Answer:
(a)25 Milligrams
(b)15%
(c)[tex]A(10) = 25(0.85)^{10}[/tex]
Step-by-step explanation:
The amount in milligrams of a drug in the body t hours after taking a pill is given by the model:
[tex]A(t) = 25(0.85)^t[/tex]
(a)Comparing this with the exponential decay model, [tex]A(t)=A_0(\frac{1}{2})^{\frac{t}{t_{1/2}} }[/tex], the initial dose given is 25 milligrams.
(b)From the model,
[tex]A(t) = 25(0.85)^t\\A(t) = 25(1-0.15)^t[/tex]
We can also use this method:
[tex]r = a - 1 = 0.85 - 1 = -0.15=-15\%[/tex]
We can see that for every hour, 15% of the drug leaves the body.
(c)After 10 hours
When t=10
[tex]A(10) = 25(0.85)^{10}[/tex]
The amount of drug left after 10 hours is given above in function notation.
a. The initial dose given is 25 milligrams. b. 85(0.85)^t percent of the drug leaves the body each hour. c. The amount of drug left after 10 hours is 0.2147 milligrams.
Explanation:a. The initial dose given can be found by substituting t = 0 into the function A(t) = 25(0.85)^t. This gives A(0) = 25(0.85)^0 = 25(1) = 25 milligrams.
b. To find the percent of the drug that leaves the body each hour, we need to find the rate of change of A(t) with respect to time. Taking the derivative of A(t) gives dA/dt = 25(0.85)^t * ln(0.85) = 21.25(0.85)^t. This represents the rate of change of A(t) with respect to time. To find the percent, we can divide this rate by the initial dose and multiply by 100: (21.25(0.85)^t / 25) * 100 = 85(0.85)^t percent.
c. To find the amount of drug left after 10 hours, we substitute t = 10 into the function A(t) = 25(0.85)^t: A(10) = 25(0.85)^10 = 25(0.0859) = 0.2147 milligrams.
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find a coterminal angle to 20 degrees answer choices r 320 760 690 and 740
Answer:
740°
Step-by-step explanation:
2 *360° + 20° = 720° + 20° = 740°
PLEASE HURRY!!! Dwight has 3 baseball cards, and Ellis has 9 baseball cards. If Dwight and Ellis put their baseball cards together and then divide them up equally, how many will each one of them have?
3
6
9
12
Answer:
6
Step-by-step explanation:
3+9=12,
So since there are 2 people,
12 divided by 2 is 6.
Your answer would be 6.
9+3=12
12÷2=6
Dwight and Ellis both have 6 cards equally.
Hope this helps!!!
4. The diagonal of a rectangle is 13cm. The breadth is 5cm. Find it's length. *
Answer:
The length of the rectangle is
12
c
m
and the area of the rectangle is
60
c
m
2
.
Explanation:
By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.
Recall that the Pythagorean Theorem states that the sun of the squares of the legs of a right triangle is equal to the square of the hypotenuse.
a
2
+
b
2
=
c
2
5
2
+
b
2
=
13
2
25
+
b
2
=
169
25
−
25
+
b
2
=
169
−
25
b
2
=
144
√
b
2
=
√
144
b
=
±
12
Since the length of the side is a measured distance, the negative root is not a reasonable result. So the length of the rectangle is
12
cm.
The area of a rectangle is given by multiplying the width by the length.
A
=
(
5
c
m
)
(
12
c
m
)
A
=
60
c
m
2
Answer:
[tex] {5}^{2} + {x}^{2} = {13}^{2} \\ 25 + {x}^{2} = 169 \\ {x}^{2} = 169 - 25 \\ {x}^{2} = 144 \\ x = \sqrt{144} \\ x = 12cm[/tex]
Step-by-step explanation:
use the Pythagorean theorem
hope this helps you
What is the area of a rectangle with the numbers as 6 and 14
Answer:
I believe its 84
Step-by-step explanation:
6 multiplied by 14
A consumer organization estimates that over a 1-year period 17% of cars will need to be repaired once, 10% will need repairs twice, and 2% will require three or more repairs. If you own two cars, what is the probability that a) neither will need repair? b) both will need repair? c) at least one car will need repair?
Answer:
a) 50.41% probability that neither will need repair.
b) 8.41% probability that both will need repair.
c) 49.59% probability that at least one car will need repair.
