A circle has a radius of 16 ft. What is the area of the circle in terms of π?
Responses
A. 256π ft2
B. 128π ft2
C. 64π ft2
D. 32π ft2
The area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
First, let us understand the circle:
A circle is nothing more than a round form with no corners or line segments. In geometry, it is a closed curve shape.
Some formulas related to circle:
Area of the circle = πr^2
Circumference of the circle = 2πr
where, r = radius of the circle.
We are given;
A circle has a radius of 16 ft.
We need to find the area of the circle in terms of π.
Area of the circle = πr^2
Put the value of r in the above formula:
Area of the circle = π 16^2 * ft^2
Area of the circle = 256 ft^2
Thus, the area of the circle in terms of π if the circle has a radius of 16 ft is 256 π ft^2. Option A is correct.
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Answer:
option A
Step-by-step explanation:
there are 6 circles and 9 triangles what is the simplest ratio of circles to triangles?
What would be the compound interest obtained on an amount of $4800 at a rate of 5% per annum for 3 years?
A $448.7
B) $817.8
C)$623.5
D $756.6
The total compound interest obtained is $756.6.
We are given an initial amount equal to $4,800. This is the principal amount that is denoted by the variable "P". The rate of interest is 5% per annum and is denoted by "r". The interest is compounded annually and denoted by "I". The time duration is 3 years, denoted by the variable "t". Let the final amount be represented by the variable "A". We can use the given formula.
A = P(1 + r)^t
A = $4,800*(1 + 0.05)³
A = $4,800*(1.05)³
A = $4,800*1.157625
A = $5,556.6
The compound interest earned is the difference between the initial and the final amount.
I = A - P
I = $5,556.6 - $4,800
I = $756.6
Hence, the interest amount is $756.6.
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[50 Points help!] A circle graph shows that an office supply store spends a total of $1200 per month on expenses. If the company spends $300 on paper, what would be the measure of the central angle for paper in the circle graph?
A. 75 degrees
B. 90 degrees
C. 120 degrees
D. 150 degrees
E. 175 degrees
Answer:
B. 90 degreesStep-by-step explanation:
The circle represents a 360° angle.
Total spending corresponds to full circle and part of it spent on paper.
The ratio of paper over total is:
300/1200 = 1/4This is the part of circle which is:
360°*1/4 = 90°Correct choice is B.
Answer:
b) 90 degrees
Step-by-step explanation:
Forming the expression,
→ 360° × (300/1200)
Let's solve given expression,
→ 360° × (300/1200)
→ 360° × (1/4)
→ (360°/4)
→ 90°
Hence, the answer is 90°.
for 50 points and brainliest! (Part 2)
Lesson: Linear Inequalities in Two Variables
Directions: Answer the following problem. And graph it.
Please I want a complete answer with a clear explanation. Thank you in advance :)
Answer:
4.a) Broken line.
4.b) True.
5.a) Solid line.
5.b) True.
Step-by-step explanation:
When graphing inequalities:
< or > : broken line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Question 4Given inequality:
[tex]y < -\dfrac{1}{2}x+2[/tex]
a) As the "<" sign has been used, the line will be a broken line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 0 & < -\dfrac{1}{2}(0)+2\\0 & < 0+2\\0 & < 2\end{aligned}[/tex]
As zero is less than 2, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-2: \quad y &=-\dfrac{1}{2}(-2)+2\\y &=1+2\\y&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=4: \quad y &=-\dfrac{1}{2}(4)+2\\y &=-2+2\\y&=0\end{aligned}[/tex]
Plot the points (-2, 3) and (4, 0).
Draw a broken straight line through the points.
Shade below the line.
Question 5Given inequality:
[tex]2x+5y \leq 10[/tex]
a) As the "≤" sign has been used, the line will be a solid line.
b) Substitute (0, 0) into the inequality:
[tex]\begin{aligned}\textsf{When $x=0$ and $y=0$}: \quad 2(0)+5(0) &\leq 10\\0+0 &\leq 10\\0 &\leq 10\end{aligned}[/tex]
As zero is less than 10, the solution at (0, 0) is true.
Graphing the inequality
Change the inequality sign to an equals sign, then substitute two values of x into the equation and solve for y to find two points on the line:
[tex]\begin{aligned}x=-5: \quad 2(-5)+5y &=10\\-10+5y &=10\\5y &=20\\y&=4\end{aligned}[/tex]
[tex]\begin{aligned}x=5: \quad 2(5)+5y &=10\\10+5y &=10\\5y &=0\\y&=0\end{aligned}[/tex]
Plot the points (-5, 4) and (5, 0).
Draw a solid straight line through the points.
Shade below the line.
Tiffany’s allowance is reduced $1. 25 every time she forgets to clean her room. If she forgets to clean her room 7 times this month, by how much money is tiffany’s allowance reduced?.
