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?

The Height (in Centimeters) Of A Candle Is A Linear Function Of The Amount Of Time (in Hours) It Has

Answers

Answer 1

Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters


Related Questions

A normal distribution has a mean of 30 and a variance of 5.Find N such that the probability that the mean of N observations exceeds 30.5 is 1%.​

Answers

Answer:

109

Step-by-step explanation:

Use a chart or calculator to find the z-score corresponding to a probability of 1%.

P(Z > z) = 0.01

P(Z < z) = 0.99

z = 2.33

Now find the sample standard deviation.

z = (x − μ) / s

2.33 = (30.5 − 30) / s

s = 0.215

Now find the sample size.

s = σ / √n

s² = σ² / n

0.215² = 5 / n

n = 109

Figure out if the figure is volume or surface area.​

(and the cut out cm is 4cm)

Answers

Answer:

Surface area of the box = 168 cm²

Step-by-step explanation:

Amount of cardboard needed = Surface area of the box

Since the given box is in the shape of a triangular prism,

Surface area of the prism = 2(surface area of the triangular bases) + Area of the three rectangular lateral sides

Surface area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{height})[/tex]

                                                           = [tex]\frac{1}{2}(6)(4)[/tex]

                                                           = 12 cm²

Surface area of the rectangular side with the dimensions of (6cm × 9cm),

= Length × width

= 6 × 9

= 54 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Area of the rectangle with the dimensions (9cm × 5cm),

= 9 × 5

= 45 cm²

Surface area of the prism = 2(12) + 54 + 45 + 45

                                           = 24 + 54 + 90

                                           = 168 cm²

Consider the surface f(x,y) = 21 - 4x² - 16y² (a plane) and the point P(1,1,1) on the surface.

Required:
a. Find the gradient of f.
b. Let C' be the path of steepest descent on the surface beginning at P, and let C be the projection of C' on the xy-plane. Find an equation of C in the xy-plane.
c. Find parametric equations for the path C' on the surface.

Answers

Answer:

A) ( -8, -32 )

Step-by-step explanation:

Given function : f (x,y) = 21 - 4x^2 - 16y^2

point p( 1,1,1 ) on surface

Gradient of F

attached below is the detailed solution

consider the bevariate data below about Advanced Mathematics and English results for a 2015 examination scored by 14 students in a particular school.The raw score of the examination was out of 100 marks.
Questions:
a)Draw a scatter graph
b)Draw a line of Best Fit
c)Predict the Advance Mathematics mark of a student who scores 30 of of 100 in English.
d)calculate the correlation using the Pearson's Correlation Coefficient Formula
e) Determine the strength of the correlation

Answers

Answer:

Explained below.

Step-by-step explanation:

Enter the data in an Excel sheet.

(a)

Go to Insert → Chart → Scatter.

Select the first type of Scatter chart.

The scatter plot is attached below.

(b)

The scatter plot with the line of best fit is attached below.

The line of best fit is:

[tex]y=-0.8046x+103.56[/tex]

(c)

Compute the value of x for y = 30 as follows:

[tex]y=-0.8046x+103.56[/tex]

[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]

Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.

(d)

The Pearson's Correlation Coefficient is:

[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]

  [tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]

Thus, the Pearson's Correlation Coefficient is -0.71.

(e)

A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.

The correlation between Advanced Mathematics and English results is -0.71.

This implies that there is a strong negative correlation.

For a certain instant lottery game, the odds in favor of a win are given as 81 to 19. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.

Answers

Answer: 0.81

Step-by-step explanation:

[tex]81:19\ \text{can be written as the fraction}\ \dfrac{81}{81+19}=\dfrac{81}{100}=\large\boxed{0.81}[/tex]

A fair die is tossed once, what is the probability of obtaining neither 5 nor 2?​

Answers

Answer:

4/6 or 66.666...%

Step-by-step explanation:

If you want to find the probability of obtaining neither a 5 nor a 2 you find how many times they occur and add them together in this case 5 occurs once and 2 also occurs once out of 6 numbers so 1/6 + 1/6 equals 2/6, you now know that 4/6 of them won't be a 5 nor a 2 and because it is a fair die the likelihood of it falling on a number is the same for all sides so the answer is 4/6 or 66.67%.

