Answer:
Step-by-step explanation:
We can use the concept of unit rate to find the constant of proportionality between the number of packets and the number of beads.
For the first case, with 3 packets and 36 beads, the unit rate is 36/3 = 12 beads per packet.
For the second case, with 4 packets and 48 beads, the unit rate is 48/4 = 12 beads per packet.
We can see that the unit rate is the same for both cases, so we can conclude that the relationship between the number of packets and the number of beads is proportional, and the constant of proportionality is 12 beads per packet.
Therefore, the equation that models this relationship is:
b = 12p,
where b is the number of beads and p is the number of packets.
What is the image point of (-2, 5) after a translation left 5 units and up 3 units?
Answer:
(-7, 8)
Step-by-step explanation:
Hope it helps! =D
Each of the 110 students in a statistics class selects a different random sample of 35 quiz scores from a population of 5000 scores. Using their data, each student constructs a 90% confidence interval for μ the average quiz score of the 5000 students. Which of the following conclusions is correct? A) About 10% of the sample means will not be included in the confidence intervals. B) About 90% of the confidence intervals will contain μ C) It is probable that 90% of the confidence intervals will be identical. D) About 10% of the raw scores in the samples will not be found in these confidence intervals.
B) About 90% of the confidence intervals will contain μ
The 90% confidence interval is a range of values that is constructed from a sample of data that has a 90% probability of containing the true population mean, μ. To calculate the 90% confidence interval from a sample, we use the formula:
[tex]CI = X ± z* (σ/√n)[/tex]
Where X is the sample mean, z is the z-score corresponding to a 90% confidence level, σ is the population standard deviation, and n is the sample size.
In this case, 110 students each selected a sample of 35 quiz scores from a population of 5000. So the sample size is n = 35. Assuming the population standard deviation is known, then we can use the formula to calculate the 90% confidence interval for each student. We expect that around 90% of the confidence intervals will contain μ, the true population mean.
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item is regularly priced at $80. Maya bought it on sale for 65% off the regular price. How much did Maya pay?
Answer:
52$
Step-by-step explanation:
Well, because we know our price was originally 80 dollars and maya bought it 65% off, we know that our answer is 65% of 80. 65% can be rewritten as .65, and we can now write our new equation as 80 x .65 = Mayas new price. Using a calculator we can find out that the answer is 52$
suppose f ( t ) represents the particles' combined distance from the wall in feet t seconds after they started moving. define the function f in terms of a and b .
The function f(t) can be represented as f(t) = a + bt, where a and b are constants that depend on the initial position and velocity of the particles.
In this function, a represents the initial distance from the wall when t = 0 and b represents the rate of change of the distance from the wall over time. The value of a and b can be determined from the initial conditions and the velocity of the particles.
The function f(t) is a linear function that models the combined distance of the particles from the wall as a function of time. As t increases, the value of f(t) increases linearly with a slope of b, representing the increase in distance from the wall over time.
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Solve by graphing
x + 3y = 1
-3 - 3y = -15
The solution of the given equation is (-11, 4). the graph is attached below.
What are Systems of equations?Simultaneous equations, a system of equations are Two or more equations in algebra that must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given a system of equation x + 3y = 1 and -3 - 3y = -15
Before solving it with a graph we need to simplify the equation:
From equation 1
=> -3 - 3y = -15
=> -3y = -12
=> y = 4
From substitution in equation 1
x = -11
therefore, The solution of the given equation is (-11, 4).
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Please see picture thanks
Using compound interest, The future value of this investment at the end of year 1 is $16321.6.
Compound interest is defined.Compound interest is the type of interest that is calculated using both the principal and the interest that has accumulated over the preceding period. In contrast to simple interest, compound interest does not factor in the principal when calculating the interest for a subsequent period.
Every six months, or every semi-annually, the compound interest is added up.
Thus,
Rate = 4% / 2 = 2% =0.02
P = $16,000
n = 2
The compound interest is given by:
[tex]A = P (1 + \frac{r}{n})^n[/tex]
[tex]A = 16000(1 + \frac{0.02}{2})^2[/tex]
A = 16321.6
Hence, the future value of this investment at the end of year 1 is $16321.6.
