Answer:
a. Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are
b. Theoretical Probability. Experimental Probability.
Use theoretical probability by counting the favorable outcomes and put that in a fraction above all possible outcomes.
Use experimental probability by comparing the number of times the event occurs to the total number of trials.
Step-by-step explanation:
I don't really know what to explain. :v
7.75 in expanded form
Answer: 7+0.7+0.05
Since 7 is in the ones place it goes in front of the decimal. .7 is in the tenth place because it's behind the decimal. .05 is also behind the decimal so it's in the hundredths place.
At the end of a snow storm, Tristan saw there was a lot of snow on his front lawn. The
temperature increased and the snow began to melt at a steady rate. After the storm,
the snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours
after the storm ended, the depth of snow was down to 9 inches. Write an equation for
S, in terms of t, representing the depth of snow on Tristan's lawn, in inches, t hours
after the snow stopped falling.
Answer:[tex]S(t)=12-0.75t[/tex]
Step-by-step explanation:
Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours after the storm ended, after the storm ended, the depth of snow was down to 9 inches.
Snow melted in 4 hours = [tex]0.75\times4 =3\text{ inches}[/tex]
Initial depth of snow = 9 + 3 inches = 12 inches.
Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)
Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.
Then, [tex]S(t)=12-0.75t[/tex]
The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling is:
[tex]S(t) = 12 - 0.75t[/tex]
A linear function in the model will have the following format:
[tex]S(t) = S(0) - mt[/tex]
In which:
S(0) is the initial amount of snow.m is the melting rate, which is the slope.The snow melts at a rate of 0.75 inches per hour, thus [tex]m = 0.75[/tex] and:
[tex]S(t) = S(0) - 0.75t[/tex]
After 4 hours, there were 9 inches, that is, when [tex]t = 4, S(t) = 9[/tex], and this is used to find S(0).
[tex]S(t) = S(0) - 0.75t[/tex]
[tex]9 = S(0) - 0.75(4)[/tex]
[tex]S(0) = 9 + 0.75(4)[/tex]
[tex]S(0) = 12[/tex]
Hence, the equation is:
[tex]S(t) = 12 - 0.75t[/tex]
A similar problem is given at https://brainly.com/question/16302622
What is the product of the fractions belo?
1/8*4/5
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
cross simplify
[tex]\frac{1}{8}[/tex] • [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex]
multiply
[tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{10}[/tex]
List the next three numbers for the sequence:
27, 41, 55, 69, ...
Answer:
83, 97, 111 i think that is what you are asking
Answer:
83, 97,111
Step-by-step explanation:
You find yourself stuck in a traffic jam. It is not rush hour. You feel frustrated and wonder what is holding up traffic Which of the following are plausible hypotheses for explaining the problem?
Check all that apply.
a) It is Friday the 13th, and you think that because this is considered a day for bad luck, that must be why there is a traffic jam. ?
b) You were in a hurry this morning, and you forgot to bring your lucky rabbit's foot with you. That's why you are now stuck in traffic.
c) There is an accident ahead, which often causes traffic to slow.
d) There is a sale at the mall near an exit up ahead, and everyone on the road is going to the sale
e) Road repairs are being made today, and you didn't know about it.
Answer:
There is an accident ahead, which often causes traffic to slow.
Step-by-step explanation:
Looking at the question closely, we understand that the traffic jam occurred at a time that is not generally regarded as a rush hour.
A traffic jam due to road repair is not really an option because roads are closed during repairs. Shop malls announce their special sales days ahead of time so that many people will hear about it.
However, it is likely that an accident occurred. An road accident may suddenly occur on an otherwise less busy road. This often leads to an unusual delay in traffic irrespective of the hour of the day when it occurs.
factorise : 64a cube minus 27b cube minus 144a square b plus 108ab square .
Plz Answer this question
Answer:
The answer is [tex]4a(16a^2+27b^2)-3b(9b^2+48b)[/tex]Step-by-step explanation:
step one:
let us re-write the expression in mathematical terms for clarity
we have the expression stated below
[tex]64a^3-27b^3-144b^2+108ab^2[/tex]
step two:
We are going to collect like terms before factorization we have
[tex]64a^3+108ab^2-27b^3-144b^2[/tex]
We can now factorize the expression we have
[tex]4a(16a^2+27b^2)-3b(9b^2+48b)[/tex]
3.28 in expanded form
Answer:
3 ones
2 tenths
8 hundredths
I'm sorry if I misunderstood.
