Using the direct and inverse variations, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
What is proportionality constant?The ratio between two proportional quantities' constant values is known as the constant of proportionality. When either their ratio or their product gives a constant, two changing values are said to be in a proportionate relationship. The Direct Variation and Inverse Variation types of proportions between the two provided values determine the proportionality constant's value.
Given that the time t needed to paint a fence varies directly as the length L and inversely as the number of workers w.
This is represented as follows:
t = k(l/p)
Where, k is the proportionality constant.
Given that, it takes 10 hours to paint 400 feet of fence with six workers.
Substitute the value of t = 10, l = 400 and w = 6 in the equation we have:
10 = k (400 / 6)
10 = k (66.66)
k = 10 / 66.66
k = 0.15
Now, for or 10 workers to paint 1000 ft fence, take l = 1000, w = 10, and k - 0.15:
t = (0.15) (1000 / 10
t = (0.15) (100)
t = 15
Hence, the time taken by 10 workers to paint a fence of 1000 ft is 15 hours.
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A polynomial function is represented by the data in the table.
Choose the function represented by the data.
f(x) = −14x − 11
f(x) = −12x + 1
f(x) = 2x2 + 1
f(x) = x2 − 6x + 1
find the length x. round to the nearest tenth
The numerical value of to the nearest tenth is 14.3.
What is the value of x ?From the diagram, we have a right angle triangle.
Angle Ф = 40 degreeOpposite to angle 40 degree = 12Adjacent to angle 40 degree = xUsing trig ratio, Tangent = Opposite / Adjacent.
Hence;
tan( Ф ) = Opposite / Adjacent
Plug in the given values and solve for x
tan( 40° ) = 12/ x
tan( 40° ) × x = 12
x = 12 / tan( 40° )
x = 12 / 0.8390996
x = 14.3
Therefore, the value of x is approximately 14.3.
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The post office’s human resources manager wants to determine an optimal hiring plan. Day Number of full-time employees required 1 = Monday 17 2 = Tuesday 13 3 = Wednesday 15 4 = Thursday 19 5 = Friday 14 6 = Saturday 16 7 = Sunday 11 Union rules state that each full-time employee must work 5 consecutive days and then receive 2 days off. Formulate an IP to minimize the number of fulltime employees who must be hired, and solve it using Excel Solver to find the optimal solution
Here is a simple framework to model the problem as an Integer Programming (IP) problem and solve it using Excel Solver:
Define decision variables:Let x(i,j) be the number of full-time employees assigned to work on day i (1 <= i <= 7) and given day off on day j (1 <= j <= 7).
Set constraints:a. Work days constraint: For each day i, the number of employees working must meet the demand:
∑(j=1 to 7) x(i,j) = demand(i) (1 <= i <= 7)
b. Availability constraint: Each employee can work only 5 consecutive days, so for each day j (1 <= j <= 7), the number of employees given day off on day j must be less than or equal to the number of employees working on day j-5:
∑(i=1 to 7) x(i,j) <= ∑(i=j-5 to j-1) x(i,j-5) (1 <= j <= 7)
Set objective:The objective is to minimize the total number of full-time employees hired, so the objective function is:
minimize: ∑(i=1 to 7) ∑(j=1 to 7) x(i,j)
Solve using Excel Solver:Excel Solver can be used to find the optimal solution to the IP problem. The constraints and objective function should be set up in the spreadsheet, and Solver should be configured to use the integer constraint option. The solution will give the optimal number of full-time employees hired and their assignment on each day.
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the average weekly work hours of full-time u.s. workers have approximately a normal distribution with mean 37 hours and standard deviation hours. suppose 200 u.s. citizens are randomly chosen. find an approximate probability that less than 10 of them are working more than 50 hours a week on average (round off to third decimal place).
The approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.019
We can use the normal distribution to approximate the probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average.
To do this, we have to standardize the variable by subtracting the mean and dividing by the standard deviation.
