A stone is thrown vertically upward from a platform that is 20 feet height at a rate of 160 ft/sec. Use the quadratic function h(t) = −16t^2 + 160t + 20 to find how long it will take the stone to reach its maximum height, and then find the maximum height.

The approximate probability that at most 125 transmission errors occur when transmitting 1000 bits is 0.9998.

To calculate the probability, we can use the binomial distribution formula. In this case, we want to find the probability of at most 125 transmission errors occurring out of 1000 bits transmitted. The probability of a transmission error is 10% or 0.1.

The binomial distribution formula is given by\(P(X ≤ k) = ∑(i=0 to k) [C(n,i) * p^i * (1-p)^(n-i)]\), where P(X ≤ k) is the probability of at most k successes, n is the total number of trials, p is the probability of success, and C(n,i) is the binomial coefficient.

In our case, n = 1000, p = 0.1, and we want to find P(X ≤ 125). We can calculate this using the formula:

\(P(X ≤ 125) = ∑(i=0 to 125) [C(1000,i) * (0.1)^i * (0.9)^(1000-i)]\)

Using a statistical software or calculator, we can find that the probability is approximately 0.9998.

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Answer:

x=0.8712, y=1.1818

Step-by-step explanation:

1.2x+1.4y=2.7 --(1)

0.4x-0.3y=0.9--(2)

1.2x=2.7-1.4y

x=(2.7-1.4y) / 1.2 --(3)

substitute (3) in (2)

\(0.4(2.7-1.4y) / 1.2 -0.3y=0.9\)

\((1.8 - 0.56y) \frac{1}{3} - 0.3y = 0.9\)

times both sides with 1/3

\( \frac{1}{3} (1.08 - 0.56y( \frac{1}{3} ) - 0.3y = 0.9)\)

1.08-0.3=0.56y+0.1y

0.78=0.66y

y=1.1818

substitute y in (3)

x=2.7-1.4(1.1818) /1.2

x=0.8712

Answer:

0.75

Step-by-step explanation:

Okay, let's calculate the average rate of change:

On day 3, the high temperature was 59 degrees.

On day 5, the high temperature was 53 degrees.

So the temperature change from day 3 to day 5 was 59 - 53 = 6 degrees.

And the number of days was 5 - 3 = 2 days.

So the average rate of change = (6 degrees) / (2 days) = 3 degrees per day

The closest choice is:

The high temperature changed by an average of −4 degrees per day from day 3 to day 5.

So the answer is:

5

Answer:

Below

Step-by-step explanation:

Most of these can be found by knowing that the internal angles of a triangle sum to 180 degrees.....

Answer:

m divided by three equals 3 times two m plus 1.

Step-by-step explanation:

Answer:

Answer:

= − 4 3

Step-by-step explanation:

Answer:

x+62=19

x=19-62

x=-43

I hope this help

Answer:

B

Step-by-step explanation:

Because the range are the y values

The range of the given function is {-3, 1, 5,9}. Therefore, option B is the correct answer.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively. For example, if the relation is, R = {(1, 2), (2, 2), (3, 3), (4, 3)}, then:

Domain = the set of all x-coordinates = {1, 2, 3, 4}

Range = the set of all y-coordinates = {2, 3}

The solution set of the given function is {(-1, -3), (0, 1), (1,5), (3,9)}.

Range is the set of all y-coordinates

So, the range is {-3, 1, 5, 9}

Therefore, option B is the correct answer.

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The ratio of c:d:e is 1:3:2.

To find the ratio, you can multiply the first ratio by the second ratio: 1 * 2 = 2 and 3 * 3 = 9, so the ratio becomes 2:9:6, which can be simplified to 1:3:2.

A ratio is a comparison between two values. To calculate a ratio, divide the first value by the second value. For example, if you have three apples and seven bananas, the ratio of apples to bananas would be 3/7.

You can also simplify a ratio by dividing both values by their greatest common divisor. For example, if the ratio of apples to bananas is 6/14, you could simplify it to 3/7.

It's also possible to express a ratio as a fraction, decimal, or percentage. To convert a ratio to a fraction, simply divide the two values. To convert a ratio to a decimal, divide the numerator by the denominator. To convert a ratio to a percentage, multiply the ratio by 100.

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Answer:

Quotient: 2

Remainder: 0

50 = 25 × 2 + 0

Step-by-step explanation:

Answer:0.516

Step-by-step explanation:You need to divide 29.25 by 50.25.

Answer:

$ 800

Step-by-step explanation:

number of books sold = 50

money earned = $ 890.00

profit = $ 90.00

Then the price of 50 books will be (money earned) - (profit)

= 890 - 90

= 800

So, the cost of 50 books is $ 800

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A piecewise function is a function that behaves differently in different intervals of its domain.

The piecewise function is:

Here the given information for the function is:

Then if we define x as the age of the person, the function f(x) that tells the cost of the ticket will be:

So as you can see, depending on the value of x and in which interval it belongs, the function behaves differently.

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Step-by-step explanation:

When (f + g)(x) = 0,

f(x) + g(x) = x² + 6x + 4 = 0.

Therefore (x + 3)² - 5 = 0, we have

x = sqrt5 - 3 or x = -sqrt5 - 3.

Answer:

$415.6

Step-by-step explanation:

Given data

Gross weekly pay = $440.00

Taxes/deductible

Medical insurance = $14.40

Union dues= $10.00

Total deductible= 14.4+10= $24.4

Hence the net pay

= $440-24.4

=$415.6

The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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Triangle ABC, we are given the measure of angle A as 30 degrees, the length of side AC as 10.7 cm, and the length of side BC as 6.5 cm.

To work out the value of sin(ABC), we can use the trigonometric ratio of the sine function.

The sine function relates the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle.

In the given information, we don't have a right triangle or the length of the side opposite angle ABC.

Without this information, it is not possible to calculate the value of sin(ABC) accurately.

If you have any other information regarding the triangle, such as the length of side AB or the measure of angle B or C, please provide it so that I can assist you further in calculating sin(ABC).

We may utilise the sine function's trigonometric ratio to get the value of sin(ABC).

The sine function connects the ratio of the hypotenuse length of a right triangle to the length of the side opposite an angle.

A right triangle or the length of the side opposite angle ABC are absent from the provided information.

The value of sin(ABC) cannot be reliably calculated without these information.

Please share any more information you may have about the triangle, such as the length of side AB or the size of angles B or C, so I can help you with the calculation of sin(ABC).

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The given system of equations is expressed as

y = x + 5

y = x + 1

We would apply the method of substitution. It means that

x + 5 = x + 1

x - x = 1 - 5

0 = - 4

We know that 0 is not equal to - 4. Therefore, there is no solution

The angle of 0.42 radians is swiped out by the car while revolving about the vertex at the center of the circular race track.

For the stated question;

Then,

Ф = radius / arc length

Ф = r/s

Ф = 2.9 /6.9

Ф = 0.42 radians

Thus, angle of 0.42 radians is swiped out by the car while revolving about the vertex at the center of the circular race track.

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Answer:

In this subtraction, PR5T and 47Y6 represent 4-digit numbers. What number does PR5T represent?

PR5T - 47Y6 = 1998

Answer:

Step-by-step explanation:

In a fourth-grade class, students are making cookies to learn about fractions. They are measuring using measuring cups and spoons. This learning is best described as formal standard measurement.

A standard unit of measurement is a quantifiable language that helps everyone understand the association of the object with the measurement. It is expressed in inches, feet, and pounds, in the United States, and centimeters, meters, and kilograms in the metric system.

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When the graph is decreasing, the rectangles give an underestimate and when the graph is increasing, they give an overestimate. These trends are accentuated to a greater extent by areas of the graph that are steeper.

We only need to add up the areas of all the rectangles to determine the area beneath the graph of f. It is known as a Riemann sum. The area underneath the graph of f is only roughly represented by the Riemann sum. The subinterval width x=(ba)/n decreases as the number of subintervals n increases, improving the approximation. Increased sections result in an underestimation while decreasing sections result in an overestimation. We now arrive at the middle rule. The height of the rectangle is equal to the height of its right edges for a right Riemann sum and its left edges for a left Riemann sum. The rectangle height is the height of the top edge's midpoint according to the midpoint rule, a third form of the Riemann sum.

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Answer:

$12.31

Step-by-step explanation:

11.62 divided by 2 =0.69

$11.62+$0.69=12.31

Answer:

b

Step-by-step explanation:

. The y intercept is pretty easy, thats just where the line crosees the y axis, or where x is 0

.The slope is just the rise over run, so the rise would be how much you go up, or y2-y1. As for the run, that is how much you go across, or "run" across the grid, that is calculated by doing x2-x1

Slope Formula: y2-y1/x2-x1

Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

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Answer:

It's either 4000pi/3 or 4188.79020478

Step-by-step explanation:

Hope this helped

Since 50 is an even number, we know that x will be even if y is even (50 times an even number is still even) and odd if y is odd (50 times an odd number is odd). Therefore, the only answer choice that must be odd is x+y.

Given that x and y are integers and x = 50y + 69, let's determine which of the following expressions must be odd.

1. xy: Since x is odd (50y + 69), when it is multiplied by any integer y, the result will always be odd. Therefore, xy must be odd.

2. x + y: If x is odd, adding it to an even integer (y) would result in an odd number. However, adding it to an odd integer (y) would result in an even number. Therefore, x + y does not necessarily have to be odd. xy: We can't determine if this is odd or even without knowing the values of x and y.
- x+y: This expression is always odd. To see why, consider two cases:

If x and y are both odd, then x+y is even+odd=odd.
If x and y are both even, then x+y is even+even=even.
If one of x and y is odd and the other is even, then x + y is odd + even =odd.

3. x+2y: We can't determine if this is odd or even without knowing the values of x and y.
3x-1: This expression will be odd if x is odd (3 times an odd number is odd) and even if x is even (3 times an even number is even).
3x+1: This expression will be odd if x is even (3 times an even number plus 1 is odd) and even if x is odd (3 times an odd number plus 1 is even).
x + 2y: Since x is odd and 2y is always even, their sum must be odd. Therefore, x + 2 y must be odd.

4. 3x - 1: This expression is odd, since 3x will always be odd (as x is odd) and subtracting 1 from an odd number results in an even number. Therefore, 3x - 1 does not necessarily have to be odd.

5. 3x + 1: This expression is odd, since 3x will always be odd (as x is odd) and adding 1 to an odd number results in an even number. Therefore, 3x + 1 must be odd.

In conclusion, the expressions that must be odd are xy, x + 2y, and 3x + 1.

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Answer:

10.5 %

Step-by-step explanation:

Here .

let the Cost Price be 'x'

the..

by the question..

the marked price was fixed to make 30% profit

then..

the marked price will be

x+ 30% of x

= x + 30/100 × x

=x+ 0.3x

=1.3x

soo .. the marked price is 1.3x

now.. after allowing 15% discount..

the selling price will be

1.3x - 15% of 1.3x

= 1.3x - 0.195x

= 1.105x

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now..

profit made = 1.105x-x

= 0.105x

soo .

in percentage..

profit percent = profit/cp × 100%

= 0.105x/x × 100%

= 10.5 %

(a) The proportion of corporations for which the rate of return was higher than 16%, we need to calculate the area under the normal distribution curve to the right of 16%.

(b) The proportion of corporations for which the rate of return was negative, we need to calculate the area under the normal distribution curve to the left of 0%.

(c) The proportion of corporations for which the rate of return was between 5% and 15%, we need to calculate the area under the normal distribution curve between these two values.

(a) The proportion of corporations for which the rate of return was higher than 16%, we can use the cumulative probability function of the normal distribution. By calculating 1 minus the cumulative probability up to 16%, we obtain the proportion of corporations with a rate of return higher than 16%.

(b) The proportion of corporations for which the rate of return was negative, we again use the cumulative probability function. Since the mean rate of return is 10.4%, we need to calculate the cumulative probability up to 0% to find the proportion of corporations with a negative rate of return.

(c) The proportion of corporations for which the rate of return was between 5% and 15%, we calculate the cumulative probability up to 15% and subtract the cumulative probability up to 5%. This gives us the proportion of corporations with a rate of return within this range.

To perform these calculations, we can use a statistical software or a standard normal distribution table. By plugging in the appropriate values into the cumulative probability function or referring to the table, we can determine the proportions of corporations for each scenario.

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