3|5x+2|+10=4
Absolute value

Answer:

It's a parabola with a minimum.

C(x)= 500,000 + 80x + 0.003x^2

C'(x) = 80 + 0.006x = 0

x = 80/0/006 = 13,333 units

Step-by-step explanation:

A company that produces chemicals used in manufacturing sells a certain product for $200 per unit. The total production cost for the product is

C(x)= 500,000 + 80x + 0.003x^2

The company can produce no more than 30,000 units during a given time period. How

many units of the chemical product should be manufactured and sold to maximize profit?

The statement suggests that the worst-case time complexity of Insertion Sort is approximately proportional to n²/2, while the average-case time complexity is approximately proportional to n²/4.

The worst-case and average-case time complexities of Insertion Sort indicate that the algorithm's performance is quadratic, with the average case being more efficient than the worst case due to a smaller constant factor.

The worst-case time complexity refers to the scenario where the input array is in reverse order or nearly sorted in reverse order. While the average-case time complexity represents the average performance of the algorithm over all possible inputs.

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In mathematics, there are several types of inequalities that are commonly studied, including linear inequalities, quadratic inequalities, absolute value inequalities, rational inequalities, logarithmic inequalities and trigonometric inequalities.

Linear inequalities: These are inequalities involving a linear function and a single variable. They can be represented in the form of "ax + b > c" or "ax + b < c" where a, b, and c are constants, and x is the variable.

Quadratic inequalities: These are inequalities involving a quadratic function and a single variable. They can be represented in the form of "ax^2 + bx + c > 0" or "ax^2 + bx + c < 0" where a, b, and c are constants, and x is the variable.

Absolute value inequalities: These are inequalities involving the absolute value of a variable or expression. They can be represented in the form of "|x| > a" or "|x| < a" where x is the variable and a is a constant.

Rational inequalities: These are inequalities involving a rational function (a function with a fraction) and a single variable. They can be represented in the form of "f(x) = (ax+b)/(cx+d) > 0" or "f(x) = (ax+b)/(cx+d) < 0" where a, b, c, d are constants, and x is the variable.

Logarithmic inequalities: These are inequalities involving logarithmic functions and a single variable. They can be represented in the form of "loga(x) > b" or "loga(x) < b" where a and b are constants, and x is the variable.

Trigonometric inequalities: These inequalities involve trigonometric functions such as sine, cosine, and tangent. These inequalities can be used to describe the range of possible values for an angle or a real-valued function.

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a) To find g(-6), we can estimate the value of g(-6) by finding the equation of the line that passes through the points (-5,0) and (-3,-2). To do this, we can use the slope-intercept formula:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the points on the line.

m = (y2 - y1) / (x2 - x1) = (-2 - 0) / (-3 - (-5)) = -1/2

Using the point-slope formula with (x1, y1) = (-5, 0), we get:

y - 0 = (-1/2)(x - (-5))

y = (-1/2)x + 5/2

Therefore, g(-6) is approximately equal to g(-5), which we can find by substituting x = -5 into the equation:

g(-5) = (-1/2)(-5) + 5/2 = 5/2

So, g(-6) is approximately equal to 5/2.

b) To find g(4), we look for the value of y when x is 4. From the table, we can see that when x is 4, g(x) is equal to -6. Therefore, g(4) = -6.

c) To find the value of x when g(x) is 0, we look for the row where g(x) is 0. From the table, we can see that when x is -5, g(x) is equal to 0. Therefore, x = -5 when g(x) = 0.

Answer:

2x+ 2y = -2

Step-by-step explanation:

Given the equation of a line as x + y = -1

To get the equation of the line P so the set of equations has infinitely many solutions, we will have to multiply the given equation by a factor

Multiplying the given equation by a factor of 2;

Given x + y = -1

Multiplying both sides by 2;

2(x + y) = 2(-1)

2x+ 2y = -2

Hence the required equation is 2x+ 2y = -2

Given that X has k-stage Erlang distribution with parameter 1. Therefore, the probability density function of X can be given as follows: f(x)={λkxk−1e−λx(k−1)!for x≥0otherwiseY=2XX2 = 2kXX has the chi-square distribution with 2k degrees of freedom.

