En una granja hay 500 animales. Si hay el triple de vacas que de ovejas, ¿ cuantas animales hay de cada especie

Answer:

(mn+n²)/(m+n)

Step-by-step explanation:

probability of blue marble= n/(n+m)

probability of red marble= m/(n+m)

probability that process stops = Probability of both blue + probability of both red=  n/(n+m) × n/(n+m) + m/(n+m)×m/(n+m)

                        = (n²+m²)/(n+m)²

P(1st marbel is blue)= P(blue and red) + P(blue and blue)

                                  = mn/(n+m) + n²/(n+m)

                                   = (mn+n²)/(m+n)

P(1st marble is blue | process stops)= ( (mn+n²)/(m+n)× (n²+m²)/(n+m)²)/ ((n²+m²)/(n+m)²)

= (mn+n²)/(m+n)

Answer:

.08

Step-by-step explanation:

Divide the percentage by 100.

8 / 100 = .08

Answer: 8% = .08

Step-by-step explanation: simple. if you use d2p. meaning decimal two percent. you take your decimal like .36 and move the dot two places forward making it 36%. same from percent to decimal by reversing it.

Answer:

  salary

Step-by-step explanation:

Salary is the term generally used to refer to the annual amount of wages.

_____

tuition is the amount paid to an educational institution for the classes they offer.

hourly wage refers to the amount earned in an hour, not a year.

expense is the name given to any expenditure, not an amount earned.

Answer:

C. Salary

Step-by-step explanation:

EDg

Answer:

A = $ 8,951.33

Step-by-step explanation:

A = $ 8,951.33

A = P + I where

P (principal) = $ 6,500.00

I (interest) = $ 2,451.33

Formula:

Continuous Compounding Formulas (n → ∞)

Calculate Accrued Amount (Principal + Interest)

A = Pe^rt

Calculate Principal Amount, solve for P

P = A / e^rt

Calculate rate of interest in decimal, solve for r

r = ln(A/P) / t

Calculate rate of interest in percent

R = r * 100

Calculate time, solve for t

t = ln(A/P) / r

A = Accrued Amount (principal + interest)

P = Principal Amount

I = Interest Amount

R = Annual Nominal Interest Rate in percent

r = Annual Nominal Interest Rate as a decimal

r = R/100

t = Time Involved in years, 0.5 years is calculated as 6 months, etc.

n = number of compounding periods per unit t; at the END of each period

Compound Interest Equation

A = P(1 + r/n)^nt

Answer:

Parasite

Step-by-step explanation:

It feeds off of other organisms by living on or in the animal.

Answer: f(-2)=3

Step-by-step explanation:

Answer: D. f(–2) = 3

Step-by-step explanation: EDGE 2022

Answer:

can you please post the pyramid

Step-by-step explanation:

The statements that are true concerning the rectangular pyramids include the following:

What are the properties of a rectangular pyramid?

The properties of a rectangular pyramid include the following:

From the given rectangular pyramid, The area of the base is 24 cm² because, 6*4= 24cm²

There are four lateral faces which are triangular in shape.

Answer:

Explanation:

Answer:

Explanation:

Answer:

Step-by-step explanation:

Socratic had the answer on there I think

Answer:

We conclude that the average height of hobbit is taller than Yoda.

Step-by-step explanation:

We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.

From a sample of 7 hobbits, you find their mean height [tex]\bar X[/tex] = 80 cm with standard deviation s = 10.8 cm.

Let [tex]\mu[/tex] = average height of hobbit.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 66 cm      {means that the average height of hobbit is shorter than or equal to Yoda}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 66 cm      {means that the average height of hobbit is taller than Yoda}

The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;

                     T.S. =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean height = 80 cm

             s = sample standard deviation = 10.8 cm

             n = sample of hobbits = 7

So, test statistics  =  [tex]\frac{80-66}{\frac{10.8}{\sqrt{7}}}[/tex]  ~ [tex]t_6[/tex]

                              =  3.429

The value of t test statistics is 3.429.

Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the average height of hobbit is taller than Yoda.

Answer:

-6 ÷ -2 and  (-1)(-3)

Step-by-step explanation:

To find which expressions have a value of 3, set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply.

To find which expressions have a value of 3, we can set each expression equal to 3 and solve for the variable. The expressions that have a value of 3 when the variable is substituted are the ones that apply. Let's go through each expression:

So, the only expression that has a value of 3 is 2x - 1 = 3 when x = 2.

