determine the area of the shaded region of a wooden patch in a circular park if the radius of the circle is: a. 8m b. 12
Answers
Answer:
22.88
Step-by-step explanation:
O/360 * π r squared
90/360 * 8 squared
1/4 * π (64)
4 π
Next:
b*h/2
8*12/2 = 48
8π - 48
8π = 25.12
48-25.12 = 22.88
Related Questions
Select all the expressions that have the same value. a \large 3^3 b \large 3^4 c \large 6^2 d \large 6^3 e \large 9^2 f \large 9^3
Answers
The expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
Selecting all expressions that have the same value.To compare the expressions, we can simplify them using the rules of exponents:
a) 3^3 = 27
b) 3^4 = 81
c) 6^2 = 36
d) 6^3 = 216
e) 9^2 = 81
f) 9^3 = 729
Using the above as a guide, we have the following:
Therefore, the expressions that have the same value are: b) 3^4 = 81 and e) 9^2 = 81
So, options b and e have the same value.
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The distance of 15 miles on a map is represented by 2 inches.
If the distance between two cities on the map is 8 inches, what is the actual distance
between them?
A 60 miles
B 75 miles
C 90 miles
D 120 miles
awing of an airplane. The airplane has a 100-foot wings
Answers
Answer:
A. 60 miles
Step-by-step explanation:
2 in. = 15mi or like 2in+2in+2in+2in = 8in
15mi+15mi+15mi+15mi = 60mi
2×4 =8
/
/
v
4 × 15mi = 60mi
The piecewise function g(x) is shown in the graph.
Graph with three pieces. The first piece is a horizontal line from the left with an open right endpoint at negative 2 comma negative 1. The second piece is curved with a solid point at negative 1 comma 0, which ends at 1 comma 1. The last piece starts with a solid circle at 0 comma 1 and increases to the right as it passes through 4 comma 5.
Which of the following represents g(x)?
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than or equal to x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than or equal to x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0.
g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x plus 1 end quantity squared, when negative 1 is less than x is less than 0, and it equals x plus 1, when x is greater than or equal to 0.
Answers
The description that correctly represents g(x) is g of x is a piecewise function, which equals negative 2, when x is less than or equal to negative 1, and it equals the quantity x minus 1 end quantity squared, when negative 1 is less than x is less than or equal to 0, and it equals negative x plus 1, when x is greater than 0 (third option).
What represents g (x)?Looking at the graph, we can see that:
g(x) is equal to -2 for x ≤ -1.g(x) is a quadratic function that passes through the point (-1,0) and (1,1), with a vertex at (0,1), for -1 < x ≤ 0.g(x) is a linear function that passes through the point (0,1) and (4,5), for x > 0.Thus, the correct piecewise function that represents g(x) is:
g(x) = {-2 if x ≤ -1
{ (x-1)^2 if -1 < x ≤ 0
{ -x+1 if x > 0
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if k(x) = 3x, then f'(x)=? A. x³Ln3 B. 3xLn3 C. 3x/Lnx D. 3/3xLn3
Answers
The correct answer is not listed among the options. The correct answer is E. 1/x.
What is function?
In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.
To find f'(x), we need to differentiate the function f(x) with respect to x. Since we are given k(x) = 3x, we can use the chain rule to differentiate f(x) = ln(k(x)) = ln(3x) as follows:
f'(x) = d/dx [ln(3x)]
= 1/(3x) * d/dx [3x] (applying the chain rule)
= 1/(3x) * 3
= 1/x
Therefore, the correct answer is not listed among the options. The correct answer is E. 1/x.
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Evander Holyfield (the champion boxer who had part of his ear bitten off by Mike Tyson) made $290 million during his boxing career but declared bankruptcy because of poor financial choices. His July interest at 18% was $248. What was Evander’s principal at the beginning of July? (Use 360 days a year. Do not round intermediate calculations. Round your final answer to the nearest whole dollar.)
Answers
Evander's principal at the beginning of July was approximately $16,533. Rounded to the nearest whole dollar, this is $16,533.
How do we calculate?Applying the formula for simple interest:
Interest = Principal x Rate x Time
Here, we know the interest ($248), the rate (18%), and the time (1/12 of a year for one month, since we're using a 360-day year).
Let the principal = "P":
$248 = P x 0.18 x (1/12)
$248 = P x 0.015
P = $248 / 0.015
P ≈ $16,533.33
Simple interest is described as an interest charge that borrowers pay lenders for a loan.