A work shift for an employee at Starbucks consists of 8 hours (whole).
What FRACTION (part) of the employees work shift is represented by 2
hours? *

Answers

Answer:

1/4 of an hour

Step-by-step explanation:

2 divided by 8 = 1/4

Answer:

1/4

Step-by-step explanation:

A whole shift is 8 hours

Part over whole is the fraction

2/8

Divide top and bottom by 2

1/4

A soccer player has made 3 of her last 10 field goals, which is a field goal percentage of 30%. How many more consecutive field goals would she need to make to raise her field goal percentage to 50%?

Answers

Answer:

4 consecutive goals

Step-by-step explanation:

If 3 of last 10 field goals = 30%

Which is equivalent to

(Number of goals scored / total games played) * 100%

(3 / 10) * 100% = 30%

Number of consecutive goals one has to score to raise field goal to 50% will be:

Let y = number of consecutive goals

[(3+y) / (10+y)] * 100% = 50%

[(3+y) / (10+y)] * 100/100 = 50/100

[(3+y) / (10+y)] * 1 = 0.5

(3+y) / (10+y) = 0.5

3+y = 0.5(10 + y)

3+y = 5 + 0.5y

y - 0.5y = 5 - 3

0.5y = 2

y = 2 / 0.5

y = 4

Therefore, number of consecutive goals needed to raise field goal to 50% = 4

2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)

Answers

Answer:

16/45x-11/12

Step-by-step explanation:

Multiply across

2/15x-30/40-1/6+2/9x=

Get common denominators of like terms

6/45x+10/45x-9/12-2/12=

Combine like terms

16/45x-11/12

The simplified expression is: (16/45)x - (11/12)

To simplify the given expression, we'll follow the steps:

Step 1: Distribute the fractions through the parentheses.

Step 2: Simplify the expression by combining like terms.

Let's proceed with the simplification:

Step 1: Distribute the fractions through the parentheses:

2/5 * (1/3x - 15/8) - 1/3 * (1/2 - 2/3x)

Step 2: Simplify the expression:

To distribute 2/5 through (1/3x - 15/8):

2/5 * 1/3x = 2/15x

2/5 * (-15/8) = -15/20 = -3/4

So, the first part becomes: 2/15x - 3/4

To distribute -1/3 through (1/2 - 2/3x):

-1/3 * 1/2 = -1/6

-1/3 * (-2/3x) = 2/9x

So, the second part becomes: -1/6 + 2/9x

Now, the entire expression becomes:

2/15x - 3/4 - 1/6 + 2/9x

Step 3: Combine like terms:

To combine the terms with "x":

2/15x + 2/9x = (2/15 + 2/9)x

Now, find the common denominator for (2/15) and (2/9), which is 45:

(2/15 + 2/9) = (6/45 + 10/45) = 16/45

So, the combined x term becomes:

(16/45)x

Now, combine the constant terms:

-3/4 - 1/6 = (-18/24 - 4/24) = -22/24

To simplify -22/24, we can divide both numerator and denominator by their greatest common divisor (which is 2):

-22 ÷ 2 = -11

24 ÷ 2 = 12

So, the combined constant term becomes:

(-11/12)

Putting it all together, the simplified expression is:

(16/45)x - (11/12)

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Complete question is:

Simplify the given expression: 2/5 ( 1/3 x− 15/8 )− 1/3 ( 1/2 − 2/3 x)

Let f(x) = x - 1 and g(x) = x^2 - x. Find and simplify the expression. (f + g)(1) (f +g)(1) = ______

Answers

Answer:

The simplified answer of the given expression is 1.

Step-by-step explanation:

When you see (f + g)(x), then it means that you are going to add f(x) and g(x) together. So, we are going to add the terms together that are given in the problem. We are also given the value of x which is 1. So, we are going to combine this information together so we can simplify the expression.

(f + g)(1)

f(x) = x - 1

g(x) = x²

(f + g)(1) = (1 - 1) + (1²)

Simplify the terms in the parentheses.

(f + g)(1) = 0 + 1

Add 0 and 1.

(f + g)(1) = 1

So, (f + g)(1) will have a simplified answer of 1.

