A NASA test rocket is launched from the top of a 101 foot cliff with an initial
velocity of 116 feet per second. The function h(t) = -16t2 +116t + 101 gives the
height, h(t), in feet of the rocket t seconds after it's launched.
How long does it take for the rocket to reach the ground?
​

The value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.

The equation 2x2 + 2x - 1 = 0 can be written in the form ax2 + bx + c = 0, where a = 2, b = 2 and c = -1. The formula for calculating b2 - 4ac for this equation is

[tex]b2 - 4ac = (b2) - (4)(a)(c)= (2)2 - (4)(2)(-1)= 4 - (-8)= 12[/tex]

Therefore, the value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.

To calculate this value, the formula first finds the value of b2, which is the square of the coefficient of the x-term (2). Then it multiplies the coefficient of the x2-term (2) by the constant term (-1), and multiplies the result by 4. Finally, it subtracts the result of this multiplication from the value of b2.

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Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

The collection of all potential inputs for a function is its domain.

For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.

The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.

A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.

So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.

A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.

Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.

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Tommy and Zach will be 16 miles apart after 2.90 hours.

Let the time taken for Tommy and Zach to run until they are 16 miles apart be t hours.

Tommy runs North at a speed of 5 miles per hour.

Therefore, the distance covered by Tommy in t hours is 5 multiplied by t hours:

=5t miles

Zach runs East at a speed of 8 miles per hour.

Zach started running 2 hours later so that he would run for (t - 2) hours.

Distance covered by Zach in (t - 2) hours running at a speed of 8 miles per hour :

=8(t - 2) miles

Since they are now 16 miles apart, Pythagoras's theorem, a²+ b² = c², is applied.

[8(t - 2)]²+ (5t)² = 16²

64(t - 2)² + 25t² = 256

64(t² + 4 - 4t) + 25t² = 256

64t² + 256 - 256t + 25t² = 256

89t² -256t + 256 - 256 = 0

89t² - 256t = 0

t( 89t - 256) = 0

(89t - 256) = 0

9t = 256

= 256÷9

t = 2.90 hours

Therefore, for 2.90 hours, Zach and Tommy will be 16 miles apart.

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The table showing trading account is given below

he trading account gives details of total sales, total purchases and direct expenses relating to purchase and sales. Trading account format for the year contains Particulars, Amount, Dr., Cr., Purchases, Sales, etc.

Given here,

Particulars                         Amount

Cash purchases               Rs.4,50,000

Credit purchases              Rs.27,00,000

Returns inwards                Rs.60,000

Cash sales                         Rs.4,80,000

credit sales                        Rs.33,00,000

Returns outward               Rs.30,000

freight inwards                 Rs.9000

carriage inwards              Rs.9000

Wages and salaries         Rs.12000

Opening stock                Rs. 4,50,000

closing stock                  Rs. 2,64,000

Market value                     Rs.2,52,000​

Hence the trading account for the year ended 31st March, 2013 is given above

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Answer:

Calculate: 48.78/0.9 = 54.2

Write a situation: Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice.

What does the quotient mean: The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.

y = 3/x equation is an example of inverse variation between the variables x and y .

Now, According to the question:

The equation with the inverse variation between the variables 'x' and 'y' .

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.

y = 3/x is an example of inverse variation.

Hence, y = 3/x equation is an example of inverse variation between the variables x and y .

Let's know:

What is an Inverse variation equation?

Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.

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Using the linear function y = -5/3x + 3000, the boulder will touch the ground at 1800m

A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

A model of a linear function is given as y = mx + c

where m is the slope or rate of change of the function and c is the constant value or y - intercept

In this function;

The slope is - 5/3 and the constant is 3000

The linear function can be written as

y = -5/3x + 3000

The height at which the boulder will strike the ground, the value of y = 0

0 = -5/3x + 3000

5/3x = 3000

x = 1800

The point is at 1800m

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By using the the application of ASA we can determine the two angles are congruent by AAS.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

AAS congruence can be proved in easy steps.

Suppose we have two triangles ABC and DEF, where,

Diagram attaches at the end of the solution.

