Answer:
The number is 72.
Step-by-step explanation:
Let the number be xy.
x = y + 5
10x + y - 2(10y + x) = 0.25(10x + y)
10x - 2x + y - 20y = 2.5x + 0.25y
5.5x - 19.25y = 0
Substituting for x:
5.5y + 27.5 - 19.25y = 0
-13.75y = -27.5
y = 2.
So x = 2 + 5 = 7.
The height of a soccer ball that is kicked from the ground can
be approximated by the function: y = -16x² + 48x, where y is the height of
the soccer ball in feet x seconds after it is kicked.
Find the time, in seconds, it takes from the moment the soccer ball is kicked until it
returns to the ground.
The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
How to determine the time to hit the ground?The function is given as:
y = -16x^2 + 48x
When the ball hits the ground, we have
y = 0
Substitute the known values in the above equation
-16x^2 + 48x = 0
Factor out -16x
-16x(x - 3) = 0
Divide through by -16x
x - 3 = 0
Add 3 to both sides
x = 3
Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds
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25. Jen ran x miles last week and 18 miles
this week. Write an expression to represent
the total number of miles Jen ran over the
last two weeks.
Solve: If she ran 34 miles over the last two
weeks, how many did she run last week?
Answer:
Step-by-step explanation:
If Jen ran 34 miles over the last 2 weeks and only 18 miles the second week, she would've had to have run 16 miles the first week.
34= 18+x
I hope this helps!
Darren wins a coupon for $4 off the lunch special for each of 5 days. He pays $75 for his 5 lunch specials. Write and solve the equation to find the original price p for one lunch special.
Answer:
19
Step-by-step explanation: (75/5) + 4= p
15+4=p
19=p
The original price for one lunch meal is $19
p = $15 + $4
p = $19
Work out the circumference of this circle.
Take it to be 3. 142 and give your answer to 1 decimal place.
4 cm
The circumference of the given circle is 25.1 cm.
According to the statement
we have given that the the radius of circle which is 4cm.
And we have to find the circumference of the circle.
So, For this purpose
The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).
The formula to calculate it is
C = 2(pi)r
So, substitute the values in it then
Here use pi value is 3.14
C = 2 *3.14*4
C = 25.12.
The circumference of the given circle is according to one decimal place is 25.12 cm.
So, The circumference of the given circle is 25.1 cm.
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Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint. The average
15 + 3x
3+x
15+ 3x dollars per pint. If the equation y =
=
is graphed in the
3+x
cost of all the berries he bought was
xy-plane, what quantity will be represented by the y-intercept of the graph?
O The total cost, in dollars, of all the raspberries Ethan bought
O The average cost, in dollars per pint, of all the raspberries Ethan bought
O The total cost, in dollars, of all the blueberries Ethan bought
O The average cost, in dollars per pint, of all the blueberries Ethan bought
The y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought. Therefore, option B is the correct answer.
Given that, Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint.
The average is (15 + 3x)/(3+x) per pint.
We need to find what quantity will be represented by the y-intercept of the graph.
How to find the y-intercept of the graph?Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
Now, the graph of y=(15 + 3x)/(3+x)is given below.
To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.
x-intercept(s): (−5,0)
y-intercept(s): (0,5)
So, the y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought.
Therefore, option B is the correct answer.
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Marta’s mother shared a funny video of their cat on the Internet. The total number of people who had viewed the video over the first 30 days could be modeled using the function f(x) = 33(1.3)x where x is the number of days the video has been online.
About how many people had viewed the video once it had been online for 20 days?
190
858
6,271
86,460
The number of people that have watched the video is 858 people
What is a function?A function is a mathematic rule. We know that a function shows the rule that is to be carried out and is often written in the form of an equation.
Now we have the function shown as; f(x) = 33(1.3)x. Since we know that the term x is referred as the number of days the video has been online.
Thus, f(x) = 33(1.3)(20) thus we can now say that the number of people who have vied the video in twenty days is 858 people.
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Answer: the answer is B or 858
Step-by-step explanation: The answer is B or 858
Given: circle k(O) with diameter AB and CD ⊥ AB
Prove: AD·CB=AC·CD
For a circle k(O) with diameter AB and CD ⊥ AB, it is proved that AD·CB=AC·CD, using similarity of triangles.
Given:
circle k(O) with diameter AB
CD ⊥ AB
To Prove: AD·CB=AC·CD
Proof:
In ΔADC and ΔCDB,
∠ADC = ∠CDB = 90°
[∵Both are right angle triangles]
CB = CB [Common side]
⇒ AC / CB = CD / DB
Thus, ΔACD is similar to ΔCDB by RHS similarity.