Good luck though! :)
Please add Brainliest if you'd like, not that it matters.
Please help me with this
Answer:8^20
Step-by-step explanation:
I just say 10x2=20 lol
Answer:
[tex]8^{20}[/tex]
Step-by-step explanation:
8^10*2
8^20
A paycheck is issued for $329.40. The paystub reflects an amount earned of $400.00, Medicare tax of $5.80, Social Security tax of $24.80, and a federal tax of $40.00. What is the net income for the paycheck? Group of answer choices
Answer:
gross income is $400
The net is $329.40
Deductions are $$70.6
Step-by-step explanation:
Based on the gross amount earned and the various deductions, the net income is $329.40
What is Net Income?Net income is the amount that will be earned after all the taxes have been subtracted from the paystub amount.
The net income is therefore:
= 400 - 5.80 - 24.80 - 40
= $329.40
In conclusion, the net income is $329.40.
Find out more about net income at https://brainly.com/question/25273589.
The friends collected a total of 43 shells on the beach. Paula collected x shells. Bethany collected 3 less than twice as many shells as Paula. Jerrell collected 2 more than half as many shells as Paula. How many shells did Paula collect?
A. 8 shells
B. 12 Shells
C. 21 shells
D. 29 Shells
Answer:
12
Step-by-step explanation:
The number of shells collected by Paula is 12 shells
The correct answer is B.
The given expression:
total number of shells collected by the friends, t = 43 shells
number of shells collected by Paula = x
number of shell collected by Bethany = 2x - 3
number of shell collected by Jerrell = [tex]\frac{x}{2} + 2[/tex]
To find:
the number of shells collected by PaulaThe number of shells collected by Paula is calculated as follows:
[tex]x + (2x-3 ) + (\frac{x}{2} + 2) = 43\\\\3x + \frac{x}{2} - 1 = 43\\\\\frac{6x + x}{2} = 43 + 1\\\\\frac{7x}{2} = 44\\\\7x = 88\\\\x = \frac{88}{7} \\\\x \approx 12 \ shells[/tex]
Thus, the number of shells collected by Paula is 12 shells
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You invested $17,000 in two accounts paying 6% and 7% annual interest, respectively.
If the total interest earned for the year was $1160, how much was invested at each rate?
Answer:
Total Earnings = 18,160
1) 1.07 * principal1 * + 1.06 * principal2= 18,160
2) principal1 + principal2 = 17,000
We'll multiply equation 2) by -1.06
2) -1.06*principal1 -1.06*principal2 = -18,020 then adding equation 1)
1) 1.07 * principal1 * + 1.06 * principal2= 18,160
.01*principal1 = 140
principal 1 = 14,000
and therefore principal 2 = 3,000
Step-by-step explanation:
identify rules of algebra with (x+3)-(x+3)=0
Taking any number x, and adding on its opposite -x, leads to x+(-x) = x-x = 0
This is the inverse property of addition.
A numeric example would be 7 + (-7) = 7-7 = 0
Going back to x-x = 0, we can replace x with any expression (whether simple or complicated) we want.
So in this case, we replace each 'x' with 'x+3' to get (x+3)-(x+3) = 0
The equation (x+3)-(x+3) = 0 has infinitely many solutions. The solution set is the set of all real numbers. We can replace x with any number and the original equation will simplify to a true statement.
