Find the average rate of change of h (x) = -2x²-3x from x=2 to x = 4. Simplify your answer as much as possible.
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On solving the provided question, we can say that the variable x while retaining the inequality [tex]- 2 \geq 4x = > -1/2 \geq x[/tex]

An inequality in mathematics is a relationship between two expressions or values that is not equal. Thus, imbalance leads to inequality. An inequality creates the link between two values that are not equal in mathematics. Egality is distinct from inequality. When two values are not equal, most commonly use the not equal sign (). Different inequalities are used to contrast values, no matter how little or large. Many simple inequalities may be resolved by modifying the two sides until the variables are all that remain. But a number of things contribute to inequality: Negative values on both sides are divided or added. Trade off the left and right.

Inequality is 2x - 6 ≥ 6(x - 2) + 8

the variable x while retaining the inequality

[tex]2x - 6 \geq 6x - 12 + 8\\-6 + 12 - 8 \geq 6x - 2x\\- 2 \geq 4x\\-1/2 ≥ x[/tex]

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A function is considered a one-to-one function, also called an injective function, if it assigns a unique output value to each input value. In other words, a function is one-to-one if no two different input values have the same output value.

A function f(x) is one-to-one if and only if for any two distinct inputs x1 and x2, it holds that f(x1) ≠ f(x2).

One way to determine if a function is one-to-one is to use the horizontal line test:

if any horizontal line intersects the graph of the function at most once, then the function is one-to-one.

A one-to-one function has an inverse function. The inverse function, f^-1(x), is also a function, it assigns to each output value of f(x), an input value such that f^-1(f(x)) = x.

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When a 6-sided die is rolled, P(3 or 5) is equal to B. 1/3.

A 6-sided die has six possible outcomes: 1, 2, 3, 4, 5, and 6. To find P(3 or 5) or the probability of rolling a 3 or a 5, we need to add the probabilities of rolling each of those numbers separately and then subtract the probability of rolling both numbers (3 and 5) at the same time to avoid overcounting.

The probability of rolling a specific number on a fair die is 1/6, since there are 6 possible outcomes.

So, P(rolling a 3) = 1/6 and P(rolling a 5) = 1/6

P(3 or 5) = P(rolling a 3) + P(rolling a 5) - P(rolling 3 and 5) = 1/6 + 1/6 - 0 (since rolling 3 and 5 is not possible)

= 2/6 = 1/3

Therefore, the probability of rolling 3 or 5 on a fair 6 sided die is 1/3.

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Answer: [tex]y-1=\frac{1}{4}(x-5)[/tex]

Step-by-step explanation:

The median from vertex [tex]A[/tex] passes through [tex]A[/tex] and the midpoint of [tex]\overline{BC}[/tex].

Using the midpoint formula, the midpoint of [tex]\overline{BC}[/tex] has coordinates [tex]\left(\frac{3+7}{2}, \frac{5-3}{2} \right)=(5, 1)[/tex].

Therefore, we need the equation of the line passing through [tex](-3,-1)[/tex] and [tex](5,1)[/tex].

The slope of this line is [tex]\frac{-1-1}{-3-5}=\frac{1}{4}[/tex].

Using point-slope form, the equation is y[tex]y-1=\frac{1}{4}(x-5)[/tex].

By calculating the given equations with points none of the equation represents equation of this graphed line.

What is the equation of the line?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.

We have given the,

y = 2x+2

y=-2x-2

y=6x+6

y=-6x-6

And, the graph.

From the line in the graph we can take the cordinate points which represents the equation of line.

point (1, 2)

By putting this point we can decide the given equation of line:

y=2(1)+2 = 4

y=-2(1)-2 = 0

y=6(1)+6 =12

y=-6(1) - 6 =-12

Hence, by calculating the given equations with points none of the equation represents equation of this graphed line.

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The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

The linear equation to represent how much Martina collects for one night of stay in her home is:

y = 25 + 10x - 5z

where:

y is the total amount collected in dollars

x is the number of additional guests (besides the first one)

z is the number of hours the guests check out late

This equation represents the flat fee of $25 per night for the first guest, the additional fee of $10 per person per night for additional guests, and the extra fee of $5 per hour for late checkouts.

Therefore, The linear equation that correctly represents how much Martina collects for one night of stay in her homey is 25 + 10x - 5z

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The minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

What is the positive real number?

In mathematics, the set of positive real numbers is the subset of those real numbers that are greater than zero. The non-negative real numbers, also include zero.

