-16t^2 +100t+2 = 0 at what time does the rocket return to the ground

Answer:

10

Step-by-step explanation:

To find the median in a set of data, organize the data from least to greatest.

Here, our data is the homework scores, those being:

10, 7, 8, 12, 9, 11, 13

Let's organize them in ascending order, like so:

7, 8, 9, 10, 11, 12, 13

The next step in finding the median is figuring out which number is in the middle. Since the amount of data we have is an odd number (7), there will be only one number in the middle.

We can find that the number in the middle is 10.

Thus, the median of the scores is 10.

The cost of the utility pole is approximately $1273.99 when rounded to the nearest cent.

To calculate the cost of the utility pole, we need to find its volume first. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the base of the cylinder and h is its height.

Here, the diameter of the utility pole is given as 1.5 ft. We need to find the radius, which is half of the diameter, so r = 0.75 ft. The height is given as 30 ft.

Using the formula, we get:

V = πr^2h = π(0.75 ft)^2(30 ft) = 53.36 ft^3

Now, we can calculate the cost of the utility pole by multiplying its volume by the cost of wood per cubic foot, which is $23.89 per cubic foot.

Cost = 53.36 ft^3 x $23.89/ft^3 ≈ $1273.99

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The domain of  the composition function fog(x) when f(x)= √6x and g(x)= 1/ (x-6) is equal to  (-∞, 6) U (6, ∞).

Function f(x) = √6x

And g(x)= 1/ (x-6

Composition function fog is ,

fog(x) = f(g(x))

Domain of fog(x),

First, find the domain of g(x),

Here,

g(x) = 1/(x-6)

The denominator of g(x) cannot be equal to zero,

So we must exclude x = 6 from the domain of g(x).

The domain of g(x) is equal to ,

domain of g(x) = {x | x ≠ 6}

The range of g(x) is,

As x approaches 6 from the left, g(x) approaches negative infinity,

And as x approaches 6 from the right, g(x) approaches positive infinity.

Range of g(x) = (-∞, 0) U (0, ∞)

Now, the domain of fog(x),

fog(x)

= f(g(x))

= √6g(x)

=√ 6 (1 /(x - 6 ) )

Square root sign must be non-negative.

Since the range of g(x) does not include zero,

Exclude the part of the range that is less than zero.

The domain of fog(x) is,

domain of fog(x)

= {x | g(x) > 0}

= {x | x < 6} U {x | x > 6}

The domain of fog(x) consists of all real numbers except x = 6.

Therefore, the domain of fog(x) is (-∞, 6) U (6, ∞).

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The above question is incomplete, the complete question is :

Given f(x)= √6x and g(x)= 1/ (x-6) Which value is in the domain of fog.

Answer:

To find the circumference of a circle with diameter 25cm, we can use the formula:

Circumference = π × Diameter

where π (pi) is a mathematical constant approximately equal to 3.14159.

Substituting the diameter of 25cm, we get:

Circumference = π × 25cm

= 3.14159 × 25cm

= 78.53975cm

Therefore, the circumference of the circle with diameter 25cm is approximately 78.54cm.

To find the circumference of a circle with diameter 2.5cm, we can again use the same formula:

Circumference = π × Diameter

Substituting the diameter of 2.5cm, we get:

Circumference = π × 2.5cm

= 3.14159 × 2.5cm

= 7.85398cm

Therefore, the circumference of the circle with diameter 2.5cm is approximately 7.85cm.

The unit price for the first bag is $2.12 per kilogram and the unit price for the second bag is $2.09 per kilogram.

To find the unit price, we need to divide the total cost by the weight of the bag.

For the first bag

Unit price = Total cost / Weight

Unit price = $15.84 / 7.48 kg

Unit price = $2.12/kg

Therefore, the unit price for the first bag is $2.12 per kilogram.

For the second bag

Unit price = Total cost / Weight

Substitute the values in the equation

Unit price = $16.58 / 7.94 kg

Unit price = $2.09/kg

Therefore, the unit price for the second bag is $2.09 per kilogram.

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The values of trigonometric-ratios in the given triangle whose legs are 4 and [tex]4\sqrt{3}[/tex] are:

a)sinθ=0.5

b)cosθ=0.866

c)tanθ=0.577

What is trigonometric-ratios ?

A right angle triangle has six trigonometric ratios: Sin, Cos, Tan, Cosec, Sec, and Cot. Sine, Cosine, Tangent, Cosecant, Secant, and Cotangent are their respective acronyms. These ratios show the ratio of various sides depending on the angle selected.

Given sides of triangle: 4 and [tex]4\sqrt{3}[/tex]

hypotenuse=[tex]\sqrt{perpendicular^{2}+base^{2} }[/tex]

                  =[tex]\sqrt{4^{2}+\((4\sqrt{3}) ^{2} }[/tex]

                  =[tex]\sqrt{16+48}[/tex]

                  =8

a)Sin θ=[tex]\frac{side opposite to the given angle}{hypotenuse}[/tex]

Sin θ=[tex]\frac{4 }{8}[/tex]

Sin θ=[tex]\frac{1}{2}[/tex]

Sin θ=0.5

b)Cos θ=[tex]\frac{side adjacent to the given angle}{hypotenuse}[/tex]

            =[tex]\frac{4\sqrt{3} }{8}[/tex]

            =[tex]\frac{\sqrt{3} }{2}[/tex]

            =[tex]\frac{1.732}{2}[/tex]

Cos θ=0.866

c)tan θ=[tex]\frac{side opposite to the given angle}{side adjacent to the given angle}[/tex]

            =[tex]\frac{4}{4\sqrt{3} }[/tex]

            =[tex]\frac{1}{\sqrt{3} }[/tex]

tan θ=0.577

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Answer:3/16

Step-by-step explanation:

√1 is the same thing as 1

so (3*1)/16

3/16

Answer: 320π or approximately 1005.31 mi

Step-by-step explanation:

The formula for the volume of a cylinder is

π r² h

we need to find the radius which is 16/2 = 8

plug in and solve

π 8² *5

π 64 *5

320π or approximately 1005.31 mi

The total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.

Let's start by finding the number of £1 coins in the bottle. We know that ſ (one-half) of the coins are £1 coins, so:

ſ × 549 = 1/2 × 549 = 274.50

Since we can't have half a coin, we know that there are either 274 or 275 £1 coins in the bottle.

Next, we know that there are 164 50p coins in the bottle.

To find the number of 20p coins, we can subtract the number of £1 and 50p coins from the total number of coins:

549 - 274 (or 275) - 164 = 111 (or 110)

So, there are either 110 or 111 20p coins in the bottle.

To calculate the total value of the coins, we can multiply the number of each type of coin by its value and then add them up:

Value of £1 coins = £1 × 274 (or 275) = £274 (or £275)

Value of 50p coins = £0.50 × 164 = £82

Value of 20p coins = £0.20 × 111 (or 110) = £22.20 (or £22)

Total value = £274 (or £275) + £82 + £22.20 (or £22) = £378.20 (or £379)

Therefore, the total value of the 549 coins in pounds (£) is £378.20 (or £379), depending on whether there are 110 or 111 20p coins.

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B. save time in arriving at solutions to problems. Heuristics are problem-solving shortcuts or rules of thumb that can save time when arriving at solutions to problems.

The use of heuristics rather than algorithms is most likely to save time in arriving at solutions to problems. Heuristics are mental shortcuts or rules of thumb that are used to solve problems quickly and efficiently, whereas algorithms are step-by-step procedures for solving problems. While algorithms may produce more accurate solutions, they can be time-consuming to apply. Heuristics, on the other hand, allow for quick problem-solving and are often based on our language skills and prior knowledge. However, relying too heavily on heuristics can sometimes lead to errors or the overconfidence phenomenon.

They might not always yield the most accurate solutions compared to algorithms, which are step-by-step, systematic procedures that guarantee a correct solution. Heuristics usually rely less on language skills and do not necessarily minimize the overconfidence phenomenon.

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Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently.

B. save time in arriving at solutions to problems . The correct answer is:

Heuristics are mental shortcuts or rules of thumb that people use to make decisions or solve problems quickly and efficiently. They are simple and often automatic strategies that allow individuals to make judgments or decisions without engaging in a lengthy, deliberate, and systematic process of problem-solving.

One of the main advantages of using heuristics is that they can save time in arriving at solutions to problems. Instead of analyzing all available information and considering all possible alternatives, heuristics allow individuals to quickly narrow down options and make decisions based on simplified cognitive processes. This can be especially useful in situations where time is limited or when individuals need to make decisions on the spot.

However, heuristics are not always foolproof and can sometimes lead to errors or biases in decision-making.

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Answer: 2 girls to 3 non-girls

Step-by-step explanation:

80 are girls

120 are boys (200-80)

80:120

simplify

2:3

There are 216 possible outcomes for each trial of rolling three standard dice.

In probability theory, an outcome is defined as the result of a single experiment or trial. The total number of outcomes in a trial can be determined by the multiplication principle, which states that if there are m ways to do one thing, and n ways to do another, then there are m x n ways to do both.

In this case, Michelle is rolling three standard dice simultaneously, which means that there are six possible outcomes for each die. Therefore, the total number of outcomes for a single trial is calculated by multiplying the number of outcomes for each die. Using the multiplication principle, we get:

Number of outcomes for each die = 6

Total number of outcomes for a single trial = 6 x 6 x 6 = 216

It is important to note that not all outcomes are equally likely, and the probability of getting a specific outcome can be calculated by dividing the number of favorable outcomes by the total number of outcomes.

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Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.

Fractions with a numerator less than the denominator are said to be proper fractions. When the numerator exceeds the denominator, the fraction is said to be inappropriate.

Given data:

fraction of crate brought by friend = 1/2

Total number of ice buckets = 6

Fraction of crate in each bucket = fraction of crate brought by friend / Total number of ice buckets

Fraction of crate in each bucket = (1/2) / 6

Fraction of crate in each bucket =  1 / (2*6)

Fraction of crate in each bucket = 1/12

Thus, the fraction of crate that will go in each of the ice bucket is found as - 1/12.

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The next four equivalent fractions of 8/13 are:

Equivalent fractions are fractions that represent the same value but have different numerator and denominator. To find equivalent fractions of 8/13, we can multiply both the numerator and the denominator by the same non-zero integer.

In this case, we multiplied the numerator and denominator by 2, 3, 4, and 5, respectively, to obtain the next four equivalent fractions: 16/26, 24/39, 32/52, and 40/65. These fractions have different numerators and denominators, but they are equivalent to 8/13 as they represent the same value or amount.

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The ounces of  beeswax needed by Leah to make 15 more small candles is equal to 49.95 ounces.

Let us consider 'x' be the ounces of beeswax required by Leah to make 15 candles.

To make 6 small candles, Leah uses 20 ounces of beeswax.

So, to make one small candle,

Ounces of beeswax used by Leah ,

= 20 ounces / 6 candles

= 3.33 ounces/candle (rounded to two decimal places)

To make 15 more small candles,

Ounces of beeswax Leah will need is equals to,

⇒ x = 15 candles x 3.33 ounces/candle

⇒ x = 49.95 ounces (rounded to two decimal places)

Therefore, Leah needs 49.95 ounces of beeswax to make 15 more small candles.

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The closest choice to the actual number of ways to choose 52 different winners out of 52 contestants is 16,497,400,

To solve this problem, we can use the formula for permutations, which is:

nPr = n! / (n - r)!

where n is the total number of objects (in this case, 52), and r is the number of objects we are choosing (in this case, the number of prizes, which is also 52).

Since no one can win more than one prize, we need to choose 52 different winners for the prizes. Therefore, the number of ways to do this is:

52P52 = 52! / (52 - 52)! = 52!

Using a calculator or computer program, we can find that 52! is approximately equal to 8.0658 × 10^67.

Therefore, the answer is 16,497,400, which is the closest choice to the actual number of ways to choose 52 different winners out of 52 contestants.

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Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

An instrument for comparing the sizes of two or more quantities in proportion to one another is called a ratio. A list of the structured equivalent ratios of every given ratio is called a ratio table. By multiplying as well as dividing the 2 terms of such a ratio by an identical number, equivalent ratios can be created.

Given data:

Area of triangle = 1/2* base * height

Ratios:

area of larger triangle / area of smaller triangle = (1/2*B*H) / (1/2*b*h)

area of larger triangle / area of smaller triangle = B*H / b*h

area of larger triangle / area of smaller triangle = 10*5 / 5*2

area of larger triangle / area of smaller triangle = 50 / 10

area of larger triangle / area of smaller triangle = 5/ 1 = 5:1

Thus, the ratio of the area of larger triangle to the area of smaller triangle

is found as 5:1.

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Complete question:

what is the ratio of the area of larger triangle to the area of smaller triangle ? express your answer as a common fraction.

Dimension of  larger triangle: base B = 10 cm, Height H = 5 cm.

Dimension of  smaller triangle : base b = 5 cm, Height H = 2 cm.

The length of arc XW is 9,60 metres

The length of arc YVU is 44.93 metres

A. M<XZW = 180 degrees - M<VZW

= 180 - 108

= 72 degrees.

XV = 180/360 x 2\pi r =

r = 7.639

XW= 72/360 x 2\pi r

= 9.60 metres.

B. M<UZY = M<XZW = 72 degrees

MYVU= 85 + 180 + 72 = 337 degrees

YVU = 337/360 x 2 pi r

=44.93 metres

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In the graph, line k with equation y = -k makes a 45° angle with the x- and y- axes. The correct option is 1. (-2, 5).

The angle formed by the line y = - x with the x-axis is 45 degrees, and the angle formed by the y-axis with the positive x-axis is 135 degrees.

The coordinates of the reflected point, when a point (p,q) is reflected over the line y=x, are (q,p)

Moreover, the coordinates of the reflected point, when point (p,q) is reflected over the line y= -x, will be (-q, -p).

Hence, the coordinates of the reflected point when point (2,5) is reflected over the line y= - x will be (-5,-2).

The point (2,5) will change to if it is reflected across the line y=x (5,2).

Therefore, the correct option is 1. (-2, 5).

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The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

A number line is a diagram that depicts numbers on a straight line. It is a tool for comparing and sorting numbers. It can represent any real number, including whole numbers and natural numbers.

Jesse currently has 520 signatures and needs at least 1000 signatures, which means he still needs to collect 1000 - 520 = 480 signatures.

He has 6 more weeks to collect the signatures he needs, so he wants to collect the same number of signatures each week. Let's call this number x, representing the number of signatures he collects each week. Then, the total number of signatures he collects in the remaining 6 weeks would be 6x.

We want to find the range of values for x that would allow Jesse to collect at least 480 signatures in the remaining 6 weeks. In other words, we want to solve the inequality:

6x ≥ 480

Dividing both sides by 6, we get:

x ≥ 80

This means that Jesse needs to collect at least 80 signatures per week in order to have enough signatures to submit the petition.

The number line that represents all of the possible number of signatures Jesse could collect in each of the remaining weeks so he can have enough signatures to submit the petition is option B.

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The statement "Both IPv4 and IPv6 provide for subnetting, but the much larger IPv6 address field makes this a lot simpler to design and manage" is correct for subnetting.

Hence, the correct option is B.

In IPv4, subnetting involves dividing a network into smaller subnetworks using the Classless Inter-Domain Routing (CIDR) protocol at Layer 3, which allows for more efficient use of IP addresses. The subnet mask determines the network and host portions of the IP address.

IPv6 also supports subnetting, but uses a different approach called prefix notation, where the network and subnet are represented by a prefix length rather than a subnet mask. Since the address field in IPv6 is much larger than IPv4, there are more available addresses and therefore it is easier to subnet.

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To estimate the sample size required for estimating the proportion of college students who are working while going to school with a desired accuracy of 4% at a 90% confidence level, we can use the following formula:

n = (Z^2 * p * (1-p)) / (E^2)

where:

n is the sample size

Z is the Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of 1.645)

p is the estimated proportion (or expected proportion) of the population

E is the desired margin of error

Given:

Desired accuracy (E): 4% or 0.04

Confidence level (Z-score): 1.645 (corresponding to 90% confidence level)

Estimated proportion (p): 0.40 (or 40%)

Plugging the values into the formula, we get:

n = (1.645^2 * 0.40 * (1-0.40)) / (0.04^2)

n = 0.1239 / 0.0016

n ≈ 77.4375

Rounding up to the nearest whole number, the estimated sample size required to achieve the desired accuracy is 78.

So, a sample size of at least 78 college students would be needed to estimate the proportion of college students who are working while going to school with a margin of error of 4% at a 90% confidence level, assuming an estimated proportion of 40%.

Answer:

Roots = (1, 0) and (-5, 0)

Vertex = (-2, -9)

Two additional points = (-4, -5) and (0, -5)

Step-by-step explanation:

The given equation y = x² + 4x - 5 is a quadratic equation with a positive leading coefficient. Therefore, the shape of the curve is a parabola that opens upwards.

The roots of a quadratic equation are the x-values that satisfy the equation y = 0. They are the points at which the curve crosses the x-axis.

To calculate the roots of the given equation, set it to zero and solve for x.

[tex]\begin{aligned}x^2+4x-5&=0\\x^2+5x-x-5&=0\\x(x+5)-1(x+5)&=0\\(x-1)(x+5)&=0\\\\\implies x-1&=0 \implies x=1\\\implies x+5&=0 \implies x=-5\end{aligned}[/tex]

Therefore, the roots of the equation are (1, 0) and (-5, 0).

The x-value of the vertex of a quadratic function in the form ax² + bx + c is -b/2a.

For the given equation y = x² + 4x - 5, a = 1 and b = 4.

To find the x-value of the vertex, substitute these values into the formula:

[tex]x_{\sf vertex}=\dfrac{-b}{2a}=\dfrac{-4}{2(1)}=-2[/tex]

To find the y-value of the vertex, substitute the x-value of the vertex into the given equation:

[tex]y_{\sf vertex}=(-2)^2+4(-2)-5=-9[/tex]

Therefore, the vertex is (-2, -9).

To find two other points on the curve, substitute two values of x into the equation.

[tex]\begin{aligned}x=-4 \implies y&=(-4)^2+4(-4)-5\\&=16-16-5\\&=0-5\\&=-5\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies y&=(0)^2+4(0)-5\\&=0+0-5\\&=0-5\\&=-5\end{aligned}[/tex]

The axis of symmetry of a quadratic equation is the vertical line that divides the parabola into two mirror images. The x-value of the vertex is the axis of symmetry. Therefore, the axis of symmetry is x = -2.

To graph the given equation:

suppose that x is a normal random variable with a mean of 5. if p{x > 9} = .2, So, the approximate variance of the normal random variable X is 22.66.

To find the variance of a normal random variable X with mean 5 and given P(X > 9) = 0.2, we will follow these steps:

1. Recognize that X follows a normal distribution: X ~ N(μ, σ²), where μ = 5 and σ² is the variance we want to find.

2. Convert the probability statement P(X > 9) = 0.2 to a standard normal distribution (Z) by finding the corresponding Z-score:
  Z = (X - μ) / σ

3. Look up the Z-score that corresponds to the given probability (0.2) in a standard normal (Z) table. Since the table typically gives P(Z < z), we'll find P(Z < z) = 1 - 0.2 = 0.8. The corresponding Z-score is approximately 0.84.

4. Plug in the known values and solve for σ:
  0.84 = (9 - 5) / σ
  σ ≈ 4 / 0.84
  σ ≈ 4.76

5. Finally, find the variance, which is σ²:
  σ² ≈ 4.76²
  σ² ≈ 22.66

So, the approximate variance of the normal random variable X is 22.66.

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The approximate variance of the normal random variable X is the square of the standard deviation:

Var(X) ≈ [tex](4.76)^2[/tex] ≈ 22.65 (rounded to two decimal places).

To approximate the variance of the normal random variable X with a mean of 5, given that P(X > 9) = 0.2, we can use the z-score and standard normal distribution.

First, we calculate the z-score using the standard normal distribution formula:

z = (X - μ) / σ

where X is the value of interest (in this case, 9), μ is the mean (5), and σ is the standard deviation.

Plugging in the values, we get:

z = (9 - 5) / σ = 4 / σ

Next, we use the standard normal distribution table or a calculator to find the z-score that corresponds to a cumulative probability of 0.2. Let's assume that z = -0.84.

Now, we can use the z-score formula to solve for the standard deviation σ:

-0.84 = 4 / σ

Cross-multiplying, we get:

-0.84σ = 4

Dividing both sides by -0.84, we get:

σ ≈ 4 / -0.84 ≈ -4.76

Since the standard deviation cannot be negative, we discard the negative value and take the absolute value, resulting in:

σ ≈ 4.76

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Answer:

6 examinations

Step-by-step explanation:

We Know

A doctor can complete 3 examinations in 2 hours.

How many examinations can the doctor complete in 4 hours?

We see

4 hours is 2 hours times 2

We take

3 x 2 = 6 examinations

So, the doctor can complete 6 exams in 4 hours.

Three distances that are equivalent to 1/2 mile are:

880 yards

1,609.34 meters

2,640 feet

Step-by-step explanation:

I know it not all but this is what I have

1. A hamburger combo meal in Poland costs approximately $1.13.

2. A hamburger combo meal in Mozambique costs approximately $5.12.

To find the dollar price of a hamburger combo meal in Poland, we need to divide the price in Polish Zlotys by the exchange rate for January:

= 5.08 Polish Zlotys / 4.5

= $1.13

To find the dollar price of a hamburger combo meal in Mozambique, we need to divide the price in Mozambique Meticals by the exchange rate for February:

= 338 Mozambique Meticals / 66.00

= $5.12

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Answer:

-5d + 5.5 < 17

-5d < 11.5

d > -2.3

A is the correct solution.