms in the numerator:
[tex][(5(x^2+ 2) cos(x))'] = 10xcos(x) - 5(x^2+ 2)sin(x)[/tex]
[tex][(sin(x)(2sin(x) - cos(x)))'] = 3cos^2 (x) - 4sin^2(x)[/tex]
Now we can substitute these back into our original equation for f'(x):
[tex]f'(x) = [(10xcos(x) - 5(x^2 + 2)sin(x))sin(x)(2sin(x) - cos(x)) - (5(x^2 + 2) cos(x))(3cos^2(x) - 4sin^2 x))]/(sin(x)(2sin(x) - cos(x))^2)[/tex]
Simplifying further:
[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 5(x^2 + 2)sin^2 (x)(2sin(x) - cos(x)) - 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]
[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2+ 2)sin^ 2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]
Therefore, the derivative of f(x) is:
[tex]f'(x) = [10xsin(x)cos(x)(2sin(x) - cos(x)) - 10(x^2 + 2)sin^3(x) + 15(x^2 + 2)cos^3(x) + 20(x^2 + 2)sin^2(x)cos(x)]/(sin(x)(2sin(x) - cos(x))^2)[/tex]
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A company's daily profit from the production and sale of electrical components can be described by the equation P(x)=6.30x-1,777 dollars, where x is the number of units produced and sold. What level of production and sales will give a daily profit of more than $8,9337
Answer:1,777...)-(1,555)= B)1,333...+4,666
Step-by-step explanation:1,777...)-(1,555)= B)1,333...+4,666
Let f (x) = x²e² the value of = lim [ƒ (x)]* i 1-lim is: 4x-
a)
b) 1
c) 0
d) 1 4e
Answer:
d) 1/(4e)
Step-by-step explanation:
You want the value of the limit of 1/4f(x)^(1/x) as x approaches -1, where f(x) = x^2·e^(x^2).
LimitThe function is continuous and defined at x=-1, so the limit can be evaluated directly.
[tex]\lim=\dfrac{1}{4}((-1)^2\cdot e^{(-1)^2})^{(1/-1)}=\dfrac{1}{4}(1\cdot e^1)^{-1}=\boxed{\dfrac{1}{4e}}[/tex]
what is 0.357 divided by 6.7
Answer:
0.05328358208955223880597014925373
Step-by-step explanation:
A student purchased a used car for $15,200. The value of the car depreciates exponentially at
a rate of 5.8% per year. What is the value of the car after 4 years? Show your work or
explain how you determined your answer.
(2 points)
15,1
15.8%.
As a result, after fοur years οf depreciatiοn, the car is wοrth abοut $12,914.96.
Hοw dο I determine depreciatiοn?Subtract the asset's cοst frοm its scrap value (what yοu anticipate it tο be wοrth just at end οf the useful life) tο determine depreciatiοn using the straight-line technique. The quantity that can be depreciated, οr the depreciable basis, is the οutcοme. Take this amοunt and deduct it frοm the lifespan οf the asset, which is expressed in years.
This fοrmula fοr expοnentially decaying can be used tο determine the value οf a vehicle after fοur years οf depreciatiοn:
[tex]A = P * e^{(-rt)} (-rt)[/tex]
where A represents a finaI vaIue, P represents its initiaI price, r represents the yearIy depreciatiοn rate in decimaI fοrm, and t is the periοd οf time.
Inputting the specified vaIues resuIts in:
P = $15,200 (the οriginaI vaIue) (the initiaI vaIue)
Given that the annuaI depreciatiοn rate is 5.8%, r is equaI tο 0.058.
t = 4 (because we want tο find the vaIue after 4 years)
When we enter these vaIues, we οbtain:
[tex]A = $15,200 * e^{(-0.058 * 4)}[/tex]
Hence, When we condense an expression, we get:
[tex]A = $15,200 * e^{(-0.232)} (-0.232)[/tex]
A = $12,914.96
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Precision Aviation had a profit margin of 8.50%, a total assets turnover of 1.5, and an equity multiplier of 1.8. What was the firm's ROE?
