Answer:
(2/9)cis(30°)
Step-by-step explanation:
We can express the two numbers in magnitude∠angle form, then find their ratio.
|z1| = 3√((-1)² +(√3)²) = 3√4 = 6
∠z1 = arctan((3√3)/(-3)) = -arctan(√3) = 120°
z2 = 27∠90°
So, the ratio is ...
z1/z2 = (6∠120°)/(27∠90°) = (6/27)∠(120°-90°)
z1/z2 = (2/9)∠30°
solve for x x/25 > 5
Answer:
x > 125
Step-by-step explanation:
x/25 > 5
Multiply both sides by 25
x/25 × 25 > 5 × 25
x > 125
Which would be the most appropriate subject line for
the e-mail with this claim?
Claim: Cell phones should be allowed in schools
because banning them is no longer universally
accepted as the best policy.
YOUR POLICY IS TERRIBLE
Cell phones as an educational tool
Help! Students are at a disadvantage!
You should know that.
Answer:
B ✔️
Step-by-step explanation:
"Cell phones as an educational tool"
-4.0 -y=24
Complete the missing value in the solution to the equation.
8)
Answer:
y=-28
Step-by-step explanation:
add 4 to both sides which gets you -y =28. Then you have to move the negative sign to the other side because y can't end with a negative
The heights of all adult males in Croatia are approximately normally distributed with a mean of 180 cm and a standard deviation of 7 cm. The heights of all adult females in Croatia are approximately normally distributed with a mean of 158 cm and a standard deviation of 9 cm. If independent random samples of 10 adult males and 10 adult females are taken, what is the probability that the difference in sample means (males – females) is greater than 20 cm?
Answer:
Step-by-step explanation:
.7104
The probability that the difference in sample means (males – females) is greater than 20 cm is; 0.7088
How to find difference between two means?The formula for z-score of difference between two means is;
z = (x₁' - x₂' - Δ)/√[(√σ₁²/n₁) + (σ₂²/n₂)]
We are given;
Sample mean 1; x₁' = 180 cm
Sample mean 2; x₂' = 158 cm
Standard deviation 1; σ₁ = 7 cm
Standard Deviation 2; σ₂ = 9 cm
hypothesized difference; Δ = 20 cm
Sample size; n₁ = n₂ = 10
Thus;
z = (180 - 158 - 20)/√[(7²/10) + (9²/10)]
z = 0.55
From online z-score table, we have;
p = 0.71
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In 2001 polls indicated that 74% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2001? We test the hypothesis that the percentage supporting mandatory testing is less than 74% this year. The P-value is 0.015. Which of the following interpretation of this P-value is valid? Group of answer choices The probability that Americans have changed their opinion on this issue since 2001 is 0.015. If 74% of Americans still favor mandatory testing this year, then there is a 1.5% chance that poll results will show 71% or fewer with this opinion. There is a 1.5% chance that the null hypothesis is true.
Answer:
The correct option is option 2.
Step-by-step explanation:
In this case we need to test whether the previous data for the proportion of Americans who favored mandatory testing of students in public schools as a way to rate the school has decreased this year or not.
The hypothesis can be defined as follows:
H₀: The proportion supporting mandatory testing is not less than 74% this year, i.e. p ≥ 0.74.
Hₐ: The proportion supporting mandatory testing is less than 74% this year, i.e. p < 0.74.
It is provided that the p-value of the test is,
p-value = 0.015
The p-value is well defined as per the probability, [under the null hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was truly observed.
The p-value of 0.015 or 1.5% implies that, if it is true that 74% of Americans still favor mandatory testing this year, then the probability that the poll results will show that 71% or less with the same opinion is 1.5%.
Thus, the correct option is option 2.
A polling organization had taken a survey of a sample of 200 people for one of their clients, in order to estimate a population percentage. Now the client would like them to reduce the margin of error by 50% (that is, the new margin of error should be half the original margin of error), while keeping the same level of confidence. To do this, how many people should they now survey
Answer:
They now should survey 800 people.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem:
Same level of confidence, so same z
Same proportion, so same [tex]\pi[/tex]
We have to change n
We want to reduce the margin of error by half.