Therefore, we can write,
AD/CD = AC/CB [Since corresponding sides of similar triangles are proportional]
⇒ AD·CB = AC·CD
Hence proved.
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Solve: 25x2 − 30 = 0 round the answer to the nearest hundredth. x = −1.10 and x = 1.10 x = −26.15 and x = 1.15 x = 0 x = −0.83 and x = 0.83
Answer:
(a) x = -1.10 and x = 1.10
Step-by-step explanation:
A straightforward square root will give the value of x.
SolutionDivide by the coefficient of x^2:
x^2 -30/25 = 0
x^2 -1.20 = 0
Add 1.20, and take the square root.
x^2 = 1.20
x = ±√1.20 ≈ ±1.0954
x ≈ -1.10 and 1.10 . . . . . round to hundredths
__
Additional comment
For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.
Geometry: complete this proof, ASAP!!!!!!!!
Answer:
1. Given
2. Definition of Congruent Angles
3. Triangle Interior Angle Sum Theorem
4. Transitive Property of Equality
5. Substitution Property of Equality
6. Definition of Congruent Angles
I found this proof by induction that all people in canada are the same height, i was wondering what is the incorrect step?
Step 1: In any group that consists of just one person, everybody in the group has the same age, because after all there is only one person!
Step 2: Therefore, statement S(1) is true.
Step 3: The next stage in the induction argument is to prove that, whenever S(n) is true for one number (say n=k), it is also true for the next number (that is, n = k+1).
Step 4: We can do this by (1) assuming that, in every group of k people, everyone has the same age; then (2) deducing from it that, in every group of k+1 people, everyone has the same age.
Step 5: Let G be an arbitrary group of k+1 people; we just need to show that every member of G has the same age.
Step 6: To do this, we just need to show that, if P and Q are any members of G, then they have the same age.
Step 7: Consider everybody in G except P. These people form a group of k people, so they must all have the same age (since we are assuming that, in any group of k people, everyone has the same age).
Step 8: Consider everybody in G except Q. Again, they form a group of k people, so they must all have the same age.
Step 9: Let R be someone else in G other than P or Q.
Step 10: Since Q and R each belong to the group considered in step 7, they are the same age.
Step 11: Since P and R each belong to the group considered in step 8, they are the same age.
Step 12: Since Q and R are the same age, and P and R are the same age, it follows that P and Q are the same age.
Step 13: We have now seen that, if we consider any two people P and Q in G, they have the same age. It follows that everyone in G has the same age.
Step 14: The proof is now complete: we have shown that the statement is true for n=1, and we have shown that whenever it is true for n=k it is also true for n=k+1, so by induction it is true for all n.
The incorrect step in the induction that all people in Canada are the same height is; Step 9
How to prove Mathematical Induction?The principle of mathematical induction as follows:
For example, we have a set of natural numbers. Now, suppose that 1 is in the set. Now, we assume that anytime n is in the set, n + 1 is also in the set. Therefore we can say that every natural number is in the set.
The wrong step in the given mathematical Induction is Step 9. This is because;
We might not be to see anyone else in the arbitrary group G other than groups P or Q!
Recall that G is a group of k + 1 people. Thus, provided that k > 1, k + 1 > 2 and that a third person R in G does not exist, then the rest of the proof will work.
The steps above proves that;
S(k) = S(k + 1), for every k > 1.
Thus, we can also say that if S(2) is true, then it equally means S(3) is true and so on till infinity.
From our induction process written so far, we have see that S(1) was true. However, our induction step in the question does not show us that that S(1) = S(2) = true.
So: Thus, from the induction I have done It shows that S(1) not imply S(2) and as a result the proof is fallacious.
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What is the slope?
What is the slope?
What is the slope?
What is the slope?
What is the slope?
Answer:
okay it's name is Muhammad Deco alfansia ( ◜‿◝ )
Answer:
Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.
Step-by-step explanation: Hope this helps you!
help please !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!111
Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
Given solution of a question done by two people.
Jenna's method
5(30+4)
(5)(30)+(5)(4)
150+20=170
Mia's method
5(30+4)
5(34)=170
We are required to find why they have achieved at the same answer.
Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.
Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.
