The height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. When graphed, the function gives a line with a slope of −0.4. See the figure below. Suppose that the height of the candle after 11 hours is 16.6 centimeters. What was the height of the candle after 6 hours?

Answer:

y = -3    m = -1     b = 3

Step-by-step explanation:

-3y=3x-9

To isolate the y variable, divide both sides by -3.

y = -1x + 3

y = -3

m = -1

b = 3

Answer:

finding the value of x first

2x + 3x + 10 = 180 (linear pair)

5x = 180 - 10

x = 170 / 5

x = 34

3x = 102

Answer:

W = 9 * g

Step-by-step explanation:

W/9 = g

W = 9 * g

The expression W/9 = g can be written as W = 9g after cross multiplication.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

W/9 = g

To solve for W

Make subject as W:

W = 9g

By cross multiplication.

Thus, the expression W/9 = g can be written as W = 9g after cross multiplication.

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Answer:

see below

Step-by-step explanation:

Part A

The slope is found by

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

    = ( 1200-1500)/(4-0)

    = -300/4

    =-75

Part B

point slope  y-y1 = m(x-x1)  where m is the slope and (x1,y1) is a point on the line

y-1200 = -75(x-4)

slope intercept  y = mx+b  where m is the slope and b is the y intercept

y = -75x + 1500

standard form  Ax+By =C

75x + y = 1500

Part C

Change y to g(x) in the slope intercept form

g(x) = -75x + 1500

Part D

Let x = 5

g(5) = -75(5) + 1500

      =-375+1500

      =1125

Answer:

x^6 y^3

Step-by-step explanation:

(x²y)³

We know that (ab) ^c = a^c * b^c

(x²y)³ = x^2 ^3  * y^3

We know that a^b^c = a^(b*c)

(x²y)³ = x^2 ^3  * y^3 = x^( 2*3) y^3 = x^6 y^3

Answer:

1/2 inch per month

Step-by-step explanation:

The average rate hair grows is about half an inch per month which is 6 inches per year.

Answer:

1/32v²sin2θ

Step-by-step explanation:

Given the expression r(theta) = 1/16v²sinθcosθ

According to double angle of trigonometry identity;

Sin2θ = sin(θ+θ)

Sin2θ = sinθcosθ + cosθsinθ

Sin2θ = 2sinθcosθ

sinθcosθ = sin2θ/2 ... **

Substituting equation ** into the question

1/16v²sinθcosθ = 1/16v²(sin2θ/2)

1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)

1/16v²sinθcosθ = 1/32v²sin2θ

Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ

Answer:

No the sample does not show that the average age  was different in 2010      

Step-by-step explanation:

From the question we are told that

   The sample size is n =  50

    The  sample mean is  [tex]\= x = 38.5[/tex]

    The population mean is  [tex]\mu = 37[/tex]

     The standard deviation is  [tex]\sigma = 16[/tex]

     The level of significance is  [tex]\alpha = 5 \% = 0.05[/tex]

 The null hypothesis is  [tex]H_o : \mu = 37[/tex]

  The alternative hypothesis is  [tex]H_a : \mu \ne 37[/tex]

The critical value of the level of  significance obtained from the normal distribution table is  ([tex]Z_{\alpha } = 1.645[/tex] )

Generally the test statistics is mathematically evaluated as

          [tex]t = \frac{ \= x - \mu }{ \frac{\sigma }{\sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 38.5 - 37}{ \frac{16}{\sqrt{50} } }[/tex]        

         [tex]t = 0.663[/tex]

Now looking at the value  t and  [tex]Z_{\alpha }[/tex] we see that [tex]t < Z_{\alpha }[/tex] hence we fail to reject the null hypothesis.

This mean that there is no sufficient evidence to state that the sample shows that the average age was different in 2010      

Answer:

2x^3 - 9x^2 + 7x + 6

Step-by-step explanation:

(2x + 1)(x - 3)(x - 2)=2x^3 - 9x^2 + 7x + 6

Answer: hey

Step-by-step explanation:

Answer:

30.10

Step-by-step explanation:

First find the amount of tax

28 * 7.5%

28 * .075

2.10

Add this to the price of the pants

28+2.10 =30.10

Answer:

Step-by-step explanation:

It is possible that after an elastic collision a moving mass (1) strikes a stationary mass (2) and the two objects will have exactly the same final speed.

During an elastic collision, the momentum and kinetic energy are both conserved. Since one of the object is a stationary object, its velocity will be zero hence the other moving object will collide with the stationary object and cause both of them to move with a common velocity. The expression for their common velocity can be derived using the law of conservation of energy.

