Answers
The measure of ∠AOB is 80°.
Describe Angles?In geometry, an angle is a figure formed by two rays, or half-lines, that originate from a common endpoint, which is called the vertex. The rays can be thought of as emanating from the vertex and extending infinitely in opposite directions.
The measure of an angle is typically given in degrees, where a full circle is 360 degrees. Angles can be classified according to their size:
An acute angle is less than 90 degrees.
A right angle measures exactly 90 degrees.
An obtuse angle is greater than 90 degrees but less than 180 degrees.
A straight angle measures exactly 180 degrees.
A reflex angle is greater than 180 degrees but less than 360 degrees.
A full angle measures exactly 360 degrees.
In a parallelogram, opposite angles are equal, so we have:
∠OAD = ∠OCB = a2 + b2 (1)
∠OAB = ∠ODC = a1 + d1 (2)
∠OAB + ∠OAD = ∠BOC = 180° (3)
∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)
From (1), (2), and (3), we have:
∠AOB = 180° - (a1 + b2 + a2 + d1)
= 180° - (a1 + a2 + b1 + b2 + c1 + d1 + d2)
= 180° - ∠ABD - ∠BCD
Since ABCD is a parallelogram, we have ∠ABD = ∠BCD. Therefore,
∠AOB = 180° - 2∠ABD
Let x be the measure of angle ABD. Then we have:
∠ABD + ∠BCD = 180°
x + (d1 + d2) = 180° (5)
In triangle ADO, we have:
∠ADO + ∠ODA + ∠OAD = 180°
d2 + x + a2 = 180° (6)
From (5) and (6), we get:
d1 + d2 + a2 + x = 180°
Substituting this expression into (3), we obtain:
∠AOB = 180° - 2(d1 + d2 + a2 + x)
= 80°
Therefore, the answer is (d) 80°.
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The measure of ∠AOB is 80°. The required answer for the given question is option (d). 80°.
Describe Angles?An angle is a figure in geometry made up of two rays, or half-lines, that start from a single endpoint known as the vertex. You can imagine the
rays coming from the vertex and continuing in opposing directions indefinitely.
A whole circle has 360 degrees, hence an angle is commonly measured in degrees. Angles can be grouped based on their size:
Acute angle is one that is less than 90 degrees.
A right angle has a 90 degree angle.
Obtuse angles are those that are greater than 90 degrees and less than 180 degrees.
A straight angle has a 180 degree length.
Greater than 180 degrees and less than 360 degrees is a reflex angle.
360 degrees makes up a whole angle.
Since opposite angles in a parallelogram are equal, we have:
∠OAD = ∠OCB = [tex]a_2+b_2[/tex] (1)
∠OAB = ∠ODC = [tex]a_1+d_1[/tex] (2)
∠OAB + ∠OAD = ∠BOC = 180° (3)
∠OAD + ∠BOC = ∠AOB + ∠ODC = 180° (4)
From (1), (2), and (3), we have:
∠AOB = 180° - [tex](a_1 + b_2 + a_2 + d_1)[/tex]
= 180° - [tex](a_1 + a_2 + b_1 + b_2 + c_1 + d_1 + d_2)[/tex]
= 180° - ∠ABD - ∠BCD
Due to the parallelogram that is ABCD, we have ∠ABD = ∠BCD.
∠AOB = 180° - 2∠ABD
Let x be the measure of angle ABD. Then we have:
∠ABD + ∠BCD = 180°
x + [tex](d_1 + d_2)[/tex] = 180° (5)
In triangle ADO, we have:
∠ADO + ∠ODA + ∠OAD = 180°
[tex]d_2[/tex] + x + [tex]a_2[/tex] = 180° (6)
From (5) and (6), we get:
[tex]d_1 + d_2 + a_2[/tex] + x = 180°
Substituting this expression into (3), we obtain:
∠AOB = 180° - 2[tex](d_1 + d_2 + a_2 + x)[/tex]
= 80°
Therefore, the answer is (d) 80°.