Therefore, we need to prove the moment generating function of Y equals the moment generating function of a chi-square distribution with 2k degrees of freedom. Moment generating function of X can be given as follows: MX(t) = (1−t/λ)−k Therefore, moment generating function of Y can be given as follows: MY(t) = E(etY)= E[et(2kXX2)] ... Equation (1)Since X has k-stage Erlang distribution with parameter 1, let’s represent it as the sum of k independent exponentially distributed random variables with mean 1/λ as follows: X=∑i=1kExpiwhere Exp is an exponentially distributed random variable with mean 1/λ.

Therefore, Equation (1) can be written as follows:MY(t) = E [et(2kX(Expi)22)] = E [et∑i=1k(2kExpi)22] = ∏i=1k E [et(2kExpi)22] ... Equation (2)The moment generating function of an exponentially distributed random variable Exp with parameter λ can be given as follows:ME(t) = E(etExp) = ∫0∞etxe−λxdx = λλ−tThe moment generating function of Xpi can be calculated by replacing λ with kλ in the moment generating function of Exp.

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The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

Part A
Option C

Part B
Option A

Step-by-step explanation:

Part A

The equation for revenue gained for x tickets sold by Alpacas team

is y = 7.5x

This indicates the slope is 7.5 which means for every ticket sold the revenue increases by $7.50

Or in other words, cost of each ticket = $7.50

The revenue - ticket relationship for the Stingrays is given in the form of a graph with a linear equation

The slope of the graph can be found by rise/run where rise

= difference in y values for 2 points on the graph and run

= difference in the corresponding x values

Let's take points (0, 0) and (100, 1500) to find the slope
rise = (1500 - 0)/(10-0) = 1500/10 = 150

run = 10 - 0 = 10

Slope = 150/10 = 15

Equation is y = 15x

So for every ticket sold, the revenue increases by $15

Or in other words, cost of each ticket = $15

Therefore each Stingrays ticket costs 15/7.5 = 2 times each Alpacas ticket

Correct Answer:
Option C

---------------------------------------------------------------------------------------------------------

Part B

For the Geckos swim team we can see that as the number of tickets increases from 6 to 18(difference of 18- 6 = 12), the revenue increases by 180 - 60 = $120

Cost for ticket between 6 and 18 tickets = $120/12 = $10

When tickets sold increases from 18 to 54 (difference of 54 - 18= 36), the revenue increases by $540 - $180 = $360

Therefore the price for each ticket within this range = $360/36 = $10

So the price per ticket is the same regardless of the number of tickets sold

Therefore Gecko's revenue can be modeled as y = 10x

Alpacas charge $7.50 per ticket and Gecko's charge $10 per ticket
So the difference between a Gecko's ticket and an Alpacas ticket

= $10 - $7.50

= $2.50 more than Alpacas

or, alternatively

Alpacas charge $2.50 less than Gecko per ticket

Correct Answer

Option A

Answer:

The equation in standard form is:

x^2-40x-6000 = 0

Step-by-step explanation:

Let the length of the field be x yards.

Now the width of the field is 40 yards less than the length of the field.

Thus, the width of the field would be (x-40) yards

Now, to calculate the area of the field, we simply multiply the length of the field by the width of the field.

Hence;

Since the shape is rectangular, the area is the product of the length and that of the width

x(x-40) =6,000

x^2 -40x = 6,000

x^2-40x-6000 = 0

The value of a is -1/2 when the slope of a line passing through points A(2a,3) and B(-1,3) is 6.

The slope formula can be used to find the value of a in the equation,  which states that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula (y2 - y1) / (x2 - x1).

In this case, the two points are A(2a, 3) and B(-1, 3), and we know that the slope is 6.

By substituting values into the slope formula:

(3 - 3) / (-1 - 2a) = 6

Simplifying the equation:

0 / (-1 - 2a) = 6

-1 - 2a = 0

-1 = 2a

Dividing both sides by 2:

-1/2 = a

So, the value of "a" is -1/2.

