find the point of intersection of lines given
y=2x+1
y=-x+11

The average rate of change of f over intervals of x from x = 3 to  = 3.5 is - 159.

Given that the function is,

f (x) = - 5x³

Used the formula for the average rate of change of function f at interval [a, b] is,

f' (x) = [ f (b) - f (a) ] / (b - a)

Here, f (x) = - 5x³

At x = 3;

f (3) = - 5 × 3³

= - 135

At x = 3.5;

f (3.5) = - 5 × (3.5)³

= - 214.4

Hence, the average rate of change of f over intervals of x from x = 3 to  = 3.5 is,

f ' (x) = [- 214.5 - (- 135)] / (3.5 - 3)

f ' (x) = [- 79.5] / 0.5

f ' (x) = - 159

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Final answer:

The average rate of change of the function f(x) = -5[tex]x^3[/tex] from x = 3 to x = 3.5 is -158.75.

Explanation:

The average rate of change (ARoC) can be determined using the formula:

ARoC = (f(x2) - f(x1)) / (x2 - x1)

In this case, the given function is f(x) = -5x^3. To find the ARoC from x = 3 to x = 3.5, substitute these values into the formula:

ARoC = (-5[tex](3.5)^3 - (-5(3)^3)[/tex]) / (3.5 - 3)

Simplifying the equation gives:

ARoC = (-5(42.875) - (-5(27))) / (0.5)

ARoC = (-214.375 + 135) / 0.5

ARoC = -79.375 / 0.5

ARoC = -158.75

Therefore, the average rate of change of f(x) from x = 3 to x = 3.5 is -158.75.

Answer:

Please see the attached pictures for full solution.

Answer:

1) $1966.62

2) $1968.12

3) $1968.88

Step-by-step explanation:

1) 1500 × (1 + .034/4)³²

= 1966.618592

2) 1500 × (1 + .034/12)⁹⁶

= 1968.123402

3) 1500 × (e^(8×0.0314))

= 1968.880502

Answer:

1968.880502

Step-by-step explanation:

Answer:

y = mx + b

Hope I helped!!! :)

~Nuha

Answer:

30%

Step-by-step explanation:

Given:

Every morning he starts with 150 tomatoes.

On Sunday Austin sells 45 of the 150 tomatoes.

Question asked:

What percent of the tomatoes he sold ?

Solution:

As Austin sells 45 tomatoes out of 150 tomatoes, we will find percent of the tomatoes he sold by using :

Percent of the tomatoes he sold = Number of tomatoes he sold divided by total number of tomatoes he starts with.

[tex]Percentage =\frac{45}{150} \times100\\[/tex]

                  [tex]=\frac{4500}{150} \\ = 30[/tex]

Therefore, 30% of the tomatoes he sold on Sunday.

the answer is 30%

step by step problem

Answer

Answer:

  y = 4x -3

Step-by-step explanation:

The line perpendicular to the given line can be written as the same equation with the coefficients of x and y swapped, and one of them negated. The constant may be different, so we'll call it "c".

  4x -y +c = 0 . . . . . line perpendicular to that given

The y-intercept of the second given line can be found by setting x=0. That gives the equation -y -3 = 0. The perpendicular line with x=0 would have equation ...

  -y +c = 0

Comparing these two tells us c = -3.

So, the general form of the perpendicular line we want is ...

  4x -y - 3 = 0

We can add y to put this in slope-intercept form:

  y = 4x -3

Answer:

It is likewise significant on the grounds that it causes you decide if your business has enough cash to run or to grow it in future. Thus budget and cash flow spreadsheet is an absolute necessity in a simulation to grow.

Step-by-step explanation:

Cash flow spreadsheet alludes to the announcement of planned cash inflows and outflows. Budget cash flow spreadsheet is utilized to assess the momentary cash necessity and it can likewise be utilized to distinguish where the most extreme cash is going out and from where is the greatest inflow.

Answer:

a) Mean = 1205

Standard Deviation = 2.89

b) P( 1195 < x < 1205) = 0.5

50% of the cables lie within the given specification.