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Related Questions
7. Roberta and Eugene were trying to work out how
much charge there was stored in different electric
toothbrush batteries. They measured the current
flowing into toothbrush when it was switched on
and timed how long it took to run the batteries
down. The toothbrush required two batteries.
They repeated their experiment twice.
(Results in picture attached)
a) Circle the anomalous result in the table.
b) Calculate the mean average for each brand of
battery.
c) Calculate the amount of charge stored by each
brand of battery.
d) How would you present the results of this
experiment? Justify your answer.
Please help I have a test tmrw
Answers
a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.
b) The mean averages for each brand of battery are 955.33, 852 and 908 seconds.
c) the amount of charge stored by each brand of battery is 1098.6 coulombs, 1065 coulombs and 1089.6 coulombs.
d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery.
What is anomalous result?It is an unexpected or unusual outcome that does not agree with the expected or accepted outcome. It may be a result of a mistake, an anomaly in the data, or a misinterpretation of the data.
a) The anomalous result in the table is the Durablast battery in the second trial, which recorded a time taken of 768 seconds.
b) The mean averages for each brand of battery are:
Longalast: 955.33 seconds
Durablast: 852 seconds
Morelife: 908 seconds
c) The amount of charge stored by each brand of battery can be calculated by multiplying the current flowing into the toothbrush (amps) by the mean time taken (seconds) for each battery:
Longalast: 1.15 amps x 955.33 seconds = 1098.6 coulombs
Durablast: 1.25 amps x 852 seconds = 1065 coulombs
Morelife: 1.20 amps x 908 seconds = 1089.6 coulombs
d) The results of this experiment can be presented in a table format, showing the current flowing, the mean time taken, and the amount of charge stored for each brand of battery. This would allow the reader to easily compare the performance of each battery, as well as to identify any anomalous results.
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Suppose that y varies directly as the square root of x, and that y=43 when x=289 . What is y when x=191 ? Round your answer to two decimal places if necessary.
Please hurry i need it asap
Answers
Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).
Define about the direct variation?When two quantities, including such time and distance or hours and compensation, change directly, they do so at a predictable rate.
The constant of variation is another name for the constant rate of increase or decline. We will examine three different methods of showing direct variation in this lesson: an equation, a table, and just a graph.
For the given question:
y varies directly as the square root of x.
y ∝ √x
y = k√x
Here, k is the constant of proportionality
Now,
y=43 when x=289 .
43 = k√289
k = 43/√289
k = 2.53
Now, y when x=191.
y = k√x
y = 2.53√191
y = 34.96
Thus, the value of y for the given direct variation is found as y = 34.96 (Rounded up to two decimal places).
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Use formula to find the area of the figure(show the formula,work,and units)
Answers
Answer:
25
Step-by-step explanation:
Formula 1/2(B1+B2)H
1/2(10)5
1/2 x 10=5
5 x 5 =25
how do we check for normality of the sampling distribution of for a one sample z confidence interval for proportions? group of answer choices large sample size (n>30) no skewness or outliers in sample data n > 10 and n(1- ) > 10 n > 10 and n(1- ) > 10
Answers
To check the normality of the sampling distribution for a one-sample z confidence interval for proportions, the sample size should be large (typically n > 30), and the number of successes and failures in the sample should both be at least 10.
To check for normality of the sampling distribution for a one-sample z confidence interval for proportions, we need to ensure that the following conditions are met:
Large sample size: The sample size should be sufficiently large (typically n > 30). This is because the central limit theorem states that for large enough sample sizes, the sampling distribution of the sample proportion will be approximately normal, regardless of the underlying distribution of the population.
Success-Failure Condition: The number of successes (np) and failures (n(1-p)) in the sample should both be at least 10. This condition ensures that the binomial distribution of the sample proportion is approximately normal.
If these conditions are met, then we can assume that the sampling distribution of the sample proportion is approximately normal, and we can proceed to construct a one-sample z confidence interval for proportions.
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Which equation of a circle represents the picture?
