Suppose that when a car goes over a bump, the impact hat must be absorbed by the suspension is directly proportional to the square of the car's speed. Of a car going 12 mph receives 4000 units of impact, ow much impact will a car received at 30 mph

Answer:

angles that add up to 180 degrees

Step-by-step explanation:

Answer:

Two angles who's sums are 180 degrees.

Step-by-step explanation:

Answer:

Given information:

To obtain the equation of the regression line for the given data.

The equation of regression line of y on x is given by:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

;

w

h

e

r

e

,

y

=

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

x

=

i

n

d

e

p

e

n

d

e

n

t

v

a

r

i

a

b

l

e

b

y

x

=

s

l

o

p

e

o

f

r

e

g

r

e

s

s

i

o

n

l

i

n

e

¯

x

=

m

e

a

n

o

f

x

¯

y

=

m

e

a

n

o

f

y

y−y¯=byx(x−x¯);where,y=dependentvariablex=independentvariablebyx=slopeofregressionlinex¯=meanofxy¯=meanofy

The calculations for the equation of regression line is tabulated below:

The regression coefficient of y on x is given by:

b

y

x

=

∑

x

y

−

1

n

∑

x

∑

y

∑

x

2

−

1

n

(

∑

x

)

2

=

1944

−

1

5

×

98

×

69

2580

−

1

5

(

98

)

2

=

591.6

659.2

=

0.898

byx=∑xy−1n∑x∑y∑x2−1n(∑x)2=1944−15×98×692580−15(98)2=591.6659.2=0.898

Mean of x is calculated as:

¯

x

=

1

n

∑

x

=

1

5

×

98

=

19.6

x¯=1n∑x=15×98=19.6

Mean of y is calculated as:

¯

y

=

1

n

∑

y

=

1

5

×

69

=

13.8

y¯=1n∑y=15×69=13.8

The equation of regression line is given as:

y

−

¯

y

=

b

y

x

(

x

−

¯

x

)

y

−

13.8

=

0.898

(

x

−

19.6

)

y

=

0.898

x

−

3.8

y−y¯=byx(x−x¯)y−13.8=0.898(x−19.6)y=0.898x−3.8

Therefore, the required equation of regression line is y = 0.898x - 3.8.

Answer:

The answer is 6 rides that cost $26.

Step-by-step explanation:

Plan A: $20 plus $1 per ride.

Plan B: $8 plus $3 per ride.

Turn that into a linear equation to graph.

Plan A: \(y=1x + 20\)

Plan B: \(y=3x + 8\)

The x-axis is rides and the y-axis is $.

On the graph appears that it takes 6 rides for Plan A and B to be the same a cost of $26.

The sets of ordered pairs  that represents a function is: B. {10,5), (-10,-5), (5,10), (-5,-10)}.

Option A: The input value 1 is associated with two different output values (6 and -10), so this set does not represent a function.

Option B: Each input value is associated with only one output value, so this set represents a function.

Option C: The input values 3 and -17 are associated with two different output values (5 and -5, and -5 and 5, respectively) so this set does not represent a function.

Option D: The input value 10 is associated with two different output values (5 and -5) so this set does not represent a function.

Therefore the correct option  is B.

Learn more about function here:https://brainly.com/question/25638609

#SPJ1

Answer:

not equivalent to meteorologists ratio

Step-by-step explanation:

meteorologists ratio is

rainy days : sunny days = 2 : 5

last months weather is

rainy days : sunny days

= 10 : 20 ( divide both parts by LCM of 10 )

= 1 : 2 ← not equivalent to 2 : 5

Answer:

^4+2x^3+x+2

Step-by-step explanation:

1. Combine exponents

(+2)(^2x+1)

(x+2)(x^3+1)

2. Distribute

x (x^3+1)+2(x^3+1)

x^4+x+ 2(x^3+1)

3. Solution is x^4 + 2x^3 + x+2

Answer:

46

Step-by-step explanation:

-5(-2-5)-x-1=-12

-5(-7)-x-1=- 12

35 - x - 1 = -12

34 - x = -12

-x = -12 - (-34)

-x = - 46

x = 46

Answer:

\(x=46\)

Step-by-step explanation:

\(-5\left(-2-5\right)-x-1=-12\)

⟹ Subtract -2 and 5 = -7

⟹ Remover parentheses:

\(-\left(-35\right)-x-1=-12\)

⟹ Apply rule: \(-\left(-a\right)=a\)

\(35-x-1=-12\)

⟹ Combine like terms:

⟹ Subtract 34 from both sides:

⟹ Divide both sides by -1:

___________________

       OAmalOHopeO      

___________________

Answer:

5:3

Step-by-step explanation:

hope this helps

Answer:

It's (C) But if you do it like this you get 13/6

Step-by-step explanation:

Answer:

The original price is $90.

