Answer:
2n^3
Step-by-step explanation:
twice a number cubed
n=number
512^2/3
Evaluate and explain how pls
Answer:
64
Step-by-step explanation:
Use \((x^a)^b=x^{ab}\)
So \(512^{\frac{2}{3}}=(512^\frac{1}{3})^2 =8^2=64\)
PLEASE HELP!! URGANT!
Answer:
80
Step-by-step explanation:
HIG+GIJ=HIJ
x=6
12(6)+8=80
What must be done to categorical variables in order to use them in a regression analysis?
Choose one answer.
a. categorical coding
b. nothing
c. problem coding
d. dummy coding
d. Dummy coding. Categorical variables need to be converted into numerical variables to be used in regression analysis. Dummy coding involves creating binary variables for each category of the categorical variable.
For example, if the categorical variable is "color" with categories "red," "green," and "blue," dummy coding would involve creating three binary variables: "red" (0 or 1), "green" (0 or 1), and "blue" (0 or 1). These binary variables can then be used in the regression analysis. In conclusion, to use categorical variables in regression analysis, dummy coding is necessary.
In order to use categorical variables in a regression analysis, they must be converted into numerical values. This process is called dummy coding (also known as one-hot encoding). Dummy coding involves creating new binary variables (0 or 1) for each category of the categorical variable. This allows the regression model to incorporate the categorical data while maintaining its numerical nature.
To use categorical variables in a regression analysis, you must apply dummy coding to convert them into numerical values.
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helpppppppppppppppppppppppppp
The answer is: 8m=152
Stephanie needs to buy birthday gifts for her family. She wants to stick to a budget of . $150.She buys a board game for her brother that costs,$49.50 a book for her sister that costs,$19.99 and a toy for her dog that costs.$15.00 She needs to buy a gift for her spouse, but she cannot decide between a watch that costs.$75.00 and a pair of shoes that costs. $59.99
Part A: How much has Stephanie spent on gifts so far?
Part B: How much does Stephanie have left to spend on gifts?
Part C: Which gift should Stephanie buy? Justify your answer.
Answer:
A. 84.50
B. She has 65.5$ left
C. Shoes
Step-by-step explanation:
A. If you add them it is 84.5
B. subtract 150 by 84.5 it is 65.5
C. Shoes because they are within the budget
PLEASE HELP WITH ALGEBRA!!!
Answer: aₙ = 3 + 4ⁿ⁻¹
So the formula would be:
aₙ = 3 + 4ⁿ⁻¹
Where a₁ = 3
Common Ratio (r) = 4
And n = the term number that needs to be found out
Step-by-step explanation:
Let's check if the answer is right:
To find the 1st number in the term we can substitute 1 in for n in the equation:
a₁ = 3 + 4¹⁻¹
a₁ = 3 + 4⁰
a₁ = 3 + 1
a₁ = 4
And if going back and checking the first number in the sequence given is indeed 4, therefore this equation is correct
Hope this helps!
the population of a town increased from 3300 in 2008 to 4750 in 2012. find the absolute and relative (percent) increase.
The population of the town increased by 1450 from 2008 to 2012. The relative increase, expressed as a percentage, is approximately 43.94%.
To find the absolute increase, we subtract the initial population from the final population: 4750 - 3300 = 1450.
Therefore, the population of the town increased by 1450 individuals over the four-year period.
To calculate the relative increase as a percentage, we use the following formula:
Relative Increase (%) = (Absolute Increase / Initial Population) × 100
Substituting the values into the formula, we have:
Relative Increase (%) = (1450 / 3300) × 100 ≈ 43.94%
This means that the population of the town increased by approximately 43.94% from 2008 to 2012.
The relative increase gives us a measure of the percentage change in the population size.
In this case, the town experienced a significant population growth of 43.94% over the four-year period.
This information can be useful for understanding demographic trends, planning infrastructure, and making policy decisions to accommodate the increased population.
