The total cost incurred by time t in the production of a certain commodity is f(t) dollars. The number of products produced by time t is g(t) units. What does the function f(t)/g(t) represent?

Answer:

  see below

Step-by-step explanation:

The leading minus sign tells you the graph opens downward. (x-3) in the squared term tells you the x-coordinate of the vertex is x=3. The graph that matches these characteristics is shown below.

Final answer:

Greg bought 12 books online. To find the number of books, set up the equation 6n + 3 = 75, subtract the shipping fee, and divide by the price per book.

Explanation:

Greg ordered books online for $6 each and paid a total of $75, which includes a $3 shipping fee. To determine the number of books Greg bought, you need to set up an equation that represents the total cost.

The cost of the books alone can be represented by 6 times the number of books (6n), and when you add the shipping cost of $3, it equals the total cost of $75. So the equation would be:

6n + 3 = 75

To solve for n, which is the number of books Greg purchased, follow these steps:

Subtract the shipping fee from the total cost: 75 - 3 = 72.

Divide the result by the cost per book: 72 ÷ 6 = 12.

Therefore, Greg bought 12 books.

Answer:

There are 7 dimes, 3 nickels, and 4 quarters.

Answer:

Step-by-step explanation:

If angle 1 and angle 2 are supplementary, then

∠1 + ∠2 = 180°

If angle 2 and angle 3 are complementary, then

∠2 + ∠3 = 90°

We are given the values for angles 1 and 2, so:

(8x + 3) + ( 5x - 18) = 180 so

13x - 15 = 180 and

13x = 195 so

x = 15

Sub 15 in for x in angle 2 to find the measure of angle 2:

∠2 = 5(15) - 18 so

∠2 = 57°

That means that to find angle 3,

57° + ∠3 = 90 so

∠3 = 33°

The measure of angle 3 is found to be 33 degrees, using the relationships that angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3, along with their given expressions in terms of x.

To find the measure of angle 3, we must use the relationships between the angles given: angle 1 is supplementary to angle 2 and angle 2 is complementary to angle 3.

Since angle 1 and angle 2 are supplementary, their sum is 180 degrees. The equation is therefore:

(8x + 3) + (5x - 18) = 180

Solving for x gives:

13x - 15 = 180

x = 195 / 13

x = 15

Substitute x back into the expression for angle 2:

(5x - 18) = (5(15) - 18) = 57 degrees

Since angle 2 and angle 3 are complementary, they add up to 90 degrees:

angle 2 + angle 3 = 90

57 + angle 3 = 90

Subtract 57 from both sides to find angle 3:

angle 3 = 90 - 57

angle 3 = 33 degrees

Therefore, the measure of angle 3 is 33 degrees.

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Answer:

The cubic polynomial is: x³ - x² - 6x.

Step-by-step explanation:

Given the degree and the roots of the polynomial we can find it.

An n - degree polynomial has n roots.

Here, given that the degree of the polynomial is 3 and three roots are given. Also, if (x - a) is a factor of a polynomial then x = a is a root of the polynomial. The converse is also true.

Since, the roots of the polynomial are given to -2, 0, 3 then it should have had the following factors.

(x + 2)(x - 0)(x - 3) = 0

Multiplying them we get:

⇒ [tex]$ (x^2 + 2x)(x - 3) $[/tex]

[tex]$ = x^3 - 3x^2 + 2x^2 - 6x $[/tex]

[tex]$ = x^3 - x^2 - 6x $[/tex] which is the required cubic polynomial.

Hence, the answer.

Answer:

the answer would be C. The mean would increase.

Step-by-step explanation:

The mean has increased, the correct option is C.

Average is the mean of the data set obtained by summing all the values of the data set and then dividing it by the number of data in the set.

The total number of students is 19.

The outlier is 81

An outlier is a number that is different from the other set of numbers, it is obtained due to variability in the observation or due to experimental error.

The mean including the outlier of 81 equals 94.

For the mean including the outlier, it can be observed that the outlier is the left outlier or the smallest number.