g 3.24 Socks in a drawer. In your sock drawer you have 4 blue, 5 gray, and 3 black socks. Half asleep one morning you grab 2 socks at random and put them on. Find the probability you end up wearing (a) 2 blue socks (b) no gray socks (c) at least 1 black sock (d) a green sock (e) matching socks
Answer:
a) 1/11 (b) 7/22 (c) 5/11 (d) 0 (e) 19/66
Step-by-step explanation:
Given the following :
Number of Blue socks = n(B) = 4
Number of Gray socks = n(G) =5
Number of black socks = n(Bl) = 3
Total number of socks = (4 + 5 + 3) = 12
Probability = ( number of required outcomes / number of total possible outcomes)
Picking 2 socks at random:
A) probability of two blue socks :
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(2 blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
B) No gray socks :
Number of non - gray socks = (4 + 3) = 7
1st pick = 7/12
After 1st pick non-gray socks left = 6
Total socks left = 11
2nd pick = 6 / 11
P(non-gray) = (7/12 × 6/11) = 42/132 = 7/22
C.) Atleast one black socks = (1 - P(no black))
Number of non-black socks = (4 +5) = 9
1st pick = 9/12 = 3/4
After 1st pick, non-black left = 8, total = 11
2nd pick = 8/11
P(non - black) = (3/4 × 8/11) = 24/44 = 6/11
P(atleast 1 black) = (1 - 6/11) = 5 /11
D.) A green socks
Number of green socks = 0
P(green) = 0
E.) A matching socks :
1) matching black socks :
Ist pick = p(Bl) = (3/12) = 1/4
Number of Black socks left = (3 - 1) =2
Total socks left = 12 - 1 = 11
2nd pick = p(Bl) = (2/11)
P(matching black socks) = (1/4 * 2/11) = 2 /44 = 1/22
11) matching blue socks:
Ist pick = p(B) = (4/12) = 1/3
Number of Blue socks left = (4 - 1) =3
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (3/11)
P(matching blue socks) = (1/3 * 3/11) = 3 /33 = 1/11
111) matching gray socks :
Ist pick = p(B) = (5/12) = 5/12
Number of Blue socks left = (5 - 1) =4
Total socks left = 12 - 1 = 11
2nd pick = p(B) = (4/11)
P(matching gray socks) = (5/12 * 4/11) = 20/132 = 5 /33
Summing the probabilities :
(1/22 + 1/11 + 5/33) = (3 + 6 + 10) / 66 = 19/66
Using the hypergeometric distribution, it is found that there is a:
a) 0.0909 = 9.09% probability that you end up with 2 blue socks.
b) 0.3182 = 31.82% probability that you end up with no gray socks.
c) 0.4545 = 45.45% probability that you end up with at least 1 black sock.
d) 0% probability that you end up with a green sock.
e) 0.2879 = 28.79% probability that you end up with matching socks.
Hypergeometric distribution:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. N is the size of the population. n is the size of the sample. k is the total number of desired outcomes.In this problem:
There is a total of 4 + 5 + 3 = 12 socks, hence [tex]N = 12[/tex].2 are grabbed, hence [tex]n = 2[/tex].Item a:
4 are blue, hence [tex]k = 4[/tex]The probability is P(X = 2), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,4) = \frac{C_{4,2}C_{8,0}}{C_{12,2}} = 0.0909[/tex]
0.0909 = 9.09% probability that you end up with 2 blue socks.
Item b:
5 are gray, hence [tex]k = 5[/tex]The probability is P(X = 0), hence:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,12,2,5) = \frac{C_{5,0}C_{7,2}}{C_{12,2}} = 0.3182[/tex]
0.3182 = 31.82% probability that you end up with no gray socks.
Item c:
3 are black, hence [tex]k = 3[/tex].The probability is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,12,2,3) = \frac{C_{3,0}C_{9,2}}{C_{12,2}} = 0.5455[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5455 = 0.4545[/tex]
0.4545 = 45.45% probability that you end up with at least 1 black sock.
Item d:
There are no green socks, hence 0% probability that you end up with a green sock.
Item e:
0.0909 probability of two blue.The probability of two gray is P(X = 2) when k = 5.The probability of two black is P(X = 2) when k = 3.Hence, for two gray:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,5) = \frac{C_{5,2}C_{7,0}}{C_{12,2}} = 0.1515[/tex]
Then, for two black:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 2) = h(2,12,2,3) = \frac{C_{3,2}C_{9,0}}{C_{12,2}} = 0.0455[/tex]
Then, the probability of matching socks is:
[tex]p = 0.0909 + 0.1515 + 0.0455 = 0.2879[/tex]
0.2879 = 28.79% probability that you end up with matching socks.
A similar problem is given at https://brainly.com/question/24826394
3ab - 2bc = 12 solve for b
Question 8 options: Solve for the value of X. 23X = 6
Answer:
divide both sides by 23
making it to be 0.26
The value of x from the equation 23x =6 is x= 6/23.