A) (x)^2+(y)^2=10
B) (x-5)^2+(y-5)^2=25
C) (x)^2+(y^2)=25
D) (x+5)^2+(y+5)^2=10
Answers
Answer:
C) x² + y² = 25
Step-by-step explanation:
the center is (0, 0).
so, the generic circle equation
(x−h)² + (y−k)² = r². The center is (h, k) and the radius is r units.
for (h, k) = (0, 0) this gives us the equation above.
and r we can easily see as the distance from the center to one of the points on the circle arc. which is 5, as the coordinates tell us.
2. ? 0.13 6.02 ? what are the two numbers to fill the question marks?
Answers
The missing numbers to fill the question marks are 2.1 and 7.11
Completing the missing numbersTo solve the question, we need to look for a pattern or relationship between the given numbers. One way to approach this is to consider the decimal representation of each number.
If we look at the first number, 0.13, we can see that it has 2 digits after the decimal point.
The second number, 6.02, has 2 digits before the decimal point.
So, it's possible that the missing numbers also follow a pattern where one number has 2 digits before the decimal point, and the other has n digits after the decimal point.
Using the decimal points, one possible pattern is 2, 2.1, 0.13, 6.02, 7.11
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a bucket that weighs 5 pounds and a rope of negligible weight are used to draw water from a well that is 76 feet deep. the bucket is filled with 37 pounds of water and is pulled up at a rate of 1.8 feet per second, but water leaks out of a hole in the bucket at a rate of 0.25 pounds per second. find the work done pulling the bucket to the top of the well.
Answers
The work done pulling the bucket to the top of the well of depth 76 feet is equals to the 346.56 pounds/ feet.
Work is the product of force and distance, W=F×d. A Riemann Sum is a collection of rectangles used to approximate the area underneath a curve. In this case the "height" of the rectangle will be the force being exerted, and the "width" of the rectangle will be the amount of distance it moved. The work done by the force on the object can be expressed as an integral, [tex]W = \int_{a}^{b}F(x)dx[/tex]
Weigh of bucket = 5 pounds
A rope with negligible weight is used to draw water from a well. The depth of well = 76 feet.
Initially, Water in bucket = 37 pounds
Rate of pulling rope = 1.8 feet per second
Rate of water leaking in bucket = 0.25 pounds per second
Changing rate of leaking from pounds/sec to pounds/ feet : Q = 0.25/1.8 pounds/feet
= 0.139 pounds per feet
Thus, the rate of water leak from bucket hole is 0.12 pounds per feet. Let 'x' be height of bucket in feet from bottom of well. So, the total water leaked from hole = 0.12x
After leakage Remaining water in bucket = (37 - 0.12x )pounds
Also, add the weigh of buket in above expression. The limits of integration varies with depth of well that is 0 to 76 feet. Using Riemann sum method, work done pulling the bucket to the top of the well, [tex]W = \int_{0}^{76} ( 37 - 0.12x + 5 ) dx [/tex]
=>[tex]W = \int_{0}^{76} ( 42 - 0.12x ) dx [/tex]
=> [tex]W = [0 - \frac{0.12x²}{2}]_{0}^{76} \\ [/tex]
=> [tex]W = \frac{0.12×76²}{2} - 0 [/tex]
=> W = 0.12× 38×76 = 346.56 pounds/ feet. Hence required work done is 346.56 pounds/ feet.
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since the mid 1950s both men and women in the u.s. have experienced a steady in the proportion of the population never married. group of answer choices decline decrease increase none of these options are correct.
Answers
Since the mid 1950s, both men and women in the U.S. have experienced an increase in the proportion of the population never married. The correct answer is "increase".
This trend has been attributed to various factors such as the rise of individualism, changing gender roles, economic factors, and the decline of traditional social norms. In 1960, only 9% of women and 6% of men aged 25-34 had never been married, while in 2020, these numbers increased to 33% for women and 23% for men.