Let x represent the sum of all the test scores

x / 19 = 94

x = 94 * 19

x = 1786

The sum without the outlier is 1786 - 81 = 1705

The mean without the outlier is

= 1705 / 18

= 94  13 /18

This is greater than 94.

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The point 6 cm away from the center travels in a circle of circumference 2π*(6 cm) = 12π cm, so that it covers this distance per revolution, 12π cm/1 rev.

So the disk has a linear speed of

(6000 rev/min) * (12π cm/rev) = 72,000π cm/min

which is equivalent to

(72,000π cm/min) * (1/100,000 km/cm) * (60 min/h)

or approximately 135.7 km/h.

Answer:the equations are

x + y = 8

20x + 110y = 340

Step-by-step explanation:

Let x represent the number of commercials on which Alexa's songs were played.

Let y represent the number of movies on which Alexa's songs were played.

The total number of movies and commercials on which Alexa earned is 8. It means that

x + y = 8 - - - - - - - - - - - -1

Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that

20x + 110y = 340 - - - - - - - - - - - -2

Answer:

variables:

c= the number of commercials

m= number of movies

system of equations:

20c+110m= 340

c+m= 8

Answer:the fraction of Mary's garden that has tulips is 2/3

Step-by-step explanation:

Let x represent the full area if Mary's garden.

Mary plants roses in 1/4 of her garden. This means that the portion of the garden on which she planted roses would be 1/4 × x = x/4

She also plants some tulips in her garden. She has 1/12 of the garden left to plant more flowers. This means that the portion if the garden that she has left to plant more flowers would be 1/12 × x = x/12

The portion of the garden on which she planted tulips would be

x - (x/4 + x/12) = x - (3x + x)/12 = x - 4x/12

x - x/3 = (3x - x)/3 = 2x/3

Therefore, the fraction of Mary's garden that has tulips would be

(2x/3) /x = 2/3

Final answer:

Mary has 2/3 of her garden planted with tulips.

Explanation:

To find the fraction of Mary's garden that has tulips, we need to first determine the fraction of her garden that she has planted with roses. We are given that Mary plants roses in 1/4 of her garden, so the fraction of her garden that she has planted with roses is 1/4. Since she has 1/12 of her garden left to plant more flowers, the fraction of her garden that she has planted with tulips is the remaining fraction, which is 1 - 1/4 - 1/12.

Let's simplify this expression. First, find a common denominator for 1/4 and 1/12, which is 12. Rewrite 1/4 with the denominator 12 as 3/12, and rewrite 1/12 with the denominator 12 as 1/12. Now we can subtract these fractions:

1 - 3/12 - 1/12 = 12/12 - 3/12 - 1/12 = 8/12 = 2/3

Therefore, 2/3 of Mary's garden has tulips.

Final answer:

To solve the problem, set up a system of equations representing the total number of chickens and the total cost. Solve the system using substitution or elimination method to find the number of Americana and Delaware chickens that Allysa bought.

Explanation:

Allysa spent a total of $35 to purchase 12 chickens. Let's denote the number of Americana chickens as 'x' and the number of Delaware chickens as 'y'. The cost of Americana chickens is $3.75 each, while the cost of Delaware chickens is $2.50 each. Based on this information, we can establish two equations:

x + y = 12 (equation 1, representing the total number of chickens)

We can solve this system of equations using substitution or elimination method. Let's use substitution:

Therefore, Allysa bought 4 Americana chickens and 8 Delaware chickens.

Alyssa purchased 4 Americana chickens and 8 Delaware chickens. By solving the system of equations, we determined the number of each type of chicken. At the end of the first week, she expects to take in $22.5  from selling eggs.

To determine the number of Americana chickens, A, and the number of Delaware chickens, D, Alyssa purchased, we set up a system of equations based on the given information:

Now, to solve the system, we can use substitution or elimination. Let's use substitution:

So, Alyssa purchased 4 Americana and 8 Delaware chickens.

To determine Alyssa's expected income from selling eggs at the end of the first week:

Therefore, Alyssa expects to take in $22.5 at the end of the first week from selling eggs.

