Answer:
a) probability that the sample will have between 50% and 60% of the identification correct = 0.498
b) The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65% = 0.01
Step-by-step explanation:
Sample size, n = 200
Since the brands are equally likely, p = 0.5, q = 0.5
The Standard deviation, [tex]\sigma_p = \sqrt{\frac{pq}{n} }[/tex]
[tex]\sigma_p = \sqrt{\frac{0.5 * 0.5}{200} } \\\sigma_p = 0.0353[/tex]
a) probability that the sample will have between 50% and 60% of the identification correct.
[tex]P(0.5 < X < 0.6) = P(\frac{0.5 - 0.5}{0.0353} < Z < \frac{0.6 - 0.5}{0.0353} )\\P(0.5 < X < 0.6) = P( 0 < Z < 2.832)\\P(0.5 < X < 0.6) = P(Z < 2.832) - P(Z < 0)\\P(0.5 < X < 0.6) = 0.998 - 0.5\\P(0.5 < X < 0.6) = 0.498[/tex]
Probability that the sample will have between 50% and 60% of the identification correct is 0.498
b) p = 90% = 0.9
Getting the z value using excel:
z = (=NORMSINV(0.9) )
z = 1.281552 = 1.28 ( 2 dp)
Then we can calculate the symmetric limits of the population percentage as follows:
[tex]z = \frac{X - \mu}{\sigma_p}[/tex]
[tex]-1.28 = \frac{X_1 - 0.5}{0.0353} \\-1.28 * 0.0353 = X_1 - 0.5\\-0.045+ 0.5 = X_1\\X_1 = 0.455[/tex]
[tex]1.28 = \frac{X_2 - 0.5}{0.0353} \\1.28 * 0.0353 = X_2 - 0.5\\0.045+ 0.5 = X_2\\X_2 = 0.545[/tex]
The probability is 90% that the sample percentage is contained 45.5% and 54.5% of the population percentage
c) Probability that the sample percentage of correct identifications is greater than 65%
P(X>0.65) = 1 - P(X<0.65)
[tex]P(X<0.65) = P(Z< \frac{X - \mu}{\sigma} )\\P(X<0.65) = P(Z< \frac{0.65 - 0.5}{0.0353} )\\P(X<0.65) = P(Z < 4.2372) = 0.99\\P(X>0.65) = 1 - P(X<0.65)\\P(X>0.65) = 1 - 0.99\\P(X>0.65) = 0.01[/tex]
h(1)=0. h(n)=h(n-1)-9 explicit formula for h(n)=
Answer:
0-9(n-1)
Step-by-step explanation:
We can tell the first term of the sequence is 0 and the common difference is -9. So the explicit formula would be h(n)=0-9(n-1)
The explicit formula for h(n) comes to be h(n)=9-9n.
What is an arithmetic progression?An arithmetic progression is a list of numbers where the difference between consecutive terms is always constant.
[tex]h(n)=h(n-1)-9[/tex]
[tex]h(n)-h(n-1)=-9[/tex]
So the common difference of the arithmetic progression will be -9.
[tex]h(1)=0[/tex] means the first term of the AP is 0.
We know that [tex]n^{th}[/tex] term of an AP is given by:
[tex]h(n)=a+(n-1)d[/tex]
Where a is the first term and d is a common difference.
Fo the given series [tex]a=0[/tex] and [tex]d=-9[/tex]
So, [tex]h(n)=0+(n-1)(-9)[/tex]
[tex]h(n)=9-9n[/tex]
So, the explicit formula for h(n) is [tex]h(n)=9-9n[/tex]
Hence, the explicit formula for h(n) comes to be [tex]h(n)=9-9n[/tex].
To get more about arithmetic progressions visit:
https://brainly.com/question/6561461
Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?
a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)
Answer:
Step-by-step explanation:
Since we are dealing with binomial probability in this scenario, then the outcome is either a success or a failure. A success in this case means that a chosen adult has a bachelor's degree. The probability of success, p would be 20/100 = 0.2
The number of adults sampled, n is 100
The number of success, x is 60
The probability that more than 60 adults have a bachelor's degree P(x >60) would be represented as
d. P(x<60)=binomcdf (100.0.20.60)
binompdf is used when we want to determine P(x = 60)
what value of x in the solution set of -5×-15>10+20
Answer:
ⁱ ʰᵒᵖᵉ ᵗʰⁱˢ ʷᵒᵘˡᵈ ʰᵉˡᵖ ʸᵒᵘ ᵗᵒ ᵍᵉᵗ ʳᵉᵃˡ ᵃⁿˢʷᵉʳ...
