Answers
Using the given table:
a) the average rate of change is 32.5 jobs/year.
b) the average rate of change is 12.5 jobs/year.
How to find the average rate of change?
For a function f(x), the average rate of change on an interval [a, b] is:
[tex]\frac{f(b) - f(a)}{b - a}[/tex]
a) The average rate of change between 1997 and 1999 is:
[tex]A = \frac{695 - 630}{1999 - 1997} = 32.5[/tex]
So the average rate of change is 32.5 jobs/year.
b) Now the interval is 1999 to 2001.
The rate this time is:
[tex]A ' = \frac{720 - 695}{2001 - 1999} = 12.5[/tex]
So the average rate of change is 12.5 jobs/year.
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Related Questions
Which graph is the sequence defined by the function f(x) = 3(2)x-1?
On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).
On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).
On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).
On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Answers
Answer: On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).
Step-by-step explanation:
When x=1, f(x)=3. So, it passes through (1,3).
So, everything is eliminated except for option (4).
Answer:
D!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Step-by-step explanation:
Can someone help?
what do both of these functions have in common?
f(x) = 5e^x+5 - 5 g(x) = 0.5(x-5)^2 -5
o a. they have the same vertical stretch
ob. they have the same horizontal translation
c. they have the same vertical shift
d. they have the same end behavior
Answers
c. They have the same vertical shift.
A vertical shift is just an alternate within the y-price of each characteristic. it's miles literally picking up the entire characteristic or graph and moving the whole element up or down. If it's far moved up, we add to the y-cost, if it's far moved down, we subtract from the y-cost.
Vertical shift and lateral shift are phenomena because of the refraction of mild rays once they journey from one medium into every other. while light rays travel across two parallel surfaces, the emergent rays from the second one floor are parallel to the incident rays on the primary floor.
The segment Shift is how far the function is shifted horizontally from the standard position. The Vertical Shift is how long way the function is shifted vertically from the same old function.
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Seventy percent of kids who visit a doctor have a fever and 21% of kids have fever and sore throats . what is the probability that a kid who goes the doctor has a sore throat given that he has a fever? (when entering your answer remember that the probability is a number between 0 and 1)
Answers
The probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%. Computed using conditional probability.
The probability of any event A given that event B has already taken place is found using the formula P(A|B) = P(A ∩ B)/P(B). This is known as conditional probability, where P(A ∩ B) is the probability of events A and B, and P(B) is the probability of event B.
In the question, we are given that 70% of kids who visit a doctor have a fever and 21% of kids have a fever and sore throats.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever.
We suppose the event of going to the doctor while having a fever to be B, and going to a doctor while having a sore throat to be A.
We are given that 70% of kids who visit a doctor have a fever, that is, the probability of event B, P(B) = 70% = 0.7.
We are given that 21% of kids who visit a doctor have a fever and sore throats, that is, the probability of event A and event B, P(A ∩ B) = 21% = 0.21.
We are asked to find the probability that a kid who goes to the doctor has a sore throat given that he has a fever, that is, we are asked to find the conditional probability of event A, when event B has already taken place, that is, P(A|B).
By formula, we know that:
P(A|B) = P(A ∩ B)/P(B) = 0.21/0.70 = 0.30.
Thus, the probability that a kid who goes to the doctor has a sore throat given that he has a fever is 0.30 or 30%.
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A poll worker analyzing the ages of voters found that mu = 65 and sigma = 5. what is a possible voter age that would give her zx = 1.14? round your answer to the nearest whole number.
Answers
If the value of μ is 65, σ is 5 and z is 1.14 then the value of possible voter age would be 70.6 years.
Given that value of μ is 65, σ is 5 and z is 1.14.
We have to calculate the possible voter age that can satisfy the given values of σ,μ and z.
We know that in z test,
z=X-μ/σ
in which μ is population mean,σ is population standard deviation.
We have to just put the values in the above formula to get the value of X which is our possible voter age.