In this case, X = (50 - 37) / hours = 1.83
We know that for a standard normal distribution, the probability of X being less than a certain value can be found using a standard normal table or a calculator with a built-in standard normal cumulative distribution function (CDF).
Now, we will use the cumulative distribution function to find the probability of less than 10 out of 200 working more than 50 hours a week on average. Using a standard normal table or calculator, we can find the probability of having X < -2.04.
P(X < -2.04) = 0.0188
So the approximate probability that less than 10 out of 200 U.S. citizens are working more than 50 hours a week on average is 0.0188 which rounding it off to the third decimal place we get 0.019.
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Solve 35 / 2 using an area model. Use long division and the distributive property to record your work
Answer by solving the expression 35 /2 using different methods are:
a. Area model : 35 /2 can be expressed as 17. 5 + 17.5 .(attached figure)
b. Long division method : 35 /2 = 17 + 1/2
c. Distributive property expressed as 35/2 = ( 34 + 1 ) × 1/ 2.
a. Area model.
Expression 35 /2 solved by area model is attached in the figure.
One part of 35 is divided into two parts each of 17.5 .
17.5 + 17.5 = 35
b. Long division.
How many 2's are there in 3
Answer is 1.
3−1⋅2=3−2=1
Write down the next digit of the dividend.
How many 2's are there in 15
Answer is 7
15−7⋅2=15−14=1.
( 35 /2 ) = 17 + ( 1/2)
c. Distributive property
35 /2
= ( 34 + 1 ) × 1/ 2
= 34 /2 + 1 /2
= 17 + 1 /2
= 17 + 0.5
= 17.5
Therefore, the solution of 35/2 using different methods are:
a. Using area model : 17.5 + 17.5 represent 35/2.
b. long division : 35 /2 = 17 + 1/2
c. Distributive property: 35/2 = ( 34 + 1 ) / 2
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Jaxson bought a pair of sunglasses online for $66. He used a coupon code to
get a 30% discount. The website also applied a 15% processing fee to the price
after the discount. How much was the discount, in dollars and cents?
The discount was 17 dollars and 87 cents.
What is a discount?
A discount is a reduction in the price of a product or service. It can be offered for a variety of reasons, such as to encourage sales or to reward loyal customers.
We have,
price of pair of sunglasses for $66,
coupon code discount of 30%,
15% processing fee to the price.
The final price is:
$66 * (1 - 30%) * (1 + 15%)
$66 * 0.7 * 1.15
$53.13
So, the actual discount is,
$(71 - 53.13)
= $17.87
Hence, the discount was 17 dollars and 87 cents.
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how many 6-digit numbers (leading zeros are allowed) contain exactly one 3, one 4, and one 5 as digits? g
246960 6-digit numbers contain exactly one 3, one 4, and one 5 as digits.
There are a total of 6 digits that make up any of the numbers in 0 to 999999 with the given condition
The total numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
This can be represented as UVWXYZ
Digit 3 can occupy any of the 6 positions
Digit 4 can occupy any of the (6 - 1) positions
Digit 5 can occupy any of the (6 - 2) positions
The remaining 7 digits will occupy the last 3 positions in the following ways:
The first of the 7 digits can be selected from any of 7 ways
The second can be selected from any of 7 ways
The third can be selected from any of 7 ways
So, the total number of selection is:
= 6 × 6 × (6 - 1) × (6 - 2) × 7 × 7 × 7
= 36 × 5 × 4 × 343
= 246960
Therefore there are 246960 numbers.
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Rectangle URST undergoes a dilation centered at the origin. The result is rectangle U'R'S'T'. Which rule describes the dilation? A) (x, y) → (2x, 2y) B) (x, y) → (3x, 3y) C) (x, y) → ( 1 2 x, 1 2 y) D) (x, y) → (− 1 2 x, − 1 2 y)
Option A, (x,y) → (2x,2y) This rule describes an origin-centered stretch with a factor of 2. That is, the image doubles its original size in both the x and y directions.