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Answer:

Move all the terms to the left and set equal to zero.

Then set each factor equal to zero.

Step-by-step explanation:

I hope this helps

The correct answer is that the expression [tex]\(a^2 + 2ab + b^2\)[/tex]  equals 44.

To solve the given mathematical expression [tex]\(a^2 + 2ab + b^2\),[/tex] we recognize that it is a perfect square trinomial. The perfect square trinomial can be factored into the square of a binomial:

[tex]\[ (a + b)^2 = a^2 + 2ab + b^2 \][/tex]

Given that this expression equals 44, we can set the factored form equal to 44:

[tex]\[ (a + b)^2 = 44 \][/tex]

To find the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we take the square root of both sides of the equation. Remembering that the square root of 44 is not a whole number, we can express it as the product of prime factors:

[tex]\[ \sqrt{44} = \sqrt{4 \cdot 11} = \sqrt{2^2 \cdot 11} = 2\sqrt{11} \][/tex]

 Therefore, we have:

[tex]\[ a + b = \pm 2\sqrt{11} \][/tex]

This equation tells us that the sum of [tex]\(a\)[/tex] and [tex]\(b\)[/tex] is either [tex]\(2\sqrt{11}\) or \(-2\sqrt{11}\).[/tex] Without additional information about [tex]\(a\)[/tex] and [tex]\(b\)[/tex], we cannot determine unique values for [tex]\(a\)[/tex] and [tex]\(b\)[/tex], but we know that their sum must equal one of these two values.

The expression [tex]\(a^2 + 2ab + b^2\)[/tex] is indeed equal to 44, and the relationship between [tex]\(a\)[/tex]  and [tex]\(b\)[/tex] is given by [tex]\(a + b = \pm 2\sqrt{11}\).[/tex]

Answer:

  see below for a graph

  x = 4

Step-by-step explanation:

The perimeter is given by the formula ...

  P = 2(L +W)

The area is given by the formula ...

  A = LW

We want these two values to be equal. Using "y" for both perimeter and area, and substituting the given values for L and W, we have the equations ...

  y = 2(4 +x)

  y = 4x

The graph of these equations (below) shows the value of x is 4.

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4-0.25(10)+0.5(5)

Multiply -0.25 by 10 and you get -2.5

4-2.5+0.5(5)

Multiply 0.5 by 5 and you get 2.5

4-2.5+2.5

Subtract 4 minus 2.5 and you get 1.5

1.5+2.5

Add 1.5 plus 2.5 and you get 4

4

Answer:

[tex]I'(t)=12I-0.004I^2, I_o=500[/tex]

Step-by-step explanation:

Population of the Community=3000

Let the number of infected=I

The number of uninfected=3000-I

The rate at which disease is spreading is proportional to the product of number of people infected and the number of people not yet infected.

[tex]\frac{dI}{dt}\propto I(3000-I) \\\frac{dI}{dt}=k I(3000-I)\\\frac{dI}{dt}=0.004 I(3000-I)\\$Let I_o$=Initial Number of Infected=500\\Therefore, the initial value problem is given as:\\I'(t)=12I-0.004I^2, I_o=500[/tex]

Answer:

i hope that helps......

For the given equation, the value of [tex]x[/tex] is [tex]2[/tex].

[tex]8^{\frac{1}{6}} \times 2^{x} = 32^{\frac{1}{2}}[/tex]

[tex](2^{3})^{\frac{1}{6}} \times 2^{x} = (2^{5})^{\frac{1}{2}}[/tex]

[tex]2^{\frac{1}{2}} \times 2^{x} = 2^{\frac{5}{2}}[/tex]

[tex]2^{\frac{1}{2}+x}=2^{\frac{5}{2}}[/tex]

Since, the bases are equal, we can compare the powers.

[tex]\frac{1}{2}+x=\frac{5}{2}[/tex]

[tex]x=\frac{5}{2}-\frac{1}{2}[/tex]

[tex]x=\frac{5-1}{2}[/tex]

[tex]x=\frac{4}{2}[/tex]

[tex]x=2[/tex]

So, the value of [tex]x[/tex] is [tex]2[/tex].

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Answer:

Probability that the potential candidate will run for President election is 0.0096.

