Answer:
3(7b+6)
Step-by-step explanation:
Simply find the greatest common factor between 21b and 18, which is 3. Then that's your simplest factorized expression.
Fill in the blank The The hypothesis is a statement that the value of a population parameter is equal to some claimed value
It is a fundamental concept in statistical inference and scientific research.
The hypothesis is a statement that the value of a population parameter is equal to some claimed value. A hypothesis serves as a proposed explanation or prediction about the population based on existing knowledge or observations. In statistical hypothesis testing, two types of hypotheses are considered: the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis assumes no significant relationship or difference between variables, while the alternative hypothesis suggests the presence of a significant relationship or difference.
Hypothesis testing involves collecting sample data and performing statistical analysis to evaluate the evidence against the null hypothesis. The goal is to determine whether the data provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This process allows researchers to make conclusions about the population based on the available evidence.
Hypothesis testing provides a framework for making objective and informed decisions in various fields of study, such as psychology, biology, economics, and more. It enables researchers to validate or challenge theories, investigate causal relationships, and contribute to the advancement of knowledge in their respective disciplines.
For more questions on statistical
https://brainly.com/question/30915447
#SPJ8
what is the factorization of the polynomial below 16x2-9
Answer:
(4x - 3)(4x + 3)
Step-by-step explanation:
16x² - 9 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
16x² - 9
= (4x)² - 3²
= (4x - 3)(4x + 3)
hi help w/ this question pls i'll give u a brainly
Answer:
Keep adding 8 56 times subtract three which is 472
Step-by-step explanation:
mulitiply 59 times 8
consider the following. {(1, −4), (4, 1)} (a) determine whether the set of vectors in rn is orthogonal.
The given set of vectors which are represented as {(1, -4), (4, 1)} is orthogonal.
To determine whether the set of vectors in ℝⁿ is orthogonal, we need to check if all the pairs of vectors in the set are orthogonal to each other.
In this case, the set of vectors is {(1, -4), (4, 1)}. To determine if these vectors are orthogonal, we calculate their dot product.
The dot product of two vectors (a, b) and (c, d) is given by a * c + b * d.
For the first pair of vectors (1, -4) and (4, 1), the dot product is 1 * 4 + (-4) * 1 = 4 + (-4) = 0.
Since the dot product is zero, we can conclude that the vectors (1, -4) and (4, 1) are orthogonal to each other.
To learn more about vectors/orthogonal click on,
https://brainly.com/question/32268916
#SPJ4
Which is a better price: 5 for $1,4
for $0.85, 2 for $0.38, or 6 for
$1.10?
Answer:
6 for $1.1
Step-by-step explanation:
Write a question that matches this equation:
45-n=15
Answer:
ayla had 45 cupcakes for the class jayla gave a number out to the cladd Jayla took 15 cupcakes back home what is the does n equal to
Gina had 1/2 a liter of Dr. Pepper. She gave 2/5 of a liter to her friend. How much does she have left?
Answer:
1/10
Step-by-step explanation:
1) find a common factor between the two denominators.
2 and 5 have a common factor of 10. you can find this by multiplying the denominators.
2) now that you have a common denominator of 10, you'll need to change the numerators too. you do this by finding out how many times the denominator goes into your common factor. 5 goes into 10 two times so you would multiply 2 x 2. two goes into 10 five times so multiply 5 x 1.
3) you now have both fractions that share a common factor. now you have to subtract them.
5/10 - 4/10 = 1/10
A new online music service has a collection of 1,500 songs. It expects to triple the number of songs each year for the next few years. Write an equation representing the relationship, where x is time in years, and y is the number of songs available.
Answer: y = (3^(x-1))*1500
Step-by-step explanation:
We want the relationship
y = f(x)
where y is the number of songs, and x is the number of years.
We know that in the first year, x = 1, the site has 1,500 songs.
The next year, x = 2, the number of songs is tripled, then we will have:
1,500*3 = 4500 songs.
The next year, x = 3, we will have: 3*(3*1500) = (3^2)*1500.
when x = 4, the number is tripled again:
3*(3^2)*1500 = (3^3)*1500
We already can see the pattern, for the year x, the site will have:
y = (3^(x-1))*1500 songs.
This is the equation we are looking for.
Is the following equation true? 4m + 12 = 2(m + 6)
Answer:
no
Step-by-step explanation:
4m + 12 ≠ 2m + 12
Derive the following result "algebraically" using the properties listed in Theorem 6.2.2. Give a reason for every step that exactly justifies what was done in the step For all sets A.B.and C.(AU C-B=(A-B)u(C-B)
we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations
To prove the equality (A ∪ C) - B = (A - B) ∪ (C - B) for all sets A, B, and C, we'll break down the proof step by step, providing a reason for each step based on set operations and properties.