given:f(x)=x-7 and h(x)=2x+3 write the rule for f(h(x))
Answer:
Step-by-step explanation:
h(x) = 2x + 3
f(2x+3)
2x+3 - 7
2x - 4
Cory is picking out some movies to rent, and he is primarily interested in comedies and horror films. He has narrowed down his selections to 14 comedies and 19 horror films. How many different combinations of 4 movies can he rent if he wants at least one comedy
Answer:
37044 different combinations of 4 movies can he rent if he wants at least one comedy
Step-by-step explanation:
The order in which the movies are selected is not important, so we use the combinations formula to solve this question.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
How many different combinations of 4 movies can he rent if he wants at least one comedy
The easier way to solve this is subtract the total from the number of combinations with no comedies.
Total:
4 movies from a set of 14 + 19 = 33. So
[tex]C_{33,4} = \frac{33!}{4!(33-4)!} = 40920[/tex]
No comedies:
4 movies from a set of 19.
[tex]C_{19,4} = \frac{19!}{4!(19-4)!} = 3876[/tex]
At least one comedy:
40920 - 3876 = 37044
37044 different combinations of 4 movies can he rent if he wants at least one comedy
Darren wanted to see how contagious yawning can be. To better understand this, he conducted a social experiment in which he yawned in front of a large, random crowd and observed how many people yawned as a result. The relationship between the elapsed time ttt, in minutes, since Darren yawned, and the number of people in the crowd, P(t)P(t)P, left parenthesis, t, right parenthesis, who yawned as a result is modeled by the following function: P(t)=5⋅4t10.5
Answer:
10.5 minutes
Step-by-step explanation:
Thinking about the problem
The modeling function is of the form P(t)=A⋅Bf(t), where B=4B=4B, equals, 4 and f(t)=\dfrac{t}{10.5}f(t)=
10.5
t
f, left parenthesis, t, right parenthesis, equals, start fraction, t, divided by, 10, point, 5, end fraction.
Note that each time f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111, the quantity is multiplied by B=4B=4B, equals, 4.
Therefore, we need to find the ttt-interval over which f(t)f(t)f, left parenthesis, t, right parenthesis increases by 111.
Hint #22 / 3
Finding the appropriate unit interval
fff is a linear function whose slope is \dfrac{1}{10.5}
10.5
1
start fraction, 1, divided by, 10, point, 5, end fraction.
This means that whenever ttt increases by \Delta tΔtdelta, t, f(t)f(t)f, left parenthesis, t, right parenthesis increases by \dfrac{\Delta t}{10.5}
10.5
Δt
start fraction, delta, t, divided by, 10, point, 5, end fraction.
Therefore, for f(t)f(t)f, left parenthesis, t, right parenthesis to increase by 111, we need \Delta t=10.5Δt=10.5delta, t, equals, 10, point, 5. In other words, the ttt-interval we are looking for is 10.510.510, point, 5 minutes.
Hint #33 / 3
Summary
The number of people who yawned quadruples every 10.510.510, point, 5 minutes.
An excavation crew is digging a tunnel under a bay. The crew has dug 573 meters of the tunnel, which is 34 meters past the halfway point. What will be the length of the tunnel when the crew has finished digging?
Answer:
The total length of the tunnel when the crew has finished digging is 1078 meters
Step-by-step explanation:
total length of the tunnel dug by the crew = 573 meters
let the halfway point of the tunnel = h
if the crew digs 34 meters past the halfway point, then we will this equation below;
h + 34 meters = 573 meters
h = 573 - 34
h = 539 meters
halfway point of the tunnel is 539 meters
Then, the total length of the tunnel when the crew has finished digging = 2h
= 2 x 539 meters
= 1078 meters
Therefore, the total length of the tunnel when the crew has finished digging is 1078 meters
Suppose a batch of metal shafts produced in a manufacturing company have a variance of 2.89 and a mean diameter of 211 inches. If 86 shafts are sampled at random from the batch, what is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Answer:
27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation(which is the square root of the variance) [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 211, \sigma = \sqrt{2.89} = 1.7, n = 86, s = \frac{1.7}{\sqrt{86}} = 0.1833[/tex]
What is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches.
Either greater than 211 + 0.2 = 211.2 or smaller than 211 - 0.2 = 210.8. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.