The amount of money that is reduced from Tiffany's allowance is $8.75
The amount of allowance reduced every time she forget to clean her room = $1.25
Number of times that she forgets to clean her room = 7 times this month
The amount of money is reduced from Tiffany's allowance = Number of times that she forgets to clean her room × The amount of allowance reduced every time she forget to clean her room
Here we have to use the multiplication to find the amount
Substitute the values in the equation
The amount of money is reduced from Tiffany's allowance = 7 × 1.25
Multiply the terms
= $8.75
Hence, the amount of money that is reduced from Tiffany's allowance is $8.75
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an airplane flying at an elevation of 3,500 ft., directly above a straight highway. two motorists are driving cars on the highway on opposite sides of the plane. the angle of depression to one car is 31 degrees and to the other is 53 degrees. how far apart are the cars?
The first and second cars are 7724 feet apart from each other.
The angle of depression is the angle we have to move your eyes downwards to look at the car from the plane. Let's start with the first car, with the 31° angle of depression. Draw an upside-down right triangle with vertices at the plane, the car, and the point 3500 feet in the air above the car (level with the plane). The vertex at the plane is 31° and the right angle is the vertex in the air above the car. The length of the leg from the car to the point in the air above the car is 3500 feet. We like to find the length of the leg from the plane to the point in the air above the car. Since the two sides involved are the legs of the triangle, use tangent:
tan = opposite/ adjacent
⇒ tan(31°) = 3500/x
⇒ 0.60086 = 3500/x
⇒ 0.67 x = 3500 [ rounding up 0.60086 = 0.67]
⇒ x = 5223.88
That means the first car is 5223.88 feet from the point on the highway below the plane.
We can do something similar with the second car, which has an angle of depression of 53° from the plane. Again, the leg from the car to the point in the air above the car (level with the plane) is 3500 feet, the right angle is at the vertex at the point in the air above the car, and the 53° angle is at the vertex at the plane. We are looking for the length of the other leg, which runs from the plane to the point in the air above the car. Use tangent:
tan(53°) = 3500/x
⇒ 1.327 = 3500/x
⇒ 1.4x = 3500 [ rounding 1.327 = 1.4]
⇒ x = 3500/1.4
⇒ x = 2500
That means the second car is 2500 feet from the point on the highway below the plane.
Add the two distances together to get the total distance from car to car:
5223.88 + 2500.00 = 7723.88
So, rounded to the nearest foot, the cars are 7724 feet apart.
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fill in the table using this function rule y=-2x-5
For given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
In this question we have been given an equation y = -2x - 5
We need to complete the table using given function rule.
for x = -4,
y = -2(-4) - 5
y = 8 - 5
y = 3
for x = -2,
y = -2(-2) - 5
y = 4 - 5
y = -1
for x = 0,
y = -2(0) - 5
y = -5
for x = 2,
y = -2(2) - 5
y = -4 - 5
y = -9
Therefore, for given equation y = -2x - 5,
x y
-4 3
-2 -1
0 -5
2 -9
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Which function ha real zero at x = –8 and x = 5?
g(x) = x2 3x – 40
g(x) = x2 3x 40
g(x) = x2 14x – 40
g(x) = x2 14x 40
The function which has real zero at x = –8 and x = 5 is x² + 3x - 40
Given the real zeroes at x = -8 and x = 5.
Factor theorem states that (x-r) is a factor of the polynomial function f(x) if and only if r is a root of the function f(x).
Since, we know that the root of the function i.e g(x) are -8 and 5 then the function has the following factor:
(x+8) = 0 and (x-5) =0
Zero product property states that if ab = 0 if and only if a =0 and b =0.
By zero product property,
(x+8)(x-5) = 0
Now, distribute each terms of the first polynomial to every term of the second polynomial we get;
x(x - 5) + 8(x - 5)
Now, when you multiply two terms together you must multiply the coefficient (numbers) and add the exponent.
x² + 8x - 5x - 40
Combine like terms;
x² + 3x - 40
therefore, the function has real zeros at x = -8 and x =5 is x² + 3x - 40
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A student club plans to buy food for a soup kitchen. A case of vegetables coats $10.68. The club can spend at most $50 for this project. What are all the possible numbers of cases c that the club can buy?
Answer:
0,1,2,3,4
Step-by-step explanation:
[tex]\frac{50}{16.68}[/tex] = 4.68 rounded to the nearest hundredths.
Which graph represents a function with direct variation?
Graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
It is given that:
The graph is shown in the pictures
As we know,
The proportional relationship can be defined as:
y ∝ x
y = kx
k is the constant of proportionality:
y = kx is the equation of the line which passes through the origin.
Graph four passes through origin.
