Answer:
5
Step-by-step explanation:
y=mx+b
B is always the y intercept.
The time intervals between successive barges passing a certain point on a busy waterway have an exponential distribution with mean 8 minutes.
(a) Find the probability that the time interval between two successive barges is less than 5 minutes.
(b) Find a time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t.
Answer:
a) 0.4647
b) 24.6 secs
Step-by-step explanation:
Let T be interval between two successive barges
t(t) = λe^λt where t > 0
The mean of the exponential
E(T) = 1/λ
E(T) = 8
1/λ = 8
λ = 1/8
∴ t(t) = 1/8×e^-t/8 [ t > 0]
Now the probability we need
p[T<5] = ₀∫⁵ t(t) dt
=₀∫⁵ 1/8×e^-t/8 dt
= 1/8 ₀∫⁵ e^-t/8 dt
= 1/8 [ (e^-t/8) / -1/8 ]₀⁵
= - [ e^-t/8]₀⁵
= - [ e^-5/8 - 1 ]
= 1 - e^-5/8 = 0.4647
Therefore the probability that the time interval between two successive barges is less than 5 minutes is 0.4647
b)
Now we find t such that;
p[T>t] = 0.95
so
t_∫¹⁰ t(x) dx = 0.95
t_∫¹⁰ 1/8×e^-x/8 = 0.95
1/8 t_∫¹⁰ e^-x/8 dx = 0.95
1/8 [( e^-x/8 ) / - 1/8 ]¹⁰_t = 0.95
- [ e^-x/8]¹⁰_t = 0.96
- [ 0 - e^-t/8 ] = 0.95
e^-t/8 = 0.95
take log of both sides
log (e^-t/8) = log (0.95)
-t/8 = In(0.95)
-t/8 = -0.0513
t = 8 × 0.0513
t = 0.4104 (min)
so we convert to seconds
t = 0.4104 × 60
t = 24.6 secs
Therefore the time interval t such that we can be 95% sure that the time interval between two successive barges will be greater than t is 24.6 secs
a.) we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.
b.) the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.
Given to us:
exponential distribution with mean = E(T) = 8,
The mean of the exponential
E(T) = 1/λ
1/λ = 8
λ = 1/8
∴ [tex]t(t) =\frac{1}{8} \times e^\frac{-t}{8} }\ ;\ [ t > 0][/tex]
(a) The probability that the time interval between two successive barges is less than 5 minutes.
Now the probability we need
[tex]\begin{aligned} \ [T<5] &= \int\limits^5_0 {t(t)} \, dt\\&= \int\limits^5_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\&= \frac{1}{8} \int\limits^5_0 { (e^\frac{-t}{8} })dt\\\\&= [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^5\\&= - [ e^{-t/8}]_0^5\\&= - [ e^{-5/8} - 1 ]\\&= 1 - e^{-5/8}\\&= 0.4647\end{aligned}[/tex]
So, we can conclude that probability for the time interval between two successive barges is less than 5 minutes is 46.47%.
b) Now we find t such that;
[tex]\begin{aligned} \ &p[T>t]=0.95\\ & \int\limits^{10}_0 {t(t)} \, dt=0.95\\& \int\limits^{10}_0 { (\frac{1}{8} \times e^\frac{-t}{8} })dt=0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt = 0.95\\& \frac{1}{8} \int\limits^{10}_0 { (e^\frac{-t}{8} })dt=0.95 \\\\& [ \dfrac{(e^\frac{-t}{8})}{\frac{-1}{8}} ]_0^{10}=0.95\\\\& - [ 0 - e^{-t/8} ] = 0.95&\ \ e^{-t/8} = 0.95\\\end{aligned}[/tex]
taking logs,
t = 24.6 secs
Hence,the time interval 't' such that we can be 95% sure that the time interval between two successive barges will be greater than 't' is 24.6 secs.
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Cindy measured and recorded the temperature of a liquid for an experiment. She used a poorly calibrated thermometer and noted the temperature as 100.5 degrees Fahrenheit. The actual temperature of the liquid was 95 degrees Fahrenheit. The percent error in her calculation is:______.
a. -5.79%.
b. 4.08%.
c. 4.08%.
d. 5.79%.
Answer:
5.79%
Step-by-step explanation:
The percentage error in the measurement is obtained by;
|measured temperature - actual temperature|/actual temperature ×100
actual temperature= 95°F
measured temperature= 100.5°F
|100.5 - 95|/95×100
%error= 5.79%
If f(x)=1-x^2+x^3, then f(-1)=
Answer:
Well, we know that there exists a function f(x) such that f(x-1) is a direct transformation of its parent function. First we want to set x=x-1. Conceptually, it might be easier just to annotate one of the x’s as a completely different variable, because we know that x doesn’t equal x-1. So let’s rewrite as x=y-1 and solve for y.