Answer:
Step-by-step explanation:
We can use the DuPont model to calculate the ROE (Return on Equity):
ROE = Profit margin * Total assets turnover * Equity multiplier
Substituting the given values, we get:
ROE = 0.085 * 1.5 * 1.8 = 0.2295 or 22.95%
Therefore, Precision Aviation's ROE was 22.95%.
Find 4/5 of twelve times a
third of sixty-nine
Answer:
220.8
Step-by-step explanation:
4/5 × (12 × 1/3) × 69
4/5 × (4) × 69
3.2 × 69
= 220.8
Probability and statistics question
(a) There are 0.1271 percent of poodles that weigh more than 7.9 kilograms. (b) The region to a left , z1 is 0.2389, and the proportion of pups with weights of no more than 7.4 kilos is 0.2852.
How much does a kilogram weigh?a. i. To determine how many times the revenue in 2017 was greater than the revenue in 2016, divide the revenue in 2017 by the revenue in 2016:
$164,900\div 138,200 = 1.1939$
Revenue in 2017 was 1.1939 times greater than revenue in 2016.
ii. To calculate the revenue in 2017 as a percentage of the revenue in 2016, divide the revenue in 2017 by the revenue in 2016 and multiply by 100:
$dfrac164,900138,200 multiplied by 100% = 119.39%$In 2017, revenue was 119.39% higher than in 2016.
b. i. To determine how many times the population of Huntersville was greater than the population of Wright's Park in 2015, divide the population of Huntersville by the population of Wright's Park:
(a) To find the proportion of poodles with weights over 7.9 kilograms, we need to find the area under the standard normal distribution curve to the right of z = (7.9 - 7) / 0.7 = 1.14. From the standard normal distribution table, the area to the right of z = 1.14 is 0.1271. Therefore, the proportion of poodles with weights over 7.9 kilograms is 0.1271.
(b) To find the proportion of poodles with weights of at most 7.4 kilograms, we need to find the area under the standard normal distribution curve to the left of z = (7.4 - 7) / 0.7 = -0.86. From the standard normal distribution table, the area to the left of z = -0.86 is 0.1949. Therefore, the proportion of poodles with weights of at most 7.4 kilograms is 0.1949.
(c) To find the proportion of poodles with weights between 6.5 and 7.8 kilograms inclusive, we need to find the area under the standard normal distribution curve between z = (6.5 - 7) / 0.7 = -0.714 and z = (7.8 - 7) / 0.7 = 1.14. From the standard normal distribution table, the area to the left of z = -0.714 is 0.2389 and the area to the right of z = 1.14 is 0.1271. Therefore, the proportion of poodles with weights between 6.5 and 7.8 kilograms inclusive is 1 - 0.2389 - 0.1271 = 0.634.
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his annual salary is $91 520 and he has $7300 in allowable tax deductions.
What is his taxable income?
Taxable income = $
Answer:
$84,220
Step-by-step explanation:
To calculate the taxable income, we need to subtract the allowable tax deductions from the annual salary:
Taxable income = Annual salary - Allowable tax deductions
Taxable income = $91,520 - $7,300
Taxable income = $84,220
Therefore, his taxable income is $84,220.
13. Find x.
E(7x°
D- (4x+10)°
A-(4x + 5)°
C-(5x - 5)
B-(6x + 10)°
Answer: 14ex
Step-by-step explanation:
The function c(t) = 54 (1.12) models the cost in dollars, c, of 1 ounce of insulin, the input, t,
represents the number of years since 2010.
a. Does the cost of insulin increase or decrease over time, and by what percentage per year
does it do so?
b.
How much does an ounce of insulin cost in 2018? Show your reasoning.
How much would an ounce of insulin have cost in 2006? Show your reasoning.
Therefore, we cannot calculate the cost of an ounce of insulin in 2006 using this function. (a). the cost of insulin increases by 12% per year.