Step-by-step explanation:

We are given the following information in the question:

[tex]f(x) = 0.1[/tex]

a = 1200, b = 1210

We are given a uniform distribution.

a) Mean:

[tex]\mu = \displaystyle\frac{a+b}{2}\\\\\mu = \frac{1200+1210}{2} = 1205[/tex]

Standard Deviation:

[tex]\sigma = \sqrt{\displaystyle\frac{(b-a)^2}{12}}\\\\= \sqrt{\displaystyle\frac{(1210-1200)^2}{12}} = \sqrt{8.33} = 2.89[/tex]

b) P( 1195 < x < 1205)

[tex]=\displaystyle\int_{1195}^{1205} f(x) dx\\\\=\displaystyle\int_{1200}^{1205} (0.1) dx\\\\=0.1[x]_{1200}^{1205} = (0.1)(1205-1200) = 0.5[/tex]

50% of the cables lie within the given specification.

Answer: the total area where roses will be planted is 1520 feet²

Step-by-step explanation:

The formula for determining the area of a parallelogram is expressed as

Area = base × height

From the information given,

Base = 20 + 40 = 60 feet

Height = 38 feet

Area of the rose garden = 60 × 38 = 2280 feet²

The formula for determining the area of a rectangle is expressed as

Area = length × width

From the information given,

Length = 38 feet

Width = 20 feet

Area of the rectangular walkway is

20 × 38 = 760 feet²

Therefore, the total area where roses will be planted is

2280 - 760 = 1520 feet²

Answer:

The answers to the question are;

(a) 0.042 to three decimal places.

(b) 0.115 to three decimal places.

(c) μ = 8.25, σ = 1.44 to two decimal places.

Step-by-step explanation:

To solve the question, we note that this is a binomial distribution problem

(a) The probability that all 11 will be available is given by

P(11) = ₁₁C₁₁ × 0.75¹¹×0.25¹¹⁻¹¹ = 0.0422

(b) Probability of 6 or less success = P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0)

P(6)  = ₁₁C₆ × 0.75⁶×0.25⁵ = 0.080299

P(5) = ₁₁C₅ × 0.75⁵×0.25⁶ = 0.026766

P(4) = ₁₁C₄ × 0.75⁴×0.25⁷ = 0.063729

P(3) = ₁₁C₃ × 0.75³×0.25⁸ = 0.001062

P(2) = ₁₁C₂ × 0.75²×0.25⁹ = 0.0001180

P(1) = ₁₁C₁ × 0.75¹×0.25¹⁰ = 0.000007867

P(0) = ₁₁C₀ × 0.75⁰×0.25¹¹ = 0.00000002384

Therefore P(6) + P(5) +P(4) +P(3) + P(2) + P(1) +P(0) = 0.11462

Which is 0.115 to three decimal places

(c) The expected number of those available to serve on the jury =

Probability of success = n·p = 11×0.75 = 8.25

μ = 8.25

The standard deviation,σ [tex]=\sqrt{npq}[/tex] =[tex]\sqrt{11*0.75*0.25}[/tex] = 1.43614 ≅ 1.44 to two decimal places

The probability of everyone being available for jury duty can be calculated by multiplying the individual probabilities. More complex probabilities, such as the chance of more than 5 not being available, can be determined using a binomial distribution or a normal approximation. The expected number and standard deviation are calculated from these probabilities.

The probability of different outcomes for jury duty service can be calculated based on known probabilities and using principles of statistics. If 25% of those called find an excuse to avoid it, that means 75% are available. We can use that data to find the probability of all 11 individuals being available, or more than 5 being unavailable.

a) Probability that all 11 will be available: The probability would be (0.75)^11 = 0.042. Because all events are independent, we multiply the individual probabilities.

b) Probability that 5 or more will not be available: You would use a binomial distribution or a normal approximation to a binomial distribution to find this probability (0.115).

c) Expected number and standard deviation: The expected number of people available to serve would be the total people called multiplied by the probability of being available (11*0.75) = 8.25 people. The standard deviation, which is a bit more complex to compute, would be about 1.436 people.

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The probability that both of the interviewed students are from Middle Georgia State College is 2/7 or 0.2857 rounded to four decimal places.

To calculate the probability that both interviewed students are from Middle Georgia State College, one would use the formula for conditional probability, considering the process as two sequential events. The first student being from the college and then the second one, given the first is already from the college. Since there are four students from the college out of a total of seven, the probability of picking one Middle Georgia State College student first is 4/7. After the first student from the college has been picked, there are now three remaining Middle Georgia students out of the remaining six students. Thus, the probability for the second pick is 3/6, which simplifies to 1/2. The total probability is the product of these two probabilities: (4/7) * (1/2) = 2/7, or approximately 0.2857 when rounded to four decimal places.

Answer:

24000 pieces.      

