The radius of a circle is 10 cm. What is the approximate area of the circle? What is the exact area of the circle? Show your work.
First let's review the area formula for a circle.
Area=π\(r^2\)
Now that we know the radius, r is 10. The area is
10*10*π=100π
I will approximate π to 3.14 although you could do it more precise or less precise. The final answer will be 100*3.14=314 squared centimeter.
Any question you have about this just ask in the comment of this answer :)
Answer:
\(\large\boxed{\mathtt{Exact = 100 \pi \ cm^{2}}}\)
\(\large\boxed{\mathtt{Approximate: 314.16cm^{2}}}\)
Step-by-step explanation:
\(\textsf{We are asked to identify the area of the circle with the given radius.}\)
\(\large\underline{\textsf{What is the Radius?}}\)
\(\textsf{The \underline{Radius} is a straight \underline{line segment} that covers the distance to the \underline{center} of the}\)
\(\textsf{circle, to the \underline{circumference}.}\)
\(\large\underline{\textsf{What is the Formula for Area?}}\)
\(\textsf{The formula we use for area is;} \mathtt{ \ Area = \pi(radius)^{2}.}\)
\(\textsf{Pi is used to help equal out the ratio of the formula. Mainly, it's helpful to find the area.}\)
\(\textsf{Now that we have the Radius, we can begin solving.}\)
\(\Large\underline{\textsf{Substitute:}}\)
\(\mathtt{Area = \pi(10)^{2}}\)
\(\mathtt{Area = 100 \pi}\)
\(\textsf{For our answer,} \ 100 \pi \ \textsf{is the \underline{exact answer} for the area of this circle.}\)
\(\Large\underline{\textsf{Evalulate 100 pi:}}\)
\(\mathtt{Area = 100 \pi \approx 314.16cm^{2}}\)
\(\textsf{314.16cm is the approximate area of this circle.}\)
cuanto mide diametro si el radio es de 11 pulgadas? ;-;
Answer:
14 pulgadas
Step-by-step explanation:
a 7 pulgadas, entonces el diámetro es 2(7) = 14 pulgadas.
A 95% confidence interval for the population mean is constructed as 6 ± 2. What is the confidence coefficient?.
Confidence coefficient or confidence level for the interval is 0.95.
What is confidence coefficient?
The proportion of samples of a given size that may be anticipated to contain the true mean is all that the confidence coefficient is.
Confidence level:
Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.
For example,
A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.
Main Body :
Confidence Interval = 95%
Hence the confidence interval would be 0.95.
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Does this equation y=87.2/x represent a direct or inverse variation?
Answer:
Inverse relationship
Step-by-step explanation:
The equation we are looking at is;
y = 87.2/x
which implies xy = 87.2
If it was a direct relationship
y = constant * x
if it was inverse, it would have been
y * x = constant
since 87.2 is a constant, the question looks exactly like the second scenario.
This means that what we have is an inverse relationship
what is the value of 1 1/2 - 3/4
Answer:
It is 3/4
Step-by-step explanation:
You take the 3/4 out of the 1 and are left with 1/4 and then add that to the 1/2 and you get 3/4
f(x) = = -x + 9
g(x) = x2 - 6x + 9
What is the value of g(f(0))
=========================================================
Explanation:
f(x) = -x+9
f(0) = -0+9 .... replace x with 0
f(0) = 9
We will replace f(0) with 9 in the g(x) function. In other words, we plug in x = 9 into the g(x) function
This is because g( f(0) ) = g( 9 )
g(x) = x^2 - 6x + 9
g(9) = 9^2 - 6*9 + 9 ... replace x with 9
g(9) = 81 - 54 + 9
g(9) = 36
Therefore, g(f(0)) = g(9) = 36 or simply g(f(0)) = 36
-----------------------
Another method is to compute g(f(x)) algebraically first
g(x) = x^2 - 6x + 9
g(f(x)) = ( f(x) )^2 - 6*( f(x) ) + 9 .... replace every x with f(x)
g(f(x)) = ( -x+9 )^2 - 6*( -x+9 ) + 9 .... replace f(x) with -x+9
g(f(x)) = x^2 - 18x + 81 + 6x - 54 + 9
g(f(x)) = x^2 - 12x + 36
then we plug in x = 0
g(f(x)) = x^2 - 12x + 36
g(f(0)) = 0^2 - 12*0 + 36 ... replace x with 0
g(f(0)) = 36
which measure of variation is affected most by a few extreme scores? which measure of variation is affected most by a few extreme scores? standard deviation mode range median mean
Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.