Putting the values we get,
1.14=x-65/5
5.7=X-65
X=65+5.7
X=67.7
Hence the possible voter age is 67.7 which would satisfy the value of μ=65,σ=5 and z=1.14.
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Which type of graph would you want to use to show the frequency of an interval?
line graph
histogram
box-and-whisker plot
stem-and-leaf plot
Answers
M<2=7x+,m<3=4y,and m<4=122 , find the values of x and y.
Answers
The values of x and y in the equation are 15 and 28 respectively
How to find the variables in an equation?Let's find the x and y values in the equation,
m = 7x + 7
m = 4y
m = 112
Therefore,
4y = 7x + 7
4y - 7x = 7
4y = 112
y = 112 / 4
y = 28
Therefore,
4(28) - 7x = 7
112 - 7x = 7
112 - 7 = 7x
105 = 7x
x = 105 / 7
x = 15
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The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to eliminate the
y-varlable, and what is the solution for this system?
x+3y=42
2x-y=1
Answers
=======================================================
Explanation:
The 3y in the first equation must add to -3y so the y terms go away. We have -y in the second equation, which is why we triple everything in that equation
2x-y = 1 becomes 6x - 3y = 3 after tripling everything. This is the same as multiplying both sides by 3.
This is the updated equivalent system
[tex]\begin{cases}x+3y = 42\\6x-3y = 3\end{cases}[/tex]
Add the terms straight down
x+6x becomes 7x3y+(-3y) becomes 0y or 0. The y variables are eliminated.The right hand sides 42 and 3 add to 45We have the equation 7x = 45 which solves to x = 45/7.
Unfortunately it doesn't turn into a nice single whole number because 45 isn't a multiple of 7. So I would leave it as a fraction.
Optionally you could note that 45/7 = 6.42857 approximately. But I prefer the fraction form since it's most exact.
--------------
Use this x value to find y. Pick any equation involving x and y. Plug in that x value and solve for y.
x + 3y = 42
45/7 + 3y = 42
3y = 42 - 45/7
3y = 42*(7/7) - 45/7
3y = 294/7 - 45/7
3y = (294 - 45)/7
3y = 249/7
y = (249/7)*(1/3)
y = 83/7
Like with x, we also don't get a nice whole number.
I used WolframAlpha to confirm the solutions. GeoGebra is another tool you could use.
In your rectangular backyard, you know the width of the yard is three less than four times the length. If the perimeter of your yard is 24 yards, what is the width?
Answers
Answer: 9 yards
Step-by-step explanation:
Let's make equations to represent each situation.
The first equation says that the width is 3 less than 4 times the length, so let's put that into an equation:
[tex]w=4l-3[/tex]
Next, we can use the perimeter equation that [tex]P=2l+2w[/tex]. Since we know the perimeter is 24 yards, we can replace it for P.
[tex]24=2l+2w[/tex]
Now that we have two equations with two variables, we can use either elimination or substitution to solve them. Since w is already solved for in the first equation, let's plug it in the second equation.
[tex]24=2l+2(4l-3)\\ 12=l+4l-3\\ 12=5l-3\\ 15=5l\\ l=3[/tex]
Now, let's put l back into the first equation to solve for w.
[tex]w=4(3)-3\\ w=12-3\\ w=9[/tex]
The width is 9 yards
PLEASE HELP OUT ASAP!!!!!!
WILL GIVE 15 POINTS!!!!
Answers
a) The approximate area below the curve using five rectangles is 1280 square units.
b) The approximate area below the curve using ten rectangles is 1320 square units.
c) The approximate area below the curve using infinite number of rectangles is 1333.333 square units.