The new rectangle is similar to the original, but with larger dimensions, so the correct rule is A) (x, y) → (2x, 2y).
In this case, the rule described in option A) (x, y) → (2x, 2y) specifies that the image is twice the size of the original rectangle in both the x and y directions increase. This means that the scale factor is 2. This will result in a similar shape but with larger dimensions. This is the correct rule describing stretching the rectangle URST to the rectangle U'R'S'T'.
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how to graph y=2x+1
-2x=y=-2
Answer:
For y=2x+1
The line y=2x+1 has a y-intercept of +1, so begin with a point at (0,1)
and its slope is 2/1, which means from there you go Up 2 and Right 1.
Follow that pattern until you can draw a straight line through all the points.
For -2x=y=-2
In this point it only passes (0,2) and (1.0)
Have a wonderful day! :-)
8112 equals 2 ^ 4 times 3 times 13 ^ 2 find the value of the smallest square number that is a mutiple of 8112
The factor 3 does not occur in pair. Thus, ‘3’ is the smallest number by which 8112 should be divided to get a perfect square.
What is the lowest square number?The LCM of 8, 15, and 20 is 120. Prime factors 2, 3, and 5 do not have a pair in this case. To construct a perfect square, 120 must be multiplied by 2 x 3 x 5. As a result, the least square number divisible by 8, 15, and 20 is 3600.
The smallest square matrix is 2 2 2 2 ; there is no theoretical limit to the highest size square matrix, however anything larger than 10 10 10 10 becomes impossible to manage numerically.4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, and 961
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Determine whether each set of side lengths could be the sides of a right triangle.
The side length that could be a right triangle are
6 8 105 12 13How to find out side lengths of right triangleApplying Pythagoras theorem, for each side length we solve for the longest side in each case assuming the longest side is x
Using Pythagoras theorem given by the the formula
hypotenuse² = opposite² + adjacent²
checking for 4 7 8
let x be the required distance
x² = 4² + 7²
x² = 16 + 49
x² = 65
x = √65
this is not a right triangle
checking for 6 8 10
let x be the required distance
x² = 6² + 8²
x² = 36 + 64
x² = 100
x = √100
x = 10
this is a right triangle
checking for 5 12 13
let x be the required distance
x² = 5² + 12²
x² = 25 + 144
x² = 169
x = √169
x = 13
this is a right triangle
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In the parallelogram above, AE = 7x+4, BE=15x-12, and DE= 9x. What is the length of BD?
Answer:
BD = 36
Step-by-step explanation:
• the diagonals of a parallelogram bisect each other , so
BE = DE , that is
15x - 12 = 9x ( subtract 9x from both sides )
6x - 12 = 0 ( add 12 to both sides )
6x = 12 ( divide both sides by 6 )
x = 2
Then
BD = BE + ED
= 15x - 12 + 9x
= 24x - 12 ( substitute x = 2 )
= 24(2) - 12
= 48 - 12
= 36
I buy 4 gallons of milk at the grocery store. Each gallon sells for $3. 50. Is this relationship a function? Justify your claim
Yes, this relationship is a Funtion.
The relationship between the no of gallons of milk purchased and the total cost can be represented by this equation:
y = 3.5x
where y is the total cost and x represents the number of gallons of milk purchased. A function is a collection of ordered pairs (x, y) with exactly one value of y for each value of x. for each input (x), just one output (y) is created.
In this situation, there is only one equivalent value of y for each value of x .We may see this by putting different value of x into the equation and get ing a different result for y.
For example, when x = 1, y = 3.5 ×1 = 3.5
when x = 2, y = 3.5 × 2 = 7
when x = 3, y = 3.5 × 3 = 10.5
and so on.
So, the relationship between the number of gallons of milk purchased and the total cost is a Funtion.
