For the function

h(x)=−x3−3x2+15x+3 , determine the absolute maximum and minimum values on the interval [-6, 3]. Keep 1 decimal place (rounded) (unless the exact answer is an integer).

Answer: Absolute maximum = 21 at x= -6

Absolute minimum = -43.40 at x= -3.4

Answer:

22

Step-by-step explanation:

g(x) = 3x + 1

g(7) = 3(7) + 1

= 21 + 1

= 22

hope this helps! :D

have a miraculous day!! <3

Answer:

OC. $57.28

Step-by-step explanation:

It depends on how much she sells them for.

Let's say Anne sells them for $x.

Then her profit is:

8x-(8*7.16)

=8x-57.28

To make a minimum to at least make even is $57.28 and sell for $7.16 a piece.

Anne makes a profit of $57.28 on the sale of these 8 canvases. which is the correct answer would be option (C).

The profit is equal to the difference between the selling price and the original cost price.

Anne purchases art supplies for her business from a wholesaler. She spends $7.16 on eight 16 by 20-inch canvases.

To calculate the profit that Anne makes on the sale of these 8 canvases, you need to know the price at which she sells them and the cost of buying them from the wholesaler. If the cost of each canvas is $7.16 and she buys 8 of them, the total cost of the canvases is :

⇒ 8 × $7.16

Apply the multiplication operation and we get

⇒ $57.28.

Therefore, she makes a profit of $57.28 on the sale of these 8 canvases.

Hence, the correct answer would be an option (C).

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The derivative dx/dy of the equation 2x+3y=sin(x) is (3y) / cos(x).

To find dx/dy of the equation 2x+3y=sin(x), we can differentiate both sides using the chain rule and solve for dx/dy.

To find dx/dy, we need to differentiate both sides of the equation 2x+3y=sin(x) with respect to y. Let's start by differentiating the left-hand side (LHS) and the right-hand side (RHS) separately.

For the LHS, we have two terms: 2x and 3y. The derivative of 2x with respect to y is 0 since x does not depend on y. The derivative of 3y with respect to y is simply 3, as y is being differentiated with respect to itself.

Now, let's differentiate the RHS. The derivative of sin(x) with respect to y requires the chain rule. The chain rule states that if u = f(x) and x = g(y), then du/dy = (du/dx) * (dx/dy). In this case, u = sin(x) and x = g(y) (which means x is a function of y).

The derivative of sin(x) with respect to x is cos(x), and the derivative of x with respect to y is dx/dy. Therefore, applying the chain rule, we have du/dy = cos(x) * (dx/dy).

Now, equating the derivatives obtained for both sides of the equation, we have 0 + 3y = cos(x) * (dx/dy). Simplifying, we find dx/dy = (3y) / cos(x).

Therefore, the derivative dx/dy of the equation 2x+3y=sin(x) is (3y) / cos(x).

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Answer:

x = 14

y = 31/2

Step-by-step explanation:

\(y = \dfrac{5}{4}x-2 ---------------(i)\\\\\\y =\dfrac{-1}{4}x + 19 --------------(ii)\\\\\\Substitute \ y =\dfrac{5}{4}x -2 \ in \ equation \ (2) \\\\\\\dfrac{5}{4}x-2=\dfrac{-1}{4}x+19\\\\\\\dfrac{5}{4}x-2+\dfrac{1}{4}x=19\\\\\\\dfrac{6}{4}x-2=19\\\\\\\dfrac{6}{4}x=19+2\\\\\\\dfrac{6}{4}x=21\\\\\\x=21*\dfrac{4}{6}\\\\\\x=\dfrac{7*4}{2}\\\\\\x=7*2=14\\\\\\substitute \ x= 14\ in \ equation (1)\\\\\\y=\dfrac{5}{4}*14 }-2\\\\y=\dfrac{35}{2}-2\\\\\\\)

\(y=\dfrac{35}{2}-\dfrac{2*2}{1*2}\\\\\\y=\dfrac{35}{2}-\dfrac{4}{2}\\\\y=\dfrac{31}{2}\)

a.8.25 kg is equivalent to 8250 grams.

b. 0.0002948 Ms is equivalent to 0.2948 seconds.

c. 6,400,000,000 nL is equivalent to 0.0064 L.

d. 9,113 mg is equivalent to 9.113 grams.

e. 0.0048 ks is equivalent to 4.8 seconds.

f. 3.0 cL is equivalent to 0.03 L.