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Evaluate - 3.28 - (-4.4) + (-p) where p = 9.7.
Answer:
-8.58
Step-by-step explanation:
-3.28+4.4-9.7=-8.58
PLEASE HELP 50 points
The situation that could not be represented by the algebraic expression b + 5 is given as follows:
If there are b ounces of water in a bottle, b + 5 could represent the amount of water after you drink 5 bottles.
How to interpret the algebraic expression?The algebraic expression for this problem is defined as follows:
b + 5.
Meaning that an unknown amount b is increased by a value of 5.
For the answer of this problem, the correct expression would be of b - 5 instead of b + 5, hence it is the option that could not be represented by the algebraic expression b + 5.
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Mhanifa Please help
Identify the error in this outline.
error in capitalization
error in indentation
error in parallel structure
error in punctuation
error in division of points
Answer:
Step-by-step explanation:
Error in the division of points is the error in this outline. Thus option (E) is correct. Each heading's first word needs to be capitalized. Any proper nouns contained within each header must be capitalized. period.
What is a division
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.
In order to emphasize related ideas in a sentence, parallelism is the use of comparable words, clauses, phrases, sentence structure, or other grammatical characteristics. It makes the statement succinct, understandable, and simple to read. Particularly in series, pairs, and items in an outline or list, parallel structuring is crucial.
Therefore, Thus option (E) is correct.
write the algorithm for the following tasks. to calculate the sum of 9 and 4.
The algorithm to calculate the sum of 9 and 4. is:
Input 9Add 4 to 9Prnt the result 13How to determine the algorithmFrom the question, we have the following parameters that can be used in our computation:
algorithm to calculate the sum of 9 and 4
This implies that we write the steps to calculate the sum of 9 and 4
So, the steps are
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find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.
The equation of the tangent at (2,7) is y = 4x - 1.y = x^2 + 3; t = 2
Given: y = x^2 + 3 and t = 2
We need to find the equation of the tangent at (2,7).
First, we find the slope of the tangent line by taking the derivative of the function:
y' = 2x
At x = 2, the slope is 2*2 = 4.
Now, we can use the point-slope form of the equation of a line to find the equation of the tangent line:
y - y1 = m(x - x1)
y - 7 = 4(x - 2)
Simplifying:
y = 4x - 1
Therefore, the equation of the tangent at (2,7) is y = 4x - 1.
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RISE AIRLINES- WE RISE TOGETHER!
With the recent crisis in the country's airline industry failing to meet customer needs and
demand, Rise Airlines is re-evaluating its overbooking policy for its most common routes on
their small aircraft. They have hired your team to perform a study of the cost of overbooking
vs flying with empty seats using several types of demand distributions. They have provided
your team with some information about their last 60 days of flites and cancellations as well as
their estimates on demand. On average, a ticket sells for $200 and there are 50 seats on each
aircraft. The fixed cost for running their operations is $100,000 per DAY and their variable
cost of operations is $2,000 per flite, per day. Rise airlines has the current capacity to fly a
mean of 15 flites a day with a standard deviation of 12. The minimum amount of flites they can
fly per day and still maintain their gate space is 13 and the maximum they can fly before they
run out of functional aircraft is 25. Management is requesting a study of their distributions,
the breakeven point, SL and SO. Management would also like recommendations on which
distribution should be used and what other factors they should consider. In order to prepare
this analysis, you and your team have gathered information and will answer the following
questions using excel, graphs, and the case study shell:
A. What is the expression for total cost per month? Assume 30 days in the month
B. What is the expression for total revenue per month? Assume 30 days in a month
C. How many flites need to fly on a daily basis for Rise to breakeven?
D. What percentage of Rise's total flite capability must be in the air that day?
Hint- set these calculations up in excel to help make any graphics easier.
Total cost of Airline per month = 3,900,000$. Total revenue of airline per month = $ 90,000. The break even point= 55.56. Rise in flight to make end meet = 222.24%
What is percentage rise?The growth rate formula is the ratio of the increased value to the original value multiplied by 100, expressed as a percentage. As the value of something increases, the percentage of the value increases.