The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.
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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the
highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure
of variation.
The measure of variation that is affected most by a few extreme scores is the standard deviation.
The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared
deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.
On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.
The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.
The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.
The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme
enough to change the position of the middle value.
The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less
pronounced than on the standard deviation.
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Find the inverse of the given function f(x)=-5x-9
Answer:
f-1(x)= x+9/-5
Step-by-step explanation:
1. To determine the inverse of the given function, first change f(x) to y. Then, switch x and y in the equation.
2. Now, solve the equation for y.
3. Finally, change y to f -1(x).
Work out x^2- 2x
when x =4
Answer:
8
Step-by-step explanation:
\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)
9.656 divided by 1,000
Answer:
0.00656
Step-by-step explanation:
5)Write an algebraic equation for each statement, and then SOLVE for x
The sum of a number and six is fourteen. __________________________
The quotient of fifteen and a number equals three. __________________________
The product of seven and a number equals fifty-six. __________________________
The difference between the square of a number four is twelve. __________________________
One quarter of a number is ten. __________________________
Three times a number decreased by nine equals eighteen. __________________________
Ten less than half a number equals fourteen. __________________________
A number divided by eight is nine. __________________________
The product of double a number and three equals twenty-four. __________________________
The product of twenty and a number equals one hundred and forty.
Answer:
Step-by-step explanation:
1. x+6=14
14-6=8
x=8
2. 15/x=3
15/3=x
x=5
3. 7*x=56
56/7=8
x=8
4. x^2-4=12
x=4, x=-4
5. 1/4x=10
x/4 = 10
x = 40
6. 3x-9=18
x=9
7. 1/2x-10=14
x/2-10=14
x=48
8.x/8=9
8*9=72
x=72
9.2x+3=24
2x=21
x=21/2
10.20*x=140
140/20=7
x=7
is 3 x 10 to the 5th power real, imaginary, rational, or irrational?
Answer:
real
Step-by-step explanation:
300000
whst is the answer to 3x – 11 =
The value of x in the expression 3x – 11 =0 is: x = 11/3.
Here, we have,
given that,
the expression is : 3x – 11 =0
now, we have to solve it for x.
so, we have,
3x – 11 =0
simplifying we get,
=> 3x=11
now, dividing both side by 3, we get,
=> 3x/3=11 /3
=>x=11/3
this is the answer in a fraction.
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complete question is:
what is the answer to 3x – 11 = 0, find the value of x.
Q1: Using MATLAB instruction: \[ z 1=[2+5 i 3+7 i ; 6+13 i 9+11 i], z 2=\left[\begin{array}{lll} 7+2 i & 6+8 i ; 4+4 s q r t(3) i & 6+s q r t(7) i \end{array}\right] \] i. Find z1z2 and display the re
Here is the answer to your question.Q1: Using MATLAB instruction:\(\[ z_1=[2+5 i 3+7 i ; 6+13 i 9+11 i], z_2=\left[\begin{array}{lll} 7+2 i & 6+8 i ; 4+4 s q r t(3) i & 6+s q r t(7) i \end{array}\right] \] i.\) Find z1z2 and display the result in rectangular form.