The following is the conversion of given terms to grams, liters or seconds: a. 8.25 kg

To convert kg to grams, multiply by 1000

Thus, 8.25 kg is equivalent to 8250 grams.

b. 0.0002948Ms

To convert Ms to seconds, multiply by 1000. Thus, 0.0002948 Ms is equivalent to 0.2948 seconds.

c. 6,400,000,000 nL

To convert nL to liters, divide by 1,000,000,000. Thus, 6,400,000,000 nL is equivalent to 0.0064 L.

d. 9,113 mg

To convert mg to grams, divide by 1000. Thus, 9,113 mg is equivalent to 9.113 grams.

e. 0.0048 ks

To convert ks to seconds, multiply by 1000. Thus, 0.0048 ks is equivalent to 4.8 seconds.

f. 3.0 cL

To convert cL to liters, divide by 100. Thus, 3.0 cL is equivalent to 0.03 L.

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Answer:

d

Step-by-step explanation:

the graph increases then goes horizontal

Answer:

D

Step-by-step explanation:

D is the choice you have to make. The culprit is the word quickly. You can't tell if the speed is increasing quickly or not.

The correct part of d is that the bicycle stays at a constant rate until  the end of the timing of the graph.

A solution of the differential equation is given by:

F(x,y) = (x^5 - 2xy + C/(|7x-3y^3|^3))|7x-3y^3|^3

where C is an arbitrary constant.

To determine whether the differential equation (4x^4 − 4y)dx + (3y^3 − 7x)dy = 0 is exact, we need to check if its partial derivatives with respect to x and y are equal:

∂/∂y (4x^4 − 4y) = -4

∂/∂x (3y^3 − 7x) = -7

Since these partial derivatives are not equal, the differential equation is not exact.

To find a solution of the form F(x,y) = C, where C is a constant, we can try to find an integrating factor μ(x,y) such that μ(x,y)(4x^4 − 4y)dx + μ(x,y)(3y^3 − 7x)dy = 0 becomes exact. If we can find such a function, then we can multiply both sides of the differential equation by μ(x,y) and obtain an exact differential equation which can be solved using standard methods.

To find the integrating factor μ(x,y), we can use the formula:

μ(x,y) = e^(∫(∂M/∂y - ∂N/∂x)/N dx)

where M = 4x^4 − 4y and N = 3y^3 − 7x.

Substituting these into the formula, we get:

μ(x,y) = e^(∫((-4-(-7))/(3y^3-7x)) dx)

= e^(∫3/(7x-3y^3) dx)

= e^(3ln|7x-3y^3|)

= |7x-3y^3|^3

Multiplying both sides of the differential equation by μ(x,y) = |7x-3y^3|^3, we get:

(4x^4 − 4y)|7x-3y^3|^3 dx + (3y^3 − 7x)|7x-3y^3|^3 dy = 0

This equation is exact, since its partial derivatives with respect to x and y are equal. Therefore, we can find a solution F(x,y) by integrating its differential form:

dF = (4x^4 − 4y)|7x-3y^3|^3 dx + (3y^3 − 7x)|7x-3y^3|^3 dy

Integrating the first term with respect to x and the second term with respect to y, we get:

F(x,y) = (x^5 - 2xy + g(y))|7x-3y^3|^3

where g(y) is an arbitrary function of y.

To determine g(y), we can use the fact that F(x,y) is constant, i.e., F(x,y) = C for some constant C. Substituting this into the above expression, we get:

C = (x^5 - 2xy + g(y))|7x-3y^3|^3

Solving for g(y), we get:

g(y) = (C/(|7x-3y^3|^3)) - x^5 + 2xy

Therefore, a solution of the differential equation is given by:

F(x,y) = (x^5 - 2xy + C/(|7x-3y^3|^3))|7x-3y^3|^3

where C is an arbitrary constant.