A. To calculate your total cost per month, you need to find the sum of your fixed and variable costs. The fixed cost is $100,000 per day and the variable cost is $2,000 per flight per day. So the formula for total cost per month is:
$100,000 * 30 + $2,000 * 15 * 30 = $3,000,000 + $900,000 = $3,900,000
B. To calculate your total revenue per month, multiply your average revenue per flight ($200) by the average number of flights per day (15), then multiply by the number of days in a month (30) is needed. So the formula for total sales per month is:
$200 * 15 * 30 = $90,000
C. To calculate your break-even point, you must determine the number of flights required per day so that your total revenue equals your total cost. We can formulate an equation for this:
$200 * x = $100,000 + $2,000 * x
200x = 100,000 + 2,000x
-1,800x = -100,000
x = 55.56 (rounded to two decimal places)
Therefore, the breakeven point is 55.56 flights per day.
D. To find the percentage of Rise's total flight capacity that needs to be in the air each day to break even, divide the number of flights required to reach breakeven into the maximum number of flights you can fly in a day. You need to divide by the number of times (25). . This can be expressed as:
55.56/25 = 2.2224
2.2224 * 100 = 222.24D
44 Therefore, about 222.24% of Rise's total flight capacity needs to be in the air that day to make ends meet.
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exercise 2-20 (static) record transactions, post to t-accounts, and prepare a trial balance (lo2-4, 2-5, 2-6)
For the given transactions, the general journal, T accounts, and trial balance is attached.
In the given case, it is required to record all transactions using the general journal, post them into corresponding T accounts. After posting all transactions, ending balances are calculated. The ending balances are used to create a Trial Balance.
The general journal is a book of original entries where the raw business transactions is recorded according to the date events occur. It is the first place where data is recorded . The general journal for the provided data is attached (figure 1).
Each transaction from the journal to corresponding T-accounts and their ending balances are calculated by subtracting credits from debits for accounts with debit balance and subtracting debits from credits for account with credit balance. A T-account is an informal term which is used for a set of financial records that use double-entry bookkeeping. It is a graphical representation of a general ledger where business’ transactions are recorded. It consists of the an account title at the top, a debit side on the left, and a credit side on the right. It is called a T-account because the bookkeeping entries are laid out in a way that resembles a T-shape. The T-account for the given data is attached (figure 2 and 3).
Trial balance is prepared by entering corresponding ending balances from T accounts and calculating the sums of debit and credit. A trial balance refers to a bookkeeping worksheet where the balances of all ledgers are compiled into debit and credit account column totals that are equal. The general purpose is to ensure that the entries in a company’s bookkeeping system are mathematically correct. The trial balance for the given data is attached (figure 4).
Note: The question is incomplete. The complete question probably is: Boilermaker House Painting Company incurs the following transactions for September. Record each transaction. Boilermaker uses the following accounts: Cash, Accounts Receivable, Supplies, Equipment, Accounts Payable, Deferred Revenue, Common Stock, Retained Earnings, Service Revenue, Salaries Expense, Advertising Expense, and Rent Expense. 2. Post each transaction to T-accounts and compute the ending balance of each account. 3. After calculating the ending balance of each account, prepare a trial balance.
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I need help with this question
The procedure used to show the converse of the Pythagorean Theorem is given as follows:
D. Knowing that 3² + 4² = 5², draw the 3-foot side and the 4-foot side with a right angle between them. The five foot side will fit to form a right triangle.
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
Hence:
h² = 3² + 4²
h² = 25
h = 5.
The hypotenuse has the larger side length, hence the sides that are connected by the right triangle must be the two smaller sides, the three foot side and the four foot side, hence option D is correct.
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y-6≤-3(x+4) in slope intercept form WITH STEPS!!!
The slope intercept form of the inequality is y ≤ -3x - 6.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
Slope intercept form of a linear equation is of the form y = mx + c.
m : slope and c : y intercept
In the case of inequalities, symbol change from equality sign to inequality sign.
Given linear inequality is,
y - 6 ≤ -3(x + 4)
y - 6 ≤ -3x - 12
y ≤ -3x - 12 + 6
y ≤ -3x - 6
Hence the slope intercept form of the inequality is y ≤ -3x - 6.