We now have y=x+1 where y(x) is actually our parent function and y(x)=f(x+1). So take our equation f(x-1) and substitute each x with (x+1). So f(x)=2(x+1) + 3
f(x)= 2x + 5. We can check this by finding f(x-1) because it should equal 2x+3.
f(x-1)= 2(x-1) + 5
f(x-1)= 2x + 3.
Hoped I helped
A supply company sells packs of paper by the box. Each box contains the same number of packs of paper, P. Which equation could be used to find the total number of packs of paper , T that would be in B boxes ordered?
Answer:
T = BP
Step-by-step explanation:
Boxes = B
Pack of paper in each box = P
Total number of packs = T
T = BPIs the equation for total number of packs of paper
For which of these reasons would you create a scatterplot between two variables?
a. To get an initial sense of whether the means of the groups are different from each other.
b. To determine if your research hypothesis has been proven.
c. To determine if the relationship is bi-directional.
d. To see if the relationship is positive or negative.
The answer should be c) To determine if the relationship is bi-directional.
What is a scatterplot?
Scatterplot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed
To get an initial sense of whether the means of the groups are different from each other. scatterplot is used to show relation between the two variables. So option a is wrong.
To determine the research hypothesis has been proven. Scatterplot is no where related to research hypothesis. so option b is wrong
determine if the relationship is bi-directional. Scatterplot is used to determine that the variables are dependent or not i.e they have a relation or not ,option c is correct
To see if the relationship is postive or negative . Scatterplot is used to show dispersed data, it can't be used to show positive or negative.So option d is wrong
Therefore, option c is correct
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1+tanA.tan2A = sec2A
Answer:
Step-by-step explanation:
1+tan2A(tanA)=sec2A
Right hand side
sec2A=1cos2A=1cos2A−sin2A
=cos2A+sin2Acos2A−sin2A
=1+tan2A1−tan2A
=1−tan2A+2tan2A1−tan2A
=1−tan2A1−tan2A+2tan2A1−tan2A
=1+2tanA1−tan2A×tanA
=1+tan2A×tanA
=Left hand side
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the remains of an ancient ball court include a rectangular playing alley with a perimeter of about 64 M. the length of the alley is 2 times the width. find the length and the width of the playing alley
Answer:
The length is 21.3 metersThe width is 10.6 metersStep-by-step explanation:
This problem is on the mensuration of flat shapes, a rectangular shape
we are required to solve for the length and width of the rectangular ball court
we know that the perimeter is expressed as
[tex]P= 2(L)+2(W)[/tex]
let the width be x
hence the length is 2x
Given data
perimeter = 64 meters
length l= 2x
width w= x
Substituting our data and solving for x we have
[tex]64= 2(2x)+2(x)\\\\64= 4x+2x\\\\64= 6x[/tex]
Dividing both sides by 6 we have
[tex]x=\frac{64}{6}\\\\ x= 10.66[/tex]
Hence the width is 10.66 meters
The length is 2x= 2(10.66)= 21.33 meters
6 + x is an example of _____. a formula a constant a variable an expression
Answer:
it is an example of an expression
Step-by-step explanation:
it is an example of an expression because it is asking a question without an equal sign. so its not a question, but an expression
19=7X+3-3x
Solve equation
Answer:
x=4
Step-by-step explanation:
19=7X+3-3x
Combine like terms
19 = 4x +3
Subtract 3 from each side
19-3 = 4x+3-3
16 = 4x
Divide each side by 4
16/4 = 4x/4
4 =x
Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9.
Answer:
0
Step-by-step explanation:
∫∫8xydA
converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.
So,
∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ
So we integrate r from 0 to 9 and θ from 0 to 2π.
∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ
= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ
= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ
= 8[6561/4]∫(cosθsinθ)dθ
= 13122∫(cosθsinθ)dθ
Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2
Substituting this we have
13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ
= 13122/2[-cos2θ]/2 from 0 to 2π
13122/2[-cos2θ]/2 = 13122/4[-cos2(2π) - cos2(0)]
= -13122/4[cos4π - cos(0)]
= -13122/4[1 - 1]
= -13122/4 × 0
= 0
What are the steps for using integer tiles to evaluate the expression 45 divided by 15
Answer:
45 / 15 = 3
Step-by-step explanation:
Required
Steps to divide 45 by 15 using integer tiles
Step 1: We start by writing out 45 items;
See attachment 1 where I used 45 boxes as illustration
Step 2: Then, we group these 45 items into groups (15 per groups)
See attachment 2 for illustration
Step 3: Count the number of groups
There are 3 groups;
Hence, 45 / 15 = 3
Answer:
The answer is B
Step-by-step explanation:
bc its 45/15 :)
Simplify. This algebraic expression y-3/3+12
Answer:
y-11
Step-by-step explanation:
First you divide 3 by 3 to get one. Then you add 12 to -1 to get 11. Then you will have y-11. PEMDAS saves lives.