Choose the algebraic description that maps ΔABC onto ΔA′B′C′ in the given figure. Question 9 options:
A) (x, y) → (x, y – 6)
B) (x, y) → (x – 6, y)
C) (x, y) → (x, y + 6)
D) (x, y) → (x + 6, y)

Answers

Answer:

  B) (x, y) → (x – 6, y)

Step-by-step explanation:

Each x-value in the image is 6 less than in the pre-image. Each y-value is the same. That means x gets mapped to x-6, and y gets mapped to y:

  (x, y) → (x – 6, y)

find the 5th term in the sequence an=n÷n+1

Answers

Answer:

The 5th term of a sequence is defined as the term with n = 5.  So for this sequence, a sub 5 = 5/6

What is 5 feet and 11 inches in inches

Answers

Answer:

60

Step-by-step explanation:

5 is 60 inch

evaluate the expression 4x^2-6x+7 if x = 5

Answers

Answer:

77

Step-by-step explanation:

4x^2-6x+7

Let x = 5

4* 5^2-6*5+7

4 * 25 -30 +7

100-30+7

7-+7

77

Please answer this correctly without making mistakes

Answers

Answer:

355/12

Step-by-step explanation:

Answer:

355/12mi

Step-by-step explanation:

9 1/2 = 19/2

20 1/12 = 241/12

19/2 + 241/12 = 355/12mi

A survey​ asked, "How many tattoos do you currently have on your​ body?" Of the males​ surveyed, responded that they had at least one tattoo. Of the females​ surveyed, responded that they had at least one tattoo. Construct a ​% confidence interval to judge whether the proportion of males that have at least one tattoo differs significantly from the proportion of females that have at least one tattoo. Interpret the interval.

Answers

Complete Question

The complete question is shown on the first uploaded image

Answer:

The  95% interval for [tex]p_1 - p_2[/tex] is  [tex]-0.0171 ,0.0411[/tex]

Option A is correct

Step-by-step explanation:

From the question we are told that

   The sample size of male  is [tex]n_1 = 1211[/tex]

    The number of males that  said they have at least one tattoo is [tex]r = 182[/tex]

   The sample size of female is [tex]n_2 = 1041[/tex]

     The number of females that  said they have at least one tattoo is [tex]k = 144[/tex]

Generally the sample proportion of male is  

            [tex]\r p_1 = \frac{r}{ n_1}[/tex]

substituting values

            [tex]\r p_1 = \frac{ 182}{1211}[/tex]

             [tex]\r p_1 = 0.1503[/tex]

Generally the sample proportion of female is  

            [tex]\r p_2 = \frac{k}{ n_2}[/tex]

substituting values

           [tex]\r p_2 = \frac{ 144}{1041}[/tex]

           [tex]\r p_2 = 0.1383[/tex]

Given that the confidence level is  95% then the level of  significance is mathematically represented as

          [tex]\alpha =100-95[/tex]

          [tex]\alpha =5\%[/tex]

          [tex]\alpha =0.05[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the value is

          [tex]Z_\frac{\alpha }{2} = 1.96[/tex]

Generally the margin of error is mathematically represented as

        [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p_1 (1- \r p_1)}{n_1} + \frac{\r p_2 (1- \r p_2)}{n_2} }[/tex]

substituting values

       [tex]E = 1.96 * \sqrt{\frac{ 0.1503 (1- 0.1503)}{1211} + \frac{0.1383 (1- 0.1383)}{1041} }[/tex]

       [tex]E = 0.0291[/tex]

The 95% confidence interval is mathematically represented as

        [tex](\r p_1 - \r p_2 ) - E < p_1-p_2 < (\r p_1 - \r p_2 ) + E[/tex]

substituting values

         [tex](0.1503- 0.1383 ) - 0.0291 < p_1-p_2 < (0.1503- 0.1383 ) + 0.0291[/tex]

          [tex]-0.0171 < p_1-p_2 < 0.0411[/tex]

So the interpretation is that there is 95% confidence that the difference of the proportion is in the interval .So conclude that there is insufficient evidence of a significant difference in the proportion of male and female that have at least one tattoo

This because the difference in proportion is less than [tex]\alpha[/tex]

Which graph shows the polar coordinates (-3,-) plotted

Answers

Graph 1 would be the answer

Oregon State University is interested in determining the average amount of paper, in sheets, that is recycled each month. In previous years, the average number of sheets recycled per bin was 59.3 sheets, but they believe this number may have increase with the greater awareness of recycling around campus. They count through 79 randomly selected bins from the many recycle paper bins that are emptied every month and find that the average number of sheets of paper in the bins is 62.4 sheets. They also find that the standard deviation of their sample is 9.86 sheets. What is the value of the test-statistic for this scenario

Answers

Answer:

