Answer:
The 95% confidence interval is [tex] 101.13 < \mu < 104.87 [/tex]
The 99% confidence interval is [tex] 100.54 < \mu < 105.46 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 110
The sample mean is [tex]\= x = 103 \ mg[/tex]
The population standard deviation is [tex]\sigma = 10 \ mg[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =1.8688 [/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 1.8688 < \mu < 103 + 1.8688 [/tex]
=> [tex] 101.13 < \mu < 104.87 [/tex]
Considering question b
From the question we are told the confidence level is 99% , hence the level of significance is
[tex]\alpha = (100 - 99 ) \%[/tex]
=> [tex]\alpha = 0.01[/tex]
Generally from the normal distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] is
[tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 2.58 * \frac{ 10 }{\sqrt{110} }[/tex]
=> [tex]E =2.4599 [/tex]
Generally 99% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]103 - 2.4599 < \mu <103 + 2.4599 [/tex]
=> [tex] 100.54 < \mu < 105.46 [/tex]
2x-y=5 in slope intercept form?
Answer:
y = 2x - 5
I hope this helps!
A consultant for an association of personnel directors wants to find the proportion of clerical personnel that change jobs because they are bored with their work. The consultant queries a random sample of 400 clerical workers who recently changed jobs, 200 of which state that they changed jobs because they were bored. The consultant wishes to prepare a 95% confidence interval for the true proportion changing jobs because of boredom. What is the margin of error for this interval
Answer:
the margin of error for this interval is 0.049
Step-by-step explanation:
The computation of the margin of error for this interval is shown below;
Given that
n = 400
x = 200
Now
p = x ÷ n = 200 ÷ 400 = 0.5
Now the margin of error is
= [tex]z \times \sqrt{\frac{p(1-p)}{n}} \\\\1.96 \times \sqrt{\frac{0.5 \times 0.5}{400} }[/tex]
= 0.049
Hence the margin of error for this interval is 0.049
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, -0.75); f(x) = x2 - x + 1
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = -x2 + x
Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + 2x + 1
Answer:
Option A: Axis of symmetry: x = -0.5; Vertex: (-0.5, 0.75); f(x) = x2 + x + 1
Step-by-step explanation:
1) The axis of symmetry of quadratic graph is the vertical line that divides the graph curve into two congruent halves. In this case, it is: x = -0.5
2) Vertex is the point at which the graph curve changes direction or simply coordinates of the crest or trough of the curve.
The graph given has a trough with the coordinates: x = -0.5, y = 0.75. This is (-0.5, 0.75)
3) The roots of a quadratic equation are the points where the curve crosses the x-axis. In this case, it doesn't cross and so we have imaginary roots.
Now, formula for line of symmetry is; x = -b/2a
Thus; -b/2a = -0.5 or -b/2a = -1/2
Thus, b = 1 and a = 1
Our first and second terms will now be;
x² + x
Looking at the options, the only one with x² + x as it's first 2 terms is option A.
Thus, the complete equation will be x² + x + 1
I need help with this
Answer:
(-2, -4)
Step-by-step explanation: because its going backwards it should be a negative slope :)
I'm sorry if I'm wrong but i hope this helps :)
The probability of rolling a number less than 3 on a number cube is 2/6. Jennifer rolls a number cube 60 times. How many times should Jennifer expect to roll a number less than 3?
A. 10
B. 20
C. 30
D. 40
E. 50
Please help me!!
What are the domain and range of the function ? domain: all real numbers range: all real numbers greater than or equal to –5 domain: all real numbers range: all real numbers greater than or equal to –4 domain: all real numbers between –2.5 and 2.5 range: all real numbers domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Answer:
Option A Domain: all real numbers between –2.5 and 2.5 range: all real numbers greater than or equal to –5
Step-by-step explanation:
Domain corresponds to the values of x and Range corresponds to the value of y. If sketch the graph on an online calculator we can see that the domain lies between -2.5 and 2.5 for x and the range corresponds to y as in this case
range ≥ -5.
Answer:
a
Step-by-step explanation:
I want to make sure if this was the right answer
Answer:
no, I believe the correct answer would be D. (-4, 4)
Answer:
(-4, 4)
Step-by-step explanation:
Even though I don't see it explained anywhere, it seems that what looks like the coordinates of two points is really the coordinates of the first point and the translation.
That means that (-9, 6) is the original point.
(5, -2) is the translation which is a translation of 5 in x and a translation of -2 in y.
