solve these inequalities 1a.4x+12>or equals to 40 1b.3(x+8) 3x+15

Answer:

B ( 432 units^2)

Step-by-step explanation:

Total surface area= 2*(6*6)+ 4*(15*6)

There are 2 squares at each end of the same size so total area will be 2*(6*6)

If we look at the rectangles( bottom, top and the sides), we can see that all are of same dimensions and there are 4 of them so it's 4*(15*6)

In short, total surface area= 2*(6*6)+ 4*(15*6) = 432 units^2

(a) The values of f(0) = 3 and g(2) = 2.

(b) The values of x for which f(x) = g(x) are -2, 2.

(c) The solutions of the equation f(x) = −1 are x = -3, 4.

(d) The interval on which f is decreasing is [0, 4].

(e) The domain and range of f are:

domain = [-4, 4].

range = [-2, 3].

(f) The domain and range of g are:

domain = [-4, 3].

range = [-0.5, 4].

In Mathematics and Geometry, a function is an equation which defines and represents the relationship that exist between two or more variables.

Part a.

By critically observing the graph of f(x) and g(x) shown in the image attached below, the corresponding output values are as follows:

f(0) = 3.

g(2) = 2.

Part b.

The values of x for which f(x) is equal to g(x) are x = -2 and x = 2;

f(-2) = g(-2) = 1.

f(2) = g(2) = 2.

Part c.

The estimated solutions of the equation f(x) = −1 are as follows;

f(-3) = -1

f(4) = -1

Therefore, x = -3, 4.

Part d.

The function f(x) is decreasing over this interval [0, 4].

Part e.

By critically observing the graph of f(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 4].

range = [-2, 3].

Part f.

By critically observing the graph of g(x) shown in the image attached below, we can logically deduce the following domain and range:

domain = [-4, 3].

range = [-0.5, 4].

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Missing information:

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

Answer

$12.41

Step-by-step explanation

1 pound is equivalent to $0.85 in the shipping fee.

To find the shipping fee equivalent to 14.6 pounds, we can use the next proportion:

Cross-multiplying and omitting the units:

Answer:

13 x 50 = 650

Step-by-step explanation:

Answer:

75 ft

Step-by-step explanation:

It's the first one. y can equal x as long as y doesn't equal x multiple times. We also know the last two are wrong because they're saying the same thing. A linear function is a straight line.

Hi there!

-10-2 is equal to -12, not -8. This changes everything.

The fraction would be -12/16, which simplifies to -3/4.

I hope this helps!

Answer:

1st red box:

-10 - 2 = -12

2nd box above:

-3

3rd box:

4

The solutions of the inequality \(2x^{2} + x - 6 = 0\) are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form \(ax^{2} +bx + c = 0\), the solutions are \(x = -b +/-\sqrt{b^{2} -4ac} /2a\).

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = \(-b + \sqrt{b^{2} -4ac} /2a\) = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = \(-b-\sqrt{b^{2} -4ac} /2a\)= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

\(2x^{2} +4x -3x-6=0\)

\(2x(x+2) -3(x+2) = 0\)

\((2x-3)(x+2) = 0\)

x = 3/2, -2

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Hey there! I'm happy to help!

Since we are using graphs, we will do not need to algebraically solve this system of equations.

When you graph a system of equations, the solution is always the point at which the two lines intersect.

Here is our system of equations graphed. We see that the lines intersect at about (1 1/3, 2 1/3). Therefore, the correct answer is C. x=1 1/3, y=2 1/3

Have a wonderful day! :D

Answer:

Segment U T is congruent to segment X V

Segment S T is congruent to segment W V

Angle V is congruent to angle T

Answer:

AC is approximately 0.3178

Step-by-step explanation:

The given parameters are;

In ΔPAB

CD ║ EF ║ AB

The area of triangle ΔPEF = 1/3 × area of triangle ΔPAB

Therefore, PE = 1/√3·PA

PA = √3

We have area of ΔPCD = 2/3 × area of triangle ΔPAB

∴ PC = √(2/3) × PA = √(2/3) × √3

PC = √2

Therefore, AC = PA - PC = √3 - √2

AC = √3 - √2 ≈ 0.3178

Steps to solve:

3x - 5y = 20

~Subtract 3x to both sides

-5y = 20 - 3x

~Divide everything by -5

y = -4 + 3/5x

Best of Luck!