Since the sizes of z1 and z2 are compatible, we can multiply them. The MATLAB code for multiplying z1 and z2 is shown below:>>z1
=\([2+5i 3+7i; 6+13i 9+11i]; > > z2=[7+2i 6+8i; 4+4*sqrt(3)*i 6+sqrt(7)*i]; > > z1z2=z1*z2 The result of z1z2 is:z1z2\)
= -39.0000 + 189.0000i -50.0000 - 97.0000i -152.0000 - 50.0000i -42.0000 +154.0000iTo represent the result in rectangular form, we need to use the real() and imag() functions to get the real and imaginary parts of the product. .
Then, we can combine these parts using the complex() function to get the result in rectangular form. The MATLAB code for this is shown below:>>rectangular_result
= complex(real(z1z2), imag(z1z2))
= -39.0000 + 189.0000i -50.0000 - 97.0000i -152.0000 - 50.0000i -42.0000 +154.0000i
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I need help with this!And also can they play 6 levels during their free trial?
Answer: B and they can play 6 levels
Step-by-step explanation: first solve the mixed fractions
Then solve the factions
ill give brainliest to the first person who answers correctly
How many solutions does this equation have?
–5d + 6 = 6 − 5d
Answer:
Infinite
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
its 0 beacause there is no solution
I will give a Step by step solution to this equation
Let's solve your equation step-by-step.
−5d + 6 = 6 −5d
Step 1: Simplify both sides of the equation.
−5d + 6 = 6 −5d
−5d + 6 = 6 + −5d
−5d + 6 = −5d + 6
Step 2: Add 5d to both sides.
−5d + 6 + 5d = −5d + 6 + 5d
6 = 6
Step 3: Subtract 6 from both sides.
6 − 6 = 6 − 6
0 = 0
Answer:
0
help pls
this is the question
Answer:
x=2
Step-by-step explanation:
<=> 3x+12-2=16
<=> 3x+10=16
<=> 3x=6
<=> x=2
Antonio is ready to move out of his parent's house and live on his own. He found a great apartment that has all utilities included. His job as an assistant plumber requires him to have a car, but his hours are flexible enough to give him time on the weekends to have fun with his friends. What is the best way Antonio's budget can be modified to help him save enough for the $200 down payment and make the $500 monthly rental payment?
Monthly Budget
Old Budget
New Budget
Income
Wages
$1500
$1500
Expenses
Food
Cell Phone
Savings
Entertainment
Car Expenses
.
$250
$175
$200
$200
$300
.
$____
$____
$____
$____
$____
Net Income
$375
$____
a.
Antonio could keep his budget the same and hope he gets a raise at work.
b.
Antonio could reduce his monthly entertainment expenses by $100 to help pay the monthly rent. He could take $200 out of savings once for the deposit.
c.
Antonio could live at his parent’s house for one more month and save his net income. After one month of living at home, he would have enough additional money for the deposit and one year’s rent at the apartment.
d.
Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit.
Please select the best answer from the choices provided
A
B
C
D
The best way Antonio's budget can be modified to help him save enough is D. Antonio could reduce his monthly entertainment expenses by $75 and his food expenses by $50 to pay the monthly rent. He could take $200 out of savings once for the deposit
What is a budget?A budget is an estimate of revenue and expenses for a given period of time that is usually compiled and re-evaluated on a regular basis. A budget expresses intended expenditures as well as recommendations for how to meet them with resources.
Saving is the portion of one's income that is not spent on current expenses. In other words, it is money set aside for future use rather than being spent immediately. An expense is a cost incurred by businesses in the course of their operations. Wages, salaries, maintenance, rent, and depreciation are expenses.
In this case, the way to reduce the budget is illustrated.
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consider a symmetric matrix a. if the vector v is in the image of a and w is in the kernel of a, is v necessarily orthogonal to w?
Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A.
Yes, the vector v is necessarily orthogonal to w if v is in the image of the symmetric matrix A and w is in the kernel of A. This is due to the fact that for any symmetric matrix A, the image (column space) and kernel (null space) are orthogonal subspaces. Since v is in the image of A and w is in the kernel of A, their dot product must be zero, indicating orthogonality.
