Answer:
The values is [tex]P(52.3 < X < 54.7 ) = 0.17142[/tex]
Step-by-step explanation:
From the question we are told that
The lower limit of the interval is a = 43 minutes
The upper limit of the interval is b = 57 minutes
Generally the probability distribution function of uniform distribution is mathematically represented as
[tex]F(x) = \left \{ {{\frac{1}{(b - a)}\ \ \ for \ x \ \epsilon\ | a, b | } \atop {0 } \ \ \ \ \ \ otherwise} \right.[/tex]
Generally the probability it takes between 52.3 and 54.7 min is mathematically represented as
[tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {F(x)} \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {\frac{1}{57- 43} } \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \int\limits^{52.4}_{54.7} {\frac{1}{14} } \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = {\frac{1}{14} } \int\limits^{52.4}_{54.7} \, dx[/tex]
=> [tex]P(52.3 < X < 54.7 ) = {\frac{1}{14} } [x] \ | \left 54.7} \atop {52.3}} \right.[/tex]
=> [tex]P(52.3 < X < 54.7 ) = \frac{54.7 -52.3}{14}[/tex]
=> [tex]P(52.3 < X < 54.7 ) = 0.17142[/tex]
To rent a meeting room a college charges a reservation fee of $14 an additional fee of four dollars per hour. The chemistry club wants to spend less than $50 in renting a room. What are the possible numbers of ours a chemistry club could rent the meeting room?
This question concerns bit strings of length six. These bit strings can be divided up into four types depending on their initial and terminal bit. Thus the types are: 0XXXX0, 0XXXX1, 1XXXX0, 1XXXX1. How many bit strings of length six must you select before you are sure to have at least 6 that are of the same type?
Answer:
We have to choose 21 strings to be sure we have chosen at least 6 strings of the same type.
Step-by-step explanation:
Since the string type is determined by the initial and terminal bits as understood from the question, then the value of the bits between the initial and terminal bits is of no concern to us.
Now, to be sure you have atleast 6 of the same type, we select each string five times. By doing this, we have already selected 20 strings because we have 4 strings there. Now if you choose any of the string one more time, we are certain that we must have chosen atleast 6 strings that are the same. This means we have to choose 21 strings to be sure we have chosen at least 6 strings of the same type.
A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Match the vocabulary word with its corresponding example.
Answer:
1. All heart attack patients that the cardiologist has cared for or will care for in the future ⇒ B. POPULATION (entire group of individuals from where the sample must be chosen)
2. The 32 heart attack patients who were observed by the cardiologist ⇒ D. SAMPLE (the group that was observed)
3. The average recovery time for all heart attack patients that the cardiologist has or will treat ⇒ A. PARAMETER (the mean of the whole population)
4. The average recovery time for the 32 heart attack patients ⇒ E. STATISTICS (the mean of the sample)
5. The recovery time for a heart attack patient ⇒ F. VARIABLE (the data's attribute or value)
6. The list of all 32 heart attack patients' recovery times ⇒ C. DATA (information collected form the sample)
If ex + e⁻¹= 2, then x =..
Answer:
[tex] \rm x = \dfrac{2e - 1}{ {e}^{2} } [/tex]
Step-by-step explanation:
[tex] \rm Solve \: for \: x: \\ \rm \longrightarrow ex + {e}^{ - 1} = 2 \\ \\ \rm \longrightarrow e x + \dfrac{1}{e} = 2 \\ \\ \rm Subtract \: \dfrac{1}{e} \: from \: both \: sides: \\ \rm \longrightarrow e x + \dfrac{1}{e} - \dfrac{1}{e} = 2 - \dfrac{1}{e} \\ \\ \rm \longrightarrow ex = \dfrac{2e}{e} - \dfrac{1}{e} \\ \\ \rm \longrightarrow ex = \dfrac{2e - 1}{e} \\ \\ \rm Divide \: both \: sides \: by \: e: \\ \rm \longrightarrow \dfrac{ex}{e} = \dfrac{2e - 1}{e \times e} \\ \\ \rm \longrightarrow x = \dfrac{2e - 1}{ {e}^{2} } [/tex]
Solve the system of equations by any method.
5x+9y =16
x+2y =4
Answer:
The system of equations has one solution at (-4, 4).
