Answer:
56
Step-by-step explanation:
Answer:
56
Step-by-step explanation:
the answer is 56
eric from exercise 3.30 continues driving. after three years, he still has no traffic accidents. now, what is the conditional probability that he is a high-risk driver?
The conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. Generally, insurance companies use the number of traffic violations and/or the number of claims a driver has had within a certain time period as indicators of their riskiness.
As Eric has had no accidents or traffic violations, the probability that he is a high-risk driver is very low. However, this does not mean that the probability is zero. There are many other factors which can contribute to a driver's risk, such as age, gender, experience, and location.
If Eric is an experienced driver, who has been driving for many years with no traffic accidents, then the probability of him being a high-risk driver will be lower than the average driver. On the other hand, if Eric is a new driver, or is located in an area with a high rate of traffic accidents, then the probability of him being a high-risk driver may be higher than the average driver.
Overall, the conditional probability that Eric is a high-risk driver, given that he has had no traffic accidents in the past three years, is very low. However, this probability can change depending on other factors, such as his age, experience, and location.
See more about conditional probability at: https://brainly.com/question/23382435
#SPJ11
if a continuous probability distribution is symmetric above and below the mean and displays a bell-shaped function, what type of distribution does this indicate?
There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.
This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.
In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.
Learn more about normal distribution here:
https://brainly.com/question/29509087
#SPJ4
Please help anyone!!
Answer options
2 units
4 units
6 units
10 units
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
what is triangle ?Three straight lines that cross at three different locations create the two-dimensional geometric outline of a triangle. A triangle's vertices, which are the three places at which those three lines intersect, are referred to as the triangle's sides. The dimensions of a triangle's edges and angles can be used to classify it. For instance, an isosceles triangle has two equal sides and two equal angles while an equilateral triangle has three equal sides and three equal angles of 60 degrees. An angle or side of a scalene triangle cannot be equivalent.
given
The right-angled triangle XYZ in the provided illustration has a side length of 6 units and an angle opposite to it that is labelled as 30°. The extent of the side YZ, denoted as x, must be determined.
To find x, we can use the trigonometric sine relation. The length of the side directly across from the angle divided by the length of the hypotenuse is known as the sine of an angle. The hypotenuse in this instance is designated as 2x.
As a result, we have:
sin 30° = (6/2x)
Adding two times to both sides:
2x * sin 30° = 6
Using sin 30°, which has a value of 0.5:
x = (6/(2 * 0.5)) = 6/1 = 6
Consequently, the side YZ is 6 units long.
As the length of the side immediately across from the angle, choice (c) 6 units is the correct answer.
To know more about triangle visit:
https://brainly.com/question/2773823
#SPJ1
if 80% of all marketing personnel are extroverted, then what is the probability that 10 or more are extroverts at a party of 15 marketing personnel
The probability that 10 or more of 15 marketing personnel are extroverts is 0.719.
Since 80% of all marketing personnel are extroverts, the probability of any single marketing personnel being an extrovert is 0.8. The probability that 10 or more marketing personnel at the party of 15 are extroverts can be calculated using the Binomial Distribution formula:
P(X>=10) = 1 - [P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9)]
P(X>=10) = 1 - [15C0*0.80*0.215 + 15C1*0.81*0.214 + 15C2*0.82*0.213 + 15C3*0.83*0.212 + 15C4*0.84*0.211 + 15C5*0.85*0.210 + 15C6*0.86*0.29 + 15C7*0.87*0.28 + 15C8*0.88*0.27 + 15C9*0.89*0.26]
P(X>=10) = 0.719
Therefore, 0.79 is the probability that 10 or more of the 15 marketing personnel at the party are extroverts.
To know more about probability refer here:
https://brainly.com/question/1596693#
#SPJ11
HELP FAST I DONT HAVE TIME ASAP
Answer:772
Step-by-step explanation:
SA=PH+2b
SA=(10+8+10+8)(17)+2(8x10)
SA=772
Answer:
Step-by-step explanatin
multiply all of them
23. (p. 434-435) Which of the following factors work to reduce conflict and promote positive interaction between grieving couples who have lost a child by death?
