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]
Solve plz, this is due Tomorrow!!
.
Step-by-step explanation:
25) h=11
26). two sides are same = 12cm
27). time = 15 hours
28). veronica travelled = 6+1 = 7 days
29). number of tickets buyed by people each showing : 231
30) ©
2logx+3logy=0 find y in term of x
Answer:
y = x^(-2/3)Step-by-step explanation:
Given
2log x + 3log y = 0Finding y in terms of x
3log y = -2log xlog y = -2/3log xlog y = log x^(-2/3)y = x^(-2/3)Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 2log_x+3log_y=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 3log_y=-2log_x [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf {\cancel {log}}_y={\dfrac {2}{3}}{\cancel{log}}_x [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf y={\dfrac{2}{3}}x [/tex]
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A simple random sample of 36 bulbs is taken. a. What are the expected value, standard deviation, and shape of the sampling distribution of
Answer:
Answer and Explanation:
We have:
Population mean,
μ
=
3
,
000
hours
Population standard deviation,
σ
=
696
hours
Sample size,
n
=
36
1) The standard deviation of the sampling distribution:
σ
¯
x
=
σ
√
n
=
696
√
36
=
116
2) As per the central limit theorem, the expected value of the sampling distribution is equal to the population mean.
Therefore:
The expected value of the sampling distribution is equal to the population mean,
μ
¯
x
=
μ
=
3
,
000
The standard deviation of the sampling distribution,
σ
¯
x
=
116
The shape of the sampling distribution of
¯
x
is approximately normal. As the sample size is more than
30
.
3) The probability that the average life in the sample will be between
2670.56
and
2809.76
hours:
P
(
2670.56
<
x
<
2809.76
)
=
P
(
2670.56
−
3000
116
<
z
<
2809.76
−
3000
116
)
=
P
(
−
2.84
<
z
<
−
1.64
)
=
P
(
z
<
−
1.64
)
−
P
(
z
<
−
2.84
)
=
0.0482
Using Excel: =NORMSDIST(-1.64)-NORMSDIST(-2.84)
4) The probability that the average life in the sample will be greater than
3219.24
hours:
P
(
x
>
3219.24
)
=
P
(
z
>
3219.24
−
3000
116
)
=
P
(
z
>
1.89
)
=
0.0294
Using Excel: =NORMSDIST(-1.89)
5) The probability that the average life in the sample will be less than
3180.96
hours:
P
(
x
<
3180.96
)
=
P
(
z
<
3180.96
−
3000
116
)
=
P
(
z
<
1.56
)
=
0.9406
The expected value, standard deviation, and shape of the sampling distribution of will be 116.
What is Standard deviation?Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Given that;
The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Now,
Since, The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours.
And, A simple random sample of 36 bulbs is taken.
Hence, The expected value, standard deviation, and shape of the sampling distribution of is,
⇒ Standard error = 696 / √ 36
= 696 / 6
= 116
Thus, The expected value, standard deviation, and shape of the sampling distribution of = 116.
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What is the sum of two consecutive numbers is 141
The two consecutive integers such that their sum is 141 will be 70 and 71.
What is a number system?The number system is a way to represent or express numbers.
Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.
Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.
Let's say that two consecutive integers are x and x + 1.
x + x + 1 = 141
2x + 1 = 141
2x = 140
x = 70
So, x + 1 = 71
Thus, it will be 70 and 71.
Hence "The two consecutive integers such that their sum is 141 will be 70 and 71".
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A box of 11 transistors has 4 defective ones.
A) If 2 transistors are drawn from the box together, what is the probability that both transistors are defective?
B) If 2 transistors are drawn from the box together, what is the probability that neither transistor is defective?
C) If 2 transistors are drawn from the box together, what is the probability that one transistor is defective?
Answer:
(a) 0.1325
(b) 0.4045
(c) 0.463
Step-by-step explanation:
Let X denote the number of defective transistors.
The proportion of defective transistors is, p = 4/11 = 0.364.
All the transistors are independent of the others.
The random variable X follows a binomial distribution.
(a)
Compute the probability that both transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=2)={2\choose 2}(0.364)^{2}(1-0.364)^{2-2}\\\\=1\times 0.132496\times 1\\\\=0.132496\\\\\approx 0.1325[/tex]
(b)
Compute the probability that neither transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=0)={2\choose 0}(0.364)^{0}(1-0.364)^{2-0}\\\\=1\times 1\times 0.404496\\\\=0.404496\\\\\approx 0.4045[/tex]
(c)
Compute the probability that one transistors are defective, if 2 transistors are drawn from the box together as follows:
[tex]P(X=1)={2\choose 1}(0.364)^{1}(1-0.364)^{2-1}\\\\=2\times 0.364\times 0.636\\\\=0.463008\\\\\approx 0.463[/tex]
Two less than three-fourths of a number is, at most, negative seventeen. what is the range of values for the number?