To solve for the value of x in the equation 23x = 6, we need to isolate x on one side of the equation.
Divide both sides of the equation by 23:
(23x) / 23 = 6 / 23
Simplifying:
x = 6 / 23
Therefore, the value of x is 6 divided by 23, which can be left as a fraction or decimal depending on the desired form.
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Write an equation that illustrates the following: a number with two decimal places multiplied by a number with one decimal place the product has only 2 nonzero digits.
Answer:
Step-by-step explanation:
Represent the equation as follows:
[tex]a * b = c[/tex]
Where a,b and c are decimal numbers
To solve further, we make use of trial by error method
Let
[tex]a = 2.52[/tex]
[tex]b = 0.6[/tex]
Such that
[tex]2.5 * 0.6 = c[/tex]
[tex]1.512 = c[/tex]
[tex]c = 1.512[/tex]
This set of digits do not follow the rule in the question
Let
[tex]a = 2.55[/tex]
[tex]b = 1.6[/tex]
[tex]2.55 * 1.6 = c[/tex]
[tex]4.08 = c[/tex]
[tex]c = 4.08[/tex]
The result has only 2 non zeros (4 and 8)
Hence
[tex]2.55 * 1.6 = 4.08[/tex] answers the question.
However, there are other set of numbers that can be used too
One of the equation which illustrates and meets the conditions given is :
First number = 1.25First number = 1.25Second number = 0.2.Product = 0.25First number, x = 1.25
First number, x = 1.25 Second number, y = 0.2
Result = first Number × second number
Result = 1.25 × 0.2
Result = 1.25 × 0.2 Result = 0.25
Evaluating the result : 0.25
Number of digits = 3
Non - zero digits = 2
There are several values of x and y which will satisfy the 3 conditions given.
Therefore, the product of the values 1.25 and 0.2 gives the required output.
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A cabinet costs $149. If the sales tax is 7.5%, what is the total cost of the cabinet? Round to the nearest cent
Answer: $160.18
Step-by-step explanation:
Answer:
$160.18
Step-by-step explanation:
The cabinet's sale price (or in this case, sub-total) is $149. The sales tax is 7.5%, which means you must multiply 149 x 7.5% to get 11.175. After you do this, you must add the 11.175 (which we will round to $11.18 for your tax) to your subtotal ($149). Since $149 + $11.18 = $160.18, you will have to pay a total of $160.18 for the cabinet.
are ray AB and ray BA same? why
Answer:
A length of a ray cannot be measured therefore it's refferd to as infinite. same
Please help!
Explain how changes in the dimensions of a cube dimensions affect the volume of a cube. Be specific, explaining how much the volume will change with each increase of 1 unit on the side lengths.
Answer:
Difference = 3x² + 3x + 1
See Explanation
Step-by-step explanation:
Required: How changes in sides of a cube affects its volume.
Take for instance the side of the cube is x.
The initial volume would be:
Volume = x * x * x
Volume = x³
When then dimension is increased by 1 unit, the new volume would be
Volume = (x + 1) * (x + 1) * (x + 1)
Expand the brackets
New Volume = (x² + 2x + 1)(x + 1)
New Volume = x³ + 3x² + 3x + 1
[Calculate the difference between both volumes]
Difference = New Volume - Initial Volume
Difference = x³ + 3x² + 3x + 1 - x³
[Collect like terms]
Difference = x³ - x³ + 3x² + 3x + 1
Difference = 3x² + 3x + 1
So, there will be a difference of 3x² + 3x + 1 when the dimension is increased from x to x + 1
Take for instance: a dimension of 2 units is increased to 3 units
Initial Volume = 2³ = 8
New Volume = 3³ = 27
Difference = 27 - 8
Difference = 19
Using the derived formula (x = 2)
Difference = 3x² + 3x + 1
Substitute 2 for x
Difference = 3 * 2² + 3 * 2 + 1
Difference = 3 * 4 + 6 + 1
Difference = 12 + 6 + 1
Difference = 19
You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die and 5 on red die). (Enter your answer as a fraction.) (c) Find P(5 on green die and 1 on red die). (Enter your answer as a fraction.) (d) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)). (Enter your answer as a fraction.)