M is inverse proportion to the square root of n. That is, as n increases, M decreases.
We want to decrese M by half. So we need to increase n by a factor of 2^2 = 4
The first survey had a sample of 200 people
Increasing by a factor of 4.
200*4 = 800
They now should survey 800 people.
The mean number of sick days per employee taken last year by all employees of a large city was 10.6 days. A city administrator is investigating whether the mean number of sick days this year is different from the mean number of sick days last year. The administrator takes a random sample of 40 employees and finds the mean of the sample to be 12.9. A hypothesis test will be conducted as part of the investigation.
Which of the following is the correct set of hypotheses?
A. H0:μ=10.6Ha:μ>10.6 AB. H0:μ=10.6Ha:μ≠10.6 BC. H0:μ=10.6Ha:μ<10.6 CD. H0:μ=12.9Ha:μ≠12.9 DE. H0:μ=12.9Ha:μ<12.9 E
Answer:
H0:μ=10.6
Ha:μ≠10.6
Step-by-step explanation:
you do not find out about the 12.9 until after stating the hypothesis.
The correct hypothesis set for testing whether the mean number of sick days has changed is H0: μ = 10.6 against Ha: μ ≠ 10.6, which represents a two-tailed test.
Explanation:The correct set of hypotheses for the city administrator to test whether the mean number of sick days this year is
different from last year would be:
H0: μ = 10.6Ha: μ ≠ 10.6This is because the administrator is investigating if there is a change in either direction (increase or decrease), which is
considered a two-tailed test.
The null hypothesis (H0) always states that there is no difference or no effect, while the alternative hypothesis (Ha)
suggests that there is a difference from the norm, in that the mean is not equal to 10.6 days.
Based on the information given, the correct answer would be:
B. H0: μ = 10.6
Ha: μ ≠ 10.6
A new alloy is made by mixing 72 grams of iron with 9 grams of zinc. How many grams of iron are required to make the alloy when combined with 144 grams of zinc?
A) 992 grams
B) 1,152 grams
C) 1,226 grams
D) 1,445 grams
Answer:
B) 1,152 grams
Step-by-step explanation:
Gary used 8 gallons of gas to travel 176 miles. How many miles can Gary travel on 1 gallon of gas
Answer: Gary can travel 22 miles on 1 gallon gas.
Step-by-step explanation:
176/8 = 22
Haala buys 13 identical shirts and 22 identical ties for £363.01
The cost of a shirt is £15.35
Find the cost of a tie.
Answer:
£7.43
Step-by-step explanation:
The total cost is ...
13s +22t = 363.01
13(15.35) +22t = 363.01 . . . . fill in the cost of a shirt
22t = 163.46 . . . . . . . . . . . . . subtract 199.55
t = 7.43 . . . . . . . . . . . divide by 22
The cost of a tie is £7.43.
x 2 + 13x + 40 = 0
solving quadratic
Answer: x=-5 or x=-8
Step-by-step explanation:
x^2+13x+40=0
x^2 + 8x + 5x +40=0
x(x+8)+5(x+8)=0
(x+5)(x+8)=0
x+5=0 or x+8=0
x=-5 or x=-8
3
0 +
x+1
2
≤ −
3x+1
4
Answer:
solve for x
x ≤ − 7
Suppose we know that the birth weight of babies is normally distributed with mean 3500g
and standard deviation 500g.
(1) What is the probability that a baby is born that weighs less than 3100g?
a. What are the parameters?
b. Construct the normal distribution density curve, then shade your seeking area.
c. Find the Z-score, and construct the standard normal distribution density curve,
then shade your seeking area.
d. Find the probability.
Answer:
a) [tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
b) For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
c) For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
d) We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
Step-by-step explanation:
For this problem we define the random variable of interest X defined as "the birth weigth of babies" and the distribution for this variable is normal
Part a
The parameters are given:
[tex]\mu = 3500 gr, \sigma = 500g[/tex]
[tex]X \sim N(\mu =3500, \sigma =500)[/tex]
Part b
For this case we want to find this probability:
[tex] P(X< 3110)[/tex]
And in the firt figure attached we see the normal standard distirbution with the parameters given and the green area represent the probability that we want to find.
