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A gardener makes a new circular flower bed. The bed is ten feet in diameter.Calculate the circumference and the area of the circular flower bed
Answer:
It will be 31.4 cm rounded off for circumference
It will be 78.53 cm2 rounded off for area
Step-by-step explanation:
Diameter = 10 cm
Radius = 10/2 cm = 5 cm
Circumference = 2×pi×radius
= 2pi×5
= 31.4 cm
Area = pi × r square
= 25 pi
= 78.53cm2
inverse of f(x)=e^(3x-1)
Answer:
f(x) = 3ex - e
Step-by-step explanation:
In this equation we have basically the times e by 3x and -1
so first let's do e times 3x
here...
e X 3x = 3ex
so let's rewrite the equation
3ex - 1
now we times e by 1. (Note - Negative sign stays)
3ex - 1e
we don't have to write 1e cause 1e = e, they are the same.
Therefore the answer is 3ex - 1e
Following are the calculation of inverse:
Given:
[tex]\to f(x)=e^{3x-1}[/tex]
To find:
inverse function=?
Solution:
A function g is the inverse of function F if for [tex]y=f(x), x=g(y)[/tex]
[tex]\to y=e^{3x-1}[/tex]
Replacing the value of x with y
[tex]\to x=e^{3y-1}[/tex]
Solve for [tex]y, x=e^{3y-1}[/tex]
Therefore, the answer is [tex]\frac{\log(x)+1}{3}[/tex].
Learn more about the inverse function:
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1/10
9/10
Q
Find the perimeter of the rectangle pictured above. Give your answer as a reduced mixed number.
Answer:2
Step-by-step explanation:
-p/3-8=3 what is the variable
Answer:
-33
Step-by-step explanation:
-p/3-8=3
or,(-p-24)/3=3
or,(-p-24)=9
or,-p=33
Therefore, p=-33
(x-1)(x-3)(x+5)(x+7)=297
First simplify the expression into polynomial form,
[tex](x-1)(x-3)(x+5)(x+7)=297[/tex]
[tex]x^4+8x^3-10x^2-104x+105=297[/tex]
[tex]x^4+8x^3-10x^2-104x-192=0[/tex]
Now factor into,
[tex](x-4)(x+8)(x^2+4x+6)=0[/tex]
Which means the solutions are,
[tex]x-4=0\implies\boxed{x_1=4}[/tex]
[tex]x+8=0\implies\boxed{x_2=-8}[/tex]
and then two complex solutions because determinant of the third factor [tex]D\lt0[/tex],
[tex]x^2+4x+6=0[/tex]
[tex]x^2+4x+4=-2[/tex]
[tex](x+2)^2=-2\implies\boxed{x_3=i\sqrt{2}-2},\boxed{x_4=-i\sqrt{2}-2}[/tex]
Hope this helps :)
Answer:
x=4
Step-by-step explanation:
(4-1)(4-3)(4+5)(4+7)=297
Identify the domain of the graph given below.
Answer:
(-∞,∞) is the domain.
2 is the range
Step-by-step explanation:
please help i need this by tonight
Answer:
The measure of ∠1 and ∠2 is 105° and 75° respectively
Step-by-step explanation:
In the given figure, line a is parallel to line b.
We need to find the measure of angles 1 and 2.
∠2 = 75° (because they form corresponding angles)
We know that, interior angles add up to 180. So,
∠1 +75 = 180
∠1 = 180-75
∠1 = 105°
So, the measure of ∠1 and ∠2 is 105° and 75° respectively.
What is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101 . . .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256 . . .?
Answer:
a.
[tex] \frac{36}{40} [/tex]
An investment of $8,120 is earning interest at the rate of 5.8% compounded quarterly over 11 years. How much
interest is earned on the investment? Show your work.
Answer:
5180.56 Dollars...........
The rate of change for yyy as a function of xxx is
, therefore the function is
.
For all values of xxx, the function value y\:yy
\:000.
The yyy-intercept of the graph is the function value y=\:y=y, equals
.
When x=1x=1x, equals, 1, the function value y=\:y=y, equals
.
everything seems to be correctly filled.
if you wanted confidence by confirmation: here, take some
It is an exponentially decaying function.
What is an exponential function ?An exponential function is where the independent variable is in the exponent. Generally the the independent variable is in the power of a constant term e.
Exponential functions are of two types one is exponentially growing function and exponentially decaying function.
when the we have a positive exponent the function is exponentially growing and when we have a negative exponent the function is exponentially decaying.
