The independent variables, the ones that are intentionally manipulated, are temperature and surface time.
The dependent variable, the one that you measure the response in, is the reaction time.
The physical concept of temperature indicates in the numerical form how hot or cold something is. Temperature is measured with a thermometer.
Thermometers are calibrated in numerous temperature scales that historically have depended on various reference factors and thermometric materials for definition. The most common scales are the Celsius scale with the unit image °C (previously referred to as centigrade), the Fahrenheit scale (°F), and the Kelvin scale (okay), the latter being used predominantly for clinical functions. The kelvin is one of the seven base units within the worldwide machine of gadgets (SI).
Absolute zero, i.e. 0 kelvin or −273.15 °C, is the bottom factor within the thermodynamic temperature scale. Experimentally, it can be approached simplest very intently, however, no longer genuinely reached, as diagnosed in the 0.33 law of thermodynamics. it'd be not possible to extract power as the warmth from a body at that temperature.
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liz is baking cookies. a single batch uses ¾ teaspoons of vanilla. if liz is mixing the ingredients for five batches at the same time, how many tablespoons of vanilla will she use?
Step-by-step explanation:
Liz is baking cookies. a single batch uses ¾ teaspoons of vanilla. if Liz is mixing the ingredients for five batches at the same time, how many tablespoons of vanilla will she use?
3/4 = 0.75 teaspoons
0.75 teaspoons * 5 batches = 3.75 teaspoons
There are 3 teaspoons in a tablespoon so:
Liz will use:
1 1/4 tablespoons
if you need in decimal form: 1.25 tablespoons
Help please i am stuck! More points!
Answer:
I belive it would be 102
Step-by-step explanation:
Answer:
306 cm
Step-by-step explanation:
the opposite side is the same as the shaded side
18 x 17 = 306 cm
Given rhombus ABCD, find mLADC.
The measure of the required angle of the given rhombus ABCD is m∠ADC = 64°.
Properties of a rhombus:In a rhombus, the opposite angles are equal in measure.The diagonals in a rhombus are the angle bisectors.The two diagonals bisect each other.The adjacents angles of a rhombus are supplementary.Calculation:The given rhombus has four angles as
∠ADC, ∠DCB, ∠CBA, and ∠BAD
It has two diagonals that bisect each other at point E.
And we have ∠ABD = 32° and ∠ACD = 58°
Here, the angles ∠ABD and ∠BDC are alternate angles. Since we know that, the alternate angles are equal in measure, we can write
∠ABD = ∠BDC
⇒ 32° = ∠BDC
Since we know that the diagonals of a rhombus bisect the angles, we get
∠ADC = 2∠BDC
⇒ ∠ADC = 2 × 32° = 64°
Therefore, the required angle of the rhombus is ∠ADC = 64°.
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Which one is an undefined term?(A) Point
(B) Line
(C) Plane
(D) All of the above
Answer:
all the above
Step-by-step explanation:
examples of undefined term are point line and plane
3 =
% of 7 percent with rounding
3 of 7 in percentage with rounding is 42.86%
How to determine 3 of 7 as a percent?
Percentage is a way of expressing a number as a fraction of 100. It is often used to express how much of something there is compared to the total amount.
For example, if you have 20 apples and the total number of apples is 100, you can express the fraction of the total number of apples you have as a percentage. That is 20/100 = 0.2, which is equal to 20%.
In order to write 3 of 7 as a percent, we can say:
3/7 × 100 = 42.86%
Thus, with rounding 3 of 7 is 42.86%
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Complete Question
3 of 7 percent with rounding = ___ %
bookword code G06 calculate length of AD
Aiyub vai loves to eat apples. He eats apples in an interesting way. After buying apples, on the first day, he eats 1 apple; on second day, he eats 2 apples; on the third day, he eats 3 apples. For the next few days he eats apples in a way such that, on day N , he eats n apples more than that he ate 3 days before. How many apples will he eat more in day 99 than that of in day 98?