Answer:
y = - 11
Step-by-step explanation:
Let y - 3/3 + 12 = 0
Multiply through by 3, we have as follow:
3y - 3 + 36 = 0
3y + 33 = 0
3y = - 33
y = -33/3 = -11
To evaluate the effect of a treatment, a sample of n = 9 is obtained from a population with a mean of μ = 40, and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M = 33. If the sample has a standard deviation of s = 9, do we reject or accept the null hypothesis using a two-tailed test with alpha = .05?
Answer:
Yes we reject the null hypothesis
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 9[/tex]
The population mean is [tex]\mu = 40[/tex]
The sample mean is [tex]\= x = 33[/tex]
The standard deviation is [tex]\sigma = 9[/tex]
The level of significance is [tex]\alpha = 0.05[/tex]
For a two-tailed test
The null hypothesis is [tex]H_o : \mu = 40[/tex]
The alternative hypothesis is [tex]H_a : \mu \ne 40[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{\sqrt{n} } }[/tex]
=> [tex]t = \frac{ 33 - 40 }{ \frac{9}{\sqrt{9} } }[/tex]
=> [tex]t = -2.33[/tex]
The p-value for the two-tailed test is mathematically represented as
[tex]p-value = 2 P(z > |-2.33|)[/tex]
From the z-table
[tex]P(z > |-2.33|) = 0.01[/tex]
[tex]p-value = 2 * 0.01[/tex]
[tex]p-value = 0.02[/tex]
Given that [tex]p-value < \alpha[/tex] Then we reject the null hypothesis
what are the domain and range of this function y=(x+3)^2 -5
a. domain: (-∞, ∞) range: (-5, ∞)
b. domain: (-∞, ∞) range: (-∞, ∞)
c. domain: (-5, ∞) range: (-5, ∞)
d. domain: (-5, ∞) range (-∞, ∞)
Answer: Choice A
Note: the range should be [tex][-5, \infty)[/tex]. See explanation below.
===================================================
We can plug in any real number for x to get some output for y. The domain is the set of all real numbers in which we say [tex](-\infty, \infty)[/tex] which is interval notation. It represents the interval from negative infinity to positive infinity.
The range is the set of possible outputs. The smallest output possible is y = -5 which occurs at the vertex (3,-5). We can get this y value or larger. So we can describe the range as the set of y values such that [tex]y \ge -5[/tex] and that translates to the interval notation [tex][-5, \infty)[/tex].
The square bracket says "include this endpoint" while the curved parenthesis says to exclude the endpoint. Your teacher mistakenly wrote [tex](-5, \infty)[/tex] for choice A, when they should have written [tex][-5, \infty)[/tex]
I think either your teacher made a typo or somehow the formatting messed up. Either way, choice A is the closest to the answer.
Option A is the correct choice .
Domain will be → all real numbers .
Range will be → y belongs to R : y greater than or equal to -5 .
→ (x+3)^2 It means 0 to infinity
So (x+3)^2-5= (-5, infinity)
→ Range = (-5, infinity )
Solve the Multi-Step Equations and check. Solve for x
15x - 24 - 4x = -79
Answer:
x = -5
Step-by-step explanation:
Step 1: Write out equation
15x - 24 - 4x = -79
Step 2: Combine like terms
11x - 24 = -79
Step 3: Add 24 to both sides
11x = -55
Step 4: Divide both sides by 11
x = -5
Step 5: Check step
Plug in -5 into the original equation
15(-5) - 24 - 4(-5) = -79
-75 - 24 + 20 = -79
-99 + 20 = -79
-79 = -79
Answer:
x = -5
Step-by-step explanation:
15x - 24 - 4x = -79
11x - 24 = -79
11x = -55
x = -5
Check:
15 * -5 - 24 - 4 * -5
= -75 - 24 + 20
= -79
PLEASE HELP ME, I DON'T UNDERSTAND!
