1. Todd purchased a jumper for his infant son. The jumper clamps to the top of a door frame and has a spring from which the body of the jumper hangs to allow the infant to jump up and down. Included with the jumper are small weights, each identical in weight and size. The weights allow the user to adjust the initial height of the jumper by stretching the spring a certain distance. Todd adds 8 of the weights and notes the spring stretches 2 centimeters.
(a) According to Hook's Law, the amount that a spring is stretched, s, varies directly with the force applied to the spring by the weights, $F$. Write an equation that relates F and s for the spring on the jumper. (3 points)

F=ks 8=k 2
k=8/2 F=4 x

Answer: 11.36

Step-by-step explanation:

↓ Please look in the screenshot below...

All values of t for which the ball's height is 8 feet are 0.82 or 0.305.

What is quadratic equation?

Quadratics are often outlined as a polynomial equation of a second degree, which means that it contains a minimum of 1 term that's square. it's conjointly known as quadratic equations.

Main Body:

The actual equation is

h=  4- 18t +16t²

initial height of ball = 4 ft

The problem asks for a time when the ball's height will be 8 ft. To find these times, I plug 8 in for h and solve for t:

8 = 4+18t -16t²

16t² - 18t +4 =0

Using the quadratic equation:

t = {18 ±√((18)² - 4*16 *4 )}/2*16

t = 18 ± √(324 - 256)/32

t = (18 ± √68) /32

t = (18±8.24)/32

t =  0.82 or 0.305

Hence ,all values of t for which the ball's height is 8 feet are 0.82 or 0.305.

To know more about quadratic equation , visit:

https://brainly.com/question/28038123

#SPJ1

Step-by-step explanation:

I just answered this with all explanations.

the 2 solutions are

x = 6

x = -12

12. The customer should use 120 units in a quarter for company A to be      cheaper.

What is cost management?

Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.

Solution:

Company A charges $14 for first 100 units = 14×100

                                                                        = $1400

After that 11% of 14 = 1.54 per unit

Company B charges $12 per unit so for 100 units = $12×100

                                                                                     = $1200

For company A to be cheaper, customer must use 120 units of electricity from company B as expense for 120 units from company B will be  $12×120 = $1440

and,

For 120 units of electricity from company A would be

$14×100 + 1.54×20 as after 100 units company A will charge 11%.

∴ for 120 units = 1400 + 30.8

                        = $1430.8

To learn more about cost management click on the link below:

https://brainly.com/question/28536789

#SPJ4

13. For taxi company A to be cheaper customer must travel a minimum of 6 miles.

What is cost management?

Cost management is the process of estimating, allocating, and controlling costs. The cost management process allows a business or a customer to predict future expenses to reduce the chances of budget overrun.

Solution:

Given:

Company A charges $2.25 for a minimum of 2 miles journey and after that 85 cents per mile.

Company B charges 95 cents per mile without any minimum mile condition.

Let's assume

no. of miles = 4

fare from A = $2.25(2 miles) + 85 cents(1 mile) + 85 cents(1 mile)

                  = $3.95

fare from B = 95 cents × no. of miles

                  =  95 cents × 4

                  = $3.8

∵ Fare of company A is greater than B, minimum number of miles should be greater than 4.

now,

Let's assume

no. of miles = 5

fare from A = $2.25 + 85 cents + 85 cents + 85 cents

                  = $4.8

fare from B = 95 cents × no. of miles

                  =  95 cents × 5

                  = $4.75

∵ Fare of company A is greater than B minimum number of miles should be greater than 5.

now,

Let's assume

no. of miles = 6

fare from A = $2.25 + 85 cents + 85 cents + 85 cents + 85 cents

                  = $5.65

fare from B = 95 cents × no. of miles

                  =  95 cents × 6

                  = $5.7

∵ Fare of company A is less than B.

∴ Minimum number of miles should be 6.

To learn  more about cost management click on the link below:

https://brainly.com/question/28536789

#SPJ4

The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is closest to (d) 0.04

The margin of error is a statistic that describes how much random sampling error there is in survey results.

Given in question,

n = 400

p = 317/400

  = 0.7925

Confidence Level = 95%

                          = 0.95

Formula for margin error, E = [tex]z\sqrt{\frac{p(1-p)}{n} }[/tex]

Confidence level corresponding to 95 % confidence interval, z = 1.96

Therefore,

Margin Error, E = [tex]1.96\sqrt{\frac{0.7925(1-0.7625)}{400} }[/tex]

                         = 0.0397

                         ≈ 0.04

Hence, The margin of error for a 95% confidence interval for the true proportion of tongue rollers among students is 0.0397 which is closest to 0.04.