Probability of being less than 210.8:
This is the pvalue of Z when X = 210.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{210.8 - 211}{0.1833}[/tex]
[tex]Z = -1.09[/tex]
[tex]Z = -1.09[/tex] has a pvalue of 0.1379
Probability of differing from the population mean by greater than 0.2 inches :
2*0.1379 = 0.2758
27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches
Answer:
Probability is 86.24%
Step-by-step explanation:
We can solve this by using the Z-score formula.
Z = (X - μ)/σ
Where;
μ is mean = 211 inches
σ is standard deviation
Now, we are given variance as 2.89
Formula for standard deviation using variance is;
SD = √variance
SD = √2.89
SD = 1.7
To find the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches, we will find the p-value of z and subtract 1 from it.
Since we are told that the sample shafts would differ by 0.2 inches, thus;
X = 211 + 0.2 = 211.2
Since we are working with sample mean of 86, then we have;
Z = (X - μ)/s
s = σ/√86
s = 1.7/√86
s = 0.1833
So,
Z = (211.2 - 211)/0.1833
Z = 1.0911
From z-score calculator, the p-value is gotten to be 0.1376
Thus, probability that mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches is;
Probability = 1 - 0.1376 = 0.8624 = 86.24%
A random sample of 100 pumpkins is obtained and the mean circumference is found to be 40.5 cm. Assuming that the population standard deviation is known to be 1.6 cm, use a 0.05 significance level to test the claim that the mean circumference of all pumpkins is equal to 39.9 cm.Do the following:_________.a) Write the hypotheses H0 and H1b) Calculate the z-scorec) Find corresponding probability to z-scoree) Write the decision and conclusion of the test of hypothesis.
Answer:
it should be 40.5 i believe
Step-by-step explanation:
According to a survey conducted by the Associated Press (AP) and petside in 2009, 63% of dog owners and 53% of cat owners would be at least somewhat likely to give CPR to their pet in the event of a medical emergency. The survey involved a nationwide sample of 1,166 pet owners. Use this information to answer the following questions.
Requried:
a. Produce a well-labeled segmented bar graph to display these percentages.
b. Identify the two categorical variables displayed in the graph.
c. What additional information would you need in orde to construct a 2 x 2 table?
Answer:
a) Check the bar graph in the picture attached
b) The two categorical variables are:
1) Type of owners
2) Likelihood to give CPR
c) Information on the population( in number or percentage) of the dog/cat owners.
Step-by-step explanation:
a) the bar chart is drawn with % of owners likely to give CPR to their pets on the y-axis and the owner types on the x - axis.
b) The two categorical variables are:
1) Type of owners
2) Likelihood to give CPR
c) To construct a 2 x 2 table, the percentage (or number) of either dog owners or cat owners.
Since we know that the total number of pet owners that were sampled = 1166.
If the number of dog owners is known, it can be subtracted from the total number of pet owners to know the number of cat owners and vice versa. If this information is gotten, then the 2 x 2 table can be constructed.
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer:
A: f(x) = (3/4 x)^2 - 1
Step-by-step explanation:
As you can see in the first image i attached, option A is the function that matches the one in your image. the "- 1" in the function is the y-intercept, and the 3/4 is what stretches your parabola which made it larger. You could also use process of elimination to get rid of option B and D since the y-intercepts do not match. Then you are left with A and C. the 4 in "(4x)^2" would make the parabola shrink, as you can see in the second image.
At a certain car dealership, the probability that a customer purchases an SUV is . Given that a customer purchases an SUV, the probability that it is black is . What is the probability that a customer purchases a black SUV? Round your answer to four decimal places, if necessary.
Answer:
The probability that a customer purchases a black SUV is 0.05.
Step-by-step explanation:
The question is incomplete:
At a certain car dealership, the probability that a customer purchases an SUV is 0.20. Given that a customer purchases an SUV, the probability that it is black is 0.25.
The probability that a customer purchases a black SUV can be calculated as the multiplication of this 2 factors:
The probability of a customer purchasing a SUV: P(SUV).The probability that it is black, given that he or she purchases a SUV (conditional probabilty): P(B|SUV)We know then:
[tex]P(SUV)=0.25\\\\P(B | SUV)=0.20[/tex]
We can now calculate the probability as:
[tex]P(B\,\&\,SUV)=P(B|SUV)\cdot P(SUV)=0.25\cdot0.20=0.05[/tex]
A group consists of five men and five women. Three people are selected to attend a conference.