In the given question f(x) = 8e⁻ˣ
when, x = 0 f(x) = 8
f(x) = 8e⁻ˣ
f(0) = 8e⁰
f(0) = 8
Learn more about Exponential functions here :
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For the same random sample of adult women, with a sample mean height of x¯=64.3 inches and sample standard deviation of s=2.4 inches, use the Empirical Rule to determine the approximate percent of heights that lie between 59.5 inches and 69.1 inches.
Round your answer to the nearest whole number (percent).
Answer:
95%
Step-by-step explanation:
Mean , xbar = 64.3; standard deviation, s= 2.4
Using the empirical formula where ;
68% of the distribution is within 1 standard deviation from the mean ;
95% of the distribution is within 2 standard deviation from the mean
percent of heights that lie between 59.5 inches and 69.1 inches.
Number of standard deviations from the mean /
Z = (x - μ) / σ
(x - μ) / σ < Z < (x - μ) / σ
(59.5 - 64.3) / 2.4 < Z < (69.1 - 64.3) / 2.4
-2 < Z < 2
Thia is within 2 standard deviations of the means :
2 standard deviation form the mean = 95% according to the empirical rule.
Suppose a certain study reported that 27.7% of high school students smoke.
Random samples are selected from high school that has 632 students.
(i) If a random sample of 60 students is selected, what is the probability that
fewer than 19 of the students smoke?
(ii) If a random sample of 75 students is selected, what is the probability that
more than 17 of the students smoke?
The correct answer of the question is "0.7062" and "0.835". The further solution is provided below.
Given:
Probability of student smoke,
P = 27.7%
= 0.277
Number of students (n) = 632
[tex]q = 1-p[/tex]
[tex]=1-0.277[/tex]
[tex]=0.723[/tex]
(i)
Here,
Number of students (n) = 60
then,
⇒ [tex]n_P=60\times 0.277[/tex]
[tex]=16.62[/tex]
⇒ [tex]n_q=60\times 0.723[/tex]
[tex]=43.38[/tex]
We can see that [tex]n_P > 10[/tex] and [tex]n_q>10[/tex] so the normal approximation condition are met.
Now,
[tex]\mu = n_P= 16.62[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]= \sqrt{60\times 0.277\times 0.723}[/tex]
[tex]=3.9664[/tex]
Now,
⇒ [tex]P(X<19) = P(X<18.5)[/tex]
[tex]=P(Z_{18.5})[/tex]
The Z-score is:
= [tex]\frac{18.5-16.62}{3.4664}[/tex]
= [tex]0.5423[/tex]
hence,
The probability will be:
⇒ [tex]P(Z_{18.5}) = 0.7062[/tex]
or,
⇒ [tex]P(Z<19) = 0.7062[/tex]
(ii)
Here,
Number of students (n) = 75
[tex]\mu = n_P = 75\times 0.277[/tex]
[tex]=20.775[/tex]
[tex]\sigma = \sqrt{n_{Pq}}[/tex]
[tex]=\sqrt{75\times 0.277\times 0.723}[/tex]
[tex]=3.8756[/tex]
Now,
⇒ [tex]P(X>17) = P(X> 17.5)[/tex]
[tex]=1-P(X \leq 17.5)[/tex]
[tex]=1-P(Z_{17.5})[/tex]
The Z-score is:
= [tex]\frac{17.5-20.775}{3.8756}[/tex]
= [tex]-0.9740[/tex]
then, [tex]P(Z_{17.5}) = 0.165[/tex]
hence,
The probability will be:
⇒ [tex]P(X>17) = 1-0.165[/tex]
[tex]=0.835[/tex]
Learn more about Probability here:
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The two rectangles have the same perimeters, find the value of x.
Answer:
x = 8ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
Answer:
x=4
Step-by-step explanation:
2x-2+x+2x-2+x=3+7+3+7
6x-4=20
6x=24
x=4
double the sum of a number w and 3
Answer:
2(w+3)
Step-by-step explanation:
2(w+3) or 2w+6
(PLEASE ITS ACTUALLY MY LAST ONE HELP)
Which two figures represent circles of the same size?
A) D and G
B) C and G
C) none of them.
D) C and D
Answer:
B) C and G
Step-by-step explanation:
The radius is equal to 1/2 the diameter
r = 1/2 d
G has a diameter of 45
1/2 (45) = 22.5
C and G are the same
Answer:
c and g!
Step-by-step explanation:
The decimal for an irrational number never terminates or repeats. The
rational and irrational numbers together form the set of real numbers.
If false, explair:
Answer:
Step-by-step explanation:
No that is true. I can't make anything more out of it.