1. Open and honest communication
2. Expressing emotions in each other's company
3. Crying separately to minimize the open grief and pain
4. Ability of partners to reframe each other's behavior in a positive way
A. 1, 2, and 3
B. 1, 2, and 4
C. 1, 3, and 4
D. 2, 3, and 4
The following factors work to reduce conflict and promote positive interaction between grieving couples who have lost a child by death is open and honest communication, expressing emotions in each other's company, and the ability of partners to reframe each other's behavior in a positive way. The correct option is B. 1, 2, and 4
When grieving couples lose a child due to death, it can lead to tension in their relationship, leading to conflicts between the couple. However, some factors work to reduce conflicts and promote positive interaction between grieving couples who have lost a child by death.
These factors include the following:
:Open and honest communication: Open communication is essential when it comes to expressing emotions, needs, and expectations from one another. It helps to build understanding, trust, and positive interaction between the couples. Honest communication provides room for clarification and better comprehension of each other's feelings and needs
Reframing each other's behavior in a positive way helps to build a healthy relationship and reduce conflicts.Crying separately to minimize the open grief and pain: Crying separately does not help reduce conflicts between the couple as it promotes distance and an unhealthy way of dealing with grief. It is important to grieve together and find support from each other to heal and move forward.
To know more about conflicts:
https://brainly.com/question/1638202
#SPJ11
there are 75 people at the city swim park today. everyone in the park was wearing swim suits or sunglasses, some people had both. how many people had swim suits on but not sunglasses, if you know 63 people have swim suits on and 43 have sunglasses?
If you know 63 people have swim suits on and 43 have sunglasses, 32 people have swim suits on but not sunglasses.
To find out how many people have swim suits on but not sunglasses, we can use the principle of inclusion-exclusion.
We know that there are 75 people in the park, and 63 of them have swim suits on. We also know that 43 people have sunglasses. However, some people have both swim suits and sunglasses. Let's denote the number of people who have both by x. Then we can use the formula:
total = swim suits + sunglasses - both
Substituting in the given values, we get:
75 = 63 + 43 - x
Simplifying, we get:
x = 31
Therefore, 31 people have both swim suits and sunglasses, and the number of people who have swim suits on but not sunglasses is:
63 - 31 = 32
To learn more about inclusion-exclusion click on,
https://brainly.com/question/18958304
#SPJ4
Solve the following quadratic function by utilizing the square root method.
Answer:
x = ±9
Step-by-step explanation:
If x² = k, then x = ±√k.
x² - 81 = 0
x² = 81
x = ±√81
x = ±9
which set of numbers can make the inequality below true? 26> n + 15
Answer:
[tex]26 > n + 15[/tex]
[tex]11 > n[/tex]
[tex]n < 11[/tex]
Mattew is going on a trip to Hawaii and takes a limo to the airport. The driver says it will cost $20 plus 20 cents a mile. Mattew lives 50 miles from the airport
Matthew can travel up to 150 miles for $50, assuming the cost of the limo ride remains constant at a $20 fixed cost plus $0.20 per mile. Let's say Matthew has $50 to spend on the limo ride.
We know that the cost per mile is $0.20, so we can set up an equation:
Cost = $20 + $0.20 x Distance
We can substitute $50 for Cost and solve for Distance:
$50 = $20 + $0.20 x Distance
$30 = $0.20 x Distance
Distance = $30 / $0.20
Distance = 150 miles
Find out more about Distance
brainly.com/question/29063730
#SPJ4
a dance delegation of 4 people must be chosen from 5 pairs of dance partners. if 2 dance partners can never be together on the delegation, how many different ways are there to form the delegation?
There are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
The total number of ways to form the delegation from five pairs of dance partners can be calculated using the combination formula. The combination formula is used to calculate the number of different combinations of n objects taken r at a time without repetition.
In this question, n is the total number of dance partners (5) and r is the number of people on the delegation (4).
Therefore, the calculation is as follows:
total number of ways = nCr
= 5C4
= 5! / 4!(5-4)!
= 5! / 4!1!
= 5 x 4 x 3 x 2 x 1 / 4 x 1 x 1
= 5 x 4 x 3 x 2
= 120
Hence, there are 120 different ways to form the dance delegation from five pairs of dance partners if two dance partners can never be together on the delegation.
Learn more about combination here:
https://brainly.com/question/20211959
#SPJ4
a collection of five positive integers has mean $4.4$, unique mode $3$ and median $4$. if an $8$ is added to the collection, what is the new median? express your answer as a decimal to the nearest tenth.