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what is the answer (x+80)(x-20)
Answers
Answer:
Using the FOIL method to multiply (x + 80)(x - 20), we get:
(x + 80)(x - 20) = x^2 - 20x + 80x - 1600
Simplifying the expression, we get:
(x + 80)(x - 20) = x^2 + 60x - 1600
Therefore, the answer is x^2 + 60x - 1600.
Valerie bought a clownfish for $47 at the pet store. She planned to spend her remaining money on smaller fish that cost $9 each. If Valerie began with $120, which inequality could be used to find f, the number of smaller fish she can buy?
A 9 +47f≤ 120
B 47 +9f≤ 120
C 56+9f≤ 120
D 38 + 47f≤ 120
Answers
Answer:
Step-by-step explanation:
b
Answer:
47 + 9f [tex]\leq[/tex] 120
Step-by-step explanation:
B is the correct answer.
What is the opposite of 12 written in simplest terms?
Answers
Answer:
Step-by-step explanation:
It is -12.
The opposite of a positive number would be its negative.
What is 6 5/6-5 1/2
6 5
6
-
5 1
2
Answers
The difference between 6 5/6 and 5 1/2 is 4/3 .
How to subtract these mixed numbers?To subtract these mixed numbers, we need to first convert them into improper fractions:
6 5/6 = (6 x 6 + 5)/6 = 41/6
5 1/2 = (5 x 2 + 1)/2 = 11/2
Now we can subtract:
41/6 - 11/2
To deduct divisions with various denominators, we really want to track down a shared factor. 6 is the smallest common multiple of 6 and 2 in this instance. Therefore, we can use denominator 6 to convert 11/2 into an equivalent fraction:
11/2 = (11 x 3)/(2 x 3) = 33/6
Now we can subtract the fractions with the same denominator:
41/6 - 33/6 = 8/6
Working on the portion by partitioning both the numerator and denominator by their most prominent normal component, we get:
8/6 = 4/3
As a result, in mixed numbers, the difference between 6 5/6 and 5 1/2 is 4/3, or 1 1/3..
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The complete question is:
What is the rule for the sequence
5/6, 1 1/2, 2 1/6, 2 5/6.....
1 1 Jemima has three boxes with a total weight of 51 kg. Box B weighs 5 kg more than box A and box C weighs 3 kg more than box B. Ch the correct statement. Select one: a. Box C weighs 21 O b. O c. kg. 30 1 Box A weighs 42 kg. 1 Box B weighs 12 kg. O d. 5 Box A weighs 17 kg.
Answers
On solving the question, we can say that Therefore, none of the answers to the question's assertions are true.
What is equation?A mathematical equation is a formula that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The symbol and the single variable are frequently the same. as in, 2x - 4 equals 2, for instance.
Let's use "x" to symbolise box A's weight. Then, we could type:
Given that box B weighs 5 kg more than box A, its weight is "x + 5".
Given that box C weighs 3 kg more than box B, its weight is calculated as "x + 5 + 3" = "x + 8".
We can write: Since we are aware that the combined weight of the three boxes is 51 kg:
[tex]x + (x + 5) + (x + 8) = 51\\3x + 13 = 51\\3x = 38\\x = 12.67\\[/tex]
Therefore, box A weights around 12.67 kg. The weights of boxes B and C may also be ascertained using the equations we discovered earlier:
17.67 kg (x + 5) is the estimated weight of Box B.
The approximate weight of Box C is 25.67 kg (x + 8).
Therefore, none of the answers to the question's assertions are true.
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HELLLLLLP!!! I WILL GIVE BRAINLIEST!!!
Answers
The expression that is equivalent to 6x2y + 2xy^5 include:
2(3x²y + xy^5).
2xy(3x + y⁴)
xy(6x + 2y⁴)
What is an expression?An expression can refer to a variety of things depending on the context in which it is used.
In mathematics and computer programming, an expression typically refers to a combination of numbers, variables, operators, and/or functions that are evaluated to produce a value. For example, "2 + 3" is an expression that evaluates to "5"
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The concentration C of a drug in a patient's bloodstream t hours after injection is given by C(t) = 100t/2 t^2 + 85.
Use a calculator to approximate the time when the concentration is highest. (Round your answer to two decimal places.)
Answers
Approximately 1.18 hours the concentration is highest.
The given function is c(t)=100t/t² +85.
When the concentration is highest, the function becomes
100t/t² +85 =0
100/t +85=0
100+85t=0
85t=100
t=100/85
t=1.18 hours
Therefore, approximately 1.18 hours the concentration is highest.
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I need help solving this question
Answers
Answer:
C. y = 3/2x + 4
Step-by-step explanation:
C. y = 3/2x + 4
If (x -1) is a factor of the polynomial f(x) = 4x²- 4x² - x - K, where K is a Constant.