Step-by-step explanation:

We are given that a potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy.

To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy.

Let p = % of Americans voice support for her candidacy

The z score probability distribution for sample proportion is given by;

                               Z  =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of Americans support her candidacy = 35%

            n = sample of Americans = 500

Now, probability that the potential candidate will obtain a p^ ≥ 0.30 and run for President is given by = P( [tex]\hat p[/tex] ≥ 0.30)

      P( [tex]\hat p[/tex] ≥ 0.30) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ≥ [tex]\frac{0.35-0.30}{\sqrt{\frac{0.35(1-0.35)}{500}} }[/tex] ) = P(Z ≥ 2.34) = 1 - P(Z [tex]\leq[/tex] 2.34)

                                                                      = 1 - 0.9904 = 0.0096

The above probability is calculated by looking at the value of x = 2.34 in the z table which has an area of 0.9904.

Hence, the required probability is 0.0096.

Answer:

[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]  

Since we conduct a bilateral test we have the p value given by:

[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance

Step-by-step explanation:

Information given

[tex]\bar X_{boys}=70.5[/tex] represent the mean weigth for ten year boys

[tex]\bar X_{girls}=68.7[/tex] represent the mean weigth for ten year girls

[tex]s_{boys}=5.3[/tex] represent the sample deviation for 10 year boys

[tex]s_{girls}=4.3[/tex] represent the sample standard deviation for 10 year girls

[tex]n_{boys}=360[/tex] sample size for boys

[tex]n_{girls}=329[/tex] sample size for girls

t would represent the statistic

[tex]\alpha=0.01[/tex] significance level assumed

System of hypothesis to check

We need to conduct a hypothesis in order to check if the true means are different for boys and girls, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{boys}=\mu_{girls}[/tex]

Alternative hypothesis:[tex]\mu_{boys} \neq \mu_{girls}[/tex]

The statistic for this case would be given by:

[tex]t=\frac{\bar X_{boys}-\bar X_{girls}}{\sqrt{\frac{s^2_{boys}}{n_{boys}}+\frac{s^2_{girls}}{n_{girsl}}}}[/tex] (1)

Replacing we got:

[tex]t=\frac{70.5-68.7}{\sqrt{\frac{5.3^2}{360}+\frac{4.3^2}{329}}}}=4.913[/tex]  

P value

We can assume that the degrees of freedom for this case are large enough to assume that the t distribution is approximately the normal distribution.

Since we conduct a bilateral test we have the p value given by:

[tex]p_v =2*P(z>4.913)=8.97x10^{-7}[/tex]

Since the p value is very low compared to the significance level we have enough evidence to reject the null hypothesis and we can conclude that the true means for girls and boys are different at 1% of significance

Answer:

1/3

Step-by-step explanation:

Let the probability of selecting all coloured chips in the bag be 1.

If the probability of randomly selecting a red chip from the bag is 1/8 and the probability of selecting a blue chip from the bag is 13/24, then the probability of selecting both will be 1/8+13/24

1/8+13/24

= (3+13)/24

= 16/24

= 2/3

If the probability of selecting both ted and blue chip is 2/3, then the probability that there are other colors in the bag too will be expressed as 1-2/3 which is equivalent to 1/3

Final answer:

To find the probability of picking a chip that is neither red nor blue from the bag, we subtract the probabilities of picking a red or blue chip from 1. The calculation shows that the probability of selecting a different color chip is 1/3.

Explanation:

The student's question pertains to the calculation of probabilities when selecting poker chips of different colors from a bag. We are given that the probability of selecting a red chip is 1/8, and the probability of selecting a blue chip is 13/24. The aim here is to find the probability of selecting a chip of a different color. Since probabilities sum up to 1 for all possible outcomes, we would subtract the given probabilities from 1 to find the probability of selecting a chip that's neither red nor blue.

The total probability for all colors in the bag is always 1 (or 100%), which can be mathematically expressed as:

P(red) + P(blue) + P(other colors) = 1

Given P(red) = 1/8 and P(blue) = 13/24, we can substitute to find P(other colors):

P(other colors) = 1 - (P(red) + P(blue))

P(other colors) = 1 - (1/8 + 13/24)

First, we need to find a common denominator to combine the fractions:

P(other colors) = 1 - (3/24 + 13/24)

P(other colors) = 1 - 16/24

P(other colors) = 1 - 2/3

P(other colors) = 1/3

Therefore, the probability of selecting a chip that is neither red nor blue is 1/3.