Step-by-step explanation:
For each car, there are only two possible outcomes. Either it will need repairs, or it will not need repairs. The probability of a car needing repairs is independent of other cars. So we use the binomial probability distribution to solve this question.
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.
17% of cars will need to be repaired once, 10% will need repairs twice, and 2% will require three or more repairs.
This means that [tex]p = 0.17+0.1+0.02 = 0.29[/tex]
Two cars:
This means that [tex]n = 2[/tex]
a) neither will need repair?
This is P(X = 0).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{2,0}.(0.29)^{0}.(0.71)^{2} = 0.5041[/tex]
50.41% probability that neither will need repair.
b) both will need repair?
This is P(X = 2).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{2,2}.(0.29)^{2}.(0.71)^{0} = 0.0841[/tex]
8.41% probability that both will need repair.
c) at least one car will need repair?
Either none will need repair, or at least one will. The sum of these probabilities is 100%.
From a)
50.41% probability that neither will need repair.
p = 100 - 50.41 = 49.59%
49.59% probability that at least one car will need repair.
what is the h?
h/6 = 20/24
Answer:
h = 5
Step-by-step explanation:
[tex] \frac{h}{6} = \frac{20}{24} \\ 24 \times h = 20 \times 6 \\ 24h = 120 \\ h = \frac{120}{24} \\ h = 5[/tex]
Total
Last July, 160 babies were born in a hospital in Maine;
Š of the babies were girls. Seventy babies weighed 8
pounds or more. Fifty boys weighed 8 pounds or more.
b
REFERATER
O a = 64, b = 14, c = 76, d = 20, e = 90
o a = 14, b = 64, c = 90 d = 20, e = 76
14, b = 76, c = 64, d = 90, e = 20
a = 14, b = 64, c = 76, d = 20, e = 90
11
Answer:
D
Step-by-step explanation:
If you work backwards and add everything up it works.
Answer:
D
Step-by-step explanation:
principal: $1000, annual interest rate: 4.8%, time: 2 yr
The question involves calculating compound interest using a given principal, interest rate, and time period. The calculation is performed using the compound interest formula, which takes into account the principal amount of $1000, an annual interest rate of 4.8%, and a time span of 2 years.
Explanation:The question pertains to calculating compound interest over a certain period using a principal amount, an annual interest rate, and a given time frame. Given a principal of $1000, an annual interest rate of 4.8%, and a time period of 2 years, we can find the amount of interest accrued using the formula:
Interest = Principal imes rate imes time
Compound Interest = Principal imes (1 + interest rate)time
In this case, the formula would be:
Compound Interest = $1000 imes (1 + 0.048)2
Performing this calculation would give us the total amount after 2 years, including both the principal and the interest earned.
An online vendor requires that customers select a password that is a sequence of upper-case letters, lower-case letters and digits. A valid password must be at least 10 characters long, and it must contain at least one character from each of the three sets of characters. What is the probability that a randomly selected string with exactly ten characters results in a valid password? The alphabet for the strings in the sample space from which the string is drawn is the union of the three sets of characters.
Answer:
What is the probability that a randomly selected string with exactly ten characters results in a valid password? = 0.02836
Step-by-step explanation:
CHECK THE ATTACHMENT BELOOW
Final answer:
The probability of a randomly selected string with exactly ten characters resulting in a valid password can be determined using combinatorics. The probability is given by (62! / (52!*10!)) / (62^10)
Explanation:
To find the probability of a randomly selected string with exactly ten characters resulting in a valid password, we need to determine how many valid passwords exist out of all possible strings of length ten. Since the password must contain at least one character from each of the three sets (upper-case letters, lower-case letters, and digits), we can calculate the probability using combinatorics.
There are 26 upper-case letters, 26 lower-case letters, and 10 digits, so the total number of characters in the union of the three sets is 26 + 26 + 10 = 62.
The probability of selecting a valid password is then:
P(valid password) = (Number of valid passwords) / (Total number of passwords)
For a valid password, the first character can be any of the 62 characters, the second character can be any of the remaining 61 characters, and so on. Therefore, the number of valid passwords is: 62 * 61 * 60 * ... * 53.
Since there are 10 characters in a valid password, the number of valid passwords is:
62 * 61 * 60 * ... * 53 = 62! / (52!*10!).
The total number of passwords of length 10 is: 62^10.
Therefore, the probability of a randomly selected string with exactly ten characters resulting in a valid password is:
P(valid password) = (62! / (52!*10!)) / (62^10).