Therefore, it is evident that the proportion of the U.S. population never married has increased steadily over the past few decades
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) the average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. a lot contains 200 of these vehicles, brand new. (a) how many of the 200 would you expect to fail in their first 2 years? (b) what is the approximate probability that 50 or more of them fail in their first 2 years? (c) if you have learned that 30 vehicles have already failed in under 2 years, what is the approximate probability that no more than 10 of the rest of them fail in their first 2 years?
Answers
a) We would expect approximately 0.2325 × 200 = 46.5 vehicles
to fail in their first 2 years. Since we cannot have a fraction of a vehicle
failing, we would expect around 46 or 47 vehicles to fail in their first 2
years.
b) The approximate probability that 50 or more vehicles fail in
the first 2 years is 0.0004.
c) The approximate probability that no more than 10 of the remaining
vehicles fail in their first 2 years, given that 30 have already failed, is 0.0002.
a) The average lifespan of the vehicle is 8 years, and it follows an
exponential distribution, which has a probability density function of
[tex]f(x) = (1/θ) \times e^(-x/θ)[/tex],
where θ is the mean of the distribution. Thus, θ = 8.
The probability that a vehicle fails in the first 2 years can be found by
integrating the exponential probability density function from 0 to 2:
P(X ≤ 2) = ∫[0,2] f(x) dx = ∫[0,2] (1/8) × e^(-x/8) dx
Using a calculator or a table of integrals, we can find this probability to
be approximately 0.2325.
b) The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 200 × P(X ≤ 2) = 200 × 0.2325 = 46.5.
The probability that 50 or more vehicles fail in the first 2 years can be
found using the Poisson distribution with parameter λ = 46.5:
P(X ≥ 50) = 1 - P(X < 50)
Using a Poisson distribution table or a calculator, we can find that P(X <
50) is approximately 0.9996.
Thus, P(X ≥ 50) = 1 - 0.9996 = 0.0004 (approximately).
c) Given that 30 vehicles have already failed in under 2 years, we need
to find the probability that no more than 10 of the remaining 170 vehicles
fail in their first 2 years.
The number of vehicles that fail in the first 2 years follows a Poisson
distribution with parameter λ = 170 × P(X ≤ 2) = 170 × 0.2325 = 39.525
(rounded to 40).
Thus, we need to find P(Y ≤ 10), where Y is a Poisson random variable
with parameter λ = 40.
Using a Poisson distribution table or a calculator, we can find that P(Y ≤
10) is approximately 0.0002.
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100 points!!!
Express the function graphed on the axes below as a piecewise function.
Answers
It seems like your question is incomplete. Please provide the complete question or topic you would like me to discuss,
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if f(x) = -x-11 ; find the following.
the fraction of f(9) and f(-6)
Answers
Answer:
f(x) = -x -11
= -9-11 = -20
f(x) = -x-11
= -6-11= -17
Step-by-step explanation:
Shawn makes 15 1/5% of free throw shots he attempts. That means on average he makes 15 1/5 shots for every 100 shots he attempts. About how many free throw shots does Shawn make out of 300 shots?
Answers
Answer: To find how many free throw shots Shawn makes out of 300 shots, we can first find how many he makes out of 100 shots, and then multiply by 3 to get the number of shots he makes out of 300.
If he makes 15 1/5 shots out of 100, we can convert this to a decimal by dividing 15 by 100 and adding 1/5, which is the same as adding 0.2. This gives:
15/100 + 1/5 = 0.15 + 0.2 = 0.35
So, on average, Shawn makes 35% of the free throw shots he attempts.
To find how many shots he makes out of 300, we can multiply this percentage by 300:
0.35 x 300 = 105
Therefore, Shawn makes about 105 free throw shots out of 300 shots.
Step-by-step explanation:
Which statements are true for the following expression? (8 + 7)(11+7) Check all that are true. The solution is the sum of two terms. The solution is the difference between two terms. The first factor is itself the sum of two terms. 4 The solution is the product of two factors. The second factor is itself the sum of two terms.