Thus, graph fourth represents a function with direct variation and the equation of the graph will be y = kx option (D) is correct.
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Write the equation of the line
that is perpendicular to y=-2x
and passes through (-2, -1)
A) y = 1/2x + 1
B) y = -3x - 7
C) y = -2x - 5
D) y = 1/2x
E) y = 1/2
Farmer joe separates his farm into 10 regions. He then randomly selected 5 trees from each region to estimate the number of apples produced on his apple tree farm. What type of sampling is this?.
it's a Stratified sampling
Given the exponential growth function †(x) = 75(1.0025)*
What is the initial value of the function?
What is the growth factor, or growth rate of the function (as a percent)?
The initial value of the function is 75.
The growth factor or growth rate of the function as a percent is 0.25%
An exponential growth model is defined as :
F(x) = A( 1 + r)^x
Where;
A = Initial amount,
r = rate of increase
x = time
Comparing the exponential growth function with the exponential growth model given;
f(x)=75(1.0025)ˣ
A = 75 = Initial amount
The growth rate of the model expressed as a percentage :
Taking :
(1 + r) = 1.0025
1 + r = 1.0025
r = 1.0025 - 1
r = 0.0025
Expressing r as a percentage:
r = 0.0025×100
= 0.25%
Hence we get the required answers.
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Distribute to create an equivalent expression with the fewest symbols possible.
4(x - 2 + y) =4(x−2+y)
The equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is 4(x - 2 + y). The equivalent expression will be solved as,
E = 4(x - 2 + y)
E = 4x - 8 + 4y
Therefore, the equivalent expression of the given expression 4(x - 2 + y) is 4x-8+4y.
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a raft left port a and traveled toward port b. at the same time, a motorboat left port b and traveled toward port a. how many hours after departure will the two meet if the raft travels the distance between ports a and b after 30 hours and the motorboat travels the same distance in 6 horus?
If the raft travels the distance between ports a and b after 30 hours and the motorboat travels the distance in 6 hours. After the departure the two boats will after 5 hours 4 minutes.
Given that,
After leaving the port,
Raft travels the distance between a and b ports = 30 hours
Motorboats travels the distance between a and b ports = 6 hours
The triangle formed by their tracks and the line joining their current positions in a right angled triangle.
According to the Pythagoras Theorem,
a² + b² = c²
⇒ (30)²+ (6)² = c²
⇒ 900 + 36 = c²
⇒ 936 = c²
⇒ c = √936
⇒ c = 30.59
Rounding up 30.59 in 30.6.
Therefore, the boats will the two meet by 30 hours and 6 minutes after they leave the port.
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write the percent 144 as a decimal
suppose that pulse rates among healthy adults are normally distributed with a mean of 80 beats/minute and a standard deviation of 10 beats/minute. what proportion of healthy adults have pulse rates that are more than 86 beats/minute? round your answer to at least four decimal places.
The Proportion of healthy adults have pulse rates that are more than 86 beats/minute is 27.42%
Z- Score gives an idea how far a data point is from mean .
z = x- μ / σ where numerator is difference between the random variable and the actual mean dividing by the standard deviation .
Given , mean = 80beats/minute
standard deviation = 10 beats/minute
x = 86 beats/minute
Applying z score formula :
z-score = (x-mean)/standard deviation
P(x>86) = P(z > 86-80/10)
=P(z>6/10)
=P(z>0.6) = 1 - P(z<0.6)
= 1 -0.7257
= 0.2742
Hence, the proportion of healthy adults have pulse rates that are more than 86 beats/minute is 0.2742
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Select the correct answer.
Solve the following equation by completing the square.
4z²-16z +8=0
O A z = 2 + √2 orz = 2-√2
OB.
z = 2 + √2 or z = − 2 + √2
z = −2+ √2 orz = -2-√2
z = 4 or z = 0
O C.
O. D.
Reset
Next
Step-by-step explanation:
4z-16z+8=0
[4×8]=32
factors of 32
1,2,4,8,....
The ratio of cats to dogs in a shelter is 3:8.
Check all statements that must be true based on the statement above.
If none of the statements is true, check "None of the above".
There are 8 cats to every 3 dogs in the shelter.
O For every 8 cats in the shelter, there are 3 dogs.
There are 3 dogs to every 8 cats in the shelter.
There are 8 dogs to every 3 cats in the shelter.
None of the above
Answer:
Step-by-step explanation:
no
I need help please!!!!!
HELP! I WILL NAME YOU THE BRAINLIEST. Solve the system by graphing.
y = x + 4
-x + y = -3
QUESTION 9/10 HELP ASAPP
Answer:
y = 3x + 8Step-by-step explanation:
GivenThe y-intercept b = 8,Slope m = 3.The equation is y = mx + by = 3x + 8Write a linear equation that has m=-4 and passes through (5,9)!