Complete Question:

Alyssa spent $35 to purchase 12 chickens. She bought two different types of chickens. Americana chickens cost $3.75 each and Delaware chickens cost $2.50 each. Write a system of equations that can be used to determine the number of Americana chickens, A, and the number of Delaware chickens, D, she purchased. Determine algebraically how many of each type of chicken Allysa purchased. Each Americana chicken lays 2 eggs per day and each Delaware chicken lays 1 egg per day. Allysa only sells eggs by the full dozen for $2.50. Determine how much money she expects to take in at the end of the first week with her 12 chickens.

Answer:

Park is 5 miles from Billy's home.

Step-by-step explanation:

Given:

Billy left home at 9 a.m. And rode his bicycle to the park at an average speed of 10 miles per hour here and got the park at 9:30 a.m.

Now, to find the distance from park to Billy,s home.

Time it took Billy to rode his bicycle from park to home is from 9.30 a.m to 9.30 p.m.

So, the time = (9.30 - 9.00) = 30 minutes

[tex]=\frac{30}{60}[/tex]  [tex]=0.5\ hour.[/tex]

Speed = 10 miles per hour.

Now, to get the distance from park to Billy's home we put formula:

[tex]Distance=Speed\times Time.[/tex]

[tex]Distance=10\times 0.5[/tex]

[tex]Distance=5\ miles.[/tex]

Therefore, park is 5 miles from Billy's home.

The coordinates of the point on the graph when x=3 are C. (3, 5)

Step-by-step explanation:

Given piece-wise function is:

[tex]y = \left \{ {{4x+1\ \ \ x<3 } \atop {2x-1\ \ \ x\geq 3 }} \right.[/tex]

In order to determine the coordinates of the point on the graph where x=3 we will see which part of the function we have to consider as the function is in two pieces.

By observing we see that the second piece  of function will be used as it is for x≥ 3 so it includes 3.

Putting x = 3 in y = 2x-1

[tex]y = 2(3) -1\\y = 6-1\\y = 5[/tex]

Hence,

The coordinates of the point on the graph when x=3 are C. (3, 5)

Keywords: Functions, graph

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Answer: Christina's age is 13, Joanne's age is 42 and Devin's age is 21.

Step-by-step explanation: If Devin's age is represented by d, then Joanne's age will be 2d because Joanne is two times Devin's age. Also, if Devin is 8 years older than Christina, then Christina's age would be d - 8. If the sum of their ages is equal to 76, then;

2d + d + (d - 8) = 76

2d + d + d - 8 = 76

4d - 8 = 76

Add 8 to both sides of the equation

4d = 84

Divide both sides of the equation by 4

d = 21

Therefore, Devin is 21 years old

Joanne is 42 years old and

Christina is 13 years old.

Christina is 13 years old, Devin is 21 years old, and Joanne is 42 years old. This is found by defining Christina's age as x, then setting up and solving an equation based on the problem's provided relationships.

In this math problem, we have three individuals: Joanne, Devin, and Christina, and we know their ages in relation to each other's.

We know that Joanne's age is two times Devin's. We also know Devin is eight years older than Christina. Finally, we know the sum of all three ages is 76.

Let's denote Christina's age as x. Consequently, Devin's age would be x + 8 because he is 8 years older than Christina. As Joanne's age is two times Devin's age, Joanne's age would be 2*(x + 8).

The sum of their ages is 76, which gives us the following equation:
x (Christina's age) + x + 8 (Devin's age) + 2*(x + 8) (Joanne's age) = 76.

Solving this equation, we get:
4x + 24 = 76
Subtract 24 from both sides gives us 4x = 52, and dividing both sides by 4 gives x = 13.

So, Christina's age is 13, Devin's age is 13 + 8 = 21, and Joanne's age is 2*21 = 42.

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Answer: Angelo is 13 years old.

Aaron is 15 years old

Alfred is 34 years old

Step-by-step explanation:

Let x represent the age of Angelo.

Let y represent the age of Aaron.