Part c
For this case the z score is defined as:
[tex] z =\frac{X-\mu}{\sigma}[/tex]
And replacing we got:
[tex] Z= \frac{3100-3500}{500}= -0.8[/tex]
And in the second figure attached we illustrate the probability desired in terms of the z score. With the shaded area representing the probability that z<-0.8
Part d
We can find this probability using the normal standard distribution or excel and we got:
[tex] P(X<3100) =P(Z<-0.8) = 0.212[/tex]
suppose the null hypothesis is rejected. state the conclusion based on the results of the test. six years%E2%80%8B ago, 11.4% of registered births were to teenage mothers. a sociologist believes that the percentage has increased since then. which of the following is the correct%E2%80%8B conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Answer: the correct option is B
Step-by-step explanation:
The question is incorrect. The correct one is:
Suppose the null hypothesis is rejected. State the conclusion based on the results of the test. Six years ago, 11.4% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then. which of the following is the correct conclusion? a. there is sufficient evidence to conclude that the percentage of teenage mothers has increased. b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same. c. there is not sufficient evidence to conclude that the percentage of teenage mothers has increased. d. there is sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Solution:
This is a test of two population proportions. We would set up the hypothesis. The given proportion is 11.4/100 = 0.114
For the null hypothesis,
p = 0.114
For the alternative hypothesis,
p < 0.114
Since the null hypothesis is rejected, it means that there was sufficient evidence to reject it and the alternative hypothesis is accepted. the correct conclusion would be
b. there is not sufficient evidence to conclude that the percentage of teenage mothers has remained the same.
Final answer:
When the null hypothesis is rejected, it indicates there is enough evidence to support the alternative hypothesis. In this case, the result would suggest an increase in the percentage of teenage mothers from six years ago.
Explanation:
If the null hypothesis is rejected, the correct conclusion would be that there is sufficient evidence to support the alternative hypothesis. In this scenario, the sociologist believes that the percentage of teenage mothers has increased since six years ago. Therefore, if we reject the null hypothesis, our conclusion would be option (a) - there is sufficient evidence to conclude that the percentage of teenage mothers has increased.
F(x)=4x-1 and G(x) =x2+7 what is G(F(x)
Answer:
The answer is 16x^2-8x+8
The answer is c
Step-by-step explanation:
If liam ate 4 apples out of a tree of 100 apples how many does he have left?
Answer:
96 apples
Step-by-step explanation:
100-4=96
Answer:
96
Step-by-step explanation:
Bruh just subtract 4 from 100 like seriously XD
A roller coaster travels 80 ft of track from the loading zone before reaching its peak. The horizontal distance between the loading zone and the base of the peak is 50 ft. At what angle, to the nearest degree, is the roller coaster rising?
Answer:
the answer is answer b, or 30.83ft
Step-by-step explanation:
The distance travelled in (m) by a ball dropped from a height are 128/9,32/3,8,6,...
How much distance will it travel before coming to rest
Answer: it will trave 56.89 meters before coming to rest.
Step-by-step explanation:
This is a geometric progression since the distance travelled (height) by the ball is reducing by a constant ratio, r. Since the number of times that the ball will bounce is infinite, then we would apply the formula for determining the sum of the terms in a geometric progression to infinity which is expressed as
S = a/(1 - r)
where
S = sum of the distance travelled by the ball
a = initial distance or height of the ball
r = common ratio
From the information given,
a = 128/9
r = (32/3)/(128/9) = 0.75
Therefore,
S = (128/9)/(1 - 0.75) = 56.89 meters
The distance travelled is an illustration of the sum to infinity of a geometric sequence.
