The circumference of a circle is given by the following formula
[tex]C=2\pi r[/tex]where r represents the radius.
The ratio between two circumferences is equal to the ratio of the radius.
[tex]\frac{C_1}{C_2}=\frac{2\pi r_1}{2\pi r_2}=\frac{r_1}{r_2}[/tex]The area of a circle is given by the following formula
[tex]A=\pi r^2[/tex]Then, the ratio between two circle areas is equal to the square of the ratio of the radius, which is the square of the ratio between the circumferences.
[tex]\frac{A_1}{A_2}=\frac{\pi r_1^2}{\pi r_2^2}=(\frac{r_1}{r_2})^2=(\frac{C_1}{C_2})^2[/tex]Then, applying this relation in our problem, the ratio between the areas is:
[tex]\frac{A_1}{A_2}=(\frac{30}{12})^2=\frac{25}{4}[/tex]The ratio between the areas is 25/4.
Algebra 1B CP find the zeros of the function by factoringexercise 2 please
2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
1) Factoring these quadratic functions we have:
2) y = 8x² +2x -15
Let's call u, and v two factors.
Multiplying 8 by -15 = we have u*v = -120 Adding u + v= 2, so u = 12 and v =-10
12 x -10 = -120
12 +(-10) = 2
So, now we can rewrite it following this formula:
(ax² + ux) +(vx +c)
(8x² +12x) +(-10x-15) Rewriting each binomial in a factored form
4x(2x +3) -5(2x+3)
(4x -5)(2x +3)
Equating each factor to zero to find out the roots:
(4x -5) =0
4x =5
x=5/4
(2x +3) = 0
2x = -3
x= -3/2
Hence, the solution set is S={-3/2, 5/4}
3) y= 4x² +20x +24
Proceeding similarly we have:
u * v = 96
u + v = 20
So u = 12, and v =8 12x 8 = 96 12 +8= 20
Rewriting into (ax²+ux)+(vx +c)
(4x²+12x) +(8x+24) Factoring out each binomial
4x(x+3) +8(x+3) As we have a repetition we can write:
(4x +8)(x +3)
3.2) Now to find out the roots equate each factor to zero, and solve it for x:
4x +8 = 0
4x = -8
x =-2
x+3 =0
x=-3
4) Hence, the answers are:
2) y = 8x² +2x -15
(4x -5)(2x +3)
S={-3/2, 5/4}
3) y= 4x² +20x +24
(4x +8)(x +3)
S={-2,3}
Can anybody help me out with this? I would really appreciate it! I don't need a huge explanation just the answer and a BRIEF explanation on how you got it.
The range of the following function is
[tex]\mleft\lbrace y>1\mright\rbrace[/tex]We can also call the range of a function an image, the range or image of a function is a set, we can see this set looking at the graph and see which values of y the function have, remember that we can have the same y value for different x value, looking at our graph we can see that this function comes from high y values, have a vertex on (3,1), in other words, it stops at y = 1 and then start growing again, and go on repeated values of y, then we can say that the image (values of y that the function assumes) is all values bigger than 1, therefore {y > 1}.
Hello I need help with this . Thanks ok ok
Answer:
The given graph is not a graph of a function because a vertical line can be drawn that will intersect this graph more than once.
Explanation:
A vertical line test is generally used to determine if a relation is a function or not by drawing a vertical line across the graph of the relation.
If the vertical line intersects the graph of the relation more than once, it means that the relation is not a function because one x-value will have more than one y-value.
If the vertical line intersects the graph just once, then we can say that the relation is a function since one x-value will be associated with only one y-value.
Looking at the given graph, we can see that a vertical line can be drawn across the graph that will intersect the graph more than once, therefore the given graph is not a graph of a function because a vertical line can be drawn that will intersect the graph more than once.
Laura needs summer blouses. She bought 1 blouseand 2 sweaters. How much did she spend? Did shebuy clothes that matched her summer needs?
Given:-
Cost of blouse is $27.50
Cost of sweater is $34.99
To find the cost if laura bought :-
So since laura bought one blouse and two sweaters, we get
[tex]27.50+2(34.99)=97.48[/tex]So the cost is $97.48 and she bought the cloths of her summer needs.
In a class of students, the following data table summarizes the gender of the studentsand whether they have an A in the class. What is the probability that a student whohas an A is a female?Female MaleHas an A24Does not have an A176
We are asked to find the probability that a student is female given that they have an A.
Since this is the case, we limit ourselves to observing the row "Has an A".
In said row, there is a total of 6 students who have an A. Out of those 6, 2 are female.
Thus, P(Female|A) = 2/6 = 1/3 = 33.33%.
Find the volume of the solid. Round your answer to the nearest hundredth. I keep getting the wrong answer. Need help!