Answer:
[tex]x\leq -20[/tex]
values ranging from minus infinity to negative 20
Step-by-step explanation:
we write the inequality associated with the text in terms of the unknown number "x" as:
[tex]\frac{3}{4} x-2\leq -17[/tex]
then, we solve for "x" by adding 2 to both sides, and then isolating "x" on the left as shown below:
[tex]\frac{3}{4} x-2\leq -17\\\frac{3}{4} x\leq -17+2\\\frac{3}{4} x\leq -15\\3\,x\leq -60\\x\leq -\frac{60}{3} \\x\leq -20[/tex]
then, the range of x-values is from minus infinity to negative 20
A Fahrenheit thermometer shows that the temperature is 13 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit
Answer:
-13??? weird question... do you mean celcius themometer?
Step-by-step explanation:
Answer:
The integer that represents 13 degrees below 0 is -13°F.
Step-by-step explanation:
This is because the phrase "13 degrees below 0" is obviously not an integer meaning that the corresponding integer to this phrase would be -13.
P.S.
This question was asked by somebody else and I answered already so I am not copying the answer!
Hope this helps! :)
Christen has to run around the rectangular soccer field during practice. The soccer field measures 60 meters
long by 45 meters wide.
How far did Christen run?
Answer:
210m
Step-by-step explanation:
60+60+45+45
120+90
210m
12k-15=35+2k
answer pleasseeeeeeeee thank youu!!
Answer:
K=5
Step-by-step explanation:
12k-15=35+2k
12k=50+2k
10k=50
k=5
Answer:
[tex]k = 5[/tex]
Step-by-step explanation:
[tex]12k - 15 = 35 + 2k[/tex]
Our goal is to isolate k
[tex]12k - 15 = 35 + 2k\\\;\;\;\;+15 \;\;\;\;\;\;\; +15[/tex]
[tex]12k = 50 + 2k\\-2k \;\;\;\;\;\;\;\; -2k[/tex]
[tex]10k = 50[/tex]
Now we have k isolated to one side. Our final step is to have k be just k, no coefficient. We can do this by dividing each side by the coefficient.
[tex]\large\frac{10k}{10} = \frac{50}{10} \\\\10k\;\div\;10 = k\\50\;\div\;10 = 5\\[/tex]
[tex]\large\boxed {k \;=\;5}[/tex]
~[tex]InLoveWithPugs[/tex]
[tex]Moderator\\Math\ Enthusiast[/tex]
The sum of three consecutive odd integers is 153. Find the three odd integers.
First integer =
Second integer =
Third integer =
PLEASE HELPPPP!!
Answer:
49, 51, 53
Step-by-step explanation:
Let the first odd integer be n.
Then the consecutive odd integer will be (n+2).
This will be followed by (n+4).
We know that the sum of these three is 153. In other words:
[tex]n+(n+2)+(n+4)=153[/tex]
Solve for n. Combine like terms:
[tex]3n+6=153[/tex]
Subtract 6 from both sides:
[tex]3n=147[/tex]
Divide both sides by 3:
[tex]n=49[/tex]
Therefore, our first odd number is 49.
So, our consecutive numbers must be 51 and 53.
Hence, our sequence is:
49, 51, 53
Notes:
If we get an even number for n or a non-integer value, then there are no three consecutive odd integers that sum to 153.
Answer:
49, 51, 53
Step-by-step explanation:
All odd numbers:
49 + 51 = 100
100 + 53 = 153
please help can yall solve this
The pumpkin patch had two corn mazes, as shown by the shaded and non-shaded sections in the model below.
A model with 4 rows of 7 squares, representing 28 acres, and 2 rows of 7 squares, representing 14 acres.
Which expression is shown by the model?
Answer :
D - 28 + 14 = 7(4+2)
The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by K(x) 5x/x^2 + 9. a. Find the time at which the concentration is a maximum. b. Find the maximum concentration.
Given :
The percent of concentration of a certain drug in the bloodstream x hours after the drug is administered is given by [tex]K(x) = \dfrac{5x}{x^2+9}[/tex].
To Find :
Find the time at which the concentration is a maximum. b. Find the maximum concentration.
Solution :
For maximum value of x, K'(x) = 0.
[tex]K'(x) = \dfrac{5(x^2+9)- 5x(2x)}{(x^2+9)^2}=0\\\\5x^2+45-10x^2=0\\\\5x^2 = 45\\\\x = \pm 3[/tex]
Since, time cannot be negative, so ignoring x = -3 .