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An airplane is headed for the airport, 15 miles away. If the airplane is at an altitude of 5000 feet, what is the angle of depression, to the nearest tenth of a degree, from the airplane to the airport? (1 mile = 5280 feet)
The angle of depression of the airplane is 3.6⁰.
What is the angle of depression of the airplane?
The angle of depression of the airplane is calculated by forming a triangle with base displacement of the airplane and the altitude.
base of the right triangle = 15 miles = 79,200 ft
height of the right triangle = 5,000 ft
The angle of depression is calculated as follows;
θ = arc tan ( h / b )
θ = arc tan ( 5000 / 79,200 )
θ = 3.6⁰
Thus, the angle of depression of the airplane is a function of the altitude and base displacement of the airplane.
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If U And V Are Orthogonal, What Is The Magnitude Of U Times V?
If U and V are orthogonal then the magnitude of U times V will be U.V = 0 or |UxV| = uv.
U and V are two orthogonal vectors.
since the angle between them is θ = 90⁰
let u and v be the magnitudes of the vectors U and V respectively.
so first dot-product: If two non-zero vectors are orthogonal than the dot product of these vectors will be zero. Dot product of two vectors is expressed by:
U.V = uv cosθ
since these vectors are orthogonal so,
U.V = uv cos90⁰ = 0
And Cross-product: Magnitude Cross product of two orthogonal vectors will be equal to product of magnitude of these vectors.
|UxV| = uv sin θ
|UxV| = uv sin 90⁰ = uv
Therefore, U.V = 0, |UxV| = uv.
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∠TWP≅
∠HGD
∠DGH
∠GHD
∠GDH
on a drive from your home to town, you wish to average 64 mph. the distance from your home to town is 88 miles. however, at 44 miles (half way), you find you have averaged only 48 mph. what average speed must you maintain in the remaining distance in order to have an
The average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph is 50.39 mph.
We have to find the average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph.
Let the speed be x.
The total average we want = 33.6 mph
The distance from your home to town = 90 miles
Time = Distance/Speed
Time = 90/33.6
At 45 miles (half way), you find you have averaged only 25.2 mph. So
Time first leg = 45/25.2
Time second leg= 45/x
Now the average speed;
45/25.2 + 45/x = 90/33.6
Subtract 45/25.2 on both side, we get
45/x = 90/33.6 - 45/25.2
After solving the ratio, we get
45/x = 0.893
Multiply by x on both side, we get
0.893x = 45
Divide by 0.893 on both side, we get
x = 45/0.893
x = 50.39 mph
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The complete question is:
On a drive from your home to town, you wish to average 33.6 mph. The distance from your home to town is 90 miles. However, at 45 miles (half way), you find you have averaged only 25.2 mph. What average speed must you maintain in the remaining distance in order to have an overall average speed of 33.6 mph?
Californians use 75 BTU of energy per home per year which is 25% less than the national average.
How many BTU does an average American household use? Show Work
Proportionately, an average American household uses 100 BTU of energy per home per year while Californians use 75 BTU, which is 25% less than the national average.
What is the proportion?Proportion refers to the ratio or relative size of a value or number compared to another.
Proportions are fractional values equated to each other.
Generally, proportions may be depicted as fractions, decimals, or percentages.
The level of energy per home per year in California = 75 BTU
The national average of BTU use = 100%
California's use = 75% (100 - 25)
Proportionately, if 75% = 75 BTU, 100% = 100 BTU (75/0.75)
Thus, the national average use of energy is expected to be 100 BTU.
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define partial products. what partial products can you use to find how many 6 bags of cat food will cost?
Partial products can be used to multiply two or more numbers.
In Mathematics, partial products mean multiplying each digit of a number with each digit of another number where each digit maintains its place value6 bags × cat food cost
The bug has friends in nearby trees.
For each description, write equations similar to Problem 2.
Assume each bug starts at the same position as the bug in Problem 2.