Answer:
33
Step-by-step explanation:
Difference from
Day Number of apples previous day
1 1 -
2 2 1
3 3 1
4 5 2
5 7 2
6 9 2
7 12 3
8 15 3
9 18 3
10 22 4
11 26 4
12 30 4
13 35 5
14 40 5
15 45 5
16 51 6
17 57 6
18 63 6
19 70 7
20 77 7
21 84 7
The differences between consecutive days started at 1, then 2, then 3, etc. The last day of any specific difference is a multiple of 3.
For example, day 3 was the last day of a difference of 1.
Day 6 was the last day of a difference of 2.
Day 9 was the last day of a difference of 3.
Day 12 was the last day of a difference of 4.
In each case, 6/2 = 3; 9/9 = 3; 12/4 = 3.
99 is a multiple of 3, so it will be the last day with a difference of 99/3 = 33
Answer: 33
which expression is equivalent to −10.75 (20x +15.2)
The expression which is equivalent to −10.75(20x +15.2) is -215x - 163.4.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical terms.
As per the given expression,
−10.75 (20x +15.2)
By multiplying or opening the bracket,
When a bracket opens then the outer number will multiply with all inner variables as,
⇒ (-10.75 × 20x) + (- 10.75 × 15.2)
⇒ -215x - 163.4
Hence "The expression which is equivalent to −10.75(20x +15.2) is -215x - 163.4".
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Write a linear function that relates your distance to the number of seconds. In the same coordinate plane, graph the linear functions that represent the distances of you and your friend.
The linear function that relates your distance to the number of seconds is y = Sx, and the graph is attached below.
What is a linear function?A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.
The formula for distance covered is given by,
[tex]Distance = Speed \times time[/tex]
Assume the speed is constant,
D = S × t
Assume distance is in y direction and time is in x direction, the equation can be written as,
y = Sx
Suppose my speed of mine is 5 m / s and the speed of my friend's is 10 m/s then the function of distance for my friend,
Y = 10X
And for me
y = 5x
The graph of this is attached below, the red line in the graph is my distance equation and the green line is of my friend.
Therefore, the linear function that relates your distance to the number of seconds is y = Sx.
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Determine which of the following are examples of independent events.
Rolling a 5 on one die and rolling a 5 on a second die.
Choosing a cookie from the cookie jar and choosing a jack from a deck of cards.
Winning a hockey game and scoring a goal.
Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.
What is independent events?
Events classified as independent do not depend on other events for their occurrence. For instance, if we toss a coin in the air and it lands on head, we can toss it again and this time it will land on tail. Both instances involve independent occurrences of the two events.In probability, two events are deemed independent if the knowledge that one occurred has no impact on the likelihood of the other event.Winning a hockey game and scoring a goal is dependent because if we score a goal then only we can win the game.
Hence, Rolling a 5 on one die and rolling a 5 on a second die and Choosing a cookie from the cookie jar and choosing a jack from a deck of cards are the independent events.
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Which statement justifies why (2, 1,985.5) is a solution to y = 2,200(0.95)x?
(2, 1,985.5) is not a solution of the equation y = 2200(0.95)x.
What is solution of an equation?
An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself.
Consider, the given equation
y = 2200(0.95)x
And the point given is, (2, 1985.5).
From this x = 2, y = 1985.5
Plug x = 2 in the above equation,
y = 2200(0.95)(2)
y = 4180 ≠ 1985.5
Hence, the given point (2, 1985.5) is not a solution to the equation
y = 2200(0.95)x.
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The population of a city decreases by 3.3% per year. If this year's population is 72,000, what will next year's population be, to the nearest individual?
Using the given information, the city's next year population will be 69,840
Determining the population of a cityFrom the question, we are to determine what the population of the city will be the following year
From the given information,
"The population of a city decreases by 3.3% per year"
and
This year's population is 72,000
Thus,
The population of the following year will be
72000 - 3% of 72000
Next year population = 72000 - 3% of 72000
Next year population = 72000 - 3% × 72000
Next year population = 72000 - 0.03 × 72000
Next year population = 72000 - 2160
Next year population = 69,840
Hence, the population will be 69,840
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Match each system of equations with the number of solutions the system has. 1. No solutions 2. One solution 3. Infinitely many solutions A. y=-4/3x+4 y=-4/3x-1 B. y=4x-5 y=-2x+7 C. 2x+3y=8 4x+6y=17 D. y=5x-15 y=5(x-3)
A. y = - (4/3)x + 4.
y = - (4/3)x - 1.
