The Total outcome with replacement will be given by ,3² = 9, the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
What is Mean ?Mean predicts the central tendency of a data set , It is determined by the ratio of sum of all the numbers to the total numbers in the data set.
On the basis of given data
The number given is 2,4,7
Size of the sample = 2 with replacement
The Total outcome with replacement will be given by
3² = 9
Possible outcome can be
2,2 2,4 2,7 4,4 4,2 4,7 7,7 7,2 7,4
The sample mean can be calculated as
(a+b)/2
(2+2)/2 = 2
similarly the mean of the samples will be 2 , 4.5 , 3 , 7 , 4
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Giving a test to a group of students, the grades and gender are summarized below
Grades vs. Gender
A B C
Male 17 18 5
Female 12 3 14
If one student was chosen at random,
find the probability that the student was female.
Probability = (Round to 4 decimal places)
I will give lots of points please help
Answer:
a) 81π in³
b) 27 in³
c) divide the volume of the slice of cake by the volume of the whole cake
d) 10.6%
e) see explanation
Step-by-step explanation:
Part (a)The cake can be modeled as a cylinder with:
diameter = 9 inheight = 4 in[tex]\sf Radius=\dfrac{1}{2}diameter \implies r=4.5\:in[/tex]
[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]
[tex]\begin{aligned}\sf \implies \textsf{Volume of the cake} & =\pi (4.5)^2(4)\\ & = \sf \pi (20.25)(4)\\ & = \sf81 \pi \:\: in^3\end{aligned}[/tex]
Part (b)[tex]\begin{aligned}\textsf{Circumference of the cake} & = \sf \pi d\\& = \sf 9 \pi \:\:in\end{aligned}[/tex]
If each slice of cake has an arc length of 3 in, then the volume of each slice is 3/9π of the entire volume of the cake.
[tex]\begin{aligned}\implies \textsf{Volume of slice of cake} & = \sf \dfrac{3}{9 \pi} \times \textsf{volume of cake}\\\\& = \sf \dfrac{3}{9 \pi} \times 81 \pi\\\\& = \sf \dfrac{243 \pi}{9 \pi}\\\\& = \sf 27\:\:in^3\end{aligned}[/tex]
Part (c)The volume of each slice of cake is 27 in³.
The volume of the whole cake is 81π in³.
To calculate the probability that the first slice of cake will have the marble, divide the volume of a slice by the volume of the whole cake:
[tex]\begin{aligned}\implies \sf Probability & = \sf \dfrac{27}{81 \pi}\\\\& = \sf 0.1061032954...\\\\ & = \sf 10.6\% \:\:(1\:d.p.)\end{aligned}[/tex]
Part (d)Probability is approximately 10.6% (see above for calculation)
Part (e)If the four slices of cake are cut and passed out before anyone eats or looks for the marble, the probability of getting the marble is the same for everyone. If one slice of cake is cut and checked for the marble before the next slice is cut, the probability will increase as the volume of the entire cake decreases, until the marble is found. So it depends upon how the cake is cut and distributed as to whether Hattie's strategy makes sense.
As a unit price, a half-dozen for
$6.00 is
a. $36.00 each
b. $6.00 each
c. $0.50 each
d. $1.00 each
If you currently makes 425 What is the gross they will earn If they work every week If the year
They will earn If they work every week If the year is $22100.
We have given that,
you currently make 425
We have to determine what is the gross they will earn If they work a week If the year.
We know that
A worker currently makes $425 per week
How many weeks in a year?1year=52 weeks
So by proportion find the amount that the worker will earn in one year
[tex]\frac{425}{x}\times \frac{\$}{weeks}[/tex]
[tex]=\frac{x}{52}\times \frac{\$}{weeks}[/tex]
[tex]x=52\times 425[/tex]
x=22,100
Therefore, The answer is $22100.
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On December 13, 2007, one British pound was worth 2.04 U.S. dollars.