∠B = ∠E [Corresponding angles]

∠C = ∠F [Corresponding angles]

AC = DF [Adjacent sides]

By angle sum property of triangle, we know that;

∠A + ∠B + ∠C = 180 ………(1)

∠D + ∠E + ∠F = 180 ……….(2)

From equation 1 and 2 we can say;

∠A + ∠B + ∠C = ∠D + ∠E + ∠F

∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D

Hence, in triangle ABC and DEF,

∠A = ∠D

AC = DF

∠C = ∠F

Hence, by ASA congruency, (AAS: the application of ASA)

Δ ABC ≅ Δ DEF

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Answer:

f(x) and G(x)

Step-by-step explanation:

When you want to write a function of something, you can write it as the letter followed by "(x)"

The graph of y=3x-1 will be a straight line that does not passes through origin.

A line is a geometry object that extends on both sides and is defined by zero width. Simply put, a straight line is a line devoid of bends. A straight line is one that has no curves and continues to infinity on both sides.

ax+by=c is the standard form of straight line.

A straight line serves as the visual representation of a linear function's graph.

The given function is as follows:

y=3x-1

A linear function looks like this:

y=mx+c

Where:

m=3:  the slope

c=-1: the y-intercept

So given function has a different y-intercept than 0.

So, the resulting graph o does not cross through the origin.

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The z-scores are (-1.85, 1.85)

An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.

If a Z-score is 0, it indicates that the data point's score is identical to the mean score

Given:

If we look at the z score table we will get the value of z- score.

The value 0.0322 lies in horizontal row 1.8 and column 0.05.

Then, for left value 0.0322 is -1.85

and, for right value 0.0322 is 1.85.

Hence, the z-scores are (-1.85, 1.85)

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Answer:

4.9 miles

Step-by-step explanation:

(.01)(490)=4.9

Y- intercept for the line y = 5x is 0. This can be get from the standard equation for a line.

For the The standard equation for a line is,

     y = ax + b

y is called the dependent variable because its value depends on the value of x

a is the slope of the line

x is called the independent variable because it can be any value

b is the y-intercept

Here y is a function of x. You could simply write it as y = 5x.  Thus if we compare to the standard form equation y = ax + b, a=5 and b=0.  Thus the y-intercept is zero.  The reason that this is the case is that when you set x=0 the value is plotted on the y axis because the equation for the y axis is the line defined by x=0.  Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.

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Answer:

31

Step-by-step explanation:

What is the median of 35 27 51 31 28 19 33?

Median: center most value when values are arranged in numerical order so:

19 , 27 , 28 , 31 , 33 , 35 , 51

we will find the length of rectangle when area is divided by the breadth of rectangle.

Some properties are rectangle are stated below:

1. rectangle has four right angles

2. rectangles has four sides and equal opposite sides which are parallel to each other.

3.rectangle has two diagonals which are similar in length.

The bigger side lengths are called length and the smaller sides are called breadth of rectangle.

if area of rectangle is given, we can find length when area is divided by its breadth.

 length = area/breadth

hence, length of rectangle is determined from the value of area and breadth.

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The mean number who have immunity in samples of size 17  is 13.6

Sample Size =17

Immunity to a Particular disease=0.8

=17*0.8

=13.6

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Answer:

43.1

Step-by-step explanation:

2.5 % = .025    look for this value on the z-score table to find this corresponds to z = - 1.96   Standard Deviations

72.5      - 1.96 * 15    = 43.1  

(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.

f(x) is equal to (n pick x) * p * x * (1-p) (n-x)

Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).

(b) The formula for the anticipated value of X, or E[X], is

E[X] = np = 20 * (1/5) = 4

Var X, the variance of X, is defined as follows:

Var X = np(1-p) = 20*1/5*4/5=3.2

(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:

Sum(i=3 to n) f for P[X >= 3] (i)

Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:

Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]

(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.

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Therefore , the solution to this problem is yes 8 has multiple which are 16,24,32 etc.

A multiple in mathematics refers to the product produced by multiplying two numbers or variable. In this instance, the number 7 is multiple by 56.

The expression is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.

Here,

There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.

There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.

