Mr. Jensen throws an eraser at a sleeping student. The equation that models the flight of the eraser is: h(t)=-16t^(2)+35t+6 The student hos his head laying on the desk about 3 feet off the ground. How long does it take for the eraser to hit the student in the head?

With speed = 10 m/s, the rope will hit ground after 3.36 seconds.

Speed is a measure of how fast an object is moving, usually measured in units of distance per unit time, such as meters per second (m/s) or kilometers per hour (km/h). It is a scalar quantity, meaning it only has magnitude and no direction.

Mathematically, speed is defined as the distance an object travels per unit time. The formula for calculating speed is:

Speed = Distance / Time

where Distance is the distance traveled by the object, and Time is the time taken to cover that distance.

Now,

To find when the rope will hit the ground, we can use the kinematic equation:

y = vi * t + (1/2) * a * t²

where:

y = 50 m (the height of the cliff)

vi = 10 m/s (the initial velocity of the rope)

a = 9.8 m/s² (the acceleration due to gravity, acting downward)

t = time it takes for the rope to hit the ground

We can solve for t by setting y=50 and solving for t:

50 = 10t + (1/2) * 9.8 * t²

50 = t(10 + 4.9t)

t = 50/14.9=3.36 s

Therefore, the rope will hit the ground after 3.36 seconds.

To know more about speed visit the link

https://brainly.com/question/7359669

#SPJ1

The experimental probability of spinning a number less than 3 is given as follows:

0.38.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The outcomes for this problem are given as follows:

Hence the experimental probability of spinning a number less than 3 is given as follows:

p = 38/100

p = 0.38.

The bars are given as follows:

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

The antenna's height is 12.1 meters, as stated throughout the announcement.

Building type refers to a grouping of buildings according to their purpose, location, and style that serves as the standard for evaluating and categorizing variants. Buildings must be categorized as either support, civic, commercial, industrial, or residential. Any kind of fella construction is a structural. It could be anything: a dam or a bridge, for instance. In contrast, a building is a closed construction with walls and a roof. Once more, the more precise phrase is "building," although "structure" is far more generic.

Based on the graph.

[tex]$$\begin{aligned}& \overline{O H}=\overline{C D}=1.51 \mathrm{~mm} . \\& \overline{O C}=24 \mathrm{~m} . \\& \angle O C A=20^{\circ} . \quad \angle O C B=41^{\circ} .\end{aligned}$$[/tex]

In RT [tex]$\triangle A O C_,$[/tex]

[tex]$$\begin{aligned}& \tan 20^{\circ}=\frac{A_0}{O C}=\frac{A_0}{24} \\& \text { So } A_0=\tan 20^{\circ} \times 24=8.74 \mathrm{~m}\end{aligned}$$[/tex]

In Rt ΔOBC.

[tex]$$\begin{aligned}\tan 41^{\circ} & =\frac{O B}{O C}=\frac{O B}{24} \\O B & =\tan 41^{\circ} \times 24=20.86 \mathrm{~m} .\end{aligned}$$[/tex]

[tex]A B=O B-O A=20.86-8.74=12.12 \mathrm{~m} \approx 12.1 \mathrm{~m} .[/tex]

To know more about Building visit:

https://brainly.com/question/27243378

#SPJ1

Answer:

12.1

Step-by-step explanation:

I got the question right

The equation that represents the line of best fit for the scatterplot is given as follows:

B. y = -10x + 100.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

From the graph, we have that:

Hence option B is correct.

More can be learned about line of best fit at https://brainly.com/question/1441182

#SPJ1

The solutions to the quadratic equation are x = -1/3 and x = -8.

To solve the quadratic equation 3x^2 + 1 = -25x - 7 by factoring, we first need to rearrange the equation so that all the terms are on one side of the equal sign:

3x^2 + 25x + 8 = 0

Next, we need to find two numbers that multiply to give us 8 (the constant term) and add to give us 25 (the coefficient of the x term). These numbers are 20 and 1, so we can factor the trinomial as follows:

(3x + 1)(x + 8) = 0

Now we can use the zero product property to set each factor equal to zero and solve for x:

3x + 1 = 0 or x + 8 = 0

x = -1/3 or x = -8

So the solutions to the quadratic equation are x = -1/3 and x = -8.

Learn more about quadratic equation

brainly.com/question/30098550

#SPJ11

Y= 3.2

When \( y \) varies directly as \( x \) and inversely as \( z \), the equation is given by:
\( y = \frac{kx}{z} \)

Where \( k \) is a constant.