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Use the binomial series to find the maclaurin series for the function. f(x) = 4 1 x
Answer:
We note that,
x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³
now we can use binomial series on (1+x²)²ᐟ³
(1+x²)²ᐟ³ = ( 1+2x²/3+((2/3)*(2/3 -1)/2) x⁴ + ((2/3)*(2/3 -1)(2/3–2)/6) x⁶ +o(x⁶) =
= 1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶)
The last step is to differentiate,
x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³
= (3/4) d/dx (1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶) )
= (3/4) ( 0 + (4/3)x - 4/9 x³ + 24x⁵/81 + o(x⁵))
= x - x³/3 + 2x⁵/9 + o(x⁵)
The complete Question is- How do I find the Maclaurin series using binomial series in the function f(x) = x/³√1+x^2?
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Find a power series representation for the function. (center your power series representation at x = 0. ) f(x) = 1 9 x f(x) = [infinity] n = 0
The power series representation for the function, so the interval of convergence is (-9,9).
The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.
Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.
The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.
We have given f(x)=1/(9+x)
f(x)=(1/9)*(1/(1-(-x/9))
f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]
=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]
Let an=(-1)n*(xn/9n+1)
using the Ratio Test
L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|
=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|
=lim n-->infinity|(-1)*(x)/9)|
=|-x/9|<1
x/9<1 and x>9>-1
x<9 and x>-9
x is -9<x<9
for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)n]
By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges
=1/9*diverges
the series diverges for x=9
for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]
=1/9*summation of (n=0 to infinity) [(-1)2n]
which is diverges
so the interval of convergence is (-9,9)
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Which of the following represents the series in summation notation?
−2 + 4 − 8 + 16 − 32 + 64 − 128.
Answer:
ummation of n=1 to n=7 (-2)^n
Step-by-step explanation:
summation of n=1 to n=7 (-2)^n
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days. Assuming that the chance of rain is independent of the day, what is the probability that it will rain both days?
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
According to the question
Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.
Assuming that the chance of rain is independent of the day
Probability is the chance that some event will happen.
It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.
Probability = Number of ways it can occur/Total number of outcomes
Probability of rain on first day = 1/2
Probability of rain on second day = 1/2
Then
Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4
Hence,
The probability that it will rain both days is [tex]\frac{1}{4}[/tex].
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What type of number is -√/81?
Choose all answers that apply:
A. whole number
B. integer
C. rational
D. irrational
Answer:
Step-by-step explanation:
integer and rational
You randomly choose a block from each
set in the diagram. What is the probability
that you will choose a block labeled with a
Tor a block labeled with a 6?
Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:
There are 8 outcomes with a T and a block from the second square.Removing the 2 outcomes below with a 6 and a T, as they are already counted, there are 7 outcomes with a six.Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:
p = 15/64 = 0.2344.
0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.
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find the total surface area and volume, then multiply by 0.0004
The Total surface area of the rectangular prism = 168 in.²
The Volume of the rectangular prism = 108 in.³
What is the Total Surface Area of a Rectangular Prism?The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:
w = width of the rectangular prism
h = height of the rectangular prism
l = length of the rectangular prism
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = l × w × h
Find the Total surface area of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²
Find the volume of the rectangular prism:
Length (l) = 9 in.
Width (w) = 2 in.
Height (h) = 6 in.
Volume of the rectangular prism = l × w × h = 9 × 2 × 6
Volume of the rectangular prism = 108 in.³
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A nonnative fern species is introduced into an area and quickly begins to spread. The number of plants can be modeled by
P(n) = 1,200(1.68)", where n is the number of months since the ferns were introduced. Use this information to complete the
statements.
Select the correct answer from each drop-down menu.
Based on the model, there were initially
The monthly percent rate of change is
This situation is modeled by an exponential
%.
ferns.
function.
Submit
Based on the information, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
How to complete the information?The given parameters from the question are:
P(n) = 1200(1.68)^n
Where
n represent the number of months
An exponential growth function is represented as:
P(n) = a * (1 + r)^n
Where
a represents the initial value
r represents the rate
By comparison, we have
a = 1200
1 + r = 1.68
This gives
r = 0.68 = 68%
Hence, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function
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1,200
68
growth
Got it right on Edmentum
Which equation represents the function? f(x)=−1/2x+4 f begin argument x end argument equals negative fraction 1 over 2 end fraction x plus 4 f(x)=2x+12 f begin argument x end argument equals 2 x plus 1 half f(x)=4x−2 f begin argument x end argument equals 4 x minus 2 f(x)=−2x+4
The equation that represents the function is y = -x - 1
How to determine the equation of the function?The complete question is added as an attachment
From the table of values, we have the following points
(x, y) = (-1,0) and (0,-1)
Calculate the slope (m) using
m = (y2 - y1)/(x2 - x1)
Substitute the known values in the above equation
m = (-1 -0)/(0 + 1)
Evaluate the exponent
m = -1
The equation is then calculated as:
y = mx + c
This gives
y = -x + c
Using the point (0,-1), we have:
0 = 1 + c
Solve for c
c = -1
So, we have
y = -x - 1
Hence, the equation that represents the function is y = -x - 1
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5. In a recent year, the population of Springfield, Illinois was one hundred
sixteen thousand, four hundred eighty-two. Write this number in standard
form. Show your work in the space below. Remember to check your solution
Answer: 16482
Step-by-step explanation:
Let's divide the number into three parts:
sixteen thousand | four hundred |eighty-two
A thousand is 1000, so sixteen thousand should be 16000.