How to find the area below the curve by Riemann's sum
In this problem we must estimate the value of the area below the curve by finite number of rectangles using Riemann sums, whose expression is:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n], for i = {0, 1, 2, 3, ..., n - 1} (1)
Where:
n - Number of rectanglesa - Lower limit of the interval.b - Upper limit of the interval.i - Index of the rectangle.The approximate area below the curve using five rectangles is: f(x) = 20 · x - x², a = 0, b = 20, n = 5
A ≈ [(20 - 0) / 5] · ∑ f[0 + i · (20 - 0) / 5]
A ≈ 4 · ∑ f(4 · i)
A ≈ 4 · [f(0) + f(4) + f(8) + f(12) + f(16)]
f(0) = 20 · 0 - 0² = 0
f(4) = 20 · 4 - 4² = 64
f(8) = 20 · 8 - 8² = 96
f(12) = 20 · 12 - 12² = 96
f(16) = 20 · 16 - 16² = 64
A ≈ 4 · (0 + 64 + 96 + 96 + 64)
A ≈ 1280
And using ten rectangles:
A ≈ [(20 - 0) / 10] · ∑ f[0 + i · (20 - 0) / 10]
A ≈ 2 · ∑ f(2 · i)
A ≈ 2 · [f(0) + f(2) + f(4) + f(6) + f(8) + f(10) + f(12) + f(14) + f(16) + f(18)]
f(0) = 20 · 0 - 0² = 0
f(2) = 20 · 2 - 2² = 36
f(4) = 20 · 4 - 4² = 64
f(6) = 20 · 6 - 6² = 84
f(8) = 20 · 8 - 8² = 96
f(10) = 20 · 10 - 10² = 100
f(12) = 20 · 12 - 12² = 96
f(14) = 20 · 14 - 14² = 84
f(16) = 20 · 16 - 16² = 64
f(18) = 20 · 18 - 18² = 36
A ≈ 2 · (0 + 36 + 64 + 84 + 96 + 100 + 96 + 84 + 64 + 36)
A ≈ 1320
And using infinite rectangles:
A ≈ [(b - a) / n] · ∑ f[a + i · (b - a) / n]
A ≈ (20 / n) · ∑ [20 · (20 / n) · i - (20 / n)² · i²]
A ≈ (20 / n) · ∑ [400 · i / n - 400 · i² / n²]
A ≈ ∑ (8000 · i / n² - 8000 · i² / n³)
A ≈ (8000 / n²) · ∑ i - (8000 / n³) · ∑ i²
A ≈ (8000 / n²) · [n · (n + 1) / 2] - (8000 / n³) · [n · (n + 1) · (2 · n + 1) / 6]
A ≈ (8000 / n²) · [(n² + n) / 2] - (8000 / n³) · [(n² + n) · (2 · n + 1) / 6]
A ≈ 4000 · (n² + 2) / n² - (8000 / n³) · [(2 · n³ + 3 · n² + n) / 6]
A ≈ 4000 · (1 + 2 / n²) - (4000 / 3) · [2 + 3 · (1 / n) + (1 / n²)]
As n → + ∞, then:
A ≈ 4000 - 8000 / 3
A ≈ 1333.333
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Let your dependent variable in the function be y. Write the function that models the independent variable in terms of y, using logarithms.
Function: [tex]f(x)=2.56(1.04)^x[/tex]
Answers
The function that models the independent variable, x, in terms of y, is:
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
How to write the independent variable in terms of y?
Here we have the relation:
[tex]y = 2.56*(1.04)^x[/tex]
We want to write x in terms of y, so we just need to isolate x.
We have:
[tex]\frac{y}{2.56} = (1.04)^x[/tex]
Now we can apply the natural logarithm in both sides, so we get:
[tex]ln(\frac{y}{2.56}) = ln((1.04)^x)\\\\ln(\frac{y}{2.56}) = ln((1.04))*x[/tex]
Now we can just isolate x.
[tex]x = ln(\frac{y}{2.56})/ln(1.04)[/tex]
That is the function that models the independent variable, x, in terms of y.
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URGENT PLEASE ANSWER THESE
Answers
The distance of the cruise liner from me 20 seconds later will be; 2600ft.