We can simplify the expression as follows:

a^2 b^2 c = (ab)^2 c.

Now, we can use the AM-GM inequality to find the minimum value of the expression:

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

As the minimum value is achieved when equality holds, we can set the equation to the original expression and simplify it.

[tex][(ab)^2 c \ge \left(\frac{(ab)^2 + c}{2}\right)^2 = \left(\frac{(ab + c)^2 - 2abc}{4}\right)^2.][/tex]

[tex]$a^2b^2c = \frac{(a^2b^2+ 2ab^2c+c^2b^2) - 2abc}{4}$[/tex]

[tex]$4a^2b^2c = (a^2b^2+ 2ab^2c+c^2b^2) - 2abc$[/tex]

4abc = (ab + c)(ab + c) - 2abc

4abc = (ab + c)^2 - 2abc

6abc = (ab + c)^2

so the minimum value is: [tex]$(\frac {(ab+c)^2}{6})^{\frac{1}{2}}$[/tex]

[tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex]

Hence, the minimum value of the expression is [tex]$\sqrt{\frac{abc(a+b+c)^2}{6}}$[/tex], with a, b, and c be positive real numbers.

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Answer:

FIRST ONE IS 7

Step-by-step explanation:

SECOUND ONE IS 12THIRD ONME IS 2

Part A:Coefficients in  are 85 and 15.

X represents theatrical shifts, Y represents dog-walking gigs.

Part B: Two phrases, the first of which indicates the amount of money he makes from his work in the theater and the second, from dog-walking. A sum or a deduct sign is used to demarcate each phrase.

Part A: The information we don't know is contained in an expression's variable. In this instance, we don't know how many dog-walking jobs he has in addition to his theater duties. We have 2 variables—x and y—because of this. The variable is multiplied by the coefficient, which is a number. Since there are two variables in this situation, there are two coefficients: 85 and 15.

Part B: A sum or a subtract sign is used to denote the separation of each term in an equation. The terms are the numbers and variables that occur before and after the sum sign because there is only one sum in this situation. 85x and 15y are involved. He initially discloses how much money he makes for each shift at his total annual salary at the theater is determined by multiplying his hourly wage by the number of shifts he works. The second one is the sum of the money he makes from each dog-walking work multiplied by the number of jobs he completes; this is the total amount he makes from the dog-walking jobs.

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On solving the provided question, we can say that the range of the function f(x) = 2(3)x is best described by y > 0.

The variable's range is obtained by finding its largest observed value (maximum) and subtracting its smallest observed value (minimum). Variational bounds or possible range: various steel prices; various styles; The extent or magnitude of a procedure or action: insight. the maximum or expected range of a weapon's projectile. The range of a list or set is the number between the minimum and maximum. Prior to identifying the region, align all the numbers. Remove (remove) the lowest number from the highest number next. The list's range is provided in the solution.

The range of the function f(x) = 2(3)x is best described by y > 0.

Especially when the constant is e, a function whose value is a constant increased to the power of the argument.

An exponential function is a function with the form, where b is referred to as the base and x can be any real number, if b is any number such that and.

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Answer:

  33 mm

Step-by-step explanation:

Given a triangle with sides 48 mm and 55 mm, and angles x and w such that cos(x) = 4/5 and cos(w) = 1/2, you want the length of the third side (r) opposite angle x.

For sides a, b, c and angle C opposite side c, the Law of Cosines gives the relation ...

  c² = a² +b² -2ab·cos(C)

Filling in the given values, we have ...

  r² = 48² +55² -2·48·55·(4/5) = 1105

  r = √1105 ≈ 33 . . . . millimeters

The length r is about 33 mm.

__

Additional comment

Side r is irrational, so the triangle cannot have exactly the measures shown. Using other measures as true, the value of cos(w) is about 0.4994, not 1/2.

Taking cos(w) as true, side r is found using the law of cosines as 33.43717. Taking cos(x) as true, side r is found using the law of cosines as 32.24154. Taking the angle measures and 48 mm to be true, side r is found using the law of sines as 33.25538. All round to 33 mm.

The attachment shows the solution using cos(w)=1/2, or w=60°.

On solving the provide question, we can say that by unitary method each person get = 24/14 = 1.7142857143 pounds of beef

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

a group of = 24 people

equally shared  = 14 pounds of ground beef.

each person get = 24/14 = 1.7142857143 pounds of beef

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Ratio grade 7 is a mathematical concept that involves comparing two or more quantities using a ratio. It is a common part of mathematics curriculums for middle and high school students.