Un padre paga la mesada a sus tres hijas de forma que a cada una le corresponde una cantidad
proporcional a su edad. A la mayor, que tiene 20 años, le da 5.000 pesos. ¿Cuánto dará a las otras
dos hijas de 15 años y 8 años de edad?
las otras dos hijas obtendrán 3750 pesos y 2000 pesos.
¿Qué es razón y proporción?Cuando dos números son divisibles se pueden escribir en la forma p:q, cuando dos razones son iguales se dice que son proporcionales.
El padre da dinero a las hijas en la proporción de su edad.
La hija mayor, que tiene 20 años, da 5.000 pesos.
La relación es 5000: 20 = 250:1
la edad de las otras hijas es 15 y 8
Que la hija de 15 años se lleve x pesos
y la hija de 8 años recibe y pesos
por lo que se forma la relación x: 15 y x: 8 que es igual a 250: 1
Comparando las dos proporciones
x/15 = 250/1
X = 15*250
x = 3750 pesos
x/8 = 250/1
x = 2000 pesos
Por lo tanto, las otras dos hijas obtendrán 3750 pesos y 2000 pesos.
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Application of the least squares method results in values of the y intercept and the slope that minimizes the sum of the squared deviations between the
a. observed values of the independent variable and the estimated values of the independent variable
b. actual values of the independent variable and estimated values of the dependent variable
c. observed values of the dependent variable and the estimated values of the dependent variable
d. None of these answers is correct.
Answer:
Копиравать
Step-by-step explanation:
Копиравать ладно
The National Collegiate Athletic Association (NCAA) measures the Graduation Success Rate (GSR), which is the percentage of eligible athletes who graduate within six years of entering college. According to the NCAA, the GSR for all scholarship athletes in a particular division is 57%. The GSR for all students in this division is 62%. Suppose the NCAA report was based on a sample of 500 student-athletes, of which 285 graduated within six years. Is this sufficient information to conclude that the GSR for all scholarship athletes in this division differs from 62%? Carry out the test using a Type I error rate of 0.05.
Answer:
Yes. There is enough evidence to support the claim that the GSR for all scholarship athletes in this division differs from 62%.
Step-by-step explanation:
We have to perform a hypothesis test on a proportion.
The claim is that the GSR for all scholarship athletes in this division differs from 62%. Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.62\\\\H_a:\pi<0.62[/tex]
The significance level, named here as Type I error rate, is 0.05.
The sample size is n=500.
The sample proportion is:
[tex]p=X/n=285/500=0.57[/tex]
The standard deviation of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.62(1-0.62)}{500}}=\sqrt{0.0004712}=0.022[/tex]
The z-statistic is then:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.57-0.62+0.5/500}{0.022}=\dfrac{-0.049}{0.022} = -2.227[/tex]
The P-value for this left tailed test is:
[tex]P-value=P(z<-2.227)=0.013[/tex]
The P-value is smaller than the significance level, so the effect is significant. The null hypothesis is rejected.
There is enough evidence to support the claim that the GSR for all scholarship athletes in this division differs from 62%.
Answer:
[tex]z=\frac{0.57 -0.62}{\sqrt{\frac{0.62(1-0.62)}{500}}}=-2.303[/tex]
[tex]p_v =2*P(z<-2.303)=0.0213[/tex]
So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of student athletes who graduate within 6 years is significantly different from 0.62 or 62%
Step-by-step explanation:
Data given and notation
n=500 represent the random sample taken
X=285 represent the student athletes who graduate within 6 years
[tex]\hat p=\frac{285}{500}=0.57[/tex] estimated proportion of student athletes who graduate within 6 years
[tex]p_o=0.62[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that true proportion differs from 0.62.:
Null hypothesis:[tex]p=0.62[/tex]
Alternative hypothesis:[tex]p \neq 0.62[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.57 -0.62}{\sqrt{\frac{0.62(1-0.62)}{500}}}=-2.303[/tex]
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-2.303)=0.0213[/tex]
So the p value obtained was a very low value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of student athletes who graduate within 6 years is significantly different from 0.62 or 62%
Brawdy Plastics, Inc., produces plastic seat belt retainers for General Motors at the Brawdy Plastics plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds.
The following data were collected. If required, enter negative values as negative numbers.