Answers
Answer:
the last 3 are true
Step-by-step explanation:
hope this helps
ASAP PLEASE 25 POINTS YALL
find the 43th term for the sequence -19, -15, -11
Answers
The 43rd term of the sequence is 149.
What is arithmetic progression?Arithmetic progression is a sequence of numbers in which the difference between any two consecutive numbers is a constant value. The constant value is called a common difference.
Equation:We can see that the common difference between consecutive terms in the sequence is 4. So, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n - 1)d
where a1 is the first term, d is the common difference, and n is the term number we want to find.
To find the 43rd term, we plug in the values:
a1 = -19, d = 4, n = 43
an = -19 + (43 - 1)4
an = -19 + 42(4)
an = -19 + 168
an = 149
Therefore, the 43rd term of the sequence is 149.
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Write an inequality for the following statement. a is less than or equal to 2
Answers
Answer: a ≤ 2
Step-by-step explanation:
How to write an inequality statement:
Step 1: Write the two values being compared in the problem.
Step 2: Determine whether the first value is larger or smaller than the second value.
Step 3: Express the inequality with the right symbols:
≤ = less than or equal to
≥ = greater than or equal to
Therefore, the answer would be a≤2.
Hope this helped!
Question 1) What fraction of this shape is shaded?
Answers
The required fraction for the given condition is [tex]\frac{1}{3}[/tex]
What is fraction?A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.
According to question:Give shape contain 12 squares out of then four squares are shaded.
so, required fraction can be determine as
[tex]$Fraction=\frac{4}{12}[/tex]
[tex]$Fraction=\frac{1}{3}[/tex]
Thus, required fraction is [tex]\frac{1}{3}[/tex]
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Complete question;
The area of a composite figure is 84 square inches. The figure is decomposed into one rectangle and two congruent triangle. The length of the rectangle is 12 inches. The width of the rectangle is 5 inches. The heigh of both triangles is 4 inches. What is the base of both triangles?
________Inches
Answers
Answer:
3 inches
Step-by-step explanation:
area of a rectangle
12×5
he difference between the value of the number increased by 20% and the value of the number decreased by 25% is 36. what is the number? (1 point) 720 80 7.2 0.8
Answers
The number described in the question, whose stated percentage difference is 36, is 80.
Let us represent the number as x. So, the increased number will be -
Increased number = x + 20%×x
Simplify percentage
Increases number = x + 0.2x
Add the digits
Increased number = 1.2x
Similarly, decreased number = x - 25%×x
Converting percentage
Decreased number = x - 0.25x
Subtract the digits
Decreased number = 0.75x
Representing the difference
1.2x - 0.75x = 36
Subtract
0.45x = 36
Divide
x = 80
Hence, the number is 80.
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A bag with 8 marbles has 2 yellow marbles, 3 red marbles and 3 blue marbles. A marble is chosen from the bag at random. What is the probability that it is yellow? Write your answer as a fraction in simplest form.
Answers
The probability that it is yellow is 1/4.
What is probability?
The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
Here, we have
Given: A bag with 8 marbles has 2 yellow marbles, 3 red marbles, and 3 blue marbles. A marble is chosen from the bag at random.
We have to find the probability that it is yellow.
the probability that it is yellow:
= 2/8
= 1/4
Hence, the probability that it is yellow is 1/4.
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In a cooking contest, the mean score for taste was 20, with a standard deviation of 2.8. One of the contestants received a score of 14. Convert this score to a z score and tell if it is “usual” or “unusual.”
Answers
To convert the score of 14 to a z-score, we use the formula:
z = (x - μ) / σ
where x is the raw score, μ is the population mean, and σ is the population standard deviation.
Substituting the given values, we get:
z = (14 - 20) / 2.8
z = -2.14
The z-score of -2.14 indicates that the score of 14 is quite far from the mean of 20, which makes it an unusual score. To determine how unusual it is, we can compare the z-score to the standard normal distribution table.