To begin, we know that the median of the original collection of five positive integers is 4, which means that the middle number is 4. We also know that the unique mode is 3, which means that there is only one number in the collection that occurs more frequently than any other number.
Let's call the five positive integers in the original collection a, b, c, d, and e.
Since the mean of the original collection is 4.4, we can set up the equation:
(a+b+c+d+e)/5 = 4.4
Multiplying both sides by 5 gives:
a+b+c+d+e = 22
We also know that the mode is 3, which means that one of the numbers in the collection must be 3. Let's assume that a = 3, then we have:
3+b+c+d+e = 22
b+c+d+e = 19
Since the median is 4 and 3 is the unique mode, we can conclude that b, c, d, and e must be either 4 or 5. However, since there is only one unique mode, we know that there is only one number in the collection that is equal to 3. Therefore, we can conclude that the collection of five positive integers must be: 3, 4, 4, 4, 5.
If we add 8 to this collection, the new collection becomes: 3, 4, 4, 4, 5, 8. The new collection has six numbers, so the median is now the average of the two middle numbers. Since the middle two numbers are 4 and 5, the median is (4+5)/2 = 4.5.
Therefore, the new median is 4.5, expressed as a decimal to the nearest tenth.
For more details about median click here:
https://brainly.com/question/28060453#
#SPJ11
A person runs in a straight line across a field. The velocity of the person, v(t) is a differentiable function and selected values of v(t) are given above on the interval 0
Therefore, the average velocity of the person over the interval 0 ≤ t ≤ 12 can be calculated as follows:Average Velocity = Total distance travelled / Total time taken= 6.6 / 12= 0.55 m/s.
In the given question, we need to find the average velocity of a person running in a straight line across a field, given differentiable function v(t) on the interval [0,12]. Therefore, to calculate the average velocity of a person, we use the following formula:Average Velocity = Total distance travelled / Total time takenWe have a graph with the velocity of the person, which is a differentiable function v(t) given above on the interval 0 ≤ t ≤ 12.
We need to find the distance travelled by the person. Therefore, we use the following formula:Distance travelled = ∫v(t)dt From the given graph, the velocity of the person is zero when t = 0 and when t = 5. Similarly, the velocity of the person is 0 when t = 10 and when t = 12.So, we have to calculate the distance travelled from 0 to 5, from 5 to 10, and from 10 to 12 to determine the total distance travelled by the person over the given interval .Distance travelled from 0 to 5 can be calculated as follows :
Distance travelled from 0 to 5 = ∫v(t)dt from [tex]0 to 5= 5 x 0.6 = 3[/tex]Distance travelled from 5 to 10 can be calculated as follows :Distance travelled from 5 to 10 = [tex]∫v(t)dt[/tex] from [tex]5 to 10= 5 x 0.4 = 2[/tex]
Distance travelled from 10 to 12 can be calculated as follows: Distance travelled from 10 to 12 = ∫v(t)dt from 10 to 12= 2 x 0.8 = 1.6Total distance travelled = Distance travelled from 0 to 5 + Distance travelled from 5 to 10 + Distance travelled from 10 to [tex]12= 3 + 2 + 1.6= 6.6[/tex]
for such more questions on average velocity
https://brainly.com/question/1844960
#SPJ11
Can you solve this with workings out please
Answer:
Eighty biscuits.
Step-by-step explanation:
We need to find the limiting factor. We can do that by comparing ratio of mass of ingredient given to mass of ingredient needed for 20 biscuits
[tex]Butter:\\800:150\\=16:3\\=5.33\\Sugar:\\700:75=28:3\\=9.33\\Flour:\\1000:180\\=50:9\\=5.56\\Chocolate Chips:200:50\\=4:1\\=4\\[/tex]
We can clearly see that the choco. chips are the limiting factor since it has the lowest ratio, basically meaning we will run out of choco chips before anything else.
[tex]Biscuits=4*20=80[/tex]
Since we only have 4 times the choco chips needed to make 20 biscuits, we can only make 80 biscuits. Now you can see, we have other ingredients left, but choco chips have ran out which is why it was the limiting factor.
[tex]Flour:\\1000-4(180) = 280g[/tex]
After making 4 servings we still have 280g of flour left.
five observations taken for two variables follow. xi4611316 yi5050406030 what does the scatter diagram indicate about the relationship between the two variables?