(b).Therefore, an ounce of insulin would have cost approximately $114.08 in 2018.
(c).Therefore, the cost of insulin increases by 12% per year.
What is function?
a function is a relationship between two sets of objects, where each object in the first set (called the domain) is associated with exactly one object in the second set (called the range). The domain and range can be any set, including numbers, geometric shapes, or other mathematical objects.
A function is typically represented by a rule or formula that describes how to map each element in the domain to an element in the range. For example, the function f(x) = 2x maps each value of x to its double, so that f(1) = 2, f(2) = 4, f(3) = 6, and so on.
The cost of insulin increases over time because the value of 1.12 is greater than 1, meaning the function's output grows with increasing t. To find the percentage increase per year, we can calculate the difference in cost between two consecutive years and divide it by the cost of the earlier year. For example, to find the percentage increase between 2010 and 2011:
[tex]c(1) - c(0) = 54(1.12) - 54 = 6.48[/tex]
Percentage increase = (6.48/54) x 100% = 12%
Therefore, the cost of insulin increases by 12% per year.
b. To find the cost of an ounce of insulin in 2018, we need to find the value of t for that year. Since t represents the number of years since 2010, we can subtract 2010 from 2018 to get:
[tex]t = 2018 - 2010 = 8[/tex]
[tex]c(8) = 54(1.12)^8 =$114.08[/tex]
Therefore, an ounce of insulin would have cost approximately $114.08 in 2018.
c. To find the cost of an ounce of insulin in 2006, we need to find the value of t for that year. Since t represents the number of years since 2010, we can subtract 2010 from 2006 to get:
[tex]t = 2006 - 2010 = -4[/tex]
However, a negative value of t is not meaningful in this context because the function assumes t represents the number of years since 2010. Therefore, we cannot calculate the cost of an ounce of insulin in 2006 using this function.
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A bag contains 3 gold marbles, 26 silver marbles, and 28 black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win $3. If it is silver, you win $2. If it is black, you lose $1. What is your expected value if you paid $1 to play this game?
3+26+28 = 57
chance of gold is 3/57
chance of silver = 26/57
chance of black = 28/57
the expected value of playing this game = a weighted average of the winnings (or losses) multiplied by the odds of winning: (3/57)3 + (26/57)2 + (28/57)(-1) = 9/57 + 54/57 - 58/57 = 60/57 -58/17 = 2/57 = about 0.578 winnings = $0.578 = 0.58 cents
You will win 0.58 cents each time you play this game, on average.
but the mode is on black. You're more likely to lose (28/57)(-1) about 0.49 cents on your first time to play
but if you stick it out, and play enough times, you'll average 0.58 cents a game
When 3x^2+18x–21=0 is written in the form (x–p)^2=q, what is the value of q?
The value of q is 16.
What is a quadratic equation?
Any equation can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. An equation containing a single variable of degree 2.
Here, we have
Given: Equation: 3x²+18x–21 = 0 is written in the form (x–p)²=q.
We have to find the value of q.
3x²+18x–21 = 0
3(x²+6x-7) = 0
x²+6x-7 = 0
(x+3)²-7-9 = 0
(x+3)² - 16 = 0
(x+3)² = 16
(x-p)² = q
Hence, the value of q is 16.
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The triangles below are similar. Find the length of x.
Answer:
D
Step-by-step explanation:
If the triangles are similar, their side ratios are equal
[tex] \frac{54}{12} = \frac{x}{15} [/tex]
Cross-multiply to find x:
[tex]x = \frac{54 \times 15}{12} = 67.5[/tex]
How can I solve this?
The polynomial that models the company's profit is 1.0x² + 3.5x, which represents the profit in thousands of dollars.
Define polynomial equationA polynomial equation is an algebraic equation that involves a polynomial, which is an expression consisting of variables and coefficients that are combined using addition, subtraction, multiplication, and exponentiation (raising to a power).