Let z represent the age of Alfred

The sum of three guys ages is 62. It means that

x + y + z = 62 - - - - - - - - - - -1

Angelo is two years younger than Aaron. It means that

x = y - 2

Alfred is four years older than twice Aaron's age. It means that

z = 2y + 4

Substituting x = y - 2 and z = 2y + 4 into equation 1, it becomes

y - 2 + y + 2y + 4 = 62

4y + 2 = 62

4y = 62 - 2 = 60

y = 60/4 = 15

x = y - 2 = 15 - 2

x = 13

z = 2y + 4 = 2 × 15 + 4

z = 34

Answer:

The distance that the conveyor belt moves the bottle is less than 90 meters

Step-by-step explanation:

Speed of the conveyor belt

120 cm/s

Time it takes to move the conveyor belt less than 1.2 minutes to move the bottle from the loading dock to the unloading dock.

But 60s = 1 minute

This gives

1.2 minutes = 1.2×60s seconds = 72 seconds

But speed = distance/time

so that distance = speed × time = 120cm/s ×(<72s)

From where distance = <8640cm<90m (90m×100=9000cm)

Time it takes to move the conveyor belt more than 1.1 minutes to move the bottle from the loading dock to the unloading dock.

Again 60s = 1 minute

This gives

1.1 minutes = 1.1×60s seconds = 66 seconds

Time it takes is more than 66s

But speed = distance/time

so that distance = speed × time = 120cm/s × (>66s)

From where distance >7920cm

However

7920cm < 90m (90m×100=9000cm)

So that

The distance that the conveyor belt moves the bottle is less than 90 meters

Answer:

B. A continuous continuous data set because there are infinitely many possible values and those there are infinitely many possible values and those values cannot be counted values cannot be counted

Step-by-step explanation:

Given that the  volume of cola in a can is 12.1 oz

We have to find out whether discrete or continuous.

We can say a random variable is discrete if it takes values which have one to one correspondence with the set of natural numbers.

continuous if a one to one correspondence with set of natural numbers cannot be established.

In our case, we have volume of cola as 12.1 oz.  Between two readings say,12.1 oz and 12.15 oz. there may be infinite other values which the volume can take

i.e. this is a continuous data.

B. A continuous continuous data set because there are infinitely many possible values and those here are infinitely many possible values and those values cannot be counted values cannot be counted

is right answer

The volume of cola in a can, measured as 12.1 oz, is an example of continuous data because it could theoretically take any value in a certain range, unlike discrete data which can only have certain distinct values.

The volume of cola in a can being 12.1 oz represents continuous data. This is because continuous data can take on any value within a certain range or interval. In this case, the volume of the cola in the can could theoretically have been any number between certain limits, for example, 0 to 12.2 oz. This differs from discrete data, which can only take certain distinct or separate values, such as the number of cans of cola you might buy (1,2,3, etc.).

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Answer:

64%

Step-by-step explanation:

pain

The answer is B) 64%.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Let X be the number of students out of 40 who like to hike. We know that P(X ≤ 15) = 0.36 and we want to find P(X ≥ 16).

Note that P(X ≥ 16) is the complement of P(X ≤ 15). That is,

P(X ≥ 16) = 1 - P(X ≤ 15) = 1 - 0.36 = 0.64

Therefore, the answer is B) 64%.

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Answer:

Step-by-step explanation:

A female bunny gained three pounds per. It means that the total number of pounds that the female bunny gained in 6 weeks would be

3 × 6 = 18 pounds.

A male bunny gained 8 pounds per week. It means that the total number of pounds that the male bunny gained in 6 weeks would be

8 × 6 = 48 pounds.

Therefore, the number of pounds that the male bunny gained more the female bunny would be

48 - 18 = 30 pounds

Step-by-step explanation:

Female Bunny: Doe

Male Bunny: Buck

A doe gained three lbs per week for six weeks.

3 x 6 = 18

A buck gained eight lbs per week for six weeks.

8 x 6 = 48

How many more lbs did the buck get than the doe?

48-18= 30

Answer:

The male bunny gained thirty more pounds than the female bunny.