A. In how many ways can three people be selected from this group of ten?
B. In how many ways can three women be selected from the five women?
C. Find the probability that the selected group will consist of all women.
Answer:
a) 120
b) 10
c) 1/12
Step-by-step explanation:
The number of ways that a sample of r can be selected from a population of n is:
nCr = n! / (r! (n−r)!)
a) 3 people selected from a group of 10
₁₀C₃ = 120
b) 3 women selected from a group of 5
₅C₃ = 10
c) Of the 120 committees that can be chose, 10 are all women. So the probability is 10/120 = 1/12.
The average weight of the entire batch of the boxes of cereal filled today was 20.5 ounces. A random sample of four boxes was selected with the following weights: 20.05, 20.56, 20.72, and 20.43. The sampling error for this sample is ________.
Answer:
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s= 0.286[/tex]
And then the estimator for the standard error is given by:
[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]
Step-by-step explanation:
For this case we have the following dataset given:
20.05, 20.56, 20.72, and 20.43
We can assume that the distribution for the sample mean is given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
And the standard error for this case would be:
[tex] SE= \frac{\sigma}{\sqrt{n}}[/tex]
And we can estimate the deviation with the sample deviation:
[tex] s= \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]
And replacing we got:
[tex] s= 0.286[/tex]
And then the estimator for the standard error is given by:
[tex] SE= \frac{0.286}{\sqrt{4}}= 0.143[/tex]
Lauren drove the 75 miles to the coast at 75mph, but got stuck in traffic and averaged 25mph on the way back.
-How many total miles did Lauren drive in this round-trip?
-How many total hours did Lauren drive in this round-trip?
-What was the average speed Lauren was driving during this round-trip?
Answer:
Step-by-step explanation:
1) The distance that Lauren drove to the coast is the same as the distance he drove back from the coast. It means that the total miles that Lauren drove in this round-trip is
75 + 75 = 150 miles
2) time = distance/speed
Time spent in driving to the coast is
75/75 = 1 hour
His return speed is 25 mph
Time spent in driving back from the coast is
75/25 = 3 hours
3) Average speed = total distance/total time
Total distance = 75 + 75 = 150 miles
Total time = 1 + 3 = 4 hours
Average speed = 150/4 = 37.5 mph
A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt. The recipe can be scaled up to make multiple loaves of bread. Complete the table that shows the quantities to use for multiple loaves of bread.
Answer:
For 2 loaves of bread, 4 cups of flour, 24 tablespoons of water, and 2 teaspoons of salt are required
For 4 loaves of bread, 8 cups of flour, 48 tablespoons of water, and 4 teaspoons of salt are required
Step-by-step explanation:
Given: A recipe for 1 loaf of bread calls for 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt
To find: the missing terms in the box
Solution:
As for 1 loaf of bread, 2 cups of flour, 12 tablespoons of water, and 1 teaspoon of salt are required
So, for 2 loaves of bread, double the quantity.
So, for 2 loaves of bread, 2×2=4 cups of flour, 12×2=24 tablespoons of water, and 1×2=2 teaspoons of salt are required
For 4 loaves of bread, double the quantity used to make 2 loaves of bread.
For 4 loaves of bread, 4×2=8 cups of flour, 24×2=48 tablespoons of water, and 2×2=4 teaspoons of salt are required
See the image attached.
Question 7 of 10
2 Points
Which number produces a rational number when multiplied by 0.5%
A. V
C. -1.73205089
O D. 0.54732814
BUBMIT
Find the product in simplest form. (3√2) ( √10) 3 √10 3 √20 6 √5 6 √10
Answer:
6 sqrt(5)
Step-by-step explanation:
(3√2) ( √10)
We know that sqrt(a) * sqrt(b) = sqrt(ab)
3 sqrt(2*10)
3 sqrt(20)
3 sqrt(4*5)
We know that sqrt(a) * sqrt(b) = sqrt(ab)
3 sqrt(4) sqrt(5)
3 * 2 * sqrt(5)
6 sqrt(5)
When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of the trachea, making a narrower channel for the expelled air to flow through. For a given amount of air to escape in a fixed time, it must move faster through the narrower channel than the wider one. The greater the velocity of the airstream, the greater the force on the foreign object. X rays show that the radius of the circular tracheal tube contracts to about two-thirds of its normal radius during a cough. According to a mathematical model of coughing, the velocity v of the airstream is related to the radius r of the trachea by the equation v(r)= k (r 0- r) r ^ 2, 1/2 r 0 less than r less than r0where k is a constant and r0 is the normal radius of the trachea. The restriction on r is due to the fact that the tracheal wall stiffens under pressure and a contraction greater than 1/2r0 is prevented (otherwise the person would suffocate). Determine the value of r in the interval [1/2r0, r0] at which v has an absolute maximum. How does this compare with experimental evidence?