(a) On that date, how many pounds was 10.79 dollars worth?
Round your answer to the nearest hundredth of a pound.
pounds
(b) On that date, how many dollars was 178.98 pounds worth?
Round your answer to the nearest hundredth of a dollar.
dollars i need help with this problem.
Answer:
a) 5 pounds
b) 365 dollars
Which value is a solution to the inequality x – 4 > 15.5? A) x = 21.4 B) x = 17.3 C) x = 15.5 D) x = 19.3
Answer:
A.) x = 21.4
Step-by-step explanation:
When solving the inequality, you can treat the sign like an equal sign. To isolate the "x" variable, you can add "4" to both sides. This eliminates the -4 from the right side.
You are left with the inequality:
x > 19.5
If "x" must be greater than 19.5, the only answer that satisfies this is A.) x = 21.4. All of the other answers are less than 19.5.
[tex]\bf{x -4 > 15.5}[/tex]
[tex]\bf{Add \ 4 \ to \ both \ sides.}[/tex]
[tex]\bf{x-4+4 > 15.5+4 }[/tex]
[tex]\bf{x > 19.5 === > Answer }[/tex]
[tex]\red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]
What data collection
used in face-to-face
or written questionnaires?
method is
interview
O A. survey
O B. observation
O C. experiment
O D. publication
Answer:
survey (A)
A questionnaire (or someone asking questions) is considered to be a survey. It is "surveying" someone's opinion on data.
hope this helps!!
Determine the equation of the tangent line in both cases
1. x^2/x+2 at (2,1)
2. x^3+2y^2=10y at (2,1)
Differentiate the function/equation with respect to x and solve for the derivative, dy/dx. The value of dy/dx at the given point is the slope of the tangent line to the curve at that point. Then use the point-slope formula to get the equation of the tangent.
1.
[tex]y = \dfrac{x^2}{x+2} \implies \dfrac{dy}{dx} = \dfrac{2x\times(x+2) - x\times1}{(x+2)^2} = \dfrac{x(x+4)}{(x+2)^2}[/tex]
When x = 2, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{x=2} = \dfrac{2(2+4)}{(2+2)^2} = \dfrac34[/tex]
Then the equation of the tangent line at (2, 1) is
[tex]y - 1 = \dfrac34 (x - 2) \implies \boxed{y = \dfrac{3x}4 - \dfrac12}[/tex]
2.
[tex]x^3 + 2y^2 = 10y \implies 3x^2 + 4y \dfrac{dy}{dx} = 10 \dfrac{dy}{dx} \implies \dfrac{dy}{dx} = \dfrac{3x^2}{10-4y}[/tex]
When x = 2 and y = 1, the derivative is
[tex]\dfrac{dy}{dx}\bigg|_{(x,y)=(2,1)} = \dfrac{3\times2^2}{10-4\times1} = 2[/tex]
Then the tangent at (2, 1) has equation
[tex]y - 1 = 2 (x - 2) \implies \boxed{y = 2x - 3}[/tex]
Tìm số dư trong phép chia 3^{2020} chia cho 13
Your question translates to computing [tex]3^{2020} \pmod {13}[/tex].
Recall Euler's theorem: if [tex]\gcd(a,n)=1[/tex] (that is, [tex]a[/tex] and [tex]n[/tex] are relatively prime), then [tex]a^{\varphi(n)}\equiv1\pmod n[/tex], where [tex]\varphi(n)[/tex] denotes Euler's totient function, which counts the number of positive integers relatively prime to [tex]n[/tex].
Since 13 is prime, we have [tex]\phi(13)=12[/tex]. Then by Euler's theorem,
[tex]3^{12} \equiv 1 \pmod{13}[/tex]
Now, observe that 2020 = 168×12 + 4, so that
[tex]3^{2020} \equiv 3^{168\times12+4} \equiv \left(3^{12}\right)^{168} \times 3^4 \equiv 1^{168} \times 3^4 \equiv 3^4 \pmod{13}[/tex]
and since 3⁴ = 81 = 6×13 + 3, we end up with
[tex]3^{2020} \equiv 81 \equiv 3 \pmod{13}[/tex]
so the remainder upon dividing 3²⁰²⁰ by 13 is 3.