The ball will a travel 56.89 meters before coming to rest
The sequence is given as:
[tex]\mathbf{128/9, 32/3, 8, 6....}[/tex]
From the sequence above, we have:
[tex]\mathbf{a = 128/9}[/tex] --- the first term
[tex]\mathbf{r = 6/8 = 3/4}[/tex] -- the common ratio
The sum to infinity of a geometric progression is:
[tex]\mathbf{S_{\infty} = \frac{a}{1-r}}[/tex]
So, we have:
[tex]\mathbf{S_{\infty} = \frac{128/9}{1-3/4}}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128/9}{1/4}}[/tex]
Divide
[tex]\mathbf{S_{\infty} = \frac{128}{9} \times 4}[/tex]
[tex]\mathbf{S_{\infty} = \frac{128\times 4}{9} }[/tex]
[tex]\mathbf{S_{\infty} = \frac{512}{9} }[/tex]
[tex]\mathbf{S_{\infty} = 56.89}[/tex]
Hence, the ball will a travel 56.89 meters before coming to rest
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Anthony is informed that there is a 10% chance that he will be hired by the prestigious Acme corporation. He believes that, given his outstanding skill as a golfer, once he is hired there is an 80% chance that he will earn a spot on the celebrated Acme Corporation golf team. Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
Answer:
8% probability that Anthony will soon be playing on the Acme golf team
Step-by-step explanation:
We have these following probabilities:
10% probability that he is hired by the corporation.
If he is hired by the corporation, an 80% probability that he will earn a spot on the golf team.
Given this information we can estimate that the likelihood that Anthony will soon be playing on the Acme golf team to be:
80% of 10%
So
P = 0.8*0.1 = 0.08
8% probability that Anthony will soon be playing on the Acme golf team
Find the circumference of circle L. Write your answer as a decimal, rounded to the nearest hundredth.
please show work
find the leght of the arch for one degree by doing
2.25 ÷ 114°
u will get
0.0197368421 ft every 1°
and since a full circumference is equal to 360°, just do this:
0.0197368421 ft × 360° = 7.10526315789 ft
ROUND IT OFFFFFF
u get 7.105 ft
VOILA
Find the length of the arc. Round to the nearest tenth.
Answer:28.8 m
Step-by-step explanation:
length of arc=theta/360 x 2 x π x radius
Length of arc=150/360 x 2 x3.14x11
length of arc=(150x2x3.14x11) ➗ 360
Length of arc =10362 ➗ 360
Length of arc =28.8
The two-way table below describes the practice habits of members of the school band and choir.
Practice Habits of School Musicians
Less than
30 Minutes per Day
38
At Least
30 Minutes per Da
26
12
Band Students
Choir Students
Which statement best describes the relationship between the two variables?
O
O
There is an association because the relative frequencies by row are different.
There is an association because the relative frequencies by row are similar.
There is no association because the relative frequencies by row are different.
There is no association because the relative frequencies by row are similar.
O
Mark this and return
Save and Exit
Next
Answer:
D.
Step-by-step explanation:
i took the quiz
What’s the distance between point A (32,15) and point B (32,29
Answer:
14 units
Step-by-step explanation:
Both points lie on the vertical line x=32, so the distance between them is the difference of their y-coordinates:
29 -15 = 14 . . . . units
The two points are 14 units apart.
Answer:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
Step-by-step explanation:
When we have a two points on a dimensional space A and B we can find the distance between the two points with the following formula:
[tex] d= \sqrt{(x_A -x_B)^2 +(y_A -y_B)^2}[/tex]
Where (x_A,y_A) represent the coordinates for the point A and (x_B,y_B) represent the coordinates for the point B. And we know that the coordinates are :
A= (32,15) and B= (32,29)
And replacing in the formula for the distance we got:
[tex] d = \sqrt{(32-32)^2 +(15-29)^2} = \sqrt{196}= 14[/tex]
So then we can conclude that the smallest distance between the point A (32,15) and the point B(32,39) is 14
A survey was conducted at two colleges. 500 students at College A participated in the study. The results indicated that on average, the students spent 15 hours per week doing online assignments and its standard deviation was 5 hours. At College B, 400 students participated in the study. The average hours they worked for online assignments was 20 with a standard deviation of 4 hours. Please test whether there is a true difference in the time students spent for online assignments between the two colleges (using a confidence level of 99%).