Answer:
c
Step-by-step explanation:
We need to divide [tex]9x^2-6x+2[/tex] by 3x -1
we know that 2 = 1+1 so
[tex](9x^2-6x+1)+1[/tex]
if you notice the thing that it's inside the parenthesis it's a perfect square
[tex]((3x)^2-2(3x)+1)+1\\=(3x-1)^2+1\\[/tex]
if we divide this by 3x -1 we get
[tex]\frac{(3x-1)^2+1}{3x-1} \\\\=\frac{(3x-1)^2}{3x-1}+\frac{1}{3x-1} \\\\=3x-1 + \frac{1}{3x-1}[/tex]
so answe is c
large cheese pizzas cost $5 each and large one topping pizzas cost $6 each. write an equation that represents the total cost, T , of c large cheese pizzas and d large one-topping pizzas.
Answer:
T = 5c +5d, where unit of the equation is $.
Step-by-step explanation:
Cost of 1 large cheese pizza = $5
No. of large cheese pizza = c
therefore
cost of c large cheese pizza = c*Cost of 1 large cheese pizza = $5c
Cost of 1 large one topping pizza = $6
No. of large one topping pizza = d
therefore
cost of d large one topping pizza = d*Cost of 1 large one topping pizza = cost of d large one topping pizza = $6d
Total cost of c large cheese pizza and cost of d large one topping pizza
= $5c +$6d
total cost is represented by T
thus, T = $5c +$5d Answer
(2x-3)^2 - (3x-2)^2
Answer:
im Pretty sure x
Step-by-step explanation: Distribute:
=4x2+−12x+9+−9x2+12x+−4
Combine Like Terms:
=4x2+−12x+9+−9x2+12x+−4
=(4x2+−9x2)+(−12x+12x)+(9+−4)
=−5x2+5
Answer: −5x2+5
can someone solve this for me????? (10−523)⋅(−2)+x=823
Answer:
the answer is -203 i got 100%
Step-by-step explanation:
3. An electric bill is an essential expense for young people who get their first
apartment. The following is a list of Jordan's monthly electric bills for the past
10 months.
$115,
$150, $144, $126, $90, $90, $95, $110, $120, $88
Round your answers to the nearest cent.
a. What is the mean monthly electric bill?
b. What is the range?
c. What is the variance?
d. What is the standard deviation?
Answer:
Mean = $123.8
Range= $72
Variance= $607.344
Standard deviation=$ 24.64
Step by step explanation:
The list of the data of electricity bill on ascending order
$88,$90,$90,$95,$110,$115,$120,$126,$144,$150
Mean = (summation of($88,$90,$90,$95,$110,$115,$120,$126,$144,$150))/10
Mean = 1238/10
Mean = $123.8
Range= highest value- Lowest VA
Range= 150-88
Range= $72
Variance=( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)/10
Variance= (1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)/10
Variance= 6073.44/10
Variance=$ 607.344
Standard deviation= √variance
Standard deviation= √ 607.344
Standard deviation=$ 24.64
The mean monthly electric bill is $123.8
The Range is $72
The variance is $607.344
The standard deviation is $ 24.64
What is the arithmetic mean?Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean
The formula for the mean of a given set of data is as follows:
Mean = Sum of Observations/Total number of observations
Σx = 88+90+90+95+110+115+120+126+144+150
Σx = 1238
Here n = 10
⇒ Mean = Σx/n
⇒ Mean = 1238/10
⇒ Mean = $123.8
Hence, the mean monthly electric bill is $123.8
⇒ Range = Largest value - Least value
⇒ Range = 150-88
⇒ Range= $72
Hence, the Range is $72
⇒ Σ(x -mean)² = ( (88-123.8)²+(90-123.8)²+(90-123.8)²+(95-123.8)²+(110-123.8)²+(115-123.8)²+(120-123.8)²+(126-123.8)²+(144-123.8)²+(150-123.8)²)
⇒ Σ(x -mean)² =(1281.64+1142.44+1142.44+829.44+190.44+77.44+14.44+4.84+295.84+408.04+686.44)
⇒ Σ(x -mean)² = 6073.44
Here n = 10
⇒ Variance = Σ(x -mean)²/10
⇒ Variance = 6073.44/10
⇒ Variance = $607.344
⇒ Standard deviation = √variance
⇒ Standard deviation = √607.344
⇒ Standard deviation = $24.64
Hence, the standard deviation is $24.64.
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You reflect triangle PQR, with vertices P(-2, -4), Q(-3, -1), and R(-4, -4), across the y-axis to get triangle P′Q′R′. What are the coordinates of triangle P′Q′R′?
A.
P′(-2, 4), Q′(-3, 1), R′(-4, 4)
B.
P′(2, -4), Q′(3, -1), R′(4, 4)
C.
P′(-2, 4), Q′(-3, 1), R′(4, -4)
D.