No solution.
B. y = 4x - 5.
y = - 2x + 7.
one solution.
C. 2x + 3y = 8
4x + 6y = 17.
No solution.
D. y = 5x - 15.
y = 5(x - 3).
Infinitely many solutions.
What is the graphical solution of a system of equations?Graphical solutions of a system of equations are a way of finding the intersection points of all the equations given.
A system with two or more than two equations has a solution only when they have a common intersection point.
We'll graph each system of equations, If they intersect at one point they have one solution, if they are parallel to each other they have no solution and if they are coinciding with each other they have infinitely many solutions.
y = - (4/3)x + 4.
y = - (4/3)x - 1.
These are parallel lines no solution.
y = 4x - 5.
y = - 2x + 7.
These lines intersect at (2, 3) one solution.
2x + 3y = 8
4x + 6y = 17.
They are parallel to each other.
y = 5x - 15.
y = 5(x - 3).
These are coinciding lines if we distribute the terms hence infinitely many solutions.
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Only 20 of a sample of 275 students say they are vegetarians. Of these, nine eat both fish and eggs, three eat eggs but not fish, and eight eat neither. If we choose one of those 275 students at random and the chosen student turns out to be a vegetarian, what is the probability that the chosen student eats neither fish nor eggs?
0.5
8/20 - 0.4
8/275 - 0.03
1
0
20/275 - 0.07
0.65 is the probability that the chosen student eats neither fish nor eggs.
What are examples and probability?
A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
The likelihood of an event occurring increases as its probability increases. The flip of a fair (impartial) coin serves as a straightforward illustration.
We know that there is sample of 275 MHS Students
20 are vegetarians
9 eat both fish and eggs
3 eat eggs but not fish
8 eat neither
Total 20
In a table
FISH FISHc TOTAL
EGGS 9 3 12
EGGSc 1 7 8
TOTAL 10 10 20
P(F U E) = 9 + 3 + 1 / 20 = 13/20 = 0.65
Or
P(F U E) = 10/20 + 12/20 -9/20 = 13/20 = 0.65
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how many bit strigs of length 5 do have 3 consecutive zeros such that the remaining two bits are not not equal?. show all your work step by step to get credit. final answers must be provided in decimal form three important considerations for this problem: (a) brute force is not allowed in this problem. it must be solved using either permutations, combinations or both. (b) a bit can be 0 or 1 (c) repetitions are not allowed in the final results.
Based on the permutation concept, the allowed final result is 20
Permutation method
In statistics, permutation means a mathematical calculation of the number of ways a particular set can be arranged.
Given
Here we need to find how many bit strings of length 5 do have 3 consecutive zeros such that the remaining two bits are not not equal.
Let us consider T denote the number of bit strings of length containing 3 consecutive 0's.
Total no. of bit strings of length = 5
And the no. of bit strings of length not containing 3 consecutive 0's = 3
Then the possible combination of permutation is calculated as,
=> T = 5!/3!
=> T = 20
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determine whether or not the vectors U=(1, 1, 2), v=(2, 3, 1), and w=(4, 5, 5) in R³ are linearly dependent
The u(1, 1, 2), v(2, 3, 1), and w(4, 5, 5) supplied vectors are linearly dependent.
What is a Vector?A vector is a quantity with both magnitude and direction in physics. It is often depicted by an arrow with the same direction as the amount and a length proportionate to the size of the quantity. A vector lacks position, but has magnitude and direction. A vector is therefore unaffected by displacement parallel to itself as far as its length is unaltered.
