David drops a ball from the top of a building with a height of 64 feet. The height (h) of the ball, in feet, after (t) seconds can be found using the formula h = -16t^2 + 64. How long will it take the ball to reach the ground? 1 seconds 2 seconds 3 seconds none of the choices are correct

The parabola \(y = √(x - 4)\) opens upward.

The parabola y = √(x - 4) represents the square root function of x minus 4. To determine the direction in which the parabola opens, we examine the behavior of the square root function.

The square root function (√x) returns non-negative values for non-negative inputs. Since the expression inside the square root, (x - 4), must be non-negative for real solutions, we have x - 4 ≥ 0. Solving this inequality, we find x ≥ 4.

This means that the parabola is defined for x values greater than or equal to 4. As we increase x from 4, the value of √(x - 4) will also increase. Therefore, the graph of the parabola opens upward.

The parabola \(y = √(x - 4)\) opens upward.

For more such questions on parabola

https://brainly.com/question/29635857

#SPJ8

Answer:

a) The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is 10.02.

Step-by-step explanation:

The t-distribution is used to solve this question:

a) n = 14

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 14 - 1 = 13

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 13 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.9}{2} = 0.95\). So we have T = 1.7709

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.7709\frac{40}{\sqrt{14}} = 18.93\)

In which s is the standard deviation of the sample and n is the size of the sample.

The margin of error for a 90% confidence interval when n = 14 is 18.93.

b) n = 28

27 df, T = 1.7033

\(M = T\frac{s}{\sqrt{n}} = 1.7033\frac{40}{\sqrt{28}} = 12.88\)

The margin of error for a 90% confidence interval when n=28 is 12.88.

c) The margin of error for a 90% confidence interval when n = 45 is

44 df, T = 1.6802

\(M = T\frac{s}{\sqrt{n}} = 1.6802\frac{40}{\sqrt{45}} = 10.02\)

The margin of error for a 90% confidence interval when n = 45 is 10.02.

By using the graph, the employee's hourly wages is calculated as $10.6

Graph:

Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.

Given,

Here we have the graph with straight line.

And we need to determine the employee's hourly wage.

While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.

In order to find the wages for one hour, we need to select one point from the graph.

Here we have take the point  (5,53)

The first point refers the number of hours that is 5.

And the second one refers the wages for 5 hours that is 53.

So, the one hour wages is calculated as,

=> 53/5

=> 10.6

Therefore, the employee's hourly wage is $10.6.

To know more about Graph here.

https://brainly.com/question/17267403

#SPJ1

The set of rational expressions are closed under subtraction because the subtraction will result to a rational expression

The ratio of two polynomials is a rational expression.

A rational expression can be expressed in the form p/q, where p and q are polynomials,

Closure property of rational expression

According to the closure property, a - b is also a rational number for any pair of two rational numbers, a and b. The outcome is a rational number. Therefore, under subtraction, the rational numbers are closed.

In the polynomial subtraction

= P(x) /q(x) - r(x)/s(x)

= (P(x) * s(x) - r(x) * q(x)) / (q(x) * r(x))) also a rational number

Learn more about closure property of rational numbers at:

https://brainly.com/question/9353272

#SPJ1

If water flows into the container at a constant rate of 6 cubic feet per minute, the rate at which the water level rising when the height of the water is 5 feet is; 0.688 ft/min

When we are given an equation that gives the relationship between two or more variables, then by differentiating the equation with respect to time would give us a new equation that involves the rate of change of each of the given variables.

We are given the dimensions of the tank as;

Radius; r = 4 feet

Height; h = 12 feet.

The water in the tank will also have a conical shape.

By similar triangles, we know that;

r/h = 4/12

r = h/3

Now the volume of the water is;

V = ¹/₃πr²h

Put h/3 for r in this volume equation to get;

V = ¹/₃π(h/3)²h

V = (1/27)πh³

Differentiating with respect to time gives;

dV/dt = (3/27)πh²(dh/dt)

We are given;

dV/dt = 6 cubic feet per minute

h = 5

Thus;

6 = (3/27)π(5²)(dh/dt)

dh/dt = 0.688 ft/min

Read more about rate of change at; https://brainly.com/question/20245412

#SPJ1

Answer:

52500

Step-by-step explanation:

first do 5*105 to get 525 then mutiply by 100 to get 52500

Answer:

The standard error of the mean = 2

Step-by-step explanation:

Given that:

The standard deviation σ = 14

The sample size n = 49

The sample mean \(\overline x\) = 56

The formula for calculating the standard error can be expressed as:

\(S.E = \dfrac{\sigma}{\sqrt{n}}\)

\(S.E = \dfrac{14}{\sqrt{49}}\)

\(S.E = \dfrac{14}{7}\)

S.E = 2

Therefore, the standard error of the mean = 2

Answer:

2000 + 600+ 2

Step-by-step explanation:

expanded form is: way to write a number by adding the value of its digits

The value of the expression two thousand,six hundred two is given by the equation A = 2,602

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = two thousand,six hundred two

Substituting the values in the equation , we get

Two thousand = 2000

Six hundred = 600

Two = 2

So , the equation is A = 2000 + 600 + 2

On simplifying the equation , we get

A = 2,602

Therefore , the value of A is 2,602

Hence , the number is 2,602

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ2

Answer:

228

Step-by-step explanation:

absolute value is total steps away from zero. it's always positive. so the abs of a negative number is just the positive of that number.