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maria and joan went shopping. maria bought 3 pair of jeans that each cost the same amount and 5 t-shirts that each cost the same amount. joan bought 4 pair of jeans that each cost the same amount, and 10 t-shirts that each cost the same amount. what is the cost of one pair of jeans and one t-shirt?
The cost of one pair of jeans and one t-shirt is the same for both Maria and Joan.
To determine the cost of one pair of jeans and one t-shirt, we need to first calculate the total cost of Maria's purchase. The cost of 3 pair of jeans is 3 times the cost of one pair of jeans. Similarly, the cost of 5 t-shirts is 5 times the cost of one t-shirt.
We then add the cost of the jeans and the cost of the t-shirts together to get the total cost of Maria's purchase. We do the same for Joan's purchase- calculate the cost of 4 pairs of jeans and 10 t-shirts, and add them together.
Since the cost of one pair of jeans and one t-shirt is the same for both Maria and Joan, we can subtract the total cost of Maria's purchase from the total cost of Joan's purchase and be left with the cost of one pair of jeans and one t-shirt.
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In 2017, 60 wild boars were released in the wild. By 2019, there were 88 boars. Knowing that boars reproduce exponentially, a) find the function modeling their growth and b) calculate the expected number of boars by 2020, assuming this patter holds. Round to two decimal places where needed.
a) The function modeling the growth of the wild boar population is given by: P(t) = 60 * e^(0.5 * t)
b) The expected number of boars by 2020 is approximately 268.90 (rounded to two decimal places).
a) To model the exponential growth of the wild boar population, we can use the general form of the exponential growth function:
P(t) = P₀ * e^(r * t)
where:
P(t) is the population size at time t
P₀ is the initial population size
r is the growth rate
t is the time elapsed
In this case, the initial population size in 2017 is P₀ = 60. We need to find the growth rate (r). Using the given information that the population increased from 60 to 88 over a span of 2 years (2017-2019), we can calculate the growth rate as follows:
88 = 60 * e^(r * 2)
Dividing both sides by 60:
88/60 = e^(2r)
Taking the natural logarithm (ln) of both sides:
ln(88/60) = 2r
Now we can solve for r:
r = ln(88/60) / 2
b) To calculate the expected number of boars by 2020, we need to substitute the obtained growth rate (r) and the corresponding time (t = 3 years) into the exponential growth function:
P(3) = 60 * e^(r * 3)
Using the calculated growth rate:
P(3) = 60 * e^(ln(88/60)/2 * 3)
) To calculate the expected number of boars by 2020 (which is 3 years after 2017), we substitute t = 3 into the exponential growth function:
P(3) = 60 * e^(0.5 * 3)
P(3) = 60 * e^1.5
P(3) ≈ 60 * 4.4817
P(3) ≈ 268.90
Therefore, the expected number of boars by 2020 is approximately 268.90 (rounded to two decimal places).
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you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable preliminary estimation for the population proportion. you would like to be 95% confident that you estimate is within 3% of the true population proportion. how large of a sample size is required?
Rounding up to the nearest whole number, the required sample size is approximately 8478.
To determine the required sample size to estimate a population proportion with a specified level of confidence and margin of error, we can use the formula:
\(n = (Z^2 * p * q) / (E^2)\)
where:
n = required sample size
Z = Z-score corresponding to the desired level of confidence (in this case, for a 95% confidence level, Z ≈ 1.96)
p = estimated population proportion (since we don't have a preliminary estimation, we can use p = 0.5 as it maximizes the sample size, making it more conservative)
q = 1 - p
E = desired margin of error (in this case, E = 0.03)
Plugging in the values into the formula:
\(n = (1.96^2 * 0.5 * 0.5) / (0.03^2)\)
n = (3.8416 * 0.25) / 0.0009
n ≈ 8477.44
Rounding up to the nearest whole number, the required sample size is approximately 8478.
Therefore, to be 95% confident that the estimate is within 3% of the true population proportion, a sample size of at least 8478 is required.
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Evaluate the expression using x=-1 and y=3 (6^4y^3)
The value of the expression when evaluated is: 162.