Answer:
[tex]y=-4x+29[/tex]
Step-by-step explanation:
Using point-slope form,
[tex]y-9=-4(x-5) \\ \\ y-9=-4x+20 \\ \\ y=-4x+29[/tex]
a college believes that 28% of applicants to that school have parents who have remarried. how large a sample is needed to estimate the true proportion of students who have parents who have remarried to within 6 percentage points with 95% confidence?
The sample size required for the true proportion of students who have parents who have remarried is 607.
What is termed the Confidence Interval?
The confidence interval is indeed the range of values within which you expect your forecast to fall a certain proportion of the time if you repeat your experiment or re-sample a population in the same manner.
The alpha value determines the confidence level, which is the percentage of times you anticipate reproducing an approximate between both the upper and lower limits of the confidence interval.
The above problem is based on the use of determining sample size to estimate the true percentage of students given the constraints.
We may also need to consult the table to determine the Z value.
For the given question,
α = 0.5
Consider the Z-table,
Zα/2 = Z (0.1/2)
Z (0.025) = 1.96
Let 'n' be the sample size required for the true proportion of students who have parents who have remarried.
For calculating the margin error 'E' is given 3%.
n = Z² (α/2) / E² × (P°(1 - P°))
Put the given values.
n = (1.96)² / (0.03)² × (0.28(1 - 0.28))
On solving,
n = 4268.444(0.2016)
n = 860.51
n ≈ 860.51
Thus, the sample size required for the true proportion of students who have parents who have remarried is 860.
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2) Ahmad had 15 coins in nickels and quarters. He knows he has a $2.95 in change. How many
quarters and nickels does he have?
Answer:
11 quarters and 4 nickels
Hope this helps! :3
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Jess has to spend 12000 on expenses each year. If that amount of money is 30 percent of her salary, then how much much does jess make as an administrador per year? Round your answer to the nearest whole number if necessary
Jess makes $40000 per year as an administrator .
What is an administrator?
Administrators support the efficient operation of offices by carrying out clerical jobs and initiatives. You can be planning project meetings in the construction business as an administrator.
Main Body:
Expenses incurred by Jess = $12000
According to the question , 30% of his annual salary is his expenses
Let his annual salary be x.
so,
⇒30% of x = 12000
⇒ (30/100)*x = 12000
⇒x = 12000*100/30
⇒x= 40000
Hence the salary made by Jess in a year is $40000.
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Find the value of 49^-1/2
Find the value of (27/125)^2/3
The value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
According to the question,
We have the following expressions:
[tex]49^{-1/2}[/tex]
Now, we will convert the base of these expressions in exponential form in such a way the denominator of powers will get divided:
[tex]7^{2*(-1/2)}[/tex]
[tex]7^{-1}[/tex]
Or it can be 1/7 because we have positive exponents.
Now, we have another expression:
[tex](\frac{27}{125}) ^{2/3}[/tex]
We will follow the same steps to solve this expression:
[tex](\frac{3}{5}) ^{3*2/3}[/tex]
[tex]\frac{3}{5} ^{2}[/tex]
Now, expanding the numerator and denominator of the fraction by multiplying them two times, we have the following fraction:
9/25
Hence, the value of [tex]49^{-1/2}[/tex] is 1/7 and the value of [tex](\frac{27}{125}) ^{2/3}[/tex] is 9/25.
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in a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green?
If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
In the question ,
it is given that ,
total numbers of car in the parking lot = 200 cars
number of white cars = 50
number of red cars = 30
number of silver cars = 20
let the number of green cars be "x" ,
So , the number of green cars possible = 200 - 100 = 100
that means x ≤ 100 .
So , P(green) = x/200
Option(a)
p = 0.2 ,
So , x/200 = 0.2
x = 40
Option(b)
p = 0.1 ,
So , x/200 = 0.1
x = 20
Option(c)
p = 0.6 ,
So , x/200 = 0.6
x = 120
Option(d)
p = 0.5 ,
So , x/200 = 0.5
x = 100 ,
We can see that only option(c) gives the number of green cars as 120 , which is not possible .
Therefore , If each car in the parking has only one color , then the option which cannot be the probability that the selected car will be green is 0.6 , the correct option is (c) .
The given question is incomplete , the complete question
In a parking lot with 200 cars, 50 cars are white, 30 cars are red, and 20 cars are silver. one car will be selected at random from the parking lot. if each car in the parking has only one color, which of the following cannot be the probability that the selected car will be green ?
(a) 0.2
(b) 0.1
(c) 0.6
(d) 0.5
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Please help! ASAP!! i really don't understand
Answer: B
Kyler earns more money in one week. Kyler earns $1,150 and Xiang earns $685 in one week.
Step-by-step explanation:
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