Answer:
1. 100[tex]\pi[/tex]
2. 27 [tex]cm^{3}[/tex]
3. 30
Step-by-step explanation:
Area = [tex]\pi[/tex][tex]r^{2}[/tex]
= [tex]\pi[/tex] x [tex]10x^{2}[/tex]
= 100[tex]\pi[/tex]
Volume = l x w x h
= 3 x 3 x 3
= 27
Math Is TU parallel to VW explain
Answer: C ( yes, both lines have a slope of 2/3. )
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Set C is the set of two-digit even numbers greater than 34 that are divisible by 5
C=
Express (In 35+ln(1/7))/ In 25 in terms of In 5 and In 7
Properties of the logarithm: for any base of logarithm,
log(a*b) = log(a) + log(b)
If we replace b with 1/b, or b^-1, we have
log(a/b) = log(a) + log(1/b) = log(a) - log(b)
since
log(1/b) = log(b^-1) = - log(b)
using the power property of logarithms,
log(b^n) = n log(b)
Now,
ln35 = ln(5*7) = ln5 + ln7
ln(1/7) = - ln7
ln25 = ln(5^2) = 2 ln5
Putting everything together, we have
(ln35 + ln(1/7))/ln25 = (ln5 + ln7 - ln7)/(2 ln5) = ln5/(2 ln5) = 1/2
simplify : 3/5x+x , find the answer ?
Answer:
8x/5
There’s a 1 in front of the x also remember to always simplify
3/5x + 1x
Answer:8x/5
Step-by-step explanation:
Formula to find the number of subsets of a set that has "n" number of elements. 2 raise 1)to the nth power 2)n squared 3)2 times n 4)All of these
Answer:
(A)[tex]2^n[/tex]
Step-by-step explanation:
Given a set with "n" number of elements, the collection of all subsets of the set is referred to as the Power set of the given set.
To find the number of possible subsets of any set, we use the formula: [tex]2^n[/tex]
Take for example the set: A={2,3,4)
A has 3 elements, therefore n=3
The number of possible subsets of A is: [tex]2^3=8$ subsets[/tex]
A flexible cable always hangs in the shape of a catenary curve y = c + a cosh(x/a), where cand a are constants, a > 0. Suppose a telephone line hangs between two poles 18 meters apart, in the shape of the catenary y = 30 cosh(x/15) - 4, where x and y are measured in meters. a. (3 pts.) Find the slope of this curve where it meets the right pole. (Round to 3 decimal places.] b. (3 pts.) Find the angle between the line and the right pole. [Give your answer in degrees, rounded to the nearest hundredth.) Expert Answer
Answer:
The slope of this curve where it meets the right pole is 1.130
The angle between the line and the right pole is 41.51 °
Step-by-step explanation:
Given that ;
[tex]y = 30 \ cos h (\dfrac{x}{15} - 4)[/tex]
[tex]\dfrac{dy}{dx}= \dfrac{30}{15} sinh(\dfrac{x}{15})[/tex]
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{x}{15})[/tex]
x = 9 m;( i.e half of the distance of the two poles at 18 meters apart.
[tex]\dfrac{dy}{dx}=2 \ sinh(\dfrac{9}{15})[/tex]
= 1.130
The slope of this curve where it meets the right pole is 1.130
The angle between the line an the right rope can be determined by using the tangent of the slope .
tan ∝ = 1.130
∝ = tan⁻¹ (1.130)
∝ = 48.49°
The angle is θ; so
θ = 90 - ∝
θ = 90 - 48.49°
θ = 41.51 °
Thus; the angle between the line and the right pole is 41.51 °
The mean of 6 numbers is 32.If one of the numbers is excluded, the mean reduces by 2.Find the excluded number.
Answer:
42
Step-by-step explanation:
Mean = Sum of numbers/ Total numbers
Sum of 6 numbers = 32 x 6
= 192
If one number is excluded the mean reduce by 2 . so it becomes 30
Sum of 5 Numbers = 5 x 30
=150
Therefore the excluded number is
= 192 - 150
= 42.