9514 1404 393

Answer:

  ray

Step-by-step explanation:

The dashed part of the figure is a "half-line", a line that extends in one direction from a point. Such a line is called a "ray."

Answer:

The value of x any y are "-5.29 and 0.79" and "3.79 and -2.29"

Step-by-step explanation:

Given values:

[tex]2xy =6.....(a)\\\\x-y= 3.....(b)\\\\[/tex]

After solve equation (a) we get

[tex]\ equation: \\\\2xy= 6\\\\xy =\frac{6}{2} \\\\xy = 3.....(x)\\\\[/tex]

After solve equation (b) we get

[tex]\ equation: \\\\x-y =3\\\\x= 3+y....(x1)\\[/tex]

put the value of x in to equation (x)

[tex](3+y)y = 3\\[/tex]

[tex]y^2+3y-3=0\\\\\ compare \ the \ value \ with \ ay^2+by+c=0\\a= 1\\b=3\\c=-3\\\ Formula: \\y= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\y= \frac{-3\pm \sqrt{9+12}}{2}\\y= \frac{-3\pm \sqrt{21}}{2}\\[/tex]

The value of y is = -5.29 and 0.79, put the value of y in x1 equation so, we get: 3.79 and -2.29

Answer:

The mean of the samples is 21

Step-by-step explanation:

Mean is defined as the average sum of numbers i.e total sum of given numbers divided by the total number.

Given the randomly selected numbers as shown;

7, 100, 1, 3, 7, 10, 15, 12, 17, 38

Total sum of numbers = 7+ 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38

= 210

Total numbers given = 10

Mean = 210/10

Mean = 21

Answer:mean is 21 i did it on edge 2023

Step-by-step explanation:

A table titled Text messages sent has entries 7, 100, 1, 3, 17, 10, 15, 12, 7, 38.

What is the mean of this sample, which consists of 10 values randomly selected from the table?

Mean = 7 + 100 + 1 + 3 + 7 + 10 + 15 + 12 + 17 + 38

10

The mean of the third sample is

21

.

Answer:

1. x-2y

2. 2(13a-5)

Step-by-step explanation:

1. it's asking to expand the equation, so you should distribute the -1/2. -1/2*-2x becomes 1x or just x and -1/2*4y becomes -2y, so the answer is x-2y.

2. it's asking to factor, so you should find the greatest common factor of 26a and 10, which is 2. (a isn't on both terms, but if it was, then you would factor out the a also.) 26a/2 is 13a and -10/2 is -5, so the answer is 2(13a-5).

hope this helped!

Answer:

tanx·secx

Step-by-step explanation:

To simply this, you can begin by factoring sin x out of the numerator to become:

[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]

Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:

[tex]\frac{sinx}{cos^{2}x }[/tex]

First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.

Finally, we get our answer as tanx·secx.

Answer:

(x+5)² + (y-2)² =58

Step-by-step explanation:

"Your answer needs to be at least 20 characters long"

The equation of circle C will be;

⇒ (x + 5)² + (y - 2)² = 7.61²

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.

Now,

Since, The points j(-8,9) and k(-2,-5) are endpoints of a diameter of circle C.

Hence, The diameter of circle = √(- 2 - (-8))² + (- 5 - 9)²

                                               = √ 6² + 14²

                                               = √36 + 196

                                               = √232

                                               = 15.23

Thus, The radius of circle = 15.23 / 2

                                        = 7.61

And, The center of the circle = (- 8 + (-2)) / 2 , (9 + (-5))/2

                                             = (- 5, 2)

So, The equation circle C is,

⇒ (x - (-5))² + (y - 2)² = 7.61²

⇒ (x + 5)² + (y - 2)² = 7.61²

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Answer:

Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.

Step-by-step explanation:

We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.

And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.