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Answer:

Required system of inequalities to represent this situation:

Given:

Opal makes $15 per hour working for a photographer.

She also coaches a competitive soccer team for $10 per hour.

Defining variables

Let x = Number of hours she works as a photographer, y= Number of hours she works as coach.

Explanation

As she needs to earn at least $90 per week i.e.  

but she does not want to work more than 20 hours per week.

i.e.  

Required system of inequalities to represent this situation:

Step-by-step explanation:

HOPE THIS HELPS

Required system of inequalities to represent this situation 15x + 10y ≥ 20 and x + y ≤ 20.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

Given that Opal makes $15 per hour working for a photographer. She also coaches a competitive soccer team for $10 per hour.

Defining variables Let x = Number of hours she works as a photographer, y= Number of hours she works as a coach.

As she needs to earn at least $90 per week i.e. but she does not want to work more than 20 hours per week. The required system of inequalities to represent this situation.

15x + 10y ≥ 20

x + y ≤ 20.

Therefore, the required system of inequalities to represent this situation is 15x + 10y ≥ 20 and x + y ≤ 20.

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Sequence of P1, P2, and P3 are 6 8 6

Needs matrix = Claim matrix - Allocation matrix

R1 R2 R3 R1 R2 R3

P1 0 1 2 P1 -1 -1 1

P2 2 0 0 P2 2 2 0

P3 0 0 2 P3 0 0 -2

Resource vector = Sum of Allocation matrix - Available vector

R1 R2 R3

6 7 5

Available vector = Resource vector - Sum of Allocation matrix

R1 R2 R3

3 4 2

According to the Banker's algorithm

Then, the available vector becomes:

R1 R2 R3

4 5 3

P2's needs satisfied Hence, P2 selected for execution.

R1 R2 R3

6 8 4

P3's needs satisfied. Hence, P3 selected for execution.

R1 R2 R3

6 8 6

So, we have a safe sequence of P1, P2, and P3.

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Conditions I and II must be met in order to use the formula for the standard deviation of the sampling distribution for sample mean. The correct option is E.

Let's first understand what the formula for the standard deviation of the sampling distribution for sample mean is. This formula is used to calculate the standard deviation of the means of all possible samples of a certain size that can be taken from a population. It is given by the equation: σ=σ/√. Where σ is the standard deviation of the sampling distribution for sample mean, σ is the population standard deviation, and is the sample size. Condition I states that the population's distribution is approximately Normal. This condition is important because if the population's distribution is not Normal, the sample means may not follow a Normal distribution, and the formula for the standard deviation of the sampling distribution for sample mean may not be accurate.

Conditions I and II must be met to use the formula for the standard deviation of the sampling distribution for sample mean. If only one of these conditions is met, the formula may not be accurate. If both conditions are met, the formula can be used to calculate the standard deviation of the sampling distribution for sample mean.

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The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.

A statistical question is a question that can be answered by collecting and analyzing data. It is a question that involves variability, uncertainty, or randomness and cannot be answered with a single definitive answer.

Instead, it requires the use of statistical methods to analyze and summarize data to make informed decisions.

Here we have

A video game company will make a new game. The manager must choose between role-playing the game and an action game. He asks his sales staff which of the last 10 released games sold the most copies.

This is a statistical question because it involves collecting and analyzing data to make an informed decision.

The manager is seeking information from the sales staff about the last 10 released games to determine which type of game - role-playing or action - is more likely to sell well.

By analyzing the sales data, the manager can make a data-driven decision about which game to develop, rather than relying solely on intuition or personal preferences.

To answer the question, the sales staff would need to collect data on the sales figures of each of the last 10 released games, which involves using statistical methods to analyze and summarize data.v

Therefore,

The question is statistical because it requires data analysis, statistical methods, and interpretation of results to make a decision.