Therefore the value of a is -1/2 when the slope of a line passing through points A(2a,3) and B(-1,3) is 6.

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The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

Let X the random variable that represent the diameters of interest for this case, and for this case we know the following info

Where \($\mu=205$\) and \($\sigma=1.5$\)

Let the probability be

\($P(205-0.3=204.7 < \bar{X} < 205+0.3=205.3)$$\)

For this case they select a sample of n = 79 > 30, so then we have enough evidence to utilize the central limit theorem and the distribution for the sample mean can be approximated with:

\($\bar{X} \sim N\left(\mu, \frac{\sigma}{\sqrt{n}}\right)$$\)

To simplify this problem is utilizing the normal standard distribution and the z score given by:

\($z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$$\)

To find the z scores for each limit and we got:

\($z=\frac{204.7-205}{\frac{1.5}{\sqrt{79}}}=-1.778$$\)

\($z=\frac{205.3-205}{\frac{1.5}{\sqrt{79}}}=1.778$$\)

To find this probability:

P(-1.778 < Z < 1.778) = P(Z < 1.778) - P(Z < -1.778)

simplifying the above equation, we get

= 0.962 - 0.0377

= 0.9243

The interest exists the probability that the mean diameter of the sample shafts would vary from the population mean by more than 0.3 inches utilizing the complement rule we got:

P = 1 - 0.9243 = 0.0757

The probability that the mean diameter of the sample shafts would vary from the population mean by less than 0.3 inches exists 0.0757.

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Answer:

For the function: \(g(x)=-x^2-3x+5\), the average rate of change of function over the interval \(-7\leq x\leq 2\) is 2

Step-by-step explanation:

We are given function: \(g(x)=-x^2-3x+5\), we need to find average rate of change of function over the interval \(-7\leq x\leq 2\)

The formula used is: \(Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\)

We have b=2 and a= -7

Finding f(b) and f(a)

Finding g(b) by putting x=2

\(g(x)=-x^2-3x+5\\g(2)=-(2)^2-3(2)+5\\g(2)=-4-6+5\\g(2)=-10+5\\g(2)=-5\)

Finding g(a) by putting x=-7

\(g(x)=-x^2-3x+5\\g(-7)=-(-7)^2-3(-7)+5\\g(-7)=-49+21+5\\g(-7)=-23\)

Now, finding average rate of change when g(b)=-5 and g(a)=-23

\(Average \ rate \ of \ change=\frac{g(b)-g(a)}{b-a}\\Average \ rate \ of \ change=\frac{-5-(-23)}{2-(-7)}\\Average \ rate \ of \ change=\frac{-5+23}{2+7}\\Average \ rate \ of \ change=\frac{18}{9}\\Average \ rate \ of \ change=2\)

So, Average rate of change = 2

Therefore for the function: \(g(x)=-x^2-3x+5\), the average rate of change of function over the interval \(-7\leq x\leq 2\) is 2

Answer:

x=5 and y=2

Step-by-step explanation:

Let's solve your system by substitution.

3x+y=17;4x−y=18

Step: Solve 3x+y=17 for y:

3x+y=17

3x+y+−3x=17+−3x(Add -3x to both sides)

y=−3x+17

Step: Substitute−3x+17 for y in 4x−y=18:

4x−y=18

4x−(−3x+17)=18

7x−17=18(Simplify both sides of the equation)

7x−17+17=18+17(Add 17 to both sides)

7x=35

7x

7

=

35

7

(Divide both sides by 7)

x=5

Step: Substitute 5 for x in y=−3x+17:

y=−3x+17

y=(−3)(5)+17

y=2(Simplify both sides of the equation)

The probability of the new engine design being approved given that it is low-energy is 0.2, or 20%.

To find the probability of the new engine design being approved, we need to use the concept of conditional probability.

We can use Bayes' Theorem to calculate this conditional probability:

P(A|H) = P(H|A) x P(A) / P(H)

where P(A|H) is the probability of the engine being approved given that it is high-energy, P(H|A) is the probability of the engine being high-energy given that it is approved, P(A) is the overall probability of the engine being approved (irrespective of energy consumption), and P(H) is the overall probability of the engine being high-energy.