Step-by-step explanation:

100% - 40% = 60%

\(\frac{54}{y} :\frac{60}{100}\)

y × 60 = 54 × 100

60y = 5400

60y ÷ 60 = 5400 ÷ 60

y = 90

Answer:

90

Step-by-step explanation:

If the discount is 40%, we are still paying 100-40% or 60 %

original price * 60% = sale price

original price * .6 = 54

Divide each side by .6

original price = 54/.6

original price =90

Answer:

D

Step-by-step explanation:

Answer:

The circumference is:

14.6 x 3.14 = 45.844 (m)

Step-by-step explanation:

The equation of the circle in standard form is: x² + y² = 100. And in general, form is: x² + y² - 100 = 0.

The center of the circle with the given endpoints of the radius is the midpoint of the line segment from (-8, 6) to the origin, (0, 0). We can use the midpoint formula to find the center of the circle, and then use the distance formula to find the radius, which is the distance from the center to either endpoint. Midpoint formula: $[(x_1+x_2)/2,(y_1+y_2)/2]$ Distance formula: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Now let's calculate: Midpoint of (-8, 6) and (0, 0):$\left[\frac{(-8)+(0)}{2}, \frac{(6)+(0)}{2}\right] = (-4, 3)$Radius: $\sqrt{(0-(-8))^2 + (0-6)^2} = \sqrt{64+36} = \sqrt{100} = 10$. Therefore, the equation of the circle in standard form is: x² + y² = 100. And in general, form is: x² + y² - 100 = 0. The equation of the circle with center at the origin and radius of length 10 is x² + y² = 100 (standard form) and x² + y² - 100 = 0 (general form).

To know more about circle: https://brainly.com/question/23989157

#SPJ11

The probability of drawing a seven and then a four when randomly drawing two cards without replacement is 0.0045 or approximately 0.45%.

The probability of drawing a seven and then a four when randomly drawing two cards without replacement can be calculated using the following steps:

First, we need to determine the total number of possible outcomes when drawing two cards from a standard deck of 52 cards without replacement. This can be found using the combination formula:

C(52,2) = 52! / (2! * (52-2)!) = 1,326

Next, we need to determine the number of favorable outcomes where we draw a seven and then a four.

There are four sevens and four fours in a deck of 52 cards, so the probability of drawing a seven on the first draw is 4/52. Since we are not replacing the card, there are now 51 cards left in the deck, and three of them are fours. Therefore, the probability of drawing a four on the second draw is 3/51.

The probability of drawing a seven and then a four is the product of the probabilities of drawing a seven on the first draw and a four on the second draw:

P(seven and then four) = (4/52) * (3/51) = 0.0045 or approximately 0.45%.

Therefore, the probability of drawing a seven and then a four when without replacement is 0.0045 or approximately 0.45%.

To learn more about probability, click here:

https://brainly.com/question/30034780

#SPJ11

In the context of racial and ethnic relations, ethnocentrism refers to the tendency to regard one's own culture and group as the standard, and thus superior, whereas all other groups are seen as inferior. Ethnocentrism is a belief system rooted in the notion that one's own cultural practices, values, and beliefs are superior to those of others.

It often leads to prejudice, discrimination, and the marginalization of individuals or groups who do not conform to the dominant culture. This mindset can hinder intercultural understanding and perpetuate stereotypes and biases. Ethnocentrism can manifest in various ways, such as the imposition of cultural norms on others, the dismissal or devaluation of alternative perspectives, and the reinforcement of social hierarchies based on ethnicity or race. Overcoming ethnocentrism requires open-mindedness, empathy, and a willingness to learn and appreciate different cultures and perspectives. Promoting cultural diversity, inclusivity, and intercultural dialogue can help challenge ethnocentric attitudes and foster a more inclusive and equitable society.

