if a ball is thrown into the air with a velocity of 20 ft/second it's height in feet and seconds is given by f(t) = 20t - 10t^2. find average velocity for the time period t0 = 1 to t=2

Answer:

Quadratic Formula

Step-by-step explanation:

x^2-11x+10=

x^2-x-10x+10=

x(x-1)-10(x-1)=(x-10)(x-1)

Answer:

HELP WITH WHAT?

Step-by-step explanation:

The required radius and error in radius is 13.8 cm and ± 0.12cm

Given that,
A machinist is required to manufacture a circular metal disk with an area of 600cm².
(a) What radius produces such a disk is to be determined
(b) If the machinist is allowed an error tolerance of ±5cm2 in the area of the disk, how close to the ideal radius in part is to be determined.

The area of a circle is given by the pie times square of the radius.

Area of circle = πr^2

Here,
a) The given area of disk = 600 cm²
   πr² = 600
   r = √600/3.14
   r = 13.8 cm

b) an error tolerance of ± 5 cm² in the area of the disk,
So the percentage of error is 0.84%
Now, 0.84% of radius = 0.84 *13.8/100 = 0.12
The required error in radius will be ±0.12 cm

Similarly,
c) limx→a f(x) = L
Where a is the area of the disk and L is length, and f(x) is function of area.

Thus, the required radius and error in radius is 13.8 cm and ± 0.12cm.

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Answer:

400

Step-by-step explanation:

Change the 16 and the 64 in the numerator to exponents

2^4 x 10^2 x 4^3/2^4 x 4^2

Simplify

10^2 x 4

100 x 4

Part A  The quadratic expression in factored form is 2t(19 - 8t)

Part B The height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft

Since Callie kicks a soccer ball from the ground. The height of the ball, in feet, above the ground t seconds after the ball is kicked can be represented by the expression 38t- 16t².

So, the expression is a quadratic expression, we have that h(t) = 38t- 16t².

To write the expression in factored form, we find the common factors of both terms and factor them out.

So,  h(t) = 38t- 16t²

= 2 × 19 × t - 2 × 8 × t × t

Factoring out 2 and t, we have

= 2 × t × (19 - 8 × t)

= 2t(19 - 8t)

So, the quadratic expression in factored form is 2t(19 - 8t)

Since the quadratic expression h(t) = 38t- 16t² represents the height of the ball above the ground in feet, to find the height of the ball after 1.25 second,we substitute t = 1.25 s into the expression.

So, h(t) = 38t- 16t²

h(1.25) = 38(1.25) - 16(1.25)²

h(1.25) = 47.5 - 16(1.5625)

h(1.25) = 47.5 - 25

h(1.25) = 22.5 ft

So, the height of the soccer ball 1.25 seconds after Callie kicks it is 22.5 ft

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If total revenue given by the function R=16.5x and has total cost given by C=14x+400, where x is the number of items produced and sold then the number of units that gives break even for the product is 160.

In mathematics, a function is an expression, rule, or law that specifies a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are commonplace in mathematics and are required for expressing physical relationships in the sciences. The present concept of function was proposed by German mathematician Peter Dirichlet in 1837.

If a variable y is so tied to a variable x that there is a rule that determines a unique value of y whenever a numerical value is assigned to x, then y is referred to as a function of the independent variable x.

If the manufacturer will break even for the products then

Revenue = Cost

F(R) = F(C)

14x+400 = 16.5x

On solving the equation

16.5x - 14x = 400

2.5x = 400

x = 400/2.5

x = 160

In the graph the value of x is 160 as well

Thus, to break the product even the number of units =

160

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Answer:

Step-by-step explanation:

x + x + 16 = 90

2x +16 = 90

2x = 74

x = 37

The average speed of person during her commute is 28 miles/ hour.

What do you mean by average speed ?

The entire distance that an object travels in a given amount of time is defined as the average speed for that object.

Total time of driving is 12 minutes.

This can be written as hours which will be :

= 12 / 60

= 1/5 hour

Time of stopping at red lights is 3 minutes and speed is 35 miles per hour.

So , the total distance using the formula will be :

Total distance = Speed × time

Here , the time taken will be equal to :

= [(12 + 3) / 60]

= 15 / 60

= 1/4 hour

So ;

Total distance = 35 × (1/4 hour)

Total distance = 7 miles

And the average speed will be ;

Average speed = Distance / Time

or

Average speed = 7 miles / (1/4) hour

Average speed = 7 × 4 miles/hour

Average speed = 28 miles / hour

Therefore , the average speed of person during her commute is 28 miles/ hour.

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The small will grow 19/4 inch in 3 weeks and the method which will not give the correct inches will be the first option which is

                       multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.

According to the question we have been given that

The height of the small plant = [tex]2\frac{1}{2}[/tex] inch

In  1 week the plant grows = [tex]\frac{3}{4}[/tex] inch

We need to find the height of the small plant after 3 weeks.

