Qn2. Two functions f and g are defined as follows: f(x) = 2x – 1 and g(x) = x +4. Determine: i) fg(x) ii) value of x such that fg(x) = 20

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

The correct compound inequality to represent the scenario is:

60 ≤ 1.36x + 34 ≤ 85

To solve for x, we need to isolate it in the middle of the inequality:

60 - 34 ≤ 1.36x ≤ 85 - 34

26 ≤ 1.36x ≤ 51

Finally, we divide by 1.36 to isolate x:

19.12 ≤ x ≤ 37.5

Therefore, the recommended range of water consumption is between 19.1 and 37.5 HCF. The answer is (D) 60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

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complete question

To conserve water, many communities have developed water restrictions. The water utility charges a fee of $34, plus an additional $1.36 per hundred cubic feet (HCF) of water. The recommended monthly bill for a household is between $60 and $85 dollars per month. If x represents the water usage in HCF in a household, write a compound inequality to represent the scenario and then determine the recommended range of water consumption. (Round your answer to one decimal place.)

60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 69.1 and 87.5 HCF.

60 ≤ 1.36x − 34 ≤ 85; To stay within the range, the usage should be between 44.1 and 87.5 HCF.

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 37.5 and 44.1 HCF.

60 ≤ 1.36x + 34 ≤ 85; To stay within the range, the usage should be between 19.1 and 37.5 HCF.

Use first two points and the slope equation to find the slope:

The slope is 745.

Use the first point and point-slope equation to find the y-intercept:

The y-intercept is 500.

The slope of 745 represents the profit per month and the y-intercept of 500 represents the initial profit.

0.135 or 13.5%  is the probability that he had 3 âhits

The probability that the player had 3 hits in 5 at-bats can be calculated using the binomial probability formula, which is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where:
- P(x) is the probability of getting x hits
- n is the number of at-bats (in this case, 5)
- x is the number of hits we want to find the probability for (in this case, 3)
- p is the probability of getting a hit in one at-bat (in this case, 0.343)
- (1-p) is the probability of not getting a hit in one at-bat (in this case, 0.657)

Plugging in the values, we get:

P(3) = (5C3) * 0.343^3 * 0.657^(5-3)
P(3) = (10) * 0.039304527 * 0.4305961
P(3) = 0.134912947

Therefore, the probability that the player had 3 hits in 5 at-bats is approximately 0.135 or 13.5%.

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The integral of f(x, y) = x + y over the given curve is 8.

To integrate the function f(x, y) = x + y over the curve C: x² + y² = 4 in the first quadrant from (2, 0) to (0, 2), we will use the line integral. Since the curve is a circle, we can parameterize it using polar coordinates as follows:

x = 2cos(θ)
y = 2sin(θ)

Now, let's find the derivatives:

dx/dθ = -2sin(θ)
dy/dθ = 2cos(θ)

Next, we substitute x and y in f(x, y):

f(x, y) = 2cos(θ) + 2sin(θ)

Now, we can set up the line integral:

∫[f(x, y) * ||dr/dθ||]dθ

Since ||dr/dθ|| = sqrt((-2sin(θ))^2 + (2cos(θ))^2) = 2, the line integral becomes:

∫[2cos(θ) + 2sin(θ)] * 2 dθ

To find the limits of integration, we can use the points (2, 0) and (0, 2). In polar coordinates, these points correspond to θ = 0 and θ = π/2.

So, the line integral becomes:

∫[4cos(θ) + 4sin(θ)]dθ from 0 to π/2

Now, we can integrate and evaluate:

[4sin(θ) - 4cos(θ)] from 0 to π/2 = [4(1) - 4(0)] - [4(0) - 4(1)] = 8

Thus, the integral of f(x, y) = x + y over the given curve is 8.

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The same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.

To estimate the amount of fabric Gabby has left, we can subtract the amount of fabric she used from the amount she started with:

57878 - 3215215 ≈ -3157337

However, we can see that this result is negative, which doesn't make sense in the context of the problem. It's not possible for Gabby to have negative yards of fabric left.

It's likely that there was a mistake in the problem statement or in the numbers given. If the problem were corrected, we could use the same method of subtracting the amount of fabric used from the amount she started with to estimate the amount of fabric Gabby has left.

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Answer:

10.24 gallons

$276.48

Step-by-step explanation:

The area of the wall can be calculated by multiplying the length and height of the wall:

Area of wall = length x height = 32 x 16 = 512 square feet

To calculate the number of gallons of paint needed, we need to divide the area of the wall by the coverage of one gallon of paint:

Number of gallons of paint = Area of wall / Coverage of one gallon of paint

Number of gallons of paint = 512 / 50

Number of gallons of paint = 10.24

Therefore, it will take approximately 10.24 gallons of paint to paint the wall.