The test statistic is [tex]t = 2.79[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 59.3[/tex]

    The sample size is  [tex]n = 79[/tex]

    The  sample mean is  [tex]\= x = 62.4[/tex]

    The  standard deviation is  [tex]\sigma = 9.86[/tex]

Generally the test statistics is mathematically represented as

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

substituting values

          [tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]

          [tex]t = 2.79[/tex]

find the range of the inequality 2e-3< 3e-1​

Answers

Answer:

[tex]x = { - 1, 0,1 ,2 ...}[/tex]

Step-by-step explanation:

[tex]2e - 3 < 3e - 1 = 2e - 3e < - 1 + 3 = - 1e < 2 = e > - 2[/tex]

Hope this helps ;) ❤❤❤

You are going to your first school dance! You bring $20,
and sodas cost $2. How many sodas can you buy?
Please write and solve an equation (for x sodas), and
explain how you set it up.

Answers

Answer:

10

Step-by-step explanation:

Let the no. of sodas be x

Price of each soda = $2

Therefore, no . of sodas you can buy = $2x

2x=20

=>x=[tex]\frac{20}{2}[/tex]

=>x=10

you can buy 10 sodas

Answer: 10 sodas

Step-by-step explanation:

2x = 20       Divide both sides by 2  

x = 10

If I brought 20 dollars and I  want to by only sodas and each sodas cost 2 dollars, then I will divide the total amount of money that I brought  by 2 to find out how many sodas I could by.

The odds in favor of a horse winning a race are 7:4. Find the probability that the horse will win the race.

Answers

Answer:

7/11 = 0.6363...

Step-by-step explanation:

7 + 4 = 11

probability of winning: 7/11 = 0.6363...

The probability that the horse will in the race is [tex]\mathbf{\dfrac{7}{11}}[/tex]

Given that the odds  of the horse winning the race is 7:4

Assuming the ratio is in form of a:b, the probability of winning the race can be computed as:

[tex]\mathbf{P(A) = \dfrac{a}{a+b}}[/tex]

From the given question;

The probability of the horse winning the race is:

[tex]\mathbf{P(A) = \dfrac{7}{7+4}}[/tex]

[tex]\mathbf{P(A) = \dfrac{7}{11}}[/tex]

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Which of the following is an even function? f(x) = (x – 1)2 f(x) = 8x f(x) = x2 – x f(x) = 7

Answers

Answer:

f(x) = 7

Step-by-step explanation:

f(x) = f(-x) it is even

-f(x)=f(-x) it is odd

f(x) = (x – 1)^2 neither even nor odd

f(x) = 8x   this is a line  odd functions

f(x) = x^2 – x  neither even nor odd

f(x) = 7  constant  this is an even function

Answer:

answer is f(x)= 7

Step-by-step explanation:

just took edge2020 test

anyone can help me with these questions?
please gimme clear explanation :)​

Answers

Step-by-step explanation:

The limit of a function is the value it approaches.

In #37, as x approaches infinity (far to the right), the curve f(x) approaches 1.  As x approaches negative infinity (far to the left), the curve f(x) approaches -1.

lim(x→∞) f(x) = 1

lim(x→-∞) f(x) = -1

In #38, as x approaches infinity (far to the right), the curve f(x) approaches 2.  As x approaches negative infinity (far to the left), the curve f(x) approaches -3.

lim(x→∞) f(x) = 2

lim(x→-∞) f(x) = -3

What is the value of the product (3 – 2i)(3 + 2i)?

Answers

Answer:

13

Step-by-step explanation:

(3 - 2i)(3 + 2i)

Expand

(9 + 6i - 6i - 4i^2)

Add

(9 - 4i^2)

Convert i^2

i^2 = ([tex]\sqrt{-1}[/tex])^2 = -1

(9 - 4(-1))

Add

(9 + 4)

= 13

Answer:

13.

Step-by-step explanation:

(3 - 2i)(3 + 2i)

= (3 * 3) + (-2i * 3) + (2i * 3) + (-2i * 2i)

= 9 - 6i + 6i - 4[tex]\sqrt{-1} ^{2}[/tex]

= 9 - 4(-1)

= 9 + 4

= 13

Hope this helps!

Find all values of x on the graph of f(x) = 2x3 + 6x2 + 7 at which there is a horizontal tangent line.

Answers

Answer:

the equation is not correct, u have to write like

ax'3+bx'2+cx+d

Answer:

x=-2 and x=0

Step-by-step explanation:

So I know it isn't x=-3 and x=0. So my guess is that it is x=0 and x=-2 and heres why.

First, I find the derivative of f(x)=2x^3+6x^2+7 which is 6x^2+12x

Then, I plugged in all the values of x's I had and I found out that you get 0 for -2 and 0 when you plug them in

So, in conclusion I believe the answer to be x=-2 and x=0

99 litres of gasoline oil is poured into a cylindrical drum of 60cm in diameter. How deep is the oil in the drum? ​

Answers

Answer:

  35 cm

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

We want to find h for the given volume and diameter. First, we must convert the given values to compatible units.

  1 L = 1000 cm³, so 99 L = 99,000 cm³

  60 cm diameter = 2 × 30 cm radius

So, we have ...

  99,000 cm³ = π(30 cm)²h

  99,000/(900π) cm = h ≈ 35.01 cm

The oil is 35 cm deep in the drum.

AB is dilated from the origin to create A'B' at A' (0, 8) and B' (8, 12). What scale factor was AB dilated by?

Answers

Answer:

4

Step-by-step explanation:

Original coordinates:

A (0, 2)

B (2, 3)

The scale is what number the original coordinates was multiplied by to reach the new coordinates

1. Divide

(0, 8) ÷ (0, 2) = 4

(8, 12) ÷ (2, 3) = 4

AB was dilated by a scale factor of 4.

If f(x) = 2x2 – 3x – 1, then f(-1)=

Answers

ANSWER:
Given:f(x)=2x^2-3x-1
Then,f(-1)=2(-1)^2-3(-1)-1
f(-1)=2(1)+3-1
f(-1)=5-1
f(-1)=4


HOPE IT HELPS!!!!!!
PLEASE MARK BRAINLIEST!!!!!

The value of function at x= -1 is f(-1) = 4.

We have the function as

f(x) = 2x² - 3x -1

To find the value of f(-1) when f(x) = 2x² - 3x -1, we substitute x = -1 into the expression:

f(-1) = 2(-1)² - 3(-1) - 1

      = 2(1) + 3 - 1

      = 2 + 3 - 1

      = 4.

Therefore, the value of function at x= -1 is f(-1) = 4.

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Please Solve
F/Z=T for Z

Answers

Answer:

F /T = Z

Step-by-step explanation:

F/Z=T

Multiply each side by Z

F/Z *Z=T*Z

F = ZT

Divide each side by T

F /T = ZT/T

F /T = Z

Answer:

[tex]\boxed{\red{ z = \frac{f}{t} }}[/tex]

Step-by-step explanation:

[tex] \frac{f}{z} = t \\ \frac{f}{z} = \frac{t}{1} \\ zt = f \\ \frac{zt}{t} = \frac{f}{t} \\ z = \frac{f}{t} [/tex]

g A random sample of size 16 taken from a normally distributed population revealed a sample mean of 50 and a sample variance of 36. The upper limit of a 95% confidence interval for the population mean would equal:

Answers

Answer:

The  upper limit is    

                   [tex]k = 52.94[/tex]

Step-by-step explanation:

From the question we  told that

     The  sample size is [tex]n = 16[/tex]

      The sample mean is  [tex]\= x = 50[/tex]

      The sample variance is  [tex]\sigma ^2 = 36[/tex]

For  a  95% confidence interval the confidence level is  95%

Given that the confidence level is 95% then the level of significance is  mathematically evaluated  as  

             [tex]\alpha = 100 - 95[/tex]

              [tex]\alpha = 5 \%[/tex]

              [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table(reference- math dot armstrong dot edu), the value is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

             

Generally the margin of error is mathematically represented as

             [tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]

 Here  [tex]\sigma[/tex] is the standard deviation which is mathematically evaluated as

                  [tex]\sigma = \sqrt{\sigma^2}[/tex]

substituting values

                  [tex]\sigma = \sqrt{36}[/tex]

=>                [tex]\sigma = 6[/tex]

So

                    [tex]E = 1.96 * \frac{6}{\sqrt{16} }[/tex]

                     [tex]E = 2.94[/tex]

The 95% confidence interval is mathematically represented as

                 [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

                [tex]50 -2.94 < \mu <50 +2.94[/tex]

                [tex]47.06 < \mu <52.94[/tex]

The  upper limit is    

                   [tex]k = 52.94[/tex]

   

                 

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