For that we will first find how much tall it will be in 3 weeks using unitary method that is,

                              1 week = [tex]\frac{3}{4}[/tex] inch

                               3 week = [tex]\frac{3}{4}[/tex]  * 3 inch

                                          = 9/4 inch

Therefore the height of the small plant after 3 weeks will be

                         [tex]=2\frac{1}{2} + \frac{9}{4} \\= \frac{5}{2} + \frac{9}{4}\\= \frac{10+9}{4} \\= \frac{19}{4}[/tex]

hence the height is 19/4 inch

And the method which will not give the correct number of inches is the first option which is

               multiply [tex]2\frac{1}{2} * 3[/tex] and then add 3/4.

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[tex]76000\times1.08=\boxed{82,080}[/tex]

Answer:

82,080

Step-by-step explanation:

To increase a number by it's percentage, you must first extract what 8% of 76,000 is (6080). Then, you must add the original number to what is 8% of it, to get 82,080, and that, is the final answer.

The INEFFICIENT point of production in the given graph is represented by Point A , the correct option is option (a).

The given graph is for skateboards vs Bikes .

We need to find the point representing the Inefficient Point of Production.

The Production Possibility Curve points are said to be Inefficient when the resources are not utilized to the fullest.

In the given Production Possibility Curve between Skateboards and Bikers the point A is the inefficient point of production .

Therefore , the Inefficient point of production in the given curve is represented by Point A , the correct option is option (a)

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Answer:

8.9 ÷ 0.4 = 22.25

so the answer is 22.25

hope this helps

Answer:

22.25 is your answer

Step-by-st

The total laps your friend runs is 3.

A fraction is a non-integer that is made up of a numerator and a denominator. The numerator is the number above and the denominator is the number below.

A proper fraction is a fraction where the numerator is less than the denominator. A mixed fraction is a fraction that is made up of a whole number and a proper fraction.

The first step is to determine the total miles you run

Total miles run  = length of the side walk x total number of laps

9/10 x (3 + 2)

9/10 x 5 = 45 / 10 = 4.5 miles

The second step is to determine the total number of laps she runs:

4.5 miles / 1 1/2 miles

4.5 / 1.5 = 3 laps

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You need to add 6 red marbles for the ratio to stay the same

The given parameters are:

Black = 6

Red = 4

Represent as ratio

Ratio = Red : Black

This gives

Red : Black = 4 : 6

When you add 4 red marbles, we have:

4 + 4 : 6 + x = 4 : 6

Where x represents the additional number of black marbles

This gives

8 : 6 + x = 4 : 6

Multiply 4 : 6 by 2

So, we have:

8 : 6 + x = 8 : 12

By comparing both sides, we have

6 + x = 12

This gives

x = 6

Hence, you need to add 6 red marbles for the ratio to stay the same

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Answer: x=68

Step-by-step explanation:

(x-5)/3=21

(x-5)*3/3=21*3     ==> Multiply both sides by 3 to remove fractions

x-5=21*3

x-5=63

x+5-5=63+5     ==> Add 5 on both sides to isolate the x variable

x=63+5

x=68

Let's solve the problem,

→ (x - 5)/3 = 21

→ x - 5 = 21 × 3

→ x = 63 + 5

→ [ x = 68 ]

Hence, the value is 68.

Answer:The cost should be 300,000 dollars

Step-by-step explanation:

Answer:

Here's an answer to part of your question.

Step-by-step explanation:

The older the kids get, the less you have to change their diapers. Therefore, that is why the graph is going down

The turning point of the equation of the graph f(x) = |x - 4| is (4, 0)

The equation of the graph is given as

f(x) = |x - 4|

The above equation is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the vertex is

Vertex = (h, k)

The vertex also represents the turning point of the absolute value function

From the given equation, we have

(h, k) = (4, 0)

Hence, the turning point of the graph is (4, 0)

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The expression 6-3/6-4 after simplification will look like 1.5.

Given that the expression is 6-3/6-4.

We are required to find the value after simplification.

Simplification or simplify fractions basically means to simplify a complicated mathematical expression to get a single or direct answer.

We have to use BODMAS rule for the simplification. The full form of BODMAS is Brackets, Open, Division, Multiplication,Addition and Subtraction. Simplication is nothing but to reduce the expression.

The expression is  6-3/6-4.

We have to do division first.

6-3/6-4 =6-0.5-4

Now we have to do subtraction now.

6-0.5-4=5.5-4=1.5

Hence the expression 6-3/6-4 after simplification will look like 1.5.

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Answer:

You save $ 14.27

Step-by-step explanation:

12 dozen = 11.53

2.15 x 12 = 25.80

25.80 - 11.53 = 14.27

After juggling for several minutes i.e., 2.5 minutes and [tex]1\frac{1}{3}[/tex] minutes (mixed fraction), the total number of bowling pins by clown is 37 pins

As per the question statement, a clown juggles 12 bowling for the first 2.5 minutes then he bump it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute (Mixed Fraction form)

We are supposed to find the total number if pins by the clown.

Let's calculate the total time first that will be 2.5 minutes + [tex]1\frac{1}{3}[/tex] minutes

[tex]1\frac{1}{3} =\frac{3*1 +1}{3} =\frac{4}{3} =1.34[/tex] minutes.