To calculate the cost of the paint, we need to multiply the number of gallons of paint by the cost per gallon:

Cost of paint = Number of gallons of paint x Cost per gallon

Cost of paint = 10.24 x $27

Cost of paint = $276.48

Therefore, it will cost $276.48 to paint the wall.

Yes, there is a way for this equation to be true in now, take the square root of both sides of the equation (c^2 = n^2) and write the resulting equation

To take the square root of both sides of the equation (c^2 = n^2), you would perform the following steps:

1. Take the square root of both sides:
√(c^2) = √(n^2)

2. Simplify the square roots:
c = n

The resulting equation is c = n.

This equation can be true if both c and n have the same value. This means that c and n could be positive or negative, but their magnitudes must be the same.

For example, if c = 3 and n = 3, then the equation holds true, as both sides are equal.

Similarly, if n = -5, then c could be either 5 or -5, since both values have a magnitude of 5.

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Answer: hopefully the image helps

Step-by-step explanation:

Answer:

First, convert R as a percent to r as a decimal

r = R/100

r = 3.5/100

r = 0.035 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 500.00(1 + 0.035/4)(4)(15)

A = 500.00(1 + 0.00875)(60)

A = $843.30

A = $843 (round-off)

The value of v in the equation is 26

The equation is given as

v= u + at

The parameters given are

u= 6

a= 10

t= 2

v= 6 + 10(2)

v= 6 + 20

v= 26

Hence the value of v in the equation is 26

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I have gotten 113

Step-by-step explanation:

The right angle triangle has three angles and the value of its two angles are 90°and30°.We need to find the third angle which is the sum of 90°and 30°subtract from 180°=60°.60° is vertically opposite to angle C. We'll be having a quadrilateral whose angles add up to 360° .Subtract the sum of the three angles from 360° and you'll get 113°

The correct number of beads is; 4 black, 8 red, and 4 blue. Option A

A molecular model is a depiction of molecules or chemical compounds made physically, visually, or mathematically in order to comprehend their behavior and characteristics. These models can range from real models made of plastic or metal to computer-generated graphics or mathematical formulae, and they can be straightforward or sophisticated.

There are four carbon atoms, eight hydrogen atoms and four oxygen atoms.

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The difference between the abscissa of P and Q is 1.

The abscissa of a point is its x-coordinate, or horizontal distance from the origin (usually measured along the x-axis).

In the given problem, the abscissa of point P is -2, which means it is located 2 units to the left of the origin on the x-axis. The abscissa of point Q is -3, which means it is located 3 units to the left of the origin on the x-axis.

To find the difference between the abscissas of P and Q, we simply subtract the abscissa of Q from the abscissa of P:

(abscissa of P) - (abscissa of Q) = (-2) - (-3) = -2 + 3 = 1

Therefore, the difference between the abscissas of P and Q is 1 unit.

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Answer:

72.5 square inches

Step-by-step explanation:

See attachment.

The areas of the 2 shapes are in blue, but when added together:

60+12.5=72.5

Hope this helps!

Determine whether the two figures are similar: D. No, the two figures are not similar.

In Geometry, two (2) quadrilaterals are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.

Additionally, two (2) geometric figures such as quadrilaterals are considered to be congruent only when their corresponding side lengths are congruent (proportional) and the magnitude of their angles are congruent;

Ratio = 12/8 = 10/6 = 10/6

Ratio = 3/2 ≠ 5/3 = 5/3

In conclusion, the two figures are not similar because the ratio of their corresponding sides is not proportional.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The approximate values of y at x = 0.1, 0.2, 0.3, and 0.4 are all equal to y1 = y2 = y3 = y4 = 0.5, as we only used the first step of Euler's method.

We can use Euler's method with a step size of 0.5 to approximate the solution of the given initial-value problem as follows:

First, we need to find the slope at the initial point (0, -3):

y' = 1 - 2x - 2y

y'(0, -3) = 1 - 2(0) - 2(-3) = 7

Using Euler's method, we can approximate the solution at x = 0.5:

y(0.5) ≈ y(0) + hy'(0, -3) = -3 + 0.57 = 0.5

Next, we can use the approximate value y(0.5) to approximate the solution at x = 1:

y(1) ≈ y(0.5) + hy'(0.5, 0.5) = 0.5 + 0.5(1 - 2(0.5) - 2(0.5)) = -0.5

Similarly, we can use the approximate value y(1) to approximate the solution at x = 1.5:

y(1.5) ≈ y(1) + hy'(1, -0.5) = -0.5 + 0.5(1 - 2(1) - 2(-0.5)) = -1.25

Finally, we can use the approximate value y(1.5) to approximate the solution at x = 2:

y(2) ≈ y(1.5) + hy'(1.5, -1.25) = -1.25 + 0.5(1 - 2(1.5) - 2(-1.25)) = -2.4375

Therefore, the approximate values of y at x = 0.1, 0.2, 0.3, and 0.4 are all equal to y1 = y2 = y3 = y4 = 0.5, as we only used the first step of Euler's method.