To learn more about margin of error here:

https://brainly.com/question/10501147

#SPJ4

Answer:84

Step-by-step explanation:21x4=84

Answer: Length (in feet) x width (in feet) = area in sq. ft. 

Step-by-step explanation:

After solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, 2 equations can be formed:

Let a be adults and c be children.

3a + 4c = 96 ...(1)

2a + 3c = 68 ...(2)

Now, take equation (1):

3a + 4c = 96

3a = 96 - 4c

a = 96 - 4c/3

Now, substitute a = 96 - 4c/3 in equation (2):

2a + 3c = 68

2(96 - 4c/3) + 3c = 68

96 - 4c/3 + 3c = 68/2

96 - 4c + 3c = 34*3

-c = 102 - 96

c = $6

Now, substitute c = 6 in equation (1):

3a + 4c = 96

3a + 4(6) = 96

3a + 24 = 96
3a = 96 - 24

3a = 72

a = 72/3

a = $24

Therefore, after solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.

Know more about equations here:

https://brainly.com/question/28937794

#SPJ1

The required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the equation of the line will be:

The needed line will have the same slope as the parallel line.

The slope of the parallel line:
x - y = 5

y = x - 5

The parallel line's slope is 1.

Equation of a line with a slope of 1 through the point (-5,-2).

(y - y1) = m(x  x1)

(y + 2) = 1(x + 5)

x - y + 3 = 0

Therefore, the required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.

Know more about the equation of the line here:

https://brainly.com/question/18831322

#SPJ1

The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

Learn more about equations of circle at;

brainly.com/question/16039879

#SPJ1

Answer:

The tree is 396 feets height

Step-by-step explanation:

1 m = 3.3 ft

then

12 meters to feet is:

(12)*(3.3) = 396

The smallest possible value of x - y will be -6 when x = -4  and y = 2. The largest possible value of {2x}/{y}  will be 3/2 when x = 6  and y = 8. The largest possible value of x²+y² will be 100 when x = 6  and y = 8.

Given that -4 ≤ x ≤6 and 2≤ y ≤ 8,

The smallest possible value of x - y

⇒ (x - y)

As per the given, the smallest values of x and y are - 4 and 2

So, substitute the values of x = -4  and y = 2 in the expression (x - y)

⇒ - 4 - 2

⇒ - 6

The largest possible value of {2x}/{y}

⇒ {2x}/{y}

As per the given, the largest values of x and y are 6 and 8

So, substitute the values of x = 6  and y = 8 in the expression {2x}/{y}

⇒ 2(6)/8

⇒ 12/8

⇒ 3/2

The largest possible value of x²+y².

⇒ x²+y²

As per the given, the largest values of x and y are 6 and 8

So, substitute the values of x = 6  and y = 8 in the expression x²+y²

⇒ 6²+8²

⇒ 36 + 64

⇒ 100

Learn more about the algebraic expression here :

brainly.com/question/21751419

#SPJ1

Answer:

Slope = 2

y-intercept = -1

Step-by-step explanation:

In the slope-intercept form of the equation of a line (y=mx+b), m equals the slope and b represents the y-intercept.

So, for this problem, m=2 and b=-1.  This means the slope is 2 and the y-intercept is -1.

Answer:

y = 3x + 17

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (- 5, 2) , that is x = - 5, y = 2 into the partial equation

2 = - 15 + c ⇒ c = 2 + 15 = 17

y = 3x + 17 ← equation of line

Answer: 100 feet

Step-by-step explanation:

   If there are 100 square floor tiles, and each side is one foot long, we will multiply the number of tiles by the length of each tile to find the length of each side of the room.

100 tiles * 1 foot length = 100 feet

Answer:

16/24

Step-by-step explanation:

To raise a fraction, we have to multiply by 24/3, which is 8:
2 * 8 / 3 * 8 =

16/24

The value of G = F/MH for H

Mathematical expression is the combination of numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent all of the numerical constants, variables, operations, functions, brackets, punctuation, and grouping. They can also be used to denote the logical syntax's operation order and other properties.