Learn more about challenge here:https://brainly.com/question/9207784

#SPJ11

Answer:

Hows it going young blood Y=5x-13 is the answer

Step-by-step explanation:

Answer:

m = 3/2

General Formulas and Concepts:

Pre-Alg

Alg I

Slope-Intercept Form: y = mx + b

Step-by-step explanation:

Step 1: Define function

3x - 2y = 5

Step 2: Rewrite

Step 3: Identify

Slope m = 3/2

y-intercept b = -5/2

HUD (Housing and Urban Development) is responsible for overseeing housing programs and community development initiatives.

The U.S. Department of Housing and Urban Development (HUD) is a government agency tasked with promoting affordable housing, addressing housing discrimination, and facilitating community development. HUD's primary goal is to ensure that individuals and families have access to safe and affordable housing options.

HUD supervises a wide range of programs and initiatives aimed at meeting housing needs and fostering community development. These include rental assistance programs, public housing initiatives, homeownership programs, and support for housing rehabilitation and revitalization projects. Additionally, HUD works to enforce fair housing laws to prevent discrimination in housing-related activities.

Through its various programs, HUD provides financial support, resources, and guidance to local communities, housing authorities, and nonprofit organizations to address housing challenges and promote sustainable, inclusive communities.

Learn more about HUD here:

https://brainly.com/question/28166985

#SPJ11

Answer:

Answer:

speed = 43.974 miles per hour

= 43.974 mi/h

Step-by-step explanation: speed calculator

Answer:

(-3/2, -13/2)

Step-by-step explanation:

To solve the system of equations graphically, we need to plot the two equations on the same set of axes and find the point of intersection.

To plot the first equation y = x - 5, we can start by finding the y-intercept, which is -5. Then, we can use the slope of 1 (since the coefficient of x is 1) to find other points on the line. For example, if we move one unit to the right (in the positive x direction), we will move one unit up (in the positive y direction) and get the point (1, -4). Similarly, if we move two units to the left (in the negative x direction), we will move two units down (in the negative y direction) and get the point (-2, -7). We can plot these points and connect them with a straight line to get the graph of the first equation.

To plot the second equation y = -x - 8, we can follow a similar process. The y-intercept is -8, and the slope is -1 (since the coefficient of x is -1). If we move one unit to the right, we will move one unit down and get the point (1, -9). If we move two units to the left, we will move two units up and get the point (-2, -6). We can plot these points and connect them with a straight line to get the graph of the second equation.

The point of intersection of these two lines is the solution to the system of equations. We can estimate the coordinates of this point by looking at the graph, or we can use algebraic methods to find the exact solution. One way to do this is to set the two equations equal to each other and solve for x:

x - 5 = -x - 8 2x = -3 x = -3/2

Then, we can plug this value of x into either equation to find the corresponding value of y:

y = (-3/2) - 5 y = -13/2

So the solution to the system of equations is (-3/2, -13/2).

The area of the garden is equal to 12.5 m².

In Mathematics and Geometry, the area of a triangle can be calculated by using this formula:

Area = 1/2 × b × h

Where:

Next, we would determine the side lengths of this right triangle by using the distance between coordinates formula;

Distance AB = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance AB = √[(0 - 4)² + (-2 - 1)²]

Distance AB = √[(-4)² + (-3)²]

Distance AB = √[16 + 9]

Distance AB = 5 meters.

Distance BC = √[(3 - 0)² + (2 + 2)²]

Distance BC = √[(3)² + (4)²]

Distance BC = √[9 + 16]

Distance BC = 5 meters.

Area of garden = 1/2 × AB × BC

Area of garden = 1/2 × 5 × 5

Area of garden = 25/2

Area of garden = 12.5 m².

Read more on distance here: brainly.com/question/12470464

#SPJ1

The product of 56.2 and 9.2057 to the appropriate number of significant digits is 517.00.

The significant digits in a number are the digits that contribute to its precision. When multiplying numbers, the result should be rounded to the same number of significant digits as the factor with the least number of significant digits.

In this case, 56.2 has three significant digits, and 9.2057 has five significant digits. The factor with the least number of significant digits is 56.2. Therefore, the product should be rounded to three significant digits.

Multiplying 56.2 by 9.2057 gives 517.38134. Rounding this result to three significant digits gives us 517.00. The trailing zeros after the decimal point are significant in this case as they indicate the precision of the result. Hence, the correct answer is 517.00.

To learn more about significant digits refer:

https://brainly.com/question/28052368

#SPJ11

Answer:

4 × 4000 = 16000cm or 160 meters

The optimal solution for the given linear programming model is:

max z = 38

when x1 = 5, x2 = 10, x3 = 0

To solve the given linear programming model using the simplex algorithm, we start by converting the inequalities into equations and introducing slack variables. The initial tableau is constructed with the coefficients of the decision variables and the right-hand side constants.