1. What is the Value of K?
2. What are the roots of the equation
Answers
Answer:
If (x-1) is a factor of the polynomial f(x) = 4x² - 4x² - x - K, then we know that (x-1) divides evenly into the polynomial, which means that the polynomial can be written as:
f(x) = (x-1)(ax + b)
where a and b are constants that we need to determine. We can use the distributive property to expand this expression and equate it with the original polynomial:
f(x) = (x-1)(ax + b) = 4x² - 4x - K
Expanding the left side of the equation, we get:
ax² + bx - ax - b = ax² - (a-b)x - b = 4x² - 4x - K
Now we can equate the coefficients of the like terms on both sides of the equation.
The coefficient of x^2 on the left side is a, and on the right side it is 4. Therefore, we have:
a = 4
The coefficient of x on the left side is b - a, and on the right side it is -4. Therefore, we have:
b - a = -4
Substituting a=4, we get:
b - 4 = -4
Solving for b, we get:
b = 0
So the polynomial can be written as:
f(x) = (x-1)(4x + 0) = 4x² - 4x
Therefore, K = 0.
To find the roots of the equation, we need to set f(x) = 0 and solve for x:
4x² - 4x = 0
Factor out 4x:
4x(x - 1) = 0
So the roots of the equation are x = 0 and x = 1.
The segmented bar graph shows the relative frequencies regarding your arrival time to school using three different routes. How many times more likely are you to be on time than be late to school if you take Route C?
Answers
Therefore, you are three times more likely to be on time than be late if you take Route C to school.
What is relative frequency?Relative frequency is a statistical term that refers to the proportion or percentage of times an event or a particular value occurs within a larger set of data. It is calculated by dividing the number of times the event or value occurs by the total number of observations in the data set.
Here,
To determine how many times more likely you are to be on time than late if you take Route C, we need to compare the heights of the green and red bars for Route C. From the graph, we can see that the green bar (representing on-time arrivals) is approximately three times taller than the red bar (representing late arrivals) for Route C.
To calculate how many times more likely you are to be on time than late if you take Route C, we need to find the ratio of the heights of the green and red bars:
Ratio = height of green bar / height of red bar
Looking at the segmented bar graph, we can see that the height of the green bar for Route C is approximately 0.45, and the height of the red bar is approximately 0.15.
Ratio = 0.45 / 0.15
= 3
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Is the figure line symmetric?
If yes, how many lines of symmetry does the figure have?
a picture of a snow flake
Answers
Answer:
Yes, the figure is line symmetric.
A snowflake has six lines of symmetry. Therefore, the correct answer is: 6.
A car is purchased for $19,500. After each year, the resale value decreases by 20%. What will the resale value be after 3 years? Use the calculator provided and round your answer to the nearest dollar.
Answers
The resale value of the car after 3 years is $9,984.
How to find the resale value after 3 years?Since the resale value decreases by 20%. Thus, the resale value of the car will be 80% of its original value.
After the first year, the resale value of the car will be 80% of its original value:
Resale value after 1 year = 80/100 * $19,500 = $15,600
After the second year, the resale value of the car will be 80% of its value after the first year:
Resale value after 2 years = 80/100 * $15,600 = $12,480
After the third year, the resale value of the car will be 80% of its value after the second year:
Resale value after 3 years = 80/100 * $12,480 = $9,984
Therefore, the resale value of the car after 3 years will be $9,984.
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NO LINKS!! URGENT HELP PLEASE!!
For what value of c is the number "a" a solution of the equation? (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, enter INFINITELY MANY.)
4x + 1 + 7c = 8c - 3x + 6; a = -5
c = ________
Answers
Answer:
To find the value of "c" for which the number "a" (-5 in this case) is a solution of the equation, we can substitute "a" into the equation and solve for "c".
Given equation: 4x + 1 + 7c = 8c - 3x + 6
Substituting x with "a": 4(-5) + 1 + 7c = 8c - 3(-5) + 6
Simplifying the equation: -20 + 1 + 7c = 8c + 15 + 6
Combining like terms: -19 + 7c = 8c + 21
Moving all "c" terms to one side: 7c - 8c = 21 + 19
Simplifying: -c = 40
Dividing both sides by -1 to isolate "c": -c/-1 = 40/-1
Flipping the sign when dividing by a negative number: c = -40
So, the value of "c" for which the number "a" (-5) is a solution of the equation is c = -40.