Answer:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
Step-by-step explanation:
Data given
[tex]\bar X_{1}=15[/tex] represent the mean for sample A
[tex]\bar X_{2}=20[/tex] represent the mean for sample B
[tex]s_{1}=5[/tex] represent the sample standard deviation for A
[tex]s_{f}=4[/tex] represent the sample standard deviation for B
[tex]n_{1}=500[/tex] sample size for the group A
[tex]n_{2}=400[/tex] sample size for the group B
[tex]\alpha=0.01[/tex] Significance level provided
t would represent the statistic
System of hypothesis
The system of hypothesis is the true difference in the time students spent for online assignments between the two colleges, the system of hypothesis would be:
Null hypothesis:[tex]\mu_{1}-\mu_{2}=0[/tex]
Alternative hypothesis:[tex]\mu_{1} - \mu_{2}\neq 0[/tex]
Since we don't know the deviations the statistic is given by:
[tex]t=\frac{(\bar X_{1}-\bar X_{2})-\Delta}{\sqrt{\frac{\sigma^2_{1}}{n_{1}}+\frac{\sigma^2_{2}}{n_{2}}}}[/tex] (1)
The degrees of freedom are given by [tex]df=n_1 +n_2 -2=500+400-2=898[/tex]
Replacing the info given we got:
[tex]t=\frac{(15-20)-0}{\sqrt{\frac{5^2}{500}+\frac{4^2}{400}}}}=-16.67[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{898}<-16.67) \approx 0[/tex]
Since the p value is a very low value we have enough evidence to reject the null hypothesis and we can conclude that we have significant difference in the means of time spent for online assignments between the two colleges
g According to a New York Times/CBS News poll conducted during June 24–28, 2011, 55% of the American adults polled said that owning a home is a very important part of the American Dream (The New York Times, June 30, 2011). Suppose this result was true for the population of all American adults in 2011. In a recent poll of 1810 American adults, 62% said that owning a home is a very important part of the American Dream. Perform a hypothesis test to determine whether it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%. Use a 2% significance level, and use both the p-value and the critical-value approaches.
Answer:
Step-by-step explanation:
We would set up the hypothesis test.
a) For the null hypothesis,
P = 0.55
For the alternative hypothesis,
P > 0.55
Considering the population proportion, probability of success, p = 0.55
q = probability of failure = 1 - p
q = 1 - 0.55 = 0.45
Considering the sample,
Probability of success, P = 0.62
Number of samples, n = 1810
We would determine the test statistic which is the z score
z = (P - p)/√pq/n
z = (0.62 - 0.55)/√(0.55 × 0.45)/1810 = 5.98
Since this is a right tailed test, the critical value would be the p value to the right of z = 5.98
p value = 0.00001
Since alpha, 0.02 > than the p value, 0.00001, then we would reject the null hypothesis.
Using the critical value approach, By using the critical region method,
the calculated test statistic is 5.98 for the right tail and - 5.98 for the left tail
Since α = 0.02, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.02/2 = 0.01
The z score for an area to the left of 0.01 is - 2.325
For the right, α/2 = 1 - 0.01 = 0.99
The z score for an area to the right of 0.995 is 2.325
In order to reject the null hypothesis, the test statistic must be smaller than - 2.325 or greater than 2.325
Since - 5.98 < - 2.325 and 5.98 > 2.325, we would reject the null hypothesis.
Therefore, it is reasonable to conclude that the percentage of all American adults who currently hold this opinion is higher than 55%.
14. Find the height of a cylinder if the surface area is 408.41 square inches and the radius is 5
inches.
Final answer:
To find the height of a cylinder with a given surface area and radius, use the formula for the surface area of a cylinder. In this case, the height is approximately 4 inches.
Explanation:
Surface Area of a Cylinder Formula: S = 2πrh + 2πr²
Given: surface area = 408.41 sq in, radius = 5 in
Plug in the values: 408.41 = 2π(5)h + 2π(5)²
Solve for height: h = (408.41 - 50π) / 10π ≈ 4 in
Therefore, the height of the cylinder is approximately 4 inches.
There were 47 ducks swimming in a pond. A dog jumped into the pond and scared 29 of the ducks away. After
the dog got out, 5 groups of 3 ducks returned to the pond.
Answer:
Step-by-step explanation:
Originally, there were 47 ducks. After the dog jumped in, there were 29. This means there were 18 ducks.