Volume is area * height
area of pentagon is 1/4 * root(5(5 + 2root(5))) a^2
a being length of 1 side
if a =2, area is 6.88
6.88 * 4 = 27.52 yards^3
The transformation T-2,3 maps the point (7,2) onto the point whose coordinates are
we know that
the rule of the translation in this problem is 2 units at left and 3 units up
so
(x,y) ------> (x-2,y+3)
Apply the rule
(7,2) ------> (7-2,2+3)
(5,5)The function used to compute the probability of x successes in n trials, when the trials are dependent, is the _____. a.binomial probability functionb.Poisson probability functionc.hypergeometric probability functiond.exponential probability function
Given:
The function used to compute the probability of x successes in n trials, when the trials are dependent.
Required:
To choose the correct option for the given statement.
Explanation:
The hypergeometric distribution is a discrete probability distribution. It is used when you want to determine the probability of obtaining a certain number of successes without replacement from a specific sample size.
Therefore the option c is correct.
Final Answer:
c ) hypergeometric probability function.
Suppose that $6000 is placed in an account that pays 19% interest compounded each year. Assume that no withdrawals are made from the account.
We are going to use the formula for the compound interest, which is
[tex]A=P\cdot(1+\frac{r}{n})^{nt}[/tex]A = the future value of the investment
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per unit t
t = the time the money is invested or borrowed for
Replacing the values in the first question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=1 \\ A=6000\cdot(1+\frac{0.19}{1})^1=7140 \end{gathered}[/tex]Answer for the first question is : $7140
Then, replacing the values in the second question we have:
[tex]\begin{gathered} A=P\cdot(1+\frac{r}{n})^{nt} \\ A=6000,r=0.19,n=1,t=2 \\ A=6000\cdot(1+\frac{0.19}{1})^2=8497 \end{gathered}[/tex]Answer for the second question is : $8497
At the end of 2008, the number of text messages sent one month was
110.4 billion. If 270.3 million people used text messaging, about how
many did each person send that month? Round to the nearest whole
number.
The average number of text messages sent during the month by each person was 408.
What is the average?The average is the total number of a data set divided by the number of items on the data set.
The average is the same as the mean, which is a central value of a data set.
The total number of text messages sent in a month in 2008 = 110.4 billion
(110,400,000,000)
The total number of people using text messaging = 270.3 million (270,300,000)
Average text messages per person = 408. 44 (110,400,000,000/270,300,000)
Thus, we can conclude that, on average, each person in the population texted 408 messages per month in 2008.
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csc 0 (sin2 0 + cos2 0 tan 0)=sin 0 + cos 0= 1
Okay, here we have this:
Considering the provided expression, we are going to prove the identity, so we obtain the following:
[tex]\frac{csc\theta(sin^2\theta+cos^2\theta tan\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos^2\theta\frac{sin\theta}{cos\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{\frac{1}{sin\vartheta}(sin^2\theta+cos\text{ }\theta sin\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{(\frac{sin^2\theta}{sin\theta}+\frac{cos\text{ }\theta sin\theta}{sin\theta})}{sin\theta+cos\theta}=1[/tex][tex]\frac{(sin\text{ }\theta+cos\text{ }\theta)}{sin\theta+cos\theta}=1[/tex][tex]\frac{1}{1}=1[/tex][tex]1=1[/tex]You borrow $12,000 from your bank to help pay for some emergency home repairs.
.
This loan is paid back by making quarterly payments of $1100 for a total of 3 years.
.
What is total amount of interest paid on this loan?
The amount of interest paid is $21000
What is interest?
In finance and economics, interest is the payment of an amount over repayment of the principle sum (that is, the amount borrowed) by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate by a borrower or deposit-taking financial institution. It differs from a charge that the borrower may pay to the lender or a third party. Interest is also distinct from a dividend, which is given by a firm to its shareholders (owners) from its profit or reserve, but not at a fixed rate, but rather on a pro rata basis as a portion of the reward achieved by risk-taking entrepreneurs when revenue exceeds total expenditures.
Total amount paid = $11000x3 = $33000
Interest paid = $(33000-12000) = $21000
Hence, the amount of interest paid is $21000
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18 area = in. 114, 134, Jordan's game started at 6:05 pm. The game finished at 7:10 pm, and it took 20 minutor to got home what time did
Notice that the first term is 114 and the third term is 134, then, between the first and the third, there are 20 units of difference.
Then, the common difference between each term must be 10, thus, the complete sequence is:
[tex]114,124,134,144,154[/tex]What are the unknown angles?
The expression below is scientificnotation for what number? 4.58 • 10^-2
We are given the number in scientific notation:
[tex]4.58\times10^{-2}[/tex]To convert it to decimal format, we need to move the decimal point two spaces to the left.