Step-by-step explanation:
We are given the system of equations:
[tex]\displaystyle\left \{ {{5x+9y=16} \atop {x+2y=4}} \right.[/tex]
We can use elimination to solve this system. We need to multiply the second equation by -5 so we can cancel out our x-terms.
[tex]-5\times(x+2y=4) \rightarrow -5x - 10y = -20[/tex]
Therefore, our system now becomes:
[tex]\displaystyle\left \{ {{5x+9y=16} \atop {-5x-10y=-20}} \right.[/tex]
Now, we can add these two equations together and solve for y.
[tex]\displaystyle(5x + 9y) + (-5x - 10y) = 0 - y\\\\16 + (-20) = -4\\\\-y = -4\\\\\frac{-y}{-1}=\frac{-4}{-1}\\\\y = 4[/tex]
Now, we can substitute our value for y into one of the equations and solve for x.
[tex]x+2(4)=4\\\\x + 8 = 4\\\\x = -4[/tex]
Therefore, our final solution is (-4, 4).
Find the equation of the linear function represented by the table below in slope-intercept form.
Noah is thinking of two fractions that have a sum of 35. Each fraction has a numerator of 1.
What are the denominators of the fractions?
Answer:
2 and 10
Step-by-step explanation:
The equation of the line that passes through points (0, negative 7) and (2, negative 1) is shown below. What value is missing from the equation?
y = _______x – 7
Answer:
1/3
Step-by-step explanation:
2-0=2
-1 - -7 = 6
2/6. = 1/3
Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?
Answer:
n = 1, this means the interest compounds ANNUALLY.
Step-by-step explanation:
Carlos deposited $7,924 into a savings account 30 years ago. The account has an interest rate of 4.6% and the balance is currently $30,541.83. How often does the interest compound?
Compound Interest Formula
: A = P(1 + r/n)^nt
A = Amount after time t
P = Principal (Initial Amount Invested)
r = Interest rate
n = Number of times the interest is compounded
t = time in years
A = $30,541.83
r = 4.6% = 0.046
t = 30
P = $7,924
Hence,
$30,541.83 = $7924(1 + 0.046/n)^30n
Divide both sides by 7924
$30,541.93/$7924 = (1 + 0.046/n)^30n
$30,541.93/$7924 = (n + 0.046/n)^30n
3.8543576477 = (n + 0.046/n)^30n
We take the logarithm of both sides
log 3.8543576477 = log (n + 0.046/n)^30n
Solving for n,
n = 1
Therefore, from the calculation above, since n = 1, this means the interest compounds ANNUALLY.
Someone help me out with this
Write an equation in standard form of the line shown.
Answer: y= -2x + 4
Hope this helps.
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Please Help! WILL GIVE BRAINLIEST
Answer:
{-1, 0, 1, 2}
Step-by-step explanation:
EXPONENTIAL FUNCTION
Evaluate the following:
1.) 2^-3
2.) 5^-3
3.)6^-6
4.) (5/2)^-2
5.) (7/3)^-3
can somone help me please
Answer:
The slides is 36 and the angle is 180.
Step-by-step explanation:
14.4m+15.6m+6m=36
90+30+50=180
If they ask why it is 180 because when adding all the angles it has to give you a total of 180.
Which equation has a slope of -2 and passes through the point (1,-6)?
A. y=-2x-4
B. y=-10x+3
C. y=3x-10
D. y=3x+10
Answer:
y=-2x-4
Step-by-step explanation:
Given that,
Slope, m = -2
It passes through the point (1,-6).
We need to find the equation of line that passes throgh the given point. It can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]
Put y₁ = -6, x₁ = 1 and m = -2
[tex]y-(-6)=(-2)(x-1)\\\\y+6=-2x+2\\\\y+2x+6-2=0\\\\y=-2x-4[/tex]
Hence, the equation of line is y=-2x-4.
WILL GIVE BRAINLIEST! What is the constant of proportionality between cups of rice and cups of water shown in this table?
Cups of Rice Cups of Water
1 1.5
2 3
3 4.5
4 6
5 7.5
1.5
0.5
2
This is a trick question as this is not proportional.
None of the Above
Answer:
E (none of the above)
Step-by-step explanation:
1 = k(1.5)
2 = k(3)
Therefore, k = 2/3
and when we put k = 2/3 into all values in the table we notice it is right
but it could be "A" also if the relationship was cups of water to cups of rice
The ratio of boys to girls in a classroom was 9:8. Half of the girls left the classroom, and then there were 15 more boys than girls. Part i.) How many children were in the classroom in the beginning?