A hundred is 100, so four hundred should be 400.
Eighty-two is just 82.
Let's add all of these:
[tex]16000+400+82=16482[/tex]
Find the solution for the system of linear equations by substitution: 2x - y = 3 y − x = 1
The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the solution to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2x- y = 3
y - x = 1
Make y the subject in the second equation, by adding x to both sides of the equation
y - x + x = x + 1
This gives
y = x + 1
Substitute y = x + 1 in 2x- y = 3
2x- x - 1 = 3
Evaluate the like terms
x = 4
Substitute x = 4 in y = x + 1
y = 4 + 1
Evaluate
y = 5
Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5
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PLEASE HELP!!!!!! I CAN’T UNDERSTAND!!!! How to do this one
The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
What is binomial expansion?Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.
What is Pascal's triangle?Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.
What is the coefficient of t²s⁵ in the expansion of (2t + s)⁷?
The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.
So, each term is ⁿCₓaˣbⁿ⁻ˣ.
Comparing (a + b)ⁿ with (2t + s)⁷,
a = 2t, b = s and n = 7.So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ
= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ
So, the coefficient term is ⁷Cₓ(2)ˣ
Now for the term t²s⁵, x = 2.
So, the coeficient term is ⁷Cₓ(2)ˣ = ⁷C₂(2)²
= 7!/2!(7 - 2)! × 4
= 7!/2!5! × 4
= 7 × 6 × 5!/(2! × 5!) × 4
= 7 × 6/2 × 4
= 7 × 3 × 4
= 84
So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84
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identify all values of that make the equation true.
Please explain them as step by step !!
Thank you!!
Part a
[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]
Part C
[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]
Rajini throws a die. What is the chance of her getting a number 8?
Answer:
Hey there!
Step-by-step explanation:
This is ur answer...
0/6She has no chance getting an 8 because 8 doesn't exist in a dice....She can get 1-6 only....Hope it helps!
Brainliest pls!
Have a good day!^^
Consider the line 4x + 2y = 8.
What is the slope of a line perpendicular to this line?
Answer:
supposed to make the subject y then slope is -2
A man made a loss of 15% by selling an article for $595. Find the cost price of the article
Answer:
$700
Step-by-step explanation:
If he made a loss of 15%, then it means that selling price is 85% of the cost price.
If the cost price is x, then we have;
0.85x = 595
x = 595/0.85
x = $700
A large company has offices in cities across the country. The facilities director of the company was asked to survey employees about their office furniture. Rather than survey all employees in the company, the director decided to take a sample of employees. Which groups would be most representative of the opinions of all employees in the company? Select each correct answer.
A.
5% of randomly selected employees from each office location
B.
Employees with office phone numbers ending in 3 and 7
C.
Employees who are randomly selected by a computer from a list of all company employees
D.
Employees who have worked for the company for more than 10 years
E.
Randomly selected employees in the cafeteria of one of the offices
F.
Employees answering phone calls in the company’s customer service departme
The groups which would be most representative of the opinions of all employees in the company are: A sample of 5% of randomly selected employees from each office location, Employees who are randomly selected by a computer from a list of all company employees and Employees who have worked for the company for more than 10 years.
Options (A),(C) and (D) are correct.
A sizable business has locations around the nation. The company's facilities director was tasked with asking employees about their office furnishings. Instead of polling every worker at the company, the director chose to select a sample. We are supposed to find the groups which would be most representative of the opinions of all employees in the company.
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Which of the graphs below represents the equation 3x-2y=-12?
Answer:
Graph B
Step-by-step explanation:
Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
3x - 2y = -12
2y = 3x + 12
y = 3/2x + 6
Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.