The results of multiplying any integer by other natural numbers are known as multiples.

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The average change in the volume of water per day is obtained as 0.625  litres.

The rate change of volume is the change of volume with respect to time.

For instantaneous change the derivative of the expression of volume can be taken.

The average change in the volume of water can be obtained as follows,

Average change = Volume of water ÷ Number of days

                            = 2.5 ÷ 4 = 0.625

Hence, the average change in water volume is given as  0.625 liters per day.

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Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent

The classification which best describes the system of equations is; Consistent and dependent

A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.

Additionally, the system of equations is dependent because the value of each variable is dependent on the others.

Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.

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The equation that represents a proportional relationship is y/X = 2.5. That is option D.

A proportional relationship is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.

The relationship between these two variables can either be directly proportional or indirectly proportional.

The relationship that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.

y = 2.5 X

= y/X = 2.5. Where 2.5 is the constant.

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Answer:

145

Step-by-step explanation:

Cuánto es means what is the answer

35 - (-110)

Two negative signs equal a positive sign

35 + 110 = 145

Answer:

it means multiply like the × symbol

Step-by-step explanation:

The value of angle x is 70° and angle y is 60° in the given figure with exterior angle = 120°

From the given figure, we know that the Exterior angle = 120°

To find the values of x and y we will follow the following steps.

We know that the sum of interior opposite angles is equal to the exterior angle of the triangle.

The exterior angle of the triangle=120°

The interior angles are x and 50°

50° + x = 120°

x = 120°- 50°

x = 70°

Also, we know that the sum of the y and the exterior angle is 180° because they are forming a linear pair.

Hence we have,

y + 120° = 180°

y = 180° - 120°

y = 60°

Therefore, the value of angle x is 70° and angle y is 60°.

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A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.

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Yes, a 4 year old can typically count to 100.

Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.

Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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A function is continuous if it is defined for all values of the independent variable and there are no breaks, jumps, or gaps in its graph. In other words, a function is continuous if you can draw its graph without lifting your pen from the paper.

To check whether a function is continuous at a particular point, you can use the following methods:

The two-part definition of continuity: A function is continuous at a point if the following two conditions are met:

The limit of the function as it approaches the point from the left and the right exists and is equal to the function's value at that point.

The function is defined at the point.

The Epsilon-Delta definition of continuity: A function is continuous at a point if, for every epsilon (a small positive number) there exists a delta (also a small positive number) such that, for all points x within delta units of the point in question, the function's value at x is within epsilon units of the function's value at the point.

The graph of the function: You can also check the continuity of a function by looking at its graph. If the graph is a continuous curve with no breaks or jumps, then the function is continuous. If the graph has breaks or jumps, then the function is discontinuous.

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The Epsilon-Delta definition of continuity states that a function is continuous at a point if there is an epsilon (a small positive number) and a delta (also a small positive number) such that the value of the function at x is within epsilon units of the value of the function at the point for all points x within delta units of the point in question.

The function's graph: Additionally, you can examine a function's graph to see whether it is continuous. The function is continuous if the graph displays a continuous curve without any interruptions or leaps. The function is discontinuous if the graph has breaks or jumps.

The total cost for Bob's ride is C = x + m and no. of minutes of the ride is

m = C - x.

A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.

Given,  A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.

Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.

Therefore, The total bill(C) for Bob's ride is,

C = x + m.

The no. of minutes Bob ride the scooter is simply,

m = C - x.

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To simplify this expression, we can start by simplifying the square roots:

2√12 + 3√48 - 75

= 2√(12) + 3√(48) - 75

= 2√(43) + 3√(412) - 75

= 2√4 * √3 + 3√4 * √12 - 75

= 2 * √3 + 3 * √12 - 75

We can then combine like terms:

= 2 * √3 + 3 * √12 - 75

= (2 * √3 + 3 * √12) - 75

= 5 * √12 - 75

Finally, we can simplify the expression to get our final answer:

= 5 * √12 - 75

= 5 * 2√3 - 75

= 10√3 - 75

= -75 + 10√3

= -75 + 10√3

So the simplified expression is -75 + 10√3.

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