1. A ratio is a comparison of two or more numbers.

2. Ratios can be expressed as a fraction, a decimal, or a percentage.

3. Ratios are used to compare quantities of different kinds and are used to find relationships between them.

4. In grade 7, students will learn about ratios and how to use them to solve various problems. They will also learn about proportionality, rates, and unit rates.

5. Ratios can also be used to compare measurements, such as lengths, weights, and areas.

6. Students will also use ratios to calculate proportions, which can be used to solve problems involving proportional relationships.

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The probability of 30 random people having weight more than 6000 pounds is 0.3134 or 31.34%.

To find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds, we can use the Central Limit Theorem (CLT) which states that the sum of a large number of independent and identically distributed random variables will tend to be normally distributed, regardless of the underlying distribution of the individual variables.

Since we know the average weight of a passenger (190 pounds) and a reasonable standard deviation (35 pounds), we can use this information to calculate the mean and standard deviation of the total weight of 30 passengers.

The mean weight of 30 passengers is:

30*190 = 5700 pounds

The standard deviation of the weight of 30 passengers is:

sqrt(30)*35 = 59.8076211353316

Now we can use the standard normal distribution table, or z-score formula to find the probability that the total weight of 30 randomly selected passengers exceeds 6000 pounds.

z = (6000-5700)/59.8076211353316

z = 0.50251572

The probability of a z-score being greater than 0.50251572 is 0.3134, this means that there is a 31.34% chance that the total weight of 30 randomly selected passengers will exceed 6000 pounds.

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Answer: 32

Step-By-Step Explanation: 1/8 times 32 = 4

I multiplied 8 by 4 to get 32 then checked my answer by multiplying 1/8 and 32.

if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time

mr. earl e. bird leaves his house for work at exactly 8:00 a.m. every morning

when he averages 40 miles per hour, he arrives at his workplace thirty minutes late.

when he averages 60 miles per hour, he arrives thirty minutes early.

at what average speed, in miles per hour, should mr. bird drive to arrive at his workplace precisely on time?

if 40 makes him 30 mins late and 60 makes him 30 mins early then it only would make since that in between both 40 and 60 is 50 and that would make him go on time

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The correct answer is 5 white triangles coincide.

3 red, 5 blue, and 8 white triangles are present on each side. The 2 pairs of red triangles are also utilized, leaving 1 red triangle, 5 blue triangles, and 8 white triangles on each half.

Additionally, there are 3 pairs of blue triangles that are used up, leaving 1 red triangle, 2 blue triangles, and 8 white triangles on each half. Additionally, we offer 2 red-white pairs. Since there is only 1 on each side, it is evident that we cannot utilize 2 red triangles on one side.

As a result, we must use 1 red and 1 white triangle per side, leaving 2 blue and 7 white triangles on each. The remaining blue triangles must be coupled with white triangles in order to create 4 blue-white pairings, one for each of the remaining blue triangles.

Blue triangles cannot be matched with other blue triangles because it would result in more than 3 worth of blue pairs. This leaves 5 white triangles per side, which must be coupled with each other to create $5 white-white pairings.

Therefore, The correct answer is 5 white triangles coincide.

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So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

The Poisson distribution is a discrete probability distribution that describes the number of events that occur in a fixed interval of time or space, given the average number of events per interval.

For a Poisson distribution with mean λ, the variance is equal to λ.

Given that at least one tornado occurs in a year, the mean number of tornadoes is 3. Therefore, the variance is also equal to 3.

So, the variance of the number of tornadoes in a year given that at least one tornado occurs is 3.

It's worth noting that this result is based on the assumption that the number of tornadoes follows a Poisson distribution with mean 3, which may not always be the case in real-world scenarios. The actual number of tornadoes in a given year can be influenced by various factors such as climate, weather patterns, and geography.

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Answer:

Step-by-step explanation:

A polynomial function of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros -2, 1, 3 is (x- -2)(x-1)(x-3) = x^3 - 6x^2 + 11x - 6

The line which passes through the points (2,-1) and (4,-1) has the slope-intercept equation as y = -1.

What is the slope-intercept form?

The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The line passes through point (x1,y1) = (2,-1) and (x2,y2) = (4,-1)

The formula to find slope is -

m = (y2-y1)/(x2-x1)

m = (-1+1)/(4-2)

m = 0/2

m = 0

Now use the slope and point (2,-1) to find the y-intercept.

y = mx + b

-1 = 0(2) + b

-1 = 0 + b

b = -1

Write the equation in slope-intercept form as -

y = mx + b

y = 0x + (-1)

y = -1

Therefore, the equation is obtained as y = -1.