If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values for y increases as well.
[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]
[tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]
For this part we use excel in order to create the scatterplot and we got the result on the figure attached
If we see the scatter plot we can conclude that the possible relation between x and y is linear and with a positive correlation since when the values of x increase the values of y increase as well
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this
[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]
:
[tex]Cov(x,y) =\frac{\sum_1^n(x_i-X')(y_i-Y')}{n-1}[/tex]
[tex]\sum_1^5(6-16)(6-10)+(11-16)(9-10)....(27-16)(12-10)=106\\\\and\\Cov(x,y)=\frac{106}{4}=26.5\\\\r=0.693[/tex]
learn more about scatter plot
https://brainly.com/question/29231735
#SPJ4
I NEED HELP ON THIS ASAP!
Answer:
16 represents the hours available to sew gloves.
2 represents the cost of producing gloves for a small pair.
Step-by-step explanation:
draw a quadratic function that only has one root at 3
The quadratic function that only has one root at 3 and passes through the point (0,4) is: f(x) = (4/9)(x - 3)^2
What is quadratic equation?A quadratic equation is a polynomial equation of degree 2, meaning that the highest exponent of the variable is 2. It has the general form:
ax^2 + bx + c = 0
If a quadratic function has only one root at 3, then it must be of the form:
f(x) = a(x - 3)^2
where a is a constant. This is because a quadratic function with only one root must have a double root, meaning that the parabola only touches the x-axis at that point and does not cross it. And a quadratic function with vertex at (3,0) and opening upwards satisfies this condition.
To determine the value of a, we can use any additional information that may be provided, such as the value of the function at another point. For example, if we know that f(0) = 4, then we can substitute these values into the equation to get:
4 = a(0 - 3)^2
4 = 9a
a = 4/9
To know more about quadratic function visit:
https://brainly.com/question/30929439
#SPJ1
The quadratic function that has only one root at 3 and passes through (0,4) is: [tex]f(x)=(\frac{4}{9} )(x-3)^{2}[/tex]
Why is it called a quadratic equation?A quadratic equation is a second-degree algebraic problem in x. In its standard form, the quadratic equation is [tex]ax^2+bx+c=0[/tex], where an as well as b are the coefficients, x is the variable, and c is the value of the constant component. The essential requirement for a formula to be a quadratic equation is that the coefficient of [tex]x^2[/tex] is not zero (a 0). When writing an equation with quadratic equations in conventional format, the [tex]x^2[/tex] term comes first, then the x term, and lastly the constant term.
A quadratic equation is a polynomial expression of degree 2, which means that the variable's greatest exponent is 2. It takes the following basic form:
[tex]ax^2+bx+c=0[/tex]
If the quadratic function has only one root at 3, it must have the following form:
[tex]f(x)=a(x-3)^2[/tex]
This requirement is satisfied by a quadratic function with a vertex at (3,0) and an opening upwards.
We know that f(0) = 4, so we can plug these numbers into the equation to get:
[tex]4=a(0-3)^2[/tex]
simplify the above equation
4 = 9a
The value is,
a = 4/9
To know more about quadratic function, visit:
https://brainly.com/question/1214333
#SPJ1
what effect does increasing the sample size, n, have on the center of the sampling distribution of sample means?
Increasing the sample size leads to a more accurate estimation of the population mean.
What is Probability ?
Probability can be defined as ratio of number of favourable outcomes and total number outcomes.
As the sample size, n, increases, the center of the sampling distribution of sample means becomes more precise and closer to the true population mean. This is known as the central limit theorem, which states that as the sample size increases, the distribution of sample means becomes approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
In other words, as we take larger and larger samples, we are more likely to obtain sample means that are closer to the true population mean. This is because larger samples are less affected by random fluctuations and more likely to provide a representative picture of the population as a whole.
Therefore, increasing the sample size leads to a more accurate estimation of the population mean.
To learn more about Probability from given link.
brainly.com/question/30034780
#SPJ1
can someone help me please i don't understand this
The transformation that would not result in a congruent figure when performed on triangle RST is A. A dilation by a scale factor of 2 with respect to point R.
The equation that has the same solution as the system of equations is C. 4x + 9y = 10
4x + 6y = 24.