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Last year, the numbers of skateboards produced per day at a certain factory were normally distributed with a mean of 20,300 skateboards and a standard deviation of 60 skateboards. On what percent of the days last year did the factory produce 20,420 skateboards or fewer? On what percent of the days last year did the factory produce 20,240 skateboards or fewer? On what percent of the days last year did the factory produce 20,480 skateboards or more?
The percentages are given as follows:
20,240 skateboards or fewer: 15.87%.20,420 skateboards or fewer: 97.72%.20,480 skateboards or more: 0.13%.How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.The mean and the standard deviation for this problem are given as follows:
[tex]\mu = 20300, \sigma = 60[/tex]
The proportion of 20,240 of fewer is the p-value of Z when X = 20240, hence:
Z = (20240 - 20300)/60
Z = -1
Z = -1 has a p-value of 0.1587.
The proportion of 20,420 of fewer is the p-value of Z when X = 20420, hence:
Z = (20420 - 20300)/60
Z = 2
Z = 2 has a p-value of 0.9772.
The proportion of 20480 or more is one subtracted by the p-value of Z when X = 20480, hence:
Z = (20480 - 20300)/60
Z = 3
Z = 3 has a p-value of 0.9987.
1 - 0.9987 = 0.0013.
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What is the probability of landing on a 5 when rolling a six-sided number cube?
Answer: 1/6
Step-by-step explanation: there are 6 sides, so we know the answer will be something/6. There is only one 5 on this 6-sided cube which is why the probability of rolling it would be 1/6
(50 POINTS AND BRAINLYEST)
Answer:
Question 1:
Diameter: 10
radius: 5
circumference: 15.70796
Area: 78.53981
Question 2:
98 Gallons of paint
Step-by-step explanation:
Question 1:
Diameter: 10
radius: 5
circumference: 2π x 5
= 15.70796
Area: π x [tex]5^{2}[/tex]
= 78.53981
Question 2:
To find the radius of the sphere: r=(3V4π)⅓
=(3·66844·π)⅓
≈11.68555
To find the surface area of the sphere: A=4πr2
=4·π·11.692
≈1715.96403
Since surface area is 1715.96403 and each gallon of paint can cover 350 square feet the number of gallons of paint needed to paint the water tower is:
1715.96403÷35x2
=98 gallons of paint is needed to paint the entire water tower twice
Answer: x = 666
Step-by-step explanation:
solve for the area while doing pi squared and then solve it with the hypotenuse of the area
Michael has $16 and wants to buy a mixture of cupcakes and fudge to feed at least 4 siblings. Each cupcake costs $4, and each piece of fudge costs $2.
This system of equations models the scenario:
4x + 2y ≤ 16
x + y ≥ 4
Part A: Describe the graph of the system, including shading and the types of lines graphed. Provide a description of the solution set. (4 points)
Part B: Is the point (2, 3) included in the solution area for the system? Justify your answer mathematically. (3 points)
Part C: Choose a different point in the solution set and interpret what it means in terms of the real-world context. (3 points)
Note that the solution of the given inequalities [4x+2y ≤ 16 and x+y>4.] is (4, 0).
What is inequality in Math?Inequalities are mathematical expressions in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), larger than (or greater than or equal to), or not equal to sign.
Part A: The solution of the inequalities is (4, 0)
Part B: In figure attached, we can see that the point (2, 3) included in the solution area for the system.
Therefore, the solution of the given inequalities is (4, 0).
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2 3/8 x 5 3/4
Preform the indicated operation
The solution to the given fraction 2 3/8 x 5 3/4 is 13 21/32
How to solve fractions?A fraction is a number which has a numerator and a denominator. A numerator is the top or upper value while a denominator is the bottom or lower value.
2 3/8 x 5 3/4
= 19/8 × 23/4
Multiply numerator and denominator respectively
= (19 × 23) / (8 × 4)
= 437 / 32
= 13 21/32
Therefore, 13 21/32 is the solution to the fraction.
