) A random sample of size 36 is selected from a normally distributed population with a mean of 16 and a standard deviation of 3. What is the probability that the sample mean is somewhere between 15.8 and 16.2
Answer:
The probability is 0.31084
Step-by-step explanation:
We can calculate this probability using the z-score route.
Mathematically;
z = (x-mean)/SD/√n
Where the mean = 16, SD = 3 and n = 36
For 15.8, we have;
z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4
For 16.2, we have
z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4
So the probability we want to calculate is;
P(-0.4<z<0.4)
We can get this using the standard normal distribution table;
So we have;
P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)
= 0.31084
A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Answer:
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Step-by-step explanation:
Given
[tex]Sections = 10[/tex]
[tex]n(Gray) = 5[/tex]
[tex]n(Blue) = 5[/tex]
Required
Determine P(Gray and Blue)
Using probability formula;
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
Calculating P(Gray)
[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]
[tex]P(Gray) = \frac{5}{10}[/tex]
[tex]P(Gray) = \frac{1}{2}[/tex]
Calculating P(Gray)
[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]
[tex]P(Blue) = \frac{5}{10}[/tex]
[tex]P(Blue) = \frac{1}{2}[/tex]
Substitute these values on the given formula
[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]
[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]
Question 36 of 40
The distance of a line bound by two points is defined as
L?
O A. a line segment
B. a ray
O
c. a plane
O D. a vertex
SUBMI
Answer:
A. a line segment
Step-by-step explanation:
a ray is directing in one dxn, and has no end pointa plane is a closed, so more than 2 points a vertex is a single point itself6(x + 2) = 30Solve the following linear equation
Answer:
[tex]\huge \boxed{x=3}[/tex]
Step-by-step explanation:
[tex]6(x+2)=30[/tex]
[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]
[tex]x+2=5[/tex]
[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]
[tex]x=3[/tex]
Answer:
3
Step-by-step explanation:
30 = 6(x+2)
30/6 = 5
5 = x+2
5-2 = 3
3=x
This is a pretty simple question and I tried to make it as simple as possible when explaining it.
The cost of performance tickets and beverages for a family of four can be modeled using the equation 4x+12=48,where x represents the cost of a. Ticket.how much is one ticket
Answer:
x=9; one ticket is $9
Step-by-step explanation:
4x+12=48
4x=48-12
4x=36
x=36/4
x=9
The coffee cups can hold 7/9 of a pint of liquid. If Emily pours 2/3 of a pint of coffee into a cup,how much milk can a customer add? PLZ HELP!
Answer:
1/9
Step-by-step explanation:
easy 2/3 is equivalent to 6/9. So there is 1/9 of a pint left
The radius of a sphere is measured as 7 centimeters, with a possible error of 0.025 centimeter.
Required:
a. Use differentials to approximate the possible propagated error, in cm3, in computing the volume of the sphere.
b. Use differentials to approximate the possible propagated error in computing the surface area of the sphere.
c. Approximate the percent errors in parts (a) and (b).
Answer:
a) dV(s) = 15,386 cm³
b) dS(s) = 4,396 cm²
c) dV(s)/V(s) = 1,07 % and dS(s)/ S(s) = 0,71 %
Step-by-step explanation:
a) The volume of the sphere is
V(s) = (4/3)*π*x³ where x is the radius
Taking derivatives on both sides of the equation we get:
dV(s)/ dr = 4*π*x² or
dV(s) = 4*π*x² *dr
the possible propagated error in cm³ in computing the volume of the sphere is:
dV(s) = 4*3,14*(7)²*(0,025)
dV(s) = 15,386 cm³
b) Surface area of the sphere is:
V(s) = (4/3)*π*x³
dV(s) /dx = S(s) = 4*π*x³
And
dS(s) /dx = 8*π*x
dS(s) = 8*π*x*dx
dS(s) = 8*3,14*7*(0,025)
dS(s) = 4,396 cm²
c) The approximates errors in a and b are:
V(s) = (4/3)*π*x³ then
V(s) = (4/3)*3,14*(7)³
V(s) = 1436,03 cm³
And the possible propagated error in volume is from a) is
dV(s) = 15,386 cm³
dV(s)/V(s) = [15,386 cm³/1436,03 cm³]* 100
dV(s)/V(s) = 1,07 %
And for case b)
dS(s) = 4,396 cm²
And the surface area of the sphere is:
S(s) = 4*π*x³ ⇒ S(s) = 4*3,14*(7)² ⇒ S(s) = 615,44 cm²
dS(s) = 4,396 cm²
dS(s)/ S(s) = [ 4,396 cm²/615,44 cm² ] * 100
dS(s)/ S(s) = 0,71
can you please help ?
Answer:
69
Step-by-step explanation:
The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.
We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.
[tex]\frac{5(x)}{2} -6[/tex]
[tex]\frac{5(30)}{2}-6[/tex]
[tex]\frac{150}{2}-6[/tex]
[tex]75-6[/tex]
[tex]69[/tex]
Which expression is equal to 7 times the sum of a number and 4
Answer:
7(n + 4)
Step-by-step explanation:
Represent the number by n. Then the verbal expression becomes
7(n + 4).