Which transformations changes congruency ?Transformations that change the shape or size of a figure can change its congruency. A dilation is a transformation that changes the size of a figure so this would mean that RST dilated would not result in a congruent figure.
How to find the equation?When the system of equations, 4x + 9y = 10, 2x + 3y = 12 is solved, we find that x = 13 and y = - 14/ 3.
Options A,B, and D cannot have the same value because the numbers are the same and so they should have different values., Only option C can be the same and when the values are slotted in, this is proven.
Option C, 4x + 9y = 10 , 4x + 6y = 24 is therefore correct.
Find out more on equations at https://brainly.com/question/25869125
#SPJ1
Rewrite each equation without absolute value for the given conditions.
(Please help)ASAP
1. y = |x − 3| + |x +2| − |x − 5| if x >5
2. y = |x − 3| + |x +2| − |x − 5| if x < −2
3. y = |x − 3| + |x +2| − |x − 5| if 3
The equations without absolute value for the given conditions are: 1. y = -3x + 6 if x > 5; 2. y = -x - 6 if x < -2; 3. y = x - 6 if 3 ≤ x ≤ 5, and y = -x - 6 if x < 3.
1. When x > 5, the expression (x - 3) is positive, (x + 2) is positive, and (x - 5) is positive. Thus, to get absolute value we can rewrite the equation as:
y = (x - 3) + (x + 2) - (x - 5)
Simplifying this, we get:
y = 2x - 4
2. When x < -2, the expression (x - 3) is negative, (x + 2) is negative, and (x - 5) is negative. Thus, we can rewrite the equation as:
y = -(x - 3) - (x + 2) + (x - 5)
Simplifying this, we get:
y = -2x + 6
3. When -2 ≤ x ≤ 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is negative. Thus, we can rewrite the equation as:
y = -(x - 3) + (x + 2) - (x - 5)
Simplifying this, we get:
y = 10 - x
When x > 3, the expression (x - 3) is negative, (x + 2) is positive, and (x - 5) is positive. Thus, we can rewrite the equation as:
y = -(x - 3) + (x + 2) + (x - 5)
Simplifying this, we get:
y = -2x + 6
To learn more about absolute value please click on below link
https://brainly.com/question/29764645
#SPJ1
The speed of the ISS is 27,576 kilometres per hour.
The station travels 42,600 in 1 orbit
Work out the number of full orbits the station does in 1 day.
Answer:
15 Full orbits per day
Step-by-step explanation:
To work out the number of full orbits the ISS does in 1 day, we need to know how long it takes for the ISS to complete one orbit around the Earth.
We can use the information given to us to calculate the time it takes for the ISS to complete one orbit:
Distance traveled in one orbit = 42,600 kilometers
Speed of the ISS = 27,576 kilometers per hour
To calculate the time taken for one orbit:
Time taken = Distance traveled / Speed
Time taken = 42,600 kilometers / 27,576 kilometers per hour
Time taken = 1.54 hours (rounded to 2 decimal places)
So, the ISS takes approximately 1.54 hours to complete one orbit around the Earth.
Now, we can calculate the number of orbits the ISS does in one day:
Number of orbits per day = 24 hours / Time taken for one orbit
Number of orbits per day = 24 hours / 1.54 hours
Number of orbits per day = 15.58 (rounded to 2 decimal places)
Therefore, the ISS completes approximately 15 full orbits around the Earth in one day.
volume of a sphere = ³, where r is the radius. The radius of a spherical planet is 6052 km, and its mass is 4.87 × 1027g. Calculate the density of the planet in kilograms per cubic metre (kg/m³). Give your answer in standard form to 3 s.f.
Answer:
5240 kg/m³
Step-by-step explanation:
You want the average density of a planet with radius 6052 km and mass 4.87×10^27 g.
Unit conversionThe mass is given in grams, and the corresponding unit in the desired answer is kilograms. There are 1000 g in 1 kg, so 4.87×10^27 g = 4.87×10^24 kg.
The radius is given in km, and the corresponding unit in the desired answer is meters. There are 1000 meters in 1 km, so 6052 km = 6052×10^3 m. (We could adjust the decimal point, but we choose to let the calculator do that.)
DensityThe units of density tell you it is computed by dividing the mass by the volume:
ρ = mass/volume
The volume of the sphere is found using the given formula, so the density is ...