Let the Probability that pointer will stop on an odd number = P(A)

Probability that pointer will stop on a number greater than 5 = P(B)

Probability that pointer will stop on an odd number and on a number greater than 5 =  [tex]P(A\bigcap B)[/tex]

Probability that pointer will stop on an odd number or on a number greater than 5 =  [tex]P(A\bigcup B)[/tex]

Here, Odd numbers = {1, 3, 5, 7} = 4

Numbers greater than 5 = {6, 7, 8} = 3

Also, Number which is odd and also greater than 5 = {7} = 1

Total numbers = 8

Now, Probability that pointer will stop on an odd number =  [tex]\frac{4}{8}[/tex]  = 0.5

Probability that pointer will stop on a number greater than 5 =  [tex]\frac{3}{8}[/tex]  = 0.375

Probability that pointer will stop on an odd number and on a number greater than 5 =  [tex]\frac{1}{8}[/tex]  = 0.125

Now,    [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]

                            =  0.5 + 0.375 - 0.125

                            =  0.75

Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.

The probability that the pointer will stop on an odd number or a number greater than 5 is 3/4

The sample space is:

[tex]\mathbf{S = \{1,2,3,4,5,6,7,8\}}[/tex]

Count = 8

The odd numbers are:

[tex]\mathbf{Odd = \{1,3,5,7\}}[/tex]

Count = 4

The probability of odd is:

[tex]\mathbf{P(odd) = \frac{4}{8} }[/tex]

The numbers greater than 5 are:

[tex]\mathbf{Greater= \{6,7,8\}}[/tex]

Count = 3

The probability of numbers greater than 5 is:

[tex]\mathbf{P(Greater) = \frac{3}{8}}[/tex]

Odd numbers greater than 5 are:

[tex]\mathbf{OddGreater= \{7\}}[/tex]

Count =1

The probability of odd numbers greater than 5 is:

[tex]\mathbf{P(OddGreater) = \frac{1}{8}}[/tex]

So, the probability that the pointer will stop on an odd number or a number greater than 5 is:

[tex]\mathbf{Pr = P(Odd) + P(Greater) - P(OddGreater)}[/tex]

This gives

[tex]\mathbf{Pr = \frac 48 + \frac 38 - \frac 18}[/tex]

[tex]\mathbf{Pr = \frac 68}[/tex]

Simplify

[tex]\mathbf{Pr = \frac 34}[/tex]

Hence, the required probability is 3/4

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Answer:

35 square units.

Step-by-step explanation:

To find the area of a parallelogram, the formula is the exact same as finding the area of a rectangle. So 7 x 5 is 35.

Answer:

a) The function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Written in interval form

(-∞, -1.45) and (3.45, ∞)

- The function, f(x) is decreasing at the interval (-1.45 < x < 3.45)

(-1.45, 3.45)

b) Local minimum value of f(x) = -78.1, occurring at x = 3.45

Local maximum value of f(x) = 10.1, occurring at x = -1.45

c) Inflection point = (x, y) = (1, -16)

Interval where the function is concave up

= (x > 1), written in interval form, (1, ∞)

Interval where the function is concave down

= (x < 1), written in interval form, (-∞, 1)

Step-by-step explanation:

f(x) = x³ - 6x² - 15x + 4

a) Find the interval on which f is increasing.

A function is said to be increasing in any interval where f'(x) > 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

the function is increasing at the points where

f'(x) = 3x² - 6x - 15 > 0

x² - 2x - 5 > 0

(x - 3.45)(x + 1.45) > 0

we then do the inequality check to see which intervals where f'(x) is greater than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

So, the function (x - 3.45)(x + 1.45) is positive (+ve) at the intervals (x < -1.45) and (x > 3.45).

Hence, the function, f(x) is increasing at the intervals (x < -1.45) and (x > 3.45)

Find the interval on which f is decreasing.

At the interval where f(x) is decreasing, f'(x) < 0

from above,

f'(x) = 3x² - 6x - 15

the function is decreasing at the points where

f'(x) = 3x² - 6x - 15 < 0

x² - 2x - 5 < 0

(x - 3.45)(x + 1.45) < 0

With the similar inequality check for where f'(x) is less than 0

Function | x < -1.45 | -1.45 < x < 3.45 | x > 3.45

(x - 3.45) | negative | negative | positive

(x + 1.45) | negative | positive | positive

(x - 3.45)(x + 1.45) | +ve | -ve | +ve

Hence, the function, f(x) is decreasing at the intervals (-1.45 < x < 3.45)

b) Find the local minimum and maximum values of f.