To ______ a function, you need to stretch or compress it
Answer: It’s to change the shape of a function
Step-by-step explanation:
To change the shape of a function, you need to stretch or compress it.
How to stretch or compress a function?In math terms, you can stretch or compress a function horizontally by multiplying x by some number before any other operations. To stretch the function, multiply by a fraction between 0 and 1. To compress the function, multiply by some number greater than 1.
Is there a function for every shape?By definition, a function has one possible output for any given input. So if you want your function defined as some y=f(x), then not every shape can be written as a function. Any shape that has two points directly above each other (relative to the x-axis) cannot be written as a function, even a piecewise one.
Learn more about the shape of a function, here: https://brainly.com/question/1884491
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Find f(g(−1)), f(g(−1))=___
Answer:
Find g(f(−1)).
g(f(−1)) = 64
Find f(g(−1)).
f(g(−1)) = -6
f(g(−1)) is - 8.
What is a composite function ?A composite functions is a function where two or more than two functions are combined.The output of the previous function is the input of the next function.
According to the given question we have to find a composite function.
Assuming f(x) = x² + 9x and g(x) = x³.
To find f(g(-1)) first we have to put x = -1 for g(x) which is
= g(-1) = (-1)³ = -1.
Now we put this value of g(-1) in f(x).
∴ f(g(-1))
= f(-1)
= (-1)² + 9(-1)
= 1 - 9
= - 8.
learn more about composite functions here :
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A public relations firm found that only 27% of voters in a certain state are satisfied with their U.S. senators. How large a sample of voters should be drawn so that the sample proportion of voters who are satisfied with their senators is approximately normally distributed?a) 38b) 14c) 10d) 48
Answer:
a) 38
Step-by-step explanation:
The normal distribution can be applied if:
[tex]np \geq 5[/tex] and [tex]n(1-p) \geq 5[/tex]
In this question:
[tex]p = 0.27[/tex]
Then
a) 38
n = 38.
Then
38*0.27 = 10.26
38*0.73 = 27.74
Satisfies. But is this the smallest sample of the options which satisfies.
b) 14
n = 14
Then
14*0.23 = 3.22
14*0.77 = 10.78
Does not satisfy
c) 10
Smaller than 14, which also does not satisfy, so 10 does not satisfy.
d) 48
Greater than 38, which already satisfies. So the answer is a)
my last question and im done, please help!
Answer:
2 acute and one right.
Step-by-step explanation:
plz mark brainliest!
Answer:
2 acute 1 right, you asked for ASAP so theres no explanation
You cant mix right and obtuse, and you cant have more than 1 obtuse in a triangle. There has to be at least 2 acute angles.
In a random sample of six cell phones, the mean full retail price was $538.00 and the standard deviation was $184.00. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 90% confidence interval for the population mean mu. Interpret the results. Identify the margin of error. Construct a 90% confidence interval for the population mean. Interpret the results. Select the correct choice below and fill in the answer box to complete your choice.
Answer:
The margin of error is 370.8.
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
90% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.0150
The margin of error is:
M = T*s = 2.0150*184 = 370.8.
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 538 - 370.8 = $167.2
The upper end of the interval is the sample mean added to M. So it is 538 + 370.8 = $908.8
The 90% confidence interval for the population mean is between $167.2 and $908.8
The correct interpretation is that we are 90% sure that the true mean price for all cellphones in within the interval end-points, so option B.
Express the following in usual form
Answer:
52300
Step-by-step explanation:
When you multiply by ten the decimal dot moves one space to the right, so here you multiply by ten four times, so you move the dot four spaces to the right and you get 52300
What is the volume of a cone with a height of 27 cm
and a radius of 13 cm? Round your answer to the
nearest tenth.