ρ = (4.87×10^24 kg)/(4/3π(6052×10^3 m)^3)
ρ ≈ 5240 kg/m³
The average density of the planet is about 5240 kg/m³.
__
Additional comment
This is comparable to the average density of Earth, which is about 5520 kg/m³.
what are the advantages of a best-guess (trial and error) experiment versus a factorial or design experiment
One advantage of best-guess experiments is that they are often faster and more cost-effective than factorial or design experiments.
Best-guess (trial and error) experiments involve making a hypothesis and testing it through a series of trials until a satisfactory result is achieved. On the other hand, factorial or design experiments involve manipulating multiple variables simultaneously to determine their individual and interactive effects on a response variable.
Both approaches have their advantages and disadvantages depending on the specific research question and goals. They may also be useful in situations where there is limited knowledge about the variables of interest or when the system is too complex to be modeled accurately.
However, best-guess experiments may suffer from issues such as biased or subjective interpretation of results, a lack of control over extraneous variables, and a potential for false positives or negatives.
In contrast, factorial or design experiments provide a more systematic approach to testing hypotheses and offer greater control over variables, leading to more reliable and generalizable results. They may, however, be more time-consuming and expensive to conduct.
Ultimately, the choice between best-guess and factorial or design experiments depends on the research question, available resources, and desired level of precision and control.
To learn more about experiment click on,
https://brainly.com/question/30455826
#SPJ4
A factory produces components of which 1% are defective. The components are
packed in boxes of 10. A box is selected at random
the probability that there are at most 2 defective components in the box is approximately 0.9044 and the probability of having at most 3 defective components out of 250 boxes is very close to zero.
a) Let X be the number of defective components in a box of 10 components. Then X follows a binomial distribution with n=10 and p=0.01, since the probability of a component being defective is 0.01. We want to find the probability that there are at most 2 defective components in the box, i.e., P(X ≤ 2).
Using the binomial probability formula, we get:
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
= (10 choose 0) × 0.01⁰ × 0.99¹⁰ + (10 choose 1) × 0.01¹ × 0.99⁹ + (10 choose 2) × 0.01² × 0.99⁸
= 0.90438222
Therefore, the probability that there are at most 2 defective components in the box is approximately 0.9044 (rounded to four decimal places).
b) We want to find the probability of having at most 3 defective components out of 250 boxes, each containing 10 components. Since np = 100.01 = 0.1 < 5 and n × (1-p)=10 × 0.99=9.9 > 5, we can use the normal approximation to the binomial distribution, with mean μ = np = 2.5 and standard deviation σ = √np(1-p) = 1.577.
Let X be the number of boxes with at most 3 defective components. Then X follows an approximate normal distribution with mean μ' = np=2.5250 = 625 and standard deviation σ' = √np(1-p)) = 12.5 × 1.577 = 19.712.
We want to find P(X ≤ 250), which can be written as P(X < 251) since X is a discrete variable. Using the continuity correction, we can approximate this probability as P(X < 251.5). Then we standardize the variable:
z = (251.5 - μ')/σ' = (251.5 - 625)/19.712 = -18.919
Using a standard normal table or calculator, we find that P(Z < -18.919) is a very small number, practically zero. Therefore, the probability of having at most 3 defective components out of 250 boxes is very close to zero.
To learn more about probability click here
brainly.com/question/30034780
#SPJ4
Complete Question
factory produces components of which 1% are defective. The components are packed in boxes of 10. A box is selected by random a) Find the probability that there are at most 2 defective components in the box b) Use a suitable approximation to find the probability of having at most 3 defective (inclusive 3 cases) components out of 250.
a. Is there a value of x, for -3≤x≤2, such that g(x)= 0
b. Find the absolute minimum value of g and the absolute maximum value of g on the interval -7≤x≤9. Justify your answer.
For x = -2, g(-2) = 2(-2)^3 - 5(-2)^2 + 4(-2) - 1 = 0, so there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2.
The absolute minimum value of g on the interval -7 ≤ x ≤ 9 is -765, and the absolute maximum value of g on the interval is 1720.
How to Solve the Problem?a. To determine if there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2, we can plug in each value of x in the interval into the equation and see if we get 0.
g(x) = 2x^3 - 5x^2 + 4x - 1
For x = -3, g(-3) = 2(-3)^3 - 5(-3)^2 + 4(-3) - 1 = -55, which is not 0.