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Under the federal list, the total amount of exemptions that Jerry would be allowed is $27,900.

Under the state list, the total amount of exemptions that Jerry would be allowed is $37,500.

Under the federal list, Jerry's exemptions can only be be:

Equity in home:                     $15,000

Motor vehicle:                        $2,400

Household goods:                  $8,000

Tools (for debtor’s trade):       $1,500

Total exemptions              =   $27,900

Under the state list, Jerry's exemptions can only be be

Equity in home:                               $25,000

Motor vehicle:                                $1,500

Household goods:                          $6,000

Tools:                                               $5,000

Total exemptions =                       $37,500

Based on the above, the state list can be more favorable for Jerry as it will give him  a lot of exemption a higher total value of assets.

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See full question below

Computing Exemptions Under Chapter 7 Bankruptcy

Assume the current federal bankruptcy exemptions are listed at the left, and the state exemptions are

listed at the right. The debtor may use the exemption table that best benefits him or her. For the two

circumstances shown below, compute the exemption amounts and decide which will be better for the

debtor—the federal list or the state list.

LIST A. FEDERAL EXEMPTIONS

Equity in home .......................................$15,000

Motor vehicle .............................................2,400

Household goods .......................................8,000

($400 limit for a single item)

Jewelry .......................................................1,000

Other property ..............................................800

Tools (for debtor’s trade) ...........................1,500

LIST B. STATE EXEMPTIONS

Equity in home ....................................... $25,000

Motor vehicle ............................................. 1,500

Household goods ..................................... 10,000

($1,000 limit for a single item)

Jewelry .......................................................... 500

Other property .............................................. 100

Tools ........................................................... 5,000

1. Jerry has the following assets: a house with equity of $15,000, a car with equity of $2,500, and household goods worth $6,000 (no single item over $400). He also has tools worth $5,800 that he needs for his business. What is the total amount of exemptions Jerry would be allowed using the federal list? The state list? Which list will be more favorable for him? SHOW YOUR WORK!

The function that models this situation is f(n) = -3n + 24.

To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).

1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.

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The red car is actually traveling along the road at a speed of approximately 26.67 feet per second.

We can start by drawing a diagram of the situation:

     P (police car)

      |

      |

      |

40    |    S (stop sign)

-------|--------------------

      | 160

      |    R (red car)

Let's use the Pythagorean theorem to find the distance between the police car and the red car at any time t:

d(t)² = 40² + (160 - v*t)²

Where v is the speed of the red car in feet per second, and d(t) is the distance between the police car and the red car at time t.

We want to find how fast the red car is actually traveling along the road, so we need to find v when the distance between the police car and the red car is decreasing at a rate of 100 feet per second:

d'(t) = -100

We can take the derivative of the equation for d(t) with respect to time:

2d(t)d'(t) = 0 + 2(160 - v*t)(-v)

Simplifying and plugging in d'(t) = -100, we get:

-4000 + 2v²t = -100(160 - vt)

Solving for v, we get:

v = 80/3 ≈ 26.67 feet per second

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The depth of trail mix box that is shaped like a rectangular prism must be 2.4 inches.

We are going to use the formula for determining volume to work out the depth of the rectangular prism.

The volume of a rectangular prism is given by the formula:

V = l × w × h

where:

V = the volume

l = the length

w = the width

h = the height.

Given:

w = 7.5 inches

h = 9 inches

V = 162 cubic inches

Now, we are to find the value of d, the depth of the box, which corresponds to the length of the rectangular prism.

Substituting the values into the formula for volume:

162 = d × 7.5 × 9

Simplifying the right-hand side:

162 = 67.5d

Dividing both sides by 67.5, we get:

d = 162 ÷ 67.5

d = 2.4 inches

Therefore, the depth of the box shaped as rectangular prism = 2.4 inches.

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The unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is

:
y(x) = [-(6x⁸ - 64)]¹/³

Determine the unique solution?

To determine the unique solution, y(x), to the given differential equation with initial condition y(0) = 4, we first need to separate the variables and integrate both sides with respect to x and y, respectively.

dy/y⁴ = 8x⁷ dx

Integrating both sides, we get:

-1/3y³ = 2x⁸ + C

where C is the constant of integration.