1. The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be x = -2 × 28
2. The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be: y = -8.1 × 3.2
3. The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
How to solve the equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
The equation when Buggo crawls did 28 minutes at a rate of -2 centimeters per minute will be:
Let x = total centimeters
x = -2 × 28
The equation when Buggy slides for 3.2 seconds at -8.1 millimeters per second will be:
Let y = ital millimeters
y = -8.1 × 3.2
The equation when Buggum creeps for 3.5 seconds and finishes at -28.5 centimeters will be 3.5x = -28.5
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Consider absolute value function f
f(x) = -2/3|x + 4|
The vertex of the function is a (minimum/maximum) at (0,4)(0,-4)(4,0)(-4,0)
For the absolute value function, the vertex is at its maximum at (-4,0).
What is function?A function is an expression, rule, or law in mathematics that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are common in mathematics and are required for the formulation of physical relationships in the sciences. A function is defined as a relationship between a set of inputs that each have one output. A function is a relationship between inputs in which each input is related to exactly one output.
Here,
The vertex for the absolute value function is at its maximum at (-4,0).
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URGENT!! HOMEWORK DUE SOON!!
The difference between two positive numbers is 50. One number is four times the other number. What are the two numbers?
The two missing positive numbers are; 50/3 and 200/3
How to solve algebra word problems?The difference between two positive numbers is 50. Let the two numbers be x and y and as such we have;
x - y = 50 -----(1)
One number is four times the other number. Thus;
x = 4y -----(2)
Put 4y for x in eq 1 to get;
4y - y = 50
3y = 50
y = 50/3
Thus;
x = 4(50/3)
x = 200/3
We conclude that x and y above are the two positive numbers.
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Nick is splitting 3 quarts of ice cream with 15 members of thw team. If the ice cream is split evenly how many cups will each person get 1 quart equals=
whixh equals = _cups
so 3 quarts equaks _cups divibg thw ice cream among _ people means each gets _ cups
1 quart equals 2 pints, which equals 4 cups, so 3 quarts equals 12 cups. Dividing the ice cream among 15 people means each gets 1 3/12 cup(s).
Nick has 3 quarts of ice and he wants to split it with 15 members of the team.
To solve this, we have to convert quarts to cups. We have that:
1 quart = 2 pints
and 1 pint = 2 cups
This means that:
1 quart = 2 × 2 cups
1 quart = 4 cups
So, 3 quarts will be:
3 quarts=3 × 4
3 quarts =12
Therefore, dividing the ice cream among 15 people would mean that we have to divide 12 cups by 15 people.
That is:
= 15/12
= [tex]1\frac{3}{12}[/tex]
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The complete question is:
Nick is splitting 3 quarts of ice cream with 15 members of the team. If the ice cream is split evenly, how many cups will each person get?
Explain 1 quart equals _ pints, which equals _ cups, so 3 quarts equals _ cups. Dividing the ice cream among _ people means each gets _ cup(s).
Convert 4 liters into gallons. Round your answer to the nearest hundredth.
*Note: you must use these exact conversion factors to get this question right.
1 cup (cup) = 8 fluid ounces (fl oz)
1 liter (L) 1000 milliliters (mL)
1 pint (pt) = 2 cups (cups)
1 cubic meter (m³) = 1000 liters (L)
1 quart (qt) = 2 pints (pt)
1 gallon (gal) = 3.785 liters (L)
1 gallon (gal) = 4 quarts (qt)
1 fluid ounce (fl oz) = 29.574 milliliters (ml)
1 cubic foot (ft³) = 7.481 gallons (gal)
Answer:
= (blank) gallons
Use the graph of the parabola to fill in the table.
PLEASE HURRY
a) Upwards
b) x = -1
c) (-1,-9) (-1,-9)
d) Intercepts of x; and (2, 0) (-4,0)
is y intercept (0,-8)
What is intercept calculation?a) The parabola, as seen, faces upward.
b) To identify the point through the parabola's vertex that precisely divides the parabola into two equal sections, we look at the plot of the graph.