P′(2, -4), Q′(3, -1), R′(4, -4)
Answer:
D. (2, -4),(3, -1), (4, -4)
Step-by-step explanation:
Hello!
When you reflect over the y-axis you reverse the x.
Negatives become positives and positives become negatives
(-2, -4) turns into (2, -4)
(-3, -1) turns into (3, -1)
(-4, -4) turns into (4, -4)
look for the answer that has (2, -4),(3, -1), and (4, -4)
The answer is D
Hope this helps!
Answer:
the answer is D
Step-by-step explanation:
because i said so
please help me asap!!:)
Answer:
Hey there!
Basically, you are either going to North Dakota, New Hampshire, New Jersey, New York, New Mexico or North Carolina, as those are the only two word states beginning with N.
Thus, the chance of picking one of those is 6/50, or 3/25.
You have to choose one state, so this is Mutually Exclusive.
Let me know if this helps :)
6-7 Please help BRAINLEST!
Answer:
18
Step-by-step explanation:
25=7+r 25-7=18 7-7=0
r=18 Do you understand? I really hoped I helped. I was in your position when i was learning that.
Find the equation of the line graphed below. Write the equation in the form y=mx+b and identify m and b.
Answer:
m = 1/2 and b = 1.
Step-by-step explanation:
The y intercept (b) is at y = 1 so we have
y = mx + 1 so b = 1
The m is the slope of the line.
The graph passes through the point (4, 2)
From the graph, the slope = 2/4 = 1/2.
So it is y = 1/2x + 1.
A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, that would be an example of probability.
Answer: Experimental probability
Step-by-step explanation:
There are two kinds of probability: Theoretical probability and Experimental probability.
To calculate theoretical probability we divide favorable outcomes by total outcomes.
To calculate experimental probability we divide number of times an event occurs by the total number of trials or times the activity is performed.
Here, A child gets 20 heads out of 30 tosses of a coin. If he declared the chance of getting a head with that coin were 2/3, which is dependent on the activity he performed, thus it is an experimental probability.
. The number of parking tickets handed out at BCCC was twice the number of tickets handed out last year. The number of tickets handed out this year was what percent of the number handed out last year
Answer:
200% of tickets handed out this year
Step-by-step explanation:
Let
Tickets handed out last year=x
Tickets handed out this year=2x
The number of tickets handed out this year was what percent of the number handed out last year
Last year was x%
Then, this year would be 200x%
200% tickets was handled out this year
(10c^6d^-5)(2c^-5d^4)
Answer:
The value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].
Step-by-step explanation:
In this problem, we need to evaluate [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex]. Here, c and d are variable with exponents.
Taking both c together
[tex]=(10c^6{\cdot} 2c^{-5})\\\\=20(c^6{\cdot} c^{-5})\\\\=20c^{6-5}\\\\=20[/tex]
Taking both d together
[tex]=(d^{-5}{\cdot}d^4)\\\\=d^{-5+4}\\\\=d^{-1}[/tex]
So,
[tex](10c^6d^{-5})(2c^{-5} d^4)=20d^{-1}[/tex]
Hence, the value of [tex](10c^6d^{-5})(2c^{-5} d^4)[/tex] is [tex]20d^{-1}[/tex].
Find the number that completes each of the following proportions: a.8120=4c b.n0.5=0.71 c.8x=23 d. 7:6=k:120
Answer:
a. c = 2030,
b. n = 1.42,
c. x = 2.875,
d. k = 140
Step-by-step explanation:
a ) 8120 = 4c,
c = 8120 / 4 = 2030
b ) 0.5n = 0.71,
n = 0.71 / 0.5 = 1.42
c ) 8x = 23,
x = 23 / 8 = 2.875
d ) 7 : 6 = k : 120
Here we want to convert this ratio into fraction form,
7 / 6 = k / 120
And now we can cross - multiply to determine the value of k,
6k = 7(120) = 840,
k = 840 / 6 = 140
We can check the value of k, by plugging it back into our ratio, and see if it reduces to 7 : 6,
140 : 120,
14 : 12,
7 : 6
Will give brqinlist if correct
Answer:
7 + 8x
Step-by-step explanation:
-11 + 2 (4x -1) + 6
=> -11 + 8x -2 + 6
=> -13 + 8x + 6
=> -7 + 8x
So, the simplified expression is 7 + 8x.
An is mathematical sentence that compares expression that are not equal
Answer:
Inequality
Step-by-step explanation:
An inequality is mathematical sentence that compares expression that are not equal.
Instead of using an equal sign = , you use an inequality symbol (>, <, ≥, ≤, ≠) with an inequality.