How far will the cruise liner be in 20 seconds?a) Since, the speed of the liner is 30ft/sec, it follows that after 20secs, the liner would cover; (30×20)ft = 600ft more; and consequently, the distance is now; √(2000²+600²) = ft.
b) For the boat to be 2500 ft away given the speed 30ft per sec; Time taken = 2500/30 = 83.3seconds. Hence, the boat will be more than 2500 feets away after 2 minutes.
c) If the boat's distance is 2000ft from me; it follows that the distance covered is 10 seconds is; √(2000²-1500²) = 1322.9ft
Hence, the speed to attain this distance is; 1322.9/10 = 132.29ft/sec.
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PLEASE ANSWER QUICKLY
Answers
Answer:
Option (4)
Step-by-step explanation:
See attached image.
Solve the following linear system algebraically. State why you chose the method you used.
x + 3y = 7
2x + 4y = 11
Answers
There are two methods of solving systems of equations:
substitutioneliminationSubstitution is where we substitute one equation into the other by isolating a certain variable, or a group of terms.
Elimination is where we subtract the two equations. Before doing this, we may have to multiply one equation by a certain number to make sure one variable cancels out.
Solving the QuestionWe're given the following equations:
[tex]x + 3y = 7[/tex][tex]2x + 4y = 11[/tex]Because they are organized in the same manner (i.e. x [operation] y [equals] number), it is easier for us to use elimination.
First, multiply the first equation by 2:
[tex]x + 3y = 7\\2(x + 3y) = 2(7)\\2x + 6y = 14[/tex]
Now, subtract the second equation from the one we just created:
[tex]\hspace{10}2x + 6y = 14\\-2x + 4y = 11\\\rule{67}{0.3}\\2y=3[/tex]
Solve for y:
[tex]y=\dfrac{3}{2}[/tex]
To solve for x, we can use substitution in the first equation:
[tex]x + 3y = 7\\\\x + 3(\dfrac{3}{2}) = 7\\\\x + \dfrac{9}{2} = 7\\\\x = 7- \dfrac{9}{2}\\\\x = 7- 4.5\\\\x = 2.5\\\\x=\dfrac{5}{2}[/tex]
Answer[tex]x=\dfrac{5}{2}[/tex]
[tex]y=\dfrac{3}{2}[/tex]
What is the reason for statement 7 in the given proof?
A) definition of midpoint
B) definition of slope
C) parallel lines have equal slopes.
D) using point-slope formula
Answers
Answer: definition of slope
Step-by-step explanation:
The results in step 7 come from substituting the coordinates into the slope formula.
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
Answers
The predicted value of y when x =7 is -8.5
How to predict the y value?Start by drawing the line of best fit through the points
See attachment for the graph.
From the attached graph, we have the following value
y = -8.5 when x = 7
Hence, the predicted value of y when x =7 is -8.5
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At a restaurant, Lana gets a bill that is $40 for the food plus a 5% sales tax. Lana decides to tip 20% on the total bill. How much will Lana pay in total?
Answers
Answer:
$50.40
Step-by-step explanation:
To find how much Lana will pay in total follow these steps.
First, multiply 40 by 1.05.
40×1.05=42.
This is how much she will pay for the food plus tax.
Now, multiply 42 by 1.2.
42×1.2=50.40
This is how much she will pay for the food, tax, and tip.
Lana will pay a total of $50.40.
Hope this helps!
What is the maximum number of consecutive odd positive integers that can be added together before the sum exceeds $401$
Answers
The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
According to the statement
We have a given that the maximum sum of the positive integers is 400.
And we have to find the value of n which is a maximum number of integers by which the value of sum become 400.
So, to find the value of the n we use the
A.P. Series'Summation formula
According to this,
S = n (n+1)/2
Here the value of s is 401
Then
S = n (n+1)/2
401 = n (n+1)/2
401*2 = n (n+1)
802 =n (n+1)
n (n+1) = 802
n^2 + n -802 =0
By the use of the Discriminant formula the
value of n becomes n = -28 and n = 27.
The negative value of n is neglected.
Therefore the value of n is 27.