Now we can use the initial condition y(0) = 4 to solve for C:

-1/3(4)³ = 2(0)⁸ + C

C = -64/3

Substituting C back into the previous equation, we get:

-1/3y³ = 2x⁸ - 64/3

Multiplying both sides by -3 and taking the cube root, we get:

y(x) = [-(6x⁸ - 64)]¹/³

Therefore, the unique solution, y(x), to the given differential equation with initial condition y(0) = 4 is:

y(x) = [-(6x⁸ - 64)]¹/³

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According to the question the  graph the line -3x + 5y = 15, we can start by solving for y:

-3x + 5y = 15

5y = 3x + 15

y = (3/5)x + 3

As an algebraic framework that depicts a specific function by joining a collection of points, a graph is defined. It establishes a pairwise connection among the items. The graph is made up of nodes (vertices) linked by edges. (lines).

Briefing :

Now we have the equation in slope-intercept form (y = mx + b) where the slope is 3/5 and the y-intercept is 3.

To graph the line, we can start at the y-intercept (the point (0, 3)) and then use the slope to find additional points. Since the slope is 3/5, we can move up 3 units to the right 5 units to get to the point (5, 6), and down 3 units to the left 5 units to get to the point (-5, 0). Connect these points to get the line.

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There are 42 yellow skittles in the box.

Based on the given information, we know that the ratio of green skittles to yellow skittles is 5:7. This means that for every 5 green skittles, there are 7 yellow skittles.

To find out how many yellow skittles are in the box, we need to know how many sets of 5 green skittles there are. We can do this by dividing the total number of skittles in the box (30) by 5 (since there are 5 green skittles for every set).
30 ÷ 5 = 6

This means there are 6 sets of 5 green skittles in the box.

Now we can use the ratio of 5:7 to find out how many yellow skittles there are in each set:
5 green skittles : 7 yellow skittles

Since there are 7 yellow skittles in each set, we can find the total number of yellow skittles by multiplying 7 by the number of sets (6):
7 x 6 = 42

There are 42 yellow skittles in the box.

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A.  The number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.

B. The number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.

What is combinatorics?

Combinatorics is a branch of mathematics that deals with counting and arranging the possible outcomes of different arrangements and selections of objects.

For part (a), the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is given by the product of the number of shortest lattice paths from (2, 2) to (8, 10) and from (8, 10) to (11, 11).

To find the number of shortest lattice paths from (2, 2) to (8, 10), we can count the number of ways to choose 6 steps up out of 8 total steps (the remaining 2 steps are to the right), which is 8 choose 6 = 28.

Similarly, the number of shortest lattice paths from (8, 10) to (11, 11) is the number of ways to choose 1 step up out of 4 total steps (the remaining 3 steps are to the right), which is 4 choose 1 = 4.

Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10) is 28 * 4 = 112.

b) To find the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10), we can use the principle of inclusion-exclusion.

Let's first count the number of shortest lattice paths from (2, 2) to (11, 11) without any restrictions. Since we can only move up or to the right, the number of such paths is the number of ways to choose 9 steps up out of 18 total steps (the remaining 9 steps are to the right), which is 18 choose 9 = 48620.

Next, we count the number of shortest lattice paths from (2, 2) to (11, 11) that pass through (8, 10). Using the method described in part (a), we found that the number of such paths is 28 * 4 = 112.

Therefore, the number of shortest lattice paths from (2, 2) to (11, 11) that avoid (8, 10) is the total number of paths minus the number of paths that pass through (8, 10), which is 48620 - 112 = 48508.

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Step-by-step explanation:

the answer will be "15" according to the question.

We need to make some assumptions. Let's assume that the survey allowed students to choose one favorite hobby and that bike riding was one of the options.

We also need to know the percentage of students who chose bike riding as their favorite hobby. If this information is not given, we cannot accurately estimate the number of students who would say that bike riding is their favorite hobby.

Suppose that 30% of the surveyed students chose bike riding as their favorite hobby. To find out how many students this represents, we can use the following formula:

Expected number of students = Percentage of students x Total number of students surveyed

Plugging in the values we have, we get:

Expected number of students who say bike riding is their favorite hobby = 0.30 x 60 = 18

Therefore, we can expect that approximately 18 of the 60 seventh-grade students surveyed would say that bike riding is their favorite hobby, based on the assumption that 30% of the students chose this option.

It's important to remember that this is just an estimate based on the information we have. The actual number may be different depending on the survey results.

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Hello beautiful people! I hope you're all doing well today. As for me, I'm feeling great and ready for the weekend! I plan on spending some quality time with my loved ones, exploring new places, and trying out new activities.

I believe that weekends are meant for rest, relaxation, and rejuvenation, so I'm looking forward to taking a break from my busy work schedule.

One of the things I love about weekends is the opportunity to disconnect from the stresses of everyday life and focus on things that bring me joy. Whether it's going for a hike, trying out a new recipe, or catching up with friends over a cup of coffee, there's always something to look forward to.

this weekend I plan on making the most of my free time by doing things that make me happy and help me recharge. I hope you all have a great weekend as well, and that you find time to do the things you love with the people you care about. Remember, life is short, so let's make the most of every moment we have!

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