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Step-by-step explanation:

Solution:

Given,

So,

n(S) = 8

n(E) = 4+3 = 7

Here,

P(getting blue or yellow marble)

\( \frac{n( e)}{n(s)} \)

= 7 /8

Therefore , probability of getting blue or yellow marble is 7/8.

Answer:

6400

Step-by-step explanation:

To find the number that makes the perfect square of 80, multiply 80 times 80 (square 80).

80 squared equals 6400, which means the square root of 6400 would be the perfect square 0f 80.

The given fraction (x^2-25)/(x^2-x-20) expressed in simplest form is (x+5)/(x+4). (Option C)

A fraction is in simplest form if the numerator and denominator have no common factors other than 1. In order to solve the given fraction, the numerator and denominator must be factorized, and the common factor will be canceled out.

Factoring x^2 – 25 using the difference of squares formula that states that a^2 – b^2 = (a + b)(a - b)

x^2 – 25 = x^2 – 5^2 = (x + 5)(x – 5)

Factoring x^2 – x – 20,

x^2 – x – 20 = x^2 + 4x – 5x – 20 = x(x + 4) -5(x + 4) = (x + 4)(x – 5)

Hence, factor (x – 5) is there in both numerator and denominator, it is canceled out. Hence the fraction in the simplest form is:

(x + 5)(x – 5)/ (x + 4)(x – 5) = (x + 5)/(x + 4)

Note: The question is incomplete.  The complete question probably is:  What fraction represents(x^2-25)/(x^2-x-20) expressed in simplest form. A) 5/4 B) (x-5)/(x-4) C) (x+5)/(x+4) D)25/(x+20)

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Answer:

\(\frac{1}{7}\,\,miles/minute\)

Step-by-step explanation:

Given: Travis and Tony took 40 minutes to skate 5 miles and the return trip took them 30 minutes

To find: average speed for the trip

Solution:

Total distance = 5 + 5 = 10 miles

Total time = 40 + 30 = 70 minutes

So,

Average speed for the trip = Total distance/Total time = \(\frac{10}{70}=\frac{1}{7}\) miles/minute

Answer:

the time spent

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4-4 =0 so therefore the answer is 4

Answer:

I think it's 2 sorry if I am wrong but

Step-by-step explanation:

2 squared equals 4 and 4 minus 4 equals zero

The magnitude of the magnetic dipole moment of the coil is approximately 0.079 A·m². The magnitude of the torque acting on the coil is approximately 0.068 N·m.

(a) To find the magnitude of the magnetic dipole moment (M) of the coil, we can use the formula M = NIA, where N is the number of turns, I is the current flowing through the coil, and A is the area of the coil. For the circular coil, the area is given by A = πr², where r is the radius. Substituting the values N = 21, I = 11.8 mA = 0.0118 A, and r = 4.8 cm = 0.048 m, we can calculate the magnetic dipole moment as M = NIA = 21 * 0.0118 * π * (0.048)² ≈ 0.079 A·m².

(b) The torque acting on the coil can be calculated using the formula τ = M x B, where M is the magnetic dipole moment and B is the magnetic field strength. The magnitude of the torque is given by |τ| = M * B, where |τ| is the absolute value of the torque. Substituting the values M ≈ 0.079 A·m² and B = 0.350 T, we can calculate the magnitude of the torque as |τ| = M * B ≈ 0.079 A·m² * 0.350 T ≈ 0.068 N·m.

Therefore, the magnitude of the magnetic dipole moment of the coil is approximately 0.079 A·m², and the magnitude of the torque acting on the coil is approximately 0.068 N·m.

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The probability of spinning an even number or a prime number is 5/6.

The total number of possible outcomes is 12 since there are 12 sections on the spinner.

Therefore, the probability of spinning an even number or a prime number is:

Probability = (Number of favorable outcomes) / (Total number of possible outcomes)

Probability = 10 / 12

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Probability = (10 / 2) / (12 / 2)

Probability = 5 / 6

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Answer: 20/3

Step-by-step explanation:

To write 6 2/3 as a fraction greater than 1, we simply have to convert it from a mixed fraction to an improper fraction. This will be:

6 2/3 = [(6 × 3) + 2]/3

= (18 + 2)/3

= 20/3

Therefore, the answer is 20/3.