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The Bureau of Economic Analysis estimates that in 2015, personal consumption expenditures of American totaled $12.3 trillion. The major categories of these expenditures were durable goods ($1.36 trillion: for example, cars, furniture, recreational equipment), nondurable goods ($2.66 trillion: for example, food, clothing, fuel), and services ($8.3 trillion: for example, health care, education, transportation).
a. What was the approximate annual per capita spending on personal consumption? Assume a population of 321 million.
B. What was the approximate daily per capita spending on personal consumption?
c. On average, about what percentage of personal consumption spending was devoted to services? Is this figure consistent with your own spending ?
d. Spending on health care was estimated to be $2.1 trillion. About what percentage of all personal consumption spending was devoted to health care?
e. In 2000, the total spending on personal consumption was $6.8 trillion, while health care spending was $918 billion. Compare the percentage increase in total spending and health care spending between 2000 and 2015.
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
a. The approximate annual per capita spending on personal consumption in 2015 was $38,218. This figure was calculated by dividing the estimated total personal consumption expenditure of $12.3 trillion by the population of 321 million.
b. The approximate daily per capita spending on personal consumption in 2015 was $104.89. This figure was calculated by dividing the approximate annual per capita spending of $38,218 by 365 days.
c. Services accounted for approximately 67.2% of personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on services of $8.3 trillion by the total personal consumption expenditure of $12.3 trillion. This figure is consistent with my own spending, as the majority of my expenditure is devoted to services such as transportation, food delivery, and entertainment.
d. Health care accounted for approximately 17.1% of all personal consumption spending in 2015. This figure was calculated by dividing the estimated total spending on health care of $2.1 trillion by the total personal consumption expenditure of $12.3 trillion.
e. The percentage increase in total spending between 2000 and 2015 was 77.5%, while the percentage increase in health care spending between 2000 and 2015 was 129.9%. This was calculated by first subtracting the total spending on personal consumption in 2000 of $6.8 trillion from the total spending on personal consumption in 2015 of $12.3 trillion, and then dividing the result by the total spending in 2000. This was done for both total spending and health care spending, and the results were then multiplied by 100 to get the percentage increase.
From 2000 to 2015, total spending on personal consumption increased by 77.5%, while health care spending increased by 129.9%.
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graph g has vertex set {v1, v2, v3, v4, v5} and end edge set {e1, e2, e3, e4}, with edge point function as follow:
Graph H is a simple undirected graph, meaning that it has no self-loops or multiple edges between the same pair of vertices. The vertex set is {v1, v2, v3, v4, v5}. The edge set is {e1, e2, e3, e4}.
To draw the graph, we start by placing the vertices on a plane and then connecting them with edges according to the edge-endpoint function.
For example:
Edge e1 connects vertex v1 to itself. This means that v1 has a self-loop.Edges e2 and e3 connect vertices v2 and v3. This means that v2 and v3 are adjacent and there is an edge between them.Edge e4 connects vertices v1 and v3. This means that v1 and v3 are adjacent and there is an edge between them.Note that v4 and v5 are not included in the edge-endpoint function and are not part of the graph.
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Complete Question:
Graph H has a vertex set {v1, v2, v3, v4, v5}, edge set {e1, e2, e3, e4} and edge-endpoint function: Edge Endpoints e1 {v1} e2 {v2, v3} e3 {v2, v3} e4 {v1, v3} Draw the graph.
Find the area and perimeter.
The figure shows a rectangle. The length of the rectangle is given by 9 x units. The width of the rectangle is given by 2 x plus 7 units.
Answer:
Step-by-step explanation:
Perimeter:
2(9x) + 2(2x + 7)
18x + 4x + 14 = 22x + 14
Area:
9x(2x + 7)
18x^2 + 63x
9x(2x + 7)
to draw accurate conclusions about change in an experiment, which of the following is required? a. experimental control b. correlation c. causation d. single case study
Option A and C, To draw accurate conclusions about change in an experiment, both experimental control and causation are required.
Experimental control means that the experiment is designed and conducted in a way that allows for a clear determination of the effect of the independent variable on the dependent variable, by controlling for extraneous variables and minimizing the effects of confounding variables.
Causation means that a relationship exists between the independent variable and the dependent variable, such that a change in the independent variable directly and consistently results in a change in the dependent variable.