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
use the product of powers property to simplify the numeric expression.
4 1/3 • 4 1/5 = _____
Answer:
The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Step-by-step explanation:
We need to simplify the numeric expression using property. The expression is as follows :
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]
The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]
This property is valid if the base is same. Here, base is x.
In this given problem, x = 4, a = 1/3 and b = 1/5
So,
[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]
So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex] is [tex]4^{\dfrac{8}{15}}[/tex] .
Find the first term in the sequence when u(subscript)31=197 and d= 10.
Answer:
197 = 10(31-1) + a
197 = 300 + a
-103 = a
The chief business officer of a construction equipment company arranges a loan of $9,300, at 12 1 /8 % interest for 37.5 months. Find the amount of interest. (Round to the nearest cent)
a. $2,761.21
b. $3,583.83
c. $3,523.83
d. $3,722.47
Answer:
C). $3523.83
Step-by-step explanation:
loan of principles p= $9,300,
at rate R= 12 1 /8 % interest
Rate R = 12.125%
for duration year T = 37.5 months
T= 37.5/12 = 3.125 years
Interest I=PRT/100
Interest I =( 9300*12.125*3.125)/100
Interest I = (352382.8125)/100
Interest I = 3523.83
Interest I= $3523.83
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
A cardboard box without a lid is to be made with a volume of 4 ft 3 . Find the dimensions of the box that requires the least amount of cardboard.
Answer:
2ft by 2ft by 1 ftStep-by-step explanation:
Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;
S = lw+2wh+2lh ... 1
Given the volume V = lwh = 4ft³ ... 2
From equation 2;
h = 4/lw
Substituting into r[equation 1;
S = lw + 2w(4/lw)+ 2l(4/lw)
S = lw+8/l+8/w
Differentiating the resulting equation with respect to w and l will give;
dS/dw = l + (-8w⁻²)
dS/dw = l - 8/w²
Similarly,
dS/dl = w + (-8l⁻²)
dS/dw = w - 8/l²
At turning point, ds/dw = 0 and ds/dl = 0
l - 8/w² = 0 and w - 8/l² = 0
l = 8/w² and w =8/l²
l = 8/(8/l² )²
l = 8/(64/I⁴)
l = 8*l⁴/64
l = l⁴/8
8l = l⁴
l³ = 8
l = ∛8
l = 2
Hence the length of the box is 2 feet
Substituting l = 2 into the function l = 8/w² to get the eidth w
2 = 8/w²
1 = 4/w²
w² = 4
w = 2 ft
width of the cardboard is 2 ft
Since Volume = lwh
4 = 2(2)h
4 = 4h
h = 1 ft
Height of the cardboard is 1 ft
The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft
12-(3-9) 3*3 help please
Step-by-step explanation:
42 is your answer according to bodmas
please help
-3(-4x+4)=15+3x
Answer:
x=3
Step-by-step explanation:
● -3 (-4x+4) = 15 + 3x
Multiply -3 by (-4x+4) first
● (-3) × (-4x) + (-3)×(4) = 15 + 3x
● 12 x - 12 = 15 +3x
Add 12 to both sides
● 12x - 12 + 12 = 15 + 3x +12
● 12 x = 27 + 3x
Substract 3x from both sides
● 12x -3x = 27 + 3x - 3x
● 9x = 27
Dividr both sides by 9
● 9x/9 = 27/9
● x = 3
Which choice is equivalent to the expression below? √-12
A. 12i
B. -12i
C. -2√3
D. 2i √3
E. -2√3i
PLEASE DON’T GUESS
Answer:
D. 2i√3
Step-by-step explanation:
You have the expression √-12. You can divide the number in the radical sign into the numbers that make up the expression. After you do this, you will be able to take numbers out of the radical sign
√(-12)
√(-1 × 4 × 3)
√-1 = i
√4 = 2
√3 = √3
2i√3
The answer is D.
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
Can someone explain to me what a “derivative” means? How do you find the derivative of f(x)=x^3+1?
The range of values for x?
Answer:
x = 32
but
I would say anything from 30 to 33
but truly i have no clue about the range
Step-by-step explanation:
3x-9=87 (because 180 -93 =87)
3x = 96
x = 32
Answer:
it is 32
Step-by-step explanation:
An evergreen nursery usually sells a certain shrub after 9 years of growth and shaping. The growth rate during those 9 years is approximated by
dh/dt = 1.8t + 3,
where t is the time (in years) and h is the height (in centimeters). The seedlings are 10 centimeters tall when planted (t = 0).
(a) Find the height after t years.
h(t) =
(b) How tall are the shrubs when they are sold?
cm
Answer:
(a) After t years, the height is
18t² + 3t + 10
(b) The shrubs are847 cm tall when they are sold.
Step-by-step explanation:
Given growth rate
dh/dt = 1.8t + 3
dh = (18t + 3)dt
Integrating this, we have
h = 18t² + 3t + C
When t = 0, h = 10cm
Then
10 = C
So
(a) h = 18t² + 3t + 10
(b) Because they are sold after every 9 years, then at t = 9
h = 18(9)² + 3(9) + 10
= 810 + 27 + 10
= 847 cm
What is the first step in mathematical induction?