Law of conservation of energy states that the sum of momentum of bodies before collision is equal to the sum of momentum of the bodies after  collision.

Since momentum = mass*velocity

Before collision

Momentum of body of mass m1 and velocity u1  = m1u1

Momentum of body of mass m2 and velocity u2  = m2u2

Since the second body is stationary, u2 = 0m/s

Momentum of body of mass m2 and velocity u2  = m1(0) = 0kgm/s

Sum of their momentum before collision = m1u1+0 = m1u1 ... 1

After collision

Momentum of body of mass m1 and velocity vf  = m1vf

Momentum of body of mass m2 and velocity vf  = m2vf

vf is their common velocity.

Sum of their momentum before collision = m1vf+m2vf ... 2

Equating 1 and 2 according to the law;

m1u1 = m1vf+m2vf

m1u1 = (m1+m2)vf

vf = m1u1/m1+m2

vf s their common velocity after collision. This shows that there is possibility that they have the same velocity after collision.

Complete Question

The complete question is shown on the first uploaded image

Answer:

the null hypothesis is  [tex]H_o : \mu = 122[/tex]

the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

The test statistics is  [tex]t = - 1.761[/tex]

The p-value is  [tex]p = P(Z < t ) = 0.039119[/tex]

so

    [tex]p \ge 0.01[/tex]

Step-by-step explanation:

From the question we are told that

   The population mean is  [tex]\mu = 122[/tex]

     The sample size is  n=  38

    The sample mean is  [tex]\= x = 116 \ feet[/tex]

     The standard deviation is [tex]\sigma = 21[/tex]

Generally the null hypothesis is  [tex]H_o : \mu = 122[/tex]

                the alternative hypothesis is [tex]H_a : \mu \ne 122[/tex]

Generally the test statistics is mathematically evaluated as

         [tex]t = \frac { \= x - \mu }{\frac{ \sigma }{ \sqrt{n} } }[/tex]

substituting values

         [tex]t = \frac { 116 - 122 }{\frac{ 21 }{ \sqrt{ 38} } }[/tex]

         [tex]t = - 1.761[/tex]

The p-value is mathematically represented as

      [tex]p = P(Z < t )[/tex]

From the z- table  

     [tex]p = P(Z < t ) = 0.039119[/tex]

So  

     [tex]p \ge 0.01[/tex]

Answer:

t = -1.862, df = 399, p > 0.05

Step-by-step explanation:

The null hypothesis is the statement which is test for its validity. The decision to accept or reject the null hypothesis is based on the test statistics value. In the given question the null hypothesis is H0 = 34. There is one sample t-test for the testing of null hypothesis. The null hypothesis will be same for each type of one sample t-test. The null hypothesis assumes that the difference between the true mean and comparison value is zero.

Answer:

He can be on either the lower end of that 95%, or on the higher end. this guy is not a too short, nor is he extremely tall.

Sry if it's nor right, It was a little confusing.

Hope this helps!（づ￣3￣）づ╭❤～

He can be on either the lower end of that 95%, or on the higher end.

This guy is not too short, nor is he extremely tall.

We have given that

Height =2

Everything on the normal model is within 2 standard deviations away from the mean.

The standard deviation is a measure of the amount of variation or dispersion of a set of values.

So He can be on either the lower end of that 95%, or on the higher end.

This guy is not too short, nor is he extremely tall.

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Answer:

Yes

Step-by-step explanation:

18 × 200 = 3600

120 × 25 = 3000

270 × 5 = 1350

in total 7950

tickets = 10 × 1000 = 10000

7950 < 10000

Answer:

C. Graph C

Step-by-step explanation:

In a scatter plot, a positive correlation coefficient suggests that as one variable increases the other increases as well, or as one decreases, the other decreases.

Also, the more clustered the data points are along the line of best fit, the higher the value of the coefficient, whether positive or negative.

Graph C shows a positive correlation because as the variable on the x-axis increases, the variable on the y-axis also increases. The data points are more clustered along the line if best fit, if we draw one. This suggest a positive correlation coefficient (r) as strong as 0.75.

Graph C has a correlation coefficient, r, that is closer to 0.75.

Answer: graph A ‼️

Step-by-step explanation:

Answer:

x = 7

Step-by-step explanation:

L and M would be parallel if angle 2x -3 and the angle x + 4 are equal.

Thus, 2x - 3 = x + 4, so that x = 7

Answer: B. This is sometimes true.

Step-by-step explanation:

A positive correlation between 2 variables means that they generally move in the same direction meaning that as one variable rises, the other rises as well and as the other falls, the other falls as well.

However, the correlation can be strong, weak or anything in-between. This means that just because one variable increases by 12 does not mean the other would as well. It could increase by 1 alone and still have a positive correlation albeit a small one.

