A toy rocket is shot vertically into the air from a launching pad 7 feet above the ground with an initial velocity of 72 feet per second. The height h, in feet, of the rocket above the ground at t seconds after launch is given by the function h(t)=-16 t²+72 t+7. How long will it take the rocket to reach its maximum height? What is the maximum height?
The rocket reaches its maximum height at ? second(s) after launch.
(Simplify your answer.)
The maximum height reached by the object is ? feet.
(Simplify your answer.)

Answer:

A. Yes

Step-by-step explanation:

Each input corresponds to only one output, which satisfies the definition of a function.

The level of production that minimizes the average cost is the quantity of units produced when the value of the average cost function has a minimum value, which is 110 units of production

The minimum value of a function is given by the point of the graph of the function where the value is minimum.

The total cost function is C(x) = 0.2·(0.01·x² + 120)

x = The number of units produced (manufactured)

The average cost is the cost to produce one unit

Therefore;

[tex]Average\, cost, \, AC = \dfrac{Total \, cost }{Quantity \, produced}[/tex]
Therefore;

[tex]Average\, cost \, function,\, f(x) = \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}[/tex]

The quantity that minimizes the average cost is given by the minimum value of the average cost function, which is the point at which the slope of the function, f'(x) is zero as follows;

[tex]f'(x) =\dfrac{d}{dx} \left( \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}\right) = 0[/tex]

[tex]\dfrac{d}{dx} \left( \dfrac{0.2\cdot (0.01\cdot x^2 + 120)}{x}\right) =\dfrac{x^2-12000}{500\cdot x^2} = 0[/tex]

x² - 12000 = 0

x² = 12000

x = √(12000) = 20·√(30) ≈ 110

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Answer:

2

Step-by-step explanation so, you got the question 1+1? let me help.  So the first 1 in the question right? You add another 1 that equals 2 hope this helps.

Answer:

24

Step-by-step explanation:

well u see 1+1 would usually = 2 but because i dont like the number 2 by its self i add another 2 therefore its 22 and then i like to spice it up with adding another 2 to the last 2 then u have 24.

HOPED THIS HELPED!!!!! :b

Answer:

the answer is A

Step-by-step explanation:

you are dividing with a - so the signs will switch

The image of the rotation in the transformation is (-1, 4)

The coordinates of the point are given as

Point = (3, -5)

The transformations are given as

T₁, ₄ rₓ-axis R₉₀°

Mathematically, this is represented as

(x, y) = (x + 1, y + 4) = (x + 1, -y - 4) = (y + 4, x + 1)

So, we have

(x, y) ⇒ (y + 4, x + 1)

Recall that

Point = (3, -5)

This gives

Image = (-5 + 4, 3 + 1)

Evaluate

Image = (-1, 4)

Hence, the coordinates of the image are (-1, 4)

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[tex]\fbox{64 or 8*8}[/tex]

[tex]2^6=64[/tex]

[tex]8\times8=64[/tex]

Answer:

Hopefully this image helps, I am pretty sure you just have to rotate the shape by 270 degrees on the graph.

Answer:

A

Step-by-step explanation:

Answer:

A)

Step-by-step explanation:

To find the percentage of the Pie-Chart , Divide each corresponding Number by the Total Frequency

Total Frequency = 9 + 20 + 25 + 39 = 93

% of Motorcycle = [tex]\frac{9}{93}* 100=9.7 %[/tex] %

% of Sedan  = [tex]\frac{20}{93}* 100=21.5 %[/tex] %

% of SUV  = [tex]\frac{25}{93}* 100=26.9 %[/tex] %

% of Truck  = [tex]\frac{39}{93}* 100=41.9 %[/tex] %

This is represented by Choice A)

The cost for a child ticket was $4 less than the cost of an adult ticket.

Given that, 4 adults took their 5 children to a movie. The price for 9 people was $160.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the cost of adult tickets be x.

The 5 children received a 20% discount on their tickets.

Now, x-20% of x

= x-20/100 × x

= x-0.2x

= 0.8x

Here, 4x+5×0.8x=160

⇒ 4x+4x=160

⇒ 8x=160

⇒ x=20

So, the cost of children is 20-20% of 20

= 20-0.2×20

= 20-4

= 16

Therefore, the cost for a child ticket was $4 less than the cost of an adult ticket.

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Answer:

The transformations that have been done are reflected vertically -1/2 and moved to the right by 3 units.

Step-by-step explanation:

To find out what transformations differ from your parent graph, look at the a,h, and k values.

A value means if it is being vertically stretched or reflected

In this case, -1/2 is a vertically reflection(upside down).

We also have -3 as our h value. This tells us how many units right or left our graph moves. If the value is negative, it moves to the right. If the value is positive, it moves to the left.