Answer:
Show that the statement is true for n=1
Step-by-step explanation:
Hey,
Show that the statement is true for n=1
You can check my other answer there which explains a little bit more the ideas.
https://brainly.com/question/17162256
thank you
Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.
Answer:
The portfolio beta is [tex]\alpha = 1.354[/tex]
Step-by-step explanation:
From the question we are told that
The first investment is [tex]i_1 = \$ 25,000[/tex]
The first beta is [tex]k = 0.8[/tex]
The second investment is [tex]i_2 = \$ 40,000[/tex]
The second beta is [tex]w = 1.7[/tex]
Generally the portfolio beta is mathematically represented as
[tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]
substituting values
[tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]
[tex]\alpha = 1.354[/tex]
what are the comparison symbols for 5/6 and 2/5, 4/10 and 7/8, and 3/12 and 1/4
Answer like this: Example
=
<
>
Answer:
5/6 > 2/44/10 < 7/83/12 = 1/4Step-by-step explanation:
The comparison will be the same if you subtract the right side and compare to zero:
a/b ?? c/d . . . . . . . using ?? for the unknown comparison symbol
a/b - c/d ?? 0 . . . . subtract the fraction on the right
(ad -bc)/bd ?? 0 . . . combine the two fractions
ad - bc ?? 0 . . . . . . multiply by bd to make the job easier
__
5/6 and 2/5
5(5) -6(2) = 25 -12 > 0 ⇒ 5/6 > 2/5
4/10 and 7/8
4(8) -10(7) = 48 - 70 < 0 ⇒ 4/10 < 7/8
3/12 and 1/4
3(4) -12(1) = 0 ⇒ 3/12 = 1/4
_____
Of course, you can use your calculator (or your memory) to change each of these to a decimal equivalent. The comparison should be easy at that point.
0.833 > 0.400
0.400 < 0.875
0.250 = 0.250
6x - 10 = 4(x + 3) x = ? x = 9 x = 10 x = 11 x = 12
Answer:
x=11
Step-by-step explanation:
Answer:
x = 11
Step-by-step explanation:
6x - 10 = 4(x+3)
6x - 10 = 4*x + 4*3
6x - 10 = 4x + 12
6x - 4x = 12 + 10
2x = 22
x = 22/2
x = 11
check:
6*11 - 10 = 4(11+3)
66 - 10 = 4*14 = 56
You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each. If you sold twice as many silly string tickets as car wash tickets, and you have $1460 total. Write the matrix in the box below. Write the solution set for this system and include any necessary work.
Answer:
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Solution Set : { x = 123, y = 246, z = 11 }
Step-by-step explanation:
Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,
x + y + z = 380,
And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.
5x + 3y + 10z = 1460
The silly string tickets were sold for twice as much as the car wash tickets.
y = 2x
Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.
System of Equations :
[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]
Matrix :
[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]
Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,
[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows
[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three
And we can continue, canceling the leading co - efficient in each row until this matrix remains,
[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]
x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold
Can somebody explain how trigonometric form polar equations are divided/multiplied?
Answer:
Attachment 1 : Option C
Attachment 2 : Option A
Step-by-step explanation:
( 1 ) Expressing the product of z1 and z2 would be as follows,
[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]
Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,
cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],
sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]
cos(3π / 2) = 0,
sin(3π / 2) = - 1
Let's substitute those values in our expression,
[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]
And now simplify the expression,
[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]
The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.
( 2 ) Here we will apply the following trivial identities,
cos(π / 3) = [tex]\frac{1}{2}[/tex],
sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],
cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],
sin(- π / 6) = [tex]-\frac{1}{2}[/tex]
Substitute into the following expression, representing the quotient of the given values of z1 and z2,
[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒
[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]
The simplified expression will be the following,
[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]
The solution will be option a, as you can see.
On a coordinate plane, a line goes through (negative 3, 3) and (negative 2, 1). A point is at (4, 1). What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (4, 1)? y − 1 = −2(x − 4) y – 1 = Negative one-half(x – 4) y – 1 = One-half(x – 4) y − 1 = 2(x − 4)
Answer:
y - 1 = -2(x - 4).
Step-by-step explanation:
First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).
(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.
The line will be parallel to the given line, so the slope is the same.
Now that we have a point and the slope, we can construct an equation in point-slope form.
y1 = 1, x1 = 4, and m = -2.
y - 1 = -2(x - 4).
Hope this helps!
The slope of the line passing parallel to the given line and passes through the point (4, 1) is y = -2x + 9
The equation of a straight line is given by:
y = mx + b
where y, x are variables, m is the slope of the line and b is the y intercept.
The slope of the line passing through the points (-3,3) and (-2,1) is:
[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]
Since both lines are parallel, hence they have the same slope (-2). The line passes through (4,1). The equation is:
[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]
Find out more at: https://brainly.com/question/18880408
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