V=
Answer: V=4778.4 cm³
Step-by-step explanation:
[tex]V=\pi r^2\frac{h}{3}[/tex] is the formula for volume. Since we are given the height and radius, we can directly plug it into the equation
[tex]V=\pi (13)^2(\frac{27}{3})[/tex]
[tex]V=169\pi (9)[/tex]
[tex]V=1521\pi[/tex]
[tex]V=4778.4cm^3[/tex]
Aakash has a liability of 6000 due in four years. This liability will be met with payments of A in two years and B in six years. Aakash is employing a full immunization strategy using an annual effective interest rate of 5%.Calculate |A-B|
Answer:
|A-B|= 586.411565Step-by-step explanation:
We know that = Liability
[tex]PLiability= \frac{6000}{1.05^{4} }[/tex]
[tex]\frac{6000}{1.05^{4} }=\frac{A}{1.05^{2} }+\frac{B}{1.05^{6} }\\\\6000(1.05^{2} ) = (1.05^{4} ) +B\\B= 6000(1.05^{2} )-(1.05^{4} )----------(1)\\\\[/tex]
dAssets =dLiability
[tex]4=2*\frac{\frac{A}{1.05^2} }{\frac{6000}{1.05^4} } +6*\frac{\frac{B}{1.05^6} }{\frac{6000}{1.05^4} } \\4={\frac{6000}{1.05^4}= 2*\frac{A}{1.05^2} +6*\frac{B}{1.05^6}\\\\4[6000(1.05^2)]= 2*A(1.05^4)+6*B[/tex]
From equation 1 we have
[tex]4[6000(1.05^2)]= 2*A(1.05^4)+6*6000(1.05^2)-6*A(1.05^4)\\4*A(1.05^4)=2*6000(1.05^2)\\A=\frac{2*6000(1.05^2)}{4*(1.05^4)} \\A=272.088435\\[/tex]
Going back to equation 1 we have
[tex]B= 6000(1.05^2)-A(1.05^4)\\B= 3307.5\\|A-B|= |2721.088435-3307.5|= 586.411565[/tex]
If Romeo earns 8% more than Juliet, Romeo’s salary is how many times Juliets salary?
A) 1.08
B) 0.92
C) 80
D) 108
Answer:
1.08
Step-by-step explanation:
If Romeo earns 8% more than Juliet,
Example?
If Juliet earns $80
80x8% = 6.40 So his pay would be 80 + 6.40
If you times 80 by 1.08 (this would also be 108%) you would get $86.40
How do you solve this?
Answer:
.75 teaspoons per ounce
Step-by-step explanation:
Take the number of teaspoons and divide by the number of ounces
10.5 / 14
.75 teaspoons per ounce
What is the simplified value of the exponential expression 27 1/3
1/3
1/9
3
9
Answer:
I think its 1/9
Answer:
B
Step-by-step explanation:
Which ordered pair is a solution of the equation? y=-6x+1y=−6x+1y, equals, minus, 6, x, plus, 1 Choose 1 answer: Choose 1 answer:Only (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis (Choice B) B Only (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice C) C Both (-2,13)(−2,13)left parenthesis, minus, 2, comma, 13, right parenthesis and (-1,7)(−1,7)left parenthesis, minus, 1, comma, 7, right parenthesis (Choice D) D Neither
Answer:
C Both (-2,13) and (-1,7)
Step-by-step explanation:
Try the offered points in the equation and see if they work
y = -6x +1
For (-2, 13):
13 = -6(-2) +1 = 12 +1 . . . . true
For (-1. 7):
7 = -6(-1) +1 = 6 +1 . . . . true
Both ordered pairs are solutions.
Isaac is a professional swimmer who trains, in part, by running. She would like to
estimate the average number of miles she runs in each week. For a random sample
of 20 weeks, the mean is
x
= 17.5 miles with standard deviation s = 3.8 miles. Find
a 99% confidence interval for the population mean number of weekly miles Isaac runs.
