Bob just crash landed on the island too. He doesn’t have quite the stamina that Alice does so he can only work 6 hours a day. He finds that he can gather a bundle of wood in 2 hours or 1 coconut per hour.

Well, most books define critical values of a function as x-values where f'(x)=0 or f'(x) is undefined, so they occur there because that's the definition of what a critical value is.

But the reason we define it that way is that when you're looking for local extrema (local mins and/or local maxs), these must occur when f'(x)=0 or f'(x) is undefined.  

If f has a local extremum at a point x=c, then f'(c)=0 or f'(c) is undefined.

Answer:

[tex]\frac{(s + 15.4)(8.1)}{2}[/tex] = 81

8.1s + 124.74 = 162

8.1s = 37.26

s = 4.6

The correct option that can be used to prove that ∠ABC = ∠FDE is option (A). It is done using rules of congruency.

What is meant by congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

For the construction of the congruent angle, the compass measurement used is the same for both figures.

Now we draw a line through points A and C and another line through points F and E.

We can then say that

AB = FD

BC = DE

CA = EF

These are the sides of the triangles ΔABC and ΔFDE

As all sides are equal, we can say that

ΔABC ≅ ΔFDE by SSS congruency rule.

Now CPCTC rule says that "corresponding parts of congruent triangles are congruent". This means that the corresponding angles and sides of two or more triangles must also be identical in order for them to be considered congruent.

So ∠ABC ≅ ∠FDE by CPCTC as they are corresponding angles.

Therefore the correct congruency rules that can be used to prove that

∠ABC = ∠FDE is option (A).

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Answer:

Step-by-step explanation:

48 miles = 1 hour

??           = 4.5hr

=> cross multiplicationt

4.5/1 *48Miles

= 216Miles

Using simple division we know that 86 people or citizens dies each day in 2015.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

Division in mathematics is the process of dividing an amount into equal parts.

For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

So, we know that:

31,500 people died in 2015.

We also know that 2015 had 365 days.

Then, people died easily day would be:

= 31,500/365

= 86.30

Rounding off: 86 people

Therefore, using simple division we know that 86 people or citizens dies each day in 2015.

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Answer:

h=V/πr2

Step-by-step explanation:

Rewrite the equation as π r 2 h = V . π r 2 h = V

Divide each term in π r 2 h = V by π r 2 and simplify.

It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.

Expected to give that it has three sections and three vertices, a triangle qualifies as a rectangle. It belongs to the core geometric shapes. Triangle ABC is the term utilized to refer to a triangle only with vertices A, B, and C. When the three principles are not collinear, a unique rectangle and square in Geometry and trigonometry are discovered. Triangles are polygons because they have sides and three corners. The points at which three sides of the triangle coincide are referred to as the triangle's edges. Three triangle angles are multiplied to generate 180 degrees.

given

FGH and JKL in the specified right angle

GF ≅ KJ ( one side of both right angle triangles) ( one side of both right angle triangles)

∠F≅ ∠J (right angle) (right angle)

FH ≅ JL (opposite side of both right angle triangles ) (other side of both right angle triangles )

Then ,

We can conclude that GH KL (hypotenuse of both right angle triangles)

In two right triangles, if the hypotenuse and one side of one triangle are identical to the hypotenuse and one side of the other triangle, then the two triangles are congruent according to the RHS congruence rule.

It is true that both triangles meet the prerequisites listed before. FGH and JKL are then consistent.

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The number of people in Indiana residents is given by the equation

A = 5,750,000 or 5.75 million

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of people in Indiana residents aged 5 years and older be A

Now , the equation will be

Substituting the values in the equation , we get

The percentage of population residents aged 5 years and older = 5.6 %

The number of residents aged 5 years and older = 322,000

So , the total population A is calculated as

( 5.6 % ) of A = 322,000

On simplifying the equation , we get

( 5.6 / 100 ) A = 322,000

Divide by 6.6 on both sides of the equation , we get

A / 100 = 57,500

Multiply by 100 on both sides of the equation , we get

A = 5,750,000

A = 5.75 million

Hence , the population of Indiana is A = 5,750,000 or 5.75 million

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Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

The similar symbol (=) is used in arithmetic equations to signify equality between two statements. It is shown that it is possible to compare various numerical factors by applying mathematical algorithms, which have served as expressions of reality. For instance, the equal sign divides the number 12 or even the solution y + 6 = 12 into two separate variables many characters are on either side of this symbol can be calculated. Conflicting meanings for symbols are quite prevalent.