Step-by-step explanation:

Given:

Side lengths of cube = [tex]\frac{1}{4} \ foot[/tex]

The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.

Question asked:

What is the greatest number of packages that can fit in the truck?

Solution:

First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.

[tex]Volume\ of\ cube =a^{3}[/tex]

                          [tex]=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot[/tex]

Length = 8 foot, Breadth = [tex]6\frac{1}{4} =\frac{25}{4} \ foot[/tex], Height =[tex]7\frac{1}{2} =\frac{15}{2} \ foot[/tex]

[tex]Volume\ of\ rectangular\ prism =length\times breadth\times height[/tex]

                                                [tex]=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot[/tex]

The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube

The greatest number of packages that can fit in the truck = [tex]\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube[/tex]

Thus, the greatest number of packages that can fit in the truck is 24000 pieces.                                

Answer:

0.57 yr  

Step-by-step explanation:

To find the doubling time with continuous compounding, we should look at the formula:

[tex]FV = PVe^{rt}[/tex]

FV = future value, and

PV = present value

If FV is twice the PV, we can calculate the doubling time, t

[tex]\begin{array}{rcl}2 & = & e^{rt}\\\ln 2 & = & rt\\t & = & \dfrac{\ln 2}{r} \\\end{array}[/tex]

1. David's doubling time

[tex]\begin{array}{rcl}t & = & \dfrac{\ln 2}{0.06125}\\\\& = & \textbf{11.317 yr}\\\end{array}[/tex]

2. Violet's doubling time

The formula for interest compounded periodically is

[tex]FV = PV\left (1 + \dfrac{r}{n} \right )^{nt}[/tex]

where

n = the number of payments per year

[tex]\begin{array}{rcl}9600 & = & 4800\left (1 + \dfrac{0.065}{4} \right )^{4t}\\\\2 &= & (1 + 0.01625 )^{4t}\\& = & 1.01625^{4t}\\\ln 2& = & 4 (\ln 1.01625)\times t \\& = & 0.064478t\\t& = & \dfrac{\ln 2}{0.064478}\\\\& = & \textbf{10.750 yr}\\\end{array}[/tex]

3. David's doubling time vs Violet's

11.317 - 10.750 = 0.57 yr

It would take 0.57 yr longer for David's money to double than Violet's.

First problem: let [tex]b[/tex] and [tex]h[/tex] be the base and height of the rectangle, respectively. We know that [tex]b=11+h[/tex] (the base if 11 longer than the height), and that [tex]2(b+h)=58[/tex] (the perimeter is 58 centimeters).

So, we have the system

[tex]\begin{cases}b=11+h\\2(b+h)=58\end{cases}\iff\begin{cases}b=11+h\\b+h=29\end{cases}[/tex]

Use the first equation to substitute into the second:

[tex]b+h=11+h+h=2h+11=29 \iff 2h=18 \iff h=9[/tex]

And since the base is 11 centimeters longer, we have

[tex]b=11+h=11+9=20[/tex]

Second problem: Let [tex]m,n,o[/tex] be the number of cards owned by Mark, Norm and Oscar, respectively. We know that:

[tex]m+n+o=810[/tex] (they have 810 cards in total)

[tex]n=m+30[/tex] (Norm has 30 more than Mark)

[tex]o=2m[/tex] (Oscar has twice as much as Mark)

The second and third equation express [tex]n[/tex] and [tex]o[/tex] in terms of [tex]m[/tex], and substituting those expressions in the first equation we have

[tex]m+n+o=m+(m+30)+2m=810 \iff 4m+30=810 \iff 4m=780 \iff m=195[/tex]

And then we can use again the second and third equations:

[tex]n=m+30=195+30=225[/tex]

[tex]o=2m=2\cdot 195=390[/tex]

The expression that does not belong with the other three is −58+(−34) because it results in a more negative value compared to the other expressions.

The expression that does not belong with the other three is −58+(−34).

−58−34 and −34+58 are both addition expressions, while −34−58 is a subtraction expression. These three expressions involve adding or subtracting two numbers.

However, −58+(−34) is different because it involves adding a negative number to another negative number, which results in a more negative value. The other three expressions all result in a positive value.

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Answer: Osvoldo did not meet his goal.