For x = -2, g(-2) = 2(-2)^3 - 5(-2)^2 + 4(-2) - 1 = 0, so there is a value of x such that g(x) = 0 for -3 ≤ x ≤ 2.
b. To find the absolute minimum and maximum values of g on the interval -7 ≤ x ≤ 9, we can use the Extreme Value Theorem, which states that a continuous function on a closed interval will have both an absolute minimum and maximum value on that interval.
To find these values, we can take the derivative of g(x) and set it equal to 0 to find critical points, and then evaluate g(x) at those critical points as well as at the endpoints of the interval.
g(x) = 2x^3 - 5x^2 + 4x - 1
g'(x) = 6x^2 - 10x + 4 = 2(3x-2)(x-1)
Setting g'(x) = 0, we get critical points x = 2/3 and x = 1.
g(-7) = -765, g(2/3) = -23/27, g(1) = 0, and g(9) = 1720.
Therefore, the absolute minimum value of g on the interval -7 ≤ x ≤ 9 is -765, and the absolute maximum value of g on the interval is 1720.
Learn more about inequality here: https://brainly.com/question/14993153
#SPJ1
a professor at a local university noted that the exam grades of her students were normally distributed with a mean of 68 and a standard deviation of 17. according to the professor's grading scheme only the top 12.3 percent of her students receive grades of a. what is the minimum score needed to receive a grade of a? write your answer to two decimal points.
A minimum score of 88.95 is required to receive an "A" grade on the exam.
To determine the minimum score required to receive an "A" grade on an exam, we must first understand the meaning of standard deviation and mean. The mean is the average of a set of values, whereas the standard deviation is a measure of how far apart the values are from the mean. The minimum score required to receive an "A" grade is determined by calculating the z-score that corresponds to the top 12.3 percent of exam scores.
The formula for calculating the z-score is given as: z = (x - μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation. Solving for z, we have: z = invNorm(1 - 0.123) = invNorm(0.877) ≈ 1.15. The inverse normal distribution function is used to determine the value of z that corresponds to the area to the right of the z-score. We can then use the formula for the z-score to solve for the raw score (x):
x = zσ + μ
Substituting the values we have, we get:
x = 1.15(17) + 68 ≈ 88.95
Therefore, a minimum score of 88.95 is required to receive an "A" grade in the exam.
To know more about mean click here:
https://brainly.com/question/30112112
#SPJ11
Pls help me with 10 asap I will mark brainiest if it’s correct
The value of p from the given equation is 4.5.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign [tex]=\\[/tex].
The given equation is [tex]0.5p-3.45=-1.2[/tex]
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The equation can be solved as follows
[tex]0.5p-3.45=-1.2[/tex]
[tex]0.5p= -1.2+3.45[/tex]
[tex]0.5p= 2.25[/tex]
[tex]p= 2.25\div0.5[/tex]
[tex]p= 4.5[/tex]
Therefore, the value of p is 4.5.
To learn more about an equation visit:
https://brainly.com/question/14686792.
Write the equation of the line that is parallel to y=- 3/2and passes through
point (2,3).
Answer:
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
Step-by-step explanation:
In order to find an equation that is parallel, it must have the same slope. This means the y intercept could literally be anything.
By equation of the line, we can write it in point slope form
[tex]y-y1=m(x-x1)[/tex]
where y1 and x1 are points on the coordinate plane and m is the slope.
We are already given the slope, so we just plug in the numbers.
[tex]y-3=-\frac{3}{2}(x-2)[/tex]
A rhombus has an area of 20 cm^2. One diagonal is 10 cm. What is the other diagonal
The other diagonal of the rhombus is 4 cm.
The other diagonal of the rhombus can be found using the formula for the area of a rhombus, which is A = (d₁ × d₂)/2, where d₁ and d₂ are the lengths of the diagonals.
We're given that the area of the rhombus is 20 cm² and that one diagonal (d1) is 10 cm. Plugging these values into the formula, we get:
20 = (10 × d₂)/2
Simplifying, we get:
20 = 5 d₂
Dividing both sides by 5, we get:
d₂ = 4
Find out more about rhombus
brainly.com/question/14192697
#SPJ4