Answer:
1) yes ; 2) 1/36 ; 3) 1/36 ; 4) 1/18
Step-by-step explanation:
Given the following :
Two fair dice : 1 green ; 1 red
A) Are the outcomes on the dice independent:
Yes, becomes the outcome of the green dice does not have any effect on the outcome of the red dice.
B) Find P(1 on green die and 5 on red die).
Probability = (number of required outcome) / (total possible outcomes)
Total outcomes of a dice = 6
P(1 on green) = 1 / 6
P(5 on red) = 1/6
P(1 on green die and 5 on red die) :
(1/ 6) × (1/6) = 1/36
C) Find P(5 on green die and 1 on red die)
P(5 on green) = 1/6
P(1 on red) = 1/6
Find P(5 on green die and 1 on red die):
1/6 × 1/6 = 1/36
D) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die))
P(5 on green die and 1 on red die) = 1/36
P(1 on green die and 5 on red die) = 1/36
P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) =
P(5 on green die and 1 on red die) + P(1 on green die and 5 on red die)
= (1/36 + 1/36) = 2 /36 = 1/18
Rebecca Clarke's Nursery sells border plants for home gardeners at a discounted price of
$12.99. Rebecca Clarke's has 335 plants it needs to sell. Fixed costs for all these plants were
$1,675 and variable costs per plant are $3.65. What is the maximum profit Rebecca Clarke's
will make if it sells all the plants at the discounted price?
Answer:
$1,540.70
Step-by-step explanation:
1675/335 = 5
3.65 * 335 = 1222.75
Cost of $8.65 per plant, or $2,897.75 for every plant.
12.99 - 8.65 = 4.34
Profit of $4.34 per plant, or $1,540.70 total.
ANSWER brainliest if right
Answer:
c)
The distribution is skewed down the middle,
Therefore it is symmetric.
What values of x make the equation x2 + 9x – 22 = 0 true?
To solve this polynomial equation, we will need to factor the left side.
On the left, we have a a trinomial in a special form that
can be factored as the product of two binomials.
The trinomial on the left can be factored which makes life easier.
This factors as (x + 11)(x - 2) = 0.
This means that either x + 11 = 0 or x - 2 = 0.
Solving each equation from here, we get x = -11 or x = 2.
So the solution is {-11, 2}.
Answer:
2 and -11
Step-by-step explanation:
Step 1: Use the quadratic formula to solve for x
[tex]x=\frac{-b+-\sqrt{b^{2-4ac} } }{2a} \\x=\frac{-9+-\sqrt{9^{2}-4(1) (-22)} }{2(1)} \\x=\frac{-9+-\sqrt{169} }{2(1)}\\x=\frac{-9+-13 }{2}\\x1=\frac{-9+13 }{2}\\x1=\frac{4}{2} \\x1 = 2\\x2 = \frac{-9-13 }{2}\\x2 = \frac{-22 }{2}\\x2 = -11\\[/tex]
Therefore the values of 'x' that make the equation true is 2 and -11
The slant height of a cone is 8.45cm
and the diameter of the base is 14cm.
Calculate, three significant figures, the
curved surface area of the cone (Take
= 22÷7
[tex]\bf \underline{ \underline{Given : }}[/tex]
Slant height,l = 8.45 cmDiameter of base = 14 cm[tex]\bf \underline{ \underline{To \: be \: calculated : }}[/tex]
Calculate the curved surface area of the cone .
[tex]\bf \underline{ \underline{Formula \: applied : }}[/tex]
Curved surface area of cone = πrl
[tex]\bf \underline{ \underline{Solution : }}[/tex]
First of all,
Radius = Diameter/2
=> Radius,r = 14/2
=> Radius,r = 7 cm
Now,
[tex] \sf{Curved \: surface \: area \: of \: cone =\pi rl}[/tex]
[tex] \sf \: \implies \: \dfrac{22}{ \cancel7} \times \cancel7 \times 8.45[/tex]
[tex] \sf\implies22 \times 8.45[/tex]
[tex] \sf \implies 185.9 \: {cm}^{2} [/tex]
Hence,the Curved surface area of cone is 185.9 cm².
which number rounds to 341 when rounded to the nearest whole number
Answer:
341.5 because it makes the most sense
Answer:
340.511
Step-by-step explanation:
The five in the tenths place would make you round up.