Here,

Given :

customer uses 390 minutes , the monthly cost will be $178.

customer uses 940 minutes, the monthly cost will be $398.

To find an equation ,

where x is number of monthly minutes

and y is total monthly of splint plan.

So , equation is :

=> y =mx +b

For first case :

=> 178 = 390x + b

Second case :

=> 398 = 940x + b

Solve for x:

=> 178 - 390x = 398 - 940x

=> -200x = - 550

=> x = 550/200

=>x = 55/20

=>x = 11/4

=> x = 2.75

For value of b

=>  178 = 390(2.75) + b

=> 178 - 1072.5 = b

=> -894.5 = b

B)

=> y = 866(2.75) - 894.5

=> y = 2381.5 - 894.5

=> y = 1487

Therefore , the solution of the given problem of equation comes out to be total cost for 866 minutes is $1487.

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Answer:

======================================================

Reason:

The number of weeks can be any number from the set {0,1,2,3,...} so we say that this value is independent. It does not depend on the number of stickers.

But the number of stickers does depend on the number of weeks. As w changes, so does the value of 's'.

The equation would be:  s = 2w+12

And so on. Each time 'w' goes up by 1, 's' goes up by 2.

Family's fuel efficiency is 32.67 miles per gallon.

Unit conversion is the conversion between different units and measurements of the same quantity done by the division or multiplication.

Mitchell family's fuel efficiency in km/l =[tex]\frac{750}{54}[/tex]

                                                               =13.89 km/l

The fuel efficiency in miles per gallon = 13.89*2.35

                                                               = 32.67 m/g

(1 kilometer per liter = 2.35 miles per gallon)

Hence, mitchell family's fuel efficiency is 32.67 miles per gallon.

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Answer: After 39 minutes, both pools will have the same amount of water.

Step-by-step explanation:

Let's call the number of minutes elapsed t. Then the amount of water in Destiny's pool after t minutes is 800 + 25t gallons, and the amount of water in Jabez's pool after t minutes is 20 + 45t gallons.

We want to find the time t at which the two pools have the same amount of water, so we set their amounts equal:

800 + 25t = 20 + 45t

Subtracting 20 from both sides of the equation:

780 + 25t = 45t

Subtracting 25t from both sides of the equation:

780 = 20t

Dividing both sides of the equation by 20:

39 = t

So, after 39 minutes, both pools will have the same amount of water.

a)The events A1, A2, and A3 are pairwise independent.

b)  The events are not mutually independent.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Observe the given numbers:

Out of 4 numbers, 2 have 1 at first position

so outcomes in event A1 is

A1 ={ 110, 101}

Similarly, possible outcomes in A2 is

A2 ={110, 011}

A3 = {101,111}

The probabilities of events are

P(A1) = 2/4 = 0.5

P(A2) = 2/4 = 0.5

P(A3) = 2/4 = 0.5

Also,

(A1 and A2) = {110}

(A1 and A3) = {101}

(A2 and A3) = {011}

The probabilities are

P(A1 and A2) = 1 /4 = 0.25

P(A1 and A3) = 1 /4 = 0.25

P(A2 and A3) = 1 /4 = 0.25

a)

From above we have

P(A1 and A2) = P(A1)P(A2) = 0.25

P(A1 and A3) = P(A1)P(A3) = 0.25

P(A2 and A3) = P(A2)P(A3) = 0.25

So events A1, A2, and A3 are pairwise independent.

b)

Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.

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a)The events A1, A2, and A3 are pairwise independent.

b)  The events are not mutually independent.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Observe the given numbers:

Out of 4 numbers, 2 have 1 at first position

so outcomes in event A1 is

A1 ={ 110, 101}

Similarly, possible outcomes in A2 is

A2 ={110, 011}

A3 = {101,111}

The probabilities of events are

P(A1) = 2/4 = 0.5

P(A2) = 2/4 = 0.5

P(A3) = 2/4 = 0.5

Also,

(A1 and A2) = {110}

(A1 and A3) = {101}

(A2 and A3) = {011}

The probabilities are

P(A1 and A2) = 1 /4 = 0.25

P(A1 and A3) = 1 /4 = 0.25

P(A2 and A3) = 1 /4 = 0.25

a)

From above we have

P(A1 and A2) = P(A1)P(A2) = 0.25

P(A1 and A3) = P(A1)P(A3) = 0.25

P(A2 and A3) = P(A2)P(A3) = 0.25

So events A1, A2, and A3 are pairwise independent.

b)

Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.