The equivalent value of the expression is y = ( 3x - 20 ) / 5

Given data ,

Let the equation be represented as A

Now , the value of A is

3x - 5y = 20

On simplifying the equation , we get

3x - 5y = 20

So , the left hand side of the equation is equated to the right hand side by the value of 20

Adding 5y on both sides , we get

3x = 20 + 5y

Subtracting 20 on both sides , we get

5y = 3x - 20

Divide by 5 on both sides , we get

y = ( 3x - 20 ) / 5

Therefore , the value of y = ( 3x - 20 ) / 5

Hence , the expression is y = ( 3x - 20 ) / 5

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Answer:Rounding a number is when you take a number and "bump it up" or "bump it down" to a nearby and "cleaner" number. A number can be rounded to any place value you want. If you type in a number you wish to round below, and select what place value you want to round it to, this selection will show you how to round it!

Step-by-step explanation:

To construct X-bar and S control charts, we need to calculate the control limits.

For X-bar chart:

Centerline (CLx-bar) = Target value = 21.00 cm

Upper Control Limit (UCLx-bar) = CLx-bar + 3 * (Average range/1.128) = CLx-bar + A2 * Sample Standard Deviation / sqrt(sample size)

Lower Control Limit (LCLx-bar) = CLx-bar - 3 * (Average range/1.128) = CLx-bar - A2 * Sample Standard Deviation / sqrt(sample size)

For S chart:

Centerline (CLs) = Average range

Upper Control Limit (UCLs) = D4 * Average range

Lower Control Limit (LCLs) = D3 * Average range

To determine the percentage of out-of-control points, we need to plot the sample data on the control charts and count the number of points outside the control limits. Divide this count by the total number of subgroups and multiply by 100.

To calculate the percentage of bottles that are reworked and scrapped, we need additional information on the criteria for rework and scrap. Without this information, it is not possible to provide an accurate answer.

Cp (Process Capability Index) measures the ability of a process to meet the specifications. Cpk (Process Capability Index with respect to a target) measures the process capability considering both the spread and centering of the process. To calculate Cp and Cpk, we need the specification limits and the process standard deviation.

With a new process mean of 20.84 cm, the calculations for rework, scrap, Cp, and Cpk will change based on the new process center and the specification limits.

Whether the change in the process center is a wise decision depends on the specific circumstances and the impact on process capability, customer requirements, and other factors. It is important to analyze the consequences and evaluate the overall effect before making a decision.

To center the process and reduce scrap, adjustments need to be made to bring the process mean closer to the target value. The specific actions to center the process depend on the underlying causes of variation and may involve process optimization, adjustments to machine settings, or other corrective measures.

Apart from shifting the mean, process behavior can change through other factors such as variation reduction, process stabilization, implementing quality control measures, improving equipment or tooling, and enhancing operator training. These actions can help reduce process variability and improve overall process performance.

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This equation assumes a constant price per cubic yard of mulch and a fixed delivery charge. If there are any additional fees or discounts based on specific conditions, the equation may need to be modified accordingly to reflect those changes.

The linear equation that computes the total cost of mulch (M) to deliver x cubic yards of mulch can be expressed as follows:

M = 41x + 26

In this equation, x represents the number of cubic yards of mulch to be delivered. The term 41x corresponds to the cost of the mulch itself, where $41 is charged per cubic yard. The term 26 represents the delivery charge, which is a fixed amount added to the total cost regardless of the quantity of mulch.

By multiplying the number of cubic yards (x) by the cost per cubic yard (41) and adding the delivery charge (26), we obtain the total cost of the mulch delivery (M) in dollars.

It's important to note that this equation assumes a constant price per cubic yard of mulch and a fixed delivery charge. If there are any additional fees or discounts based on specific conditions, the equation may need to be modified accordingly to reflect those changes.