Line Speed Devective number
20 23
20 21
30 19
30 16
40 15
40 17
50 14
50 11
a. Select a scatter diagram with the line speed as the independent variable.b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
Scatter plot shows negative correlation; regression equation: Defective Parts = [tex]27.5 - 0.3 \times \text{Line Speed}[/tex]; 20 defects predicted at 25 fpm.
a. The scatter diagram with the line speed as the independent variable is displayed. It shows the number of defective parts found at various line speeds.
(DIAGRAM IS GIVEN BELOW)
b. The scatter diagram indicates that there is a negative relationship between the two variables. As the line speed increases, the number of defective parts found decreases. This suggests that at higher speeds, perhaps the inspectors are not able to identify all the defective parts due to the speed at which the parts are moving past the inspection station.
c. Using the least squares method to develop the estimated regression equation with line speed as the independent variable (to 1 decimal), we get:
Defective Parts = [tex]27.5 - 0.3 \times \text{Line Speed}[/tex]
where 27.5 is the y-intercept and -0.3 is the slope of the line.
d. To predict the number of defective parts found for a line speed of 25 feet per minute, we can substitute x = 25 into the regression equation:
Defective Parts = [tex]27.5 - 0.3 \times 25 = 20.0[/tex]
Therefore, the model predicts that for a line speed of 25 feet per minute, there would be 20 defective parts found.
The complete question is here:
Brawdy Plastics, Inc. produces plastic seat belt retainers for General Motors at their plant in Buffalo, New York. After final assembly and painting, the parts are placed on a conveyor belt that moves the parts past a final inspection station. How fast the parts move past the final inspection station depends upon the line speed of the conveyor belt (feet per minute). Although faster line speeds are desirable, management is concerned that increasing the line speed too much may not provide enough time for inspectors to identify which parts are actually defective. To test this theory, Brawdy Plastics conducted an experiment in which the same batch of parts, with a known number of defective parts, was inspected using a variety of line speeds. The following data were collected. If required, enter negative values as negative numbers.
(DATA IS GIVEN BELOW)
a. Select a scatter diagram with the line speed as the independent variable.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Use the least squares method to develop the estimated regression equation (to 1 decimal). = + x d. Predict the number of defective parts found for a line speed of 25 feet per minute.
Please help me answer thanks.
Answer:
see explanation
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, thus
160 = k × 4³ = 64k ( divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of variation
(a)
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
(b)
When M = 540, then
540 = 2.5r³ ( divide both sides by 2.5 )_
216 = r³ ( take the cube root of both sides )
r = [tex]\sqrt[3]{216}[/tex] = 6
The task involves summarizing previous answers and reflecting upon them using a paragraph planner to organize and provide clarity to the response. This process aids in addressing the questions effectively and personally.
Explanation:To approach the task at hand, one must begin by summarizing the answers provided previously. It is essential to distill the content into a coherent summary that accurately represents the experiences and advice shared. Upon doing so, reflection on these insights will lead to a personal understanding that is both informed and enriched by the various perspectives.
An effective strategy for this analysis is to use a paragraph planner. This tool assists in organizing thoughts and structuring the response in a logical and clear manner. By leveraging such a planner, the responses to the posed questions will not only address the directly asked matters but also encapsulate a broader interpretation of the information received.
Tonight's endeavor is to answer critical questions that resonate with the audience's collective curiosity. This act of addressing inquiries serves as a bridge between the speaker and the listener, fostering a shared understanding and grounding the conversation in mutual interests and concerns.
A study is conducted to determine whether sunshine affects depression. Eight individuals are given a questionnaire measuring depression immediately following a run of 10 consecutive days when the sun shone for over 80% of the daylight hours. The same individuals have their depression measured immediately following 10 consecutive days without any sunshine. The following data are collected. The higher the score the greater the depression.
Individuals 1 2 3 4 5 6 7 8
Sunshine 10 12 14 11 12 10 14 15
No Sunshine 20 21 17 14 18 8 18 14
Using the Wilcoxon signed ranks test to evaluate the data, with a = 0.052 tail, Tcrit =
a.- 3
c.33
b.3
d.4
Based on the information given, it should be noted that the Wilcoxon signed rank test will be 3.
From the table, it can be seen that the first tank is assigned to the first absolute value. The second rank is assigned to the second absolute value while the average of the third and the fourth value are given the value of 3.
The sum of the positive ranks will be:
= 1 + 2 = 3
The sum of the negative ranks will be:
= 8 + 7 + 3.5 + 3.5 + 6 + 5 = 33.
Therefore, the Wilcoxon signed-rank will be the minimum of 33 and 3 which is 3.