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decide whether enough information is given to prove that $\triangle abc\cong\triangle dbe$ using the sss congruence theorem. explain. two triangles, triangle a c b and triangle d e b that share a common vertex b. point b is on the segment a d. in triangle a c b, side a c is marked with single tick, side b c is marked with double ticks and side a b is marked with three ticks. in triangle d e b, side d e is marked with single tick, side b e is marked with double ticks and side b d is marked with three ticks.put responses in the correct input to answer the question. select a response, navigate to the desired input and insert the response. responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. responses can also be moved by dragging with a mouse.you are given that $\overline{ab}\cong$ response area, $\overline{bc}\cong$ response area, and $\overline{ac}\cong$ response area. so, the triangles response area be proven congruent using the sss congruence theorem.
No, enough information is not given to prove that triangles are congruent using the SSS congruence theorem.
The SSS congruence theorem expresses that assuming in two triangles, three sides of one are consistent to three sides of the other, then, at that point, the two triangles are said to be congruent.
Now, we are given that triangle ACB and triangle DEB that share a common vertex b. So, both triangles share a common side. So, one side is same for both of triangles.
From the diagram, we can see that both triangles opposite side are equal. So, second side is equal for both of triangles.
Now, from the diagram, we can see that both triangles vertically opposite angles are equal. So, we have two sides equal and one angle is equal.
So, given triangle is proved to congruent by SAS congruency not by SSS congruency.
Hence, enough information is not given.
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What is f(4) for the function f(x)=7x+1?
Answer:
29
Step-by-step explanation:
substitute 4 for x into the function so 7x+1 would be (7*4)+1
7*4=28
28+1=29
Find an equation of the line through the points (−3,5) and (9,10) and write it in standard form Ax+By=C, with A>0a. 6x-10y=-75b. 5x-12y=-75c. 4x-11y=-65d. x-6y=-15
The required equation is 5x - 12y = -75
What is slope of line?
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate points and calculating the slope of a line are related tasks. Typically, in order to determine the slope of a line, we need to know the values of any two separate line coordinates.
Given points are (−3,5) and (9,10)
The slope of the line is given by:
m= \(\frac{(10-5)}{9-(-3)} =\frac{5}{12}\)
The equation becomes:
\(y-5=\frac{5}{12} [x-(-3)]\\\\y-5=\frac{5}{12} (x+3)\)
12y − 60 = 5x + 15
5x − 12y = −75
Hence, The required equation is 5x - 12y = -75
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The values in the table represent a function.
f(x)
8
X
-6
7
4
3
-5
3
-5
-2
12
Use the drop-down menus to complete the
statements.
The ordered pair given in the first row of the table can
be written using function notation as
f(3) is
◊
f(x) = -5 when x is
Done
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
The table represents a function where the input values (x) correspond to the output values (f(x)). Let's analyze the given information to complete the statements:
The ordered pair given in the first row of the table can be written using function notation as (x, f(x)) = (8, f(8)). This means that when x is equal to 8, the corresponding function value is f(8).
To find f(3), we look for the row in the table where x is equal to 3. From the given table, we can see that when x is 3, the corresponding function value f(x) is 7. Therefore, f(3) is equal to 7.
Similarly, to find when f(x) is equal to -5, we look for the rows in the table where the function value is -5. From the table, we can see that when x is equal to -6 and -2, the function value f(x) is -5. Therefore, we can say that f(x) = -5 when x is -6 or -2.
In summary:
The ordered pair given in the first row of the table can be written as (8, f(8)).
f(3) is equal to 7.
f(x) = -5 when x is -6 or -2.
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Can someone please help
Answer:
5\(\sqrt{6}\)
Step-by-step explanation:
Using the rule of radicals
\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\)
Given
\(\sqrt{150}\)
= \(\sqrt{25(6)}\)
= \(\sqrt{25}\) × \(\sqrt{6}\)
= 5\(\sqrt{6}\)
Partial Derivative Applications, Vectors and Matrices
If z = F(u, v, w) where u = r 2 , v = −2s 2 , and w = lnr + lns,
find ∂z/∂r and ∂z/∂s.
The values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.
To find ∂z/∂r and ∂z/∂s, we need to differentiate z = F(u, v, w) with respect to r and s.