Step-by-step explanation:

If he ate 220 grams of carbohydrates today and 55 grams were from whole grains, it means that the percentage of the carbohydrates he ate today that came from whole grains is

55/220 × 100 = 25%

Since he has a goal of getting at least 30% percent of his grams of carbohydrates each day from whole grains, then he did not meet his goal because 25% is lesser than 30% and he needs 30% or more

Answer:

[tex]2\dfrac{2}{3}[/tex] cups of flour

Step-by-step explanation:

Each batch uses 2/3 cup of flour.

If Eduardo makes 4 batches, he is going to need [tex]4X\frac{2}{3}[/tex] cups of flour.

[tex]4 X \dfrac{2}{3}=\dfrac{8}{3}=2\dfrac{2}{3}[/tex]

Eduardo is going to need [tex]2\dfrac{2}{3}[/tex] cups of flour.

Final answer:

Eduardo will need 2 2/3 cups of flour for 4 batches.

Explanation:

To find the total cups of flour Eduardo needs for 4 batches:

Amount of flour for 1 batch: 2/3 cup

Total cups for 4 batches: (2/3 cup) x 4 = 8/3 cups = 2 2/3 cups

So, Eduardo will need 2 2/3 cups of flour for 4 batches.

Answer:

4/3*π*[tex]100^{3}[/tex]

Step-by-step explanation:

water level rises to the 200 mL mark, it means the ball diameter is 200, and the radius is: 100

So the  voulume of the ball is: 4/3*π*[tex]r^{3}[/tex]

= 4/3*π*[tex]100^{3}[/tex]

Hope it will find you well.

Answer:

Eli used 1.25 pounds of butter to make mashed potato.            

Step-by-step explanation:

We are given the following in the question:

Amount of potato used by Eli = 12.5 pounds

Amount of butter used =

[tex]\dfrac{1}{10}(\text{Amount of potato used})[/tex]

Thus, pounds of butter used by Eli is:

[tex]\dfrac{1}{2}\times 12.5\\\\=1.25[/tex]

Thus, Eli used 1.25 pounds of butter to make mashed potato.

Answer:

Therefore, the probability is P=0.000142.

Step-by-step explanation:

We have a weighted coin which lands on Heads with probability 0.17. You decide to toss it 5 times.

We calculate the  probability that the total number of times the coin lands on Heads. We get:

[tex]P=0.17^5\\\\P=0.000142[/tex]

Therefore, the probability is P=0.000142.

The answer involves using the binomial distribution to calculate the probabilities of getting different numbers of heads when tossing a weighted coin five times. The outcome of interest is the sum of probabilities of getting 0, 1, or 4 heads, as these are not prime numbers, unlike 2, 3, and 5.

The probability of a weighted coin landing on heads is given as 0.17. When tossing this coin 5 times, there are several outcomes, but we're interested in the probability that the total number of heads is not a prime number. To address the question, we need to calculate the binomial probabilities for obtaining 0, 1, 2, 3, 4, or 5 heads, since these cover all possible outcomes.

Then, we need to identify which of these are prime numbers, and which are not. Prime numbers within our range are 2, 3, and 5. Therefore, we want the probabilities of getting 0, 1, or 4 heads. These probabilities can be computed using the binomial probability formula:

P(X = k) = (n choose k) * (p^k) * ((1-p)^(n-k))

Where 'n' is the number of trials, 'k' is the number of successes (heads in this case), 'p' is the probability of getting a head on a single toss, and 'n choose k' is the binomial coefficient.

The probability of getting a total number of heads that is not a prime number is the sum of the probabilities of getting 0, 1, or 4 heads.

Answer:

The answer to your question is 34°

Step-by-step explanation:

Data

m∠1 = 34°

m∠2 = 116°

m∠3 = ?

Process

1.- If lines l and m are parallel then angles 1 and 3 are interior alternate angles.

2.- Interior alternate angle measure the same.

3.-  m∠1 = m∠3

4.- m∠3 = 34°

5.- Another information given is not necessary to answer this question.

Answer: 34°

Step-by-step explanation:

There may be another way to do it; angle 1 is equal to 34°, angle one and the supplement of 3(we will call it angle 4) are supplementary. So if angle 1 equals 34, angle 4 = 180-34 (which equals 146). since angles 3 and 4 are supplementary, angle 3; would equal 180 - 146 (which equals 34).

Have a nice day! Good luck with the exam.

Answer:

a) The marginal cost function is given by

C'(x) = 4 + 0.04x + 0.0003x² (in dollars)

b) C'(70) = $8.27

Step-by-step explanation:

C(x) = 1000 + 4x + 0.02x² + 0.0001x³

a) Marginal cost is usually defined as the cost of producing one extra unit of product. It expresses how much the total cost is changing with respect to number of units of product.