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The smallest angle of a right triangle is 20-degree angle. What is the measure of the medium angle?
Answer:
70 degrees.
Step-by-step explanation:
Hello!
It says that this triangle is a right triangle. That means one angle is 90°. Since there are 180° in a triangle, all we have to do is subtract 90 + 20 from 180.
90 + 20 = 110
180 - 110 = 70.
So the medium angle is 70°.
Hope this helps!
Find the perimeter of the figure to the nearest hundredth.
Please consider helping!
Any help is appreciated!
Hello!
Your answer should be 26.85.
We can use the formula of pi d or 2 pi r for the circumference.
You would get 5 pi.
But since its not a full circle you would divide it in half and get 2.5 pi.
2.5 pi is equal to 7.85.
Now we can use the equation 7.85 + 7 + 7 + 5
That would equal our answer... 26.85!
Hope this helps!
Clark and Phil are each running to raise money. The amount of money (y), in dollars, they each raise is based on the distance (x), in miles, they each run. Clark has an initial donation that he has received regardless of how many miles he runs. The graphs model the amount of money each will raise based on the distance they each run. What is the unit rate for the person for whom the amount of money and the number of miles are proportionally related? A) $5.00 per mile B) $7.50 per mile C) $15.00 per mile D) $30.00 per mile
Answer:
Your answer is B
Step-by-step explanation:
i just did the test
Answer:$7.50
Step-by-step explanation:
Assume that 0 < x < pi/2 and 0 < y < pi/2. Find the exact value of cos(x-y) if cos(x)=3/5 and cos(y)=4/5
a. 25/24
b. -25/24
c. 24/25
d. -24/25
Answer: The answer is C
I ready probability concepts quiz
work out 5 power 8 x 5 to power -2 divide by 5 to power 4
Answer: 25
Step-by-step explanation:
2.06. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor. Is there a significant difference between the proportions of urban and suburban residents who favor the construction of the nuclear plant at 5% significance level
Answer:
[tex]z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795[/tex]
[tex]p_v =2*P(Z>2.795)= 0.005[/tex]
So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.
Step-by-step explanation:
Data given and notation
[tex]X_{1}=74[/tex] represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
[tex]X_{2}=70[/tex] represent the number of people suburban residents are in favor
[tex]n_{1}=100[/tex] sample 1 selected
[tex]n_{2}=125[/tex] sample 2 selected
[tex]p_{1}=\frac{74}{100}=0.74[/tex] represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant
[tex]p_{2}=\frac{70}{125}=0.56[/tex] represent the proportion of suburban residents are in favor
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the value for the test (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to check if the proportions are different, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} = p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]
We need to apply a z test to compare proportions, and the statistic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{74+70}{100+125}=0.64[/tex]
Calculate the statistic
Replacing in formula (1) the values obtained we got this:
[tex]z=\frac{0.74-0.56}{\sqrt{0.64(1-0.64)(\frac{1}{100}+\frac{1}{125})}}=2.795[/tex]
Statistical decision
The significance level provided is [tex]\alpha=0.05[/tex] ,and we can calculate the p value for this test.
Since is a two tailed test the p value would be:
[tex]p_v =2*P(Z>2.795)= 0.005[/tex]
So if we compare the p value and using any significance level for example [tex]\alpha=0.05[/tex] we see that [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and we can conclude that the proportions are different at 5% of significance.
Weights of Elephants A sample of 7 adult elephants had an average weight of 11,647 pounds. The standard deviation for the sample was 24 pounds. Find the 95 % confidence interval of the population mean for the weights of adult elephants. Assume the variable is normally distributed. Round intermediate answers to at least three decimal places. Round your final answers to the nearest whole number.
The 95% confidence interval for the population mean weight of adult elephants is approximately (11628, 11666) pounds.
Explanation:To find the 95% confidence interval of the population mean for the weights of adult elephants, we can use the formula:
CI = x ± Z * (σ/√n)
where CI is the confidence interval, x is the sample mean, Z is the z-score corresponding to the desired confidence level (in this case, 95%), σ is the population standard deviation, and n is the sample size.
Using the given values, x = 11,647 lb, σ = 24 lb, and n = 7, we can calculate the confidence interval:
CI = 11647 ± 1.96 * (24/√7)
CI ≈ 11647 ± 19.12
Therefore, the 95% confidence interval for the population mean weight of adult elephants is approximately (11628, 11666) pounds.
