Answer:
There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
P-value=0.01923.
Step-by-step explanation:
We have to test the hypothesis that the proportion of defective circuits is under 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
We will assume a level of significance of 0.05.
The sample, of size n=1000, has 35 defecteive circuits, so the sample proportion is:
[tex]p=35/1000=0.035[/tex]
The standard error is calculated as if the null hypothesis is true, so it is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1000}}}=\sqrt{0.0000475}=0.007[/tex]
The z-statistic can be calculated as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.035-0.050+0.5/1000}{0.007}=\dfrac{-0.0145}{0.007}= -2.07[/tex]
For this one-tailed test, the P-value is:
[tex]P-value=P(z<-2.07)=0.01923[/tex]
As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected. There is statistical evidence to support the claim that the goal of reducing the rate of undercutting to less than 5% has been met.
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).
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.
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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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!!!
Find the 107th term of the sequence -9, -5, -1, 3, 7
Answer:
4×107 = 428
428-(5×4) =
428-20= 408
how many 1/4 kilograms are there in 15 1/2 kg
Answer:
20
Step-by-step explanation:
as u have to divide the answr and convert it
Answer:
62 is the answer because
15x4=60 + 1/2x4 = 62
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
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.
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).
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:
work out 5 power 8 x 5 to power -2 divide by 5 to power 4
Answer: 25
Step-by-step explanation:
When we slice a three-dimensional object, we expose new faces that are two dimensional. The two-dimensional face is called ______________.
Answer:
Cross section
Step-by-step explanation:
Cross section refers to the new two dimensional face exposed when we slice through a three dimensional objects.
It can also be the surface or shape exposed by making a straight cut through something, especially at right angles to an axis.
Cross section is the plane surface(two-dimensional objects) formed by cutting across a solid shape (three-dimensional shape) especially perpendicular to its longest axis.
Bob is the owner of a home improvement store. He has hired you to check his machine’s calibration prior to starting production on a large order. To check this, you set the machine to create 1.5 inch bolts and manufacture a random sample of 200 bolts. That sample of bolts has an average length of 1.521 inches with a standard deviation of 0.204 inches. Does this sample provide convincing evidence that the machine is working properly or should it be shut down for repairs?
Parameter:
Null hypothesis: μ = 1.5 (the machines work as needed)
Alternative hypothesis: μ ≠ 1.5 (The machines don't work properly)
Since we don't know the population deviation, we will apply a t-test to compare the actual mean to the reference value
Conditions:
Simple random sample: The problem states the sample was chosen at random.
Independence: You can assume there are more than 10(200) = 2000 screws.
Normality: (200 ≥ 30) the sample is large enough for sampling distribution to assume Normality
Calculations:
Since the conditions are met we will carry out a T-test using a calculator for μ≠μ0
μ = population mean = 1.5
σ= standard dev = 0.204
xbar = sampe mean = 1.521
n = sample size= 200
After adding all of this data into the calculator in the T-test program we get a p-value of 0.147
Conclusion:
We will assume a 0.05 sig level for our conclusion.
Since 0.147 > 0.05 we will fail to reject the null hypothesis meaning that we have enough evidence to show that the machines work as needed.
Given the average length and standard deviation of the manufactured bolts, the machine might require recalibration since the lengths produced are slightly larger than desired, and there's a wide spread in lengths. Application of the empirical rule can provide further insight about the need for machine repair. A larger sample size might give a more accurate assessment.
Explanation:Given that the machine is set to manufacture bolts of 1.5 inches and a random sample of 200 bolts showed an average length of 1.521 inches with a standard deviation of 0.204 inches, it seems the machine may not be calibrated correctly. The average length is slightly larger than the desired length, a factor that may be important depending on the tolerances required for these bolts. The standard deviation is also relatively high, implying that there is a wide spread in the lengths of bolts being produced.
One way to determine if the machine needs to be repaired or not is to apply the empirical rule, also known as the 68-95-99.7 rule, which says approximately 68% of data falls within one standard deviation from the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations in a normal distribution. In this case, it means 95% of the bolts should fall between 1.113 inches (1.521 - 2*0.204) and 1.929 inches (1.521 + 2*0.204). If these lengths are acceptable for the operation, the machine can continue working. If not, it might need to be shut down for repair.
Also, it's also worth noting that a larger sample size could provide a more accurate assessment of whether the machine is working correctly or not. While a sample size of 200 is decent, a larger sample size would reduce the margin of error from sample to population.
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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%
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!
if the perimeter of a square is 236 inches, how long is each side?
Answer:
59 inches
Step-by-step explanation:
a square has 4 equal sides
if the sum of all sides(perimeter) is 236 you can do the inverse of that and divide by 4
so your answer should be 59
Answer:
59 inches
Step-by-step explanation:
All of the 4 sides in a square are equal, and the perimeter is all the sides added together.
s+s+s+s=236
4s=236
Divide both sides by 4
s=59
Each side is 59 inches
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°
hree TAs are grading a final exam. There are a total of 60 exams to grade. (a) How many ways are there to distribute the exams among the TAs if all that matters is how many exams go to each TA? (b) Now suppose it matters which students' exams go to which TAs. How many ways are there to distribute the exams? (c) Suppose again that we are counting the ways to distribute exams to TAs and it matters which students' exams go to which TAs. The TAs grade at different rates, so the first TA will grade 25 exams, the second TA will grade 20 exams and the third TA will grade 15 exams. How many ways are there to distribute the exams?