Answer:
Step-by-step explanation:
(a)
[tex]= kr^2(r_0 - r )[/tex]
[tex]= ( kr_0)r^2 - kr^3 \\\\=>v '(r) = ( 2kr_0 )r -3kr^2\\\\= ( -3k)r^2 + ( 2kr_0 )r[/tex]
v has an absolute maximum when v '(r) = 0
v '(r) = 0 =>
( -3k )r2 + ( 2kr0 )r = 0 =>
r = [ -( 2kr0 ) ± sqrt[ ( 2kr0)2 - ( 4 )( -3k )( 0 ) ] ] / [ ( 2 )( -3k ) ]
= [ -2kr0 ± 2kr0 ] / ( -6k)
= 0 or ( -4kr0 / -6k )
= 0 or (2/3)r0
since [tex]r > (1/2)r_0[/tex] in the given interval,[tex]r =(2/3)r_0[/tex], which matches its experimental value.
Solve for x
A) 7
B) 10
C) 5
D) -7
Answer:
D) -7
Step-by-step explanation:
[tex] \because \: PQ + QR = PR \\ \therefore \: 2x + 17 + 12 = 22 + x \\ \therefore \: 2x + 29 = 22 + x \\ \therefore \: 2x - x = 22 - 29 \\ \therefore \: x = - 7 \\ [/tex]
Please answer this correctly without making mistakes
Answer:
10.99 inches
Step-by-step explanation:
7*2=14
diameter=14
circumference=diameter*pi
14*3.14=43.96
quarter circle
43.96/4=10.99
10.99 inches
Answer:
the quarter circle's perimeter = 24.99 inch
Step-by-step explanation:
1. Calculate circumference of a complete circle.
2. Divide by 4 and you have the quarter part. (This is the same as multiplying by 0.25).
3. Just like a pie chart, there are 2 sides from the center to the left and right side edge of the quarter circle. Both are equal to the radius r.
4. Add the numbers found in step 2 and step 3 and you will have found the quarter circle's perimeter.
Given: use 3.14 for pi and r = 7 inch
1. Circumference = 2* pi * r
2. 1/4 * ( 2 * pi * r )
1/4 * ( 2 * 3.14 * 7 ) = 10.99 inch
3 Since r = 7 and we have to sides.
So you just add 2 * 7 = 14 inch
4. Add 10.99 + 14 = 24.99 inch
[Pic] Name a face of the solid.
Answer:
Option C.
Step-by-step explanation:
Solid in the given picture is a rectangular prism and a rectangular prism has 6 faces. Each face is formed by joining 4 vertices of the prism.
All the faces joining four vertices are: AFGB, BGHC, ADEF, DCHE, FEHG, ADCB.
From the given options,
Option (C). ADEF will be one of the face of the solid.
In the USA today internet poll 73 percent of readers indicated that they were satisfied with their lives.
1. 73 percent of readers are satisfied with their lives.
A. The population B. The sample
C. a population statistic D. a sample statistic
Answer:
c) Population parameter or Population statistic
Step-by-step explanation:
Population:-
The totality of observation with which we are concerned , whether this number be finite or infinite is called population
Sample :
A sample is subset of a Population
Given data the USA today internet poll is called Population
Given data 73 percent of readers are satisfied with their lives.
This is called Population parameter.
Suppose a jar contains 10 red marbles and 34 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.
Answer:
The probability that both are red is [tex]P(red\:and \:red)=\frac{45}{946}\approx0.04756\approx4.756\%[/tex].
Step-by-step explanation:
Probability is simply how likely something is to happen and its given by
Probability of an event = (# of ways it can happen) / (total number of outcomes)
Two events are dependent when the outcome of the first event influences the outcome of the second event. The probability of two dependent events is the product of the probability of X and the probability of Y AFTER X occurs.
[tex]P(A\:and\: B)=P(A)\cdot P(A|B)[/tex]
At our first pull, there is an [tex]P(red)=\frac{10}{10+34}[/tex] chance that a red will be pulled.
At the second pull there is a [tex]P(red)=\frac{9}{9+34}[/tex] chance that the second marble will be red.