How to Evaluate an Expression?To evaluate the expression, 6x^4y^3, substitute x = -1 and y = 3 into the expression and solve.
6(-1^4) × 3^3
6(1) × 27
6 × 27
162
The value of the expression, 6x^4y^3, is: 162.
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WHY DOES NODBODY HELP ME PLZZ HELP
Answer: your answer is A.
From the graph, we can find the y-intercept, or where the line intercepts the y-axis, and the slope of the line to formulate our equation.
y-intercept = 3slope = -5With this information, we can write the equation of the line:
C. y = -5x + 3
*Note: the slope-intercept formula for a line is y = mx + b, where m is slope and b is the y-intercept.
In the above figure, m∠A = 30° and m∠B = (2x + 10)°. If angles A and B are complementary angles, what are the value of x and the measure of angle B?
A.
x = 55, m∠B = 60°
B.
x = 25, m∠B = 60°
C.
x = 70, m∠B = 150°
D.
x = 25, m∠B = 50°
Answer:
Step-by-step explanation:
option B
Complementary angles add up to 90°
m∠A + m∠B = 90
30 + 2x + 10 = 90
2x + 40 = 90
To find the value of x, we have to isolate x. To isolate x, first we have subtract 40 from both sides.
2x = 90 -40
2x = 50
Now, divide both sides by 2
x = 50/2
x = 25°
∠B = 2x + 10
= 2*25 + 10
= 50 + 10
∠B = 60°
what is the average student headcount for the spring terms of the $'02$-$'03$, $'03$-$'04$ and $'04$-$'05$ academic years? express your answer to the nearest whole number.
The average student headcount for the spring terms is: 10700
What is a graph with examples?A graph is a non-linear kind of data structure made up of nodes or vertices and edges. The edges connect any two nodes in the graph, and the nodes are also known as vertices. This graph has a set of vertices V= { 1,2,3,4,5} and a set of edges E= { (1,2),(1,3),(2,3),(2,4),(2,5),(3,5),(4,50 }.
We have the information:
From the graph,
Number of headcounts for spring '0.2 - 0.3' = 10900
Number of headcounts for spring '0.3 - 0.4' = 10500
Number of headcounts for spring '0.4 - 0.5' = 10700
The average student headcount for the spring terms is:
= 1/3 (10900 + 10500 + 10700)
= 10700
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For complete question, to see the attachment.
Please answer this question
Step-by-step explanation:
a ) 19 + 7 = 26
26 ÷ 2 = 13
13 - 5 = 8 ans
b) (19+7/2)-5
\(( \frac{19 + 7}{2} ) - 5\)
hope this answer helps you dear...
5p + 3 = 15
Write a situation that this equation could help you solve and explain how each part of the equation relates to the situation you create.
The given expression represents a number whose 5 times is 3 less than 15 which is 12/5.
Given that,
An expression is given we have to discuss what the expression 5p + 3 = 15 implies.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
Given expression,
5p + 3 = 15
5p = 15 - 3
p = 12 / 5
Thus, the given expression represents a number whose 5 times is 3 less than 15 which is 12/5.
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Lois made a dish with61/3 cups of pasta. One serving of the pasta is 0.2 cups. How many servings of pasta were in the dish Lois made?
A.
B.
C.
D.
The number of servings of pasta were in the dish Lois made is 31.67.
Unit valueNumber of cups of pasta Lois made = 6 1/3 cupsA serving of the pasta = 0.2 cupsNumber of servings of pasta were in the dish Lois made = Number of cups of pasta Lois made / A serving of the pasta
= 6 1/3 ÷ 0.2
= 19/3 ÷ 0.2
= 19/3 × 1/0.2
= (19×1) / (3 × 0.2)
= 19/0.6
= 31.6666666666666
Approximately,
Number of servings of pasta were in the dish Lois made is 31.67 servings
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What is necessary to determine the z-score for a raw score in a particular set of scores?.
Answer:
See below
Step-by-step explanation:
The mean score and the standard deviation are needed