Solve, finding all solutions in [0, 2(pi)]
Answer:
x = π/12, 5π/12
Step-by-step explanation:
We can work this problem a couple of ways. We can convert it to single trig function, shifted horizontally. Or we can convert it to a double-angle equation.
__
horizontal shiftWe recall the sum of angles formula is ...
sin(x+y) = sin(x)cos(y) +cos(x)sin(y)
Using this, we can rewrite the left side of the equation using some angle offset y, and some scale factor k.
k·sin(x +y) = k·sin(y)·cos(x) +k·cos(y)·sin(x) = 2cos(x) +2sin(x)
finding the shift
Equating coefficients of cos(x) and sin(x), we can solve for k and y:
k·sin(y) = 2
k·cos(y) = 2
The ratio of these equations is ...
(k·sin(y))/(k·cos(y)) = 2/2
tan(y) = 1 ⇒ y = π/4
k = 2/sin(π/4) = 2√2
shifted equation
So, our original equation becomes ...
2√2·sin(x +π/4) = √6
Dividing by √2 and using the inverse sine function, we have ...
x +π/4 = arcsin((√3)/2) = π/2 ±π/6
x = π/4 ±π/6
x = π/12, 5π/12
__
double-angle equationIf we square both sides of the original equation, we get ...
(2sin(x) +2cos(x))² = (√6)²
4sin²(x) +8sin(x)cos(x) +4cos²(x) = 6
2sin(x)cos(x) = (6 -4)/4 = 1/2 . . . . use sin² +cos² = 1, subtract 4, divide by 4
Using the trig identity 2sin(x)cos(x) = sin(2x), we can find ...
2x = arcsin(1/2) = π/2 ±π/3 +2kπ . . . . k = an integer;
x = π/4 ±π/6 +kπ . . . . for integer k
x = {π/12, 5π/12, 13π/12, 17π/12}
We know that squaring the equation can introduce extraneous solutions, so we need to try these out. For x in the third quadrant, the sine and cosine values are both negative, so the only useful solutions here are ...
x = π/12, 5π/12
_____
Additional comment
Based on the above, we now know that any trig expression of the form ...
a·sin(x) +b·cos(x)
can be rewritten to the form ...
(√(a² +b²))·sin(x +arctan(b/a)) . . . . . a scaled and shifted sine function
The arctangent will have to take the signs of 'a' and 'b' into account in order to get the angle quadrant right.
Out of 310 racers who started the marathon, 289 completed the race, 18 gave up, and 3 were disqualified. What percentage did not complet
Answer:
7.1%
Step-by-step explanation:
Those that did not complete the race either gave up or were disqualified. This means that 18 + 3 = 22 people did not complete the race. The percentage is 22/310 × 100% = 7.1%
I really need help on this question. Im stuck any help?
Answer:
170
Step-by-step explanation:
[tex]x+40=210\\x=170[/tex]
If a number, x, is increased by 40 (+40) and is now equal to 210 (=210), then the number, x, is equal to 170.
Expression Math problem...help and get 15 pts!
When h = 0 , [f(x + h) - f(x)]/h = 2x +2 for the given expression.
The missing expression is f(x) = x² + 2x.
What is formula of difference quotient ?f(x+h)-f(x)/h is called the formula of difference quotient.
When h---> 0 ,
the expression f'(x) = (f(x-h) - f(x)) / h is the equation for tangent to the line
Here the the expression is
f(x) = x² + 2x
Determining f(x + h) by substituting x = x + h on both sides of the given f(x).