The polynomial that models the company's sales in thousands of dollars is simply the given sales volume polynomial:
Sales = 5.9x² + 8.5x + 4.7 (in thousands of dollars)
To find the polynomial that models the company's profit, we need to subtract the cost polynomial from the sales polynomial:
Profit = Sales - Cost
Profit = (5.9x² + 8.5x + 4.7) - (4.9x²+ 5x + 4.7)
Profit = (5.9 - 4.9)x² + (8.5 - 5)x
Profit = 1.0x²+ 3.5x
So the polynomial that models the company's profit is 1.0x² + 3.5x, which represents the profit in thousands of dollars.
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2. Use the Factor Theorem to determine if (x-4) is a factor of the polynomial function
P(x) = x5 + 4x4 - 17x³ - 60x²
Clearly state that (x-4) is a factor, or that (x-4) is not a factor. Show all work.
Answer:
Yes, (x - 4) is a factor of polynomial function P(x) = x⁵ + 4x⁴ - 17x³ - 60x².
Step-by-step explanation:
The Factor Theorem states that if f(x) is a polynomial, and f(a) = 0, then (x - a) is a factor of f(x).
Therefore, according to the Factor Theorem, if (x - 4) is a factor of P(x) then P(4) = 0.
To determine if (x - 4) is a factor of P(x), substitute x = 4 into the function and solve.
[tex]\begin{aligned}x=4 \implies P(4)&=(4)^5+4(4)^4-17(4)^3-60(4)^2\\&=1024+4(256)-17(64)-60(16)\\&=1024+1024-1088-960\\&=2048-1088-960\\&=960-960\\&=0\end{aligned}[/tex]
As P(4) = 0, this confirms that (x - 4) is a factor of polynomial function P(x) = x⁵ + 4x⁴ - 17x³ - 60x².
[tex]\hrulefill[/tex]
Additional comments
The fully factored form of the given polynomial function is:
[tex]P(x)=x^2\left(x+3\right)\left(x-4\right)\left(x+5\right)[/tex]
Use distributive property to evaluate 4(2x-1) when x=6.
The answer is 44.
What is unitary method?
"A method to find a single unit value from a multiple unit value and to find a multiple unit value from a single unit value."
We always count the unit or amount value first and then calculate the more or less amount value.
For this reason, this procedure is called a unified procedure.
Many set values are found by multiplying the set value by the number of sets.
A set value is obtained by dividing many set values by the number of sets.
4*(12-1)
44
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Ronaldo has three and three-sevenths sandwiches. He shares three-fourths of them with his family. How many sandwiches did Ronaldo share?
Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .
what is unitary method ?A mathematical strategy for resolving proportionality issues is the unitary method. Finding the value of one unit of a quantity and utilising that value to determine the value of a different number of units of the same quantity is what this process entails. The unitary technique can be used, for instance, to determine the cost of any quantity of apples if you know that 5 apples cost $10. $10/5 = $2 would be the price of one apple. By multiplying the quantity of apples by the price of one apple, you could then calculate the price of any other number of apples. For instance, 8 apples would cost 8 x $2, or $16, to purchase.
given
Ronaldo eats sandwiches that are three and three-sevenths of a sandwich, which is an incorrect fraction:
3 3/7 = (7*3 + 3)/7 = 24/7
He divides these sandwiches into thirds and fourths among his family, making a total of:
(3/4) * (24/7) = (324)/(47) = 18/7
We can change this incorrect fraction into a mixed number because:
18/7 = 2 and 4/7
Ronaldo therefore feeds his family 2 and 4/7 sandwiches as he eats sandwiches that are three and three-sevenths .
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Which of the following is the best estimate of the area of the irregular shape?