Answer:
[tex]c=-40[/tex]
Step-by-step explanation:
Since a is a Solution to the Equation , then it satisfies the Equation
Substitute by [tex]x=a=-5[/tex] into the Equation [tex]4x+1+7c=8c-3x+6[/tex]
Then [tex]4(-5)+1+7c=8c-3(-5)+6[/tex]
Then [tex]-20+1+7c=8c+15+6[/tex]
By adding like-terms
Then [tex]-19+7c=8c+21[/tex]
Then [tex]8c-7c=-19-21[/tex]
Then [tex]c=-40[/tex]
Hi I need help finding the degree measure of Radian on a triangle with hypotenuse =7 and opposite =3
Answers
Answer:
24.6 degrees.
Step-by-step explanation:
To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.
sin(θ) = opposite/hypotenuse
sin(θ) = 3/7
Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.
θ = sin^-1(3/7)
θ ≈ 0.429 radians
To find the degree measure, we must convert radians to degrees by multiplying by 180/π.
θ ≈ 0.429 x 180/π
θ ≈ 24.6 degrees
Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.
Lauren works at a reception hall and is setting tables for a retirement party. She takes a basket of 98 soup spoons, and she places 8 soup spoons on every table she sets.
Write an equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x.
y=
Answers
The equation that shows how the number of soup spoons remaining, y, depends on the number of tables Lauren sets, x, is:
y = 98 - 8x
The initial number of soup spoons, 98, is reduced by 8 for each table Lauren sets. Therefore, the number of soup spoons remaining after x tables have been set is 98 - 8x.
What expression is equivalent to 4- 1/3-7/8+1/6?
A. 6/24-8/24-21/24+4/24?
Answer for brainliest. Don't care if its wrong.
Answers
The simplified form of the expression is 71/24.
What is the simplified form?
To simplify the expression 4 - 1/3 - 7/8 + 1/6, we can follow the order of operations, which dictates that we perform multiplication and division before addition and subtraction.
Here's the step-by-step solution:
Find a common denominator for the fractions involved. In this case, the least common denominator (LCD) is 24, which is the least common multiple of 3, 8, and 6.
Convert the fractions to have the same denominator, which is 24:
4 - 1/3 - 7/8 + 1/6
= 4 * 24/24 - 1/3 * 8/8 - 7/8 * 3/3 + 1/6 * 4/4 (Multiplying each fraction by the appropriate form of 1 to get the common denominator)
= 96/24 - 8/24 - 21/24 + 4/24 (Performing the multiplication)
Combine the numerators over the common denominator:
= (96 - 8 - 21 + 4)/24 (Combining numerators)
= 71/24 (Performing the subtraction)
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50 points! Multiple choice algebra question. Gilda used the formula f(x) = x/144 to convert square inches to square feet. Find the inverse of f(x). Photo attached. Thank you,
Answers
To find the inverse of f(x), we need to switch x and f(x) and solve for x:
x = f(f^(-1)(x))
In this case, f(x) = x/144, so we have:
x = f(f^(-1)(x))
x = (f^(-1)(x))/144
Simplifying for f^(-1)(x), we multiply each side by 144:
144x = f^(-1)(x)
Therefore, the inverse of f(x) is:
f^(-1)(x) = 144x
Write an equation of the line below.
Answers
Which equation is correct for the circle shown on the graph?
(x+3)²+ (y-6)² = 4
(x-3)² + (y+6)² = 4
(x+3)² + (y-6)² = 2
(x-3)² + (y-6)² = 4
Answers
Option 2 is the correct answer, that is, the equation of the given circle is (x+3)² + (y - 6)² = 4 with center at (-3,6) and radius 2.
What is a distance formula?The distance formula is a mathematical formula used to determine the distance between two points in a coordinate plane. It is derived from the Pythagorean theorem as:
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
where (x₁, y₁) and (x₂, y₂) are the x and y coordinates of the said two points. This formula works for any two points in a two-dimensional space with a Cartesian coordinate system.
To answer this we need to know the equation of a circle.
Let (a,b) be the center of a circle with radius r, then the equation of the circle can be written as:
(x - a)² + (y - b)² = r²
We see that from the given graph center of the circle is the point (-3,6) and radius will be 2.
We can now substitute these information in the circle equation,
(x - -3)² + (y - 6)² = 2²
(x+3)² + (y - 6)² = 4
That is the equation of the given circle is (x+3)² + (y - 6)² = 4.
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A carpenter has two different-sized circular saws. The smaller saw has the radius shown. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
.
Answers
If the radius of smaller-saw is 1.25 in, and radius of larger-saw is 2 inches, then larger-saw is 4.71 inches greater the smaller-saw.