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(b) No, The branch manager's argument that dispatching buses every 0.5 minutes will reduce the average traveling time (a round trip) to 3.5 minutes is not correct.

To calculate the average time, we need to consider the time it takes for the bus to travel to the airport and back, as well as the time spent waiting for the bus.

If buses are dispatched every 3 minutes, and the average traveling time (a round trip) is 21 minutes, it means that passengers spend 18 minutes waiting for the bus (21 minutes - 3 minutes of traveling time).

If buses are dispatched every 0.5 minutes, the waiting time will be significantly reduced. However, the traveling time remains the same at 21 minutes for a round trip.

Therefore, the average traveling time will not be reduced to 3.5 minutes but will remain at 21 minutes (assuming the traveling time remains constant).

(c) The average traveling time, following the branch manager's suggestion of dispatching buses every 0.5 minutes, would still be 21 minutes.

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Complete question:

The Avis Company is a car rental company and is located three miles from the Los Angeles airport (LAX). Avis is dispatching a bus from its offices to the airport every 3 minutes. The average traveling time (a round trip) is 21 minutes.

(a) The branch manager wants to improve the service and suggests dispatching buses every 0.5 minute. She argues that this will reduce the average traveling time (a round trip) to 3.5 minutes. Is she correct? (Enter "Yes" or "No" in the following blank).

c. Following the branch manager's suggestion (dispatch busses every 0.5 min), what will the average traveling time be? average travelling time ____(mins) (enter the numbers only)

Answer:

B

Both systems can be sloved by susbituding (1,2)

Step-by-step explanation:

(1)- x−4y=−7

Substitute in the x and y values: 1 - 4 (2) = -7

Multiply the numbers : 1 - 8 = -7

Calculate the difference: -7 = -7

(2) - −x+2y=3

Substitute in the x and y values: -1 + 2 (2) = 3

Multiply the numbers : -1 + 4 = 3

Calculate the sum: 3 = 3

Here is a tree diagram that shows all the possible ways to choose 2 balls from a set of blue, red, and green balls,

where you are allowed to choose two of the same color:

Copy code

    B           R           G

  /   \       /   \       /   \

 B     B     R     R     G     G

/ \   / \   / \   / \   / \   / \

B   B B   B R   R R   R G   G G   G

Alternatively, we can list all the probability ways to choose 2 balls:

Blue and blue

Blue and red

Blue and green

Red and blue

Red and red

Red and green

Green and blue

Green and red

Green and green

Note that we have included all possible combinations, including duplicates (e.g., blue and red and red and blue).

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The measure of ∠t is 135 degrees.

If we know that ∠t and ∠s are supplementary angles, it means that their measures add up to 180 degrees.

Let's assume that the measure of ∠s is x degrees. Since ∠t and ∠s are supplementary, the measure of ∠t is 180 - x degrees.

Given that m∠t is 3 times the measure of ∠s, we can write the equation:

m∠t = 3(m∠s)

180 - x = 3x

Now, we can solve this equation to find the value of x and then determine the measure of ∠t.

180 - x = 3x

180 = 4x

x = 45

Substituting the value of x back into the equation for ∠t:

∠t = 180 - x

∠t = 180 - 45

∠t = 135

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The objective function (a) can be written as:
\(a = s^2 + 4s(864 / s^2)\)

The dimensions for minimum surface area are: s=12ft and h(height)= 6ft

To find the dimensions of the tank that has the minimum surface area, we can start by finding the objective function.

Let's assume that the length of one side of the square base is "s". Since the base is square, the width of the base would also be "s".

The surface area of the tank consists of the area of the base and the four sides. The area of the base would be \(s^2\), and the area of each side would be s times the height of the tank (h). Since the tank is rectangular, the height would be \(864 ft^3\) divided by the area of the base \((s^2).\)

So, the objective function (a) can be written as:
\(a = s^2 + 4s(864 / s^2)\)

Taking derivative of the area function,

\(a=2s-3456/s^2\)

Now, for minimum surface area

\(a=0\\2s-3456/s^2=0\\2s^3=3458\\s=\sqrt[3]{1728} \\s=12 ft\\\)

We have calculated above that:

\(h=864/s^2\\h=864/12^2\\h=6ft\)

Therefore, the dimensions for minimum surface area are: s(length of one of the side of the square base)=12ft and h(height)= 6ft

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Answer:

The equation of the line is -1/3x + 4

Step-by-step explanation:

You would do rise over run or use the slope formula

y2-y1/x2-x1=

2-4/6-0 = -2/6 = -1/3

The y-intercept is when the line hits the y-axis so it would be (0,4) or 4

The instantaneous rate of change for the function at the given value,

g(x) = x² + 11x - 15 + 4ln(3x + 7) at x = 1 is 28 + 4/10ln(10).