Putting value of x = 3, we get, K(3) = 15/( 9 + 9) = 5/6
Therefore, maximum value drug in bloodstream is 5/6 at time x = 3 units.
Hence, this is the required solution.
Find the value of θ from the following equation.(θ≤90°)
Answer: 10°
__________________________________________________________
We are given:
Sin(6θ) = Cos(3θ)
Solving for θ:
Simplifying Cos(3θ):
We know that:
Cos(θ) = Sin(90-θ)
So, we can say that:
Cos(3θ) = Sin(90 - 3θ)
Finding the value of θ:
Sin(6θ) = Cos(3θ)
Sin(6θ) = Sin(90 - 3θ) [Since Cos(3θ) = Sin(90 - 3θ)]
6θ = 90 - 3θ [If Sin(θ) = Sin(A) ; θ = A]
9θ = 90 [adding 3θ on both sides]
θ = 10° [dividing both sides by 9]
A birdbath is filled to the top. On Day 1, the volume of water in the bowl decreases by 7/8 cup. On Day 2, the volume in the bowl decreases by 3/4 cup. What number represents the total change in the volume of water in the bowl after two days? Write your answer as a mixed number.
Answer:
-1 5/8
Step-by-step explanation:
Let the total amount in the bowl be x;
If on Day 1, the volume of water in the bowl decreases by 7/8 cup, the remaining water will be;
x - 7/8
If on day 2, the volume in the bowl decreases by 3/4 cup, the remaining volume of water after the second day will be;
= x - 7/8 - 3/4
= x - (7-2(3))/8
= x - (7+6)/8
= x - 13/8
This shows that the total change after the two days is -13/8
As a mixed fraction;
-13/8 = -1 5/8
what is the answer for 6.8×10²
Answer:
680
Step-by-step explanation:
Answer:
680
Step-by-step explanation:
10 to the 2nd power is 10 times 10 which is 100.
Now, 6.8 times 100 is 680.
Hope this helps you!!
What proportion results in the equation 9m=10n?
Answer:
the 2 nd one 9/m=10/n
Step-by-step explanation:
in how many distinct ways can the letters in philosophy be arranged
Answer:
3 Letters Word: 6 Distinct Ways: 4 Letters Word: 24 Distinct Ways: 5 Letters Word: 120 Distinct Ways: 6 Letters Word: 720 Distinct Ways: 7 Letters Word: 5,040 Distinct Ways: 8 Letters Word: 40,320 Distinct Ways: 9 Letters Word: 362,880 Distinct Ways: 10 Letters Word: 3,628,800 Distinct Ways
Step-by-step explanation:
The number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
What is a factorial?The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.
As we can see that the word 'PHILOSOPHY' has 10 letters therefore, the letters of the word can be arranged in the 10! manner, but it contains the letter P, H and O twice therefore, there will be words that will look the same and are counted twice. Thus, the number of ways the word PHILOSOPHY can be arranged are,
[tex]\text{Number of ways} = \dfrac{10!}{2! \times 2! \times 2!} = 453,600[/tex]
Hence, the number of ways in which the word 'PHILOSOPHY' can be arranged is 453,600.
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Clayton opens a savings account with 11 dollars he got from his grandmother
Answer:
The answer is "$3640.58"
Step-by-step explanation:
This question is incomplete, that's why we add another question in the attached file. Please find it.
P = [tex]\$ \ 1300[/tex] and effective per year is = interest rate per year = 7.2
Total [tex]\$ \ 1300[/tex] due after 8 years is P+PRT:
[tex]\to 1300(1+0.072 \times 8)\\\\\to 1300(1+ 0.576)\\\\\to 1300(1.576)\\\\\to \$ \ 2048.8[/tex]
[tex]\to Total \ X = \$ \ (7000-2048.8) \\\\[/tex]
[tex]= \$ \ 4951.2 \\\\= X(1 +0.072 \times 5)\\\\=1.36 X \\\\[/tex]
The number of dollars is X [tex]= \frac{4951.2}{1.36} = \$ \ 3640.58[/tex]
Lines QS and NR intersect at P. Ray PM is perpendicular to line SQ.
What is the value of y?
Answer:
A. 13
Step-by-step explanation:
[tex] (6y - 14) + 90 + (2y) = 180 [/tex] (angles on a straight line)
Solve for y
[tex] 6y - 14 + 90 + 2y = 180 [/tex]
Collect like terms
[tex] 6y + 2y - 14 + 90 = 180 [/tex]
[tex] 8y + 76 = 180 [/tex]
Subtract 76 to both sides
[tex] 8y + 76 - 76 = 180 - 76 [/tex]
[tex] 8y = 104 [/tex]
Divide both sides by 8
[tex] \frac{8y}{8} = \frac{104}{8} [/tex]
[tex] y = 13 [/tex]
what is the slope of the following line?