Start with (-9, 6)
Apply the translation to x and y (-9 + 5, 6 + (-2))
You get (-4, 4)
Answer: (-4, 4)
Find the solution for a system of equations by elimination
3x – 6y = 12
5x - 2y = 10
Answer:
y=2, x=1
Step-by-step explanation:
3x-6y=12(x2)
5x-2y=10(x6)
Eliminate y
6x-12y=12
30x-12y=60
-24x =-48
divide both sides by -24
-24x/-24=-48/-24
y=2
to get our x
3x-6(2)=12
3x-12=12
3x=12+12
3x=24(divide both sides by 3)
x=1
Very confusing not sure
Answer:
This describes a translation.
A friend offers to play a game, in which you roll 3 standard 6-sided dice. If all the dice roll
different values, you give him $1. If any two dice match values, you get $2. What is the expected value of this game?
Answer: The expected value is $0.32
Step-by-step explanation:
The expected value can be calculated as:
EV = ∑xₙ*pₙ
Where:
xₙ is the n-th event.
pₙ is the probability of the n-th event.
First, let's see the events in this situation and the probability of each event.
Lossing $1.
This happens when you roll all different numbers.
To calculate the number of combinations where you roll all different values, we first need to count the number of possible options for each roll, this is:
First dice: you have 6 options
Second dice: You have 5 options, because we remove the option that was rolled in the first dice.
Third dice: You have 4 options, because we removed the two outcomes showed in the two previous rolls.
Then the number of combinations is:
c = 6*5*4 = 120.
And the total number of combinations for rolling 3 dice is equal to the product between the number of outcomes for each dice, each dice has 6 possible outcomes, then the total number of outcomes is:
C = 6*6*6 = 216
The probability of rolling all different numbers will be equal to the quotient between the number of combinations where you roll all different values and the total number of combinations:
P₁ = 120/216 = 0.56
In the other case, where you roll at least two equal outcomes, you win $2.
The probability for this case will be the complement of the previous one, then the probability can be calculated as:
P₂ = 1 - P₁ = 1 - 0.56 = 0.44
Then the expected value will be:
EV = -$1*0.56 + $2*0.44 = $0.32
The expected value is $0.32
You deposit $6000 in and account earning 2% interest compounded monthly How much will you have in the account in 10 years
Answer:
14400 $. do u need an explanation:
so if 6000 is 100 percent
then ??? is 2 percent
to find out that you need to 6000×2 and divide by 2=120$
so you get this monthly.
in ten years you will have 14400 because
10 year=120 month
120month×120$=14400.
btw I cant speak English well. I hope it will help
Show that a vector
[tex]u = x _{1}i + y_{1}j + z_{1}k[/tex]
with direction cosines (cos α, cos β, cos gamma) can be written as
[tex]u = |u| ( \cos \alpha i + \cos\beta j + \cos \gamma k)[/tex]
Answer:
u = |u|(cos∝+cosβ+cosγ)
Step-by-step explanation:
Explanation
Proof:-
Given a vector u = x₁ i + y₁j +z₁k
let O X, OY, O Z be the positive co-ordinate axes
P(x₁,y₁,z₁) be any point in the space
Let OP makes angles α,β,γ with co-ordinate axes OX , OY ,OZ .
The angle α,β,γ are known as direction angles and cosine of the angle
l =cosα , m= cosβ , n=cosγ
The perpendicular PA,PB,PC are drawn co-ordinate axes OX,OY,OZ respecctively
InΔOAP , ∠A =90° , cos∝ =[tex]\frac{x}{r}[/tex]
x₁ = rcos∝
InΔOBP , ∠B =90° , cosβ =[tex]\frac{y}{r}[/tex]
y₁ = rcosβ
InΔOCP , ∠C =90° , cosγ =[tex]\frac{z}{r}[/tex]
z₁ = rcosγ
Given u = x₁ i + y₁j +z₁k
|u| = [tex]\sqrt{(x_{1})^{2} +(x_{2} )^{2} +(x_{3} )^{2} }[/tex]
Therefore u = x₁ i + y₁j +z₁k
u = |u|(cos∝+cosβ+cosγ)
Daniel plays two games in the casino. The first game he believes he has 60% chance to win. If he wins the first game, he will win the second game with 35% chance, if he loses the first game, he will win the second game with 65% chance. The winning prices for the first and second game are $1 and $2 respectively. a. If he wins the second game, what is the probability that he lost the first game
Answer:
0.5532
Step-by-step explanation:
We have these events
WF = Wins the first game
LF = lose the first game
WS = Wins the second game
LS = lose the second game
Then
Prob(WF) = 0.6
Prob(LF) = 0.4
Prob(WS|WF) = 0.35
Prob(WS|LF) = 0.65
1. If he wins the second game, the probability that he lost the first =
P(Lf|WS)
= 0.4x0.65/0.4x0.65+0.6x0.35
= 0.21/0.47
= 0.5532
0.5532 is the probability that he lost the first game given that he wins the second
The regular price of a television is $250. A discount offered on the television is 20% of the regular price. What is the discount amount?