Answer:

228

Step-by-step explain

The absolute value is the distance. ... If there is an absolute value of a negative number (l-6l), the distance of it away from zero cannot be a negative distance. So if the distance is always positive, then the absolute value will always be positive.

Answer:

$\(45\)

Step-by-step explanation:

\(30\)% \(\mathrm{of}\) $\(150\)

\(=\frac{30}{100}\times 150\\\)

\(=\) $\(45\)

Answer:

The measure of an exterior angle is found by the following formula: Aˆ0B=^AB-^CD2. An interior angle has its vertex at the intersection of two lines that intersect inside a circle. The sides of the angle lie on the intersecting lines. You can find a measure of an exterior angle of a regular polygon with  

N  sides.  It is equal to   360 o N .

Step-by-step explanation:  

Angles of a general polygon (exterior and interior) with more than 3 sides are not defined by the lengths of its sides.  

However, we can calculate the sum of all interior or exterior angles of any convex polygon. It equals to  360 o .

It can be proven geometrically since each exterior angle describes a rotation by some angle and a sum of all exterior angles describes a rotation by full angle of  

360 o . So, if all exterior angles are equal, like in a regular polygon, each one equals to  360 o N .

It can also be defined with some algebraic calculations based on the fact that a sum of all interior angles is  ( N − 2 ) ⋅ 180 o .  

Dividing the above by  N

we will obtain a value of an interior angle:  ( N − 2 ) ⋅ 180o N .  

Therefore, exterior angle of a regular polygon is  180 o − ( N − 2 ) ⋅ 180 o N = 360 o N

1. The velocity of the object is 3 m/s.

2. The object is moving in positive direction.

3. The total distance travelled is 5√10.

1. The velocity of the object is

= displacement / time

= 12/ 4

= 3 m/s

2. The object is moving in positive direction.

3. The total distance travelled

= √225+ 25

= √250

= 5√10

4. The displacement is

= 1/2 x base x height

= 1/2 x 5 x 15

= 37.5 m

Learn more about velocity here:

https://brainly.com/question/30559316

#SPJ1

A table that best represent the equation include the following: H. table H.

In order to determine the table that best represent the equation, we would have to substitute each of the values of x (x-values) into the linear function and then evaluate as follows;

When the value of x = 1 in table F, the linear function is given by;

y = x - 12

y = 1 - 12

y = -11 (False).

When the value of x = 0 in table G, the linear function is given by;

y = x - 12

y = 0 - 12

y = -12 (True).

When the value of x = 2 in table G, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (False).

When the value of x = 0 in table H, the linear function is given by;

y = x - 12

y = 2 - 12

y = -10 (True).

When the value of x = 4 in table H, the linear function is given by;

y = x - 12

y = 4 - 12

y = -8 (True).

When the value of x = 6 in table H, the linear function is given by;

y = x - 12

y = 6 - 12

y = -6 (True).

Read more on linear function here: brainly.com/question/27325295

#SPJ1

Missing information:

The question is incomplete and the complete question is shown in the attached picture.

9514 1404 393

Answer:

  -1/7

Step-by-step explanation:

To find the x-intercept, set y=0 and solve for x.

  0 = 7/4x +1/4

Multiply by 4/7

  0 = x + 1/7

Subtract 1/7

  -1/7 = x

The x-intercept is -1/7.

_____

In decimal, that is -0.142857... (6-digit repeating decimal)

Answer:

(-1,-2)

Step-by-step explanation:

Hello!

The solution to the system is at the intersection between the two graphed lines.

Remember that a coordinate is written in (x,y) format, so we take the x-value of the points and the y-value of the point.

The coordinate is (-1, -2).

The mean of a distribution is 217, while the median is 217.The statements is likely to be true about the distribution is  option  D. It is not symmetrical.

The distribution is likely to be asymmetrical if the mean and median have different values. If the mean and median of a distribution are equal, it is likely that the distribution is symmetrical, which means it has equal tail sizes on both sides. However, if the mean and median are not equal, it indicates that the distribution is skewed.

A negatively skewed distribution means that the mean is less than the median, whereas a positively skewed distribution means that the mean is greater than the median.In this case, since the mean and median of the distribution are equal, it is likely to be symmetrical. Since none of the options say "symmetrical," option D, "It is not symmetrical," is the correct answer.