So, The maximum number of integers is 27 that can be added together before the summation of the A.P. Series exceeds 401.
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X: -1/2
-6(x-2)
pls i need a result
Answers
Answer:
15
Step-by-step explanation:
First, we can plug -1/2 into the equation and get -6(-1/2 -2). Then, we can convert -2 into a fraction to get -4/2. If we subtract -4/2 from -1/2, we get -6(-5/2). We then multiply this and get 30/2 which simplifies to 15
If f(-1) for the polynomial….
Answers
Answer:
Yes ,because (x+1) is the factor of all degree 4 polynomial
. Distribute the among the atoms, giving ( for hydrogen) to as many atoms as possible. First get electrons atoms, then atoms.
Answers
Answer:
Bonding theories predict
Step-by-step explanation:
how atoms bond together to form compounds. They predict what combinations of atoms form compounds and what combinations do not. Bonding theories explain the shapes of molecules, which in turn determine many of their physical and chemical properties
Write an equation of a line in slope intercept form going through the points (1,6) and (3,0)
Answers
Answer:
y = -3x + 9
Step-by-step explanation:
The slope is
[tex] \frac{6 - 0}{1 - 3} = - 3[/tex]
Substituting into point-slope form, we get
y = -3(x-3)
y = -3x + 9
The volume of the cylindrical water tank shown below is 490π feet^3. If the tank is 10 feet high, what does its radius r equal?
Answers
The cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of 7 feet.
The volume of a cylinder having a radius of r units, and a height of h units, is given by the formula, V = πr²h.
In the question, we are asked to find the radius (r), of a cylindrical water tank, with a volume of 490π feet³, and a height of 10 feet.
Substituting the value of V = 490π feet³, and h = 10 feet, in the formula for the volume of a cylinder, V = πr²h, we get:
490π feet³ = π.(r²)(10 feet).
Rearranging this, we can write:
r² = (490π)/(10π) feet²,
or, r² = 49 feet²,
or, r = √49 feet,
or, r = 7 feet.
Thus, the cylindrical water tank with a volume of 490π feet³, and a height of 10 feet, has a radius of 7 feet.
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In the given circle the m∠DFB is 41°, mArc EF is 52° what is the m∠C ?
Answers
Check the picture below.
The requried measure of the angle m∠C in the given circle is 15°.
In the given circle the m∠DFB is 41°, mArc EF is 52°
To find out the measure of the angle m∠C.
Following the properties of arcs in the circle,
arc BD = 2m∠BFD
arc BD=2*41 = 82
Now we know that,
The angle subtended by two sectants drawn from the single point that lies outside the circle is given by the difference in larger and minor arcs divided by 2.
∠c= BD- EF / 2
∠c = 82°-52°/2
∠c = 15°
Thus, the requried measure of the angle m∠C in the given circle is 15°.
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a vendor sold 25 dozens of mangoes. He was able to sell 3/5 of the total number of mangoes at 15.50 pesos and the remaining at 19.00 pesos each. How much was the total sales?
Answers
Answer: 422.5
Step-by-step explanation: To find how many mangoes were sold at 15.50 pesos, find 3/5 of the total number of mangoes. 3/5 of 25 is 15 because 3 (numerator) times 25 (mangoes) divided by 5 (denominator) is 15. 15 times 15.50 (price) is 232.5 pesos. Next we take the remaining mangoes (10) and multiply it by the price (19) to get 190 pesos. Add the sales and you get 422.5 pesos.
Answer:
422.50 pesos total
Step-by-step explanation:
3/5 ths of 25 = 15
(1/5th of 25 is 5, so we can multiply that number by 3 (3)(5) to get what 3/5ths of 25 are)
So, 15 mangoes were sold at 15.50 pesos
15 × 15.50 = 232.50
(why is this multiplication?
remember that repeated addition is multiplication. We are adding the cost of each mango (15.50) 15 times, which we could write as 15.50 + 15.50... 15 times, or we could simply multiply the two values :) )
Because this vendor has sold 15 of his mangoes, he has 10 left (25 - 15 = 10), so we multiply
10 × 19.00 to find the combined cost:
10 × 19.00 = 190.00
Now, we want to find the total sale (how much money he made in total, from all 25 mangoes)
So, let's add our two values together:
232.50
+ 190.00
422. 50
So, the vendor made 422.50 pesos total from his mangoes
hope this helps! have a lovely day :)
3. A train travels 20 km at a uniform speed of 60 km/h and the next 20 km at a uniform speed of 80km/h. Calculate its average speed.