The buck gained 30 more lbs than the doe.

Answer:

x=22.5

Step-by-step explanation:

BM||DT

Using Intercept theorem/Intercept theorem

[tex]\frac{6}{6+15} =\frac{9}{9+x}[/tex]

6(9+x)=9*21

54+6x=189

6x=135

x=22.5

At least I think so

Answer:

[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]

Step-by-step explanation:

We have been given that the desert temperature, H, oscillates daily between 40◦F at 5 am and 80◦F at 5 pm. We are asked to write a formula H in terms of t, measured in hours from 5 am.

We will use cosine function to write our required formula.

[tex]y=A\text{cos}[B(x-C)]+D[/tex], where,

A = Amplitude,

[tex]\text{Period}=\frac{2\pi}{|B|}[/tex]

C = Phase shift,

D = Vertical shift.

First of all, we will find amplitude using maximum and minimum values as:

[tex]A=\frac{\text{Maximum value}-\text{Minimum value}}{2}[/tex]

[tex]A=\frac{80-40}{2}[/tex]

[tex]A=\frac{40}{2}[/tex]

[tex]A=20[/tex]

Since period is 24 hours (5 am to 5 pm), so let us find B as:

[tex]24=\frac{2\pi}{|B|}[/tex]

[tex]B=\frac{2\pi}{24}[/tex]

[tex]B=\frac{\pi}{12}[/tex]

[tex]\text{Vertical shift}=\frac{\text{Maximum value}+\text{Minimum value}}{2}[/tex]

[tex]D=\frac{80+40}{2}=\frac{120}{2}=60[/tex]

There is no phase shift.

Since temperature is minimum when [tex]t=0[/tex], so we will use negative cosine as:

[tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex]

Therefore, our required function would be [tex]H(t)=-20\text{cos}(\frac{\pi}{12}t)+60[/tex].

To model the desert temperature, use the sinusoidal function H(t) = 20 * cos(π/12 * t) + 60, which captures daily temperature changes between 40°F and 80°F, with parameters tuned to fit the given data.

To write a formula for the desert temperature H in terms of t, measured in hours from 5 am, we can use a sinusoidal function that models the daily temperature oscillation.

We know:

The general form for the sinusoidal function is:

H(t) = A * sin(B*(t - C)) + D

Where:

From the given data:

Thus, the sinusoidal function becomes:

H(t) = 20 * cos(π/12 * t) + 60.

Answer: 162  sq. yds.

Step-by-step explanation:

Given : A square that is 5yd on a side is placed inside a rectangle that has a width of 11yd and a length of 17 yd.

Then , Area of rectangle = length x width

= 11 yd  x 17 yd = 187 sq. yds.

Area of square = (side)²  

= (5 yd)² = 25  sq. yds.

Now , the area of the region inside the rectangle that surrounds the square will be Area of rectangle - Area of square

= 187 sq. yds.- 25  sq. yds.

=162  sq. yds.

Hence, the area of the region inside the rectangle that surrounds the square is 162  sq. yds. .

Answer:

1 minute = 1080 - 960 = 120 m

5 minutes = 5400 - 4800 = 600 m

8 minutes = 8640 - 7680 = 960 m

Step-by-step explanation:

I think the easiest way is to just see how far they get at each time.  So I'm going to go one horse at a time.

16 m/s

1 minute = 60 seconds, every second is 16 meters so 16 m/s * 60 s = 960 m

5 minutes = 300 seconds so 16 m/s * 300 s = 4800 m

8 minutes = 480 seconds, 16 m/s * 480 s = 7680 m

I also want to point out that unites cancel out.  m/s * s is kinda like variables so the seconds being multiplied by m/s cancels witht eh seconds in the denominator.

Now the next horse

18 m/s

1 minute totals to 1080 m

5 minutes = 5400 m

8 minutes = 8640 m

Now we take the differences of each time

1 minute = 1080 - 960 = 120 m

5 minutes = 5400 - 4800 = 600 m

8 minutes = 8640 - 7680 = 960 m

Another way to do this is to take the difference of speed and then multiply that by the time.  so 18-16 = 2, then multiply each time by 2.  For me it just makes more intuitive sense the way I showed.  