Then f(x + h) = (x + h)² + 2(x + h)
= x² + 2xh + h² + 2x + 2h
the difference f(x + h) - f(x).
f(x + h) - f(x) = [x² + 2xh + h² + 2x + 2h] - [x² + 2x]
= 2xh + h² + 2h
Divide the difference from h as in the formula of difference coefficient
[f(x + h) - f(x)]/h = (2xh + h² + 2h) / h
= 2x + h + 2
So, when h = 0 , [f(x + h) - f(x)]/h = 2x +2
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What is the solution to the linear equation?
-12 +3b-1-5-b
b=-2
b = -1.5
b = 1.5
b = 2
Answer:
[tex]b = 2[/tex]
Step-by-step explanation:
[tex]( - 12 - 1 - 5) + (3b - b) \\ - 18 + 2b \\ 2b - 18 \\ b = 2[/tex]
Select the correct answer from each drop-down menu.
Consider functions hand k.
h(t) = 5r2 – 1
k(x) = √5x + 1
For > 0, the value of h(k(x)) is
0, functions hand k
For
the value of k(h(r
inverse functions.
Answer:
h(t)= 5r2-1
That the answer for the question
Please answer the question down below!
Answer:
144°Step-by-step explanation:
regular decagon = all side equal and all angles congruent, so your answer is 144°
Skylar models the volume of a popcorn box as a right rectangular prism and the box can hold 69 cubic inches of popcorn when it is full. Its width is 33 in and its height is 5 3/4 in. Find the length of the popcorn box in inches. Round your answer to the nearest tenth if necessary.
Answer:
4/11 of an inch (about .4 of an inch)
Step-by-step explanation:
[tex]l \times 33 \times 5.75 = 69[/tex]
[tex]189.75l = 69[/tex]
[tex]l = \frac{69}{189.75} = \frac{4}{11} = .3636[/tex]
So the length of the popcorn box is 4/11 of an inch, or about .4 of an inch.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
In this graph, the number of containers is plotted along the x-axis and the amount of water in the containers is along the y-axis.
The proportionality constant of the graph (y to x) is
The constant of the proportional relationship graphed in this problem is of 10.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, the points on the graph are: (0,0), (2,20), (4,40), ..., hence the constant is:
k = 40/4 = 20/2 = 10.
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Considering only the values of β for which (1+cosβ)(1−cosβ)sinβ is defined, which of the following expressions is equivalent to (1+cosβ)(1−cosβ)sinβ?
Select the correct answer below:
sinβ
sin3β
secβ
1
sec2β
The following expressions (1+cosβ)(1−cosβ)sinβ is equivalent to sin³β
What are Trigonometric Ratios ?In a Right angled triangle , trigonometric ratios can be used to determine the value of angles and sides of the triangle.
The trigonometric expression given in the question is
(1+cosβ)(1−cosβ)sinβ
(a+b)(a-b) = a² - b²
( 1 - cos²β)sinβ
By the trigonometric Identity
1-cos²β = sin² β
sin² β x sin β
sin³β
Therefore Option B is the correct answer.
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Bacteria colonies can increase by 73%
every 2 days. If you start with 55 bacteria
microorganisms, how large would the
colony be after 10 days?
Future Amount = [?] microorganisms
←time
Hint: Future Amount = 1(1+r) periods
↑
initial growth
amount rate
Round to the nearest whole number.
The size of the colony after 10 days is 852.
What is the size of the colony after 10 days?The growth rate of the colony can be represented with an exponential equation with the form:
FV = P(1 + r)^n
Where:
p = present population r = rate of growth n = growth factor = 10 days / 2 days = 555(1.73)^5 = 852
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a u.s dollar bill remains in circulation about 1 1/4 years. A u.s coin is in circulation about 22 1/2 times longer. About how long is a coin circulation brainly
Answer:
28.125
Step-by-step explanation:
22.5×1.25=28.125
Answer:
28 1/8
Step-by-step explanation:
1.25 x 22.5 = 28.125
The graph of y=x^3 is transformed as shown in the graph below. Which equation represents the transformed function?