For the local maximum and minimum points,

f'(x) = 0

but f"(x) < 0 for a local maximum

And f"(x) > 0 for a local minimum

From (a) above

f'(x) = 3x² - 6x - 15

f'(x) = 3x² - 6x - 15 = 0

(x - 3.45)(x + 1.45) = 0

x = 3.45 or x = -1.45

To now investigate the points that corresponds to a minimum and a maximum point, we need f"(x)

f"(x) = 6x - 6

At x = -1.45,

f"(x) = (6×-1.45) - 6 = -14.7 < 0

Hence, x = -1.45 corresponds to a maximum point

At x = 3.45

f"(x) = (6×3.45) - 6 = 14.7 > 0

Hence, x = 3.45 corresponds to a minimum point.

So, at minimum point, x = 3.45

f(x) = x³ - 6x² - 15x + 4

f(3.45) = 3.45³ - 6(3.45²) - 15(3.45) + 4

= -78.101375 = -78.1

At maximum point, x = -1.45

f(x) = x³ - 6x² - 15x + 4

f(-1.45) = (-1.45)³ - 6(-1.45)² - 15(-1.45) + 4

= 10.086375 = 10.1

c) Find the inflection point.

The inflection point is the point where the curve changes from concave up to concave down and vice versa.

This occurs at the point f"(x) = 0

f(x) = x³ - 6x² - 15x + 4

f'(x) = 3x² - 6x - 15

f"(x) = 6x - 6

At inflection point, f"(x) = 0

f"(x) = 6x - 6 = 0

6x = 6

x = 1

At this point where x = 1, f(x) will be

f(x) = x³ - 6x² - 15x + 4

f(1) = 1³ - 6(1²) - 15(1) + 4 = -16

Hence, the inflection point is at (x, y) = (1, -16)

- Find the interval on which f is concave up.

The curve is said to be concave up when on a given interval, the graph of the function always lies above its tangent lines on that interval. In other words, if you draw a tangent line at any given point, then the graph seems to curve upwards, away from the line.

At the interval where the curve is concave up, f"(x) > 0

f"(x) = 6x - 6 > 0

6x > 6

x > 1

- Find the interval on which f is concave down.

A curve/function is said to be concave down on an interval if, on that interval, the graph of the function always lies below its tangent lines on that interval. That is the graph seems to curve downwards, away from its tangent line at any given point.

At the interval where the curve is concave down, f"(x) < 0

f"(x) = 6x - 6 < 0

6x < 6

x < 1

Hope this Helps!!!

This question involves finding the increasing and decreasing intervals, local maximum and minimum values, and concavity of a cubic function f(x) = x3 – 6x2 – 15x + 4. These are found by taking the first and second derivative and applying various tests.

The subject of this question is Calculus, more specifically, regarding the properties of the function f(x) = x3 – 6x2 – 15x + 4. To find the intervals where the function is increasing or decreasing, we need to find the derivative of f(x), set it to zero and solve for x to find critical points. Then we set up a number line with these critical numbers and analyze the sign of f'(x) in each interval.

The local maximum and minimum values can also be found from the critical numbers. To find where the function is concave up or down, we find the second derivative (f''(x)) and perform a similar process we did with the first derivative.

The inflection points, where the function changes its concavity, can also be found from evaluating the second derivative.

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Answer: 36 cubic inches

Step-by-step explanation:

Answer:

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

Step-by-step explanation:

Given:

A = {t, u, v, w}

S1 = set of all subsets of A that do not contain w.

S2 = set of all subsets of A that contains w.

Therefore S1 & S2 in set roster notation will be given as:

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

S2 = { {w}, {t,w}, {u,w}, {v,w}, {t,u,w}, {t,v,w}, {u,v,w}, {t,u,v,w} }

a) We can see that,

S1 = {∅, {t}, {u}, {v}, {t,u}, {t,v}, {u,v}, {t,u,v} }

The problem involves finding subsets of a given set. The set S1, which includes subsets of the original set A that do not contain the element 'w', includes eight such subsets.

The given set A contains the elements {t, u, v, w}. The set S1 consists of all the subsets of A that do not contain the element 'w'. Similarly, the set S2 consists of all the subsets of A that do contain the element 'w'.

To find S1, we can start by listing out each possible subset of A without the element 'w'. These include {}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, and {t, u, v}. So, S1 = {{}, {t}, {u}, {v}, {t, u}, {t, v}, {u, v}, {t, u, v}}.

We ignore S2 as it's not relevant to the question asked.

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