Answer:
The discounted TV would cost $200 because the 20% discount takes off $50
If <1 <2
, which lines are parallel?HELP PLEASE
Answer: C. n//p
Step-by-step explanation:
The length of a rectangular picture frame is 2 inches shorter than its width. If the perimeter of
the picture frame is 52 inches, what is the length, l, and width, w, of the frame? Write and
solve an equation to model the problem. Explain the meaning of the solution.
Answer:
Length = 12 inches
Width = 14 inches
Step-by-step explanation:
Formula for perimeter of a rectangle is;
P = 2(L + W)
Where;
L is length
W is width
We are told that the length is 2 inches shorter than its width. Thus;
L = (W - 2)
Thus,perimeter is now;
P = 2(W - 2 + W)
P = 2(2W - 2)
P = 4W - 4
We are told that the perimeter is 52. Thus;
4W - 4 = 52
4W = 52 + 4
4W = 56
W = 56/4
W = 14 inches
From L = (W - 2) ;
L = 14 - 2
L = 12 inches
f(x)= -8x
Find the value of x so that
f(x) = 40
Answer:
x=-5
Step-by-step explanation:
f(x)=-8x
f(x)=40
substitute f(x) with 40 in the first equation
40=-8x
s=-5 (slove)
Maria has a savings account that is earning simple interest. If she started with $200 in the account and has earned a total of $8 in interest in two years, what is the rate of the account?
Answer:
The rate of the interest for savings account is: 2%
Step-by-step explanation:
Simple interest is given by the formula
[tex]I = Prt[/tex]
Here
I is the interest,
P is the principal amount
r is the interest rate
and
t is the time period in years
Now, it is given that
P = $200
I = $8
t = 2 years
Putting the values in the formula
[tex]8 = 200 * r * 2\\8 = 400 * r\\r =\frac{8}{400}\\r = 0.02[/tex]
Converting into percentage
r = 2%
Hence,
The rate of the interest for savings account is: 2%
Answer:
0.02
Step-by-step explanation
<8 and <6 are ___________.
0443e860-aba2-49e1-952c-862061d9e91a?w=400&h=400
a
Same-side Interior Angles
b
Alternate Exterior Angles
c
Alternate Interior Angles
d
Corresponding Angles
What inequality is represented by this number line?
x > -4
x ≤ -4
x < -4
x ≥ -4
quadrilateral ABCD is dilated by a scale factor of 2 centered around (2,2). Which statement is true about the dilation?
Answer:
The vertices of the image will have the coordinates
A(-5, 1) → A'(2x-2, 2y-2) → A'(-12, 0)
B(-4, 3) → B'(2x-2, 2y-2) → B'(-10, 4)
C(1, 2) → C'(2x-2, 2y-2) → C'(0, 2)
D(-3, 0) → D'(2x-2, 2y-2) → D'(-8, -2)
Step-by-step explanation:
Note: You missed to mention the vertices of a quadrilateral ABCD. So, I am assuming the following vertices. It would anyways clear your concept.
Let us suppose
A(-5, 1)B(-4, 3)C(1, 2)D(-3, 0)We know that the rule of the dilation with the center of dilation at (2,2) by a scale factor of 2 is:
(x, y) → (2x-2, 2y-2)Therefore, the vertices of the image will have the coordinates
A(-5, 1) → A'(2x-2, 2y-2) → A'(-12, 0)
B(-4, 3) → B'(2x-2, 2y-2) → B'(-10, 4)
C(1, 2) → C'(2x-2, 2y-2) → C'(0, 2)
D(-3, 0) → D'(2x-2, 2y-2) → D'(-8, -2)
A parabola has x-intercepts at (3,0) and (9,0) and a maximum at 4. Write the equation of the
parabola in vertex form.
Then, convert the equation of the parabola to standard form.
Answer:
H!
Step-by-step explanation:
what is the combined mass of the moon(7.3*10^22)earth(590*10^22)and pluto(1.3*10^22)
It's the sum of the three masses:
[tex]7.3\cdot10^{22} + 590\cdot10^{22} + 1.3\cdot10^{22} = (7.3 + 590 + 1.3)10^{22} = 598.6\cdot10^{22}[/tex]
There are 3 fourth grade clases with a total of 90 scholars. 2/5 of the scholars have a sister. 1/2 of the scholars have a brother. How many scholars have a sisters?