Answers
Answer:
Given,
Distance traveled = 20 km
Speed = 60 km/h
So, timetaken=DistanceSpeed=2060=13h
For the next journey
Distance traveled = 20 km
Speed = 80 km/h
So, timetaken=DistanceSpeed=2080=14h
Now,
Total distance traveled = 20 + 20 = 40 km
Total time taken = 13+14=712
We know,
Averagespeed=TotaldistancetraveledTotaltimetaken=40712=68.5 km/h
Hence the average speed of the train is 68.5 km/h
The probability of an outcome being more than three standard deviations away from the mean in a normal distribution is approximately ___ percent.
Answers
The probability in a normal distribution is approximately 90% percent.
According to the statement
we have given that the
Probability of the more three standard deviations and we have to find the percentage in a normal distribution.
We know that the
A normal distribution is a type of continuous probability distribution for a real-valued random variable.
So, In the presence of a more than three standard deviations the normal distribution is about 95%.
Because in the normal distribution is 95% due to the empirical rule.
The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.
So, The probability in a normal distribution is approximately 90% percent.
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Drag each expression to the correct location on the table.
Simplify each exponential expression using the properties of exponents and match it to the correct answer.
Answers
An exponential expression is one in which a number has been raised to a certain power.
What is an exponential expression?An exponential expression is one in which a number has been raised to a certain power.
Now;
1) 3^2 . (3^3)^2 . 3^-8 = 3^2 + 6 - 8= 3^0 = 1
2) (3^2) (2.3)^-3/2^-2 = 3^2 . 2^-3 . 3^-3/2^-3 = 1/3
3) (2^-1) . (3 . 2)^4/(3 . 2)^3 = 2^-1. 3^4 . 2^4/ 3^3. 2^3 = 3
4) 2^5 . 3^5 . 6^-5 = 32 * 243/7776 = 1
5) (2^3) . (2 . 3)^-1/2^2 = 2^3 . 2^-1 . 3^-1/2^2 = 1/3
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(6. Factorise:
(a) 4a²-28ab-a+7b
(b) 2a²-366²
(c) 12ce-9c-8de+6d
(d) a² +b²+2ab-2a-2b-3
(e) 5-45a²
(f) p(y-2)-q(z-y)
(g)
³-y²z-y₂² +2³
J
Answers
Answer:
a. 1ab (4 -28+7)
b 2(a² - 183²)
c. cde(12-9-8+6)
d ab(a+b +2 -2-2 -3)
e 5(1- 9a²)
f py- 2p - qz -qy
pqy (1 - 2 -z -1)
WILL GIVE BRAINLIES!! How can one data display be used to create a data display of a different form?
Answers
The method whereby data display can be used to create a data display of a different form is as done below.
How to create a programming model?To answer this question means we are trying to create a view page where we need to display data as well as a form to insert data.
Now, for us to insert data we can use a bootstrap modal which is;
public ActionResult GetFirm()
{
return View(db.FirmModels.ToList());
}
The view page would be given and then the way to do it is;
Pass a list to the view and define your view model as:
model IEnumerable<models.FirmModel>
The IEnumerable interface is implementing the GetEnumerator() method used to iterate through the collection.
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the product of 1540 and m is a square number. find the smallest possible value of m
Answers
Answer:
Step-by-step explanation:
the smallest value is 96.25 or rounded to the nearest whole number it is 96
what i did was put in my calculator 1540 divided by 4^2 because it is squared and has 4 sides