According to the given information

F = MGH

we need to find the value for G

Dividing the above equation by MH

F/MH = MGH/MH

SO

G = [tex]\frac{F}{MH}[/tex]

So the value of G = F/MH for H

To know more about Expression

https://brainly.com/question/3089268

#SPJ1

r≈10.75cm

Answer:

r≈10.75cm

V=πr^2h/3

Answer:

The correct answer is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

If she has 6 classes, then the total hours of classes are:

[tex]\frac{6}{1}[/tex] · [tex]\frac{7}{6}[/tex] = [tex]7[/tex]

[tex]7[/tex] · [tex]\frac{1}{2}[/tex] - [tex]7[/tex] = [tex]\frac{1}{2}[/tex]

The angle between 0 and 2π coterminal with the angle 23π/3 will be equal to 17π/3.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the angle between 0 and 2π coterminal with the angle 23π/3. The coterminal angle will be calculated as,

To calculate the coterminal angle subtract 2π from 23π/3. Solve mathematically,

Coternimal = ( 23π / 3 ) - 2π

Coterminal = 9 23π  - 6π ) / 3

Coterminal = 17π / 3

To know more about trigonometry follow

https://brainly.com/question/10871286

#SPJ1

The value of k in the point (2, k) which lies on the line is -4.

How to find the value of k?

Every point lying on the curve of the line satisfies the equation of curve. Therefore, substitute the point in the given equation of line to find the value of k.

According to the given question:

The given equation is: 2y = - 3x - 2.

This is written as: 3x + 2y + 2 = 0.

Given the point (2, k) lies on the line given.

That means it should satisfy the given equation.

So, to find the value of 'k', simply substitute the point on the line.

So, it becomes: 3(2) + 2(k) + 2 = 0

⇒ 6 + 2k + 2 = 0

⇒ 2k = - 8

Dividing by 2 throughout, we get: k = - 4

Hence, (2, -4) lies on the line.

To know more about equation of line visit

https://brainly.com/question/13078415

#SPJ1

The value of z-score of a person who scored 115 on the exam will be;

⇒ z - score = - 1

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

The scores are normally distributed with a mean of 135 and a standard deviation of 20.

Now,

Since, The scores are normally distributed with a mean of 135 and a standard deviation of 20.

We know that;

⇒ z - score = X - μ / σ

Substitute all the values, we get;

⇒ z - score = 115 - 135 / 20

⇒ z - score = - 20/20

⇒ z - score = - 1

Thus, The value of z-score of a person who scored 115 on the exam will be;

⇒ z - score = - 1

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ1

Answer:

Yes

Step-by-step explanation:

let x = one boy

let y = another boy

let z = a third boy

x + 2 + y + 2 + z + 2 = 15  Combine like terms

6 + x + y + z = 15  Subtract 6 apples from both sides

x + y + x = 9

When we subtract out the 2 apples each brother know that they ate at lease 2 apples each we are left with a total of 9 apples.

One boy could have eaten 4 additional apples?  Yes.

4 + 1 + 1 < 9

The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’

Multiply the coordinates of point P by the scale factor 7/4  to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

          = P(-8.75, 5.25)

Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).

Learn more about scale factor at:https://brainly.com/question/25722260

#SPJ1

Answer:

x is (2,0) and y is (0, -2)

Step-by-step explanation:

Hope this helps

Answer:

Exact form: 13/4

Decimal form: 3.25

Mixed form: 3 1/4

Step-by-step explanation:

Answer:

The number of students in the seventh grade is 550.

Step-by-step explanation:

To find the number of students in the seventh grade, we need to use the information given in the problem: the number of students in the Environmental Club (11 students) and the percentage of students in the seventh grade that the Environmental Club represents (2%).

We can set up an equation to represent this information:

11 students / 2% = X students / 100%

The left side of the equation represents the number of students in the Environmental Club and the percentage of the seventh grade that they represent. The right side of the equation represents the total number of students in the seventh grade and the percentage that represents the whole.

Since percentages are just fractions with a denominator of 100, we can rewrite the equation as:

11 students / 0.02 = X students / 1

Then, we can use algebraic techniques to solve for X. One way to do this is to cross-multiply:

X = (11 students * 1) / 0.02

= 550 students

Therefore, there are 550 students in the seventh grade.

This question is incomplete , I am answering this question in general as per my knowledge.

No, because you gave T a Boolean when T expected a student as its first argument and a course as its second parameter. This will be less formal if.

The expected,

T(‘‘user2012813",‘‘discrete math")=true

However, the function F(x) and A both yield either true or false (y). Thus, you are attempting to assess

T(F(‘‘user2012813"),A(‘‘discrete math"))=T(true, false)= NULL

Only the first formulation makes sense, but after relations are established, these kinds of structures can be used.

Null functions as both a value and a pointer in computer programming. A built-in constant called null has a value of zero. It is the same as how strings in C are terminated with the letter 0.

Null is another possible value for a pointer, and unless the CPU supports a unique bit pattern for a null pointer, it has the same value as zero.

To learn more about Boolean

brainly.com/question/2467366

#SPJ4