Hope this helps! Can I get Brainliest? I’ve never had it before.
Please help me please thank
Answer:
x=20
Step-by-step explanation:
<2 = <3 when the lines are parallel
3x-10 = x+30
Subtract x from each side
3x-10 -x = x+30-x
2x-10 = 30
Add 10 to each side
2x-10 +10 = 30+10
2x = 40
Divide by 2
2x/2= 40/2
x =20
Can someone describe the process of Simplifying -12x + x - 3x - 9 + 5 - 1
first lets collect the x's so -12x + x is -11x (think about a number line if you are not sure) then we minus 3x so we get -14x
-9 + 5 is -4 then if we minus 1 we get -5 so
- 14x - 5
Answer: Combine each like term. Any number in this expression with the variable x is a like term. -12x+1x-3x=-14x. The numbers with no variable are like terms. -9+5-1=-5. The simplified expression is -14x-5.
Step-by-step explanation:
What is the value of X in the given triangle?
==================================================
Work Shown:
cos(angle) = adjacent/hypotenuse
cos(x) = 5/12
x = arccos(5/12)
x = 65.375681647836 which is approximate
x = 65.4 after rounding to one decimal place
Make sure your calculator is in degree mode. The arccosine function is the same as the inverse cosine function (shortened to [tex]\cos^{-1}[/tex] ).
Fast Food and Gas Stations Forty percent of all Americans who travel by car look for gas stations and food outlets that are close to or visible from the highway. Suppose a random sample of n = 25 Americans who travel by car are asked how they determine where to stop for food and gas. Let x be the number in the sample who respond that they look for gas stations and food outlets that are close to or visible from the highway.
a. What are the mean and variance of x?
b. Calculate the interval p-±2a. What values of the binomial random variable x fall into this interval?
c. Find P(6 ≤ x ≤ 14). How does this compare with the fraction in the interval WO for any distribution? For mound-shaped distributions?
Answer:
a
mean [tex]\mu = 10[/tex] variance [tex]\sigma^2 = 6[/tex]
b
The binomial random variable x fall into this interval ranges from
- 5 to 5
c
[tex]P(6 \le x \le 14) = 0.8969[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 25[/tex]
The percentage that look for gas stations and food outlets that are close to or visible from the highway is [tex]p = 0.40[/tex]
Generally the mean is mathematically represented as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 0.40 * 25[/tex]
=> [tex]\mu = 10[/tex]
The variance is mathematically represented as
[tex]\sigma^2 = np(1- p )[/tex]
=> [tex]\sigma^2 = 25 * 0.40(1- 0.40 )[/tex]
=> [tex]\sigma^2 = 6[/tex]
The standard deviation is mathematically evaluated as
[tex]\sigma = \sqrt{\sigma^2}[/tex]
[tex]\sigma = \sqrt{6}[/tex]
[tex]\sigma = 2.45[/tex]
The interval is evaluated as
[tex]p\pm 2 \sigma[/tex]
=> [tex]p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma[/tex]
=> [tex]0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45[/tex]
=> [tex]-4.5\ \ \ , \ \ \ 5.3[/tex]
The binomial random variable x fall into this interval ranges from
- 5 to 5
Generally
[tex]P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ][/tex]
[tex]P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ][/tex]
[tex]P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]][/tex]
From the z-table
[tex]P(Z > 1.63 ) = 0.051551[/tex]
And
[tex]P(Z >- 1.63 ) =0.94845[/tex]
=> [tex]P(6 \le x \le 14) = [1-0.051551] -[1-0.94845][/tex]
=> [tex]P(6 \le x \le 14) = 0.8969[/tex]
What is the equation of the line that passes through the point (-6, -8) and has an
undefined slope?
Answer: x=-6
Step-by-step explanation:
Undefined slopes are vertical lines, so there's no y variable in the equation. so you look at the point (-6, -8) and take out the y, which is negative eight. So your answer is negative six.
The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
Then the equation of the line that passes through the point (-6, -8) and has an undefined slope will be
y + 8 = m (x + 6)
The equation of the line that passes through the point (-6, -8) and has an undefined slope will be y + 8 = m (x + 6).
More about the linear equation link is given below.
https://brainly.com/question/11897796
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