Since we don't have enough digits before the decimal point, we add two zeros before the 4:
[tex]004.58\times10^{-2}[/tex]Now we move the point as required:
[tex]004.58\times10^{-2}=0.0458[/tex]The required number is 0.0458
How else can you write 6p in mathematic terms?
In mathematic terms, the expression 6p is written as 6 times p.
Mathematic terms
Mathematic terms means a single mathematical expression. The terms may be a single number, a single variable, several variables multiplied but never added or subtracted. Some of the terms contain variables with a number in front of them. Those number in front of a term is called a coefficient.
Given,
Here we have the expression 6p.
Now, we have to write it as a mathematic term.
While we looking into the expression 6p.
The only operation word in this expression is p which is multiplied with the constant that is the number 6.
So, in the verbal phrase it can be written as 6 times p.
Here p take any valid number in the real numbers.
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Use the point-slope formula to write an equation of the line that passes through (- 1, 4) and (1, 5 ) .Write the answer in slope-intercept form (if possible).The equation of the line is Hi everyone, this is very hard for me I have tried 18 times by myself before I found you folks .I need this in the simplest terms as i don't get it if it is too involved .
To solve this problem, we will compute the slope of the line and then we will use it to find the equation of the line.
To determine the slope of a line that passes through points (x₁,y₁), and (x₂,y₂), we can use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}.[/tex]Substituting
[tex]\begin{gathered} (x_2,y_2)=(-1,4), \\ (x_1,y_1)=(1,5), \end{gathered}[/tex]in the above formula, we get:
[tex]s=\frac{4-5}{-1-1}=\frac{-1}{-2}=\frac{1}{2}.[/tex]Now, with the above slope, we use the following formula for the equation of a line with slope m:
[tex]y-y_1=m(x-x_1).[/tex]Finally, we substitute one of the points:
[tex]y-5=\frac{1}{2}(x-1)[/tex]and take the equation to its slope-intercept form:
[tex]\begin{gathered} y-5=\frac{1}{2}(x-1), \\ y-5=\frac{1}{2}x-\frac{1}{2}, \\ y=\frac{1}{2}x+\frac{9}{2}. \end{gathered}[/tex]Answer: [tex]y=\frac{1}{2}x+\frac{9}{2}=0.5x+4.5.[/tex]find the rate of the discount of a $12 99 novel on sale for $5.50
In order to find the rate of discount, calculate what is the associated percentage of 5.50 related to 12.99, just as follow:
(5.50/12.99)(100) = 42.34
5.50 is the 42.34% of 12.99.
Hence, the discount was 100% - 42.34% = 57.65%
Find the slope and y intercept of the line 5x - 3y =12
Answer:
slope = 5/3
y-intercept = -4
Step-by-step explanation:
First, move the x to the other side of the equation:
-3y=-5x+12
Then, divide BOTH sides by -3, so that there is no coefficient next to y:
y=5/3x-4
Then, just look at the constant and coefficient next to x (m). The slope is 5/3 and the y-intercept is -4.
Hope this helps!
Answer:
[tex]y = \frac{5}{3}x - 4[/tex]
Step-by-step explanation:
move the 5x to a -5x
-3y= -5x+12
-3/-3= -5x÷ -3 12÷ -3
Find the value of 5y-7 given that -2y+1=3.Simplify your answer as much as possible.
-2y + 1 = 3
Solving for y:
Add 2y to both sides:
-2y + 1 +
one month Mark measure the rainfall each day the data is shown below which statement is true about the two sets of data
Given
Data from graph
Procedure
It is more likely to rain on the first 15 days of the month
5. Monty compared the minimum of the function f(x) = 2x2 - x + 6 to theminimum of the quadratic function that fits the values in the table below.X-3-2-101g(x)0-5-6-34What is the horizontal distance between the minimums of the twofunctions?A 0.25B. 1C. 1.5D. 12
The function f is given by:
[tex]\begin{gathered} f(x)=2x^2-x+6 \\ \text{ Rewrite the quadratic function in vertex form} \\ f(x)=2(x^2-\frac{1}{2}x)+6 \\ =2((x-\frac{1}{4})^2-(-\frac{1}{4})^2)+6 \\ =2(x-\frac{1}{4})^2-2(\frac{1}{16})+6 \\ =2(x-\frac{1}{4})^2+\frac{47}{8} \end{gathered}[/tex]If a quadratic function is written in the form:
[tex]\begin{gathered} a(x-h)^2+k \\ where: \\ a>0 \end{gathered}[/tex]Then the function has a minimum point at (h,k)
And the minimum is k
In this case,
[tex]\begin{gathered} a=2\gt0 \\ h=\frac{1}{4}=0.25 \\ k=\frac{47}{8}=5.875 \end{gathered}[/tex]Therefore, the minimum of the function f is at (0.25, 5.875)
The minimum of the function given by the table is at (-1, -6).