Given that u = r^2, v = -2s^2, and w = ln(r) + ln(s), we can substitute these values into z = F(u, v, w).
So, z = F(r^2, -2s^2, ln(r) + ln(s)).
To find ∂z/∂r, we differentiate z with respect to r while treating s as a constant. This gives us:
∂z/∂r = ∂F/∂u * ∂u/∂r + ∂F/∂w * ∂w/∂r.
Similarly, to find ∂z/∂s, we differentiate z with respect to s while treating r as a constant. This gives us:
∂z/∂s = ∂F/∂v * ∂v/∂s + ∂F/∂w * ∂w/∂s.
Since we don't have the specific function F(u, v, w) mentioned in the question, we cannot determine the values of ∂z/∂r and ∂z/∂s. These partial derivatives will depend on the specific function F(u, v, w) provided.
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Find the series in A.P whose sum to n terms is n*(n+2)
Answer:
3, 5, 7, 9, 11, .........
Step-by-step explanation:
Given
\(S_{n}\) = n(n + 2) , then
S₁ = 1(1 + 2) = 1(3) = 3 ⇒ a₁ = 3
S₂ = 2(2 + 2) = 2(4) = 8
S₃ = 3(3 + 2) = 3(5) = 15
Thus
a₂ = S₂ - S₁ = 8 - 3 = 5
a₃ = S₃ - S₂ = 15 - 8 = 7
The first 3 terms are 3, 5, 7
This is an AP with common difference d = 2, then
a₄ = a₃ + 2 = 7 + 2 = 9
a₅ = a₄ + 2 = 9 + 2 = 11
and so on
Write a function rule for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, k.A. 100 = 0.20 × kB. p = 0.20 × 100 × kC. p = 0.20k + 100D. 0.20k = 100 + p
A function rule for finding the amount of daily pay, p, in the following situation: A bus driver gets paid $100 each day plus $0.20 per kilometer, k is p = 0.20k + 100. Correct option is C.
The given situation states that a bus driver gets paid a fixed amount of $100 per day plus an additional amount of $0.20 per kilometer driven. This means that the driver's daily pay, p, is directly proportional to the number of kilometers driven, k.
To find the function rule that relates p and k, we can start by setting up a linear equation in slope-intercept form:
p = mk + b
where m is the slope (the rate of change in pay per kilometer driven) and b is the y-intercept (the fixed daily amount of $100).
From the given information, we know that m = 0.20 (the pay rate per kilometer) and b = 100 (the fixed daily amount). Therefore, we can substitute these values into the equation:
p = 0.20k + 100
This is the function rule for finding the amount of daily pay, p, in the given situation.
Therefore, Correct option is C.
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The ruthless queen has asked the royal physician to come
up with a cure for laziness for her son Reginald. The
physician, not knowing what else to do, mixed 1 ounce of
a substance containing 3.7% ground cinnamon with
another substance containing 7.9% ground cinnamon to
create a substance with 6.5% ground cinnamon. How
many ounces of the 7.9% substance did he use?
The amount of ounces of the 7.9% substance is 2 ounces
How to determine the how many ounces of the 7.9% he used?We know that amount m = CV where
c = concentration and V = volumeLet
m = amount of 3.7 % ,m' = amount of 7.9 % and M = amount of 6.5 %We have that m + m' = M
cv + c'v' = CV where
c = 3.7 % conentration = 0.037 v = volume of 3.7 % = 1 ounce , c = 7.9% concentration = 0.079, v' = volume of 7.9%, C = 6.5 % concentration = 0.065 and V = volume of 6.5% = v + v'Since cv + c'v' = CV
Substituting the values of the variables into the equation, we have
3.7% × 1/3.7% + 7.9 %v' = 6.5%(v + v')
3.7% + 7.9 %v' = 6.5%(1 + v')
3.7% + 7.9 %v' = 6.5% + 6.5%v'
7.9%v' - 6.5%v' = 6.5% - 3.7%
1.4%v' = 2.8%
v' = 2.8%/1.4%
v' = 2 ounces
So, the amount of ounces of the 7.9% substance is 2 ounces
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Consider the wave packet: ψ(x)=[ 2πa 2
1
] 1/2
exp[− 4a 2
(x−⟨x⟩) 2
+i ℏ
px
]. Calculate the uncertainties ⟨Δx 2
⟩=⟨( x
^
−⟨x⟩) 2
⟩ and ⟨Δp 2
⟩=⟨( p
^
−⟨p⟩) 2
⟩, where ⟨ A
^
⟩ denotes the expectation value ⟨ψ∣ A
^
∣ψ⟩ of the observable A
^
on the state ∣ψ>.
The uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
To calculate the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ for the given wave packet, we need to find the expectation values of the observables (x^ - ⟨x⟩)^2 and (p^ - ⟨p⟩)^2, respectively.
The wave packet is represented by the function ψ(x) = [2πa^2]^(1/2) exp[-4a^2(x - ⟨x⟩)^2 + iℏpx]. Here, a is a constant, ⟨x⟩ represents the expectation value of x, and p is the momentum operator.
To find ⟨Δx^2⟩, we calculate the expectation value of (x^ - ⟨x⟩)^2 with respect to ψ(x). By integrating (x - ⟨x⟩)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δx^2⟩ = a^2/2.
Similarly, to find ⟨Δp^2⟩, we calculate the expectation value of (p^ - ⟨p⟩)^2 with respect to ψ(x). Since p is the momentum operator, its expectation value is ⟨p⟩ = 0 for the given wave packet. By integrating (p^ - 0)^2 multiplied by the squared magnitude of the wave packet over all x values, we obtain the result ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
Therefore, the uncertainties ⟨Δx^2⟩ and ⟨Δp^2⟩ are given by the expressions ⟨Δx^2⟩ = a^2/2 and ⟨Δp^2⟩ = (ℏ^2)/(8a^2).
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Test the polar equation for symmetry with respect to the polar axis, the pole, and the line θ = π 2 . (Select all that apply.) r = 3 + 6 cos(θ)
The polar equation r = 3+6cosθ is symmetric to the polar axis with respect to the polar axis.
To test the polar equation r = 3 + 6 cos(θ) for symmetry, we will consider each type of symmetry one by one:
1. Polar axis symmetry: Replace θ with -θ and check if the equation remains the same.
r = 3 + 6 cos(-θ) = 3 + 6 cos(θ) (since cosine is an even function)
Since the equation remains the same, the curve is symmetric with respect to the polar axis.
2. Pole symmetry: Replace r with -r and check if the equation remains the same.
-r = 3 + 6 cos(θ)
This equation is not equivalent to the original equation, so the curve is not symmetric with respect to the pole.
3. Line θ = π/2 symmetry: Replace θ with (π - θ) and check if the equation remains the same.
r = 3 + 6 cos(π - θ) = 3 - 6 cos(θ) (since cos(π - θ) = -cos(θ))
This equation is not equivalent to the original equation, so the curve is not symmetric with respect to the line θ = π/2.
In conclusion, the polar equation r = 3 + 6 cos(θ) is symmetric with respect to the polar axis, but not with respect to the pole or the line θ = π/2.
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Can someone pls help me with this?
Answer: Graph B.
Step-by-step explanation: If he is traveling on the highway we know he starts out fast. This means it can't be graph c. After he pulls over and stops which would mean he has no speed at all he accelerates or speeds up quickly. The only graph that represents this is Graph B.
Starts fast
Slows Down and stops
Speeds Up Only represented by graph B
A new bank customer with $4,000 wants to open a money market account. The bank is offering a simple interest rate of1.4 %. how much will the customer earn in 10 years
Answer: they would earn $560
Step-by-step explanation:
10% = 400
1% = 40
0.1% = 4
40+16 = 56*10=560
If you could be so kind to press brainliest on this answer
Which of the following types of harm resulting from technological innovations can engineers be held most morally blameworthy? O Foreseen harms O Foreseeable harms O Unforeseen harms O Unforeseeable harms
Engineers can be held most morally blameworthy for foreseeable harms resulting from technological innovations, engineers have a responsibility to anticipate the potential consequences of their work,
and to take steps to mitigate those consequences. If they fail to do so, and their work results in harm, they can be held morally blameworthy. When engineers develop new technologies, they have a responsibility to consider the potential consequences of their work.