*The answer is not 19.5*
Option (D) 15.5 units²
Step-by-step explanation:Number of clear squares = 9 = 9 squares
Number of half squares = 7 = 3.5 squares
Number of more than half squares = 1 = 1 squares
Number of less than half squares = 8 = 2 squares
Grand total = 9 + 3.5 + 1 + 2
= 15.5 units²
Please mark my answer as the BRAINLIEST. Plssssssss
Hope my answer helps:)The following graph depicts which inverse trigonometric function
It should be noted that cpnsidering that when x = 1, y = 0, it is found that the inverse trigonometric function depicted in the graph is given by: A. y = Arccos x
What is an inverse trigonometric function?It has the format y = f(x), with f being an inverse trigonometric function, and it basically is what angle y has a trigonometric function value of x.
In this graph, we have that when x = 1, y = 0, and considering that cos(0) = 1, the inverse trigonometric function depicted in the graph is given by y = Arccos x
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Find the surface area of each of the following right prisms using the formula SA=LA+2B
calculate the following expression and give answer in the standard form z=a+bi
use the De Moivre's theorems to calculate
[tex] \frac{(cis22.5)(5cis67.5)}{3 {}^{2} ( \cos(12) + i \sin(12)) } [/tex]
As a result, the expression can be expressed in the following standard form: -32 sin(102) + 32i cos = 32i (cos(102) + I sin(102)) (102).
what is expression ?In mathematics, programming, or other subjects, an expression is typically a grouping of numbers, symbols, and operators that denotes a value or computation. When used to indicate a mathematical relationship or formula, an expression in mathematics can be made up of a number of different variables, operators, and digits. For instance, the statement 3x + 2y denotes a linear equation. A combination of variables, constants, operators, and functions can make up an expression in programming, which can then be evaluated to create a value. For instance, the expression 5 + 3 evaluates to 8 as an expression.
given
First, we can use De Moivre's theorem to simplify the expression:
(cis(22.5+67.5)) = (cis(22.5+67.5)) = cis(22.5+90) = I
We then have:
Cos(12) + I sin(12) = 32cis (12)
When we multiply these two outcomes, we obtain:
32i cis(90+12) = 32i cis(i * 32cis(12)) = 32i cis102
Thus, the phrase can be worded as follows:
(cis22.5) (5cis67.5) (5cis67.5) 32(cos (12) + I sin (12)) = 32i cis (102).
Using Euler's formula, cis102 can be written as follows:
102 + I sin + cos(102) = cis102 (102)
As a result, the expression can be expressed in the following standard form: -32 sin(102) + 32i cos = 32i (cos(102) + I sin(102)) (102)
The final response is thus: Z = 32i cos + 32sin(102) (102)
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Ms. grimes walks up to a tank of water that can hold up to 12 gallons. When it is active, a drain empties water from the tank at a constant rate. When jada first sees the tank it contains 8 gallons of water. Four minutes later the tank contains 6 gallons of water. At what rate is the amount of water in the tank changing? Use a signed number, and include the unit of measurement in your answer.
The rate at which the amount of water in the tank is changing is -0.5 gallons/minute. This means that the amount of water in the tank is decreasing at a rate of 0.5 gallons per minute.
Rate of change:
The rate of change is a measure of how a quantity changes with respect to another quantity. It tells us how much a particular quantity is changing for a given change in another quantity.
It is often represented as a ratio of the change in the quantity of interest to the change in the other quantity, usually with units of measurement.
Here we have
Ms. Grimes walks up to a tank of water that can hold up to 12 gallons.
When it is active, a drain empties water from the tank at a constant rate. When Jada first sees the tank it contains 8 gallons of water. Four minutes later the tank contains 6 gallons of water.
We can use the following formula for the rate of change of a quantity:
Rate of change = (change in quantity) / (change in time)
Given that when Jada first saw the tank, 8 gallons. Four minutes later, the amount of water in the tank decreased to 6 gallons.
So the change in the amount of water in the tank is:
change in water = 6 gallons - 8 gallons = -2 gallons
The change in time is:
change in t = 4 minutes - 0 minutes = 4 minutes
So, the rate of change of the amount of water in the tank is:
= (change in W) / (change in t)
= (-2 gallons) / (4 minutes) = -0.5 gallons/minute
Therefore,
The rate at which the amount of water in the tank is changing is -0.5 gallons/minute. This means that the amount of water in the tank is decreasing at a rate of 0.5 gallons per minute.
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a tourist bought a statue at a discount of 20% with 13% VAT and got Rs 416 back for VAT airport, what was the labeled price of the statue ?
Let the labeled price be 100x
20% discount, sale price = 80x
13% of 80x = 13x*4/5= 52x/5 = 10.4x
10.4x = 416
100x = ?
100/10.4 X416 = 41600/10.4 = Rs 4, 000 ANSWER
4 (7x +5)
Please show me how to work this out
Answer:
28x + 20
Step-by-step explanation:
you just need to distribute
4(7x + 5)
you multiply 4 X 7x which would give you 28 and because 7 has a variable and 4 doesn't have a variable the x stays there so it would be 28x.
45, you need to multiply 4 x 5 which would give you 20, and because neither 4 or 5 have a variable it will stay 20
So now you just 28x with 20
28x + 20.
Omaya picked as amount of apples, took a break, and then picked v more. Write the expression that models the total number of apples Omaya picked
The formula that describes how many apples Omaya picked in total is Y=x + v.
What does a linear equation mean in mathematics?
A linear equation is one that only has a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Occasionally, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The term "linear equation" refers to equations with power 1 variables. Where ax+b = 0 is one example with only one variable, where a and b are real numbers and x is the variable.
Let Total number of apples= Y
so,
Y=x + v
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Can someone pls help me on this?
Worth 50 points!!
+
1st to answer gets Brainliest!!
The measure of the sector that represents the probability of the medicine curing one person is 216°. So correct option is A.
Describe Sector?In geometry, a sector is a region of a circle enclosed by two radii and an arc. The two radii form an angle, called the central angle, which defines the boundary of the sector.
The area of a sector can be calculated using the following formula:
Area of sector = (central angle / 360) * π * r²
where:
central angle is the angle formed by the two radii
r is the radius of the circle
π is the mathematical constant pi, which is approximately 3.14159
The perimeter of a sector is the sum of the length of the arc and the length of the two radii. The length of the arc can be calculated using the formula:
Length of arc = (central angle / 360) * 2 * π * r
Sectors are often used in real-world applications, such as calculating the area of a pizza slice or the distance traveled by a car in a circular racetrack. They are also used in trigonometry to calculate angles and side lengths of triangles formed by intersecting chords and tangents in circles.
The probability of the medicine curing one person is given by P(curing) = 3/5. Since the spinner is a circle of 360°, the measure of the sector that represents the probability of the medicine curing one person is:
360° × P(curing) = 360° × 3/5 = 216°
Therefore, the answer is A) 216 degrees.
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Solve for d in the equation below. Isolate [tex]d[/tex] on the left hand side. Show all work.
[tex]A=B\left(1+\dfrac{c}{d} \right)^{dk}[/tex]
The solution for ‘d’ in the given equation is d = (ln(A) - ln(B))/ln(1+c/d).
What is natural log?Natural log is a logarithmic function commonly used in mathematics and in calculators to simplify equations. It is the inverse of the exponential function and is written as ln(x).
In order to solve for ‘d’ in the given equation, we need to isolate it on the left side of the equation.
To do this, we can begin by taking the natural log of both sides of the equation, as shown below.
ln(A) = ln(B) + d*ln(1+c/d)
We can now rearrange the terms in this equation such that ‘d’ is isolated on the left side of the equation.
d*ln(1+c/d) = ln(A)-ln(B)
We can now divide both sides of the equation by ln(1+c/d) in order to solve for ‘d’, as shown below.
d = (ln(A) - ln(B))/ln(1+c/d)
Therefore, the solution for ‘d’ in the given equation is
d = (ln(A) - ln(B))/ln(1+c/d).
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