Using the values given in the problem, we can substitute in these probabilities:

P(H|A) = 0.1 (given)

P(A) = P(H)P(A|H) + P(L)P(A|L) = 0.50.1 + 0.50.2 = 0.15

P(H) = 0.5 (given)

Therefore, we can calculate:

P(A|H) = 0.1 x 0.5 / 0.15 = 1/3 = 0.333

This means that the probability of the new engine design being approved given that it is high-energy is 0.333, or approximately one-third. Similarly, we can find the probability of the engine being approved given that it is low-energy:

P(A|L) = P(L|A) x P(A) / P(L)

P(L|A) = 1 - P(H|A) = 0.9 (given)

P(L) = 0.5 (given)

P(A|L) = 0.2 * 0.5 / 0.5 = 0.2

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Answer:

y = -1/3x + 2

Step-by-step explanation:

Divide everything by 2

Answer: 50 ml of butter

Step-by-step explanation:

Answer:

60000

Step-by-step explanation:

You should treat the first son with the 1 ratio as x. Because of this, the second son would be 3x and the third would be 6x. All of them need to equal 120000 so 10x=120000. Next you isolate the and x= 12000. Fill in 1200 for x and the first son gets 12000, the second gets 36000, and the third gets 72000. Lastly you subtract and you get 60000.

Answer:

The 1st step in evaluating the expression is doing the equation in the paranthesis. PEMDAS states we do the paranthesis 1st.

The training heart rate function, T(M) for a person with a resting heart rate of 62 beats per minute is 0.6M.

a. The maximum heart rate function, M() for a person a years of age. M(x) is 220 - x.

The formulas provided are:

T(M, R) = R + 0.6(M - R)M(z) = 220 - z

where R is the resting heart rate, M is the maximum heart rate, and z is the age.

Using the formula T(M, R) = R + 0.6(M - R), we can find the training heart rate function, T(M), for a person with a resting heart rate of 62 beats per minute:

T(M, R) = R + 0.6(M - R)T(M, 62) = 62 + 0.6(M - 62)T(M, 62) = 62 + 0.6M - 37.2T(M, 62) = 24.8 + 0.6M

Therefore, the training heart rate function for a person with a resting heart rate of 62 beats per minute is T(M) = 24.8 + 0.6M.

To find the maximum heart rate function, M(x), for a person a years of age, we can use the formula M(z) = 220 - z:

M(z) = 220 - z

M(a) = 220 - a

Therefore, the maximum heart rate function for a person a years of age is M(x) = 220 - x.

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Answer:

19

Step-by-step explanation:

The number of shares remaining after the stockbroker buys shares for her customers is 57500

Also, The number of the most important pretty definitely really variable for finding the number of shares the company particularly definitely for all intents and purposes has left in a generally really big way in a fairly big way. Also, The number of shares the company generally really definitely has left after stockbroker's purchase = 95000 - 150×250 = 5750 in a subtle way.

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Answer: (14)(-2/4.89)

i’m currently doing a test with the same expression as yours, i tried googling the answer which was no help. i eventually decided to work it out on my own and i came up with this answer

Answer:

The weight is 100.

Step-by-step explanation:

65 divided by 13 = 5

500 divided by 5 = 100

Given functionis`y = 2 cos 3/2 (u - 40°)`. We are required to find the amplitude, period, phase shift, and sketch one cycle of its graph on the given interval. The amplitude of the given function is `2`. The period of the given function is `4π / 3`. The phase shift of the given function is `- 80 / 3`

.

Let's find these one by one.Amplitude

Given function: `y = 2 cos 3/2 (u - 40°)

The amplitude of a cosine function is the absolute value of the coefficient of `cos u` .So, the amplitude of the function `y = 2 cos 3/2 (u - 40°)` is `2`.

Therefore, the amplitude of the given function is `2`.Period

The period of a cosine function is given by the formula `2π/ b`, where `b` is the coefficient of `u`.So, the period of the function `y = 2 cos 3/2 (u - 40°)` is `2π / (3/2) = 4π / 3`.