They need to think about how their technology could be used, and whether it could be used to harm people or the environment.
They also need to consider how their technology could be misused, and what steps they can take to prevent misuse.
If engineers fail to consider the potential consequences of their work, and their work results in harm, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.
For example, engineers who develop new weapons systems have a responsibility to consider the potential consequences of their work. They need to think about how their weapons could be used,
and whether they could be used to kill or injure innocent people. They also need to consider how their weapons could be misused, and what steps they can take to prevent misuse.
If engineers fail to consider the potential consequences of their work, and their weapons are used to kill or injure innocent people, they can be held morally blameworthy. This is because they have a duty to protect the public from harm, and they have failed to fulfill that duty.
It is important to note that engineers cannot be held morally blameworthy for unforeseeable harms. This is because they did not have the opportunity to anticipate the harm, and they could not have taken steps to prevent it.
For example, engineers who develop new medical treatments cannot be held morally blameworthy if the treatments have unforeseen side effects. This is because the engineers did not have the opportunity to anticipate the side effects, and they could not have taken steps to prevent them.
In conclusion, engineers can be held morally blameworthy for foreseeable harms resulting from technological innovations.
This is because they have a responsibility to anticipate the potential consequences of their work, and to take steps to mitigate those consequences.
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Who can access your credit report? a. friends b. employers c. neighbors d. teachers Please select the best answer from the choices provided. Group of answer choices A B C D
The best answer from the choices provided is b. employers.The friends, neighbors, and teachers do not typically have access to Credit report, employers may request it under specific Circumstances .
Your credit report contains sensitive financial information and is typically accessed by entities that have a legitimate need for it. While friends, neighbors, and teachers do not typically have a legitimate reason to access your credit report, employers may request access as part of their hiring process, especially when evaluating candidates for positions that involve handling financial matters or require a certain level of trust.
Employers may request your credit report to assess your financial responsibility, integrity, and overall suitability for a particular role. However, it's important to note that employers must comply with legal requirements and obtain your consent before accessing your credit report. In some jurisdictions, laws and regulations govern the permissible use of credit reports for employment purposes.
It's crucial to be aware of your rights and protections regarding the access and use of your credit report. In many countries, individuals have the right to review their credit reports, dispute inaccuracies, and request corrections. Additionally, credit reporting agencies are required to follow specific procedures to ensure the security and privacy of your credit information.
while friends, neighbors, and teachers do not typically have access to your credit report, employers may request it under specific circumstances and with your consent.
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Snowflake Skate is an
ice-skating rink that charges a
flat rate for skate rentals plus
an hourly skating rate. Cara
skated for three hours and paid
$17. Marcus skated for one
hour and paid $11.
Answer:
I am not sure what the questions is, but I think that you ae looking for the equation
y = 3x + 8
Step-by-step explanation:
Let m = the cost per hour
Let b= the cost for the skates
17 = 3m + b
11 = m + b Solve for b; b = 11 - m Substitute 11 -m for b in the first equation
17 = 3m + b
17 = 3m + 11 - m Combine like terms
17 = 2m + 11 Subtract 11 from both sides
6 = 2m Divide both sides by 2
3 = m
Substitute 3 for m to solve for b
b = 11 -m
b = 11 - 3
b = 8
y = mx + b Substitute 3 for m and 8 for b.
y = 3x + 8
What is the product of (a+b) (a-b)
Answer:
\(a^{2}+b^{2}\)
Step-by-step explanation:
(a+b)(a-b)
\(a^{2}\)-ab+ab-\(b^{2}\)
\(a^{2} + b^{2}\)
An entity has the following balances: Bank: R5 000; Machinery: R3 000: Trade payables: R2 000.
The equity of the entity according to the basic accounting equation is …
NB: Instructions
1. Use a full stop to indicate any decimals (eg: 1000.01)
2. Only show the amount, do not show the R (eg: 12141.72)
The equity of the entity, according to the basic accounting equation, is R6 000. The basic accounting equation is Assets = Liabilities + Equity. To find the equity of the entity, we need to subtract the total liabilities from the total assets.
