The probability that x is between 7 and 8 is 1/21 or approximately 0.0476.
The question seems to have an error as it asks for the probability that x is less than 67, but the range of x is from -4 to 17.
Therefore, it is impossible for x to be greater than 17, let alone 67. However, I can still answer the second part of the question, which asks for the probability that x is between 7 and 8.
Using the given information, we know that the minimum value of x is -4 and the maximum value of x is 17, and the probability of any value of x between these two values is equally likely, due to the uniform distribution.
To find the probability that x is between 7 and 8, we can use the formula for the probability density function of a uniform distribution:
f(x) = 1 / (b - a)
where f(x) is the probability density function of x, a is the minimum value of x, and b is the maximum value of x.
In this case, a = -4 and b = 17, so f(x) = 1 / (17 - (-4)) = 1 / 21.
Now, we need to find the area under the probability density function between x = 7 and x = 8.
This can be done by integrating the probability density function between these two values:
P(7 ≤ x ≤ 8) = ∫[7,8] f(x) dx
= ∫[7,8] 1 / 21 dx
= [1/21 * x]7^8
= (1/21 * 8) - (1/21 * 7)
= 1/21
Therefore, the probability that x is between 7 and 8 is 1/21 or approximately 0.0476.
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Rearrange the equation so q is the independent variable.
-7q+12r=3q-4r
Rearranging the equation so q is the independent variable is; q = -1.6r
How to change the subject of a subject?We are given the expression;
-7q + 12r = 3q - 4r
Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;
-7q - 3q = -4r - 12r
-10q = -16r
q = 16r/10
q = -1.6r
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Every time I use a piece of scrap paper, I crumple it up and try to shoot it inside the recycling bin across the room. I'm pretty good at it: If I shoot $5$ pieces of paper at the recycling bin, at least one of them will make it inside the recycling bin with probability $\frac{211}{243}$. If I shoot $6$ pieces of paper at the recycling bin, what's the probability at least two of them make it inside the recycling bin
Using the binomial distribution, it is found that there is a 0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.With 5 shoots, the probability of making at least one is [tex]\frac{211}{243}[/tex], hence the probability of making none, P(X = 0), is [tex]\frac{232}{243}[/tex], hence:
[tex](1 - p)^5 = \frac{232}{243}[/tex]
[tex]\sqrt[5]{(1 - p)^5} = \sqrt[5]{\frac{232}{243}}[/tex]
1 - p = 0.9908
p = 0.0092
Then, with 6 shoots, the parameters are:
n = 6, p = 0.0092.
The probability that at least two of them make it inside the recycling bin is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which:
[P(X < 2) = P(X = 0) + P(X = 1)
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.0092)^{0}.(0.9908)^{6} = 0.9461[/tex]
[tex]P(X = 1) = C_{6,1}.(0.0092)^{1}.(0.9908)^{5} = 0.0527[/tex]
Then:
P(X < 2) = P(X = 0) + P(X = 1) = 0.9461 + 0.0527 = 0.9988
[tex]P(X \geq 2) = 1 - P(X < 2) = 1 - 0.9988 = 0.0012[/tex]
0.0012 = 0.12% probability at least two of them make it inside the recycling bin.
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Please solve for X: 11/2-x = 1/3 + 1/6
Answer: 5
Step-by-step explanation:
11/2-x = 1/3 + 1/6
-x+11/2 = 1/2
- 11/2 - 11/2
-x = -5
Divide -1 by both sides
And it gives you the answer 5.
i need help with this page
Step-by-step explanation:
what is not clear that you cannot answer this by yourself ?
please let me know what you need explained.
1. Rhombus
2. rectangle
3. square
4. rhombus
5. square
6. rectangle
7. rhombus
8. parallelogram
Is there a way to find the intersections only by the equations?
I just know how to find the intersections by graphing them.
Answer:
see explanation
Step-by-step explanation:
to find the intersection equate g(x) and h(x) , that is
(x + 7)(x - 5) = x - 5 ← expand left side using FOIL
x² + 2x - 35 = x - 5 ( subtract x - 5 from both sides )
x² + x - 30 = 0 ← in standard quadratic form
(x + 6)(x - 5) = 0 ← in factored form
equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x - 5 = 0 ⇒ x = 5
substitute these values into either g(x) or h(x) for corresponding values of y
substituting into h(x)
h(- 6) = - 6 - 5 = - 11 ⇒ (- 6, - 11 )
h(5) = 5 - 5 = 0 ⇒ (5, 0 )
Systematic random sampling has become a popular method of drawing samples in research practices because _____.
it is a relatively easy way to draw a sample while ensuring randomness is the answer.
Systematic sampling is a probabilistic sampling method in which a researcher selects members of a population at regular intervals. For example, select every 15 people from the list of populations. If the population is in random order, this can mimic the benefits of a simple random sample.
These are generally preferred by researchers because they are easy to implement and understand. The important assumption that the results represent the majority of the normal population ensures that the entire population is sampled equally. The process also provides a higher level of control for systematic sampling compared to other sampling methods. systematic sampling also has a lower risk factor because the data is unlikely to be contaminated.
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Which of the following sets is equal to {1, 2, 3, ...}?
{x | x R, x ≥ 1}
{x | x R, x > 1}
{x | x N, x ≥ 1}
From the list of options, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}
How to determine the set?The set is given as:
{1, 2, 3, ...}
The three dots (...) after 3 implies that the elements of the set include other values such as 4, 5, 6 and so on
Using the above scenario, we can see that the set {1, 2, 3, ...} contains only positive integers.
All positive integers are natural numbers and they are denoted by N
From the list of options, we have:
{x | x R, x ≥ 1}
This represents the set of all real numbers greater than or equal to 1.
Note that this set includes decimal numbers i.e. 1, 1.5, 1.89 and so on
This does not represent the set {1, 2, 3, ...}
{x | x R, x > 1}
This represents the set of all real numbers greater than 1.
Note that this set includes decimal numbers i.e. 1.5, 1.89 and so on
This does not represent the set {1, 2, 3, ...}
{x | x N, x ≥ 1}
This represents the set of all natural numbers greater than or equal to 1.
Note that this set does not include decimal numbers i.e. 1, 2, 3, 4 and so on
This does represent the set {1, 2, 3, ...}
Hence, the set that is equal to the set {1, 2, 3, ...} is {x | x N, x ≥ 1}
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On the 405 freeway one can travel 65 miles per hour (mph), how many kilometers per hour (kph) is the car travelling
Answer:
104.607kph
Step-by-step explanation:
Conversion from mph to kph = 1.609mph
The equation i= ;δv / r is called __________.
Answer:
Step-by-step expl
2.73 A,16.3 V
Can someone help me
Answer: Choice B
All real numbers except 2 and 5
===========================================================
Explanation:
Factor the denominator. We need to find two numbers that multiply to 10 and add to -7.
Through trial and error, those two numbers are -2 and -5
-2 times -5 = 10
-2 plus -5 = -7
This means the denominator [tex]\text{x}^2 - 7\text{x} + 10[/tex] factors to [tex](\text{x}-2)(\text{x}-5)[/tex]. You can use the FOIL rule to confirm this.
Then each piece is set equal to zero to solve for x
x-2 = 0 leads to x = 2
x-5 = 0 leads to x = 5
------------
In short, if x = 2 or x = 5, then it causes the the denominator [tex]\text{x}^2 -7\text{x}+10[/tex] to turn into 0.
Dividing by 0 is not allowed; therefore, x = 2 nor x = 5 is allowed in the domain. Any other x value is valid.
Can someone please help me
Answer:
Right option is B.
Step-by-step explanation:
[tex] \sf \longrightarrow \frac{ \sec x \sin( - x) + \tan( - x) }{1 + \sec( - x) } \\ \\ \sf \longrightarrow \frac{ \sec x( - \sin x) - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \frac{1}{ \cos x } \times \sin x - \tan x }{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - \tan x - \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ - 2 \tan x}{1 + \sec x} \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{1 + \frac{1}{ \cos x} } \\ \\ \sf \longrightarrow \frac{ \frac{ - 2 \sin x}{ \cos x} }{ \frac{ \cos x + 1}{ \cos x} } \\ \\ \boxed{ \sf{\longrightarrow \frac{ - 2 \sin x}{ \cos x + 1} }}[/tex]
Kiran is driving on a long road trip. he currently has 13 gallons of gas in his car. each hour that he drives, his car uses up 2 gallons of gas. how much gas would be in the tank after driving for 5 hours? how much gas would be left after t t hours?
Step-by-step explanation:
"t t hours" ????
you mean 11 hours ?
13 gallons now.
2 gallons are used (and therefore disappear from the tank) per hour.
so, in 5 hours 5×2 = 10 gallons will be used.
that leaves 13 - 10 = 3 gallons in the tank.
in 11 hours 11×2 = 22 gallons would have been used.
but there are only 13 gallons in the tank.
so, if he does not fill up, he will have 0 gallons left after 11 hours. in fact, already after 13/2 = 6.5 hours.
the point :
when you use 2 gallons per hour, that means in t hours you are using t × 2 or 2t gallons.
Solve m=10x−x for x.
Answer:
x=m/9
Steps:
m=9x
m/9=x
x=m/9
A lifeguard sitting in a tower 10ft off the ground spots swimmer in trouble at a 55 angle of depression. If the lifeguard tosses a ring in a 15ft rope to the swimmer, can the ring reach the swimmer? Finish solving the problem below to determine your answer
Based on the given parameters, the 15 ft rope will reach the swimmer
How to determine if the ring reach the swimmer?From the question, we have the following equation:
sin 55 = 10/x
Multiply both sides of the equation by x
x * sin 55 = 10/x * x
Evaluate the product
x * sin 55 = 10
Divide both sides by sin 55
x = 10/sin 55
Evaluate sin 55
x = 10/0.8192
Evaluate the quotient
x = 12.21
From the question, the lifeguard tosses a ring in a 15ft rope to the swimmer
15 is greater than 12.21
This means that the 15 ft rope will reach the swimmer
Hence, the 15 ft rope will reach the swimmer
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Find the missing side lengths. Show work.
x=______ y=_____
PLEASE HELP IM SERIOUSLY STUCK E
Answer: 2.12 × [tex]10^{-3}[/tex]
The coefficient (in green) will be 2.12
Step-by-step explanation:
Scientific notation is written by multiplying the number by a power of 10. This number is a number between 1 and 10.
Since this is a smaller number, we will be multiplying it by a power of 10 to a negative number.
To get this value to a number between 1 and 10, we must multiply it by 10 3 times (also shown as 10³) which gives us 2.12.
To get back to the original value, we multiply this by [tex]10^{-3}[/tex]. This gives us our answer.
I think of a number. i add 7 to it and then divide by 10. my answer is 3.8. what number did i start with
Answer:
31
Step by step:
You need to do it in reverse:
Devidng Becomes multiplying so its 3.8x10=38
Then same for this + = - do its 38-7=31
So answer is 31
Help solve these (find the slope of each line) 8 problems don’t just give the answer show your work please
Answer:
Khan Academy.
Step-by-step explanation:
You can go on khan academy and search up "area and graphs." The videos should immediately pop up. there are also lessons if you don't want to risk getting your problem wrong. If you are still confused and do not understand please just comment and I will respond.
In which quadrant is the point ( - 2, 3) located?
O Quadrant II
Quadrant III
O Quadrant I
O Quadrant IV
ANSWER:
Quadrant ll
________________________________
________________________________HOPE IT HELPS
The prime factors of 13195 are 5, 7, 13 and 29. What is the largest prime factor of the number 600851475143 ?