Answer:
-2
Hope this helps,
PumpkinSpice1
The slope of the line will be ( -1 / 2 ). The correct option is C.
Slope or the gradient is the number or the ratio which determines the direction or the steepness of the line.
An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The two points are (0,3) and ( 6,0). The slope of the line will be calculated by using the formula below;-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( 0 - 3 ) / ( 6 - 0 )
Slope = -3 / 6 = -1 / 2
Therefore, the slope of the line will be ( -1 / 2 ). The correct option is C.
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A rock is thrown upward with a velocity of 17 meters per second from the top of a 31 meter high cliff and it missies the cliff on the way back down when will the rock ve 8 meters from the ground level
Answer:
[tex]4.5\ \text{s}[/tex]
Step-by-step explanation:
t = Time taken
u = Initial velocity =17 m/s
v = Final velocity
s = Displacement
a = Acceleration
g = Acceleration due to gravity = 9.81 m/s² = a
[tex]v^2-u^2=2as\\\Rightarrow s=\dfrac{v^2-u^2}{2a}\\\Rightarrow s=\dfrac{0^2-17^2}{2\times -9.81}\\\Rightarrow s=14.73\ \text{m}[/tex]
Total height the rock is to fall when it is 8 meters from the ground is [tex]14.73+(31-8)=37.73\ \text{m}[/tex]
[tex]v=u+at\\\Rightarrow t=\dfrac{v-u}{a}\\\Rightarrow t=\dfrac{0-17}{-9.81}\\\Rightarrow t=1.73\ \text{s}[/tex]
Time taken to reach the maximum height is 1.73 s.
[tex]s=ut+\dfrac{1}{2}at^2\\\Rightarrow 37.73=0+\dfrac{1}{2}\times 9.81t^2\\\Rightarrow t=\sqrt{\dfrac{37.76\times 2}{9.81}}\\\Rightarrow t=2.77\ \text{s}[/tex]
Time taken from the maximum height to the point which is 8 m from the ground is 2.77 s.
So, time taken from the moment of the throw to the point 8 m from the ground is [tex]1.73+2.77=4.5\ \text{s}[/tex].
find the value of x and the measure of MNW
Answer:
VALUE OF X:
3x-13+61 = 90
3x+48 = 90
3x = 42
x = 14
MEASURE OF <MNQ:
3x-13
= 3(14)-13
= 42-13
= 29
Factorise fully 2x+8
Answer:
2(x+4)
Step-by-step explanation:
To factor you have to divide both terms by the greatest common factor, which in this case is 2. Using distribution you can check your answer.
Answer: 2(x + 4)
Explanation: If you're asked to factor a polynomial,
the first thing you want to look for is the greatest common factor
for the terms that are involved.
The greatest common factor of 2x and 8 is 2.
So a 2 can factor out.
Inside the parenthses, we have each term divided by
the 2 that factored out of the polynomial.
So we have 2(x + 4).
A professional language translator gets paid an average of $320 per hour with a standard deviation of $41.75 per hour. What proportion of professional language translators get paid less than $250 per hour? Assume the population is normally distributed. Round your answer to four decimal places
Answer:
0.0475 or 4% professional language translators get paid less than $250 per hour
Step-by-step explanation:
Mean = 320
Standard Deviation = 41.75
We need to find proportion of professional language translators get paid less than $250 per hour i.e P(x<250)
First we will find value of z
Using formula: [tex]z=\frac{x-\mu}{\sigma}[/tex]
We have x=250, finding z
[tex]z=\frac{x-\mu}{\sigma}\\z=\frac{250-320}{41.75}\\z=-1.67[/tex]
Now we will find P(z<-1.67) by looking into the normal distribution table
[tex]P(z<-1.67)=0.0475\\[/tex]
So,0.0475 or 4% professional language translators get paid less than $250 per hour
Find the quotient:
7/8
Answer:
c.) 2 1/3
Step-by-step explanation:
i know
100.6 + 296.5 using
mental math
Answer:397.1....i think
Step-by-step explanation:
Answer:
397.1
Step-by-step explanation:
I used mental math
swear no calculator or work done
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Help please as soon as possible :)))
Answer:
24m 10+3+3+2+6
Step-by-step explanation:
Answer:
i believe its 24m surface area
Step-by-step explanation:
sorry if wrong
A restaurant offers $12 dinner specials that has 6 choices for an appetizer, 10 choices for an entree, and 3 choices for dessert. How many different meals
Answer:
19
Step-by-step explanation:
a window washer clean 38 windows in 2 hours at this rate how many windows did he clean in 7 hours?
Answer:
133 windows
Step-by-step explanation: