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.)

a) The binomial distribution is suitable to use when:

b) The probabilities are given as follows:

The mass probability formula, giving the probability of x successes, is of:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are given by:

The binomial distribution is used when there is a fixed number n of trials, with each trial having only two possible outcomes, success or failure, and trials are independent, that is, the probability of success on any trial is the same.

For item b, the parameter p is obtained as follows:

The sum of all the probabilities is of one, hence:

5 x 0.5p + p = 1

3.5p = 1.

p = 1/3.5

p = 0.2857.

For item i, the probability is obtained as follows:

Hence:

p = (1 - 0.2857)^5 x 0.2857 = 0.0531 = 5.31%.

For item ii, the probability is P(X = 3) when n = 8, hence:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{8,3}.(0.2857)^{3}.(0.7143))^{5} = 0.2428[/tex]

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The total number of days for which the food supply will last is 37 days.

Given,

The number of days that the food supply would last is = ?

The number of pounds of grain = 10656 pounds

The number of cattle is = 24 cattle

The number of pounds eaten by each cow each day = 12 pounds.

Therefore if one cow eat 12 pounds a day then 24 cows=

12 × 24 = 288 pounds a day

Therefore if,

288 pounds = 1 day

10656 pounds = 10656/288

= 37 days

Therefore, the number of days that the food supply would last is  37 days.

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Answer:

12 ÷ 3 = 24 ÷ 6

Step-by-step explanation:

12/3 = 4 and 24/6 = 4

So 4 = 4

The smallest possible number Hannah could be thinking of will be 351.

And, the largest possible number Hannah could be thinking of will be 355.

Rounding numbers refers to changing a number's digits such that it approximates a value. The provided number is more simply represented by this value. For instance, 700,000 rather than 698,869 could be used to express a town's population.

Given that;

Hannah thinks of a whole number.

Rounded to the nearest 10, her number is 350.

And, Rounded to 1 significant figure, her number is 300.

Now,

Since, Hannah thinks of a whole number.

Rounded to the nearest 10, her number is 350.

And, Rounded to 1 significant figure, her number is 300.

Hence, We get;

The smallest possible number Hannah could be thinking of = 351.

And, The largest possible number Hannah could be thinking of = 355.

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The amount that the cell phone owner will pay for the overages is $14.91.

The overage is the difference between the actual usage in minutes and the estimated usage.

For instance, if the plan estimates that the phone usage per year would be 4,000 minutes, but the plan holder uses 4,010 minutes, the extra 10 minutes are regarded as overages.

The opposite of overages is underages.  If underages are part of the phone plan, the plan holder will be refunded accordingly.

Usually, overages attract a variable plan rate per minute.

Fixed charge per month = $35.98

Utilities tax APR = 6.5%

Overages = 40 minutes

Rate per overage minute = $0.35

The total charge for overage = $14 ($0.35 x 40)

Interest on the overages = $0.91 ($14 x 6.5%)

Total payment for the overages = $14.91 ($14 + $0.91)

Thus, for going over the plan by 40 minutes at $0.35 plus an APR of 6.5%, you will pay $14.91 for the overages.

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The length of the garden is 63ft, in the rectangle

What is a rectangle?

Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral,

Quadrilaterals are typically four-sided closed shapes, and there are numerous varieties of them. Square, rectangle, rhombus, kite, and trapezoid are the most typical shapes. Four closed sides make up a quadrilateral. Quadrilaterals are the following figures: a four-sided figure. The form features a single set of parallel sides and no right angles.

The given perimeter is 210ft

let l be the length and 2/3 of l is the breadth.

We know that 2(a+b) = 210

2(l + 2/3l) = 210

5/3 l = 105

l = 105* 3/5 = 63ft

Hence the length of the garden is 63ft.

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The values of the vertical motion modelled by the quadratic function, h(t) = -16·t² + 54·t + 3 of the object are;

The maximum height reached is approximately 48.6 units

The time of flight is approximately 3.4 seconds

A quadratic function is a polynomial of the form y = a·x² + b·x + c, where the value of a is larger than or lesser than 0

First part;

The function, for the vertical motion, h(t) = -16·t² + 54·t + 3, is a quadratic function;

The maximum height is found by using the equation that gives the value of x at the maximum value, which is presented as follows;

At the maximum point, [tex]x = \dfrac{-b}{2\cdot a}[/tex]

From the equation, a = -16, b = 54, c = 3, and x = t, which gives;

[tex]t = \dfrac{-54}{2\times (-16)} = 1.6875[/tex]

The maximum height is therefore;

h(1.6875) = -16 × 1.6875² + 54 × 1.6875 + 3 = 48.6

The time the object is in the air is found using the equation;

h(t) = 0 = -16·t² + 54·t + 3

Using the quadratic formula, [tex]x= \dfrac{-b\pm \sqrt{b^2 - 4\cdot a \cdot c} }{2 \cdot a}[/tex], we have;

[tex]t= \dfrac{-54\pm \sqrt{54^2 - 4\times (-16)\times 3} }{2 \times (-16)}=\dfrac{27\pm \sqrt{777} }{16}[/tex]

The time of flight is therefore;

[tex]t=\dfrac{27+ \sqrt{777} }{16}\approx 3.4[/tex]

The time of flight is 3.4 seconds

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The domain of given graph is [-8,8].

The domain of a function is a set of all x values i.e. the numbers for which function is defined. All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range. When viewing a graph, the whole range of numbers from left to right comprise the domain.

As seen from the graph graph is limited from -8 to +8 that means the domain of the graph is [-8,8].

Or it can be written as [tex]-8\leq x \leq 8[/tex]

Therefore, the domain of the function is [-8,8].

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Answer:The answer is 4

Step-by-step explanation:BEcause of the mail´s mystery number

Example:

120 and 45

10 and 12 can go into 120. 10 can go into 5 and 2, while 12 can go into 3 and 4. 4 can be still divisible, so it would be 2 and 2.

45 is 9x5. 9 can be divisible, so you would turn them into 3 and 3.

The LCM will be the product of the largest multiple of each prime that appears on at least one list. For example, we have a 2, 3, and 5, so I’ll choose the largest multiples of each and find their product. There are three 2's, three 3's, and 5, or 8 x 9 x 5. That would get you 360.

See how you could get that with your problem?

P.S. I don't answer questions directly, instead, I use examples. Feel free to use other suggestions if this one doesn't appeal to you.

Answer:

Step-by-step explanation: use your brain  please you will get it ahhh

The highest amount that can be charged to your credit account is called credit limit and is therefore denoted as option A.

This is referred to as a type of banking arrangement which involves a customer receiving goods from a store and paying for them over a period of time.

The credit card which is linked to the account is used for such type of transactions and the highest amount that can be charged to it is known as credit limit which is therefore the reason why option A was chosen as the correct choice.

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Answer:

I think its false

Step-by-step explanation:

Answer: True i think

Step-by-step explanation: If Nancy is two years older than Mark who is 13, then Nancy would be 15, 15 + 13 equals 28.

Answer:

The width of the rectangle should be 8 units.

Calculation of the width:

Since The width of a rectangle is 1 units less than the length. The area of the rectangle is 72 units.

Here we know that

Area = (length) (width)

Here we assume length be x

So, width be = x - 1

So,

(x) (x - 1) = 72

(x + 8) (x - 9)

So, the width should be

= 9 - 1

= 8

hence,

Answer: no.

Step-by-step explanation: no.

Proof:

L.H.S. = A - (B - C)

= A - (B ∩ C'), since A - B = A ∩ B'

= A ∩ (B ∩ C')'

= A ∩ {B' U (C')'}, since (A ∩ B)' = A' U B'

= A ∩ (B' U C)

= (A ∩ B') U (A ∩ C)

= (A - B) U (A ∩ C) = R.H.S.

∴ A - (B - C) = (A - B) U (A ∩ C)

Hence, This completely the proof.

Some properties of set algebra:

1. A U Φ = A, A ∩ Φ = Φ

2. A U U = U, A ∩ U = A

3. A U A = A, A ∩ A = A

4. A U (B U C) = (A U B) U C

5. A ∩ (B ∩ C) = (A ∩ B) ∩ C

6. A U (B ∩ C) = (A U B) ∩ (A U C)

7. A ∩ (B U C) = (A ∩ B) U (A ∩ C)

8. A U A' = U

9. A ∩ A' = Φ

10. (A U B)' = A' ∩ B'

11. (A ∩ B)' = A' U B'

12. A - B = A ∩ B'

13. A - (B ∩ C) = (A - B) U (A - C)

14. A - (B U C) = (A - B) ∩ (A - C)

15. A Δ B = (A - B) U (B - A)

16. A Δ B = B Δ A

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Answer:

1  1/2 gallons

Step-by-step explanation:

there are two pints in one quart so 2 quarts plus 8 pints equals

2 quarts plus 4 quarts, or 6 quarts

there are 4 quarts in one gallon so 6 quarts is the same as 1 gallon and 2 quarts

2 quarts is half of one gallon

Mina uses 17/18 inches of chalk.

What is algebra?

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions. In algebra, we utilize integers with fixed or definite values, such as 2, 7, 0.068, etc. In algebra, we combine integers with variables like x, y, and z.

Here, we have

she used 1/3 of a piece of chalk that was originally 2 5/6 inches long.

Now, we have to find how many inches of chalk did she use?

= 1/3 × 2 5/6

= 1/3 × 17/6

= 17/18 inches.

Hence, Mina uses 17/18 inches of chalk.

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Answer:

17/18

Step-by-step explanation:

The probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June is 0.266.

We are given information about the temperatures in Los Angeles for the month of June. The average daily high temperature in June in LA is 80°F. The standard deviation in the temperature values is 8°F. The temperatures in June closely followed a normal distribution. We need to find the probability of observing an 85°F temperature or higher in Los Angeles during a randomly chosen day in June. Let the mean, standard deviation, value, z-score, and probability be represented by the variables M, S, X, Z, and P. First of all, we will find the z-score for the given temperature value.

Z = (X - M)/S = (85 - 80)/8 = 5/8 = 0.625

We want to find the probability for Z-values greater than or equal to the calculated z-score. We need to use the z-score table to find the corresponding probability.

P(z ≥ 0.625) = 0.26599

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Step-by-step explanation:

1 have to make number cross the top number n sce

You apply the rule for a pair of parallel angles cut by a line. So that means that 59 degrees equals 2x-15.

59=2x-15

59+15 = 2x

74=2x

x= 37

Answer:9

Step-by-step explanation:um

The given triangle  ∆QRT is isosceles triangle.

What is isosceles triangle?

  Triangles with two equal sides are referred to as isosceles triangles. Also equal are the two angles that face the two equal sides. To put it another way, "An isosceles triangle is a triangle with two congruent sides." Assume that the sides AB and AC of the triangle ABC are equal, in which case the triangle ABC is an isosceles triangle with B = C. According to the theorem, "if the two sides of a triangle are congruent, then the angle opposite to them is also congruent."

Here the given points are Q(-2,-1) , R(1,5) , T(-8,-4).

Using distance formula

Now , The Distance between the points can be measure as :

D=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

QR = [tex]\sqrt{(1+2)^2+(5+1)^2}[/tex]

=>QR=[tex]\sqrt{3^2+6^2} = \sqrt{9+36} =\sqrt{45}=3\sqrt{5[/tex] unit

Now RT = [tex]\sqrt{(-8-1)^2+(-4-5)^2} =\sqrt{9^2+9^2} \\[/tex]

=>RT=[tex]\sqrt{81+81}=\sqrt{162} = 9\sqrt{2}[/tex] unit

Now TQ  = [tex]\sqrt{(-2+8)^2+(-1+4)^2} =\sqrt{6^2+3^2} \\[/tex]

=>TQ=[tex]\sqrt{36+9}=\sqrt{45}=3\sqrt{5}[/tex] unit.

Here QR=TQ then

Hence the given triangle is isosceles triangle.

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The larger angle in the straight line is 101°.

What is straight line angle?

   A straight angle in mathematics is one with a sine angle of 180 degrees. Due to the fact that it resembles a straight line, it is called straight. Those angles that make a straight line are known as straight angle pairs. Each angle in this pair adds up to 180 degrees, regardless of how many angles make up the pair. A straight angle in geometry is one that is equal to 180 degrees. It looks like a straight line, hence the name "straight angle." It is an angle, then, whose sides are in the same straight line but opposite to the vertex.

We know that , In straight line angle at any point is 180°.

Here,

=> (14x+3)°+(11x+2)°=180°

=>14x+3+11x+2=180

=>25x+5=150

=>25x=180-5=175

=> x = 175/25 = 7.

Then , 14(7)+3=101° and 11(7)+2=79°.

Hence the larger angle is 101°.

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Answer:

Step-by-step explanation:

5x+30-35

5x-5

Answer:

[tex]5x[/tex] - [tex]5[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

√(16) - √(-2) + √(16) + √(-200) =

8 + 12.7279221 i

The distance between the points M=(-4, 9 ) and L=(-1. 1) in the coordinate plane is [tex]\sqrt{73}[/tex].

Explain Coordinate Plane.

In a plane, a Cartesian coordinate system is a system of a coordinate that designates each point uniquely by a pair of numerical coordinate in a plane, which are the signed distances from two fixed perpendicular oriented lines to the point on the same plane, measured in the same unit of length.

Solution Explained:

Using the distance formula, we have

[tex]\sqrt{(x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }[/tex]

Substituting the values using the values of the points

[tex]\sqrt{(-1 + 4) ^{2} + (1 - 9) ^{2} }[/tex]

[tex]\sqrt{(3) ^{2} + (-8) ^{2} }[/tex]

[tex]\sqrt{9 + 64}[/tex]

[tex]\sqrt{73}[/tex]

Hence, the distance between the two points is [tex]\sqrt{73}[/tex]

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The salary is $55100 when [tex]a_n=55100[/tex].

[tex]55100=41900+1100n\\\\13200=1100n\\\\12=n[/tex]

So, her salary will be $55,100 after 12 years.

The salary is $55100  after 12 years.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given that construction worker's starting salary is $43,000. Each year she receives a $1100 raise.

Therefore, an = 41,900 + 1100n

An explicit formula of the form an = bn + c to model this situation.

When n = 10,

= 41,900 + 1100n

= 41,900 + 1100(10)

= 41,900 + 11000

= 52,900

when an  = 55,100

Then an = 41,900 + 1100n

55,100 = 41,900 + 1100n

1100n = 55,100 - 41,900

1100n = 13200

n = 13200/ 1100

n = 12

So, her salary will be $55,100 after 12 years.

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Answer:

Step-by-step explanation:

216÷3=72

72 is your answer