The instantaneous rate of change is also known as the derivative. It is the rate at which the function changes at a specific point. The formula for finding the derivative is

f'(x) = limh→0 [f(x + h) - f(x)]/h.

Using this formula to find the derivative of the function,

g(x) = x² + 11x - 15 + 4ln(3x + 7), we can get

g'(x) = 2x + 11 + [12/(3x + 7)] = (6x² + 68x - 78)/(3x + 7)².

To find the instantaneous rate of change at x = 1, we need to evaluate g'(x) at x = 1. Thus,

g'(1) = (6(1)² + 68(1) - 78)/(3(1) + 7)² = 28 + 4/10ln(10).

Therefore, the instantaneous rate of change for the function g(x) at x = 1 is 28 + 4/10ln(10).

The instantaneous rate of change for the given function g(x) at x = 1 is 28 + 4/10ln(10).

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Answer:

-4/3

Step-by-step explanation:

Trust me

Coating the seed typically improves seed quality and germination rates, so the same seeding rate can be maintained even with coated seed.

To convert mass-based seeding rates to population-based establishment rates, we need to consider the area conversion factors provided:

a. Given a seeding rate of 60 lbs/acre for cereal rye, we can convert it to seeds per square foot by using the conversion factor of 1 acre = 43,560 square feet.

b. Given a seeding rate of 15 kg/ha for crimson clover, we can convert it to seeds per square meter using the conversion factor of 1 hectare = 10,000 square meters.

To convert population-based seeding rates to mass-based seeding rates, we can use the given area conversion factors:

a. Given a seeding rate of 30 plants/square foot for oats, we can convert it to pounds of seed per acre.

b. Given a seeding rate of 20 plants/square meter for hairy vetch, we can convert it to kilograms of seed per hectare.

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The histrogram that best represents the data collected by the surfer is "A histogram titled Tides For 15 Days with an x-axis labeled Measurement ...  There is a shaded bar above 1 to 5 that stops at 2, above 6 to 10 that stops at 4" (First option).

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Answer:

Burger Calories Individual: 450

Fry Calories Indicidual: 280

Step-by-step explanation:

First, since there are 2 burgers and each burger has 170 more calories, we will subtract 170 + 170.

170 + 170 = 340.

1740 - 340 = 1400 ( this makes it good for the next part )

Since we have 2 burgers and 3 fries, that will be 5 in total.

All we will have to do is divide 1400 by 5 to get our answer.

1400 ÷ 5 = 280.

Now we know that each of the fries had 280 calories.

280 + 170 = 450 ( add 170 because the instructions say the burger had 170 calories more. )

Therefore, the burgers each had 450 calories and the fries each had 280.

-kiniwih426

The difference between the number of correct and incorrect answers is 34.

To find the difference between the number of correct and incorrect answers, we first need to determine the number of correct answers. We know that the point score is obtained by dividing the final score by 10. In this case, the point score is 45. Since each correct answer is worth 1 point, the number of correct answers is equal to the point score. Therefore, the student answered 45 questions correctly.  

Next, we need to find the number of incorrect answers. Each incorrect answer is worth 4 1-point, so we divide the point score by 4. In this case, 45/4 equals 11.25.

Rounding to the nearest whole number, we get 11. Therefore, the student answered 11 questions incorrectly.  

Finally, we calculate the difference between the number of correct and incorrect answers by subtracting the number of incorrect answers from the number of correct answers: 45 - 11 = 34.

Thus, the difference between the number of correct and incorrect answers is 34.

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