Therefore, the probability that both are red is
[tex]P(red\:and \:red)=\frac{10}{10+34}\cdot \frac{9}{9+34}=\frac{45}{946}\approx0.04756\approx4.756\%[/tex]
Courtney sold 48 cantaloupes at the farmers' market and had 25 left. Which equation could be used to find x, the number of cantaloupes Courtney had originally?
Answer:
48+25=x
Step-by-step explanation:
Answer:
The answer is D :)
Thank me later.
Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n =8, p = 0.6, P(3 or fewer) Group of answer choices
Answer:
[tex]P(X \leq 3) = 0.1738[/tex]
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this question, we have that:
[tex]n = 8, p = 0.6[/tex]
P(3 or fewer)
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{8,0}.(0.6)^{0}.(0.4)^{8} = 0.0007[/tex]
[tex]P(X = 1) = C_{8,1}.(0.6)^{1}.(0.4)^{7} = 0.0079[/tex]
[tex]P(X = 2) = C_{8,2}.(0.6)^{2}.(0.4)^{6} = 0.0413[/tex]
[tex]P(X = 3) = C_{8,0}.(0.6)^{3}.(0.4)^{5} = 0.1239[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.0007 + 0.0079 + 0.0413 + 0.1239 = 0.1738[/tex]
3. Show why, for linear functions, a vertical translation is equivalent to a horizontal
translation. For a linear function, what horizontal translation is equivalent to a vertical
translation of 3 units up?
4. Alex says that the function f(x) = (3x)represents a vertical stretch of the quadratic
parent function by a factor of 3. Marta says that it represents a horizontal compression
1
by a factor of 3. Decide whether one student is correct, both are correct, or neither is
correct.
5. For an unknown parent function f(x), write a function g(x) that is:
O
o vertically stretched by a factor of 2,
shifted up 5 units, and
o shifted right 4 units.
6. Explain how your function accomplishes these transformations.
Answer:
3. Vertical is the same as horizontal for linear equations because when moving the function up, it moves the whole line left along the x-axis too. When moving it down, it moves the equation right on the x-axis.
4. Alex is correct
5. g(x)=(2x-8)^2+5
6. This accomplishes these transformations because I made a graph about it
Step-by-step explanation:
Solve for y 6(y-1/3) = 4(3y-5)
Answer:
y = 3
Step-by-step explanation:
It can work well to start by eliminating parentheses.
6(y -1/3) = 4(3y -5)
6y -2 = 12y -20
18 = 6y . . . . . . . . . add 20-6y to both sides
3 = y . . . . . . . . . . . divide by 6
Answer:
y=3
Step-by-step explanation:
6(y−13)=4(3y−5)
(6)(y)+(6)(−13)=(4)(3y)+(4)(−5)(Distribute)
6y+−2=12y+−20
6y−2=12y−20
Step 2: Subtract 12y from both sides.
6y−2−12y=12y−20−12y
−6y−2=−20
Step 3: Add 2 to both sides.
−6y−2+2=−20+2
−6y=−18
Step 4: Divide both sides by -6.
−6y−6=−18−6
y=3
(2/5 + 3/4) x [ 3 - (1/4 : 1/5)]
Answer & Step-by-step explanation:
(2/5 + 3/4) * [ 3 - (1/4 : 1/5)]
When you see this sign, : , it usually means to divide the numbers because they represent some form of a ratio. So, we will divide 1/4 by 1/5.
First, do all of the operations in the parentheses ().
(2/5 + 3/4)*[ 3 - (1/4 : 1/5)]
(23/20) * [ 3 - (5/4)]
(23/20) * (7/4)
Now, we multiply 23/20 by 7/4.
(23/20) * (7/4)
161/80
This number can not be simplified so we will keep it as it is.
So, the answer to this expression is 161/80
Requiem needs to know if the triangle shown is a right triangle. Which equation could he use to help ?
Answer:
Pythagoras theorem: hypotenuse² = opposite² + adjacent²
Step-by-step explanation:
To know if a triangle is a right angle, we need to have the length of each sides of the triangle. Then we would apply Pythagoras theorem to determine if it is truly a right angled triangle.
Pythagoras theorem is a theorem in the form of an equation which shows the relationship between the sides of a right angled triangle.
let the sides of the right angled triangle be:
opposite =a, adjacent = b and hypotenuse = c
Using Pythagoras theorem
hypotenuse² = opposite² + adjacent²
c² = a² + b²
If the left hand side of the equation = the right hand side of the equation, it is a right angled triangle.