The table shows that a z-score of -2.14 corresponds to a probability of approximately 0.016. This means that only about 1.6% of contestants would receive a score of 14 or lower in this cooking contest. Therefore, we can conclude that the score of 14 is unusual.
a researcher wants to test the hypothesis that the mean rating of guilt will be higher for unattractive defendants than for attractive defendants. the appropriate statistical test would be the
Answers
The appropriate statistical test for whether the mean rating of guilts are greater for unattractive defendants than for attractive is:
B. 1 tailed t-test.
What are the hypothesis test?At the null hypothesis, it is tested if the mean rating of guilt will not be higher for unattractive defendants than for attractive defendants, that is:
H0 : uU <=uA
At the alternative hypothesis, it is tested if the rating is greater, that is:
H1 : uU> uA
We are comparing the means, hence a t-test is used. We are testing if one is greater than other(not different), hence a 1-tailed test is used, and option B is correct.
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PLS HELP THIS PROGRAM IS UNNECESSARY
Answers
Answer: -32.00
Step-by-step explanation:
Answer:
A) -32.00
Step-by-step explanation:
-32.00 would be more debt than -25
Helping in the name of Jesus.
-8x+y=25 system of equations help
Answers
-8x+y=25 can be rewritten in slope intercept form to be…
Answer: y=8x+25
What is the value of x?
Triangle A B C is shown with its exterior angles. Line B A extends through point D. Line A B extends through point E. Line A C extends through point F.
Which angle’s measure is equal to the sum of the measures of ∠BAC and ∠BCA?
Answers
The measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.
What is the exterior angle?An exterior angle is an angle that forms a linear pair with an interior angle of a polygon. It is formed by extending one of the sides of the polygon. In other words, it is the angle formed between a side of a polygon and the extension of an adjacent side.
Based on the problem description, we can see that the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA. Therefore, we need to find the measure of the exterior angle at vertex A.
We know that the sum of the measures of the angles in a triangle is 180 degrees. So, we can find the measure of angle BAC by subtracting the measures of angles BCA and ABC from 180 degrees:
angle BAC = 180 - angle BCA - angle ABC
We can find the measure of angle ABC by subtracting the measure of angle A from 180 degrees:
angle ABC = 180 - angle A
Similarly, we can find the measure of angle BCA by subtracting the measure of angle C from 180 degrees:
angle BCA = 180 - angle C
Substituting these expressions into the equation for angle BAC, we get:
angle BAC = 180 - (180 - angle A) - (180 - angle C)
= angle A + angle C
Therefore, the measure of the exterior angle at vertex A is equal to the sum of the measures of angles BAC and BCA, which is angle A + angle C.
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Identify the slope and y-intercept of the following equation:
y = 1/3x
Answers
Answer: Slope: 1/3
Y-intercept: 0 (since there is no constant term)
The dance team is making banners to advertise an upcoming performance. (Screenshot)
Answers
Answer:
[tex]6.45ft^{2}[/tex]
Step-by-step explanation:
You've decided you want a plant for your room. At the gardening store, there are
4
44 different kinds of plants (tulip, fern, cactus, and ficus) and
4
44 different kinds of pots to hold the plants (clay pot, plastic pot, metal pot, and wood pot).
If you randomly pick the plant and the pot, what is the probability that you won't get a clay pot or a cactus?
Answers
The probability of not getting a clay pot or a cactus when randomly picking a plant and a pot from a selection of 4 plants and 4 pots is 0.75 or 75%.
There are a total of 4 x 4 = 16 possible outcomes when randomly picking a plant and a pot. Out of these, we need to count the number of outcomes where we don't get a clay pot or a cactus.
Let's start by counting the number of outcomes where we get a clay pot or a cactus. There are 4 possible outcomes for the plant (cactus or one of the three other plants) and 1 possible outcome for the pot (clay pot). So there are 4 x 1 = 4 outcomes where we get a cactus or a clay pot.