Substituting the given values of \( x \), \( y \) and \( z \), we get:
\( 24 = \frac{k(120)}{16} \)

Solving for \( k \):
\( k = \frac{24*16}{120} = 4.8 \)

Substituting the values of \( k \), \( x \) and \( z \) into the equation, we get:
\( y = \frac{(4.8)*4}{15} \)

Therefore, the value of \( y \) when \( x=4 \) and \( z=15 \) is \( 3.2 \).

Learn more about fractions

brainly.com/question/10354322

#SPJ11

To find the hypotenuse of a right triangle, we can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
Where c is the hypotenuse, and a and b are the other two sides of the triangle.

In this case, we are given the lengths of the two legs of the triangle, 11 inches and 24 inches.
We can plug these values into the formula and solve for the hypotenuse:
c^2 = 11^2 + 24^2
c^2 = 121 + 576
c^2 = 697
c = √697
c ≈ 26.4 inches

Therefore, the hypotenuse of the triangle is approximately 26.4 inches.

To know more about hypotenuse refer here:

https://brainly.com/question/29407794

#SPJ11

The expression b^(2)-7b+1 evaluates to -9 when b=5.

To evaluate the expression when b=5, we simply need to substitute the value of b into the expression and then simplify.

Here's how we do it step-by-step:

Step 1: Substitute the value of b into the expression:

b^(2)-7b+1 = (5)^(2)-7(5)+1

Step 2: Simplify the expression by following the order of operations (PEMDAS):

= 25-35+1

Step 3: Combine like terms:

= -9

So, the final answer is -9.

Therefore, the expression b^(2)-7b+1 evaluates to -9 when b=5.

For more about quadratic expression:

https://brainly.com/question/14083225

#SPJ11

The missing side of the triangle is 16 mm.

Trigonometry is the branch of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six common uses for an angle in trigonometry.

As per the given diagram:

The sides and angles of the right-angled triangle is given:

To find v using the trigonometric ratio:

sinθ = (P/H) {P is perpendicular and H is hypotunese}

for θ = 30°

sin30° = (8/v)

1/2 = 8/v

v = 16 mm

Hence, the missing side of the triangle is 16 mm.

To learn more about Trigonometry, click:

brainly.com/question/29002217

#SPJ1

The least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6) is 14(x-3).

To find the least common denominator of the two fractions (2x)/(7x-21) and (1)/(2x-6), we need to find the least common multiple of the denominators 7x-21 and 2x-6.

Step 1: Factor the denominators.
7x-21 = 7(x-3)
2x-6 = 2(x-3)

Step 2: Identify the common factors.
Both denominators have the factor (x-3).

Step 3: Multiply the unique factors together.
7 * 2 * (x-3) = 14(x-3)

Step 4: The least common denominator is 14(x-3).

To know more about least common multiple  click on below link:

https://brainly.com/question/30060162#

#SPJ11

Answer:

the quotient of 100 and the sum of B and 24

Step-by-step explanation:

The word expression is: "the quotient of 100 and the sum of B and 24"

The algebraic expression is: 100 / (B + 24)

To evaluate this expression for the values 1, 6, and 13.5, we substitute each value in turn for B and simplify:

When B = 1:

100 / (1 + 24) = 100 / 25 = 4

When B = 6:

100 / (6 + 24) = 100 / 30 = 3.33...

When B = 13.5:

100 / (13.5 + 24) = 100 / 37.5 = 2.666...

Therefore, the values of the expression for B = 1, 6, and 13.5 are approximately 4, 3.33, and 2.67, respectively.

When solving a polynomial equation by factoring, we can apply the zero-product property to the factors that are equal to zero.

The zero-product property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero. For example, if (x-2)(x+3) = 0, then either (x-2) = 0 or (x+3) = 0.

In the case of a polynomial equation, we can apply the zero-product property to the factors that are equal to zero in order to find the values of x that make the equation true.

For example, if we have the equation x^2 - 5x + 6 = 0, we can factor the left-hand side of the equation to get (x-2)(x-3) = 0. We can then apply the zero-product property to find that either (x-2) = 0 or (x-3) = 0, which means that x = 2 or x = 3 are the solutions to the equation.

In summary, when solving a polynomial equation by factoring, we can apply the zero-product property to the factors that are equal to zero in order to find the values of x that make the equation true.