Now you know how to find transformations that differ from the parent graph

the difference between 9 and 2 is 7

Answer:

7?

Step-by-step explanation:

Uhhhh
You subtract 9 and 2
7
That's crazy now

The compound inequality that represents this range is D) -19≤temp≤33.

What is inequality?

A mathematical statement known as an inequality in algebra uses the inequality symbol to show the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa. Literal inequalities are relationships between two algebraic expressions that are expressed using the inequality symbols. When the symbols ">," <"  are used to connect two real numbers or algebraic expressions, the relationship is referred to as an inequality.

Here during the recent year the temperature in Chicago ranged from -19 degree celsius to 33 degree celsius.

Here from -19 degree increased to 33 degree. then the inequality is ,

=> -19 [tex]\leq temp\leq 33[/tex]

Hence the correct option is D)  -19 [tex]\leq temp\leq 33[/tex] .

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The equation in slope - intercept form is y = x + 6

Given,

In the question:

A line has slope is 1 and passes through the point (-9, -3)

To find the equation in slope - intercept form.

Now, According to the question:

Based on the given conditions:

Slope (m) = 1

and, x = -9 , y = -3

Substitute the values into

y = mx + b

-3 = -9 +b

Calculate the sum or difference

-b = -6

Divide both sides of the equation by the coefficient of variable

b = 6

Substitute m = 1 and b = 6 into y = mx + b

y = x + 6

Rewrite y = x + 6 in slope intercept form.

Hence, The equation in slope - intercept form is y = x + 6.

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Answer:

B. Rewarding yourself with a small treat every now and then is probably okay

Step-by-step explanation:

The lesson talks about shopping and how it’s not bad to go shopping.

Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.

Given that,

A sample has n = 18, SS = 102, and M = 12 for one sample. In a second sample, the n is 5, the SS is 171, and the M is 8.

We have to find The mean difference in confidence between the two samples' 95% confidence interval falls between which of the following ranges.

n₁=18 and SS=102

We get,

S₁=[tex]\sqrt{SS/n_{1}-1 }[/tex]=[tex]\sqrt{102/18-1}[/tex]=2.45

n₂=5 and SS=8

We get,

S₂=[tex]\sqrt{SS/n_{2}-1 }[/tex]=[tex]\sqrt{8/5-1}[/tex]=6.54

C is 95%=0.95

d=0.05

Pooled variance is

S²p=273.13/21=13.01

Standard error= S₁-S₂= 1.82

Confidence interval is

μ₁-μ₂

4±3.7856

Therefore, Option-3 is correct. The mean difference in confidence between the two samples' 95% confidence interval falls between 4±3.7856.

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There are two pairs of triangles given. Using transformation of triangles we can say that ΔABC and ΔEFG are congruent. ΔDEF and ΔJKL are non-congruent to each other.

There are three types of transformations in triangles. They are translations, rotations and reflections.

Translation is nothing but changing the position of the figure without disturbing its shape and size. Two triangles are said to be congruent if their corresponding sides and angles are proportional.

In triangles ΔABC and ΔEFG, the sides AB and EF are proportional to each other, AC and EG are proportional to each other and BC and FG are proportional to each other. Translation is seen in ΔABC and ΔEFG.

In triangles ΔDEF and ΔJKL, neither the sides nor the angles are proportional to each other. Hence, ΔDEF and ΔJKL are not congruent to each other.

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Answer:

The answer is C

Step-by-step explanation:

-3/9 is bigger than -1 and -9/3 is smaller than -1

Answer:

89 decimeters I THINK...

Step-by-step explanation:

1 m → 10 dm

8.9 m → L(dm)

Solve the above proportion to obtain the length L in decimeters:

L(dm) = 8.9 m × 10 dm

L(dm) = 89 dm

The final result is:

8.9 m → 89 dm

Answer:

89 decimeters

Step-by-step explanation:

8.9 m × 10 = 89 dm

The Volume of the Ball Bearings is 1.76 cubic. inches

Given :

The diameter of the ball bearings = 3/2 inches

The radius of the ball bearings = 3/4 inches

Now, The Volume of the Sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

Putting the value of radius = 3/4 in the formula of the Volume,

We have :

The volume of the ball bearings =

[tex]V =\frac{4}{3} \pi (\frac{3}{4} )^{3} = \frac{4}{3} *\frac{22}{7}*\frac{3}{4} *\frac{3}{4} *\frac{3}{4}\\ \\V = 1.76[/tex]

Hence, The Volume of the Ball Bearings =  1.76 cubic. inches

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i wish you good luck

The kangaroo traveled 1.2 km in 3 minutes.

What is distance?