Answer:
There are 36 scholars who have a sister.
Step-by-step explanation:
Given that:
Total number of scholars in classes = 90
Fraction of scholars who have a sister = 2/5
Fraction of scholars who have a brother = 1/2
Number of scholars who have sisters = 2/5 of 90
Number of scholars who have sisters = [tex]\frac{2}{5}*90[/tex]
Number of scholars who have sisters = 36
Hence,
There are 36 scholars who have a sisters.
what is the angle of elevation to the nearest tenth of a degree to the top of a 35ft building from 75ft away?
Answer:25°
Step-by-step explanation:
tanθ= 35/72
PLEASE HELP!! PLEASE SHOW WORK OR EXPLAIN!! I WILL GIVE BRAINLIEST!!
Answer:
-4
Step-by-step explanation:
The equation for slope is as follows:
[tex]\frac{y2 - y1}{x2 - x1}[/tex]We can use point P and point V's coordinates to find the slope.
Point P is at (2,4)
Point V is at (3,0)
Let's define all the variables:
y2 = 0 (from point V)
y1 = 4 (from point P)
x2 = 3 (from point V)
x1 = 2 (from point P)
Now that we have all the variables we can plug it into the equation:
[tex]\frac{0-4}{3-2} = \frac{-4}{1} = -4[/tex]
Therefore, the slope of line PV is -4.
I hope this helps!!
Feel free to ask any questions!
- Kay :)
A farmer notices that there is a linear relationship between the number of bean stalks, n, she plants and the yield, Y. When she plants 2 stalks, each plant yields 70 ounces of beans. When she plants 8 stalks, each plant yields 160 ounces of beans.
Which of these equations correctly represents this situation?
Select the correct answer below:
Y(n)=19n+32
Y(n)=11n+72
Y(n)=11n+48
Y(n)=19n+8
Y(n)=15n+30
Y(n)=15n+40
Answer:
Y(n)=15n+40
Step-by-step explanation:
Lets represent the number of bean stalks she plant by n and
the yield by Y.
It says in the question that when she plants 2 stalks, each plant yields 70 ounces of beans. When she plants 8 stalks, each plant yields 160 ounces of beans.
Which means 2 stalks correspond to 70 ounces and 8 stalks corresponds to 160 ounces we could write the data Mathematically like:
(2 , 70) and (8 , 160) are our coordinates where the x-axis would be n the number of beans stalks planted and y-axis would be Y the yield in ounces.
So we have two coordinates and to find the linear relationship we must find out the slope/gradient(m) of the linear function by the formula of slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{160-70}{8-2} \\\\m=\frac{90}{6} \\\\m=15[/tex]
so we plug in one of the coordinates and our slope in the point-slope formula :
[tex]y-y_1=m(x-x_1)[/tex]
where,
[tex](x_1,y_1)\ represent\ the\ coordinate\ (2,70)[/tex]
so plugging in the coordinate and the value of m we get:
[tex]y-y_1=m(x-x_1)\\y-70=15(x-2)\\y-70=15x-30\\y=15x-30+70\\y=15x+40\\[/tex]
so our the answer is the last option
Y(n)=15n+40
here x corresponds to n and y corresponds to Y(n)
reduce the ratio to its simpliest form 208/52
Answer:
4
Step-by-step explanation:
208 ÷ 52 = 4
52 × 4 = 208
Hope this helped a little!
208/52
= 4
you could have simply cancelled out or even use a calculator
A suppliers sold a machine levying 13% vat on rupees 320000 to a retailer. the retailer spent rupees 10000 for transportation and rupees 5000 for the local tax if the retailer sold it at a profit of rupees 15000 to a customer how much did the customer pay for the machine with 13% vat?
Answer:
395,500
Step-by-step explanation:
The computation is shown below:
Supplier to retailer = 320,000
Vat tax = 13%
Retailer spent for transportation = 10,000
local tax = 5,000
Profit = 15,000
Now based on the above information
the customer would pay the amount with 13% vat is
= (320,000 + 10,000 + 5,000 + 15,000) + 13% of total
= 350,000 + 13% of 350,000
= 350,000 + 45,500
= 395,500
PLEASE PLEASE HELP ME
Which of the following angles is coterminal with -610?
1. 110
2. 70
3. 250
4. 20
Answer:
1. 110°Step-by-step explanation:
Given angle - 610°
Coterminal angle is an angle in the interval 0°- 360° added or subtracted to multiples of 360°:
-610° + 2*360° = -610° + 720° = 110°Correct option is 1.