Next, we apply the simplex algorithm to iteratively improve the solution. By performing pivot operations, we move towards the optimal solution. In each iteration, we select the pivot column based on the most negative coefficient in the objective row and the pivot row based on the minimum ratio test.

After several iterations, we reach the optimal tableau, where all the coefficients in the objective row are non-negative. The optimal solution is obtained by reading the values of the decision variables from the tableau.

In this case, the optimal solution is z = 38 when x1 = 5, x2 = 10, and x3 = 0. This means that to maximize the objective function, the decision variables x1 and x2 should be set to 5 and 10 respectively, while x3 is set to 0.

Learn more about optimal solution

brainly.com/question/30575901

#SPJ11

Dante's Commedia consists of three books, each containing 33 cantos, for a total of 100 cantos.

The Commedia is a famous literary work by Dante Alighieri, an Italian poet from the 14th century. It is divided into three books: Inferno, Purgatorio, and Paradiso. Each book consists of 33 cantos, making a total of 100 cantos in the entire work.

Inferno is the first book and depicts Dante's journey through Hell. It starts with Dante being guided by the Roman poet Virgil and encountering various sinners and punishments in the different circles of Hell.

Purgatorio is the second book and portrays Dante's ascent up Mount Purgatory, where souls undergo purification to reach Heaven. In this book, Dante is guided by Virgil and later by Beatrice, his beloved.

Paradiso is the final book and represents Dante's ascent to Heaven. In Paradiso, Dante is guided by Beatrice and encounters various heavenly spheres, learning about theology, cosmology, and the nature of God's love.

Each book explores different themes, symbolism, and allegorical representations. Dante's Commedia is renowned for its vivid imagery, complex allegories, and its profound exploration of moral, spiritual, and philosophical themes.

In conclusion, Dante's Commedia consists of three books, each containing 33 cantos, for a total of 100 cantos. It is a monumental work of Italian literature that delves into the realms of Hell, Purgatory, and Heaven, offering a rich exploration of various themes and ideas.

Know more about Commedia here,

https://brainly.com/question/33450792

#SPJ11

the solution to the equation \(4(1.7)^(x) = 7(1.08)^(x)\)  is approximately

x = 8.732.

The other technique to write exponents in mathematics is using logarithms. A number's base-based logarithm is equal to another number. A logarithm performs exponentiation's exact opposite function. For instance, log10 100 = 2 if 102 = 100.

from the question:

By separating the variable on one side of the equation and then taking the logarithm of both sides, we can find the value of x.

Starting with:

\(4(1.7)^(^x^) = 7(1.08)^(^x^)\)

Dividing both sides by \(7(1.08)^(x)\), we get:

\((4/7)(1.7)^(^x^) = (1.08)^(^x^)\)

Taking the logarithm of both sides (with any base), we get:

\(log[(4/7)(1.7)^(^x^)] = log[(1.08)^(^x^)]\)

Using the properties of logarithms, we can simplify this to:

log(4/7) + xlog(1.7) = xlog(1.08)

Subtracting x*log(1.7) from both sides, we get:

log(4/7) = xlog(1.08) - xlog(1.7)

Factoring out x, we get:

log(4/7) = x*[log(1.08) - log(1.7)]

Dividing both sides by [log(1.08) - log(1.7)], we get:

x = log(4/7) / [log(1.08) - log(1.7)]

We can evaluate this statement with a calculator and obtain:

x ≈ 8.732

As a result, x = 8.732 is about the answer to the equation 4(1.7)(x) = 7(1.08)(x).

Learn more about logarithms here:

brainly.com/question/30085872

#SPJ1

The mistake in the equation that javier made is in the multiplication

When you take a single number and multiply it by several, you are multiplying. A 5 multiplied by a 4 results in 20 (5 + 5 + 5 + 5). We multiplied the number five by four times. Due to this, multiplication is occasionally referred to as "times."

Any integer multiplied by zero always equals zero.

Any integer multiplied by one is always the same.

When multiplying by 10, add a 0 to the original value.

The product is unaffected by the order of the elements.

When multiplying consecutively sign-matched numbers, the products are always positive.

In the above question

8(9x)=192

72x=192

x=8/3

To learn more about multiplication, click the following link:-

https://brainly.com/question/10873737

#SPJ4