Bank balance: R5 000
Machinery balance: R3 000
Trade payables: R2 000
Total assets = Bank + Machinery
= R5 000 + R3 000
= R8 000
Total liabilities = Trade payables
= R2 000
Equity = Total assets - Total liabilities
= R8 000 - R2 000
= R6 000
Therefore, the equity of the entity, according to the basic accounting equation, is R6 000.
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The equation of line j is
y= -6/7+7. Line k is perpendicular to j. What is the slope of line K
Answer:
7/6
Step-by-step explanation:
in order for it to perpendicular then its need to be the negative reciprocal of it, so you flip the sign making it positive and do the opposite of the slope like for ex if it was 1/2 it would have been 2
2. Realiza la siguientes sumas de números enteros usando el método de tener y deber
a) –4 + 5 –3 =
b ) +3 –5 +7 =
c) –3 + 5 –8 =
d) +4 – 7 –8 = 9.
Answer:
a is the answer
Step-by-step explanation:
The average earnings per share (EPS) for 9 industrial stocks randomly selected from those listed on the Dow-Jones Industrial Average (DJIA) was found to be 1.85 with a standard deviation of 0.395.
Calculate a 90% confidence interval for the average EPS of all the industrials listed on the DJIA.
To calculate the 90% confidence interval for the average EPS of all industrials listed on the DJIA, we will use the formula:
Confidence interval = sample mean ± (critical value * standard deviation / √sample size)
Step 1: Find the critical value.
Since we want a 90% confidence interval, the corresponding critical value can be obtained from the z-table. The critical value for a 90% confidence level is 1.645.
Step 2: Calculate the margin of error.
The margin of error is given by (critical value * standard deviation / √sample size).
Substituting the values, we get: 1.645 * 0.395 / √9 = 0.29175.
Step 3: Calculate the confidence interval.
The confidence interval is given by the sample mean ± margin of error.
Substituting the values, we get: 1.85 ± 0.29175.
The 90% confidence interval for the average EPS of all industrials listed on the DJIA is (1.55825, 2.14175).
We can be 90% confident that the true average EPS of all industrials listed on the DJIA falls within the range of 1.55825 to 2.14175.
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A friend of yours was interested in determining whether the news media noticed campus events. Your friend decided to do a content analysis of the local paper.Your friend counted each story that mentioned his university's name. At the end of two months, 136 events had been counted. Your friend asked for your comments on his research. You told your friend:
The inference is that the person will tell the friend that he did manifest coding and he should have recorded the base.
What is an inference?The options are:
He did manifest coding.
He did latent coding.
He should have recorded the base.
He did manifest coding and he should have recorded the base.
It should be noted that an inference simply means the conclusion that can be deduced based on the information given.
In this case, the friend was interested in determining whether the news media noticed campus events and decided to do a content analysis of the local paper.
Therefore, the the person will tell the friend that he did manifest coding and he should have recorded the base.
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You told your friend: d. he did manifest coding and he should have recorded the base.
How to determine the true statement?The missing options are:
a. he did manifest coding. b. he did latent coding.
c. he should have recorded the base.
d. he did manifest coding and he should have recorded the base.
e. he did latent coding and he should have recorded the base.
From the question, we understand that:
Each story is counted136 events were counted after 2 monthsAs a general rule, manifest coding include making use of the contents at the surface gotten from available data and questionnaires.
Because the stories that mentioned the university name can be gotten from publications, it means that your friend used manifest coding
Hence, the true statement is (d) he did manifest coding and he should have recorded the base.
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The school band will sell pizzas to raise money for new uniforms. The supplier charges $143 plus $5 per
pizza. The band members sell the pizzas for $7 each. Enter and solve an inequality to find how many
pizzas the band members will have to sell to make a profit. Let p be the number of pizzas sold.
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Answer:
7 x > 4 x + 100
7 x - 4 x > 100
3 x > 100
x > 100 : 3
x > 33.33
Answer: they have to sell 34 pizzas to make a profit.
Step-by-step explanation: