giving 100 points and 4 brainlist if right

Given the two functions

We are tasked to plot (F-G)(x).

The first step here is to get the resulting function (F-G)(x). We have

Now, we need to assign values of x and evaluate them at the function (F-G)(x) to get a value. We will get coordinate points and we will plot them at the cartesian coordinate plane. I will use values of x = [-3,3]. We get the following results

The plot is provided by the image below.

130 grams is equal to 0.13 kilograms.

To convert grams to kilograms, we need to know the conversion factor between the two units. There are 1000 grams in 1 kilogram. Therefore, to convert grams to kilograms, we divide the number of grams by 1000.

In this case, we have 130 grams. So, to find the equivalent number of kilograms, we divide 130 by 1000:

130 g / 1000 = 0.13 kg

Therefore, 130 grams is equal to 0.13 kilograms.

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To solve quadratic equations on a calculator by access to equation mode.

What is a quadratic equation?

Equations of degree 2 with a single variable are known as quadratic equations. a\(x^{2}\) + bx + c = 0 is its general form, where x is the variable, a, b, and c are constants or coefficient values, and a ≠ 0.

The quadratic formula, which is saved on the calculator and accessible via the equation mode, can be used to solve quadratic equations, by substituting the value of the coefficient of \(x^{2}\) , x and the constant term.

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To prove that 3x ≤ y, assume the opposite, that is, 3x > y, rearrange the inequality substitute x < 2y and simplify, contradict the given condition that x < 2y, therefore, concluding that 3x ≤ y.

Start by assuming the opposite, that is, 3x > y.

From the given inequality,\(7xy \leq 3x^2 + 2y^2,\), we can rearrange to get:
\(7xy - 3x^2 \leq 2y^2\)

We can substitute \(x < 2y\) into this inequality:
\(7(2y)x - 3(2y)^2 \leq 2y^2\)

Simplifying, we get:
\(y(14x - 12y) \leq 0\)

Since y is a real number, this means that either y ≤ 0 or 14x - 12y ≤ 0.

If y ≤ 0, then 3x ≤ y is trivially true.

If 14x - 12y ≤ 0, then we can rearrange to get:
3x ≤ (12/14)y
3x ≤ (6/7)y
3x < y (since we assumed 3x > y)

But this contradicts the given condition that x < 2y, so our assumption that 3x > y must be false.

Therefore, we can conclude that 3x ≤ y.

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Answer:

The cousins have 4 bags of white marbles and 4 bags of pink marbles.

Step-by-step explanation:

If x is the number of bags with white marbles and y is the number of bags with pink marbles, we can write the following system:

x + y = 8 -- Equation 1

5x + 7y = 48 -- Equation 2

5x + 5y = 40 -- Equation 3 (Multiply Equation 1 by 5)

2y = 8 -- (Subtract Equation 3 from 2)

y = 4 -- (Divide both sides by 2)

x + 4 = 8 -- (Substitute y = 4 into Equation 1)

x = 4 -- (Subtract 4 from both sides)

To test the hypothesis of mean differences in artificially sweetened drink consumption among BMI groups, assuming a normal distribution, the researcher might use a one-way ANOVA.

The one-way ANOVA compares the means of three or more independent groups and determines if there are statistically significant differences among them. In this case, the BMI groups (normal weight, overweight, and obese) represent the independent groups, and the number of artificially sweetened drinks consumed is the dependent variable. By conducting a one-way ANOVA, the researcher can assess if there are significant differences in mean consumption among the BMI groups and draw conclusions regarding their hypothesis.

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The fire stations should be placed in neighborhoods 1, 3, and 4.

The shipping plan that minimizes the total number of sailing days is as follows: Ship 1 from Origin 1 to Destination 2, Ship 1 from Origin 1 to Destination 3, Ship 2 from Origin 2 to Destination 2, Ship 1 from Origin 2 to Destination 4, Ship 1 from Origin 3 to Destination 2, and Ship 3 from Origin 3 to Destination 4.

The optimal flow plan for the network is as follows:

Flow from Node A to Node D with a capacity of 6 units.

Flow from Node A to Node B with a capacity of 3 units.

Flow from Node B to Node C with a capacity of 3 units.

Flow from Node B to Node D with a capacity of 3 units.

Flow from Node C to Node D with a capacity of 3 units.

The optimal flow through the network is 6 units.

To solve this problem, we can use a graph-based approach. Each neighborhood can be represented as a node in a graph, and the borders between neighborhoods can be represented as edges connecting the corresponding nodes. We need to find the minimum number of fire stations required to cover all neighborhoods while considering adjacency.

To do this, we can use a graph algorithm such as minimum spanning tree (MST) or maximum flow to determine the optimal locations for fire stations. In this case, neighborhoods 1, 3, and 4 will host the fire stations.

This is a transportation problem that can be solved using the transportation simplex method. We have three origins and four destinations, with given numbers of ships available at each origin and the number of ships required at each destination. We also have the sailing times between origins and destinations. By formulating the problem as a transportation model and solving it using the simplex method, we can find the optimal shipping plan that minimizes the total number of sailing days.

The specific steps of the simplex method involve setting up the initial feasible solution, finding the optimal solution by iterating through iterations, and updating the solution until an optimal solution is reached. The optimal shipping plan will determine which ships should sail from each origin to each destination.

To formulate the problem as a maximum flow problem, we can represent the network as a directed graph with nodes representing the source (Node A), intermediate nodes (Nodes B and C), and the sink (Node D). The edges between the nodes represent the capacity of the flow. We need to determine the maximum flow from the source to the sink while respecting the capacity constraints of the edges.

By using a flow algorithm such as the Ford-Fulkerson algorithm or the Edmonds-Karp algorithm, we can find the optimal flow plan for the network. The optimal flow plan will indicate the flow values through each edge, maximizing the flow from the source to the sink while considering the capacity limitations.

In a spreadsheet model, we can set up the nodes and edges of the network, assign capacities to the edges, and use a flow algorithm to calculate the maximum flow through the network. The optimal flow plan will specify the flow values for each edge, indicating how much flow should pass through each edge to achieve the maximum flow from the source to the sink. The optimal flow through the network will be the maximum flow value obtained from the flow algorithm.

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Answer:

71.0

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

1/12 - 5/6 = -9/12

We need to get a common denominator of 12

1/12 - 5/6*2/2 = -9 /12

1/12 - 10/12 = -9/12

Since the denominators are the same, we can subtract the numerators

1-10 = -9

-9/12 = - 9/12

We can simplify -9/12 by dividing the top and bottom by 3

-9/3 = -3

12 /3 = 4

-9/12 = -3/4

Answer:

see below

Step-by-step explanation:

1/12 - 5/6 = -9/12

1st, we need to identify the Least Common Multiplier of 12 and 6

in this case, the LCM is 12

for 5/6 = (5*2) / (6*2) = 10/12

2nd, adjust the fractions based on the LCM

= 1 / 12  -  10 / 12

= 1 - 10 / 12

= -9 / 12 ---- simplify   -3 / 4

Answer:

-1/4

Step-by-step explanation:

Simply draw a slope triangle

Answer:

its -1/4 which is the third option

Step-by-step explanation:

negative because it's going down, 1/4 because every four blocks to the right it goes down by only one block

We can find a using the trig. ratio

From the diagram,

Theta= 45 opposite =17 hypotenuse = a

substitute the values into the formula

cross-multiply

Divide both-side by sin45

but sin45 = 1/√2

Rationalize the above

Answer: 56.548

Step-by-step explanation:  Circumfrance = (radius x pi) x2

Answer:

The answer is 56.57miles

Step-by-step explanation:

The home's price is worth today's compared to the original price, which increased by 9% per year, equal to $803,310.

Purchase price of the house bought by Sunita in 1992 = $289,000

Percent increase in the average home price from 1992 to today per year

= 9% per year.

Let us consider 'y' be the home price worth today.

Total number of years = 2023 - 1992

                                     = 31 years

Todays price = 289,000 × 9 % × 31

                      = ( 289,000 × 9 × 31 )/100

                      = $803,310

Therefore, for the increased in home price by 9% per year the worth todays home price is equal to $803,310.

The given question is incomplete, I answer the question in general according to my knowledge:

From 1992 to today the average home price increased by 9% per year. In 1992 Sunita Bath bought a house for $289,000. What was it worth today?

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The correct answer is a. H0: u≥2 hours and H1:u<2 hours. When testing a right-tailed hypothesis using a significance level of 0.025, a sample size of n=13, and with the population standard deviation unknown, the critical value is as follows:

To determine the critical value, we need to use the t-distribution since the population standard deviation is unknown.

Using a t-distribution table or calculator with 12 degrees of freedom (n-1), a one-tailed test, and a significance level of 0.025, the critical value is 2.1604.

If the test statistic is greater than or equal to this value, we can reject the null hypothesis in favor of the alternative hypothesis, which is a right-tailed hypothesis.

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The graph of the solution set for the given system of inequalities can be seen below.

Here we have two inequalities:

2x + y < 0

y ≥ -4 - 2x

First, we can write both of these in slope-intercept form, to get:

y < -2x

y ≥ -2x - 4

To graph the first one, we need to graph a dashed line along:

y = -2x (we use a dashed line because the symbol < means that the points on the line are not solutions).

And then we shade the region below that line.

For the second one, we need to graph a solid line along:

y = -2x - 4 (this time we sue a solid line, because the points on the line are solutions).

And then we must shade the region above the line.

The graph of the system of inequalities can be seen below. The double shaded region is the solution set for the system.

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The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

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Answer: D) 602.88

Step-by-step explanation:

A cylinder is basically a circle prism.  Any prism volume can be found by taking the area of the base * the height.  The circle area is 4^2*3.14 = 50.24.  Then multiply that by the height(12)  50.24*12 = 602.88

Also, so far all of your questions that I've answered have been D...

Hope it helps <3

To determine if equations are parallel, perpendicular, or neither, you need to examine the slopes of the lines represented by the equations.

The slope of a line is calculated using the formula m = (y2 - y1) / (x2 - x1). The slope-intercept equation y = mx + c can be used to identify the slope and y-intercept of a line, where m represents the slope, while c represents the y-intercept.

If two equations are parallel, they will have the same slope.

If two equations are perpendicular, then the product of the two slopes should equal -1. This also means that if one slope is m, the other must be -1/m. If the slope of one line is zero, the line is horizontal, and any line perpendicular to it has a slope of undefined.

The two lines are neither parallel nor perpendicular if their slopes are not the same or opposite reciprocals of each other.

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a) The taxes to be paid for someone with a taxable income of $39,000 are of: $4,680.

b) The piece-wise function is defined as follows:

c) The tax rates are used as the slope for each linear definition of the piece-wise functions, while the bounds of the intervals are used to calculate the intercept.

The amount of taxes owed is obtained applying the proportion of the tax rate relative to the annual salary.

The tax rate for a taxable income of $39,000 is of 12%, hence the amount is given as follows:

0.12 x 39000 = $4,680.

The piece-wise functions for this problem are all derived considering the intervals with the tax brackets,

For the first tax bracket, the proportion is merely applied, as follows:

0.1x, 0 ≤ x ≤ 10275;

For each bracket, starting on the second, the maximum tax rate of the previous rate is calculated, and added to the excess of the income relative to the maximum of the previous tax bracket multiplied by the proportion.

For the first tax bracket, the maximum income is of:

$10,275.

The maximum tax of the first tax bracket is of:

0.1 x 10275 = 1027.5. -> the maximum value of the nth bracket is the starting value of the nth+1 bracket.

Then the function for the second bracket rate is obtained as follows:

f(x) = 1027.5 + 0.12(x - 10275), 10276 ≤ x ≤ 41175.

The same procedure is applied to any of the remaining brackets, taking the previous bracket to obtain the function.

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Recall that the inequality x>b in interval notation is:

Subtracting 3 to the given inequality we get:

Which in interval notation is:

Answer:

Answer:

$3.0375

Step-by-step explanation:

Original price of dinner = $2.25

If cost percentage of 35%, then the additional cost paid will be;

35% * 2.25

= 0.35 * 2.25

= $0.7875

Target price = Original price + additional cost

Target price = $2.25 + $0.7875

Target price = $3.0375

The solutions to the questions are:

The function is an exponential function.

So, the parent function has the form

y = ab^x

Using the function in (c), the parent function is: y = -7/8 * 2^x and the form of the function is g(x) = -7/8(2^[-5x]) + 7

First, the function is horizontally stretched by -5

This gives

g(x) = -7/8(2^[-5x])

Next, the function is shifted up by 7 units

g(x) = -7/8(2^[-5x]) + 7

The equation of the function is given as:

g(x) = -28/[2^(5x + 5)] + 7

Rewrite the equation as follows:

g(x) = -28/[2^(5x) * 2^5] + 7

Evaluate the exponent

g(x) = -28/[2^(5x) * 32] + 7

Divide

g(x) = -7/[2^(5x) * 8] + 7

Rewrite as:

g(x) = -7/[8 * 2^(5x)] + 7

Further, rewrite as:

g(x) = -7/8 * 2^(-5x) + 7

Rewrite properly as:

g(x) = -7/8(2^[-5x]) + 7

We have:

g(x) = -7/8 * 2^(-5x) + 7

Set the radical to 0

g(x) = 0 + 7

Evaluate

g(x) = 7

This represents the horizontal asymptote (it has no vertical asymptote)

Hence, the horizontal asymptote is y = 7 and the function is an example of exponential decay

The function can take any input

So, the domain is -∝ < x < ∝

We have the horizontal asymptote to be

y = 7

The function cannot equal or exceed this value.

So, the range is y < 7

Set x = 0

g(0) = -7/8 * 2^(-5 * 0) + 7

This gives

g(0) = -7/8 * 2^(0) + 7

Evaluate the exponent

g(0) = -7/8 + 7

Evaluate the sum

g(0) = 49/8

So, the y-intercept is 49/8

Set g(x) = 0

0 = -7/8 * 2^(-5x) + 7

This gives

-7 = -7/8 * 2^(-5x)

Divide by -7

1 = 1/8 * 2^(-5x)

Multiply by 8

8 = 2^(-5x)

Solve for x

x = -0.6

So, the x-intercept is -0.6

See attachment for the sketch

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Answer:

n+5

Step-by-step explanation:

Answer:

n + 5 or 5 + n

Step-by-step explanation:

add 5 to n, tanya's current age, to find how old she'll be in 5 years.

since the variable n is not defined, the answer cannot be simplified further than n + 5.

if n had been defined, you would be able to figure out her exact age after 5 years, which would be the fully simplified answer. for example, if n were to equal 10, then tanya would currently be 10 years old. by plugging in 10 for n in n + 5, you would figure out that in 5 years (aka 10 + 5) tanya would be 15.

i hope this helped! have a great day <3

To find an equation of the plane tangent to the surface 8xy + 5yz + 7xz − 80 = 0 at the point (2, 2, 2), we need to find the gradient vector of the surface at that point.

The gradient vector is given b

grad(f) = (df/dx, df/dy, df/dz)

where f(x, y, z) = 8xy + 5yz + 7xz − 80.

Taking partial derivatives,

df/dx = 8y + 7z

df/dy = 8x + 5z

df/dz = 5y + 7x

Evaluating these at the point (2, 2, 2), we get:

df/dx = 8(2) + 7(2) = 30

df/dy = 8(2) + 5(2) = 26

df/dz = 5(2) + 7(2) = 24

So the gradient vector at the point (2, 2, 2) is:

grad(f)(2, 2, 2) = (30, 26, 24)

This vector is normal to the tangent plane. Therefore, an equation of the tangent plane is given by:

30(x − 2) + 26(y − 2) + 24(z − 2) = 0

Simplifying, we get:

30x + 26y + 24z − 136 = 0

So the equation of the plane to the surface at the point (2, 2, 2) is 30x + 26y + 24z − 136 = 0.

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The average velocity from t = 2s to t = 4s would be - 48 ft/s.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that an object is thrown upward with initial velocity of 48 feet per second from a high of 120 feet. The height of the object t seconds after it is thrown is given by h(t) = - 16t² + 48t + 120.

Average rate of change of velocity with time is called average velocity. Mathematically -

v{avg.} = Δx/Δt                                                         .... Eq { 1 }

Δx = x(4) - x(2)

Δx = - 16(4)² + 48(4) + 120 - {- 16(2)² + 48(2) + 120}

Δx = - 96

Δt = 4 - 2 = 2

So -

v{avg.} = Δx/Δt = -96/2 = - 48 ft/s

Therefore, the average velocity from t = 2s to t = 4s would be - 48 ft/s.

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Answer:

49 sq ft.

Step-by-step explanation:

The area of a square is calculated by multiplying the length by the width which, since it is a square, are both the same value. Therefore, since we are given the area of the new patio we can simply square root that area to find the value of the length/width

\(\sqrt{144}\) = 12 feet

Since the new sides of the patio are 5ft more than the original we need to subtract 5 feet.

12 - 5 = 7 feet

Now we can multiply the original width/length together to calculate the original area of the patio.

7 * 7 = 49 sq ft.

(a) The top of the ladder is sliding down the wall at a rate of 3/2 m/sec.

(b) The angle between the ladder and the ground is changing at a rate of 1/2 rad/sec.

To solve this problem, we can use related rates, considering the ladder as a right triangle formed by the ladder itself, the wall, and the ground.

Let's denote:

x: the distance from the base of the ladder to the house (in meters)

y: the height of the ladder on the wall (in meters)

θ: the angle between the ladder and the ground (in radians)

Given:

dx/dt = -2 m/sec (the rate at which the base of the ladder is moving away from the house)

Using the Pythagorean theorem, we have:

x^2 + y^2 = 5^2 (since the ladder has a length of 5 meters)

Taking the derivative of both sides with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 0

(a) To find dy/dt:

We can solve the equation above for dy/dt:

2x(dx/dt) + 2y(dy/dt) = 0

2(3)(-2) + 2y(dy/dt) = 0 (substituting x = 3 and dx/dt = -2)

-12 + 2y(dy/dt) = 0

2y(dy/dt) = 12

dy/dt = 12/(2y)

dy/dt = 6/y

Now, we need to find y. Using the Pythagorean theorem again:

x^2 + y^2 = 5^2

3^2 + y^2 = 5^2

9 + y^2 = 25

y^2 = 25 - 9

y^2 = 16

y = 4 (taking the positive value as y represents a length)

Substituting y = 4 into dy/dt = 6/y:

dy/dt = 6/4

dy/dt = 3/2 m/sec

Therefore, the top of the ladder is sliding down the wall at a rate of 3/2 m/sec.

(b) To find dθ/dt:

We can use trigonometry to relate θ, x, and y:

tan(θ) = y/x

Differentiating both sides with respect to time (t), we get:

sec^2(θ)dθ/dt = (x(dy/dt) - y(dx/dt))/x^2

Substituting the given values:

sec^2(θ)dθ/dt = (3(3/2) - 4(-2))/3^2

sec^2(θ)dθ/dt = (9/2 + 8)/9

sec^2(θ)dθ/dt = (25/2)/9

sec^2(θ)dθ/dt = 25/18

Since sec^2(θ) is equal to 1 + tan^2(θ) and tan(θ) = y/x:

sec^2(θ) = 1 + (y/x)^2

sec^2(θ) = 1 + (4/3)^2

sec^2(θ) = 1 + 16/9

sec^2(θ) = (9 + 16)/9

sec^2(θ) = 25/9

Substituting sec^2(θ) = 25/9 into the equation:

(25/9)dθ/dt = 25/18

Simplifying and solving for dθ/dt:

dθ/dt = (25/18) * (9/25)

dθ/dt = 1/2 rad/sec

Therefore, (b) the angle between the ladder and the ground is changing at a rate of 1/2 rad/sec.

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Step-by-step explanation:

m1:90 degrees . .... angles in a perpendicular line

m2: 180-(90+27).....angles in a triangle add to 180 degrees

m3:63 degrees ... angles in an iscolese triangle

The measure of angles 1, 2, 3 are -  \(90^{o} ,\;63^{0} ,\;63^{0}\).

Consider the figure attached.

We have a labelled kite similar to mentioned in the question. We have angle ABO = \(27^{o}\).

We have to find the measure of angle 1, 2, 3.

Here are some of the properties of kite -

According to the question -

In ΔAOB,

\(\angle2 + \angle ABO+\angle AOB = 180^{o} \\\angle2+27^{o} +90^{o}=180^{o}\\\angle2+117^{o} =180^{o}\\\angle2 = 63^{o}\)

Th, the two angles opposite to the two equal sides are also equal, since BA and BC are equal, therefore - \(\angle2=\angle3\)\(=63^{o}\).

Since the diagonals of the kite intersect each other perpendicularly, therefore -

\(\angle1=90^{o}\)

Hence the measure of angles 1, 2, 3 are -  \(90^{o} ,\;63^{0} ,\;63^{0}\).

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Hello!

58, 65, 72, 79, 86

86+7 = 93

93+7 =100

100+7 =107