Answer: the probability that the first toss wins is:

P = 1/6 or 0.1667

Step-by-step explanation:

A die has six sides (that is 6 outcome per die)

For a pair of dice:

The Total number of possible outcomes = 6 × 6 = 36

The possible outcomes of 7 is:

(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)

= 6

The probability P of getting 7 is:

P = number of possible outcomes of 7/total number of possible outcomes

P = 6/36 = 1/6

The probability that the first toss wins

P = 1/6 or 0.1667

Answer:

the answer is 16ft

step-by-step explanation:

in order to make a triangle with non-zero area, the sum of the shorter two sides must be greater than the longest side.

here, 4 + 4 > 7, so the lengths can form a triangle.

The correct answer was given: Brain

7+8= 15

hope this

The correct answer was given: Brain

36 cm is the final : )

The Answer is

5 by 9

Answer:

-6, 8

Step-by-step explanation:

Let the numbers be represented by y

Square of y = y^2

Double y = 2 × y = 2y

Square of the number is 48 more than double the number is written mathematically as

y^2 = 2y +48

y^2 - 2y - 48 = 0

This is a quadratic equation and can be solved by method of factorisation

y^2 -2y - 48 = 0

y^2 + 6y - 8y - 48 = 0

(y^2 + 6y) - (8y - 48) = 0

y(y + 6) - 8(y + 6) = 0

(y + 6)(y - 8) = 0

y = -6, 8

The numbers are -6, 8

Answer:

8, -6

Step-by-step explanation:

Let the number be $n$, so we have $n^2 =48 + 2n$. Rearranging this equation gives $n^2 -2n-48=0$ and factoring gives $(n-8)(n+6)=0$. So, the numbers that fit the problem are $\boxed{n = -6~\text{and}~n = 8}$.

Answer:

Another way to decompose the number would be

43  taking the 4 of the left with tens like 40 ( 4*10) and 3 of the right as three separate ones ( 3*1= 3) .Adding 10s four times with  three one times would make 43

Final answer:

The student's question deals with decomposing numbers into tens and ones and relates to the concept of powers of ten in mathematics. Powers of ten notation is foundational in understanding place value, large, and small numbers. By breaking down numbers into tens and ones, students can grasp numerical values more effectively.

Explanation:

The question pertains to the mathematical concept of decomposing numbers into tens and ones using a ten-frame and involves powers of ten. In mathematics, numbers can be broken down into tens and ones to understand their value better. It's essential to note that each place in our numbering system is ten times greater than the place to the right of it. This is part of the reason we use powers-of-ten notation.

Decomposing Numbers

When decomposing a number like 24, for example, we can break it down into two tens (20) and four ones (4). If we used a ten-frame, we would fill in two full ten-frame grids to represent the tens and then add four individual marks to represent the ones.

Understanding Powers of Ten

When we discuss powers of ten, we're talking about how the counting system is structured, with each place value being ten times greater than the one before it. The digital numbering system got started because humans have ten fingers and counted with them, leading to an increase by tens.

A positive exponent, like 10³, tells us to multiply the base (10) by itself the number of times indicated by the exponent (3), which results in 1000. On the other hand, a negative number as the power indicates a division, so a power like 10⁻¹=0.1. If we have 10⁻⁴, it means 0.0001, which is ten times smaller than 0.001 (10⁻³).

When dividing by powers of ten, we move the decimal point to the left by the number of zeros indicated by the power. This process simplifies understanding large and small numbers by expressing them in terms of powers of ten or powers of one thousand for very large numbers.

Answer:

4

Step-by-step explanation:

in similarity the ratio of the similar sides is the same i.e

10/5 =8/x

2x=8

x= 4

Answer:

He paid = $20,500

Step-by-step explanation:

Let the amount he bought the car originally be X

so from the statement,

(2/5)*X + $200 = $8,400

(2/5)*X = $8,400 - $200

solving for X

X = $8200 * 5/2

X = $20,500