Find the dy/dx from
y=3×^2+5×^4 -10
Solve 2x2 – 3x = 12 using the quadratic formula.
Quadratic Formula: (-b +/- sqrt(b^2 - 4ac)) / 2a
2x^2 - 3x = 12
2x^2 - 3x - 12 = 0
a = 2
b = -3
c = -12
(--3 +/- sqrt( (-3)^2 - 4(2)(-12) )) / 2(2)
3 +/- sqrt( 9 + 96 ) / 4
3 +/- sqrt(105) / 4
Answers: [tex]\frac{3 + \sqrt{105} }{4}[/tex], [tex]\frac{3 - \sqrt{105} }{4}[/tex]
Hope this helps!
HaLP a beggar in need
Answer:
C) 2
Step-by-step explanation:
From the point (2,0), the next point on the graph is up 2, right 1, meaning that the slope is a positive 2.
Help. The graph shows the system of equations below.
2x -3y = -6
y = - 1/3x -4
9514 1404 393
Answer:
(a) The blue line ... solution ... (-6, -2)..
Step-by-step explanation:
The second equation describes a line with negative slope and a y-intercept of -4. This is clearly the red line on the graph.
The blue line represents the equation 2x -3y = -6.
The point of intersection of the two lines is (-6, -2), so that is the solution to the system of equations. This, by itself, is sufficient for you to choose the correct answer.
3. (02.01)
Solve for x:
wim
(x – 4) = 2x. (1 point)
2
-2
-8
-4
PLEASE HELP! 50 POINTS
Identify the intervals on which the function is increasing, decreasing or constant. Write your answers in interval notation. Write the end behavior for each function in limit notation.
f(x)=-4x^4+3x^3-2x^2+x-9
(Type a 0 before the decimal to hold the ones place for answers that don't have a value in the ones place. Ex. 0.24)
Use inf for infinity
6( n - 2) in word form please c:
Answer:
six in parenthesis n minus two
Step-by-step explanation:
2 ways could be:
A. N minus two then multiply by six
B. Six times parentheses n minus two end parentheses
The sum of two positive integers is 67. When the smaller integer is subtracted from twice the larger, the result is 38. Find the two integers.
Answer:
Step-by-step explanation:
x+y = 67
2x-y = 38
Add the equations together
3x = 108
x = 36
y = 67-x = 31
I need help please thank you
Answer:
A
Step-by-step explanation:
in the question given, the goal is to rationalize the denominator, or in other words get rid of any square roots.
recall this formula :
(a-b)(a+b) = a^2 - b^2
in this case, to rationalize the denominator of 3 - [tex]\sqrt{6x}[/tex] , we will multiply it and the numerator by its conjugate. the conjugate of 3 -
after multiplying the denominator by its conjugate, we get:
(3 - [tex]\sqrt{6x}[/tex]) (3 +
at this point there is no need to solve the numerator as there is only one answer with this denominator.
hope this helps :)
Answer:
Step-by-step explanation:
What effect will replacing x with (x - 4) have on the graph of the equation y = (x - 3) ^ 2
A. Slides the graph 4 units up
B. Slides the graph 7 units down
C. Slides the graph 4 units right
D. Slides the graph 1 units
Answer:
C)slides graph 4 units to the right
HELP! NO SCAMS PLZ, i need to know how to write the proportion.
Answer:
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
4+z/y = 36/18
Step-by-step explanation:
a) Since both triangles are similar triangles, then the ratio of their similar sides is equal to a constant k. Therefore:
16/4 = 18/y
Note that the arrangement depends on which of the triangles sides cones first.
Terry misappropriately represented the ratio on the left-hand side. Instead of 16/4, he wrote 4/16.
b) Same rule in (a) applies to the sum as well. Hence;
4+z/y = 16+20/18
4+z/y = 36/18
What is the purpose for post tests?
Answer:
The real reason of post test is to measure it's result in comparison to a pre test and determine d how much student has progressed over a term of instruction.
find the area of the semi circle plss
Answer:
Step-by-step explanation:
What should be subtracted from 13/(-56) to get 11/28
Answer:
-5/8
Step-by-step explanation:
13/ -56 -x = 11/28
Add 13/56 to each side
13/ -56 + 13/56 -x = 11/28+ 13/56
-x = 11/28 + 13/56
Get a common denominator
-x = 11/28 *2/2 +13/56
-x = 22/56 + 13/56
-x = 35/56
Divide top and bottom by 7
-x = 5/8
Multiply both side by -1
x = -5/8