As per the given information in the question,
The given vectors are:
u = (1, 1, 2)
v = (2, 3, 1) and,
w = (4, 5, 5)
If there are three scalars that are not all zero and that are dependent on a set of vectors (u, v, and w), they have been shown to be linearly dependent.
au + bv + cw = 0
⇒ a(1, 1, 2) + b(2, 3, 1) + c(4, 5, 5) = (0, 0, 0)
⇒ (a + 2b + 4c, a + 3b + 5c, 2a+ b + 5c) = (0, 0, 0)
So,
a + 2b + 4c = 0 (i)
a + 3b + 5c = 0 (ii)
2a+ b + 5c = 0 (iii)
From equation (i) and (ii)
b = -c
From equation (i)
a - 2c + 4c = 0
⇒ a = -2c
Let's assume that c = 1
So,
a = -2 and,
b = -1
Then, from the obtained values,
-2u - v + w = 0
As a result, there is a set of non-zero values for a, b, and c such that:
au + bv + cw = 0
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Find the measure of the missing angle
The measures of the missing angles are:
1. x = 41°
2. x = 100°
3. x = 42°
4. x = 47°
5. x = 65°
6. x = 73°
7. x = 70°
8. x = 43°
How to Find the Missing Measures of the Angles?To find the missing measures of each of the angles given, we need to apply one of the property of isosceles triangles which states that the base angles of an isosceles triangle has the same measure.
1. x = 41° [base angles]
2. x = 180 - 2(40) = 100°
3. x = 180 - 2(69) = 42°
4. x = 1/2(180 - 86) = 47°
5. x = 65° [base angles are equal]
6. 2x = 146
2x/2 = 146/2
x = 73°
7. x = 180 - 2(180 - 125)
x = 70°
8. 2x = 86
2x/2 = 86/2
x = 43°
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The length and width of a rectangle are consecutive odd integers. The area of the rectangle is 323 square inches. Find the length and width of the rectangle.
Answer:17cm x 19cm
Step-by-step explanation:
Answer: length is 19 inches
width is 17 inches
Step-by-step explanation:
Let the length and the width are x>0 and (x+2)>0
Hence,
x(x+2)=323
x²+2x=323
x²+2x-323=0
x²+(19x-17x)-323=0
(x²+19x)-(17x+323)=0
x(x+19)-17(x+19)=0
(x+19(x-7)=0
x+19=0
x=-19∉ (x>0)
x-17=0
x=17 inches
x+2=17+2
x+2=19 inches
the linear factors of the cubic are ✔ (x – 2)(x – 3)(x – 5) . to solve for the leading coefficient, use ✔ –5 = a(0 – 2)(0 – 3)(0 – 5) . a = ✔ 1/6 write the function: f(x) = x3 – x2 x –
For the linear factors of the cubic, which are (x - 2)(x - 3)(x – 5), the function will be f(x)=1/6x³–5/3x²+31/6x–5.
What is linear factors?The first-degree equations that make up a polynomial's linear factors serve as the foundation for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. A linear factor model establishes a linear equation-based relationship between the return on an asset (such as a stock, bond, mutual fund, or other type of investment) and the values of a small number of factors.
Here,
The linear factors of the cubic are
=(x – 2)(x – 3)(x – 5)
To solve for the leading coefficient, use
–5 = a(0 – 2)(0 – 3)(0 – 5)
a = 1/6
f(x)=1/6x³–5/3x²+31/6x–5
The function will be f(x)=1/6x³–5/3x²+31/6x–5 for the the linear factors of the cubic that is (x – 2)(x – 3)(x – 5).
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help please i need to answer it
Answer: 4ft/s
Step-by-step explanation:
I think
2 + 6 = 8
8 / 2 = 4
If B is the midpoint of AC, find the length of AC.
10
23
46
None of these choices are correct.
Answer: [C]: " 46 units ."
______
Step-by-step explanation:
The question (and corresponding image) asks:
" If B is the midpoint of AC, find the length of AC. "
Note:
The midpoint refers to the point in the middle of the line [segment].
In this particular question:
⇒ The line segment; AC is divided into 2 (two) equal segments of the same length:
AB = (x + 13) ; and:
BC = (2x + 3) ; {as per 'posted image'} ;
We are asked to find the length of AC.