Correlation refers to the statistical relationship between two variables, but does not necessarily imply causation. A single case study provides information about a specific individual or situation, but may not be generalizable to a larger population.
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To draw accurate conclusions about change in an experiment, which of the following is required?
a. experimental control
b. correlation
c. causation
d. single case study
CAN SOMEONE HELP WITH THIS QUESTION?✨
The percentage error in the density of metal will be 3.4%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that the density of the metal in the handbook is 4.018 g/mL and the measured value of the density is 4.16 g/mL.
The percentage error will be calculated as:-
Percentage = [ ( 4.16 - 4.018 ) / 4.16 ] x 100
Percentage = 0.034x 100
Percentage = 3.4%
Hence, the percentage error will be 3.4% for the densities.
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What kind of angle is this
This triangle is similar by the rule of (d)SAS.
What is similar shape?When applying a scale factor, similar shapes are enlarged versions of one another. All of the corresponding angles and lengths in related shapes are equal and in the same ratio.
We divide the length of the enlarged shape by the length of the original shape to calculate the length scale factor.
In this given diagram, there are two triangle ΔRST and ΔRUV
where, RS/SU = RT/RV
and ∠SRT = ∠URV
So ΔRST ~ ΔRUV by the rule of SAS
So that option (d) is correct answer.
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if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is .
if the correlation between two variables is close to 1.0, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.
Two variables are said to be causally related in statistics if the occurrence of one variable influences or modifies the other variable. In this case, one variable is the cause and the other is the effect.
We are unable to draw the conclusion that changes in one variable are responsible for changes in the other.An outcome of a study is measured by a response variable. A response variable changes are explained by or affected by an explanatory variable. You will often find explanatory variables called independent variables and response variables called dependent variables.
If their values change so that as the value of one variable increases or decreases so does the value of the other variable (although it may be in the opposite direction).So, we cannot conclude that the explanatory variable causes changes in the response variable when the study is observational.
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6(2d-3) but we don't know what d is
D is zero
Answer:12d-18
Step-by-step explanation:
Find the values of the six trigonometric functions of an angle in standard position if the given point lies on its terminal side
The point being used in the problem is (-1,5)
we need to use the concept of the right triangle formed by the angle and the point in the coordinate plane.
Let's call the angle in standard position θ. The point (-1, 5) lies on the terminal side of θ. We can use the Pythagorean Theorem to find the length of the adjacent side (x) and the opposite side (y) of the right triangle formed by θ and the point.
x = √((-1)^2 + 5^2) = √(1 + 25) = √26
y = 5
The values of the six trigonometric functions of θ can then be found as follows:
sin(θ) = y/r = 5/√26
cos(θ) = x/r = -1/√26
tan(θ) = y/x = 5/(-1) = -5
csc(θ) = 1/sin(θ) = √26/5
sec(θ) = 1/cos(θ) = -√26
cot(θ) = 1/tan(θ) = -1/5
where r is the distance from the origin to the point, which can be found using the distance formula:
r = √((-1)^2 + 5^2) = √26
So the values of the six trigonometric functions of the angle in standard position with a point of (-1, 5) on its terminal side are: sin(θ) = 5/√26, cos(θ) = -1/√26, tan(θ) = -5, csc(θ) = √26/5, sec(θ) = -√26, and cot(θ) = -1/5.
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Determine whether y varies directly with x. If so find the constant of variation k and write the equation.
x y
4 6.4
7. 11.2
10 16
13. 20.8
Please show the steps
In this situation, y varies directly with x since the constant of variation, k, is 1.6 and can be represented by the equation, y = 1.6x.
What is the constant of variation?The constant of variation refers to the ratio or unit rate (slope) between two variables in a direct variation.
In an inverse variation, the constant of variation is the product of the two variables of interest.
In this situation, the constant of variation is the quotient of the division operation between y and x.
x y Ratio
4 6.4 1.6 (6.4/4)
7. 11.2 1.6 (11.2/7)
10 16 1.6 (16/10)
13. 20.8 1.6 (20.8)
Thus, as y increases, x directly increases at a constant rate of 1.6.
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