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Answer:

- 8

Step-by-step explanation:

the absolute value function always gives a positive value, that is

| - a | = | a | = a

then

| - 13 | - | 21 |

= | 13 | - | 21 |

= 13 - 21

= - 8

The lengths of q and r are 2.5 , 2.5 respectively if the perimeter of an isosceles triangle pqr is 9 cm.

A triangle can be defined in which it consists of three sides , three angles and the sum of three angles is always 180 degrees.

here, Given that,

The perimeter of an isosceles triangle (2 equal sides) pqr is 9 cm.

the length of side p is 4 cm

Let the lengths of q and r are x and y respectively.

The perimeter of an isosceles triangle  =  (p+2q)

So,

p+2q = 9

4+2q = 9

2q = 9-4

2q = 5

q = 5/2

q = 2.5 cm

Hence , the lengths of q and r are 2.5 , 2.5 cm respectively .

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Answer:

23.8

Step-by-step explanation:

Solve for the missing side, x, by using the pythagorean theorem:

5² + 3² = x²        **(8-5=3)

x² = 25+9 = 34

x = √34 = 5.831

P = sum of all sides = 5 + 5 + 8 + 5.831 = 23.8

Answer: 14.7

Step-by-step explanation:

The remaining interior angle is [tex]135^{\circ}[/tex].

[tex]\frac{x}{\sin 19^{\circ}}=\frac{32}{\sin 135^{\circ}}\\ \\ x=\frac{32 \sin 19^{\circ}}{\sin 135^{\circ}} \\ \\ x \approx 14.7[/tex]

The value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.

For the stated question:

(x + 12) + (3x + 48) = 180  (co exterior angles are supplementary)

4x + 60 = 180

4x = 180 - 60

4x = 120

x = 30

Thus, the value of 'x' for the given co exterior angles for the parallel lines PQ ans SR is found as: x = 30.

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At 12 seconds, the cart will be moving at 24 cm per second.Rebecca is using a fan cart and measuring the rate of the cart at different times.

Rebecca is using a fan cart and measuring the rate of the cart at different times. At 10 seconds, the cart has a speed of 20 cm per second. To calculate the speed at 12 seconds, you can use the formula rate x time = distance. The rate is the speed of the cart at 10 seconds, which is 20 cm per second. The time is the difference between 10 seconds and 12 seconds, which is 2 seconds. Thus, the equation becomes 20 cm/s x 2s = 40 cm. Therefore, the speed at 12 seconds is 24 cm per second.

At 12 seconds, the cart will be moving at 24 cm per second.

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Because the temperature is greater, the relative humidity of the atmosphere is higher.

Water vapor is also measured by relative humidity (RH), which is stated as a percentage but RELATIVE to the air's temperature. In plenty of other terms, it is a comparison between the quantity of water vapor that is really present in the air and the maximum amount water vapor that is possible for the air at the current temperature.

By deducting the temperature just on wet-bulb thermometer from of the temperature just on dry-bulb thermometers and utilizing a relative humidity chart, one may determine the relative humidity.

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Answer:

Step-by-step explanation:

The equation of line passing from point (x1,y1) and having slope m is

y- y1 =m(x- x1)

m=-3, x1=1, y1=-3

y-(-3) = -3(x-1)

y+3=-3(x-1)

y+3=-3x+3

y=-3x

3x+y=0

Answer:

y + 3x = 0

Step-by-step explanation:

The formula for equation of the line is :

y - y1 = m ( x - x1 )

NB: The m is the slope, then use substitution, solve and equate everything to 0

A reasonable prediction for the number of times a Red or Yellow Marble Draws = (7/20) x 180 = 126.

The total number of marbles in the bag is 20 (5 red, 6 blue, 3 green, 4 black, and 2 yellow). Therefore, the probability of drawing a red or yellow marble is 7/20. Applying this probability to the 180 times a marble is drawn and replaced, we can calculate that the number of times a red or yellow marble is likely to be drawn is 126 (7/20 x 180). This can be expressed as a formula as follows: Red or Yellow Marble Draws = (Number of Red and Yellow Marbles / Total Number of Marbles) x Number of Draws. In this case, Red or Yellow Marble Draws = (7/20) x 180 = 126.

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