Know more about polynomial here:

https://brainly.com/question/1496352

#SPJ11

The equation of line is y = -4x - 3 and the slope is m = -4

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( -2 , 5 )

Let the second point be Q ( -1 , 1 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 1 - 5 ) / ( -1 - ( -2 ) )

On simplifying , we get

Slope m = ( -4 ) / 1

Slope m = -4

Now , the equation of line is y - y₁ = m ( x - x₁ )

y - 5 = -4 ( x - ( -2 ) )

y - 5 = -4 ( x + 2 )

y - 5 = -4x - 8

Adding 5 on both sides , we get

y = -4x - 3

Hence , the equation of line is y = -4x - 3

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ9

The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:

Where L = 400, A [tex]\approx[/tex] 12.82

Where L = 700 A [tex]\approx[/tex] 44.43

Where L = 1,100 A [tex]\approx[/tex]  86.13

The length of the pipe is given by the function:

L =  111.25√A.

Where a = (L/111.25)²

Thus, for L = 400inches

A =  (400/111.24)²

(400/111.24)² = (400²)/(111.24)²

(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:

(160000)/(12369.5776) = 12.820128200735

Therefore, A = 12.820128200735,

A [tex]\approx[/tex] 12.82

Thus:

Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43

Where L = 1,100
A = 86.129479

A [tex]\approx[/tex] 86.13

Learn more about area at:

https://brainly.com/question/27683633

#SPJ1

Answer:

I'm sorry, but it is not clear what you are asking for. Can you please provide more information or a specific question?

The answer to the quadratic equation -9d^(2)+6=-6d is 11/20 and -11/20. To solve the given quadratic equation f -9d^(2)+6=-6d, we need to rearrange the terms and use the quadratic formula.

Step 1: Rearrange the terms to get the equation in the standard form of ax^(2) + bx + c = 0
-9d^(2) + 6d + 6 = 0

Step 2: Identify the values of a, b, and c.
a = -9
b = 6
c = 6

Step 3: Use the quadratic formula to find the solutions for d.
The quadratic formula is given by:

d = (-b ± √(b^(2) - 4ac))/(2a)

Substitute the values of a, b, and c into the formula:

d = (-(6) ± √((6)^(2) - 4(-9)(6)))/(2(-9))

Step 4: Simplify the expression inside the square root:

d = (-(6) ± √(36 + 216))/(-18)

d = (-(6) ± √(252))/(-18)

Step 5: Simplify the expression further:

d = (-(6) ± 15.87)/(-18)

Step 6: Solve for d using both the positive and negative values inside the square root:

d = (-(6) + 15.87)/(-18) = 0.55

d = (-(6) - 15.87)/(-18) = -0.55

So, the solutions for d are 0.55 and -0.55 or 11/20 and -11/20 using the quadratic formula to solve the given quadratic equation.

Know more about quadratic formula here:

https://brainly.com/question/11540485

#SPJ11

The statement g(5) = 33.75 represents total cost of $33.75 when the purchase of a stuffed giraffe added to 5 accessories to it, the total cost

From the question, we have the following parameters that can be used in our computation:

g(x) = the cost of a stuffed giraffe.

The giraffe costs $15 and accessories cost $3.75 each.

This means that

g(5) = 33.75

Using the above as a guide, we have the following:

The statement g(5) = 33.75 means that if we purchase a stuffed giraffe and add 5 accessories to it, the total cost will be $33.75.

Read more about function at

https://brainly.com/question/28277110

#SPJ1

Answer:

The answer is [tex](u + 3)(5u^{2} - 1)[/tex]

Answer:

the paper is too blurry i would help if i could.

Step-by-step explanation:

The sum of the squares of n standard gaussians is known as a Chi square and denoted by x2. In other words, if Z1, Z2, ..., Zn are independent N(0, 1) then x2 = Z1^2 + Z2^2 + ... + Zn^2.  to use the Central Limit Theorem (CLT) to find P(x2 > 30). The closest value is (C) 0.20 The correct option is C) 0.20

The CLT states that the sum of a large number of independent and identically distributed random variables will be approximately normally distributed. In this case, the sum of the squares of n standard gaussians (x2) will be approximately normally distributed with mean n and variance 2n.

Therefore, we can standardize x2 to find the probability that it is greater than 30:

Z = (x2 - n) / sqrt(2n)

We want to find P(x2 > 30), which is equivalent to P(Z > (30 - n) / sqrt(2n)). Using the standard normal table, we can find the closest value to this probability. The closest value is (C) 0.20. Therefore, the answer is (C) 0.20.

To learn more about Central Limit Theorem here:

https://brainly.com/question/18403552#

#SPJ11

In response to the given query, the result we have is Hence, each expressions container contains 1/2 gallon of paint.