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A round ball has a diameter of 10 inches. What is the approximate volume of the ball?
Answer:
523.333333333
Step-by-step explanation:
Using the formula 4/3πr³:
(4/3)(3.14)(5^3)
Hope this helps :)
Solve the equation
1
4
(4x − 24) + x = 14.
Distribute the
1
4
to the quantity to get:
Combine the like terms to get:
Add 6 to both sides to get:
x =
Answer:
Distribute the
1
4
to the quantity to get:
✔ x – 6 + x = 14
Combine the like terms to get:
✔ 2x – 6 = 14
Add 6 to both sides to get:
✔ 2x = 20
x =
✔ 10
Step-by-step explanation:
i got is right so i hope it helps :)
The required solution is [tex]x=10[/tex].
Important equation:
The given equation is [tex]\dfrac{1}{4}(4x-24)+x=14[/tex].We need to find the value of [tex]x[/tex].
Linear equation:The given linear equation can be written as:
[tex]\dfrac{1}{4}(4x)-\dfrac{1}{4}(24)+x=14[/tex]
[tex]x-6+x=14[/tex]
[tex]2x=14+6[/tex]
[tex]2x=20[/tex]
Divide both sides by 2.
[tex]x=\dfrac{20}{2}[/tex]
[tex]x=10[/tex]
Thus, the required solution is [tex]x=10[/tex].
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In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether the proportions have changed, a random sample of 300 students from ABC University was selected. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. Refer to Exhibit 12-4. If the proportions are the same as they were in the past, the expected frequency for the Business College is
Answer: The expected frequency for the Business college is 31.5.
Step-by-step explanation:
Since we have given that
Number of students from ABC university = 300
Number of students from Liberal Arts college = 120
Number of students in Education college = 90
Number of students in Business college = 90
Probability of students in Business college = 35% = 0.35
Probability of students in Liberal arts college = 0.35
Probability of students in Education college = 0.30
So, Expected frequency for the Business College is given by
[tex]0.35\times 90=31.5[/tex]
Hence, the expected frequency for the Business college is 31.5.
−8x+4y=24 What does X and Y equal?
−7x+7y=28
Answer:(x,y) = (-2,2)
Step-by-step explanation:
Does the function model exponential growth or decay?
$(t) = 5. (3/7)*
Answer:
decay
Step-by-step explanation:
Answer:
khan
Step-by-step explanation:
Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size?
a. A small mean difference and small sample variances
b. A large mean difference and small sample variances
c. A small mean difference and large sample variances
d. A large mean difference and large sample variances
Answer:
Correct option: (b).
Step-by-step explanation:
Effect size (η) is a statistical measure that determines the strength of the association (numerically) between two variables. For example, if we have data on the weight of male and female candidates and we realize that, on average, males are heavier than females, the difference between the weight of male and the weight of female candidates is known as the effect size.
The larger the effect size, the larger the weight difference between male and female will be.
Statistic effect size helps us in analyzing if the difference is factual or if it is affected by a change of factors.
In hypothesis testing, effect size, power, sample size, and critical significance level are related to each other.
The effect size formula for a hypothesis test of mean difference is:
[tex]\eta =\frac{\bar x_{1}-\bar x_{2}}{\sqrt{s^{2}}}[/tex]
The denominator s² is combined sample variance.
[tex]s^{2}=\frac{n_{1}s_{1}^{2}+n_{2}s_{2}^{2}}{n_{1}+n_{2}-2}[/tex]
The effect size is affected by two components:
Sample mean differenceSample variance.As the sample mean difference is directly proportional to the effect size, on increasing the sample mean difference value the effect size will also increase.
Ans the sample variance is inversely proportional to the the effect size, on decreasing the sample variance value the effect size will increase and vice-versa.
Thus, the correct option is (b).
The manager of the toy store at the mall is curious about why nobody is buying the new robot toys. He's very annoyed because he paid a lot of money for inventory, and wants to know how to get the merchandise sold. What is the best method of sampling for him to get his answers?
A.
use a convenience sample of customers in other toy stores
B.
survey customers as they leave the store
C.
survey the toy store employees
D.
random sampling of people walking in the mall
Answer: B
Step-by-step explanation: I believe it's B because if you're able to get the opinions of others about your store. You'll be able to see whats the customers are more interested in, so therefore be able to supply your store with stuff people are more intrigued in. (Let me know if I'm wrong, have a good day)