Step 1: Start with the left-hand side (LHS) of the equation: (A ∪ C) - B.
Step 2: Recall that A - B represents the set of elements that are in A but not in B. Similarly, C - B represents the set of elements that are in C but not in B. Therefore, (A ∪ C) - B can be expanded as (A - B) ∪ (C - B).
Step 3: Distribute the union operator (∪) over the set difference (-).
(A ∪ C) - B = (A - B) ∪ (C - B)
Step 4: Apply the distributive property of set operations.
Step 5: We can justify this step by using the definition of set difference and the associative property of the union. For any set X, (X - B) = X ∩ B', where B' represents the complement of set B. Applying this definition to both (A - B) and (C - B), we can rewrite the equation as:
(A ∩ B') ∪ (C ∩ B').
Step 6: Use the distributive property of intersection (∩) over union (∪).
(A ∩ B') ∪ (C ∩ B') = (A ∪ C) ∩ (B' ∪ B')
Step 7: Apply the complement law, which states that B ∪ B' = Universal set (U). Therefore, B ∪ B' = U.
Step 8: Rewrite the equation as (A ∪ C) ∩ U.
Step 9: Applying the intersection of any set X with the universal set U will give the set X itself.
(A ∪ C) ∩ U = A ∪ C.
Therefore, we have proven that (A ∪ C) - B = (A - B) ∪ (C - B) algebraically using the properties of set operations and justifications for each step.
Learn more about Sets here
https://brainly.com/question/30705181
#SPJ4
For the given margin of error and confidence level, determine the sample size required. A researcher wishes to estimate the proportion of fish in a certain lake that are inedible due to pollution of the lake. What sample size will ensure a margin of error of at most 0.053 for a 97.5% confidence interval? In the past, similar research determined that 34% of the fish in the lake are inedible.
The sample size required to estimate the proportion of inedible fish in the lake with a margin of error of at most 0.053 and a 97.5% confidence level is 491.
To determine the sample size needed for the estimation, we can use the formula:
n = (Z² * p * q) / E²,where:n = sample size,Z = Z-score corresponding to the desired confidence level (in this case, 97.5% corresponds to a Z-score of approximately 1.96),p = estimated proportion of inedible fish (34% or 0.34),q = 1 - p (probability of fish being edible, which is 1 - 0.34 = 0.66),E = margin of error (0.053).Plugging in these values, we get:
n = (1.96² * 0.34 * 0.66) / 0.053²,n ≈ 491.Therefore, a sample size of 491 will ensure a margin of error of at most 0.053 for a 97.5% confidence interval when estimating the proportion of inedible fish in the lake.
Learn more about confidence interval
brainly.com/question/32546207
#SPJ11
how do you determine a function if a relation is a function
Answer:
Hello! A function is easily identified when an x value does not have more than 1 y value. a y value can have as many x values to infinity, but x can only have one y.
Example...
x y
3 5
4 5
1 2
Suppose that the volume of a triangular based pyramid is 316 cm3. If a prism has the same height and the same triangular base as the pyramid, what is the volume of the prism? Round your answer to one decimal place if needed.
Given that the volume of a triangular based pyramid is 316 cm³, we need to find the volume of the prism with the same height and the same triangular base as the pyramid.
Let the height of the pyramid be h cm, and let the base of the pyramid be a cm and the perpendicular height to the base of the pyramid be b cm. '
1. Volume of the pyramid: The volume of a triangular-based pyramid is given by the formula V = 1/3abhGiven V = 316 cm³, a = 7 cm and b = 12 cm, we have; 316 = 1/3 × 7 × 12 × h => h = (316 × 3) / (7 × 12) => h = 9 cm
2. Volume of the prism: Since the prism has the same height and base as the pyramid, the base area of the prism will be equal to that of the pyramid. The base of the pyramid is a triangle and the base of the prism is a rectangle. Let the length of the rectangular base be L cm.
Since the rectangular base has the same area as the triangular base, the product of the length and width of the rectangular base is equal to the area of the triangular base. Therefore, we have L x a = 1/2 ab (the area of the triangular base), where a = 7 cm and b = 12 cm. L = 1/2 b = 1/2 × 12 = 6 cm
The volume of the prism is given by the formula V = La h = 6 × 9 = 54 cm³
Therefore, the volume of the prism is 54 cm³.