Answer:
The prime factors of 13195 are 5, 7, 13 and 29. The largest prime factor of the number 600851475143 is 6857
A fair die is tossed 5 times. Let $\dfrac{m}{n}$ be the probability that at least two consecutive tosses have the same number, where $m$ and $n$ are relatively prime positive integers. Find $m$.
The probability that no two consecutive heads will occur is 13/32.
What is probability?It should be noted that probability simply means the likelihood of the occurence of an event based on chance.
In this case, the fair coin is tossed 5 times and we simony want it find the probability that no two consecutive heads will occur.
This will be:
Let n be the number of strings of h
Let t be the length n with two adjacent H's.
Therefore, the probability will be:
= (8+5)/2^5
= 13/32
In conclusion, the probability that no two consecutive heads will occur is 13/32.
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Please help and explain!!!
As x increases, y value decreases.
The rate of change for y as a function of x is decreasing, therefore the function is a decreasing function.
For all values of x, the function value y, decreases to 0.
The y intercept of the graph is the function value y=8
When x=1, the function value y=5.
From the given graph, it is clear that the curve is decreasing for all values of x. Hence, the rate of change of the give curve is decreasing.
Therefore, the giving function is called as decreasing function.
Since, the function is decreasing for all values of x, the value of y decreases to 0.
Form the graph, it is clear that the y-intercepts is at y=8.
Also, the value of y at x=1 is 5 from the graph.
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Solve for x in the diagram below.
Answer:
x = 20
Step-by-step explanation:
x°
2x°
(x + 10)°
little box on the bottom left means this is a right angle which is 90°
add up all the angles and make it equal to 90°
( x° + 2x° + (x + 10)° ) = 90°
4x + 10 = 90
4x = 80
x = 20
Since we can see the "square" at the bottom left corner of the angle, the square indicates that the angle is a right angle (which measures 90°).
We can also see three smaller angles forming the right angle. Therefore, the sum of the measure of the smaller angles = 90°.
According to the diagram, the measures of the smaller angles are x°, 2x°, and (x + 10)° respectively. Then we get the following equation:
[tex]\implies x + 2x + (x + 10) = 90\°[/tex]
Step-2: Solving the equation obtained in step-1Here, we had the equation: [tex]\underline{x + 2x + (x + 10) = 90\°}[/tex]
[tex]\implies x + 2x + x + 10 = 90\°[/tex] [tex]\text{(Ope} \text{ning the parentheses)}[/tex]
[tex]\implies 4x + 10 = 90\°[/tex] [tex]\text{(Combining like terms)}[/tex]
[tex]\implies 4x + 10 - 10 = 90 - 10[/tex] [tex]\text{(Subtracting 10 on both sides)}[/tex]
[tex]\implies 4x = 80[/tex] [tex]\text{(Simplifying both sides)}[/tex]
[tex]\implies \dfrac{4x}{4} = \dfrac{80}{4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \text{(Dividing 4 on both sides)}[/tex]
[tex]\implies \boxed{x = 20}[/tex] [tex]\text{(Simplifying both sides)}[/tex]
Therefore, the value of x, in the diagram provided, is 20.
Area=
Help me please asap thanks
Answer:
10 unit^2.
Step-by-step explanation:
The base of the triangle (CE)
= 6 - 2 = 4 units
The height = 5
Area = 1/2 * 4 * 5
= 10 unit^2.