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Answer:

A regular prism with 10 faces and 12 vertices has 6 sides. This is because the number of faces and vertices are related by the equation F+2 = E+2V, where F is the number of faces, E is the number of edges, and V is the number of vertices. In this case, 10+2 = 12+2V, so V = 6 and the number of sides of the prism is also 6

Step-by-step explanation:

1. A regular prism has 10 faces and 12 vertices.

2. The number of faces and vertices is related by the equation F+2 = E+2V.

3. Where F is the number of faces, E is the number of edges, and V is the number of vertices.

4. In this case, 10+2 = 12+2V, so V = 6.

5. Therefore, the number of sides of the prism is also 6.

Answer:

Step-by-step explanation:

The number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is calculated as follows:

The number of ways the hospital can receive exactly 2 defective machines is C(4,2) = 6, where C(n, k) is the number of combinations of n things taken k at a time.

The number of ways the hospital can receive exactly 3 defective machines is C(4,3) = 4.

The number of ways the hospital can receive exactly 4 defective machines is C(4,4) = 1.

So, the total number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is 6 + 4 + 1 = 11.

The required values of the given composite functions follow as:

(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.

Composite functions are mathematical functions that are formed by taking the output of one function and using it as the input for another function.

(a) To find fog(x), we need to evaluate g(f(x)).

Since function f(x) = 2x, we have:

g(f(x)) = g(2x) = (2x)² = 4x²

Therefore, fog(x) = 4x².

(b) To find gof(x), we need to evaluate f(g(x)).

Since g(x) = x², we have:

f(g(x)) = f(x²) = 2(x²) = 2x²

Therefore, gof(x) = 2x².

(c) To find gog(x), we need to evaluate g(g(x)).

Since function g(x) = x², we have:

g(g(x)) = g(x²) = (x²)² = x⁴

Therefore, gog(x) = x⁴.

Thus, the required values of the given composite functions follow as:

(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.

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The required length of the third side of the right-angle triangle is 15 units.

In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.

Here,
For the right triangle lenght of the two legs to be 9 and 12 units, a measure of the third side is to be determined.

So, Applying the Pythagoras theorem,
h² = p² + b²
h = √9² + 12²
h = √225
h = 15

Thus, the required length of the third side of the right-angle triangle is 15 units.

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Answer: To calculate the total, we need to first calculate the discount and then the tip.

First, calculate the discount: $21.50 x 10% = $2.15

Then, subtract the discount from the subtotal: $21.50 - $2.15 = $19.35

Next, calculate the tip: $19.35 x 20% = $3.87

Finally, add the tip to the subtotal after the discount to find the total: $19.35 + $3.87 = $23.22

Therefore, Abdiel's total would be $23.22 if he uses a coupon for 10% off the subtotal and leaves a 20% tip before the discount.

Step-by-step explanation:

The average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.

In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.

The average daily balance can be determined by dividing the total daily balances for January by the number of days in January.

The average daily balance = Total balance / Total number of days in January.

Total balance = (800 x 1 days) + (1000 x10 days) + (1250 x 10 days) + (1650 x 10 days)

Total balance = 800 + 10,000 + 12,500 + 16,500 = 39800

The average daily balance = 39800/31 = $1283.87

Therefore, the average daily balance of the credit card for the January 1 - January 31 billing period is $1283.87.

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In isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.

What is the isosceles triangle?

An isosceles triangle is a triangle having any two sides equal in length. The third side is called the base of the isosceles triangle. In an isosceles triangle, the angles opposite to equal sides are equal in measure.

1.∠ABC ≅ ∠AED (Given)

2.  Isosc. △ABE, base BE (Given)

3.  AB ≅ BE (Def. of Isosc. △)

4.  ∠A ≅ ∠A (Reflex. Prop. of ≅)

5.  △ABC ≅ △AED (ASA Steps 1, 3, 4)

6.  BC ≅ ED (CPCTC)

option 1 is wrong in that the step 3. AB is not congurent with BE,

option 3 is wrong in that step 5.   △ABC≅△AED  should be prove by BD ≅ CE, ∠A BE ≅ ∠AEB, BE  ≅ BE

hence, in isosceles triangle ΔABE, the correct option is option D. which proves that BC ≅ ED.

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The derivative of the given function is  23t^22 ln |t| +  t^22

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The product rule  will be most helpful in beginning this problem.