Know more about  symmetrical   here:

https://brainly.com/question/31331083

#SPJ8

Answer:

x = -5 , 3

Step-by-step explanation:

(x₁ , y₁) = (-1, -2)    & (x₂, y₂) = (x , 2)

\(Distance =\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\\\\\\sqrt{(x - [-1])^{2}+(2-[-2])^{2}}=2\sqrt{5}\\\\\sqrt{(x+1)^{2}+(2+2)^{2}}=2\sqrt{5}\\\\\sqrt{(x)^{2}+2x+1+(4)^{2}}=2\sqrt{5}\\\\\sqrt{x^{2}+2x+1+4}=2\sqrt{5}\\\\\sqrt{x^{2}+2x+5}=2\sqrt{5}\)

Take square both sides,

x² + 2x + 5 = (2)²(√5)²               {(√5)² = √5*√5 = 5 }

x² + 2x +5 = 4 * 5

x² + 2x + 5 = 20

x² + 2x + 5 - 20 = 0

x² + 2x  -15 = 0

x² + 5x - 3x  - 5*3 = 0

x(x + 5) -3(x + 5)=0

(x + 5)(x - 3) = 0

x + 5 = 0     ; x - 3 = 0

x = -5        ;    x = 3

x = -5 , 3

Answer:

convert the task into ratios

(1) if $24 = 4 walks

how many $ for a walk

= (24/4) $/walk

= $6 per walk

•the first one is correct

•the second is wrong, cause it interprete $12/3 walks, which is rationalized to $3 per walk

•the third one is correct, cause it can also be rationalized ($30/5walks) to $6 per walk.

also, rationalizing this would equate to 3 miles per hour (6miles/2hrs)

• one is wrong cause it's 4 miles per hour

•two is correct, it's saying 3 miles per hour (12/4)

• third, likewise is correct 3 miles per hour (9/3) miles/hrs

Answer:

It is a function.

Step-by-step explanation:

If you use the Vertical Line Test, you can see that each x-value has its own y-value.

Answer: This curved line passes the vertical line test. Therefore, the curved line represents a function.

]

Given:

In 2010 the population was 5800.

2012 the population had dropped to 4,600.

Let 't=0' be the year 2010.

P(t) represents the year population of the town t years after 2010.

Slope of a function P(t) is

Population of town t years after 2010.

Population in the year 2016 that is t=6

Population in the year 2016 is 2200

Answer:

Step-by-step explanation:

The vertex is at (-3, -1)  and the leading coefficient is negative ( because  the curve is inverted)

y = -a(x + 3)^2 - 1

One point on the curve is (-2, -3) so

-3 = -a(-2+3)^2 - 1

-3 = -a - 1

-a = -2

So we have

y = -2(x + 3)^2 -  1

y = -2(x^2 + 6x + 9) - 1

y = -2x^2 - 12x - 19.

using SOH CAH TOA

Tan 85.144 =h/130

h=tan 85.144*130

h=1530.19 fr

Answer:

Step-by-step explanation:

a) gradient of AB

  or

  Slope of AB

  \(Slope , m = \frac{y_B - y_A}{x_B - x_A}\)

               \(=\frac{1 - 3 }{7 - 1 } \\\\=\frac{-2}{6}\\\\=-\frac{1}{3}\)

b)

when lines are perpendicular to each other, the product of their slope = - 1

That is ,

           \(m_{AB} \times m_{perpendicular} = - 1 \\\\- \frac{1}{3} \times m_{perpendicular} = - 1\\\\m_{perpendicular} = - 1 \times \frac{-3}{1} = 3\)

c) Equation of the line perpendicular to line AB and passing through ( 4 , 2 )

  \(( y - y_1) = m_{perpendicular} ( x - x_1) \ where \ (x_1 , y_ 1 ) = ( 4 , 2 ) \\\\( y - 2 ) = 3(x - 4 ) \\\\y = 3x - 12 + 2\\\\y = 3x - 10\)

Answer:

i think the fourth one is equvilent ratio

Step-by-step explanation:

Answer:

$66.03 in total.

Step-by-step explanation:

$66.03 because 6.5% is 0.065 and $62.00 times 0.065 equals $4.03. $62.00 plus $4.03 is $66.03.

Trawler B should take a course that is 18 degrees east of north.

In order to intercept Trawler A, Trawler B must travel in a direction that will bring it closer to Trawler A. Since Trawler A is traveling due west, Trawler B must travel in a direction that is east of north. The angle that is 18 degrees east of north will bring Trawler B closest to Trawler A.

Here are the steps to find the course that Trawler B should take:

Draw a diagram of the situation.

Label the two trawlers A and B.

Draw a line representing the direction that Trawler A is traveling.

Draw a line representing the direction that Trawler B should travel.

Measure the angle between the two lines.

The angle between the two lines will be 18 degrees. Therefore, Trawler B should take a course that is 18 degrees east of north.

Learn more about angle on

https://brainly.com/question/25716982

#SPJ1

The quantity of candy that Eric ate would be = 14/15

The quantity of Candy Kim had = 2⅓ pounds.

The quantity of Kims candy that Eric ate = 2/5

That is 2/5 of 2⅓.

The actual quantity of candy that Eric ate = 2/5× 7/3 = 14/15

Learn more about fraction here:

https://brainly.com/question/28699958

#SPJ1