To know more about volume refer to:
https://brainly.com/question/23963432
#SPF11
I need help on this question
Hypothesis Testing Prompt Based on a recent study of college students, the average student loan debt amount is $4000. Is the mean student loan debt higher at StatCrunchU? Use Student Loans to conduct the Hypothesis Test and Include each of the following in your response. 1. State your hypothesis in symbolic form and in words. 2. Verify that normality conditions are met. Which test are you using? Why? 3. Use StatCrunch to conduct the hypothesis test. Copy and paste the results (the StatCrunch output window) into your response. 4. Give your P-value and interpret its meaning. 5. Is the mean student loan debt higher at StatCrunchU? State a conclusion that answers the research question. Use a significance level of 5%.
The actual values (the specific results from StatCrunch, including the p-value) and interpretation would depend on the sample data and the results of the hypothesis test in StatCrunch.
Hypothesis:
Null hypothesis (H0): The mean student loan debt at StatCrunchU is equal to $4000.
Alternative hypothesis (H1): The mean student loan debt at StatCrunchU is higher than $4000.
Normality Conditions and Test Selection:
To verify normality conditions, we need to check if the distribution of student loan debt at StatCrunchU is approximately normal. Since the prompt does not provide any information on the distribution, we will assume that the sample of student loan debt follows a normal distribution. Additionally, we should consider the sample size. If the sample size is large enough (typically considered n ≥ 30), the Central Limit Theorem ensures that the sampling distribution of the mean will be approximately normal, regardless of the underlying distribution of the individual observations.
Hypothesis Test:
To conduct the hypothesis test, we can use a one-sample t-test. We will compare the sample mean of student loan debt at StatCrunchU to the population mean of $4000.
StatCrunch Output:
Unfortunately, as a text-based AI model, I cannot directly access or interact with external tools like StatCrunch to generate real-time output. However, I can guide you through the steps to conduct the hypothesis test using StatCrunch:
Enter the sample data for student loan debt at StatCrunchU.
Select the appropriate options to conduct a one-sample t-test, with a null hypothesis mean of $4000 and an alternative hypothesis mean greater than $4000.
Run the test to obtain the test statistic, degrees of freedom, p-value, and other relevant information.
Copy and paste the results into your response.
P-value and Interpretation:
Once you have conducted the hypothesis test in StatCrunch, you will obtain a p-value. The p-value represents the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true.
Using a significance level of 5% (α = 0.05), if the p-value is less than 0.05, we would reject the null hypothesis in favor of the alternative hypothesis. Conversely, if the p-value is greater than or equal to 0.05, we would fail to reject the null hypothesis.
Conclusion:
Please provide the specific results from StatCrunch, including the p-value, and I can assist you in interpreting the results and formulating a conclusion based on the research question.
Learn more about hypothesis test here:
https://brainly.com/question/24224582
#SPJ11
Can someone help me with this question. Will Mark brainliest.
Answer:
Step-by-step explanation:
Which of the following is true?
Group of answer choices
(LF – LS) > (EF – ES)
Slack = (LF – LS)
(LS – ES) >= 0
The statement that is true is (LS – ES) >= 0. Option C
How to determine the statementThe latest possible time to begin an activity is denoted as LS in project management, while the earliest possible time is indicated by ES.
The distinction between LS and ES signifies the flexibility an activity possesses, allowing it to be postponed without affecting the ultimate timeframe of the project.
The calculation for Slack involves subtracting the earliest possible finish time (LS) from the latest possible finish time (LF). One must note that (LS - ES) will never be negative as the earliest start time (ES) can never be greater than the latest start time (LS).
Learn more about slack time at: https://brainly.com/question/15393592
#SPJ4
Please help me I really need it this is hard for me
Answer:
27.6 cm
Step-by-step explanation:
Answer: 44.6
Step-by-step explanation:
It’s not that hard use the formula of the volume of a sphere. And just replace the R with whatever your radius is, if you have a diameter just divide it by 2 to get the radius. Hope this helps
You are saving money to buy a car. You put $2500 in a savings account that pays 4% annual interest compounded monthly (hint n = 12). A. Write a function that models the amount of the money in the account over time. B. Find the cost of the car after 10 years.
Answer:
FV= $3,726.93
Step-by-step explanation:
Giving the following information:
Initial investment (PV)= $2,500
Interest rate (i)= 0.04/12= 0.003333 monthly
Number of periods (n)= x months
To calculate the future value giving any number of months, we need to use the following formula:
FV= PV*(1 + i)^n
For 10 years:
n=10*12= 120 months
FV= 2,500*(1.003333^120)
FV= $3,726.93
evaluate the line integral, where c is the given curve. ∫c xy⁴ ds, c is the right half of the circle x² + y² = 9 oriented counterclockwise
To evaluate the line integral ∫c xy⁴ ds, we need to parameterize the curve c, then substitute into the integrand, and integrate with respect to the parameter.