Answer:
i pretty sure it's 17
Step-by-step explanation:
Answer:
17
Step-by-step explanation:
12 = -4(-6x - 3)
What does x=
Answer:
x=0
Step-by-step explanation:
Answer:
x=24
Step-by-step explanation:
12= -4(-6x-3)
12=24x+12
-24x= 12-12
-24x=0
X=24
An online auction charges sellers a flat fee of $1.20 and 2% of the amount of the sale. Let A be the amount of the sale in dollars and C be the charge of the online auction. Explain whether the solutions A=−5 and C=1.1 are viable.
The solutions are not viable because the amount charged is not a whole number.
The solutions are viable because the amount of the sale is an integer.
The solutions are viable because the amount charged is positive.
The solutions are not viable because the amount of the sale cannot be negative
Answer:
The solutions are not viable because the amount of the sale cannot be negative
Step-by-step explanation:
We are told that;
Let A be the amount of the sale in dollars and C be the charge of the online auction
This means that both values of A and B should be non-negative integers.
Now, we are also told that An online auction charges sellers a flat fee of $1.20 and 2% of the amount of the sale.
We can conclude that the solution is not viable because the amount of sale of -1.1 cannot be negative.
Answer asap. Just the image below.
Answer:
x>9
Step-by-step explanation:
Remark
You have to watch this question when you divide by a minus. We should try to eliminate that possibility.
Equation
7 - 2/3 x < x - 8 Add 2/3 x to both sides
7 < x + 2/3 x - 8 Combine the like terms on the right.
7 < 1 2/3 x - 8 Add 8 to both sides
7 + 8 < 5/3 x Combine the left
15 < 5/3 x Multiply both sides by 3/5
15*3/5 < 5/3*3/5 x
9 < x
Since all the answers have the x on the left, we have to put this answer so that x is on the left. Be very careful. The big end of the arrow is towards the x. We have to make sure it stays that way.
x > 9
The answer is A
The table shows the highest and lowest golf scores for your cousin and your friend over the summer. Find the ranges of golf scores for your cousin and your friend. Who has the greater range of scores?
highest +6, +3
lowest -2, -3
Answer:
Cousin has a greater range of score.
Step-by-step explanation:
Range = Highest No. - Lowest No.
Range of cousin's score = +6 - (-2)
= +6+2 = 8
Range of friend's score = -2 - (-3)
= -2 + 3 = 1
Cousin has a greater range of score.
[tex]\rule[225]{225}{2}[/tex]
Hope this helped!
~AnonymousHelper1807Find the additive inverse of 0.25
Find tan θ if sec θ = root 37/6 and sin θ < 0
which of the equations is the correct representation of the following?
six is the product of two consecutive integers
x(x+1)=16
x+(x+1)=6
x(x-2)=6
x(x+1)=6
Answer:
x(x+1)=6
Step-by-step explanation:
6= 2 numbers, one after the other, so you have the same number and add 1 to make the second number.
Example:
6=2.5 and 3.5
Answer:
X * (x+1) = 6
Step-by-step explanation:
Please answer this simple math question(CLICK TO SEE PICTURE) ITS MULTIPLE CHOICE. Answers are not exact! (it's not the one I chose) TY!
Look at the figure. Find the value of x?
Answer:
since they both bisect themselves it means they are equal
i.e 3x=5x-30
3x-5x=-30
-2x=-30
minus cancels minus
2x=30
x=15
Answer:
x = 15
Step-by-step explanation:
3x = 5x - 30
-2x = -30
x = 15
The sum of 56x2 and 56x2 is 56x______?
Answer:
56x4
Step-by-step explanation:
56x2= 112 so since you have 56x2 twice you want to add 112+112 to get 224 now what you wanna do is to divide 56 from 224 and your answer will be 4 so you can say 56x4
The sum of two numbers is 17. The difference of the numbers is 3
Ashe feels she needs $45,000 per year in retirement. If she receives $2,500 a month from Social Security, at what interest rate must Asha invest her $250,000 of savings for her income to be AT LEAST $45,000 per year? PLEASE HURRYYY
Answer:
15,000 from her savings
Step-by-step explanation:2,500*12=30,000 45000-30,000=15,000