y = x^3 - 4
y = (x - 4)^3
y = (-x - 4)^3
y = (-x)^3 - 4
please help with this problem
thanks so much
Answer:
5/17
Step-by-step explanation:
If we do the multiplication first, we get:
[tex]\frac{4-(12\div-12)}{13+(-8\div-2)}[/tex]
If we do the division next, we get:
[tex]\frac{4+1}{13+4} = 5/17[/tex]
NEED HELP ASAP PLEASEE
Answer:
2nd one is the correct
Which of the following slopes of a line pass through points (1, -3) and (0, 2)?
m=5
m = -5
m = undefined
None of these choices are correct.
The slope of the line that passes through (1, -3) and (0, 2) is: B. m = -5.
What is the Slope of a Line?Slope (m) = rise / run = change in y / change in x.
Given the points, (1, -3) and (0, 2):
Slope (m) = (-3 - 2)/(1 - 0)
Slope (m) = -5/1
Slope (m) = -5
Therefore, the slope of the line is: B. m = -5.
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Last year over 10,000 students took an entrance exam at a certain state university. Ivanna's score was at the 36th percentile. Aldo's score was at the 19th percentile.
Ivanna's score was at the 36th percentile, will be 99.64 and Aldo's score was at the 19th percentile, will be 99.81.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
Last year, over 10,000 students took an entrance exam at a certain state university.
Let the maximum score be 100.
Ivanna's score was at the 36th percentile, will be
⇒ [(10,000 – 36) / 10,000] x 100
⇒ 99.64
Aldo's score was at the 19th percentile, will be
⇒ [(10,000 – 19) / 10,000] x 100
⇒ 99.81
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Figure ABCD is a rhombus. Find the value of x.
58°
x = [ ? ]°
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 32°[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Diagonals of a Rhombus bisect each other at 90°
[tex]\qquad \tt \rightarrow \: x + 58 + 90 = 180[/tex]
[ Sum of interior angles of a triangle ]
[tex]\qquad \tt \rightarrow \: x + 148 = 180[/tex]
[tex]\qquad \tt \rightarrow \: x = 180 - 148[/tex]
[tex]\qquad \tt \rightarrow \: x = 32 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The diagonals of the rhombus intersect at right angle. Then the value of x will be 32°.
What is a rectangle?It is a polygon with four sides. The total interior angle is 360 degrees. In a rhombus, opposite sides are parallel and equal.
Figure ABCD is a rhombus.
Its diagonals intersect at right angle.
Let the another angle be x. Then we have
x + 58° + 90° = 180°
x + 148° = 180°
x = 32°
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3. What are the roots of the polynomial y = x³ - 8?
Step-by-step explanation:
x^3 is a perfect cube, 8 is a perfect cube, so we use difference of cubes.
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
Cube root of x^3 is x.
Cube root of 8 is 2
So
a=x
b= 2.
[tex](x - 2)( {x}^{2} - 2x + 4)[/tex]
Set these equations equal to zero
[tex]x - 2 = 0[/tex]
[tex]x = 2[/tex]
[tex] {x}^{2} - 2x + 4 = 0[/tex]
If we do the discriminant, we get a negative answer so we would have two imaginary solutions,
Thus the only real root is 2.
If you want imaginary solutions, apply the quadratic formula.
[tex]1 + i \sqrt{ 3 } [/tex]
and
[tex]1 - i \sqrt{3} [/tex]
What to do when forget the pasword to the account?
Answer:
usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"
Given A(-2, 5) and B(13, -7), find the midpoint of AB.
Answer:
The mid-point is (9,-9/2)
Step-by-step explanation:
You would use the mid-point formula for this
[tex](\frac{x_{2} +x_{1} }{2} , \frac{y_{2}+y_{1} }{2} )[/tex]
if you plug that in it is ([tex]\frac{13-2}{2}, \frac{-7+5}{2}[/tex])
resulting in (11/2,-2/2) = (11/2,-1)