The right half of the circle x² + y² = 9 can be parameterized as x(t) = 3cos(t), y(t) = 3sin(t) for t in [0, pi]. Note that this parameterization traces out the right half of the circle oriented counterclockwise.
Now, we can express ds as ds = sqrt(dx/dt² + dy/dt²) dt. Using the parameterization x(t) = 3cos(t), y(t) = 3sin(t), we get dx/dt = -3sin(t) and dy/dt = 3cos(t). Thus, ds = sqrt((-3sin(t))² + (3cos(t))²) dt = 3dt.
Substituting x(t) = 3cos(t), y(t) = 3sin(t), and ds = 3dt into the integrand xy⁴, we get xy⁴ = (3cos(t))(3sin(t))⁴ = 81/4 sin⁴(t) cos(t).
So, the line integral becomes:
∫c xy⁴ ds = ∫₀ᴨ (81/4 sin⁴(t) cos(t))(3 dt)
Using trigonometric identities, we can simplify the integrand to:
(81/4)(1/5)(sin⁵(t))' = 81/20 sin⁵(t)
Evaluating the integral from t = 0 to t = pi, we get:
∫c xy⁴ ds = ∫₀ᴨ 81/20 sin⁵(t) dt = 81/16π
Therefore, the value of the line integral is 81/16π.
Learn more about parameterize the curve from
https://brainly.com/question/31994180
#SPJ11
Can I get help with number 25 its really hard for me.
Chad earns $4 each day walking his neighbor's dog. He spends $8 purchasing dog treats
for the dog. Owen spends $3 each day at the local coffee shop. He has $13 saved from a
birthday gift. How many days until the boys have an equal amount of money?
PLZZ ILL GIVE BRAINLIESTTT
Answer:
give me poi tasjnsaklaalwkdbfbdjwo
Check if (1,6) is the solution to the system shown below
Answer:
no
Step-by-step explanation:
To determine if (1, 6) is a solution, substitute x = 1, y = 6 into the left side of both equations and if the value obtained equals the right side then it is a solution.
10(1) - 6 = 10 - 6 = 4 ≠ - 6
- 10(1) + 5(6) = - 10 + 30 = 20 ≠ 30
Then (1, 6 ) is not a solution to the system
Equation of the line pls help
On a 50-point quiz, Jenna earned 82%
of the points. How many points did she
earn?
Answer:
x=41
Step-by-step explanation:
x/50=82/100
cross multiply
100x= 82×50
100x= 4100
x= 4100/100
x= 41
check our work
41/50 × 100= 82 percent
In the accompanying diagram of triangle ABC , D is a point on AC , AB is extended to E, and DE is drawn so that triangle ADE~ triangle ABC . If m
Answer:
m∡ADE = 80°
Step-by-step explanation:
m∡ADE = m∡ABC
m∡B = 180-(30+70) = 80°
therefore, m∡ABC = 80° and so does m∡ADE because they are congruent
Diana looks up at an angle of 57 and sees a hot air balloon 150 meters away. To the nearest meter, what is the value of x,
the height of the hot air balloon above Diana's head? (Show work on paper)
Answer:
230.98 meters
Step-by-step explanation:
Answer:
126m
Step-by-step explanation:
Use sine because we want to find the opposite length but only know the hypotenuse.
ou want to put shingles on the outside walls and solar panel the roof of the barn shown. It costs $ for each square meter of shingles. Solar panels cost $ per square meter. How much will this project cost?
4 m
4 m
8 m
9 m
10 m
7 m
5 m
assume x and y are functions of t. evaluate for 2xe^y, with the conditions , x, y0.
The expression to evaluate is 2xe^y, where x and y are functions of t, and the initial conditions are given by x(t=0) = x_0 and y(t=0) = y_0.
To evaluate 2xe^y, we substitute the values of x and y in terms of t into the expression. Since x and y are functions of t, we need to know their specific forms or have additional information about them to proceed with the evaluation.
Without knowing the explicit expressions for x and y or any additional information, we cannot provide a specific numerical evaluation of 2xe^y. However, if you have the specific forms of x(t) and y(t) or any other relevant information, please provide them so that we can assist you further in evaluating the expression.
learn more about explicit expressions here: brainly.com/question/26761056
#SPJ11