(a) 15.01 to 19.99 miles (b) 15.07 to 19.93 miles
(c) 15.34 to 19.66 miles (d) 15.31 to 19.69 miles
(e) 15.08 to 19.92 miles
Answer: (b) 15.07 to 19.93 miles
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 3.8
n = number of samples = 20
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 20 - 1 = 19
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.02/2 = 0.005
the area to the right of z0.005 is 0.025 and the area to the left of z0.025 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.861
Margin of error = 2.861 × 3.8/√20
= 2.43
the lower limit of this confidence interval is
17.5 - 2.43 = 15.07 miles
the upper limit of this confidence interval is
17.5 + 2.43 = 19.93 miles
5.2 times a number is 46.8
Answer:
9
Step-by-step explanation:
"5.2 times a number is 46.8" as an equation is:
[tex]5.2*n=46.8[/tex]
Solve for 'n':
[tex]5.2*n=46.8\\5.2/5.2*n=46.8/5.2 \leftarrow \text {Division Property of Equality} \\\boxed {n=9}[/tex]
What is the result of adding these two equations? 2x+3y=-5 5x-y=-12
Answer:
[tex]x = \frac{-41}{17} , y = \frac{-1}{17}[/tex]
Step-by-step explanation:
Step(i):-
Given equations are 2 x+3 y=-5 ...(i)
5 x-y=-12 ...(ii)
Multiply equation (ii) by '3'
2 x + 3 y = -5
15 x - 3 y = - 36
17 x = - 41
[tex]x = \frac{-41}{17}[/tex]
Step(ii):-
Substitute [tex]x = \frac{-41}{17}[/tex] in equation (i)
2 ([tex]\frac{-41}{17}[/tex]+3 y=-5
3 y = - 5 + [tex]\frac{82}{17}[/tex]
[tex]3 y = \frac{-85 + 82}{17} = \frac{-3}{17}[/tex]
[tex]y = \frac{-1}{17}[/tex]
The solution of the two equations
( x, y ) = [tex](\frac{-41}{17} , \frac{-1}{17})[/tex]
At a football game, a vender sold a combined total of 152 sodas and hot dogs. The number of sodas sold was three times the number of hot dogs sold. Find the number of sodas and the number of hot dogs sold.
Answer:
38 hot dogs114 sodasStep-by-step explanation:
Sometimes problems of this nature are easily worked by considering groups of items. Here, it is convenient to consider a group as 1 hot dog and 3 sodas, so the number of sodas in the group is 3 times the number of hotdogs in the group.
Each group is 4 items, so 152/4 = 38 groups were sold.
In the 38 groups, there were 38 hot dogs and 3×38 = 114 sodas.
114 sodas and 38 hot dogs were sold.
128 less than a number is 452
Answer:
580
Step-by-step explanation:
"128 less than a number is 452" is represented by:
n - 128 = 452
Solve for 'n':
n - 128 + 128 = 452 + 128 (Addition Property of Equality)
n = 580
NEED GEOMETRY HELP ASAP PLEASE (11 POINTS)
Answer:
d = 2[tex]\sqrt{17}[/tex]
Step-by-step explanation:
P1 (-5, 4) P2 (-3, -4)
Use the distance formula: d = [tex]\sqrt{(x2 - x1)^{2} + (y2 - y1)^{2} }[/tex]
Plug in the values and simplify
d = [tex]\sqrt{(-3 + 5)^{2} + (-4 -4)^{2} }[/tex]
d = [tex]\sqrt{(2)^{2} + (-8)^{2} }[/tex]
d = [tex]\sqrt{4 + 64 }[/tex]
d = [tex]\sqrt{68}[/tex]
d = 2[tex]\sqrt{17}[/tex]
I hope this helps :)
HELP PLEASE!!
NEED ANSWER ASAP!!!
A farmer in China discovers a mammal
hide that contains 54% of its original
Find age of the mammal hide to the nearest year.
amount of C-14
N=N0e^-kt
N = Noe
No = inital amount of C-14 (at time t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Answer:
6163.2 years
Step-by-step explanation:
A_t=A_0e^{-kt}
Where
A_t=Amount of C 14 after “t” year
A_0= Initial Amount
t= No. of years
k=constant
In our problem we are given that A_t is 54% that is if A_0=1 , A_t=0.54
Also , k=0.0001
We have to find t=?