Therefore, if the value of one variable is above the mean, it doesn't always follow that the other with a positive correlation will as well as they just might not have that strong a correlation.

Answer: Rational, integer, whole, natural, real

So basically everything but irrational

====================================================

Explanation:

109 is a rational number because 109 = 109/1. Any rational number is a fraction of two integers. Because of this, it cannot be irrational as "irrational" means "not rational".

An integer is anything that does not have a fractional or decimal part. So it involves the set of positive and negative whole numbers, and zero as well. So we can see that 109 is an integer.

A whole number is very similar to an integer, but we're referring to the set {0, 1, 2, 3, ..} meaning we ignore the negative integers. This makes 109 a whole number as well.

A natural number is from the set {1, 2, 3, ...}. We've kicked 0 out from the set of whole numbers. This is the set of counting numbers. So 109 is also a natural number.

A real number is any number you have encountered so far assuming your teacher has not introduced complex and imaginary numbers yet. Effectively a real number is any number that can be written as decimal. This makes 109 to be a real number.

Answer:

the Portuguese

The History of The Republic of Ghana

The earliest Europeans to set foot on the land were the Portuguese in the 15th century (1471). On their arrival, they found so much gold between the rivers Ankobra and the Volta that they named the area “da Mina”, meaning “The Mine”.

Step-by-step explanation:

This was all I could really find :( Hope this helps! <3

I think it was Portugal

Answer:

The second quartile in the data set is $130 per night.

Step-by-step explanation:

Quartile is a type of quantile which divides the number of data set into even numbered sub groups. The second quartile is median of data set. This means that 5% of data lies within this point. The middle value between the median and highest value of data set. The second quartile in the data set must be 50% so the statement is not correct.

Answers:

There is a  max   value of   81/8   located at (x,y) =   (9/8, 9)  

=============================================================

Explanation:

Solve the second equation for y

8x+y = 18

y = 18-8x

Plug this into the first equation

f(x,y) = x*y

g(x) = x*(18-8x)

g(x) = 18x-8x^2

This graphs out a parabola that opens downward, and has a max point at the vertex.

If you apply the derivative to this, you get g ' (x) = 18 - 16x

Set this equal to zero and solve for x

g ' (x) = 0

18 - 16x = 0

18 = 16x

16x = 18

x = 18/16

x = 9/8

Use this x value to find y

y = 18 - 8x

y = 18 - 8(9/8)

y = 18 - 9

y = 9

So the max is x*y = (9/8)*9 = 81/8

Or we could say

g(x) = 18x-8x^2

g(9/8) = 18(9/8)-8(9/8)^2

g(9/8) = 81/8

----------------

To summarize,

There is a  max   value of   81/8   located at (x,y) =   (9/8, 9)  

When saying "max value of something", we're basically talking about the largest f(x,y) value. Which in this case is the largest x*y value based on the fact that 8x+y = 18.

A practical real world example of a problem like this would be if you wanted to max out a certain rectangular area based on constraints of how much building material you have for the fence.

Answer:

15/22

Step-by-step explanation:

Of the 66 students who have no chores, 45 have a curfew.  So the probability is 45/66 = 15/22.

Answer:

First, let's find how far away the pier is.

Using the distance formula, we can see that the pier is [tex]\sqrt{58}[/tex] units away.

So, the radius is sqrt 58.

Area = pi (r)^2

So,  the area is 182.82 square units.

Let me know if this helps!

We have that The area that the light covers is  is mathematically given as

[tex]A=\pi x^2[/tex]

From the Question we are told that

Revolving beam of light as far as the pier

Let distance to pier be x

Generally the revolving beam turns a complete angle of 360

Therefore

Its goes in a circle

The area that the light covers is  is mathematically given as

[tex]A=\pi r^2[/tex]

[tex]A=\pi x^2[/tex]

In conclusion

The area that the light covers is  is mathematically given as

[tex]A=\pi x^2[/tex]

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Answer:

[tex]\boxed{\sf 24\ cookies}[/tex]

Step-by-step explanation:

1 cookie = 1/16 of a pound of cookie

If we want to find how many cookies can be made by 3/2 pounds ( 1.5 pounds) then we need to divide 3/2 pounds by 1/16

=> [tex]\frac{3}{2} / \frac{1}{16}[/tex]

=> [tex]\frac{3}{2} * 16[/tex]

=> 3*8

=> 24 cookies

Answer:

24 cookies

Step-by-step explanation:

3/2= 1.5 and 1/16= 0.0625

if you divide the amount of dough you have by the amount needed for each cookie you will have 24

1.5/0.0625=24