Final answer:
The solutions to the three parts of the question use different combinatorial methods: for part (a), the stars and bars method is used; for part (b), permutations are appropriate; and for part (c), combinations with fixed capacities are needed. Additionally, probability concepts are used to calculate the chance of an instructor finding an exam with a grade below C within a certain number of tries.
Explanation:
The student's question revolves around combinatorics, which is a field of mathematics that deals with counting, both as an art and as a science. Let's break down the responses to parts (a), (b), and (c) of the question provided by the student:
Part (a): We need to determine the number of ways to distribute 60 exams among three TAs regardless of which specific exams they receive. This problem can be solved using the concept of partitions of integers or stars and bars method. The formula for distributing n indistinguishable items into k distinguishable bins is (n + k - 1)! / [n!(k - 1)!]. Here, n=60 exams, and k=3 TAs.
Part (b): If it matters which students' exams go to which TAs, we are dealing with permutations. The total ways to distribute the exams in this case is 60!, because each exam is distinct and can be assigned to each TA.
Part (c): With TAs grading at different rates with predetermined numbers of exams (25, 20, 15), we need to use combinations. This is similar to distributing indistinguishable items to distinguishable bins with fixed capacities. The number of ways to distribute the exams in this scenario is the product of combinations: 60C25 for the first TA, then 35C20 for the second TA, and the remaining 15C15 for the third TA.
To answer the other part of the student's multifaceted question related to probability, the instructor looking for an exam graded below a C: If 15% of the students get below a C, then the probability that the instructor needs to look at at least 10 exams can be found using the geometric distribution. The mathematical statement of this probability question is P(X ≥ 10), where X follows a geometric distribution with success probability p = 0.15.
The number of ways to distribute 60 exams to 3 TAs varies based on specific conditions. If only the count of exams per TA matters, there are 1891 ways. If specific exams matter, there are approximately 4.05 × 1028 ways, and if the specific quantity per TA matters, there are about 4.28 × 1016 ways.
Distribution of Exams Among TAs
Let's break down the problem into three parts:
(a) Distribution Based on Number of Exams Each TA Grades
→ This problem can be approached using the stars and bars combinatorial method. We need to distribute 60 → → indistinguishable exams to 3 TAs.
→ The formula for this is:
C(n + r - 1, r - 1) where n = 60 exams and r = 3 TAs.
C(60 + 3 - 1, 3 - 1) = C(62, 2)
→ Calculating this combination:
C(62, 2) = 62! / (2!(60!))
62! / (2! × 60!) = (62 × 61) / (2 × 1)
= 1891
Thus, there are 1891 ways to distribute the exams such that only the number of exams per TA matters.
(b) Distribution Where Specific Exams Matter
Now, we are interested in which specific exams go to which TA.
→ This is a permutations problem with repetition. Each of the 60 exams can go to any of the 3 TAs.
3⁶⁰
→ Calculating this value:
3⁶⁰ ≈ 4.0528564 × 10²⁸
Therefore, there are approximately 4.05 × 10²⁸ ways to distribute the specific exams to the TAs.
(c) Distribution with Specific Numbers and Specific Exams
Here, we need to distribute the exams where each TA has a predetermined number of exams (25, 20, and 15).
→ This scenario uses the multinomial coefficient:
C(60, 25, 20, 15)
→ This is calculated as:
60! / (25! 20! 15!)
→ Finding the exact value:
60! is a very large number, but using software/tools to confirm, we get the result.
Thus, there are 60! / (25! 20! 15!) ≈ 4.28 × 10¹⁶ ways to distribute the exams under these conditions.
I ready probability concepts quiz
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
The distance a car travels can be found using the formula d=r t where d is distance, r is the rate of speed, and t is time. How many miles does the car travel, if it drives at an average speed of 70 miles per hour for 1/2 of an hour?
Answer:
35 miles
Step-by-step explanation:
70miles per hour x1/2 hour =35distance the car travels
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
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!
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 functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2? Check all that apply. p(x) = 14(x + 7)2 + 1
q(x) = –5(x + 10)2 – 1
s(x) = –(x – 1)2 + 0.5
g(x) = 2x2 + 10x – 35
t(x) = –2x2 – 4x – 3
Answer:q(x)=-5(x+10)2-1
t(x)=-2x2-4x-3
Step-by-step explanation:
The functions that have a maximum and are transformed to the left and down of the parent function, f(x) = x2 include:
q(x) = –5(x + 10)2 – 1t(x) = –2x2 – 4x – 3What is a function?It should be noted that a function simply means a rule the shows the relationship between the variables. The variables are the dependent and the independent variables.
In order to determine whether the function will have a minimum or a maximum depending on the coefficient of the x² term. When the x² coefficient is positive, the function has a minimum and when it is negative, the function has a maximum.
In this case, the above functions have a maximum and are transformed to the left and down of the parent function, f(x) = x2.
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The graph below show Layla’s Pay as a hairdresser. How much does Layla charge per haircut?
A. $5
B. $20
C. $1
D. $10
Answer:
i assume 20 dollars per haircut
Step-by-step explanation:
i do not know what the bottom numbers stand for because there is no label
Answer:
The Answer is B. $20 per haircut.
Step-by-step explanation:
−8x+4y=24 What does X and Y equal?
−7x+7y=28
Answer:(x,y) = (-2,2)
Step-by-step explanation:
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.
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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