Therefore, the required horizontal distance is given by:
[tex]0.25-(-1)=1.25[/tex]Therefore, the horizontal distance is 1.25
I really need help with this can somebody help me ?
Answer
a. Vertical shrink by a factor of 1/3
Step-by-step explanation
Function transformation
• a,f(x) vertically compresses f(x) when 0 < a < 1
Given the function:
[tex]f(x)=x^2[/tex]Multiplying f(x) by a = 1/3, we get:
[tex]\frac{1}{3}f(x)=\frac{1}{3}x^2=h(x)[/tex]Then, f(x) is vertically shrunk by a factor of 1/3
Find the midpoint M of the line segment joining the points R = (-5. -9) and S = (1. -1).
Answer:
(-2,-5)
Step-by-step explanation:
(-5+1÷2, -9+(-1)÷2)
=(-4÷2, -10÷2)
=(-2,-5)
13(10+2) could be used to simplify which of the following problems?A 013/20)B O13(12)C 0130(26)
Explanation:
The expression is given below as
help meeeeeeeeee pleaseee !!!!!
The solution of the composition functions are represented as follows;
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3How to solve composite functions?Composite functions are when the output of one function is used as the input of another.
In other words, a composite function is generally a function that is written inside another function.
Therefore, the composite function can be solved as follows:
f(x) = √x
g(x) = - 2x + 3
Hence,
(fog)(x) = f(g(x)) = [tex]\sqrt{-2x+3}[/tex]
(g o f)(x) = g(f(x)) = - 2√x + 3 = -2√x + 3
Therefore, the composite function expression is as follows:
(fog)(x) = [tex]\sqrt{-2x+3}[/tex](g o f)(x) = -2√x + 3learn more on composite function here: https://brainly.com/question/24464747
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3)A space shuttle achieves orbit at 9:23am. At 9:31am it has traveled an additional 2309.6 miles in orbit. Find the rate of change in miles per minutes.
Answer: 288.7 miles per minute.
Step-by-step explanation:
Considering:
Distance = Rate / Time
We are given the distance as 2309.6 miles in orbit.
We can calculate the time required to travel 2309.6 miles by doing:
End time - Start time.
In this case it would be 9:31 - 9:23 = 8 minutes.
Therefore it takes 8 minutes to travel 2309.6 miles.
Now we need to find the Rate of Change in miles per minutes.
In other words we need how many miles the shuttle traveled every minute.
Right now we have the shuttle traveled 2309.6 miles in 8 minutes. To find how many traveled in 1 minute, we need to divide.
2309.6 / 8 = 288.7 miles per minute.
Identify the inverse g(x) of the given relation f(x). f(x)={(8,3),(0,-1),(-4,-3)}
The function is given as.
f(x)={(8,3),(4,1),(0,-1),(-4,-3) }
The inverse function is determined as a function, which can reverse into another function.
Therefore the inverse function g(x) is obtained as
[tex]g(x)=\lbrace(3,8),(1,4),(-1,0),(-3,-4)\rbrace[/tex]Hence the correct option is D.
Use the given information to select the factors of f(x).
ƒ(4) = 0
f(-1) = 0
f(³/²) = 0
options are:
(2x-3)
(2x+3)
(x-4)
(3x-2)
(x-1)
(x+4)
(3x+2)
(x+1)
The factors of f(x) are (x-4), (x+1) and (2x-3) respectively.
How to select the factors of f(x)To select the factors of f(x), we are to pick the functions that satisfy the conditions of the given information.
For f(4) = 0:
The function that evaluates to 0 when x = 4 is (x - 4). That is:
f(x) = (x - 4)
f(4) = (4 - 4) = 0
For f(-1) = 0:
The function that evaluates to 0 when x = -1 is (x + 1). That is:
f(x) = (x + 1)
f(-1) = (-1 + 1) = 0
For f(3/2) = 0:
The function that evaluates to 0 when x = 3/2 is (2x-3). That is:
f(x) = (2x-3)
f(3/2) = (2 × 3/2 - 3) = 0
Therefore, (x-4), (x+1) and (2x-3) are the corresponding factors of f(x)
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Can the numbers 12, 6, 6 be used to form the sides of a triangle? Why or why not?
Enter your answer and also a 2-3 sentence explanation that describes how you determined your answer.
Using the numbers 12, 6, 6, the triangle can not be formed.
The given numbers are 12, 6 and 6.
What is the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Here, 6 + 6 = 12 but not greater than 12
Therefore, using the numbers 12, 6, 6, the triangle can not be formed.
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