Therefore, the number of outcomes where we don't get a cactus or a clay pot is:
16 - 4 = 12
So the probability of getting a plant and a pot where neither the plant is a cactus nor the pot is a clay pot is:
P = number of outcomes where we don't get a cactus or a clay pot / total number of outcomes
= 12 / 16
= 0.75
Therefore, the probability of not getting a clay pot or a cactus is 0.75 or 75%.
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the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
Answers
The average speed of a falling object during the first 3 seconds of its fall is h(3)-h(0)/3.
The model of the motion of the body is given by, and the function of the motion of the body is given by h(t) = 300 - 16t².
The speed of object after 3 seconds is given by . The falling speed of object during the first 3 seconds of falling is calculated as follows, v = dh(t)/dt = -32t.
So now the average speed of the movement is calculated as follows,
v = h(3)-h(0)/3.
Option d is therefore the correct option.
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Complete question - the height, h, of a falling object t seconds after it is dropped from a platform 300 feet above the ground is modeled by the function . what is the average rate at which the object falls during the first 3 seconds?
A.) h(3) – h(0)
B.) h(3/3)-h(0/3)
C.) h(3)/3
D.) (h(3)-h(0))/3
PLEASE HELP!!
Fill in the table below.
Level
3
7
Toothpicks
Part D Extension
Sum of
Toothpicks
sxordinoni 10 # IRIOL
120
100
80
60
40
20
Number of Levels
What do you notice about the points being graphed?
Do they appear linear, quadratic or exponential?
Defend your choice.
Answers
The table of values when completed using y = 10x is a linear function
Completing the table of valuesFrom the question, we have the following parameters that can be used in our computation:
The incomplete table
When completed, we have
Levels Toothpicks
1 10
2 20
3 30
4 40
5 50
6 60
7 70
8 80
The means that
Toothpicks = 10 * Level
So, we have the equation to be
y = 10x
This is a linear function
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it is known that 5% of the books bound at a certain bindery have defective bindings. find the probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution.
Answers
Answer:
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
Step-by-step explanation:
We can use the Poisson approximation to the binomial distribution when n (the number of trials) is large and p (the probability of success) is small. In this case, n = 100 and p = 0.05, so np = 5, which is not too small. However, we can still use the approximation as long as we adjust for continuity, by adding and subtracting 0.5 from the number of successes we're interested in.
Let X be the number of books with defective bindings out of 100. We want to find the probability that X = 2. Using the Poisson approximation, we have:
λ = np = 5
P(X = 2) ≈ P(1.5 < Y < 2.5), where Y is a Poisson random variable with parameter λ
To find this probability, we can use the cumulative distribution function (CDF) of Y:
P(X = 2) ≈ P(1.5 < Y < 2.5) = F(2.5) - F(1.5), where F(x) is the CDF of Y evaluated at x
The CDF of a Poisson distribution with parameter λ is given by:
F(x) = e^(-λ) * Σ(λ^k / k!, k = 0 to floor(x))
where floor (x) is the greatest integer less than or equal to x. Using this formula, we can calculate:
F(1.5) = e^(-5) * Σ(5^k / k!, k = 0 to 1) ≈ 0.0337
F(2.5) = e^(-5) * Σ(5^k / k!, k = 0 to 2) ≈ 0.1247
Therefore, P(X = 2) ≈ 0.1247 - 0.0337 ≈ 0.091, or about 9.1%.
The probability that 2 of the 100 books bound by this bindery will have defective bindings using the poisson approximation to the binomial distribution is 0.0842.
Since the number of books bound, n = 100, is large and the probability of defective bindings, p = 0.05, is small, we can use the Poisson approximation to the binomial distribution.
The mean, µ, of the Poisson distribution is µ = np = 100 x 0.05 = 5.
The probability of 2 defective bindings can be calculated using the Poisson probability formula:
P(X = 2) = (e^-µ) * (µ^x) / x!
= (e^-5) * (5^2) / 2!
= 0.0842 (rounded to four decimal places)
Using the Poisson approximation to the binomial distribution, the likelihood that 2 of the 100 volumes bound by this bindery will have faulty bindings is roughly 0.0842.
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