[length of AB] + [length of BC] = [length of AC].
(x + 13) + (2x + 3) = [length of AC; for which we solve] :
We shall solving for x ; & then plug in the value to solve.
Note:
[length of AB] = [length of BC] ; Plug in our known values:
⇒ that is; (x + 13) = (2x + 3) ;
So, we have: " x + 13 = 2x + 3 "
_____________________
" x + 13 = 2x + 3 " ;
− x − 3 = − x − 3 " ;
_____________________
0 + 10 = x + 0 ;
→ " 10 = x " ;
↔ {Note: According to the "symmetric property" algebra:
"a = b " ; then " b = a"};
→ " x = 10 " ; {according to the "symmetric property of alm
__________________
Another method:
When we have:
" x + 13 = 2x + 3 " ;
→ Subtract each side of the equation by x ; & subtract each side of the equation by 3 ;
to isolate x on one side of the equation —
[in this case, the 'right-hand' side of the equation];
and to solve for x ; as follows:
" x + 13 = 2x + 3 ";
Now; for each side of the question—on a separate 'left-hand' side; and: on a separate 'right-hand' side basis; we can combine the 'like terms' and simply:
For the left-hand side:
" x + 13 − x − 3 " : Combine the 'like terms":
+ x − x = 0 ; [that is: " +1x − 1x = 0"];
+ 13 − 3 = + 10 ; We have: " 0 + 10 = + 10 ".
Now, For the right-hand side:
" 2x + 3 − x − 3 " : Combine the 'like terms'; as follows:
" + 2x − x = x " ; {that is: " +2x − 1x = 1x = x "} ;
" + 3 − 3 " = 0 " . " x + 0 = x "
So: [left-hand side = right-hand side] ;
→ 10 = x ; ↔ " x = 10 ."
Both methods result in the same value for x ; that is: x = 10 ; which happens to suggest credibility.
Now, to find the length of AC ; which equals:
→ " x + 13 + 2x + 3 " ;
Then, we plug in our calculated value; 10 —for the values of x ;
and solve!
→ " 10 + 13 + (2*10) + 3 " = " 10 + 13 + 20 + 3 " = " 46 units ".
⇒ which corresponds to the correct answer: [C]: " 46 units."
_______
Hope this answer with explanation is helpful.
Best wishes!
_______
Write the complex number 8/1+i in standard form?
Answer: 8 + i
Step-by-step explanation:
The complex number 8/1+i can be written in standard form as 8 + i. In standard form, a complex number is written as a+bi, where a is the real part and bi is the imaginary part. In this case, the real part is 8 and the imaginary part is i. Therefore, the standard form of the complex number 8/1+i is 8 + i.
Answer: 4-4i
Step-by-step explanation:
[tex]\displaystyle\\\frac{8}{1+i} =\\\\\frac{8(1-i)}{(1+i)(1-i)}=\\\\\frac{8(1-i)}{1^2-i^2} =\\\\\frac{8(1-i)}{1-(\sqrt{-1})^2 }=\\\\\frac{8(1-i)}{1-(-1)}=\\\\\frac{8(1-i)}{1+1} =\\\\\frac{8(1-i)}{2} =\\\\4(1-i)=\\\\4-4i[/tex]
Which expression is equivalent to 3(−5.5b − 3) − (5b + 7)?
11.5b + 4
−21.5b − 2
−21.5b − 16
11.5b − 16
Answer:
-21.5b - 16
Step-by-step explanation:
Simplify the expression
3(−5.5b − 3) − (5b + 7)
-16.5b - 9 - 5b - 7 [Expand the parentheses]
-21.5b - 16 [Add like terms]
This matches the third option.
A computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in hundreds of dollars) he can make on the full version of the new shareware. Following is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed:
Regression Statistics Multiple R 0.8691 R Square 0.7554 Adjusted R Square 0.7467 44.4765 Standard Error Observations 30,0000 ANOVA SS MS Significance F 1 171062.9193 171062.9193 86.4759 Regression 0.0000 28 55388.4309 1978.1582 Residual Total 29 226451.3503 Coefficients Standard Emor t Stat P-value Lower 95% Upper 95% 95.0614 26.9183 3.5315 0.0015 150.2009 39,9218 intercept 4.5513 Download 3,7297 9.2992 0.0000 0.4011 2.9082
a) Write down the regression equation.
b) What is the correct interpretation for the slope coefficient?
c) Predict the revenue when the number of downloads is 30,000.
Answer: ______________________________
d) What is the correct interpretation for the coefficient of determination (R2)?
e) The 95% confidence interval estimate for the population slope is (______________ , ______________)
f) Is there sufficient evidence that revenue and the number of downloads are linearly related at a 5% level of significance? Give a reason why.
Here is sufficient evidence that revenue and the number of downloads are linearly related.
A computer software developer would like to use the number of downloads for the trial version of his new shareware to predict the amount of revenue.
The Null hypothesis is the common statistical theory that asserts that no statistical relationship or significance exist between two sets of observed data and measure phenomena based on a single observed variable.
Therefore the null hypothesis become,
H₀ : ρ₁ = 0
and the adjacent hypothesis will become,
H₁ : ρ ≠ 0
Now we will calculate test statistic,
t = r × [tex]\sqrt{\frac{n-2}{1-r^{2} } }[/tex]
= (0.8691) × [tex]\sqrt{\frac{30 - 2}{0.1309^{2} } }[/tex]
t = 9.2974
we know that degree of freedom = n - 2 = 28
p-value at t = 9.2974 is 0.00
α = 0.05
since p-value < α
so null hypothesis will be rejected.
Hence we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.
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What is 15 cm/year converted to inches per month? Round to the nearest hundreth.
The required conversion of the 15 cm/year is given as 0.5 inches per month.
Given that,
15 cm/year converted to inches per month is to be determind.
Conversion of the units is defined as the multiplying the original value with the unit factor.
Here,
1 cm = 0.4 inch
1 year = 12 month,
Substitute these values in the expression = 15 cm / year
= 15 × 0.4 / 12
= 0.5 inches per month.
Thus, the required conversion of the 15 cm/year is given as 0.5 inches per month.
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goodness of fit 5. a buyer for a t-shirt shop wants to compare the proportion of t-shirts of each size that are sold to the proportion that were ordered. the buyer counts the number of t-shirts of each size that are sold in a week. size sold small medium 25 41 large 91 extra large 68 percentage ordered 10% 20% 40% 30% does the distribution of the sold items follow the distribution of the ordered items? state the conclusion.
The buyer concludes that there is not a significant difference between the observed t-shirt sales and the expected t-shirt sales.
Given :
goodness of fit 5. a buyer for a t-shirt shop wants to compare the proportion of t-shirts of each size that are sold to the proportion that were ordered. the buyer counts the number of t-shirts of each size that are sold in a week.
Test :
Test Contribution
Category Observed Proportion Expected to Chi-Square
Small 25 0.1 22.5 0.277778
Medium 41 0.2 45.0 0.355556
Large 91 0.4 90.0 0.011111
Extra Large 68 0.3 67.5 0.003704
The overall chi-square statistic is 0.648 and has a p-value of 0.885. Because the p-value is greater than the significance level of 0.05, the buyer fails to reject the null hypothesis.
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g(x) = 1/3x - 6
Linear, Quadratic, Expodential, or None and why?
The given equation is a linear equation.
What is the linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
We have,
g(x) = 1/3x - 6
We need to identify whether the given equation is Linear, Quadratic, Exponential, or None and why.
g(x) is the term that shows the rate of change with respect to x.
1/3 is the coefficient of the variable x
and the 6 is the constant term in the equation.
so, comparing the given equation with standard form of linear equation,
y = mx + c.
we can say here,
y = g(x)
m = 1/3,
c = 6
Hence, the given equation is a linear equation.