Answer:
10
Step-by-step explanation:
area = hight ×base÷2
hight = 5-0
= 5
base = 6-2
= 4
area = 4×5÷2
=10
What is the logarithmic form of 13^2=169
The logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]
How to determine the logarithmic form?The equation is given as
13^2=169
Take the logarithm of both sides
log(13^2) = log(169)
This gives
2log(13) = log(169)
Divide both sides by log(13)
[tex]\log_{13}(169) = 2[/tex]
Hence, the logarithmic form of 13^2=169 is [tex]\log_{13}(169) = 2[/tex]
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Which system models this situation? y = 26x and y = 8,400(x-500)2 15,900 y = 26x and y = -0.030(x-500)2 15,900 y = x/26 and y = -0.030(x-500)2 15,900 y = x/26 and y =8,400(x-500)2 15,900
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
According to the statement
we have given that Vertex
(h,k) = (500, 15900)
And One of the points on the graph
(x,y) = (0,8400)
FIRST PART: we have to find the quadratic function
We can find the quadratic function by parabola's equation formula
y = a (x - h)² + k -(1)
Input the numbers to the formula, to find the value of a
y = a (x - h)² + k
8400 = a(0 - 500)² + 15900
8400 = a (500)² + 15900
8400 = 250000a + 15900
-250000a = 15900 - 8400
-250000a = 7500
a = 7500/-250000
a = 0.03
Now,
Submit a to the formula (1)
y = a (x - h)² + k
y = 0.03 (x - 500)² + 15900
this is the quadratic equation.
SECOND PART: Find the linear function
the total cost = cost each helmet × the number of helmet
y = 26x
So,
The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.
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Disclaimer: This question was incomplete. Please find the full content below.
Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)
x= number of helmets
y = amount in dollars
Which system models this situation?
a) y = 26x and y = 8,400(x-500)2+15,900
b) y = 26x and y = -0.030(x-500)2+15,900
c) y = x/26 and y = -0.030(x-500)2+15,900
d) y = x/26 and y =8,400(x-500)2+15,900
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Answer:
B. y = 26x and y = -0.030(x-500)2+15,900
Step-by-step explanation:
Given: AD BC and ZBCD ZADC
Prove: DE CE
D
Assemble the proof by dragging tiles to
the Statements and Reasons columns.
Intro
Angles Segments Triangles Statements Reasons
ZADC
ZDEA
Statements
ZECD
ZBCD
ZEDC
ZCBE
Reasons
ZCEB
ZDAE
The proofing of the triangle is illustrated below.
How to illustrate the triangle?Based on the information, the reflexive property of equality states that an angle or shape is always congruent to itself.
The alternate interior angle theorem is that when two parallel lines are cut by a transversal, then the alternate interior angles are the same.
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Answer:
answer in picture
Step-by-step explanation:
A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. what is the value of the quantity after 1.2 minutes, to the nearest hundredth?
The value of the quantity after 1.2 minutes, to the nearest hundredth, is 313.56
What is the calculated quantity?A quantity is a measurable attribute of a particular thing or group of objects. One quantity might be more than, less than, or equal to another quantity when comparing them. Quantity is a notion that is used frequently in both mathematics and the sciences.
A quantity cannot be a property that cannot be compared. The conventional format for presenting a quantity is as the product of a magnitude and a unit.
According to the question,
Initial value of the quantity=310
Rate of growth= 8.5% per second
Value of the quantity after 1.2 minutes,
=[tex]310(1+\frac{8.5}{100}) ^{1.2*60}[/tex]
=[tex]310(\frac{108.5}{100})^{72}[/tex]
=313.56
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Answer:
141008.06
Step-by-step explanation:
Please help me i need to turn this in soon and i don't understand
circumference of the mirror = 175.84 cm
area of the mirror = 2461.76 cm²
The measure needed to find the amount of wire round the mirror is the circumference.
The measure needed to find the amount of glass needed is the area.
How to find area and circumference of a circle?The circumference and area of a circle can be found as follows:
circumference of the mirror = 2πr
circumference of the mirror = 2 × 3.14 × 28 = 175.84 cm
area of the mirror = πr²
area of the mirror = 3.14 × 28²
area of the mirror = 2461.76 cm²
The measure needed to find the amount of wire round the mirror is the circumference.
The measure needed to find the amount of glass needed is the area.
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Write the quotient in scientific notation and in
standard form.
(3.64 x 10000000) (2.6 x 10000)
Answer:
3.64 × 10(raised to the power 7)
2.6 × 10⁴