Multiplying, dividing, adding, and subtracting are all mathematical operations. As an example, consider the following expression: Expression, mathematics, and a numeric value Numbers, parameters, and functions are the components of an expression in mathematics. Using opposing words and phrases is possible. An expression, sometimes referred to as an algebraic expression, is any mathematical statement that includes variables, numbers, and a mathematical action between them. For instance, the expression 4m + 5 is made up of the expressions 4m and 5, as well as the variable m from the previous equation, all of which are separated by the mathematical symbol +.

The remaining paint would be as follows if the art teacher had 8 gallons and the students had used 3/4 of it:

8 x 1 - 3/4 = 8 x 1/4 = 2 gallons.

The 4 bottles of the remaining 2 gallons of paint each contain the following amounts of paint:

1/2 gallon is equal to 2/4.

Hence, each container contains 1/2 gallon of paint.

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

The relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

What is frequency ?

In statistics, frequency refers to the number of times a particular observation or value occurs in a given dataset or sample. It is often represented in a frequency table, which organizes the data by category or value and shows the number of occurrences for each.

To find the relative frequency for the total number of boys in this survey, we need to divide the number of boys who prefer math or social studies by the total number of students in the survey, which is 120.

Relative frequency of boys who prefer math = 43/52 ≈ 0.83

Relative frequency of boys who prefer social studies = 9/52 ≈ 0.17

Relative frequency of total number of boys = 52/120 ≈ 0.43

Therefore, the relative frequency for the total number of boys in this survey, rounded to the nearest hundredth, is 0.43.

To know more about frequency visit :

brainly.com/question/254161

#SPJ1

The value of f(3) using synthetic division is 72.

To find f(3) using synthetic division, we need to divide the polynomial f(v) by the factor (v - 3). This will give us the quotient and the remainder, which will help us find the value of f(3).

Write the coefficients of the polynomial in a row: 12 -40 4 17 21

Write the value of the factor we are dividing by to the left of the row: 3 | 12 -40 4 17 21

Bring down the first coefficient: 3 | 12 -40 4 17 21
          ------------------
             12

Multiply the first coefficient by the factor and write the result under the second coefficient: 3 | 12 -40 4 17 21
          ------------------
             12  36

Add the second coefficient and the result from step 4: 3 | 12 -40 4 17 21
          ------------------
             12  -4

Repeat steps 4 and 5 for the remaining coefficients: 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51

The last number in the bottom row is the remainder. This is the value of f(3): 3 | 12 -40 4 17 21
          ------------------
             12  -4  0  51  72

So, f(3) = 72.

Therefore, the value of f(3) using synthetic division is 72.

Learn more about Synthetic division

brainly.com/question/29631184

#SPJ11

Answer:

Part A: To find the expression for the length of the rectangular space, we can use the formula for the area of a rectangle, which is length multiplied by width. We have the expression for the area as 8x² - 12x, and the expression for the width as 4x. So, we can write:

Area = Length × Width

8x² - 12x = Length × 4x

Simplifying the right side by multiplying, we get:

8x² - 12x = 4x × Length

2x² - 3x = Length

Therefore, the expression for the length of the rectangular space is 2x² - 3x.

Part B: To prove that the expression for the length from Part A is correct, we can multiply it by the expression for the width and simplify:

Length × Width = (2x² - 3x) × (4x)

= 8x³ - 12x²

= 4x(2x² - 3x)

= 4x(2x(x - 3))

This is in fact the same as the expression for the area of the rectangular space, 8x² - 12x, in standard form.

Precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

To make a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point, follow these steps:

1. Draw the given circle using a compass.
2. Mark the given point on the paper with a pencil.
3. Place the point of the compass at the given point and extend the compass until it touches the edge of the circle.
4. Draw a circle with the compass. This circle will intersect the given circle at two points.
5. Use a ruler to draw a line from the given point to each of the intersection points. These lines are the tangent lines to the given circle that pass through the given point.
6. Label the tangent lines and the given point for clarity.

By following these steps, you can create a ruler-and-compass construction of the lines tangent to a given circle that pass through a given point. Remember to be precise and accurate in your construction, using the ruler and compass correctly to create the desired lines.

Learn more about  ruler-and-compass

brainly.com/question/14811499

#SPJ11

The function  f(g(x)) = x/(3+2x)-2 and g(f(x)) = (-x+2)/(1-2x) after simplifying.