The distance between two points is the length of a straight line segment that links them. The distance of a point from a line is the length of the shortest line segment from the point to the line. This will also be perpendicular to the line.

Given,

kangaroo travel the distance in 5 min = 2

in 1 min, the distance covered by kangaroo = 2/5

and in 3 minutes, kangaroo will traveled = 2/5(3) = 1.2 km.

Hence, the distance covered by the Kangaroo in 3 minutes is 1.2 km.

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The slope of the line passing through (-4,5) and (-7,8) is -1.

Slope of line is the ratio of change in y-coordinate with the change in x-coordinate. It measures the steepness and direction of the line with x-axis (non vertical line.

Slope of line passing through two points (x₁,y₁) and (x₂,y₂) is given by

Slope of line = (y₂-y₁)/(x₂-x₁)

The given points are (-4,5) and (-7,8).

Here x₁ = -4, y₁ = 5

x₂ = -7, y₂ =8

Hence,

Slope of the line  = (8-5)/{-7-(-4)}

= (8-5)/(-7+4)

= 3/(-3)

= -3/3

= -1

The slope of line is given by -1.

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Answer: B

Step-by-step explanation: A is a translation, C is reflection and B is the reflection.

Hoped This Helped!

The radical expressed using the imaginary unit i  is ±(√77)*i  .

The iota(i) is an imaginary unit number that is denoted by i and the value of iota(i) is √-1  , that is √-1 = i .

In the question,

it is given that

the the radical expression is ±√-77 , we have to express it using the imaginary unit (i) .

So , ±√-77 can be written as

= ±√(-1 × 77)

= ±√-1 × √77

Substituting the value of i that is  √-1 = i ,

we get

= ± i * √77

= ±(√77)*i

Therefore ,The radical expressed using the imaginary number i  is ±(√77)*i .

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The side length x of the following triangle is √40 or 2√10 when hypotenuse is 11 and one side is 9.

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.

a² + b² = c²

where a and b are sides of right angled triangle and c is the hypotenuse.

According to the given question:

Check the attachment below for figure

Hypotenuse = 11

Length of one side = 9

Length of other side = x

By Pythagoras theorem

9² + x² = 11²

81 + x² = 121

x² = 40

x = 2√10

Therefore side length x = 2√10

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A. Her estimate is not reasonable, as she does not have enough money to buy the 3 sunglasses.

B. The change that she will receive is of $4.67.

C. Her $30 will be enough to take advantage of the deal.

The values are obtained applying the proportions, which are the prices of each product in this problem.

For item a, the cost of three sunglasses should be of:

3 x 14.72 = $44.16.

The estimate to the nearest tenth is not reasonable, as she does not have enough money to buy the sunglasses.

The cost in item b is given as follows:

9.83 + 2 x 2.75 = $15.33.

The change is given by the amount paid subtracted by the total cost, hence:

Change = 20 - 15.33 = $4.67.

The amount paid in item c is of:

3 x 9.83 = $29.49.

Which is less than $30, hence her $30 will be enough to take advantage of the deal.

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Answer:

6 cookies

Step-by-step explanation:

himself + 6 friend = 7

(17+25)/7

= 42/7

= 6

Each friende get:

6 cookies

Answer:

6 cookies each person

Step-by-step explanation:

(17+25=42)

Answer:

x=8

Step-by-step explanation:

2x+122=154-2x

4x+122=154

4x=32

X=8

hopes this helps

Yes At = 0.025 is there enough evidence to reject the claim.

Given:

A random sample of 10 buildings is selected, and the heights in feet are shown.

485 511 841 725 615 520 535 635 616 582

Mean x = 6065/10

= 606.5

H : μ ≤ 700

n = 10

s = 109.08

α = 0.25

Test stat t = x - μ / s/[tex]\sqrt{n}[/tex]

on submitting the above values

t = -2.71.

so reject h.

Therefore Yes At = 0.025 is there enough evidence to reject the claim.

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The point-slope form of the equation is y - 1 = 0

From the graph, we have the following points

(-2, 1) and (0, 1)

Start by calculating the slope of the points

This is calculated as

slope = (y₂ - y₁)/(x₂ - x₁)

This can be rewritten as

m = (y₂ - y₁)/(x₂ - x₁)

Where

slope = m

(x, y) = (-2, 1) and (0, 1)

So, we have

m = (1 - 1)/(0 + 2)

Evaluate the expression

m = 0

From the question, we understand that:

(x₁, y₁) = (-2, 1)

The equation of the line is then calculated as

y - y₁ = m(x - x₁)

Substitute the known values in the above equation, so, we have the following representation

y - 1 = 0(x + 2)

Evaluate

y - 1 = 0

Hence, the equation of the line is y - 1 = 0

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