47 - 29 = 18
After the dog got out 5 groups of 3 ducks came. This means that 15 ducks came back.
5 × 3 = 15
To find the total amount of ducks, add the ducks together.
18 + 15 = 33
To find the number of ducks remaining in the pond, subtract the 29 ducks scared away from the initial 47, then add the 15 ducks that returned in 5 groups of 3, resulting in 33 ducks now present in the pond.
Explanation:The student has asked a question related to a basic arithmetic problem involving ducks in a pond. Initially, there were 47 ducks in the pond. A dog scares 29 ducks away. After the dog leaves, 5 groups of 3 ducks each return to the pond. To solve this, we perform two main steps:
Subtract the number of ducks that were scared away by the dog: 47 - 29 = 18 ducks remaining.Calculate the total number of ducks returning: 5 groups * 3 ducks/group = 15 ducks returning.Add the ducks that returned to the remaining ducks in the pond: 18 + 15 = 33 ducks are now in the pond after the disturbance and return.
What is the measure of c?
45°
56°
60°
66°
Answer:
56
Step-by-step explanation:
Just took the quiz
Hope this helps!
A flock of broiler chickens has a mean weight gain of 700 g between ages 5 and 9 weeks, and the narrow-sense heritability of weight gain in this flock is 0.80. Selection for increased weight gain is carried out for 5 consecutive generations, and in each generation the average of the parents is 50 g greater than the average of the population from which the parents were chosen.
Assuming that the heritability remains constant at 0.80, what is the expected mean weight gain after the 5 generations of selection?
The expected mean weight gain of the broiler chickens after 5 generations of selection is 900 grams.
Explanation:The expected mean weight gain of the broiler chickens can be calculated using the equation:
Σ = µ + (h^2 * S * t)
where µ is the initial population mean, h^2 is the heritability, S is the selection differential, and t is the number of generations.
From the question:
µ = 700gh^2 = 0.80S = 50gt = 5 generationsSubstituting these values into the equation gives:
Σ = 700g + (0.80 * 50g * 5) = 700g + 200g = 900g
So, the expected mean weight gain after 5 generations of selection is 900 grams.
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After 5 generations of selection with a heritability of 0.80 and a selection differential of 50 g, the expected mean weight gain for the flock is 900 g.
To determine the expected mean weight gain after 5 generations, we use the breeder's equation, which is R = h²S, where R is the response to selection, h² is the narrow-sense heritability, and S is the selection differential.
The narrow-sense heritability h² is given as 0.80 and the selection differential S is 50 g. Therefore, the response to selection for one generation is:⇒ R = h² x S
⇒ 0.80 x 50 g = 40 g
After 5 generations, the total expected gain can be calculated by multiplying the response by the number of generations:⇒ Total gain = R x 5
⇒ 40g/generations x 5 generations = 200 g
Starting with the initial mean weight gain of 700 g, we add the total gain:⇒ Expected mean weight gain after 5 generations = 700 g + 200 g
= 900 g
Thus, the expected mean weight gain after 5 generations of selection is 900 g.
Determine the measures of the unknown angles in the figure.
m∠APD =
m∠CPE =
m∠BPD =
Answer:
Step-by-step explanation:
Lines A B, C D, and D P intersect at point P. Angle A P C is 65 degrees, Angle C P E is blank, angle E P B is 90 degrees, and angle B P D is blank.
Determine the measures of the unknown angles in the figure.
m∠APD =
✔ 115°
m∠CPE =
✔ 25°
m∠BPD =
✔ 65°
The measure of unknown angles
m∠APD = 115
m∠CPE = 25
m∠BPD = 65
What is Linear Pair?When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. They are also referred to as additional angles. Angles that share a vertex are said to be neighbouring. Hence, the linear angles have a common vertex in this instance as well.
Using Linear Pair
<APC + <CPE + <EPB = 180
65 + <CPE + 90 = 180
<CPE = 180 - 155
<CPE = 25
So, <APD = 90 + 25 = 115 degree
<CPE = 25 degree
<BPD = <APC = 65 degree (Vertically opposite angle)
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