Mathematically,

MC = (dC/dx) = C'(x)

For this question,

C'(x) = 4 + 0.04x + 0.0003x²

b) C'(70) means the marginal cost at x = 70 units, that is, how much the total cost is changing after the production of 70 units; the cost of producing one extra unit of product after producing 70 units.

C'(x) = 4 + 0.04x + 0.0003x²

C'(70) = 4 + 0.04(70) + 0.0003(70²)

C'(70) = $8.27

Hope this helps!

Answer:

The range is 9,100

Step-by-step explanation:

Six different figures for the account balance for the six months are given.

The range of a set of numbers is defined as the difference between the highest and the lowest of the numbers.

In this question, we have;

Highest: 9200

Lowest: 100

Range = Highest - Lowest = 9200 - 100 = 9100

Answer:

There is a typo in your question it's supposed to be 200 not 9200

Step-by-step explanation:

Answer:

The -15°C temperature of the ice in their snow cones mean that the temperature of that ice is 15° below the freezing point of water.

Step-by-step explanation:

It is explained that Celsius scale was calibrated based on water. The scientists use 0°C to represent the freezing point of water and subsequently use positive numbers to indicate temperatures above the freezing point of water and negative numbers to indicate temperatures lower than the freezing point of water.

So, a temperature of -15°C simply means that the temperature is 15° lower than the freezing point of water.

Hope this Helps!!!

Answer:

Its A

Step-by-step explanation:

Answer:

60 combinations for single file.

Step-by-step explanation:

Bloopin has 12 combinations where he leads the single file line of 3 only reindeer's at a time including the reindeer that leads the file. This is not a file of five but as the question asks for 3 there are 5 reindeer's that each have a turn of 12 each, to single file 3 reindeer's, it is here we get 12 for each combination.

12 x 5 = 60 combination.

Answer:

3

Step-by-step explanation:

A mandatory relationship means that for every A there must be a B and vice versa. The excessive is saying that you have a relationship with 3 records each, therefore the bridge relation cannot have less than 3 records otherwise the mandatory aspect will be broke.

I hope you find this information useful and interetsing! Good luck!

Final answer:

The trigonometric functions and their inverse functions are related to each other because they undo each other's actions. Inverse trigonometric functions give the angle whose trigonometric ratio is a given value. The domains and ranges of inverse trigonometric functions are restricted to ensure that they are well-defined.

Explanation:

The trigonometric functions and their inverse functions are related to each other because they undo the actions of the other function. Let's take the sine function as an example. The sine function takes an angle as input and gives the ratio of the opposite side to the hypotenuse as output. Its inverse function, arcsine, takes a ratio as input and gives the angle whose sine is that ratio as output.

These comparisons make sense in the light of the definition of the inverse of a function because an inverse function undoes the action of the original function. In the case of trigonometric functions, they represent a ratio between the sides of a right-angled triangle, and their inverses give the corresponding angle.

The domains and ranges of the inverse trigonometric functions make sense in relation to their parent functions because they are restricted to a specific range to ensure that the inverse function is well-defined. For example, the domain of arcsine function is [-1, 1] because the output of sine function is always between -1 and 1. By restricting the domain, we can ensure that the inverse function is a one-to-one mapping and has a well-defined output for each input.

Answer:

5 dollars and 19 cents

Step-by-step explanation:

hsgd

Answer:

  check your math

Step-by-step explanation:

The first subtraction was correct:

  36 -7 3/4 = 28 1/4

The second subtraction needs to be revisited.

  28 1/4 -6 2/4 = 27 5/4 -6 2/4 = 21 3/4

__

You can do what you did, but you need to pay attention to the signs.

  28 1/4 -6 2/4 = (28 -6) +(1/4 -2/4) = 22 - 1/4 = 21 3/4

The result of subtracting 2/4 from 1/4 is -1/4, not +1/4.

_____

The length of the first cut piece was 21 3/4 inches.

Answer:

21 ¾ inches

Step-by-step explanation:

36 - 6½ - 7¾

36 - (6½ + 7¾)

36 - (6 + 7 + ½ + ¾)

36 - (13 + [2+3]/4) lcm:4

36 - (13 + 5/4)

36 - (13 + 1 + ¼)

36 - 14 - ¼

22 - ¼

21¾ inches