Therefore, the period of the given function is `4π / 3`Phase Shift

The phase shift is given by the formula `(h / b)` where `h` is the value inside the bracket. `h` is positive for shifts to the left and negative for shifts to the right. In this case, `h = 40`.Since there is a minus sign, the function is shifted to the right. So, the phase shift of the function `y = 2 cos 3/2 (u - 40°)` is `-40° / (3/2) = - 80 / 3` .

Therefore, the phase shift of the given function is `- 80 / 3`.Graph of `y = 2 cos 3/2 (u - 40°)`

One cycle of the graph of the given function can be plotted as follows:

The function `y = 2 cos 3/2 (u - 40°)` starts from its maximum value `2` when `(u - 40°) = 0°`.

At this point, the value of `u` is `40°`.

The next maximum value occurs when `cos 3/2 (u - 40°) = 1`.

This occurs when `3/2 (u - 40°) = 0` or `(u - 40°) = 0`.

Therefore, `u = 40° + 0° = 40°`.

The next minimum value occurs when `cos 3/2 (u - 40°) = -1`.

This occurs when `3/2 (u - 40°) = π` or `(u - 40°) = 2π/3`.

Therefore, `u = 40° + 2π/3`.

The next maximum value occurs when `cos 3/2 (u - 40°) = 1`.

This occurs when `3/2 (u - 40°) = 2π` or `(u - 40°) = 4π/3`. Therefore, `u = 40° + 4π/3`.

Therefore, the graph of the given function over the interval `0° ≤ u ≤ 360°` is as follows:Answer:

The amplitude of the given function is `2`.

The period of the given function is `4π / 3`.

The phase shift of the given function is `- 80 / 3`.

The graph of the given function over the interval `0° ≤ u ≤ 360°` is as follows:

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Answer:

FIRST ONE IS 300

Step-by-step explanation:

5X8X7.5=300 l x w x h

Answer:

Question A:
Your Answer would be:
C.) 300ft2

5 x 8 x 7.5 =
(5 x 8) x 7.5 =
40 x 7.5 = 300ft2


Question B:
Your answer would be:
C.) 39.25in2
(not very sure about this one let me know if it's right or wrong)



Step-by-step explanation:

Have a great rest of your day
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Answer:-8

Step-by-step explanation:

Answer:

This is an example of task abstraction, which refers to identifying the fundamental goals and objectives of a data visualization task by abstracting it from the specific context and formulating it in general terms. In this case, the task abstraction is to visualize the correlation between two numeric variables.

Step-by-step explanation:

The the distance between the school and Nokesville be on the map is 0.7 inches.

What is scaling ?

It is the technique to resize drawing with comparing to actual size of object which uses proportion or ratio. For example, Mapping of earth, drawing prototype of automobiles.

It is given that :

The distance between the school and Target is 4.2 miles and on a map the ratio is 0.5 inches is equal to 3 miles that is :

3 miles = 0.5 inches on map

Now to find the distance between the school and Nokesville be on the map we first find for 1 miles on the map and then multiply it by 4.2 miles :

3 miles = 0.5 inches on map

1  miles = 0.5/3 inches on map

4.2 miles = (0.5/3) x 4.2 inches on map

4.2 miles = 0.7 inches inches on map

Therefore, the the distance between the school and Nokesville be on the map is 0.7 inches.

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(-∞, -1.96) ∪ (1.96, ∞) is the rejection region.

Consider the given hypothesis,

H0:=μ=7, S=5, ⎯⎯⎯⎯⎯=5X¯=5, n=46

H1:=μ≠7

The rejection region is given as follows:

Step 1: Find the level of significance α=0.05

Step 2: Find the rejection region, which can be found using the Z-distribution, given as

Z> zα/2, Z< -zα/2

where

zα/2 is the critical value of the Z-distribution such that P(Z > zα/2) = α/2 and P(Z < -zα/2) = α/2

The rejection region can be written as (-∞, -zα/2) ∪ (zα/2, ∞)

The rejection region is ( -∞, -1.96) ∪ (1.96, ∞)

Round off to 2 decimal places, (-∞, -1.96) ∪ (1.96, ∞) is the rejection region.

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