Therefore total time = 3.84minutes

Given that he bumps it up to an average of 18 bowling pins per minute for the last [tex]1\frac{1}{3}[/tex]  minute so, the number of pins in the last  [tex]1\frac{1}{3}[/tex]  minute will be = [tex]18*1.34 = 24.12 = 25[/tex] (approx.)

So total number of bowling pins = [tex]12+25 = 37[/tex] pins

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Answer:

The equation in slope-intercept form is: [tex]y=5x+32[/tex]

Step-by-step explanation:

To calculate the slope, [tex]m[/tex], we use the formula [tex]\frac{y_{2} -y_{1}}{x_{2}-x_{1} }[/tex] where [tex]y[/tex] are the [tex]y[/tex]-values of the points and [tex]x[/tex] are the [tex]x[/tex]-values.

Pugging our numbers into the formula, we get [tex]\frac{(-3)-12}{-7-(-4)}[/tex]. This simplifies to 5.

To calculate the [tex]y[/tex]-intercept, we first substitute one of our points into the formula. Substituting -4  and 12, we get [tex]12=5(-4)+b[/tex].

Then we can solve for [tex]b[/tex].

[tex]12=5(-4)+b[/tex]

[tex]12=-20+b[/tex]

[tex]32=b[/tex]

So, our slope is 32.

We can then plug these values into the slope-intercept form [tex]y=mx+b[/tex]

The slope ( option A) best describes the number 3.

An equation can be represented by a linear function. The standard form for the linear equation is: y= ax+b , for example, y=7x+2. Where:

a= the slope. It can be calculated for  [tex]\frac{\Delta y}{\Delta x}[/tex].

b= the constant term that represents the y-intercept.

For the given example: a=7 and b=2.

The equation of the question is y=3x+7, when you compare this equation with the  standard form for the linear equation is: y= ax+b. You find that a=3, where a represents the slope.

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The work in process(Job C) is $14,250

The finished goods(job B) is $23,000

The cost of goods sold(job A) is $31,500

What are work in process, finished goods and cost of goods sold in this case?

The work in process refers to the total costs incurred on Job C, since it was not completed at the end of the month, the finished goods refers to the costs incurred on job B which has been completed but not yet sold and cost of goods sold means the cost incurred on Job A which has been sold since it has been completed.

Job A:

Cost of job in process=$12,000

direct materials used=$2,000

direct labor=$10,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$10,000/$20=500 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=500*$15=$7,500

cost of goods sold=$12,000+$2,000+$10,000+$7,500

cost of goods sold=$31,500

Job B:

Cost of job in process=$1,000

direct materials used=$8,000

direct labor=$8,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$8,000/$20=400 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=400*$15=$6,000

finished goods=$1,000+$8,000+$8,000+$6,000

finished goods=$23,000

Job C:

Cost of job in process=$0

direct materials used=$9,000

direct labor=$3,000

number of direct labor hours=direct labor cost/ direct labor rate

number of direct labor hours=$3000/$20=150 hours

Applied Manufacturing Overhead=labor hours*predetermined overhead rate per direct labor hour

Applied Manufacturing Overhead=150*$15=$2,250

work in progress=$0+$9,000+$3,000+$2,250

work in progress=$14,250

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The amount to  report for Plant Assets in the Classified Balance Sheet of the company is $24,600

What are plant assets?

Plant assets are long-term fixed assets used to manufacture or sell products and services for Adventure Travel. These assets are of tangible nature and of monetarily benefits to the company for more than one accounting year.

The only plant assets in this case is the office equipment bearing in mind that it has a contra entry, in other words, the $29,600 is the cost of the office equipment , we need to deduct the accumulated depreciation on it so as to determine its current book value

plant assets=$29,600-$5,000

plant assets=$24,600

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Answer:

22, 24

Step-by-step explanation:

Hello!

Consecutive integers are integers that come after each other. We want to find two consecutive even integers that when added give us 46.

Let the first consecutive even integer be x. Since even integers come every 2 integers (even, odd, even), the second even integer should be x + 2.

That means x + 2 should be 24.

The two numbers are 22 and 24.

Answer:

-29⁰F

Step-by-step explanation:

Because -19-10=-29.

Part a: Resulting mixture: 92.2 milliliters.

Part b: Percentage of acid in the resulting mixture = 36.88%.

Part a: Find the both values from the given percentage;

225 millilitres of a solution contains is 39% acid.

39% of 225 = (39×225)/100 = 87.75 millilitres.

Now, 25 milliliters of a solution contains is 19% acid.

19% of 25 = (19×25)/100 = 4.75 millilitres.

Mixture solution = 87.75 + 4.75

Mixture solution = 92.2 milliliters of acid.

Part b: percentage of the resulting mixture is acid.

92.2 milliliters of the total 250 milliliters is acid.

= 92.2/250 × 100

= 36.88 %

Thus, 36.88% of the the resulting mixture contains acid.

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Answer:

x^2

Step-by-step explanation:

it's a quadratic equation so the parent function is x^2.