The place where the line has an x-value of -1 is where the axis of symmetry's equation is located.
d) In this case, the vertex marks the circle's lowest point.
As we can see, this is the location where the axis of symmetry passes to divide the parabola symmetrically.
The location's coordinates are as follows:
(-1,-9)
The intercepts (d)
The parabola crosses the x-axis at two places, which are known as the x-intercept.
We have 2 and -4 for this point.
the coordinates of the x-intercepts are (2,0) and
In terms of the y-intercept, it is the y-coordinate of the location where the parabola crosses the y-axis.
The Complete Question.
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find the measure of each interior angle and each exterior angle of a regular 45-gon.
The measure of each interior angle is calculated to be 172° and each exterior angle is calculated to be 8°.
Each interior angle in a polygon can be calculated using the formula, (n - 2) ×180°/n
where, n is the polygon's number of vertices.
So, each exterior angle can be calculated as, 180 - (n - 2) 180°/n
Now, let us put the number of vertices into these formulae,
Each interior angle = (45 - 2)×180°/45 = 43×180°/45 = 172°
Each exterior angle = 180 - (45 - 2) 180°/45 = 8°
So, the interior angle is 172° and the exterior angle is 8°.
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in a sample of 2000 people, 430 people have their ears pierced. two unrelated people are selected at random without replacement, find the probability that neither of the people have their ears pierced.
The probability that neither of the people have their ears pierced is 0.6157
What is the probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain.
The probability of A happening is the number of people who do not have their ears pierced divided by the total number of people in the sample, which is:
P(A) = (2000 - 430) / 2000 = 1570 / 2000 = 0.785
The conditional probability of B given A is the number of people who do not have their ears pierced and are still available to be selected as the second person divided by the total number of people available to be selected as the second person, which is:
P(B|A) = (2000 - 430 - 1) / (2000 - 1) = 1569 / 1999 = 0.7845
Therefore, the probability that neither of the people have their ears pierced is:
P(A) * P(B|A) = 0.785 * 0.7845 = 0.6157
Hence, the probability that neither of the people have their ears pierced is 0.6157
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Target is having a sale, Every item in the store is 20% off the orignal price . if a tvs oringal price is 250$ , what was the sale price
The final sales price is equal to $200.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to decrease 250 dollars by 20 percent (20%), we would have to multiply the given amount of money by 80 percent (80%) because it denotes a percentage decrease:
Percentage decrease = 250 × 80/100
Percentage decrease = 250 × 0.8
Percentage decrease = $200.
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Let S(t) be the number of students enrolled in a school district in terms of the number of years, t, after 2000.
Which statements regarding function S are true? Select TWO that apply.
Answer:
S(t) is a function, because there is a unique output value (number of students) for each input value (number of years after 2000)
S(t) can be represented by a graph, where the horizontal axis represents the number of years after 2000, and the vertical axis represents the number of students
Step-by-step explanation:
The statements regarding function S are true are:
S(5) = 2024 means there were 2024 students in 2005.
S(10)= S(5) there same number of students in 2005 and 2010.
We have function,
S(t)= 2000t
First, S(0) in 2000 means that there were 2000 students in starting.
Second, S(5) = 2024 means there were 2024 students in 2005.
Third, S(10)= S(5) there same number of students in 2005 and 2010.
Fourth, S(15)- S(10)= -40 means that there were 40 less students in 2015 than in 2010.
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Step by step. Integrated 2 Checkpoint 4 Picture Below
The value of 'x' in the equation 8 - x/x = 3/2 is x equal to [tex]3\frac{1}{5}[/tex].
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, An equation in 8 - x/x = 3/2 fractions.
Now, The LCM of both the denominators is 2x, So we'll multiply each term by 2x.
2(8 - x) = 3x.
16 - 2x = 3x.
- 2x - 3x = - 16.
- 5x = - 16.
5x = 16.
x = 16/5.
x = [tex]3\frac{1}{5}[/tex].
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