The "Circumference" of a circle is defined as the distance around the boundary of a circle, it is also called perimeter of circle;
The diameter of the smaller saw can be calculated as:
⇒ diameter = 2 × radius = 2 × 1.25 inches = 2.5 inches;
The diameter of the larger saw is 1.5 inches greater than the diameter of the smaller saw, which means,
⇒ diameter of larger saw = diameter of smaller saw + 1.5 inches,
⇒ diameter of larger saw = 2.5 inches + 1.5 inches = 4 inches;
So, Circumference of circle is = 2 × π × radius;
The Circumference of "smaller-saw" = 2 × 3.14 × 1.25 inches,
⇒ circumference of smaller saw = 7.85 inches;
circumference of "larger-saw" = 2 × 3.14 × 2 inches
⇒ circumference of larger saw = 12.56 inches;
The difference in circumference between the two saws is:
⇒ circumference of larger saw - circumference of smaller saw
⇒ 12.56 inches - 7.85 inches = 4.71 inches;
Therefore, the circumference of the larger saw is 4.71 inches greater than the circumference of the smaller saw.
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The given question is incomplete, the complete question is
A carpenter has two different-sized circular saws. The smaller saw has the radius as 1.25 inch. The larger saw has a diameter that is 1.5 inches greater than the diameter of the smaller one.
How much greater is the circumference of the larger saw than the smaller saw? Use 3.14 for π
9. The Donut Shoppe sells "day old" donuts at 40% off original price. If a customer buys three "day old" donuts for $2.75, what is the cost after the discount?
Answers
the cost of day old donuts after the discount is $4.95.
what is discount?A discount is a decrease in the cost of a good or service. Discount is the reduction in the price of goods or services offered by shopkeepers at the marked price.
Discounts are offers or rebates made to customers on the marked-down prices of goods. We come across phrases like cost price, tagged price, discount, and selling price when making a purchase. Shop owners give discounts to customers to encourage product sales. Let's examine the connections between these concepts.
The formula to calculate the discount is:
Discount = List Price - Selling Price
Discount (%) = (Discount/List Price) × 100
the discount is 40% ⇒0.4
customer buys 3 donuts.
price of 1 donut = $2.75
total cost for 3 donuts= $2.75 x 3 = $8.25
discount for 1 donut= [tex]\frac{0.4}{100}* 2.75[/tex]=$1.1
so, for 3 donuts discount = $1.1 x 3 = $3.3
therefore the final price to be paid by customer is
=$8.25-$3.3
=$4.95
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4/7 of the length of a car ride is 8 miles. How many miles is the whole car ride ?
Answers
hi
4/7 = 8
7/7 = ?
so ? = 7/7 * 8 /4/7 = 8/4/7 = 8 *7/4 = 4*2*7 /4 = 2*7 = 14
so whole thing is 14
let's check : 14 * 4/7 = 56/7 = 8
Match initial data. answer is correct.
Choose the scatterplot(s) that DO NOT suggest a linear relationship between x and y.
O a
Ob
Oc
Od
y
y
*
y
LOVE
y
X
Answers
The scatter plots that do not show a linear relationship are B and C
How can a scatter plot show a linear relationship?The distribution of points on a scatter plot's graph can show a linear relationship between two variables. A linear relationship exists between two variables when there is a consistent change in one variable for every change in the other.
The horizontal axis and the vertical axis of a scatter plot each indicate a separate variable. Each data point is plotted on the graph based on its values for the two variables. If the variables are related to one another linearly, the points will often fall in a straight line.
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1. The relationship between distance
measured on a map and the actual
distance on the ground
A. A sketch
B. A statement
C. Layout
D. Scale
What if the correct answer
Answers
Answer: A Map Scale.
Step-by-step explanation:
A Map Scale is the relationship with the ground.
The definition given in the question is referring to the concept of "scale" in cartography. Scale is the ratio between the distance on a map and the actual distance on the ground, and it is an important consideration when creating and using maps. Therefore, the correct answer is D. Scale.
The value of y is directly proportional to the value
of x. If x = 8, then y = 12. What is the value of x when y = 30?
Answers
Answer:
If the value of y is directly proportional to the value of x, we can use the formula for direct variation to find the value of x when y = 30. The formula for direct variation is:
y = kx
where k is the constant of proportionality.
To find the value of k, we can use the values given in the problem:
y = kx
12 = k(8)
Solving for k, we get:
k = 12/8 = 3/2
Now that we know k, we can use the formula for direct variation to find the value of x when y = 30:
y = kx
30 = (3/2)x
Solving for x, we get:
x = (30)/(3/2) = 20
Therefore, when y = 30, x = 20