Answer:

Step-by-step explanation:

ummm so it doesnt have a y axis...

i think it should be

y=4x which is the parallel

and y= -1/4x which is perpendicular, it doesnt really pass through (4,3) so ot sure what ur teacher wants really

The total amount Lusac have in his savings after 3 more years with 1.8% saving interest is $1055.10.

Simple interest is the amount charged on the principal amount with a fixed rate of interest for a time period. Simple interest calculated only on the principal amount.

The formula for the simple interest can be given as,

\(I=\dfrac{Prt}{100}\)

Here, (I) is the interest amount earned on the principal amount of (P) with the rate of (r) in the time period of (t).

Lucas spends $83.42 in additional interest and charges on monthly payments as the result of a prior bankruptcy. The amount save in a year (12 months) is,

\(P=83.42\times12\\P=1001.04\)

The interest earned on this principal amount with earning 1.8% simple interest, after 3 years is,

\(I=\dfrac{1001.04\times1.83}{100}\\I=54.06\)

The total total amount in his bank account after 3 years is,

\(A=P+I\\A=1001.04+54.06\\A=1055.10\)

Hence, the total amount Lusac have in his savings after 3 more years with 1.8% saving interest is $1055.10.

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Answer:

b.

$1,055.10

Step-by-step explanation:

right on edg 22

The probability that Nandini will reach her hometown without having to head back is 0.50, or 50%. To understand why, let's analyze the scenario step by step. At the first four-way junction, Nandini randomly chooses one of the ways in front of her.

There are four possible directions she can take, and she selects one randomly. At the second four-way junction, again she randomly chooses one of the available paths. Since each junction has four possible directions, there are a total of 4 x 4 = 16 different combinations of paths Nandini can take. Out of these 16 possibilities, only 8 will lead her towards her hometown, while the remaining 8 will lead her away from her destination.

Since Nandini's choices at each junction are independent of each other, the probability of choosing a path that leads to her hometown at each junction is 1/2. Thus, the probability of reaching her hometown without heading back is (1/2) x (1/2) = 1/4 = 0.25. However, since there are two junctions involved, we need to multiply this probability by itself, resulting in a final probability of (1/4) x (1/4) = 1/16 = 0.0625. This can be rounded to 0.06 or 6% when expressed as a percentage.

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Answer:

A 0

Step-by-step explanation:

Since x = 2 is a vertical line, the slope is undefined. The slope of a perpendicular line to a vertical line is zero. So, the answer is A

Answer:

The choose a. – 2

Step-by-step explanation:

\(f( - 8) = \frac{ - 8}{4} = - 2\)

Answer:

1) greater than

2) less than

3) greater than

4)less than

5) greater than

6) greater than

Step-by-step explanation:

The test to use when there's an independent group design and ordinal data is the Kruskal Wallis test

Given: Independent group and ordinal data. To find which test to use.

What's the Kruskal Wallis test?

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The Kruskal Wallis test is used when you have one independent variable with two or further situations and an ordinal dependent variable. In other words, it's thenon-parametric interpretation of ANOVA and a generalized form of the Mann- Whitney test system since it permits two or further groups.

The null thesis for the Kruskal- Wallis test simply states that there are no methodical or harmonious differences among the treatments being compared.

How to calculate the Kruskal Wallis test?

The computation of the Kruskal- Wallis statistic requires

Hence as is mentioned for an independent group design and ordinal data so we use the Kruskal Wallis test.

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We can use the Kruskal Wallis test when we have an independent group design and ordinal data.

We are given an independent group design and ordinate data.

We need to tell which test to use on them.

The Kruskal Wallis test is used when you have one independent variable with two or more situations and one ordinal dependent variable. In other words, it is an interpretation of ANOVA table and a generalized form of the Mann- Whitney test system.

The null hypothesis for the Kruskal- Wallis test tells us that:

There are no methodical or harmonious differences among the treatments being compared.

Therefore, we can use the Kruskal Wallis test when we have an independent group design and ordinal data.

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