S = t^23 ln|t|

Differentiate with respect to t

D(s) = ds/dt = D( t^23 ln|t| )

Apply the rule :

D(uv) = u'v+uv'

u' =du/dt , v'=dv/dt

D(s) = 23t^22 ln |t| +  t^23 (1/t)

D(s) = 23t^22 ln |t| +  t^22

The derivative of the given function is  23t^22 ln |t| +  t^22

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The derivative of the given function is  23t²² ln |t| +  t²².

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a complete sentence. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

The product rule will be most helpful in beginning this problem.

S = t²³ ln |t|

Differentiate with respect to t

D(s) = ds/dt = D( t²³ln|t| )

Apply the rule :

D(uv) = u'v+uv'

u' =du/dt , v'=dv/dt

D(s) = 23t²² ln |t| +  t²³ (1/t)

D(s) = 23t²² ln |t| +  t²²

The derivative of the given function is  23t²² ln |t| +  t²²

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Answer:

The answers are x=-37 and x=3

Step-by-step explanation:

The solution set for the equation (7x+3)(2x-6)=0 is {−37,3}. To solve for x, one can use the distributive property to expand the equation and then solve for x. For example, 7x² - 3x - 12x - 18 = 0 can be rearranged to 7x² - 15x - 18 = 0 and then solved using the quadratic formula.

Answer: 96 m.

Step-by-step explanation: Let's call the length of the rectangular field "L".

We know the perimeter of the field is equal to the sum of all its sides, so:

350 = 2L + 2 * 79

Expanding the right side, we have:

350 = 2L + 158

Subtracting 158 from both sides:

192 = 2L

Dividing both sides by 2:

L = 96 m

So the length of the rectangular field is 96 m.

Answer: The formula for continuously compounded interest is given by:

A = P * e^(rt)

Where:

A = the final account balance

P = the initial investment (principal)

r = the annual growth rate as a decimal

t = the number of years the investment is held

In this case, P = 540, r = 0.091 and t = t years.

So, the function showing the value of the account after t years is:

A = 540 * e^(0.091t)

To find the percentage of growth per year (APY), we can use the formula:

APY = (e^r - 1) * 100

Substituting r = 0.091, we find:

APY = (e^0.091 - 1) * 100 = 9.56%

So, the APY is approximately 9.56%, to the nearest hundredth of a percent.

Step-by-step explanation:

Here are some examples of quantitative survey or simulation questions:

On a scale of 1 to 5, how likely are you to recommend our product to a friend or colleague?

1 (Not at all likely)

2

3

4

5 (Extremely likely)

How often do you use our app?

Daily

3-4 times a week

Once a week

Once every two weeks

Rarely

How much time do you spend using our app in an average day?

Less than 30 minutes

30 minutes to 1 hour

1 to 2 hours

More than 2 hours

How satisfied are you with the overall performance of our app?

Very dissatisfied

Dissatisfied

Neutral

Satisfied

Very satisfied

How do you rate the usability of our app?

Poor

Fair

Good

Very good

Excellent

A quantitative survey uses statistics to gather facts and figures. It's most frequently utilized to support or refute a conclusion you may have reached after conducting qualitative research.

A survey may be qualitative, quantitative, or a combination of the two. A quantitative survey is one that uses a questionnaire with scaleable responses. If your survey has descriptive questions with in-depth answers then it is a qualitative survey. Your survey is a mixed-method survey if it uses both of them.

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Answer:

6 GB

Step-by-step explanation:

First find the rate per day. You can do that by dividing 4GB by 20 days.

4/20 = 1/5 = 0.2GB per day

Then, just multiply 30 days by the rate of 0.2GB/day.

30 x 0.2 = 6

The percentages of the weights are given as follows:

a) Over 15.5 pounds: 2.07%.

b) Under 11.9 pounds: 75.8%.

c) Between 11.9 pounds and 15.9 pounds: 22.13%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 10, \sigma = 2.7[/tex]

The proportion over 15.5 pounds is one subtracted by the p-value of Z when X = 15.5, hence:

Z = (15.5 - 10)/2.7

Z = 2.04

Z = 2.04 has a p-value of 0.9793.

1 - 0.9793 = 0.0207.

The proportion under 11.9 pounds is the p-value of Z when X = 11.9, hence:

Z = (11.9 - 10)/2.7

Z = 0.7

Z = 0.7 has a p-value of 0.7580.

The proportion between is the subtraction of the p-values, hence:

0.9793 - 0.7580 = 0.2213 = 22.13%.

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