The composition of two functions f and g is denoted by (f∘g)(x) and is defined as f(g(x)). In other words, we apply the function g to the input x, and then apply the function f to the result.

For the first part of the question, let f(x)=2x+2 and g(x)=2x²+2x. To find (f∘g)(x), we apply g(x) to the input x and then apply f(x) to the result:

(f∘g)(x) = f(g(x)) = f(2x²+2x) = 2(2x²+2x)+2 = 4x^2+4x+2

So, (f∘g)(x) = 4x^2+4x+2 after simplifying.

For the second part of the question, let f(x)=1/x-2 and g(x)=3/x+2. To find f(g(x)), we apply g(x) to the input x and then apply f(x) to the result:

f(g(x)) = f(3/x+2) = 1/(3/x+2)-2 = 1/(3+2x)/x-2 = x/(3+2x)-2

To find g(f(x)), we apply f(x) to the input x and then apply g(x) to the result:

g(f(x)) = g(1/x-2) = 3/(1/x-2)+2 = 3x/(1-2x)+2 = (3x+2-4x)/1-2x = (-x+2)/(1-2x)

So, f(g(x)) = x/(3+2x)-2 and g(f(x)) = (-x+2)/(1-2x) after simplifying.

learn more about of function here

brainly.com/question/28992757

#SPJ11

The equation which represents the total length of the siding is given by A , where A = 50 x 4 = 200 meters

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign.

It displays the similarity of the connections between the phrases on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are examples of the parts of an equation. When creating an equation, the "=" symbol and terms on both sides are necessary.

Given data ,

Let the total length of the siding be represented as A

Now , the value of A is

Let the number of pieces be n = 48 pieces

Let the length of each piece be l = 3.7 meters

Now , total length of the siding A = number of pieces x length of each piece

On simplifying the equations , we get

The total length of siding A = 48 x 3.7 = 177.6 meters

Now , n ≈ 50 pieces

l ≈ 4 meters

So , total length of siding A = 50 x 4 = 200 meters

Hence , the equation is A = 50 x 4 = 200 meters

To learn more about equations click :

https://brainly.com/question/10413253

#SPJ9

When two straight lines or rays intersect at a single endpoint then an angle is created. The vertex of an angle is that location where two points are come together.

The sum of angles equal to 180° is called Supplementary Angle.

Complementary Angle, Sum of the angle is equal to 90°.

a. (10x + 7) + (4x + 5) = 180 ( Supplementary angle )

14x + 12 = 180

14x = 180 -12

x = 12

10x + 7 = 127°

4x + 5 = 53°

c. (5x -11) + (8x -3) = 90 ( Complementary Angle )

13x - 14 = 90

13x = 90 + 14

x = 8

5x - 11 = 29°

8x - 3 = 61°

To learn more about Supplementary angle , visit :

https://brainly.com/question/30759856

#SPJ1

The  true about the volumes of the triangular prism and the triangular pyramid is D; triangular pyramid has a volume one-third the volume of the triangular prism.

Suppose a triangle. Now, strech it up so as to make a stack of triangles up above another. This new 3d object is called a triangular prism.

Usually, about triangular prism, we talk about the triangular prism, whose stack goes straight up, thus, we talk about a right triangular prism.

In order for us to know the volume of the triangular pyramid, first we need to know the ratio of the volume of triangular prism and the volume of the triangular pyramid.

Take a traingle as a base then take 3 triangles such that each of them are connected to one-one side of the first traingle and when they're taken together, they form a closed object, called as a triangular pyramid.

Volume of the pyramid = 1/3 volume of the prism.

Learn more about volumes of prisms here:

https://brainly.com/question/16909441

#SPJ1

The triangular pyramid has a volume one-third the volume of the triangular prism .

Correct option is D.

Volume is the measure of the capacity that an object holds. Volume can also be defined as the amount of space occupied by a 3-dimensional object. The volume of a solid like a cube or a cuboid is measured by counting the number of unit cubes it contains. The best way to visualize volume is to think of it in terms of the space enclosed/occupied by any 3-dimensional object or solid shape.

Given,

A triangular prism and a triangular pyramid have the same base and height.

Let the height be h unit and area of base be x square unit

Volume of triangular prism

= base area × height

= Ah cubic unit

Volume of triangular pyramid

= (1/3)× base area × height

= (1/3)Ah

= (1/3) volume of triangular prism

Hence, volume of triangular pyramid is one-third of  volume of triangular prism.

Learn more about volume here:

https://brainly.com/question/1578538

#SPJ1