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14.25 Hot Spot. Hot Spot is a California lottery game. Players pick 1 to 10 Spots (sets of numbers, each from 1 to 80) that they want to play per draw. For example, if you select a 4 Spot, you play four numbers. The lottery draws 20 numbers, each from 1 to 80. Your prize is based on how many of the numbers you picked 27% Page 1584 of 6452 Location Co match one of those selected by the lottery. The odds of winning depend on the number of Spots you choose to play. For example, the overall odds of winning some prize in 4 Spot is approximately 0.256. You decide to play the 4 Spot game and buy 5 tickets. Let X be the number of tickets that win some prize. 6452 Location 18277 of 68468 32°F Mostly cloudy 6:10 3/14 the location of the mean on your histogram. a. Xhas a binomial distribution. What are n and p? b. What are the possible values that x can take? e, Find the probability of each value of X. Draw a probability histogram for the distribution of X. (See Figure 14.2 on page 331 for an example of a probability histogram.) d. What are the mean and standard deviation of this distribution? Mark 14.26 Roulette-Betting on Red. A roulette wheel has 38 slots, numbered 0, 00, and 1 to 36. The slots o and 00 are colored green, 18 of the others are red, and 18 are black. The dealer spins the wheel and at the same time rolls a small ball along the wheel in the opposite direction. The wheel is carefully a Page 1585 32°F Mostly cloudy
The answers to each part are as follows -
a. n refers to the number of bought tickets. p is representative of the probability that I will win some prize after taking a single ticket.
b. The values of X will be in the range 0 to 5. It is indicative of number of won tickets. Hence, values that are possible are 0, 1, 2, 3, 4 and 5.
c. The probability of each value of x will be calculated using Binomial formula. The formula is-
P(x) = (n choose x) × [tex] {p}^{x} [/tex] × [tex] {(1 - p)}^{n - x} [/tex]
In this formula, n is the number of trials, p is probability of success and x is number of successes.
Keep the values in formula for calculation -
P(0) = (5 choose 0) * 0.256^0 * (1-0.256)^(5-0)
P(0) = 0.326
P(1) = (5 choose 1) * 0.256^1 * (1-0.256)^(5-1)
P(1) = 0.410
P(2) = (5 choose 2) * 0.256^2 * (1-0.256)^(5-2)
P(2) = 0.219
P(3) = (5 choose 3) * 0.256^3 * (1-0.256)^(5-3)
P(3) = 0.062
P(4) = (5 choose 4) * 0.256^4 * (1-0.256)^(5-4)
P(4) = 0.011
P(5) = (5 choose 5) * 0.256^5 * (1-0.256)^(5-5)
P(5) = 0.001
d. For the probability histogram stating the distribution of x, the x-axis will have x values and y-axis will have the probability of each x value. The mean of distribution will be calculated by the formula -
mean = n × p
mean = 5 × 0.256
mean = 1.28
Further, the standard deviation will be calculated by the formula -
Standard Deviation = [tex] \sqrt{n × p × (1-p)} [/tex]
Keep the values in formula -
Standard Deviation = [tex] \sqrt{5 × 0.256 × (1-0.256)} [/tex]
Standard Deviation = 0.995
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jim is considering pursuing an ms in information systems degree. he has applied to two different universities. the acceptance rate for applicants with similar qualifications is 30% for university x and 40% for university y. what is the probability that jim will not be accepted at either university?
Probability that jim will not be accepted at either university is 0.42
He has applied to two different universities.
the acceptance rate for applicants with similar qualifications is 30% for university x
the acceptance rate for applicants with similar qualifications is 40% for university Y
Here, getting accepted into the two different universities are two independent events.
P(A or B) = P(A) x P(B)
Probability of not getting accepted in university X is 1 - 0.30
Probability of not getting accepted in university Y is 1 - 0.40
Probability that jim will not be accepted at either university
P'(X or Y) = P'(X) x P'(Y)
=(1 - 0.30) x(1 - 0.40) = 0.70 x 0.60 = 0.42
Therefore, Jim will not be accepted at either university has a probaility of 0.42 or 42%
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on average, how many murders will an american child have seen on various media before middle school?
Answer:
around 8,000 or 100,000 is the answer