Let us substitute these values in the formula
0.54=1* e^{-0.0001t}
Taking log on both sides to the base 10 we get
log 0.54=log e^{-0.0001t}
-0.267606 = -0.0001t*log e
-0.267606 = -0.0001t*0.4342
t=\frac{-0.267606}{-0.0001*0.4342}
t=6163.20
t=6163.20 years
PLEASE MARK BRAINLY
Which expression would be easier to simplify if you used the associative
property to change the grouping?
A. 0.85+ (0.15 +(-3)
B. [(-3)+(-3)] +(-3)
C. (160 + 40 + 27
O D. 1+*+(-))
SUBMIT
P
Answer:
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
Step-by-step explanation:
Explanation:-
Associative property with addition
(a+(b+c)) = (a+b) + c
A)
Given 0.85 + (0.15 +(-3)) = (0.85 +0.15)+(-3)
= 1 - 3
= -2
B) Given [(-3)+(-3)]+(-3) = ( (-3)+[( -3)+(-3))]
= ( -3 +[-3-3]
= -3 -6
= -9
Final answer:-
A . 0.85 + (0.15 +(-3)) = -2
B . [(-3)+(-3)]+(-3) = - 9
Define a function sinc(x) (pronounced "sink of x") by: text(sinc)(x)={(sin(x)/x text(if)\ x != 0, 1 text(if)\ x = 0.) (This function is used frequently in electrical engineering and signal processing.) Use this list of Basic Taylor Series to find the Taylor Series for f(x) = sinc(x) based at 0. Give your answer using summation notation and give the largest open interval on which the series converges. (If you need to enter [infinity] , use the [infinity] button in CalcPad or type "infinity" in all lower-case.)
Answer:
Step-by-step explanation:
To find the Taylor series of sinc(x) we will use the taylor series of sin(x). We have that
[tex]\sin(x) = \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n+1}}{(2n+1)!}[/tex]
which is the taylor series expansion based at 0. Then for [tex]x\neq 0[/tex], by dividing both sidex by x, we have that
[tex]\text{sinc}(x) = \frac{\sin(x)}{x}= \sum_{n=0}^{\infty}\frac{(-1)^n x^{2n}}{(2n+1)!}[/tex]
which is the taylor series expansion for the sinc function. Since the series of sine converges for every value of x. Then the taylor series of sinc converges for every value of x, but 0.
If sin(θ -π/2) = 0.73.. find cos (-θ) plz explain how to solve
Answer:
[tex]cos(-\theta) = -0.73[/tex]
Step-by-step explanation:
It is given that:
[tex]sin(\theta -\dfrac{\pi}{2}) = 0.73[/tex]
Formula to be used:
[tex]1.\ sin(-x) = -sinx\\2.\ sin(\dfrac{\pi}{2}-x) = cosx\\3.\ cos(-x) = cosx[/tex]
Using Formula (1) written above:
[tex]\Rightarrow sin (\theta - \dfrac{\pi}{2})=sin(-(\dfrac{\pi}{2}-\theta ))\\\Rightarrow -sin(\dfrac{\pi}{2}-\theta)[/tex]
Now, using Formula (2) written above:
[tex]\Rightarrow -sin(\dfrac{\pi}{2}-\theta) = -cos \theta[/tex]
So, we can say that:
[tex]sin(\theta -\dfrac{\pi}{2}) = -cos\theta = 0.73 ...... (1)[/tex]
We have to find the value of [tex]cos(-\theta)[/tex].
Using Formula (3) written above:
[tex]cos(-\theta) = cos\theta[/tex]
So, ultimately we need to find the value of [tex]cos\theta[/tex]
Using equation (1):
[tex]-cos\theta = 0.73\\\Rightarrow cos\theta = -0.73[/tex]
So, the answer is [tex]cos(-\theta) = -0.73[/tex].
please very soon I offer the crown !!! + 10 points urgently !!!
Answer:
a. 3
b. 5
c. 4
d. 4
e. 10
Step-by-step explanation:
Answer:
read below
Step-by-step explanation:
a.3
b.5
c.2
d.2
6. 8p
